Van der Waerden spaces and Hindman spaces are not the same

A Hausdorff topological space $X$ is van der Waerden if for every sequence $(x_n)_{n\in\omega}$ in $X$ there is a converging subsequence $(x_n)_{n\in A}$ where $A\subseteq \omega$ contains arithmetic progressions of all finite lengths. A Hausdorff topological space $X$ is Hindman if for every sequence $(x_n)_{n\in\omega}$ in $X$there is an IP-converging subsequence $(x_n)_{n\in FS(B)}$for some infinite $B\subseteq\omega$.

We show that the continuum hypothesis implies the existence of a van der Waerden space which is not Hindman.