Free theorem provers

thumb|300x300px|An interactive proof session in CoqIDE, showing the proof script on the left and the proof state on the right.

software for interactive and automated theorem proving

Metamath is a formal language and an associated computer program (a proof assistant) for archiving and verifying mathematical proofs. Several databases of proved theorems have been developed using Metamath covering standard results in logic, set theory, number theory, algebra, topology and analysis, among others.

higher-order logic (HOL) automated theorem prover