Tags:First Order Logic, Higher Order Logic, Large Theory Proving, Machine Learning, Many Sorted Logic and Theorem Proving
Abstract:
We describe a large set of related theorem proving problems obtained by translating theorems from the HOL4 standard library into multiple ATP formalisms. The translations give representations in higher-order logic (with and without type variables) and first-order logic (possibly with multiple types and possibly with type variables). The problem sets allow us to run theorem provers designed for different logics on related problem sets and compare their performance. 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 ATP formalisms in complementary ways and jointly learn from the accumulated knowledge.