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Testing a Saturation-Based Theorem Prover: Experiences and Challenges [chapter]

Giles Reger, Martin Suda, Andrei Voronkov
2017 Lecture Notes in Computer Science  
This paper attempts to address the question of how best to assure the correctness of saturation-based automated theorem provers using our experience with developing the theorem prover Vampire.  ...  We describe the techniques we currently employ to ensure that Vampire is correct and use this to motivate future challenges that need to be addressed to make this process more straightforward and to achieve  ...  Introduction This paper considers the problem of checking that a saturation-based automated theorem prover is correct.  ... 
doi:10.1007/978-3-319-61467-0_10 fatcat:x7cutte3jrb6tijcmyozrkjysq

Testing a Saturation-Based Theorem Prover: Experiences and Challenges (Extended Version) [article]

Giles Reger and Martin Suda and Andrei Voronkov
2017 arXiv   pre-print
This paper attempts to address the question of how best to assure the correctness of saturation-based automated theorem provers using our experience developing the theorem prover Vampire.  ...  We describe the techniques we currently employ to ensure that Vampire is correct and use this to motivate future challenges that need to be addressed to make this process more straightforward and to achieve  ...  Introduction This paper considers the problem of checking that a saturation-based automated theorem prover is correct.  ... 
arXiv:1704.03391v1 fatcat:oq3ex3t2bvhilkvb55aoozwbxa

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.  ...  Unlike in Wang & Deng (2020) , who train a theorem generator based on human-written theorems from Metamath, neither proposer nor prover see any TPTP problems until test time.  ... 
arXiv:2103.03798v2 fatcat:ysjigv7xevc6rg3zjxyuru7ada

Learning as Abduction: Trainable Natural Logic Theorem Prover for Natural Language Inference [article]

Lasha Abzianidze
2020 arXiv   pre-print
We implement the learning method in a tableau theorem prover for natural language and show that it improves the performance of the theorem prover on the SICK dataset by 1.4% while still maintaining high  ...  The main reasons for such a conception are that (a) logic-based methods are usually brittle when it comes to processing wide-coverage texts, and (b) instead of automatically learning from data, they require  ...  This work was supported by the NWO-VICI grant (288-89-003) while I was at the University of Groningen and by the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation  ... 
arXiv:2010.15909v2 fatcat:n2mmfo7uxjczrarcmis645oqpy

AUTO2, A Saturation-Based Heuristic Prover for Higher-Order Logic [chapter]

Bohua Zhan
2016 Lecture Notes in Computer Science  
We introduce a new theorem prover for classical higher-order logic named auto2. The prover is designed to make use of human-specified heuristics when searching for proofs.  ...  We implemented the prover in Isabelle/HOL, and applied it to several formalization projects in mathematics and computer science, demonstrating the high level of automation it can provide in a variety of  ...  The author thanks Jasmin Blanchette for extensive comments on a first draft of this paper, and also Jeremy Avigad, Adam Chlipala, and Larry Paulson for feedbacks and discussions during the project.  ... 
doi:10.1007/978-3-319-43144-4_27 fatcat:zwlitqglmnawnp2laenjfhwnla

Formalizing Bachmair and Ganzinger's Ordered Resolution Prover [chapter]

Anders Schlichtkrull, Jasmin Christian Blanchette, Dmitriy Traytel, Uwe Waldmann
2018 Lecture Notes in Computer Science  
We present an Isabelle/HOL formalization of the first half of Bachmair and Ganzinger's chapter on resolution theorem proving, culminating with a refutationally complete first-order prover based on ordered  ...  We developed general infrastructure and methodology that can form the basis of completeness proofs for related calculi, including superposition.  ...  first-order version of the ordered resolution rule and a first-order prover, RP, based on that rule.  ... 
doi:10.1007/978-3-319-94205-6_7 fatcat:hmjoecj5obe2ji6ldifhh3yfbu

Coupling saturation-based provers by exchanging positive/negative information [chapter]

Dirk Fuchs
1998 Lecture Notes in Computer Science  
We examine di erent possibilities of coupling saturation-based theorem provers by exchanging positive/negative information.  ...  Based on this study, we introduce a basic model for cooperative theorem proving.  ...  In contrast to saturation-based provers information on bad facts can easily be used in analytic theorem provers.  ... 
doi:10.1007/bfb0052379 fatcat:tg5xccaqbffpxgffxkntzo7xjm

A Survey on Theorem Provers in Formal Methods [article]

M. Saqib Nawaz, Moin Malik, Yi Li, Meng Sun, M. Ikram Ullah Lali
2019 arXiv   pre-print
Technically, mathematical formalisms and automated reasoning based-approaches are employed to perform inferences and to generate proofs in theorem provers.  ...  In this work, more than 40 theorem provers are studied in detail and compared to present a comprehensive analysis and evaluation of these tools.  ...  ACKNOWLEDGMENTS The work has been supported by the National Natural Science Foundation of China under grant no. 61772038, 61532019 and 61272160, and the Guandong Science and Technology Department (Grant  ... 
arXiv:1912.03028v1 fatcat:fabxqg75xjhxlh7u3uyypgyzdy

