TSTP Solution File: GRA007+2 by iProver---3.9
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.9
% Problem : GRA007+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n002.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 20.43s 3.67s
% Output : CNFRefutation 20.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 200 ( 26 unt; 0 def)
% Number of atoms : 829 ( 283 equ)
% Maximal formula atoms : 18 ( 4 avg)
% Number of connectives : 1032 ( 403 ~; 419 |; 165 &)
% ( 5 <=>; 33 =>; 0 <=; 7 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 2 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 494 ( 50 sgn 261 !; 45 ?)
% 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(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/sandbox/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/sandbox/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/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(f19,conjecture,
( complete
=> ! [X1,X2,X6,X7,X3] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ? [X8] :
( tail_of(X6) = head_of(X8)
& tail_of(X8) = head_of(X7)
& edge(X8) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',back_edge) ).
fof(f20,negated_conjecture,
~ ( complete
=> ! [X1,X2,X6,X7,X3] :
( ( precedes(X6,X7,X3)
& shortest_path(X1,X2,X3) )
=> ? [X8] :
( tail_of(X6) = head_of(X8)
& tail_of(X8) = head_of(X7)
& edge(X8) ) ) ),
inference(negated_conjecture,[],[f19]) ).
fof(f21,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(f24,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(f25,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(f26,plain,
! [X0,X1] :
( sequential(X0,X1)
<=> ( head_of(X0) = tail_of(X1)
& X0 != X1
& edge(X1)
& edge(X0) ) ),
inference(rectify,[],[f8]) ).
fof(f27,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(f28,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(f29,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(f30,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(f37,plain,
~ ( complete
=> ! [X0,X1,X2,X3,X4] :
( ( precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ? [X5] :
( tail_of(X2) = head_of(X5)
& head_of(X3) = tail_of(X5)
& edge(X5) ) ) ),
inference(rectify,[],[f20]) ).
fof(f39,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(ennf_transformation,[],[f1]) ).
fof(f40,plain,
! [X0] :
( ( vertex(tail_of(X0))
& vertex(head_of(X0)) )
| ~ edge(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f41,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,[],[f21]) ).
fof(f42,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,[],[f41]) ).
fof(f46,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,[],[f24]) ).
fof(f47,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,[],[f46]) ).
fof(f48,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,[],[f25]) ).
fof(f49,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,[],[f48]) ).
fof(f50,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,[],[f27]) ).
fof(f51,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,[],[f50]) ).
fof(f52,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,[],[f28]) ).
fof(f53,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,[],[f29]) ).
fof(f54,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,[],[f30]) ).
fof(f55,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,[],[f54]) ).
fof(f64,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] :
( tail_of(X2) != head_of(X5)
| head_of(X3) != tail_of(X5)
| ~ edge(X5) )
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
& complete ),
inference(ennf_transformation,[],[f37]) ).
fof(f65,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] :
( tail_of(X2) != head_of(X5)
| head_of(X3) != tail_of(X5)
| ~ edge(X5) )
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
& complete ),
inference(flattening,[],[f64]) ).
fof(f66,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,[],[f42]) ).
fof(f67,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,[],[f66]) ).
fof(f68,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(f69,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])],[f67,f68]) ).
fof(f76,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(f77,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])],[f49,f76]) ).
fof(f78,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,[],[f26]) ).
fof(f79,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,[],[f78]) ).
fof(f80,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,[],[f52]) ).
fof(f81,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,[],[f80]) ).
fof(f82,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,[],[f81]) ).
fof(f83,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(f84,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])],[f82,f83]) ).
fof(f85,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,[],[f53]) ).
fof(f86,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,[],[f85]) ).
fof(f87,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,[],[f86]) ).
fof(f88,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(f89,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])],[f87,f88]) ).
fof(f92,plain,
( ? [X0,X1,X2,X3,X4] :
( ! [X5] :
( tail_of(X2) != head_of(X5)
| head_of(X3) != tail_of(X5)
| ~ edge(X5) )
& precedes(X2,X3,X4)
& shortest_path(X0,X1,X4) )
=> ( ! [X5] :
( head_of(X5) != tail_of(sK10)
| tail_of(X5) != head_of(sK11)
| ~ edge(X5) )
& precedes(sK10,sK11,sK12)
& shortest_path(sK8,sK9,sK12) ) ),
introduced(choice_axiom,[]) ).
