--- /dev/null
+include "logic/equality.ma".
+
+(* Inclusion of: LAT051-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LAT051-1 : TPTP v3.7.0. Released v2.5.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Problem : Lattice is not ortholattice *)
+
+(* Version : [McC88] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+
+(* : [RW01] Rose & Wilkinson (2001), Application of Model Search *)
+
+(* Source : [RW01] *)
+
+(* Names : mace-e1.in [RW01] *)
+
+(* Status : Satisfiable *)
+
+(* Rating : 0.33 v3.2.0, 0.67 v3.1.0, 0.33 v2.5.0 *)
+
+(* Syntax : Number of clauses : 12 ( 0 non-Horn; 12 unit; 1 RR) *)
+
+(* Number of atoms : 12 ( 12 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 7 ( 4 constant; 0-2 arity) *)
+
+(* Number of variables : 19 ( 2 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : First part of the problem. The second part, mace-e2.in, requires *)
+
+(* MACE specific input. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Invertability (5) *)
+
+(* ----Denial of compatibility (6) *)
+ntheorem prove_compatibility_law:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀a:Univ.
+∀b:Univ.
+∀complement:∀_:Univ.Univ.
+∀join:∀_:Univ.∀_:Univ.Univ.
+∀meet:∀_:Univ.∀_:Univ.Univ.
+∀n0:Univ.
+∀n1:Univ.
+∀H0:∀X:Univ.eq Univ (complement (complement X)) X.
+∀H1:∀X:Univ.eq Univ (meet (complement X) X) n0.
+∀H2:∀X:Univ.eq Univ (join (complement X) X) n1.
+∀H3:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).
+∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).
+∀H5:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X).
+∀H6:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).
+∀H7:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.
+∀H8:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.
+∀H9:∀X:Univ.eq Univ (join X X) X.
+∀H10:∀X:Univ.eq Univ (meet X X) X.eq Univ (complement (join a b)) (meet (complement a) (complement b)))
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#b ##.
+#complement ##.
+#join ##.
+#meet ##.
+#n0 ##.
+#n1 ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+#H10 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9,H10 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)