%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT036-3 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n005.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 12:02:09 PM UTC 2026
% Result : Unsatisfiable 2.62s 1.33s
% Output : Refutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 16 ( 6 unt; 0 def)
% Number of atoms : 46 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 68 ( 38 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 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 : 21 ( 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( subpopulations(X2,X1,X0,X3)
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations_1) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater_or_equal(growth_rate(X2,X3),zero)
| ~ greater(zero,growth_rate(X1,X3))
| outcompetes(X2,X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_2) ).
fof(f5,axiom,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_5) ).
fof(f6,axiom,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_6) ).
fof(f7,axiom,
greater_or_equal(growth_rate(first_movers,sk2),zero),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_7) ).
fof(f8,axiom,
greater(zero,growth_rate(efficient_producers,sk2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_star_8) ).
fof(f9,negated_conjecture,
! [X0,X1] :
( ~ outcompetes(first_movers,efficient_producers,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_star_9) ).
fof(f10,plain,
! [X2,X0,X1] :
( outcompetes(X1,X0,X2)
| ~ greater_or_equal(growth_rate(X1,X2),zero)
| ~ greater(zero,growth_rate(X0,X2))
| ~ subpopulations(X0,X1,sk1,X2) ),
inference(resolution,[],[f2,f5]) ).
fof(f11,plain,
! [X0,X1] :
( ~ subpopulations(efficient_producers,first_movers,sk1,X0)
| ~ greater(zero,growth_rate(efficient_producers,X0))
| ~ greater_or_equal(growth_rate(first_movers,X0),zero)
| ~ subpopulations(first_movers,efficient_producers,X1,X0)
| ~ environment(X1) ),
inference(resolution,[],[f10,f9]) ).
fof(f12,plain,
! [X0,X1] :
( ~ greater(zero,growth_rate(efficient_producers,X0))
| ~ greater_or_equal(growth_rate(first_movers,X0),zero)
| ~ subpopulations(first_movers,efficient_producers,X1,X0)
| ~ environment(X1)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ environment(sk1) ),
inference(resolution,[],[f11,f1]) ).
fof(f13,plain,
! [X0,X1] :
( ~ environment(X1)
| ~ greater_or_equal(growth_rate(first_movers,X0),zero)
| ~ subpopulations(first_movers,efficient_producers,X1,X0)
| ~ greater(zero,growth_rate(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(forward_subsumption_resolution,[],[f12,f5]) ).
fof(f14,plain,
! [X0] :
( ~ greater_or_equal(growth_rate(first_movers,X0),zero)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ greater(zero,growth_rate(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[],[f13,f5]) ).
fof(f15,plain,
! [X0] :
( ~ greater(zero,growth_rate(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ greater_or_equal(growth_rate(first_movers,X0),zero) ),
inference(duplicate_literal_removal,[],[f14]) ).
fof(f16,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ greater_or_equal(growth_rate(first_movers,sk2),zero) ),
inference(resolution,[],[f15,f8]) ).
fof(f18,plain,
~ greater_or_equal(growth_rate(first_movers,sk2),zero),
inference(forward_subsumption_resolution,[],[f16,f6]) ).
fof(f19,plain,
$false,
inference(forward_subsumption_resolution,[],[f18,f7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036-3 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 % Computer : n005.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Sun Sep 27 17:22:47 UTC 2026
% 0.11/0.40 % CPUTime :
% 0.11/0.40 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.43 Running first-order theorem proving
% 0.11/0.43 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.62/1.33 % (39385)Input is clausal, will run a generic CNF schedule.
% 2.62/1.33 % (39395)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1185772516:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.62/1.33 % (39395)First to succeed.
% 2.62/1.33 % (39395)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-39385"
% 2.62/1.33 % (39392)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2584871804:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.62/1.33 % (39396)dis-21_1_sil=8000:lcm=predicate:random_seed=1153601579: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)
% 2.62/1.33 % (39390)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=2295964563:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.62/1.33 % (39391)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1104856509:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.62/1.33 % (39393)lrs+10_1_sil=8000:sp=occurrence:random_seed=3371621848:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.62/1.33 % (39393)Also succeeded, but the first one will report.
% 2.62/1.33 % (39396)Also succeeded, but the first one will report.
% 2.62/1.33 % (39394)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2427071776:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.62/1.33 % (39394)Also succeeded, but the first one will report.
% 2.62/1.33 % (39395)Refutation found. Thanks to Tanya!
% 2.62/1.33 % SZS status Unsatisfiable for theBenchmark
% 2.62/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 2.62/1.33 % (39395)------------------------------
% 2.62/1.33 % (39395)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.62/1.33 % (39395)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.62/1.33 % (39395)CaDiCaL version: 2.1.3
% 2.62/1.33 % (39395)Termination reason: Refutation
% 2.62/1.33 % (39395)Time elapsed: 0.001 s
% 2.62/1.33 % (39395)Peak memory usage: 88 MB
% 2.62/1.33 % (39395)Instructions burned: 1 (million)
% 2.62/1.33 % (39395)------------------------------
% 2.62/1.33 % (39395)------------------------------
% 2.62/1.33 % (39385)Success in time 0.288 s
% 2.62/1.33 % Vampire exiting
%------------------------------------------------------------------------------