What is automated theorem proving?

Definition

Automated theorem proving searches a formal space of definitions, lemmas and inference rules to construct a proof. Systems may use symbolic search, decision procedures, satisfiability solvers, heuristics or learned guidance to decide which steps to attempt.

AI can improve proof search by proposing useful lemmas and tactics. A generated proof should still be checked by a trusted proof system, separating the potentially complex search process from the smaller mechanism that verifies correctness.

ELI5

Automated theorem proving uses software to search for a formal sequence of logical steps that proves a statement. The system works from precise definitions and allowed reasoning rules rather than informal confidence.

For example, AI may suggest promising lemmas or proof steps for a difficult mathematical statement. A separate trusted proof checker can then verify every step, so a creative search process cannot make an invalid proof correct merely by sounding convincing.

Acronyms and aliases

ATP acronymautomated proof search variant

Frequently asked questions

What problems can automated theorem proving solve?

It can prove logical formulas, mathematical theorems and software properties that have been expressed in a supported formal language.

Does an automated theorem prover always find a proof?

No. A statement may be false, outside the supported logic or too difficult for the available search strategy and computing resources.

Videos explaining automated theorem proving

  1. Varun Pant beside the words Prove the Code