%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT032+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 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 12:02:06 PM UTC 2026
% Result : Theorem 2.58s 1.27s
% Output : Refutation 2.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 3
% Syntax : Number of formulae : 33 ( 5 unt; 0 def)
% Number of atoms : 132 ( 0 equ)
% Maximal formula atoms : 7 ( 4 avg)
% Number of connectives : 179 ( 80 ~; 66 |; 26 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 59 ( 50 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& subpopulations(X1,X2,X0,X3)
& greater(growth_rate(X2,X3),growth_rate(X1,X3)) )
=> selection_favors(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates) ).
fof(f2,axiom,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) )
=> greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l1) ).
fof(f3,conjecture,
! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) )
=> selection_favors(efficient_producers,first_movers,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t1) ).
fof(f4,negated_conjecture,
~ ! [X0] :
( ( environment(X0)
& stable(X0) )
=> ? [X1] :
( in_environment(X0,X1)
& ! [X2] :
( ( subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) )
=> selection_favors(efficient_producers,first_movers,X2) ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
fof(f5,plain,
! [X0] :
( ? [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_or_equal(X2,X1) ) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f6,plain,
! [X0] :
( ? [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_or_equal(X2,X1) ) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(flattening,[],[f5]) ).
fof(f7,plain,
? [X0] :
( ! [X1] :
( ~ in_environment(X0,X1)
| ? [X2] :
( ~ selection_favors(efficient_producers,first_movers,X2)
& subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) ) )
& environment(X0)
& stable(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f8,plain,
? [X0] :
( ! [X1] :
( ~ in_environment(X0,X1)
| ? [X2] :
( ~ selection_favors(efficient_producers,first_movers,X2)
& subpopulations(first_movers,efficient_producers,X0,X2)
& greater_or_equal(X2,X1) ) )
& environment(X0)
& stable(X0) ),
inference(flattening,[],[f7]) ).
fof(f9,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3)) ),
inference(ennf_transformation,[],[f1]) ).
fof(f10,plain,
! [X0,X1,X2,X3] :
( selection_favors(X2,X1,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3)) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0] :
( ( in_environment(X0,sK0(X0))
& ! [X2] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sK0(X0)) ) )
| ~ environment(X0)
| ~ stable(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f6]) ).
fof(f12,plain,
( ! [X1] :
( ~ in_environment(sK1,X1)
| ( ~ selection_favors(efficient_producers,first_movers,sK2(X1))
& subpopulations(first_movers,efficient_producers,sK1,sK2(X1))
& greater_or_equal(sK2(X1),X1) ) )
& environment(sK1)
& stable(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X2,sK2(X1))],[f8]) ).
fof(f13,plain,
! [X2,X0] :
( greater(growth_rate(efficient_producers,X2),growth_rate(first_movers,X2))
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ greater_or_equal(X2,sK0(X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f14,plain,
! [X0] :
( in_environment(X0,sK0(X0))
| ~ environment(X0)
| ~ stable(X0) ),
inference(cnf_transformation,[],[f11]) ).
fof(f15,plain,
stable(sK1),
inference(cnf_transformation,[],[f12]) ).
fof(f16,plain,
environment(sK1),
inference(cnf_transformation,[],[f12]) ).
fof(f17,plain,
! [X1] :
( greater_or_equal(sK2(X1),X1)
| ~ in_environment(sK1,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f18,plain,
! [X1] :
( subpopulations(first_movers,efficient_producers,sK1,sK2(X1))
| ~ in_environment(sK1,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f19,plain,
! [X1] :
( ~ selection_favors(efficient_producers,first_movers,sK2(X1))
| ~ in_environment(sK1,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f20,plain,
! [X2,X3,X0,X1] :
( ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| selection_favors(X2,X1,X3) ),
inference(cnf_transformation,[],[f10]) ).
fof(f21,plain,
! [X2,X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X2,X1)
| ~ greater_or_equal(X1,sK0(X0))
| ~ environment(X0)
| ~ stable(X0)
| ~ environment(X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| selection_favors(efficient_producers,first_movers,X1) ),
inference(resolution,[],[f13,f20]) ).
fof(f22,plain,
! [X0,X1] :
( ~ greater_or_equal(sK2(X0),sK0(X1))
| ~ environment(X1)
| ~ stable(X1)
| ~ environment(sK1)
| ~ subpopulations(first_movers,efficient_producers,X1,sK2(X0))
| selection_favors(efficient_producers,first_movers,sK2(X0))
| ~ in_environment(sK1,X0) ),
inference(resolution,[],[f21,f18]) ).
