# Superposition for Lambda-Free Higher-Order Logic

arXiv: https://arxiv.org/abs/2005.02094 · HTML: https://mlsanity.com/paper/2005.02094/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2020.

## Built on by (most cited first, 2 of 2)

- [Superposition with Lambdas](https://mlsanity.com/paper/2102.00453/) (2021)
- [Superposition with Delayed Unification](https://mlsanity.com/paper/2403.04775/) (2024)

## Abstract (arXiv)

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.