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Layered Clause Selection for Saturation-based Theorem Proving

Bernhard Gleiss, Martin Suda
2020 Zenodo  
Clause selection is one of the main heuristic decision points in navigating proof search of saturation-based theorem provers.  ...  We implemented the resulting clause selection heuristics in the state-of-the-art saturation-based theorem prover Vampire and present an evaluation of these new clause-selection strategies and their combinations  ...  Acknowledgements We thank the anonymous reviewers for their useful comments and suggestions. We also thank Sibylle Ortner for a careful proofreading of a preliminary version of this paper.  ... 
doi:10.5281/zenodo.4584799 fatcat:gzosonxhsbgi3pmxeme6expmzq

Layered Clause Selection for Theory Reasoning [article]

Bernhard Gleiss, Martin Suda
2020 arXiv   pre-print
Explicit theory axioms are added by a saturation-based theorem prover as one of the techniques for supporting theory reasoning.  ...  The strategy refines a recently proposed two-layer-queue clause selection and combines it with a heuristical measure of the amount of theory reasoning in the derivation of a clause.  ...  Layered Clause Selection We assume the reader to be familiar with the saturation-based theorem proving technology (see, e.g.  ... 
arXiv:2001.09705v3 fatcat:lamgodl3e5fnxnonoydvmrv5ya

Layered Clause Selection for Theory Reasoning [chapter]

Bernhard Gleiss, Martin Suda
2020 Lecture Notes in Computer Science  
Explicit theory axioms are added by a saturation-based theorem prover as one of the techniques for supporting theory reasoning.  ...  The strategy refines a recently proposed two-layer-queue clause selection and combines it with a heuristic measure of the amount of theory reasoning in the derivation of a clause.  ...  Layered Clause Selection We assume the reader to be familiar with the saturation-based theorem proving technology (see, e.g.  ... 
doi:10.1007/978-3-030-51074-9_23 fatcat:xnv6ppimzvci5om6nd7isha4me

Learning to Prove from Synthetic Theorems [article]

Eser Aygün, Zafarali Ahmed, Ankit Anand, Vlad Firoiu, Xavier Glorot, Laurent Orseau, Doina Precup, Shibl Mourad
2020 arXiv   pre-print
A major challenge in applying machine learning to automated theorem proving is the scarcity of training data, which is a key ingredient in training successful deep learning models.  ...  Our approach outperforms a model trained on human-generated problems in most axiom sets, thereby showing the promise of using synthetic data for this task.  ...  We are also grateful to Koray Kavukcuoglu, Oriol Vinyals and Pushmeet Kohli for the helpful discussions during the course of this work.  ... 
arXiv:2006.11259v1 fatcat:7sdtudsazvdrddmbdpj5bitcuu

Learning to Guide a Saturation-Based Theorem Prover [article]

Ibrahim Abdelaziz, Maxwell Crouse, Bassem Makni, Vernon Austil, Cristina Cornelio, Shajith Ikbal, Pavan Kapanipathi, Ndivhuwo Makondo, Kavitha Srinivas, Michael Witbrock, Achille Fokoue
2021 arXiv   pre-print
TRAIL leverages (a) an effective graph neural network for representing logical formulas, (b) a novel neural representation of the state of a saturation-based theorem prover in terms of processed clauses  ...  In this work, we introduce TRAIL, a deep learning-based approach to theorem proving that characterizes core elements of saturation-based theorem proving within a neural framework.  ...  These two sets correspond to the clauses that have and have not been yet selected for inference. The actions that saturation-based theorem provers take are referred to as inferences.  ... 
arXiv:2106.03906v1 fatcat:c6hnh3zkzzalzawmxal5mhd2ge

Learning Theorem Proving Components [article]

Karel Chvalovský, Jan Jakubův, Miroslav Olšák, Josef Urban
2021 arXiv   pre-print
Saturation-style automated theorem provers (ATPs) based on the given clause procedure are today the strongest general reasoners for classical first-order logic.  ...  This has changed recently by equipping the E/ENIGMA system with a graph neural network (GNN) that chooses the next given clause based on its evaluation in the context of previously selected clauses.  ...  Introduction: Clause Selection and Context Clause selection is a crucial part of saturation-style [29] automated theorem provers (ATPs) such as E [32] , Vampire [20] , and Prover9 [22] .  ... 
arXiv:2107.10034v1 fatcat:kh5y3nebt5gbnhkfgvmjquq2dm

Dynamic Strategy Priority: Empower the Strong and Abandon the Weak

Michael Rawson, Giles Reger
2018 Conference on Automated Deduction  
Automated theorem provers are often used in other tools as black-boxes for discharging proof obligations. One example where this has enjoyed a lot of success is within interactive theorem proving.  ...  A key usability factor in such settings is the time taken for the provers to complete.  ...  for finding good strategies in saturationbased theorem proving [24] .  ... 
dblp:conf/cade/RawsonR18 fatcat:6dyzellr4neizg43vc2milxgmi

Deep Network Guided Proof Search [article]

Sarah Loos, Geoffrey Irving, Christian Szegedy, Cezary Kaliszyk
2017 arXiv   pre-print
proved.  ...  We train and compare several deep neural network models on the traces of existing ATP proofs of Mizar statements and use them to select processed clauses during proof search.  ...  Theorem Proving Preliminaries The First-Order Logic Prover E We target the saturation-based first-order logic theorem prover E (Schulz, 2013) .  ... 
arXiv:1701.06972v1 fatcat:kym7bgfagvh6ji3kw2zhyeqjfy

