%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEG021_1 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 09:50:00 AM UTC 2026
% Result : Theorem 3.40s 1.36s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 1
% Syntax : Number of formulae : 13 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 118 ( 100 equ)
% Maximal formula atoms : 16 ( 9 avg)
% Number of connectives : 115 ( 10 ~; 0 |; 101 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 10 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 127 ( 17 atm; 7 fun; 103 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 : 44 ( 44 !; 0 ?; 44 :)
% 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,
( ( ( d(berlin,frankfurt) = 420 )
& ( d(hamburg,cologne) = 360 )
& ( d(munich,frankfurt) = 300 )
& ( d(hamburg,kiel) = 90 )
& ( d(munich,saarbruecken) = 360 )
& ( d(cologne,frankfurt) = 150 )
& ! [X0: city] : ( d(X0,X0) = 0 )
& ( d(hamburg,frankfurt) = 390 )
& ( d(berlin,cologne) = 480 )
& ( d(berlin,munich) = 510 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(hamburg,berlin) = 250 )
& ( d(saarbruecken,frankfurt) = 160 )
& ! [X1: city,X0: city,X2: city] : $lesseq(d(X0,X2),$sum(d(X0,X1),d(X1,X2)))
& ! [X0: city,X1: city] : ( d(X0,X1) = d(X1,X0) ) )
=> $lesseq(d(cologne,berlin),500) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',city_distance_1) ).
tff(f2,negated_conjecture,
~ ( ( ( d(berlin,frankfurt) = 420 )
& ( d(hamburg,cologne) = 360 )
& ( d(munich,frankfurt) = 300 )
& ( d(hamburg,kiel) = 90 )
& ( d(munich,saarbruecken) = 360 )
& ( d(cologne,frankfurt) = 150 )
& ! [X0: city] : ( d(X0,X0) = 0 )
& ( d(hamburg,frankfurt) = 390 )
& ( d(berlin,cologne) = 480 )
& ( d(berlin,munich) = 510 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(hamburg,berlin) = 250 )
& ( d(saarbruecken,frankfurt) = 160 )
& ! [X1: city,X0: city,X2: city] : $lesseq(d(X0,X2),$sum(d(X0,X1),d(X1,X2)))
& ! [X0: city,X1: city] : ( d(X0,X1) = d(X1,X0) ) )
=> $lesseq(d(cologne,berlin),500) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ( ( d(berlin,frankfurt) = 420 )
& ( d(hamburg,cologne) = 360 )
& ( d(munich,frankfurt) = 300 )
& ( d(hamburg,kiel) = 90 )
& ( d(munich,saarbruecken) = 360 )
& ( d(cologne,frankfurt) = 150 )
& ! [X0: city] : ( d(X0,X0) = 0 )
& ( d(hamburg,frankfurt) = 390 )
& ( d(berlin,cologne) = 480 )
& ( d(berlin,munich) = 510 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(hamburg,berlin) = 250 )
& ( d(saarbruecken,frankfurt) = 160 )
& ! [X1: city,X0: city,X2: city] : ~ $less($sum(d(X0,X1),d(X1,X2)),d(X0,X2))
& ! [X0: city,X1: city] : ( d(X0,X1) = d(X1,X0) ) )
=> ~ $less(500,d(cologne,berlin)) ),
inference(theory_normalization,[],[f2]) ).
tff(f16,plain,
~ ( ( ! [X5: city,X4: city] : ( d(X4,X5) = d(X5,X4) )
& ! [X2: city,X1: city,X3: city] : ~ $less($sum(d(X2,X1),d(X1,X3)),d(X2,X3))
& ( d(hamburg,berlin) = 250 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(berlin,munich) = 510 )
& ( d(berlin,frankfurt) = 420 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(munich,frankfurt) = 300 )
& ( d(hamburg,kiel) = 90 )
& ( d(hamburg,cologne) = 360 )
& ( d(berlin,cologne) = 480 )
& ( d(cologne,frankfurt) = 150 )
& ! [X0: city] : ( d(X0,X0) = 0 )
& ( d(hamburg,frankfurt) = 390 )
& ( d(munich,saarbruecken) = 360 ) )
=> ~ $less(500,d(cologne,berlin)) ),
inference(rectify,[],[f3]) ).
tff(f17,plain,
( $less(500,d(cologne,berlin))
& ! [X5: city,X4: city] : ( d(X4,X5) = d(X5,X4) )
& ! [X2: city,X1: city,X3: city] : ~ $less($sum(d(X2,X1),d(X1,X3)),d(X2,X3))
& ( d(hamburg,berlin) = 250 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(berlin,munich) = 510 )
& ( d(berlin,frankfurt) = 420 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(munich,frankfurt) = 300 )
& ( d(hamburg,kiel) = 90 )
& ( d(hamburg,cologne) = 360 )
& ( d(berlin,cologne) = 480 )
& ( d(cologne,frankfurt) = 150 )
& ! [X0: city] : ( d(X0,X0) = 0 )
& ( d(hamburg,frankfurt) = 390 )
& ( d(munich,saarbruecken) = 360 ) ),
inference(ennf_transformation,[],[f16]) ).
