TSTP Solution File: GRA003+1 by iProver---3.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n026.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 : Thu Aug 31 00:03:09 EDT 2023
% Result : Theorem 2.43s 1.15s
% Output : CNFRefutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 85 ( 17 unt; 0 def)
% Number of atoms : 443 ( 112 equ)
% Maximal formula atoms : 20 ( 5 avg)
% Number of connectives : 549 ( 191 ~; 171 |; 158 &)
% ( 3 <=>; 20 =>; 0 <=; 6 <~>)
% Maximal formula depth : 15 ( 7 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 : 280 ( 22 sgn; 192 !; 44 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(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(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(f12,axiom,
! [X1,X2,X6,X7,X3] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ( ~ precedes(X7,X6,X3)
& ~ ? [X8] :
( head_of(X8) = head_of(X7)
& tail_of(X8) = tail_of(X6) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',shortest_path_properties) ).
fof(f18,conjecture,
! [X1,X2,X6,X7,X3] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ( path(X1,X2,X3)
& X6 != X7
& edge(X7)
& edge(X6)
& X1 != X2
& vertex(X2)
& vertex(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vertices_and_edges) ).
fof(f19,negated_conjecture,
~ ! [X1,X2,X6,X7,X3] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ( path(X1,X2,X3)
& X6 != X7
& edge(X7)
& edge(X6)
& X1 != X2
& vertex(X2)
& vertex(X1) ) ),
inference(negated_conjecture,[],[f18]) ).
fof(f22,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(f23,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(f27,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(f28,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(f29,plain,
! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ~ precedes(X3,X2,X4)
& ~ ? [X5] :
( head_of(X3) = head_of(X5)
& tail_of(X2) = tail_of(X5) ) ) ),
inference(rectify,[],[f12]) ).
fof(f35,plain,
~ ! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( path(X0,X1,X4)
& X2 != X3
& edge(X3)
& edge(X2)
& X0 != X1
& vertex(X1)
& vertex(X0) ) ),
inference(rectify,[],[f19]) ).
fof(f42,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,[],[f22]) ).
fof(f43,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,[],[f23]) ).
fof(f44,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,[],[f43]) ).
fof(f49,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,[],[f27]) ).
fof(f50,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,[],[f28]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ) )
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(ennf_transformation,[],[f29]) ).
fof(f52,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ precedes(X3,X2,X4)
& ! [X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5) ) )
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(flattening,[],[f51]) ).
fof(f59,plain,
? [X0,X1,X2,X3,X4] :
( ( ~ path(X0,X1,X4)
| X2 = X3
| ~ edge(X3)
| ~ edge(X2)
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) )
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) ),
inference(ennf_transformation,[],[f35]) ).
fof(f60,plain,
? [X0,X1,X2,X3,X4] :
( ( ~ path(X0,X1,X4)
| X2 = X3
| ~ edge(X3)
| ~ edge(X2)
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) )
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) ),
inference(flattening,[],[f59]) ).
fof(f61,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 )
& ( ? [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(nnf_transformation,[],[f42]) ).
fof(f62,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 )
& ( ? [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(flattening,[],[f61]) ).
fof(f63,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 )
& ( ? [X5] :
( path_cons(X3,X5) = X2
& path(head_of(X3),X1,X5) )
| ( 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,[],[f62]) ).
fof(f64,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 )
& ( ? [X5] :
( path_cons(X3,X5) = X2
& path(head_of(X3),X1,X5) )
| ( path_cons(X3,empty) = X2
& head_of(X3) = X1 ) )
& tail_of(X3) = X0
& edge(X3) )
=> ( ( ! [X4] :
( path_cons(sK0(X0,X1,X2),X4) != X2
| ~ path(head_of(sK0(X0,X1,X2)),X1,X4) )
| path_cons(sK0(X0,X1,X2),empty) != X2
| head_of(sK0(X0,X1,X2)) != X1 )
& ( ? [X5] :
( path_cons(sK0(X0,X1,X2),X5) = X2
& path(head_of(sK0(X0,X1,X2)),X1,X5) )
| ( path_cons(sK0(X0,X1,X2),empty) = X2
& head_of(sK0(X0,X1,X2)) = X1 ) )
& tail_of(sK0(X0,X1,X2)) = X0
& edge(sK0(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0,X1,X2] :
( ? [X5] :
( path_cons(sK0(X0,X1,X2),X5) = X2
& path(head_of(sK0(X0,X1,X2)),X1,X5) )
=> ( path_cons(sK0(X0,X1,X2),sK1(X0,X1,X2)) = X2
& path(head_of(sK0(X0,X1,X2)),X1,sK1(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f66,plain,
! [X0,X1,X2] :
( ( ( ! [X4] :
( path_cons(sK0(X0,X1,X2),X4) != X2
| ~ path(head_of(sK0(X0,X1,X2)),X1,X4) )
| path_cons(sK0(X0,X1,X2),empty) != X2
| head_of(sK0(X0,X1,X2)) != X1 )
& ( ( path_cons(sK0(X0,X1,X2),sK1(X0,X1,X2)) = X2
& path(head_of(sK0(X0,X1,X2)),X1,sK1(X0,X1,X2)) )
| ( path_cons(sK0(X0,X1,X2),empty) = X2
& head_of(sK0(X0,X1,X2)) = X1 ) )
& tail_of(sK0(X0,X1,X2)) = X0
& edge(sK0(X0,X1,X2))
& vertex(X1)
& vertex(X0) )
| ~ path(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f63,f65,f64]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(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) )
| ~ path(X1,X2,X0) ),
inference(nnf_transformation,[],[f49]) ).
