TSTP Solution File: GRA002+3 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---1.0
% Problem : GRA002+3 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% Computer : n001.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 : Wed Aug 31 16:13:31 EDT 2022
% Result : Theorem 2.20s 0.65s
% Output : Refutation 2.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 21
% Syntax : Number of formulae : 105 ( 19 unt; 0 def)
% Number of atoms : 351 ( 43 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 391 ( 145 ~; 141 |; 69 &)
% ( 10 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 17 ( 15 usr; 9 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 10 con; 0-3 aty)
% Number of variables : 238 ( 207 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1364,plain,
$false,
inference(avatar_sat_refutation,[],[f212,f214,f409,f416,f1282,f1297,f1361,f1363]) ).
fof(f1363,plain,
~ spl15_83,
inference(avatar_contradiction_clause,[],[f1362]) ).
fof(f1362,plain,
( $false
| ~ spl15_83 ),
inference(resolution,[],[f1277,f108]) ).
fof(f108,plain,
shortest_path(sK1,sK2,sK0),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
( complete
& shortest_path(sK1,sK2,sK0)
& ~ less_or_equal(minus(length_of(sK0),n1),number_of_in(triangles,graph)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f63,f64]) ).
fof(f64,plain,
( ? [X0,X1,X2] :
( shortest_path(X1,X2,X0)
& ~ less_or_equal(minus(length_of(X0),n1),number_of_in(triangles,graph)) )
=> ( shortest_path(sK1,sK2,sK0)
& ~ less_or_equal(minus(length_of(sK0),n1),number_of_in(triangles,graph)) ) ),
introduced(choice_axiom,[]) ).
fof(f63,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,[],[f45]) ).
fof(f45,plain,
( complete
& ? [X2,X0,X1] :
( shortest_path(X0,X1,X2)
& ~ less_or_equal(minus(length_of(X2),n1),number_of_in(triangles,graph)) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
~ ( complete
=> ! [X1,X0,X2] :
( shortest_path(X0,X1,X2)
=> less_or_equal(minus(length_of(X2),n1),number_of_in(triangles,graph)) ) ),
inference(rectify,[],[f20]) ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [X1,X2,X3] :
( 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
=> ! [X1,X2,X3] :
( shortest_path(X1,X2,X3)
=> less_or_equal(minus(length_of(X3),n1),number_of_in(triangles,graph)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',maximal_path_length) ).
fof(f1277,plain,
( ! [X10,X9] : ~ shortest_path(X9,X10,sK0)
| ~ spl15_83 ),
inference(avatar_component_clause,[],[f1276]) ).
fof(f1276,plain,
( spl15_83
<=> ! [X9,X10] : ~ shortest_path(X9,X10,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_83])]) ).
fof(f1361,plain,
( spl15_86
| spl15_23
| ~ spl15_84 ),
inference(avatar_split_clause,[],[f1360,f1279,f402,f1290]) ).
fof(f1290,plain,
( spl15_86
<=> ! [X2,X3] : ~ path(X2,X3,sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_86])]) ).
fof(f402,plain,
( spl15_23
<=> number_of_in(triangles,sK0) = sF13 ),
introduced(avatar_definition,[new_symbols(naming,[spl15_23])]) ).
fof(f1279,plain,
( spl15_84
<=> triangle(sK5(sK0),sK4(sK0),sK9(sK4(sK0),sK5(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_84])]) ).
fof(f1360,plain,
( ! [X0,X1] : ~ path(X0,X1,sK0)
| spl15_23
| ~ spl15_84 ),
inference(subsumption_resolution,[],[f1359,f403]) ).
fof(f403,plain,
( number_of_in(triangles,sK0) != sF13
| spl15_23 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f1359,plain,
( ! [X0,X1] :
( number_of_in(triangles,sK0) = sF13
| ~ path(X0,X1,sK0) )
| ~ spl15_84 ),
inference(forward_demodulation,[],[f1352,f235]) ).
fof(f235,plain,
sF13 = number_of_in(sequential_pairs,sK0),
inference(forward_demodulation,[],[f234,f177]) ).
fof(f177,plain,
minus(sF12,n1) = sF13,
introduced(function_definition,[]) ).
fof(f234,plain,
minus(sF12,n1) = number_of_in(sequential_pairs,sK0),
inference(forward_demodulation,[],[f233,f176]) ).
fof(f176,plain,
sF12 = length_of(sK0),
introduced(function_definition,[]) ).
