%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT036-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n003.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 0.88s 1.14s
% Output : Refutation 2.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 69 ( 13 unt; 4 def)
% Number of atoms : 200 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 282 ( 151 ~; 127 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 5 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 130 ( 0 sgn 130 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_FM_and_EP_1) ).
fof(f2,axiom,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships_3) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( ~ greater(zero,growth_rate(X0,X3))
| subpopulations(X0,X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships_4) ).
fof(f5,axiom,
! [X0,X1] :
( ~ greater_or_equal(growth_rate(X0,X1),zero)
| ~ greater(zero,growth_rate(X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_growth_rate_relationships_5) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( greater_or_equal(growth_rate(X2,X3),zero)
| ~ subpopulations(X1,X2,X0,X3)
| ~ outcompetes(X2,X1,X3)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_8) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ subpopulations(X1,X2,X0,X3)
| ~ outcompetes(X2,X1,X3)
| greater(zero,growth_rate(X1,X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_9) ).
fof(f10,axiom,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ in_environment(X0,X1)
| greater(zero,growth_rate(X2,X1))
| ~ greater(resilience(X3),resilience(X2))
| ~ greater(zero,growth_rate(X3,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a12_10) ).
fof(f11,axiom,
greater(resilience(efficient_producers),resilience(first_movers)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a2_11) ).
fof(f12,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_12) ).
fof(f13,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t5_13) ).
fof(f14,negated_conjecture,
outcompetes(first_movers,efficient_producers,sk2),
file('/export/starexec/sandbox2/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(f22,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| in_environment(X0,X1) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f2,f20]) ).
fof(f24,plain,
( ! [X0,X1] :
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f1,f20]) ).
fof(f27,plain,
( ! [X2,X3,X0,X1] :
( greater(zero,growth_rate(X1,X3))
| ~ outcompetes(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f9,f20]) ).
fof(f36,definition,
( spl0_3
<=> ! [X0] : in_environment(X0,sk2) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f37,plain,
( ! [X0] : in_environment(X0,sk2)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f36]) ).
fof(f42,plain,
( ! [X2,X3,X0,X1] :
( greater(zero,growth_rate(X2,X1))
| ~ in_environment(X0,X1)
| ~ greater(resilience(X3),resilience(X2))
| ~ greater(zero,growth_rate(X3,X1)) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f10,f20]) ).
fof(f44,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ greater(resilience(X2),resilience(X3))
| ~ in_environment(X0,X1)
| ~ greater(zero,growth_rate(X2,X1))
| subpopulations(X3,X4,X5,X1) )
| ~ spl0_2 ),
inference(resolution,[],[f42,f4]) ).
fof(f45,plain,
( ! [X2,X3,X0,X1] :
( ~ greater(zero,growth_rate(efficient_producers,X1))
| ~ in_environment(X0,X1)
| subpopulations(first_movers,X2,X3,X1) )
| ~ spl0_2 ),
inference(resolution,[],[f44,f11]) ).
fof(f49,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( subpopulations(first_movers,X2,X3,X1)
| ~ in_environment(X0,X1)
| ~ outcompetes(X4,efficient_producers,X1)
| ~ subpopulations(efficient_producers,X4,X5,X1) )
| ~ spl0_2 ),
inference(resolution,[],[f45,f27]) ).
fof(f52,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ subpopulations(efficient_producers,X2,X3,X1)
| ~ outcompetes(X2,efficient_producers,X1)
| ~ in_environment(X0,X1)
| in_environment(X4,X1) )
| ~ spl0_2 ),
inference(resolution,[],[f49,f22]) ).
fof(f56,plain,
( ! [X2,X3,X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X3,X0)
| ~ in_environment(X1,X0)
| in_environment(X2,X0)
| ~ outcompetes(first_movers,efficient_producers,X0) )
| ~ spl0_2 ),
inference(resolution,[],[f52,f24]) ).
fof(f62,plain,
( ! [X0,X1] :
( ~ in_environment(X0,sk2)
| in_environment(X1,sk2)
| ~ outcompetes(first_movers,efficient_producers,sk2) )
| ~ spl0_2 ),
inference(resolution,[],[f56,f13]) ).
fof(f65,plain,
( ! [X0,X1] :
( ~ in_environment(X0,sk2)
| in_environment(X1,sk2) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f62,f14]) ).
