%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEG022_1 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n010.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 09:50:04 AM UTC 2026
% Result : Theorem 0.16s 0.49s
% Output : Refutation 0.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG022_1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.38 % Computer : n010.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Sun Sep 27 06:29:17 UTC 2026
% 0.13/0.38 % CPUTime :
% 0.13/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.16/0.43 Running first-order model finding
% 0.16/0.43 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
% 0.16/0.49 % (581651)Will run a generic schedule for satisfiability detection.
% 0.16/0.49 % (581661)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2699293168:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.49 % (581657)% WARNING: option uhcvi not known.
% 0.16/0.49 % (581662)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2291638919:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.16/0.49 % (581656)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2666118669_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.49 % (581658)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4171321198:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.49 % (581657)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2970988806:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.49 % (581659)dis+10_1_sil=32000:sp=arity:random_seed=1040748387:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.49 % (581660)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1295119868:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.49 % (581656)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.16/0.49 % (581656)Terminated due to inappropriate strategy.
% 0.16/0.49 % (581656)------------------------------
% 0.16/0.49 % (581656)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.49 % (581656)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.49 % (581656)CaDiCaL version: 2.1.3
% 0.16/0.49 % (581656)Termination reason: Inappropriate
% 0.16/0.49 % (581656)Time elapsed: 0.001 s
% 0.16/0.49 % (581656)Peak memory usage: 10 MB
% 0.16/0.49 % (581656)------------------------------
% 0.16/0.49 % (581656)------------------------------
% 0.16/0.49 % (581659) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-581651-581659"...
% 0.16/0.49 % (581659)...printing done.
% 0.16/0.49 % (581660) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-581651-581660"...
% 0.16/0.49 % (581659)Refutation found. Thanks to Tanya!
% 0.16/0.49 % SZS status Theorem for theBenchmark
% 0.16/0.49 % SZS output start Proof for theBenchmark
% 0.16/0.49 tff(type_def_5, type, city: $tType).
% 0.16/0.49 tff(func_def_0, type, d: (city * city) > $int).
% 0.16/0.49 tff(func_def_1, type, kiel: city).
% 0.16/0.49 tff(func_def_2, type, hamburg: city).
% 0.16/0.49 tff(func_def_3, type, berlin: city).
% 0.16/0.49 tff(func_def_4, type, cologne: city).
% 0.16/0.49 tff(func_def_5, type, frankfurt: city).
% 0.16/0.49 tff(func_def_6, type, saarbruecken: city).
% 0.16/0.49 tff(func_def_7, type, munich: city).
% 0.16/0.49 tff(f1,conjecture,(
% 0.16/0.49 (! [X0 : city,X1 : city] : d(X0,X1) = d(X1,X0) & ! [X0 : city,X1 : city,X2 : city] : $lesseq(d(X0,X2),$sum(d(X0,X1),d(X1,X2))) & ! [X0 : city] : d(X0,X0) = 0 & d(berlin,munich) = 510 & d(berlin,cologne) = 480 & d(berlin,frankfurt) = 420 & d(saarbruecken,frankfurt) = 160 & d(saarbruecken,cologne) = 190 & d(hamburg,cologne) = 360 & d(hamburg,frankfurt) = 390 & d(cologne,frankfurt) = 150 & d(hamburg,kiel) = 90 & d(hamburg,berlin) = 250 & d(munich,frankfurt) = 300 & d(munich,saarbruecken) = 360) => $lesseq(d(hamburg,munich),700)),
% 0.16/0.49 file('/export/starexec/sandbox2/benchmark/theBenchmark.p',city_distance_2)).
