%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT036+2 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 12:02:08 PM UTC 2026
% Result : Theorem 3.03s 1.26s
% Output : Refutation 3.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 9
% Syntax : Number of formulae : 63 ( 17 unt; 2 def)
% Number of atoms : 184 ( 0 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 213 ( 92 ~; 78 |; 28 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 2 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 106 ( 0 sgn 102 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& subpopulations(X1,X2,X0,X3) )
=> subpopulations(X2,X1,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations) ).
fof(f2,axiom,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> in_environment(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur) ).
fof(f3,axiom,
! [X0,X1,X2,X3] :
( ( ( environment(X0)
& subpopulations(X1,X2,X0,X3) )
=> greater_or_equal(growth_rate(X1,X3),zero) )
<=> ~ greater(zero,growth_rate(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_relationships) ).
fof(f4,axiom,
! [X0,X1,X2,X3] :
( ( 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) ).
fof(f5,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2) ).
fof(f6,axiom,
! [X0,X1,X2,X3] :
( ( environment(X0)
& in_environment(X0,X3)
& ~ greater(zero,growth_rate(X1,X3))
& greater(resilience(X2),resilience(X1)) )
=> ~ greater(zero,growth_rate(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13) ).
fof(f7,conjecture,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> ~ outcompetes(first_movers,efficient_producers,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> ~ outcompetes(first_movers,efficient_producers,X1) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0,X1,X2,X3] :
( ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
<=> outcompetes(X2,X1,X3) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(ennf_transformation,[],[f4]) ).
fof(f10,plain,
! [X0,X1,X2,X3] :
( ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
<=> outcompetes(X2,X1,X3) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1,X2,X3] :
( ~ greater(zero,growth_rate(X2,X3))
| ~ environment(X0)
| ~ in_environment(X0,X3)
| greater(zero,growth_rate(X1,X3))
| ~ greater(resilience(X2),resilience(X1)) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,plain,
! [X0,X1,X2,X3] :
( ~ greater(zero,growth_rate(X2,X3))
| ~ environment(X0)
| ~ in_environment(X0,X3)
| greater(zero,growth_rate(X1,X3))
| ~ greater(resilience(X2),resilience(X1)) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
? [X0,X1] :
( outcompetes(first_movers,efficient_producers,X1)
& environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f14,plain,
? [X0,X1] :
( outcompetes(first_movers,efficient_producers,X1)
& environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1,X2,X3] :
( subpopulations(X2,X1,X0,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(ennf_transformation,[],[f1]) ).
fof(f16,plain,
! [X0,X1,X2,X3] :
( subpopulations(X2,X1,X0,X3)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(growth_rate(X1,X3),zero)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) )
<=> ~ greater(zero,growth_rate(X1,X3)) ),
inference(ennf_transformation,[],[f3]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(growth_rate(X1,X3),zero)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) )
<=> ~ greater(zero,growth_rate(X1,X3)) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f20,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
! [X0,X1,X2,X3] :
( ( ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
| ~ outcompetes(X2,X1,X3) )
& ( outcompetes(X2,X1,X3)
| ~ greater_or_equal(growth_rate(X2,X3),zero)
| ~ greater(zero,growth_rate(X1,X3)) ) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(nnf_transformation,[],[f10]) ).
fof(f22,plain,
! [X0,X1,X2,X3] :
( ( ( ( greater_or_equal(growth_rate(X2,X3),zero)
& greater(zero,growth_rate(X1,X3)) )
| ~ outcompetes(X2,X1,X3) )
& ( outcompetes(X2,X1,X3)
| ~ greater_or_equal(growth_rate(X2,X3),zero)
| ~ greater(zero,growth_rate(X1,X3)) ) )
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3) ),
inference(flattening,[],[f21]) ).
fof(f23,plain,
( outcompetes(first_movers,efficient_producers,sK1)
& environment(sK0)
& subpopulations(first_movers,efficient_producers,sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f14]) ).
fof(f24,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(growth_rate(X1,X3),zero)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| greater(zero,growth_rate(X1,X3)) )
& ( ~ greater(zero,growth_rate(X1,X3))
| ( ~ greater_or_equal(growth_rate(X1,X3),zero)
& environment(X0)
& subpopulations(X1,X2,X0,X3) ) ) ),
inference(nnf_transformation,[],[f18]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ( greater_or_equal(growth_rate(X1,X3),zero)
| ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| greater(zero,growth_rate(X1,X3)) )
& ( ~ greater(zero,growth_rate(X1,X3))
| ( ~ greater_or_equal(growth_rate(X1,X3),zero)
& environment(X0)
& subpopulations(X1,X2,X0,X3) ) ) ),
inference(flattening,[],[f24]) ).
