GRUNGE: A Grand Unified ATP Challenge

This paper describes a large set of related theorem proving problems obtained by translating theorems from the HOL4 standard library into multiple logical formalisms. The formalisms are in higher-order logic (with and without type variables) and first-order logic (possibly with types, and possibly with type variables). The resultant problem sets allow us to run automated theorem provers that support different logical formalisms on corresponding problems, and compare their performances. This also results in a new “grand unified” large theory benchmark that emulates the ITP/ATP hammer setting, where systems and metasystems can use multiple formalisms in complementary ways, and jointly learn from the accumulated knowledge.