I think I solved it. Since (by axiom group 2 of Enderton's book and modus ponens) and by assumption, which means , i.e., inconsistent.
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.