Consider the following premises. forall x_6: T_1(x_6). forall x_6: ~P_6(x_6). forall x_6: P_6(x_6). Can we infer forall x_6: R_2(x_6) from them? If possible, name the inference rules being used at each step.
 From forall x_6: P_6(x_6) we can infer forall x_6: P_6(x_6) or R_2(x_6) via universal addition. Finally, from forall x_6: P_6(x_6) or R_2(x_6), forall x_6: ~P_6(x_6) we can infer forall x_6: R_2(x_6) via universal disjunctive syllogism. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.