TSTP Solution File: GRA002+3 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : GRA002+3 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 11:42:35 EDT 2024
% Result : Theorem 0.22s 0.42s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 44
% Syntax : Number of formulae : 227 ( 14 unt; 0 def)
% Number of atoms : 839 ( 125 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 953 ( 341 ~; 362 |; 174 &)
% ( 29 <=>; 39 =>; 0 <=; 8 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 37 ( 35 usr; 22 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 8 con; 0-3 aty)
% Number of variables : 463 ( 419 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f729,plain,
$false,
inference(avatar_sat_refutation,[],[f217,f226,f230,f268,f271,f402,f411,f485,f488,f515,f520,f573,f575,f661,f673,f728]) ).
fof(f728,plain,
( spl17_15
| spl17_5
| ~ spl17_6 ),
inference(avatar_split_clause,[],[f727,f265,f261,f568]) ).
fof(f568,plain,
( spl17_15
<=> ! [X2,X3] : ~ path(X2,X3,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_15])]) ).
fof(f261,plain,
( spl17_5
<=> number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_5])]) ).
fof(f265,plain,
( spl17_6
<=> on_path(sK13(sK5),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_6])]) ).
fof(f727,plain,
( ! [X0,X1] : ~ path(X0,X1,sK5)
| spl17_5
| ~ spl17_6 ),
inference(subsumption_resolution,[],[f726,f267]) ).
fof(f267,plain,
( on_path(sK13(sK5),sK5)
| ~ spl17_6 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f726,plain,
( ! [X0,X1] :
( ~ path(X0,X1,sK5)
| ~ on_path(sK13(sK5),sK5) )
| spl17_5 ),
inference(subsumption_resolution,[],[f725,f262]) ).
fof(f262,plain,
( number_of_in(sequential_pairs,sK5) != number_of_in(triangles,sK5)
| spl17_5 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f725,plain,
( ! [X0,X1] :
( number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
| ~ path(X0,X1,sK5)
| ~ on_path(sK13(sK5),sK5) )
| spl17_5 ),
inference(resolution,[],[f566,f276]) ).
fof(f276,plain,
( on_path(sK14(sK5),sK5)
| spl17_5 ),
inference(subsumption_resolution,[],[f275,f262]) ).
fof(f275,plain,
( on_path(sK14(sK5),sK5)
| number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5) ),
inference(resolution,[],[f151,f193]) ).
fof(f193,plain,
path(sK6,sK7,sK5),
inference(resolution,[],[f191,f108]) ).
fof(f108,plain,
shortest_path(sK6,sK7,sK5),
inference(cnf_transformation,[],[f72]) ).
fof(f72,plain,
( ~ less_or_equal(minus(length_of(sK5),n1),number_of_in(triangles,graph))
& shortest_path(sK6,sK7,sK5)
& complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5,sK6,sK7])],[f38,f71]) ).
fof(f71,plain,
( ? [X0,X1,X2] :
( ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph))
& shortest_path(X1,X2,X0) )
=> ( ~ less_or_equal(minus(length_of(sK5),n1),number_of_in(triangles,graph))
& shortest_path(sK6,sK7,sK5) ) ),
introduced(choice_axiom,[]) ).
fof(f38,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,[],[f21]) ).
fof(f21,plain,
~ ( complete
=> ! [X0,X1,X2] :
( shortest_path(X1,X2,X0)
=> less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [X3,X1,X2] :
( shortest_path(X1,X2,X3)
=> less_or_equal(minus(length_of(X3),n1),number_of_in(triangles,graph)) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f19,conjecture,
( complete
=> ! [X3,X1,X2] :
( shortest_path(X1,X2,X3)
=> less_or_equal(minus(length_of(X3),n1),number_of_in(triangles,graph)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',maximal_path_length) ).
fof(f191,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(resolution,[],[f166,f161]) ).
fof(f161,plain,
! [X2,X0,X1] :
( ~ sP4(X0,X1,X2)
| path(X2,X1,X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0,X1,X2] :
( ( sP4(X0,X1,X2)
| ( ~ less_or_equal(length_of(X0),length_of(sK15(X0,X1,X2)))
& path(X2,X1,sK15(X0,X1,X2)) )
| X1 = X2
| ~ path(X2,X1,X0) )
& ( ( ! [X4] :
( less_or_equal(length_of(X0),length_of(X4))
| ~ path(X2,X1,X4) )
& X1 != X2
& path(X2,X1,X0) )
| ~ sP4(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15])],[f101,f102]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ less_or_equal(length_of(X0),length_of(X3))
& path(X2,X1,X3) )
=> ( ~ less_or_equal(length_of(X0),length_of(sK15(X0,X1,X2)))
& path(X2,X1,sK15(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f101,plain,
! [X0,X1,X2] :
( ( sP4(X0,X1,X2)
| ? [X3] :
( ~ less_or_equal(length_of(X0),length_of(X3))
& path(X2,X1,X3) )
| X1 = X2
| ~ path(X2,X1,X0) )
& ( ( ! [X4] :
( less_or_equal(length_of(X0),length_of(X4))
| ~ path(X2,X1,X4) )
& X1 != X2
& path(X2,X1,X0) )
| ~ sP4(X0,X1,X2) ) ),
inference(rectify,[],[f100]) ).
