### Learning Proof Search in Proof Assistants

Michael FärberPhD thesis, University of Innsbruck, 2018.

### Abstract

Proof assistants are programs that verify the correctness of formal proofs. They can increase the confidence in results from domains such as mathematics, informatics, physics, and philosophy. However, it requires extensive labour and expertise to write proofs accepted by proof assistants. In this thesis, we improve proof automation in proof assistants. Automated theorem provers are programs that search for proofs automatically. Our goal is to find proofs in proof assistants using automated theorem provers. However, this is not directly possible when the logic of an automated theorem prover and that of a proof assistant differ. In this case, the integration of the automated theorem prover into the proof assistant requires the translation of statements to the logic of the automated theorem prover and the translation of proofs to the logic of the proof assistant. To restrict the search space of the automated theorem prover, only a selection of facts relevant to the current conjecture is translated. The success rate of the automatic proof search in proof assistants depends on the various translations, the selection of relevant facts as well as on the automated theorem prover itself. We improve several components of the integration of automated theorem provers into proof assistants. Among others, we learn from previous proofs to select relevant facts as well as to guide automated theorem provers to make good decisions. Furthermore, we create automated proof translations for several automated theorem provers for which such a translation was not previously available. Our work increases the success ratio of proof search in proof assistants.

### BibTeX

@phdthesis{MF18, author = "Michael F\"arber", title = "Learning Proof Search in Proof Assistants", school = "University of Innsbruck", year = 2018 }