TSTP Solution File: GRA003+1 by SnakeForV-SAT---1.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : SnakeForV-SAT---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_sat --cores 0 -t %d %s
% Computer : n005.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 0.19s 0.49s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 11
% Syntax : Number of formulae : 76 ( 13 unt; 0 def)
% Number of atoms : 430 ( 110 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 532 ( 178 ~; 162 |; 163 &)
% ( 3 <=>; 20 =>; 0 <=; 6 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-3 aty)
% Number of variables : 261 ( 212 !; 49 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f238,plain,
$false,
inference(subsumption_resolution,[],[f221,f228]) ).
fof(f228,plain,
~ precedes(sK4,sK4,sK5),
inference(backward_demodulation,[],[f190,f220]) ).
fof(f220,plain,
sK4 = sK7,
inference(subsumption_resolution,[],[f219,f151]) ).
fof(f151,plain,
! [X2,X1] : ~ shortest_path(X1,X1,X2),
inference(equality_resolution,[],[f133]) ).
fof(f133,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( ( ! [X3] :
( ~ path(X0,X1,X3)
| less_or_equal(length_of(X2),length_of(X3)) )
& path(X0,X1,X2)
& X0 != X1 )
| ~ shortest_path(X0,X1,X2) )
& ( shortest_path(X0,X1,X2)
| ( path(X0,X1,sK10(X0,X1,X2))
& ~ less_or_equal(length_of(X2),length_of(sK10(X0,X1,X2))) )
| ~ path(X0,X1,X2)
| X0 = X1 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK10])],[f86,f87]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ? [X4] :
( path(X0,X1,X4)
& ~ less_or_equal(length_of(X2),length_of(X4)) )
=> ( path(X0,X1,sK10(X0,X1,X2))
& ~ less_or_equal(length_of(X2),length_of(sK10(X0,X1,X2))) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ( ( ! [X3] :
( ~ path(X0,X1,X3)
| less_or_equal(length_of(X2),length_of(X3)) )
& path(X0,X1,X2)
& X0 != X1 )
| ~ shortest_path(X0,X1,X2) )
& ( shortest_path(X0,X1,X2)
| ? [X4] :
( path(X0,X1,X4)
& ~ less_or_equal(length_of(X2),length_of(X4)) )
| ~ path(X0,X1,X2)
| X0 = X1 ) ),
inference(rectify,[],[f85]) ).
fof(f85,plain,
! [X1,X2,X0] :
( ( ( ! [X3] :
( ~ path(X1,X2,X3)
| less_or_equal(length_of(X0),length_of(X3)) )
& path(X1,X2,X0)
& X1 != X2 )
| ~ shortest_path(X1,X2,X0) )
& ( shortest_path(X1,X2,X0)
| ? [X3] :
( path(X1,X2,X3)
& ~ less_or_equal(length_of(X0),length_of(X3)) )
| ~ path(X1,X2,X0)
| X1 = X2 ) ),
inference(flattening,[],[f84]) ).
fof(f84,plain,
! [X1,X2,X0] :
( ( ( ! [X3] :
( ~ path(X1,X2,X3)
| less_or_equal(length_of(X0),length_of(X3)) )
& path(X1,X2,X0)
& X1 != X2 )
| ~ shortest_path(X1,X2,X0) )
& ( shortest_path(X1,X2,X0)
| ? [X3] :
( path(X1,X2,X3)
& ~ less_or_equal(length_of(X0),length_of(X3)) )
| ~ path(X1,X2,X0)
| X1 = X2 ) ),
inference(nnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X1,X2,X0] :
( ( ! [X3] :
( ~ path(X1,X2,X3)
| less_or_equal(length_of(X0),length_of(X3)) )
& path(X1,X2,X0)
& X1 != X2 )
<=> shortest_path(X1,X2,X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0,X2,X1] :
( shortest_path(X1,X2,X0)
<=> ( ! [X3] :
( path(X1,X2,X3)
=> less_or_equal(length_of(X0),length_of(X3)) )
& X1 != X2
& path(X1,X2,X0) ) ),
inference(rectify,[],[f11]) ).
