Consider the following premises. forall x: W(x) <-> U_4(x). forall x: U_3(x) or T_2(x). forall x: U_3(x) -> U_4(x). forall x: ~W(x). Can we infer exists x: ~T_2(x) from them? If possible, name the inference rules being used at each step.
 From forall x: W(x) <-> U_4(x), forall x: ~W(x) we can infer forall x: ~U_4(x) via universal biconditional elimination. From forall x: U_3(x) -> U_4(x), forall x: ~U_4(x) we can infer forall x: ~U_3(x) via universal modus tollens. Finally, from forall x: U_3(x) or T_2(x), forall x: ~U_3(x) we can infer forall x: T_2(x) via universal disjunctive syllogism, which contradicts exists x: ~T_2(x). Therefore, the answer is no.