%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEG022_1 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 09:50:01 AM UTC 2026
% Result : Theorem 2.57s 1.04s
% Output : Refutation 2.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 127 ( 102 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 125 ( 17 ~; 3 |; 101 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 148 ( 24 atm; 11 fun; 109 num; 4 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 : 23 ( 9 usr; 21 con; 0-2 aty)
% Number of variables : 52 ( 52 !; 0 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
city: $tType ).
tff(func_def_0,type,
d: ( city * city ) > $int ).
tff(func_def_1,type,
kiel: city ).
tff(func_def_2,type,
hamburg: city ).
tff(func_def_3,type,
berlin: city ).
tff(func_def_4,type,
cologne: city ).
tff(func_def_5,type,
frankfurt: city ).
tff(func_def_6,type,
saarbruecken: city ).
tff(func_def_7,type,
munich: city ).
tff(func_def_24,type,
'$inst0': $int ).
tff(f1,conjecture,
( ( ( d(cologne,frankfurt) = 150 )
& ( d(berlin,frankfurt) = 420 )
& ( d(hamburg,berlin) = 250 )
& ( d(berlin,cologne) = 480 )
& ! [X0: city] : ( d(X0,X0) = 0 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(hamburg,cologne) = 360 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(hamburg,frankfurt) = 390 )
& ( d(munich,frankfurt) = 300 )
& ( d(munich,saarbruecken) = 360 )
& ! [X1: city,X0: city] : ( d(X0,X1) = d(X1,X0) )
& ! [X0: city,X1: city,X2: city] : $lesseq(d(X0,X2),$sum(d(X0,X1),d(X1,X2)))
& ( d(berlin,munich) = 510 )
& ( d(hamburg,kiel) = 90 ) )
=> $lesseq(d(hamburg,munich),700) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',city_distance_2) ).
tff(f2,negated_conjecture,
~ ( ( ( d(cologne,frankfurt) = 150 )
& ( d(berlin,frankfurt) = 420 )
& ( d(hamburg,berlin) = 250 )
& ( d(berlin,cologne) = 480 )
& ! [X0: city] : ( d(X0,X0) = 0 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(hamburg,cologne) = 360 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(hamburg,frankfurt) = 390 )
& ( d(munich,frankfurt) = 300 )
& ( d(munich,saarbruecken) = 360 )
& ! [X1: city,X0: city] : ( d(X0,X1) = d(X1,X0) )
& ! [X0: city,X1: city,X2: city] : $lesseq(d(X0,X2),$sum(d(X0,X1),d(X1,X2)))
& ( d(berlin,munich) = 510 )
& ( d(hamburg,kiel) = 90 ) )
=> $lesseq(d(hamburg,munich),700) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ( ( d(cologne,frankfurt) = 150 )
& ( d(berlin,frankfurt) = 420 )
& ( d(hamburg,berlin) = 250 )
& ( d(berlin,cologne) = 480 )
& ! [X0: city] : ( d(X0,X0) = 0 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(hamburg,cologne) = 360 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(hamburg,frankfurt) = 390 )
& ( d(munich,frankfurt) = 300 )
& ( d(munich,saarbruecken) = 360 )
& ! [X1: city,X0: city] : ( d(X0,X1) = d(X1,X0) )
& ! [X0: city,X1: city,X2: city] : ~ $less($sum(d(X0,X1),d(X1,X2)),d(X0,X2))
& ( d(berlin,munich) = 510 )
& ( d(hamburg,kiel) = 90 ) )
=> ~ $less(700,d(hamburg,munich)) ),
inference(theory_normalization,[],[f2]) ).
tff(f10,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) ),
introduced(definition,[],[tha_transitivity]) ).
tff(f16,plain,
~ ( ( ( d(cologne,frankfurt) = 150 )
& ! [X0: city] : ( d(X0,X0) = 0 )
& ( d(munich,saarbruecken) = 360 )
& ( d(berlin,cologne) = 480 )
& ( d(berlin,munich) = 510 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(berlin,frankfurt) = 420 )
& ( d(hamburg,frankfurt) = 390 )
& ! [X1: city,X2: city] : ( d(X1,X2) = d(X2,X1) )
& ! [X4: city,X3: city,X5: city] : ~ $less($sum(d(X3,X4),d(X4,X5)),d(X3,X5))
& ( d(hamburg,cologne) = 360 )
& ( d(hamburg,kiel) = 90 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(munich,frankfurt) = 300 )
& ( d(hamburg,berlin) = 250 ) )
=> ~ $less(700,d(hamburg,munich)) ),
inference(rectify,[],[f3]) ).