fof(f11,axiom,
! [X9,X1,X2] :
( ( path(X1,X2,X9)
& X1 != X2
& ! [X3] :
( path(X1,X2,X3)
=> less_or_equal(length_of(X9),length_of(X3)) ) )
<=> shortest_path(X1,X2,X9) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shortest_path_defn) ).
fof(f219,plain,
( sK4 = sK7
| shortest_path(sK6,sK6,sK5) ),
inference(superposition,[],[f127,f214]) ).
fof(f214,plain,
( sK6 = sK8
| sK4 = sK7 ),
inference(resolution,[],[f176,f184]) ).
fof(f184,plain,
edge(sK4),
inference(resolution,[],[f181,f160]) ).
fof(f160,plain,
path(sK8,sK6,sK5),
inference(resolution,[],[f134,f127]) ).
fof(f134,plain,
! [X2,X0,X1] :
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f88]) ).
fof(f181,plain,
! [X4,X5] :
( ~ path(X4,X5,sK5)
| edge(sK4) ),
inference(resolution,[],[f178,f143]) ).
fof(f143,plain,
! [X2,X3,X0,X1] :
( ~ on_path(X0,X3)
| edge(X0)
| ~ path(X1,X2,X3) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2,X3] :
( ~ path(X1,X2,X3)
| ~ on_path(X0,X3)
| ( edge(X0)
& in_path(tail_of(X0),X3)
& in_path(head_of(X0),X3) ) ),
inference(rectify,[],[f52]) ).
fof(f52,plain,
! [X3,X1,X2,X0] :
( ~ path(X1,X2,X0)
| ~ on_path(X3,X0)
| ( edge(X3)
& in_path(tail_of(X3),X0)
& in_path(head_of(X3),X0) ) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X3,X1,X0,X2] :
( ( edge(X3)
& in_path(tail_of(X3),X0)
& in_path(head_of(X3),X0) )
| ~ on_path(X3,X0)
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,plain,
! [X3,X1,X0,X2] :
( ( on_path(X3,X0)
& path(X1,X2,X0) )
=> ( edge(X3)
& in_path(tail_of(X3),X0)
& in_path(head_of(X3),X0) ) ),
inference(rectify,[],[f6]) ).
fof(f6,axiom,
! [X3,X1,X2,X0] :
( ( path(X1,X2,X3)
& on_path(X0,X3) )
=> ( in_path(head_of(X0),X3)
& in_path(tail_of(X0),X3)
& edge(X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',on_path_properties) ).
fof(f178,plain,
on_path(sK4,sK5),
inference(resolution,[],[f168,f160]) ).
fof(f168,plain,
! [X0,X1] :
( ~ path(X0,X1,sK5)
| on_path(sK4,sK5) ),
inference(resolution,[],[f140,f126]) ).
fof(f126,plain,
precedes(sK4,sK7,sK5),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
( shortest_path(sK8,sK6,sK5)
& precedes(sK4,sK7,sK5)
& ( ~ edge(sK7)
| sK6 = sK8
| sK4 = sK7
| ~ path(sK8,sK6,sK5)
| ~ edge(sK4)
| ~ vertex(sK6)
| ~ vertex(sK8) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5,sK6,sK7,sK8])],[f78,f79]) ).
fof(f79,plain,
( ? [X0,X1,X2,X3,X4] :
( shortest_path(X4,X2,X1)
& precedes(X0,X3,X1)
& ( ~ edge(X3)
| X2 = X4
| X0 = X3
| ~ path(X4,X2,X1)
| ~ edge(X0)
| ~ vertex(X2)
| ~ vertex(X4) ) )
=> ( shortest_path(sK8,sK6,sK5)
& precedes(sK4,sK7,sK5)
& ( ~ edge(sK7)
| sK6 = sK8
| sK4 = sK7
| ~ path(sK8,sK6,sK5)
| ~ edge(sK4)
| ~ vertex(sK6)
| ~ vertex(sK8) ) ) ),
introduced(choice_axiom,[]) ).
fof(f78,plain,
? [X0,X1,X2,X3,X4] :
( shortest_path(X4,X2,X1)
& precedes(X0,X3,X1)
& ( ~ edge(X3)
| X2 = X4
| X0 = X3
| ~ path(X4,X2,X1)
| ~ edge(X0)
| ~ vertex(X2)
| ~ vertex(X4) ) ),
inference(rectify,[],[f50]) ).
