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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

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

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

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

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

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

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.  ...  This is probably due to different versions of the systems tested, for instance, the TPTP uses Vampire version 7, while the results reported in [14] are based on version 5.  ... 
doi:10.1007/978-3-540-32275-7_27 fatcat:vllvzeicvbdixmzafcjhtee7ca

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.  ...  We explain how to extend the prover's data structures, algorithms, and heuristics to λ-free higher-order logic, a formalism that supports partial application and applied variables.  ...  Brown's Satallax [12] is based on a higher-order tableau calculus, guided by a SAT solver; recent versions also cooperate with first-order provers.  ... 
doi:10.1007/978-3-030-17462-0_11 fatcat:eg3yugmhdveqdgicjqxqtn2crm

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.  ...  This paper is a revised and extended version of "Distributed Deduction by Clause-Diffusion: the Aquarius Prover", Miola, A. (ed.), Proc. of the Third Int.  ... 
doi:10.1006/jsco.1995.1014 fatcat:mfqvijzk6rhvlpetd3iyz6liii

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

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 results update and extend those in [35] by using more recent versions of the provers involved, presenting additional experimental results and considering the performance of portfolios of provers.  ... 
doi:10.1007/s10817-018-09503-x fatcat:rhvht7pvnnfp3ggvvaq6d6whdm

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

Invariant Generation in Vampire [chapter]

Kryštof Hoder, Laura Kovács, Andrei Voronkov
2011 Lecture Notes in Computer Science  
This paper describes a loop invariant generator implemented in the theorem prover Vampire. It is based on the symbol elimination method proposed by two authors of this paper.  ...  The generator accepts a program written in a subset of C, finds loops in it, analyses the loops, generates and outputs invariants.  ...  We used a computer with a 2GHz processor and 2GB RAM and ran experiments using Vampire version 0.6.  ... 
doi:10.1007/978-3-642-19835-9_7 fatcat:hvnbjil23jen5dtyozasycpt3e

Extensional Crisis and Proving Identity [chapter]

Ashutosh Gupta, Laura Kovács, Bernhard Kragl, Andrei Voronkov
2014 Lecture Notes in Computer Science  
We illustrate this by running the VAMPIRE theorem prover with extensionality resolution on a number of set theory and array problems.  ...  In this paper we show how addition of a new inference rule, called extensionality resolution, allows first-order theorem provers to easily solve problems no modern first-order theorem prover can solve.  ...  S11410-N23), and the WWTF PROSEED grant ICT C-050.  ... 
doi:10.1007/978-3-319-11936-6_14 fatcat:fj7nwcr54rhhfjgnbqtypfb3zy

Faster, Higher, Stronger

Bruce K. Rubin
2013 American Journal of Respiratory and Critical Care Medicine  
E 2.3 is a theorem prover for many-sorted first-order logic with equality. We describe the basic logical and software architecture of the system, as well as core features of the implementation.  ...  The paper also gives an overview of the performance of the system, and describes ongoing and future work.  ...  The prover is available as free and open source software, and has been used and extended by a large number of parties.  ... 
doi:10.1164/rccm.201307-1371ed pmid:24032379 fatcat:wkohfj6vdncqjaesh5utfffx7i
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