Consider the following premises. forall x_14: P_14(x_14). P_14(f) <-> q. Can we infer ~q from them? If possible, name the inference rules being used at each step.
 From forall x_14: P_14(x_14) we can infer P_14(f) via universal instantiation. From P_14(f) <-> q we can infer P_14(f) -> q via biconditional elimination. Finally, from P_14(f) -> q, P_14(f) we can infer q via modus ponens, which contradicts ~q. Therefore, the answer is no.