%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT028-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 29 12:02:34 PM UTC 2026
% Result : Unsatisfiable 0.10s 0.45s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 14
% Syntax : Number of formulae : 44 ( 9 unt; 1 def)
% Number of atoms : 184 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 281 ( 141 ~; 139 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 2 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 45 ( 0 sgn 45 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ stable(X0)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(sk2(X0),appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_1) ).
fof(f2,axiom,
! [X0,X1] :
( greater_or_equal(sk1(X1,X0),X1)
| ~ stable(X0)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| greater(sk2(X0),appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_2) ).
fof(f3,axiom,
! [X2,X0,X1] :
( ~ greater_or_equal(X2,sk2(X0))
| ~ stable(X0)
| ~ in_environment(X0,X1)
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ environment(X0)
| greater(zero,growth_rate(first_movers,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_3) ).
fof(f4,axiom,
! [X2,X0,X1] :
( greater_or_equal(sk1(X1,X0),X1)
| ~ greater_or_equal(X2,sk2(X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ stable(X0)
| greater(zero,growth_rate(first_movers,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_4) ).
fof(f5,axiom,
! [X0,X1] :
( ~ in_environment(X0,X1)
| ~ stable(X0)
| ~ environment(X0)
| ~ greater(zero,growth_rate(first_movers,sk1(X1,X0)))
| greater(sk2(X0),appear(efficient_producers,X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_5) ).
fof(f6,axiom,
! [X2,X0,X1] :
( ~ greater_or_equal(X2,sk2(X0))
| ~ stable(X0)
| ~ in_environment(X0,X1)
| ~ greater(zero,growth_rate(first_movers,sk1(X1,X0)))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ environment(X0)
| greater(zero,growth_rate(first_movers,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_first_movers_negative_growth_6) ).
fof(f7,axiom,
! [X0] :
( in_environment(X0,sk3(X0))
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l11_7) ).
fof(f9,axiom,
! [X0,X1] :
( ~ greater_or_equal(X1,sk3(X0))
| ~ stable(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(zero,growth_rate(first_movers,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l11_9) ).
fof(f10,negated_conjecture,
environment(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_10) ).
fof(f11,negated_conjecture,
stable(sk4),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_11) ).
fof(f12,negated_conjecture,
! [X0] :
( subpopulations(first_movers,efficient_producers,sk4,sk5(X0))
| ~ greater(X0,appear(efficient_producers,sk4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_12) ).
fof(f13,negated_conjecture,
! [X0] :
( greater_or_equal(sk5(X0),X0)
| ~ greater(X0,appear(efficient_producers,sk4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_13) ).
fof(f14,negated_conjecture,
! [X0] :
( ~ greater(zero,growth_rate(first_movers,sk5(X0)))
| ~ greater(X0,appear(efficient_producers,sk4)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l10_14) ).
fof(f17,plain,
! [X0,X1] :
( ~ stable(X0)
| ~ in_environment(X0,sk3(X1))
| ~ environment(X0)
| greater(sk2(X0),appear(efficient_producers,X0))
| ~ stable(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,sk1(sk3(X1),X0))
| ~ environment(X1)
| greater(zero,growth_rate(first_movers,sk1(sk3(X1),X0))) ),
inference(resolution,[],[f2,f9]) ).
fof(f18,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X1,sk1(sk3(X1),X0))
| ~ in_environment(X0,sk3(X1))
| ~ environment(X0)
| greater(sk2(X0),appear(efficient_producers,X0))
| ~ stable(X1)
| ~ stable(X0)
| ~ environment(X1) ),
inference(forward_subsumption_resolution,[],[f17,f5]) ).
fof(f28,definition,
( spl0_1
<=> greater(sk2(sk4),appear(efficient_producers,sk4)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f29,plain,
( ~ greater(sk2(sk4),appear(efficient_producers,sk4))
| spl0_1 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f30,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f28]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ greater_or_equal(X2,sk2(X1))
| ~ in_environment(X1,sk3(X0))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ stable(X1)
| greater(zero,growth_rate(first_movers,X2))
| ~ stable(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sk1(sk3(X0),X1))
| ~ environment(X0)
| greater(zero,growth_rate(first_movers,sk1(sk3(X0),X1))) ),
inference(resolution,[],[f4,f9]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ greater_or_equal(X2,sk2(X1))
| ~ in_environment(X1,sk3(X0))
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,X2)
| ~ stable(X1)
| greater(zero,growth_rate(first_movers,X2))
| ~ stable(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sk1(sk3(X0),X1))
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[],[f36,f6]) ).
fof(f46,plain,
! [X0,X1] :
( ~ stable(X0)
| ~ in_environment(X0,X1)
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ subpopulations(first_movers,efficient_producers,X0,sk5(sk2(X0)))
| ~ environment(X0)
| greater(zero,growth_rate(first_movers,sk5(sk2(X0))))
| ~ greater(sk2(X0),appear(efficient_producers,sk4)) ),
inference(resolution,[],[f3,f13]) ).
fof(f51,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| ~ subpopulations(first_movers,efficient_producers,X0,sk5(sk2(X0)))
| ~ stable(X0)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| ~ greater(sk2(X0),appear(efficient_producers,sk4)) ),
inference(forward_subsumption_resolution,[],[f46,f14]) ).
