%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : GRA002+4 : 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 : n012.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 09:55:19 AM UTC 2026
% Result : Theorem 2.32s 0.94s
% Output : Refutation 2.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 29 ( 8 unt; 0 def)
% Number of atoms : 95 ( 17 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 108 ( 42 ~; 32 |; 24 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 2 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-3 aty)
% Number of variables : 77 ( 71 !; 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/sandbox/benchmark/theBenchmark.p',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/sandbox/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/sandbox/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/sandbox/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/sandbox/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(f21,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(f22,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(f25,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1)
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f15]) ).
fof(f26,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(f29,plain,
( ~ less_or_equal(minus(length_of(sK0),n1),number_of_in(triangles,graph))
& shortest_path(sK1,sK2,sK0)
& complete ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f22]) ).
fof(f33,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,[],[f26]) ).
fof(f34,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,[],[f33]) ).
fof(f35,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,[],[f34]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| X0 = X1
| ( ~ less_or_equal(length_of(X2),length_of(sK4(X0,X1,X2)))
& path(X0,X1,sK4(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,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f35]) ).
fof(f37,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ shortest_path(X1,X2,X0)
| ~ complete ),
inference(cnf_transformation,[],[f21]) ).
fof(f38,plain,
complete,
inference(cnf_transformation,[],[f29]) ).
fof(f39,plain,
shortest_path(sK1,sK2,sK0),
inference(cnf_transformation,[],[f29]) ).
fof(f40,plain,
~ less_or_equal(minus(length_of(sK0),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[],[f29]) ).
fof(f47,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f25]) ).
fof(f50,plain,
! [X2,X0,X1] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f36]) ).
fof(f53,plain,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf_transformation,[],[f17]) ).
fof(f58,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ shortest_path(X1,X2,X0) ),
inference(forward_subsumption_resolution,[],[f37,f38]) ).
fof(f60,plain,
! [X2,X0,X1] :
( less_or_equal(number_of_in(sequential_pairs,X0),number_of_in(triangles,graph))
| ~ shortest_path(X1,X2,X0) ),
inference(superposition,[],[f53,f58]) ).
fof(f63,plain,
! [X0,X1] :
( ~ less_or_equal(number_of_in(sequential_pairs,sK0),number_of_in(triangles,graph))
| ~ path(X0,X1,sK0) ),
inference(superposition,[],[f40,f47]) ).
fof(f66,plain,
! [X2,X3,X0,X1] :
( ~ shortest_path(X2,X3,sK0)
| ~ path(X0,X1,sK0) ),
inference(resolution,[],[f63,f60]) ).
fof(f69,plain,
! [X0,X1] : ~ path(X0,X1,sK0),
inference(resolution,[],[f66,f39]) ).
fof(f70,plain,
! [X0,X1] : ~ shortest_path(X0,X1,sK0),
inference(resolution,[],[f69,f50]) ).
fof(f72,plain,
$false,
inference(resolution,[],[f70,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRA002+4 : TPTP v9.3.1. Bugfixed v3.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.04/0.32 % Computer : n012.cluster.edu
% 0.04/0.32 % Model : x86_64 x86_64
% 0.04/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.32 % Memory : 8046.5625MB
% 0.04/0.32 % OS : Linux 6.8.0-71-generic
% 0.04/0.32 % CPULimit : 300
% 0.04/0.32 % WCLimit : 300
% 0.04/0.32 % DateTime : Sun Sep 27 08:45:20 UTC 2026
% 0.04/0.32 % CPUTime :
% 0.04/0.32 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.34 Running first-order theorem proving
% 0.08/0.34 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
% 2.32/0.94 % (2071413)Detected formulas, will run a generic FOF schedule.
% 2.32/0.94 % (2071423)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2419675867:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.32/0.94 % (2071420)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=499879389:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.32/0.94 % (2071421)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2443244491:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.32/0.94 % (2071422)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1266761309:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.32/0.94 % (2071418)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=1201455470:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.32/0.94 % (2071419)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=457625413:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.32/0.94 % (2071424)dis-21_1_sil=8000:lcm=predicate:random_seed=3821728477: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)
% 2.32/0.94 % (2071422)First to succeed.
% 2.32/0.94 % (2071421)Also succeeded, but the first one will report.
% 2.32/0.94 % (2071422)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2071413"
% 2.32/0.94 % (2071423)Also succeeded, but the first one will report.
% 2.32/0.94 % (2071424)Instruction limit reached!
% 2.32/0.94 % (2071424)------------------------------
% 2.32/0.94 % (2071424)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/0.94 % (2071424)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.94 % (2071424)CaDiCaL version: 2.1.3
% 2.32/0.94 % (2071424)Termination reason: Instruction limit
% 2.32/0.94 % (2071424)Termination phase: Saturation
% 2.32/0.94 % (2071424)Time elapsed: 0.035 s
% 2.32/0.94 % (2071424)Peak memory usage: 88 MB
% 2.32/0.94 % (2071424)Instructions burned: 133 (million)
% 2.32/0.94 % (2071422)Refutation found. Thanks to Tanya!
% 2.32/0.94 % SZS status Theorem for theBenchmark
% 2.32/0.94 % SZS output start Proof for theBenchmark
% See solution above
% 2.32/0.94 % (2071422)------------------------------
% 2.32/0.94 % (2071422)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.32/0.94 % (2071422)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.32/0.94 % (2071422)CaDiCaL version: 2.1.3
% 2.32/0.94 % (2071422)Termination reason: Refutation
% 2.32/0.94 % (2071422)Time elapsed: 0.002 s
% 2.32/0.94 % (2071422)Peak memory usage: 88 MB
% 2.32/0.94 % (2071422)Instructions burned: 3 (million)
% 2.32/0.94 % (2071422)------------------------------
% 2.32/0.94 % (2071422)------------------------------
% 2.32/0.94 % (2071413)Success in time 0.297 s
% 2.32/0.94 % Vampire exiting
%------------------------------------------------------------------------------