First of all try to evaluate the situation from every possible perspective. If you still feel that the other person is lying and trying to prove something then you do not have to argue with the person. You have to decide what you want. Plan your actions accordingly. For example, If you know someone is constantly stealing money and lying about it then of course you would want that your money shouldn’t get stolen anymore. Instead of arguing or trying to prove the other person wrong focus on making your money safe and plan accordingly.