%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEG021_1 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n011.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 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 1
% Syntax : Number of formulae : 12 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 102 ( 86 equ)
% Maximal formula atoms : 16 ( 8 avg)
% Number of connectives : 99 ( 9 ~; 0 |; 86 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 11 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 110 ( 15 atm; 6 fun; 89 num; 0 var)
% Number of types : 2 ( 1 usr; 1 ari; 0 dat; 0 cdt)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 8 usr; 20 con; 0-2 aty)
% Number of variables : 38 ( 38 !; 0 ?; 38 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
city: $tType ).
tff(func_def_0,type,
d: ( city * city ) > $int ).
tff(func_def_1,type,
kiel: city ).
tff(func_def_2,type,
hamburg: city ).
tff(func_def_3,type,
berlin: city ).
tff(func_def_4,type,
cologne: city ).
tff(func_def_5,type,
frankfurt: city ).
tff(func_def_6,type,
saarbruecken: city ).
tff(func_def_7,type,
munich: city ).
tff(f1,conjecture,
( ( ! [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(cologne,berlin),500) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',city_distance_1) ).
tff(f2,negated_conjecture,
~ ( ( ! [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(cologne,berlin),500) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ( ! [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(500,d(cologne,berlin)) ),
inference(theory_normalization,[],[f2]) ).
tff(f16,plain,
~ ( ( ! [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(500,d(cologne,berlin)) ),
inference(rectify,[],[f3]) ).
tff(f17,plain,
( $less(500,d(cologne,berlin))
& ! [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 ) ),
inference(ennf_transformation,[],[f16]) ).
tff(f18,plain,
( $less(500,d(cologne,berlin))
& ! [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 ) ),
inference(flattening,[],[f17]) ).
tff(f29,plain,
d(berlin,cologne) = 480,
inference(cnf_transformation,[],[f18]) ).
tff(f33,plain,
! [X0: city,X1: city] : ( d(X0,X1) = d(X1,X0) ),
inference(cnf_transformation,[],[f18]) ).
tff(f34,plain,
$less(500,d(cologne,berlin)),
inference(cnf_transformation,[],[f18]) ).
tff(f35,plain,
$less(500,d(berlin,cologne)),
inference(forward_demodulation,[],[f34,f33]) ).
tff(f36,plain,
$less(500,480),
inference(forward_demodulation,[],[f35,f29]) ).
tff(f37,plain,
$false,
inference(evaluation,[],[f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEG021_1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 06:29:00 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 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
% 0.16/0.46 % (2039460)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (2039473)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2728903866_2999 on theBenchmark for (2999ds/0Mi)
% 0.16/0.46 % (2039473)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.16/0.46 % (2039473)Terminated due to inappropriate strategy.
% 0.16/0.46 % (2039473)------------------------------
% 0.16/0.46 % (2039473)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (2039473)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (2039473)CaDiCaL version: 2.1.3
% 0.16/0.46 % (2039473)Termination reason: Inappropriate
% 0.16/0.46 % (2039473)Time elapsed: 0.0000 s
% 0.16/0.46 % (2039473)Peak memory usage: 10 MB
% 0.16/0.46 % (2039473)------------------------------
% 0.16/0.46 % (2039473)------------------------------
% 0.16/0.46 % (2039474)% WARNING: option uhcvi not known.
% 0.16/0.46 % (2039475)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=928055392:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.16/0.46 % (2039476)dis+10_1_sil=32000:sp=arity:random_seed=2340777363:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (2039474)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3190487833:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.16/0.46 % (2039477)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3972242457:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.16/0.46 % (2039476) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2039460-2039476"...
% 0.16/0.46 % (2039477) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2039460-2039477"...
% 0.16/0.46 % (2039474) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-2039460-2039474"...
% 0.16/0.46 % (2039477)...printing done.
% 0.16/0.46 % (2039476)...printing done.
% 0.16/0.46 % (2039474)...printing done.
% 0.16/0.46 % (2039478)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1538021580:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.16/0.46 % (2039477)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (2039477)------------------------------
% 0.16/0.46 % (2039477)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (2039477)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (2039477)CaDiCaL version: 2.1.3
% 0.16/0.46 % (2039477)Termination reason: Refutation
% 0.16/0.46 % (2039477)Time elapsed: 0.002 s
% 0.16/0.46 % (2039477)Peak memory usage: 12 MB
% 0.16/0.46 % (2039477)Instructions burned: 2 (million)
% 0.16/0.46 % (2039460)Success in time 0.045 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------