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Formalizing mathematical argument is a fascinating activity in itself and (we hope!) also bears important practical applications. While traditional proof theory investigates deducibility of an individual statement from a collection of premises, a mathematical proof, with its structure and continuity, can hardly be presented as a single sequent or a set of… (More)

In this paper, a proof assistant, called SAD, is presented. SAD deals with mathematical texts that are formalized in the ForTheL language (brief description of which is also given) and checks their cor-rectness. We give a short description of SAD and a series of examples that show what can be done with it. Note that abstract notion of cor-rectness on which… (More)

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… (More)

A research project aimed at the development of an automated theorem proving system was started in Kiev (Ukraine) in early 1960s. The mastermind of the project, Academician V. Glushkov, baptized it "Evidence Algorithm", EA1. The work on the project lasted, off and on, more than 40 years. In the framework of the project, the Russian and English versions of… (More)

In this paper we reduce the question of validity of a first-order intu-itionistic formula without equality to generating ground instances of this formula and then checking whether the instances are deducible in a propositional intu-itionistic tableaux calculus, provided that the propositional proof is compatible with the way how the instances were… (More)