Consider the following premises. forall x: U(x). U(e) -> q. q -> t_3. Can we infer ~t_3 from them? If possible, name the inference rules being used at each step.
 From forall x: U(x) we can infer U(e) via universal instantiation. From U(e) -> q, q -> t_3 we can infer U(e) -> t_3 via transitivity. Finally, from U(e) -> t_3, U(e) we can infer t_3 via modus ponens, which contradicts ~t_3. Therefore, the answer is no.