Consider the following premises. forall x_12: S(x_12) or S_12(x_12). S_12(d) -> w_2. ~S(d). Can we infer ~w_2 from them? If possible, name the inference rules being used at each step.
 From forall x_12: S(x_12) or S_12(x_12) we can infer S(d) or S_12(d) via universal instantiation. From S(d) or S_12(d), ~S(d) we can infer S_12(d) via disjunctive syllogism. Finally, from S_12(d) -> w_2, S_12(d) we can infer w_2 via modus ponens, which contradicts ~w_2. Therefore, the answer is no.