Consider the following premises. q_2 <-> W_4(a). q_2 or t. forall z: Q(z) <-> W_1(z). forall z: Q(z) <-> W_4(z). forall z: ~W_1(z). Can we infer ~t from them? If possible, name the inference rules being used at each step.
 From forall z: Q(z) <-> W_1(z), forall z: ~W_1(z) we can infer forall z: ~Q(z) via universal biconditional elimination. From forall z: Q(z) <-> W_4(z), forall z: ~Q(z) we can infer forall z: ~W_4(z) via universal biconditional elimination. From forall z: ~W_4(z) we can infer ~W_4(a) via universal instantiation. From q_2 <-> W_4(a), ~W_4(a) we can infer ~q_2 via biconditional elimination. Finally, from q_2 or t, ~q_2 we can infer t via disjunctive syllogism, which contradicts ~t. Therefore, the answer is no.