-ng implemented

[helm.git] / helm / software / matita / contribs / ng_TPTP / LAT120-1.ma

diff --git a/helm/software/matita/contribs/ng_TPTP/LAT120-1.ma b/helm/software/matita/contribs/ng_TPTP/LAT120-1.ma
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+include "logic/equality.ma".
+
+(* Inclusion of: LAT120-1.p *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(*  File     : LAT120-1 : TPTP v3.2.0. Released v3.1.0. *)
+
+(*  Domain   : Lattice Theory *)
+
+(*  Problem  : Huntington equation H58 is independent of H10_dual *)
+
+(*  Version  : [McC05] (equality) axioms : Especial. *)
+
+(*  English  : Show that Huntington equation H10_dual does not imply Huntington  *)
+
+(*             equation H58 in lattice theory. *)
+
+(*  Refs     : [McC05] McCune (2005), Email to Geoff Sutcliffe *)
+
+(*  Source   : [McC05] *)
+
+(*  Names    :  *)
+
+(*  Status   : Satisfiable *)
+
+(*  Rating   : 0.33 v3.2.0, 0.67 v3.1.0 *)
+
+(*  Syntax   : Number of clauses     :   10 (   0 non-Horn;  10 unit;   1 RR) *)
+
+(*             Number of atoms       :   10 (  10 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    5 (   3 constant; 0-2 arity) *)
+
+(*             Number of variables   :   19 (   2 singleton) *)
+
+(*             Maximal term depth    :    6 (   3 average) *)
+
+(*  Comments :  *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* ----Include Lattice theory (equality) axioms *)
+
+(* Inclusion of: Axioms/LAT001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : LAT001-0 : TPTP v3.2.0. Released v1.0.0. *)
+
+(*  Domain   : Lattice Theory *)
+
+(*  Axioms   : Lattice theory (equality) axioms *)
+
+(*  Version  : [McC88] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *)
+
+(*           : [McC88] McCune (1988), Challenge Equality Problems in Lattice  *)
+
+(*           : [Wos88] Wos (1988), Automated Reasoning - 33 Basic Research Pr *)
+
+(*  Source   : [McC88] *)
+
+(*  Names    :  *)
+
+(*  Status   :  *)
+
+(*  Syntax   : Number of clauses    :    8 (   0 non-Horn;   8 unit;   0 RR) *)
+
+(*             Number of literals   :    8 (   8 equality) *)
+
+(*             Maximal clause size  :    1 (   1 average) *)
+
+(*             Number of predicates :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors   :    2 (   0 constant; 2-2 arity) *)
+
+(*             Number of variables  :   16 (   2 singleton) *)
+
+(*             Maximal term depth   :    3 (   2 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----The following 8 clauses characterise lattices  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ------------------------------------------------------------------------------ *)
+ntheorem prove_H58:
+ ∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀a:Univ.
+∀b:Univ.
+∀c:Univ.
+∀join:∀_:Univ.∀_:Univ.Univ.
+∀meet:∀_:Univ.∀_:Univ.Univ.
+∀H0:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join X (meet Y (join X Z))) (join X (meet Y (join Z (meet X (join Y Z))))).
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).
+∀H3:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X).
+∀H4:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).
+∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.
+∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.
+∀H7:∀X:Univ.eq Univ (join X X) X.
+∀H8:∀X:Univ.eq Univ (meet X X) X.eq Univ (meet a (join b c)) (meet a (join b (meet (join a b) (join c (meet a b)))))
+.
+#Univ.
+#X.
+#Y.
+#Z.
+#a.
+#b.
+#c.
+#join.
+#meet.
+#H0.
+#H1.
+#H2.
+#H3.
+#H4.
+#H5.
+#H6.
+#H7.
+#H8.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8;
+nqed.
+
+(* ------------------------------------------------------------------------------ *)