Development of the theory of continuous lattices in Mizar
Symbolic computation and automated reasoning
Automated theorem proving in software engineering
Automated theorem proving in software engineering
Journal of Automated Reasoning
Solution of the Robbins Problem
Journal of Automated Reasoning
Learning Search Control Knowledge for Equational Theorem Proving
KI '01 Proceedings of the Joint German/Austrian Conference on AI: Advances in Artificial Intelligence
Translating Mizar for First Order Theorem Provers
MKM '03 Proceedings of the Second International Conference on Mathematical Knowledge Management
Comparing Mathematical Provers
MKM '03 Proceedings of the Second International Conference on Mathematical Knowledge Management
Soft Typing for Ordered Resolution
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
Combining superposition, sorts and splitting
Handbook of automated reasoning
SNoW User Guide
AI Communications - CASC
Presenting and Explaining Mizar
Electronic Notes in Theoretical Computer Science (ENTCS)
Integrating Searching and Authoring in Mizar
Journal of Automated Reasoning
ATP cross-verification of the Mizar MPTP challenge problems
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
XML-izing mizar: making semantic processing and presentation of MML easy
MKM'05 Proceedings of the 4th international conference on Mathematical Knowledge Management
Using the TPTP language for writing derivations and finite interpretations
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Theorem proving in large formal mathematics as an emerging AI field
Automated Reasoning and Mathematics
Premise Selection for Mathematics by Corpus Analysis and Kernel Methods
Journal of Automated Reasoning
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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.