TSTP Solution File: GRA008+1 by iProver---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : GRA008+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n013.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 : Fri May 3 02:19:23 EDT 2024
% Result : Theorem 61.86s 9.24s
% Output : CNFRefutation 61.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 22
% Syntax : Number of formulae : 256 ( 14 unt; 0 def)
% Number of atoms : 1133 ( 387 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 1449 ( 572 ~; 595 |; 230 &)
% ( 7 <=>; 35 =>; 0 <=; 10 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 2 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 619 ( 57 sgn 298 !; 60 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( edge(X0)
=> head_of(X0) != tail_of(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',no_loops) ).
fof(f2,axiom,
! [X0] :
( edge(X0)
=> ( vertex(tail_of(X0))
& vertex(head_of(X0)) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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(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(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(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(f94,plain,
! [X0,X1] :
( head_of(sK0(X0,X1)) = X1
| head_of(sK0(X0,X1)) = X0
| 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(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(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(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(f122,plain,
! [X2,X3,X0,X1,X4,X5] :
( precedes(X3,X4,X0)
| ~ precedes(X5,X4,X0)
| ~ sequential(X3,X5)
| ~ 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]) ).
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_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_56,plain,
( ~ vertex(X0)
| ~ vertex(X1)
| ~ complete
| head_of(sK0(X0,X1)) = X0
| head_of(sK0(X0,X1)) = X1
| X0 = X1 ),
inference(cnf_transformation,[],[f94]) ).
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_75,plain,
( head_of(X0) != tail_of(X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f120]) ).
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_80,plain,
( ~ path(X0,X1,X2)
| ~ precedes(X3,X4,X2)
| ~ on_path(X4,X2)
| ~ on_path(X5,X2)
| ~ sequential(X5,X3)
| precedes(X5,X4,X2) ),
inference(cnf_transformation,[],[f122]) ).
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_155,plain,
( ~ precedes(X3,X4,X2)
| ~ path(X0,X1,X2)
| ~ on_path(X5,X2)
| ~ sequential(X5,X3)
| precedes(X5,X4,X2) ),
inference(global_subsumption_just,[status(thm)],[c_80,c_85,c_80]) ).
cnf(c_156,plain,
( ~ path(X0,X1,X2)
| ~ precedes(X3,X4,X2)
| ~ on_path(X5,X2)
| ~ sequential(X5,X3)
| precedes(X5,X4,X2) ),
inference(renaming,[status(thm)],[c_155]) ).
cnf(c_157,plain,
( ~ vertex(X1)
| ~ vertex(X0)
| head_of(sK0(X0,X1)) = X0
| head_of(sK0(X0,X1)) = X1
| X0 = X1 ),
inference(global_subsumption_just,[status(thm)],[c_56,c_106,c_56]) ).
cnf(c_158,plain,
( ~ vertex(X0)
| ~ vertex(X1)
| head_of(sK0(X0,X1)) = X0
| head_of(sK0(X0,X1)) = X1
| X0 = X1 ),
inference(renaming,[status(thm)],[c_157]) ).
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_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_261,plain,
( X0 != sK10
| X1 != sK11
| X2 != X3
| ~ sequential(X0,X1)
| ~ sequential(X1,X2)
| ~ sequential(X2,X0)
| ~ edge(X2) ),
inference(resolution_lifted,[status(thm)],[c_153,c_102]) ).
cnf(c_262,plain,
( ~ sequential(X0,sK10)
| ~ sequential(sK11,X0)
| ~ sequential(sK10,sK11)
| ~ edge(X0) ),
inference(unflattening,[status(thm)],[c_261]) ).
cnf(c_264,plain,
( ~ sequential(sK11,X0)
| ~ sequential(X0,sK10)
| ~ edge(X0) ),
inference(global_subsumption_just,[status(thm)],[c_262,c_103,c_262]) ).
cnf(c_265,plain,
( ~ sequential(X0,sK10)
| ~ sequential(sK11,X0)
| ~ edge(X0) ),
inference(renaming,[status(thm)],[c_264]) ).
cnf(c_273,plain,
( ~ sequential(X0,sK10)
| ~ sequential(sK11,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_265,c_78]) ).
cnf(c_525,plain,
( X0 != sK8
| X1 != sK9
| X2 != sK12
| path(X0,X1,X2) ),
inference(resolution_lifted,[status(thm)],[c_91,c_105]) ).
cnf(c_526,plain,
path(sK8,sK9,sK12),
inference(unflattening,[status(thm)],[c_525]) ).