fof(f27,plain,
! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ outcompetes(X2,X1,X3)
| ~ environment(X0)
| greater(zero,growth_rate(X1,X3)) ),
inference(cnf_transformation,[],[f22]) ).
fof(f28,plain,
! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ outcompetes(X2,X1,X3)
| ~ environment(X0)
| greater_or_equal(growth_rate(X2,X3),zero) ),
inference(cnf_transformation,[],[f22]) ).
fof(f29,plain,
greater(resilience(efficient_producers),resilience(first_movers)),
inference(cnf_transformation,[],[f5]) ).
fof(f30,plain,
! [X2,X3,X0,X1] :
( ~ greater(zero,growth_rate(X2,X3))
| ~ environment(X0)
| ~ in_environment(X0,X3)
| greater(zero,growth_rate(X1,X3))
| ~ greater(resilience(X2),resilience(X1)) ),
inference(cnf_transformation,[],[f12]) ).
fof(f31,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f32,plain,
environment(sK0),
inference(cnf_transformation,[],[f23]) ).
fof(f33,plain,
outcompetes(first_movers,efficient_producers,sK1),
inference(cnf_transformation,[],[f23]) ).
fof(f34,plain,
! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| subpopulations(X2,X1,X0,X3) ),
inference(cnf_transformation,[],[f16]) ).
fof(f37,plain,
! [X3,X1] :
( ~ greater(zero,growth_rate(X1,X3))
| ~ greater_or_equal(growth_rate(X1,X3),zero) ),
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(cnf_transformation,[],[f20]) ).
fof(f40,plain,
! [X3,X0] :
( ~ in_environment(X0,X3)
| ~ environment(X0)
| sP2(X3) ),
inference(cnf_transformation,[],[f40_D]) ).
fof(f40_D,definition,
! [X3] :
( ! [X0] :
( ~ in_environment(X0,X3)
| ~ environment(X0) )
<=> ~ sP2(X3) ),
introduced(definition,[new_symbols(definition,[sP2])],[general_splitting_component_introduction]) ).
fof(f41,plain,
! [X2,X3,X1] :
( ~ greater(resilience(X2),resilience(X1))
| greater(zero,growth_rate(X1,X3))
| ~ greater(zero,growth_rate(X2,X3))
| ~ sP2(X3) ),
inference(general_splitting,[],[f30,f40_D]) ).
fof(f44,plain,
( ~ environment(sK0)
| in_environment(sK0,sK1) ),
inference(resolution,[],[f31,f39]) ).
fof(f45,plain,
( ~ environment(sK0)
| subpopulations(efficient_producers,first_movers,sK0,sK1) ),
inference(resolution,[],[f31,f34]) ).
fof(f46,plain,
subpopulations(efficient_producers,first_movers,sK0,sK1),
inference(forward_subsumption_resolution,[],[f45,f32]) ).
fof(f47,plain,
in_environment(sK0,sK1),
inference(forward_subsumption_resolution,[],[f44,f32]) ).
fof(f48,plain,
( ~ environment(sK0)
| sP2(sK1) ),
inference(resolution,[],[f40,f47]) ).
fof(f49,plain,
sP2(sK1),
inference(forward_subsumption_resolution,[],[f48,f32]) ).
fof(f53,definition,
( spl4_1
<=> greater(zero,growth_rate(first_movers,sK1)) ),
introduced(definition,[new_symbols(definition,[spl4_1])],[avatar_definition]) ).
fof(f55,plain,
( greater(zero,growth_rate(first_movers,sK1))
| ~ spl4_1 ),
inference(avatar_component_clause,[],[f53]) ).
fof(f62,plain,
( ~ outcompetes(first_movers,efficient_producers,sK1)
| ~ environment(sK0)
| greater_or_equal(growth_rate(first_movers,sK1),zero) ),
inference(resolution,[],[f46,f28]) ).
fof(f63,plain,
( ~ outcompetes(first_movers,efficient_producers,sK1)
| ~ environment(sK0)
| greater(zero,growth_rate(efficient_producers,sK1)) ),
inference(resolution,[],[f46,f27]) ).
