Consider the following premises. forall x: U_3(x) or T(x). exists x: ~U_3(x) or Q(x). forall x: P_3(x) -> P(x). forall x: Q(x) -> P(x). forall x: ~T(x) or P_3(x). Can we infer forall x: ~P(x) from them? If possible, name the inference rules being used at each step.
 From forall x: U_3(x) or T(x), exists x: ~U_3(x) or Q(x) we can infer exists x: T(x) or Q(x) via existential resolution. From exists x: T(x) or Q(x), forall x: ~T(x) or P_3(x) we can infer exists x: Q(x) or P_3(x) via existential resolution. Finally, from forall x: Q(x) -> P(x), forall x: P_3(x) -> P(x), exists x: Q(x) or P_3(x) we can infer exists x: P(x) via existential disjunction elimination, which contradicts forall x: ~P(x). Therefore, the answer is no.