fof(f72,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(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) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f71]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(X3,X4) )
& ( ? [X6] :
( precedes(X6,X4,X0)
& sequential(X3,X6) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
! [X0,X3,X4] :
( ? [X6] :
( precedes(X6,X4,X0)
& sequential(X3,X6) )
=> ( precedes(sK3(X0,X3,X4),X4,X0)
& sequential(X3,sK3(X0,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f75,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(X3,X4) )
& ( ( precedes(sK3(X0,X3,X4),X4,X0)
& sequential(X3,sK3(X0,X3,X4)) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
| ~ precedes(X3,X4,X0) )
| ~ path(X1,X2,X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f73,f74]) ).
fof(f76,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) )
& ( ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(nnf_transformation,[],[f50]) ).
fof(f77,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) )
& ( ( ! [X3] :
( less_or_equal(length_of(X2),length_of(X3))
| ~ path(X0,X1,X3) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(flattening,[],[f76]) ).
fof(f78,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) )
& ( ( ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(rectify,[],[f77]) ).
fof(f79,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ less_or_equal(length_of(X2),length_of(X3))
& path(X0,X1,X3) )
=> ( ~ less_or_equal(length_of(X2),length_of(sK4(X0,X1,X2)))
& path(X0,X1,sK4(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ( ~ less_or_equal(length_of(X2),length_of(sK4(X0,X1,X2)))
& path(X0,X1,sK4(X0,X1,X2)) )
| X0 = X1
| ~ path(X0,X1,X2) )
& ( ( ! [X4] :
( less_or_equal(length_of(X2),length_of(X4))
| ~ path(X0,X1,X4) )
& X0 != X1
& path(X0,X1,X2) )
| ~ shortest_path(X0,X1,X2) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f78,f79]) ).
fof(f83,plain,
( ? [X0,X1,X2,X3,X4] :
( ( ~ path(X0,X1,X4)
| X2 = X3
| ~ edge(X3)
| ~ edge(X2)
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) )
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ( ~ path(sK7,sK8,sK11)
| sK9 = sK10
| ~ edge(sK10)
| ~ edge(sK9)
| sK7 = sK8
| ~ vertex(sK8)
| ~ vertex(sK7) )
& precedes(sK9,sK10,sK11)
& shortest_path(sK7,sK8,sK11) ) ),
introduced(choice_axiom,[]) ).
fof(f84,plain,
( ( ~ path(sK7,sK8,sK11)
| sK9 = sK10
| ~ edge(sK10)
| ~ edge(sK9)
| sK7 = sK8
| ~ vertex(sK8)
| ~ vertex(sK7) )
& precedes(sK9,sK10,sK11)
& shortest_path(sK7,sK8,sK11) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7,sK8,sK9,sK10,sK11])],[f60,f83]) ).
fof(f90,plain,
! [X2,X0,X1] :
( vertex(X0)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f91,plain,
! [X2,X0,X1] :
( vertex(X1)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f99,plain,
! [X2,X3,X0,X1] :
( edge(X3)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f44]) ).
fof(f112,plain,
! [X2,X3,X0,X1,X4] :
( on_path(X3,X0)
| ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f113,plain,
! [X2,X3,X0,X1,X4] :
( on_path(X4,X0)
| ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f117,plain,
! [X2,X0,X1] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f118,plain,
! [X2,X0,X1] :
( X0 != X1
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f80]) ).
