Consider the following premises. forall x_14: S(x_14) -> U_1(x_14). forall x_14: ~Q_14(x_14). forall x_14: U_1(x_14) <-> Q_14(x_14). forall x_14: U_1(x_14) -> S(x_14). p -> S(f_3). Can we infer ~p from them? If possible, name the inference rules being used at each step.
 From forall x_14: U_1(x_14) <-> Q_14(x_14), forall x_14: ~Q_14(x_14) we can infer forall x_14: ~U_1(x_14) via universal biconditional elimination. From forall x_14: S(x_14) -> U_1(x_14), forall x_14: U_1(x_14) -> S(x_14) we can infer forall x_14: S(x_14) <-> U_1(x_14) via universal biconditional introduction. From forall x_14: S(x_14) <-> U_1(x_14), forall x_14: ~U_1(x_14) we can infer forall x_14: ~S(x_14) via universal biconditional elimination. From forall x_14: ~S(x_14) we can infer ~S(f_3) via universal instantiation. Finally, from p -> S(f_3), ~S(f_3) we can infer ~p via modus tollens. Therefore, the answer is yes.