TSTP Solution File: GRA008+1 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : GRA008+1 : TPTP v8.2.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n025.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 : Mon Jun 24 06:35:26 EDT 2024
% Result : Theorem 86.39s 12.35s
% Output : CNFRefutation 86.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 27
% Syntax : Number of formulae : 315 ( 61 unt; 0 def)
% Number of atoms : 1224 ( 425 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 1487 ( 578 ~; 598 |; 254 &)
% ( 7 <=>; 40 =>; 0 <=; 10 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 13 ( 11 usr; 2 prp; 0-3 aty)
% Number of functors : 16 ( 16 usr; 6 con; 0-3 aty)
% Number of variables : 672 ( 48 sgn 343 !; 65 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( edge(X0)
=> head_of(X0) != tail_of(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',no_loops) ).
fof(f2,axiom,
! [X0] :
( edge(X0)
=> ( vertex(tail_of(X0))
& vertex(head_of(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',edge_ends_are_vertices) ).
fof(f3,axiom,
( complete
=> ! [X1,X2] :
( ( X1 != X2
& vertex(X2)
& vertex(X1) )
=> ? [X0] :
( ( ( tail_of(X0) = X2
& head_of(X0) = X1 )
<~> ( tail_of(X0) = X1
& head_of(X0) = X2 ) )
& edge(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complete_properties) ).
fof(f4,axiom,
! [X1,X2,X3] :
( ( ? [X0] :
( ( ? [X4] :
( path_cons(X0,X4) = X3
& path(head_of(X0),X2,X4) )
| ( path_cons(X0,empty) = X3
& head_of(X0) = X2 ) )
& tail_of(X0) = X1
& edge(X0) )
& vertex(X2)
& vertex(X1) )
=> path(X1,X2,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',path_defn) ).
fof(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(f7,axiom,
! [X1,X2,X3,X5] :
( ( in_path(X5,X3)
& path(X1,X2,X3) )
=> ( ? [X0] :
( ( tail_of(X0) = X5
| head_of(X0) = X5 )
& on_path(X0,X3) )
& vertex(X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in_path_properties) ).
fof(f8,axiom,
! [X6,X7] :
( sequential(X6,X7)
<=> ( head_of(X6) = tail_of(X7)
& X6 != X7
& edge(X7)
& edge(X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_defn) ).
fof(f9,axiom,
! [X3,X1,X2] :
( path(X1,X2,X3)
=> ! [X6,X7] :
( ( ( ? [X8] :
( precedes(X8,X7,X3)
& sequential(X6,X8) )
| sequential(X6,X7) )
& on_path(X7,X3)
& on_path(X6,X3) )
=> precedes(X6,X7,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',precedes_defn) ).
fof(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(f13,axiom,
! [X6,X7,X8] :
( triangle(X6,X7,X8)
<=> ( sequential(X8,X6)
& sequential(X7,X8)
& sequential(X6,X7)
& edge(X8)
& edge(X7)
& edge(X6) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',triangle_defn) ).
fof(f18,conjecture,
( complete
=> ! [X1,X2,X6,X7,X3] :
( ( sequential(X6,X7)
& precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ? [X8] : triangle(X6,X7,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_is_triangle) ).
fof(f19,negated_conjecture,
~ ( complete
=> ! [X1,X2,X6,X7,X3] :
( ( sequential(X6,X7)
& precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ? [X8] : triangle(X6,X7,X8) ) ),
inference(negated_conjecture,[],[f18]) ).
fof(f20,plain,
( complete
=> ! [X0,X1] :
( ( X0 != X1
& vertex(X1)
& vertex(X0) )
=> ? [X2] :
( ( ( tail_of(X2) = X1
& head_of(X2) = X0 )
<~> ( tail_of(X2) = X0
& head_of(X2) = X1 ) )
& edge(X2) ) ) ),
inference(rectify,[],[f3]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ( ? [X3] :
( ( ? [X4] :
( path_cons(X3,X4) = X2
& path(head_of(X3),X1,X4) )
| ( path_cons(X3,empty) = X2
& head_of(X3) = X1 ) )
& tail_of(X3) = X0
& edge(X3) )
& vertex(X1)
& vertex(X0) )
=> path(X0,X1,X2) ),
inference(rectify,[],[f4]) ).
fof(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(f24,plain,
! [X0,X1,X2,X3] :
( ( in_path(X3,X2)
& path(X0,X1,X2) )
=> ( ? [X4] :
( ( tail_of(X4) = X3
| head_of(X4) = X3 )
& on_path(X4,X2) )
& vertex(X3) ) ),
inference(rectify,[],[f7]) ).
fof(f25,plain,
! [X0,X1] :
( sequential(X0,X1)
<=> ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) ),
inference(rectify,[],[f8]) ).
fof(f26,plain,
! [X0,X1,X2] :
( path(X1,X2,X0)
=> ! [X3,X4] :
( ( ( ? [X5] :
( precedes(X5,X4,X0)
& sequential(X3,X5) )
| sequential(X3,X4) )
& on_path(X4,X0)
& on_path(X3,X0) )
=> precedes(X3,X4,X0) ) ),
inference(rectify,[],[f9]) ).
fof(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(f30,plain,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
<=> ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) ) ),
inference(rectify,[],[f13]) ).
fof(f35,plain,
~ ( complete
=> ! [X0,X1,X2,X3,X4] :
( ( sequential(X2,X3)
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ? [X5] : triangle(X2,X3,X5) ) ),
inference(rectify,[],[f19]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ( sequential(X2,X0)
& sequential(X1,X2)
& sequential(X0,X1)
& edge(X2)
& edge(X1)
& edge(X0) )
=> triangle(X0,X1,X2) ),
inference(unused_predicate_definition_removal,[],[f30]) ).
fof(f37,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f38,plain,
! [X0] :
( ( vertex(tail_of(X0))
& vertex(head_of(X0)) )
| ~ edge(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f39,plain,
( ! [X0,X1] :
( ? [X2] :
( ( ( tail_of(X2) = X1
& head_of(X2) = X0 )
<~> ( tail_of(X2) = X0
& head_of(X2) = X1 ) )
& edge(X2) )
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) )
| ~ complete ),
inference(ennf_transformation,[],[f20]) ).
fof(f40,plain,
( ! [X0,X1] :
( ? [X2] :
( ( ( tail_of(X2) = X1
& head_of(X2) = X0 )
<~> ( tail_of(X2) = X0
& head_of(X2) = X1 ) )
& edge(X2) )
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) )
| ~ complete ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
! [X0,X1,X2] :
( path(X0,X1,X2)
| ! [X3] :
( ( ! [X4] :
( path_cons(X3,X4) != X2
| ~ path(head_of(X3),X1,X4) )
& ( path_cons(X3,empty) != X2
| head_of(X3) != X1 ) )
| tail_of(X3) != X0
| ~ edge(X3) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f42,plain,
! [X0,X1,X2] :
( path(X0,X1,X2)
| ! [X3] :
( ( ! [X4] :
( path_cons(X3,X4) != X2
| ~ path(head_of(X3),X1,X4) )
& ( path_cons(X3,empty) != X2
| head_of(X3) != X1 ) )
| tail_of(X3) != X0
| ~ edge(X3) )
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(flattening,[],[f41]) ).
fof(f43,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(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(ennf_transformation,[],[f23]) ).
fof(f45,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,[],[f44]) ).
fof(f46,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( ( tail_of(X4) = X3
| head_of(X4) = X3 )
& on_path(X4,X2) )
& vertex(X3) )
| ~ in_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(ennf_transformation,[],[f24]) ).
fof(f47,plain,
! [X0,X1,X2,X3] :
( ( ? [X4] :
( ( tail_of(X4) = X3
| head_of(X4) = X3 )
& on_path(X4,X2) )
& vertex(X3) )
| ~ in_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(flattening,[],[f46]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( precedes(X3,X4,X0)
| ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
& ~ sequential(X3,X4) )
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( precedes(X3,X4,X0)
| ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
& ~ sequential(X3,X4) )
| ~ on_path(X4,X0)
| ~ on_path(X3,X0) )
| ~ path(X1,X2,X0) ),
inference(flattening,[],[f48]) ).
fof(f50,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(f51,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(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(ennf_transformation,[],[f29]) ).
fof(f53,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,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f55,plain,
! [X0,X1,X2] :
( triangle(X0,X1,X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0) ),
inference(flattening,[],[f54]) ).
fof(f60,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] : ~ triangle(X2,X3,X5)
& sequential(X2,X3)
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
& complete ),
inference(ennf_transformation,[],[f35]) ).
fof(f61,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] : ~ triangle(X2,X3,X5)
& sequential(X2,X3)
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
& complete ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
( ! [X0,X1] :
( ? [X2] :
( ( tail_of(X2) != X0
| head_of(X2) != X1
| tail_of(X2) != X1
| head_of(X2) != X0 )
& ( ( tail_of(X2) = X0
& head_of(X2) = X1 )
| ( tail_of(X2) = X1
& head_of(X2) = X0 ) )
& edge(X2) )
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) )
| ~ complete ),
inference(nnf_transformation,[],[f40]) ).
