Stuff moved from old Matita.

[helm.git] / matita / matita / contribs / ng_TPTP / BOO022-1.ma

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+include "logic/equality.ma".
+
+(* Inclusion of: BOO022-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : BOO022-1 : TPTP v3.7.0. Released v2.2.0. *)
+
+(*  Domain   : Boolean Algebra *)
+
+(*  Problem  : A Basis for Boolean Algebra *)
+
+(*  Version  : [MP96] (equality) axioms. *)
+
+(*  English  : This ntheorem starts with a (self-dual independent) 6-basis *)
+
+(*             for Boolean algebra and derives associativity of product. *)
+
+(*  Refs     : [McC98] McCune (1998), Email to G. Sutcliffe *)
+
+(*           : [MP96]  McCune & Padmanabhan (1996), Automated Deduction in Eq *)
+
+(*  Source   : [McC98] *)
+
+(*  Names    : DUAL-BA-1 [MP96] *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.11 v3.4.0, 0.12 v3.3.0, 0.14 v3.2.0, 0.07 v3.1.0, 0.22 v2.7.0, 0.00 v2.2.1 *)
+
+(*  Syntax   : Number of clauses     :    7 (   0 non-Horn;   7 unit;   1 RR) *)
+
+(*             Number of atoms       :    7 (   7 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    8 (   5 constant; 0-2 arity) *)
+
+(*             Number of variables   :   12 (   2 singleton) *)
+
+(*             Maximal term depth    :    3 (   2 average) *)
+
+(*  Comments : The other part of this problem is to prove commutativity. *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Boolean Algebra: *)
+
+(* ----Denial of conclusion: *)
+ntheorem prove_associativity_of_multiply:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀a:Univ.
+∀add:∀_:Univ.∀_:Univ.Univ.
+∀b:Univ.
+∀c:Univ.
+∀inverse:∀_:Univ.Univ.
+∀multiply:∀_:Univ.∀_:Univ.Univ.
+∀n0:Univ.
+∀n1:Univ.
+∀H0:∀X:Univ.eq Univ (multiply X (inverse X)) n0.
+∀H1:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add Y X) (add Z X)).
+∀H2:∀X:Univ.∀Y:Univ.eq Univ (add (multiply X Y) Y) Y.
+∀H3:∀X:Univ.eq Univ (add X (inverse X)) n1.
+∀H4:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply Y X) (multiply Z X)).
+∀H5:∀X:Univ.∀Y:Univ.eq Univ (multiply (add X Y) Y) Y.eq Univ (multiply (multiply a b) c) (multiply a (multiply b c)))
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#add ##.
+#b ##.
+#c ##.
+#inverse ##.
+#multiply ##.
+#n0 ##.
+#n1 ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+nauto by H0,H1,H2,H3,H4,H5 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)