Consider the following premises. forall x_10: P_10(x_10). forall x_2: T(x_2). Can we infer forall x_2: ~(P_10(x_2) and T(x_2)) from them? If possible, name the inference rules being used at each step.
 From forall x_10: P_10(x_10) we can infer P_10(a_10) via universal instantiation. From P_10(a_10) we can infer exists x_2: P_10(x_2) via existential generalization. Finally, from exists x_2: P_10(x_2), forall x_2: T(x_2) we can infer exists x_2: P_10(x_2) and T(x_2) via existential conjunction, which contradicts forall x_2: ~(P_10(x_2) and T(x_2)). Therefore, the answer is no.