Consider the following premises. t -> ~P(j). forall x_17: ~Q_17(x_17). forall x_17: ~P_17(x_17). forall x_17: P_17(x_17) or Q_17(x_17). Can we infer ~t from them? If possible, name the inference rules being used at each step.
 From forall x_17: P_17(x_17) or Q_17(x_17), forall x_17: ~P_17(x_17) we can infer forall x_17: Q_17(x_17) via universal disjunctive syllogism. From forall x_17: Q_17(x_17) we can infer forall x_17: Q_17(x_17) or P(x_17) via universal addition. From forall x_17: Q_17(x_17) or P(x_17), forall x_17: ~Q_17(x_17) we can infer forall x_17: P(x_17) via universal disjunctive syllogism. From forall x_17: P(x_17) we can infer P(j) via universal instantiation. Finally, from t -> ~P(j), P(j) we can infer ~t via modus tollens. Therefore, the answer is yes. Notice, however, that the premises were contradictory, so we can infer anything from them.