Implementing Superposition in iProver (System Description)

Duarte, André Ricardo Barbosa; Korovin, Konstantin

doi:10.1007/978-3-030-51054-1_24

Cited by 22 publications

(14 citation statements)

References 17 publications

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“…We implemented the simplifications developed in this paper -encompassment demodulation, AC joinability and AC normalisation -in a theorem prover for first-order logic, iProver [8,7]. * iProver combines superposition with Inst-Gen and resolution calculi.…”

Section: Resultsmentioning

confidence: 99%

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AC Simplifications and Closure Redundancies in the Superposition Calculus

Debenath¹,

Korovin²

2021

Preprint

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Reasoning in the presence of associativity and commutativity (AC) is well known to be challenging due to prolific nature of these axioms. Specialised treatment of AC axioms is mainly supported by provers for unit equality which are based on Knuth-Bendix completion. The main ingredient for dealing with AC in these provers are ground joinability criteria adapted for AC. In this paper we extend AC joinability from the context of unit equalities and Knuth-Bendix completion to the superposition calculus and full first-order logic. Our approach is based on an extension of the Bachmair-Ganzinger model construction and a new redundancy criterion which covers ground joinability. A by-product of our approach is a new criterion for applicability of demodulation which we call encompassment demodulation. This criterion is useful in any superposition theorem prover, independently of AC theories, and we demonstrate that it enables demodulation in many more cases, compared to the standard criterion.

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Section: Resultsmentioning

confidence: 99%

“…, where θ = mgu(s, s ), sθ tθ and tθ t θ, (7) and the selection function (underlined) selects at least one negative, or else all maximal (wrt. ' t ') literals in the clause.…”

Section: Model Constructionmentioning

confidence: 99%

AC Simplifications and Closure Redundancies in the Superposition Calculus

Debenath¹,

Korovin²

2021

Preprint

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“…Example 74 In its superposition module [20], iProver implements a rule that eliminates the chosen passive clause, or given clause, if it is redundant w.r.t. a subset of its child clauses together with the active set.…”

Section: Proofmentioning

confidence: 99%

A Comprehensive Framework for Saturation Theorem Proving

et al. 2022

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A crucial operation of saturation theorem provers is deletion of subsumed formulas. Designers of proof calculi, however, usually discuss this only informally, and the rare formal expositions tend to be clumsy. This is because the equivalence of dynamic and static refutational completeness holds only for derivations where all deleted formulas are redundant, but the standard notion of redundancy is too weak: A clause C does not make an instance $$C\sigma $$ C σ redundant. We present a framework for formal refutational completeness proofs of abstract provers that implement saturation calculi, such as ordered resolution and superposition. The framework modularly extends redundancy criteria derived via a familiar ground-to-nonground lifting. It allows us to extend redundancy criteria so that they cover subsumption, and also to model entire prover architectures so that the static refutational completeness of a calculus immediately implies the dynamic refutational completeness of a prover implementing the calculus within, for instance, an Otter or DISCOUNT loop. Our framework is mechanized in Isabelle/HOL.

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“…In its simplest form, the weight of the clause is the sum of the weights of its symbols, and clauses with a small weight are preferred for performing inferences during proof search. A clause weighting mechanism is an inherent ingredient of all of today's implementations of saturation-based theorem provers [5,18,36,38,41,45]. The hint technique introduced by Veroff adds to the clause weighting mechanism: clauses subsumed by the hint clause or clauses subsuming the hint clause receive special treatment with respect to their weight.…”

Section: Finding Relevant Instancesmentioning

confidence: 99%

“…The set of support strategy has become an integral part of many approaches to automated reasoning. It is implemented in all first-order logic resolution-based theorem provers [5,18,36,38,41,45]. In case of additional ordering restrictions, it is still complete if the set N is closed under non-redundant inferences.…”

Section: Finding Relevant Instancesmentioning

confidence: 99%