--- /dev/null
+
+include "logic/equality.ma".
+(* Inclusion of: GRP010-4.p *)
+(* -------------------------------------------------------------------------- *)
+(* File : GRP010-4 : TPTP v3.1.1. Released v1.0.0. *)
+(* Domain : Group Theory *)
+(* Problem : Inverse is a symmetric relationship *)
+(* Version : [Wos65] (equality) axioms : Incomplete. *)
+(* English : If a is an inverse of b then b is an inverse of a. *)
+(* Refs : [Wos65] Wos (1965), Unpublished Note *)
+(* : [Pel86] Pelletier (1986), Seventy-five Problems for Testing Au *)
+(* Source : [Pel86] *)
+(* Names : Pelletier 64 [Pel86] *)
+(* Status : Unsatisfiable *)
+(* Rating : 0.00 v2.1.0, 0.13 v2.0.0 *)
+(* Syntax : Number of clauses : 5 ( 0 non-Horn; 5 unit; 2 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 ( 3 constant; 0-2 arity) *)
+(* Number of variables : 5 ( 0 singleton) *)
+(* Maximal term depth : 3 ( 2 average) *)
+(* Comments : [Pel86] says "... problems, published I think, by Larry Wos *)
+(* (but I cannot locate where)." *)
+(* -------------------------------------------------------------------------- *)
+(* ----The operation '*' is associative *)
+(* ----There exists an identity element 'e' defined below. *)
+theorem prove_b_times_c_is_e:
+ \forall Univ:Set.
+\forall b:Univ.
+\forall c:Univ.
+\forall identity:Univ.
+\forall inverse:\forall _:Univ.Univ.
+\forall multiply:\forall _:Univ.\forall _:Univ.Univ.
+\forall H0:eq Univ (multiply c b) identity.
+\forall H1:\forall X:Univ.eq Univ (multiply (inverse X) X) identity.
+\forall H2:\forall X:Univ.eq Univ (multiply identity X) X.
+\forall H3:\forall X:Univ.\forall Y:Univ.\forall Z:Univ.eq Univ (multiply (multiply X Y) Z) (multiply X (multiply Y Z)).eq Univ (multiply b c) identity
+.
+intros.
+autobatch paramodulation timeout=100;
+try assumption.
+print proofterm.
+qed.
+(* -------------------------------------------------------------------------- *)