%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : GRA010+1 : 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 : n006.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 0.17s 0.49s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 30 ( 7 unt; 1 def)
% Number of atoms : 102 ( 18 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 117 ( 45 ~; 42 |; 21 &)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 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 : 83 ( 0 sgn 68 !; 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/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(f18,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/sandbox2/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).
fof(f19,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)],[f18]) ).
fof(f41,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(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(flattening,[],[f41]) ).
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) ) )
& complete ),
inference(ennf_transformation,[],[f19]) ).
fof(f44,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,[],[f43]) ).
fof(f96,plain,
! [X2,X0,X1] :
( sequential(sK6(X0),sK7(X0))
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f97,plain,
! [X2,X0,X1] :
( on_path(sK7(X0),X0)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f98,plain,
! [X2,X0,X1] :
( on_path(sK6(X0),X0)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f99,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,[],[f42]) ).
fof(f101,plain,
! [X3,X4] :
( triangle(X3,X4,sK11(X3,X4))
| ~ on_path(X4,sK8)
| ~ on_path(X3,sK8)
| ~ sequential(X3,X4) ),
inference(cnf_transformation,[],[f44]) ).
fof(f102,plain,
path(sK9,sK10,sK8),
inference(cnf_transformation,[],[f44]) ).
fof(f103,plain,
number_of_in(sequential_pairs,sK8) != number_of_in(triangles,sK8),
inference(cnf_transformation,[],[f44]) ).
fof(f305,definition,
( spl12_6
<=> ! [X0,X1] : ~ path(X0,X1,sK8) ),
introduced(definition,[new_symbols(definition,[spl12_6])],[avatar_definition]) ).
fof(f306,plain,
( ! [X0,X1] : ~ path(X0,X1,sK8)
| ~ spl12_6 ),
inference(avatar_component_clause,[],[f305]) ).
fof(f328,plain,
( $false
| ~ spl12_6 ),
inference(resolution,[],[f306,f102]) ).
fof(f329,plain,
~ spl12_6,
inference(avatar_contradiction_clause,[],[f328]) ).
fof(f465,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ on_path(sK7(X2),sK8)
| ~ on_path(sK6(X2),sK8)
| ~ sequential(sK6(X2),sK7(X2)) ),
inference(resolution,[],[f99,f101]) ).
fof(f466,plain,
! [X2,X0,X1] :
( ~ on_path(sK7(X2),sK8)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ path(X0,X1,X2)
| ~ on_path(sK6(X2),sK8) ),
inference(forward_subsumption_resolution,[],[f465,f96]) ).
fof(f638,plain,
! [X2,X3,X0,X1] :
( number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8)
| ~ path(X0,X1,sK8)
| ~ on_path(sK6(sK8),sK8)
| ~ path(X2,X3,sK8)
| number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8) ),
inference(resolution,[],[f466,f97]) ).
fof(f639,plain,
! [X2,X3,X0,X1] :
( number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8)
| ~ path(X0,X1,sK8)
| ~ on_path(sK6(sK8),sK8)
| ~ path(X2,X3,sK8) ),
inference(duplicate_literal_removal,[],[f638]) ).
fof(f640,plain,
! [X2,X3,X0,X1] :
( number_of_in(sequential_pairs,sK8) = number_of_in(triangles,sK8)
| ~ path(X0,X1,sK8)
| ~ path(X2,X3,sK8) ),
inference(forward_subsumption_resolution,[],[f639,f98]) ).
fof(f641,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,sK8)
| ~ path(X2,X3,sK8) ),
inference(forward_subsumption_resolution,[],[f640,f103]) ).
fof(f642,plain,
( spl12_6
| spl12_6 ),
inference(avatar_split_clause,[],[f641,f305,f305]) ).
cnf(s9,plain,
~ spl12_6,
inference(sat_conversion,[],[f329]) ).
cnf(s23,plain,
( spl12_6
| spl12_6 ),
inference(sat_conversion,[],[f642]) ).
cnf(s24,plain,
spl12_6,
inference(rat,[],[s23]) ).
cnf(s25,plain,
$false,
inference(rat,[],[s9,s24]) ).
fof(f643,plain,
$false,
inference(avatar_sat_refutation,[],[s25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRA010+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.39 % Computer : n006.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sun Sep 27 08:47:25 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.17/0.49 % (2693369)Will run a generic schedule for satisfiability detection.
% 0.17/0.49 % (2693378)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=4074050073:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.17/0.49 % (2693375)% WARNING: option uhcvi not known.
% 0.17/0.49 % (2693374)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=1813161345_2999 on theBenchmark for (2999ds/0Mi)
% 0.17/0.49 % (2693375)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1710727116:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.17/0.49 % (2693379)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=4143313262:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.17/0.49 % (2693376)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1582593608:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.17/0.49 % (2693377)dis+10_1_sil=32000:sp=arity:random_seed=2992569272:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.49 % (2693380)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=3146807094:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.17/0.49 % TRYING [1]
% 0.17/0.49 % TRYING [2]
% 0.17/0.49 % (2693378) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-2693369-2693378"...
% 0.17/0.49 % (2693378)...printing done.
% 0.17/0.49 % (2693378)Refutation found. Thanks to Tanya!
% 0.17/0.49 % SZS status Theorem for theBenchmark
% 0.17/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.49 % (2693378)------------------------------
% 0.17/0.49 % (2693378)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.49 % (2693378)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.49 % (2693378)CaDiCaL version: 2.1.3
% 0.17/0.49 % (2693378)Termination reason: Refutation
% 0.17/0.49 % (2693378)Time elapsed: 0.016 s
% 0.17/0.49 % (2693378)Peak memory usage: 13 MB
% 0.17/0.49 % (2693378)Instructions burned: 50 (million)
% 0.17/0.49 % (2693369)Success in time 0.055 s
% 0.17/0.49 % Vampire exiting
%------------------------------------------------------------------------------