Consider the following premises. forall x_1: P_1(x_1) -> U_4(x_1). forall x_1: P_1(x_1). Can we infer exists x_1: ~(U_4(x_1) or T(x_1)) from them? If possible, name the inference rules being used at each step.
 From forall x_1: P_1(x_1) -> U_4(x_1), forall x_1: P_1(x_1) we can infer forall x_1: U_4(x_1) via universal modus ponens. Finally, from forall x_1: U_4(x_1) we can infer forall x_1: U_4(x_1) or T(x_1) via universal addition, which contradicts exists x_1: ~(U_4(x_1) or T(x_1)). Therefore, the answer is no.