Presenting and Explaining Mizar
Electronic Notes in Theoretical Computer Science (ENTCS)
The 3rd IJCAR Automated Theorem Proving Competition
AI Communications
The CADE-21 automated theorem proving system competition
AI Communications
SRASS - A Semantic Relevance Axiom Selection System
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
MaLARea SG1 - Machine Learner for Automated Reasoning with Semantic Guidance
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Literal Projection for First-Order Logic
JELIA '08 Proceedings of the 11th European conference on Logics in Artificial Intelligence
The 4th IJCAR Automated Theorem Proving System Competition - CASC-J4
AI Communications
The TPTP Problem Library and Associated Infrastructure
Journal of Automated Reasoning
The CADE-22 automated theorem proving system competition - CASC-22
AI Communications
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
Evaluation of automated theorem proving on the Mizar mathematical library
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
Automated reasoning and presentation support for formalizing mathematics in Mizar
AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
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AISC'10/MKM'10/Calculemus'10 Proceedings of the 10th ASIC and 9th MKM international conference, and 17th Calculemus conference on Intelligent computer mathematics
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LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
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TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
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CADE'11 Proceedings of the 23rd international conference on Automated deduction
Sine Qua non for large theory reasoning
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Licensing the Mizar mathematical library
MKM'11 Proceedings of the 18th Calculemus and 10th international conference on Intelligent computer mathematics
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Automated and human proofs in general mathematics: an initial comparison
LPAR'12 Proceedings of the 18th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
The CADE-23 Automated Theorem Proving System Competition - CASC-23
AI Communications
CSR'07 Proceedings of the Second international conference on Computer Science: theory and applications
Eliciting Implicit Assumptions of Mizar Proofs by Property Omission
Journal of Automated Reasoning
ATP and Presentation Service for Mizar Formalizations
Journal of Automated Reasoning
The Mizar Mathematical Library in OMDoc: Translation and Applications
Journal of Automated Reasoning
Encoding monomorphic and polymorphic types
TACAS'13 Proceedings of the 19th international conference on Tools and Algorithms for the Construction and Analysis of Systems
CADE'13 Proceedings of the 24th international conference on Automated Deduction
MaSh: machine learning for sledgehammer
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
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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This paper describes the second version of the Mizar Problems for Theorem Proving (MPTP) system and first experimental results obtained with it. The goal of the MPTP project is to make the large formal Mizar Mathematical Library (MML) available to current first-order automated theorem provers (ATPs) (and vice versa) and to boost the development of domain-based, knowledge-based, and generally AI-based ATP methods. This version of MPTP switches to a generic extended TPTP syntax that adds term-dependent sorts and abstract (Fraenkel) terms to the TPTP syntax. We describe these extensions and explain how they are transformed by MPTP to standard TPTP syntax using relativization of sorts and deanonymization of abstract terms. Full Mizar proofs are now exported and also encoded in the extended TPTP syntax, allowing a number of ATP experiments. This covers, for example, consistent handling of proof-local constants and proof-local lemmas and translating of a number of Mizar proof constructs into the TPTP formalism. The proofs using second-order Mizar schemes are now handled by the system, too, by remembering (and, if necessary, abstracting from the proof context) the first-order instances that were actually used. These features necessitated changes in Mizar, in the Mizar-to-TPTP exporter, and in the problem-creating tools. Mizar has been reimplemented to produce and use natively a detailed XML format, suitable for communication with other tools. The Mizar-to-TPTP exporter is now just a XSLT stylesheet translating the XML tree to the TPTP syntax. The problem creation and other MPTP processing tasks are now implemented in about 1,300 lines of Prolog. All these changes have made MPTP more generic, more complete, and more correct. The largest remaining issue is the handling of the Mizar arithmetical evaluations. We describe several initial ATP experiments, both on the easy and on the hard MML problems, sometimes assisted by machine learning. It is shown that on the nonarithmetical problems, countersatisfiability (completions) is no longer detected by the ATP systems, suggesting that the `Mizar deconstruction' done by MPTP is in this case already complete. About every fifth nonarithmetical theorem is proved in a fully autonomous mode, in which the premises are selected by a machine-learning system trained on previous proofs. In 329 of these cases, the newly discovered proofs are shorter than the MML originals and therefore are likely to be used for MML refactoring. This situation suggests that even a simple inductive or deductive system trained on formal mathematics can be sometimes smarter than MML authors and usable for general discovery in mathematics.