Stuff moved from old Matita.

[helm.git] / matita / matita / contribs / ng_TPTP / GRP428-1.ma

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+include "logic/equality.ma".
+
+(* Inclusion of: GRP428-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : GRP428-1 : TPTP v3.7.0. Released v2.6.0. *)
+
+(*  Domain   : Group Theory *)
+
+(*  Problem  : Axiom for group theory, in product & inverse, part 2 *)
+
+(*  Version  : [McC93] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     : [Neu81] Neumann (1981), Another Single Law for Groups *)
+
+(*           : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+
+(*  Source   : [TPTP] *)
+
+(*  Names    :  *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.11 v3.4.0, 0.12 v3.3.0, 0.00 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    :    4 (   2 constant; 0-2 arity) *)
+
+(*             Number of variables   :    4 (   0 singleton) *)
+
+(*             Maximal term depth    :    9 (   4 average) *)
+
+(*  Comments : A UEQ part of GRP057-1 *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_these_axioms_2:
+ (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.
+∀a2:Univ.
+∀b2:Univ.
+∀inverse:∀_:Univ.Univ.
+∀multiply:∀_:Univ.∀_:Univ.Univ.
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (multiply A (inverse (multiply (multiply (inverse (multiply (inverse B) (multiply (inverse A) C))) D) (inverse (multiply B D))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2)
+.
+#Univ ##.
+#A ##.
+#B ##.
+#C ##.
+#D ##.
+#a2 ##.
+#b2 ##.
+#inverse ##.
+#multiply ##.
+#H0 ##.
+nauto by H0 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)