fof(f63,plain,
( ! [X0,X1] :
( ? [X2] :
( ( tail_of(X2) != X0
| head_of(X2) != X1
| tail_of(X2) != X1
| head_of(X2) != X0 )
& ( ( tail_of(X2) = X0
& head_of(X2) = X1 )
| ( tail_of(X2) = X1
& head_of(X2) = X0 ) )
& edge(X2) )
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) )
| ~ complete ),
inference(flattening,[],[f62]) ).
fof(f64,plain,
! [X0,X1] :
( ? [X2] :
( ( tail_of(X2) != X0
| head_of(X2) != X1
| tail_of(X2) != X1
| head_of(X2) != X0 )
& ( ( tail_of(X2) = X0
& head_of(X2) = X1 )
| ( tail_of(X2) = X1
& head_of(X2) = X0 ) )
& edge(X2) )
=> ( ( tail_of(sK0(X0,X1)) != X0
| head_of(sK0(X0,X1)) != X1
| tail_of(sK0(X0,X1)) != X1
| head_of(sK0(X0,X1)) != X0 )
& ( ( tail_of(sK0(X0,X1)) = X0
& head_of(sK0(X0,X1)) = X1 )
| ( tail_of(sK0(X0,X1)) = X1
& head_of(sK0(X0,X1)) = X0 ) )
& edge(sK0(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
( ! [X0,X1] :
( ( ( tail_of(sK0(X0,X1)) != X0
| head_of(sK0(X0,X1)) != X1
| tail_of(sK0(X0,X1)) != X1
| head_of(sK0(X0,X1)) != X0 )
& ( ( tail_of(sK0(X0,X1)) = X0
& head_of(sK0(X0,X1)) = X1 )
| ( tail_of(sK0(X0,X1)) = X1
& head_of(sK0(X0,X1)) = X0 ) )
& edge(sK0(X0,X1)) )
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0) )
| ~ complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f63,f64]) ).
fof(f66,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,[],[f43]) ).
fof(f67,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,[],[f66]) ).
fof(f68,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,[],[f67]) ).
fof(f69,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(sK1(X0,X1,X2),X4) != X2
| ~ path(head_of(sK1(X0,X1,X2)),X1,X4) )
| path_cons(sK1(X0,X1,X2),empty) != X2
| head_of(sK1(X0,X1,X2)) != X1 )
& ( ? [X5] :
( path_cons(sK1(X0,X1,X2),X5) = X2
& path(head_of(sK1(X0,X1,X2)),X1,X5) )
| ( path_cons(sK1(X0,X1,X2),empty) = X2
& head_of(sK1(X0,X1,X2)) = X1 ) )
& tail_of(sK1(X0,X1,X2)) = X0
& edge(sK1(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f70,plain,
! [X0,X1,X2] :
( ? [X5] :
( path_cons(sK1(X0,X1,X2),X5) = X2
& path(head_of(sK1(X0,X1,X2)),X1,X5) )
=> ( path_cons(sK1(X0,X1,X2),sK2(X0,X1,X2)) = X2
& path(head_of(sK1(X0,X1,X2)),X1,sK2(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f71,plain,
! [X0,X1,X2] :
( ( ( ! [X4] :
( path_cons(sK1(X0,X1,X2),X4) != X2
| ~ path(head_of(sK1(X0,X1,X2)),X1,X4) )
| path_cons(sK1(X0,X1,X2),empty) != X2
| head_of(sK1(X0,X1,X2)) != X1 )
& ( ( path_cons(sK1(X0,X1,X2),sK2(X0,X1,X2)) = X2
& path(head_of(sK1(X0,X1,X2)),X1,sK2(X0,X1,X2)) )
| ( path_cons(sK1(X0,X1,X2),empty) = X2
& head_of(sK1(X0,X1,X2)) = X1 ) )
& tail_of(sK1(X0,X1,X2)) = X0
& edge(sK1(X0,X1,X2))
& vertex(X1)
& vertex(X0) )
| ~ path(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f68,f70,f69]) ).
fof(f72,plain,
! [X2,X3] :
( ? [X4] :
( ( tail_of(X4) = X3
| head_of(X4) = X3 )
& on_path(X4,X2) )
=> ( ( tail_of(sK3(X2,X3)) = X3
| head_of(sK3(X2,X3)) = X3 )
& on_path(sK3(X2,X3),X2) ) ),
introduced(choice_axiom,[]) ).
fof(f73,plain,
! [X0,X1,X2,X3] :
( ( ( tail_of(sK3(X2,X3)) = X3
| head_of(sK3(X2,X3)) = X3 )
& on_path(sK3(X2,X3),X2)
& vertex(X3) )
| ~ in_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f47,f72]) ).
fof(f74,plain,
! [X0,X1] :
( ( sequential(X0,X1)
| head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0) )
& ( ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) )
| ~ sequential(X0,X1) ) ),
inference(nnf_transformation,[],[f25]) ).
fof(f75,plain,
! [X0,X1] :
( ( sequential(X0,X1)
| head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0) )
& ( ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) )
| ~ sequential(X0,X1) ) ),
inference(flattening,[],[f74]) ).
fof(f76,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,[],[f50]) ).
fof(f77,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,[],[f76]) ).
fof(f78,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,[],[f77]) ).
fof(f79,plain,
! [X0,X3,X4] :
( ? [X6] :
( precedes(X6,X4,X0)
& sequential(X3,X6) )
=> ( precedes(sK4(X0,X3,X4),X4,X0)
& sequential(X3,sK4(X0,X3,X4)) ) ),
introduced(choice_axiom,[]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ! [X3,X4] :
( ( ( ! [X5] :
( ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5) )
| ~ sequential(X3,X4) )
& ( ( precedes(sK4(X0,X3,X4),X4,X0)
& sequential(X3,sK4(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,[sK4])],[f78,f79]) ).
fof(f81,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,[],[f51]) ).
fof(f82,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,[],[f81]) ).
fof(f83,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,[],[f82]) ).
fof(f84,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(sK5(X0,X1,X2)))
& path(X0,X1,sK5(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f85,plain,
! [X0,X1,X2] :
( ( shortest_path(X0,X1,X2)
| ( ~ less_or_equal(length_of(X2),length_of(sK5(X0,X1,X2)))
& path(X0,X1,sK5(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,[sK5])],[f83,f84]) ).
fof(f88,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] : ~ triangle(X2,X3,X5)
& sequential(X2,X3)
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ! [X5] : ~ triangle(sK10,sK11,X5)
& sequential(sK10,sK11)
& precedes(sK10,sK11,sK12)
& shortest_path(sK8,sK9,sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
( ! [X5] : ~ triangle(sK10,sK11,X5)
& sequential(sK10,sK11)
& precedes(sK10,sK11,sK12)
& shortest_path(sK8,sK9,sK12)
& complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12])],[f61,f88]) ).
fof(f90,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f91,plain,
! [X0] :
( vertex(head_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f92,plain,
! [X0] :
( vertex(tail_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f38]) ).
fof(f93,plain,
! [X0,X1] :
( edge(sK0(X0,X1))
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ~ complete ),
inference(cnf_transformation,[],[f65]) ).
fof(f95,plain,
! [X0,X1] :
( head_of(sK0(X0,X1)) = X1
| tail_of(sK0(X0,X1)) = X1
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ~ complete ),
inference(cnf_transformation,[],[f65]) ).
fof(f96,plain,
! [X0,X1] :
( tail_of(sK0(X0,X1)) = X0
| head_of(sK0(X0,X1)) = X0
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ~ complete ),
inference(cnf_transformation,[],[f65]) ).
fof(f97,plain,
! [X0,X1] :
( tail_of(sK0(X0,X1)) = X0
| tail_of(sK0(X0,X1)) = X1
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ~ complete ),
inference(cnf_transformation,[],[f65]) ).
fof(f99,plain,
! [X2,X3,X0,X1] :
( path(X0,X1,X2)
| path_cons(X3,empty) != X2
| head_of(X3) != X1
| tail_of(X3) != X0
| ~ edge(X3)
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f102,plain,
! [X2,X0,X1] :
( vertex(X1)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f71]) ).
fof(f112,plain,
! [X2,X3,X0,X1] :
( in_path(tail_of(X3),X2)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
fof(f113,plain,
! [X2,X3,X0,X1] :
( vertex(X3)
| ~ in_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f73]) ).
fof(f116,plain,
! [X0,X1] :
( edge(X0)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f117,plain,
! [X0,X1] :
( edge(X1)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f118,plain,
! [X0,X1] :
( X0 != X1
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f119,plain,
! [X0,X1] :
( head_of(X0) = tail_of(X1)
| ~ sequential(X0,X1) ),
inference(cnf_transformation,[],[f75]) ).
fof(f120,plain,
! [X0,X1] :
( sequential(X0,X1)
| head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f121,plain,
! [X2,X3,X0,X1,X4] :
( precedes(X3,X4,X0)
| ~ sequential(X3,X4)
| ~ on_path(X4,X0)
| ~ on_path(X3,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f123,plain,
! [X2,X3,X0,X1,X4] :
( on_path(X3,X0)
| ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f124,plain,
! [X2,X3,X0,X1,X4] :
( on_path(X4,X0)
| ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f80]) ).
fof(f128,plain,
! [X2,X0,X1] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f85]) ).
