The Coq proof assistant
Science, Math, Logic and Foundations, Computational Logic - The Coq proof assistant. Allows the user to handle calculus assertions, to check mechanically proofs of these assertions, helps to find formal proofs, extracts a certified program from the constructive proof of its formal specification.
https://coq.inria.fr/
The HOL Theorem Proving System
Science, Math, Logic and Foundations, Computational Logic - The HOL Theorem Proving System. The system documented originated at the Laboratory for Applied Logic of Brigham Young University and features higher-order, classical, natural deduction with tactics.
https://hol.sourceforge.net/
Isabelle
Science, Math, Logic and Foundations, Computational Logic - Isabelle. Homepage of the theorem prover environment developed by Larry Paulson at Cambridge University and Tobias Kipkow at TU Munich.
http://isabelle.informatik.tu-muenchen.de/