integer division gives incorrect result

Question

I try to check satisfiability of x div y == 2 and x / y == 2 but got incorrect results both times. Looks like Z3 doesn't support these yet ?

(declare-fun x () Int)
(declare-fun y () Int)

(assert (=  (div x y ) 2))

(check-sat)
(get-model)
(exit)

sat
(model 
  (define-fun y () Int
    0)
  (define-fun x () Int
    38)
)



(declare-fun x () Int)
(declare-fun y () Int)

(assert (=  (/ x y ) 2))

(check-sat)
(get-model)
(exit)

sat
(model 
  (define-fun y () Int
    0)
  (define-fun x () Int
    1)
)

Answer 1

Integer division is supported, see: http://smtlib.cs.uiowa.edu/theories/Ints.smt2

Real division is also supported (from here: http://smtlib.cs.uiowa.edu/theories/Reals.smt2), the issue with division by zero you mention is covered: "Since in SMT-LIB logic all function symbols are interpreted as total functions, terms of the form (/ t 0) are meaningful in every instance of Reals. However, the declaration imposes no constraints on their value. This means in particular that - for every instance theory T and - for every closed terms t1 and t2 of sort Real, there is a model of T that satisfies (= t1 (/ t2 0))."

You should add an assertion that the divisor is not equal to zero.

(assert (not (= y 0)))

Here's the example (rise4fun link: http://rise4fun.com/Z3/IUDE ):

(declare-fun x () Int)
(declare-fun y () Int)

(assert (not (= y 0)))

(push)
(assert (=  (div x y ) 2))
(check-sat)
(get-model) ; gives x = 2, y = 1
(pop)

(push)
(assert (=  (/ x y ) 2))
(check-sat)
(get-model) ; gives x = -2, y = -1
(pop)