fof(f133,plain,
! [X2,X3,X0,X1,X4,X5] :
( head_of(X3) != head_of(X5)
| tail_of(X2) != tail_of(X5)
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(cnf_transformation,[],[f53]) ).
fof(f134,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X2,X4)
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(cnf_transformation,[],[f53]) ).
fof(f135,plain,
! [X2,X0,X1] :
( triangle(X0,X1,X2)
| ~ sequential(X2,X0)
| ~ sequential(X1,X2)
| ~ sequential(X0,X1)
| ~ edge(X2)
| ~ edge(X1)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f143,plain,
complete,
inference(cnf_transformation,[],[f89]) ).
fof(f144,plain,
shortest_path(sK8,sK9,sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f145,plain,
precedes(sK10,sK11,sK12),
inference(cnf_transformation,[],[f89]) ).
fof(f146,plain,
sequential(sK10,sK11),
inference(cnf_transformation,[],[f89]) ).
fof(f147,plain,
! [X5] : ~ triangle(sK10,sK11,X5),
inference(cnf_transformation,[],[f89]) ).
fof(f150,plain,
! [X3,X0,X1] :
( path(X0,X1,path_cons(X3,empty))
| head_of(X3) != X1
| tail_of(X3) != X0
| ~ edge(X3)
| ~ vertex(X1)
| ~ vertex(X0) ),
inference(equality_resolution,[],[f99]) ).
fof(f151,plain,
! [X3,X0] :
( path(X0,head_of(X3),path_cons(X3,empty))
| tail_of(X3) != X0
| ~ edge(X3)
| ~ vertex(head_of(X3))
| ~ vertex(X0) ),
inference(equality_resolution,[],[f150]) ).
fof(f152,plain,
! [X3] :
( path(tail_of(X3),head_of(X3),path_cons(X3,empty))
| ~ edge(X3)
| ~ vertex(head_of(X3))
| ~ vertex(tail_of(X3)) ),
inference(equality_resolution,[],[f151]) ).
fof(f153,plain,
! [X1] : ~ sequential(X1,X1),
inference(equality_resolution,[],[f118]) ).
cnf(c_49,plain,
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f90]) ).
cnf(c_50,plain,
( ~ edge(X0)
| vertex(tail_of(X0)) ),
inference(cnf_transformation,[],[f92]) ).
cnf(c_51,plain,
( ~ edge(X0)
| vertex(head_of(X0)) ),
inference(cnf_transformation,[],[f91]) ).
cnf(c_53,plain,
( ~ vertex(X0)
| ~ vertex(X1)
| ~ complete
| tail_of(sK0(X0,X1)) = X0
| tail_of(sK0(X0,X1)) = X1
| X0 = X1 ),
inference(cnf_transformation,[],[f97]) ).
cnf(c_54,plain,
( ~ vertex(X0)
| ~ vertex(X1)
| ~ complete
| head_of(sK0(X0,X1)) = X0
| tail_of(sK0(X0,X1)) = X0
| X0 = X1 ),
inference(cnf_transformation,[],[f96]) ).
cnf(c_55,plain,
( ~ vertex(X0)
| ~ vertex(X1)
| ~ complete
| head_of(sK0(X0,X1)) = X1
| tail_of(sK0(X0,X1)) = X1
| X0 = X1 ),
inference(cnf_transformation,[],[f95]) ).
cnf(c_57,plain,
( ~ vertex(X0)
| ~ vertex(X1)
| ~ complete
| X0 = X1
| edge(sK0(X0,X1)) ),
inference(cnf_transformation,[],[f93]) ).
cnf(c_59,plain,
( ~ vertex(head_of(X0))
| ~ vertex(tail_of(X0))
| ~ edge(X0)
| path(tail_of(X0),head_of(X0),path_cons(X0,empty)) ),
inference(cnf_transformation,[],[f152]) ).
cnf(c_67,plain,
( ~ path(X0,X1,X2)
| vertex(X1) ),
inference(cnf_transformation,[],[f102]) ).
cnf(c_69,plain,
( ~ path(X0,X1,X2)
| ~ on_path(X3,X2)
| in_path(tail_of(X3),X2) ),
inference(cnf_transformation,[],[f112]) ).
cnf(c_74,plain,
( ~ path(X0,X1,X2)
| ~ in_path(X3,X2)
| vertex(X3) ),
inference(cnf_transformation,[],[f113]) ).
cnf(c_75,plain,
( head_of(X0) != tail_of(X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
cnf(c_76,plain,
( ~ sequential(X0,X1)
| head_of(X0) = tail_of(X1) ),
inference(cnf_transformation,[],[f119]) ).
cnf(c_77,plain,
~ sequential(X0,X0),
inference(cnf_transformation,[],[f153]) ).
cnf(c_78,plain,
( ~ sequential(X0,X1)
| edge(X1) ),
inference(cnf_transformation,[],[f117]) ).
cnf(c_79,plain,
( ~ sequential(X0,X1)
| edge(X0) ),
inference(cnf_transformation,[],[f116]) ).
cnf(c_81,plain,
( ~ path(X0,X1,X2)
| ~ on_path(X3,X2)
| ~ on_path(X4,X2)
| ~ sequential(X3,X4)
| precedes(X3,X4,X2) ),
inference(cnf_transformation,[],[f121]) ).
cnf(c_85,plain,
( ~ path(X0,X1,X2)
| ~ precedes(X3,X4,X2)
| on_path(X4,X2) ),
inference(cnf_transformation,[],[f124]) ).
cnf(c_86,plain,
( ~ path(X0,X1,X2)
| ~ precedes(X3,X4,X2)
| on_path(X3,X2) ),
inference(cnf_transformation,[],[f123]) ).
cnf(c_91,plain,
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f128]) ).
cnf(c_92,plain,
( ~ precedes(X0,X1,X2)
| ~ precedes(X1,X0,X2)
| ~ shortest_path(X3,X4,X2) ),
inference(cnf_transformation,[],[f134]) ).
cnf(c_93,plain,
( head_of(X0) != head_of(X1)
| tail_of(X1) != tail_of(X2)
| ~ precedes(X2,X0,X3)
| ~ shortest_path(X4,X5,X3) ),
inference(cnf_transformation,[],[f133]) ).
cnf(c_94,plain,
( ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0)
| ~ edge(X0)
| ~ edge(X1)
| ~ edge(X2)
| triangle(X0,X1,X2) ),
inference(cnf_transformation,[],[f135]) ).
cnf(c_102,negated_conjecture,
~ triangle(sK10,sK11,X0),
inference(cnf_transformation,[],[f147]) ).
cnf(c_103,negated_conjecture,
sequential(sK10,sK11),
inference(cnf_transformation,[],[f146]) ).
cnf(c_104,negated_conjecture,
precedes(sK10,sK11,sK12),
inference(cnf_transformation,[],[f145]) ).
cnf(c_105,negated_conjecture,
shortest_path(sK8,sK9,sK12),
inference(cnf_transformation,[],[f144]) ).
cnf(c_106,negated_conjecture,
complete,
inference(cnf_transformation,[],[f143]) ).
cnf(c_144,plain,
( ~ vertex(X1)
| ~ vertex(X0)
| X0 = X1
| edge(sK0(X0,X1)) ),
inference(global_subsumption_just,[status(thm)],[c_57,c_106,c_57]) ).
cnf(c_145,plain,
( ~ vertex(X0)
| ~ vertex(X1)
| X0 = X1
| edge(sK0(X0,X1)) ),
inference(renaming,[status(thm)],[c_144]) ).
cnf(c_147,plain,
( ~ edge(X0)
| path(tail_of(X0),head_of(X0),path_cons(X0,empty)) ),
inference(global_subsumption_just,[status(thm)],[c_59,c_51,c_50,c_59]) ).
cnf(c_153,plain,
( ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0)
| ~ edge(X2)
| triangle(X0,X1,X2) ),
inference(global_subsumption_just,[status(thm)],[c_94,c_79,c_78,c_94]) ).
cnf(c_160,plain,
( ~ vertex(X1)
| ~ vertex(X0)
| head_of(sK0(X0,X1)) = X1
| tail_of(sK0(X0,X1)) = X1
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_55,c_106,c_55]) ).
cnf(c_161,plain,
( ~ vertex(X0)
| ~ vertex(X1)
| head_of(sK0(X0,X1)) = X1
| tail_of(sK0(X0,X1)) = X1
| X0 = X1 ),
inference(renaming,[status(thm)],[c_160]) ).
cnf(c_162,plain,
( ~ vertex(X1)
| ~ vertex(X0)
| head_of(sK0(X0,X1)) = X0
| tail_of(sK0(X0,X1)) = X0
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_54,c_106,c_54]) ).
cnf(c_163,plain,
( ~ vertex(X0)
| ~ vertex(X1)
| head_of(sK0(X0,X1)) = X0
| tail_of(sK0(X0,X1)) = X0
| X0 = X1 ),
inference(renaming,[status(thm)],[c_162]) ).
cnf(c_164,plain,
( ~ vertex(X1)
| ~ vertex(X0)
| tail_of(sK0(X0,X1)) = X0
| tail_of(sK0(X0,X1)) = X1
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_53,c_106,c_53]) ).