Can a Higher-Order and a First-Order Theorem Prover Cooperate? [chapter]

Christoph Benzmüller, Volker Sorge, Mateja Jamnik, Manfred Kerber
2005 Lecture Notes in Computer Science  
We present a solution to this challenge by combining a higher-order and a first-order automated theorem prover, both based on the resolution principle, in a flexible and distributed environment.  ...  We demonstrate the effectiveness of our approach on a set of problems still considered non-trivial for many first-order theorem provers.  ...  Our approach to the cooperation between a higher-order and a first-order theorem prover has many advantages.  ... 
doi:10.1007/978-3-540-32275-7_27 fatcat:vllvzeicvbdixmzafcjhtee7ca

Case Studies on Invariant Generation Using a Saturation Theorem Prover [chapter]

Kryštof Hoder, Laura Kovács, Andrei Voronkov
2011 Lecture Notes in Computer Science  
used in the experiments.  ...  Automatic understanding of the intended meaning of computer programs is a very hard problem, requiring intelligence and reasoning.  ...  Kryštof Hoder is supported by the School of Computer Science at the University of Manchester and by an EPSRC Pathfinder grant.  ... 
doi:10.1007/978-3-642-25324-9_1 fatcat:ht36kixdvvgzvbdoeohs24v5bm

An automated prover for Zermelo–Fraenkel set theory in Theorema

Wolfgang Windsteiger
2006 Journal of symbolic computation  
This paper presents some fundamental aspects of the design and the implementation of an automated prover for Zermelo-Fraenkel set theory within the Theorema system.  ...  The method applies the "Prove-Compute-Solve" paradigm as its major strategy for generating proofs in a natural style for statements involving constructs from set theory.  ...  This is a highly non-trivial, mathematically very interesting and challenging, and didactically very instructive experience for the human user.  ... 
doi:10.1016/j.jsc.2005.04.013 fatcat:u6hy66okqvcypmjm7sifbyyg3i

Distributed Deduction by Clause-Diffusion: Distributed Contraction and the Aquarius Prover

Maria Paola Bonacina, Jieh Hsiang
1995 Journal of symbolic computation  
Aquarius is a distributed theorem prover for first order logic with equality, developed for a network of workstations.  ...  Then, we describe Aquarius, its design, its features and user interface. We present a set of experiments conducted with Aquarius and we analyze the results.  ...  The Aquarius theorem prover Aquarius is a distributed contraction-based theorem prover, designed according to the Clause-Diffusion methodology.  ... 
doi:10.1006/jsco.1995.1014 fatcat:mfqvijzk6rhvlpetd3iyz6liii

Extending a Brainiac Prover to Lambda-Free Higher-Order Logic [chapter]

Petar Vukmirović, Jasmin Christian Blanchette, Simon Cruanes, Stephan Schulz
2019 Lecture Notes in Computer Science  
Instead of developing a new higher-order prover from the ground up, we propose to start with the state-of-the-art superposition-based prover E and gradually enrich it with higher-order features.  ...  Decades of work have gone into developing efficient proof calculi, data structures, algorithms, and heuristics for first-order automatic theorem proving.  ...  Indexing Data Structures Superposition provers like E work by saturation.  ... 
doi:10.1007/978-3-030-17462-0_11 fatcat:eg3yugmhdveqdgicjqxqtn2crm

A Resolution-Based Theorem Prover for $${\textsf {K}}_{n}^{}$$Kn: Architecture, Refinements, Strategies and Experiments

Cláudia Nalon, Ullrich Hustadt, Clare Dixon
2018 Journal of automated reasoning  
The prover implements a resolution-based calculus for both local and global reasoning. The user can choose different normal forms, refinements of the basic resolution calculus, and strategies.  ...  In this paper we describe the implementation of K S P, a resolution-based prover for the basic multimodal logic K n .  ...  The classes qbf and qbfL are more challenging.  ... 
doi:10.1007/s10817-018-09503-x fatcat:rhvht7pvnnfp3ggvvaq6d6whdm

Formalizing the metatheory of logical calculi and automatic provers in Isabelle/HOL (invited talk)

Jasmin Christian Blanchette
2019 Proceedings of the 8th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2019  
In this paper, I describe and reflect on three verification subprojects to which I contributed: a first-order resolution prover, an imperative SAT solver, and generalized term orders for λ-free higher-order  ...  IsaFoL (Isabelle Formalization of Logic) is an undertaking that aims at developing formal theories about logics, proof systems, and automatic provers, using Isabelle/HOL.  ...  Few automatic prover developers have first-hand experience with a proof assistant.  ... 
doi:10.1145/3293880.3294087 dblp:conf/cpp/Blanchette19 fatcat:n7delklh2nejvh4zspbcljamwy
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