Refractorily is an adjective that describes someone or something that is stubborn and disobedient. There are several synonyms that can be used to replace it, including recalcitrantly, intractably, obstinately, and defiantly. These words all suggest that someone or something is difficult to control and resistant to guidance or change. For example, a child who refuses to clean their room might be described as acting refractorily, while a politician who refuses to change their position on an issue might be described as acting defiantly. Overall, these synonyms all convey the sense of someone or something that is unyielding and resistant to direction or influence.