Consider the following premises. forall x_10: Q_10(x_10) -> W(x_10). forall x_10: P_10(x_10) -> Q_10(x_10). exists x_10: P_10(x_10). Can we infer forall x_10: ~(W(x_10) or T(x_10)) from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) -> Q_10(x_10), forall x_10: Q_10(x_10) -> W(x_10) we can infer forall x_10: P_10(x_10) -> W(x_10) via universal transitivity. From forall x_10: P_10(x_10) -> W(x_10), exists x_10: P_10(x_10) we can infer exists x_10: W(x_10) via existential modus ponens. Finally, from exists x_10: W(x_10) we can infer exists x_10: W(x_10) or T(x_10) via existential addition, which contradicts forall x_10: ~(W(x_10) or T(x_10)). Therefore, the answer is no.