MDE is a software development process where models constitute pivotal elements of the software to be built. If models are well-specified, transformations can be employed for various purposes, e.g., to produce final code. However, transformations are only meaningful when they are 'correct': they must produce valid models from valid input models. A valid model has conformance to its meta-model and fulfils its constraints, usually written in OCL. In this paper, we propose a novel methodology to perform automatic, unbounded verification of ATL transformations. Its main component is a novel first-order semantics for ATL transformations, based on the interpretation of the corresponding rules and their execution semantics as first-order predicates. Although, our semantics is not complete, it does cover a significant subset of the ATL language. Using this semantics, transformation correctness can be automatically verified with respect to non-trivial OCL pre- and postconditions by using SMT solvers, e.g. Z3 and Yices.