We present a new approach to checking assertion properties for register-transfer level (RTL) design verification. Our approach combines structural word-level automatic test pattern generation (ATPG) and modular arithmetic constraint-solving techniques to solve the constraints imposed by the target assertion property. Our word-level ATPG and implication technique not only solves the constraints on the control logic, but also propagates the logic implications to the datapath. A novel arithmetic constraint solver based on modular number system is then employed to solve the remaining constraints in datapath. The advantages of the new method are threefold. First, the decision-making process of the word-lever ATPG is confined to the selected control signals only. Therefore, the enumeration of enormous number of choices at the datapath signals is completely avoided. Second, our new implication translation techniques allow word-level logic implication being performed across the boundary of datapath and control logic and, therefore, efficiently cut down the ATPG search space. Third, our arithmetic constraint solver is based on modular instead of integral number systems. It can thus avoid the false-negative effect resulting from the bit-vector value modulation. A prototype system has been built that consists of an industrial front-end hardware description language (HDL) parser, a property-to-constraint converter, and the ATPG/arithmetic constraint-solving engine. The experimental results on some public benchmark and industrial circuits demonstrate the efficiency of our approach and its applicability to large industrial designs.