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Automated and Human Proofs in General Mathematics: An Initial Comparison

  • Jesse Alama
  • Daniel Kühlwein
  • Josef Urban
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7180)

Abstract

First-order translations of large mathematical repositories allow discovery of new proofs by automated reasoning systems. Large amounts of available mathematical knowledge can be re-used by combined AI/ATP systems, possibly in unexpected ways. But automated systems can be also more easily misled by irrelevant knowledge in this setting, and finding deeper proofs is typically more difficult. Both large-theory AI/ATP methods, and translation and data-mining techniques of large formal corpora, have significantly developed recently, providing enough data for an initial comparison of the proofs written by mathematicians and the proofs found automatically. This paper describes such an initial experiment and comparison conducted over the 50000 mathematical theorems from the Mizar Mathematical Library.

Keywords

Automate Theorem Prove Initial Comparison General Mathematic Mizar Mathematical Library Proof Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jesse Alama
    • 1
  • Daniel Kühlwein
    • 2
  • Josef Urban
    • 2
  1. 1.New University of LisbonPortugal
  2. 2.Radboud University NijmegenNetherlands

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