Consider the following premises. forall z: ~U(z). forall z: U(z) or T_3(z). forall z: T_3(z) -> P(z). Can we infer exists z: ~P(z) from them? If possible, name the inference rules being used at each step.
 From forall z: U(z) or T_3(z), forall z: ~U(z) we can infer forall z: T_3(z) via universal disjunctive syllogism. Finally, from forall z: T_3(z) -> P(z), forall z: T_3(z) we can infer forall z: P(z) via universal modus ponens, which contradicts exists z: ~P(z). Therefore, the answer is no.