Consider the following premises. q_1 -> t_2. P(i_1) -> t_2. forall x: P(x). Can we infer ~t_2 from them? If possible, name the inference rules being used at each step.
 From forall x: P(x) we can infer P(i_1) via universal instantiation. From P(i_1) we can infer P(i_1) or q_1 via addition. Finally, from P(i_1) -> t_2, q_1 -> t_2, P(i_1) or q_1 we can infer t_2 via disjunction elimination, which contradicts ~t_2. Therefore, the answer is no.