%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GEG024_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 : n004.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 3.72s 1.49s
% Output : Refutation 3.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 180 ( 150 equ)
% Maximal formula atoms : 24 ( 11 avg)
% Number of connectives : 176 ( 12 ~; 6 |; 154 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 12 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 202 ( 29 atm; 7 fun; 166 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 : 53 ( 49 !; 4 ?; 53 :)
% 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,
( ( ( inh(saarbruecken) = 175810 )
& ( d(berlin,frankfurt) = 420 )
& ( inh(kiel) = 238281 )
& ! [X0: city] : ( d(X0,X0) = 0 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(munich,saarbruecken) = 360 )
& ! [X1: city,X0: city,X2: city] : $lesseq(d(X0,X2),$sum(d(X0,X1),d(X1,X2)))
& ( d(hamburg,cologne) = 360 )
& ( d(hamburg,berlin) = 250 )
& ( inh(berlin) = 3442675 )
& ( d(berlin,cologne) = 480 )
& ( inh(cologne) = 998105 )
& ( d(hamburg,frankfurt) = 390 )
& ( inh(munich) = 1330440 )
& ( d(berlin,munich) = 510 )
& ( d(munich,frankfurt) = 300 )
& ( inh(hamburg) = 1774224 )
& ( inh(frankfurt) = 671927 )
& ( d(cologne,frankfurt) = 150 )
& ( d(saarbruecken,frankfurt) = 160 )
& ! [X0: city,X1: city] : ( d(X0,X1) = d(X1,X0) )
& ( d(hamburg,kiel) = 90 ) )
=> ? [X0: city] :
( $lesseq(d(kiel,X0),100)
& $lesseq(1000000,inh(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exists_big_city_distance_1) ).
tff(f2,negated_conjecture,
~ ( ( ( inh(saarbruecken) = 175810 )
& ( d(berlin,frankfurt) = 420 )
& ( inh(kiel) = 238281 )
& ! [X0: city] : ( d(X0,X0) = 0 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(munich,saarbruecken) = 360 )
& ! [X1: city,X0: city,X2: city] : $lesseq(d(X0,X2),$sum(d(X0,X1),d(X1,X2)))
& ( d(hamburg,cologne) = 360 )
& ( d(hamburg,berlin) = 250 )
& ( inh(berlin) = 3442675 )
& ( d(berlin,cologne) = 480 )
& ( inh(cologne) = 998105 )
& ( d(hamburg,frankfurt) = 390 )
& ( inh(munich) = 1330440 )
& ( d(berlin,munich) = 510 )
& ( d(munich,frankfurt) = 300 )
& ( inh(hamburg) = 1774224 )
& ( inh(frankfurt) = 671927 )
& ( d(cologne,frankfurt) = 150 )
& ( d(saarbruecken,frankfurt) = 160 )
& ! [X0: city,X1: city] : ( d(X0,X1) = d(X1,X0) )
& ( d(hamburg,kiel) = 90 ) )
=> ? [X0: city] :
( $lesseq(d(kiel,X0),100)
& $lesseq(1000000,inh(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ( ( inh(saarbruecken) = 175810 )
& ( d(berlin,frankfurt) = 420 )
& ( inh(kiel) = 238281 )
& ! [X0: city] : ( d(X0,X0) = 0 )
& ( d(saarbruecken,cologne) = 190 )
& ( d(munich,saarbruecken) = 360 )
& ! [X1: city,X0: city,X2: city] : ~ $less($sum(d(X0,X1),d(X1,X2)),d(X0,X2))
& ( d(hamburg,cologne) = 360 )
& ( d(hamburg,berlin) = 250 )
& ( inh(berlin) = 3442675 )
& ( d(berlin,cologne) = 480 )
& ( inh(cologne) = 998105 )
& ( d(hamburg,frankfurt) = 390 )
& ( inh(munich) = 1330440 )
& ( d(berlin,munich) = 510 )
& ( d(munich,frankfurt) = 300 )
& ( inh(hamburg) = 1774224 )
& ( inh(frankfurt) = 671927 )
& ( d(cologne,frankfurt) = 150 )
& ( d(saarbruecken,frankfurt) = 160 )
& ! [X0: city,X1: city] : ( d(X0,X1) = d(X1,X0) )
& ( d(hamburg,kiel) = 90 ) )
=> ? [X0: city] :
( ~ $less(100,d(kiel,X0))
& ~ $less(inh(X0),1000000) ) ),
inference(theory_normalization,[],[f2]) ).