cnf(c_165,plain,
( ~ vertex(X0)
| ~ vertex(X1)
| tail_of(sK0(X0,X1)) = X0
| tail_of(sK0(X0,X1)) = X1
| X0 = X1 ),
inference(renaming,[status(thm)],[c_164]) ).
cnf(c_198,plain,
( ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0)
| triangle(X0,X1,X2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_153,c_78]) ).
cnf(c_940,plain,
( X0 != sK10
| X1 != sK11
| X2 != X3
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0) ),
inference(resolution_lifted,[status(thm)],[c_198,c_102]) ).
cnf(c_941,plain,
( ~ sequential(X0,sK10)
| ~ sequential(sK11,X0)
| ~ sequential(sK10,sK11) ),
inference(unflattening,[status(thm)],[c_940]) ).
cnf(c_943,plain,
( ~ sequential(sK11,X0)
| ~ sequential(X0,sK10) ),
inference(global_subsumption_just,[status(thm)],[c_941,c_103,c_941]) ).
cnf(c_944,plain,
( ~ sequential(X0,sK10)
| ~ sequential(sK11,X0) ),
inference(renaming,[status(thm)],[c_943]) ).
cnf(c_2328,plain,
( ~ sequential(X0_13,sK10)
| ~ sequential(sK11,X0_13) ),
inference(subtyping,[status(esa)],[c_944]) ).
cnf(c_2332,plain,
( ~ vertex(X0_14)
| ~ vertex(X1_14)
| tail_of(sK0(X0_14,X1_14)) = X0_14
| tail_of(sK0(X0_14,X1_14)) = X1_14
| X0_14 = X1_14 ),
inference(subtyping,[status(esa)],[c_165]) ).
cnf(c_2333,plain,
( ~ vertex(X0_14)
| ~ vertex(X1_14)
| head_of(sK0(X0_14,X1_14)) = X0_14
| tail_of(sK0(X0_14,X1_14)) = X0_14
| X0_14 = X1_14 ),
inference(subtyping,[status(esa)],[c_163]) ).
cnf(c_2334,plain,
( ~ vertex(X0_14)
| ~ vertex(X1_14)
| head_of(sK0(X0_14,X1_14)) = X1_14
| tail_of(sK0(X0_14,X1_14)) = X1_14
| X0_14 = X1_14 ),
inference(subtyping,[status(esa)],[c_161]) ).
cnf(c_2337,plain,
( ~ edge(X0_13)
| path(tail_of(X0_13),head_of(X0_13),path_cons(X0_13,empty)) ),
inference(subtyping,[status(esa)],[c_147]) ).
cnf(c_2338,plain,
( ~ vertex(X0_14)
| ~ vertex(X1_14)
| X0_14 = X1_14
| edge(sK0(X0_14,X1_14)) ),
inference(subtyping,[status(esa)],[c_145]) ).
cnf(c_2339,negated_conjecture,
shortest_path(sK8,sK9,sK12),
inference(subtyping,[status(esa)],[c_105]) ).
cnf(c_2340,negated_conjecture,
precedes(sK10,sK11,sK12),
inference(subtyping,[status(esa)],[c_104]) ).
cnf(c_2341,negated_conjecture,
sequential(sK10,sK11),
inference(subtyping,[status(esa)],[c_103]) ).
cnf(c_2348,plain,
( head_of(X0_13) != head_of(X1_13)
| tail_of(X1_13) != tail_of(X2_13)
| ~ precedes(X2_13,X0_13,X0_15)
| ~ shortest_path(X0_14,X1_14,X0_15) ),
inference(subtyping,[status(esa)],[c_93]) ).
cnf(c_2349,plain,
( ~ precedes(X0_13,X1_13,X0_15)
| ~ precedes(X1_13,X0_13,X0_15)
| ~ shortest_path(X0_14,X1_14,X0_15) ),
inference(subtyping,[status(esa)],[c_92]) ).
cnf(c_2350,plain,
( ~ shortest_path(X0_14,X1_14,X0_15)
| path(X0_14,X1_14,X0_15) ),
inference(subtyping,[status(esa)],[c_91]) ).
cnf(c_2355,plain,
( ~ path(X0_14,X1_14,X0_15)
| ~ precedes(X0_13,X1_13,X0_15)
| on_path(X0_13,X0_15) ),
inference(subtyping,[status(esa)],[c_86]) ).
cnf(c_2356,plain,
( ~ path(X0_14,X1_14,X0_15)
| ~ precedes(X0_13,X1_13,X0_15)
| on_path(X1_13,X0_15) ),
inference(subtyping,[status(esa)],[c_85]) ).
cnf(c_2360,plain,
( ~ path(X0_14,X1_14,X0_15)
| ~ on_path(X0_13,X0_15)
| ~ on_path(X1_13,X0_15)
| ~ sequential(X0_13,X1_13)
| precedes(X0_13,X1_13,X0_15) ),
inference(subtyping,[status(esa)],[c_81]) ).
cnf(c_2361,plain,
( ~ sequential(X0_13,X1_13)
| edge(X0_13) ),
inference(subtyping,[status(esa)],[c_79]) ).
cnf(c_2362,plain,
( ~ sequential(X0_13,X1_13)
| edge(X1_13) ),
inference(subtyping,[status(esa)],[c_78]) ).
cnf(c_2363,plain,
~ sequential(X0_13,X0_13),
inference(subtyping,[status(esa)],[c_77]) ).
cnf(c_2364,plain,
( ~ sequential(X0_13,X1_13)
| head_of(X0_13) = tail_of(X1_13) ),
inference(subtyping,[status(esa)],[c_76]) ).
cnf(c_2365,plain,
( head_of(X0_13) != tail_of(X1_13)
| ~ edge(X0_13)
| ~ edge(X1_13)
| X0_13 = X1_13
| sequential(X0_13,X1_13) ),
inference(subtyping,[status(esa)],[c_75]) ).
cnf(c_2366,plain,
( ~ path(X0_14,X1_14,X0_15)
| ~ in_path(X2_14,X0_15)
| vertex(X2_14) ),
inference(subtyping,[status(esa)],[c_74]) ).
cnf(c_2371,plain,
( ~ path(X0_14,X1_14,X0_15)
| ~ on_path(X0_13,X0_15)
| in_path(tail_of(X0_13),X0_15) ),
inference(subtyping,[status(esa)],[c_69]) ).
cnf(c_2373,plain,
( ~ path(X0_14,X1_14,X0_15)
| vertex(X1_14) ),
inference(subtyping,[status(esa)],[c_67]) ).
cnf(c_2382,plain,
( ~ edge(X0_13)
| vertex(tail_of(X0_13)) ),
inference(subtyping,[status(esa)],[c_50]) ).
cnf(c_2383,plain,
( head_of(X0_13) != tail_of(X0_13)
| ~ edge(X0_13) ),
inference(subtyping,[status(esa)],[c_49]) ).
cnf(c_2384,negated_conjecture,
sequential(sK10,sK11),
inference(demodulation,[status(thm)],[c_2341]) ).
cnf(c_2385,negated_conjecture,
precedes(sK10,sK11,sK12),
inference(demodulation,[status(thm)],[c_2340]) ).
cnf(c_2386,negated_conjecture,
shortest_path(sK8,sK9,sK12),
inference(demodulation,[status(thm)],[c_2339]) ).
cnf(c_2388,plain,
X0_13 = X0_13,
theory(equality) ).
cnf(c_2389,plain,
X0_14 = X0_14,
theory(equality) ).
cnf(c_2392,plain,
( X0_13 != X1_13
| X2_13 != X1_13
| X2_13 = X0_13 ),
theory(equality) ).
cnf(c_2393,plain,
( X0_14 != X1_14
| X2_14 != X1_14
| X2_14 = X0_14 ),
theory(equality) ).
cnf(c_2397,plain,
( X0_13 != X1_13
| tail_of(X0_13) = tail_of(X1_13) ),
theory(equality) ).
cnf(c_2404,plain,
( X0_13 != X1_13
| X2_13 != X3_13
| ~ sequential(X1_13,X3_13)
| sequential(X0_13,X2_13) ),
theory(equality) ).
cnf(c_2412,plain,
( sK10 != sK10
| tail_of(sK10) = tail_of(sK10) ),
inference(instantiation,[status(thm)],[c_2397]) ).
cnf(c_2418,plain,
sK10 = sK10,
inference(instantiation,[status(thm)],[c_2388]) ).
cnf(c_2442,plain,
~ sequential(sK10,sK10),
inference(instantiation,[status(thm)],[c_2363]) ).
cnf(c_2458,plain,
( ~ edge(sK10)
| vertex(tail_of(sK10)) ),
inference(instantiation,[status(thm)],[c_2382]) ).
cnf(c_3402,plain,
( ~ sequential(sK10,sK11)
| edge(sK10) ),
inference(instantiation,[status(thm)],[c_2361]) ).
cnf(c_3403,plain,
( ~ sequential(sK10,sK11)
| edge(sK11) ),
inference(instantiation,[status(thm)],[c_2362]) ).
cnf(c_3406,plain,
( X0_13 != sK10
| X1_13 != sK11
| ~ sequential(sK10,sK11)
| sequential(X0_13,X1_13) ),
inference(instantiation,[status(thm)],[c_2404]) ).
