Consider the following premises. forall x_5: Q_5(x_5). exists x_5: P_1(x_5) -> Q_3(x_5). forall x_5: P_1(x_5). Can we infer forall x_5: ~Q_3(x_5) from them? If possible, name the inference rules being used at each step.
 From forall x_5: P_1(x_5), forall x_5: Q_5(x_5) we can infer forall x_5: P_1(x_5) and Q_5(x_5) via universal conjunction. From forall x_5: P_1(x_5) and Q_5(x_5) we can infer forall x_5: P_1(x_5) via universal simplification. Finally, from exists x_5: P_1(x_5) -> Q_3(x_5), forall x_5: P_1(x_5) we can infer exists x_5: Q_3(x_5) via existential modus ponens, which contradicts forall x_5: ~Q_3(x_5). Therefore, the answer is no.