tff(f17,plain,
( $less(700,d(hamburg,munich))
& ( d(cologne,frankfurt) = 150 )
& ! [X0: city] : ( d(X0,X0) = 0 )
& ( d(munich,saarbruecken) = 360 )
& ( d(berlin,cologne) = 480 )
& ( d(berlin,munich) = 510 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(berlin,frankfurt) = 420 )
& ( d(hamburg,frankfurt) = 390 )
& ! [X1: city,X2: city] : ( d(X1,X2) = d(X2,X1) )
& ! [X4: city,X3: city,X5: city] : ~ $less($sum(d(X3,X4),d(X4,X5)),d(X3,X5))
& ( d(hamburg,cologne) = 360 )
& ( d(hamburg,kiel) = 90 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(munich,frankfurt) = 300 )
& ( d(hamburg,berlin) = 250 ) ),
inference(ennf_transformation,[],[f16]) ).
tff(f18,plain,
( $less(700,d(hamburg,munich))
& ! [X4: city,X3: city,X5: city] : ~ $less($sum(d(X3,X4),d(X4,X5)),d(X3,X5))
& ( d(munich,saarbruecken) = 360 )
& ( d(hamburg,berlin) = 250 )
& ( d(berlin,munich) = 510 )
& ( d(berlin,frankfurt) = 420 )
& ! [X1: city,X2: city] : ( d(X1,X2) = d(X2,X1) )
& ( d(hamburg,cologne) = 360 )
& ( d(cologne,frankfurt) = 150 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(berlin,cologne) = 480 )
& ( d(munich,frankfurt) = 300 )
& ( d(hamburg,frankfurt) = 390 )
& ( d(hamburg,kiel) = 90 )
& ! [X0: city] : ( d(X0,X0) = 0 ) ),
inference(flattening,[],[f17]) ).
tff(f19,plain,
( $less(700,d(hamburg,munich))
& ! [X0: city,X1: city,X2: city] : ~ $less($sum(d(X1,X0),d(X0,X2)),d(X1,X2))
& ( d(munich,saarbruecken) = 360 )
& ( d(hamburg,berlin) = 250 )
& ( d(berlin,munich) = 510 )
& ( d(berlin,frankfurt) = 420 )
& ! [X3: city,X4: city] : ( d(X3,X4) = d(X4,X3) )
& ( d(hamburg,cologne) = 360 )
& ( d(cologne,frankfurt) = 150 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(berlin,cologne) = 480 )
& ( d(munich,frankfurt) = 300 )
& ( d(hamburg,frankfurt) = 390 )
& ( d(hamburg,kiel) = 90 )
& ! [X5: city] : ( 0 = d(X5,X5) ) ),
inference(rectify,[],[f18]) ).
tff(f22,plain,
d(hamburg,frankfurt) = 390,
inference(cnf_transformation,[],[f19]) ).
tff(f23,plain,
d(munich,frankfurt) = 300,
inference(cnf_transformation,[],[f19]) ).
tff(f29,plain,
! [X3: city,X4: city] : ( d(X3,X4) = d(X4,X3) ),
inference(cnf_transformation,[],[f19]) ).
tff(f34,plain,
! [X2: city,X0: city,X1: city] : ~ $less($sum(d(X1,X0),d(X0,X2)),d(X1,X2)),
inference(cnf_transformation,[],[f19]) ).
tff(f35,plain,
$less(700,d(hamburg,munich)),
inference(cnf_transformation,[],[f19]) ).
tff(f41,plain,
300 = d(frankfurt,munich),
inference(superposition,[],[f29,f23]) ).
tff(f66,plain,
! [X0: city] : ~ $less($sum(390,d(frankfurt,X0)),d(hamburg,X0)),
inference(superposition,[],[f34,f22]) ).
tff(f142,plain,
! [X0: $int] :
( $less(X0,d(hamburg,munich))
| ~ $less(X0,700) ),
inference(resolution,[],[f10,f35]) ).
