; Automatically generated by map2smt

(set-logic HORN)

(declare-datatypes ((listOfInt 0) )
(((cons-listOfInt (head-listOfInt Int) (tail-listOfInt listOfInt)) (nil-listOfInt))))



(declare-fun leq (Int Int Bool) Bool)
(declare-fun plus (Int Int Int) Bool)
(declare-fun count (Int listOfInt Int) Bool)
(declare-fun ff () Bool)

(assert
  (forall ( (A Int) (B Int) (C Int) )
    (=>
      (and
        (= B (- C A))
        (>= A 0)
        (>= (- C A) 0)
      )
      (plus A B C)
    )
  )
)
(assert
  (forall ( (A Int) (B Int) )
    (=>
      (= B 0)
      (count A nil-listOfInt B)
    )
  )
)
(assert
  (forall ( (A Int) (B listOfInt) (C Int) (D Int) )
    (=>
      (and
        (= C (+ 1 D))
        (count A B D)
      )
      (count A (cons-listOfInt A B) C)
    )
  )
)
(assert
  (forall ( (A Int) (B Int) (C listOfInt) (D Int) )
    (=>
      (and
        (>= (- B A) 1)
        (count A C D)
      )
      (count A (cons-listOfInt B C) D)
    )
  )
)
(assert
  (forall ( (A Int) (B Int) (C listOfInt) (D Int) )
    (=>
      (and
        (<= (- B A) (- 1))
        (count A C D)
      )
      (count A (cons-listOfInt B C) D)
    )
  )
)
(assert
  (forall ( (A Int) (B Int) (C Int) (D Int) (E Int) (F listOfInt) )
    (=>
      (and
        (= (+ A B) C)
        (count D (cons-listOfInt E nil-listOfInt) A)
        (count D F B)
        (count D (cons-listOfInt E F) C)
      )
      ff
    )
  )
)

(assert (not ff))
(check-sat)