fof(f50,plain,
? [X0,X2,X4,X3,X1] :
( shortest_path(X1,X4,X2)
& precedes(X0,X3,X2)
& ( ~ edge(X3)
| X1 = X4
| X0 = X3
| ~ path(X1,X4,X2)
| ~ edge(X0)
| ~ vertex(X4)
| ~ vertex(X1) ) ),
inference(flattening,[],[f49]) ).
fof(f49,plain,
? [X1,X2,X3,X0,X4] :
( ( ~ edge(X3)
| X1 = X4
| X0 = X3
| ~ path(X1,X4,X2)
| ~ edge(X0)
| ~ vertex(X4)
| ~ vertex(X1) )
& precedes(X0,X3,X2)
& shortest_path(X1,X4,X2) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,plain,
~ ! [X1,X2,X3,X0,X4] :
( ( precedes(X0,X3,X2)
& shortest_path(X1,X4,X2) )
=> ( vertex(X1)
& edge(X3)
& vertex(X4)
& X1 != X4
& path(X1,X4,X2)
& X0 != X3
& edge(X0) ) ),
inference(rectify,[],[f19]) ).
fof(f19,negated_conjecture,
~ ! [X6,X1,X3,X7,X2] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ( X1 != X2
& edge(X6)
& X6 != X7
& path(X1,X2,X3)
& edge(X7)
& vertex(X1)
& vertex(X2) ) ),
inference(negated_conjecture,[],[f18]) ).
fof(f18,conjecture,
! [X6,X1,X3,X7,X2] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ( X1 != X2
& edge(X6)
& X6 != X7
& path(X1,X2,X3)
& edge(X7)
& vertex(X1)
& vertex(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vertices_and_edges) ).
fof(f140,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X4,X3,X1)
| on_path(X4,X1)
| ~ path(X2,X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ~ precedes(X4,X3,X1)
| ( on_path(X4,X1)
& on_path(X3,X1)
& ( ! [X5] :
( ~ sequential(X4,X5)
| ~ precedes(X5,X3,X1) )
| ~ sequential(X4,X3) )
& ( ( sequential(X4,sK11(X1,X3,X4))
& precedes(sK11(X1,X3,X4),X3,X1) )
| sequential(X4,X3) ) ) )
| ~ path(X2,X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK11])],[f91,f92]) ).
fof(f92,plain,
! [X1,X3,X4] :
( ? [X6] :
( sequential(X4,X6)
& precedes(X6,X3,X1) )
=> ( sequential(X4,sK11(X1,X3,X4))
& precedes(sK11(X1,X3,X4),X3,X1) ) ),
introduced(choice_axiom,[]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ~ precedes(X4,X3,X1)
| ( on_path(X4,X1)
& on_path(X3,X1)
& ( ! [X5] :
( ~ sequential(X4,X5)
| ~ precedes(X5,X3,X1) )
| ~ sequential(X4,X3) )
& ( ? [X6] :
( sequential(X4,X6)
& precedes(X6,X3,X1) )
| sequential(X4,X3) ) ) )
| ~ path(X2,X0,X1) ),
inference(rectify,[],[f90]) ).
fof(f90,plain,
! [X2,X0,X1] :
( ! [X3,X4] :
( ~ precedes(X4,X3,X0)
| ( on_path(X4,X0)
& on_path(X3,X0)
& ( ! [X5] :
( ~ sequential(X4,X5)
| ~ precedes(X5,X3,X0) )
| ~ sequential(X4,X3) )
& ( ? [X5] :
( sequential(X4,X5)
& precedes(X5,X3,X0) )
| sequential(X4,X3) ) ) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X2,X0,X1] :
( ! [X3,X4] :
( ~ precedes(X4,X3,X0)
| ( on_path(X4,X0)
& on_path(X3,X0)
& ( ! [X5] :
( ~ sequential(X4,X5)
| ~ precedes(X5,X3,X0) )
| ~ sequential(X4,X3) )
& ( ? [X5] :
( sequential(X4,X5)
& precedes(X5,X3,X0) )
| sequential(X4,X3) ) ) )
| ~ path(X1,X2,X0) ),
inference(nnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X2,X0,X1] :
( ! [X3,X4] :
( ~ precedes(X4,X3,X0)
| ( on_path(X4,X0)
& on_path(X3,X0)
& ( sequential(X4,X3)
<~> ? [X5] :
( sequential(X4,X5)
& precedes(X5,X3,X0) ) ) ) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,plain,
! [X2,X1,X0] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( precedes(X4,X3,X0)
=> ( on_path(X4,X0)
& on_path(X3,X0)
& ( sequential(X4,X3)
<~> ? [X5] :
( sequential(X4,X5)
& precedes(X5,X3,X0) ) ) ) ) ),
inference(rectify,[],[f10]) ).
