### Abstract

Mizar is a proof assistant used for formalization and mechanical verification of mathematics. The main use of Mizar is in the development of the Mizar Mathematical Library (MML), in which proofs are verified by the Mizar proof checker. The Mizar proof checker has a quite complex implementation, and also lacks the ability to print out detailed atomic proof steps in a format that is easy to verify by an independent proof-checking tool. This can raise concerns about the correctness of the MML. This paper describes how a Mizar-to-ATP translation (the MPTP system), ATP verification tools (the GDV system), and Automated Theorem Proving (ATP) systems, have been used for an independent cross-verification of a part of the MML.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 546-560 |

Number of pages | 15 |

Volume | 4790 LNAI |

State | Published - 2007 |

Event | 14th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2007 - Yerevan, Armenia Duration: Oct 15 2007 → Oct 19 2007 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 4790 LNAI |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 14th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2007 |
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Country | Armenia |

City | Yerevan |

Period | 10/15/07 → 10/19/07 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Biochemistry, Genetics and Molecular Biology(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 4790 LNAI, pp. 546-560). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4790 LNAI).

**ATP cross-verification of the mizar MPTP challenge problems.** / Urban, Josef; Sutcliffe, Geoffrey.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 4790 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4790 LNAI, pp. 546-560, 14th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2007, Yerevan, Armenia, 10/15/07.

}

TY - GEN

T1 - ATP cross-verification of the mizar MPTP challenge problems

AU - Urban, Josef

AU - Sutcliffe, Geoffrey

PY - 2007

Y1 - 2007

N2 - Mizar is a proof assistant used for formalization and mechanical verification of mathematics. The main use of Mizar is in the development of the Mizar Mathematical Library (MML), in which proofs are verified by the Mizar proof checker. The Mizar proof checker has a quite complex implementation, and also lacks the ability to print out detailed atomic proof steps in a format that is easy to verify by an independent proof-checking tool. This can raise concerns about the correctness of the MML. This paper describes how a Mizar-to-ATP translation (the MPTP system), ATP verification tools (the GDV system), and Automated Theorem Proving (ATP) systems, have been used for an independent cross-verification of a part of the MML.

AB - Mizar is a proof assistant used for formalization and mechanical verification of mathematics. The main use of Mizar is in the development of the Mizar Mathematical Library (MML), in which proofs are verified by the Mizar proof checker. The Mizar proof checker has a quite complex implementation, and also lacks the ability to print out detailed atomic proof steps in a format that is easy to verify by an independent proof-checking tool. This can raise concerns about the correctness of the MML. This paper describes how a Mizar-to-ATP translation (the MPTP system), ATP verification tools (the GDV system), and Automated Theorem Proving (ATP) systems, have been used for an independent cross-verification of a part of the MML.

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M3 - Conference contribution

SN - 9783540755586

VL - 4790 LNAI

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 546

EP - 560

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -