Consider the following premises. exists x_16: P_14(x_16) -> W(x_16). forall x_16: P_16(x_16) -> U(x_16). forall x_16: P_16(x_16). forall x_16: P_14(x_16) and Q_14(x_16). Can we infer forall x_16: ~W(x_16) from them? If possible, name the inference rules being used at each step.
 From forall x_16: P_16(x_16) -> U(x_16), forall x_16: P_16(x_16) we can infer forall x_16: U(x_16) via universal modus ponens. From forall x_16: P_14(x_16) and Q_14(x_16) we can infer forall x_16: P_14(x_16) via universal simplification. From exists x_16: P_14(x_16) -> W(x_16), forall x_16: P_14(x_16) we can infer exists x_16: W(x_16) via existential modus ponens. From forall x_16: U(x_16), exists x_16: W(x_16) we can infer exists x_16: U(x_16) and W(x_16) via existential conjunction. Finally, from exists x_16: U(x_16) and W(x_16) we can infer exists x_16: U(x_16) via existential simplification, which contradicts forall x_16: ~W(x_16). Therefore, the answer is no.