Consider the following premises. exists x_19: Q_19(x_19) <-> Q_16(x_19). forall x_19: ~P_19(x_19) or R_19(x_19). forall x_19: ~Q_16(x_19). forall x_19: P_19(x_19) or Q_19(x_19). forall x_19: Q(x_19). Can we infer forall x_19: ~(R_19(x_19) and Q(x_19)) from them? If possible, name the inference rules being used at each step.
 From forall x_19: P_19(x_19) or Q_19(x_19), forall x_19: ~P_19(x_19) or R_19(x_19) we can infer forall x_19: Q_19(x_19) or R_19(x_19) via universal resolution. From exists x_19: Q_19(x_19) <-> Q_16(x_19), forall x_19: ~Q_16(x_19) we can infer exists x_19: ~Q_19(x_19) via existential biconditional elimination. From forall x_19: Q_19(x_19) or R_19(x_19), exists x_19: ~Q_19(x_19) we can infer exists x_19: R_19(x_19) via existential disjunctive syllogism. Finally, from exists x_19: R_19(x_19), forall x_19: Q(x_19) we can infer exists x_19: R_19(x_19) and Q(x_19) via existential conjunction, which contradicts forall x_19: ~(R_19(x_19) and Q(x_19)). Therefore, the answer is no.