% 0.16/0.49 tff(f2,negated_conjecture,(
% 0.16/0.49 ~((! [X0 : city,X1 : city] : d(X0,X1) = d(X1,X0) & ! [X0 : city,X1 : city,X2 : city] : $lesseq(d(X0,X2),$sum(d(X0,X1),d(X1,X2))) & ! [X0 : city] : d(X0,X0) = 0 & d(berlin,munich) = 510 & d(berlin,cologne) = 480 & d(berlin,frankfurt) = 420 & d(saarbruecken,frankfurt) = 160 & d(saarbruecken,cologne) = 190 & d(hamburg,cologne) = 360 & d(hamburg,frankfurt) = 390 & d(cologne,frankfurt) = 150 & d(hamburg,kiel) = 90 & d(hamburg,berlin) = 250 & d(munich,frankfurt) = 300 & d(munich,saarbruecken) = 360) => $lesseq(d(hamburg,munich),700))),
% 0.16/0.49 inference(negated_conjecture,[status(cth)],[f1])).
% 0.16/0.49 tff(f3,plain,(
% 0.16/0.49 ~((! [X0 : city,X1 : city] : d(X0,X1) = d(X1,X0) & ! [X0 : city,X1 : city,X2 : city] : ~$less($sum(d(X0,X1),d(X1,X2)),d(X0,X2)) & ! [X0 : city] : d(X0,X0) = 0 & d(berlin,munich) = 510 & d(berlin,cologne) = 480 & d(berlin,frankfurt) = 420 & d(saarbruecken,frankfurt) = 160 & d(saarbruecken,cologne) = 190 & d(hamburg,cologne) = 360 & d(hamburg,frankfurt) = 390 & d(cologne,frankfurt) = 150 & d(hamburg,kiel) = 90 & d(hamburg,berlin) = 250 & d(munich,frankfurt) = 300 & d(munich,saarbruecken) = 360) => ~$less(700,d(hamburg,munich)))),
% 0.16/0.49 inference(theory_normalization,[],[f2])).
% 0.16/0.49 tff(f10,definition,(
% 0.16/0.49 ( ! [X2 : $int,X0 : $int,X1 : $int] : (~$less(X1,X2) | ~$less(X0,X1) | $less(X0,X2)) )),
% 0.16/0.49 introduced(theory,[tha_transitivity])).
% 0.16/0.49 tff(f16,plain,(
% 0.16/0.49 ~((! [X0 : city,X1 : city] : d(X0,X1) = d(X1,X0) & ! [X2 : city,X3 : city,X4 : city] : ~$less($sum(d(X2,X3),d(X3,X4)),d(X2,X4)) & ! [X5 : city] : 0 = d(X5,X5) & d(berlin,munich) = 510 & d(berlin,cologne) = 480 & d(berlin,frankfurt) = 420 & d(saarbruecken,frankfurt) = 160 & d(saarbruecken,cologne) = 190 & d(hamburg,cologne) = 360 & d(hamburg,frankfurt) = 390 & d(cologne,frankfurt) = 150 & d(hamburg,kiel) = 90 & d(hamburg,berlin) = 250 & d(munich,frankfurt) = 300 & d(munich,saarbruecken) = 360) => ~$less(700,d(hamburg,munich)))),
% 0.16/0.49 inference(rectify,[],[f3])).
% 0.16/0.49 tff(f17,plain,(
% 0.16/0.49 $less(700,d(hamburg,munich)) & (! [X0 : city,X1 : city] : d(X0,X1) = d(X1,X0) & ! [X2 : city,X3 : city,X4 : city] : ~$less($sum(d(X2,X3),d(X3,X4)),d(X2,X4)) & ! [X5 : city] : 0 = d(X5,X5) & d(berlin,munich) = 510 & d(berlin,cologne) = 480 & d(berlin,frankfurt) = 420 & d(saarbruecken,frankfurt) = 160 & d(saarbruecken,cologne) = 190 & d(hamburg,cologne) = 360 & d(hamburg,frankfurt) = 390 & d(cologne,frankfurt) = 150 & d(hamburg,kiel) = 90 & d(hamburg,berlin) = 250 & d(munich,frankfurt) = 300 & d(munich,saarbruecken) = 360)),
% 0.16/0.49 inference(ennf_transformation,[],[f16])).
