ProofWatch: Watchlist Guidance for Large Theories in E

Watchlist (also hint list) is a mechanism that allows related proofs to guide a proof search for a new conjecture. This mechanism has been used with the Otter and Prover9 theorem provers, both for interactive formalizations and for human-assisted proving of open conjectures in small theories. In this work we explore the use of watchlists in large theories coming from first-order translations of large ITP libraries, aiming at improving hammer-style automation by smarter internal guidance of the ATP systems. In particular, we (i) design watchlist-based clause evaluation heuristics inside the E ATP system, and (ii) develop new proof guiding algorithms that load many previous proofs inside the ATP and focus the proof search using a dynamically updated notion of proof matching. The methods are evaluated on a large set of problems coming from the Mizar library, showing significant improvement of E's standard portfolio of strategies, and also of the previous best set of strategies invented for Mizar by evolutionary methods.Comment: 19 pages, 10 tables, submitted to ITP 2018 at FLO

Genomic epidemiology of SARS-CoV-2 in a UK university identifies dynamics of transmission

AbstractUnderstanding SARS-CoV-2 transmission in higher education settings is important to limit spread between students, and into at-risk populations. In this study, we sequenced 482 SARS-CoV-2 isolates from the University of Cambridge from 5 October to 6 December 2020. We perform a detailed phylogenetic comparison with 972 isolates from the surrounding community, complemented with epidemiological and contact tracing data, to determine transmission dynamics. We observe limited viral introductions into the university; the majority of student cases were linked to a single genetic cluster, likely following social gatherings at a venue outside the university. We identify considerable onward transmission associated with student accommodation and courses; this was effectively contained using local infection control measures and following a national lockdown. Transmission clusters were largely segregated within the university or the community. Our study highlights key determinants of SARS-CoV-2 transmission and effective interventions in a higher education setting that will inform public health policy during pandemics.</jats:p