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Mizar System

The Mizar system is a formal proof-checking system intended to fully automate the process of checking mathematical proofs written in natural language for accuracy. Mizar is used to create and verify formalized mathematics, helping to ensure that published proofs are correct and free from errors. The programming language supporting this activity was designed by Andrzej Trybulec in 1973 at the University of Warsaw, incorporating set theory and higher-order logic. Proofs and definitions can be written using the Mizar language or converted to it from other systems, then thoroughly checked by computer analyses for consistency within the given axioms and logical correctness.