Partial Redundancy in Saturation

TL;DR

This paper introduces a new redundancy notion based on partial clauses that enhances saturation-based proof search efficiency, demonstrated by solving previously unsolvable problems in theorem proving.

Contribution

It proposes a novel redundancy concept and a superposition calculus on partial clauses, improving proof search and solving capabilities in theorem proving.

Findings

Solved 24 previously unsolvable TPTP problems

Implemented the approach in Vampire prover

Enhanced redundancy elimination effectiveness

Abstract

Redundancy elimination is one of the crucial ingredients of efficient saturation-based proof search. We improve redundancy elimination by introducing a new notion of redundancy, based on partial clauses and redundancy formulas, which is more powerful than the standard notion: there are both clauses and inferences that are redundant when we use our notions and not redundant when we use standard notions. In a way, our notion blurs the distinction between redundancy at the level of inferences and redundancy at the level of clauses. We present a superposition calculus PaRC on partial clauses. Our calculus is refutationally complete and is strong enough to capture some standard restrictions of the superposition calculus. We discuss the implementation of the calculus in the theorem prover Vampire. Our experiments show the power of the new approach: we were able to solve 24 TPTP problems not previously solved by any prover, including previous versions of Vampire.