fof(f233,plain,
minus(length_of(sK0),n1) = number_of_in(sequential_pairs,sK0),
inference(resolution,[],[f106,f219]) ).
fof(f219,plain,
path(sK1,sK2,sK0),
inference(resolution,[],[f158,f108]) ).
fof(f158,plain,
! [X2,X0,X1] :
( ~ shortest_path(X2,X0,X1)
| path(X2,X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2] :
( ( ( path(X2,X0,X1)
& X0 != X2
& ! [X3] :
( less_or_equal(length_of(X1),length_of(X3))
| ~ path(X2,X0,X3) ) )
| ~ shortest_path(X2,X0,X1) )
& ( shortest_path(X2,X0,X1)
| ~ path(X2,X0,X1)
| X0 = X2
| ( ~ less_or_equal(length_of(X1),length_of(sK8(X0,X1,X2)))
& path(X2,X0,sK8(X0,X1,X2)) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f94,f95]) ).
fof(f95,plain,
! [X0,X1,X2] :
( ? [X4] :
( ~ less_or_equal(length_of(X1),length_of(X4))
& path(X2,X0,X4) )
=> ( ~ less_or_equal(length_of(X1),length_of(sK8(X0,X1,X2)))
& path(X2,X0,sK8(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f94,plain,
! [X0,X1,X2] :
( ( ( path(X2,X0,X1)
& X0 != X2
& ! [X3] :
( less_or_equal(length_of(X1),length_of(X3))
| ~ path(X2,X0,X3) ) )
| ~ shortest_path(X2,X0,X1) )
& ( shortest_path(X2,X0,X1)
| ~ path(X2,X0,X1)
| X0 = X2
| ? [X4] :
( ~ less_or_equal(length_of(X1),length_of(X4))
& path(X2,X0,X4) ) ) ),
inference(rectify,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( ( path(X2,X0,X1)
& X0 != X2
& ! [X3] :
( less_or_equal(length_of(X1),length_of(X3))
| ~ path(X2,X0,X3) ) )
| ~ shortest_path(X2,X0,X1) )
& ( shortest_path(X2,X0,X1)
| ~ path(X2,X0,X1)
| X0 = X2
| ? [X3] :
( ~ less_or_equal(length_of(X1),length_of(X3))
& path(X2,X0,X3) ) ) ),
inference(flattening,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( ( path(X2,X0,X1)
& X0 != X2
& ! [X3] :
( less_or_equal(length_of(X1),length_of(X3))
| ~ path(X2,X0,X3) ) )
| ~ shortest_path(X2,X0,X1) )
& ( shortest_path(X2,X0,X1)
| ~ path(X2,X0,X1)
| X0 = X2
| ? [X3] :
( ~ less_or_equal(length_of(X1),length_of(X3))
& path(X2,X0,X3) ) ) ),
inference(nnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ( path(X2,X0,X1)
& X0 != X2
& ! [X3] :
( less_or_equal(length_of(X1),length_of(X3))
| ~ path(X2,X0,X3) ) )
<=> shortest_path(X2,X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,plain,
! [X1,X2,X0] :
( shortest_path(X2,X0,X1)
<=> ( path(X2,X0,X1)
& ! [X3] :
( path(X2,X0,X3)
=> less_or_equal(length_of(X1),length_of(X3)) )
& X0 != X2 ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X2,X9,X1] :
( ( path(X1,X2,X9)
& ! [X3] :
( path(X1,X2,X3)
=> less_or_equal(length_of(X9),length_of(X3)) )
& X1 != X2 )
<=> shortest_path(X1,X2,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_defn) ).
fof(f106,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2] :
( ~ path(X0,X1,X2)
| number_of_in(sequential_pairs,X2) = minus(length_of(X2),n1) ),
inference(rectify,[],[f38]) ).
fof(f38,plain,
! [X0,X2,X1] :
( ~ path(X0,X2,X1)
| number_of_in(sequential_pairs,X1) = minus(length_of(X1),n1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,plain,
! [X1,X2,X0] :
( path(X0,X2,X1)
=> number_of_in(sequential_pairs,X1) = minus(length_of(X1),n1) ),
inference(rectify,[],[f15]) ).
fof(f15,axiom,
! [X1,X3,X2] :
( path(X1,X2,X3)
=> number_of_in(sequential_pairs,X3) = minus(length_of(X3),n1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_length_sequential_pairs) ).
