Critical flaws continue to exist at the level of domain, requirement, and/or design specification, and specification verification (i.e., to check whether a specification has desirable properties) is still one of the most important challenges in software/system engineering. CafeOBJ is an executable algebraic specification language system and domain/requirement/design engineers can write proof scores for improving quality of specifications by the specification verification. This paper describes advances of the proof scores for the specification verification in CafeOBJ.