Consider the following premises. forall x: U(x) or ~T_3(x). forall x: R_2(x) -> U(x). forall x: W_3(x) or T_3(x). forall x: ~W_3(x) or R_2(x). Can we infer ~U(h) from them? If possible, name the inference rules being used at each step.
 From forall x: U(x) or ~T_3(x) we can infer forall x: T_3(x) -> U(x) via universal rewriting. From forall x: W_3(x) or T_3(x), forall x: ~W_3(x) or R_2(x) we can infer forall x: T_3(x) or R_2(x) via universal resolution. Finally, from forall x: T_3(x) -> U(x), forall x: R_2(x) -> U(x), forall x: T_3(x) or R_2(x) we can infer forall x: U(x) via universal disjunction elimination, which contradicts ~U(h). Therefore, the answer is no.