In 2005, Dunfield, Gukov, and Rasmussen inferred the existence of a spectral sequence from the reduced three-step Khovanov-Rozansky homology of a knot to its knot Floer homology defined by Ozsv\’ath and Szab\’o. Did. The main result of this paper is a proof of this conjecture. For this purpose, we construct a bigrade spectral sequence from the $\mathfrak{gl}_0$ homology constructed by the last two authors of his to the Knot Floer homology. We use the fact that the $\mathfrak{gl}_0$ homology is equipped with the spectral sequence from the reduced three-step homology to obtain the main result. The first spectral sequence is Boxstein-type and results from subtle manipulation of the coefficients. The main tools are the quantum traces of bubbles and singular Soergel bimodules and the $\mathbb Z $ is the value cube. As an application, we speculate that the $\mathfrak{gl}_0$ homology and the reduced three-step Khovanov-Rozansky homology detect an unknot, two trefoils, a figure-eight knot and a sinkfoil.