cnf(c_983,plain,
( ~ sequential(X0_13,sK10)
| ~ sequential(sK11,X0_13) ),
inference(subtyping,[status(esa)],[c_273]) ).
cnf(c_986,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_988,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_989,plain,
( ~ vertex(X0_14)
| ~ vertex(X1_14)
| head_of(sK0(X0_14,X1_14)) = X0_14
| head_of(sK0(X0_14,X1_14)) = X1_14
| X0_14 = X1_14 ),
inference(subtyping,[status(esa)],[c_158]) ).
cnf(c_990,plain,
( ~ path(X0_14,X1_14,X0_15)
| ~ precedes(X0_13,X1_13,X0_15)
| ~ on_path(X2_13,X0_15)
| ~ sequential(X2_13,X0_13)
| precedes(X2_13,X1_13,X0_15) ),
inference(subtyping,[status(esa)],[c_156]) ).
cnf(c_992,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_993,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_1003,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_1004,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_1010,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_1011,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_1015,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_1016,plain,
( ~ sequential(X0_13,X1_13)
| edge(X0_13) ),
inference(subtyping,[status(esa)],[c_79]) ).
cnf(c_1017,plain,
( ~ sequential(X0_13,X1_13)
| edge(X1_13) ),
inference(subtyping,[status(esa)],[c_78]) ).
cnf(c_1020,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_1028,plain,
( ~ path(X0_14,X1_14,X0_15)
| vertex(X1_14) ),
inference(subtyping,[status(esa)],[c_67]) ).
cnf(c_1037,plain,
( ~ edge(X0_13)
| vertex(tail_of(X0_13)) ),
inference(subtyping,[status(esa)],[c_50]) ).
cnf(c_1038,plain,
( head_of(X0_13) != tail_of(X0_13)
| ~ edge(X0_13) ),
inference(subtyping,[status(esa)],[c_49]) ).
cnf(c_1049,plain,
( ~ path(X0_14,X1_14,X0_15)
| ~ sP1_iProver_def(X0_15) ),
inference(splitting,[splitting(split),new_symbols(definition,[sP1_iProver_def])],[c_990]) ).
cnf(c_1065,plain,
( ~ shortest_path(X0_14,X1_14,X0_15)
| ~ sP2_iProver_def(X0_15) ),
inference(splitting,[splitting(split),new_symbols(definition,[sP2_iProver_def])],[c_1003]) ).
cnf(c_1066,plain,
( ~ precedes(X0_13,X1_13,X0_15)
| sP2_iProver_def(X0_15)
| ~ sP3_iProver_def(X0_13,X1_13) ),
inference(splitting,[splitting(split),new_symbols(definition,[sP3_iProver_def])],[c_1003]) ).
cnf(c_1067,plain,
( head_of(X0_13) != head_of(X1_13)
| tail_of(X1_13) != tail_of(X2_13)
| sP3_iProver_def(X2_13,X0_13) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1003]) ).
cnf(c_1071,plain,
( ~ precedes(X0_13,X1_13,X0_15)
| ~ precedes(X1_13,X0_13,X0_15)
| sP2_iProver_def(X0_15) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1004]) ).
cnf(c_1079,plain,
( ~ precedes(X0_13,X1_13,X0_15)
| on_path(X0_13,X0_15)
| sP1_iProver_def(X0_15) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1010]) ).
cnf(c_1082,plain,
( ~ precedes(X0_13,X1_13,X0_15)
| on_path(X1_13,X0_15)
| ~ sP4_iProver_def(X0_15) ),
inference(splitting,[splitting(split),new_symbols(definition,[sP4_iProver_def])],[c_1011]) ).
cnf(c_1083,plain,
( ~ path(X0_14,X1_14,X0_15)
| sP4_iProver_def(X0_15) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1011]) ).
cnf(c_1095,plain,
( ~ on_path(X0_13,X0_15)
| ~ on_path(X1_13,X0_15)
| ~ sequential(X0_13,X1_13)
| precedes(X0_13,X1_13,X0_15)
| sP1_iProver_def(X0_15) ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_1015]) ).
cnf(c_1134,plain,
X0_13 = X0_13,
theory(equality) ).
cnf(c_1139,plain,
( X0_14 != X1_14
| X2_14 != X1_14
| X2_14 = X0_14 ),
theory(equality) ).
cnf(c_1142,plain,
( X0_13 != X1_13
| head_of(X0_13) = head_of(X1_13) ),
theory(equality) ).
