%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : MGT021+1 : 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 : n007.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 : Theorem 0.87s 1.14s
% Output : Refutation 2.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 14 unt; 2 def)
% Number of atoms : 164 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 192 ( 87 ~; 73 |; 19 &)
% ( 2 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 3 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 45 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> in_environment(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_time_point_in_environment) ).
fof(f2,axiom,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> greater(number_of_organizations(X0,X1),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_environment_not_empty) ).
fof(f3,axiom,
! [X0] :
( increases(X0)
=> ~ decreases(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_increase_not_decrease) ).
fof(f5,axiom,
! [X0,X1] :
( ( environment(X0)
& in_environment(X0,X1)
& greater(number_of_organizations(X0,X1),zero) )
=> ( ( greater(equilibrium(X0),X1)
=> decreases(resources(X0,X1)) )
& ( ~ greater(equilibrium(X0),X1)
=> constant(resources(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a3) ).
fof(f6,axiom,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> ( ( decreases(resources(X0,X1))
=> increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) )
& ( constant(resources(X0,X1))
=> ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l4) ).
fof(f7,conjecture,
! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_l3) ).
fof(f8,negated_conjecture,
~ ! [X0,X1] :
( ( environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) )
=> ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [X0,X1] :
( ( ( decreases(resources(X0,X1))
| ~ greater(equilibrium(X0),X1) )
& ( constant(resources(X0,X1))
| greater(equilibrium(X0),X1) ) )
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(number_of_organizations(X0,X1),zero) ),
inference(ennf_transformation,[],[f5]) ).
fof(f10,plain,
! [X0,X1] :
( ( ( decreases(resources(X0,X1))
| ~ greater(equilibrium(X0),X1) )
& ( constant(resources(X0,X1))
| greater(equilibrium(X0),X1) ) )
| ~ environment(X0)
| ~ in_environment(X0,X1)
| ~ greater(number_of_organizations(X0,X1),zero) ),
inference(flattening,[],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( ( ( increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ decreases(resources(X0,X1)) )
& ( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ constant(resources(X0,X1)) ) )
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f12,plain,
! [X0,X1] :
( ( ( increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ decreases(resources(X0,X1)) )
& ( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ constant(resources(X0,X1)) ) )
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f11]) ).
fof(f13,plain,
? [X0,X1] :
( decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
& environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f14,plain,
? [X0,X1] :
( decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
& environment(X0)
& subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f16,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f18,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0] :
( ~ decreases(X0)
| ~ increases(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f20,plain,
( decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(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(f21,plain,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| constant(resources(X0,X1)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f22,plain,
! [X0,X1] :
( ~ greater(number_of_organizations(X0,X1),zero)
| ~ greater(equilibrium(X0),X1)
| ~ environment(X0)
| ~ in_environment(X0,X1)
| decreases(resources(X0,X1)) ),
inference(cnf_transformation,[],[f10]) ).
fof(f23,plain,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ constant(resources(X0,X1))
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(cnf_transformation,[],[f12]) ).
fof(f24,plain,
! [X0,X1] :
( increases(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(cnf_transformation,[],[f12]) ).
fof(f25,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f20]) ).
fof(f26,plain,
environment(sK0),
inference(cnf_transformation,[],[f20]) ).
fof(f27,plain,
decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))),
inference(cnf_transformation,[],[f20]) ).
fof(f28,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(number_of_organizations(X0,X1),zero) ),
inference(cnf_transformation,[],[f16]) ).
fof(f29,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f30,plain,
! [X0] :
( ~ decreases(X0)
| ~ increases(X0) ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
( ~ environment(sK0)
| in_environment(sK0,sK1) ),
inference(resolution,[],[f25,f29]) ).
fof(f32,plain,
( ~ environment(sK0)
| greater(number_of_organizations(sK0,sK1),zero) ),
inference(resolution,[],[f25,f28]) ).
fof(f33,plain,
greater(number_of_organizations(sK0,sK1),zero),
inference(forward_subsumption_resolution,[],[f32,f26]) ).
fof(f34,plain,
in_environment(sK0,sK1),
inference(forward_subsumption_resolution,[],[f31,f26]) ).
fof(f35,plain,
~ increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))),
inference(resolution,[],[f27,f30]) ).
fof(f36,plain,
( greater(equilibrium(sK0),sK1)
| ~ environment(sK0)
| ~ in_environment(sK0,sK1)
| constant(resources(sK0,sK1)) ),
inference(resolution,[],[f21,f33]) ).
fof(f37,plain,
( greater(equilibrium(sK0),sK1)
| ~ in_environment(sK0,sK1)
| constant(resources(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f36,f26]) ).
