--- /dev/null
+include "logic/equality.ma".
+
+(* Inclusion of: LAT165-1.p *)
+
+(* ------------------------------------------------------------------------------ *)
+
+(* File : LAT165-1 : TPTP v3.2.0. Released v3.1.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Problem : Huntington equation H76 implies H77 *)
+
+(* Version : [McC05] (equality) axioms : Especial. *)
+
+(* English : *)
+
+(* Refs : [McC05] McCune (2005), Email to Geoff Sutcliffe *)
+
+(* Source : [McC05] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.86 v3.2.0, 0.93 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 : 6 ( 4 constant; 0-2 arity) *)
+
+(* Number of variables : 20 ( 2 singleton) *)
+
+(* Maximal term depth : 7 ( 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_H77:
+ ∀Univ:Type.∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀a:Univ.
+∀b:Univ.
+∀c:Univ.
+∀d:Univ.
+∀join:∀_:Univ.∀_:Univ.Univ.
+∀meet:∀_:Univ.∀_:Univ.Univ.
+∀H0:∀U:Univ.∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet X (join Y (meet Z (join Y U)))) (meet X (join Y (meet Z (join U (meet X Y))))).
+∀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 (meet c (join b d)))) (meet a (join b (meet c (join d (meet a (meet b c))))))
+.
+#Univ.
+#U.
+#X.
+#Y.
+#Z.
+#a.
+#b.
+#c.
+#d.
+#join.
+#meet.
+#H0.
+#H1.
+#H2.
+#H3.
+#H4.
+#H5.
+#H6.
+#H7.
+#H8.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8;
+nqed.
+
+(* ------------------------------------------------------------------------------ *)