In this paper, we explore the set of testable properties within the Safety-Progress classification where testability means to establish by testing that a relation, between the tested system and the property under scrutiny, holds. We characterize testable properties wrt. several relations of interest. For each relation, we give a sufficient condition for a property to be testable. Then, we study and delineate, for each Safety-Progress class, the subset of testable properties and their corresponding test oracle producing verdicts for the possible test executions. Furthermore, we address automatic test generation for the proposed framework. Finally, we present a tool implementing the results proposed by this paper.