Superposition for Lambda-Free Higher-Order Logic - Bentkamp, Alexander; Blanchette, Jasmin; Cruanes, Simon; Waldmann, Uwe (Logical methods in computer science, 2021)
We introduce refutationally complete superposition calculi for intentional and extensional clausal $λ$-free higher-order logic, two formalisms that allow partial application and applied variables. The calculi are parameterized by a term order that need not be fully monotonic, making it possible to employ the $λ$-free higher-order lexicographic path and Knuth-Bendix orders. We implemented the calculi in the Zipperposition prover and evaluated them on Isabelle/HOL and TPTP benchmarks. They appear promising as a stepping stone towards complete, highly efficient automatic theorem provers for full higher-order logic. Comment: arXiv admin note: text overlap with arXiv:2102.00453