## Escape to ATP for Mizar

Venue: | PxTP2011 (2011 |

Citations: | 5 - 0 self |

### BibTeX

@INPROCEEDINGS{Rudnicki_escapeto,

author = {Piotr Rudnicki and Josef Urban},

title = {Escape to ATP for Mizar},

booktitle = {PxTP2011 (2011},

year = {}

}

### OpenURL

### Abstract

An interactive ATP service is a new feature in the Mizar proof assistant. The functionality of the service is in many respects analogous to the Sledgehammer subsystem of Isabelle/HOL. The ATP service requires minimal user configuration and is accessible via a few keystrokes from within Mizar mode in Emacs. In return, for a given goal formula, the ATP service, when it succeeds, finds premises sufficient to prove the goal. The “escape ” to ATP uses a sound translation from Mizar’s language to that of first-order provers, the same translation that has been used in the more batch oriented Automated Reasoning for Mizar (MizAR) web services presented in [16]. We briefly present the interactive ATP service followed by an account of initial experiments with the tool. We claim with some confidence that the tool will substantially ease the process of preparing new Mizar articles. 1

### Citations

1137 | Graph Theory - Harary - 1971 |

58 |
Sur le coloriage des graphes
- Mycielski
- 1955
(Show Context)
Citation Context ...on of basic definitions was still not ironed out. The goal of the article was to develop enough theory to prove the construction of the Mycielskian of a graph. This construction was used by Mycielski =-=[5]-=- to prove existence of triangle-free graphs with arbitrarily large chromatic number. The formalization uses only very basic notions of set theory: empty set, singleton, ordered and unordered pairs, un... |

19 | Three years of experience with Sledgehammer, a practical link between automatic and interactive theorem provers
- Paulson
- 2010
(Show Context)
Citation Context ...We would like to stress that the Japanese Mizar community expressed deep interest in ATP techniques assisting in writing Mizar proofs. The growing popularity of the related Sledgehammer ATP subsystem =-=[6]-=- for Isabelle/HOL finally lead the first author to investigate the usability of the MizAR service (see Section 2) and thus provided the first valuable feedback to the second author. The first demonstr... |

17 |
MoMM—fast interreduction and retrieval in large libraries of formalized mathematics
- Urban
- 2006
(Show Context)
Citation Context ...roving a new conjecture in an article. The following tools are external to the Mizar processor and they can be launched from within the Mizar mode for Emacs. • M(ost—uch) of M(izar—ath) Matches (MoMM =-=[10]-=-), released in 2002, is a subsumption tool based on Schulz’s E Equational Theorem Prover 4 . Given a goal to prove, the tool quickly finds similar previous proof situations in the large Mizar library.... |

15 |
MPTP 0.2: Design, implementation, and initial experiments
- Urban
- 2006
(Show Context)
Citation Context ...tated the creation of various utilities based on HTML representations; see the next section for a summary and consult [13, 16] for details. An early milestone of these translations is the MPTP system =-=[11]-=-, which allows analysis of various mathematically oriented ATP benchmarks as described in [14]. Later, the XMLized MML opened the way for creating metasystems supporting reasoning in large theories [1... |

14 |
A.: Sine Qua Non for Large Theory Reasoning
- Hoder, Voronkov
- 2011
(Show Context)
Citation Context ...ke ATP help, in several simple ways, from within an Emacs session. This functionality owes much to the recent dissemination and development phase of new ATP techniques for large theories such as SInE =-=[4]-=- and MaLARea [12, 17]. The techniques are now mature enough to handle with reasonable efficiency— at least comparable to specialized ATP techniques like MoMM—simple mathematical problems in the enviro... |

14 |
Obvious inferences
- Rudnicki
- 1987
(Show Context)
Citation Context .... ... D: {x} c= L by A, ZFMISC_1:37; where the label ZFMISC 1:37 refers to a fact imported from MML. The acceptance of an inference is decided by the rather complex and still evolving Mizar checker 8 =-=[7]-=-. Finding the necessary references requires detailed knowledge of the library and even then, in more complicated cases it can be a time-consuming process. We have chosen a particularly simple example ... |

