  Cut-introduction is a technique for structuring and compressing formal
proofs. In this paper we generalize our cut-introduction method for the
introduction of quantified lemmas of the form $\forall x.A$ (for
quantifier-free $A$) to a method generating lemmas of the form $\forall
x_1\ldots\forall x_n.A$. Moreover, we extend the original method to predicate
logic with equality. The new method was implemented and applied to the TSTP
proof database. It is shown that the extension of the method to handle equality
and quantifier-blocks leads to a substantial improvement of the old algorithm.
