%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : MGT036+2 : 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 : 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 0.08s 0.37s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 7
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 91 ( 40 ~; 32 |; 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 22 !; 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/sandbox/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_subpopulations,plain,
! [E,S1,S2,T] :
( ( environment(E)
& subpopulations(S1,S2,E,T) )
=> subpopulations(S2,S1,E,T) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
cnf(0,plain,
( ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| subpopulations(X2,X1,X0,X3) ),
inference(cnf,[status(esa)],[mp_symmetry_of_subpopulations]) ).
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]) ).
cnf(l3,plain,
( ~ environment(sK1)
| ~ subpopulations(efficient_producers,first_movers,sK1,sK2)
| subpopulations(first_movers,efficient_producers,sK1,sK2) ),
inference(instantiation,[status(thm)],[0]) ).
fof(mp_time_point_occur,plain,
! [E,T] :
( ( environment(E)
& subpopulations(first_movers,efficient_producers,E,T) )
=> in_environment(E,T) ),
file('/export/starexec/sandbox/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(l4,plain,
( ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,sK1,sK2)
| in_environment(sK1,sK2) ),
inference(instantiation,[status(thm)],[1]) ).
fof(a13,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/sandbox/benchmark/theBenchmark.p',a13) ).
cnf(10,plain,
( ~ environment(X0)
| ~ greater(resilience(X1),resilience(X2))
| ~ greater(zero,growth_rate(X1,X3))
| ~ in_environment(X0,X3)
| greater(zero,growth_rate(X2,X3)) ),
inference(cnf,[status(esa)],[a13]) ).
cnf(l26,plain,
( ~ environment(sK1)
| ~ greater(resilience(efficient_producers),resilience(first_movers))
| ~ greater(zero,growth_rate(efficient_producers,sK2))
| ~ in_environment(sK1,sK2)
| greater(zero,growth_rate(first_movers,sK2)) ),
inference(instantiation,[status(thm)],[10]) ).
fof(a2,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
cnf(9,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf,[status(esa)],[a2]) ).
cnf(l27,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(instantiation,[status(thm)],[9]) ).
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/sandbox/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(l29,plain,
( ~ greater(zero,growth_rate(first_movers,sK2))
| ~ greater_or_equal(growth_rate(first_movers,sK2),zero) ),
inference(instantiation,[status(thm)],[4]) ).
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/sandbox/benchmark/theBenchmark.p',d2) ).
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(l31,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(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(l28,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(l32,plain,
outcompetes(first_movers,efficient_producers,sK2),
inference(instantiation,[status(thm)],[13]) ).
cnf(l33,plain,
outcompetes(first_movers,efficient_producers,sK2),
inference(instantiation,[status(thm)],[13]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l1,l2,l3,l4,l26,l27,l29,l31,l28,l32,l33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT036+2 : 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
% 0.08/0.35 % Computer : n007.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 7 12:38:56 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % launching worker at depth: 1
% 0.08/0.35 % launching worker at depth: 8
% 0.08/0.35 % launching worker at depth: 3
% 0.08/0.35 % launching worker at depth: 4
% 0.08/0.35 % launching worker at depth: 5
% 0.08/0.35 % launching worker at depth: 6
% 0.08/0.35 % launching worker at depth: 7
% 0.08/0.35 % launching worker at depth: 2
% 0.08/0.36 % launching worker at depth: 9
% 0.08/0.36 % launching worker at depth: 10
% 0.08/0.36 % launching worker at depth: 11
% 0.08/0.37 % SZS status Theorem for theBenchmark
% 0.08/0.37 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------