%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : MGT030+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 0.11s 0.35s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 58 ( 8 unt; 0 def)
% Number of atoms : 172 ( 0 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 204 ( 90 ~; 88 |; 17 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 5 sgn 9 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_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/sandbox/benchmark/theBenchmark.p',prove_l12) ).
fof(prove_l12_negated,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)) ) ) ),
inference(negate_conjecture,[status(cth)],[prove_l12]) ).
cnf(8,plain,
environment(sK4),
inference(cnf,[status(esa)],[prove_l12_negated]) ).
cnf(l0,plain,
environment(sK4),
inference(instantiation,[status(thm)],[8]) ).
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/sandbox/benchmark/theBenchmark.p',mp_earliest_time_growth_rate_exceeds) ).
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(l1,plain,
( ~ environment(sK4)
| ~ in_environment(sK4,sK3(sK4))
| sP0(sK4,sK5(sK2(sK4)))
| greater_or_equal(sK1(sK4,sK3(sK4)),sK3(sK4)) ),
inference(instantiation,[status(thm)],[1]) ).
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/sandbox/benchmark/theBenchmark.p',l1) ).
cnf(6,plain,
( ~ environment(X0)
| ~ stable(X0)
| in_environment(X0,sK3(X0)) ),
inference(cnf,[status(esa)],[l1]) ).
cnf(l2,plain,
( ~ environment(sK4)
| ~ stable(sK4)
| in_environment(sK4,sK3(sK4)) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(5,plain,
( in_environment(X0,sK2(X0))
| ~ sP0(X0,X1) ),
inference(cnf,[status(esa)],[mp_earliest_time_growth_rate_exceeds]) ).
cnf(l3,plain,
( in_environment(sK4,sK2(sK4))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(7,plain,
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ greater_or_equal(X1,sK3(X0))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(cnf,[status(esa)],[l1]) ).
cnf(l4,plain,
( ~ environment(sK4)
| ~ subpopulations(first_movers,efficient_producers,sK4,sK1(sK4,sK3(sK4)))
| ~ stable(sK4)
| ~ greater_or_equal(sK1(sK4,sK3(sK4)),sK3(sK4))
| greater(growth_rate(efficient_producers,sK1(sK4,sK3(sK4))),growth_rate(first_movers,sK1(sK4,sK3(sK4)))) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(9,plain,
stable(sK4),
inference(cnf,[status(esa)],[prove_l12_negated]) ).
cnf(l7,plain,
stable(sK4),
inference(instantiation,[status(thm)],[9]) ).
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(l8,plain,
( ~ environment(sK4)
| ~ in_environment(sK4,sK3(sK4))
| ~ greater(growth_rate(efficient_producers,sK1(sK4,sK3(sK4))),growth_rate(first_movers,sK1(sK4,sK3(sK4))))
| sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[2]) ).
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(l18,plain,
( ~ subpopulations(first_movers,efficient_producers,sK4,sK5(sK2(sK4)))
| ~ greater(sK5(sK2(sK4)),sK2(sK4))
| greater(growth_rate(efficient_producers,sK5(sK2(sK4))),growth_rate(first_movers,sK5(sK2(sK4))))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(11,plain,
( ~ in_environment(sK4,X0)
| greater(sK5(X0),X0)
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(cnf,[status(esa)],[prove_l12_negated]) ).
cnf(l20,plain,
( ~ in_environment(sK4,sK2(sK4))
| greater(sK5(sK2(sK4)),sK2(sK4))
| greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4))) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l5,plain,
( ~ in_environment(sK4,sK2(sK4))
| greater(sK5(sK2(sK4)),sK2(sK4))
| greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4))) ),
inference(instantiation,[status(thm)],[11]) ).
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(l26,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4)))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l41,plain,
( ~ subpopulations(first_movers,efficient_producers,sK4,sK5(sK2(sK4)))
| ~ greater(sK5(sK2(sK4)),sK2(sK4))
| greater(growth_rate(efficient_producers,sK5(sK2(sK4))),growth_rate(first_movers,sK5(sK2(sK4))))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(10,plain,
( ~ in_environment(sK4,X0)
| subpopulations(first_movers,efficient_producers,sK4,sK5(X0))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(cnf,[status(esa)],[prove_l12_negated]) ).
cnf(l42,plain,
( ~ in_environment(sK4,sK2(sK4))
| subpopulations(first_movers,efficient_producers,sK4,sK5(sK2(sK4)))
| greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4))) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(12,plain,
( ~ in_environment(sK4,X0)
| ~ greater(growth_rate(efficient_producers,sK5(X0)),growth_rate(first_movers,sK5(X0)))
| greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0)) ),
inference(cnf,[status(esa)],[prove_l12_negated]) ).