fof(f23,plain,
! [X0,X1] :
( ~ greater_or_equal(sK2(X0),sK0(X1))
| ~ environment(X1)
| ~ stable(X1)
| ~ subpopulations(first_movers,efficient_producers,X1,sK2(X0))
| selection_favors(efficient_producers,first_movers,sK2(X0))
| ~ in_environment(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f22,f16]) ).
fof(f24,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X1,sK2(X0))
| ~ environment(X1)
| ~ stable(X1)
| ~ greater_or_equal(sK2(X0),sK0(X1))
| ~ in_environment(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f23,f19]) ).
fof(f25,plain,
! [X0] :
( ~ environment(sK1)
| ~ stable(sK1)
| ~ greater_or_equal(sK2(X0),sK0(sK1))
| ~ in_environment(sK1,X0)
| ~ in_environment(sK1,X0) ),
inference(resolution,[],[f24,f18]) ).
fof(f26,plain,
! [X0] :
( ~ environment(sK1)
| ~ stable(sK1)
| ~ greater_or_equal(sK2(X0),sK0(sK1))
| ~ in_environment(sK1,X0) ),
inference(duplicate_literal_removal,[],[f25]) ).
fof(f27,plain,
! [X0] :
( ~ stable(sK1)
| ~ greater_or_equal(sK2(X0),sK0(sK1))
| ~ in_environment(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f26,f16]) ).
fof(f28,plain,
! [X0] :
( ~ greater_or_equal(sK2(X0),sK0(sK1))
| ~ in_environment(sK1,X0) ),
inference(forward_subsumption_resolution,[],[f27,f15]) ).
fof(f29,plain,
( ~ in_environment(sK1,sK0(sK1))
| ~ in_environment(sK1,sK0(sK1)) ),
inference(resolution,[],[f28,f17]) ).
fof(f30,plain,
~ in_environment(sK1,sK0(sK1)),
inference(duplicate_literal_removal,[],[f29]) ).
fof(f31,plain,
( ~ environment(sK1)
| ~ stable(sK1) ),
inference(resolution,[],[f30,f14]) ).
fof(f32,plain,
~ stable(sK1),
inference(forward_subsumption_resolution,[],[f31,f16]) ).
fof(f33,plain,
$false,
inference(forward_subsumption_resolution,[],[f32,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT032+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n009.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 17:21:15 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 2.58/1.27 % (2268199)Detected formulas, will run a generic FOF schedule.
% 2.58/1.27 % (2268207)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3959269290:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.58/1.27 % (2268207)First to succeed.
% 2.58/1.27 % (2268207)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2268199"
% 2.58/1.27 % (2268206)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=484679591:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.58/1.27 % (2268205)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1477186619:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.58/1.27 % (2268208)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3393821798:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.58/1.27 % (2268204)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=297719921:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.58/1.27 % (2268210)dis-21_1_sil=8000:lcm=predicate:random_seed=2172716403:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.58/1.27 % (2268208)Also succeeded, but the first one will report.
% 2.58/1.27 % (2268210)Also succeeded, but the first one will report.
% 2.58/1.27 % (2268209)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1133651035:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.58/1.27 % (2268209)Also succeeded, but the first one will report.
% 2.58/1.27 % (2268207)Refutation found. Thanks to Tanya!
% 2.58/1.27 % SZS status Theorem for theBenchmark
% 2.58/1.27 % SZS output start Proof for theBenchmark
% See solution above
% 2.58/1.27 % (2268207)------------------------------
% 2.58/1.27 % (2268207)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.58/1.27 % (2268207)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.58/1.27 % (2268207)CaDiCaL version: 2.1.3
% 2.58/1.27 % (2268207)Termination reason: Refutation
% 2.58/1.27 % (2268207)Time elapsed: 0.001 s
% 2.58/1.27 % (2268207)Peak memory usage: 88 MB
% 2.58/1.27 % (2268207)Instructions burned: 2 (million)
% 2.58/1.27 % (2268207)------------------------------
% 2.58/1.27 % (2268207)------------------------------
% 2.58/1.27 % (2268199)Success in time 0.306 s
% 2.58/1.27 % Vampire exiting
%------------------------------------------------------------------------------