Implementation of Lambda-Free Higher-Order Superposition

In the last decades, first-order logic (FOL) has become a standard language for describing a large number of mathematical theories. Numerous proof systems for FOL which determine what formulas are universally true emerged over time. On the other hand, higher-order logic (HOL) enables one to describe more theories and to describe existing theories more succinctly. Due to more complicated higher-order proof systems, higher-order automatic theorem provers (ATPs) aremuch lessmature than their first-order counterparts. Furthermore, manyHOLATPs are not effectively applicable to FOL problems. In this thesis, we extend E, a state-of-the-art first-order ATP, to a fragment of HOL that is devoid of lambda abstractions (LFHOL). We devise generalizations of E’s indexing data structures to LFHOL, as well as algorithms like matching and unification. Furthermore, we generalized internal structures used by E as well as inferences and simplifications to support HOL features in an efficient manner. Our generalizations exhibit exactly the same behavior and time complexity as original E on FOL problems.