TSTP Solution File: GRA003+1 by SnakeForV---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV---1.0
% Problem : GRA003+1 : 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_uns --cores 0 -t %d %s
% Computer : n020.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 16:13:20 EDT 2022
% Result : Theorem 0.19s 0.51s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 27
% Syntax : Number of formulae : 127 ( 10 unt; 0 def)
% Number of atoms : 544 ( 104 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 660 ( 243 ~; 211 |; 161 &)
% ( 19 <=>; 20 =>; 0 <=; 6 <~>)
% Maximal formula depth : 15 ( 7 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 27 ( 25 usr; 10 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 304 ( 260 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f409,plain,
$false,
inference(avatar_sat_refutation,[],[f224,f229,f245,f271,f338,f341,f354,f363,f374,f408]) ).
fof(f408,plain,
~ spl38_12,
inference(avatar_contradiction_clause,[],[f407]) ).
fof(f407,plain,
( $false
| ~ spl38_12 ),
inference(subsumption_resolution,[],[f406,f226]) ).
fof(f226,plain,
~ sP34(sK3),
inference(resolution,[],[f94,f195]) ).
fof(f195,plain,
! [X3,X0,X1] :
( ~ shortest_path(X1,X0,X3)
| ~ sP34(X3) ),
inference(general_splitting,[],[f193,f194_D]) ).
fof(f194,plain,
! [X3,X4] :
( ~ sP33(X4,X3)
| sP34(X3) ),
inference(cnf_transformation,[],[f194_D]) ).
fof(f194_D,plain,
! [X3] :
( ! [X4] : ~ sP33(X4,X3)
<=> ~ sP34(X3) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP34])]) ).
fof(f193,plain,
! [X3,X0,X1,X4] :
( ~ shortest_path(X1,X0,X3)
| ~ sP33(X4,X3) ),
inference(general_splitting,[],[f136,f192_D]) ).
fof(f192,plain,
! [X2,X3,X4] :
( ~ precedes(X4,X2,X3)
| sP33(X4,X3)
| ~ precedes(X2,X4,X3) ),
inference(cnf_transformation,[],[f192_D]) ).
fof(f192_D,plain,
! [X3,X4] :
( ! [X2] :
( ~ precedes(X4,X2,X3)
| ~ precedes(X2,X4,X3) )
<=> ~ sP33(X4,X3) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP33])]) ).
fof(f136,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X2,X4,X3)
| ~ precedes(X4,X2,X3)
| ~ shortest_path(X1,X0,X3) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ precedes(X2,X4,X3)
& ! [X5] :
( tail_of(X5) != tail_of(X4)
| head_of(X2) != head_of(X5) ) )
| ~ precedes(X4,X2,X3)
| ~ shortest_path(X1,X0,X3) ),
inference(rectify,[],[f57]) ).
fof(f57,plain,
! [X2,X3,X0,X4,X1] :
( ( ~ precedes(X0,X1,X4)
& ! [X5] :
( tail_of(X1) != tail_of(X5)
| head_of(X0) != head_of(X5) ) )
| ~ precedes(X1,X0,X4)
| ~ shortest_path(X3,X2,X4) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
! [X1,X3,X0,X4,X2] :
( ( ~ precedes(X0,X1,X4)
& ! [X5] :
( tail_of(X1) != tail_of(X5)
| head_of(X0) != head_of(X5) ) )
| ~ precedes(X1,X0,X4)
| ~ shortest_path(X3,X2,X4) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,plain,
! [X1,X3,X0,X4,X2] :
( ( precedes(X1,X0,X4)
& shortest_path(X3,X2,X4) )
=> ( ~ ? [X5] :
( head_of(X0) = head_of(X5)
& tail_of(X1) = tail_of(X5) )
& ~ precedes(X0,X1,X4) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X7,X6,X2,X1,X3] :
( ( shortest_path(X1,X2,X3)
& precedes(X6,X7,X3) )
=> ( ~ ? [X8] :
( head_of(X8) = head_of(X7)
& tail_of(X8) = tail_of(X6) )
& ~ precedes(X7,X6,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_properties) ).