cnf(c_1143,plain,
( X0_13 != X1_13
| tail_of(X0_13) = tail_of(X1_13) ),
theory(equality) ).
cnf(c_1158,plain,
( sK10 != sK10
| tail_of(sK10) = tail_of(sK10) ),
inference(instantiation,[status(thm)],[c_1143]) ).
cnf(c_1164,plain,
sK10 = sK10,
inference(instantiation,[status(thm)],[c_1134]) ).
cnf(c_1190,plain,
( ~ edge(sK10)
| vertex(tail_of(sK10)) ),
inference(instantiation,[status(thm)],[c_1037]) ).
cnf(c_1898,plain,
( ~ shortest_path(sK8,sK9,sK12)
| ~ sP2_iProver_def(sK12) ),
inference(instantiation,[status(thm)],[c_1065]) ).
cnf(c_1904,plain,
( ~ precedes(X0_13,X1_13,sK12)
| ~ precedes(X1_13,X0_13,sK12)
| sP2_iProver_def(sK12) ),
inference(instantiation,[status(thm)],[c_1071]) ).
cnf(c_1906,plain,
( ~ precedes(X1_13,X0_13,sK12)
| ~ precedes(X0_13,X1_13,sK12) ),
inference(global_subsumption_just,[status(thm)],[c_1904,c_105,c_1898,c_1904]) ).
cnf(c_1907,plain,
( ~ precedes(X0_13,X1_13,sK12)
| ~ precedes(X1_13,X0_13,sK12) ),
inference(renaming,[status(thm)],[c_1906]) ).
cnf(c_1909,plain,
( ~ precedes(sK10,sK11,sK12)
| ~ precedes(sK11,sK10,sK12) ),
inference(instantiation,[status(thm)],[c_1907]) ).
cnf(c_2139,plain,
( ~ precedes(X0_13,X1_13,sK12)
| ~ sP3_iProver_def(X0_13,X1_13)
| sP2_iProver_def(sK12) ),
inference(instantiation,[status(thm)],[c_1066]) ).
cnf(c_2140,plain,
( ~ sP3_iProver_def(X0_13,X1_13)
| ~ precedes(X0_13,X1_13,sK12) ),
inference(global_subsumption_just,[status(thm)],[c_2139,c_105,c_1898,c_2139]) ).
cnf(c_2141,plain,
( ~ precedes(X0_13,X1_13,sK12)
| ~ sP3_iProver_def(X0_13,X1_13) ),
inference(renaming,[status(thm)],[c_2140]) ).
cnf(c_2142,plain,
( ~ precedes(sK10,sK11,sK12)
| ~ sP3_iProver_def(sK10,sK11) ),
inference(instantiation,[status(thm)],[c_2141]) ).
cnf(c_2145,plain,
( tail_of(X0_13) != tail_of(sK10)
| head_of(sK11) != head_of(X0_13)
| sP3_iProver_def(sK10,sK11) ),
inference(instantiation,[status(thm)],[c_1067]) ).
cnf(c_2146,plain,
( head_of(sK11) != head_of(sK10)
| tail_of(sK10) != tail_of(sK10)
| sP3_iProver_def(sK10,sK11) ),
inference(instantiation,[status(thm)],[c_2145]) ).
cnf(c_2150,plain,
( sK11 != X0_13
| head_of(sK11) = head_of(X0_13) ),
inference(instantiation,[status(thm)],[c_1142]) ).
cnf(c_2151,plain,
( sK11 != sK10
| head_of(sK11) = head_of(sK10) ),
inference(instantiation,[status(thm)],[c_2150]) ).
cnf(c_3371,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_1139]) ).
cnf(c_3532,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_3371]) ).
cnf(c_4109,plain,
( sK11 != X0_13
| tail_of(sK11) = tail_of(X0_13) ),
inference(instantiation,[status(thm)],[c_1143]) ).
cnf(c_5084,plain,
( head_of(sK11) != tail_of(X0_13)
| tail_of(sK11) != tail_of(X0_13)
| head_of(sK11) = tail_of(sK11) ),
inference(instantiation,[status(thm)],[c_3532]) ).
cnf(c_5493,plain,
( ~ precedes(X0_13,X1_13,sK12)
| on_path(X0_13,sK12)
| sP1_iProver_def(sK12) ),
inference(instantiation,[status(thm)],[c_1079]) ).
