First-Order Theorem Proving and Vampire

Kovács, Laura; Voronkov, Andrei

doi:10.1007/978-3-642-39799-8_1

Cited by 347 publications

(321 citation statements)

References 32 publications

(33 reference statements)

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“…The winner, VampireZ3, is a newcomer to CASC. It benefits from being "built on the shoulders of giants", the well known Vampire [6] and Z3 [5] systems. VampireZ3 leveraged the new AVATAR architecture in Vampire [16], using Z3 to guide splitting decisions so that the first-order solver deals with sets of clauses whose ground part is consistent with the theories of equality and arithmetic.…”

Section: The Thf Divisionmentioning

confidence: 99%

The CADE-26 automated theorem proving system competition – CASC-26

Sutcliffe

2017

AIC

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Section: The Thf Divisionmentioning

confidence: 99%

The CADE-26 automated theorem proving system competition – CASC-26

Sutcliffe

2017

AIC

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“…Our method is implemented in the Vampire theorem prover [11] and extends Vampire with new features for theory reasoning and interpolation. Our implementation adds a general interpolation procedure to Vampire, which can be used for computing Craig interpolants, sequence interpolants and tree interpolants.…”

Section: Introductionmentioning

confidence: 99%

Tree Interpolation in Vampire

Blanc

Gupta

Kovács³

et al. 2013

Logic for Programming, Artificial Intelligence, and Reasoning

Self Cite

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Abstract. We describe new extensions of the Vampire theorem prover for computing tree interpolants. These extensions generalize Craig interpolation in Vampire, and can also be used to derive sequence interpolants. We evaluated our implementation on a large number of examples over the theory of linear integer arithmetic and integer-indexed arrays, with and without quantifiers. When compared to other methods, our experiments show that some examples could only be solved by our implementation.

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“…Most current first-order ATPs, such as E [45], iProver [34], or Vampire [36], output proofs in the TSTP (Thousands of Solutions from Theorem Provers) format [51] from the TPTP initiative [50]. 1 This format has a standard syntax and fixed conventions [53].…”

Section: Current Situationmentioning

confidence: 99%

Checkable Proofs for First-Order Theorem Proving

Reger¹,

Suda²

EPiC Series in Computing

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Inspired by the success of the DRAT proof format for certification of boolean satisfiability (SAT), we argue that a similar goal of having unified automatically checkable proofs should be sought by the developers of automatic first-order theorem provers (ATPs). This would not only help to further increase assurance about the correctness of prover results, but would also be indispensable for tools which rely on ATPs, such as "hammers" employed within interactive theorem provers. The current situation, represented by the TSTP format, is unsatisfactory, because this format does not have a standardised semantics and thus cannot be checked automatically. Providing such semantics, however, is a challenging endeavour. One would ideally like to have a proof format which covers only-satisfiability-preserving operations such as Skolemisation and is versatile enough to encompass various proving methods (i.e. not just superposition) or is perhaps even open-ended towards yet to be conceived methods or at least easily extendable in principle. Going beyond pure first-order logic to theory reasoning in the style of SMT, or beyond proofs to certification of satisfiability are further interesting challenges. Although several projects have already provided partial solutions in this direction, we would like to use the opportunity of ARCADE to further promote the idea and gather critical mass needed for its satisfactory realisation. The challengeWe would like to propose to the first-order ATP community the challenge of designing, implementing and bringing into practice a unified mechanically checkable proof format along with an efficient proof checker. The format should support the whole reasoning pipeline including formula preprocessing, be sufficiently general to cover all the solving techniques currently employed by ATPs, and be open to future extensions for proof recording of techniques yet to be developed. In this paper, we summarise the current situation regarding proof output of ATPs, explain why we think striving for a mechanically checkable proof format is a worthy effort, list the main properties we believe an ideal format should satisfy, attempt to give an overview of work already done in the first-order ATP community and related areas, and, finally, suggest possible avenues and the next steps to be taken for meeting the challenge.At this point we add the disclaimer that other people have already examined this challenge in various ways. We attempt to present this previous work and do not claim that what we are suggesting is novel, but instead we are calling for further work in this area. Our main aim at ARCADE is to solicit opinions from experts on why the proposed idea has not yet made its way to practice and on how exactly should the community proceed to achieve the envisioned goal.

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First-Order Theorem Proving and Vampire

Cited by 347 publications

References 32 publications

The CADE-26 automated theorem proving system competition – CASC-26

The CADE-26 automated theorem proving system competition – CASC-26

Tree Interpolation in Vampire

Checkable Proofs for First-Order Theorem Proving

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