Computer-Oriented Sequent Inferring without Preliminary Skolemization

Abstract

In this paper1 sequent formalism used in theorem-proving technique of a system of automated deduction, SAD2, is described. The specific feature of SAD is that a mathematical text under consideration is formalized using a certain formal language, which is close to a “natural” one and can be translated into a certain first-order language in order to apply sequent-based methods having the following features: goal-oriented reducing an assertion to be proven to a number of auxiliary assertions, quantifier-handling technique admitting efficient logical inferring in a signature of an initial theory without skolemization, separating deduction from equation solving. One of these methods is expressed here in the form of a special sequent-type calculus. Some results about its soundness and completeness are given.