fof(f65,plain,
( ~ environment(sK0)
| greater(zero,growth_rate(efficient_producers,sK1)) ),
inference(forward_subsumption_resolution,[],[f63,f33]) ).
fof(f66,plain,
( ~ environment(sK0)
| greater_or_equal(growth_rate(first_movers,sK1),zero) ),
inference(forward_subsumption_resolution,[],[f62,f33]) ).
fof(f67,plain,
greater(zero,growth_rate(efficient_producers,sK1)),
inference(forward_subsumption_resolution,[],[f65,f32]) ).
fof(f68,plain,
greater_or_equal(growth_rate(first_movers,sK1),zero),
inference(forward_subsumption_resolution,[],[f66,f32]) ).
fof(f69,plain,
! [X0] :
( ~ greater(zero,growth_rate(efficient_producers,X0))
| greater(zero,growth_rate(first_movers,X0))
| ~ sP2(X0) ),
inference(resolution,[],[f41,f29]) ).
fof(f73,plain,
( greater(zero,growth_rate(first_movers,sK1))
| ~ sP2(sK1) ),
inference(resolution,[],[f69,f67]) ).
fof(f74,plain,
greater(zero,growth_rate(first_movers,sK1)),
inference(forward_subsumption_resolution,[],[f73,f49]) ).
fof(f75,plain,
spl4_1,
inference(avatar_split_clause,[],[f74,f53]) ).
fof(f77,plain,
( ~ greater_or_equal(growth_rate(first_movers,sK1),zero)
| ~ spl4_1 ),
inference(resolution,[],[f55,f37]) ).
fof(f79,plain,
( $false
| ~ spl4_1 ),
inference(forward_subsumption_resolution,[],[f77,f68]) ).
fof(f80,plain,
~ spl4_1,
inference(avatar_contradiction_clause,[],[f79]) ).
cnf(s2,plain,
spl4_1,
inference(sat_conversion,[],[f75]) ).
cnf(s3,plain,
~ spl4_1,
inference(sat_conversion,[],[f80]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s2,s3]) ).
fof(f81,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT036+2 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.35 % Computer : n015.cluster.edu
% 0.11/0.35 % Model : x86_64 x86_64
% 0.11/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.35 % Memory : 8046.5625MB
% 0.11/0.35 % 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 17:25:46 UTC 2026
% 0.05/0.36 % CPUTime :
% 0.05/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.39 Running first-order theorem proving
% 0.05/0.39 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
% 3.03/1.26 % (1883080)Detected formulas, will run a generic FOF schedule.
% 3.03/1.26 % (1883087)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=2793439632:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.03/1.26 % (1883090)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3229007711:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.03/1.26 % (1883086)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=2111500178:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.03/1.26 % (1883089)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3554741314:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.03/1.26 % (1883088)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=3075435015:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.03/1.26 % (1883085)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=2045635075:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.03/1.26 % (1883088)First to succeed.
% 3.03/1.26 % (1883090)Also succeeded, but the first one will report.
% 3.03/1.26 % (1883088)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1883080"
% 3.03/1.26 % (1883089)Also succeeded, but the first one will report.
% 3.03/1.26 % (1883091)dis-21_1_sil=8000:lcm=predicate:random_seed=3785370514: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)
% 3.03/1.26 % (1883091)Also succeeded, but the first one will report.
% 3.03/1.26 % (1883088)Refutation found. Thanks to Tanya!
% 3.03/1.26 % SZS status Theorem for theBenchmark
% 3.03/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.64/1.46 % (1883088)------------------------------
% 3.64/1.46 % (1883088)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.64/1.46 % (1883088)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.64/1.46 % (1883088)CaDiCaL version: 2.1.3
% 3.64/1.46 % (1883088)Termination reason: Refutation
% 3.64/1.46 % (1883088)Time elapsed: 0.004 s
% 3.64/1.46 % (1883088)Peak memory usage: 89 MB
% 3.64/1.46 % (1883088)Instructions burned: 3 (million)
% 3.64/1.46 % (1883088)------------------------------
% 3.64/1.46 % (1883088)------------------------------
% 3.64/1.46 % (1883080)Success in time 0.43 s
% 3.64/1.46 % Vampire exiting
%------------------------------------------------------------------------------