fof(f10,axiom,
! [X3,X1,X2] :
( path(X1,X2,X3)
=> ! [X7,X6] :
( precedes(X6,X7,X3)
=> ( on_path(X7,X3)
& on_path(X6,X3)
& ( ? [X8] :
( precedes(X8,X7,X3)
& sequential(X6,X8) )
<~> sequential(X6,X7) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',precedes_properties) ).
fof(f176,plain,
( ~ edge(sK4)
| sK6 = sK8
| sK4 = sK7 ),
inference(resolution,[],[f175,f161]) ).
fof(f161,plain,
( ~ edge(sK7)
| sK4 = sK7
| sK6 = sK8
| ~ edge(sK4) ),
inference(resolution,[],[f160,f153]) ).
fof(f153,plain,
( ~ path(sK8,sK6,sK5)
| sK4 = sK7
| ~ edge(sK4)
| ~ edge(sK7)
| sK6 = sK8 ),
inference(subsumption_resolution,[],[f152,f100]) ).
fof(f100,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| vertex(X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ( edge(sK2(X0,X1,X2))
& tail_of(sK2(X0,X1,X2)) = X1
& ( head_of(sK2(X0,X1,X2)) != X2
| path_cons(sK2(X0,X1,X2),empty) != X0
| ! [X4] :
( path_cons(sK2(X0,X1,X2),X4) != X0
| ~ path(head_of(sK2(X0,X1,X2)),X2,X4) ) )
& ( ( head_of(sK2(X0,X1,X2)) = X2
& path_cons(sK2(X0,X1,X2),empty) = X0 )
| ( path_cons(sK2(X0,X1,X2),sK3(X0,X1,X2)) = X0
& path(head_of(sK2(X0,X1,X2)),X2,sK3(X0,X1,X2)) ) )
& vertex(X1)
& vertex(X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f66,f68,f67]) ).
fof(f67,plain,
! [X0,X1,X2] :
( ? [X3] :
( edge(X3)
& tail_of(X3) = X1
& ( head_of(X3) != X2
| path_cons(X3,empty) != X0
| ! [X4] :
( path_cons(X3,X4) != X0
| ~ path(head_of(X3),X2,X4) ) )
& ( ( head_of(X3) = X2
& path_cons(X3,empty) = X0 )
| ? [X5] :
( path_cons(X3,X5) = X0
& path(head_of(X3),X2,X5) ) ) )
=> ( edge(sK2(X0,X1,X2))
& tail_of(sK2(X0,X1,X2)) = X1
& ( head_of(sK2(X0,X1,X2)) != X2
| path_cons(sK2(X0,X1,X2),empty) != X0
| ! [X4] :
( path_cons(sK2(X0,X1,X2),X4) != X0
| ~ path(head_of(sK2(X0,X1,X2)),X2,X4) ) )
& ( ( head_of(sK2(X0,X1,X2)) = X2
& path_cons(sK2(X0,X1,X2),empty) = X0 )
| ? [X5] :
( path_cons(sK2(X0,X1,X2),X5) = X0
& path(head_of(sK2(X0,X1,X2)),X2,X5) ) ) ) ),
introduced(choice_axiom,[]) ).
