--- /dev/null
+set "baseuri" "cic:/matita/TPTP/LAT005-3".
+include "logic/equality.ma".
+
+(* Inclusion of: LAT005-3.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LAT005-3 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Problem : SAM's lemma *)
+
+(* Version : [McC88] (equality) axioms. *)
+
+(* English : Let L be a modular lattice with 0 and 1. Suppose that A and *)
+
+(* B are elements of L such that (A v B) and (A ^ B) both have *)
+
+(* not necessarily unique complements. Then, (A v B)' = *)
+
+(* ((A v B)' v ((A ^ B)' ^ B)) ^ ((A v B)' v ((A ^ B)' ^ A)). *)
+
+(* Refs : [GO+69] Guard et al. (1969), Semi-Automated Mathematics *)
+
+(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+
+(* Source : [McC88] *)
+
+(* Names : SAM's lemma [McC88] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.43 v3.2.0, 0.14 v3.1.0, 0.44 v2.7.0, 0.50 v2.6.0, 0.43 v2.5.0, 0.80 v2.4.0, 1.00 v2.3.0, 0.83 v2.2.1, 0.89 v2.2.0, 0.86 v2.1.0, 1.00 v2.0.0 *)
+
+(* Syntax : Number of clauses : 19 ( 0 non-Horn; 15 unit; 6 RR) *)
+
+(* Number of atoms : 24 ( 19 equality) *)
+
+(* Maximal clause size : 3 ( 1 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 8 ( 6 constant; 0-2 arity) *)
+
+(* Number of variables : 29 ( 4 singleton) *)
+
+(* Maximal term depth : 4 ( 2 average) *)
+
+(* Comments : [McC88] specifies that the axioms for complement should not be *)
+
+(* included ("clauses 1-13 from axioms"). However, if this makes *)
+
+(* clauses 87 and 88 pure. I have assumed a typo in the paper and *)
+
+(* included axioms 14-16. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include lattice 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 *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include modular lattice axioms *)
+
+(* Inclusion of: Axioms/LAT001-1.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LAT001-1 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Axioms : Lattice theory modularity (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 : 5 ( 0 non-Horn; 4 unit; 0 RR) *)
+
+(* Number of literals : 6 ( 6 equality) *)
+
+(* Maximal clause size : 2 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 4 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 7 ( 2 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : Requires LAT001-0.ax *)
+
+(* : These axioms, with 4 extra redundant axioms about 0 & 1, are *)
+
+(* used in [Wos88] p.217. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include 1 and 0 in the lattice *)
+
+(* ----Require the lattice to be modular *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include definition of complement *)
+
+(* Inclusion of: Axioms/LAT001-2.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : LAT001-2 : TPTP v3.2.0. Released v1.0.0. *)
+
+(* Domain : Lattice Theory *)
+
+(* Axioms : Lattice theory complement (equality) axioms *)
+
+(* Version : [McC88] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [Bum65] Bumcroft (1965), Proceedings of the Glasgow Mathematic *)
+
+(* : [McC88] McCune (1988), Challenge Equality Problems in Lattice *)
+
+(* Source : [McC88] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 3 ( 0 non-Horn; 0 unit; 3 RR) *)
+
+(* Number of literals : 7 ( 4 equality) *)
+
+(* Maximal clause size : 3 ( 2 average) *)
+
+(* Number of predicates : 2 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 4 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 2 ( 1 average) *)
+
+(* Comments : Requires LAT001-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Definition of complement *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+theorem prove_lemma:
+ ∀Univ:Set.∀X:Univ.∀Y:Univ.∀Z:Univ.∀a:Univ.∀b:Univ.∀complement:∀_:Univ.∀_:Univ.Prop.∀join:∀_:Univ.∀_:Univ.Univ.∀meet:∀_:Univ.∀_:Univ.Univ.∀n0:Univ.∀n1:Univ.∀r1:Univ.∀r2:Univ.∀H0:complement r2 (meet a b).∀H1:complement r1 (join a b).∀H2:∀X:Univ.∀Y:Univ.∀_:eq Univ (join X Y) n1.∀_:eq Univ (meet X Y) n0.complement X Y.∀H3:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (join X Y) n1.∀H4:∀X:Univ.∀Y:Univ.∀_:complement X Y.eq Univ (meet X Y) n0.∀H5:∀X:Univ.∀Y:Univ.∀Z:Univ.∀_:eq Univ (meet X Z) X.eq Univ (meet Z (join X Y)) (join X (meet Y Z)).∀H6:∀X:Univ.eq Univ (join X n1) n1.∀H7:∀X:Univ.eq Univ (meet X n1) X.∀H8:∀X:Univ.eq Univ (join X n0) X.∀H9:∀X:Univ.eq Univ (meet X n0) n0.∀H10:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (join (join X Y) Z) (join X (join Y Z)).∀H11:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (meet (meet X Y) Z) (meet X (meet Y Z)).∀H12:∀X:Univ.∀Y:Univ.eq Univ (join X Y) (join Y X).∀H13:∀X:Univ.∀Y:Univ.eq Univ (meet X Y) (meet Y X).∀H14:∀X:Univ.∀Y:Univ.eq Univ (join X (meet X Y)) X.∀H15:∀X:Univ.∀Y:Univ.eq Univ (meet X (join X Y)) X.∀H16:∀X:Univ.eq Univ (join X X) X.∀H17:∀X:Univ.eq Univ (meet X X) X.eq Univ r1 (meet (join r1 (meet r2 b)) (join r1 (meet r2 a)))
+.
+intros.
+autobatch depth=5 width=5 size=20 timeout=10;
+try assumption.
+print proofterm.
+qed.
+
+(* -------------------------------------------------------------------------- *)
projects / helm.git / blobdiff