We propose a general formal modeling and verification of the air traffic control system (ATC). This study is based on the International Civil Aviation Organization (ICAO), Federal Aviation Administration (FAA), and National Aeronautics and Space Administration (NASA) standards and recommendations. It provides a sophisticated assistance system that helps in visualizing aircrafts and presents automatic bugs detection. In such a critical safety system, the use of robust formal methods that assure bugs absence is highly required. Therefore, this work suggests a formalism of discrete transition systems based on abstraction and refinement along proofs. These ensure the consistency of the system by means of invariants preservation and deadlock freedom. Hence, all invariants hold permanently providing a handy solution for bugs absence verification. It follows that the said deadlock freedom ensures a continuous running of a given system. This specification and modeling technique enable the system to be corrected by construction.