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Conference Papers Year : 2021

Superposition for Full Higher-order Logic

Abstract

We recently designed two calculi as stepping stones towards superposition for full higher-order logic: Boolean-free $\lambda$-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 $\lambda$-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.
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Dates and versions

hal-03364032 , version 1 (04-10-2021)

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Alexander Bentkamp, Jasmin Blanchette, Sophie Tourret, Petar Vukmirović. Superposition for Full Higher-order Logic. CADE 2021 - 28th International Conference on Automated Deduction, Jul 2021, Pittsburgh, PA / online, United States. pp.396-412, ⟨10.1007/978-3-030-79876-5_23⟩. ⟨hal-03364032⟩
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