fof(f73,plain,
! [X0] :
( ~ in_environment(X0,sk3(X0))
| ~ environment(X0)
| greater(sk2(X0),appear(efficient_producers,X0))
| ~ stable(X0)
| ~ stable(X0)
| ~ environment(X0)
| ~ stable(X0)
| ~ in_environment(X0,sk3(X0))
| ~ environment(X0)
| greater(sk2(X0),appear(efficient_producers,X0)) ),
inference(resolution,[],[f18,f1]) ).
fof(f74,plain,
! [X0] :
( ~ in_environment(X0,sk3(X0))
| ~ environment(X0)
| greater(sk2(X0),appear(efficient_producers,X0))
| ~ stable(X0) ),
inference(duplicate_literal_removal,[],[f73]) ).
fof(f76,plain,
! [X0] :
( ~ stable(X0)
| greater(sk2(X0),appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[],[f74,f7]) ).
fof(f83,plain,
! [X0,X1] :
( ~ in_environment(X0,sk3(X1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sk5(sk2(X0)))
| ~ stable(X0)
| greater(zero,growth_rate(first_movers,sk5(sk2(X0))))
| ~ stable(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,sk1(sk3(X1),X0))
| ~ environment(X1)
| ~ greater(sk2(X0),appear(efficient_producers,sk4)) ),
inference(resolution,[],[f45,f13]) ).
fof(f89,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk5(sk2(X0)))
| ~ subpopulations(first_movers,efficient_producers,X1,sk1(sk3(X1),X0))
| ~ in_environment(X0,sk3(X1))
| ~ stable(X0)
| ~ stable(X1)
| ~ environment(X0)
| ~ environment(X1)
| ~ greater(sk2(X0),appear(efficient_producers,sk4)) ),
inference(forward_subsumption_resolution,[],[f83,f14]) ).
fof(f97,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk5(sk2(X0)))
| ~ in_environment(X0,sk3(X0))
| ~ stable(X0)
| ~ stable(X0)
| ~ environment(X0)
| ~ environment(X0)
| ~ greater(sk2(X0),appear(efficient_producers,sk4))
| ~ subpopulations(first_movers,efficient_producers,X0,sk5(sk2(X0)))
| ~ stable(X0)
| ~ in_environment(X0,sk3(X0))
| ~ environment(X0)
| ~ greater(sk2(X0),appear(efficient_producers,sk4)) ),
inference(resolution,[],[f89,f51]) ).
fof(f100,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk5(sk2(X0)))
| ~ in_environment(X0,sk3(X0))
| ~ stable(X0)
| ~ environment(X0)
| ~ greater(sk2(X0),appear(efficient_producers,sk4)) ),
inference(duplicate_literal_removal,[],[f97]) ).
fof(f101,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk5(sk2(X0)))
| ~ stable(X0)
| ~ environment(X0)
| ~ greater(sk2(X0),appear(efficient_producers,sk4)) ),
inference(forward_subsumption_resolution,[],[f100,f7]) ).
fof(f116,plain,
( ~ stable(sk4)
| ~ environment(sk4)
| ~ greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ greater(sk2(sk4),appear(efficient_producers,sk4)) ),
inference(resolution,[],[f101,f12]) ).
fof(f117,plain,
( ~ stable(sk4)
| ~ environment(sk4)
| ~ greater(sk2(sk4),appear(efficient_producers,sk4)) ),
inference(duplicate_literal_removal,[],[f116]) ).
fof(f214,plain,
( greater(sk2(sk4),appear(efficient_producers,sk4))
| ~ environment(sk4) ),
inference(resolution,[],[f76,f11]) ).
fof(f215,plain,
( ~ environment(sk4)
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f214,f29]) ).
fof(f216,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[],[f215,f10]) ).
fof(f217,plain,
spl0_1,
inference(avatar_contradiction_clause,[],[f216]) ).
fof(f220,plain,
( ~ environment(sk4)
| ~ greater(sk2(sk4),appear(efficient_producers,sk4)) ),
inference(forward_subsumption_resolution,[],[f117,f11]) ).
fof(f223,plain,
~ greater(sk2(sk4),appear(efficient_producers,sk4)),
inference(forward_subsumption_resolution,[],[f220,f10]) ).
fof(f226,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f223,f30]) ).
fof(f227,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f226]) ).
cnf(s3,plain,
spl0_1,
inference(sat_conversion,[],[f217]) ).
cnf(s4,plain,
~ spl0_1,
inference(sat_conversion,[],[f227]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s3,s4]) ).
fof(f230,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT028-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n003.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 17:23:26 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.45 % (806656)Will run a generic schedule for satisfiability detection.
% 0.10/0.45 % (806665)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1326447736:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.10/0.45 % (806662)% WARNING: option uhcvi not known.
% 0.10/0.45 % (806665) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-806656-806665"...
% 0.10/0.45 % (806665)...printing done.
% 0.10/0.45 % (806664)dis+10_1_sil=32000:sp=arity:random_seed=467420073:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.10/0.45 % (806665)Refutation found. Thanks to Tanya!
% 0.10/0.45 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.45 % (806665)------------------------------
% 0.10/0.45 % (806665)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.45 % (806665)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.45 % (806665)CaDiCaL version: 2.1.3
% 0.10/0.45 % (806665)Termination reason: Refutation
% 0.10/0.45 % (806665)Time elapsed: 0.005 s
% 0.10/0.45 % (806665)Peak memory usage: 12 MB
% 0.10/0.45 % (806665)Instructions burned: 15 (million)
% 0.10/0.45 % (806656)Success in time 0.03 s
% 0.10/0.45 % Vampire exiting
%------------------------------------------------------------------------------