fof(f100,plain,
! [X2,X1,X0] :
( ( sP4(X2,X1,X0)
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) )
| ~ sP4(X2,X1,X0) ) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
! [X2,X1,X0] :
( ( sP4(X2,X1,X0)
| ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) )
| ~ sP4(X2,X1,X0) ) ),
inference(nnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X2,X1,X0] :
( sP4(X2,X1,X0)
<=> ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f166,plain,
! [X2,X0,X1] :
( sP4(X2,X1,X0)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ~ sP4(X2,X1,X0) )
& ( sP4(X2,X1,X0)
| ~ shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> sP4(X2,X1,X0) ),
inference(definition_folding,[],[f55,f69]) ).
fof(f55,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) ) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( shortest_path(X0,X1,X2)
<=> ( ! [X3] :
( path(X0,X1,X3)
=> less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1
& path(X0,X1,X2) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X1,X2,X9] :
( shortest_path(X1,X2,X9)
<=> ( ! [X3] :
( path(X1,X2,X3)
=> less_or_equal(length_of(X9),length_of(X3)) )
& X1 != X2
& path(X1,X2,X9) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shortest_path_defn) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| on_path(sK14(X0),X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ( ! [X5] : ~ triangle(sK13(X0),sK14(X0),X5)
& sequential(sK13(X0),sK14(X0))
& on_path(sK14(X0),X0)
& on_path(sK13(X0),X0) )
| ~ path(X1,X2,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK13,sK14])],[f54,f95]) ).
fof(f95,plain,
! [X0] :
( ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ( ! [X5] : ~ triangle(sK13(X0),sK14(X0),X5)
& sequential(sK13(X0),sK14(X0))
& on_path(sK14(X0),X0)
& on_path(sK13(X0),X0) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( sequential(X3,X4)
& on_path(X4,X0)
& on_path(X3,X0) )
=> ? [X5] : triangle(X3,X4,X5) )
& path(X1,X2,X0) )
=> number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X3,X1,X2] :
( ( ! [X6,X7] :
( ( sequential(X6,X7)
& on_path(X7,X3)
& on_path(X6,X3) )
=> ? [X8] : triangle(X6,X7,X8) )
& path(X1,X2,X3) )
=> number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(f566,plain,
! [X2,X0,X1] :
( ~ on_path(sK14(X2),sK5)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ path(X0,X1,X2)
| ~ on_path(sK13(X2),sK5) ),
inference(subsumption_resolution,[],[f565,f152]) ).
fof(f152,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| sequential(sK13(X0),sK14(X0))
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f565,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ~ on_path(sK14(X2),sK5)
| ~ on_path(sK13(X2),sK5)
| ~ sequential(sK13(X2),sK14(X2)) ),
inference(resolution,[],[f491,f433]) ).
fof(f433,plain,
! [X0,X1] :
( precedes(X0,X1,sK5)
| ~ on_path(X1,sK5)
| ~ on_path(X0,sK5)
| ~ sequential(X0,X1) ),
inference(resolution,[],[f146,f193]) ).
fof(f146,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X1,X2,X0)
| ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| precedes(X3,X4,X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( precedes(X3,X4,X0)
| ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
& ~ sequential(X3,X4) )
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( precedes(X3,X4,X0)
| ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
& ~ sequential(X3,X4) )
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,plain,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( ( ( ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
=> precedes(X3,X4,X0) ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X3,X1,X2] :
( path(X1,X2,X3)
=> ! [X6,X7] :
( ( ( ? [X8] :
( precedes(X8,X7,X3)
& sequential(X6,X8) )
| sequential(X6,X7) )
& on_path(X7,X3)
& on_path(X6,X3) )
=> precedes(X6,X7,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',precedes_defn) ).
fof(f491,plain,
! [X2,X0,X1] :
( ~ precedes(sK13(X0),sK14(X0),sK5)
| ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(subsumption_resolution,[],[f490,f152]) ).
fof(f490,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0)
| ~ precedes(sK13(X0),sK14(X0),sK5)
| ~ sequential(sK13(X0),sK14(X0)) ),
inference(resolution,[],[f153,f357]) ).
fof(f357,plain,
! [X0,X1] :
( triangle(X0,X1,sK8(X0,X1))
| ~ precedes(X0,X1,sK5)
| ~ sequential(X0,X1) ),
inference(resolution,[],[f187,f108]) ).
fof(f187,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X0,X1,X4)
| ~ sequential(X2,X3)
| ~ precedes(X2,X3,X4)
| triangle(X2,X3,sK8(X2,X3)) ),
inference(global_subsumption,[],[f109,f108,f107,f110]) ).
fof(f110,plain,
! [X2,X3,X0,X1,X4] :
( triangle(X2,X3,sK8(X2,X3))
| ~ sequential(X2,X3)
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4)
| ~ complete ),
inference(cnf_transformation,[],[f74]) ).
fof(f74,plain,
( ! [X0,X1,X2,X3,X4] :
( triangle(X2,X3,sK8(X2,X3))
| ~ sequential(X2,X3)
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) )
| ~ complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f40,f73]) ).
fof(f73,plain,
! [X2,X3] :
( ? [X5] : triangle(X2,X3,X5)
=> triangle(X2,X3,sK8(X2,X3)) ),
introduced(choice_axiom,[]) ).
