Consider the following premises. exists x_16: Q_16(x_16) -> P_3(x_16). forall x_16: P(x_16). forall x_16: P_16(x_16) -> Q_16(x_16). forall x_16: P_8(x_16) -> P_3(x_16). forall x_16: P_8(x_16) or P_16(x_16). forall x_16: Q_14(x_16). Can we infer forall x_16: ~(P(x_16) and P_3(x_16)) from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) -> Q_16(x_16), exists x_16: Q_16(x_16) -> P_3(x_16) we can infer exists x_16: P_16(x_16) -> P_3(x_16) via existential transitivity. Finally, from forall x_16: P(x_16), forall x_16: Q_14(x_16) we can infer forall x_16: P(x_16) and Q_14(x_16) via universal conjunction, which contradicts forall x_16: ~(P(x_16) and P_3(x_16)). Therefore, the answer is no.