fof(f94,plain,
shortest_path(sK4,sK0,sK3),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
( ( ~ edge(sK2)
| sK1 = sK2
| ~ edge(sK1)
| sK4 = sK0
| ~ vertex(sK4)
| ~ vertex(sK0)
| ~ path(sK4,sK0,sK3) )
& precedes(sK1,sK2,sK3)
& shortest_path(sK4,sK0,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4])],[f39,f60]) ).
fof(f60,plain,
( ? [X0,X1,X2,X3,X4] :
( ( ~ edge(X2)
| X1 = X2
| ~ edge(X1)
| X0 = X4
| ~ vertex(X4)
| ~ vertex(X0)
| ~ path(X4,X0,X3) )
& precedes(X1,X2,X3)
& shortest_path(X4,X0,X3) )
=> ( ( ~ edge(sK2)
| sK1 = sK2
| ~ edge(sK1)
| sK4 = sK0
| ~ vertex(sK4)
| ~ vertex(sK0)
| ~ path(sK4,sK0,sK3) )
& precedes(sK1,sK2,sK3)
& shortest_path(sK4,sK0,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
? [X0,X1,X2,X3,X4] :
( ( ~ edge(X2)
| X1 = X2
| ~ edge(X1)
| X0 = X4
| ~ vertex(X4)
| ~ vertex(X0)
| ~ path(X4,X0,X3) )
& precedes(X1,X2,X3)
& shortest_path(X4,X0,X3) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
? [X0,X1,X2,X3,X4] :
( ( ~ edge(X2)
| X1 = X2
| ~ edge(X1)
| X0 = X4
| ~ vertex(X4)
| ~ vertex(X0)
| ~ path(X4,X0,X3) )
& shortest_path(X4,X0,X3)
& precedes(X1,X2,X3) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( shortest_path(X4,X0,X3)
& precedes(X1,X2,X3) )
=> ( X1 != X2
& path(X4,X0,X3)
& edge(X1)
& vertex(X0)
& X0 != X4
& vertex(X4)
& edge(X2) ) ),
inference(rectify,[],[f19]) ).
fof(f19,negated_conjecture,
~ ! [X2,X6,X7,X3,X1] :
( ( shortest_path(X1,X2,X3)
& precedes(X6,X7,X3) )
=> ( edge(X7)
& X1 != X2
& edge(X6)
& X6 != X7
& vertex(X1)
& path(X1,X2,X3)
& vertex(X2) ) ),
inference(negated_conjecture,[],[f18]) ).
fof(f18,conjecture,
! [X2,X6,X7,X3,X1] :
( ( shortest_path(X1,X2,X3)
& precedes(X6,X7,X3) )
=> ( edge(X7)
& X1 != X2
& edge(X6)
& X6 != X7
& vertex(X1)
& path(X1,X2,X3)
& vertex(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vertices_and_edges) ).
fof(f406,plain,
( sP34(sK3)
| ~ spl38_12 ),
inference(resolution,[],[f266,f194]) ).
fof(f266,plain,
( sP33(sK1,sK3)
| ~ spl38_12 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f264,plain,
( spl38_12
<=> sP33(sK1,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl38_12])]) ).
fof(f374,plain,
( ~ spl38_1
| spl38_13 ),
inference(avatar_contradiction_clause,[],[f373]) ).
fof(f373,plain,
( $false
| ~ spl38_1
| spl38_13 ),
inference(subsumption_resolution,[],[f364,f370]) ).
fof(f370,plain,
( ~ precedes(sK1,sK1,sK3)
| ~ spl38_1
| spl38_13 ),
inference(backward_demodulation,[],[f270,f207]) ).
fof(f207,plain,
( sK1 = sK2
| ~ spl38_1 ),
inference(avatar_component_clause,[],[f205]) ).
fof(f205,plain,
( spl38_1
<=> sK1 = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl38_1])]) ).
fof(f270,plain,
( ~ precedes(sK2,sK1,sK3)
| spl38_13 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f268,plain,
( spl38_13
<=> precedes(sK2,sK1,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl38_13])]) ).
fof(f364,plain,
( precedes(sK1,sK1,sK3)
| ~ spl38_1 ),
inference(backward_demodulation,[],[f95,f207]) ).
fof(f95,plain,
precedes(sK1,sK2,sK3),
inference(cnf_transformation,[],[f61]) ).
fof(f363,plain,
~ spl38_4,
inference(avatar_contradiction_clause,[],[f362]) ).