fof(f93,plain,
( ! [X5] :
( head_of(X5) != tail_of(sK10)
| tail_of(X5) != head_of(sK11)
| ~ edge(X5) )
& precedes(sK10,sK11,sK12)
& shortest_path(sK8,sK9,sK12)
& complete ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8,sK9,sK10,sK11,sK12])],[f65,f92]) ).
fof(f94,plain,
! [X0] :
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f96,plain,
! [X0] :
( vertex(tail_of(X0))
| ~ edge(X0) ),
inference(cnf_transformation,[],[f40]) ).
fof(f97,plain,
! [X0,X1] :
( edge(sK0(X0,X1))
| X0 = X1
| ~ vertex(X1)
| ~ vertex(X0)
| ~ complete ),
inference(cnf_transformation,[],[f69]) ).
fof(f98,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,[],[f69]) ).
fof(f99,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,[],[f69]) ).
fof(f101,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,[],[f69]) ).
fof(f114,plain,
! [X2,X3,X0,X1] :
( edge(X3)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f115,plain,
! [X2,X3,X0,X1] :
( in_path(head_of(X3),X2)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f116,plain,
! [X2,X3,X0,X1] :
( in_path(tail_of(X3),X2)
| ~ on_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f47]) ).
fof(f117,plain,
! [X2,X3,X0,X1] :
( vertex(X3)
| ~ in_path(X3,X2)
| ~ path(X0,X1,X2) ),
inference(cnf_transformation,[],[f77]) ).
fof(f124,plain,
! [X0,X1] :
( sequential(X0,X1)
| head_of(X0) != tail_of(X1)
| X0 = X1
| ~ edge(X1)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f79]) ).
fof(f125,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,[],[f51]) ).
fof(f127,plain,
! [X2,X3,X0,X1,X4] :
( on_path(X3,X0)
| ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f128,plain,
! [X2,X3,X0,X1,X4] :
( on_path(X4,X0)
| ~ precedes(X3,X4,X0)
| ~ path(X1,X2,X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f132,plain,
! [X2,X0,X1] :
( path(X0,X1,X2)
| ~ shortest_path(X0,X1,X2) ),
inference(cnf_transformation,[],[f89]) ).
fof(f137,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,[],[f55]) ).
fof(f138,plain,
! [X2,X3,X0,X1,X4] :
( ~ precedes(X3,X2,X4)
| ~ precedes(X2,X3,X4)
| ~ shortest_path(X0,X1,X4) ),
inference(cnf_transformation,[],[f55]) ).
fof(f148,plain,
complete,
inference(cnf_transformation,[],[f93]) ).
fof(f149,plain,
shortest_path(sK8,sK9,sK12),
inference(cnf_transformation,[],[f93]) ).
fof(f150,plain,
precedes(sK10,sK11,sK12),
inference(cnf_transformation,[],[f93]) ).
fof(f151,plain,
! [X5] :
( head_of(X5) != tail_of(sK10)
| tail_of(X5) != head_of(sK11)
| ~ edge(X5) ),
inference(cnf_transformation,[],[f93]) ).
cnf(c_49,negated_conjecture,
( head_of(X0) != tail_of(X0)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f94]) ).
cnf(c_50,plain,
( ~ edge(X0)
| vertex(tail_of(X0)) ),
inference(cnf_transformation,[],[f96]) ).
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,[],[f101]) ).
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,[],[f99]) ).
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,[],[f98]) ).
cnf(c_57,plain,
( ~ vertex(X0)
| ~ vertex(X1)
| ~ complete
| X0 = X1
| edge(sK0(X0,X1)) ),
inference(cnf_transformation,[],[f97]) ).
cnf(c_69,plain,
( ~ path(X0,X1,X2)
| ~ on_path(X3,X2)
| in_path(tail_of(X3),X2) ),
inference(cnf_transformation,[],[f116]) ).
cnf(c_70,plain,
( ~ path(X0,X1,X2)
| ~ on_path(X3,X2)
| in_path(head_of(X3),X2) ),
inference(cnf_transformation,[],[f115]) ).
cnf(c_71,plain,
( ~ path(X0,X1,X2)
| ~ on_path(X3,X2)
| edge(X3) ),
inference(cnf_transformation,[],[f114]) ).
cnf(c_74,plain,
( ~ path(X0,X1,X2)
| ~ in_path(X3,X2)
| vertex(X3) ),
inference(cnf_transformation,[],[f117]) ).
cnf(c_75,plain,
( head_of(X0) != tail_of(X1)
| ~ edge(X0)
| ~ edge(X1)
| X0 = X1
| sequential(X0,X1) ),
inference(cnf_transformation,[],[f124]) ).
