Formalizing Bachmair and Ganzinger's Ordered Resolution Prover

Abstract

Abstract. We present a formalization of the first half of Bachmair and Ganzinger's chapter on resolution theorem proving in Isabelle/HOL, culminating with a refutationally complete first-order prover based on ordered resolution with literal selection. We develop general infrastructure and methodology that can form the basis of completeness proofs for related calculi, including superposition. Our work clarifies several of the fine points in the chapter's text, emphasizing the value of formal proofs in the field of automated reasoning.

Formalizing Bachmair and Ganzinger’s Ordered Resolution Prover

“…Due to lack of space, we assume the reader has some familiarity with the chapter's content. An extended version of this paper is available as a technical report [21].…”

Reliable Reconstruction of Fine-grained Proofs in a Proof Assistant

“…To measure the performance of the v-smt tactic, we ran Mirabelle on the full HOL-Library, the theory Prime Distribution Elementary (PDE) [22], an executable resolution prover (RP) [37], and the Simplex algorithm [30]. We extended Sledgehammer's proof preplay to try all veriT strategies and added instrumentation for Table 2.…”

A Comprehensive Framework for Saturation Theorem Proving

“…On the other hand, for sets such as F ⊥ and FInf that are subsets of other sets, it was natural to use simply typed sets. Derivations, which are used to describe the dynamic behavior of a calculus, are represented by the same lazy list codatatype [13] and auxiliary definitions that were used in the mechanization of the ordered resolution prover RP (Example 29) by Schlichtkrull et al [23,24]. The framework's design and its mechanization were carried out largely in parallel.…”