%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT036-3 : TPTP v9.3.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n006.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 06:16:06 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of clauses : 19 ( 8 unt; 0 nHn; 19 RR)
% Number of literals : 43 ( 0 equ; 28 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(mp_symmetry_of_subpopulations_1,axiom,
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| subpopulations(C,B,A,D) ) ).
cnf(d2_2,hypothesis,
( ~ environment(A)
| ~ subpopulations(B,C,A,D)
| ~ greater_or_equal(growth_rate(C,D),zero)
| ~ greater(zero,growth_rate(B,D))
| outcompetes(C,B,D) ) ).
cnf(a13_star_5,hypothesis,
environment(sk1) ).
cnf(a13_star_6,hypothesis,
subpopulations(first_movers,efficient_producers,sk1,sk2) ).
cnf(a13_star_7,hypothesis,
greater_or_equal(growth_rate(first_movers,sk2),zero) ).
cnf(a13_star_8,hypothesis,
greater(zero,growth_rate(efficient_producers,sk2)) ).
cnf(prove_t5_star_9,negated_conjecture,
( ~ environment(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ outcompetes(first_movers,efficient_producers,B) ) ).
cnf(refute_0_0,plain,
( ~ environment(sk1)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| subpopulations(efficient_producers,first_movers,sk1,sk2) ),
inference(subst,[],[mp_symmetry_of_subpopulations_1:[bind(A,$fot(sk1)),bind(B,$fot(first_movers)),bind(C,$fot(efficient_producers)),bind(D,$fot(sk2))]]) ).
cnf(refute_0_1,plain,
( ~ environment(sk1)
| subpopulations(efficient_producers,first_movers,sk1,sk2) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,sk1,sk2) )],[a13_star_6,refute_0_0]) ).
cnf(refute_0_2,plain,
subpopulations(efficient_producers,first_movers,sk1,sk2),
inference(resolve,[$cnf( environment(sk1) )],[a13_star_5,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ environment(sk1)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero)
| ~ subpopulations(efficient_producers,first_movers,sk1,sk2)
| outcompetes(first_movers,efficient_producers,sk2) ),
inference(subst,[],[d2_2:[bind(A,$fot(sk1)),bind(B,$fot(efficient_producers)),bind(C,$fot(first_movers)),bind(D,$fot(sk2))]]) ).
cnf(refute_0_4,plain,
( ~ environment(sk1)
| ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero)
| outcompetes(first_movers,efficient_producers,sk2) ),
inference(resolve,[$cnf( subpopulations(efficient_producers,first_movers,sk1,sk2) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( ~ greater(zero,growth_rate(efficient_producers,sk2))
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero)
| outcompetes(first_movers,efficient_producers,sk2) ),
inference(resolve,[$cnf( environment(sk1) )],[a13_star_5,refute_0_4]) ).
cnf(refute_0_6,plain,
( ~ greater_or_equal(growth_rate(first_movers,sk2),zero)
| outcompetes(first_movers,efficient_producers,sk2) ),
inference(resolve,[$cnf( greater(zero,growth_rate(efficient_producers,sk2)) )],[a13_star_8,refute_0_5]) ).
cnf(refute_0_7,plain,
outcompetes(first_movers,efficient_producers,sk2),
inference(resolve,[$cnf( greater_or_equal(growth_rate(first_movers,sk2),zero) )],[a13_star_7,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ environment(sk1)
| ~ outcompetes(first_movers,efficient_producers,sk2)
| ~ subpopulations(first_movers,efficient_producers,sk1,sk2) ),
inference(subst,[],[prove_t5_star_9:[bind(A,$fot(sk1)),bind(B,$fot(sk2))]]) ).
cnf(refute_0_9,plain,
( ~ environment(sk1)
| ~ outcompetes(first_movers,efficient_producers,sk2) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,sk1,sk2) )],[a13_star_6,refute_0_8]) ).
cnf(refute_0_10,plain,
~ outcompetes(first_movers,efficient_producers,sk2),
inference(resolve,[$cnf( environment(sk1) )],[a13_star_5,refute_0_9]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( outcompetes(first_movers,efficient_producers,sk2) )],[refute_0_7,refute_0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036-3 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.04 % Command : metis --show proof --show saturation %s
% 0.07/0.34 % Computer : n006.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 7 12:42:31 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------