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,[],[f125]) ).
cnf(c_85,plain,
( ~ path(X0,X1,X2)
| ~ precedes(X3,X4,X2)
| on_path(X4,X2) ),
inference(cnf_transformation,[],[f128]) ).
cnf(c_86,plain,
( ~ path(X0,X1,X2)
| ~ precedes(X3,X4,X2)
| on_path(X3,X2) ),
inference(cnf_transformation,[],[f127]) ).
cnf(c_91,plain,
( ~ shortest_path(X0,X1,X2)
| path(X0,X1,X2) ),
inference(cnf_transformation,[],[f132]) ).
cnf(c_92,negated_conjecture,
( ~ precedes(X0,X1,X2)
| ~ precedes(X1,X0,X2)
| ~ shortest_path(X3,X4,X2) ),
inference(cnf_transformation,[],[f138]) ).
cnf(c_93,negated_conjecture,
( head_of(X0) != head_of(X1)
| tail_of(X1) != tail_of(X2)
| ~ precedes(X2,X0,X3)
| ~ shortest_path(X4,X5,X3) ),
inference(cnf_transformation,[],[f137]) ).
cnf(c_103,negated_conjecture,
( head_of(X0) != tail_of(sK10)
| tail_of(X0) != head_of(sK11)
| ~ edge(X0) ),
inference(cnf_transformation,[],[f151]) ).
cnf(c_104,negated_conjecture,
precedes(sK10,sK11,sK12),
inference(cnf_transformation,[],[f150]) ).
cnf(c_105,negated_conjecture,
shortest_path(sK8,sK9,sK12),
inference(cnf_transformation,[],[f149]) ).
cnf(c_106,negated_conjecture,
complete,
inference(cnf_transformation,[],[f148]) ).
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_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_227,plain,
( ~ vertex(X0_13)
| ~ vertex(X1_13)
| tail_of(sK0(X0_13,X1_13)) = X0_13
| tail_of(sK0(X0_13,X1_13)) = X1_13
| X0_13 = X1_13 ),
inference(subtyping,[status(esa)],[c_165]) ).
cnf(c_229,plain,
( ~ vertex(X0_13)
| ~ vertex(X1_13)
| head_of(sK0(X0_13,X1_13)) = X1_13
| tail_of(sK0(X0_13,X1_13)) = X1_13
| X0_13 = X1_13 ),
inference(subtyping,[status(esa)],[c_161]) ).
cnf(c_230,plain,
( ~ vertex(X0_13)
| ~ vertex(X1_13)
| head_of(sK0(X0_13,X1_13)) = X0_13
| head_of(sK0(X0_13,X1_13)) = X1_13
| X0_13 = X1_13 ),
inference(subtyping,[status(esa)],[c_158]) ).
cnf(c_235,plain,
( ~ vertex(X0_13)
| ~ vertex(X1_13)
| X0_13 = X1_13
| edge(sK0(X0_13,X1_13)) ),
inference(subtyping,[status(esa)],[c_145]) ).
cnf(c_236,negated_conjecture,
shortest_path(sK8,sK9,sK12),
inference(subtyping,[status(esa)],[c_105]) ).
cnf(c_237,negated_conjecture,
precedes(sK10,sK11,sK12),
inference(subtyping,[status(esa)],[c_104]) ).
cnf(c_238,negated_conjecture,
( head_of(X0_14) != tail_of(sK10)
| tail_of(X0_14) != head_of(sK11)
| ~ edge(X0_14) ),
inference(subtyping,[status(esa)],[c_103]) ).
