%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : MGT020-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n005.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 : Unsatisfiable 0.17s 0.47s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 16
% Syntax : Number of formulae : 59 ( 15 unt; 4 def)
% Number of atoms : 134 ( 4 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 144 ( 69 ~; 71 |; 0 &)
% ( 4 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 5 prp; 0-4 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l3_22) ).
fof(f2,axiom,
! [X0] :
( ~ environment(X0)
| ~ in_environment(X0,initial_FM_EP(X0))
| subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_point_23) ).
fof(f3,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| greater_or_equal(X1,initial_FM_EP(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_earliest_time_point_24) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( ~ environment(X0)
| ~ greater_or_equal(X1,X2)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2))
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| greater(disbanding_rate(first_movers,X3),disbanding_rate(efficient_producers,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_positive_function_difference_25) ).
fof(f5,axiom,
! [X0,X1] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| in_environment(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_time_point_occurs_26) ).
fof(f6,axiom,
! [X0] :
( ~ environment(X0)
| greater_or_equal(initial_FM_EP(X0),start_time(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_initial_time_27) ).
fof(f7,axiom,
! [X2,X0,X1] :
( ~ environment(X0)
| ~ greater_or_equal(X1,start_time(X0))
| ~ greater(X2,X1)
| ~ in_environment(X0,X2)
| in_environment(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_times_in_order_28) ).
fof(f9,axiom,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| greater(X0,X1)
| X0 = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mp_greater_or_equal_30) ).
fof(f10,axiom,
! [X0] :
( ~ environment(X0)
| greater(disbanding_rate(first_movers,initial_FM_EP(X0)),disbanding_rate(efficient_producers,initial_FM_EP(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a8_31) ).
fof(f12,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l2_33) ).
fof(f13,negated_conjecture,
subpopulations(first_movers,efficient_producers,sk1,sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l2_34) ).
fof(f14,negated_conjecture,
~ greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_l2_35) ).
fof(f15,plain,
greater_or_equal(initial_FM_EP(sk1),start_time(sk1)),
inference(resolution,[],[f6,f12]) ).
fof(f26,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| in_environment(sk1,X0) ),
inference(resolution,[],[f5,f12]) ).
fof(f28,plain,
greater(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1))),
inference(resolution,[],[f10,f12]) ).
fof(f29,plain,
in_environment(sk1,sk2),
inference(resolution,[],[f26,f13]) ).
fof(f30,plain,
! [X0] :
( ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| greater_or_equal(X0,initial_FM_EP(sk1)) ),
inference(resolution,[],[f3,f12]) ).
fof(f31,plain,
( ~ in_environment(sk1,initial_FM_EP(sk1))
| subpopulations(first_movers,efficient_producers,sk1,initial_FM_EP(sk1)) ),
inference(resolution,[],[f2,f12]) ).
fof(f33,definition,
( spl0_3
<=> subpopulations(first_movers,efficient_producers,sk1,initial_FM_EP(sk1)) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
fof(f35,plain,
( subpopulations(first_movers,efficient_producers,sk1,initial_FM_EP(sk1))
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f33]) ).
fof(f37,definition,
( spl0_4
<=> in_environment(sk1,initial_FM_EP(sk1)) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
fof(f39,plain,
( ~ in_environment(sk1,initial_FM_EP(sk1))
| spl0_4 ),
inference(avatar_component_clause,[],[f37]) ).
fof(f40,plain,
( spl0_3
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f31,f37,f33]) ).
fof(f41,plain,
! [X0,X1] :
( ~ greater(X1,X0)
| ~ greater_or_equal(X0,start_time(sk1))
| ~ in_environment(sk1,X1)
| in_environment(sk1,X0) ),
inference(resolution,[],[f7,f12]) ).
fof(f44,plain,
greater_or_equal(sk2,initial_FM_EP(sk1)),
inference(resolution,[],[f30,f13]) ).
fof(f45,plain,
! [X2,X0,X1] :
( ~ greater(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1))
| ~ greater_or_equal(X2,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X2)
| ~ greater_or_equal(X0,X1)
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| greater(disbanding_rate(first_movers,X2),disbanding_rate(efficient_producers,X2)) ),
inference(resolution,[],[f4,f12]) ).
fof(f46,plain,
( greater(sk2,initial_FM_EP(sk1))
| sk2 = initial_FM_EP(sk1) ),
inference(resolution,[],[f44,f9]) ).
fof(f48,definition,
( spl0_5
<=> sk2 = initial_FM_EP(sk1) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
fof(f50,plain,
( sk2 = initial_FM_EP(sk1)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f48]) ).
fof(f52,definition,
( spl0_6
<=> greater(sk2,initial_FM_EP(sk1)) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
fof(f54,plain,
( greater(sk2,initial_FM_EP(sk1))
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f52]) ).
fof(f55,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f46,f52,f48]) ).