fof(f1352,plain,
( ! [X0,X1] :
( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0)
| ~ path(X0,X1,sK0) )
| ~ spl15_84 ),
inference(resolution,[],[f1281,f136]) ).
fof(f136,plain,
! [X2,X0,X1,X5] :
( ~ triangle(sK5(X0),sK4(X0),X5)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ( on_path(sK4(X0),X0)
& sequential(sK5(X0),sK4(X0))
& on_path(sK5(X0),X0)
& ! [X5] : ~ triangle(sK5(X0),sK4(X0),X5) )
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f78,f79]) ).
fof(f79,plain,
! [X0] :
( ? [X3,X4] :
( on_path(X3,X0)
& sequential(X4,X3)
& on_path(X4,X0)
& ! [X5] : ~ triangle(X4,X3,X5) )
=> ( on_path(sK4(X0),X0)
& sequential(sK5(X0),sK4(X0))
& on_path(sK5(X0),X0)
& ! [X5] : ~ triangle(sK5(X0),sK4(X0),X5) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ? [X3,X4] :
( on_path(X3,X0)
& sequential(X4,X3)
& on_path(X4,X0)
& ! [X5] : ~ triangle(X4,X3,X5) )
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(rectify,[],[f57]) ).
fof(f57,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| ? [X4,X3] :
( on_path(X4,X2)
& sequential(X3,X4)
& on_path(X3,X2)
& ! [X5] : ~ triangle(X3,X4,X5) )
| number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
! [X2,X0,X1] :
( number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2)
| ? [X3,X4] :
( ! [X5] : ~ triangle(X3,X4,X5)
& sequential(X3,X4)
& on_path(X3,X2)
& on_path(X4,X2) )
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X2,X0,X1] :
( ( ! [X3,X4] :
( ( sequential(X3,X4)
& on_path(X3,X2)
& on_path(X4,X2) )
=> ? [X5] : triangle(X3,X4,X5) )
& path(X0,X1,X2) )
=> number_of_in(sequential_pairs,X2) = number_of_in(triangles,X2) ),
inference(rectify,[],[f16]) ).
fof(f16,axiom,
! [X1,X2,X3] :
( ( ! [X6,X7] :
( ( on_path(X6,X3)
& on_path(X7,X3)
& sequential(X6,X7) )
=> ? [X8] : triangle(X6,X7,X8) )
& path(X1,X2,X3) )
=> number_of_in(sequential_pairs,X3) = number_of_in(triangles,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
fof(f1281,plain,
( triangle(sK5(sK0),sK4(sK0),sK9(sK4(sK0),sK5(sK0)))
| ~ spl15_84 ),
inference(avatar_component_clause,[],[f1279]) ).
fof(f1297,plain,
~ spl15_86,
inference(avatar_contradiction_clause,[],[f1296]) ).
fof(f1296,plain,
( $false
| ~ spl15_86 ),
inference(resolution,[],[f1291,f219]) ).
fof(f1291,plain,
( ! [X2,X3] : ~ path(X2,X3,sK0)
| ~ spl15_86 ),
inference(avatar_component_clause,[],[f1290]) ).
fof(f1282,plain,
( spl15_83
| spl15_84
| ~ spl15_8
| spl15_23
| ~ spl15_24 ),
inference(avatar_split_clause,[],[f1274,f406,f402,f210,f1279,f1276]) ).
fof(f210,plain,
( spl15_8
<=> ! [X4,X0,X3,X2,X1] :
( ~ sequential(X2,X0)
| triangle(X2,X0,sK9(X0,X2))
| ~ precedes(X2,X0,X3)
| ~ shortest_path(X1,X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_8])]) ).
fof(f406,plain,
( spl15_24
<=> on_path(sK5(sK0),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl15_24])]) ).
fof(f1274,plain,
( ! [X10,X9] :
( triangle(sK5(sK0),sK4(sK0),sK9(sK4(sK0),sK5(sK0)))
| ~ shortest_path(X9,X10,sK0) )
| ~ spl15_8
| spl15_23
| ~ spl15_24 ),
inference(subsumption_resolution,[],[f1273,f472]) ).
fof(f472,plain,
( sequential(sK5(sK0),sK4(sK0))
| spl15_23 ),
inference(subsumption_resolution,[],[f471,f403]) ).
fof(f471,plain,
( number_of_in(triangles,sK0) = sF13
| sequential(sK5(sK0),sK4(sK0)) ),
inference(forward_demodulation,[],[f470,f235]) ).
