TH1: The TPTP Typed Higher-Order Form with Rank-1 Polymorphism

Abstract The TPTP world is a well established infrastructure that supports research, development, and deployment of Automated Theorem Proving (ATP) systems for classical logics. The TPTP language is one of the keys to the success of the TPTP world. Originally the TPTP world supported only first-order clause normal form (CNF). Over the years support for full first-order form (FOF), monomorphic typed firstorder form (TF0), rank-1 polymorphic typed first-order form (TF1), and monomorphic typed higher-order form (TH0) have been added. The TF0, TF1, and TH0 languages also include constructs for arithmetic. This paper introduces the TH1 form, an extension of TH0 with TF1-style rank-1 polymorphism. TH1 is designed to be easy to process by existing reasoning tools that support ML-style polymorphism. The hope is that TH1 will be implemented in many popular ATP systems for typed higher-order logic