Strong skolemization

Skolemization is a means to eliminate existential quantifiers within predicate logic sentences and that by replacing existentially quantified variables with Skolem function applications. The arguments of these Skolem functions are variables which are quantified outside the sub-formula under consideration. In this paper a Skolemization technique is introduced which abstracts from some of the arguments of the Skolem functions. It shows that the Skolemization result obtained this way is usually more general than what can be achieved from standard (classical) Skolemization. This can be of quite some importance since such generalizations often lead to a reduction of both search space and proof length