%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT023+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n009.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 : Theorem 0.15s 0.46s
% Output : Refutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 35 ( 6 unt; 0 def)
% Number of atoms : 152 ( 17 equ)
% Maximal formula atoms : 9 ( 4 avg)
% Number of connectives : 195 ( 78 ~; 83 |; 28 &)
% ( 0 <=>; 6 =>; 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 : 46 ( 39 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( environment(X0)
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& in_environment(X0,X1)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater(X2,X1) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ) )
=> X1 = critical_point(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
fof(f2,axiom,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( in_environment(X0,X1)
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater(X2,X1) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l12) ).
fof(f3,conjecture,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> in_environment(X0,critical_point(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l5) ).
fof(f4,negated_conjecture,
~ ! [X0] :
( ( environment(X0)
& stable(X0) )
=> in_environment(X0,critical_point(X0)) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0,X1] :
( X1 = critical_point(X0)
| ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| ? [X2] :
( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& subpopulations(first_movers,efficient_producers,X0,X2)
& greater(X2,X1) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f6,plain,
! [X0,X1] :
( X1 = critical_point(X0)
| ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| ? [X2] :
( ~ greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
& subpopulations(first_movers,efficient_producers,X0,X2)
& greater(X2,X1) ) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
! [X0] :
( ? [X1] :
( in_environment(X0,X1)
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,X1) ) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f8,plain,
! [X0] :
( ? [X1] :
( in_environment(X0,X1)
& ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,X1) ) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
? [X0] :
( ~ in_environment(X0,critical_point(X0))
& environment(X0)
& stable(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
? [X0] :
( ~ in_environment(X0,critical_point(X0))
& environment(X0)
& stable(X0) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( X1 = critical_point(X0)
| ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| ( ~ greater(growth_rate(efficient_producers,sK0(X0,X1)),growth_rate(first_movers,sK0(X0,X1)))
& subpopulations(first_movers,efficient_producers,X0,sK0(X0,X1))
& greater(sK0(X0,X1),X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f6]) ).
fof(f12,plain,
! [X0] :
( ( in_environment(X0,sK1(X0))
& ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater(X2,sK1(X0)) ) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X1,sK1(X0))],[f8]) ).
fof(f13,plain,
( ~ in_environment(sK2,critical_point(sK2))
& environment(sK2)
& stable(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X0,sK2)],[f10]) ).
fof(f14,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| greater(sK0(X0,X1),X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| critical_point(X0) = X1 ),
inference(cnf_transformation,[],[f11]) ).
fof(f15,plain,
! [X0,X1] :
( subpopulations(first_movers,efficient_producers,X0,sK0(X0,X1))
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| critical_point(X0) = X1 ),
inference(cnf_transformation,[],[f11]) ).
fof(f16,plain,
! [X0,X1] :
( ~ greater(growth_rate(efficient_producers,sK0(X0,X1)),growth_rate(first_movers,sK0(X0,X1)))
| ~ environment(X0)
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ in_environment(X0,X1)
| critical_point(X0) = X1 ),
inference(cnf_transformation,[],[f11]) ).
fof(f17,plain,
! [X2,X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,X2)
| greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ greater(X2,sK1(X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
! [X0] :
( ~ greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X0] :
( in_environment(X0,sK1(X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
stable(sK2),
inference(cnf_transformation,[],[f13]) ).
fof(f21,plain,
environment(sK2),
inference(cnf_transformation,[],[f13]) ).
fof(f22,plain,
~ in_environment(sK2,critical_point(sK2)),
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| critical_point(X0) = X1
| greater(growth_rate(efficient_producers,sK0(X0,X1)),growth_rate(first_movers,sK0(X0,X1)))
| ~ greater(sK0(X0,X1),sK1(X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(resolution,[],[f15,f17]) ).
fof(f26,plain,
! [X0,X1] :
( greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| critical_point(X0) = X1
| greater(growth_rate(efficient_producers,sK0(X0,X1)),growth_rate(first_movers,sK0(X0,X1)))
| ~ greater(sK0(X0,X1),sK1(X0))
| ~ stable(X0) ),
inference(duplicate_literal_removal,[],[f24]) ).
fof(f31,plain,
! [X0,X1] :
( ~ greater(sK0(X0,X1),sK1(X0))
| ~ environment(X0)
| ~ in_environment(X0,X1)
| critical_point(X0) = X1
| greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| ~ stable(X0) ),
inference(forward_subsumption_resolution,[],[f26,f16]) ).
