Consider the following premises. forall x_14: P_14(x_14) -> P_2(x_14). forall x_14: P_2(x_14) <-> W(x_14). forall x_14: ~P_14(x_14). W(a_5) or t_1. forall x_14: P_2(x_14) -> P_14(x_14). Can we infer ~t_1 from them? If possible, name the inference rules being used at each step.
 From forall x_14: P_14(x_14) -> P_2(x_14), forall x_14: P_2(x_14) -> P_14(x_14) we can infer forall x_14: P_14(x_14) <-> P_2(x_14) via universal biconditional introduction. From forall x_14: P_14(x_14) <-> P_2(x_14), forall x_14: ~P_14(x_14) we can infer forall x_14: ~P_2(x_14) via universal biconditional elimination. From forall x_14: P_2(x_14) <-> W(x_14), forall x_14: ~P_2(x_14) we can infer forall x_14: ~W(x_14) via universal biconditional elimination. From forall x_14: ~W(x_14) we can infer ~W(a_5) via universal instantiation. Finally, from W(a_5) or t_1, ~W(a_5) we can infer t_1 via disjunctive syllogism, which contradicts ~t_1. Therefore, the answer is no.