Selecting the Selection

TL;DR

This paper introduces lookahead and incomplete literal selection strategies in saturation-based theorem proving, demonstrating their effectiveness in solving complex problems more efficiently.

Contribution

It proposes the novel concept of lookahead selection and advocates for incomplete selection functions to improve proof search in theorem provers.

Findings

Lookahead selection improves proof search efficiency.

Incomplete selection functions help solve previously unsolvable problems.

Experimental results show significant performance gains in Vampire.

Abstract

Modern saturation-based Automated Theorem Provers typically implement the superposition calculus for reasoning about first-order logic with or without equality. Practical implementations of this calculus use a variety of literal selections and term orderings to tame the growth of the search space and help steer proof search. This paper introduces the notion of lookahead selection that estimates (looks ahead) the effect on the search space of selecting a literal. There is also a case made for the use of incomplete selection functions that attempt to restrict the search space instead of satisfying some completeness criteria. Experimental evaluation in the \Vampire\ theorem prover shows that both lookahead selection and incomplete selection significantly contribute to solving hard problems unsolvable by other methods.