-ng implemented

[helm.git] / helm / software / matita / contribs / ng_TPTP / LAT033-1.ma

diff --git a/helm/software/matita/contribs/ng_TPTP/LAT033-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT033-1.ma
new file mode 100644 (file)
index 0000000..c4318d9
--- /dev/null
+++ b/helm/software/matita/contribs/ng_TPTP/LAT033-1.ma
@@ -0,0 +1,82 @@
+include "logic/equality.ma".
+
+(* Inclusion of: LAT033-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : LAT033-1 : TPTP v3.2.0. Bugfixed v2.5.0. *)
+
+(*  Domain   : Lattice Theory *)
+
+(*  Problem  : Idempotency of join *)
+
+(*  Version  : [McC88] (equality) axioms. *)
+
+(*  English  : *)
+
+(*  Refs     : [DeN00] DeNivelle (2000), Email to G. Sutcliffe *)
+
+(*             [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+
+(*  Source   : [DeN00] *)
+
+(*  Names    : idemp_of_join [DeN00] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.00 v2.5.0 *)
+
+(*  Syntax   : Number of clauses     :    7 (   0 non-Horn;   7 unit;   1 RR) *)
+
+(*             Number of atoms       :    7 (   7 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    3 (   1 constant; 0-2 arity) *)
+
+(*             Number of variables   :   14 (   2 singleton) *)
+
+(*             Maximal term depth    :    3 (   2 average) *)
+
+(*  Comments :  *)
+
+(*  Bugfixes : v2.5.0 - Used axioms without the conjecture *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include lattice theory axioms *)
+
+(* include('Axioms/LAT001-0.ax'). *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem idempotence_of_join:
+ ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀join:∀_:Univ.∀_:Univ.Univ.
+∀meet:∀_:Univ.∀_:Univ.Univ.
+∀xx:Univ.
+∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).
+∀H2:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X).
+∀H3:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).
+∀H4:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.
+∀H5:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.eq Univ (join xx xx) xx
+.
+#Univ.
+#X.
+#Y.
+#Z.
+#join.
+#meet.
+#xx.
+#H0.
+#H1.
+#H2.
+#H3.
+#H4.
+#H5.
+nauto by H0,H1,H2,H3,H4,H5;
+nqed.
+
+(* -------------------------------------------------------------------------- *)