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[helm.git] / matitaB / matita / contribs / ng_TPTP / CASC_2008 / GRP506-1.ma

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+include "logic/equality.ma".
+
+(* Inclusion of: GRP506-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : GRP506-1 : TPTP v3.7.0. Released v2.6.0. *)
+
+(*  Domain   : Group Theory (Abelian) *)
+
+(*  Problem  : Axiom for Abelian group theory, in product and inverse, part 2 *)
+
+(*  Version  : [McC93] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     : [Neu81] Neumann (1981), Another Single Law for Groups *)
+
+(*           : [LW92]  Lusk & Wos (1992), Benchmark Problems in Which Equalit *)
+
+(*           : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+
+(*  Source   : [TPTP] *)
+
+(*  Names    :  *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.67 v3.4.0, 0.75 v3.3.0, 0.71 v3.2.0, 0.64 v3.1.0, 0.67 v2.7.0, 0.73 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   :    6 (   0 singleton) *)
+
+(*             Maximal term depth    :   10 (   4 average) *)
+
+(*  Comments : A UEQ part of GRP084-1 *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_these_axioms_2:
+ (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.
+∀a2:Univ.
+∀b2:Univ.
+∀inverse:∀_:Univ.Univ.
+∀multiply:∀_:Univ.∀_:Univ.Univ.
+∀H0:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.∀E:Univ.∀F:Univ.eq Univ (multiply (inverse (multiply (inverse (multiply (inverse (multiply A B)) (multiply B A))) (multiply (inverse (multiply C D)) (multiply C (inverse (multiply (multiply E (inverse F)) (inverse D))))))) F) E.eq Univ (multiply (multiply (inverse b2) b2) a2) a2)
+.
+#Univ ##.
+#A ##.
+#B ##.
+#C ##.
+#D ##.
+#E ##.
+#F ##.
+#a2 ##.
+#b2 ##.
+#inverse ##.
+#multiply ##.
+#H0 ##.
+nauto by H0 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)