cnf(c_246,negated_conjecture,
( head_of(X0_14) != head_of(X1_14)
| tail_of(X1_14) != tail_of(X2_14)
| ~ precedes(X2_14,X0_14,X0_15)
| ~ shortest_path(X0_13,X1_13,X0_15) ),
inference(subtyping,[status(esa)],[c_93]) ).
cnf(c_247,negated_conjecture,
( ~ precedes(X0_14,X1_14,X0_15)
| ~ precedes(X1_14,X0_14,X0_15)
| ~ shortest_path(X0_13,X1_13,X0_15) ),
inference(subtyping,[status(esa)],[c_92]) ).
cnf(c_248,plain,
( ~ shortest_path(X0_13,X1_13,X0_15)
| path(X0_13,X1_13,X0_15) ),
inference(subtyping,[status(esa)],[c_91]) ).
cnf(c_253,plain,
( ~ path(X0_13,X1_13,X0_15)
| ~ precedes(X0_14,X1_14,X0_15)
| on_path(X0_14,X0_15) ),
inference(subtyping,[status(esa)],[c_86]) ).
cnf(c_254,plain,
( ~ path(X0_13,X1_13,X0_15)
| ~ precedes(X0_14,X1_14,X0_15)
| on_path(X1_14,X0_15) ),
inference(subtyping,[status(esa)],[c_85]) ).
cnf(c_258,plain,
( ~ path(X0_13,X1_13,X0_15)
| ~ on_path(X0_14,X0_15)
| ~ on_path(X1_14,X0_15)
| ~ sequential(X0_14,X1_14)
| precedes(X0_14,X1_14,X0_15) ),
inference(subtyping,[status(esa)],[c_81]) ).
cnf(c_263,plain,
( head_of(X0_14) != tail_of(X1_14)
| ~ edge(X0_14)
| ~ edge(X1_14)
| X0_14 = X1_14
| sequential(X0_14,X1_14) ),
inference(subtyping,[status(esa)],[c_75]) ).
cnf(c_264,plain,
( ~ path(X0_13,X1_13,X0_15)
| ~ in_path(X2_13,X0_15)
| vertex(X2_13) ),
inference(subtyping,[status(esa)],[c_74]) ).
cnf(c_267,plain,
( ~ path(X0_13,X1_13,X0_15)
| ~ on_path(X0_14,X0_15)
| edge(X0_14) ),
inference(subtyping,[status(esa)],[c_71]) ).
cnf(c_268,plain,
( ~ path(X0_13,X1_13,X0_15)
| ~ on_path(X0_14,X0_15)
| in_path(head_of(X0_14),X0_15) ),
inference(subtyping,[status(esa)],[c_70]) ).
cnf(c_269,plain,
( ~ path(X0_13,X1_13,X0_15)
| ~ on_path(X0_14,X0_15)
| in_path(tail_of(X0_14),X0_15) ),
inference(subtyping,[status(esa)],[c_69]) ).
cnf(c_280,plain,
( ~ edge(X0_14)
| vertex(tail_of(X0_14)) ),
inference(subtyping,[status(esa)],[c_50]) ).
cnf(c_281,negated_conjecture,
( head_of(X0_14) != tail_of(X0_14)
| ~ edge(X0_14) ),
inference(subtyping,[status(esa)],[c_49]) ).
cnf(c_283,plain,
X0_13 = X0_13,
theory(equality) ).
cnf(c_284,plain,
X0_14 = X0_14,
theory(equality) ).
cnf(c_287,plain,
( X0_13 != X1_13
| X2_13 != X1_13
| X2_13 = X0_13 ),
theory(equality) ).
cnf(c_291,plain,
( X0_14 != X1_14
| head_of(X0_14) = head_of(X1_14) ),
theory(equality) ).
cnf(c_292,plain,
( X0_14 != X1_14
| tail_of(X0_14) = tail_of(X1_14) ),
theory(equality) ).
cnf(c_316,plain,
( sK10 != sK10
| tail_of(sK10) = tail_of(sK10) ),
inference(instantiation,[status(thm)],[c_292]) ).
cnf(c_331,plain,
sK10 = sK10,
inference(instantiation,[status(thm)],[c_284]) ).
cnf(c_371,plain,
( ~ edge(sK10)
| vertex(tail_of(sK10)) ),
inference(instantiation,[status(thm)],[c_280]) ).
