(declare-sort a 0)
(declare-fun x () a)
(declare-fun y () a)
(declare-fun f (a) a)
(declare-fun p1 () Bool)
(declare-fun p2 () Bool)
(assert (or p1 (= x y)))
(assert (or p1 (= y (f x))))
(assert (not (= x (f (f (f x))))))
(assert (or (not p1) p2))
(assert (or (not p1) (not p2)))
(check-sat)