cnf(l19,plain,
( ~ in_environment(sK4,sK2(sK4))
| ~ greater(growth_rate(efficient_producers,sK5(sK2(sK4))),growth_rate(first_movers,sK5(sK2(sK4))))
| greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4))) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l40,plain,
( in_environment(sK4,sK2(sK4))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l15,plain,
( ~ environment(sK4)
| ~ stable(sK4)
| in_environment(sK4,sK3(sK4)) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l6,plain,
stable(sK4),
inference(instantiation,[status(thm)],[9]) ).
cnf(l23,plain,
( ~ in_environment(sK4,sK2(sK4))
| subpopulations(first_movers,efficient_producers,sK4,sK5(sK2(sK4)))
| greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4))) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l30,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4)))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l43,plain,
( ~ in_environment(sK4,sK2(sK4))
| ~ greater(growth_rate(efficient_producers,sK5(sK2(sK4))),growth_rate(first_movers,sK5(sK2(sK4))))
| greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4))) ),
inference(instantiation,[status(thm)],[12]) ).
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(l9,plain,
( ~ environment(sK4)
| ~ in_environment(sK4,sK3(sK4))
| subpopulations(first_movers,efficient_producers,sK4,sK1(sK4,sK3(sK4)))
| sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(l24,plain,
stable(sK4),
inference(instantiation,[status(thm)],[9]) ).
cnf(l13,plain,
( ~ subpopulations(first_movers,efficient_producers,sK4,sK5(sK2(sK4)))
| ~ greater(sK5(sK2(sK4)),sK2(sK4))
| greater(growth_rate(efficient_producers,sK5(sK2(sK4))),growth_rate(first_movers,sK5(sK2(sK4))))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[3]) ).
cnf(l44,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4)))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l34,plain,
( in_environment(sK4,sK2(sK4))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l22,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4)))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l16,plain,
( ~ environment(sK4)
| ~ stable(sK4)
| in_environment(sK4,sK3(sK4)) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(l21,plain,
stable(sK4),
inference(instantiation,[status(thm)],[9]) ).
cnf(l47,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4)))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l25,plain,
( in_environment(sK4,sK2(sK4))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l46,plain,
( ~ in_environment(sK4,sK2(sK4))
| greater(sK5(sK2(sK4)),sK2(sK4))
| greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4))) ),
inference(instantiation,[status(thm)],[11]) ).
cnf(l10,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4)))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l48,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4)))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l45,plain,
( ~ in_environment(sK4,sK2(sK4))
| ~ greater(growth_rate(efficient_producers,sK5(sK2(sK4))),growth_rate(first_movers,sK5(sK2(sK4))))
| greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4))) ),
inference(instantiation,[status(thm)],[12]) ).
cnf(l27,plain,
( ~ in_environment(sK4,sK2(sK4))
| subpopulations(first_movers,efficient_producers,sK4,sK5(sK2(sK4)))
| greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4))) ),
inference(instantiation,[status(thm)],[10]) ).
cnf(l49,plain,
( in_environment(sK4,sK2(sK4))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l50,plain,
( in_environment(sK4,sK2(sK4))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(l51,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4)))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l33,plain,
( ~ greater(growth_rate(efficient_producers,sK2(sK4)),growth_rate(first_movers,sK2(sK4)))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l52,plain,
( in_environment(sK4,sK2(sK4))
| ~ sP0(sK4,sK5(sK2(sK4))) ),
inference(instantiation,[status(thm)],[5]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l4,l7,l8,l18,l20,l5,l26,l41,l42,l19,l40,l15,l6,l23,l30,l43,l9,l24,l13,l44,l34,l22,l16,l21,l47,l25,l46,l10,l48,l45,l27,l49,l50,l51,l33,l52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT030+1 : TPTP v9.3.0. Released v2.0.0.
% 0.00/0.03 % Command : /export/starexec/sandbox/solver/bin/execute.py 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n011.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Mon Sep 7 12:18:45 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % launching worker at depth: 1
% 0.09/0.35 % launching worker at depth: 3
% 0.09/0.35 % launching worker at depth: 4
% 0.09/0.35 % launching worker at depth: 7
% 0.09/0.35 % launching worker at depth: 8
% 0.09/0.35 % launching worker at depth: 5
% 0.09/0.35 % launching worker at depth: 6
% 0.09/0.35 % launching worker at depth: 2
% 0.09/0.35 % launching worker at depth: 9
% 0.09/0.35 % launching worker at depth: 10
% 0.11/0.35 % SZS status Theorem for theBenchmark
% 0.11/0.35 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------