Consider the following premises. forall x_6: W_4(x_6). forall x_6: P_6(x_6) -> Q_6(x_6). forall x_6: P_6(x_6). exists x_6: S_3(x_6). Can we infer forall x_6: ~(W_4(x_6) and S_3(x_6)) from them? If possible, name the inference rules being used at each step.
 From forall x_6: P_6(x_6) -> Q_6(x_6), forall x_6: P_6(x_6) we can infer forall x_6: Q_6(x_6) via universal modus ponens. Finally, from forall x_6: W_4(x_6), forall x_6: Q_6(x_6) we can infer forall x_6: W_4(x_6) and Q_6(x_6) via universal conjunction, which contradicts forall x_6: ~(W_4(x_6) and S_3(x_6)). Therefore, the answer is no.