--- /dev/null
+
+include "logic/equality.ma".
+(* Inclusion of: GRP491-1.p *)
+(* -------------------------------------------------------------------------- *)
+(* File : GRP491-1 : TPTP v3.1.1. Released v2.6.0. *)
+(* Domain : Group Theory *)
+(* Problem : Axiom for group theory, in double division and identity, 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 : 5 ( 2 constant; 0-2 arity) *)
+(* Number of variables : 7 ( 0 singleton) *)
+(* Maximal term depth : 6 ( 2 average) *)
+(* Comments : A UEQ part of GRP078-1 *)
+(* -------------------------------------------------------------------------- *)
+theorem prove_these_axioms_2:
+ \forall Univ:Set.
+\forall a2:Univ.
+\forall double_divide:\forall _:Univ.\forall _:Univ.Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:\forall A:Univ.eq Univ identity (double_divide A (inverse A)).
+\forall H1:\forall A:Univ.eq Univ (inverse A) (double_divide A identity).
+\forall H2:\forall A:Univ.\forall B:Univ.eq Univ (multiply A B) (double_divide (double_divide B A) identity).
+\forall H3:\forall A:Univ.\forall B:Univ.\forall C:Univ.eq Univ (double_divide (double_divide identity A) (double_divide identity (double_divide (double_divide (double_divide A B) identity) (double_divide C B)))) C.eq Univ (multiply identity a2) a2
+.
+intros.
+autobatch paramodulation timeout=100;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)