Consider the following premises. forall x_15: ~U(x_15). forall x_15: P_12(x_15) -> U(x_15). forall x_15: P_15(x_15) <-> U(x_15). exists x_15: P_12(x_15) or P_15(x_15). Can we infer forall x_15: ~T_4(x_15) from them? If possible, name the inference rules being used at each step.
 From forall x_15: P_15(x_15) <-> U(x_15) we can infer forall x_15: P_15(x_15) -> U(x_15) via universal biconditional elimination. From forall x_15: P_12(x_15) -> U(x_15), forall x_15: P_15(x_15) -> U(x_15), exists x_15: P_12(x_15) or P_15(x_15) we can infer exists x_15: U(x_15) via existential disjunction elimination. From exists x_15: U(x_15) we can infer exists x_15: U(x_15) or T_4(x_15) via existential addition. Finally, from exists x_15: U(x_15) or T_4(x_15), forall x_15: ~U(x_15) we can infer exists x_15: T_4(x_15) via existential disjunctive syllogism, which contradicts forall x_15: ~T_4(x_15). Therefore, the answer is no.