Consider the following premises. forall x: P(x) -> U_2(x). forall x: Q(x) <-> U_2(x). forall x: R(x) or P(x). exists x: ~R(x) or Q(x). Can we infer forall x: ~U_2(x) from them? If possible, name the inference rules being used at each step.
 From forall x: R(x) or P(x), exists x: ~R(x) or Q(x) we can infer exists x: P(x) or Q(x) via existential resolution. From forall x: Q(x) <-> U_2(x) we can infer forall x: Q(x) -> U_2(x) via universal biconditional elimination. Finally, from forall x: P(x) -> U_2(x), forall x: Q(x) -> U_2(x), exists x: P(x) or Q(x) we can infer exists x: U_2(x) via existential disjunction elimination, which contradicts forall x: ~U_2(x). Therefore, the answer is no.