cnf(c_5507,plain,
( ~ precedes(sK10,sK11,sK12)
| on_path(sK10,sK12)
| sP1_iProver_def(sK12) ),
inference(instantiation,[status(thm)],[c_5493]) ).
cnf(c_5536,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_1020]) ).
cnf(c_5537,plain,
( head_of(sK11) != tail_of(sK10)
| ~ edge(sK10)
| ~ edge(sK11)
| sK11 = sK10
| sequential(sK11,sK10) ),
inference(instantiation,[status(thm)],[c_5536]) ).
cnf(c_5558,plain,
( ~ sequential(X0_13,sK11)
| edge(sK11) ),
inference(instantiation,[status(thm)],[c_1017]) ).
cnf(c_5559,plain,
( ~ sequential(sK10,sK11)
| edge(sK11) ),
inference(instantiation,[status(thm)],[c_5558]) ).
cnf(c_5583,plain,
( ~ sequential(X0_13,X1_13)
| ~ on_path(X0_13,sK12)
| ~ on_path(X1_13,sK12)
| precedes(X0_13,X1_13,sK12)
| sP1_iProver_def(sK12) ),
inference(instantiation,[status(thm)],[c_1095]) ).
cnf(c_5658,plain,
( ~ path(X0_14,head_of(sK11),X0_15)
| vertex(head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_1028]) ).
cnf(c_5666,plain,
( ~ sequential(sK10,sK11)
| edge(sK10) ),
inference(instantiation,[status(thm)],[c_1016]) ).
cnf(c_5682,plain,
( ~ path(tail_of(sK11),head_of(sK11),path_cons(sK11,empty))
| vertex(head_of(sK11)) ),
inference(instantiation,[status(thm)],[c_5658]) ).
cnf(c_5719,plain,
( ~ on_path(X0_13,sK12)
| ~ sequential(sK11,X0_13)
| ~ on_path(sK11,sK12)
| precedes(sK11,X0_13,sK12)
| sP1_iProver_def(sK12) ),
inference(instantiation,[status(thm)],[c_5583]) ).
cnf(c_5720,plain,
( ~ on_path(sK10,sK12)
| ~ on_path(sK11,sK12)
| ~ sequential(sK11,sK10)
| precedes(sK11,sK10,sK12)
| sP1_iProver_def(sK12) ),
inference(instantiation,[status(thm)],[c_5719]) ).
cnf(c_5734,plain,
( head_of(sK11) != tail_of(sK11)
| ~ edge(sK11) ),
inference(instantiation,[status(thm)],[c_1038]) ).
cnf(c_5763,plain,
( ~ edge(sK11)
| path(tail_of(sK11),head_of(sK11),path_cons(sK11,empty)) ),
inference(instantiation,[status(thm)],[c_992]) ).
cnf(c_6034,plain,
( ~ vertex(head_of(X0_13))
| ~ vertex(X0_14)
| head_of(sK0(head_of(X0_13),X0_14)) = head_of(X0_13)
| head_of(sK0(head_of(X0_13),X0_14)) = X0_14
| head_of(X0_13) = X0_14 ),
inference(instantiation,[status(thm)],[c_989]) ).
cnf(c_6228,plain,
( ~ vertex(head_of(X0_13))
| ~ vertex(tail_of(X1_13))
| head_of(sK0(head_of(X0_13),tail_of(X1_13))) = head_of(X0_13)
| head_of(sK0(head_of(X0_13),tail_of(X1_13))) = tail_of(X1_13)
| head_of(X0_13) = tail_of(X1_13) ),
inference(instantiation,[status(thm)],[c_6034]) ).
cnf(c_6332,plain,
( ~ vertex(tail_of(sK10))
| ~ vertex(X0_14)
| head_of(sK0(X0_14,tail_of(sK10))) = tail_of(sK10)
| head_of(sK0(X0_14,tail_of(sK10))) = X0_14
| X0_14 = tail_of(sK10) ),
inference(instantiation,[status(thm)],[c_989]) ).
cnf(c_6339,plain,
( ~ vertex(X0_14)
| head_of(sK0(X0_14,tail_of(sK10))) = tail_of(sK10)
| head_of(sK0(X0_14,tail_of(sK10))) = X0_14
| X0_14 = tail_of(sK10) ),
inference(global_subsumption_just,[status(thm)],[c_6332,c_103,c_1190,c_5666,c_6332]) ).
