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Anomalies in past neutrino measurements have led to the discovery that these particles have non-zero mass and oscillate between their three flavors when they propagate. In the 2010's, similar anomalies observed in the antineutrino spectra emitted by nuclear reactors have triggered the hypothesis of the existence of a supplementary neutrino state that would be sterile i.e. not interacting via the weak interaction. The STEREO experiment was designed to study this scientific case that would potentially extend the Standard Model of Particle Physics. Here we present a complete study based on our full set of data with significantly improved sensitivity. Installed at the ILL (Institut Laue Langevin) research reactor, STEREO has accurately measured the antineutrino energy spectrum associated to the fission of 235U. This measurement confirms the anomalies whereas, thanks to the segmentation of the STEREO detector and its very short mean distance to the core (10~m), the same data reject the hypothesis of a light sterile neutrino. Such a direct measurement of the antineutrino energy spectrum suggests instead that biases in the nuclear experimental data used for the predictions are at the origin of the anomalies. Our result supports the neutrino content of the Standard Model and establishes a new reference for the 235U antineutrino energy spectrum. We anticipate that this result will allow to progress towards finer tests of the fundamental properties of neutrinos but also to benchmark models and nuclear data of interest for reactor physics and for observations of astrophysical or geo-neutrinos., Comment: 34 pages, 13 figures. Final version submitted to Nature