fof(f362,plain,
( $false
| ~ spl38_4 ),
inference(subsumption_resolution,[],[f355,f149]) ).
fof(f149,plain,
! [X2,X1] : ~ shortest_path(X2,X2,X1),
inference(equality_resolution,[],[f137]) ).
fof(f137,plain,
! [X2,X0,X1] :
( X0 != X2
| ~ shortest_path(X2,X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( shortest_path(X2,X0,X1)
| ~ path(X2,X0,X1)
| ( path(X2,X0,sK11(X0,X1,X2))
& ~ less_or_equal(length_of(X1),length_of(sK11(X0,X1,X2))) )
| X0 = X2 )
& ( ( path(X2,X0,X1)
& ! [X4] :
( ~ path(X2,X0,X4)
| less_or_equal(length_of(X1),length_of(X4)) )
& X0 != X2 )
| ~ shortest_path(X2,X0,X1) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f90,f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ? [X3] :
( path(X2,X0,X3)
& ~ less_or_equal(length_of(X1),length_of(X3)) )
=> ( path(X2,X0,sK11(X0,X1,X2))
& ~ less_or_equal(length_of(X1),length_of(sK11(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f90,plain,
! [X0,X1,X2] :
( ( 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 )
& ( ( path(X2,X0,X1)
& ! [X4] :
( ~ path(X2,X0,X4)
| less_or_equal(length_of(X1),length_of(X4)) )
& X0 != X2 )
| ~ shortest_path(X2,X0,X1) ) ),
inference(rectify,[],[f89]) ).
fof(f89,plain,
! [X1,X2,X0] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| ? [X3] :
( path(X0,X1,X3)
& ~ less_or_equal(length_of(X2),length_of(X3)) )
| X0 = X1 )
& ( ( path(X0,X1,X2)
& ! [X3] :
( ~ path(X0,X1,X3)
| less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1 )
| ~ shortest_path(X0,X1,X2) ) ),
inference(flattening,[],[f88]) ).
fof(f88,plain,
! [X1,X2,X0] :
( ( shortest_path(X0,X1,X2)
| ~ path(X0,X1,X2)
| ? [X3] :
( path(X0,X1,X3)
& ~ less_or_equal(length_of(X2),length_of(X3)) )
| X0 = X1 )
& ( ( path(X0,X1,X2)
& ! [X3] :
( ~ path(X0,X1,X3)
| less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1 )
| ~ shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X1,X2,X0] :
( shortest_path(X0,X1,X2)
<=> ( path(X0,X1,X2)
& ! [X3] :
( ~ path(X0,X1,X3)
| less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1 ) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,plain,
! [X1,X0,X2] :
( shortest_path(X0,X1,X2)
<=> ( path(X0,X1,X2)
& ! [X3] :
( path(X0,X1,X3)
=> less_or_equal(length_of(X2),length_of(X3)) )
& X0 != X1 ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X1,X2,X9] :
( ( X1 != X2
& path(X1,X2,X9)
& ! [X3] :
( path(X1,X2,X3)
=> less_or_equal(length_of(X9),length_of(X3)) ) )
<=> shortest_path(X1,X2,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',shortest_path_defn) ).
fof(f355,plain,
( shortest_path(sK0,sK0,sK3)
| ~ spl38_4 ),
inference(backward_demodulation,[],[f94,f219]) ).
fof(f219,plain,
( sK4 = sK0
| ~ spl38_4 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f217,plain,
( spl38_4
<=> sK4 = sK0 ),
introduced(avatar_definition,[new_symbols(naming,[spl38_4])]) ).
fof(f354,plain,
( spl38_2
| ~ spl38_3 ),
inference(avatar_split_clause,[],[f353,f213,f209]) ).
fof(f209,plain,
( spl38_2
<=> edge(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl38_2])]) ).
fof(f213,plain,
( spl38_3
<=> path(sK4,sK0,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl38_3])]) ).
fof(f353,plain,
( edge(sK1)
| ~ spl38_3 ),
inference(subsumption_resolution,[],[f349,f294]) ).
fof(f294,plain,
( ~ sP31(sK3)
| ~ spl38_3 ),
inference(resolution,[],[f214,f189]) ).
