%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRA010+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 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 09:55:21 AM UTC 2026
% Result : Theorem 2.70s 1.25s
% Output : Refutation 2.70s
% 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/sandbox/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/sandbox/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(f20,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(f21,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,[],[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) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f25,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,[],[f24]) ).
fof(f28,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))],[f21]) ).
fof(f34,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| ( ! [X5] : ~ triangle(sK5(X0),sK6(X0),X5)
& on_path(sK5(X0),X0)
& on_path(sK6(X0),X0)
& sequential(sK5(X0),sK6(X0)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5,sK6]),skolemize(X3,sK5(X0)),skolemize(X4,sK6(X0))],[f25]) ).
fof(f38,plain,
! [X3,X4] :
( triangle(X3,X4,sK3(X3,X4))
| ~ on_path(X3,sK0)
| ~ on_path(X4,sK0)
| ~ sequential(X3,X4) ),
inference(cnf_transformation,[],[f28]) ).
fof(f39,plain,
path(sK1,sK2,sK0),
inference(cnf_transformation,[],[f28]) ).
fof(f40,plain,
number_of_in(sequential_pairs,sK0) != number_of_in(triangles,sK0),
inference(cnf_transformation,[],[f28]) ).
fof(f52,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| sequential(sK5(X0),sK6(X0)) ),
inference(cnf_transformation,[],[f34]) ).
fof(f53,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,[],[f34]) ).
fof(f54,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| on_path(sK5(X0),X0) ),
inference(cnf_transformation,[],[f34]) ).
fof(f55,plain,
! [X2,X0,X1,X5] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| ~ triangle(sK5(X0),sK6(X0),X5) ),
inference(cnf_transformation,[],[f34]) ).
fof(f95,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,[],[f40,f53]) ).
fof(f96,plain,
! [X0,X1] :
( on_path(sK6(sK0),sK0)
| ~ path(X0,X1,sK0) ),
inference(trivial_inequality_removal,[],[f95]) ).
fof(f97,plain,
! [X0,X1] :
( number_of_in(sequential_pairs,sK0) != number_of_in(sequential_pairs,sK0)
| ~ path(X0,X1,sK0)
| on_path(sK5(sK0),sK0) ),
inference(superposition,[],[f40,f54]) ).
fof(f98,plain,
! [X0,X1] :
( on_path(sK5(sK0),sK0)
| ~ path(X0,X1,sK0) ),
inference(trivial_inequality_removal,[],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( number_of_in(sequential_pairs,sK0) != number_of_in(sequential_pairs,sK0)
| ~ path(X0,X1,sK0)
| sequential(sK5(sK0),sK6(sK0)) ),
inference(superposition,[],[f40,f52]) ).
fof(f100,plain,
! [X0,X1] :
( sequential(sK5(sK0),sK6(sK0))
| ~ path(X0,X1,sK0) ),
inference(trivial_inequality_removal,[],[f99]) ).
fof(f103,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,sK0) != number_of_in(sequential_pairs,sK0)
| ~ path(X0,X1,sK0)
| ~ triangle(sK5(sK0),sK6(sK0),X2) ),
inference(superposition,[],[f40,f55]) ).
fof(f104,plain,
! [X2,X0,X1] :
( ~ triangle(sK5(sK0),sK6(sK0),X2)
| ~ path(X0,X1,sK0) ),
inference(trivial_inequality_removal,[],[f103]) ).
fof(f116,plain,
! [X0,X1] :
( ~ path(X0,X1,sK0)
| ~ on_path(sK5(sK0),sK0)
| ~ on_path(sK6(sK0),sK0)
| ~ sequential(sK5(sK0),sK6(sK0)) ),
inference(resolution,[],[f104,f38]) ).
fof(f119,plain,
! [X0,X1] :
( ~ path(X0,X1,sK0)
| ~ on_path(sK6(sK0),sK0)
| ~ sequential(sK5(sK0),sK6(sK0)) ),
inference(forward_subsumption_resolution,[],[f116,f98]) ).
fof(f120,plain,
! [X0,X1] :
( ~ path(X0,X1,sK0)
| ~ sequential(sK5(sK0),sK6(sK0)) ),
inference(forward_subsumption_resolution,[],[f119,f96]) ).
fof(f121,plain,
! [X0,X1] : ~ path(X0,X1,sK0),
inference(forward_subsumption_resolution,[],[f120,f100]) ).
fof(f123,plain,
$false,
inference(resolution,[],[f121,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRA010+1 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n015.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sun Sep 27 08:51:00 UTC 2026
% 0.04/0.36 % CPUTime :
% 0.04/0.36 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.39 Running first-order theorem proving
% 0.04/0.39 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.70/1.25 % (1356209)Detected formulas, will run a generic FOF schedule.
% 2.70/1.25 % (1356218)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2278644577:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.70/1.25 % (1356218)First to succeed.
% 2.70/1.25 % (1356218)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-1356209"
% 2.70/1.25 % (1356215)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=2831918800:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.70/1.25 % (1356217)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1554587680:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.70/1.25 % (1356214)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=3672365450:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.70/1.25 % (1356216)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=2827163600:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.70/1.25 % (1356220)dis-21_1_sil=8000:lcm=predicate:random_seed=1421554202: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)
% 2.70/1.25 % (1356219)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2328406546:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.70/1.25 % (1356217)Also succeeded, but the first one will report.
% 2.70/1.25 % (1356219)Also succeeded, but the first one will report.
% 2.70/1.25 % (1356220)Instruction limit reached!
% 2.70/1.25 % (1356220)------------------------------
% 2.70/1.25 % (1356220)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.25 % (1356220)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.25 % (1356220)CaDiCaL version: 2.1.3
% 2.70/1.25 % (1356220)Termination reason: Instruction limit
% 2.70/1.25 % (1356220)Termination phase: Saturation
% 2.70/1.25 % (1356220)Time elapsed: 0.067 s
% 2.70/1.25 % (1356220)Peak memory usage: 88 MB
% 2.70/1.25 % (1356220)Instructions burned: 130 (million)
% 2.70/1.25 % (1356218)Refutation found. Thanks to Tanya!
% 2.70/1.25 % SZS status Theorem for theBenchmark
% 2.70/1.25 % SZS output start Proof for theBenchmark
% See solution above
% 2.70/1.25 % (1356218)------------------------------
% 2.70/1.25 % (1356218)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.70/1.25 % (1356218)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.70/1.25 % (1356218)CaDiCaL version: 2.1.3
% 2.70/1.25 % (1356218)Termination reason: Refutation
% 2.70/1.25 % (1356218)Time elapsed: 0.002 s
% 2.70/1.25 % (1356218)Peak memory usage: 88 MB
% 2.70/1.25 % (1356218)Instructions burned: 4 (million)
% 2.70/1.25 % (1356218)------------------------------
% 2.70/1.25 % (1356218)------------------------------
% 2.70/1.25 % (1356209)Success in time 0.314 s
% 2.70/1.25 % Vampire exiting
%------------------------------------------------------------------------------