Table-to-text systems generate natural language statements from structured data like tables. While end-to-end techniques suffer from low factual correctness (fidelity), a previous study reported gains when using manual logical forms (LF) that represent the selected content and the semantics of the target text. Given the manual step, it was not clear whether automatic LFs would be effective, or whether the improvement came from content selection alone. We present TlT which, given a table and a selection of the content, first produces LFs and then the textual statement. We show for the first time that automatic LFs improve quality, with an increase in fidelity of 30 points over a comparable system not using LFs. Our experiments allow to quantify the remaining challenges for high factual correctness, with automatic selection of content coming first, followed by better Logic-to-Text generation and, to a lesser extent, better Table-to-Logic parsing.