Superposition for Full Higher-order Logic

Alexander Bentkamp (1) , Jasmin Blanchette (2, 3, 1) , Sophie Tourret (4, 2, 5) , Petar Vukmirović (1)

1 VU - Vrije Universiteit Amsterdam [Amsterdam]
2 VERIDIS - Modeling and Verification of Distributed Algorithms and Systems
3 Computer Systems Section - Vrije Universiteit Amsterdam
4 MPII - Max-Planck-Institut für Informatik
5 MOSEL - Proof-oriented development of computer-based systems

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.

Domaines: Logique en informatique [cs.LO]

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⟩