Consider the following premises. forall x_8: P_8(x_8) and Q_8(x_8). exists x_8: W(x_8) -> ~P_8(x_8). forall x_8: Q_5(x_8). Can we infer exists x_8: ~W(x_8) from them? If possible, name the inference rules being used at each step.
 From forall x_8: P_8(x_8) and Q_8(x_8) we can infer forall x_8: P_8(x_8) via universal simplification. From forall x_8: P_8(x_8), forall x_8: Q_5(x_8) we can infer forall x_8: P_8(x_8) and Q_5(x_8) via universal conjunction. From forall x_8: P_8(x_8) and Q_5(x_8) we can infer forall x_8: P_8(x_8) via universal simplification. Finally, from exists x_8: W(x_8) -> ~P_8(x_8), forall x_8: P_8(x_8) we can infer exists x_8: ~W(x_8) via existential modus tollens. Therefore, the answer is yes.