cnf(c_3407,plain,
( sK10 != sK10
| sK10 != sK11
| ~ sequential(sK10,sK11)
| sequential(sK10,sK10) ),
inference(instantiation,[status(thm)],[c_3406]) ).
cnf(c_3410,plain,
( head_of(X0_13) != head_of(X1_13)
| tail_of(X1_13) != tail_of(X2_13)
| ~ precedes(X2_13,X0_13,sK12)
| ~ shortest_path(sK8,sK9,sK12) ),
inference(instantiation,[status(thm)],[c_2348]) ).
cnf(c_3450,plain,
edge(sK11),
inference(superposition,[status(thm)],[c_2384,c_2362]) ).
cnf(c_3461,plain,
path(sK8,sK9,sK12),
inference(superposition,[status(thm)],[c_2386,c_2350]) ).
cnf(c_3466,plain,
head_of(sK10) = tail_of(sK11),
inference(superposition,[status(thm)],[c_2384,c_2364]) ).
cnf(c_3477,plain,
( ~ edge(sK11)
| path(head_of(sK10),head_of(sK11),path_cons(sK11,empty)) ),
inference(superposition,[status(thm)],[c_3466,c_2337]) ).
cnf(c_3480,plain,
path(head_of(sK10),head_of(sK11),path_cons(sK11,empty)),
inference(forward_subsumption_resolution,[status(thm)],[c_3477,c_3450]) ).
cnf(c_3494,plain,
( X0_13 != X1_13
| sK11 != X1_13
| X0_13 = sK11 ),
inference(instantiation,[status(thm)],[c_2392]) ).
cnf(c_3495,plain,
( sK10 != sK10
| sK11 != sK10
| sK10 = sK11 ),
inference(instantiation,[status(thm)],[c_3494]) ).
cnf(c_3504,plain,
( tail_of(X0_13) != tail_of(sK10)
| head_of(sK11) != head_of(X0_13)
| ~ precedes(sK10,sK11,sK12)
| ~ shortest_path(sK8,sK9,sK12) ),
inference(instantiation,[status(thm)],[c_3410]) ).
cnf(c_3517,plain,
vertex(head_of(sK11)),
inference(superposition,[status(thm)],[c_3480,c_2373]) ).
cnf(c_3540,plain,
( head_of(X0_13) != X0_14
| tail_of(X0_13) != X0_14
| head_of(X0_13) = tail_of(X0_13) ),
inference(instantiation,[status(thm)],[c_2393]) ).
cnf(c_3553,plain,
( ~ precedes(X0_13,X1_13,sK12)
| on_path(X0_13,sK12) ),
inference(superposition,[status(thm)],[c_3461,c_2355]) ).
cnf(c_3562,plain,
( ~ precedes(X0_13,X1_13,sK12)
| on_path(X1_13,sK12) ),
inference(superposition,[status(thm)],[c_3461,c_2356]) ).
cnf(c_3624,plain,
on_path(sK10,sK12),
inference(superposition,[status(thm)],[c_2385,c_3553]) ).
cnf(c_3628,plain,
on_path(sK11,sK12),
inference(superposition,[status(thm)],[c_2385,c_3562]) ).
cnf(c_3692,plain,
head_of(sK11) = head_of(sK11),
inference(instantiation,[status(thm)],[c_2389]) ).
cnf(c_3693,plain,
( head_of(X0_13) != X0_14
| head_of(sK11) != X0_14
| head_of(sK11) = head_of(X0_13) ),
inference(instantiation,[status(thm)],[c_2393]) ).
cnf(c_3951,plain,
( head_of(sK11) != tail_of(X0_13)
| ~ edge(X0_13)
| ~ edge(sK11)
| sK11 = X0_13
| sequential(sK11,X0_13) ),
inference(instantiation,[status(thm)],[c_2365]) ).
cnf(c_3952,plain,
( head_of(sK11) != tail_of(sK10)
| ~ edge(sK10)
| ~ edge(sK11)
| sK11 = sK10
| sequential(sK11,sK10) ),
inference(instantiation,[status(thm)],[c_3951]) ).
cnf(c_4026,plain,
( head_of(X0_13) != tail_of(X1_13)
| tail_of(X0_13) != tail_of(X1_13)
| head_of(X0_13) = tail_of(X0_13) ),
inference(instantiation,[status(thm)],[c_3540]) ).
cnf(c_4184,plain,
( head_of(sK11) != X0_14
| X1_14 != X0_14
| head_of(sK11) = X1_14 ),
inference(instantiation,[status(thm)],[c_2393]) ).
cnf(c_4238,plain,
path(sK8,sK9,sK12),
inference(resolution,[status(thm)],[c_2350,c_2386]) ).
cnf(c_4333,plain,
( ~ precedes(X0_13,X1_13,sK12)
| ~ precedes(X1_13,X0_13,sK12) ),
inference(resolution,[status(thm)],[c_2349,c_2386]) ).
cnf(c_4352,plain,
~ precedes(sK11,sK10,sK12),
inference(resolution,[status(thm)],[c_4333,c_2385]) ).
cnf(c_4676,plain,
( ~ edge(X1_13)
| ~ edge(X0_13)
| head_of(X0_13) != tail_of(X1_13)
| sequential(X0_13,X1_13) ),
inference(global_subsumption_just,[status(thm)],[c_2365,c_2397,c_2365,c_2383,c_4026]) ).
cnf(c_4677,plain,
( head_of(X0_13) != tail_of(X1_13)
| ~ edge(X0_13)
| ~ edge(X1_13)
| sequential(X0_13,X1_13) ),
inference(renaming,[status(thm)],[c_4676]) ).
cnf(c_4706,plain,
( ~ sequential(X0_13,X1_13)
| ~ on_path(X0_13,sK12)
| ~ on_path(X1_13,sK12)
| precedes(X0_13,X1_13,sK12) ),
inference(resolution,[status(thm)],[c_2360,c_4238]) ).
cnf(c_4863,plain,
( ~ on_path(sK10,sK12)
| ~ on_path(sK11,sK12)
| ~ sequential(sK11,sK10) ),
inference(resolution,[status(thm)],[c_4352,c_4706]) ).
cnf(c_6832,plain,
( tail_of(X0_13) != X0_14
| head_of(sK11) != X0_14
| head_of(sK11) = tail_of(X0_13) ),
inference(instantiation,[status(thm)],[c_4184]) ).
cnf(c_9261,plain,
( head_of(sK11) != head_of(sK11)
| X0_14 != head_of(sK11)
| head_of(sK11) = X0_14 ),
inference(instantiation,[status(thm)],[c_4184]) ).
cnf(c_14552,plain,
path(sK8,sK9,sK12),
inference(superposition,[status(thm)],[c_2386,c_2350]) ).
cnf(c_14568,plain,
head_of(sK10) = tail_of(sK11),
inference(superposition,[status(thm)],[c_2384,c_2364]) ).
cnf(c_14580,plain,
( ~ in_path(X0_14,sK12)
| vertex(X0_14) ),
inference(superposition,[status(thm)],[c_14552,c_2366]) ).
cnf(c_14597,plain,
( ~ edge(sK11)
| path(head_of(sK10),head_of(sK11),path_cons(sK11,empty)) ),
inference(superposition,[status(thm)],[c_14568,c_2337]) ).
cnf(c_14601,plain,
path(head_of(sK10),head_of(sK11),path_cons(sK11,empty)),
inference(forward_subsumption_resolution,[status(thm)],[c_14597,c_3450]) ).
cnf(c_14605,plain,
vertex(head_of(sK11)),
inference(superposition,[status(thm)],[c_14601,c_2373]) ).
cnf(c_14625,plain,
( ~ precedes(X0_13,X1_13,sK12)
| on_path(X0_13,sK12) ),
inference(superposition,[status(thm)],[c_14552,c_2355]) ).
cnf(c_14646,plain,
on_path(sK10,sK12),
inference(superposition,[status(thm)],[c_2385,c_14625]) ).
cnf(c_14666,plain,
( ~ on_path(X0_13,sK12)
| in_path(tail_of(X0_13),sK12) ),
inference(superposition,[status(thm)],[c_14552,c_2371]) ).
cnf(c_14691,plain,
( ~ on_path(X0_13,sK12)
| vertex(tail_of(X0_13)) ),
inference(superposition,[status(thm)],[c_14666,c_14580]) ).
cnf(c_14704,plain,
vertex(tail_of(sK10)),
inference(superposition,[status(thm)],[c_14646,c_14691]) ).
cnf(c_16125,plain,
( ~ vertex(X0_14)
| head_of(sK0(tail_of(sK10),X0_14)) = X0_14
| tail_of(sK0(tail_of(sK10),X0_14)) = X0_14
| tail_of(sK10) = X0_14 ),
inference(superposition,[status(thm)],[c_14704,c_2334]) ).
cnf(c_16622,plain,
( tail_of(X0_13) != head_of(sK11)
| head_of(sK11) != head_of(sK11)
| head_of(sK11) = tail_of(X0_13) ),
inference(instantiation,[status(thm)],[c_6832]) ).
cnf(c_16623,plain,
( head_of(sK11) != head_of(sK11)
| tail_of(sK10) != head_of(sK11)
| head_of(sK11) = tail_of(sK10) ),
inference(instantiation,[status(thm)],[c_16622]) ).
