Consider the following premises. forall x_1: U_1(x_1) <-> T_4(x_1). forall x_1: W_3(x_1) <-> U_1(x_1). forall x_1: T_4(x_1) -> W_3(x_1). Can we infer exists x_1: ~(W_3(x_1) <-> U_1(x_1)) from them? If possible, name the inference rules being used at each step.
 From forall x_1: U_1(x_1) <-> T_4(x_1) we can infer forall x_1: U_1(x_1) -> T_4(x_1) via universal biconditional elimination. From forall x_1: W_3(x_1) <-> U_1(x_1) we can infer forall x_1: W_3(x_1) -> U_1(x_1) via universal biconditional elimination. From forall x_1: U_1(x_1) -> T_4(x_1), forall x_1: T_4(x_1) -> W_3(x_1) we can infer forall x_1: U_1(x_1) -> W_3(x_1) via universal transitivity. Finally, from forall x_1: W_3(x_1) -> U_1(x_1), forall x_1: U_1(x_1) -> W_3(x_1) we can infer forall x_1: W_3(x_1) <-> U_1(x_1) via universal biconditional introduction, which contradicts exists x_1: ~(W_3(x_1) <-> U_1(x_1)). Therefore, the answer is no.