Consider the following premises. forall x_16: Q(x_16). forall x_16: Q_10(x_16). exists x_16: ~P_16(x_16). forall x_16: P_16(x_16) or Q_16(x_16). Can we infer forall x_16: ~(Q_16(x_16) and Q(x_16)) from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) or Q_16(x_16), exists x_16: ~P_16(x_16) we can infer exists x_16: Q_16(x_16) via existential disjunctive syllogism. From exists x_16: Q_16(x_16), forall x_16: Q_10(x_16) we can infer exists x_16: Q_16(x_16) and Q_10(x_16) via existential conjunction. From exists x_16: Q_16(x_16) and Q_10(x_16) we can infer exists x_16: Q_16(x_16) via existential simplification. Finally, from exists x_16: Q_16(x_16), forall x_16: Q(x_16) we can infer exists x_16: Q_16(x_16) and Q(x_16) via existential conjunction, which contradicts forall x_16: ~(Q_16(x_16) and Q(x_16)). Therefore, the answer is no.