Consider the following premises. q_3. forall x_2: P(x_2) or T(x_2). forall x_2: ~P(x_2). Can we infer T(f) and q_3 from them? If possible, name the inference rules being used at each step.
 From forall x_2: P(x_2) or T(x_2), forall x_2: ~P(x_2) we can infer forall x_2: T(x_2) via universal disjunctive syllogism. From forall x_2: T(x_2) we can infer T(f) via universal instantiation. Finally, from T(f), q_3 we can infer T(f) and q_3 via conjunction. Therefore, the answer is yes.