fof(f123,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X2,X4)
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(cnf_transformation,[],[f52]) ).
fof(f132,plain,
shortest_path(sK7,sK8,sK11),
inference(cnf_transformation,[],[f84]) ).
fof(f133,plain,
precedes(sK9,sK10,sK11),
inference(cnf_transformation,[],[f84]) ).
fof(f134,plain,
( ~ path(sK7,sK8,sK11)
| sK9 = sK10
| ~ edge(sK10)
| ~ edge(sK9)
| sK7 = sK8
| ~ vertex(sK8)
| ~ vertex(sK7) ),
inference(cnf_transformation,[],[f84]) ).
fof(f141,plain,
! [X2,X1] : ~ shortest_path(X1,X1,X2),
inference(equality_resolution,[],[f118]) ).
cnf(c_61,plain,
( ~ path(X0,X1,X2)
| vertex(X1) ),
inference(cnf_transformation,[],[f91]) ).
cnf(c_62,plain,
( ~ path(X0,X1,X2)
| vertex(X0) ),
inference(cnf_transformation,[],[f90]) ).
cnf(c_65,plain,
( ~ path(X0,X1,X2)
| ~ on_path(X3,X2)
| edge(X3) ),
inference(cnf_transformation,[],[f99]) ).
cnf(c_79,plain,
( ~ path(X0,X1,X2)
| ~ precedes(X3,X4,X2)
| on_path(X4,X2) ),
inference(cnf_transformation,[],[f113]) ).
cnf(c_80,plain,
( ~ path(X0,X1,X2)
| ~ precedes(X3,X4,X2)
| on_path(X3,X2) ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_84,plain,
~ shortest_path(X0,X0,X1),
inference(cnf_transformation,[],[f141]) ).
cnf(c_85,plain,
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f117]) ).
cnf(c_86,plain,
( ~ precedes(X0,X1,X2)
| ~ precedes(X1,X0,X2)
| ~ shortest_path(X3,X4,X2) ),
inference(cnf_transformation,[],[f123]) ).
cnf(c_96,negated_conjecture,
( ~ path(sK7,sK8,sK11)
| ~ edge(sK9)
| ~ edge(sK10)
| ~ vertex(sK7)
| ~ vertex(sK8)
| sK7 = sK8
| sK9 = sK10 ),
inference(cnf_transformation,[],[f134]) ).
cnf(c_97,negated_conjecture,
precedes(sK9,sK10,sK11),
inference(cnf_transformation,[],[f133]) ).
cnf(c_98,negated_conjecture,
shortest_path(sK7,sK8,sK11),
inference(cnf_transformation,[],[f132]) ).
cnf(c_172,plain,
( ~ path(sK7,sK8,sK11)
| ~ edge(sK9)
| ~ edge(sK10)
| ~ vertex(sK7)
| sK7 = sK8
| sK9 = sK10 ),
inference(backward_subsumption_resolution,[status(thm)],[c_96,c_61]) ).
cnf(c_179,plain,
( ~ path(sK7,sK8,sK11)
| ~ edge(sK9)
| ~ edge(sK10)
| sK7 = sK8
| sK9 = sK10 ),
inference(backward_subsumption_resolution,[status(thm)],[c_172,c_62]) ).
cnf(c_1011,plain,
( X0 != sK7
| X1 != sK8
| X2 != sK11
| path(X0,X1,X2) ),
inference(resolution_lifted,[status(thm)],[c_85,c_98]) ).
cnf(c_1012,plain,
path(sK7,sK8,sK11),
inference(unflattening,[status(thm)],[c_1011]) ).
cnf(c_1025,plain,
( X0 != sK7
| X0 != sK8
| X1 != sK11 ),
inference(resolution_lifted,[status(thm)],[c_84,c_98]) ).
cnf(c_1026,plain,
sK7 != sK8,
inference(unflattening,[status(thm)],[c_1025]) ).
cnf(c_1083,plain,
( ~ edge(sK9)
| ~ edge(sK10)
| sK7 = sK8
| sK9 = sK10 ),
inference(backward_subsumption_resolution,[status(thm)],[c_179,c_1012]) ).
cnf(c_1087,plain,
( ~ edge(sK9)
| ~ edge(sK10)
| sK9 = sK10 ),
inference(backward_subsumption_resolution,[status(thm)],[c_1083,c_1026]) ).
