THF 0 – The Core TPTP Language for Classical Higher-Order Logic

There is a well established infrastructure that supports research, development, and deployment of first-order Automated Theorem Proving (ATP) systems, stemming from the Thousands of Problems for Theorem Provers (TPTP) problem library. One of the keys to the success of the TPTP and related infrastructure is the consistent use of the TPTP language. This paper introduces the core TPTP language for classical higher-order logic (Church’s simple type theory) – THF0. THF0 is a conservative extension of the existing first-order TPTP language. The use of THF0 in building higher-order analogs of some of the existing first-order TPTP infrastructure is explained.

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