Evidence Algorithm and Sequent Logical Inference Search

In this paper we continue to develop the approach to automated search for theorem proofs started in Kyiv in 1960-1970s. This approach presupposes the development of deductive techniques used for the processing of mathematical texts, written in a formal first-order language, close to the natural language used in mathematical papers. We construct two logical calculi, gS and mS, satisfying the following requirements: the syntactical form of the initial problem should be preserved; the proof search should be goal-oriented; preliminary skolemization is not obligatory; equality handling should be separated from the deduction process. The calculus gS is a machine-oriented sequent-type calculus with “large-block” inference rules for first-order classical logic. The calculus mS is a further development of the calculus gS, enriched with formal analogs of the natural proof search techniques such as definition handling and application of auxiliary propositions. The results on soundness and completeness of gS and mS are given.