fof(f67,definition,
( spl0_5
<=> ! [X0] : ~ in_environment(X0,sk2) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f68,plain,
( ! [X0] : ~ in_environment(X0,sk2)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f67]) ).
fof(f69,plain,
( spl0_3
| spl0_5
| ~ spl0_2 ),
inference(avatar_split_clause,[],[f65,f19,f67,f36]) ).
fof(f179,plain,
( ~ environment(sk1)
| in_environment(sk1,sk2) ),
inference(resolution,[],[f2,f13]) ).
fof(f180,plain,
in_environment(sk1,sk2),
inference(forward_subsumption_resolution,[],[f179,f12]) ).
fof(f181,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f180,f68]) ).
fof(f182,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f181]) ).
fof(f183,plain,
! [X2,X3,X0,X1] :
( ~ subpopulations(X0,X1,X2,X3)
| ~ outcompetes(X1,X0,X3)
| ~ environment(X2)
| ~ greater(zero,growth_rate(X1,X3)) ),
inference(resolution,[],[f8,f5]) ).
fof(f184,plain,
( ! [X2,X3,X0,X1] :
( ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0)
| ~ outcompetes(X2,X1,X3) )
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f9,f17]) ).
fof(f186,plain,
( ! [X0,X1] :
( ~ environment(X0)
| ~ outcompetes(first_movers,efficient_producers,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) )
| ~ spl0_1 ),
inference(resolution,[],[f184,f1]) ).
fof(f187,plain,
( ! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ outcompetes(first_movers,efficient_producers,X1)
| ~ environment(X0) )
| ~ spl0_1 ),
inference(duplicate_literal_removal,[],[f186]) ).
fof(f189,plain,
( ~ outcompetes(first_movers,efficient_producers,sk2)
| ~ environment(sk1)
| ~ spl0_1 ),
inference(resolution,[],[f187,f13]) ).
fof(f190,plain,
( ~ environment(sk1)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f189,f14]) ).
fof(f191,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[],[f190,f12]) ).
fof(f192,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[],[f191]) ).
fof(f195,plain,
( ! [X2,X3,X0,X1] :
( greater(zero,growth_rate(X1,X3))
| ~ outcompetes(X2,X1,X3)
| ~ subpopulations(X1,X2,X0,X3) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f9,f20]) ).
fof(f207,plain,
( ! [X2,X3,X0,X1] :
( greater(zero,growth_rate(X2,X1))
| ~ in_environment(X0,X1)
| ~ greater(resilience(X3),resilience(X2))
| ~ greater(zero,growth_rate(X3,X1)) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f10,f20]) ).
fof(f211,plain,
( ! [X2,X3,X0,X1] :
( ~ greater(zero,growth_rate(X1,X3))
| ~ outcompetes(X1,X0,X3)
| ~ subpopulations(X0,X1,X2,X3) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f183,f20]) ).
fof(f212,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ greater(resilience(X5),resilience(X0))
| ~ subpopulations(X1,X0,X3,X2)
| ~ in_environment(X4,X2)
| ~ outcompetes(X0,X1,X2)
| ~ greater(zero,growth_rate(X5,X2)) )
| ~ spl0_2 ),
inference(resolution,[],[f211,f207]) ).
fof(f242,plain,
( ! [X2,X3,X0,X1] :
( ~ greater(zero,growth_rate(efficient_producers,X2))
| ~ in_environment(X3,X2)
| ~ outcompetes(first_movers,X0,X2)
| ~ subpopulations(X0,first_movers,X1,X2) )
| ~ spl0_2 ),
inference(resolution,[],[f212,f11]) ).
fof(f268,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ subpopulations(efficient_producers,X4,X5,X1)
| ~ outcompetes(first_movers,X2,X1)
| ~ subpopulations(X2,first_movers,X3,X1)
| ~ outcompetes(X4,efficient_producers,X1)
| ~ in_environment(X0,X1) )
| ~ spl0_2 ),
inference(resolution,[],[f242,f195]) ).
