Consider the following premises. forall x_12: ~P_6(x_12). forall x_12: P_12(x_12). exists x_12: P_6(x_12) or T_1(x_12). forall x_12: P_12(x_12) -> S_4(x_12). Can we infer exists x_12: T_1(x_12) from them? If possible, name the inference rules being used at each step.
 From forall x_12: P_12(x_12) -> S_4(x_12), forall x_12: P_12(x_12) we can infer forall x_12: S_4(x_12) via universal modus ponens. Finally, from exists x_12: P_6(x_12) or T_1(x_12), forall x_12: ~P_6(x_12) we can infer exists x_12: T_1(x_12) via existential disjunctive syllogism. Therefore, the answer is yes.