TFF1: The TPTP Typed First-Order Form with Rank-1 Polymorphism

The TPTP World is a well-established infrastructure for automatic theorem provers. It defines several concrete syntaxes, notably an untyped firstorder form (FOF) and a typed first-order form (TFF0), that have become de facto standards in the automated reasoning community. This paper introduces the TFF1 format, an extension of TFF0 with rank-1 polymorphism. It presents its syntax, typing rules, and semantics, as well as a sound and complete translation to TFF0. The format is designed to be easy to process by existing reasoning tools that support ML-style polymorphism. It opens the door to useful middleware, such as monomorphizers and other translation tools that encode polymorphism in FOF or TFF0. Ultimately, the hope is that TFF1 will be implemented in popular automatic theorem provers.