Enderton problem 4 in Section 2.5

Let . Is consistent? Is satisfiable?

The completeness theorem says that any consistent set of formulas is satisfiable. Therefore, we only need to show that is consistent.

Suppose to the contrary, towards a contradiction, . Then, we have both and for any wff . I am looking for a counterexample , which is either or , not both.

Any help will be appreciated.