Consider the following premises. ~q. w <-> R_15(a_15). S_15(a_15) <-> q. forall x_15: R_15(x_15) -> S_15(x_15). Can we infer ~w from them? If possible, name the inference rules being used at each step.
 From forall x_15: R_15(x_15) -> S_15(x_15) we can infer R_15(a_15) -> S_15(a_15) via universal instantiation. From S_15(a_15) <-> q, ~q we can infer ~S_15(a_15) via biconditional elimination. From R_15(a_15) -> S_15(a_15), ~S_15(a_15) we can infer ~R_15(a_15) via modus tollens. Finally, from w <-> R_15(a_15), ~R_15(a_15) we can infer ~w via biconditional elimination. Therefore, the answer is yes.