Topological multiple recurrence of weakly mixing minimal systems for generalized polynomials

Let $(X, T)$ be a weakly mixing minimal system, $p_1, cdots, p_d$ be integer-valued generalized polynomials and $(p_1,p_2,cdots,p_d)$ be non-degenerate. Then there exists a residual subset $X_0$ of $X$ such that for all $xin X_0$ $${ (T^{p_1(n)}x, cdots, T^{p_d(n)}x): nin mathbb{Z}}$$ is dense in $X^d$.