tff(f16,plain,
~ ( ( ! [X2: city,X3: city,X1: city] : ~ $less($sum(d(X2,X1),d(X1,X3)),d(X2,X3))
& ( inh(saarbruecken) = 175810 )
& ( d(saarbruecken,cologne) = 190 )
& ( inh(frankfurt) = 671927 )
& ( d(hamburg,berlin) = 250 )
& ( d(berlin,munich) = 510 )
& ( d(hamburg,kiel) = 90 )
& ( inh(kiel) = 238281 )
& ( inh(hamburg) = 1774224 )
& ( inh(berlin) = 3442675 )
& ( d(cologne,frankfurt) = 150 )
& ( d(hamburg,cologne) = 360 )
& ( inh(munich) = 1330440 )
& ( d(munich,frankfurt) = 300 )
& ( inh(cologne) = 998105 )
& ! [X5: city,X4: city] : ( d(X4,X5) = d(X5,X4) )
& ( d(hamburg,frankfurt) = 390 )
& ( d(berlin,frankfurt) = 420 )
& ( d(berlin,cologne) = 480 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(munich,saarbruecken) = 360 )
& ! [X0: city] : ( d(X0,X0) = 0 ) )
=> ? [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) )
& ! [X2: city,X3: city,X1: city] : ~ $less($sum(d(X2,X1),d(X1,X3)),d(X2,X3))
& ( inh(saarbruecken) = 175810 )
& ( d(saarbruecken,cologne) = 190 )
& ( inh(frankfurt) = 671927 )
& ( d(hamburg,berlin) = 250 )
& ( d(berlin,munich) = 510 )
& ( d(hamburg,kiel) = 90 )
& ( inh(kiel) = 238281 )
& ( inh(hamburg) = 1774224 )
& ( inh(berlin) = 3442675 )
& ( d(cologne,frankfurt) = 150 )
& ( d(hamburg,cologne) = 360 )
& ( inh(munich) = 1330440 )
& ( d(munich,frankfurt) = 300 )
& ( inh(cologne) = 998105 )
& ! [X5: city,X4: city] : ( d(X4,X5) = d(X5,X4) )
& ( d(hamburg,frankfurt) = 390 )
& ( d(berlin,frankfurt) = 420 )
& ( d(berlin,cologne) = 480 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( d(munich,saarbruecken) = 360 )
& ! [X0: city] : ( d(X0,X0) = 0 ) ),
inference(ennf_transformation,[],[f16]) ).
tff(f18,plain,
( ! [X2: city,X3: city,X1: city] : ~ $less($sum(d(X2,X1),d(X1,X3)),d(X2,X3))
& ( inh(frankfurt) = 671927 )
& ! [X5: city,X4: city] : ( d(X4,X5) = d(X5,X4) )
& ( d(hamburg,frankfurt) = 390 )
& ( d(hamburg,cologne) = 360 )
& ( d(hamburg,kiel) = 90 )
& ( d(berlin,cologne) = 480 )
& ! [X6: city] :
( $less(100,d(kiel,X6))
| $less(inh(X6),1000000) )
& ( d(cologne,frankfurt) = 150 )
& ( d(saarbruecken,cologne) = 190 )
& ! [X0: city] : ( d(X0,X0) = 0 )
& ( inh(kiel) = 238281 )
& ( inh(saarbruecken) = 175810 )
& ( d(munich,frankfurt) = 300 )
& ( d(munich,saarbruecken) = 360 )
& ( inh(cologne) = 998105 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( inh(munich) = 1330440 )
& ( inh(hamburg) = 1774224 )
& ( inh(berlin) = 3442675 )
& ( d(hamburg,berlin) = 250 )
& ( d(berlin,munich) = 510 )
& ( d(berlin,frankfurt) = 420 ) ),
inference(flattening,[],[f17]) ).
