Stuff moved from old Matita.

[helm.git] / matita / matita / contribs / ng_TPTP / LAT050-1.ma

diff --git a/matita/matita/contribs/ng_TPTP/LAT050-1.ma b/matita/matita/contribs/ng_TPTP/LAT050-1.ma
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+include "logic/equality.ma".
+
+(* Inclusion of: LAT050-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : LAT050-1 : TPTP v3.7.0. Released v2.5.0. *)
+
+(*  Domain   : Lattice Theory *)
+
+(*  Problem  : Orthomodular lattice is not modular lattice *)
+
+(*  Version  : [McC88] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     : [McC88] McCune (1988), Challenge Equality Problems in Lattice  *)
+
+(*           : [RW01]  Rose & Wilkinson (2001), Application of Model Search *)
+
+(*           : [EF+02] Ernst et al. (2002), More First-order Test Problems in *)
+
+(*  Source   : [RW01] *)
+
+(*  Names    : mace-f.in [RW01] *)
+
+(*           : oml-mod [EF+02] *)
+
+(*  Status   : Satisfiable *)
+
+(*  Rating   : 0.33 v3.2.0, 0.67 v3.1.0, 0.33 v2.6.0, 0.67 v2.5.0 *)
+
+(*  Syntax   : Number of clauses     :   15 (   0 non-Horn;  15 unit;   1 RR) *)
+
+(*             Number of atoms       :   15 (  15 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    8 (   5 constant; 0-2 arity) *)
+
+(*             Number of variables   :   25 (   2 singleton) *)
+
+(*             Maximal term depth    :    4 (   2 average) *)
+
+(*  Comments : This is well known, but it is a good test problem for finite *)
+
+(*             model search. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include lattice axioms  *)
+
+(* Inclusion of: Axioms/LAT001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : LAT001-0 : TPTP v3.7.0. 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 atoms      :    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  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Compatibility (6) *)
+
+(* ----Invertability (5) *)
+
+(* ----Orthomodular law (8) *)
+
+(* ----Denial of modular law: *)
+ntheorem prove_modular_law:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀a:Univ.
+∀b:Univ.
+∀c:Univ.
+∀complement:∀_:Univ.Univ.
+∀join:∀_:Univ.∀_:Univ.Univ.
+∀meet:∀_:Univ.∀_:Univ.Univ.
+∀n0:Univ.
+∀n1:Univ.
+∀H0:∀X:Univ.∀Y:Univ.eq Univ (join X (meet (complement X) (join X Y))) (join X Y).
+∀H1:∀X:Univ.eq Univ (complement (complement X)) X.
+∀H2:∀X:Univ.eq Univ (meet (complement X) X) n0.
+∀H3:∀X:Univ.eq Univ (join (complement X) X) n1.
+∀H4:∀X:Univ.∀Y:Univ.eq Univ (complement (meet X Y)) (join (complement X) (complement Y)).
+∀H5:∀X:Univ.∀Y:Univ.eq Univ (complement (join X Y)) (meet (complement X) (complement Y)).
+∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).
+∀H7:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).
+∀H8:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X).
+∀H9:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).
+∀H10:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.
+∀H11:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.
+∀H12:∀X:Univ.eq Univ (join X X) X.
+∀H13:∀X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet b (join a c))) (meet (join a b) (join a c)))
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#c ##.
+#complement ##.
+#join ##.
+#meet ##.
+#n0 ##.
+#n1 ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+#H12 ##.
+#H13 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11,H12,H13 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)