%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRA010+2 : 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 : n015.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 10:08:27 AM UTC 2026
% Result : Theorem 0.12s 0.48s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 10 unt; 1 def)
% Number of atoms : 107 ( 19 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 120 ( 45 ~; 39 |; 27 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 79 ( 0 sgn 64 !; 15 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0,X1,X2] :
( ( path(X1,X2,X0)
& ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& sequential(X3,X4) )
=> ? [X5] : triangle(X3,X4,X5) ) )
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(f19,conjecture,
( complete
=> ! [X0,X1,X2] :
( ( path(X1,X2,X0)
& ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& sequential(X3,X4) )
=> ? [X5] : triangle(X3,X4,X5) ) )
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [X0,X1,X2] :
( ( path(X1,X2,X0)
& ! [X3,X4] :
( ( on_path(X3,X0)
& on_path(X4,X0)
& sequential(X3,X4) )
=> ? [X5] : triangle(X3,X4,X5) ) )
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f42,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& on_path(X3,X0)
& on_path(X4,X0)
& sequential(X3,X4) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f43,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& on_path(X3,X0)
& on_path(X4,X0)
& sequential(X3,X4) ) ),
inference(flattening,[],[f42]) ).
fof(f46,plain,
( ? [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
& path(X1,X2,X0)
& ! [X3,X4] :
( ? [X5] : triangle(X3,X4,X5)
| ~ on_path(X3,X0)
| ~ on_path(X4,X0)
| ~ sequential(X3,X4) ) )
& complete ),
inference(ennf_transformation,[],[f20]) ).
fof(f47,plain,
( ? [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) != number_of_in(triangles,X0)
& path(X1,X2,X0)
& ! [X3,X4] :
( ? [X5] : triangle(X3,X4,X5)
| ~ on_path(X3,X0)
| ~ on_path(X4,X0)
| ~ sequential(X3,X4) ) )
& complete ),
inference(flattening,[],[f46]) ).
fof(f65,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| ( ! [X5] : ~ triangle(sK6(X0),sK7(X0),X5)
& on_path(sK6(X0),X0)
& on_path(sK7(X0),X0)
& sequential(sK6(X0),sK7(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6,sK7]),skolemize(X3,sK6(X0)),skolemize(X4,sK7(X0))],[f43]) ).
fof(f67,plain,
( number_of_in(sequential_pairs,sK9) != number_of_in(triangles,sK9)
& path(sK10,sK11,sK9)
& ! [X3,X4] :
( triangle(X3,X4,sK12(X3,X4))
| ~ on_path(X3,sK9)
| ~ on_path(X4,sK9)
| ~ sequential(X3,X4) )
& complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9,sK10,sK11,sK12]),skolemize(X0,sK9),skolemize(X1,sK10),skolemize(X2,sK11),skolemize(X5,sK12(X3,X4))],[f47]) ).
fof(f119,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| sequential(sK6(X0),sK7(X0)) ),
inference(cnf_transformation,[],[f65]) ).
fof(f120,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| on_path(sK7(X0),X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f121,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| on_path(sK6(X0),X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f122,plain,
! [X2,X0,X1,X5] :
( ~ triangle(sK6(X0),sK7(X0),X5)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f65]) ).
fof(f126,plain,
! [X3,X4] :
( triangle(X3,X4,sK12(X3,X4))
| ~ on_path(X3,sK9)
| ~ on_path(X4,sK9)
| ~ sequential(X3,X4) ),
inference(cnf_transformation,[],[f67]) ).
fof(f127,plain,
path(sK10,sK11,sK9),
inference(cnf_transformation,[],[f67]) ).
fof(f128,plain,
number_of_in(sequential_pairs,sK9) != number_of_in(triangles,sK9),
inference(cnf_transformation,[],[f67]) ).
fof(f227,plain,
( number_of_in(sequential_pairs,sK9) = number_of_in(triangles,sK9)
| on_path(sK7(sK9),sK9) ),
inference(resolution,[],[f120,f127]) ).
fof(f228,plain,
on_path(sK7(sK9),sK9),
inference(forward_subsumption_resolution,[],[f227,f128]) ).