fof(f73,plain,
( ~ greater(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1)))
| ~ spl0_5 ),
inference(superposition,[],[f14,f50]) ).
fof(f76,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[],[f73,f28]) ).
fof(f77,plain,
~ spl0_5,
inference(avatar_contradiction_clause,[],[f76]) ).
fof(f91,plain,
! [X0,X1] :
( ~ greater_or_equal(X0,X1)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ greater_or_equal(X1,initial_FM_EP(sk1))
| decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| greater(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)) ),
inference(resolution,[],[f45,f28]) ).
fof(f92,plain,
( ~ greater_or_equal(initial_FM_EP(sk1),start_time(sk1))
| ~ in_environment(sk1,sk2)
| in_environment(sk1,initial_FM_EP(sk1))
| ~ spl0_6 ),
inference(resolution,[],[f54,f41]) ).
fof(f94,plain,
( ~ in_environment(sk1,sk2)
| in_environment(sk1,initial_FM_EP(sk1))
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f92,f15]) ).
fof(f95,plain,
( in_environment(sk1,initial_FM_EP(sk1))
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f94,f29]) ).
fof(f96,plain,
( $false
| spl0_4
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[],[f95,f39]) ).
fof(f97,plain,
( spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f96]) ).
fof(f108,plain,
( greater_or_equal(initial_FM_EP(sk1),initial_FM_EP(sk1))
| ~ spl0_3 ),
inference(resolution,[],[f35,f30]) ).
fof(f115,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ greater_or_equal(initial_FM_EP(sk1),initial_FM_EP(sk1))
| decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1))))
| greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)) ),
inference(resolution,[],[f91,f44]) ).
fof(f116,plain,
( ~ greater_or_equal(initial_FM_EP(sk1),initial_FM_EP(sk1))
| decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1))))
| greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2)) ),
inference(forward_subsumption_resolution,[],[f115,f13]) ).
fof(f118,plain,
( decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1))))
| greater(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f116,f108]) ).
fof(f119,plain,
( decreases(difference(disbanding_rate(first_movers,initial_FM_EP(sk1)),disbanding_rate(efficient_producers,initial_FM_EP(sk1))))
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f118,f14]) ).
fof(f122,plain,
( ! [X0] :
( ~ environment(X0)
| ~ subpopulations(first_movers,efficient_producers,X0,initial_FM_EP(sk1)) )
| ~ spl0_3 ),
inference(resolution,[],[f119,f1]) ).
fof(f123,plain,
( ~ subpopulations(first_movers,efficient_producers,sk1,initial_FM_EP(sk1))
| ~ spl0_3 ),
inference(resolution,[],[f122,f12]) ).
fof(f124,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[],[f123,f35]) ).
fof(f125,plain,
~ spl0_3,
inference(avatar_contradiction_clause,[],[f124]) ).
cnf(s2,plain,
( spl0_3
| ~ spl0_4 ),
inference(sat_conversion,[],[f40]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f55]) ).
cnf(s6,plain,
~ spl0_5,
inference(sat_conversion,[],[f77]) ).
cnf(s9,plain,
( spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f97]) ).
cnf(s11,plain,
~ spl0_3,
inference(sat_conversion,[],[f125]) ).
cnf(s13,plain,
spl0_6,
inference(rat,[],[s3,s6]) ).
cnf(s14,plain,
spl0_4,
inference(rat,[],[s9,s13]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s2,s14,s11]) ).
fof(f126,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT020-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n005.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 17:16:32 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.47 % (36695)Will run a generic schedule for satisfiability detection.
% 0.17/0.47 % (36709)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3260664543:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.47 % (36708)% WARNING: option uhcvi not known.
% 0.17/0.47 % (36707)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=959850472_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.47 % (36708)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4069591577:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.47 % (36710)dis+10_1_sil=32000:sp=arity:random_seed=2892913433:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.47 % (36712)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2781909688:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.47 % (36711)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4094952670:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.47 % (36713)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2094775691:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.47 % TRYING [1]
% 0.17/0.47 % TRYING [2]
% 0.17/0.47 % (36712) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-36695-36712"...
% 0.17/0.47 % TRYING [3]
% 0.17/0.47 % (36712)...printing done.
% 0.17/0.47 % (36712)Refutation found. Thanks to Tanya!
% 0.17/0.47 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.48 % (36712)------------------------------
% 0.17/0.48 % (36712)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.48 % (36712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.48 % (36712)CaDiCaL version: 2.1.3
% 0.17/0.48 % (36712)Termination reason: Refutation
% 0.17/0.48 % (36712)Time elapsed: 0.004 s
% 0.17/0.48 % (36712)Peak memory usage: 12 MB
% 0.17/0.48 % (36712)Instructions burned: 4 (million)
% 0.17/0.48 % (36695)Success in time 0.045 s
% 0.17/0.48 % Vampire exiting
%------------------------------------------------------------------------------