cnf(c_7167,plain,
( ~ vertex(head_of(X0_13))
| head_of(sK0(head_of(X0_13),tail_of(sK10))) = head_of(X0_13)
| head_of(sK0(head_of(X0_13),tail_of(sK10))) = tail_of(sK10)
| head_of(X0_13) = tail_of(sK10) ),
inference(instantiation,[status(thm)],[c_6339]) ).
cnf(c_7177,plain,
( ~ vertex(tail_of(X0_13))
| ~ vertex(head_of(sK11))
| head_of(sK0(head_of(sK11),tail_of(X0_13))) = tail_of(X0_13)
| head_of(sK0(head_of(sK11),tail_of(X0_13))) = head_of(sK11)
| head_of(sK11) = tail_of(X0_13) ),
inference(instantiation,[status(thm)],[c_6228]) ).
cnf(c_7179,plain,
( ~ vertex(tail_of(X0_13))
| head_of(sK0(head_of(sK11),tail_of(X0_13))) = tail_of(X0_13)
| head_of(sK0(head_of(sK11),tail_of(X0_13))) = head_of(sK11)
| head_of(sK11) = tail_of(X0_13) ),
inference(global_subsumption_just,[status(thm)],[c_7177,c_103,c_5559,c_5682,c_5763,c_7177]) ).
cnf(c_7181,plain,
( ~ vertex(tail_of(sK10))
| head_of(sK0(head_of(sK11),tail_of(sK10))) = head_of(sK11)
| head_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10)
| head_of(sK11) = tail_of(sK10) ),
inference(instantiation,[status(thm)],[c_7179]) ).
cnf(c_8698,plain,
( ~ vertex(head_of(sK11))
| head_of(sK0(head_of(sK11),tail_of(sK10))) = head_of(sK11)
| head_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10)
| head_of(sK11) = tail_of(sK10) ),
inference(instantiation,[status(thm)],[c_7167]) ).
cnf(c_8699,plain,
( head_of(sK0(head_of(sK11),tail_of(sK10))) = head_of(sK11)
| head_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10)
| head_of(sK11) = tail_of(sK10) ),
inference(global_subsumption_just,[status(thm)],[c_8698,c_103,c_1190,c_5666,c_7181]) ).
cnf(c_165490,plain,
( ~ precedes(X0_13,sK11,sK12)
| ~ sP4_iProver_def(sK12)
| on_path(sK11,sK12) ),
inference(instantiation,[status(thm)],[c_1082]) ).
cnf(c_165491,plain,
( ~ precedes(sK10,sK11,sK12)
| ~ sP4_iProver_def(sK12)
| on_path(sK11,sK12) ),
inference(instantiation,[status(thm)],[c_165490]) ).
cnf(c_165492,plain,
( ~ sP4_iProver_def(sK12)
| on_path(sK11,sK12) ),
inference(global_subsumption_just,[status(thm)],[c_165490,c_104,c_165491]) ).
cnf(c_165509,plain,
( ~ path(X0_14,X1_14,sK12)
| sP4_iProver_def(sK12) ),
inference(instantiation,[status(thm)],[c_1083]) ).
cnf(c_165820,plain,
( ~ path(sK8,sK9,sK12)
| sP4_iProver_def(sK12) ),
inference(instantiation,[status(thm)],[c_165509]) ).
cnf(c_165823,plain,
( ~ path(sK8,sK9,sK12)
| ~ sP1_iProver_def(sK12) ),
inference(instantiation,[status(thm)],[c_1049]) ).
cnf(c_165944,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_1020]) ).
cnf(c_165945,plain,
( head_of(sK11) != tail_of(X0_13)
| ~ edge(X0_13)
| sequential(sK11,X0_13) ),
inference(global_subsumption_just,[status(thm)],[c_165944,c_103,c_4109,c_5084,c_5536,c_5559,c_5734]) ).
cnf(c_165960,plain,
( ~ vertex(tail_of(X0_13))
| ~ vertex(head_of(sK11))
| head_of(sK0(head_of(sK11),tail_of(X0_13))) = tail_of(X0_13)
| tail_of(sK0(head_of(sK11),tail_of(X0_13))) = tail_of(X0_13)
| head_of(sK11) = tail_of(X0_13) ),
inference(instantiation,[status(thm)],[c_988]) ).
cnf(c_165962,plain,
( ~ vertex(tail_of(X0_13))
| ~ vertex(head_of(sK11))
| tail_of(sK0(head_of(sK11),tail_of(X0_13))) = tail_of(X0_13)
| tail_of(sK0(head_of(sK11),tail_of(X0_13))) = head_of(sK11)
| head_of(sK11) = tail_of(X0_13) ),
inference(instantiation,[status(thm)],[c_986]) ).
