Consider the following premises. forall x_17: P_14(x_17) <-> Q_17(x_17). forall x_17: P_17(x_17) -> Q_17(x_17). exists x_17: ~P_14(x_17). forall x_17: Q_17(x_17) -> P_17(x_17). forall x_17: Q(x_17) <-> P_17(x_17). Can we infer forall x_17: Q(x_17) from them? If possible, name the inference rules being used at each step.
 From forall x_17: P_17(x_17) -> Q_17(x_17), forall x_17: Q_17(x_17) -> P_17(x_17) we can infer forall x_17: P_17(x_17) <-> Q_17(x_17) via universal biconditional introduction. From forall x_17: P_14(x_17) <-> Q_17(x_17), exists x_17: ~P_14(x_17) we can infer exists x_17: ~Q_17(x_17) via existential biconditional elimination. From forall x_17: P_17(x_17) <-> Q_17(x_17), exists x_17: ~Q_17(x_17) we can infer exists x_17: ~P_17(x_17) via existential biconditional elimination. Finally, from forall x_17: Q(x_17) <-> P_17(x_17), exists x_17: ~P_17(x_17) we can infer exists x_17: ~Q(x_17) via existential biconditional elimination, which contradicts forall x_17: Q(x_17). Therefore, the answer is no.