Applying the framework of Tarski–Grothendieck set theory axioms, essentially the Zermelo–Fraenkel set theory supplemented by the Tarski axiom with all the objects being sets and eliminated notion of class, together with the first-order logic of the Gentzen-Jaśkowski natural deduction, in 1973 he designed the formalization system Mizar consisting of a formal language for writing mathematical definitions and proofs, a proof assistant, able to mechanically check proofs written in this language. Although the first presentation of the Mizar system on 14 November 1973 at a seminar in the Institute of Library Science and Scientific Information was an ideology understood as a visionary speculation rather than research project, his idea was later developed by himself and his collaborators to the Mizar Mathematical Library (MML), a library of formalized mathematics which can be used in the proof of new theorems and the world’s largest repository of formalized and computer-checked mathematics.
In 1973, he created the formalization system Mizar using Tarski–Grothendieck set theory axioms, which include Zermelo–Fraenkel set theory with the addition of the Tarski axiom and exclude the notion of class. This system employs first-order logic from Gentzen-Jaśkowski natural deduction to develop a formal language for mathematical definitions and proofs and a proof assistant capable of mechanically checking these proofs. Although the initial presentation at an Institute seminar on November 14, 1973, was considered visionary speculation rather than a research project, his idea later transformed into the Mizar Mathematical Library (MML), which is now a comprehensive repository of formalized mathematics used for proving new theorems and serving as the world's largest collection.