A hypothetical syllogism with three conditional propositions (hereinafter HSc) is considered invalid according to the ordinary discourse counterexamples in the existing literature. In this paper, I argue that such counterexamples cannot verify the validity of HSc. The conditional propositions in these arguments are questionable, whether that is indicative or counterfactual HSc. The arguments are considered invalid not because HSc is invalid by itself, but because there is a mismatch between the antecedent of one premise and the consequent of another premise (i.e. a violation of the common part of both premises) in the syllogism, which seems to be a fallacy of equivocation. Such sentential structures of natural-language conditionals are problematic according to possible-world semantics. However, this study does not attempt to resolve the controversy of HSc by verifying whether it is logically valid in all circumstances, but rather to disqualify the counterexamples and illustrate their unclear syllogistic schemas.