Consider the following premises. forall x_9: U(x_9) -> P_9(x_9). forall x_9: P_7(x_9) or U(x_9). forall x_9: ~P_7(x_9) or R(x_9). forall x_9: P_9(x_9) -> Q_9(x_9). forall x_9: R(x_9) -> W(x_9). exists x_9: Q_9(x_9) -> W(x_9). Can we infer forall x_9: ~W(x_9) from them? If possible, name the inference rules being used at each step.
 From forall x_9: P_9(x_9) -> Q_9(x_9), exists x_9: Q_9(x_9) -> W(x_9) we can infer exists x_9: P_9(x_9) -> W(x_9) via existential transitivity. From forall x_9: P_7(x_9) or U(x_9), forall x_9: ~P_7(x_9) or R(x_9) we can infer forall x_9: U(x_9) or R(x_9) via universal resolution. From forall x_9: U(x_9) -> P_9(x_9), exists x_9: P_9(x_9) -> W(x_9) we can infer exists x_9: U(x_9) -> W(x_9) via existential transitivity. Finally, from exists x_9: U(x_9) -> W(x_9), forall x_9: R(x_9) -> W(x_9), forall x_9: U(x_9) or R(x_9) we can infer exists x_9: W(x_9) via existential disjunction elimination, which contradicts forall x_9: ~W(x_9). Therefore, the answer is no.