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We construct a model for cohomology of a space $X$ equipped with a torus $T$action, whose homotopy orbit space $X_{T}$ is formal. This model representsKoszul complex of its equivariant cohomology. Studying homological propertiesof modules over polynomial ring we derive new bounds on homological rank(dimension of cohomology ring) of $X$ equipped with almost free torus action.We give a proof of toral rank conjecture for spaces with formal quotient in thecase of torus dimension $\le5$.

On almost free torus actions and Horrocks conjecture