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arXiv · 2510.18429

Optimistic Higher-Order Superposition

Alexander Bentkamp·Jasmin Blanchette·Matthias Hetzenberger·Uwe Waldmann
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Abstract

The $\lambda$-superposition calculus is a successful approach to proving higher-order formulas. However, some parts of the calculus are extremely explosive, notably due to the higher-order unifier enumeration and the functional extensionality axiom. In the present work, we introduce an "optimistic" version of $\lambda$-superposition that addresses these two issues. Specifically, our new calculus delays explosive unification problems using constraints stored along with the clauses, and it applies functional extensionality in a more targeted way. The calculus is sound and refutationally complete with respect to a Henkin semantics. We have yet to implement it in a prover, but examples suggest that it will outperform, or at least usefully complement, the original $\lambda$-superposition calculus.

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Alexander Bentkamp, Jasmin Blanchette, Matthias Hetzenberger, Uwe Waldmann. 2025-10-21. Optimistic Higher-Order Superposition. https://arxiv.org/abs/2510.18429

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