A Unifying Splitting Framework

Abstract

AVATAR is an elegant and effective way to split clauses in a saturation prover using a SAT solver. But is it refutationally complete? And how does it relate to other splitting architectures? To answer these questions, we present a unifying framework that extends a saturation calculus (e.g., superposition) with splitting and embeds the result in a prover guided by a SAT solver. The framework also allows us to study locking, a subsumption-like mechanism based on the current propositional model. Various architectures are instances of the framework, including AVATAR, labeled splitting, and SMT with quantifiers.

A Comprehensive Framework for Saturation Theorem Proving

“…Lemmas 10 and 11 can then be reproved for reduced static and reduced dynamic refutational completeness. Together with Theorem 19, we obtain this result: Theorem 21 The properties (i)-(iv) of Theorem 19 and the following four properties are equivalent:…”

“…Voronkov's AVATAR architecture [42] is more flexible and yields truly impressive empirical results, but he and his collaborators left the question of AVATAR's refutational completeness open. Ebner et al [21] recently provided an answer by introducing and instantiating a generic splitting framework based on our saturation framework.…”

“…When users of the framework instantiate these prover architectures with a concrete saturation calculus, they obtain the dynamic refutational completeness of the combination from the properties of the prover architecture and the static refutational completeness proof for the calculus. The framework is applicable to a wide range of calculi, including ordered resolution [6], unfailing completion [2], standard superposition [5], constraint superposition [29], theory superposition [44], and hierarchic superposition [8], It is already used in several published and ongoing works on combinatory superposition [15], λ-free superposition [12], λ-superposition [13,14], superposition with interpreted Booleans [33], AVATAR-style splitting [21], and superposition with SAT-inspired inprocessing [43].…”

Unifying Splitting

“…A shorter version of this article was presented at CADE-28 [ 14 ]. This article extends the conference paper with more explanations, examples, counterexamples, and proofs.…”