% 0.16/0.49 tff(f18,plain,(
% 0.16/0.49 $less(700,d(hamburg,munich)) & ! [X0 : city,X1 : city] : d(X0,X1) = d(X1,X0) & ! [X2 : city,X3 : city,X4 : city] : ~$less($sum(d(X2,X3),d(X3,X4)),d(X2,X4)) & ! [X5 : city] : 0 = d(X5,X5) & d(berlin,munich) = 510 & d(berlin,cologne) = 480 & d(berlin,frankfurt) = 420 & d(saarbruecken,frankfurt) = 160 & d(saarbruecken,cologne) = 190 & d(hamburg,cologne) = 360 & d(hamburg,frankfurt) = 390 & d(cologne,frankfurt) = 150 & d(hamburg,kiel) = 90 & d(hamburg,berlin) = 250 & d(munich,frankfurt) = 300 & d(munich,saarbruecken) = 360),
% 0.16/0.49 inference(flattening,[],[f17])).
% 0.16/0.49 tff(f20,plain,(
% 0.16/0.49 d(munich,frankfurt) = 300),
% 0.16/0.49 inference(cnf_transformation,[],[f18])).
% 0.16/0.49 tff(f24,plain,(
% 0.16/0.49 d(hamburg,frankfurt) = 390),
% 0.16/0.49 inference(cnf_transformation,[],[f18])).
% 0.16/0.49 tff(f32,plain,(
% 0.16/0.49 ( ! [X2 : city,X3 : city,X4 : city] : (~$less($sum(d(X2,X3),d(X3,X4)),d(X2,X4))) )),
% 0.16/0.49 inference(cnf_transformation,[],[f18])).
% 0.16/0.49 tff(f33,plain,(
% 0.16/0.49 ( ! [X0 : city,X1 : city] : (d(X0,X1) = d(X1,X0)) )),
% 0.16/0.49 inference(cnf_transformation,[],[f18])).
% 0.16/0.49 tff(f34,plain,(
% 0.16/0.49 $less(700,d(hamburg,munich))),
% 0.16/0.49 inference(cnf_transformation,[],[f18])).
% 0.16/0.49 tff(f39,plain,(
% 0.16/0.49 300 = d(frankfurt,munich)),
% 0.16/0.49 inference(superposition,[],[f33,f20])).
% 0.16/0.49 tff(f61,plain,(
% 0.16/0.49 ( ! [X0 : city] : (~$less($sum(390,d(frankfurt,X0)),d(hamburg,X0))) )),
% 0.16/0.49 inference(superposition,[],[f32,f24])).
% 0.16/0.49 tff(f130,plain,(
% 0.16/0.49 ( ! [X0 : $int] : ($less(X0,d(hamburg,munich)) | ~$less(X0,700)) )),
% 0.16/0.49 inference(resolution,[],[f10,f34])).
% 0.16/0.49 tff(f270,plain,(
% 0.16/0.49 ~$less($sum(390,d(frankfurt,munich)),700)),
% 0.16/0.49 inference(resolution,[],[f61,f130])).
% 0.16/0.49 tff(f294,plain,(
% 0.16/0.49 ~$less($sum(390,300),700)),
% 0.16/0.49 inference(forward_demodulation,[],[f270,f39])).
% 0.16/0.49 tff(f295,plain,(
% 0.16/0.49 $false),
% 0.16/0.49 inference(evaluation,[],[f294])).
% 0.16/0.49 % SZS output end Proof for theBenchmark
% 0.16/0.49 % (581659)------------------------------
% 0.16/0.49 % (581659)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.49 % (581659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.49 % (581659)CaDiCaL version: 2.1.3
% 0.16/0.49 % (581659)Termination reason: Refutation
% 0.16/0.49 % (581659)Time elapsed: 0.015 s
% 0.16/0.49 % (581659)Peak memory usage: 12 MB
% 0.16/0.49 % (581659)Instructions burned: 13 (million)
% 0.16/0.49 % (581651)Success in time 0.054 s
% 0.16/0.49 % Vampire exiting
%------------------------------------------------------------------------------