fof(f470,plain,
( sequential(sK5(sK0),sK4(sK0))
| number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ),
inference(resolution,[],[f138,f219]) ).
fof(f138,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0)
| sequential(sK5(X0),sK4(X0)) ),
inference(cnf_transformation,[],[f80]) ).
fof(f1273,plain,
( ! [X10,X9] :
( ~ sequential(sK5(sK0),sK4(sK0))
| triangle(sK5(sK0),sK4(sK0),sK9(sK4(sK0),sK5(sK0)))
| ~ shortest_path(X9,X10,sK0) )
| ~ spl15_8
| spl15_23
| ~ spl15_24 ),
inference(resolution,[],[f1264,f211]) ).
fof(f211,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ precedes(X2,X0,X3)
| triangle(X2,X0,sK9(X0,X2))
| ~ sequential(X2,X0)
| ~ shortest_path(X1,X4,X3) )
| ~ spl15_8 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f1264,plain,
( precedes(sK5(sK0),sK4(sK0),sK0)
| spl15_23
| ~ spl15_24 ),
inference(subsumption_resolution,[],[f1263,f408]) ).
fof(f408,plain,
( on_path(sK5(sK0),sK0)
| ~ spl15_24 ),
inference(avatar_component_clause,[],[f406]) ).
fof(f1263,plain,
( ~ on_path(sK5(sK0),sK0)
| precedes(sK5(sK0),sK4(sK0),sK0)
| spl15_23 ),
inference(resolution,[],[f990,f472]) ).
fof(f990,plain,
( ! [X1] :
( ~ sequential(X1,sK4(sK0))
| precedes(X1,sK4(sK0),sK0)
| ~ on_path(X1,sK0) )
| spl15_23 ),
inference(resolution,[],[f565,f420]) ).
fof(f420,plain,
( on_path(sK4(sK0),sK0)
| spl15_23 ),
inference(subsumption_resolution,[],[f419,f403]) ).
fof(f419,plain,
( on_path(sK4(sK0),sK0)
| number_of_in(triangles,sK0) = sF13 ),
inference(forward_demodulation,[],[f418,f235]) ).
fof(f418,plain,
( number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0)
| on_path(sK4(sK0),sK0) ),
inference(resolution,[],[f139,f219]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| on_path(sK4(X0),X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f565,plain,
! [X0,X1] :
( ~ on_path(X1,sK0)
| ~ on_path(X0,sK0)
| ~ sequential(X0,X1)
| precedes(X0,X1,sK0) ),
inference(resolution,[],[f152,f219]) ).
fof(f152,plain,
! [X2,X3,X0,X1,X4] :
( ~ path(X2,X1,X0)
| precedes(X3,X4,X0)
| ~ sequential(X3,X4)
| ~ on_path(X3,X0)
| ~ on_path(X4,X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ~ path(X2,X1,X0)
| ! [X3,X4] :
( ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| precedes(X3,X4,X0)
| ( ~ sequential(X3,X4)
& ! [X5] :
( ~ sequential(X3,X5)
| ~ precedes(X5,X4,X0) ) ) ) ),
inference(rectify,[],[f50]) ).
fof(f50,plain,
! [X2,X0,X1] :
( ~ path(X1,X0,X2)
| ! [X4,X3] :
( ~ on_path(X3,X2)
| ~ on_path(X4,X2)
| precedes(X4,X3,X2)
| ( ~ sequential(X4,X3)
& ! [X5] :
( ~ sequential(X4,X5)
| ~ precedes(X5,X3,X2) ) ) ) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
! [X1,X2,X0] :
( ! [X3,X4] :
( precedes(X4,X3,X2)
| ~ on_path(X4,X2)
| ~ on_path(X3,X2)
| ( ~ sequential(X4,X3)
& ! [X5] :
( ~ sequential(X4,X5)
| ~ precedes(X5,X3,X2) ) ) )
| ~ path(X1,X0,X2) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,plain,
! [X1,X2,X0] :
( path(X1,X0,X2)
=> ! [X3,X4] :
( ( on_path(X4,X2)
& on_path(X3,X2)
& ( ? [X5] :
( precedes(X5,X3,X2)
& sequential(X4,X5) )
| sequential(X4,X3) ) )
=> precedes(X4,X3,X2) ) ),
inference(rectify,[],[f9]) ).
