%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT023-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 12:02:03 PM UTC 2026
% Result : Unsatisfiable 3.56s 1.50s
% Output : Refutation 3.56s
% 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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',l12_22) ).
fof(f10,negated_conjecture,
environment(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l5_23) ).
fof(f11,negated_conjecture,
stable(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l5_24) ).
fof(f12,negated_conjecture,
~ in_environment(sk3,critical_point(sk3)),
file('/export/starexec/sandbox2/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(f17,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,[],[f17,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(f30,plain,
( critical_point(sk3) = sk2(sk3)
| ~ environment(sk3) ),
inference(resolution,[],[f28,f11]) ).
fof(f31,plain,
critical_point(sk3) = sk2(sk3),
inference(forward_subsumption_resolution,[],[f30,f10]) ).
fof(f40,plain,
( in_environment(sk3,critical_point(sk3))
| ~ stable(sk3)
| ~ environment(sk3) ),
inference(superposition,[],[f7,f31]) ).
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
% 0.00/0.03 % Problem : MGT023-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n015.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 17:21:05 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.42 Running first-order theorem proving
% 0.13/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.56/1.50 % (1878124)Input is clausal, will run a generic CNF schedule.
% 3.56/1.50 % (1878136)dis-21_1_sil=8000:lcm=predicate:random_seed=4021210877:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 3.56/1.50 % (1878136)Refutation not found, incomplete strategy
% 3.56/1.50 % (1878136)------------------------------
% 3.56/1.50 % (1878136)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.50 % (1878136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.50 % (1878136)CaDiCaL version: 2.1.3
% 3.56/1.50 % (1878136)Termination reason: Refutation not found, incomplete strategy
% 3.56/1.50 % (1878136)Time elapsed: 0.001 s
% 3.56/1.50 % (1878136)Peak memory usage: 88 MB
% 3.56/1.50 % (1878133)lrs+10_1_sil=8000:sp=occurrence:random_seed=3730111670:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 3.56/1.50 % (1878134)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=144357387:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 3.56/1.50 % (1878132)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=3240535417:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 3.56/1.50 % (1878131)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=786416256:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 3.56/1.50 % (1878130)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3885187289:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 3.56/1.50 % (1878135)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=878900390:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 3.56/1.50 % (1878133)First to succeed.
% 3.56/1.50 % (1878134)Also succeeded, but the first one will report.
% 3.56/1.50 % (1878133)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1878124"
% 3.56/1.50 % (1878135)Also succeeded, but the first one will report.
% 3.56/1.50 % (1878136)------------------------------
% 3.56/1.50 % (1878136)------------------------------
% 3.56/1.50 % (1878144)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=880569409:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 3.56/1.50 % (1878144)Also succeeded, but the first one will report.
% 3.56/1.50 % (1878133)Refutation found. Thanks to Tanya!
% 3.56/1.50 % SZS status Unsatisfiable for theBenchmark
% 3.56/1.50 % SZS output start Proof for theBenchmark
% See solution above
% 3.56/1.50 % (1878133)------------------------------
% 3.56/1.50 % (1878133)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.56/1.50 % (1878133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.56/1.50 % (1878133)CaDiCaL version: 2.1.3
% 3.56/1.50 % (1878133)Termination reason: Refutation
% 3.56/1.50 % (1878133)Time elapsed: 0.003 s
% 3.56/1.50 % (1878133)Peak memory usage: 88 MB
% 3.56/1.50 % (1878133)Instructions burned: 3 (million)
% 3.56/1.50 % (1878133)------------------------------
% 3.56/1.50 % (1878133)------------------------------
% 3.56/1.50 % (1878124)Success in time 0.414 s
% 3.56/1.50 % Vampire exiting
%------------------------------------------------------------------------------