Consider the following premises. forall x_11: P(x_11) and Q_11(x_11). forall x_11: W_4(x_11) -> S(x_11). forall x_11: ~R(x_11) or W_4(x_11). forall x_11: R(x_11). forall x_11: R_2(x_11) -> S(x_11). Can we infer exists x_11: ~(P(x_11) and S(x_11)) from them?
 From forall x_11: P(x_11) and Q_11(x_11) we can infer forall x_11: P(x_11). From forall x_11: R(x_11) we can infer forall x_11: R(x_11) or R_2(x_11). From forall x_11: R(x_11) or R_2(x_11), forall x_11: ~R(x_11) or W_4(x_11) we can infer forall x_11: R_2(x_11) or W_4(x_11). From forall x_11: R_2(x_11) -> S(x_11), forall x_11: W_4(x_11) -> S(x_11), forall x_11: R_2(x_11) or W_4(x_11) we can infer forall x_11: S(x_11). Finally, from forall x_11: P(x_11), forall x_11: S(x_11) we can infer forall x_11: P(x_11) and S(x_11), which contradicts exists x_11: ~(P(x_11) and S(x_11)). Therefore, the answer is no.