fof(f9,axiom,
! [X2,X1,X3] :
( path(X1,X2,X3)
=> ! [X7,X6] :
( ( on_path(X6,X3)
& ( ? [X8] :
( precedes(X8,X7,X3)
& sequential(X6,X8) )
| sequential(X6,X7) )
& on_path(X7,X3) )
=> precedes(X6,X7,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_defn) ).
fof(f416,plain,
~ spl15_23,
inference(avatar_contradiction_clause,[],[f415]) ).
fof(f415,plain,
( $false
| ~ spl15_23 ),
inference(subsumption_resolution,[],[f414,f179]) ).
fof(f179,plain,
~ less_or_equal(sF13,sF14),
inference(definition_folding,[],[f107,f178,f177,f176]) ).
fof(f178,plain,
number_of_in(triangles,graph) = sF14,
introduced(function_definition,[]) ).
fof(f107,plain,
~ less_or_equal(minus(length_of(sK0),n1),number_of_in(triangles,graph)),
inference(cnf_transformation,[],[f65]) ).
fof(f414,plain,
( less_or_equal(sF13,sF14)
| ~ spl15_23 ),
inference(forward_demodulation,[],[f411,f178]) ).
fof(f411,plain,
( less_or_equal(sF13,number_of_in(triangles,graph))
| ~ spl15_23 ),
inference(superposition,[],[f115,f404]) ).
fof(f404,plain,
( number_of_in(triangles,sK0) = sF13
| ~ spl15_23 ),
inference(avatar_component_clause,[],[f402]) ).
fof(f115,plain,
! [X0,X1] : less_or_equal(number_of_in(X1,X0),number_of_in(X1,graph)),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] : less_or_equal(number_of_in(X1,X0),number_of_in(X1,graph)),
inference(rectify,[],[f17]) ).
fof(f17,axiom,
! [X11,X10] : less_or_equal(number_of_in(X10,X11),number_of_in(X10,graph)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',graph_has_them_all) ).
fof(f409,plain,
( spl15_23
| spl15_24 ),
inference(avatar_split_clause,[],[f400,f406,f402]) ).
fof(f400,plain,
( on_path(sK5(sK0),sK0)
| number_of_in(triangles,sK0) = sF13 ),
inference(forward_demodulation,[],[f399,f235]) ).
fof(f399,plain,
( on_path(sK5(sK0),sK0)
| number_of_in(triangles,sK0) = number_of_in(sequential_pairs,sK0) ),
inference(resolution,[],[f137,f219]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| on_path(sK5(X0),X0)
| number_of_in(sequential_pairs,X0) = number_of_in(triangles,X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f214,plain,
spl15_2,
inference(avatar_split_clause,[],[f109,f184]) ).
fof(f184,plain,
( spl15_2
<=> complete ),
introduced(avatar_definition,[new_symbols(naming,[spl15_2])]) ).
fof(f109,plain,
complete,
inference(cnf_transformation,[],[f65]) ).
fof(f212,plain,
( ~ spl15_2
| spl15_8 ),
inference(avatar_split_clause,[],[f159,f210,f184]) ).
fof(f159,plain,
! [X2,X3,X0,X1,X4] :
( ~ sequential(X2,X0)
| ~ shortest_path(X1,X4,X3)
| ~ complete
| ~ precedes(X2,X0,X3)
| triangle(X2,X0,sK9(X0,X2)) ),
inference(cnf_transformation,[],[f99]) ).
fof(f99,plain,
( ! [X0,X1,X2,X3,X4] :
( triangle(X2,X0,sK9(X0,X2))
| ~ sequential(X2,X0)
| ~ shortest_path(X1,X4,X3)
| ~ precedes(X2,X0,X3) )
| ~ complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f97,f98]) ).
fof(f98,plain,
! [X0,X2] :
( ? [X5] : triangle(X2,X0,X5)
=> triangle(X2,X0,sK9(X0,X2)) ),
introduced(choice_axiom,[]) ).
fof(f97,plain,
( ! [X0,X1,X2,X3,X4] :
( ? [X5] : triangle(X2,X0,X5)
| ~ sequential(X2,X0)
| ~ shortest_path(X1,X4,X3)
| ~ precedes(X2,X0,X3) )
| ~ complete ),
inference(rectify,[],[f42]) ).
fof(f42,plain,
( ! [X0,X2,X4,X3,X1] :
( ? [X5] : triangle(X4,X0,X5)
| ~ sequential(X4,X0)
| ~ shortest_path(X2,X1,X3)
| ~ precedes(X4,X0,X3) )
| ~ complete ),
inference(flattening,[],[f41]) ).
