%------------------------------------------------------------------------------
% File : Vampire-SAT---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 SAT
% 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 12:02:31 PM UTC 2026
% Result : Theorem 0.17s 0.48s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 11 unt; 0 def)
% Number of atoms : 145 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 171 ( 75 ~; 66 |; 19 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 48 ( 44 !; 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(f10,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f11,plain,
! [X0,X1] :
( in_environment(X0,X1)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f10]) ).
fof(f12,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(ennf_transformation,[],[f2]) ).
fof(f13,plain,
! [X0,X1] :
( greater(number_of_organizations(X0,X1),zero)
| ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1) ),
inference(flattening,[],[f12]) ).
fof(f14,plain,
! [X0] :
( ~ decreases(X0)
| ~ increases(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f15,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(f16,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,[],[f15]) ).
fof(f17,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(f18,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,[],[f17]) ).
fof(f19,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(f20,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,[],[f19]) ).
fof(f21,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)],[f20]) ).
fof(f22,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| in_environment(X0,X1) ),
inference(cnf_transformation,[],[f11]) ).
fof(f23,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0)
| greater(number_of_organizations(X0,X1),zero) ),
inference(cnf_transformation,[],[f13]) ).
fof(f24,plain,
! [X0] :
( ~ decreases(X0)
| ~ increases(X0) ),
inference(cnf_transformation,[],[f14]) ).
fof(f25,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,[],[f16]) ).
fof(f26,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,[],[f16]) ).
fof(f27,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,[],[f18]) ).
fof(f28,plain,
! [X0,X1] :
( ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ decreases(resources(X0,X1))
| ~ environment(X0)
| increases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))) ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
subpopulations(first_movers,efficient_producers,sK0,sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f30,plain,
environment(sK0),
inference(cnf_transformation,[],[f21]) ).
fof(f31,plain,
decreases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))),
inference(cnf_transformation,[],[f21]) ).
fof(f58,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,X0,sK1)
| ~ environment(X0)
| ~ constant(resources(X0,sK1)) ),
inference(resolution,[],[f31,f27]) ).
fof(f59,plain,
~ increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))),
inference(resolution,[],[f31,f24]) ).
fof(f63,plain,
( ~ environment(sK0)
| in_environment(sK0,sK1) ),
inference(resolution,[],[f22,f29]) ).
fof(f64,plain,
in_environment(sK0,sK1),
inference(forward_subsumption_resolution,[],[f63,f30]) ).
fof(f68,plain,
( ~ environment(sK0)
| greater(number_of_organizations(sK0,sK1),zero) ),
inference(resolution,[],[f23,f29]) ).
fof(f69,plain,
greater(number_of_organizations(sK0,sK1),zero),
inference(forward_subsumption_resolution,[],[f68,f30]) ).
fof(f152,plain,
( ~ environment(sK0)
| ~ constant(resources(sK0,sK1)) ),
inference(resolution,[],[f58,f29]) ).
fof(f153,plain,
~ constant(resources(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f152,f30]) ).
fof(f165,plain,
( greater(equilibrium(sK0),sK1)
| ~ environment(sK0)
| ~ in_environment(sK0,sK1)
| constant(resources(sK0,sK1)) ),
inference(resolution,[],[f25,f69]) ).
fof(f166,plain,
( greater(equilibrium(sK0),sK1)
| ~ in_environment(sK0,sK1)
| constant(resources(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f165,f30]) ).
fof(f167,plain,
( greater(equilibrium(sK0),sK1)
| constant(resources(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f166,f64]) ).
fof(f173,plain,
greater(equilibrium(sK0),sK1),
inference(global_subsumption,[],[f167,f153]) ).
fof(f174,plain,
( ~ greater(equilibrium(sK0),sK1)
| ~ environment(sK0)
| ~ in_environment(sK0,sK1)
| decreases(resources(sK0,sK1)) ),
inference(resolution,[],[f26,f69]) ).
fof(f175,plain,
( ~ environment(sK0)
| ~ in_environment(sK0,sK1)
| decreases(resources(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f174,f173]) ).
fof(f176,plain,
( ~ in_environment(sK0,sK1)
| decreases(resources(sK0,sK1)) ),
inference(forward_subsumption_resolution,[],[f175,f30]) ).
fof(f177,plain,
decreases(resources(sK0,sK1)),
inference(forward_subsumption_resolution,[],[f176,f64]) ).
fof(f194,plain,
( ~ decreases(resources(sK0,sK1))
| ~ environment(sK0)
| increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(resolution,[],[f28,f29]) ).
fof(f195,plain,
( ~ environment(sK0)
| increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))) ),
inference(forward_subsumption_resolution,[],[f194,f177]) ).
fof(f196,plain,
increases(difference(disbanding_rate(first_movers,sK1),disbanding_rate(efficient_producers,sK1))),
inference(forward_subsumption_resolution,[],[f195,f30]) ).
fof(f197,plain,
$false,
inference(forward_subsumption_resolution,[],[f196,f59]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % 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 SAT
% 0.12/0.40 % Computer : n007.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 17:16:10 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.43 Running first-order model finding
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.48 % (1675728)Will run a generic schedule for satisfiability detection.
% 0.17/0.48 % (1675735)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3182139460:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.48 % (1675735) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1675728-1675735"...
% 0.17/0.48 % (1675734)% WARNING: option uhcvi not known.
% 0.17/0.48 % (1675735)...printing done.
% 0.17/0.48 % (1675735)Refutation found. Thanks to Tanya!
% 0.17/0.48 % SZS status Theorem for theBenchmark
% 0.17/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (1675735)------------------------------
% 0.17/0.48 % (1675735)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (1675735)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (1675735)CaDiCaL version: 2.1.3
% 0.17/0.48 % (1675735)Termination reason: Refutation
% 0.17/0.48 % (1675735)Time elapsed: 0.003 s
% 0.17/0.48 % (1675735)Peak memory usage: 11 MB
% 0.17/0.48 % (1675735)Instructions burned: 5 (million)
% 0.17/0.48 % (1675728)Success in time 0.031 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------