--- /dev/null
+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.
+
+(* -------------------------------------------------------------------------- *)