cnf(c_2704,plain,
path(sK7,sK8,sK11),
inference(superposition,[status(thm)],[c_98,c_85]) ).
cnf(c_2724,plain,
( ~ on_path(X0,sK11)
| edge(X0) ),
inference(superposition,[status(thm)],[c_2704,c_65]) ).
cnf(c_2840,plain,
( ~ precedes(X0,X1,sK11)
| on_path(X1,sK11) ),
inference(superposition,[status(thm)],[c_2704,c_79]) ).
cnf(c_2859,plain,
( ~ precedes(X0,X1,sK11)
| on_path(X0,sK11) ),
inference(superposition,[status(thm)],[c_2704,c_80]) ).
cnf(c_2884,plain,
on_path(sK10,sK11),
inference(superposition,[status(thm)],[c_97,c_2840]) ).
cnf(c_2885,plain,
edge(sK10),
inference(superposition,[status(thm)],[c_2884,c_2724]) ).
cnf(c_2886,plain,
( ~ edge(sK9)
| sK9 = sK10 ),
inference(backward_subsumption_resolution,[status(thm)],[c_1087,c_2885]) ).
cnf(c_2894,plain,
on_path(sK9,sK11),
inference(superposition,[status(thm)],[c_97,c_2859]) ).
cnf(c_2895,plain,
edge(sK9),
inference(superposition,[status(thm)],[c_2894,c_2724]) ).
cnf(c_2897,plain,
sK9 = sK10,
inference(global_subsumption_just,[status(thm)],[c_2886,c_179,c_1012,c_1026,c_2885,c_2895]) ).
cnf(c_2901,plain,
precedes(sK9,sK9,sK11),
inference(demodulation,[status(thm)],[c_97,c_2897]) ).
cnf(c_2968,plain,
( ~ shortest_path(X0,X1,sK11)
| ~ precedes(sK9,sK9,sK11) ),
inference(superposition,[status(thm)],[c_2901,c_86]) ).
cnf(c_2969,plain,
~ shortest_path(X0,X1,sK11),
inference(forward_subsumption_resolution,[status(thm)],[c_2968,c_2901]) ).
cnf(c_2970,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[c_98,c_2969]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRA003+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n026.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sun Aug 27 04:00:49 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.46 Running first-order theorem proving
% 0.20/0.46 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.43/1.15 % SZS status Started for theBenchmark.p
% 2.43/1.15 % SZS status Theorem for theBenchmark.p
% 2.43/1.15
% 2.43/1.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 2.43/1.15
% 2.43/1.15 ------ iProver source info
% 2.43/1.15
% 2.43/1.15 git: date: 2023-05-31 18:12:56 +0000
% 2.43/1.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 2.43/1.15 git: non_committed_changes: false
% 2.43/1.15 git: last_make_outside_of_git: false
% 2.43/1.15
% 2.43/1.15 ------ Parsing...
% 2.43/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 2.43/1.15
% 2.43/1.15 ------ Preprocessing... sup_sim: 0 sf_s rm: 7 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e
% 2.43/1.15
% 2.43/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 2.43/1.15
% 2.43/1.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.43/1.15 ------ Proving...
% 2.43/1.15 ------ Problem Properties
% 2.43/1.15
% 2.43/1.15
% 2.43/1.15 clauses 44
% 2.43/1.15 conjectures 2
% 2.43/1.15 EPR 15
% 2.43/1.15 Horn 31
% 2.43/1.15 unary 5
% 2.43/1.15 binary 10
% 2.43/1.15 lits 129
% 2.43/1.15 lits eq 27
% 2.43/1.15 fd_pure 0
% 2.43/1.15 fd_pseudo 0
% 2.43/1.15 fd_cond 0
% 2.43/1.15 fd_pseudo_cond 3
% 2.43/1.15 AC symbols 0
% 2.43/1.15
% 2.43/1.15 ------ Schedule dynamic 5 is on
% 2.43/1.15
% 2.43/1.15 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.43/1.15
% 2.43/1.15
% 2.43/1.15 ------
% 2.43/1.15 Current options:
% 2.43/1.15 ------
% 2.43/1.15
% 2.43/1.15
% 2.43/1.15
% 2.43/1.15
% 2.43/1.15 ------ Proving...
% 2.43/1.15
% 2.43/1.15
% 2.43/1.15 % SZS status Theorem for theBenchmark.p
% 2.43/1.15
% 2.43/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.43/1.15
% 2.43/1.15
%------------------------------------------------------------------------------