cnf(c_373,plain,
( ~ precedes(X0_14,X1_14,sK12)
| ~ precedes(X1_14,X0_14,sK12)
| ~ shortest_path(sK8,sK9,sK12) ),
inference(instantiation,[status(thm)],[c_247]) ).
cnf(c_375,plain,
( head_of(X0_14) != head_of(X1_14)
| tail_of(X1_14) != tail_of(X2_14)
| ~ precedes(X2_14,X0_14,sK12)
| ~ shortest_path(sK8,sK9,sK12) ),
inference(instantiation,[status(thm)],[c_246]) ).
cnf(c_415,plain,
path(sK8,sK9,sK12),
inference(superposition,[status(thm)],[c_236,c_248]) ).
cnf(c_424,plain,
( ~ in_path(X0_13,sK12)
| vertex(X0_13) ),
inference(superposition,[status(thm)],[c_415,c_264]) ).
cnf(c_428,plain,
( ~ on_path(X0_14,sK12)
| edge(X0_14) ),
inference(superposition,[status(thm)],[c_415,c_267]) ).
cnf(c_429,plain,
( ~ on_path(sK10,sK12)
| edge(sK10) ),
inference(instantiation,[status(thm)],[c_428]) ).
cnf(c_430,plain,
( ~ precedes(sK10,sK11,sK12)
| ~ precedes(sK11,sK10,sK12)
| ~ shortest_path(sK8,sK9,sK12) ),
inference(instantiation,[status(thm)],[c_373]) ).
cnf(c_434,plain,
( tail_of(X0_14) != tail_of(sK10)
| head_of(sK11) != head_of(X0_14)
| ~ precedes(sK10,sK11,sK12)
| ~ shortest_path(sK8,sK9,sK12) ),
inference(instantiation,[status(thm)],[c_375]) ).
cnf(c_435,plain,
( head_of(sK11) != head_of(sK10)
| tail_of(sK10) != tail_of(sK10)
| ~ precedes(sK10,sK11,sK12)
| ~ shortest_path(sK8,sK9,sK12) ),
inference(instantiation,[status(thm)],[c_434]) ).
cnf(c_448,plain,
( ~ path(X0_13,X1_13,sK12)
| on_path(sK10,sK12) ),
inference(superposition,[status(thm)],[c_237,c_253]) ).
cnf(c_460,plain,
( ~ path(X0_13,X1_13,sK12)
| on_path(sK11,sK12) ),
inference(superposition,[status(thm)],[c_237,c_254]) ).
cnf(c_463,plain,
( ~ on_path(X0_14,sK12)
| in_path(head_of(X0_14),sK12) ),
inference(superposition,[status(thm)],[c_415,c_268]) ).
cnf(c_482,plain,
( sK11 != X0_14
| head_of(sK11) = head_of(X0_14) ),
inference(instantiation,[status(thm)],[c_291]) ).
cnf(c_483,plain,
( sK11 != sK10
| head_of(sK11) = head_of(sK10) ),
inference(instantiation,[status(thm)],[c_482]) ).
cnf(c_485,plain,
head_of(sK11) = head_of(sK11),
inference(instantiation,[status(thm)],[c_283]) ).
cnf(c_486,plain,
( head_of(X0_14) != X0_13
| head_of(sK11) != X0_13
| head_of(sK11) = head_of(X0_14) ),
inference(instantiation,[status(thm)],[c_287]) ).
cnf(c_492,plain,
on_path(sK10,sK12),
inference(superposition,[status(thm)],[c_415,c_448]) ).
cnf(c_494,plain,
on_path(sK11,sK12),
inference(superposition,[status(thm)],[c_415,c_460]) ).
cnf(c_495,plain,
edge(sK11),
inference(superposition,[status(thm)],[c_494,c_428]) ).
cnf(c_496,plain,
( ~ on_path(X0_14,sK12)
| vertex(head_of(X0_14)) ),
inference(superposition,[status(thm)],[c_463,c_424]) ).
cnf(c_505,plain,
vertex(head_of(sK11)),
inference(superposition,[status(thm)],[c_494,c_496]) ).
cnf(c_640,plain,
path(sK8,sK9,sK12),
inference(superposition,[status(thm)],[c_236,c_248]) ).