fof(f41,plain,
( ! [X2,X1,X3,X4,X0] :
( ? [X5] : triangle(X4,X0,X5)
| ~ precedes(X4,X0,X3)
| ~ shortest_path(X2,X1,X3)
| ~ sequential(X4,X0) )
| ~ complete ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
( complete
=> ! [X2,X1,X3,X4,X0] :
( ( precedes(X4,X0,X3)
& shortest_path(X2,X1,X3)
& sequential(X4,X0) )
=> ? [X5] : triangle(X4,X0,X5) ) ),
inference(rectify,[],[f18]) ).
fof(f18,axiom,
( complete
=> ! [X7,X2,X1,X3,X6] :
( ( sequential(X6,X7)
& precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ? [X8] : triangle(X6,X7,X8) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sequential_is_triangle) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRA002+3 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.06/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.12/0.33 % Computer : n001.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Aug 29 22:21:30 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.49 % (29819)dis+21_1:1_av=off:er=filter:slsq=on:slsqc=0:slsqr=1,1:sp=frequency:to=lpo:i=498:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/498Mi)
% 0.19/0.49 % (29811)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 0.19/0.49 % (29803)fmb+10_1:1_fmbsr=2.0:nm=4:skr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50 % (29801)ott+33_1:4_s2a=on:tgt=ground:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50 % (29805)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.19/0.51 TRYING [1]
% 0.19/0.51 TRYING [2]
% 0.19/0.51 % (29800)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.51 % (29821)ott+10_1:1_kws=precedence:tgt=ground:i=482:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/482Mi)
% 0.19/0.52 % (29799)ott+4_1:1_av=off:bd=off:nwc=5.0:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=37:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/37Mi)
% 0.19/0.52 % (29809)ott+10_1:28_bd=off:bs=on:tgt=ground:i=101:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/101Mi)
% 0.19/0.52 % (29802)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=48:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/48Mi)
% 0.19/0.52 % (29804)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 1.38/0.52 % (29825)ott+33_1:4_s2a=on:tgt=ground:i=439:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/439Mi)
% 1.38/0.52 % (29797)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 1.38/0.52 % (29798)ott+10_1:32_abs=on:br=off:urr=ec_only:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.38/0.52 % (29812)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=75:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/75Mi)
% 1.38/0.52 TRYING [3]
% 1.38/0.52 % (29805)Instruction limit reached!
% 1.38/0.52 % (29805)------------------------------
% 1.38/0.52 % (29805)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.38/0.52 % (29805)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.38/0.52 % (29805)Termination reason: Unknown
% 1.38/0.52 % (29805)Termination phase: Property scanning
% 1.38/0.52
% 1.38/0.52 % (29805)Memory used [KB]: 1023
% 1.38/0.52 % (29805)Time elapsed: 0.004 s
% 1.38/0.52 % (29805)Instructions burned: 3 (million)
% 1.38/0.52 % (29805)------------------------------
% 1.38/0.52 % (29805)------------------------------
% 1.38/0.53 % (29824)ott+11_2:3_av=off:fde=unused:nwc=5.0:tgt=ground:i=177:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/177Mi)
% 1.38/0.53 % (29813)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.38/0.53 % (29826)ott+10_7:2_awrs=decay:awrsf=8:bd=preordered:drc=off:fd=preordered:fde=unused:fsr=off:slsq=on:slsqc=2:slsqr=5,8:sp=const_min:spb=units:to=lpo:i=355:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/355Mi)
% 1.38/0.53 % (29820)ott+11_1:1_drc=off:nwc=5.0:slsq=on:slsqc=1:spb=goal_then_units:to=lpo:i=467:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/467Mi)
% 1.38/0.53 % (29822)ott+10_1:5_bd=off:tgt=full:i=500:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/500Mi)
% 1.38/0.53 % (29804)Instruction limit reached!
