
Metamath is a proof assistant that keeps surprising outsiders by its combination of a very minimalist design with a large library of advanced results, ranking high on the Freek Wiedijk’s 100 list. In this work, we develop several translations of the Metamath logic and its large set-theoretical library into higher-order and first-order TPTP formats for automated theorem provers (ATPs). We show that state-of-the-art ATPs can prove 68% of the Metamath problems automatically when using the premises that were used in the human-written Metamath proofs. Finally, we add proof reconstruction and premise selection methods and combine the components into the first hammer system for Metamath.
Interactive theorem proving, Automated theorem proving, proof discovery, Theory of computation → Automated reasoning, Theory of computation → Higher order logic, Formal proof assistants, Metamath, Theory of computation → Logic and verification, 004, ddc: ddc:004
Interactive theorem proving, Automated theorem proving, proof discovery, Theory of computation → Automated reasoning, Theory of computation → Higher order logic, Formal proof assistants, Metamath, Theory of computation → Logic and verification, 004, ddc: ddc:004
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