cnf(c_165963,plain,
( ~ vertex(tail_of(X0_13))
| ~ vertex(head_of(sK11))
| head_of(sK11) = tail_of(X0_13)
| edge(sK0(head_of(sK11),tail_of(X0_13))) ),
inference(instantiation,[status(thm)],[c_993]) ).
cnf(c_165964,plain,
( ~ vertex(head_of(sK11))
| ~ vertex(tail_of(sK10))
| head_of(sK11) = tail_of(sK10)
| edge(sK0(head_of(sK11),tail_of(sK10))) ),
inference(instantiation,[status(thm)],[c_165963]) ).
cnf(c_165968,plain,
( ~ vertex(head_of(sK11))
| ~ vertex(tail_of(sK10))
| tail_of(sK0(head_of(sK11),tail_of(sK10))) = head_of(sK11)
| tail_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10)
| head_of(sK11) = tail_of(sK10) ),
inference(instantiation,[status(thm)],[c_165962]) ).
cnf(c_165976,plain,
( ~ vertex(head_of(sK11))
| ~ vertex(tail_of(sK10))
| head_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10)
| tail_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10)
| head_of(sK11) = tail_of(sK10) ),
inference(instantiation,[status(thm)],[c_165960]) ).
cnf(c_165980,plain,
( tail_of(X0_13) != X0_14
| head_of(sK11) != X0_14
| head_of(sK11) = tail_of(X0_13) ),
inference(instantiation,[status(thm)],[c_1139]) ).
cnf(c_165995,plain,
( head_of(sK0(head_of(sK11),tail_of(X0_13))) != tail_of(sK0(head_of(sK11),tail_of(X0_13)))
| ~ edge(sK0(head_of(sK11),tail_of(X0_13))) ),
inference(instantiation,[status(thm)],[c_1038]) ).
cnf(c_165996,plain,
( head_of(sK0(head_of(sK11),tail_of(sK10))) != tail_of(sK0(head_of(sK11),tail_of(sK10)))
| ~ edge(sK0(head_of(sK11),tail_of(sK10))) ),
inference(instantiation,[status(thm)],[c_165995]) ).
cnf(c_166007,plain,
( tail_of(sK0(head_of(sK11),tail_of(X0_13))) != head_of(sK11)
| head_of(sK11) != head_of(sK11)
| head_of(sK11) = tail_of(sK0(head_of(sK11),tail_of(X0_13))) ),
inference(instantiation,[status(thm)],[c_165980]) ).
cnf(c_166008,plain,
( tail_of(sK0(head_of(sK11),tail_of(X0_13))) != head_of(sK11)
| head_of(sK11) = tail_of(sK0(head_of(sK11),tail_of(X0_13))) ),
inference(equality_resolution_simp,[status(thm)],[c_166007]) ).
cnf(c_166009,plain,
( tail_of(sK0(head_of(sK11),tail_of(sK10))) != head_of(sK11)
| head_of(sK11) = tail_of(sK0(head_of(sK11),tail_of(sK10))) ),
inference(instantiation,[status(thm)],[c_166008]) ).
cnf(c_166027,plain,
( head_of(X0_13) != X0_14
| head_of(sK11) != X0_14
| head_of(sK11) = head_of(X0_13) ),
inference(instantiation,[status(thm)],[c_1139]) ).
cnf(c_166036,plain,
( head_of(sK0(head_of(sK11),tail_of(X0_13))) != X0_14
| tail_of(sK0(head_of(sK11),tail_of(X0_13))) != X0_14
| head_of(sK0(head_of(sK11),tail_of(X0_13))) = tail_of(sK0(head_of(sK11),tail_of(X0_13))) ),
inference(instantiation,[status(thm)],[c_1139]) ).
cnf(c_166038,plain,
( head_of(sK11) != tail_of(sK0(head_of(sK11),tail_of(X0_13)))
| ~ edge(sK0(head_of(sK11),tail_of(X0_13)))
| sequential(sK11,sK0(head_of(sK11),tail_of(X0_13))) ),
inference(instantiation,[status(thm)],[c_165945]) ).
cnf(c_166039,plain,
( head_of(sK11) != tail_of(sK0(head_of(sK11),tail_of(sK10)))
| ~ edge(sK0(head_of(sK11),tail_of(sK10)))
| sequential(sK11,sK0(head_of(sK11),tail_of(sK10))) ),
inference(instantiation,[status(thm)],[c_166038]) ).