fof(f189,plain,
! [X2,X3,X0] :
( ~ path(X2,X3,X0)
| ~ sP31(X0) ),
inference(general_splitting,[],[f131,f188_D]) ).
fof(f188,plain,
! [X0,X1] :
( ~ on_path(X1,X0)
| sP31(X0)
| edge(X1) ),
inference(cnf_transformation,[],[f188_D]) ).
fof(f188_D,plain,
! [X0] :
( ! [X1] :
( ~ on_path(X1,X0)
| edge(X1) )
<=> ~ sP31(X0) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP31])]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( edge(X1)
| ~ on_path(X1,X0)
| ~ path(X2,X3,X0) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1,X2,X3] :
( ( in_path(head_of(X1),X0)
& edge(X1)
& in_path(tail_of(X1),X0) )
| ~ on_path(X1,X0)
| ~ path(X2,X3,X0) ),
inference(rectify,[],[f59]) ).
fof(f59,plain,
! [X3,X0,X2,X1] :
( ( in_path(head_of(X0),X3)
& edge(X0)
& in_path(tail_of(X0),X3) )
| ~ on_path(X0,X3)
| ~ path(X2,X1,X3) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X2,X1,X3,X0] :
( ( in_path(head_of(X0),X3)
& edge(X0)
& in_path(tail_of(X0),X3) )
| ~ on_path(X0,X3)
| ~ path(X2,X1,X3) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,plain,
! [X2,X1,X3,X0] :
( ( on_path(X0,X3)
& path(X2,X1,X3) )
=> ( in_path(head_of(X0),X3)
& edge(X0)
& in_path(tail_of(X0),X3) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X0,X2,X1,X3] :
( ( path(X1,X2,X3)
& on_path(X0,X3) )
=> ( in_path(head_of(X0),X3)
& edge(X0)
& in_path(tail_of(X0),X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',on_path_properties) ).
fof(f214,plain,
( path(sK4,sK0,sK3)
| ~ spl38_3 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f349,plain,
( sP31(sK3)
| edge(sK1)
| ~ spl38_3 ),
inference(resolution,[],[f335,f188]) ).
fof(f335,plain,
( on_path(sK1,sK3)
| ~ spl38_3 ),
inference(subsumption_resolution,[],[f334,f291]) ).
fof(f291,plain,
( ~ sP27(sK3)
| ~ spl38_3 ),
inference(resolution,[],[f214,f181]) ).
fof(f181,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| ~ sP27(X2) ),
inference(general_splitting,[],[f179,f180_D]) ).
fof(f180,plain,
! [X2,X4] :
( ~ sP26(X4,X2)
| sP27(X2)
| on_path(X4,X2) ),
inference(cnf_transformation,[],[f180_D]) ).
fof(f180_D,plain,
! [X2] :
( ! [X4] :
( ~ sP26(X4,X2)
| on_path(X4,X2) )
<=> ~ sP27(X2) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP27])]) ).
fof(f179,plain,
! [X2,X0,X1,X4] :
( on_path(X4,X2)
| ~ path(X0,X1,X2)
| ~ sP26(X4,X2) ),
inference(general_splitting,[],[f113,f178_D]) ).
fof(f178,plain,
! [X2,X3,X4] :
( ~ precedes(X4,X3,X2)
| sP26(X4,X2) ),
inference(cnf_transformation,[],[f178_D]) ).
fof(f178_D,plain,
! [X2,X4] :
( ! [X3] : ~ precedes(X4,X3,X2)
<=> ~ sP26(X4,X2) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP26])]) ).
fof(f113,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X4,X3,X2)
| on_path(X4,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ~ precedes(X4,X3,X2)
| ( ( ~ sequential(X4,X3)
| ! [X5] :
( ~ sequential(X4,X5)
| ~ precedes(X5,X3,X2) ) )
& ( sequential(X4,X3)
| ( sequential(X4,sK8(X2,X3,X4))
& precedes(sK8(X2,X3,X4),X3,X2) ) )
& on_path(X4,X2)
& on_path(X3,X2) ) )
| ~ path(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f74,f75]) ).
