Consider the following premises. p <-> q_12. p. Can we infer ~q_12 from them? If possible, name the inference rules being used at each step.
 From p <-> q_12 we can infer p -> q_12 via biconditional elimination. Finally, from p -> q_12, p we can infer q_12 via modus ponens, which contradicts ~q_12. Therefore, the answer is no.