Rationality conjecture for bases of simply connected Seifert bundles

Let

$$f:L\to \left(S,\sum \left(1-\frac{1}{m_i}\right)D_i\right)$$

be a 5-dimensional Seifert bundle with $L$ smooth. Assume that $L$ is a simply connected rational homology sphere. Rationality conjecture. Then $S$ is a rational surface.

This conjecture is identified as the missing piece in the description of Seifert bundle structures on rational homology spheres. If true, it would impose further restrictions on the base surface $S$; the source does not establish it.