%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRA002+4 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n001.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 10:08:25 AM UTC 2026
% Result : Theorem 0.16s 0.46s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 14 unt; 2 def)
% Number of atoms : 111 ( 20 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 117 ( 45 ~; 36 |; 24 &)
% ( 4 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 4 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 67 ( 0 sgn 61 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f11,axiom,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( path(X0,X1,X2)
& X0 != X1
& ! [X3] :
( path(X0,X1,X3)
=> less_or_equal(length_of(X2),length_of(X3)) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GRA001+0.ax',shortest_path_defn) ).
fof(f15,axiom,
! [X0,X1,X2] :
( path(X0,X1,X2)
=> number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
fof(f17,axiom,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',graph_has_them_all) ).
fof(f18,axiom,
( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',triangles_and_sequential_pairs) ).
fof(f19,conjecture,
( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maximal_path_length) ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f36,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( path(X0,X1,X2)
& X0 != X1
& ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) ) ) ),
inference(ennf_transformation,[],[f11]) ).
fof(f42,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1)
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f45,plain,
( ! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ shortest_path(X1,X2,X0) )
| ~ complete ),
inference(ennf_transformation,[],[f18]) ).
fof(f46,plain,
( ? [X0,X1,X2] :
( ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph))
& shortest_path(X1,X2,X0) )
& complete ),
inference(ennf_transformation,[],[f20]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) ) )
& ( ( path(X0,X1,X2)
& X0 != X1
& ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f36]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) ) )
& ( ( path(X0,X1,X2)
& X0 != X1
& ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(flattening,[],[f61]) ).
fof(f63,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) ) )
& ( ( path(X0,X1,X2)
& X0 != X1
& ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(rectify,[],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ( ~ less_or_equal(length_of(X2),length_of(sK5(X0,X1,X2)))
& path(X0,X1,sK5(X0,X1,X2)) ) )
& ( ( path(X0,X1,X2)
& X0 != X1
& ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) ) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(X3,sK5(X0,X1,X2))],[f63]) ).
fof(f66,plain,
( ~ less_or_equal(minus(length_of(sK8),n1),number_of_in(triangles,graph))
& shortest_path(sK9,sK10,sK8)
& complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK8,sK9,sK10]),skolemize(X0,sK8),skolemize(X1,sK9),skolemize(X2,sK10)],[f46]) ).
fof(f107,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f64]) ).
fof(f114,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(cnf_transformation,[],[f42]) ).
fof(f119,plain,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf_transformation,[],[f17]) ).
fof(f120,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ shortest_path(X1,X2,X0)
| ~ complete ),
inference(cnf_transformation,[],[f45]) ).
fof(f121,plain,
complete,
inference(cnf_transformation,[],[f66]) ).
fof(f122,plain,
shortest_path(sK9,sK10,sK8),
inference(cnf_transformation,[],[f66]) ).
fof(f123,plain,
~ less_or_equal(minus(length_of(sK8),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[],[f66]) ).
fof(f132,definition,
( spl11_1
<=> complete ),
introduced(definition,[new_symbols(definition,[spl11_1])],[avatar_definition]) ).
fof(f136,definition,
( spl11_2
<=> ! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ shortest_path(X1,X2,X0) ) ),
introduced(definition,[new_symbols(definition,[spl11_2])],[avatar_definition]) ).
fof(f137,plain,
( ! [X2,X0,X1] :
( ~ shortest_path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) )
| ~ spl11_2 ),
inference(avatar_component_clause,[],[f136]) ).
fof(f138,plain,
( ~ spl11_1
| spl11_2 ),
inference(avatar_split_clause,[],[f120,f136,f132]) ).
fof(f163,plain,
spl11_1,
inference(avatar_split_clause,[],[f121,f132]) ).
fof(f164,plain,
path(sK9,sK10,sK8),
inference(resolution,[],[f107,f122]) ).
fof(f170,plain,
( number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8)
| ~ spl11_2 ),
inference(resolution,[],[f137,f122]) ).
fof(f174,plain,
( less_or_equal(number_of_in(sequential_pairs,sK8),number_of_in(triangles,graph))
| ~ spl11_2 ),
inference(superposition,[],[f119,f170]) ).
fof(f203,plain,
minus(length_of(sK8),n1) = number_of_in(sequential_pairs,sK8),
inference(resolution,[],[f114,f164]) ).
fof(f231,plain,
~ less_or_equal(number_of_in(sequential_pairs,sK8),number_of_in(triangles,graph)),
inference(superposition,[],[f123,f203]) ).
fof(f232,plain,
( $false
| ~ spl11_2 ),
inference(forward_subsumption_resolution,[],[f231,f174]) ).
fof(f233,plain,
~ spl11_2,
inference(avatar_contradiction_clause,[],[f232]) ).
cnf(s1,plain,
( ~ spl11_1
| spl11_2 ),
inference(sat_conversion,[],[f138]) ).
cnf(s8,plain,
spl11_1,
inference(sat_conversion,[],[f163]) ).
cnf(s12,plain,
~ spl11_2,
inference(sat_conversion,[],[f233]) ).
cnf(s20,plain,
$false,
inference(rat,[],[s1,s12,s8]) ).
fof(f234,plain,
$false,
inference(avatar_sat_refutation,[],[s20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA002+4 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n001.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sun Sep 27 08:51:15 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.16/0.46 % (3257403)Will run a generic schedule for satisfiability detection.
% 0.16/0.46 % (3257411)dis+10_1_sil=32000:sp=arity:random_seed=243310883:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.16/0.46 % (3257409)% WARNING: option uhcvi not known.
% 0.16/0.46 % (3257411) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3257403-3257411"...
% 0.16/0.46 % (3257411)...printing done.
% 0.16/0.46 % (3257411)Refutation found. Thanks to Tanya!
% 0.16/0.46 % SZS status Theorem for theBenchmark
% 0.16/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.46 % (3257411)------------------------------
% 0.16/0.46 % (3257411)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.16/0.46 % (3257411)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.16/0.46 % (3257411)CaDiCaL version: 2.1.3
% 0.16/0.46 % (3257411)Termination reason: Refutation
% 0.16/0.46 % (3257411)Time elapsed: 0.004 s
% 0.16/0.46 % (3257411)Peak memory usage: 12 MB
% 0.16/0.46 % (3257411)Instructions burned: 7 (million)
% 0.16/0.46 % (3257403)Success in time 0.032 s
% 0.16/0.46 % Vampire exiting
%------------------------------------------------------------------------------