fof(f387,plain,
( ! [X2,X0,X1] :
( ~ subpopulations(efficient_producers,first_movers,X0,X1)
| ~ outcompetes(first_movers,efficient_producers,X1)
| ~ outcompetes(first_movers,efficient_producers,X1)
| ~ in_environment(X2,X1) )
| ~ spl0_2 ),
inference(factoring,[],[f268]) ).
fof(f388,plain,
( ! [X2,X0,X1] :
( ~ subpopulations(efficient_producers,first_movers,X0,X1)
| ~ outcompetes(first_movers,efficient_producers,X1)
| ~ in_environment(X2,X1) )
| ~ spl0_2 ),
inference(duplicate_literal_removal,[],[f387]) ).
fof(f393,plain,
( ! [X2,X0,X1] :
( ~ outcompetes(first_movers,efficient_producers,X0)
| ~ in_environment(X1,X0)
| ~ subpopulations(first_movers,efficient_producers,X2,X0)
| ~ environment(X2) )
| ~ spl0_2 ),
inference(resolution,[],[f388,f1]) ).
fof(f395,plain,
( ! [X2,X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X2,X0)
| ~ in_environment(X1,X0)
| ~ outcompetes(first_movers,efficient_producers,X0) )
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f393,f20]) ).
fof(f402,plain,
( ! [X0] :
( ~ in_environment(X0,sk2)
| ~ outcompetes(first_movers,efficient_producers,sk2) )
| ~ spl0_2 ),
inference(resolution,[],[f395,f13]) ).
fof(f406,plain,
( ! [X0] : ~ in_environment(X0,sk2)
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[],[f402,f14]) ).
fof(f407,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f406,f37]) ).
fof(f408,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f407]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s3,plain,
( ~ spl0_2
| spl0_3
| spl0_5 ),
inference(sat_conversion,[],[f69]) ).
cnf(s9,plain,
~ spl0_5,
inference(sat_conversion,[],[f182]) ).
cnf(s10,plain,
~ spl0_1,
inference(sat_conversion,[],[f192]) ).
cnf(s16,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f408]) ).
cnf(s20,plain,
( ~ spl0_2
| spl0_3 ),
inference(rat,[],[s3,s9]) ).
cnf(s21,plain,
spl0_2,
inference(rat,[],[s1,s10]) ).
cnf(s22,plain,
~ spl0_3,
inference(rat,[],[s16,s21]) ).
cnf(s26,plain,
$false,
inference(rat,[],[s20,s22,s21]) ).
fof(f409,plain,
$false,
inference(avatar_sat_refutation,[],[s26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT036-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n003.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sun Sep 27 17:24:11 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.88/1.14 % (807897)Input is clausal, will run a generic CNF schedule.
% 0.88/1.14 % (807906)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=2534365638:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.88/1.14 % (807906)First to succeed.
% 0.88/1.14 % (807906)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-807897"
% 0.88/1.14 % (807904)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=964605349:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.88/1.14 % (807908)dis-21_1_sil=8000:lcm=predicate:random_seed=3897927928: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)
% 0.88/1.14 % (807905)lrs+10_1_sil=8000:sp=occurrence:random_seed=3996608801:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.88/1.14 % (807902)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=982144732:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.88/1.14 % (807903)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=2405003357:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.88/1.14 % (807907)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2928315849:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.88/1.14 % (807905)Also succeeded, but the first one will report.
% 0.88/1.14 % (807908)Also succeeded, but the first one will report.
% 0.88/1.14 % (807907)Also succeeded, but the first one will report.
% 0.88/1.14 % (807906)Refutation found. Thanks to Tanya!
% 0.88/1.14 % SZS status Unsatisfiable for theBenchmark
% 0.88/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 2.71/1.33 % (807906)------------------------------
% 2.71/1.33 % (807906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.71/1.33 % (807906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.71/1.33 % (807906)CaDiCaL version: 2.1.3
% 2.71/1.33 % (807906)Termination reason: Refutation
% 2.71/1.33 % (807906)Time elapsed: 0.008 s
% 2.71/1.33 % (807906)Peak memory usage: 89 MB
% 2.71/1.33 % (807906)Instructions burned: 20 (million)
% 2.71/1.33 % (807906)------------------------------
% 2.71/1.33 % (807906)------------------------------
% 2.71/1.33 % (807897)Success in time 0.299 s
% 2.71/1.33 % Vampire exiting
%------------------------------------------------------------------------------