Statistical testing procedure for lengths of formalized proofs

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library A statistical testing procedure is proposed, which enables to test, given a formula of a formalized theory, whether there exists a proof of this formula the length of which does not exceed an a priori given threshold value. Such a decision rule may be of great importance when applied to automated problem solving as it prevents us from looking for solutions which are inappropriate from applicational points of view.