# MPTP – Motivation, Implementation, First Experiments

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## Abstract

We describe a number of new possibilities for current theorem provers that arise with the existence of large integral bodies of formalized mathematics. Then we describe the implementation of the MPTP system, which makes the largest existing corpus of formalized mathematics available to theorem provers. MPTP (Mizar Problems for Theorem Proving) is a system for translating the Mizar Mathematical Library (MML) into untyped first-order format suitable for automated theorem provers and for generating theorem-proving problems corresponding to MML. The first version generates about 30,000 problems from complete proofs of Mizar theorems and about 630,000 problems from the simple (one-step) justifications done by the Mizar checker. We describe the design and structure of the system, the main problems encountered in this kind of system, their solutions, current limitations, and planned extensions. We present results of first experiments with re-proving the MPTP problems with theorem provers. We also describe first implementation of the Mizar Proof Advisor (MPA) used for selecting suitable axioms from the large library for an arbitrary problem and, again, present first results of this combined MPA/ATP architecture on MPTP.

### Keywords

ATP Mizar MPA MPTP### References

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