%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : MGT023-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% 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 06:15:21 AM UTC 2026
% Result : Unsatisfiable 0.16s 0.45s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of clauses : 41 ( 7 unt; 23 nHn; 41 RR)
% Number of literals : 126 ( 27 equ; 57 neg)
% Maximal clause size : 5 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 8 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(d1_17,hypothesis,
( ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ in_environment(A,B)
| subpopulations(first_movers,efficient_producers,A,sk1(B,A))
| B = critical_point(A) ) ).
cnf(d1_18,hypothesis,
( ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ in_environment(A,B)
| greater(sk1(B,A),B)
| B = critical_point(A) ) ).
cnf(d1_19,hypothesis,
( ~ environment(A)
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| ~ in_environment(A,B)
| ~ greater(growth_rate(efficient_producers,sk1(B,A)),growth_rate(first_movers,sk1(B,A)))
| B = critical_point(A) ) ).
cnf(l12_20,hypothesis,
( ~ environment(A)
| ~ stable(A)
| in_environment(A,sk2(A)) ) ).
cnf(l12_21,hypothesis,
( ~ environment(A)
| ~ stable(A)
| ~ greater(growth_rate(efficient_producers,sk2(A)),growth_rate(first_movers,sk2(A))) ) ).
cnf(l12_22,hypothesis,
( ~ environment(A)
| ~ stable(A)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ greater(B,sk2(A))
| greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B)) ) ).
cnf(prove_l5_23,negated_conjecture,
environment(sk3) ).
cnf(prove_l5_24,negated_conjecture,
stable(sk3) ).
cnf(prove_l5_25,negated_conjecture,
~ in_environment(sk3,critical_point(sk3)) ).
cnf(refute_0_0,plain,
( ~ environment(sk3)
| ~ stable(sk3)
| in_environment(sk3,sk2(sk3)) ),
inference(subst,[],[l12_20:[bind(A,$fot(sk3))]]) ).
cnf(refute_0_1,plain,
( ~ environment(sk3)
| in_environment(sk3,sk2(sk3)) ),
inference(resolve,[$cnf( stable(sk3) )],[prove_l5_24,refute_0_0]) ).
cnf(refute_0_2,plain,
in_environment(sk3,sk2(sk3)),
inference(resolve,[$cnf( environment(sk3) )],[prove_l5_23,refute_0_1]) ).
cnf(refute_0_3,plain,
( ~ environment(sk3)
| ~ greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| ~ stable(sk3) ),
inference(subst,[],[l12_21:[bind(A,$fot(sk3))]]) ).
cnf(refute_0_4,plain,
( ~ environment(sk3)
| ~ in_environment(sk3,sk2(sk3))
| sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(subst,[],[d1_18:[bind(A,$fot(sk3)),bind(B,$fot(sk2(sk3)))]]) ).
cnf(refute_0_5,plain,
( ~ environment(sk3)
| sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(resolve,[$cnf( in_environment(sk3,sk2(sk3)) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l5_23,refute_0_5]) ).
cnf(refute_0_7,plain,
( ~ environment(sk3)
| ~ stable(sk3)
| sk2(sk3) = critical_point(sk3)
| greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(resolve,[$cnf( greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) )],[refute_0_6,refute_0_3]) ).
cnf(refute_0_8,plain,
( ~ stable(sk3)
| sk2(sk3) = critical_point(sk3)
| greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l5_23,refute_0_7]) ).
cnf(refute_0_9,plain,
( sk2(sk3) = critical_point(sk3)
| greater(sk1(sk2(sk3),sk3),sk2(sk3)) ),
inference(resolve,[$cnf( stable(sk3) )],[prove_l5_24,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ environment(sk3)
| ~ greater(sk1(sk2(sk3),sk3),sk2(sk3))
| ~ stable(sk3)
| ~ subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3))
| greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(subst,[],[l12_22:[bind(A,$fot(sk3)),bind(B,$fot(sk1(sk2(sk3),sk3)))]]) ).
cnf(refute_0_11,plain,
( ~ environment(sk3)
| ~ in_environment(sk3,sk2(sk3))
| sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(subst,[],[d1_17:[bind(A,$fot(sk3)),bind(B,$fot(sk2(sk3)))]]) ).
cnf(refute_0_12,plain,
( ~ environment(sk3)
| sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(resolve,[$cnf( in_environment(sk3,sk2(sk3)) )],[refute_0_2,refute_0_11]) ).