fof(f38,plain,
( greater(equilibrium(sK0),sK1)
| constant(resources(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f37,f34]) ).
fof(f40,definition,
( spl2_1
<=> constant(resources(sK0,sK1)) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f44,definition,
( spl2_2
<=> greater(equilibrium(sK0),sK1) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
fof(f46,plain,
( greater(equilibrium(sK0),sK1)
| ~ spl2_2 ),
inference(avatar_component_clause,[],[f44]) ).
fof(f47,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f38,f44,f40]) ).
fof(f48,plain,
( ~ greater(equilibrium(sK0),sK1)
| ~ environment(sK0)
| ~ in_environment(sK0,sK1)
| decreases(resources(sK0,sK1)) ),
inference(resolution,[],[f22,f33]) ).
fof(f49,plain,
( ~ environment(sK0)
| ~ in_environment(sK0,sK1)
| decreases(resources(sK0,sK1))
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f48,f46]) ).
fof(f50,plain,
( ~ in_environment(sK0,sK1)
| decreases(resources(sK0,sK1))
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f49,f26]) ).
fof(f51,plain,
( decreases(resources(sK0,sK1))
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f50,f34]) ).
fof(f53,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0)
| ~ constant(resources(X0,sK1)) ),
inference(resolution,[],[f23,f27]) ).
fof(f54,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0)
| ~ decreases(resources(X0,sK1)) ),
inference(resolution,[],[f35,f24]) ).
fof(f55,plain,
( ~ environment(sK0)
| ~ constant(resources(sK0,sK1)) ),
inference(resolution,[],[f53,f25]) ).
fof(f56,plain,
~ constant(resources(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f55,f26]) ).
fof(f57,plain,
~ spl2_1,
inference(avatar_split_clause,[],[f56,f40]) ).
fof(f58,plain,
( ~ environment(sK0)
| ~ decreases(resources(sK0,sK1)) ),
inference(resolution,[],[f54,f25]) ).
fof(f59,plain,
~ decreases(resources(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f58,f26]) ).
fof(f60,plain,
( $false
| ~ spl2_2 ),
inference(forward_subsumption_resolution,[],[f59,f51]) ).
fof(f61,plain,
~ spl2_2,
inference(avatar_contradiction_clause,[],[f60]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f47]) ).
cnf(s2,plain,
~ spl2_1,
inference(sat_conversion,[],[f57]) ).
cnf(s3,plain,
~ spl2_2,
inference(sat_conversion,[],[f61]) ).
cnf(s4,plain,
$false,
inference(rat,[],[s1,s3,s2]) ).
fof(f62,plain,
$false,
inference(avatar_sat_refutation,[],[s4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT021+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n007.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sun Sep 27 17:14:55 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.87/1.14 % (1674495)Detected formulas, will run a generic FOF schedule.
% 0.87/1.14 % (1674503)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=930218870:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.87/1.14 % (1674503)First to succeed.
% 0.87/1.14 % (1674503)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1674495"
% 0.87/1.14 % (1674502)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=2595812534:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.87/1.14 % (1674505)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1324403239:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.87/1.14 % (1674504)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=14618615:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.87/1.14 % (1674506)dis-21_1_sil=8000:lcm=predicate:random_seed=3274646033: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)
% 0.87/1.14 % (1674500)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=877547644:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.87/1.14 % (1674501)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=1377054338:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.87/1.14 % (1674504)Also succeeded, but the first one will report.
% 0.87/1.14 % (1674505)Also succeeded, but the first one will report.
% 0.87/1.14 % (1674506)Also succeeded, but the first one will report.
% 0.87/1.14 % (1674503)Refutation found. Thanks to Tanya!
% 0.87/1.14 % SZS status Theorem for theBenchmark
% 0.87/1.14 % SZS output start Proof for theBenchmark
% See solution above
% 2.68/1.34 % (1674503)------------------------------
% 2.68/1.34 % (1674503)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.68/1.34 % (1674503)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.68/1.34 % (1674503)CaDiCaL version: 2.1.3
% 2.68/1.34 % (1674503)Termination reason: Refutation
% 2.68/1.34 % (1674503)Time elapsed: 0.002 s
% 2.68/1.34 % (1674503)Peak memory usage: 89 MB
% 2.68/1.34 % (1674503)Instructions burned: 3 (million)
% 2.68/1.34 % (1674503)------------------------------
% 2.68/1.34 % (1674503)------------------------------
% 2.68/1.34 % (1674495)Success in time 0.293 s
% 2.68/1.34 % Vampire exiting
%------------------------------------------------------------------------------