We present Diver, a novel technique for effectively finding critical bugs in SMT solvers. Ensuring the correctness of SMT solvers is becoming increasingly important as many applications use solvers as a foundational basis. In response, several approaches for testing SMT solvers, which are classified into differential testing and oracle-guided approaches, have been proposed until recently. However, they are still unsatisfactory in that (1) differential testing approaches cannot validate unique yet important features of solvers, and (2) oracle-guided approaches cannot generate diverse tests due to their reliance on limited mutation rules. Diver aims to complement these shortcomings, particularly focusing on finding bugs that are missed by existing approaches. To this end, we present a new testing technique that supports unrestricted random mutations without differential testing. We have used Diver to validate the most recent versions of three popular SMT solvers: CVC5, Z3 and dReal. In total, Diver found 25 new bugs, of which 21 are critical and directly affect the reliability of the solvers. We also empirically prove Diver’s own strength by showing that existing tools are unlikely to find the bugs discovered by Diver.