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[helm.git] / matitaB / matita / contribs / ng_TPTP / CASC_2008 / LAT080-1.ma

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+include "logic/equality.ma".
+
+(* Inclusion of: LAT080-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : LAT080-1 : TPTP v3.7.0. Released v2.6.0. *)
+
+(*  Domain   : Lattice Theory *)
+
+(*  Problem  : Axiom for lattice theory, part 1 *)
+
+(*  Version  : [MP96] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     : [McC98] McCune (1998), Email to G. Sutcliffe *)
+
+(*           : [MP96]  McCune & Padmanabhan (1996), Automated Deduction in Eq *)
+
+(*  Source   : [TPTP] *)
+
+(*  Names    :  *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.56 v3.4.0, 0.50 v3.3.0, 0.36 v3.1.0, 0.11 v2.7.0, 0.55 v2.6.0 *)
+
+(*  Syntax   : Number of clauses     :    2 (   0 non-Horn;   2 unit;   1 RR) *)
+
+(*             Number of atoms       :    2 (   2 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    3 (   1 constant; 0-2 arity) *)
+
+(*             Number of variables   :    7 (   1 singleton) *)
+
+(*             Maximal term depth    :   12 (   4 average) *)
+
+(*  Comments : A UEQ part of LAT015-1 *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_normal_axioms_1:
+ (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.
+∀a:Univ.
+∀join:∀_:Univ.∀_:Univ.Univ.
+∀meet:∀_:Univ.∀_:Univ.Univ.
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.∀G:Univ.eq Univ (join (meet (join (meet A B) (meet B (join A B))) C) (meet (join (meet A (join (join (meet D B) (meet B E)) B)) (meet (join (meet B (meet (meet (join D (join B E)) (join F B)) B)) (meet G (join B (meet (meet (join D (join B E)) (join F B)) B)))) (join A (join (join (meet D B) (meet B E)) B)))) (join (join (meet A B) (meet B (join A B))) C))) B.eq Univ (meet a a) a)
+.
+#Univ ##.
+#A ##.
+#B ##.
+#C ##.
+#D ##.
+#E ##.
+#F ##.
+#G ##.
+#a ##.
+#join ##.
+#meet ##.
+#H0 ##.
+nauto by H0 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)