fof(f258,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ on_path(sK6(X2),sK9)
| ~ on_path(sK7(X2),sK9)
| ~ sequential(sK6(X2),sK7(X2)) ),
inference(resolution,[],[f122,f126]) ).
fof(f259,plain,
! [X2,X0,X1] :
( ~ on_path(sK7(X2),sK9)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ on_path(sK6(X2),sK9)
| ~ path(X0,X1,X2) ),
inference(forward_subsumption_resolution,[],[f258,f119]) ).
fof(f550,definition,
( spl13_27
<=> ! [X4,X3] : ~ path(X3,X4,sK9) ),
introduced(definition,[new_symbols(definition,[spl13_27])],[avatar_definition]) ).
fof(f551,plain,
( ! [X3,X4] : ~ path(X3,X4,sK9)
| ~ spl13_27 ),
inference(avatar_component_clause,[],[f550]) ).
fof(f560,plain,
( $false
| ~ spl13_27 ),
inference(resolution,[],[f551,f127]) ).
fof(f561,plain,
~ spl13_27,
inference(avatar_contradiction_clause,[],[f560]) ).
fof(f601,plain,
! [X0,X1] :
( number_of_in(sequential_pairs,sK9) = number_of_in(triangles,sK9)
| ~ on_path(sK6(sK9),sK9)
| ~ path(X0,X1,sK9) ),
inference(resolution,[],[f259,f228]) ).
fof(f602,plain,
! [X0,X1] :
( number_of_in(sequential_pairs,sK9) = number_of_in(triangles,sK9)
| ~ path(X0,X1,sK9) ),
inference(forward_subsumption_resolution,[],[f601,f121]) ).
fof(f603,plain,
! [X0,X1] : ~ path(X0,X1,sK9),
inference(forward_subsumption_resolution,[],[f602,f128]) ).
fof(f604,plain,
spl13_27,
inference(avatar_split_clause,[],[f603,f550]) ).
cnf(s24,plain,
~ spl13_27,
inference(sat_conversion,[],[f561]) ).
cnf(s30,plain,
spl13_27,
inference(sat_conversion,[],[f604]) ).
cnf(s31,plain,
$false,
inference(rat,[],[s24,s30]) ).
fof(f605,plain,
$false,
inference(avatar_sat_refutation,[],[s31]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA010+2 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n015.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 08:51:15 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.12/0.48 % (1356613)Will run a generic schedule for satisfiability detection.
% 0.12/0.48 % (1356623)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=3952603325:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.12/0.48 % (1356618)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1609054470_2999 on theBenchmark for (2999ds/0Mi)
% 0.12/0.48 % (1356620)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3045547607:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.12/0.48 % (1356621)dis+10_1_sil=32000:sp=arity:random_seed=3707175232:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.12/0.48 % (1356622)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1312090239:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.48 % (1356624)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1807911964:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.12/0.48 % (1356619)% WARNING: option uhcvi not known.
% 0.12/0.48 % TRYING [1]
% 0.12/0.48 % TRYING [2]
% 0.12/0.48 % (1356619)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=4242361543:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.12/0.48 % TRYING [3]
% 0.12/0.48 % (1356621) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1356613-1356621"...
% 0.12/0.48 % (1356621)...printing done.
% 0.12/0.48 % (1356621)Refutation found. Thanks to Tanya!
% 0.12/0.48 % SZS status Theorem for theBenchmark
% 0.12/0.48 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.48 % (1356621)------------------------------
% 0.12/0.48 % (1356621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.48 % (1356621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.48 % (1356621)CaDiCaL version: 2.1.3
% 0.12/0.48 % (1356621)Termination reason: Refutation
% 0.12/0.48 % (1356621)Time elapsed: 0.016 s
% 0.12/0.48 % (1356621)Peak memory usage: 13 MB
% 0.12/0.48 % (1356621)Instructions burned: 23 (million)
% 0.12/0.48 % (1356613)Success in time 0.055 s
% 0.12/0.48 % Vampire exiting
%------------------------------------------------------------------------------