Consider the following premises. forall x_11: P_11(x_11) or Q_8(x_11). forall x_11: Q_8(x_11) -> R(x_11). forall x_11: Q_4(x_11) and P(x_11). forall x_11: P_11(x_11) <-> R(x_11). Can we infer exists x_11: ~(Q_4(x_11) and R(x_11)) from them?
 From forall x_11: P_11(x_11) <-> R(x_11) we can infer forall x_11: P_11(x_11) -> R(x_11). From forall x_11: P_11(x_11) -> R(x_11), forall x_11: Q_8(x_11) -> R(x_11), forall x_11: P_11(x_11) or Q_8(x_11) we can infer forall x_11: R(x_11). From forall x_11: Q_4(x_11) and P(x_11) we can infer forall x_11: Q_4(x_11). Finally, from forall x_11: Q_4(x_11), forall x_11: R(x_11) we can infer forall x_11: Q_4(x_11) and R(x_11), which contradicts exists x_11: ~(Q_4(x_11) and R(x_11)). Therefore, the answer is no.