%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT023-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 12:02:32 PM UTC 2026
% Result : Unsatisfiable 0.14s 0.44s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 9
% Syntax : Number of formulae : 25 ( 6 unt; 0 def)
% Number of atoms : 96 ( 16 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 126 ( 55 ~; 71 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| X1 = critical_point(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_17) ).
fof(f2,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,sk1(X1,X0))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| critical_point(X0) = X1 ),
inference(reorient_equations,[],[f1]) ).
fof(f3,axiom,
! [X0,X1] :
( ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| greater(sk1(X1,X0),X1)
| X1 = critical_point(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_18) ).
fof(f4,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| greater(sk1(X1,X0),X1)
| ~ in_environment(X0,X1)
| ~ environment(X0)
| critical_point(X0) = X1 ),
inference(reorient_equations,[],[f3]) ).
fof(f5,axiom,
! [X0,X1] :
( ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| X1 = critical_point(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_19) ).
fof(f6,plain,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0)))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| critical_point(X0) = X1 ),
inference(reorient_equations,[],[f5]) ).
fof(f7,axiom,
! [X0] :
( in_environment(X0,sk2(X0))
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_20) ).
fof(f8,axiom,
! [X0] :
( ~ greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| ~ stable(X0)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_21) ).
fof(f9,axiom,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ stable(X0)
| ~ environment(X0)
| ~ greater(X1,sk2(X0))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12_22) ).
fof(f10,negated_conjecture,
environment(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_23) ).
fof(f11,negated_conjecture,
stable(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_24) ).
fof(f12,negated_conjecture,
~ in_environment(sk3,critical_point(sk3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5_25) ).
fof(f14,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| critical_point(X0) = X1
| ~ stable(X0)
| ~ environment(X0)
| ~ greater(sk1(X1,X0),sk2(X0))
| greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0))) ),
inference(resolution,[],[f2,f9]) ).
fof(f16,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| critical_point(X0) = X1
| ~ stable(X0)
| ~ greater(sk1(X1,X0),sk2(X0))
| greater(growth_rate(efficient_producers,sk1(X1,X0)),growth_rate(first_movers,sk1(X1,X0))) ),
inference(duplicate_literal_removal,[],[f14]) ).
fof(f21,plain,
! [X0,X1] :
( ~ greater(sk1(X1,X0),sk2(X0))
| ~ in_environment(X0,X1)
| ~ environment(X0)
| critical_point(X0) = X1
| ~ stable(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1)) ),
inference(forward_subsumption_resolution,[],[f16,f6]) ).
fof(f23,plain,
! [X0] :
( ~ in_environment(X0,sk2(X0))
| ~ environment(X0)
| critical_point(X0) = sk2(X0)
| ~ stable(X0)
| greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0)))
| ~ in_environment(X0,sk2(X0))
| ~ environment(X0)
| critical_point(X0) = sk2(X0) ),
inference(resolution,[],[f21,f4]) ).
fof(f24,plain,
! [X0] :
( ~ in_environment(X0,sk2(X0))
| ~ environment(X0)
| critical_point(X0) = sk2(X0)
| ~ stable(X0)
| greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0))) ),
inference(duplicate_literal_removal,[],[f23]) ).
fof(f26,plain,
! [X0] :
( ~ environment(X0)
| critical_point(X0) = sk2(X0)
| ~ stable(X0)
| greater(growth_rate(efficient_producers,sk2(X0)),growth_rate(first_movers,sk2(X0))) ),
inference(forward_subsumption_resolution,[],[f24,f7]) ).
fof(f28,plain,
! [X0] :
( ~ stable(X0)
| critical_point(X0) = sk2(X0)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[],[f26,f8]) ).
fof(f34,plain,
( critical_point(sk3) = sk2(sk3)
| ~ environment(sk3) ),
inference(resolution,[],[f28,f11]) ).
fof(f35,plain,
critical_point(sk3) = sk2(sk3),
inference(forward_subsumption_resolution,[],[f34,f10]) ).
fof(f40,plain,
( in_environment(sk3,critical_point(sk3))
| ~ stable(sk3)
| ~ environment(sk3) ),
inference(superposition,[],[f7,f35]) ).
fof(f41,plain,
( ~ stable(sk3)
| ~ environment(sk3) ),
inference(forward_subsumption_resolution,[],[f40,f12]) ).
fof(f46,plain,
~ environment(sk3),
inference(forward_subsumption_resolution,[],[f41,f11]) ).
fof(f51,plain,
$false,
inference(forward_subsumption_resolution,[],[f46,f10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT023-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.36 % Computer : n010.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 17:18:07 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.14/0.39 Running first-order model finding
% 0.14/0.39 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.14/0.44 % (1183727)Will run a generic schedule for satisfiability detection.
% 0.14/0.44 % (1183734)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1000123102:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.14/0.44 % (1183733)% WARNING: option uhcvi not known.
% 0.14/0.44 % (1183732)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2874833125_2999 on theBenchmark for (2999ds/0Mi)
% 0.14/0.44 % (1183733)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=796355633:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.14/0.44 % (1183735)dis+10_1_sil=32000:sp=arity:random_seed=281407572:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.14/0.44 % (1183736)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3662572605:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.14/0.44 % (1183737)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=635772690:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.14/0.44 % (1183738)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=346937591:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.14/0.44 % TRYING [1]
% 0.14/0.44 % TRYING [2]
% 0.14/0.44 % (1183736) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1183727-1183736"...
% 0.14/0.44 % (1183737) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1183727-1183737"...
% 0.14/0.44 % (1183735) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1183727-1183735"...
% 0.14/0.44 % TRYING [3]
% 0.14/0.44 % (1183733) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1183727-1183733"...
% 0.14/0.44 % (1183738) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1183727-1183738"...
% 0.14/0.44 % (1183734) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1183727-1183734"...
% 0.14/0.44 % (1183735)...printing done.
% 0.14/0.44 % (1183736)...printing done.
% 0.14/0.44 % (1183737)...printing done.
% 0.14/0.44 % (1183734)...printing done.
% 0.14/0.44 % (1183735)Refutation found. Thanks to Tanya!
% 0.14/0.44 % SZS status Unsatisfiable for theBenchmark
% 0.14/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.44 % (1183735)------------------------------
% 0.14/0.44 % (1183735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.14/0.44 % (1183735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.14/0.44 % (1183735)CaDiCaL version: 2.1.3
% 0.14/0.44 % (1183735)Termination reason: Refutation
% 0.14/0.44 % (1183735)Time elapsed: 0.003 s
% 0.14/0.44 % (1183735)Peak memory usage: 11 MB
% 0.14/0.44 % (1183735)Instructions burned: 3 (million)
% 0.14/0.44 % (1183727)Success in time 0.04 s
% 0.14/0.44 % Vampire exiting
%------------------------------------------------------------------------------