-ng implemented

[helm.git] / helm / software / matita / contribs / ng_TPTP / GRP483-1.ma

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+include "logic/equality.ma".
+
+(* Inclusion of: GRP483-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : GRP483-1 : TPTP v3.2.0. Released v2.6.0. *)
+
+(*  Domain   : Group Theory *)
+
+(*  Problem  : Axiom for group theory, in double division and identity, part 3 *)
+
+(*  Version  : [McC93] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     : [Neu86] Neumann (1986), Yet Another Single Law for Groups *)
+
+(*           : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+
+(*  Source   : [TPTP] *)
+
+(*  Names    :  *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.00 v2.6.0 *)
+
+(*  Syntax   : Number of clauses     :    5 (   0 non-Horn;   5 unit;   1 RR) *)
+
+(*             Number of atoms       :    5 (   5 equality) *)
+
+(*             Maximal clause size   :    1 (   1 average) *)
+
+(*             Number of predicates  :    1 (   0 propositional; 2-2 arity) *)
+
+(*             Number of functors    :    7 (   4 constant; 0-2 arity) *)
+
+(*             Number of variables   :    8 (   0 singleton) *)
+
+(*             Maximal term depth    :    7 (   3 average) *)
+
+(*  Comments : A UEQ part of GRP075-1 *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_these_axioms_3:
+ ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.
+∀a3:Univ.
+∀b3:Univ.
+∀c3:Univ.
+∀double_divide:∀_:Univ.∀_:Univ.Univ.
+∀identity:Univ.
+∀inverse:∀_:Univ.Univ.
+∀multiply:∀_:Univ.∀_:Univ.Univ.
+∀H0:∀A:Univ.eq Univ identity (double_divide A (inverse A)).
+∀H1:∀A:Univ.eq Univ (inverse A) (double_divide A identity).
+∀H2:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (double_divide (double_divide A (double_divide B identity)) (double_divide (double_divide C (double_divide D (double_divide D identity))) (double_divide A identity))) B) C.eq Univ (multiply (multiply a3 b3) c3) (multiply a3 (multiply b3 c3))
+.
+#Univ.
+#A.
+#B.
+#C.
+#D.
+#a3.
+#b3.
+#c3.
+#double_divide.
+#identity.
+#inverse.
+#multiply.
+#H0.
+#H1.
+#H2.
+#H3.
+nauto by H0,H1,H2,H3;
+nqed.
+
+(* -------------------------------------------------------------------------- *)