fof(f40,plain,
( ! [X0,X1,X2,X3,X4] :
( ? [X5] : triangle(X2,X3,X5)
| ~ sequential(X2,X3)
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) )
| ~ complete ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
( ! [X0,X1,X2,X3,X4] :
( ? [X5] : triangle(X2,X3,X5)
| ~ sequential(X2,X3)
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) )
| ~ complete ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
( complete
=> ! [X0,X1,X2,X3,X4] :
( ( sequential(X2,X3)
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ? [X5] : triangle(X2,X3,X5) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
( complete
=> ! [X1,X2,X6,X7,X3] :
( ( sequential(X6,X7)
& precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ? [X8] : triangle(X6,X7,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_is_triangle) ).
fof(f107,plain,
complete,
inference(cnf_transformation,[],[f72]) ).
fof(f109,plain,
~ less_or_equal(minus(length_of(sK5),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[],[f72]) ).
fof(f153,plain,
! [X2,X0,X1,X5] :
( ~ triangle(sK13(X0),sK14(X0),X5)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f673,plain,
( ~ spl17_19
| spl17_20
| spl17_5
| ~ spl17_6 ),
inference(avatar_split_clause,[],[f475,f265,f261,f670,f666]) ).
fof(f666,plain,
( spl17_19
<=> on_path(sK8(sK13(sK5),sK14(sK5)),path_cons(sK14(sK5),empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_19])]) ).
fof(f670,plain,
( spl17_20
<=> in_path(tail_of(sK13(sK5)),path_cons(sK14(sK5),empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_20])]) ).
fof(f475,plain,
( in_path(tail_of(sK13(sK5)),path_cons(sK14(sK5),empty))
| ~ on_path(sK8(sK13(sK5),sK14(sK5)),path_cons(sK14(sK5),empty))
| spl17_5
| ~ spl17_6 ),
inference(superposition,[],[f340,f467]) ).
fof(f467,plain,
( tail_of(sK13(sK5)) = head_of(sK8(sK13(sK5),sK14(sK5)))
| spl17_5
| ~ spl17_6 ),
inference(subsumption_resolution,[],[f466,f276]) ).
fof(f466,plain,
( ~ on_path(sK14(sK5),sK5)
| tail_of(sK13(sK5)) = head_of(sK8(sK13(sK5),sK14(sK5)))
| spl17_5
| ~ spl17_6 ),
inference(subsumption_resolution,[],[f464,f267]) ).
fof(f464,plain,
( ~ on_path(sK13(sK5),sK5)
| ~ on_path(sK14(sK5),sK5)
| tail_of(sK13(sK5)) = head_of(sK8(sK13(sK5),sK14(sK5)))
| spl17_5 ),
inference(resolution,[],[f448,f298]) ).
fof(f298,plain,
( sequential(sK13(sK5),sK14(sK5))
| spl17_5 ),
inference(subsumption_resolution,[],[f296,f262]) ).
fof(f296,plain,
( sequential(sK13(sK5),sK14(sK5))
| number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5) ),
inference(resolution,[],[f152,f193]) ).
fof(f448,plain,
! [X0,X1] :
( ~ sequential(X1,X0)
| ~ on_path(X1,sK5)
| ~ on_path(X0,sK5)
| tail_of(X1) = head_of(sK8(X1,X0)) ),
inference(duplicate_literal_removal,[],[f440]) ).
fof(f440,plain,
! [X0,X1] :
( ~ on_path(X0,sK5)
| ~ on_path(X1,sK5)
| ~ sequential(X1,X0)
| ~ sequential(X1,X0)
| tail_of(X1) = head_of(sK8(X1,X0)) ),
inference(resolution,[],[f433,f364]) ).
fof(f364,plain,
! [X0,X1] :
( ~ precedes(X0,X1,sK5)
| ~ sequential(X0,X1)
| tail_of(X0) = head_of(sK8(X0,X1)) ),
inference(resolution,[],[f358,f125]) ).
fof(f125,plain,
! [X0,X1] :
( ~ sequential(X0,X1)
| head_of(X0) = tail_of(X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( ( sequential(X0,X1)
| head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0) )
& ( ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) )
| ~ sequential(X0,X1) ) ),
inference(flattening,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( ( sequential(X0,X1)
| head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0) )
& ( ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) )
| ~ sequential(X0,X1) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0,X1] :
( sequential(X0,X1)
<=> ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) ),
inference(rectify,[],[f8]) ).
fof(f8,axiom,
! [X6,X7] :
( sequential(X6,X7)
<=> ( head_of(X6) = tail_of(X7)
& X6 != X7
& edge(X7)
& edge(X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_defn) ).
fof(f358,plain,
! [X0,X1] :
( sequential(sK8(X0,X1),X0)
| ~ sequential(X0,X1)
| ~ precedes(X0,X1,sK5) ),
inference(resolution,[],[f357,f159]) ).
fof(f159,plain,
! [X2,X0,X1] :
( ~ triangle(X0,X1,X2)
| sequential(X2,X0) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ( triangle(X0,X1,X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0) )
& ( ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) )
| ~ triangle(X0,X1,X2) ) ),
inference(flattening,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2] :
( ( triangle(X0,X1,X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0) )
& ( ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) )
| ~ triangle(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
<=> ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) ) ),
inference(rectify,[],[f13]) ).
fof(f13,axiom,
! [X6,X7,X8] :
( triangle(X6,X7,X8)
<=> ( sequential(X8,X6)
& sequential(X7,X8)
& sequential(X6,X7)
& edge(X8)
& edge(X7)
& edge(X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',triangle_defn) ).
