Consider the following premises. forall x_15: P_15(x_15) -> Q_15(x_15). exists x_15: Q_15(x_15) -> R_15(x_15). forall x_15: P_13(x_15) <-> R_15(x_15). forall x_15: P_15(x_15). Can we infer forall x_15: ~P_13(x_15) from them?
 From forall x_15: P_15(x_15) -> Q_15(x_15), exists x_15: Q_15(x_15) -> R_15(x_15) we can infer exists x_15: P_15(x_15) -> R_15(x_15). From forall x_15: P_13(x_15) <-> R_15(x_15) we can infer forall x_15: R_15(x_15) -> P_13(x_15). From exists x_15: P_15(x_15) -> R_15(x_15), forall x_15: P_15(x_15) we can infer exists x_15: R_15(x_15). Finally, from forall x_15: R_15(x_15) -> P_13(x_15), exists x_15: R_15(x_15) we can infer exists x_15: P_13(x_15), which contradicts forall x_15: ~P_13(x_15). Therefore, the answer is no.