(set-logic QF_UF)
(declare-sort U 0)
(declare-fun x () U)
(declare-fun y () U)
(declare-fun z () U)
(declare-fun f (U) U)
(assert (and (not (= (f x) (f y))) (= y z) (= (f x) (f (f z))) (= x y)))
(check-sat)
(exit)