%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT055_1 : TPTP v9.3.1. Released v5.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n012.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 09:48:02 AM UTC 2026
% Result : Theorem 0.09s 0.18s
% Output : Refutation 0.09s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : DAT055_1 : TPTP v9.3.1. Released v5.0.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.00/0.11 % Computer : n012.cluster.edu
% 0.00/0.11 % Model : x86_64 x86_64
% 0.00/0.11 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.00/0.11 % Memory : 8046.5625MB
% 0.00/0.11 % OS : Linux 6.8.0-71-generic
% 0.00/0.11 % CPULimit : 300
% 0.00/0.11 % WCLimit : 300
% 0.00/0.11 % DateTime : Tue Sep 29 00:07:04 UTC 2026
% 0.00/0.11 % CPUTime :
% 0.00/0.11 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.13 Running first-order model finding
% 0.09/0.13 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
% 0.09/0.18 % (3917482)Will run a generic schedule for satisfiability detection.
% 0.09/0.18 % (3917500)% WARNING: option uhcvi not known.
% 0.09/0.18 % (3917500)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3273254703:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.09/0.18 % (3917503)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=178754207:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.18 % (3917502)dis+10_1_sil=32000:sp=arity:random_seed=1746825382:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.18 % (3917501)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=498791951:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.18 % (3917499)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1222940220_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.18 % (3917505)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=329672301:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.18 % (3917499)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.09/0.18 % (3917499)Terminated due to inappropriate strategy.
% 0.09/0.18 % (3917499)------------------------------
% 0.09/0.18 % (3917499)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.18 % (3917499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.18 % (3917499)CaDiCaL version: 2.1.3
% 0.09/0.18 % (3917499)Termination reason: Inappropriate
% 0.09/0.18 % (3917499)Time elapsed: 0.0000 s
% 0.09/0.18 % (3917499)Peak memory usage: 10 MB
% 0.09/0.18 % (3917504)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3087247749:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.18 % (3917499)------------------------------
% 0.09/0.18 % (3917499)------------------------------
% 0.09/0.18 % (3917523)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3662375601:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.09/0.18 % (3917523)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.09/0.18 % (3917523)Terminated due to inappropriate strategy.
% 0.09/0.18 % (3917523)------------------------------
% 0.09/0.18 % (3917523)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.18 % (3917523)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.18 % (3917523)CaDiCaL version: 2.1.3
% 0.09/0.18 % (3917523)Termination reason: Inappropriate
% 0.09/0.18 % (3917523)Time elapsed: 0.0000 s
% 0.09/0.18 % (3917523)Peak memory usage: 10 MB
% 0.09/0.18 % (3917523)------------------------------
% 0.09/0.18 % (3917523)------------------------------
% 0.09/0.18 % (3917500) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-3917482-3917500"...
% 0.09/0.18 % (3917500)...printing done.
% 0.09/0.18 % (3917500)Refutation found. Thanks to Tanya!
% 0.09/0.18 % SZS status Theorem for theBenchmark
% 0.09/0.18 % SZS output start Proof for theBenchmark
% 0.09/0.18 tff(type_def_5, type, list: $tType).
% 0.09/0.18 tff(func_def_0, type, a: list).
% 0.09/0.18 tff(func_def_1, type, l: $int).
% 0.09/0.18 tff(func_def_2, type, k: $int).
% 0.09/0.18 tff(func_def_3, type, min: list > $int).
% 0.09/0.18 tff(func_def_4, type, max: list > $int).
% 0.09/0.18 tff(f1,conjecture,(
% 0.09/0.18 (! [X0 : list] : $lesseq(min(X0),max(X0)) & $lesseq(l,min(a)) & $less(0,k)) => $less(l,$sum(max(a),k))),
% 0.09/0.18 file('/export/starexec/sandbox/benchmark/theBenchmark.p',boyer_moore_max_min)).
% 0.09/0.18 tff(f2,negated_conjecture,(
% 0.09/0.18 ~((! [X0 : list] : $lesseq(min(X0),max(X0)) & $lesseq(l,min(a)) & $less(0,k)) => $less(l,$sum(max(a),k)))),
% 0.09/0.18 inference(negated_conjecture,[status(cth)],[f1])).
% 0.09/0.18 tff(f3,plain,(
% 0.09/0.18 ~((! [X0 : list] : ~$less(max(X0),min(X0)) & ~$less(min(a),l) & $less(0,k)) => $less(l,$sum(max(a),k)))),
% 0.09/0.18 inference(theory_normalization,[],[f2])).
% 0.09/0.18 tff(f4,definition,(
% 0.09/0.18 ( ! [X0 : $int,X1 : $int] : ($sum(X0,X1) = $sum(X1,X0)) )),
% 0.09/0.18 introduced(theory,[tha_commutativity])).
% 0.09/0.18 tff(f10,definition,(
% 0.09/0.18 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
% 0.09/0.18 introduced(theory,[tha_transitivity])).
% 0.09/0.18 tff(f11,definition,(
% 0.09/0.18 ( ! [X0 : $int,X1 : $int] : ($less(X1,X0) | $less(X0,X1) | X0 = X1) )),
% 0.09/0.18 introduced(theory,[tha_order_totality])).
