Consider the following premises. W(a_5) <-> p_4. forall x: T(x) <-> U_4(x). forall x: U_4(x) <-> W(x). forall x: ~T(x). Can we infer p_4 from them? If possible, name the inference rules being used at each step.
 From forall x: T(x) <-> U_4(x), forall x: ~T(x) we can infer forall x: ~U_4(x) via universal biconditional elimination. From forall x: U_4(x) <-> W(x), forall x: ~U_4(x) we can infer forall x: ~W(x) via universal biconditional elimination. From forall x: ~W(x) we can infer ~W(a_5) via universal instantiation. Finally, from W(a_5) <-> p_4, ~W(a_5) we can infer ~p_4 via biconditional elimination, which contradicts p_4. Therefore, the answer is no.