Inverse of factorial function in MiniZinc

inverse.mzn

function int:factorial(int:t) =
if t = 0 then 1 else t * factorial(t-1) endif;

function int: factorial_inverse(int:n, int:factorial) =
if factorial == factorial(n) then n else factorial_inverse(n+1,factorial) endif;

function int:factorial_inverse(int:n) =
factorial_inverse(0,n);

int:a = factorial_inverse(720);

solve satisfy;

output [show(a)];