fof(f75,plain,
! [X2,X3,X4] :
( ? [X6] :
( sequential(X4,X6)
& precedes(X6,X3,X2) )
=> ( sequential(X4,sK8(X2,X3,X4))
& precedes(sK8(X2,X3,X4),X3,X2) ) ),
introduced(choice_axiom,[]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ~ precedes(X4,X3,X2)
| ( ( ~ sequential(X4,X3)
| ! [X5] :
( ~ sequential(X4,X5)
| ~ precedes(X5,X3,X2) ) )
& ( sequential(X4,X3)
| ? [X6] :
( sequential(X4,X6)
& precedes(X6,X3,X2) ) )
& on_path(X4,X2)
& on_path(X3,X2) ) )
| ~ path(X0,X1,X2) ),
inference(rectify,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ~ precedes(X4,X3,X2)
| ( ( ~ sequential(X4,X3)
| ! [X5] :
( ~ sequential(X4,X5)
| ~ precedes(X5,X3,X2) ) )
& ( sequential(X4,X3)
| ? [X5] :
( sequential(X4,X5)
& precedes(X5,X3,X2) ) )
& on_path(X4,X2)
& on_path(X3,X2) ) )
| ~ path(X0,X1,X2) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ~ precedes(X4,X3,X2)
| ( ( ~ sequential(X4,X3)
| ! [X5] :
( ~ sequential(X4,X5)
| ~ precedes(X5,X3,X2) ) )
& ( sequential(X4,X3)
| ? [X5] :
( sequential(X4,X5)
& precedes(X5,X3,X2) ) )
& on_path(X4,X2)
& on_path(X3,X2) ) )
| ~ path(X0,X1,X2) ),
inference(nnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ~ precedes(X4,X3,X2)
| ( ( ? [X5] :
( sequential(X4,X5)
& precedes(X5,X3,X2) )
<~> sequential(X4,X3) )
& on_path(X4,X2)
& on_path(X3,X2) ) )
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,plain,
! [X0,X1,X2] :
( path(X0,X1,X2)
=> ! [X3,X4] :
( precedes(X4,X3,X2)
=> ( ( ? [X5] :
( sequential(X4,X5)
& precedes(X5,X3,X2) )
<~> sequential(X4,X3) )
& on_path(X4,X2)
& on_path(X3,X2) ) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X1,X2,X3] :
( path(X1,X2,X3)
=> ! [X7,X6] :
( precedes(X6,X7,X3)
=> ( on_path(X6,X3)
& on_path(X7,X3)
& ( ? [X8] :
( sequential(X6,X8)
& precedes(X8,X7,X3) )
<~> sequential(X6,X7) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',precedes_properties) ).
fof(f334,plain,
( on_path(sK1,sK3)
| sP27(sK3) ),
inference(resolution,[],[f233,f180]) ).
fof(f233,plain,
sP26(sK1,sK3),
inference(resolution,[],[f95,f178]) ).
fof(f341,plain,
( ~ spl38_3
| ~ spl38_7 ),
inference(avatar_contradiction_clause,[],[f340]) ).
fof(f340,plain,
( $false
| ~ spl38_3
| ~ spl38_7 ),
inference(subsumption_resolution,[],[f339,f292]) ).
fof(f292,plain,
( ~ sP29(sK3)
| ~ spl38_3 ),
inference(resolution,[],[f214,f185]) ).
fof(f185,plain,
! [X2,X0,X1] :
( ~ path(X0,X1,X2)
| ~ sP29(X2) ),
inference(general_splitting,[],[f183,f184_D]) ).
fof(f184,plain,
! [X2,X4] :
( ~ sP28(X4,X2)
| sP29(X2) ),
inference(cnf_transformation,[],[f184_D]) ).
fof(f184_D,plain,
! [X2] :
( ! [X4] : ~ sP28(X4,X2)
<=> ~ sP29(X2) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP29])]) ).
fof(f183,plain,
! [X2,X0,X1,X4] :
( ~ path(X0,X1,X2)
| ~ sP28(X4,X2) ),
inference(general_splitting,[],[f112,f182_D]) ).
fof(f182,plain,
! [X2,X3,X4] :
( ~ precedes(X4,X3,X2)
| on_path(X3,X2)
| sP28(X4,X2) ),
inference(cnf_transformation,[],[f182_D]) ).
