Consider the following premises. forall x_14: P_1(x_14) -> P(x_14). forall x_14: P(x_14) -> T_3(x_14). forall x_14: P_1(x_14) or U_3(x_14). exists x_14: P(x_14) <-> U_3(x_14). Can we infer forall x_14: ~T_3(x_14) from them? If possible, name the inference rules being used at each step.
 From exists x_14: P(x_14) <-> U_3(x_14) we can infer exists x_14: U_3(x_14) -> P(x_14) via existential biconditional elimination. From forall x_14: P_1(x_14) -> P(x_14), exists x_14: U_3(x_14) -> P(x_14), forall x_14: P_1(x_14) or U_3(x_14) we can infer exists x_14: P(x_14) via existential disjunction elimination. Finally, from forall x_14: P(x_14) -> T_3(x_14), exists x_14: P(x_14) we can infer exists x_14: T_3(x_14) via existential modus ponens, which contradicts forall x_14: ~T_3(x_14). Therefore, the answer is no.