tff(f19,plain,
( ! [X0: city,X1: city,X2: city] : ~ $less($sum(d(X0,X2),d(X2,X1)),d(X0,X1))
& ( inh(frankfurt) = 671927 )
& ! [X3: city,X4: city] : ( d(X3,X4) = d(X4,X3) )
& ( d(hamburg,frankfurt) = 390 )
& ( d(hamburg,cologne) = 360 )
& ( d(hamburg,kiel) = 90 )
& ( d(berlin,cologne) = 480 )
& ! [X5: city] :
( $less(100,d(kiel,X5))
| $less(inh(X5),1000000) )
& ( d(cologne,frankfurt) = 150 )
& ( d(saarbruecken,cologne) = 190 )
& ! [X6: city] : ( 0 = d(X6,X6) )
& ( inh(kiel) = 238281 )
& ( inh(saarbruecken) = 175810 )
& ( d(munich,frankfurt) = 300 )
& ( d(munich,saarbruecken) = 360 )
& ( inh(cologne) = 998105 )
& ( d(saarbruecken,frankfurt) = 160 )
& ( inh(munich) = 1330440 )
& ( inh(hamburg) = 1774224 )
& ( inh(berlin) = 3442675 )
& ( d(hamburg,berlin) = 250 )
& ( d(berlin,munich) = 510 )
& ( d(berlin,frankfurt) = 420 ) ),
inference(rectify,[],[f18]) ).
tff(f24,plain,
inh(hamburg) = 1774224,
inference(cnf_transformation,[],[f19]) ).
tff(f35,plain,
! [X5: city] :
( $less(100,d(kiel,X5))
| $less(inh(X5),1000000) ),
inference(cnf_transformation,[],[f19]) ).
tff(f37,plain,
d(hamburg,kiel) = 90,
inference(cnf_transformation,[],[f19]) ).
tff(f40,plain,
! [X3: city,X4: city] : ( d(X3,X4) = d(X4,X3) ),
inference(cnf_transformation,[],[f19]) ).
tff(f72,plain,
! [X0: city] :
( $less(100,d(X0,kiel))
| $less(inh(X0),1000000) ),
inference(constrained_superposition,[],[f35,f40]) ).
tff(f79,plain,
( $less(100,90)
| $less(inh(hamburg),1000000) ),
inference(constrained_superposition,[],[f72,f37]) ).
tff(f81,plain,
$less(inh(hamburg),1000000),
inference(evaluation,[],[f79]) ).
tff(f83,plain,
$less(1774224,1000000),
inference(forward_demodulation,[],[f81,f24]) ).
tff(f84,plain,
$false,
inference(evaluation,[],[f83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEG024_1 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n004.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 06:30:06 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.40 Running first-order theorem proving
% 0.11/0.40 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
% 3.72/1.49 % (3145671)Detected arithmetic, will pick strategies from an ALASCA-aware ARI schedule.
% 3.72/1.49 % (3145682)lrs+10_1_tgt=ground:sas=z3:si=on:random_seed=3262799679:i=33:rtra=on_2999 on theBenchmark for (2999ds/33Mi)
% 3.72/1.49 % (3145682)Instruction limit reached!
% 3.72/1.49 % (3145682)------------------------------
% 3.72/1.49 % (3145682)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.49 % (3145682)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.49 % (3145682)CaDiCaL version: 2.1.3
% 3.72/1.49 % (3145682)Termination reason: Instruction limit
% 3.72/1.49 % (3145682)Termination phase: Saturation
% 3.72/1.49 % (3145682)Time elapsed: 0.026 s
% 3.72/1.49 % (3145682)Peak memory usage: 116 MB
% 3.72/1.49 % (3145682)Instructions burned: 34 (million)
% 3.72/1.49 % (3145681)lrs+10_1_to=lpo:sas=z3:si=on:tha=off:random_seed=3805207592:i=46:rtra=on_2999 on theBenchmark for (2999ds/46Mi)
% 3.72/1.49 % (3145676)dis+1002_16:1_to=lpo:sil=64000:sas=z3:si=on:norm_ineq=on:gve=force:uwa=one_side_constant:random_seed=3127312576:i=12:doe=on:rtra=on:gtg=exists_top:ss=axioms_2999 on theBenchmark for (2999ds/12Mi)
% 3.72/1.49 % (3145677)dis+1002_1_to=kbo:sil=128000:tgt=ground:sas=z3:si=on:spb=units:tha=off:random_seed=3742327990:i=307:kws=precedence:nm=0:rtra=on_2999 on theBenchmark for (2999ds/307Mi)
% 3.72/1.49 % (3145680)dis+21_64_to=kbo:sil=128000:si=on:sp=weighted_frequency:uwa=alasca_can_abstract:random_seed=4078423131:i=4:rtra=on_2999 on theBenchmark for (2999ds/4Mi)
% 3.72/1.49 % (3145679)lrs+1002_4:1_to=lpo:sil=64000:si=on:br=off:random_seed=1881852729:s2a=on:i=7:rtra=on:inst=on_2999 on theBenchmark for (2999ds/7Mi)
% 3.72/1.49 % (3145678)dis+10_3_slsqr=1,4:to=lpo:sil=128000:thi=strong:si=on:uwa=off:s2agt=20:slsqc=1:slsq=on:random_seed=1271845855:i=201:slsql=off:asg=cautious:rtra=on:gtg=all:ss=axioms:sgt=16_2999 on theBenchmark for (2999ds/201Mi)
% 3.72/1.49 % (3145680)First to succeed.
