Consider the following premises. P_4(d) <-> t. forall y: W(y) -> ~T(y). forall y: P_4(y) <-> W(y). forall y: T(y). Can we infer t from them? If possible, name the inference rules being used at each step.
 From forall y: W(y) -> ~T(y), forall y: T(y) we can infer forall y: ~W(y) via universal modus tollens. From forall y: P_4(y) <-> W(y), forall y: ~W(y) we can infer forall y: ~P_4(y) via universal biconditional elimination. From forall y: ~P_4(y) we can infer ~P_4(d) via universal instantiation. Finally, from P_4(d) <-> t, ~P_4(d) we can infer ~t via biconditional elimination, which contradicts t. Therefore, the answer is no.