fof(f182_D,plain,
! [X2,X4] :
( ! [X3] :
( ~ precedes(X4,X3,X2)
| on_path(X3,X2) )
<=> ~ sP28(X4,X2) ),
introduced(general_splitting_component_introduction,[new_symbols(naming,[sP28])]) ).
fof(f112,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X4,X3,X2)
| on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f76]) ).
fof(f339,plain,
( sP29(sK3)
| ~ spl38_7 ),
inference(resolution,[],[f244,f184]) ).
fof(f244,plain,
( sP28(sK1,sK3)
| ~ spl38_7 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f242,plain,
( spl38_7
<=> sP28(sK1,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl38_7])]) ).
fof(f338,plain,
( spl38_5
| ~ spl38_3
| ~ spl38_6 ),
inference(avatar_split_clause,[],[f337,f238,f213,f221]) ).
fof(f221,plain,
( spl38_5
<=> edge(sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl38_5])]) ).
fof(f238,plain,
( spl38_6
<=> on_path(sK2,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl38_6])]) ).
fof(f337,plain,
( edge(sK2)
| ~ spl38_3
| ~ spl38_6 ),
inference(subsumption_resolution,[],[f336,f294]) ).
fof(f336,plain,
( sP31(sK3)
| edge(sK2)
| ~ spl38_6 ),
inference(resolution,[],[f240,f188]) ).
fof(f240,plain,
( on_path(sK2,sK3)
| ~ spl38_6 ),
inference(avatar_component_clause,[],[f238]) ).
fof(f271,plain,
( spl38_12
| ~ spl38_13 ),
inference(avatar_split_clause,[],[f234,f268,f264]) ).
fof(f234,plain,
( ~ precedes(sK2,sK1,sK3)
| sP33(sK1,sK3) ),
inference(resolution,[],[f95,f192]) ).
fof(f245,plain,
( spl38_6
| spl38_7 ),
inference(avatar_split_clause,[],[f236,f242,f238]) ).
fof(f236,plain,
( sP28(sK1,sK3)
| on_path(sK2,sK3) ),
inference(resolution,[],[f95,f182]) ).
fof(f229,plain,
spl38_3,
inference(avatar_split_clause,[],[f225,f213]) ).
fof(f225,plain,
path(sK4,sK0,sK3),
inference(resolution,[],[f94,f139]) ).
fof(f139,plain,
! [X2,X0,X1] :
( ~ shortest_path(X2,X0,X1)
| path(X2,X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f224,plain,
( spl38_1
| ~ spl38_2
| ~ spl38_3
| spl38_4
| ~ spl38_5 ),
inference(avatar_split_clause,[],[f203,f221,f217,f213,f209,f205]) ).
fof(f203,plain,
( ~ edge(sK2)
| sK4 = sK0
| ~ path(sK4,sK0,sK3)
| ~ edge(sK1)
| sK1 = sK2 ),
inference(subsumption_resolution,[],[f202,f124]) ).
fof(f124,plain,
! [X2,X0,X1] :
( ~ path(X2,X0,X1)
| vertex(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2] :
( ( vertex(X2)
& vertex(X0)
& tail_of(sK9(X0,X1,X2)) = X2
& ( ! [X4] :
( ~ path(head_of(sK9(X0,X1,X2)),X0,X4)
| path_cons(sK9(X0,X1,X2),X4) != X1 )
| path_cons(sK9(X0,X1,X2),empty) != X1
| head_of(sK9(X0,X1,X2)) != X0 )
& ( ( path(head_of(sK9(X0,X1,X2)),X0,sK10(X0,X1,X2))
& path_cons(sK9(X0,X1,X2),sK10(X0,X1,X2)) = X1 )
| ( path_cons(sK9(X0,X1,X2),empty) = X1
& head_of(sK9(X0,X1,X2)) = X0 ) )
& edge(sK9(X0,X1,X2)) )
| ~ path(X2,X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9,sK10])],[f79,f81,f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ? [X3] :
( tail_of(X3) = X2
& ( ! [X4] :
( ~ path(head_of(X3),X0,X4)
