INTPs tend not to be interested in proving anything to anyone because they are led by an internal standard. The problem with people that you describe is that they are so intensely focused on their thought experiments, that they are willing to go at whatever great lengths to carry them. This leads them to discount the external environment. I doubt such INTPs are even clearly aware of how others perceive them, even more I doubt that they are deliberately trying to convince others of their cleverness.
The latter is mostly ENT business, or whatever is associated with applying Thinking externally. INTJs are more likely to do this than INTPs because of their Extroverted Thinking factor.