Consider the following premises. p_1 -> t. t -> q. p_1. Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From p_1 -> t, t -> q we can infer p_1 -> q via transitivity. Finally, from p_1 -> q, p_1 we can infer q via modus ponens, which contradicts ~q. Therefore, the answer is no.