cnf(refute_0_13,plain,
( sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3)))
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l5_23,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ environment(sk3)
| ~ stable(sk3)
| sk2(sk3) = critical_point(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(resolve,[$cnf( greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) )],[refute_0_13,refute_0_3]) ).
cnf(refute_0_15,plain,
( ~ stable(sk3)
| sk2(sk3) = critical_point(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l5_23,refute_0_14]) ).
cnf(refute_0_16,plain,
( sk2(sk3) = critical_point(sk3)
| subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) ),
inference(resolve,[$cnf( stable(sk3) )],[prove_l5_24,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ environment(sk3)
| ~ greater(sk1(sk2(sk3),sk3),sk2(sk3))
| ~ stable(sk3)
| sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(resolve,[$cnf( subpopulations(first_movers,efficient_producers,sk3,sk1(sk2(sk3),sk3)) )],[refute_0_16,refute_0_10]) ).
cnf(refute_0_18,plain,
( ~ greater(sk1(sk2(sk3),sk3),sk2(sk3))
| ~ stable(sk3)
| sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l5_23,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ greater(sk1(sk2(sk3),sk3),sk2(sk3))
| sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(resolve,[$cnf( stable(sk3) )],[prove_l5_24,refute_0_18]) ).
cnf(refute_0_20,plain,
( sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3))) ),
inference(resolve,[$cnf( greater(sk1(sk2(sk3),sk3),sk2(sk3)) )],[refute_0_9,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ environment(sk3)
| ~ greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3)))
| ~ in_environment(sk3,sk2(sk3))
| sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
inference(subst,[],[d1_19:[bind(A,$fot(sk3)),bind(B,$fot(sk2(sk3)))]]) ).
cnf(refute_0_22,plain,
( ~ environment(sk3)
| ~ in_environment(sk3,sk2(sk3))
| sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
inference(resolve,[$cnf( greater(growth_rate(efficient_producers,sk1(sk2(sk3),sk3)),growth_rate(first_movers,sk1(sk2(sk3),sk3))) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ in_environment(sk3,sk2(sk3))
| sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l5_23,refute_0_22]) ).
cnf(refute_0_24,plain,
( sk2(sk3) = critical_point(sk3)
| greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) ),
inference(resolve,[$cnf( in_environment(sk3,sk2(sk3)) )],[refute_0_2,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ environment(sk3)
| ~ stable(sk3)
| sk2(sk3) = critical_point(sk3) ),
inference(resolve,[$cnf( greater(growth_rate(efficient_producers,sk2(sk3)),growth_rate(first_movers,sk2(sk3))) )],[refute_0_24,refute_0_3]) ).
cnf(refute_0_26,plain,
( ~ stable(sk3)
| sk2(sk3) = critical_point(sk3) ),
inference(resolve,[$cnf( environment(sk3) )],[prove_l5_23,refute_0_25]) ).
cnf(refute_0_27,plain,
sk2(sk3) = critical_point(sk3),
inference(resolve,[$cnf( stable(sk3) )],[prove_l5_24,refute_0_26]) ).
cnf(refute_0_28,plain,
( sk2(sk3) != critical_point(sk3)
| ~ in_environment(sk3,sk2(sk3))
| in_environment(sk3,critical_point(sk3)) ),
introduced(tautology,[equality,[$cnf( in_environment(sk3,sk2(sk3)) ),[1],$fot(critical_point(sk3))]]) ).
cnf(refute_0_29,plain,
( ~ in_environment(sk3,sk2(sk3))
| in_environment(sk3,critical_point(sk3)) ),
inference(resolve,[$cnf( $equal(sk2(sk3),critical_point(sk3)) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
in_environment(sk3,critical_point(sk3)),
inference(resolve,[$cnf( in_environment(sk3,sk2(sk3)) )],[refute_0_2,refute_0_29]) ).
cnf(refute_0_31,plain,
$false,
inference(resolve,[$cnf( in_environment(sk3,critical_point(sk3)) )],[refute_0_30,prove_l5_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : MGT023-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.06 % Command : metis --show proof --show saturation %s
% 0.16/0.42 % Computer : n007.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.43 % CPULimit : 300
% 0.16/0.43 % WCLimit : 300
% 0.16/0.43 % DateTime : Mon Sep 7 12:04:26 UTC 2026
% 0.16/0.43 % CPUTime :
% 0.16/0.44 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.16/0.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.45
% 0.16/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.16/0.46
%------------------------------------------------------------------------------