Almost fifty years ago, D.E. Bell and L. LaPadula published the first formal model of a secure system, known today as the Bell-LaPadula (BLP) model. BLP is described as a state machine by means of first-order logic and set theory. The authors also formalize two state invariants known as security condition and *-property. Bell and LaPadula prove that all the state transitions preserve these invariants. In this paper we present a fully automated proof of the security condition and the *-property for all the model operations. The model and the proofs are coded in the {log} tool. As far as we know this is the first time such proofs are automated. Besides, we show that the {log} model is also an executable prototype. Therefore we are providing an automatically verified executable prototype of BLP.