Independent modeling of various modules of an information system (IS), and consequently database subschemas, may result in formal or semantic conflicts between the modules being modeled. Such conflicts may cause collisions between the integrated database schema of a whole IS and the modeled subschemas. In our previous work, we have proposed criteria and algorithms for identifying and resolving such conflicts so as to provide a consolidation of database subschemas with the integrated database schema with respect to various database concepts, such as domains, relation schemes, primary key constraints and referential integrity constraints. In this paper, we propose a new approach and algorithms for identifying conflicts and testing consolidation of subschemas with the integrated database schema against check constraints. The proposed approach is based on satisfiability modulo theory (SMT) solvers. Hereby, we propose the integration of SMT solvers into our MDSD tool, aimed at supporting a database schema integration process.