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AVATAR: The Architecture for First-Order Theorem Provers [chapter]

Andrei Voronkov
2014 Lecture Notes in Computer Science  
This paper describes a new architecture for first-order resolution and superposition theorem provers called AVATAR (Advanced Vampire Architecture for Theories and Resolution).  ...  This paper describes a new architecture for superposition theorem provers, where a superposition theorem prover is tightly integrated with a SAT or an SMT solver.  ...  We thank Krystof Hoder, who implemented the first version of AVATAR, Giles Reger, Laura Kovács and Martin Suda for discussions and reading preliminary versions of this paper.  ... 
doi:10.1007/978-3-319-08867-9_46 fatcat:jpi5e5ag4nbyxljltjtgxf55na

Playing with AVATAR [chapter]

Giles Reger, Martin Suda, Andrei Voronkov
2015 Lecture Notes in Computer Science  
Modern first-order resolution and superposition theorem provers use saturation algorithms to search for a refutation in clauses derivable from the input clauses.  ...  This paper considers the new AVATAR (Advanced Vampire Architecture for Theories And Resolution) approach to splitting which places a SAT (or SMT) solver at the centre of the theorem prover and uses it  ...  Introduction AVATAR [9] is a new architecture for first-order resolution and superposition theorem provers that places a SAT (or SMT) solver at the centre of the theorem prover to direct exploration  ... 
doi:10.1007/978-3-319-21401-6_28 fatcat:qelxxzlrvbhjlmsujj6vxbewwu

Is It Reasonable to Employ Agents in Automated Theorem Proving?

Max Wisniewski, Christoph Benzmüller
2016 Proceedings of the 8th International Conference on Agents and Artificial Intelligence  
This situation is motivating our ongoing work in the higher-order theorem prover Leo-III .  ...  The prover features a multiagent blackboard architecture for reasoning agents to cooperate and to parallelize proof construction on the term, clause and search level.  ...  ACKNOWLEDGMENTS We would like to thank all members of the Leo-III project.  ... 
doi:10.5220/0005824702810286 dblp:conf/icaart/WisniewskiB16 fatcat:ppu6zkmyvbblvg6tqbzl67mpe4

AVATAR Modulo Theories

Giles Reger, Nikolaj Bjorner, Martin Suda, Andrei Voronkov
unpublished
A recent development in first-order theorem proving has been the AVATAR architecture which uses a SAT solver to guide proof search based on a propositional abstraction of the first-order clause space.  ...  The new architecture has been implemented using the Vampire theorem prover and Z3 SMT solver.  ...  Section 7 concludes. 2 Overview of Vampire VAMPIRE [19] is an automated first-order theorem prover. For the last 15 years it has led the first-order theorem division of the CASC competition [32] .  ... 
doi:10.29007/k6tp fatcat:uqygausnrfam7b23cgikotmhjq

Superposition with Structural Induction [chapter]

Simon Cruanes
2017 Lecture Notes in Computer Science  
Several inductive goals can be attempted within a single saturation loop, by leveraging AVATAR [1] .  ...  Lemmas obtained by generalization or theory exploration can be introduced during search, used, and proved, all in the same search space.  ...  Acknowledgments The author would like to thank Jasmin Blanchette, Gilles Dowek, Guillaume Burel, Pascal Fontaine, and reviewers of previous versions of this paper (one of them, in particular, for pointing  ... 
doi:10.1007/978-3-319-66167-4_10 fatcat:jzgkbftdsvdsthbtkxg4ipmeqm

Local proofs and AVATAR

Giles Reger, Martin Suda
unpublished
With first-order interpolation as the application in mind, we study the problem of gen- erating local proofs in theorem provers employing the AVATAR architecture.  ...  The theory is complemented by experimental results based on our implementation of the techniques in theorem prover Vampire.  ...  One of the most influential improvements of first-order theorem provers of recent years is the AVATAR architecture for clause splitting [17] .  ... 
doi:10.29007/qgdk fatcat:xvk5rpc4xffkheq35i345y6rge

Layered Clause Selection for Saturation-based Theorem Proving

Bernhard Gleiss, Martin Suda
2020 Zenodo  
for clause selection (tracking relatedness to the goal, the number of split dependencies in the AVATAR architecture, and closeness to the Horn fragment, respectively).  ...  Clause selection is one of the main heuristic decision points in navigating proof search of saturation-based theorem provers.  ...  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