% 3.72/1.49 % (3145679)Also succeeded, but the first one will report.
% 3.72/1.49 % (3145680)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3145671"
% 3.72/1.49 % (3145678)Also succeeded, but the first one will report.
% 3.72/1.49 % (3145676)Instruction limit reached!
% 3.72/1.49 % (3145676)------------------------------
% 3.72/1.49 % (3145676)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.49 % (3145676)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.49 % (3145676)CaDiCaL version: 2.1.3
% 3.72/1.49 % (3145676)Termination reason: Instruction limit
% 3.72/1.49 % (3145676)Termination phase: Saturation
% 3.72/1.49 % (3145676)Time elapsed: 0.030 s
% 3.72/1.49 % (3145676)Peak memory usage: 115 MB
% 3.72/1.49 % (3145676)Instructions burned: 13 (million)
% 3.72/1.49 % (3145681)Also succeeded, but the first one will report.
% 3.72/1.49 % (3145677)Also succeeded, but the first one will report.
% 3.72/1.49 % (3145690)dis+11_3_anc=none:drc=ordering:si=on:urr=ec_only:bce=on:tha=off:sac=on:random_seed=1285508350:st=5:i=14:sd=10:rtra=on:ss=axioms:rawr=on_2998 on theBenchmark for (2998ds/14Mi)
% 3.72/1.49 % (3145690)Also succeeded, but the first one will report.
% 3.72/1.49 % (3145691)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=2381813505:i=29:thsqd=64:nm=0:thsqc=8:rtra=on:thsq=on:ev=off_2997 on theBenchmark for (2997ds/29Mi)
% 3.72/1.49 % (3145691)Instruction limit reached!
% 3.72/1.49 % (3145691)------------------------------
% 3.72/1.49 % (3145691)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.49 % (3145691)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.49 % (3145691)CaDiCaL version: 2.1.3
% 3.72/1.49 % (3145691)Termination reason: Instruction limit
% 3.72/1.49 % (3145691)Termination phase: Saturation
% 3.72/1.49 % (3145691)Time elapsed: 0.020 s
% 3.72/1.49 % (3145691)Peak memory usage: 89 MB
% 3.72/1.49 % (3145691)Instructions burned: 29 (million)
% 3.72/1.49 % (3145680)Refutation found. Thanks to Tanya!
% 3.72/1.49 % SZS status Theorem for theBenchmark
% 3.72/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.72/1.49 % (3145680)------------------------------
% 3.72/1.49 % (3145680)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.72/1.49 % (3145680)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.72/1.49 % (3145680)CaDiCaL version: 2.1.3
% 3.72/1.49 % (3145680)Termination reason: Refutation
% 3.72/1.49 % (3145680)Time elapsed: 0.005 s
% 3.72/1.49 % (3145680)Peak memory usage: 89 MB
% 3.72/1.49 % (3145680)Instructions burned: 6 (million)
% 3.72/1.49 % (3145680)------------------------------
% 3.72/1.49 % (3145680)------------------------------
% 3.72/1.49 % (3145671)Success in time 0.449 s
% 3.72/1.49 % Vampire exiting
%------------------------------------------------------------------------------