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+include "logic/equality.ma".
+
+(* Inclusion of: GRP580-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : GRP580-1 : TPTP v3.7.0. Bugfixed v2.7.0. *)
+
+(*  Domain   : Group Theory (Abelian) *)
+
+(*  Problem  : Axiom for Abelian group theory, in double div and id, part 4 *)
+
+(*  Version  : [McC93] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+
+(*  Source   : [TPTP] *)
+
+(*  Names    :  *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.00 v2.7.0 *)
+
+(*  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    :    6 (   3 constant; 0-2 arity) *)
+
+(*             Number of variables   :    7 (   0 singleton) *)
+
+(*             Maximal term depth    :    6 (   2 average) *)
+
+(*  Comments : A UEQ part of GRP102-1 *)
+
+(*  Bugfixes : v2.7.0 - Grounded conjecture *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_these_axioms_4:
+ (∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.
+∀a:Univ.
+∀b: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.eq Univ (double_divide (double_divide A (double_divide (double_divide (double_divide B A) C) (double_divide B identity))) (double_divide identity identity)) C.eq Univ (multiply a b) (multiply b a))
+.
+#Univ ##.
+#A ##.
+#B ##.
+#C ##.
+#a ##.
+#b ##.
+#double_divide ##.
+#identity ##.
+#inverse ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+nauto by H0,H1,H2,H3 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)