%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRA005+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n014.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 10:08:26 AM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : Refutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 6 unt; 0 def)
% Number of atoms : 62 ( 24 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 75 ( 32 ~; 17 |; 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 : 63 ( 48 !; 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/sandbox/benchmark/Axioms/GRA001+0.ax',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/sandbox/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(f35,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(f36,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,[],[f35]) ).
fof(f43,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(f44,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,[],[f43]) ).
fof(f61,plain,
( edge(sK12)
& tail_of(sK9) = tail_of(sK12)
& head_of(sK10) = head_of(sK12)
& shortest_path(sK7,sK8,sK11)
& precedes(sK9,sK10,sK11) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11,sK12]),skolemize(X0,sK7),skolemize(X1,sK8),skolemize(X2,sK9),skolemize(X3,sK10),skolemize(X4,sK11),skolemize(X5,sK12)],[f44]) ).
fof(f100,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,[],[f36]) ).
fof(f109,plain,
precedes(sK9,sK10,sK11),
inference(cnf_transformation,[],[f61]) ).
fof(f110,plain,
shortest_path(sK7,sK8,sK11),
inference(cnf_transformation,[],[f61]) ).
fof(f111,plain,
head_of(sK10) = head_of(sK12),
inference(cnf_transformation,[],[f61]) ).
fof(f112,plain,
tail_of(sK9) = tail_of(sK12),
inference(cnf_transformation,[],[f61]) ).
fof(f206,plain,
! [X2,X3,X0,X1,X4] :
( tail_of(X0) != tail_of(sK12)
| head_of(X0) != head_of(X1)
| ~ shortest_path(X2,X3,X4)
| ~ precedes(sK9,X1,X4) ),
inference(superposition,[],[f100,f112]) ).
fof(f235,plain,
! [X2,X3,X0,X1] :
( head_of(X0) != head_of(sK12)
| ~ shortest_path(X1,X2,X3)
| ~ precedes(sK9,X0,X3) ),
inference(equality_resolution,[],[f206]) ).
fof(f239,plain,
! [X2,X0,X1] :
( head_of(sK12) != head_of(sK12)
| ~ shortest_path(X0,X1,X2)
| ~ precedes(sK9,sK10,X2) ),
inference(superposition,[],[f235,f111]) ).
fof(f241,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| ~ precedes(sK9,sK10,X2) ),
inference(trivial_inequality_removal,[],[f239]) ).
fof(f249,plain,
~ precedes(sK9,sK10,sK11),
inference(resolution,[],[f241,f110]) ).
fof(f250,plain,
$false,
inference(forward_subsumption_resolution,[],[f249,f109]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRA005+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.37 % Computer : n014.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 08:46:59 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.10/0.40 Running first-order model finding
% 0.10/0.40 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.44 % (510123)Will run a generic schedule for satisfiability detection.
% 0.10/0.44 % (510130)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2474488150:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.10/0.44 % (510130) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-510123-510130"...
% 0.10/0.44 % (510130)...printing done.
% 0.10/0.44 % (510130)Refutation found. Thanks to Tanya!
% 0.10/0.44 % SZS status Theorem for theBenchmark
% 0.10/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.10/0.44 % (510130)------------------------------
% 0.10/0.44 % (510130)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.10/0.44 % (510130)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.10/0.44 % (510130)CaDiCaL version: 2.1.3
% 0.10/0.44 % (510130)Termination reason: Refutation
% 0.10/0.44 % (510130)Time elapsed: 0.004 s
% 0.10/0.44 % (510130)Peak memory usage: 12 MB
% 0.10/0.44 % (510130)Instructions burned: 7 (million)
% 0.10/0.44 % (510123)Success in time 0.032 s
% 0.10/0.44 % Vampire exiting
%------------------------------------------------------------------------------