cnf(c_20148,plain,
( head_of(sK0(tail_of(X0_13),X0_14)) != X0_14
| head_of(sK11) != X0_14
| head_of(sK11) = head_of(sK0(tail_of(X0_13),X0_14)) ),
inference(instantiation,[status(thm)],[c_3693]) ).
cnf(c_24094,plain,
( head_of(sK0(tail_of(sK10),head_of(sK11))) = head_of(sK11)
| tail_of(sK0(tail_of(sK10),head_of(sK11))) = head_of(sK11)
| head_of(sK11) = tail_of(sK10) ),
inference(superposition,[status(thm)],[c_14605,c_16125]) ).
cnf(c_27341,plain,
path(sK8,sK9,sK12),
inference(superposition,[status(thm)],[c_2386,c_2350]) ).
cnf(c_27357,plain,
head_of(sK10) = tail_of(sK11),
inference(superposition,[status(thm)],[c_2384,c_2364]) ).
cnf(c_27369,plain,
( ~ in_path(X0_14,sK12)
| vertex(X0_14) ),
inference(superposition,[status(thm)],[c_27341,c_2366]) ).
cnf(c_27382,plain,
( ~ edge(sK11)
| path(head_of(sK10),head_of(sK11),path_cons(sK11,empty)) ),
inference(superposition,[status(thm)],[c_27357,c_2337]) ).
cnf(c_27386,plain,
path(head_of(sK10),head_of(sK11),path_cons(sK11,empty)),
inference(forward_subsumption_resolution,[status(thm)],[c_27382,c_3450]) ).
cnf(c_27388,plain,
vertex(head_of(sK11)),
inference(superposition,[status(thm)],[c_27386,c_2373]) ).
cnf(c_27413,plain,
( ~ precedes(X0_13,X1_13,sK12)
| on_path(X0_13,sK12) ),
inference(superposition,[status(thm)],[c_27341,c_2355]) ).
cnf(c_27434,plain,
on_path(sK10,sK12),
inference(superposition,[status(thm)],[c_2385,c_27413]) ).
cnf(c_27457,plain,
( ~ on_path(X0_13,sK12)
| in_path(tail_of(X0_13),sK12) ),
inference(superposition,[status(thm)],[c_27341,c_2371]) ).
cnf(c_27482,plain,
( ~ on_path(X0_13,sK12)
| vertex(tail_of(X0_13)) ),
inference(superposition,[status(thm)],[c_27457,c_27369]) ).
cnf(c_27495,plain,
vertex(tail_of(sK10)),
inference(superposition,[status(thm)],[c_27434,c_27482]) ).
cnf(c_28869,plain,
( ~ vertex(X0_14)
| tail_of(sK0(tail_of(sK10),X0_14)) = tail_of(sK10)
| tail_of(sK0(tail_of(sK10),X0_14)) = X0_14
| tail_of(sK10) = X0_14 ),
inference(superposition,[status(thm)],[c_27495,c_2332]) ).
cnf(c_34605,plain,
( tail_of(sK0(tail_of(X0_13),X0_14)) != tail_of(sK10)
| head_of(sK11) != head_of(sK0(tail_of(X0_13),X0_14))
| ~ precedes(sK10,sK11,sK12)
| ~ shortest_path(sK8,sK9,sK12) ),
inference(instantiation,[status(thm)],[c_3504]) ).
cnf(c_41100,plain,
( tail_of(sK0(tail_of(X0_13),head_of(sK11))) != head_of(sK11)
| head_of(sK11) != head_of(sK11)
| head_of(sK11) = tail_of(sK0(tail_of(X0_13),head_of(sK11))) ),
inference(instantiation,[status(thm)],[c_9261]) ).
cnf(c_41104,plain,
( tail_of(sK0(tail_of(sK10),head_of(sK11))) != head_of(sK11)
| head_of(sK11) != head_of(sK11)
| head_of(sK11) = tail_of(sK0(tail_of(sK10),head_of(sK11))) ),
inference(instantiation,[status(thm)],[c_41100]) ).
cnf(c_42831,plain,
( tail_of(sK0(tail_of(sK10),head_of(sK11))) = head_of(sK11)
| tail_of(sK0(tail_of(sK10),head_of(sK11))) = tail_of(sK10)
| head_of(sK11) = tail_of(sK10) ),
inference(superposition,[status(thm)],[c_27388,c_28869]) ).
cnf(c_45552,plain,
( head_of(sK0(tail_of(X0_13),head_of(sK11))) != head_of(sK11)
| head_of(sK11) != head_of(sK11)
| head_of(sK11) = head_of(sK0(tail_of(X0_13),head_of(sK11))) ),
inference(instantiation,[status(thm)],[c_20148]) ).
cnf(c_45553,plain,
( head_of(sK0(tail_of(sK10),head_of(sK11))) != head_of(sK11)
| head_of(sK11) != head_of(sK11)
| head_of(sK11) = head_of(sK0(tail_of(sK10),head_of(sK11))) ),
inference(instantiation,[status(thm)],[c_45552]) ).
cnf(c_53573,plain,
( tail_of(sK0(tail_of(X0_13),head_of(sK11))) != tail_of(sK10)
| head_of(sK11) != head_of(sK0(tail_of(X0_13),head_of(sK11)))
| ~ precedes(sK10,sK11,sK12)
| ~ shortest_path(sK8,sK9,sK12) ),
inference(instantiation,[status(thm)],[c_34605]) ).
cnf(c_53574,plain,
( tail_of(sK0(tail_of(sK10),head_of(sK11))) != tail_of(sK10)
| head_of(sK11) != head_of(sK0(tail_of(sK10),head_of(sK11)))
| ~ precedes(sK10,sK11,sK12)
| ~ shortest_path(sK8,sK9,sK12) ),
inference(instantiation,[status(thm)],[c_53573]) ).
cnf(c_56773,plain,
path(sK8,sK9,sK12),
inference(superposition,[status(thm)],[c_2386,c_2350]) ).
cnf(c_56786,plain,
head_of(sK10) = tail_of(sK11),
inference(superposition,[status(thm)],[c_2384,c_2364]) ).
cnf(c_56800,plain,
( ~ edge(sK11)
| path(head_of(sK10),head_of(sK11),path_cons(sK11,empty)) ),
inference(superposition,[status(thm)],[c_56786,c_2337]) ).
cnf(c_56803,plain,
path(head_of(sK10),head_of(sK11),path_cons(sK11,empty)),
inference(forward_subsumption_resolution,[status(thm)],[c_56800,c_3450]) ).
cnf(c_56810,plain,
vertex(head_of(sK11)),
inference(superposition,[status(thm)],[c_56803,c_2373]) ).
cnf(c_56815,plain,
( ~ in_path(X0_14,sK12)
| vertex(X0_14) ),
inference(superposition,[status(thm)],[c_56773,c_2366]) ).
cnf(c_56840,plain,
( ~ precedes(X0_13,X1_13,sK12)
| on_path(X0_13,sK12) ),
inference(superposition,[status(thm)],[c_56773,c_2355]) ).
cnf(c_56861,plain,
on_path(sK10,sK12),
inference(superposition,[status(thm)],[c_2385,c_56840]) ).
cnf(c_56882,plain,
( ~ on_path(X0_13,sK12)
| in_path(tail_of(X0_13),sK12) ),
inference(superposition,[status(thm)],[c_56773,c_2371]) ).
cnf(c_56906,plain,
( ~ on_path(X0_13,sK12)
| vertex(tail_of(X0_13)) ),
inference(superposition,[status(thm)],[c_56882,c_56815]) ).
cnf(c_56919,plain,
vertex(tail_of(sK10)),
inference(superposition,[status(thm)],[c_56861,c_56906]) ).
cnf(c_57114,plain,
( ~ edge(X1_13)
| ~ edge(X0_13)
| head_of(X0_13) != tail_of(X1_13)
| sequential(X0_13,X1_13) ),
inference(global_subsumption_just,[status(thm)],[c_2365,c_4677]) ).
cnf(c_57115,plain,
( head_of(X0_13) != tail_of(X1_13)
| ~ edge(X0_13)
| ~ edge(X1_13)
| sequential(X0_13,X1_13) ),
inference(renaming,[status(thm)],[c_57114]) ).
cnf(c_58543,plain,
( ~ vertex(X0_14)
| head_of(sK0(tail_of(sK10),X0_14)) = tail_of(sK10)
| tail_of(sK0(tail_of(sK10),X0_14)) = tail_of(sK10)
| tail_of(sK10) = X0_14 ),
inference(superposition,[status(thm)],[c_56919,c_2333]) ).
cnf(c_58563,plain,
( ~ vertex(X0_14)
| head_of(sK0(tail_of(sK10),X0_14)) = X0_14
| tail_of(sK0(tail_of(sK10),X0_14)) = X0_14
| tail_of(sK10) = X0_14 ),
inference(superposition,[status(thm)],[c_56919,c_2334]) ).
cnf(c_60450,plain,
( head_of(sK0(tail_of(sK10),head_of(sK11))) = head_of(sK11)
| tail_of(sK0(tail_of(sK10),head_of(sK11))) = head_of(sK11)
| head_of(sK11) = tail_of(sK10) ),
inference(superposition,[status(thm)],[c_56810,c_58563]) ).