| path_cons(X3,X4) != X1 )
| path_cons(X3,empty) != X1
| head_of(X3) != X0 )
& ( ? [X5] :
( path(head_of(X3),X0,X5)
& path_cons(X3,X5) = X1 )
| ( path_cons(X3,empty) = X1
& head_of(X3) = X0 ) )
& edge(X3) )
=> ( tail_of(sK9(X0,X1,X2)) = X2
& ( ! [X4] :
( ~ path(head_of(sK9(X0,X1,X2)),X0,X4)
| path_cons(sK9(X0,X1,X2),X4) != X1 )
| path_cons(sK9(X0,X1,X2),empty) != X1
| head_of(sK9(X0,X1,X2)) != X0 )
& ( ? [X5] :
( path(head_of(sK9(X0,X1,X2)),X0,X5)
& path_cons(sK9(X0,X1,X2),X5) = X1 )
| ( path_cons(sK9(X0,X1,X2),empty) = X1
& head_of(sK9(X0,X1,X2)) = X0 ) )
& edge(sK9(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ? [X5] :
( path(head_of(sK9(X0,X1,X2)),X0,X5)
& path_cons(sK9(X0,X1,X2),X5) = X1 )
=> ( path(head_of(sK9(X0,X1,X2)),X0,sK10(X0,X1,X2))
& path_cons(sK9(X0,X1,X2),sK10(X0,X1,X2)) = X1 ) ),
introduced(choice_axiom,[]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ( vertex(X2)
& vertex(X0)
& ? [X3] :
( tail_of(X3) = X2
& ( ! [X4] :
( ~ path(head_of(X3),X0,X4)
| path_cons(X3,X4) != X1 )
| path_cons(X3,empty) != X1
| head_of(X3) != X0 )
& ( ? [X5] :
( path(head_of(X3),X0,X5)
& path_cons(X3,X5) = X1 )
| ( path_cons(X3,empty) = X1
& head_of(X3) = X0 ) )
& edge(X3) ) )
| ~ path(X2,X0,X1) ),
inference(rectify,[],[f78]) ).
fof(f78,plain,
! [X1,X2,X0] :
( ( vertex(X0)
& vertex(X1)
& ? [X3] :
( tail_of(X3) = X0
& ( ! [X4] :
( ~ path(head_of(X3),X1,X4)
| path_cons(X3,X4) != X2 )
| path_cons(X3,empty) != X2
| head_of(X3) != X1 )
& ( ? [X4] :
( path(head_of(X3),X1,X4)
& path_cons(X3,X4) = X2 )
| ( path_cons(X3,empty) = X2
& head_of(X3) = X1 ) )
& edge(X3) ) )
| ~ path(X0,X1,X2) ),
inference(flattening,[],[f77]) ).
fof(f77,plain,
! [X1,X2,X0] :
( ( vertex(X0)
& vertex(X1)
& ? [X3] :
( tail_of(X3) = X0
& ( ! [X4] :
( ~ path(head_of(X3),X1,X4)
| path_cons(X3,X4) != X2 )
| path_cons(X3,empty) != X2
| head_of(X3) != X1 )
& ( ? [X4] :
( path(head_of(X3),X1,X4)
& path_cons(X3,X4) = X2 )
| ( path_cons(X3,empty) = X2
& head_of(X3) = X1 ) )
& edge(X3) ) )
| ~ path(X0,X1,X2) ),
inference(nnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X1,X2,X0] :
( ( vertex(X0)
& vertex(X1)
& ? [X3] :
( tail_of(X3) = X0
& ( ( path_cons(X3,empty) = X2
& head_of(X3) = X1 )
<~> ? [X4] :
( path(head_of(X3),X1,X4)
& path_cons(X3,X4) = X2 ) )
& edge(X3) ) )
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,plain,
! [X2,X1,X0] :
( path(X0,X1,X2)
=> ( vertex(X0)
& vertex(X1)
& ? [X3] :
( tail_of(X3) = X0
& ( ( path_cons(X3,empty) = X2
& head_of(X3) = X1 )
<~> ? [X4] :
( path(head_of(X3),X1,X4)
& path_cons(X3,X4) = X2 ) )
& edge(X3) ) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X1,X2,X3] :
( path(X1,X2,X3)
=> ( vertex(X2)
& vertex(X1)
& ? [X0] :
( edge(X0)
& tail_of(X0) = X1
& ( ( path_cons(X0,empty) = X3
& head_of(X0) = X2 )
<~> ? [X4] :
( path(head_of(X0),X2,X4)
& path_cons(X0,X4) = X3 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',path_properties) ).