fof(f340,plain,
( ! [X0] :
( in_path(head_of(X0),path_cons(sK14(sK5),empty))
| ~ on_path(X0,path_cons(sK14(sK5),empty)) )
| spl17_5 ),
inference(resolution,[],[f329,f172]) ).
fof(f172,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| ~ on_path(X3,X2)
| in_path(head_of(X3),X2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1,X2,X3] :
( ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) )
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X0,X1,X2,X3] :
( ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) )
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ( on_path(X3,X2)
& path(X0,X1,X2) )
=> ( in_path(tail_of(X3),X2)
& in_path(head_of(X3),X2)
& edge(X3) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X1,X2,X3,X0] :
( ( on_path(X0,X3)
& path(X1,X2,X3) )
=> ( in_path(tail_of(X0),X3)
& in_path(head_of(X0),X3)
& edge(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',on_path_properties) ).
fof(f329,plain,
( path(head_of(sK13(sK5)),head_of(sK14(sK5)),path_cons(sK14(sK5),empty))
| spl17_5 ),
inference(subsumption_resolution,[],[f327,f279]) ).
fof(f279,plain,
( edge(sK14(sK5))
| spl17_5 ),
inference(resolution,[],[f276,f197]) ).
fof(f197,plain,
! [X0] :
( ~ on_path(X0,sK5)
| edge(X0) ),
inference(resolution,[],[f171,f193]) ).
fof(f171,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| ~ on_path(X3,X2)
| edge(X3) ),
inference(cnf_transformation,[],[f59]) ).
fof(f327,plain,
( path(head_of(sK13(sK5)),head_of(sK14(sK5)),path_cons(sK14(sK5),empty))
| ~ edge(sK14(sK5))
| spl17_5 ),
inference(superposition,[],[f312,f299]) ).
fof(f299,plain,
( head_of(sK13(sK5)) = tail_of(sK14(sK5))
| spl17_5 ),
inference(resolution,[],[f298,f125]) ).
fof(f312,plain,
! [X3] :
( path(tail_of(X3),head_of(X3),path_cons(X3,empty))
| ~ edge(X3) ),
inference(subsumption_resolution,[],[f311,f120]) ).
fof(f120,plain,
! [X0] :
( vertex(tail_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ( vertex(tail_of(X0))
& vertex(head_of(X0)) )
| ~ edge(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( edge(X0)
=> ( vertex(tail_of(X0))
& vertex(head_of(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',edge_ends_are_vertices) ).
fof(f311,plain,
! [X3] :
( path(tail_of(X3),head_of(X3),path_cons(X3,empty))
| ~ edge(X3)
| ~ vertex(tail_of(X3)) ),
inference(subsumption_resolution,[],[f185,f119]) ).
fof(f119,plain,
! [X0] :
( vertex(head_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f44]) ).
fof(f185,plain,
! [X3] :
( path(tail_of(X3),head_of(X3),path_cons(X3,empty))
| ~ edge(X3)
| ~ vertex(head_of(X3))
| ~ vertex(tail_of(X3)) ),
inference(equality_resolution,[],[f184]) ).
fof(f184,plain,
! [X3,X0] :
( path(X0,head_of(X3),path_cons(X3,empty))
| tail_of(X3) != X0
| ~ edge(X3)
| ~ vertex(head_of(X3))
| ~ vertex(X0) ),
inference(equality_resolution,[],[f183]) ).
fof(f183,plain,
! [X3,X0,X1] :
( path(X0,X1,path_cons(X3,empty))
| head_of(X3) != X1
| tail_of(X3) != X0
| ~ edge(X3)
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(equality_resolution,[],[f148]) ).
fof(f148,plain,
! [X2,X3,X0,X1] :
( path(X0,X1,X2)
| path_cons(X3,empty) != X2
| head_of(X3) != X1
| tail_of(X3) != X0
| ~ edge(X3)
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2] :
( path(X0,X1,X2)
| ! [X3] :
( ( ! [X4] :
( path_cons(X3,X4) != X2
| ~ path(head_of(X3),X1,X4) )
& ( path_cons(X3,empty) != X2
| head_of(X3) != X1 ) )
| tail_of(X3) != X0
| ~ edge(X3) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2] :
( path(X0,X1,X2)
| ! [X3] :
( ( ! [X4] :
( path_cons(X3,X4) != X2
| ~ path(head_of(X3),X1,X4) )
& ( path_cons(X3,empty) != X2
| head_of(X3) != X1 ) )
| tail_of(X3) != X0
| ~ edge(X3) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( ( ? [X4] :
( path_cons(X3,X4) = X2
& path(head_of(X3),X1,X4) )
| ( path_cons(X3,empty) = X2
& head_of(X3) = X1 ) )
& tail_of(X3) = X0
& edge(X3) )
& vertex(X1)
& vertex(X0) )
=> path(X0,X1,X2) ),
inference(rectify,[],[f4]) ).
fof(f4,axiom,
! [X1,X2,X3] :
( ( ? [X0] :
( ( ? [X4] :
( path_cons(X0,X4) = X3
& path(head_of(X0),X2,X4) )
| ( path_cons(X0,empty) = X3
& head_of(X0) = X2 ) )
& tail_of(X0) = X1
& edge(X0) )
& vertex(X2)
& vertex(X1) )
=> path(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_defn) ).
fof(f661,plain,
( spl17_17
| spl17_18 ),
inference(avatar_split_clause,[],[f652,f658,f654]) ).
fof(f654,plain,
( spl17_17
<=> sP4(sK5,sK7,sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_17])]) ).
