The phrase "study at disprove" can have several synonyms depending on the contexts in which it is used. Some alternatives to this phrase could be to "investigate to discredit" or to "analyze to refute." Similarly, "research to disprove" or "scrutinize to invalidate" are some other synonyms that could be used to convey the same meaning. Other possible options for synonymous phrases might also include "examine with skepticism" or "investigate to challenge," depending on the nuanced meaning desired. Whatever phrase is chosen, the goal is to convey the act of examining something in an attempt to disprove or discredit it.