. Dowek, Encodings of types, such as those by Bobot and Paskevich [12] and Blanchette et al. [8], are also crucial to obtain a sound encoding of higher-order logic, These ideas are implemented in proof assistant tools such as HOLyHammer and Sledgehammer, vol.19

, Robinson's [31] and Huet's [23] pioneering work stands out. Andrews [1] and Benzmüller and Miller [6] provide excellent surveys. The competitive higher-order automatic theorem provers include LEO-II, Another line of research has focused on the development of automated proof procedures for higher-order logic

, Our middle-term goal is to design higher-order superposition calculi, implement them in state-of-the-art provers such as E [33], SPASS [44], and Vampire [25], and integrate these in proof assistants to provide a high level of automation. With its stratified architecture, Otter-? [4] is perhaps the closest to what we are aiming at, but it is limited to second-order logic and offers no completeness guarantees. In preliminary work supervised by Blanchette and Schulz, Zipperposition is a convenient vehicle for experimenting and prototyping because it is easier to understand and modify than highly-optimized C or C++ provers

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