Model-based tools for automatic test generation usually can handle systems of a rather limited size. Therefore, they cannot be applied directly to systems of real industrial size. Here, we propose an approach to test generation combining enumerative data abstraction, test generation methods and constraint solving. The approach allows applying enumerative test generation tools like TGV to large and infinite systems. Given such a system, abstractions allow to derive a finite abstract system suitable for automatic test generation with enumerative tools. Abstract test cases need to be parameterized with actual test data, in order to execute them. For data selection, we make use of constraint solving techniques. Test case execution will later be done by TTCN-3