%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : MGT036+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 : n007.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 06:11:25 AM UTC 2026
% Result : Theorem 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 12 unt; 0 def)
% Number of atoms : 98 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 115 ( 52 ~; 44 |; 10 &)
% ( 2 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_t5,plain,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ~ outcompetes(first_movers,efficient_producers,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5) ).
fof(prove_t5_negated,plain,
~ ! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> ~ outcompetes(first_movers,efficient_producers,T) ),
inference(negate_conjecture,[status(cth)],[prove_t5]) ).
cnf(11,plain,
environment(sK1),
inference(cnf,[status(esa)],[prove_t5_negated]) ).
cnf(l0,plain,
environment(sK1),
inference(instantiation,[status(thm)],[11]) ).
fof(mp_symmetry_of_FM_and_EP,plain,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> subpopulations(efficient_producers,first_movers,E,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_FM_and_EP) ).
cnf(0,plain,
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| subpopulations(efficient_producers,first_movers,X0,X1) ),
inference(cnf,[status(esa)],[mp_symmetry_of_FM_and_EP]) ).
cnf(l1,plain,
( ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| subpopulations(efficient_producers,first_movers,sK1,sK2) ),
inference(instantiation,[status(thm)],[0]) ).
cnf(12,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(cnf,[status(esa)],[prove_t5_negated]) ).
cnf(l2,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(instantiation,[status(thm)],[12]) ).
fof(d2,plain,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T) )
=> ( ( greater_or_equal(growth_rate(S2,T),zero)
& greater(zero,growth_rate(S1,T)) )
<=> outcompetes(S2,S1,T) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
cnf(6,plain,
( ~ greater(zero,growth_rate(X0,X1))
| ~ environment(X2)
| ~ subpopulations(X0,X3,X2,X1)
| ~ greater_or_equal(growth_rate(X3,X1),zero)
| outcompetes(X3,X0,X1) ),
inference(cnf,[status(esa)],[d2]) ).
cnf(l3,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK2))
| ~ environment(sK1)
| ~ subpopulations(efficient_producers,first_movers,sK1,sK2)
| ~ greater_or_equal(growth_rate(first_movers,sK2),zero)
| outcompetes(first_movers,efficient_producers,sK2) ),
inference(instantiation,[status(thm)],[6]) ).
cnf(8,plain,
( ~ outcompetes(X0,X1,X2)
| ~ environment(X3)
| ~ subpopulations(X1,X0,X3,X2)
| greater(zero,growth_rate(X1,X2)) ),
inference(cnf,[status(esa)],[d2]) ).
cnf(l4,plain,
( ~ outcompetes(first_movers,efficient_producers,sK2)
| ~ environment(sK1)
| ~ subpopulations(efficient_producers,first_movers,sK1,sK2)
| greater(zero,growth_rate(efficient_producers,sK2)) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(l5,plain,
( ~ outcompetes(first_movers,efficient_producers,sK2)
| ~ environment(sK1)
| ~ subpopulations(efficient_producers,first_movers,sK1,sK2)
| greater(zero,growth_rate(efficient_producers,sK2)) ),
inference(instantiation,[status(thm)],[8]) ).
cnf(13,plain,
outcompetes(first_movers,efficient_producers,sK2),
inference(cnf,[status(esa)],[prove_t5_negated]) ).
cnf(l36,plain,
outcompetes(first_movers,efficient_producers,sK2),
inference(instantiation,[status(thm)],[13]) ).
cnf(7,plain,
( ~ outcompetes(X0,X1,X2)
| ~ environment(X3)
| ~ subpopulations(X1,X0,X3,X2)
| greater_or_equal(growth_rate(X0,X2),zero) ),
inference(cnf,[status(esa)],[d2]) ).
cnf(l12,plain,
( ~ outcompetes(first_movers,efficient_producers,sK2)
| ~ environment(sK1)
| ~ subpopulations(efficient_producers,first_movers,sK1,sK2)
| greater_or_equal(growth_rate(first_movers,sK2),zero) ),
inference(instantiation,[status(thm)],[7]) ).
fof(a12,plain,
! [E,S1,S2,T] :
( ( environment(E)
& in_environment(E,T)
& ~ greater(zero,growth_rate(S1,T))
& greater(resilience(S2),resilience(S1)) )
=> ~ greater(zero,growth_rate(S2,T)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a12) ).
cnf(9,plain,
( ~ greater(zero,growth_rate(X0,X1))
| ~ greater(resilience(X0),resilience(X2))
| ~ environment(X3)
| ~ in_environment(X3,X1)
| greater(zero,growth_rate(X2,X1)) ),
inference(cnf,[status(esa)],[a12]) ).
cnf(l7,plain,
( ~ greater(zero,growth_rate(efficient_producers,sK2))
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ environment(sK1)
| ~ in_environment(sK1,sK2)
| greater(zero,growth_rate(first_movers,sK2)) ),
inference(instantiation,[status(thm)],[9]) ).
fof(mp_time_point_occur,plain,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_occur) ).
cnf(1,plain,
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| in_environment(X0,X1) ),
inference(cnf,[status(esa)],[mp_time_point_occur]) ).
cnf(l53,plain,
( ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| in_environment(sK1,sK2) ),
inference(instantiation,[status(thm)],[1]) ).
fof(a2,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2) ).
cnf(10,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf,[status(esa)],[a2]) ).
cnf(l11,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(instantiation,[status(thm)],[10]) ).
cnf(l21,plain,
outcompetes(first_movers,efficient_producers,sK2),
inference(instantiation,[status(thm)],[13]) ).
cnf(l55,plain,
subpopulations(first_movers,efficient_producers,sK1,sK2),
inference(instantiation,[status(thm)],[12]) ).
fof(mp_growth_rate_relationships,plain,
! [E,S1,S2,T] :
( ( ( environment(E)
& subpopulations(S1,S2,E,T) )
=> greater_or_equal(growth_rate(S1,T),zero) )
<=> ~ greater(zero,growth_rate(S1,T)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships) ).
cnf(4,plain,
( ~ greater(zero,growth_rate(X0,X1))
| ~ greater_or_equal(growth_rate(X0,X1),zero) ),
inference(cnf,[status(esa)],[mp_growth_rate_relationships]) ).
cnf(l30,plain,
( ~ greater(zero,growth_rate(first_movers,sK2))
| ~ greater_or_equal(growth_rate(first_movers,sK2),zero) ),
inference(instantiation,[status(thm)],[4]) ).
cnf(l56,plain,
( ~ outcompetes(first_movers,efficient_producers,sK2)
| ~ environment(sK1)
| ~ subpopulations(efficient_producers,first_movers,sK1,sK2)
| greater_or_equal(growth_rate(first_movers,sK2),zero) ),
inference(instantiation,[status(thm)],[7]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l4,l5,l36,l12,l7,l53,l11,l21,l55,l30,l56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT036+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
% 0.11/0.37 % Computer : n007.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 7 12:37:26 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % launching worker at depth: 1
% 0.11/0.37 % launching worker at depth: 2
% 0.11/0.37 % launching worker at depth: 7
% 0.11/0.37 % launching worker at depth: 4
% 0.11/0.37 % launching worker at depth: 8
% 0.11/0.37 % launching worker at depth: 6
% 0.11/0.37 % launching worker at depth: 3
% 0.11/0.37 % launching worker at depth: 5
% 0.11/0.38 % launching worker at depth: 9
% 0.11/0.38 % launching worker at depth: 10
% 0.11/0.38 % launching worker at depth: 11
% 0.11/0.39 % SZS status Theorem for theBenchmark
% 0.11/0.39 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------