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We introduce refutationally complete superposition calculi for intentional and extensional clausal $\lambda$-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 $\lambda$-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.
Source : ScholeXplorer
IsSupplementedBy DOI 10.5281/zenodo.3975511 Source : ScholeXplorer IsSupplementedBy DOI 10.5281/zenodo.3975512
Bentkamp, Alexander ; Blanchette, Jasmin ; Cruanes, Simon ; Waldmann, Uwe ; |