EPiC Series in Computing AVATAR Modulo Theories

Nikolaj Bjøner, Giles Reger, Martin Suda, Andrei Voronkov
2016 Pages 39-52 GCAI 2016. 2nd Global Conference on Artificial Intelligence   unpublished
A recent development in first-order theorem proving has been the AVATAR architecture which uses a SAT solver to guide proof search based on a propositional abstraction of the first-order clause space.  ...  The new architecture has been implemented using the Vampire theorem prover and Z3 SMT solver.  ...  Section 7 concludes. 2 Overview of Vampire VAMPIRE [19] is an automated first-order theorem prover. For the last 15 years it has led the first-order theorem division of the CASC competition [32] .  ... 
fatcat:jm22pbggzjaglmnxbonhnvumoi

Unification with Abstraction and Theory Instantiation in Saturation-Based Reasoning [chapter]

Giles Reger, Martin Suda, Andrei Voronkov
2018 Lecture Notes in Computer Science  
These rules were implemented within the Vampire theorem prover and experimental results show that they are useful for solving a considerable number of previously unsolved problems.  ...  This abstraction is performed lazily, as needed, to allow the superposition theorem prover to make as much progress as possible without the search space growing too quickly.  ...  Our previous work on AVATAR Modulo Theories [21] uses the AVATAR architecture [23, 34] for clause splitting to integrate an SMT solver with a superposition prover.  ... 
doi:10.1007/978-3-319-89960-2_1 fatcat:qmvu5nhrdzdevgqlyq7eckcplu

Selecting the Selection [article]

Giles Reger, Martin Suda, Andrei Voronkov, Krystof Hoder
2016 arXiv   pre-print
Modern saturation-based Automated Theorem Provers typically implement the superposition calculus for reasoning about first-order logic with or without equality.  ...  Experimental evaluation in the \Vampire\ theorem prover shows that both lookahead selection and incomplete selection significantly contribute to solving hard problems unsolvable by other methods.  ...  The setting of this work is saturation-based first-order theorem provers based on the superposition calculus.  ... 
arXiv:1604.08055v1 fatcat:faa3oyfbzndkdcf4sjz5ry2xci

Selecting the Selection [chapter]

Kryštof Hoder, Giles Reger, Martin Suda, Andrei Voronkov
2016 Lecture Notes in Computer Science  
Modern saturation-based Automated Theorem Provers typically implement the superposition calculus for reasoning about first-order logic with or without equality.  ...  Experimental evaluation in the VAMPIRE theorem prover shows that both lookahead selection and incomplete selection significantly contribute to solving hard problems unsolvable by other methods.  ...  The setting of this work is saturation-based first-order theorem provers based on the superposition calculus.  ... 
doi:10.1007/978-3-319-40229-1_22 fatcat:w2llu3k2qjffrduixn2n6i3lde

A Comprehensive Framework for Saturation Theorem Proving [chapter]

Uwe Waldmann, Sophie Tourret, Simon Robillard, Jasmin Blanchette
2020 Lecture Notes in Computer Science  
We present a framework for formal refutational completeness proofs of abstract provers that implement saturation calculi, such as ordered resolution or superposition.  ...  implies the dynamic refutational completeness of a prover implementing the calculus, for instance within an Otter or DISCOUNT loop.  ...  We thank Alexander Bentkamp for discussions about prover architectures for higher-order logic and for feedback from instantiating the framework, Mathias  ... 
doi:10.1007/978-3-030-51074-9_18 fatcat:2fb33hm7djhu5pofxbdca3cggu

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  ...  At the heart of the project is the conviction that proof assistants have become mature enough to actually help researchers in automated reasoning when they develop new calculi and tools.  ...  Paulson also succeeded at verifying the second incompleteness theorem. The completeness theorem for first-order logic has been mechanized many times in proof assistants.  ... 
doi:10.1145/3293880.3294087 dblp:conf/cpp/Blanchette19 fatcat:n7delklh2nejvh4zspbcljamwy

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
The main aim to develop mechanical reasoning systems (also known as theorem provers) was to enable mathematicians to prove theorems by computer programs.  ...  Theorem provers are investigated based on various parameters, which includes: implementation architecture, logic and calculus used, library support, level of automation, programming paradigm, programming  ...  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

Boldly Going Where No Prover Has Gone Before

Giles Reger
2019 Electronic Proceedings in Theoretical Computer Science  
Many successful theorem provers employ a portfolio of different methods for solving problems.  ...  This state of affairs is particularly prominent in first-order logic, which is undecidable.  ...  the approach of searching an infinite clause space (as in proving for first-order logic).  ... 
doi:10.4204/eptcs.311.6 fatcat:e2mofcpky5birjcdbkpulkeiei
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