fof(f658,plain,
( spl17_18
<=> sK6 = sK7 ),
introduced(avatar_definition,[new_symbols(naming,[spl17_18])]) ).
fof(f652,plain,
( sK6 = sK7
| sP4(sK5,sK7,sK6) ),
inference(subsumption_resolution,[],[f651,f193]) ).
fof(f651,plain,
( sK6 = sK7
| ~ path(sK6,sK7,sK5)
| sP4(sK5,sK7,sK6) ),
inference(duplicate_literal_removal,[],[f650]) ).
fof(f650,plain,
( sK6 = sK7
| ~ path(sK6,sK7,sK5)
| sP4(sK5,sK7,sK6)
| sP4(sK5,sK7,sK6)
| sK6 = sK7
| ~ path(sK6,sK7,sK5) ),
inference(resolution,[],[f649,f164]) ).
fof(f164,plain,
! [X2,X0,X1] :
( path(X2,X1,sK15(X0,X1,X2))
| sP4(X0,X1,X2)
| X1 = X2
| ~ path(X2,X1,X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f649,plain,
! [X0,X1] :
( ~ path(sK6,sK7,sK15(sK5,X0,X1))
| X0 = X1
| ~ path(X1,X0,sK5)
| sP4(sK5,X0,X1) ),
inference(resolution,[],[f165,f247]) ).
fof(f247,plain,
! [X0] :
( less_or_equal(length_of(sK5),length_of(X0))
| ~ path(sK6,sK7,X0) ),
inference(resolution,[],[f242,f108]) ).
fof(f242,plain,
! [X2,X3,X0,X1] :
( ~ shortest_path(X0,X1,X3)
| less_or_equal(length_of(X3),length_of(X2))
| ~ path(X0,X1,X2) ),
inference(resolution,[],[f163,f166]) ).
fof(f163,plain,
! [X2,X0,X1,X4] :
( ~ sP4(X0,X1,X2)
| ~ path(X2,X1,X4)
| less_or_equal(length_of(X0),length_of(X4)) ),
inference(cnf_transformation,[],[f103]) ).
fof(f165,plain,
! [X2,X0,X1] :
( ~ less_or_equal(length_of(X0),length_of(sK15(X0,X1,X2)))
| sP4(X0,X1,X2)
| X1 = X2
| ~ path(X2,X1,X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f575,plain,
~ spl17_15,
inference(avatar_contradiction_clause,[],[f574]) ).
fof(f574,plain,
( $false
| ~ spl17_15 ),
inference(resolution,[],[f569,f193]) ).
fof(f569,plain,
( ! [X2,X3] : ~ path(X2,X3,sK5)
| ~ spl17_15 ),
inference(avatar_component_clause,[],[f568]) ).
fof(f573,plain,
( spl17_15
| spl17_16 ),
inference(avatar_split_clause,[],[f443,f571,f568]) ).
fof(f571,plain,
( spl17_16
<=> ! [X0,X1] :
( ~ on_path(X0,sK5)
| sP3(sK5,X0,X1)
| ~ on_path(X1,sK5)
| ~ sequential(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_16])]) ).
fof(f443,plain,
! [X2,X3,X0,X1] :
( ~ on_path(X0,sK5)
| ~ on_path(X1,sK5)
| ~ sequential(X1,X0)
| sP3(sK5,X0,X1)
| ~ path(X2,X3,sK5) ),
inference(resolution,[],[f433,f145]) ).
fof(f145,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X4,X0)
| sP3(X0,X4,X3)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( sP3(X0,X4,X3)
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(definition_folding,[],[f48,f67]) ).
fof(f67,plain,
! [X0,X4,X3] :
( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
| ~ sP3(X0,X4,X3) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( precedes(X3,X4,X0)
=> ( ( sequential(X3,X4)
<~> ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) ) )
& on_path(X4,X0)
& on_path(X3,X0) ) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X3,X1,X2] :
( path(X1,X2,X3)
=> ! [X6,X7] :
( precedes(X6,X7,X3)
=> ( ( sequential(X6,X7)
<~> ? [X8] :
( precedes(X8,X7,X3)
& sequential(X6,X8) ) )
& on_path(X7,X3)
& on_path(X6,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',precedes_properties) ).
fof(f520,plain,
( spl17_5
| ~ spl17_6
| spl17_13 ),
inference(avatar_contradiction_clause,[],[f519]) ).
fof(f519,plain,
( $false
| spl17_5
| ~ spl17_6
| spl17_13 ),
inference(subsumption_resolution,[],[f518,f276]) ).
fof(f518,plain,
( ~ on_path(sK14(sK5),sK5)
| spl17_5
| ~ spl17_6
| spl17_13 ),
inference(subsumption_resolution,[],[f517,f298]) ).
fof(f517,plain,
( ~ sequential(sK13(sK5),sK14(sK5))
| ~ on_path(sK14(sK5),sK5)
| ~ spl17_6
| spl17_13 ),
inference(subsumption_resolution,[],[f516,f267]) ).
fof(f516,plain,
( ~ on_path(sK13(sK5),sK5)
| ~ sequential(sK13(sK5),sK14(sK5))
| ~ on_path(sK14(sK5),sK5)
| spl17_13 ),
inference(resolution,[],[f510,f447]) ).
fof(f447,plain,
! [X0,X1] :
( edge(sK8(X1,X0))
| ~ on_path(X1,sK5)
| ~ sequential(X1,X0)
| ~ on_path(X0,sK5) ),
inference(duplicate_literal_removal,[],[f441]) ).