tff(f450,plain,
~ $less($sum(390,d(frankfurt,munich)),700),
inference(resolution,[],[f66,f142]) ).
tff(f481,plain,
~ $less($sum(390,300),700),
inference(forward_demodulation,[],[f450,f41]) ).
tff(f482,plain,
$false,
inference(evaluation,[],[f481]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEG022_1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.37 % Computer : n012.cluster.edu
% 0.04/0.37 % Model : x86_64 x86_64
% 0.04/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.37 % Memory : 8046.5625MB
% 0.04/0.37 % OS : Linux 6.8.0-71-generic
% 0.04/0.38 % CPULimit : 300
% 0.04/0.38 % WCLimit : 300
% 0.04/0.38 % DateTime : Sun Sep 27 06:28:35 UTC 2026
% 0.04/0.38 % CPUTime :
% 0.04/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.39 Running first-order theorem proving
% 0.04/0.39 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.10/0.94 % (2010432)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 1.10/0.94 % (2010437)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=1116670193:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 1.10/0.94 % (2010443)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=2611083908:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 1.10/0.94 % (2010440)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1998209534:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 1.10/0.94 % (2010441)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=2199605907:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 1.10/0.94 % (2010438)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=659703712:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 1.10/0.94 % (2010439)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=342068659:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 1.10/0.94 % (2010442)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=704086247:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 1.10/0.94 % (2010441)Instruction limit reached!
% 1.10/0.94 % (2010441)------------------------------
% 1.10/0.94 % (2010441)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.10/0.94 % (2010441)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.94 % (2010441)CaDiCaL version: 2.1.3
% 1.10/0.94 % (2010441)Termination reason: Instruction limit
% 1.10/0.94 % (2010441)Termination phase: Saturation
% 1.10/0.94 % (2010441)Time elapsed: 0.002 s
% 1.10/0.94 % (2010441)Peak memory usage: 88 MB
% 1.10/0.94 % (2010441)Instructions burned: 4 (million)
% 1.10/0.94 % (2010440)Instruction limit reached!
% 1.10/0.94 % (2010440)------------------------------
% 1.10/0.94 % (2010440)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.10/0.94 % (2010440)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.94 % (2010440)CaDiCaL version: 2.1.3
% 1.10/0.94 % (2010440)Termination reason: Instruction limit
% 1.10/0.94 % (2010440)Termination phase: Saturation
% 1.10/0.94 % (2010440)Time elapsed: 0.003 s
% 1.10/0.94 % (2010440)Peak memory usage: 88 MB
% 1.10/0.94 % (2010440)Instructions burned: 9 (million)
% 1.10/0.94 % (2010437)Instruction limit reached!
% 1.10/0.94 % (2010437)------------------------------
% 1.10/0.94 % (2010437)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.10/0.94 % (2010437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.94 % (2010437)CaDiCaL version: 2.1.3
% 1.10/0.94 % (2010437)Termination reason: Instruction limit
% 1.10/0.94 % (2010437)Termination phase: Saturation
% 1.10/0.94 % (2010437)Time elapsed: 0.019 s
% 1.10/0.94 % (2010437)Peak memory usage: 115 MB
% 1.10/0.94 % (2010437)Instructions burned: 14 (million)
% 1.10/0.94 % (2010439)First to succeed.
% 1.10/0.94 % (2010443)Instruction limit reached!
% 1.10/0.94 % (2010443)------------------------------
% 1.10/0.94 % (2010443)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 1.10/0.94 % (2010443)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.10/0.94 % (2010443)CaDiCaL version: 2.1.3
% 1.10/0.94 % (2010443)Termination reason: Instruction limit
% 1.10/0.94 % (2010443)Termination phase: Saturation
% 1.10/0.94 % (2010443)Time elapsed: 0.027 s
% 1.10/0.94 % (2010443)Peak memory usage: 115 MB
% 1.10/0.94 % (2010443)Instructions burned: 35 (million)
% 1.10/0.94 % (2010439)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2010432"
% 1.10/0.94 % (2010442)Also succeeded, but the first one will report.
% 1.10/0.94 % (2010438)Also succeeded, but the first one will report.
