--- /dev/null
+
+include "logic/equality.ma".
+(* Inclusion of: LAT045-1.p *)
+(* -------------------------------------------------------------------------- *)
+(* File : LAT045-1 : TPTP v3.1.1. Released v2.5.0. *)
+(* Domain : Lattice Theory *)
+(* Problem : Lattice orthomodular law from modular lattice *)
+(* 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 : eqp-f.in [RW01] *)
+(* Status : Unsatisfiable *)
+(* Rating : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 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 : 7 ( 4 constant; 0-2 arity) *)
+(* Number of variables : 26 ( 2 singleton) *)
+(* Maximal term depth : 4 ( 2 average) *)
+(* Comments : *)
+(* -------------------------------------------------------------------------- *)
+(* ----Include lattice axioms *)
+(* Inclusion of: Axioms/LAT001-0.ax *)
+(* -------------------------------------------------------------------------- *)
+(* File : LAT001-0 : TPTP v3.1.1. 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 *)
+(* -------------------------------------------------------------------------- *)
+(* -------------------------------------------------------------------------- *)
+(* ----Compatibility (6) *)
+(* ----Invertability (5) *)
+(* ----Modular law (7) *)
+(* ----Denial of orthomodular law (8) *)
+theorem prove_orthomodular_law:
+ \forall Univ:Set.
+\forall a:Univ.
+\forall b:Univ.
+\forall complement:\forall _:Univ.Univ.
+\forall join:\forall _:Univ.\forall _:Univ.Univ.
+\forall meet:\forall _:Univ.\forall _:Univ.Univ.
+\forall n0:Univ.
+\forall n1:Univ.
+\forall H0:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (join X (meet Y (join X Z))) (meet (join X Y) (join X Z)).
+\forall H1:\forall X:Univ.eq Univ (complement (complement X)) X.
+\forall H2:\forall X:Univ.eq Univ (meet (complement X) X) n0.
+\forall H3:\forall X:Univ.eq Univ (join (complement X) X) n1.
+\forall H4:\forall X:Univ.\forall Y:Univ.eq Univ (complement (meet X Y)) (join (complement X) (complement Y)).
+\forall H5:\forall X:Univ.\forall Y:Univ.eq Univ (complement (join X Y)) (meet (complement X) (complement Y)).
+\forall H6:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).
+\forall H7:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).
+\forall H8:\forall X:Univ.\forall Y:Univ.eq Univ (join X Y) (join Y X).
+\forall H9:\forall X:Univ.\forall Y:Univ.eq Univ (meet X Y) (meet Y X).
+\forall H10:\forall X:Univ.\forall Y:Univ.eq Univ (join X (meet X Y)) X.
+\forall H11:\forall X:Univ.\forall Y:Univ.eq Univ (meet X (join X Y)) X.
+\forall H12:\forall X:Univ.eq Univ (join X X) X.
+\forall H13:\forall X:Univ.eq Univ (meet X X) X.eq Univ (join a (meet (complement a) (join a b))) (join a b)
+.
+intros.
+autobatch paramodulation timeout=100;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)