cnf(c_643,plain,
( ~ path(X0_13,X1_13,sK12)
| on_path(sK10,sK12) ),
inference(superposition,[status(thm)],[c_237,c_253]) ).
cnf(c_644,plain,
on_path(sK10,sK12),
inference(global_subsumption_just,[status(thm)],[c_643,c_492]) ).
cnf(c_652,plain,
( ~ in_path(X0_13,sK12)
| vertex(X0_13) ),
inference(superposition,[status(thm)],[c_640,c_264]) ).
cnf(c_662,plain,
( ~ on_path(X0_14,sK12)
| in_path(tail_of(X0_14),sK12) ),
inference(superposition,[status(thm)],[c_640,c_269]) ).
cnf(c_671,plain,
( ~ on_path(X0_14,sK12)
| vertex(tail_of(X0_14)) ),
inference(superposition,[status(thm)],[c_662,c_652]) ).
cnf(c_698,plain,
vertex(tail_of(sK10)),
inference(superposition,[status(thm)],[c_644,c_671]) ).
cnf(c_785,plain,
( head_of(sK11) != tail_of(X0_14)
| ~ edge(X0_14)
| ~ edge(sK11)
| sK11 = X0_14
| sequential(sK11,X0_14) ),
inference(instantiation,[status(thm)],[c_263]) ).
cnf(c_786,plain,
( head_of(sK11) != tail_of(sK10)
| ~ edge(sK10)
| ~ edge(sK11)
| sK11 = sK10
| sequential(sK11,sK10) ),
inference(instantiation,[status(thm)],[c_785]) ).
cnf(c_797,plain,
( ~ vertex(tail_of(X0_14))
| ~ vertex(head_of(sK11))
| head_of(sK0(tail_of(X0_14),head_of(sK11))) = tail_of(X0_14)
| head_of(sK0(tail_of(X0_14),head_of(sK11))) = head_of(sK11)
| tail_of(X0_14) = head_of(sK11) ),
inference(instantiation,[status(thm)],[c_230]) ).
cnf(c_800,plain,
( ~ vertex(tail_of(X0_14))
| ~ vertex(head_of(sK11))
| tail_of(sK0(tail_of(X0_14),head_of(sK11))) = tail_of(X0_14)
| tail_of(sK0(tail_of(X0_14),head_of(sK11))) = head_of(sK11)
| tail_of(X0_14) = head_of(sK11) ),
inference(instantiation,[status(thm)],[c_227]) ).
cnf(c_801,plain,
( ~ vertex(tail_of(X0_14))
| ~ vertex(head_of(sK11))
| tail_of(X0_14) = head_of(sK11)
| edge(sK0(tail_of(X0_14),head_of(sK11))) ),
inference(instantiation,[status(thm)],[c_235]) ).
cnf(c_802,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_801]) ).
cnf(c_803,plain,
( ~ vertex(head_of(sK11))
| ~ vertex(tail_of(sK10))
| tail_of(sK0(tail_of(sK10),head_of(sK11))) = head_of(sK11)
| tail_of(sK0(tail_of(sK10),head_of(sK11))) = tail_of(sK10)
| tail_of(sK10) = head_of(sK11) ),
inference(instantiation,[status(thm)],[c_800]) ).
cnf(c_806,plain,
( ~ vertex(head_of(sK11))
| ~ vertex(tail_of(sK10))
| head_of(sK0(tail_of(sK10),head_of(sK11))) = head_of(sK11)
| head_of(sK0(tail_of(sK10),head_of(sK11))) = tail_of(sK10)
| tail_of(sK10) = head_of(sK11) ),
inference(instantiation,[status(thm)],[c_797]) ).
cnf(c_834,plain,
( head_of(X0_14) != X0_13
| tail_of(X0_14) != X0_13
| head_of(X0_14) = tail_of(X0_14) ),
inference(instantiation,[status(thm)],[c_287]) ).
cnf(c_879,plain,
( head_of(sK11) != X0_13
| X1_13 != X0_13
| head_of(sK11) = X1_13 ),
inference(instantiation,[status(thm)],[c_287]) ).
cnf(c_880,plain,
( head_of(X0_14) != head_of(sK11)
| head_of(sK11) != head_of(sK11)
| head_of(sK11) = head_of(X0_14) ),
inference(instantiation,[status(thm)],[c_486]) ).
