Consider the following premises. forall x_3: Q_1(x_3). exists x_3: P_3(x_3) or ~Q_1(x_3). Can we infer forall x_3: ~P_3(x_3) from them? If possible, name the inference rules being used at each step.
 From exists x_3: P_3(x_3) or ~Q_1(x_3) we can infer exists x_3: Q_1(x_3) -> P_3(x_3) via existential rewriting. Finally, from exists x_3: Q_1(x_3) -> P_3(x_3), forall x_3: Q_1(x_3) we can infer exists x_3: P_3(x_3) via existential modus ponens, which contradicts forall x_3: ~P_3(x_3). Therefore, the answer is no.