fof(f33,plain,
! [X0] :
( ~ environment(X0)
| ~ in_environment(X0,sK1(X0))
| critical_point(X0) = sK1(X0)
| greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
| ~ stable(X0)
| greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
| ~ environment(X0)
| ~ in_environment(X0,sK1(X0))
| critical_point(X0) = sK1(X0) ),
inference(resolution,[],[f31,f14]) ).
fof(f34,plain,
! [X0] :
( ~ environment(X0)
| ~ in_environment(X0,sK1(X0))
| critical_point(X0) = sK1(X0)
| greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
| ~ stable(X0) ),
inference(duplicate_literal_removal,[],[f33]) ).
fof(f36,plain,
! [X0] :
( ~ environment(X0)
| critical_point(X0) = sK1(X0)
| greater(growth_rate(efficient_producers,sK1(X0)),growth_rate(first_movers,sK1(X0)))
| ~ stable(X0) ),
inference(forward_subsumption_resolution,[],[f34,f19]) ).
fof(f38,plain,
! [X0] :
( ~ stable(X0)
| critical_point(X0) = sK1(X0)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[],[f36,f18]) ).
fof(f44,plain,
( critical_point(sK2) = sK1(sK2)
| ~ environment(sK2) ),
inference(resolution,[],[f38,f20]) ).
fof(f45,plain,
critical_point(sK2) = sK1(sK2),
inference(forward_subsumption_resolution,[],[f44,f21]) ).
fof(f50,plain,
( in_environment(sK2,critical_point(sK2))
| ~ environment(sK2)
| ~ stable(sK2) ),
inference(superposition,[],[f19,f45]) ).
fof(f51,plain,
( ~ environment(sK2)
| ~ stable(sK2) ),
inference(forward_subsumption_resolution,[],[f50,f22]) ).
fof(f56,plain,
~ stable(sK2),
inference(forward_subsumption_resolution,[],[f51,f21]) ).
fof(f61,plain,
$false,
inference(forward_subsumption_resolution,[],[f56,f20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT023+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n009.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 17:17:50 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.41 Running first-order model finding
% 0.10/0.41 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
% 0.15/0.46 % (2266986)Will run a generic schedule for satisfiability detection.
% 0.15/0.46 % (2266991)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1068423954_2999 on theBenchmark for (2999ds/0Mi)
% 0.15/0.46 % TRYING [1]
% 0.15/0.46 % TRYING [2]
% 0.15/0.46 % TRYING [3]
% 0.15/0.46 % (2266992)% WARNING: option uhcvi not known.
% 0.15/0.46 % (2266992)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3835128779:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.15/0.46 % (2266993)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3840108271:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.15/0.46 % (2266994)dis+10_1_sil=32000:sp=arity:random_seed=2189511120:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.15/0.46 % (2266995)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=435111568:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.15/0.46 % (2266997)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=987486479:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.15/0.46 % (2266996)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=151739524:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.15/0.46 % TRYING [4]
% 0.15/0.46 % (2266995) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2266986-2266995"...
% 0.15/0.46 % (2266992) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2266986-2266992"...
% 0.15/0.46 % (2266994) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2266986-2266994"...
% 0.15/0.46 % (2266996) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2266986-2266996"...
% 0.15/0.46 % (2266997) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2266986-2266997"...
% 0.15/0.46 % (2266995)...printing done.
% 0.15/0.46 % (2266994)...printing done.
% 0.15/0.46 % (2266992)...printing done.
% 0.15/0.46 % (2266996)...printing done.
% 0.15/0.46 % (2266994)Refutation found. Thanks to Tanya!
% 0.15/0.46 % SZS status Theorem for theBenchmark
% 0.15/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.47 % (2266994)------------------------------
% 0.15/0.47 % (2266994)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.15/0.47 % (2266994)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.15/0.47 % (2266994)CaDiCaL version: 2.1.3
% 0.15/0.47 % (2266994)Termination reason: Refutation
% 0.15/0.47 % (2266994)Time elapsed: 0.003 s
% 0.15/0.47 % (2266994)Peak memory usage: 11 MB
% 0.15/0.47 % (2266994)Instructions burned: 4 (million)
% 0.15/0.47 % (2266986)Success in time 0.044 s
% 0.15/0.47 % Vampire exiting
%------------------------------------------------------------------------------