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Superposition for Lambda-Free Higher-Order Logic

MPS-Authors
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Blanchette,  Jasmin
Automation of Logic, MPI for Informatics, Max Planck Society;

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Waldmann,  Uwe
Automation of Logic, MPI for Informatics, Max Planck Society;

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arXiv:2005.02094.pdf
(Preprint), 875KB

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Citation

Bentkamp, A., Blanchette, J., Cruanes, S., & Waldmann, U. (2020). Superposition for Lambda-Free Higher-Order Logic. Retrieved from https://arxiv.org/abs/2005.02094.


Cite as: https://hdl.handle.net/21.11116/0000-0008-0A5F-4
Abstract
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.