% 1.38/0.53 % (29804)------------------------------
% 1.38/0.53 % (29804)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.38/0.53 % (29804)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.38/0.53 % (29804)Termination reason: Unknown
% 1.38/0.53 % (29804)Termination phase: Saturation
% 1.38/0.53
% 1.38/0.53 % (29804)Memory used [KB]: 5628
% 1.38/0.53 % (29804)Time elapsed: 0.126 s
% 1.38/0.53 % (29804)Instructions burned: 7 (million)
% 1.38/0.53 % (29804)------------------------------
% 1.38/0.53 % (29804)------------------------------
% 1.38/0.53 % (29817)ott+10_1:8_bsd=on:fsd=on:lcm=predicate:nwc=5.0:s2a=on:s2at=1.5:spb=goal_then_units:i=176:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/176Mi)
% 1.38/0.53 % (29816)ott+4_1:1_av=off:bd=off:nwc=5.0:rp=on:s2a=on:s2at=2.0:slsq=on:slsqc=2:slsql=off:slsqr=1,2:sp=frequency:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.38/0.53 % (29818)ott+3_1:1_gsp=on:lcm=predicate:i=138:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/138Mi)
% 1.38/0.53 % (29807)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 1.38/0.53 % (29814)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 1.38/0.53 % (29808)ott+10_1:32_bd=off:fsr=off:newcnf=on:tgt=full:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.38/0.53 % (29806)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 1.38/0.54 % (29810)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 1.52/0.54 TRYING [1]
% 1.52/0.54 TRYING [2]
% 1.52/0.54 % (29798)Refutation not found, incomplete strategy% (29798)------------------------------
% 1.52/0.54 % (29798)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.54 % (29798)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.54 % (29798)Termination reason: Refutation not found, incomplete strategy
% 1.52/0.54
% 1.52/0.54 % (29798)Memory used [KB]: 5628
% 1.52/0.54 % (29798)Time elapsed: 0.149 s
% 1.52/0.54 % (29798)Instructions burned: 7 (million)
% 1.52/0.54 % (29798)------------------------------
% 1.52/0.54 % (29798)------------------------------
% 1.52/0.54 % (29823)ins+10_1:1_awrs=decay:awrsf=30:bsr=unit_only:foolp=on:igrr=8/457:igs=10:igwr=on:nwc=1.5:sp=weighted_frequency:to=lpo:uhcvi=on:i=68:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/68Mi)
% 1.52/0.54 TRYING [3]
% 1.52/0.55 % (29815)ott+10_1:1_tgt=ground:i=100:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/100Mi)
% 1.52/0.56 TRYING [1]
% 1.52/0.56 TRYING [2]
% 1.52/0.56 % (29803)Instruction limit reached!
% 1.52/0.56 % (29803)------------------------------
% 1.52/0.56 % (29803)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.56 % (29803)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.56 % (29803)Termination reason: Unknown
% 1.52/0.56 % (29803)Termination phase: Finite model building SAT solving
% 1.52/0.56
% 1.52/0.56 % (29803)Memory used [KB]: 7675
% 1.52/0.56 % (29803)Time elapsed: 0.100 s
% 1.52/0.56 % (29803)Instructions burned: 51 (million)
% 1.52/0.56 % (29803)------------------------------
% 1.52/0.56 % (29803)------------------------------
% 1.52/0.57 TRYING [3]
% 1.52/0.57 % (29799)Instruction limit reached!
% 1.52/0.57 % (29799)------------------------------
% 1.52/0.57 % (29799)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.57 % (29799)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.57 % (29799)Termination reason: Unknown
% 1.52/0.57 % (29799)Termination phase: Saturation
% 1.52/0.57
% 1.52/0.57 % (29799)Memory used [KB]: 1407
% 1.52/0.57 % (29799)Time elapsed: 0.169 s
% 1.52/0.57 % (29799)Instructions burned: 38 (million)
% 1.52/0.57 % (29799)------------------------------
% 1.52/0.57 % (29799)------------------------------
% 1.52/0.60 % (29811)Instruction limit reached!
% 1.52/0.60 % (29811)------------------------------
% 1.52/0.60 % (29811)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.60 % (29811)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.60 % (29811)Termination reason: Unknown
% 1.52/0.60 % (29811)Termination phase: Saturation
% 1.52/0.60
% 1.52/0.60 % (29811)Memory used [KB]: 6524
% 1.52/0.60 % (29811)Time elapsed: 0.051 s
% 1.52/0.60 % (29811)Instructions burned: 69 (million)
% 1.52/0.60 % (29811)------------------------------
% 1.52/0.60 % (29811)------------------------------
% 1.52/0.60 % (29802)Instruction limit reached!
% 1.52/0.60 % (29802)------------------------------
% 1.52/0.60 % (29802)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.60 % (29802)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.60 % (29802)Termination reason: Unknown
% 1.52/0.60 % (29802)Termination phase: Saturation
% 1.52/0.60
% 1.52/0.60 % (29802)Memory used [KB]: 6268
% 1.52/0.60 % (29802)Time elapsed: 0.198 s
% 1.52/0.60 % (29802)Instructions burned: 49 (million)
% 1.52/0.60 % (29802)------------------------------
% 1.52/0.60 % (29802)------------------------------
% 1.52/0.60 % (29806)Instruction limit reached!