fof(f441,plain,
! [X0,X1] :
( ~ on_path(X0,sK5)
| ~ on_path(X1,sK5)
| ~ sequential(X1,X0)
| ~ sequential(X1,X0)
| edge(sK8(X1,X0)) ),
inference(resolution,[],[f433,f360]) ).
fof(f360,plain,
! [X0,X1] :
( ~ precedes(X0,X1,sK5)
| ~ sequential(X0,X1)
| edge(sK8(X0,X1)) ),
inference(resolution,[],[f357,f156]) ).
fof(f156,plain,
! [X2,X0,X1] :
( ~ triangle(X0,X1,X2)
| edge(X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f510,plain,
( ~ edge(sK8(sK13(sK5),sK14(sK5)))
| spl17_13 ),
inference(avatar_component_clause,[],[f508]) ).
fof(f508,plain,
( spl17_13
<=> edge(sK8(sK13(sK5),sK14(sK5))) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_13])]) ).
fof(f515,plain,
( ~ spl17_13
| ~ spl17_14
| spl17_5
| ~ spl17_6 ),
inference(avatar_split_clause,[],[f506,f265,f261,f512,f508]) ).
fof(f512,plain,
( spl17_14
<=> tail_of(sK13(sK5)) = head_of(sK14(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_14])]) ).
fof(f506,plain,
( tail_of(sK13(sK5)) != head_of(sK14(sK5))
| ~ edge(sK8(sK13(sK5),sK14(sK5)))
| spl17_5
| ~ spl17_6 ),
inference(forward_demodulation,[],[f503,f467]) ).
fof(f503,plain,
( head_of(sK14(sK5)) != head_of(sK8(sK13(sK5),sK14(sK5)))
| ~ edge(sK8(sK13(sK5),sK14(sK5)))
| spl17_5
| ~ spl17_6 ),
inference(superposition,[],[f118,f498]) ).
fof(f498,plain,
( head_of(sK14(sK5)) = tail_of(sK8(sK13(sK5),sK14(sK5)))
| spl17_5
| ~ spl17_6 ),
inference(subsumption_resolution,[],[f497,f276]) ).
fof(f497,plain,
( ~ on_path(sK14(sK5),sK5)
| head_of(sK14(sK5)) = tail_of(sK8(sK13(sK5),sK14(sK5)))
| spl17_5
| ~ spl17_6 ),
inference(subsumption_resolution,[],[f495,f267]) ).
fof(f495,plain,
( ~ on_path(sK13(sK5),sK5)
| ~ on_path(sK14(sK5),sK5)
| head_of(sK14(sK5)) = tail_of(sK8(sK13(sK5),sK14(sK5)))
| spl17_5 ),
inference(resolution,[],[f449,f298]) ).
fof(f449,plain,
! [X0,X1] :
( ~ sequential(X1,X0)
| ~ on_path(X1,sK5)
| ~ on_path(X0,sK5)
| head_of(X0) = tail_of(sK8(X1,X0)) ),
inference(duplicate_literal_removal,[],[f439]) ).
fof(f439,plain,
! [X0,X1] :
( ~ on_path(X0,sK5)
| ~ on_path(X1,sK5)
| ~ sequential(X1,X0)
| ~ sequential(X1,X0)
| head_of(X0) = tail_of(sK8(X1,X0)) ),
inference(resolution,[],[f433,f367]) ).
fof(f367,plain,
! [X0,X1] :
( ~ precedes(X0,X1,sK5)
| ~ sequential(X0,X1)
| head_of(X1) = tail_of(sK8(X0,X1)) ),
inference(resolution,[],[f359,f125]) ).
fof(f359,plain,
! [X0,X1] :
( sequential(X1,sK8(X0,X1))
| ~ sequential(X0,X1)
| ~ precedes(X0,X1,sK5) ),
inference(resolution,[],[f357,f158]) ).
fof(f158,plain,
! [X2,X0,X1] :
( ~ triangle(X0,X1,X2)
| sequential(X1,X2) ),
inference(cnf_transformation,[],[f98]) ).
fof(f118,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0] :
( edge(X0)
=> head_of(X0) != tail_of(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_loops) ).
fof(f488,plain,
( ~ spl17_6
| spl17_12 ),
inference(avatar_contradiction_clause,[],[f487]) ).
fof(f487,plain,
( $false
| ~ spl17_6
| spl17_12 ),
inference(subsumption_resolution,[],[f486,f267]) ).
fof(f486,plain,
( ~ on_path(sK13(sK5),sK5)
| spl17_12 ),
inference(resolution,[],[f483,f203]) ).
fof(f203,plain,
! [X0] :
( in_path(tail_of(X0),sK5)
| ~ on_path(X0,sK5) ),
inference(resolution,[],[f173,f193]) ).
fof(f173,plain,
! [X2,X3,X0,X1] :
( ~ path(X0,X1,X2)
| ~ on_path(X3,X2)
| in_path(tail_of(X3),X2) ),
inference(cnf_transformation,[],[f59]) ).
fof(f483,plain,
( ~ in_path(tail_of(sK13(sK5)),sK5)
| spl17_12 ),
inference(avatar_component_clause,[],[f482]) ).
fof(f482,plain,
( spl17_12
<=> in_path(tail_of(sK13(sK5)),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_12])]) ).
