Consider the following premises. forall x_16: Q(x_16) or W(x_16). forall x_16: Q_16(x_16) -> R_16(x_16). forall x_16: P(x_16) and Q_7(x_16). forall x_16: Q(x_16) -> ~R_16(x_16). forall x_16: P_16(x_16) -> R_16(x_16). forall x_16: P_16(x_16) or Q_16(x_16). Can we infer exists x_16: ~(P(x_16) and W(x_16)) from them?
 From forall x_16: P_16(x_16) -> R_16(x_16), forall x_16: Q_16(x_16) -> R_16(x_16), forall x_16: P_16(x_16) or Q_16(x_16) we can infer forall x_16: R_16(x_16). From forall x_16: Q(x_16) -> ~R_16(x_16), forall x_16: R_16(x_16) we can infer forall x_16: ~Q(x_16). From forall x_16: P(x_16) and Q_7(x_16) we can infer forall x_16: P(x_16). From forall x_16: Q(x_16) or W(x_16), forall x_16: ~Q(x_16) we can infer forall x_16: W(x_16). Finally, from forall x_16: P(x_16), forall x_16: W(x_16) we can infer forall x_16: P(x_16) and W(x_16), which contradicts exists x_16: ~(P(x_16) and W(x_16)). Therefore, the answer is no.