Abstract

AbstractWe recently designed two calculi as stepping stones towards superposition for full higher-order logic: Boolean-free$$\lambda $$λ-superposition and superposition for first-order logic with interpreted Booleans. Stepping on these stones, we finally reach a sound and refutationally complete calculus for higher-order logic with polymorphism, extensionality, Hilbert choice, and Henkin semantics. In addition to the complexity of combining the calculus’s two predecessors, new challenges arise from the interplay between$$\lambda $$λ-terms and Booleans. Our implementation in Zipperposition outperforms all other higher-order theorem provers and is on a par with an earlier, pragmatic prototype of Booleans in Zipperposition.

Highlights

  • Superposition is a leading calculus for first-order logic with equality

  • We evaluate the calculus implementation in Zipperposition and compare it with other higher-order provers

  • We evaluate selected parameters of Zipperposition by varying only the studied parameter in a fixed well-performing configuration

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Summary

Introduction

Superposition is a leading calculus for first-order logic with equality. We have been wondering for some years whether it would be possible to gracefully generalize it to extensional higher-order logic and use it as the basis of a strong higher-order automatic theorem prover. Towards this goal, we have, together with colleagues, designed superposition-like calculi for three intermediate logics between first-order and higherorder logic. We are ready to assemble a superposition calculus for full higher-order logic. Boolean-free λ-free superposition Bentkamp et al [7] (λfSup). Superposition with Booleans Nummelin et al [23] (oSup). Boolean-free λ-superposition Bentkamp et al [6] (λSup).

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