Consider the following premises. forall x_4: ~T(x_4). exists x_4: ~P_4(x_4) or P(x_4). forall x_4: P_4(x_4). Can we infer forall x_4: ~P(x_4) from them? If possible, name the inference rules being used at each step.
 From forall x_4: P_4(x_4) we can infer forall x_4: P_4(x_4) or T(x_4) via universal addition. From forall x_4: P_4(x_4) or T(x_4), exists x_4: ~P_4(x_4) or P(x_4) we can infer exists x_4: T(x_4) or P(x_4) via existential resolution. Finally, from exists x_4: T(x_4) or P(x_4), forall x_4: ~T(x_4) we can infer exists x_4: P(x_4) via existential disjunctive syllogism, which contradicts forall x_4: ~P(x_4). Therefore, the answer is no.