--- /dev/null
+include "logic/equality.ma".
+
+(* Inclusion of: BOO013-4.p *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : BOO013-4 : TPTP v3.7.0. Released v1.1.0. *)
+
+(* Domain : Boolean Algebra *)
+
+(* Problem : The inverse of X is unique *)
+
+(* Version : [Ver94] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [Ver94] Veroff (1994), Problem Set *)
+
+(* Source : [Ver94] *)
+
+(* Names : TE [Ver94] *)
+
+(* Status : Unsatisfiable *)
+
+(* Rating : 0.00 v2.2.1, 0.22 v2.2.0, 0.29 v2.1.0, 0.25 v2.0.0 *)
+
+(* Syntax : Number of clauses : 11 ( 0 non-Horn; 11 unit; 3 RR) *)
+
+(* Number of atoms : 11 ( 11 equality) *)
+
+(* Maximal clause size : 1 ( 1 average) *)
+
+(* Number of predicates : 1 ( 0 propositional; 2-2 arity) *)
+
+(* Number of functors : 7 ( 4 constant; 0-2 arity) *)
+
+(* Number of variables : 14 ( 0 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* ----Include boolean algebra axioms for equality formulation *)
+
+(* Inclusion of: Axioms/BOO004-0.ax *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* File : BOO004-0 : TPTP v3.7.0. Released v1.0.0. *)
+
+(* Domain : Boolean Algebra *)
+
+(* Axioms : Boolean algebra (equality) axioms *)
+
+(* Version : [Ver94] (equality) axioms. *)
+
+(* English : *)
+
+(* Refs : [Ver94] Veroff (1994), Problem Set *)
+
+(* Source : [Ver94] *)
+
+(* Names : *)
+
+(* Status : *)
+
+(* Syntax : Number of clauses : 8 ( 0 non-Horn; 8 unit; 0 RR) *)
+
+(* Number of atoms : 8 ( 8 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 : 14 ( 0 singleton) *)
+
+(* Maximal term depth : 3 ( 2 average) *)
+
+(* Comments : *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+
+(* -------------------------------------------------------------------------- *)
+ntheorem prove_a_inverse_is_b:
+ (∀Univ:Type.∀X:Univ.∀Y:Univ.∀Z:Univ.
+∀a:Univ.
+∀add:∀_:Univ.∀_:Univ.Univ.
+∀additive_identity:Univ.
+∀b:Univ.
+∀inverse:∀_:Univ.Univ.
+∀multiplicative_identity:Univ.
+∀multiply:∀_:Univ.∀_:Univ.Univ.
+∀H0:eq Univ (multiply a b) additive_identity.
+∀H1:eq Univ (add a b) multiplicative_identity.
+∀H2:∀X:Univ.eq Univ (multiply X (inverse X)) additive_identity.
+∀H3:∀X:Univ.eq Univ (add X (inverse X)) multiplicative_identity.
+∀H4:∀X:Univ.eq Univ (multiply X multiplicative_identity) X.
+∀H5:∀X:Univ.eq Univ (add X additive_identity) X.
+∀H6:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (multiply X (add Y Z)) (add (multiply X Y) (multiply X Z)).
+∀H7:∀X:Univ.∀Y:Univ.∀Z:Univ.eq Univ (add X (multiply Y Z)) (multiply (add X Y) (add X Z)).
+∀H8:∀X:Univ.∀Y:Univ.eq Univ (multiply X Y) (multiply Y X).
+∀H9:∀X:Univ.∀Y:Univ.eq Univ (add X Y) (add Y X).eq Univ b (inverse a))
+.
+#Univ ##.
+#X ##.
+#Y ##.
+#Z ##.
+#a ##.
+#add ##.
+#additive_identity ##.
+#b ##.
+#inverse ##.
+#multiplicative_identity ##.
+#multiply ##.
+#H0 ##.
+#H1 ##.
+#H2 ##.
+#H3 ##.
+#H4 ##.
+#H5 ##.
+#H6 ##.
+#H7 ##.
+#H8 ##.
+#H9 ##.
+nauto by H0,H1,H2,H3,H4,H5,H6,H7,H8,H9 ##;
+ntry (nassumption) ##;
+nqed.
+
+(* -------------------------------------------------------------------------- *)