%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRA005+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/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 09:55:19 AM UTC 2026
% Result : Theorem 0.17s 1.51s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 63 ( 25 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 77 ( 33 ~; 18 |; 23 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-1 aty)
% Number of variables : 65 ( 50 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
=> ( ~ ? [X5] :
( tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
& ~ precedes(X3,X2,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shortest_path_properties) ).
fof(f18,conjecture,
! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
=> ~ ? [X5] :
( edge(X5)
& tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_short_cut_edge) ).
fof(f19,negated_conjecture,
~ ! [X0,X1,X2,X3,X4] :
( ( shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) )
=> ~ ? [X5] :
( edge(X5)
& tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) ) ),
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f22,plain,
? [X0,X1,X2,X3,X4] :
( ? [X5] :
( edge(X5)
& tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
& shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) ),
inference(ennf_transformation,[],[f19]) ).
fof(f23,plain,
? [X0,X1,X2,X3,X4] :
( ? [X5] :
( edge(X5)
& tail_of(X5) = tail_of(X2)
& head_of(X5) = head_of(X3) )
& shortest_path(X0,X1,X4)
& precedes(X2,X3,X4) ),
inference(flattening,[],[f22]) ).
fof(f25,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5] :
( tail_of(X2) != tail_of(X5)
| head_of(X3) != head_of(X5) )
& ~ precedes(X3,X2,X4) )
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) ),
inference(ennf_transformation,[],[f12]) ).
fof(f26,plain,
! [X0,X1,X2,X3,X4] :
( ( ! [X5] :
( tail_of(X2) != tail_of(X5)
| head_of(X3) != head_of(X5) )
& ~ precedes(X3,X2,X4) )
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
( edge(sK5)
& tail_of(sK2) = tail_of(sK5)
& head_of(sK3) = head_of(sK5)
& shortest_path(sK0,sK1,sK4)
& precedes(sK2,sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5)],[f23]) ).
fof(f28,plain,
precedes(sK2,sK3,sK4),
inference(cnf_transformation,[],[f27]) ).
fof(f29,plain,
shortest_path(sK0,sK1,sK4),
inference(cnf_transformation,[],[f27]) ).
fof(f30,plain,
head_of(sK3) = head_of(sK5),
inference(cnf_transformation,[],[f27]) ).
fof(f31,plain,
tail_of(sK2) = tail_of(sK5),
inference(cnf_transformation,[],[f27]) ).
fof(f35,plain,
! [X2,X3,X0,X1,X4,X5] :
( tail_of(X2) != tail_of(X5)
| head_of(X3) != head_of(X5)
| ~ shortest_path(X0,X1,X4)
| ~ precedes(X2,X3,X4) ),
inference(cnf_transformation,[],[f26]) ).
fof(f41,plain,
! [X2,X3,X0,X1,X4] :
( tail_of(X0) != tail_of(sK2)
| head_of(sK5) != head_of(X1)
| ~ shortest_path(X2,X3,X4)
| ~ precedes(X0,X1,X4) ),
inference(superposition,[],[f35,f31]) ).
fof(f43,plain,
! [X2,X3,X0,X1,X4] :
( tail_of(X0) != tail_of(sK2)
| head_of(sK3) != head_of(X1)
| ~ shortest_path(X2,X3,X4)
| ~ precedes(X0,X1,X4) ),
inference(forward_demodulation,[],[f41,f30]) ).
fof(f51,plain,
! [X2,X3,X0,X1] :
( head_of(X0) != head_of(sK3)
| ~ shortest_path(X1,X2,X3)
| ~ precedes(sK2,X0,X3) ),
inference(equality_resolution,[],[f43]) ).
fof(f64,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| ~ precedes(sK2,sK3,X2) ),
inference(equality_resolution,[],[f51]) ).
fof(f67,plain,
~ precedes(sK2,sK3,sK4),
inference(resolution,[],[f64,f29]) ).
fof(f68,plain,
$false,
inference(forward_subsumption_resolution,[],[f67,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA005+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.40 % Computer : n004.cluster.edu
% 0.12/0.40 % Model : x86_64 x86_64
% 0.12/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.40 % Memory : 8046.5625MB
% 0.12/0.40 % OS : Linux 6.8.0-71-generic
% 0.12/0.40 % CPULimit : 300
% 0.12/0.40 % WCLimit : 300
% 0.12/0.40 % DateTime : Sun Sep 27 08:47:11 UTC 2026
% 0.12/0.40 % CPUTime :
% 0.12/0.40 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 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
% 0.17/1.51 % (3209325)Detected formulas, will run a generic FOF schedule.
% 0.17/1.51 % (3209332)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=1682717762:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.17/1.51 % (3209336)dis-21_1_sil=8000:lcm=predicate:random_seed=3609750691:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 0.17/1.51 % (3209335)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2331561610:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.17/1.51 % (3209333)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4074553969:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.17/1.51 % (3209331)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=1944231157:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.17/1.51 % (3209330)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3092662922:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.17/1.51 % (3209334)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=498571880:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.17/1.51 % (3209334)First to succeed.
% 0.17/1.51 % (3209333)Also succeeded, but the first one will report.
% 0.17/1.51 % (3209334)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3209325"
% 0.17/1.51 % (3209335)Also succeeded, but the first one will report.
% 0.17/1.51 % (3209336)Also succeeded, but the first one will report.
% 0.17/1.51 % (3209334)Refutation found. Thanks to Tanya!
% 0.17/1.51 % SZS status Theorem for theBenchmark
% 0.17/1.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/1.51 % (3209334)------------------------------
% 0.17/1.51 % (3209334)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.17/1.51 % (3209334)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/1.51 % (3209334)CaDiCaL version: 2.1.3
% 0.17/1.51 % (3209334)Termination reason: Refutation
% 0.17/1.51 % (3209334)Time elapsed: 0.003 s
% 0.17/1.51 % (3209334)Peak memory usage: 88 MB
% 0.17/1.51 % (3209334)Instructions burned: 3 (million)
% 0.17/1.51 % (3209334)------------------------------
% 0.17/1.51 % (3209334)------------------------------
% 0.17/1.51 % (3209325)Success in time 0.441 s
% 0.17/1.51 % Vampire exiting
%------------------------------------------------------------------------------