cnf(c_1547,plain,
( head_of(X0_14) != head_of(X1_14)
| tail_of(X0_14) != head_of(X1_14)
| head_of(X0_14) = tail_of(X0_14) ),
inference(instantiation,[status(thm)],[c_834]) ).
cnf(c_1568,plain,
( ~ shortest_path(X0_13,X1_13,sK12)
| ~ precedes(sK11,sK10,sK12) ),
inference(superposition,[status(thm)],[c_237,c_247]) ).
cnf(c_1570,plain,
~ precedes(sK11,sK10,sK12),
inference(global_subsumption_just,[status(thm)],[c_1568,c_105,c_104,c_430]) ).
cnf(c_1580,plain,
path(sK8,sK9,sK12),
inference(superposition,[status(thm)],[c_236,c_248]) ).
cnf(c_1754,plain,
( ~ sequential(X0_14,X1_14)
| ~ on_path(X0_14,sK12)
| ~ on_path(X1_14,sK12)
| precedes(X0_14,X1_14,sK12) ),
inference(superposition,[status(thm)],[c_1580,c_258]) ).
cnf(c_1858,plain,
( ~ on_path(sK10,sK12)
| ~ on_path(sK11,sK12)
| ~ sequential(sK11,sK10) ),
inference(superposition,[status(thm)],[c_1754,c_1570]) ).
cnf(c_3095,plain,
( head_of(sK11) != head_of(sK11)
| X0_13 != head_of(sK11)
| head_of(sK11) = X0_13 ),
inference(instantiation,[status(thm)],[c_879]) ).
cnf(c_3608,plain,
( head_of(sK0(tail_of(sK10),head_of(sK11))) != tail_of(sK10)
| tail_of(sK0(tail_of(sK10),head_of(sK11))) != head_of(sK11)
| ~ edge(sK0(tail_of(sK10),head_of(sK11))) ),
inference(instantiation,[status(thm)],[c_238]) ).
cnf(c_4600,plain,
( head_of(sK0(tail_of(X0_14),head_of(sK11))) != head_of(sK11)
| tail_of(sK0(tail_of(X0_14),head_of(sK11))) != head_of(sK11)
| head_of(sK0(tail_of(X0_14),head_of(sK11))) = tail_of(sK0(tail_of(X0_14),head_of(sK11))) ),
inference(instantiation,[status(thm)],[c_1547]) ).
cnf(c_4601,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(sK0(tail_of(sK10),head_of(sK11))) = tail_of(sK0(tail_of(sK10),head_of(sK11))) ),
inference(instantiation,[status(thm)],[c_4600]) ).
cnf(c_6717,plain,
( tail_of(X0_14) != head_of(sK11)
| head_of(sK11) != head_of(sK11)
| head_of(sK11) = tail_of(X0_14) ),
inference(instantiation,[status(thm)],[c_3095]) ).
cnf(c_6718,plain,
( head_of(sK11) != head_of(sK11)
| tail_of(sK10) != head_of(sK11)
| head_of(sK11) = tail_of(sK10) ),
inference(instantiation,[status(thm)],[c_6717]) ).
cnf(c_8928,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_880]) ).
cnf(c_9673,plain,
path(sK8,sK9,sK12),
inference(superposition,[status(thm)],[c_236,c_248]) ).
cnf(c_9679,plain,
( ~ in_path(X0_13,sK12)
| vertex(X0_13) ),
inference(superposition,[status(thm)],[c_9673,c_264]) ).
cnf(c_9685,plain,
( ~ path(X0_13,X1_13,sK12)
| on_path(sK11,sK12) ),
inference(superposition,[status(thm)],[c_237,c_254]) ).
cnf(c_9687,plain,
( ~ on_path(X0_14,sK12)
| in_path(head_of(X0_14),sK12) ),
inference(superposition,[status(thm)],[c_9673,c_268]) ).
cnf(c_9691,plain,
on_path(sK11,sK12),
inference(global_subsumption_just,[status(thm)],[c_9685,c_494]) ).
cnf(c_9695,plain,
( ~ on_path(X0_14,sK12)
| vertex(head_of(X0_14)) ),
inference(superposition,[status(thm)],[c_9687,c_9679]) ).
