Consider the following premises. forall x_5: Q_2(x_5). forall x_5: Q(x_5) -> P_2(x_5). exists x_5: P_2(x_5) -> Q(x_5). forall x_5: P_2(x_5) -> ~Q_2(x_5). Can we infer forall x_5: Q(x_5) from them?
 From exists x_5: P_2(x_5) -> Q(x_5), forall x_5: Q(x_5) -> P_2(x_5) we can infer exists x_5: P_2(x_5) <-> Q(x_5). From forall x_5: P_2(x_5) -> ~Q_2(x_5), forall x_5: Q_2(x_5) we can infer forall x_5: ~P_2(x_5). Finally, from exists x_5: P_2(x_5) <-> Q(x_5), forall x_5: ~P_2(x_5) we can infer exists x_5: ~Q(x_5), which contradicts forall x_5: Q(x_5). Therefore, the answer is no.