12 | System description: SystemOnTPTP
- Sutcliffe
- 2000
(Show Context)
Citation Context ...out4.ogv 48Escape to ATP for Mizar P. Rudnicki and J. Urban Reasoning for Mizar with the suggested acronym MizAR and the main motivation for its development was Sutcliffe’s SystemOn TPTP ATP service =-=[8]-=-. MML is distributed as a collection of source Mizar articles plus an internal representation of the library for use by the Mizar verifier. The standard Mizar distribution offers a stand alone install... |

8 | MaLARea: A metasystem for automated reasoning in large theories
- Urban
- 2007
(Show Context)
Citation Context ...1], which allows analysis of various mathematically oriented ATP benchmarks as described in [14]. Later, the XMLized MML opened the way for creating metasystems supporting reasoning in large theories =-=[12, 17]-=-. The XMLized version of MML prompted a crucial application of ATPs: the cross-verification of the Mizar library. The Mizar proof checker is a complicated piece of software whose sources are publicly ... |

7 |
MPTP - Motivation, Implementation, First Experiments
- Urban
- 2004
(Show Context)
Citation Context ...f corpus in a similar way as learning of ATP premise selection. That ATPs with suitable heuristic premise selection methods can significantly help in large theories like MML has been known since 2003 =-=[9]-=-. We perceive a continuation of this effort as a chance for large-theory formal mathematics to boost development of strong semantic AI systems that are hard to envisage in less formal domains. • Autom... |

5 |
Automated reasoning and presentation support for formalizing mathematics in Mizar
- Urban, Sutcliffe
- 2010
(Show Context)
Citation Context ...nd translation from Mizar’s language to that of first-order provers, the same translation that has been used in the more batch oriented Automated Reasoning for Mizar (MizAR) web services presented in =-=[16]-=-. We briefly present the interactive ATP service followed by an account of initial experiments with the tool. We claim with some confidence that the tool will substantially ease the process of prepari... |

4 | Jiˇrí Vyskočil. MaLARea SG1 - Machine Learner for Automated Reasoning with Semantic Guidance - Urban, Sutcliffe, et al. - 2008 |

2 | Automated reasoning for Mizar: Artificial intelligence through knowledge exchange
- Urban
- 2008
(Show Context)
Citation Context ...urce code is still available only to the members of the Association of Mizar Users. Despite this difficulty, the contents of MML has been exported to other systems, independent of the Mizar processor =-=[13]-=-. For historical accuracy we cannot forget to mention the efforts of Ingo Dahn in trying to export the contents of MML to ATPs and other presentations [2]. Dahn’s effort was inspired by the (then infl... |

2 |
ATP-based cross-verification of Mizar proofs: Method, systems, and first experiments
- Urban, Sutcliffe
(Show Context)
Citation Context ...ces are publicly unavailable. Its wide, successful usage was the only external reason for trusting Mizar-checked proofs. It was natural to attempt reproving all of the theorems in MML. As reported in =-=[15]-=-, the initial experiments were encouraging: combinations of ATPs are able to reprove between 40% and 60% of MML theorems, depending on the area of mathematics covered. ATPs have been much more success... |

1 |
Andrei Voronkov. Evaluation of automated theorem proving on the Mizar mathematical library
- Urban, Hoder
- 2010
(Show Context)
Citation Context ...r a summary and consult [13, 16] for details. An early milestone of these translations is the MPTP system [11], which allows analysis of various mathematically oriented ATP benchmarks as described in =-=[14]-=-. Later, the XMLized MML opened the way for creating metasystems supporting reasoning in large theories [12, 17]. The XMLized version of MML prompted a crucial application of ATPs: the cross-verificat... |

1 | Analysis Situs, volume V - Veblen |