A Deep Reinforcement Learning Approach to First-Order Logic Theorem Proving [article]

Maxwell Crouse, Ibrahim Abdelaziz, Bassem Makni, Spencer Whitehead, Cristina Cornelio, Pavan Kapanipathi, Kavitha Srinivas, Veronika Thost, Michael Witbrock, Achille Fokoue
2020 arXiv   pre-print
In this paper we introduce TRAIL, a system that applies deep reinforcement learning to saturation-based theorem proving.  ...  theorem proving (proving around 15% more theorems).  ...  These two sets correspond to the clauses that have and have not been yet selected for inference. The actions that saturation-based theorem provers take are referred to as inferences.  ... 
arXiv:1911.02065v3 fatcat:zkajly2mnzeaxfn7dr3ma72vpe

Training a First-Order Theorem Prover from Synthetic Data [article]

Vlad Firoiu, Eser Aygun, Ankit Anand, Zafarali Ahmed, Xavier Glorot, Laurent Orseau, Lei Zhang, Doina Precup, Shibl Mourad
2021 arXiv   pre-print
We use these theorems to train a neurally-guided saturation-based prover.  ...  A major challenge in applying machine learning to automated theorem proving is the scarcity of training data, which is a key ingredient in training successful deep learning models.  ...  At each iteration of the algorithm, first we select a priority queue based on the age-cost ratio a : c: The age queue is selected for a consecutive iterations, then the cost queue is selected for c consecutive  ... 
arXiv:2103.03798v2 fatcat:ysjigv7xevc6rg3zjxyuru7ada

Teaching Automated Theorem Proving by Example: PyRes 1.2 [chapter]

Stephan Schulz, Adam Pease
2020 Lecture Notes in Computer Science  
PyRes is a complete theorem prover for classical first-order logic. It is not designed for high performance, but to clearly demonstrate the core concepts of a saturating theorem prover.  ...  PyRes uses the given-clause algorithm, optionally controlled by weight-and age evaluations for clause selection. The prover can read TPTP CNF/FOF input files and produces TPTP/TSTP proof objects.  ...  Conclusion We have described PyRes, a theorem prover developed as a pedagogical example to demonstrate saturation-based theorem proving in an accessible, readable, welldocumented way.  ... 
doi:10.1007/978-3-030-51054-1_9 fatcat:zkqfaei4cfanjjmn6zxfh5h3xu

Vampire With a Brain Is a Good ITP Hammer [article]

Martin Suda
2021 arXiv   pre-print
Vampire has been for a long time the strongest first-order automatic theorem prover, widely used for hammer-style proof automation in ITPs such as Mizar, Isabelle, HOL, and Coq.  ...  The resulting system shows good learning capability and improves on the state-of-the-art performance on the Mizar library, while proving many theorems that the related ENIGMA system could not prove in  ...  The other is the internal guidance of the ATP's proof search [43, 11] , typically focusing on the clause selection process in the predominant saturation-based proving paradigm [21, 27] .  ... 
arXiv:2102.03529v2 fatcat:h47yw3qpvfdzfas2ml2umv4kry

A verified prover based on ordered resolution

Anders Schlichtkrull, Jasmin Christian Blanchette, Dmitriy Traytel
2019 Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2019  
The superposition calculus, which underlies first-order theorem provers such as E, SPASS, and Vampire, combines ordered resolution and equality reasoning.  ...  nondeterministic specification, a verified deterministic program, written in a subset of Isabelle/HOL from which we extract purely functional Standard ML code that constitutes a semidecision procedure for  ...  Formalizing a theorem proving tool using a theorem proving tool is a thrilling (if self-referential) prospect for many researchers.  ... 
doi:10.1145/3293880.3294100 dblp:conf/cpp/SchlichtkrullBT19 fatcat:ftlcitpp7rbsbevdkf6nl6r25y

ENIGMA-NG: Efficient Neural and Gradient-Boosted Inference Guidance for E [article]

Karel Chvalovský and Jan Jakubův and Martin Suda and Josef Urban
2019 arXiv   pre-print
We describe an efficient implementation of clause guidance in saturation-based automated theorem provers extending the ENIGMA approach.  ...  Both methods are evaluated on a large dataset of theorem proving problems and compared with the previous approaches.  ...  Section 2 introduces the saturation-based automated theorem proving with the emphasis on machine learning.  ... 
arXiv:1903.03182v1 fatcat:4po7uru3s5hgli3zsrzrbiaueq

Making Higher-Order Superposition Work [chapter]

Petar Vukmirović, Alexander Bentkamp, Jasmin Blanchette, Simon Cruanes, Visa Nummelin, Sophie Tourret
2021 Lecture Notes in Computer Science  
AbstractSuperposition is among the most successful calculi for first-order logic.  ...  We describe techniques that address these issues and extensively evaluate their implementation in the Zipperposition theorem prover.  ...  We are grateful to the maintainers of StarExec for letting us use their service. Ahmed Bhayat and Giles Reger guided us through details of Vampire 4.5.  ... 
doi:10.1007/978-3-030-79876-5_24 fatcat:equtnqydmvbmrexuw2eqjr7muq
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