Consider the following premises. S_3(i). forall y: Q_3(y) or ~S_3(y). Q_3(i) -> w. Can we infer ~w from them? If possible, name the inference rules being used at each step.
 From forall y: Q_3(y) or ~S_3(y) we can infer forall y: S_3(y) -> Q_3(y) via universal rewriting. From forall y: S_3(y) -> Q_3(y) we can infer S_3(i) -> Q_3(i) via universal instantiation. From S_3(i) -> Q_3(i), S_3(i) we can infer Q_3(i) via modus ponens. Finally, from Q_3(i) -> w, Q_3(i) we can infer w via modus ponens, which contradicts ~w. Therefore, the answer is no.