SAT-Inspired Higher-Order Eliminations

TL;DR

This paper extends propositional preprocessing techniques to higher-order logic, introducing new elimination methods and demonstrating their effectiveness in theorem proving tasks.

Contribution

It generalizes existing techniques to higher-order logic and introduces quasipure literal elimination, implemented in Zipperposition, improving proof search.

Findings

Techniques sometimes improve proof success on Isabelle formalizations.

New quasipure literal elimination subsumes pure literal elimination.

Implementation in Zipperposition demonstrates practical benefits.

Abstract

We generalize several propositional preprocessing techniques to higher-order logic, building on existing first-order generalizations. These techniques eliminate literals, clauses, or predicate symbols from the problem, with the aim of making it more amenable to automatic proof search. We also introduce a new technique, which we call quasipure literal elimination, that strictly subsumes pure literal elimination. The new techniques are implemented in the Zipperposition theorem prover. Our evaluation shows that they sometimes help prove problems originating from Isabelle formalizations and the TPTP library.