fof(f485,plain,
( ~ spl17_11
| spl17_12
| spl17_5
| ~ spl17_6 ),
inference(avatar_split_clause,[],[f472,f265,f261,f482,f478]) ).
fof(f478,plain,
( spl17_11
<=> on_path(sK8(sK13(sK5),sK14(sK5)),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_11])]) ).
fof(f472,plain,
( in_path(tail_of(sK13(sK5)),sK5)
| ~ on_path(sK8(sK13(sK5),sK14(sK5)),sK5)
| spl17_5
| ~ spl17_6 ),
inference(superposition,[],[f201,f467]) ).
fof(f201,plain,
! [X0] :
( in_path(head_of(X0),sK5)
| ~ on_path(X0,sK5) ),
inference(resolution,[],[f172,f193]) ).
fof(f411,plain,
( ~ spl17_9
| spl17_10
| spl17_5 ),
inference(avatar_split_clause,[],[f376,f261,f408,f404]) ).
fof(f404,plain,
( spl17_9
<=> on_path(sK14(sK5),path_cons(sK14(sK5),empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_9])]) ).
fof(f408,plain,
( spl17_10
<=> in_path(head_of(sK13(sK5)),path_cons(sK14(sK5),empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_10])]) ).
fof(f376,plain,
( in_path(head_of(sK13(sK5)),path_cons(sK14(sK5),empty))
| ~ on_path(sK14(sK5),path_cons(sK14(sK5),empty))
| spl17_5 ),
inference(superposition,[],[f341,f299]) ).
fof(f341,plain,
( ! [X0] :
( in_path(tail_of(X0),path_cons(sK14(sK5),empty))
| ~ on_path(X0,path_cons(sK14(sK5),empty)) )
| spl17_5 ),
inference(resolution,[],[f329,f173]) ).
fof(f402,plain,
( ~ spl17_7
| spl17_8
| spl17_5 ),
inference(avatar_split_clause,[],[f375,f261,f399,f395]) ).
fof(f395,plain,
( spl17_7
<=> on_path(sK10(sK7,sK5,sK6),path_cons(sK14(sK5),empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_7])]) ).
fof(f399,plain,
( spl17_8
<=> in_path(sK6,path_cons(sK14(sK5),empty)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_8])]) ).
fof(f375,plain,
( in_path(sK6,path_cons(sK14(sK5),empty))
| ~ on_path(sK10(sK7,sK5,sK6),path_cons(sK14(sK5),empty))
| spl17_5 ),
inference(superposition,[],[f341,f205]) ).
fof(f205,plain,
sK6 = tail_of(sK10(sK7,sK5,sK6)),
inference(resolution,[],[f200,f193]) ).
fof(f200,plain,
! [X2,X0,X1] :
( ~ path(X2,X0,X1)
| tail_of(sK10(X0,X1,X2)) = X2 ),
inference(resolution,[],[f130,f139]) ).
fof(f139,plain,
! [X2,X0,X1] :
( sP2(X1,X2,X0)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( sP2(X1,X2,X0)
& vertex(X1)
& vertex(X0) )
| ~ path(X0,X1,X2) ),
inference(definition_folding,[],[f47,f65,f64]) ).
fof(f64,plain,
! [X2,X3,X1] :
( ( ( path_cons(X3,empty) = X2
& head_of(X3) = X1 )
<~> ? [X4] :
( path_cons(X3,X4) = X2
& path(head_of(X3),X1,X4) ) )
| ~ sP1(X2,X3,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f65,plain,
! [X1,X2,X0] :
( ? [X3] :
( sP1(X2,X3,X1)
& tail_of(X3) = X0
& edge(X3) )
| ~ sP2(X1,X2,X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( ( ( path_cons(X3,empty) = X2
& head_of(X3) = X1 )
<~> ? [X4] :
( path_cons(X3,X4) = X2
& path(head_of(X3),X1,X4) ) )
& tail_of(X3) = X0
& edge(X3) )
& vertex(X1)
& vertex(X0) )
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X0,X1,X2] :
( path(X0,X1,X2)
=> ( ? [X3] :
( ( ( path_cons(X3,empty) = X2
& head_of(X3) = X1 )
<~> ? [X4] :
( path_cons(X3,X4) = X2
& path(head_of(X3),X1,X4) ) )
& tail_of(X3) = X0
& edge(X3) )
& vertex(X1)
& vertex(X0) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X2,X3] :
( path(X1,X2,X3)
=> ( ? [X0] :
( ( ( path_cons(X0,empty) = X3
& head_of(X0) = X2 )
<~> ? [X4] :
( path_cons(X0,X4) = X3
& path(head_of(X0),X2,X4) ) )
& tail_of(X0) = X1
& edge(X0) )
& vertex(X2)
& vertex(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_properties) ).
fof(f130,plain,
! [X2,X0,X1] :
( ~ sP2(X0,X1,X2)
| tail_of(sK10(X0,X1,X2)) = X2 ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( sP1(X1,sK10(X0,X1,X2),X0)
& tail_of(sK10(X0,X1,X2)) = X2
& edge(sK10(X0,X1,X2)) )
| ~ sP2(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f83,f84]) ).
