Superposition for Lambda-Free Higher-Order Logic

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10900)


We introduce refutationally complete superposition calculi for intentional and extensional \(\lambda \)-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 TPTP benchmarks. They appear promising as a stepping stone towards complete, efficient automatic theorem provers for full higher-order logic.



We are grateful to the maintainers of StarExec for letting us use their service. We want to thank Christoph Benzmüller, Sander Dahmen, Johannes Hölzl, Anders Schlichtkrull, Stephan Schulz, Alexander Steen, Geoff Sutcliffe, Andrei Voronkov, Petar Vukmirović, Daniel Wand, Christoph Weidenbach, and the participants in the 2017 Dagstuhl Seminar on Deduction beyond First-Order Logic for stimulating discussions. We also want to thank Mark Summerfield, Sophie Tourret, and the anonymous reviewers for suggesting several textual improvements to this paper and to the technical report. Bentkamp and Blanchette’s research has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No. 713999, Matryoshka).


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Authors and Affiliations

  1. 1.Vrije Universiteit AmsterdamAmsterdamThe Netherlands
  2. 2.Max-Planck-Institut für Informatik, Saarland Informatics CampusSaarbrückenGermany
  3. 3.Université de Lorraine, CNRS, Inria, LORIANancyFrance
  4. 4.Aesthetic IntegrationAustinUSA

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