cnf(c_166104,plain,
( head_of(X0_13) != head_of(X1_13)
| head_of(sK11) != head_of(X1_13)
| head_of(sK11) = head_of(X0_13) ),
inference(instantiation,[status(thm)],[c_166027]) ).
cnf(c_166106,plain,
( head_of(sK0(head_of(sK11),tail_of(X0_13))) != tail_of(X0_13)
| tail_of(sK0(head_of(sK11),tail_of(X0_13))) != tail_of(X0_13)
| head_of(sK0(head_of(sK11),tail_of(X0_13))) = tail_of(sK0(head_of(sK11),tail_of(X0_13))) ),
inference(instantiation,[status(thm)],[c_166036]) ).
cnf(c_166107,plain,
( head_of(sK0(head_of(sK11),tail_of(sK10))) != tail_of(sK10)
| tail_of(sK0(head_of(sK11),tail_of(sK10))) != tail_of(sK10)
| head_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK0(head_of(sK11),tail_of(sK10))) ),
inference(instantiation,[status(thm)],[c_166106]) ).
cnf(c_166115,plain,
( ~ sequential(sK0(head_of(sK11),tail_of(X0_13)),sK10)
| ~ sequential(sK11,sK0(head_of(sK11),tail_of(X0_13))) ),
inference(instantiation,[status(thm)],[c_983]) ).
cnf(c_166116,plain,
( ~ sequential(sK0(head_of(sK11),tail_of(sK10)),sK10)
| ~ sequential(sK11,sK0(head_of(sK11),tail_of(sK10))) ),
inference(instantiation,[status(thm)],[c_166115]) ).
cnf(c_166262,plain,
( head_of(X0_13) != head_of(sK11)
| head_of(sK11) != head_of(sK11)
| head_of(sK11) = head_of(X0_13) ),
inference(instantiation,[status(thm)],[c_166104]) ).
cnf(c_166263,plain,
( head_of(X0_13) != head_of(sK11)
| head_of(sK11) = head_of(X0_13) ),
inference(equality_resolution_simp,[status(thm)],[c_166262]) ).
cnf(c_166291,plain,
( sK0(head_of(sK11),tail_of(X0_13)) != X0_13
| tail_of(sK0(head_of(sK11),tail_of(X0_13))) = tail_of(X0_13) ),
inference(instantiation,[status(thm)],[c_1143]) ).
cnf(c_166292,plain,
( sK0(head_of(sK11),tail_of(sK10)) != sK10
| tail_of(sK0(head_of(sK11),tail_of(sK10))) = tail_of(sK10) ),
inference(instantiation,[status(thm)],[c_166291]) ).
cnf(c_166628,plain,
( head_of(sK0(head_of(sK11),X0_14)) != head_of(sK11)
| head_of(sK11) = head_of(sK0(head_of(sK11),X0_14)) ),
inference(instantiation,[status(thm)],[c_166263]) ).
cnf(c_166650,plain,
( head_of(sK0(head_of(sK11),tail_of(X0_13))) != tail_of(X0_13)
| ~ edge(sK0(head_of(sK11),tail_of(X0_13)))
| ~ edge(X0_13)
| sK0(head_of(sK11),tail_of(X0_13)) = X0_13
| sequential(sK0(head_of(sK11),tail_of(X0_13)),X0_13) ),
inference(instantiation,[status(thm)],[c_1020]) ).
cnf(c_166651,plain,
( head_of(sK0(head_of(sK11),tail_of(sK10))) != tail_of(sK10)
| ~ edge(sK0(head_of(sK11),tail_of(sK10)))
| ~ edge(sK10)
| sK0(head_of(sK11),tail_of(sK10)) = sK10
| sequential(sK0(head_of(sK11),tail_of(sK10)),sK10) ),
inference(instantiation,[status(thm)],[c_166650]) ).
cnf(c_168228,plain,
( head_of(sK0(head_of(sK11),tail_of(X0_13))) != head_of(sK11)
| head_of(sK11) = head_of(sK0(head_of(sK11),tail_of(X0_13))) ),
inference(instantiation,[status(thm)],[c_166628]) ).
cnf(c_168229,plain,
( head_of(sK0(head_of(sK11),tail_of(sK10))) != head_of(sK11)
| head_of(sK11) = head_of(sK0(head_of(sK11),tail_of(sK10))) ),
inference(instantiation,[status(thm)],[c_168228]) ).