fof(f84,plain,
! [X0,X1,X2] :
( ? [X3] :
( sP1(X1,X3,X0)
& tail_of(X3) = X2
& edge(X3) )
=> ( sP1(X1,sK10(X0,X1,X2),X0)
& tail_of(sK10(X0,X1,X2)) = X2
& edge(sK10(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f83,plain,
! [X0,X1,X2] :
( ? [X3] :
( sP1(X1,X3,X0)
& tail_of(X3) = X2
& edge(X3) )
| ~ sP2(X0,X1,X2) ),
inference(rectify,[],[f82]) ).
fof(f82,plain,
! [X1,X2,X0] :
( ? [X3] :
( sP1(X2,X3,X1)
& tail_of(X3) = X0
& edge(X3) )
| ~ sP2(X1,X2,X0) ),
inference(nnf_transformation,[],[f65]) ).
fof(f271,plain,
~ spl17_5,
inference(avatar_contradiction_clause,[],[f270]) ).
fof(f270,plain,
( $false
| ~ spl17_5 ),
inference(subsumption_resolution,[],[f269,f232]) ).
fof(f232,plain,
~ less_or_equal(number_of_in(sequential_pairs,sK5),number_of_in(triangles,graph)),
inference(superposition,[],[f109,f231]) ).
fof(f231,plain,
minus(length_of(sK5),n1) = number_of_in(sequential_pairs,sK5),
inference(resolution,[],[f128,f193]) ).
fof(f128,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1,X2] :
( number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1)
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0,X1,X2] :
( path(X0,X1,X2)
=> number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X1,X2,X3] :
( path(X1,X2,X3)
=> number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
fof(f269,plain,
( less_or_equal(number_of_in(sequential_pairs,sK5),number_of_in(triangles,graph))
| ~ spl17_5 ),
inference(superposition,[],[f121,f263]) ).
fof(f263,plain,
( number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5)
| ~ spl17_5 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f121,plain,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0,X1] : less_or_equal(number_of_in(X0,X1),number_of_in(X0,graph)),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X10,X11] : less_or_equal(number_of_in(X10,X11),number_of_in(X10,graph)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',graph_has_them_all) ).
fof(f268,plain,
( spl17_5
| spl17_6 ),
inference(avatar_split_clause,[],[f259,f265,f261]) ).
fof(f259,plain,
( on_path(sK13(sK5),sK5)
| number_of_in(sequential_pairs,sK5) = number_of_in(triangles,sK5) ),
inference(resolution,[],[f150,f193]) ).
fof(f150,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| on_path(sK13(X0),X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f96]) ).
fof(f230,plain,
spl17_3,
inference(avatar_contradiction_clause,[],[f229]) ).
fof(f229,plain,
( $false
| spl17_3 ),
inference(subsumption_resolution,[],[f228,f193]) ).
fof(f228,plain,
( ~ path(sK6,sK7,sK5)
| spl17_3 ),
inference(resolution,[],[f227,f139]) ).
fof(f227,plain,
( ~ sP2(sK7,sK5,sK6)
| spl17_3 ),
inference(resolution,[],[f221,f129]) ).
fof(f129,plain,
! [X2,X0,X1] :
( edge(sK10(X0,X1,X2))
| ~ sP2(X0,X1,X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f221,plain,
( ~ edge(sK10(sK7,sK5,sK6))
| spl17_3 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f219,plain,
( spl17_3
<=> edge(sK10(sK7,sK5,sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_3])]) ).
fof(f226,plain,
( ~ spl17_3
| ~ spl17_4 ),
inference(avatar_split_clause,[],[f207,f223,f219]) ).
fof(f223,plain,
( spl17_4
<=> sK6 = head_of(sK10(sK7,sK5,sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_4])]) ).
fof(f207,plain,
( sK6 != head_of(sK10(sK7,sK5,sK6))
| ~ edge(sK10(sK7,sK5,sK6)) ),
inference(superposition,[],[f118,f205]) ).
fof(f217,plain,
( ~ spl17_1
| spl17_2 ),
inference(avatar_split_clause,[],[f206,f214,f210]) ).
fof(f210,plain,
( spl17_1
<=> on_path(sK10(sK7,sK5,sK6),sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_1])]) ).
fof(f214,plain,
( spl17_2
<=> in_path(sK6,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl17_2])]) ).
fof(f206,plain,
( in_path(sK6,sK5)
| ~ on_path(sK10(sK7,sK5,sK6),sK5) ),
inference(superposition,[],[f203,f205]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRA002+3 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 30 02:32:59 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (30034)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (30037)WARNING: value z3 for option sas not known
% 0.15/0.38 % (30035)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.38 % (30037)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.39 % (30039)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.39 % (30038)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39 % (30040)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.39 % (30041)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.39 TRYING [3]
% 0.15/0.40 % (30036)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.40 TRYING [1]
% 0.22/0.40 TRYING [2]
% 0.22/0.41 % (30037)First to succeed.
% 0.22/0.42 TRYING [3]
% 0.22/0.42 % (30037)Refutation found. Thanks to Tanya!
% 0.22/0.42 % SZS status Theorem for theBenchmark
% 0.22/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.42 % (30037)------------------------------
% 0.22/0.42 % (30037)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.42 % (30037)Termination reason: Refutation
% 0.22/0.42
% 0.22/0.42 % (30037)Memory used [KB]: 1261
% 0.22/0.42 % (30037)Time elapsed: 0.040 s
% 0.22/0.42 % (30037)Instructions burned: 58 (million)
% 0.22/0.42 % (30037)------------------------------
% 0.22/0.42 % (30037)------------------------------
% 0.22/0.42 % (30034)Success in time 0.057 s
%------------------------------------------------------------------------------