fof(f68,plain,
! [X0,X1,X2] :
( ? [X5] :
( path_cons(sK2(X0,X1,X2),X5) = X0
& path(head_of(sK2(X0,X1,X2)),X2,X5) )
=> ( path_cons(sK2(X0,X1,X2),sK3(X0,X1,X2)) = X0
& path(head_of(sK2(X0,X1,X2)),X2,sK3(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ~ path(X1,X2,X0)
| ( ? [X3] :
( edge(X3)
& tail_of(X3) = X1
& ( head_of(X3) != X2
| path_cons(X3,empty) != X0
| ! [X4] :
( path_cons(X3,X4) != X0
| ~ path(head_of(X3),X2,X4) ) )
& ( ( head_of(X3) = X2
& path_cons(X3,empty) = X0 )
| ? [X5] :
( path_cons(X3,X5) = X0
& path(head_of(X3),X2,X5) ) ) )
& vertex(X1)
& vertex(X2) ) ),
inference(rectify,[],[f65]) ).
fof(f65,plain,
! [X1,X2,X0] :
( ~ path(X2,X0,X1)
| ( ? [X3] :
( edge(X3)
& tail_of(X3) = X2
& ( head_of(X3) != X0
| path_cons(X3,empty) != X1
| ! [X4] :
( path_cons(X3,X4) != X1
| ~ path(head_of(X3),X0,X4) ) )
& ( ( head_of(X3) = X0
& path_cons(X3,empty) = X1 )
| ? [X4] :
( path_cons(X3,X4) = X1
& path(head_of(X3),X0,X4) ) ) )
& vertex(X2)
& vertex(X0) ) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X1,X2,X0] :
( ~ path(X2,X0,X1)
| ( ? [X3] :
( edge(X3)
& tail_of(X3) = X2
& ( head_of(X3) != X0
| path_cons(X3,empty) != X1
| ! [X4] :
( path_cons(X3,X4) != X1
| ~ path(head_of(X3),X0,X4) ) )
& ( ( head_of(X3) = X0
& path_cons(X3,empty) = X1 )
| ? [X4] :
( path_cons(X3,X4) = X1
& path(head_of(X3),X0,X4) ) ) )
& vertex(X2)
& vertex(X0) ) ),
inference(nnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X1,X2,X0] :
( ~ path(X2,X0,X1)
| ( ? [X3] :
( edge(X3)
& tail_of(X3) = X2
& ( ? [X4] :
( path_cons(X3,X4) = X1
& path(head_of(X3),X0,X4) )
<~> ( head_of(X3) = X0
& path_cons(X3,empty) = X1 ) ) )
& vertex(X2)
& vertex(X0) ) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,plain,
! [X2,X1,X0] :
( path(X2,X0,X1)
=> ( ? [X3] :
( edge(X3)
& tail_of(X3) = X2
& ( ? [X4] :
( path_cons(X3,X4) = X1
& path(head_of(X3),X0,X4) )
<~> ( head_of(X3) = X0
& path_cons(X3,empty) = X1 ) ) )
& vertex(X2)
& vertex(X0) ) ),
inference(rectify,[],[f5]) ).
fof(f5,axiom,
! [X2,X3,X1] :
( path(X1,X2,X3)
=> ( vertex(X2)
& vertex(X1)
& ? [X0] :
( ( ? [X4] :
( path(head_of(X0),X2,X4)
& path_cons(X0,X4) = X3 )
<~> ( path_cons(X0,empty) = X3
& head_of(X0) = X2 ) )
& edge(X0)
& tail_of(X0) = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_properties) ).
fof(f152,plain,
( ~ vertex(sK6)
| sK4 = sK7
| ~ edge(sK4)
| ~ path(sK8,sK6,sK5)
| sK6 = sK8
| ~ edge(sK7) ),
inference(subsumption_resolution,[],[f125,f101]) ).
fof(f101,plain,
! [X2,X0,X1] :
( ~ path(X1,X2,X0)
| vertex(X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f125,plain,
( ~ path(sK8,sK6,sK5)
| sK6 = sK8
| sK4 = sK7
| ~ edge(sK7)
| ~ vertex(sK6)
| ~ edge(sK4)
| ~ vertex(sK8) ),
inference(cnf_transformation,[],[f80]) ).
fof(f175,plain,
edge(sK7),
inference(resolution,[],[f174,f160]) ).
fof(f174,plain,
! [X4,X5] :
( ~ path(X4,X5,sK5)
| edge(sK7) ),
inference(resolution,[],[f170,f143]) ).