% 0.09/0.18 tff(f12,definition,(
% 0.09/0.18 ( ! [X2 : $int,X0 : $int,X1 : $int] : ($less($sum(X0,X2),$sum(X1,X2)) | ~$less(X0,X1)) )),
% 0.09/0.18 introduced(theory,[tha_order_monotonicity])).
% 0.09/0.18 tff(f16,plain,(
% 0.09/0.18 ~$less(l,$sum(max(a),k)) & (! [X0 : list] : ~$less(max(X0),min(X0)) & ~$less(min(a),l) & $less(0,k))),
% 0.09/0.18 inference(ennf_transformation,[],[f3])).
% 0.09/0.18 tff(f17,plain,(
% 0.09/0.18 ~$less(l,$sum(max(a),k)) & ! [X0 : list] : ~$less(max(X0),min(X0)) & ~$less(min(a),l) & $less(0,k)),
% 0.09/0.18 inference(flattening,[],[f16])).
% 0.09/0.18 tff(f18,plain,(
% 0.09/0.18 $less(0,k)),
% 0.09/0.18 inference(cnf_transformation,[],[f17])).
% 0.09/0.18 tff(f19,plain,(
% 0.09/0.18 ~$less(min(a),l)),
% 0.09/0.18 inference(cnf_transformation,[],[f17])).
% 0.09/0.18 tff(f20,plain,(
% 0.09/0.18 ( ! [X0 : list] : (~$less(max(X0),min(X0))) )),
% 0.09/0.18 inference(cnf_transformation,[],[f17])).
% 0.09/0.18 tff(f21,plain,(
% 0.09/0.18 ~$less(l,$sum(max(a),k))),
% 0.09/0.18 inference(cnf_transformation,[],[f17])).
% 0.09/0.18 tff(f30,plain,(
% 0.09/0.18 ~$less(l,$sum(k,max(a)))),
% 0.09/0.18 inference(superposition,[],[f21,f4])).
% 0.09/0.18 tff(f50,plain,(
% 0.09/0.18 $less(l,min(a)) | l = min(a)),
% 0.09/0.18 inference(resolution,[],[f11,f19])).
% 0.09/0.18 tff(f58,definition,(
% 0.09/0.18 spl0_1 <=> l = min(a)),
% 0.09/0.18 introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition])).
% 0.09/0.18 tff(f60,plain,(
% 0.09/0.18 l = min(a) | ~spl0_1),
% 0.09/0.18 inference(avatar_component_clause,[],[f58])).
% 0.09/0.18 tff(f62,definition,(
% 0.09/0.18 spl0_2 <=> $less(l,min(a))),
% 0.09/0.18 introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition])).
% 0.09/0.18 tff(f64,plain,(
% 0.09/0.18 $less(l,min(a)) | ~spl0_2),
% 0.09/0.18 inference(avatar_component_clause,[],[f62])).
% 0.09/0.18 tff(f66,plain,(
% 0.09/0.18 spl0_1 | spl0_2),
% 0.09/0.18 inference(avatar_split_clause,[],[f50,f62,f58])).
% 0.09/0.18 tff(f85,plain,(
% 0.09/0.18 ( ! [X2 : $int,X3 : $int,X0 : $int,X1 : $int] : (~$less(X0,X1) | ~$less(X2,$sum(X0,X3)) | $less(X2,$sum(X1,X3))) )),
% 0.09/0.18 inference(resolution,[],[f12,f10])).
% 0.09/0.18 tff(f94,plain,(
% 0.09/0.18 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X2,X1) | $less($sum(X2,X0),$sum(X0,X1))) )),
% 0.09/0.18 inference(superposition,[],[f12,f4])).
% 0.09/0.18 tff(f123,plain,(
% 0.09/0.18 ( ! [X0 : $int] : (~$less(X0,l) | $less(X0,min(a))) ) | ~spl0_2),
% 0.09/0.18 inference(resolution,[],[f64,f10])).
% 0.09/0.18 tff(f128,plain,(
% 0.09/0.18 ( ! [X0 : $int] : ($less(X0,min(a)) | $less(l,X0) | l = X0) ) | ~spl0_2),
% 0.09/0.18 inference(resolution,[],[f123,f11])).
% 0.09/0.18 tff(f160,plain,(
% 0.09/0.18 $less(l,max(a)) | l = max(a) | ~spl0_2),
% 0.09/0.18 inference(resolution,[],[f128,f20])).
% 0.09/0.18 tff(f162,definition,(
% 0.09/0.18 spl0_3 <=> l = max(a)),
% 0.09/0.18 introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition])).
% 0.09/0.18 tff(f164,plain,(
% 0.09/0.18 l = max(a) | ~spl0_3),
% 0.09/0.18 inference(avatar_component_clause,[],[f162])).
% 0.09/0.18 tff(f166,definition,(
% 0.09/0.18 spl0_4 <=> $less(l,max(a))),
% 0.09/0.18 introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition])).
