Consider the following premises. forall x_6: S_1(x_6). exists x_6: Q_4(x_6) and Q_1(x_6). Can we infer forall x_6: ~(S_1(x_6) and Q_4(x_6)) from them?
 From exists x_6: Q_4(x_6) and Q_1(x_6) we can infer exists x_6: Q_4(x_6). Finally, from forall x_6: S_1(x_6), exists x_6: Q_4(x_6) we can infer exists x_6: S_1(x_6) and Q_4(x_6), which contradicts forall x_6: ~(S_1(x_6) and Q_4(x_6)). Therefore, the answer is no.