fof(f202,plain,
( ~ edge(sK1)
| sK1 = sK2
| ~ vertex(sK0)
| ~ edge(sK2)
| sK4 = sK0
| ~ path(sK4,sK0,sK3) ),
inference(subsumption_resolution,[],[f96,f125]) ).
fof(f125,plain,
! [X2,X0,X1] :
( ~ path(X2,X0,X1)
| vertex(X2) ),
inference(cnf_transformation,[],[f82]) ).
fof(f96,plain,
( ~ vertex(sK4)
| ~ edge(sK2)
| ~ edge(sK1)
| ~ path(sK4,sK0,sK3)
| sK1 = sK2
| ~ vertex(sK0)
| sK4 = sK0 ),
inference(cnf_transformation,[],[f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRA003+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.07/0.13 % Command : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.33 % Computer : n020.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon Aug 29 22:02:45 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.45 % (14307)lrs+10_1:32_br=off:nm=16:sd=2:ss=axioms:st=2.0:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.47 % (14300)dis+1010_1:50_awrs=decay:awrsf=128:nwc=10.0:s2pl=no:sp=frequency:ss=axioms:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.47 % (14300)Refutation not found, incomplete strategy% (14300)------------------------------
% 0.19/0.47 % (14300)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.47 % (14300)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.47 % (14300)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.47
% 0.19/0.47 % (14300)Memory used [KB]: 5884
% 0.19/0.47 % (14300)Time elapsed: 0.090 s
% 0.19/0.47 % (14300)Instructions burned: 2 (million)
% 0.19/0.47 % (14300)------------------------------
% 0.19/0.47 % (14300)------------------------------
% 0.19/0.47 % (14307)Refutation not found, incomplete strategy% (14307)------------------------------
% 0.19/0.47 % (14307)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.47 % (14307)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.47 % (14307)Termination reason: Refutation not found, incomplete strategy
% 0.19/0.47
% 0.19/0.47 % (14307)Memory used [KB]: 6012
% 0.19/0.47 % (14307)Time elapsed: 0.092 s
% 0.19/0.47 % (14307)Instructions burned: 3 (million)
% 0.19/0.47 % (14307)------------------------------
% 0.19/0.47 % (14307)------------------------------
% 0.19/0.48 % (14316)ott+21_1:1_erd=off:s2a=on:sac=on:sd=1:sgt=64:sos=on:ss=included:st=3.0:to=lpo:urr=on:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.19/0.49 % (14324)lrs-11_1:1_nm=0:sac=on:sd=4:ss=axioms:st=3.0:i=24:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/24Mi)
% 0.19/0.49 % (14297)lrs+10_5:1_br=off:fde=none:nwc=3.0:sd=1:sgt=10:sos=on:ss=axioms:urr=on:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.19/0.50 % (14318)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.19/0.50 % (14295)lrs+10_1:1_gsp=on:sd=1:sgt=32:sos=on:ss=axioms:i=13:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/13Mi)
% 0.19/0.50 % (14309)lrs+10_1:1_drc=off:sp=reverse_frequency:spb=goal:to=lpo:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.50 % (14295)First to succeed.
% 0.19/0.50 % (14317)dis+1010_2:3_fs=off:fsr=off:nm=0:nwc=5.0:s2a=on:s2agt=32:i=82:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/82Mi)
% 0.19/0.50 % (14308)lrs+10_1:1_ins=3:sp=reverse_frequency:spb=goal:to=lpo:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.19/0.51 % (14301)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.19/0.51 % (14295)Refutation found. Thanks to Tanya!
% 0.19/0.51 % SZS status Theorem for theBenchmark
% 0.19/0.51 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.51 % (14295)------------------------------
% 0.19/0.51 % (14295)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.51 % (14295)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.51 % (14295)Termination reason: Refutation
% 0.19/0.51
% 0.19/0.51 % (14295)Memory used [KB]: 6268
% 0.19/0.51 % (14295)Time elapsed: 0.100 s
% 0.19/0.51 % (14295)Instructions burned: 8 (million)
% 0.19/0.51 % (14295)------------------------------
% 0.19/0.51 % (14295)------------------------------
% 0.19/0.51 % (14289)Success in time 0.163 s
%------------------------------------------------------------------------------