Consider the following premises. forall x_10: Q_10(x_10). forall x_10: T(x_10). exists x_10: W_2(x_10). Can we infer forall x_10: ~(T(x_10) and W_2(x_10)) from them? If possible, name the inference rules being used at each step.
 From exists x_10: W_2(x_10), forall x_10: Q_10(x_10) we can infer exists x_10: W_2(x_10) and Q_10(x_10) via existential conjunction. From exists x_10: W_2(x_10) and Q_10(x_10) we can infer exists x_10: W_2(x_10) via existential simplification. Finally, from forall x_10: T(x_10), exists x_10: W_2(x_10) we can infer exists x_10: T(x_10) and W_2(x_10) via existential conjunction, which contradicts forall x_10: ~(T(x_10) and W_2(x_10)). Therefore, the answer is no.