%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT036-2 : 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 : n013.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 : Unsatisfiable 2.52s 1.24s
% Output : Refutation 2.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 40 ( 15 unt; 2 def)
% Number of atoms : 81 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 87 ( 46 ~; 39 |; 0 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 3 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| subpopulations(X2,X1,X0,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations_1) ).
fof(f2,axiom,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occur_2) ).
fof(f3,axiom,
! [X2,X0,X1] :
( environment(X0)
| ~ greater(zero,growth_rate(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_relationships_3) ).
fof(f5,axiom,
! [X0,X1] :
( ~ greater_or_equal(growth_rate(X0,X1),zero)
| ~ greater(zero,growth_rate(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_growth_rate_relationships_5) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| ~ outcompetes(X2,X1,X3)
| greater_or_equal(growth_rate(X2,X3),zero) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_8) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| ~ outcompetes(X2,X1,X3)
| greater(zero,growth_rate(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_9) ).
fof(f10,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a2_10) ).
fof(f11,axiom,
! [X2,X3,X0,X1] :
( ~ greater(resilience(X3),resilience(X2))
| ~ in_environment(X0,X1)
| greater(zero,growth_rate(X2,X1))
| ~ environment(X0)
| ~ greater(zero,growth_rate(X3,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a13_11) ).
fof(f12,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_12) ).
fof(f13,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_13) ).
fof(f14,negated_conjecture,
outcompetes(first_movers,efficient_producers,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_t5_14) ).
fof(f16,definition,
( spl0_1
<=> ! [X2,X1] : ~ greater(zero,growth_rate(X1,X2)) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
fof(f17,plain,
( ! [X2,X1] : ~ greater(zero,growth_rate(X1,X2))
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f16]) ).
fof(f19,definition,
( spl0_2
<=> ! [X0] : environment(X0) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
fof(f20,plain,
( ! [X0] : environment(X0)
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f19]) ).
fof(f21,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f3,f19,f16]) ).
fof(f30,plain,
( ~ environment(sk1)
| in_environment(sk1,sk2) ),
inference(resolution,[],[f2,f13]) ).
fof(f31,plain,
in_environment(sk1,sk2),
inference(forward_subsumption_resolution,[],[f30,f12]) ).
fof(f32,plain,
( ~ environment(sk1)
| subpopulations(efficient_producers,first_movers,sk1,sk2) ),
inference(resolution,[],[f1,f13]) ).
fof(f33,plain,
subpopulations(efficient_producers,first_movers,sk1,sk2),
inference(forward_subsumption_resolution,[],[f32,f12]) ).
fof(f36,plain,
( ~ environment(sk1)
| ~ outcompetes(first_movers,efficient_producers,sk2)
| greater_or_equal(growth_rate(first_movers,sk2),zero) ),
inference(resolution,[],[f8,f33]) ).
fof(f37,plain,
( ~ outcompetes(first_movers,efficient_producers,sk2)
| greater_or_equal(growth_rate(first_movers,sk2),zero) ),
inference(forward_subsumption_resolution,[],[f36,f12]) ).
fof(f39,plain,
greater_or_equal(growth_rate(first_movers,sk2),zero),
inference(forward_subsumption_resolution,[],[f37,f14]) ).
fof(f50,plain,
( ~ environment(sk1)
| ~ outcompetes(first_movers,efficient_producers,sk2)
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(resolution,[],[f9,f33]) ).
fof(f51,plain,
( ~ outcompetes(first_movers,efficient_producers,sk2)
| greater(zero,growth_rate(efficient_producers,sk2)) ),
inference(forward_subsumption_resolution,[],[f50,f12]) ).
fof(f52,plain,
greater(zero,growth_rate(efficient_producers,sk2)),
inference(forward_subsumption_resolution,[],[f51,f14]) ).
fof(f56,plain,
~ greater(zero,growth_rate(first_movers,sk2)),
inference(resolution,[],[f39,f5]) ).
fof(f57,plain,
! [X0,X1] :
( ~ in_environment(X0,X1)
| greater(zero,growth_rate(first_movers,X1))
| ~ environment(X0)
| ~ greater(zero,growth_rate(efficient_producers,X1)) ),
inference(resolution,[],[f11,f10]) ).
fof(f58,plain,
( ! [X0,X1] :
( ~ greater(zero,growth_rate(efficient_producers,X1))
| greater(zero,growth_rate(first_movers,X1))
| ~ in_environment(X0,X1) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f57,f20]) ).
fof(f60,plain,
( ! [X0] :
( greater(zero,growth_rate(first_movers,sk2))
| ~ in_environment(X0,sk2) )
| ~ spl0_2 ),
inference(resolution,[],[f58,f52]) ).
fof(f61,plain,
( ! [X0] : ~ in_environment(X0,sk2)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f60,f56]) ).
fof(f62,plain,
( $false
| ~ spl0_2 ),
inference(resolution,[],[f61,f31]) ).
fof(f63,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[],[f62]) ).
fof(f64,plain,
( $false
| ~ spl0_1 ),
inference(resolution,[],[f17,f52]) ).
fof(f65,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f64]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s4,plain,
~ spl0_2,
inference(sat_conversion,[],[f63]) ).
cnf(s5,plain,
~ spl0_1,
inference(sat_conversion,[],[f65]) ).
cnf(s6,plain,
$false,
inference(rat,[],[s1,s4,s5]) ).
fof(f66,plain,
$false,
inference(avatar_sat_refutation,[],[s6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT036-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.38 % Computer : n013.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sun Sep 27 17:22:37 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 2.52/1.24 % (437206)Input is clausal, will run a generic CNF schedule.
% 2.52/1.24 % (437214)lrs+10_1_sil=8000:sp=occurrence:random_seed=1614552443:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 2.52/1.24 % (437214)First to succeed.
% 2.52/1.24 % (437214)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-437206"
% 2.52/1.24 % (437213)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=149170780:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 2.52/1.24 % (437211)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=1939061750:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 2.52/1.24 % (437212)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=607073993:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 2.52/1.24 % (437216)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3212634730:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 2.52/1.24 % (437217)dis-21_1_sil=8000:lcm=predicate:random_seed=3554155611: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)
% 2.52/1.24 % (437215)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1940945790:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 2.52/1.24 % (437217)Also succeeded, but the first one will report.
% 2.52/1.24 % (437216)Also succeeded, but the first one will report.
% 2.52/1.24 % (437215)Also succeeded, but the first one will report.
% 2.52/1.24 % (437214)Refutation found. Thanks to Tanya!
% 2.52/1.24 % SZS status Unsatisfiable for theBenchmark
% 2.52/1.24 % SZS output start Proof for theBenchmark
% See solution above
% 2.52/1.24 % (437214)------------------------------
% 2.52/1.24 % (437214)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.52/1.24 % (437214)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.52/1.24 % (437214)CaDiCaL version: 2.1.3
% 2.52/1.24 % (437214)Termination reason: Refutation
% 2.52/1.24 % (437214)Time elapsed: 0.002 s
% 2.52/1.24 % (437214)Peak memory usage: 89 MB
% 2.52/1.24 % (437214)Instructions burned: 2 (million)
% 2.52/1.24 % (437214)------------------------------
% 2.52/1.24 % (437214)------------------------------
% 2.52/1.24 % (437206)Success in time 0.284 s
% 2.52/1.24 % Vampire exiting
%------------------------------------------------------------------------------