fof(f170,plain,
on_path(sK7,sK5),
inference(resolution,[],[f167,f160]) ).
fof(f167,plain,
! [X0,X1] :
( ~ path(X0,X1,sK5)
| on_path(sK7,sK5) ),
inference(resolution,[],[f139,f126]) ).
fof(f139,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X4,X3,X1)
| on_path(X3,X1)
| ~ path(X2,X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f127,plain,
shortest_path(sK8,sK6,sK5),
inference(cnf_transformation,[],[f80]) ).
fof(f190,plain,
~ precedes(sK7,sK4,sK5),
inference(resolution,[],[f171,f126]) ).
fof(f171,plain,
! [X0,X1] :
( ~ precedes(X1,X0,sK5)
| ~ precedes(X0,X1,sK5) ),
inference(resolution,[],[f113,f127]) ).
fof(f113,plain,
! [X2,X3,X0,X1,X4] :
( ~ shortest_path(X1,X3,X4)
| ~ precedes(X2,X0,X4)
| ~ precedes(X0,X2,X4) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2,X3,X4] :
( ~ precedes(X0,X2,X4)
| ( ~ precedes(X2,X0,X4)
& ! [X5] :
( head_of(X5) != head_of(X2)
| tail_of(X0) != tail_of(X5) ) )
| ~ shortest_path(X1,X3,X4) ),
inference(rectify,[],[f40]) ).
fof(f40,plain,
! [X2,X1,X0,X4,X3] :
( ~ precedes(X2,X0,X3)
| ( ~ precedes(X0,X2,X3)
& ! [X5] :
( head_of(X0) != head_of(X5)
| tail_of(X5) != tail_of(X2) ) )
| ~ shortest_path(X1,X4,X3) ),
inference(flattening,[],[f39]) ).
fof(f39,plain,
! [X3,X0,X4,X1,X2] :
( ( ~ precedes(X0,X2,X3)
& ! [X5] :
( head_of(X0) != head_of(X5)
| tail_of(X5) != tail_of(X2) ) )
| ~ precedes(X2,X0,X3)
| ~ shortest_path(X1,X4,X3) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,plain,
! [X3,X0,X4,X1,X2] :
( ( precedes(X2,X0,X3)
& shortest_path(X1,X4,X3) )
=> ( ~ ? [X5] :
( tail_of(X5) = tail_of(X2)
& head_of(X0) = head_of(X5) )
& ~ precedes(X0,X2,X3) ) ),
inference(rectify,[],[f12]) ).
fof(f12,axiom,
! [X7,X1,X6,X3,X2] :
( ( shortest_path(X1,X2,X3)
& precedes(X6,X7,X3) )
=> ( ~ precedes(X7,X6,X3)
& ~ ? [X8] :
( tail_of(X8) = tail_of(X6)
& head_of(X8) = head_of(X7) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shortest_path_properties) ).
fof(f221,plain,
precedes(sK4,sK4,sK5),
inference(backward_demodulation,[],[f126,f220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GRA003+1 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.06/0.12 % 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 : n005.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 22:00:33 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.19/0.47 % (586)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)
% 0.19/0.47 % (594)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)
% 0.19/0.48 % (576)dis+10_1:1_fsd=on:sp=occurrence:i=7:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/7Mi)
% 0.19/0.48 % (565)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)
% 0.19/0.48 % (586)First to succeed.
% 0.19/0.49 % (586)Refutation found. Thanks to Tanya!
% 0.19/0.49 % SZS status Theorem for theBenchmark
% 0.19/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.49 % (586)------------------------------
% 0.19/0.49 % (586)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.19/0.49 % (586)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.19/0.49 % (586)Termination reason: Refutation
% 0.19/0.49
% 0.19/0.49 % (586)Memory used [KB]: 1151
% 0.19/0.49 % (586)Time elapsed: 0.070 s
% 0.19/0.49 % (586)Instructions burned: 8 (million)
% 0.19/0.49 % (586)------------------------------
% 0.19/0.49 % (586)------------------------------
% 0.19/0.49 % (564)Success in time 0.149 s
%------------------------------------------------------------------------------