Consider the following premises. R_16(a_16) or w_4. forall x_16: R_16(x_16) <-> S_16(x_16). w_4 -> S_16(a_16). w -> ~S_16(a_16). Can we infer w from them? If possible, name the inference rules being used at each step.
 From forall x_16: R_16(x_16) <-> S_16(x_16) we can infer R_16(a_16) <-> S_16(a_16) via universal instantiation. From R_16(a_16) <-> S_16(a_16) we can infer R_16(a_16) -> S_16(a_16) via biconditional elimination. From R_16(a_16) -> S_16(a_16), w_4 -> S_16(a_16), R_16(a_16) or w_4 we can infer S_16(a_16) via disjunction elimination. Finally, from w -> ~S_16(a_16), S_16(a_16) we can infer ~w via modus tollens, which contradicts w. Therefore, the answer is no.