Consider the following premises. forall x_14: Q_3(x_14). forall x_14: U_4(x_14) -> P_1(x_14). forall x_14: W(x_14). exists x_14: P_1(x_14) or ~W(x_14). Can we infer forall x_14: ~(Q_3(x_14) and P_1(x_14)) from them? If possible, name the inference rules being used at each step.
 From exists x_14: P_1(x_14) or ~W(x_14) we can infer exists x_14: W(x_14) -> P_1(x_14) via existential rewriting. From forall x_14: W(x_14) we can infer forall x_14: W(x_14) or U_4(x_14) via universal addition. From exists x_14: W(x_14) -> P_1(x_14), forall x_14: U_4(x_14) -> P_1(x_14), forall x_14: W(x_14) or U_4(x_14) we can infer exists x_14: P_1(x_14) via existential disjunction elimination. Finally, from forall x_14: Q_3(x_14), exists x_14: P_1(x_14) we can infer exists x_14: Q_3(x_14) and P_1(x_14) via existential conjunction, which contradicts forall x_14: ~(Q_3(x_14) and P_1(x_14)). Therefore, the answer is no.