Consider the following premises. forall x_15: Q_15(x_15) -> W(x_15). exists x_15: W(x_15) <-> P_15(x_15). forall x_15: W(x_15) -> Q(x_15). forall x_15: P_15(x_15). Can we infer exists x_15: Q(x_15) from them?
 From forall x_15: P_15(x_15) we can infer forall x_15: P_15(x_15) or Q_15(x_15). From exists x_15: W(x_15) <-> P_15(x_15) we can infer exists x_15: P_15(x_15) -> W(x_15). From exists x_15: P_15(x_15) -> W(x_15), forall x_15: Q_15(x_15) -> W(x_15), forall x_15: P_15(x_15) or Q_15(x_15) we can infer exists x_15: W(x_15). Finally, from forall x_15: W(x_15) -> Q(x_15), exists x_15: W(x_15) we can infer exists x_15: Q(x_15). Therefore, the answer is yes.