The HOL Theorem Proving System (Popularity: )
http://hol.sourceforge.net/ The system documented originated at the Laboratory for Applied Logic of Brigham Young University and features higher-order, classical, natural deduction ...
The Coq proof assistant (Popularity: )
http://coq.inria.fr/ Allows the user to handle calculus assertions, to check mechanically proofs of these assertions, helps to find formal proofs, extracts ...