% 1.10/0.94 % (2010451)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1133542353:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 1.10/0.94 % (2010452)dis+1011_2:1_to=kbo:sil=128000:tgt=full:fde=none:si=on:norm_ineq=on:spb=goal_then_units:tha=some:nwc=2:sac=on:random_seed=3620510422:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2998 on theBenchmark for (2998ds/29Mi)
% 1.10/0.94 % (2010451)Instruction limit reached!
% 1.10/0.94 % (2010451)------------------------------
% 1.10/0.94 % (2010451)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.04 % (2010451)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.04 % (2010451)CaDiCaL version: 2.1.3
% 2.57/1.04 % (2010451)Termination reason: Instruction limit
% 2.57/1.04 % (2010451)Termination phase: Saturation
% 2.57/1.04 % (2010451)Time elapsed: 0.005 s
% 2.57/1.04 % (2010451)Peak memory usage: 88 MB
% 2.57/1.04 % (2010451)Instructions burned: 15 (million)
% 2.57/1.04 % (2010452)Instruction limit reached!
% 2.57/1.04 % (2010452)------------------------------
% 2.57/1.04 % (2010452)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.04 % (2010452)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.04 % (2010452)CaDiCaL version: 2.1.3
% 2.57/1.04 % (2010452)Termination reason: Instruction limit
% 2.57/1.04 % (2010452)Termination phase: Saturation
% 2.57/1.04 % (2010452)Time elapsed: 0.011 s
% 2.57/1.04 % (2010452)Peak memory usage: 88 MB
% 2.57/1.04 % (2010452)Instructions burned: 30 (million)
% 2.57/1.04 % (2010453)ott+21_1024_to=lakbo:sil=128000:bsd=on:si=on:alasca=on:uwa=alasca_main:nwc=0.5:random_seed=1429714091:cond=on:i=16:fgj=on:ep=RS:asg=force:nm=10:rtra=on:rawr=on_2998 on theBenchmark for (2998ds/16Mi)
% 2.57/1.04 % (2010453)Instruction limit reached!
% 2.57/1.04 % (2010453)------------------------------
% 2.57/1.04 % (2010453)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.04 % (2010453)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.04 % (2010453)CaDiCaL version: 2.1.3
% 2.57/1.04 % (2010453)Termination reason: Instruction limit
% 2.57/1.04 % (2010453)Termination phase: Saturation
% 2.57/1.04 % (2010453)Time elapsed: 0.006 s
% 2.57/1.04 % (2010453)Peak memory usage: 90 MB
% 2.57/1.04 % (2010453)Instructions burned: 16 (million)
% 2.57/1.04 % (2010454)dis+1011_1_prc=on:drc=off:si=on:sac=on:random_seed=898860759:i=24:canc=force:rtra=on_2998 on theBenchmark for (2998ds/24Mi)
% 2.57/1.04 % (2010454)Instruction limit reached!
% 2.57/1.04 % (2010454)------------------------------
% 2.57/1.04 % (2010454)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.04 % (2010454)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.04 % (2010454)CaDiCaL version: 2.1.3
% 2.57/1.04 % (2010454)Termination reason: Instruction limit
% 2.57/1.04 % (2010454)Termination phase: Saturation
% 2.57/1.04 % (2010454)Time elapsed: 0.010 s
% 2.57/1.04 % (2010454)Peak memory usage: 89 MB
% 2.57/1.04 % (2010454)Instructions burned: 26 (million)
% 2.57/1.04 % (2010439)Refutation found. Thanks to Tanya!
% 2.57/1.04 % SZS status Theorem for theBenchmark
% 2.57/1.04 % SZS output start Proof for theBenchmark
% See solution above
% 2.57/1.05 % (2010439)------------------------------
% 2.57/1.05 % (2010439)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.57/1.05 % (2010439)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.57/1.05 % (2010439)CaDiCaL version: 2.1.3
% 2.57/1.05 % (2010439)Termination reason: Refutation
% 2.57/1.05 % (2010439)Time elapsed: 0.027 s
% 2.57/1.05 % (2010439)Peak memory usage: 116 MB
% 2.57/1.05 % (2010439)Instructions burned: 29 (million)
% 2.57/1.05 % (2010439)------------------------------
% 2.57/1.05 % (2010439)------------------------------
% 2.57/1.05 % (2010432)Success in time 0.333 s
% 2.57/1.05 % Vampire exiting
%------------------------------------------------------------------------------