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

Prolog Technology Reinforcement Learning Prover: (System Description)

We present a reinforcement learning toolkit for experiments with guiding automated theorem proving in the connection calculus. The core of the toolkit is a compact and easy to extend Prolog-based automated theorem prover called plCoP. plCoP builds on the leanCoP Prolog implementation and adds learning-guided Monte-Carlo Tree Search as done in the rlCoP system. Other components include a Python interface to plCoP and machine learners, and an external proof checker that verifies the validity of plCoP proofs. The toolkit is evaluated on two benchmarks and we demonstrate its extendability by two additions: (1) guidance is extended to reduction steps and (2) the standard leanCoP calculus is extended with rewrite steps and their learned guidance. We argue that the Prolog setting is suitable for combining statistical and symbolic learning methods. The complete toolkit is publicly released. © 2020, Springer Nature Switzerland AG

Testowanie potomstwa hybrydowego i różnych gatunków rodzaju Abies dla leśnictwa, ogrodnictwa ozdobnego oraz produkcji choinek

The paper evaluated dendrometric parameters of hybrid progenies of various Abies species obtained during measurements in the spring 2010 on the research plot in Kostelec nad ýernými lesy. Data were processed and compared to the measurement taken in 2004. Results show that all hybrid progenies within the plot exceeded A. alba in investigated parameters. Only two of the progenies achieved worse results in mean height – A. koreana × (A. cilicica × A. cephalonica) and progeny of spontaneous hybrid no. 2. Considering height and diameter A. nordmanniana was evaluated as the most productive. On the contrary A. gracilis is considered unsuitable for further culture and research due to the mortality of 100%.Niniejsza praca ocenia parametry dendrometryczne hybrydowego potomstwa różnych gatunków Abies otrzymane podczas pomiarów wiosną 2010 na poletku doświadczalnym w Kostelec nad Černými lesy. Otrzymane dane były przetworzone i porównane z pomiarami poczynionymi w roku 2004. Wyniki pokazują, że całe potomstwo hybrydowe na poletku przewyższało A. alba pod względem badanych parametrów. Tylko dwa osiągnęły gorsze rezultaty, jeśli chodzi o średnią wysokość – A. koreana × (A. cilicica × A. cephalonica) oraz potomek spontanicznej krzyżówki no. 2. Pod względem wysokości i średnicy, A. nordmanniana oceniono jako najbardziej produktywną. Z kolei A. gracilis uważa się za nieodpowiednią do dalszej uprawy i badań ze względu na 100% śmiertelnoś