%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT021-1 : 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 : 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 12:02:02 PM UTC 2026
% Result : Unsatisfiable 0.17s 1.51s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 24 ( 5 unt; 0 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 120 ( 65 ~; 55 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 26 ( 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( in_environment(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_in_environment_27) ).
fof(f2,axiom,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_not_empty_28) ).
fof(f3,axiom,
! [X0] :
( ~ increases(X0)
| ~ decreases(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_increase_not_decrease_29) ).
fof(f5,axiom,
! [X0,X1] :
( decreases(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| ~ greater(equilibrium(X0),X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3_31) ).
fof(f6,axiom,
! [X0,X1] :
( constant(resources(X0,X1))
| ~ in_environment(X0,X1)
| ~ greater(number_of_organizations(X0,X1),zero)
| greater(equilibrium(X0),X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3_32) ).
fof(f7,axiom,
! [X0,X1] :
( increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ decreases(resources(X0,X1))
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_33) ).
fof(f8,axiom,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ constant(resources(X0,X1))
| ~ environment(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4_34) ).
fof(f9,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l3_35) ).
fof(f10,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l3_36) ).
fof(f11,negated_conjecture,
decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l3_37) ).
fof(f12,plain,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ decreases(resources(X0,X1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(resolution,[],[f7,f3]) ).
fof(f13,plain,
! [X0] :
( ~ constant(resources(X0,sk2))
| ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0) ),
inference(resolution,[],[f8,f11]) ).
fof(f14,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0)
| ~ in_environment(X0,sk2)
| ~ greater(number_of_organizations(X0,sk2),zero)
| greater(equilibrium(X0),sk2)
| ~ environment(X0) ),
inference(resolution,[],[f13,f6]) ).
fof(f15,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0)
| ~ in_environment(X0,sk2)
| ~ greater(number_of_organizations(X0,sk2),zero)
| greater(equilibrium(X0),sk2) ),
inference(duplicate_literal_removal,[],[f14]) ).
fof(f16,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0)
| ~ greater(number_of_organizations(X0,sk2),zero)
| greater(equilibrium(X0),sk2) ),
inference(forward_subsumption_resolution,[],[f15,f1]) ).
fof(f17,plain,
! [X0] :
( greater(equilibrium(X0),sk2)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sk2) ),
inference(forward_subsumption_resolution,[],[f16,f2]) ).
fof(f18,plain,
! [X0] :
( ~ decreases(resources(X0,sk2))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sk2) ),
inference(resolution,[],[f12,f11]) ).
fof(f19,plain,
! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ in_environment(X0,sk2)
| ~ greater(number_of_organizations(X0,sk2),zero)
| ~ greater(equilibrium(X0),sk2)
| ~ environment(X0) ),
inference(resolution,[],[f18,f5]) ).
fof(f20,plain,
! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ in_environment(X0,sk2)
| ~ greater(number_of_organizations(X0,sk2),zero)
| ~ greater(equilibrium(X0),sk2) ),
inference(duplicate_literal_removal,[],[f19]) ).
fof(f21,plain,
! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ greater(number_of_organizations(X0,sk2),zero)
| ~ greater(equilibrium(X0),sk2) ),
inference(forward_subsumption_resolution,[],[f20,f1]) ).
fof(f22,plain,
! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ greater(equilibrium(X0),sk2) ),
inference(forward_subsumption_resolution,[],[f21,f2]) ).
fof(f23,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sk2)
| ~ environment(X0) ),
inference(forward_subsumption_resolution,[],[f22,f17]) ).
fof(f24,plain,
~ environment(sk1),
inference(resolution,[],[f23,f10]) ).
fof(f25,plain,
$false,
inference(forward_subsumption_resolution,[],[f24,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT021-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.39 % Computer : n015.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 17:21:31 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.43 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
% 0.17/1.51 % (1878948)Input is clausal, will run a generic CNF schedule.
% 0.17/1.51 % (1878953)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=4289749910:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 0.17/1.51 % (1878954)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=3846588657:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 0.17/1.51 % (1878957)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=1869759797:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 0.17/1.51 % (1878958)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=493136818:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 0.17/1.51 % (1878956)lrs+10_1_sil=8000:sp=occurrence:random_seed=3129196559:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 0.17/1.51 % (1878955)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2403734141:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 0.17/1.51 % (1878959)dis-21_1_sil=8000:lcm=predicate:random_seed=2536546593: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)
% 0.17/1.51 % (1878958)First to succeed.
% 0.17/1.51 % (1878959)Also succeeded, but the first one will report.
% 0.17/1.51 % (1878956)Also succeeded, but the first one will report.
% 0.17/1.51 % (1878957)Also succeeded, but the first one will report.
% 0.17/1.51 % (1878958)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1878948"
% 0.17/1.51 % (1878958)Refutation found. Thanks to Tanya!
% 0.17/1.51 % SZS status Unsatisfiable for theBenchmark
% 0.17/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.51 % (1878958)------------------------------
% 0.17/1.51 % (1878958)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.51 % (1878958)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.51 % (1878958)CaDiCaL version: 2.1.3
% 0.17/1.51 % (1878958)Termination reason: Refutation
% 0.17/1.51 % (1878958)Time elapsed: 0.002 s
% 0.17/1.51 % (1878958)Peak memory usage: 88 MB
% 0.17/1.51 % (1878958)Instructions burned: 2 (million)
% 0.17/1.51 % (1878958)------------------------------
% 0.17/1.51 % (1878958)------------------------------
% 0.17/1.51 % (1878948)Success in time 0.435 s
% 0.17/1.51 % Vampire exiting
%------------------------------------------------------------------------------