Han's iterated resultant conjecture for generic forms

Let $f(x_1,\ldots,x_n)$ be a generic form, and let $\Delta(f)$ denote its multivariate discriminant. Let ${\tt Hp}(f,[x_n,\ldots,x_1])$ be the polynomial associated with the iterated resultant in the variable order $[x_n,\ldots,x_1]$. Han's iterated resultant conjecture. For generic form $f(x_1,\ldots,x_n)$, one has

$${\tt Hp}(f,[x_n,\ldots,x_1])=\Delta(f).$$

The conjecture extends the equality proved in the paper for generic trivariate forms and the previously established case of generic quadratic forms in any number of variables. The general case remains open in the supplied text.