(set-logic AUFLIRA)
(set-info :source | Buggy list theorem |)
(set-info :smt-lib-version 2.0)
(set-info :category "crafted")
(set-info :status sat)
(declare-sort List 0)
(declare-fun cons (Real List) List)
(declare-fun nil () List)
(declare-fun car (List) Real)
(declare-fun cdr (List) List)
(declare-fun len (List) Int)
(assert (forall ((?x Real) (?y List)) (= (car (cons ?x ?y)) ?x)))
(assert (forall ((?x Real) (?y List)) (= (cdr (cons ?x ?y)) ?y)))
(assert (= (len nil) 0))
(assert (forall ((?x Real) (?y List)) (= (len (cons ?x ?y)) (+ (len ?y) 1))))
(declare-fun append (List List) List)
(assert (forall ((?x Real) (?y1 List) (?y2 List)) (= (append (cons ?x ?y1) ?y2) (cons ?x (append ?y1 ?y2)))))
(assert (not (forall ((?x Real) (?y List)) (= (append (cons ?x nil) ?y) (cons ?x ?y)))))
(check-sat)
(exit)