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+include "logic/equality.ma".
+
+(* Inclusion of: LAT040-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : LAT040-1 : TPTP v3.7.0. Released v2.4.0. *)
+
+(*  Domain   : Lattice Theory *)
+
+(*  Problem  : Another simplification rule for distributive lattices *)
+
+(*  Version  : [McC88] (equality) axioms. *)
+
+(*  English  : In every distributive lattice the simplification rule holds: *)
+
+(*             forall x, y, z: (x v y = x v z, x & y = x & z -> y = z ). *)
+
+(*  Refs     : [DeN00] DeNivelle (2000), Email to G. Sutcliffe *)
+
+(*             [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+
+(*  Source   : [DeN00] *)
+
+(*  Names    : lattice-simpl [DeN00] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.00 v2.4.0 *)
+
+(*  Syntax   : Number of clauses     :   13 (   0 non-Horn;  13 unit;   3 RR) *)
+
+(*             Number of atoms       :   13 (  13 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   :   22 (   2 singleton) *)
+
+(*             Maximal term depth    :    3 (   2 average) *)
+
+(*  Comments :  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include lattice theory 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  *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem rhs:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀join:∀_:Univ.∀_:Univ.Univ.
+∀meet:∀_:Univ.∀_:Univ.Univ.
+∀xx:Univ.
+∀yy:Univ.
+∀zz:Univ.
+∀H0:eq Univ (meet xx yy) (meet xx zz).
+∀H1:eq Univ (join xx yy) (join xx zz).
+∀H2:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y Z)) (join (meet X Y) (meet X Z)).
+∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join X (meet Y Z)) (meet (join X Y) (join X Z)).
+∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).
+∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).
+∀H6:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X).
+∀H7:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).
+∀H8:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.
+∀H9:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.
+∀H10:∀X:Univ.eq Univ (join X X) X.
+∀H11:∀X:Univ.eq Univ (meet X X) X.eq Univ yy zz)
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#join ##.
+#meet ##.
+#xx ##.
+#yy ##.
+#zz ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+#H11 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10,H11 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)