cnf(c_9697,plain,
vertex(head_of(sK11)),
inference(superposition,[status(thm)],[c_9691,c_9695]) ).
cnf(c_10586,plain,
( ~ vertex(X0_13)
| head_of(sK0(tail_of(sK10),X0_13)) = X0_13
| tail_of(sK0(tail_of(sK10),X0_13)) = X0_13
| tail_of(sK10) = X0_13 ),
inference(superposition,[status(thm)],[c_698,c_229]) ).
cnf(c_12009,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_9697,c_10586]) ).
cnf(c_13440,plain,
( head_of(sK0(tail_of(X0_14),head_of(sK11))) != tail_of(sK0(tail_of(X0_14),head_of(sK11)))
| ~ edge(sK0(tail_of(X0_14),head_of(sK11))) ),
inference(instantiation,[status(thm)],[c_281]) ).
cnf(c_13441,plain,
( head_of(sK0(tail_of(sK10),head_of(sK11))) != tail_of(sK0(tail_of(sK10),head_of(sK11)))
| ~ edge(sK0(tail_of(sK10),head_of(sK11))) ),
inference(instantiation,[status(thm)],[c_13440]) ).
cnf(c_18937,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_434]) ).
cnf(c_18938,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_18937,c_13441,c_12009,c_8928,c_6718,c_4601,c_3608,c_1858,c_806,c_803,c_802,c_786,c_505,c_495,c_494,c_492,c_485,c_483,c_435,c_429,c_371,c_331,c_316,c_104,c_105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GRA007+2 : TPTP v8.1.2. Bugfixed v3.2.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.12/0.33 % Computer : n002.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu May 2 21:43:27 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.18/0.46 Running first-order theorem proving
% 0.18/0.46 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
% 20.43/3.67 % SZS status Started for theBenchmark.p
% 20.43/3.67 % SZS status Theorem for theBenchmark.p
% 20.43/3.67
% 20.43/3.67 %---------------- iProver v3.9 (pre CASC 2024/SMT-COMP 2024) ----------------%
% 20.43/3.67
% 20.43/3.67 ------ iProver source info
% 20.43/3.67
% 20.43/3.67 git: date: 2024-05-02 19:28:25 +0000
% 20.43/3.67 git: sha1: a33b5eb135c74074ba803943bb12f2ebd971352f
% 20.43/3.67 git: non_committed_changes: false
% 20.43/3.67
% 20.43/3.67 ------ Parsing...
% 20.43/3.67 ------ Clausification by vclausify_rel & Parsing by iProver...
% 20.43/3.67
% 20.43/3.67 ------ Preprocessing... sup_sim: 0 sf_s rm: 2 0s sf_e sup_sim: 0 sf_s rm: 1 0s sf_e
% 20.43/3.67
% 20.43/3.67 ------ Preprocessing...
% 20.43/3.67
% 20.43/3.67 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 20.43/3.67 ------ Proving...
% 20.43/3.67 ------ Problem Properties
% 20.43/3.67
% 20.43/3.67
% 20.43/3.67 clauses 56
% 20.43/3.67 conjectures 10
% 20.43/3.67 EPR 18
% 20.43/3.67 Horn 38
% 20.43/3.67 unary 5
% 20.43/3.67 binary 14
% 20.43/3.67 lits 176
% 20.43/3.67 lits eq 46
% 20.43/3.67 fd_pure 0
% 20.43/3.67 fd_pseudo 0
% 20.43/3.67 fd_cond 0
% 20.43/3.67 fd_pseudo_cond 5
% 20.43/3.67 AC symbols 0
% 20.43/3.67
% 20.43/3.67 ------ Input Options Time Limit: Unbounded
% 20.43/3.67
% 20.43/3.67
% 20.43/3.67 ------
% 20.43/3.67 Current options:
% 20.43/3.67 ------
% 20.43/3.67
% 20.43/3.67
% 20.43/3.67
% 20.43/3.67
% 20.43/3.67 ------ Proving...
% 20.43/3.67
% 20.43/3.67
% 20.43/3.67 % SZS status Theorem for theBenchmark.p
% 20.43/3.67
% 20.43/3.67 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 20.43/3.67
% 20.43/3.67
%------------------------------------------------------------------------------