tff(f18,plain,
( ( d(munich,frankfurt) = 300 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(berlin,munich) = 510 )
& ( d(hamburg,berlin) = 250 )
& ( d(hamburg,cologne) = 360 )
& ( d(hamburg,kiel) = 90 )
& ( d(hamburg,frankfurt) = 390 )
& ( d(berlin,frankfurt) = 420 )
& ! [X0: city] : ( d(X0,X0) = 0 )
& ! [X2: city,X1: city,X3: city] : ~ $less($sum(d(X2,X1),d(X1,X3)),d(X2,X3))
& ( d(berlin,cologne) = 480 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(munich,saarbruecken) = 360 )
& ( d(cologne,frankfurt) = 150 )
& $less(500,d(cologne,berlin))
& ! [X5: city,X4: city] : ( d(X4,X5) = d(X5,X4) ) ),
inference(flattening,[],[f17]) ).
tff(f19,plain,
( ( d(munich,frankfurt) = 300 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(berlin,munich) = 510 )
& ( d(hamburg,berlin) = 250 )
& ( d(hamburg,cologne) = 360 )
& ( d(hamburg,kiel) = 90 )
& ( d(hamburg,frankfurt) = 390 )
& ( d(berlin,frankfurt) = 420 )
& ! [X0: city] : ( d(X0,X0) = 0 )
& ! [X1: city,X2: city,X3: city] : ~ $less($sum(d(X1,X2),d(X2,X3)),d(X1,X3))
& ( d(berlin,cologne) = 480 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(munich,saarbruecken) = 360 )
& ( d(cologne,frankfurt) = 150 )
& $less(500,d(cologne,berlin))
& ! [X4: city,X5: city] : ( d(X4,X5) = d(X5,X4) ) ),
inference(rectify,[],[f18]) ).
tff(f20,plain,
! [X4: city,X5: city] : ( d(X4,X5) = d(X5,X4) ),
inference(cnf_transformation,[],[f19]) ).
tff(f21,plain,
$less(500,d(cologne,berlin)),
inference(cnf_transformation,[],[f19]) ).
tff(f25,plain,
d(berlin,cologne) = 480,
inference(cnf_transformation,[],[f19]) ).
tff(f69,plain,
$less(500,d(berlin,cologne)),
inference(superposition,[],[f21,f20]) ).
tff(f88,plain,
$less(500,480),
inference(forward_demodulation,[],[f69,f25]) ).
tff(f89,plain,
$false,
inference(evaluation,[],[f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG021_1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n026.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 06:31:41 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.40/1.36 % (2465969)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.40/1.36 % (2466025)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=297048894:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.40/1.36 % (2466025)Instruction limit reached!
% 3.40/1.36 % (2466025)------------------------------
% 3.40/1.36 % (2466025)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.36 % (2466025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.36 % (2466025)CaDiCaL version: 2.1.3
% 3.40/1.36 % (2466025)Termination reason: Instruction limit
% 3.40/1.36 % (2466025)Termination phase: Saturation
% 3.40/1.36 % (2466025)Time elapsed: 0.019 s
% 3.40/1.36 % (2466025)Peak memory usage: 115 MB
% 3.40/1.36 % (2466025)Instructions burned: 13 (million)
% 3.40/1.36 % (2466031)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=1884153550:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.40/1.36 % (2466027)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1538960061:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.40/1.36 % (2466029)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=3492218978:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.40/1.36 % (2466026)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=129189091:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.40/1.36 % (2466028)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=3563344647:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.40/1.36 % (2466030)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=725093876:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.40/1.36 % (2466028)First to succeed.
% 3.40/1.36 % (2466029)Also succeeded, but the first one will report.
% 3.40/1.36 % (2466028)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2465969"
% 3.40/1.36 % (2466027)Also succeeded, but the first one will report.
% 3.40/1.36 % (2466030)Also succeeded, but the first one will report.
% 3.40/1.36 % (2466031)Also succeeded, but the first one will report.
% 3.40/1.36 % (2466026)Also succeeded, but the first one will report.
% 3.40/1.36 % (2466033)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=3646640505:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.40/1.36 % (2466033)Also succeeded, but the first one will report.
% 3.40/1.36 % (2466028)Refutation found. Thanks to Tanya!
% 3.40/1.36 % SZS status Theorem for theBenchmark
% 3.40/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 3.40/1.36 % (2466028)------------------------------
% 3.40/1.36 % (2466028)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.36 % (2466028)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.36 % (2466028)CaDiCaL version: 2.1.3
% 3.40/1.36 % (2466028)Termination reason: Refutation
% 3.40/1.36 % (2466028)Time elapsed: 0.004 s
% 3.40/1.36 % (2466028)Peak memory usage: 89 MB
% 3.40/1.36 % (2466028)Instructions burned: 4 (million)
% 3.40/1.36 % (2466028)------------------------------
% 3.40/1.36 % (2466028)------------------------------
% 3.40/1.36 % (2465969)Success in time 0.41 s
% 3.40/1.36 % Vampire exiting
%------------------------------------------------------------------------------