Consider the following premises. U_4(c_3) <-> t. forall z: ~P(z). forall z: U_4(z) <-> P(z). Can we infer ~t or q from them? If possible, name the inference rules being used at each step.
 From forall z: U_4(z) <-> P(z), forall z: ~P(z) we can infer forall z: ~U_4(z) via universal biconditional elimination. From forall z: ~U_4(z) we can infer ~U_4(c_3) via universal instantiation. From U_4(c_3) <-> t, ~U_4(c_3) we can infer ~t via biconditional elimination. Finally, from ~t we can infer ~t or q via addition. Therefore, the answer is yes.