cnf(c_168984,plain,
( tail_of(X0_13) != tail_of(sK10)
| head_of(sK11) != head_of(X0_13)
| sP3_iProver_def(sK10,sK11) ),
inference(instantiation,[status(thm)],[c_1067]) ).
cnf(c_168985,plain,
( head_of(sK11) != head_of(X0_13)
| tail_of(X0_13) != tail_of(sK10) ),
inference(global_subsumption_just,[status(thm)],[c_168984,c_104,c_2142,c_2145]) ).
cnf(c_168986,plain,
( tail_of(X0_13) != tail_of(sK10)
| head_of(sK11) != head_of(X0_13) ),
inference(renaming,[status(thm)],[c_168985]) ).
cnf(c_169381,plain,
( tail_of(sK0(head_of(sK11),tail_of(X0_13))) != tail_of(sK10)
| head_of(sK11) != head_of(sK0(head_of(sK11),tail_of(X0_13))) ),
inference(instantiation,[status(thm)],[c_168986]) ).
cnf(c_169382,plain,
( tail_of(sK0(head_of(sK11),tail_of(sK10))) != tail_of(sK10)
| head_of(sK11) != head_of(sK0(head_of(sK11),tail_of(sK10))) ),
inference(instantiation,[status(thm)],[c_169381]) ).
cnf(c_169383,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_169382,c_168229,c_166651,c_166292,c_166116,c_166107,c_166039,c_166009,c_165996,c_165976,c_165968,c_165964,c_165823,c_165820,c_165492,c_8699,c_5763,c_5720,c_5682,c_5666,c_5559,c_5537,c_5507,c_2151,c_2146,c_2142,c_1909,c_1190,c_1164,c_1158,c_526,c_104,c_103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GRA008+1 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.12/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n013.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 : Thu May 2 21:19:49 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --heuristic_context casc_unsat --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 46.51/7.23 % SZS status Started for theBenchmark.p
% 46.51/7.23 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|")
% 46.51/7.23 Fatal error: exception Z3.Error("Sort mismatch at argument #1 for function (declare-fun k!96 (|16777216|) |16777216|) supplied sort is |16777229|")
% 46.51/7.23 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 -t 2.00" --time_out_real 2.00 /export/starexec/sandbox/benchmark/theBenchmark.p 1>> /export/starexec/sandbox/tmp/iprover_out_10emtf71/ul5adb5b 2>> /export/starexec/sandbox/tmp/iprover_out_10emtf71/ul5adb5b_error
% 61.86/9.24 % SZS status Theorem for theBenchmark.p
% 61.86/9.24
% 61.86/9.24 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 61.86/9.24
% 61.86/9.24 ------ iProver source info
% 61.86/9.24
% 61.86/9.24 git: date: 2024-05-02 19:28:25 +0000
% 61.86/9.24 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 61.86/9.24 git: non_committed_changes: false
% 61.86/9.24
% 61.86/9.24 ------ Parsing...
% 61.86/9.24 ------ Clausification by vclausify_rel & Parsing by iProver...
% 61.86/9.24
% 61.86/9.24 ------ Preprocessing... sf_s rm: 2 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 2 0s sf_e pe_s pe_e
% 61.86/9.24
% 61.86/9.24 ------ Preprocessing... gs_s sp: 0 0s gs_e scvd_s sp: 17 0s scvd_e snvd_s sp: 0 0s snvd_e
% 61.86/9.24
% 61.86/9.24 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 61.86/9.24 ------ Proving...
% 61.86/9.24 ------ Problem Properties
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 clauses 61
% 61.86/9.24 conjectures 3
% 61.86/9.24 EPR 23
% 61.86/9.24 Horn 35
% 61.86/9.24 unary 6
% 61.86/9.24 binary 18
% 61.86/9.24 lits 182
% 61.86/9.24 lits eq 44
% 61.86/9.24 fd_pure 0
% 61.86/9.24 fd_pseudo 0
% 61.86/9.24 fd_cond 0
% 61.86/9.24 fd_pseudo_cond 5
% 61.86/9.24 AC symbols 0
% 61.86/9.24
% 61.86/9.24 ------ Input Options Time Limit: Unbounded
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------
% 61.86/9.24 Current options:
% 61.86/9.24 ------
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 ------ Proving...
% 61.86/9.24
% 61.86/9.24
% 61.86/9.24 % SZS status Theorem for theBenchmark.p
% 61.86/9.24
% 61.86/9.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 61.86/9.24
% 61.86/9.26
%------------------------------------------------------------------------------