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+include "logic/equality.ma".
+
+(* Inclusion of: GRP534-1.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(*  File     : GRP534-1 : TPTP v3.2.0. Released v2.6.0. *)
+
+(*  Domain   : Group Theory (Abelian) *)
+
+(*  Problem  : Axiom for Abelian group theory, in division, part 2 *)
+
+(*  Version  : [McC93] (equality) axioms. *)
+
+(*  English  :  *)
+
+(*  Refs     : [McC93] McCune (1993), Single Axioms for Groups and Abelian Gr *)
+
+(*  Source   : [TPTP] *)
+
+(*  Names    :  *)
+
+(*  Status   : Unsatisfiable *)
+
+(*  Rating   : 0.00 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    :    6 (   3 constant; 0-2 arity) *)
+
+(*             Number of variables   :    9 (   0 singleton) *)
+
+(*             Maximal term depth    :    5 (   2 average) *)
+
+(*  Comments : A UEQ part of GRP091-1 *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_these_axioms_2:
+ ∀Univ:Type.∀A:Univ.∀B:Univ.∀C:Univ.
+∀a2:Univ.
+∀b2:Univ.
+∀divide:∀_:Univ.∀_:Univ.Univ.
+∀identity:Univ.
+∀inverse:∀_:Univ.Univ.
+∀multiply:∀_:Univ.∀_:Univ.Univ.
+∀H0:∀A:Univ.eq Univ identity (divide A A).
+∀H1:∀A:Univ.∀B:Univ.eq Univ (inverse A) (divide (divide B B) A).
+∀H2:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (multiply A B) (divide A (divide (divide C C) B)).
+∀H3:∀A:Univ.∀B:Univ.∀C:Univ.eq Univ (divide (divide A (divide (divide A B) C)) B) C.eq Univ (multiply (multiply (inverse b2) b2) a2) a2
+.
+#Univ.
+#A.
+#B.
+#C.
+#a2.
+#b2.
+#divide.
+#identity.
+#inverse.
+#multiply.
+#H0.
+#H1.
+#H2.
+#H3.
+nauto by H0,H1,H2,H3;
+nqed.
+
+(* -------------------------------------------------------------------------- *)