%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRA010+2 : 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 : n011.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 09:55:21 AM UTC 2026
% Result : Theorem 2.69s 1.36s
% Output : Refutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 29 ( 4 unt; 0 def)
% Number of atoms : 108 ( 18 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 131 ( 52 ~; 44 |; 27 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 89 ( 74 !; 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(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/sandbox2/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(f23,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(f24,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,[],[f23]) ).
fof(f30,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(f31,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,[],[f30]) ).
fof(f34,plain,
( number_of_in(sequential_pairs,sK0) != number_of_in(triangles,sK0)
& path(sK1,sK2,sK0)
& ! [X3,X4] :
( triangle(X3,X4,sK3(X3,X4))
| ~ on_path(X3,sK0)
| ~ on_path(X4,sK0)
| ~ sequential(X3,X4) )
& complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X5,sK3(X3,X4))],[f24]) ).
fof(f46,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))],[f31]) ).
fof(f48,plain,
! [X3,X4] :
( triangle(X3,X4,sK3(X3,X4))
| ~ on_path(X3,sK0)
| ~ on_path(X4,sK0)
| ~ sequential(X3,X4) ),
inference(cnf_transformation,[],[f34]) ).
fof(f49,plain,
path(sK1,sK2,sK0),
inference(cnf_transformation,[],[f34]) ).
fof(f50,plain,
number_of_in(sequential_pairs,sK0) != number_of_in(triangles,sK0),
inference(cnf_transformation,[],[f34]) ).
fof(f76,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| sequential(sK6(X0),sK7(X0)) ),
inference(cnf_transformation,[],[f46]) ).
fof(f77,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| on_path(sK7(X0),X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f78,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| on_path(sK6(X0),X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f79,plain,
! [X2,X0,X1,X5] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| ~ triangle(sK6(X0),sK7(X0),X5) ),
inference(cnf_transformation,[],[f46]) ).
fof(f152,plain,
! [X0,X1] :
( number_of_in(sequential_pairs,sK0) != number_of_in(sequential_pairs,sK0)
| ~ path(X0,X1,sK0)
| on_path(sK7(sK0),sK0) ),
inference(superposition,[],[f50,f77]) ).
fof(f153,plain,
! [X0,X1] :
( on_path(sK7(sK0),sK0)
| ~ path(X0,X1,sK0) ),
inference(trivial_inequality_removal,[],[f152]) ).
fof(f154,plain,
! [X0,X1] :
( number_of_in(sequential_pairs,sK0) != number_of_in(sequential_pairs,sK0)
| ~ path(X0,X1,sK0)
| on_path(sK6(sK0),sK0) ),
inference(superposition,[],[f50,f78]) ).
fof(f155,plain,
! [X0,X1] :
( on_path(sK6(sK0),sK0)
| ~ path(X0,X1,sK0) ),
inference(trivial_inequality_removal,[],[f154]) ).
fof(f162,plain,
! [X0,X1] :
( number_of_in(sequential_pairs,sK0) != number_of_in(sequential_pairs,sK0)
| ~ path(X0,X1,sK0)
| sequential(sK6(sK0),sK7(sK0)) ),
inference(superposition,[],[f50,f76]) ).
fof(f163,plain,
! [X0,X1] :
( sequential(sK6(sK0),sK7(sK0))
| ~ path(X0,X1,sK0) ),
inference(trivial_inequality_removal,[],[f162]) ).
fof(f173,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,sK0) != number_of_in(sequential_pairs,sK0)
| ~ path(X0,X1,sK0)
| ~ triangle(sK6(sK0),sK7(sK0),X2) ),
inference(superposition,[],[f50,f79]) ).
fof(f174,plain,
! [X2,X0,X1] :
( ~ triangle(sK6(sK0),sK7(sK0),X2)
| ~ path(X0,X1,sK0) ),
inference(trivial_inequality_removal,[],[f173]) ).
fof(f175,plain,
! [X0,X1] :
( ~ path(X0,X1,sK0)
| ~ on_path(sK6(sK0),sK0)
| ~ on_path(sK7(sK0),sK0)
| ~ sequential(sK6(sK0),sK7(sK0)) ),
inference(resolution,[],[f174,f48]) ).
fof(f176,plain,
! [X0,X1] :
( ~ path(X0,X1,sK0)
| ~ on_path(sK7(sK0),sK0)
| ~ sequential(sK6(sK0),sK7(sK0)) ),
inference(forward_subsumption_resolution,[],[f175,f155]) ).
fof(f177,plain,
! [X0,X1] :
( ~ path(X0,X1,sK0)
| ~ sequential(sK6(sK0),sK7(sK0)) ),
inference(forward_subsumption_resolution,[],[f176,f153]) ).
fof(f178,plain,
! [X0,X1] : ~ path(X0,X1,sK0),
inference(forward_subsumption_resolution,[],[f177,f163]) ).
fof(f181,plain,
$false,
inference(resolution,[],[f178,f49]) ).
%------------------------------------------------------------------------------
%----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/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.39 % Computer : n011.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 08:48:00 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 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
% 2.69/1.36 % (2103490)Detected formulas, will run a generic FOF schedule.
% 2.69/1.36 % (2103499)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=437733823:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.69/1.36 % (2103499)First to succeed.
% 2.69/1.36 % (2103499)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2103490"
% 2.69/1.36 % (2103498)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1659629434:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.69/1.36 % (2103497)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=3288833827:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.69/1.36 % (2103501)dis-21_1_sil=8000:lcm=predicate:random_seed=1822320950: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)
% 2.69/1.36 % (2103495)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=1170261761:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.69/1.36 % (2103500)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=574119365:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.69/1.36 % (2103496)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=2328173935:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.69/1.36 % (2103498)Also succeeded, but the first one will report.
% 2.69/1.36 % (2103500)Also succeeded, but the first one will report.
% 2.69/1.36 % (2103501)Instruction limit reached!
% 2.69/1.36 % (2103501)------------------------------
% 2.69/1.36 % (2103501)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.36 % (2103501)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.36 % (2103501)CaDiCaL version: 2.1.3
% 2.69/1.36 % (2103501)Termination reason: Instruction limit
% 2.69/1.36 % (2103501)Termination phase: Saturation
% 2.69/1.36 % (2103501)Time elapsed: 0.067 s
% 2.69/1.36 % (2103501)Peak memory usage: 89 MB
% 2.69/1.36 % (2103501)Instructions burned: 131 (million)
% 2.69/1.36 % (2103499)Refutation found. Thanks to Tanya!
% 2.69/1.36 % SZS status Theorem for theBenchmark
% 2.69/1.36 % SZS output start Proof for theBenchmark
% See solution above
% 2.69/1.36 % (2103499)------------------------------
% 2.69/1.36 % (2103499)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.69/1.36 % (2103499)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.69/1.36 % (2103499)CaDiCaL version: 2.1.3
% 2.69/1.36 % (2103499)Termination reason: Refutation
% 2.69/1.36 % (2103499)Time elapsed: 0.003 s
% 2.69/1.36 % (2103499)Peak memory usage: 88 MB
% 2.69/1.36 % (2103499)Instructions burned: 6 (million)
% 2.69/1.36 % (2103499)------------------------------
% 2.69/1.36 % (2103499)------------------------------
% 2.69/1.36 % (2103490)Success in time 0.295 s
% 2.69/1.36 % Vampire exiting
%------------------------------------------------------------------------------