% 0.09/0.18 tff(f168,plain,(
% 0.09/0.18 $less(l,max(a)) | ~spl0_4),
% 0.09/0.18 inference(avatar_component_clause,[],[f166])).
% 0.09/0.18 tff(f169,plain,(
% 0.09/0.18 spl0_3 | spl0_4 | ~spl0_2),
% 0.09/0.18 inference(avatar_split_clause,[],[f160,f62,f166,f162])).
% 0.09/0.18 tff(f366,plain,(
% 0.09/0.18 ~$less(max(a),l) | ~spl0_1),
% 0.09/0.18 inference(superposition,[],[f20,f60])).
% 0.09/0.18 tff(f425,plain,(
% 0.09/0.18 ( ! [X0 : $int] : ($less($sum(0,X0),$sum(X0,k))) )),
% 0.09/0.18 inference(resolution,[],[f94,f18])).
% 0.09/0.18 tff(f433,plain,(
% 0.09/0.18 ( ! [X0 : $int] : ($less(X0,$sum(X0,k))) )),
% 0.09/0.18 inference(evaluation,[],[f425])).
% 0.09/0.18 tff(f870,plain,(
% 0.09/0.18 ( ! [X0 : $int,X1 : $int] : (~$less(X0,$sum(0,X1)) | $less(X0,$sum(k,X1))) )),
% 0.09/0.18 inference(resolution,[],[f85,f18])).
% 0.09/0.18 tff(f881,plain,(
% 0.09/0.18 ( ! [X0 : $int,X1 : $int] : (~$less(X0,X1) | $less(X0,$sum(k,X1))) )),
% 0.09/0.18 inference(evaluation,[],[f870])).
% 0.09/0.18 tff(f1048,plain,(
% 0.09/0.18 $less(l,max(a)) | l = max(a) | ~spl0_1),
% 0.09/0.18 inference(resolution,[],[f366,f11])).
% 0.09/0.18 tff(f1051,plain,(
% 0.09/0.18 spl0_3 | spl0_4 | ~spl0_1),
% 0.09/0.18 inference(avatar_split_clause,[],[f1048,f58,f166,f162])).
% 0.09/0.18 tff(f1179,plain,(
% 0.09/0.18 ~$less(l,$sum(l,k)) | ~spl0_3),
% 0.09/0.18 inference(superposition,[],[f21,f164])).
% 0.09/0.18 tff(f1190,plain,(
% 0.09/0.18 $false | ~spl0_3),
% 0.09/0.18 inference(forward_subsumption_resolution,[],[f1179,f433])).
% 0.09/0.18 tff(f1191,plain,(
% 0.09/0.18 ~spl0_3),
% 0.09/0.18 inference(avatar_contradiction_clause,[],[f1190])).
% 0.09/0.18 tff(f1288,plain,(
% 0.09/0.18 $less(l,$sum(k,max(a))) | ~spl0_4),
% 0.09/0.18 inference(resolution,[],[f168,f881])).
% 0.09/0.18 tff(f1289,plain,(
% 0.09/0.18 $false | ~spl0_4),
% 0.09/0.18 inference(forward_subsumption_resolution,[],[f1288,f30])).
% 0.09/0.18 tff(f1290,plain,(
% 0.09/0.18 ~spl0_4),
% 0.09/0.18 inference(avatar_contradiction_clause,[],[f1289])).
% 0.09/0.18 cnf(s2, plain, spl0_1 | spl0_2, inference(sat_conversion,[],[f66])).
% 0.09/0.18 cnf(s3, plain, ~spl0_2 | spl0_3 | spl0_4, inference(sat_conversion,[],[f169])).
% 0.09/0.18 cnf(s21, plain, ~spl0_1 | spl0_3 | spl0_4, inference(sat_conversion,[],[f1051])).
% 0.09/0.18 cnf(s24, plain, ~spl0_3, inference(sat_conversion,[],[f1191])).
% 0.09/0.18 cnf(s26, plain, ~spl0_4, inference(sat_conversion,[],[f1290])).
% 0.09/0.18 cnf(s27, plain, ~spl0_1, inference(rat,[],[s21,s26,s24])).
% 0.09/0.18 cnf(s28, plain, ~spl0_2, inference(rat,[],[s3,s26,s24])).
% 0.09/0.18 cnf(s29, plain, $false, inference(rat,[],[s2,s28,s27])).
% 0.09/0.18 tff(f1291,plain,(
% 0.09/0.18 $false),
% 0.09/0.18 inference(avatar_sat_refutation,[],[s29])).
% 0.09/0.18 % SZS output end Proof for theBenchmark
% 0.09/0.18 % (3917500)------------------------------
% 0.09/0.18 % (3917500)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.18 % (3917500)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.18 % (3917500)CaDiCaL version: 2.1.3
% 0.09/0.18 % (3917500)Termination reason: Refutation
% 0.09/0.18 % (3917500)Time elapsed: 0.018 s
% 0.09/0.18 % (3917500)Peak memory usage: 13 MB
% 0.09/0.18 % (3917500)Instructions burned: 51 (million)
% 0.09/0.18 % (3917482)Success in time 0.053 s
% 0.09/0.18 % Vampire exiting
%------------------------------------------------------------------------------