Abstract: For the non-cutoff soft potential Boltzmann equation, if the Boltzmann collision operator is strictly elliptic in $v$ variable, it is conjectured that the solution to the equation will  become immediately $C^\infty$ smoothness for both spatial and velocity variables for any positive time even though the initial datum has only polynomial decay at large velocity regime. The conjecture is quite important because it is related closely to the partial regularity problem on the weak solution. In this talk, we show that the conjecture might not hold for general case due to the degenerate property and the  non-local property of the collision operator.  We demonstrate it via three steps: (i). Construct so-called   {\it typical rough and  slowly decaying  data}; (ii). Prove that such kind of the data will induce the finite smoothing effect in Sobolev spaces; (iii). Prove that this finite smoothing  property will induce the  local properties for any positive time: Leibniz rule does not hold for high derivatives on the collision operator(even in the weak sense) and the discontinuity in $x$ variable of average of the solution on some certain domain in $\R^3_v$.