--- /dev/null
+include "logic/equality.ma".
+
+(* Inclusion of: GRP500-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : GRP500-1 : TPTP v3.2.0. Released v2.6.0. *)
+
+(* Domain : Group Theory *)
+
+(* Problem : Axiom for group theory, in double division and inverse, part 2 *)
+
+(* Version : [McC93] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+
+(* Source : [TPTP] *)
+
+(* Names : *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.07 v3.1.0, 0.11 v2.7.0, 0.00 v2.6.0 *)
+
+(* Syntax : Number of clauses : 3 ( 0 non-Horn; 3 unit; 1 RR) *)
+
+(* Number of atoms : 3 ( 3 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 5 ( 2 constant; 0-2 arity) *)
+
+(* Number of variables : 6 ( 0 singleton) *)
+
+(* Maximal term depth : 7 ( 3 average) *)
+
+(* Comments : A UEQ part of GRP082-1 *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_these_axioms_2:
+ ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.
+∀a2:Univ.
+∀b2:Univ.
+∀double_divide:∀_:Univ.∀_:Univ.Univ.
+∀inverse:∀_:Univ.Univ.
+∀multiply:∀_:Univ.∀_:Univ.Univ.
+∀H0:∀A:Univ.∀B:Univ.eq Univ (multiply A B) (inverse (double_divide B A)).
+∀H1:∀A:Univ.∀B:Univ.∀C:Univ.∀D:Univ.eq Univ (double_divide (inverse A) (inverse (double_divide (inverse (double_divide A (double_divide B C))) (double_divide D (double_divide B D))))) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+.
+#Univ.
+#A.
+#B.
+#C.
+#D.
+#a2.
+#b2.
+#double_divide.
+#inverse.
+#multiply.
+#H0.
+#H1.
+nauto by H0,H1;
+nqed.
+
+(* -------------------------------------------------------------------------- *)