cnf(c_63053,plain,
( head_of(sK0(tail_of(sK10),head_of(sK11))) = tail_of(sK10)
| tail_of(sK0(tail_of(sK10),head_of(sK11))) = tail_of(sK10)
| head_of(sK11) = tail_of(sK10) ),
inference(superposition,[status(thm)],[c_56810,c_58543]) ).
cnf(c_69075,plain,
( ~ vertex(tail_of(X0_13))
| ~ vertex(X0_14)
| tail_of(X0_13) = X0_14
| edge(sK0(tail_of(X0_13),X0_14)) ),
inference(instantiation,[status(thm)],[c_2338]) ).
cnf(c_69077,plain,
( tail_of(X0_13) != X0_14
| X1_14 != X0_14
| tail_of(X0_13) = X1_14 ),
inference(instantiation,[status(thm)],[c_2393]) ).
cnf(c_69303,plain,
( tail_of(X0_13) != tail_of(X0_13)
| X0_14 != tail_of(X0_13)
| tail_of(X0_13) = X0_14 ),
inference(instantiation,[status(thm)],[c_69077]) ).
cnf(c_69306,plain,
( tail_of(X0_13) != tail_of(X1_13)
| X0_14 != tail_of(X1_13)
| tail_of(X0_13) = X0_14 ),
inference(instantiation,[status(thm)],[c_69077]) ).
cnf(c_69900,plain,
( tail_of(X0_13) != tail_of(X0_13)
| tail_of(X1_13) != tail_of(X0_13)
| tail_of(X0_13) = tail_of(X1_13) ),
inference(instantiation,[status(thm)],[c_69303]) ).
cnf(c_84856,plain,
( head_of(sK0(tail_of(X0_13),head_of(sK11))) != tail_of(sK10)
| ~ edge(sK0(tail_of(X0_13),head_of(sK11)))
| ~ edge(sK10)
| sK0(tail_of(X0_13),head_of(sK11)) = sK10
| sequential(sK0(tail_of(X0_13),head_of(sK11)),sK10) ),
inference(instantiation,[status(thm)],[c_2365]) ).
cnf(c_84857,plain,
( head_of(sK0(tail_of(sK10),head_of(sK11))) != tail_of(sK10)
| ~ edge(sK0(tail_of(sK10),head_of(sK11)))
| ~ edge(sK10)
| sK0(tail_of(sK10),head_of(sK11)) = sK10
| sequential(sK0(tail_of(sK10),head_of(sK11)),sK10) ),
inference(instantiation,[status(thm)],[c_84856]) ).
cnf(c_84990,plain,
( tail_of(sK0(tail_of(X0_13),head_of(sK11))) != tail_of(sK10)
| tail_of(sK10) != tail_of(sK10)
| tail_of(sK10) = tail_of(sK0(tail_of(X0_13),head_of(sK11))) ),
inference(instantiation,[status(thm)],[c_69900]) ).
cnf(c_84993,plain,
( sK10 != sK0(tail_of(X0_13),head_of(sK11))
| tail_of(sK10) = tail_of(sK0(tail_of(X0_13),head_of(sK11))) ),
inference(instantiation,[status(thm)],[c_2397]) ).
cnf(c_84994,plain,
( sK10 != sK0(tail_of(sK10),head_of(sK11))
| tail_of(sK10) = tail_of(sK0(tail_of(sK10),head_of(sK11))) ),
inference(instantiation,[status(thm)],[c_84993]) ).
cnf(c_84997,plain,
( tail_of(sK0(tail_of(sK10),head_of(sK11))) != tail_of(sK10)
| tail_of(sK10) != tail_of(sK10)
| tail_of(sK10) = tail_of(sK0(tail_of(sK10),head_of(sK11))) ),
inference(instantiation,[status(thm)],[c_84990]) ).
cnf(c_91656,plain,
( tail_of(X0_13) != tail_of(sK0(tail_of(sK10),head_of(sK11)))
| head_of(sK11) != tail_of(sK0(tail_of(sK10),head_of(sK11)))
| tail_of(X0_13) = head_of(sK11) ),
inference(instantiation,[status(thm)],[c_69306]) ).
cnf(c_91659,plain,
( head_of(sK11) != tail_of(sK0(tail_of(sK10),head_of(sK11)))
| tail_of(sK10) != tail_of(sK0(tail_of(sK10),head_of(sK11)))
| tail_of(sK10) = head_of(sK11) ),
inference(instantiation,[status(thm)],[c_91656]) ).
cnf(c_100755,plain,
( ~ vertex(head_of(sK11))
| ~ vertex(tail_of(sK10))
| tail_of(sK10) = head_of(sK11)
| edge(sK0(tail_of(sK10),head_of(sK11))) ),
inference(instantiation,[status(thm)],[c_69075]) ).
cnf(c_102913,plain,
( sK0(tail_of(X0_13),head_of(sK11)) != X1_13
| sK10 != X1_13
| sK10 = sK0(tail_of(X0_13),head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_2392]) ).
cnf(c_102914,plain,
( sK0(tail_of(sK10),head_of(sK11)) != sK10
| sK10 != sK10
| sK10 = sK0(tail_of(sK10),head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_102913]) ).
cnf(c_109694,plain,
tail_of(sK0(tail_of(sK10),head_of(sK11))) = head_of(sK11),
inference(global_subsumption_just,[status(thm)],[c_60450,c_103,c_105,c_104,c_2418,c_2442,c_3402,c_3403,c_3407,c_3495,c_3624,c_3628,c_3692,c_3952,c_4863,c_24094,c_42831,c_45553,c_53574]) ).
cnf(c_109732,plain,
( head_of(X0_13) != head_of(sK11)
| ~ edge(sK0(tail_of(sK10),head_of(sK11)))
| ~ edge(X0_13)
| sequential(X0_13,sK0(tail_of(sK10),head_of(sK11))) ),
inference(superposition,[status(thm)],[c_109694,c_57115]) ).
cnf(c_129709,plain,
( ~ sequential(sK0(tail_of(sK10),head_of(sK11)),sK10)
| ~ sequential(sK11,sK0(tail_of(sK10),head_of(sK11))) ),
inference(instantiation,[status(thm)],[c_2328]) ).
cnf(c_146048,plain,
path(sK8,sK9,sK12),
inference(superposition,[status(thm)],[c_2386,c_2350]) ).
cnf(c_146053,plain,
head_of(sK10) = tail_of(sK11),
inference(superposition,[status(thm)],[c_2384,c_2364]) ).
cnf(c_146067,plain,
( ~ edge(sK11)
| path(head_of(sK10),head_of(sK11),path_cons(sK11,empty)) ),
inference(superposition,[status(thm)],[c_146053,c_2337]) ).
cnf(c_146070,plain,
path(head_of(sK10),head_of(sK11),path_cons(sK11,empty)),
inference(forward_subsumption_resolution,[status(thm)],[c_146067,c_3450]) ).
cnf(c_146072,plain,
vertex(head_of(sK11)),
inference(superposition,[status(thm)],[c_146070,c_2373]) ).
cnf(c_146076,plain,
( ~ in_path(X0_14,sK12)
| vertex(X0_14) ),
inference(superposition,[status(thm)],[c_146048,c_2366]) ).
cnf(c_146107,plain,
( ~ precedes(X0_13,X1_13,sK12)
| on_path(X0_13,sK12) ),
inference(superposition,[status(thm)],[c_146048,c_2355]) ).
cnf(c_146128,plain,
on_path(sK10,sK12),
inference(superposition,[status(thm)],[c_2385,c_146107]) ).
cnf(c_146151,plain,
( ~ on_path(X0_13,sK12)
| in_path(tail_of(X0_13),sK12) ),
inference(superposition,[status(thm)],[c_146048,c_2371]) ).
cnf(c_146176,plain,
( ~ on_path(X0_13,sK12)
| vertex(tail_of(X0_13)) ),
inference(superposition,[status(thm)],[c_146151,c_146076]) ).
cnf(c_146189,plain,
vertex(tail_of(sK10)),
inference(superposition,[status(thm)],[c_146128,c_146176]) ).
cnf(c_146368,plain,
( ~ edge(X1_13)
| ~ edge(X0_13)
| head_of(X0_13) != tail_of(X1_13)
| sequential(X0_13,X1_13) ),
inference(global_subsumption_just,[status(thm)],[c_2365,c_4677]) ).
cnf(c_146369,plain,
( head_of(X0_13) != tail_of(X1_13)
| ~ edge(X0_13)
| ~ edge(X1_13)
| sequential(X0_13,X1_13) ),
inference(renaming,[status(thm)],[c_146368]) ).
cnf(c_147805,plain,
( ~ vertex(X0_14)
| head_of(sK0(tail_of(sK10),X0_14)) = X0_14
| tail_of(sK0(tail_of(sK10),X0_14)) = X0_14
| tail_of(sK10) = X0_14 ),
inference(superposition,[status(thm)],[c_146189,c_2334]) ).
cnf(c_149653,plain,
( head_of(sK0(tail_of(sK10),head_of(sK11))) = head_of(sK11)
| tail_of(sK0(tail_of(sK10),head_of(sK11))) = head_of(sK11)
| head_of(sK11) = tail_of(sK10) ),
inference(superposition,[status(thm)],[c_146072,c_147805]) ).
