Consider the following premises. exists x_9: S_2(x_9) <-> S(x_9). forall x_9: ~P_2(x_9). forall x_9: P_2(x_9) or S(x_9). Can we infer forall x_9: ~S_2(x_9) from them? If possible, name the inference rules being used at each step.
 From exists x_9: S_2(x_9) <-> S(x_9) we can infer exists x_9: S(x_9) -> S_2(x_9) via existential biconditional elimination. From forall x_9: P_2(x_9) or S(x_9), forall x_9: ~P_2(x_9) we can infer forall x_9: S(x_9) via universal disjunctive syllogism. Finally, from exists x_9: S(x_9) -> S_2(x_9), forall x_9: S(x_9) we can infer exists x_9: S_2(x_9) via existential modus ponens, which contradicts forall x_9: ~S_2(x_9). Therefore, the answer is no.