% 1.52/0.60 % (29806)------------------------------
% 1.52/0.60 % (29806)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.60 % (29806)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.60 % (29806)Termination reason: Unknown
% 1.52/0.60 % (29806)Termination phase: Saturation
% 1.52/0.60
% 1.52/0.60 % (29806)Memory used [KB]: 1663
% 1.52/0.60 % (29806)Time elapsed: 0.200 s
% 1.52/0.60 % (29806)Instructions burned: 51 (million)
% 1.52/0.60 % (29806)------------------------------
% 1.52/0.60 % (29806)------------------------------
% 1.52/0.61 % (29801)Instruction limit reached!
% 1.52/0.61 % (29801)------------------------------
% 1.52/0.61 % (29801)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.61 % (29801)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.61 % (29801)Termination reason: Unknown
% 1.52/0.61 % (29801)Termination phase: Saturation
% 1.52/0.61
% 1.52/0.61 % (29801)Memory used [KB]: 6268
% 1.52/0.61 % (29801)Time elapsed: 0.209 s
% 1.52/0.61 % (29801)Instructions burned: 51 (million)
% 1.52/0.61 % (29801)------------------------------
% 1.52/0.61 % (29801)------------------------------
% 1.52/0.61 % (29814)Instruction limit reached!
% 1.52/0.61 % (29814)------------------------------
% 1.52/0.61 % (29814)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.62 % (29807)Instruction limit reached!
% 1.52/0.62 % (29807)------------------------------
% 1.52/0.62 % (29807)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.62 % (29807)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.62 % (29807)Termination reason: Unknown
% 1.52/0.62 % (29807)Termination phase: Saturation
% 1.52/0.62
% 1.52/0.62 % (29807)Memory used [KB]: 6524
% 1.52/0.62 % (29807)Time elapsed: 0.235 s
% 1.52/0.62 % (29807)Instructions burned: 51 (million)
% 1.52/0.62 % (29807)------------------------------
% 1.52/0.62 % (29807)------------------------------
% 1.52/0.62 % (29814)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.62 % (29814)Termination reason: Unknown
% 1.52/0.62 % (29814)Termination phase: Finite model building SAT solving
% 1.52/0.62
% 1.52/0.62 % (29814)Memory used [KB]: 7803
% 1.52/0.62 % (29814)Time elapsed: 0.189 s
% 1.52/0.62 % (29814)Instructions burned: 60 (million)
% 1.52/0.62 % (29814)------------------------------
% 1.52/0.62 % (29814)------------------------------
% 1.52/0.62 % (29800)Instruction limit reached!
% 1.52/0.62 % (29800)------------------------------
% 1.52/0.62 % (29800)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 1.52/0.62 % (29800)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 1.52/0.62 % (29800)Termination reason: Unknown
% 1.52/0.62 % (29800)Termination phase: Saturation
% 1.52/0.62
% 1.52/0.62 % (29800)Memory used [KB]: 6652
% 1.52/0.62 % (29800)Time elapsed: 0.238 s
% 1.52/0.62 % (29800)Instructions burned: 51 (million)
% 1.52/0.62 % (29800)------------------------------
% 1.52/0.62 % (29800)------------------------------
% 1.52/0.63 % (29825)First to succeed.
% 2.20/0.64 TRYING [4]
% 2.20/0.65 % (29825)Refutation found. Thanks to Tanya!
% 2.20/0.65 % SZS status Theorem for theBenchmark
% 2.20/0.65 % SZS output start Proof for theBenchmark
% See solution above
% 2.20/0.65 % (29825)------------------------------
% 2.20/0.65 % (29825)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 2.20/0.65 % (29825)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 2.20/0.65 % (29825)Termination reason: Refutation
% 2.20/0.65
% 2.20/0.65 % (29825)Memory used [KB]: 6268
% 2.20/0.65 % (29825)Time elapsed: 0.233 s
% 2.20/0.65 % (29825)Instructions burned: 58 (million)
% 2.20/0.65 % (29825)------------------------------
% 2.20/0.65 % (29825)------------------------------
% 2.20/0.65 % (29796)Success in time 0.298 s
%------------------------------------------------------------------------------