cnf(c_155946,plain,
tail_of(sK0(tail_of(sK10),head_of(sK11))) = head_of(sK11),
inference(global_subsumption_just,[status(thm)],[c_149653,c_109694]) ).
cnf(c_155987,plain,
( head_of(X0_13) != head_of(sK11)
| ~ edge(sK0(tail_of(sK10),head_of(sK11)))
| ~ edge(X0_13)
| sequential(X0_13,sK0(tail_of(sK10),head_of(sK11))) ),
inference(superposition,[status(thm)],[c_155946,c_146369]) ).
cnf(c_157152,plain,
( head_of(X0_13) != head_of(sK11)
| ~ edge(X0_13)
| sequential(X0_13,sK0(tail_of(sK10),head_of(sK11))) ),
inference(global_subsumption_just,[status(thm)],[c_155987,c_103,c_2418,c_2442,c_2458,c_3402,c_3403,c_3407,c_3495,c_3517,c_3624,c_3628,c_3692,c_3952,c_4863,c_16623,c_100755,c_109732]) ).
cnf(c_157165,plain,
( ~ edge(sK11)
| sequential(sK11,sK0(tail_of(sK10),head_of(sK11))) ),
inference(equality_resolution,[status(thm)],[c_157152]) ).
cnf(c_157166,plain,
sequential(sK11,sK0(tail_of(sK10),head_of(sK11))),
inference(forward_subsumption_resolution,[status(thm)],[c_157165,c_3450]) ).
cnf(c_157168,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_157166,c_129709,c_109694,c_102914,c_100755,c_91659,c_84997,c_84994,c_84857,c_63053,c_41104,c_16623,c_4863,c_3952,c_3692,c_3628,c_3624,c_3517,c_3495,c_3407,c_3403,c_3402,c_2458,c_2442,c_2418,c_2412,c_103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GRA008+1 : TPTP v8.2.0. Bugfixed v3.2.0.
% 0.04/0.13 % Command : run_iprover %s %d THM
% 0.12/0.34 % Computer : n025.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue Jun 18 15:29:54 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.21/0.50 Running first-order theorem proving
% 0.21/0.50 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 47.96/7.33 % SZS status Started for theBenchmark.p
% 47.96/7.33 ERROR - "ProverProcess:heur/379306:2.0" ran with exit code 2 and error: iprover.ml: Unexpected exception: Z3.Error("Sort mismatch at argument #1 for function (declare-fun k!96 (|16777216|) |16777216|) supplied sort is |16777229|")
% 47.96/7.33 Fatal error: exception Z3.Error("Sort mismatch at argument #1 for function (declare-fun k!96 (|16777216|) |16777216|) supplied sort is |16777229|")
% 47.96/7.33 ERROR - cmd was: ulimit -v 4096000; ./res/iproveropt_static_z3 --abstr_ref "[]" --abstr_ref_under "[]" --comb_inst_mult 3 --comb_mode clause_based --comb_res_mult 1 --comb_sup_deep_mult 6 --comb_sup_mult 32 --conj_cone_tolerance 3. --demod_completeness_check fast --demod_use_ground false --eq_ax_congr_red true --extra_neg_conj none --inst_activity_threshold 500 --inst_dismatching true --inst_eager_unprocessed_to_passive true --inst_eq_res_simp false --inst_learning_factor 2 --inst_learning_loop_flag true --inst_learning_start 3000 --inst_lit_activity_flag true --inst_lit_sel "[+prop;+sign;+ground;-num_var;-num_symb]" --inst_lit_sel_side num_symb --inst_orphan_elimination true --inst_passive_queue_type priority_queues --inst_passive_queues "[[-conj_dist;+conj_symb;-num_var];[+age;-num_symb]]" --inst_passive_queues_freq "[25;2]" --inst_prop_sim_given true --inst_prop_sim_new false --inst_restr_to_given false --inst_sel_renew solver --inst_solver_calls_frac 1. --inst_solver_per_active 1400 --inst_sos_flag false --inst_start_prop_sim_after_learn 3 --inst_subs_given false --inst_subs_new false --instantiation_flag true --out_options none --pred_elim true --prep_def_merge true --prep_def_merge_mbd true --prep_def_merge_prop_impl false --prep_def_merge_tr_cl false --prep_def_merge_tr_red false --prep_gs_sim true --prep_res_sim true --prep_sem_filter exhaustive --prep_sup_sim_all true --prep_sup_sim_sup false --prep_unflatten true --prep_upred true --preprocessing_flag true --prolific_symb_bound 256 --prop_solver_per_cl 1024 --pure_diseq_elim true --res_backward_subs full --res_backward_subs_resolution true --res_forward_subs full --res_forward_subs_resolution true --res_lit_sel adaptive --res_lit_sel_side none --res_ordering kbo --res_passive_queue_type priority_queues --res_passive_queues "[[-conj_dist;+conj_symb;-num_symb];[+age;-num_symb]]" --res_passive_queues_freq "[15;5]" --res_prop_simpl_given true --res_prop_simpl_new false --res_sim_input true --res_time_limit 300.00 --res_to_prop_solver active --resolution_flag true --schedule none --share_sel_clauses true --smt_ac_axioms fast --smt_preprocessing true --splitting_cvd false --splitting_cvd_svl false --splitting_grd true --splitting_mode input --splitting_nvd 32 --stats_out none --sub_typing true --subs_bck_mult 8 --sup_full_bw "[]" --sup_full_fw "[]" --sup_full_triv "[PropSubs;Unflattening]" --sup_fun_splitting false --sup_immed_bw_immed "[]" --sup_immed_bw_main "[]" --sup_immed_fw_immed "[Subsumption;SubsumptionRes;UnitSubsAndRes;DemodLoopTriv;ACNormalisation]" --sup_immed_fw_main "[Subsumption;UnitSubsAndRes;Demod;LightNorm;ACNormalisation]" --sup_immed_triv "[PropSubs]" --sup_indices_passive "[]" --sup_input_bw "[SubsumptionRes]" --sup_input_fw "[SMTSubs;]" --sup_input_triv "[]" --sup_iter_deepening 1 --sup_passive_queue_type priority_queues --sup_passive_queues "[[+min_def_symb;-score;+epr];[-next_state;-conj_dist;+conj_symb]]" --sup_passive_queues_freq "[3;512]" --sup_prop_simpl_given false --sup_prop_simpl_new true --sup_restarts_mult 16 --sup_score sim_d_gen --sup_share_max_num_cl 320 --sup_share_score_frac 0.2 --sup_smt_interval 10000 --sup_symb_ordering arity_rev --sup_to_prop_solver none --superposition_flag true --time_out_prep_mult 0.1 --suppress_sat_res true --proof_out true --sat_out_model pos --clausifier res/vclausify_rel --clausifier_options "--mode clausify --show_fool true -t 2.00" --time_out_real 2.00 /export/starexec/sandbox2/benchmark/theBenchmark.p 1>> /export/starexec/sandbox2/tmp/iprover_out_rtzy4mln/osk9o26c 2>> /export/starexec/sandbox2/tmp/iprover_out_rtzy4mln/osk9o26c_error
% 86.39/12.35 % SZS status Theorem for theBenchmark.p
% 86.39/12.35
% 86.39/12.35 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 86.39/12.35
% 86.39/12.35 ------ iProver source info
% 86.39/12.35
% 86.39/12.35 git: date: 2024-06-12 09:56:46 +0000
% 86.39/12.35 git: sha1: 4869ab62f0a3398f9d3a35e6db7918ebd3847e49
% 86.39/12.35 git: non_committed_changes: false
% 86.39/12.35
% 86.39/12.35 ------ Parsing...
% 86.39/12.35 ------ Clausification by vclausify_rel & Parsing by iProver...
% 86.39/12.35
% 86.39/12.35 ------ Preprocessing... sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e
% 86.39/12.35
% 86.39/12.35 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 86.39/12.35
% 86.39/12.35 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 86.39/12.35 ------ Proving...
% 86.39/12.35 ------ Problem Properties
% 86.39/12.35
% 86.39/12.35
% 86.39/12.35 clauses 56
% 86.39/12.35 conjectures 3
% 86.39/12.35 EPR 19
% 86.39/12.35 Horn 38
% 86.39/12.35 unary 6
% 86.39/12.35 binary 15
% 86.39/12.35 lits 171
% 86.39/12.35 lits eq 44
% 86.39/12.35 fd_pure 0
% 86.39/12.35 fd_pseudo 0
% 86.39/12.35 fd_cond 0
% 86.39/12.35 fd_pseudo_cond 5
% 86.39/12.35 AC symbols 0
% 86.39/12.35
% 86.39/12.35 ------ Input Options Time Limit: Unbounded
% 86.39/12.35
% 86.39/12.35
% 86.39/12.35 ------
% 86.39/12.35 Current options:
% 86.39/12.35 ------
% 86.39/12.35
% 86.39/12.35
% 86.39/12.35
% 86.39/12.35
% 86.39/12.35 ------ Proving...
% 86.39/12.35
% 86.39/12.35
% 86.39/12.35 % SZS status Theorem for theBenchmark.p
% 86.39/12.35
% 86.39/12.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 86.39/12.35
% 86.39/12.35
%------------------------------------------------------------------------------