%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GEG024_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 : n003.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 0.21s 0.53s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 7 unt; 0 typ; 0 def)
% Number of atoms : 179 ( 151 equ)
% Maximal formula atoms : 24 ( 11 avg)
% Number of connectives : 175 ( 12 ~; 5 |; 154 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 13 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 199 ( 27 atm; 7 fun; 165 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 : 31 ( 9 usr; 28 con; 0-2 aty)
% Number of variables : 52 ( 48 !; 4 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
city: $tType ).
tff(func_def_0,type,
d: ( city * city ) > $int ).
tff(func_def_1,type,
inh: city > $int ).
tff(func_def_2,type,
kiel: city ).
tff(func_def_3,type,
hamburg: city ).
tff(func_def_4,type,
berlin: city ).
tff(func_def_5,type,
cologne: city ).
tff(func_def_6,type,
frankfurt: city ).
tff(func_def_7,type,
saarbruecken: city ).
tff(func_def_8,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 )
& ( inh(berlin) = 3442675 )
& ( inh(hamburg) = 1774224 )
& ( inh(munich) = 1330440 )
& ( inh(cologne) = 998105 )
& ( inh(frankfurt) = 671927 )
& ( inh(saarbruecken) = 175810 )
& ( inh(kiel) = 238281 ) )
=> ? [X0: city] :
( $lesseq(d(kiel,X0),100)
& $lesseq(1000000,inh(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exists_big_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 )
& ( inh(berlin) = 3442675 )
& ( inh(hamburg) = 1774224 )
& ( inh(munich) = 1330440 )
& ( inh(cologne) = 998105 )
& ( inh(frankfurt) = 671927 )
& ( inh(saarbruecken) = 175810 )
& ( inh(kiel) = 238281 ) )
=> ? [X0: city] :
( $lesseq(d(kiel,X0),100)
& $lesseq(1000000,inh(X0)) ) ),
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 )
& ( inh(berlin) = 3442675 )
& ( inh(hamburg) = 1774224 )
& ( inh(munich) = 1330440 )
& ( inh(cologne) = 998105 )
& ( inh(frankfurt) = 671927 )
& ( inh(saarbruecken) = 175810 )
& ( inh(kiel) = 238281 ) )
=> ? [X0: city] :
( ~ $less(100,d(kiel,X0))
& ~ $less(inh(X0),1000000) ) ),
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 )
& ( inh(berlin) = 3442675 )
& ( inh(hamburg) = 1774224 )
& ( inh(munich) = 1330440 )
& ( inh(cologne) = 998105 )
& ( inh(frankfurt) = 671927 )
& ( inh(saarbruecken) = 175810 )
& ( inh(kiel) = 238281 ) )
=> ? [X6: city] :
( ~ $less(100,d(kiel,X6))
& ~ $less(inh(X6),1000000) ) ),
inference(rectify,[],[f3]) ).
tff(f17,plain,
( ! [X6: city] :
( $less(100,d(kiel,X6))
| $less(inh(X6),1000000) )
& ! [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 )
& ( inh(berlin) = 3442675 )
& ( inh(hamburg) = 1774224 )
& ( inh(munich) = 1330440 )
& ( inh(cologne) = 998105 )
& ( inh(frankfurt) = 671927 )
& ( inh(saarbruecken) = 175810 )
& ( inh(kiel) = 238281 ) ),
inference(ennf_transformation,[],[f16]) ).
tff(f18,plain,
( ! [X6: city] :
( $less(100,d(kiel,X6))
| $less(inh(X6),1000000) )
& ! [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 )
& ( inh(berlin) = 3442675 )
& ( inh(hamburg) = 1774224 )
& ( inh(munich) = 1330440 )
& ( inh(cologne) = 998105 )
& ( inh(frankfurt) = 671927 )
& ( inh(saarbruecken) = 175810 )
& ( inh(kiel) = 238281 ) ),
inference(flattening,[],[f17]) ).
