Consider the following premises. forall z: P(z) -> Q(z). P(e_2) <-> t. forall z: ~Q(z). forall z: Q(z) -> P(z). Can we infer t from them?
 From forall z: P(z) -> Q(z), forall z: Q(z) -> P(z) we can infer forall z: P(z) <-> Q(z). From forall z: P(z) <-> Q(z), forall z: ~Q(z) we can infer forall z: ~P(z). From forall z: ~P(z) we can infer ~P(e_2). Finally, from P(e_2) <-> t, ~P(e_2) we can infer ~t, which contradicts t. Therefore, the answer is no.