tff(f19,plain,
( ! [X0: city] :
( $less(100,d(kiel,X0))
| $less(inh(X0),1000000) )
& ! [X1: city,X2: city] : ( d(X1,X2) = d(X2,X1) )
& ! [X3: city,X4: city,X5: city] : ~ $less($sum(d(X3,X4),d(X4,X5)),d(X3,X5))
& ! [X6: city] : ( 0 = d(X6,X6) )
& ( 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 )
& ( inh(berlin) = 3442675 )
& ( inh(hamburg) = 1774224 )
& ( inh(munich) = 1330440 )
& ( inh(cologne) = 998105 )
& ( inh(frankfurt) = 671927 )
& ( inh(saarbruecken) = 175810 )
& ( inh(kiel) = 238281 ) ),
inference(rectify,[],[f18]) ).
tff(f25,plain,
inh(hamburg) = 1774224,
inference(cnf_transformation,[],[f19]) ).
tff(f30,plain,
d(hamburg,kiel) = 90,
inference(cnf_transformation,[],[f19]) ).
tff(f41,plain,
! [X2: city,X1: city] : ( d(X1,X2) = d(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
tff(f42,plain,
! [X0: city] :
( $less(100,d(kiel,X0))
| $less(inh(X0),1000000) ),
inference(cnf_transformation,[],[f19]) ).
tff(f43,plain,
90 = d(kiel,hamburg),
inference(superposition,[],[f41,f30]) ).
tff(f68,plain,
( $less(100,90)
| $less(inh(hamburg),1000000) ),
inference(superposition,[],[f42,f43]) ).
tff(f69,plain,
$less(inh(hamburg),1000000),
inference(evaluation,[],[f68]) ).
tff(f70,plain,
$less(1774224,1000000),
inference(forward_demodulation,[],[f69,f25]) ).
tff(f71,plain,
$false,
inference(evaluation,[],[f70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG024_1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.40 % Computer : n003.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sun Sep 27 06:31:55 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.47 Running first-order model finding
% 0.13/0.47 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
% 0.21/0.53 % (144958)Will run a generic schedule for satisfiability detection.
% 0.21/0.53 % (144963)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3138509024_2999 on theBenchmark for (2999ds/0Mi)
% 0.21/0.53 % (144963)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.53 % (144963)Terminated due to inappropriate strategy.
% 0.21/0.53 % (144963)------------------------------
% 0.21/0.53 % (144963)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.53 % (144963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.53 % (144963)CaDiCaL version: 2.1.3
% 0.21/0.53 % (144963)Termination reason: Inappropriate
% 0.21/0.53 % (144963)Time elapsed: 0.001 s
% 0.21/0.53 % (144963)Peak memory usage: 10 MB
% 0.21/0.53 % (144963)------------------------------
% 0.21/0.53 % (144963)------------------------------
% 0.21/0.53 % (144964)% WARNING: option uhcvi not known.
% 0.21/0.53 % (144969)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=211204569:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.21/0.53 % (144964)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1735111755:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.21/0.53 % (144966)dis+10_1_sil=32000:sp=arity:random_seed=3240398348:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.21/0.53 % (144965)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4164540542:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.21/0.53 % (144967)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1331316806:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.21/0.53 % (144968)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1093019261:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.21/0.53 % (144969) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-144958-144969"...
% 0.21/0.53 % (144966) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-144958-144966"...
% 0.21/0.53 % (144968) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-144958-144968"...
% 0.21/0.53 % (144969)...printing done.
% 0.21/0.53 % (144966)...printing done.
% 0.21/0.53 % (144968)...printing done.
% 0.21/0.53 % (144967) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-144958-144967"...
% 0.21/0.53 % (144966)Refutation found. Thanks to Tanya!
% 0.21/0.53 % SZS status Theorem for theBenchmark
% 0.21/0.53 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.53 % (144966)------------------------------
% 0.21/0.53 % (144966)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.53 % (144966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.53 % (144966)CaDiCaL version: 2.1.3
% 0.21/0.53 % (144966)Termination reason: Refutation
% 0.21/0.53 % (144966)Time elapsed: 0.007 s
% 0.21/0.53 % (144966)Peak memory usage: 12 MB
% 0.21/0.53 % (144966)Instructions burned: 5 (million)
% 0.21/0.53 % (144958)Success in time 0.045 s
% 0.21/0.53 % Vampire exiting
%------------------------------------------------------------------------------