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The study of nuclear fragmentation plays a central role in many important applications: from the study of Particle Therapy (PT) up to radiation protection for space (RPS) missions and the design of shielding for nuclear reactors. The FragmentatiOn Of Target (FOOT) collaboration aims to study the nuclear reactions that describe the interactions with matter of different light ions (like H1, He4, C12, O16) of interest for such applications, performing double differential fragmentation cross section measurements in the energy range of interest for PT and RPS. In this manuscript, we present the analysis of the data collected in the interactions of an oxygen ion beam of 400 MeV/u with a graphite target using a partial FOOT setup, at the GSI Helmholtz Center for Heavy Ion Research facility in Darmstadt. During the data taking the magnets, the silicon trackers and the calorimeter foreseen in the final FOOT setup were not yet available, and hence precise measurements of the fragments kinetic energy, momentum and mass were not possible. However, using the FOOT scintillator detectors for the time of flight (TOF) and energy loss (ΔE) measurements together with a drift chamber, used as beam monitor, it was possible to measure the elemental fragmentation cross sections. The reduced detector set-up and the limited available statistics allowed anyway to obtain relevant results, providing statistically significant measurements of cross sections eagerly needed for PT and RPS applications. Whenever possible the obtained results have been compared with existing measurements helping in discriminating between conflicting results in the literature and demonstrating at the same time the proper functioning of the FOOT ΔE-TOF system. Finally, the obtained fragmentation cross sections are compared to the Monte Carlo predictions obtained with the FLUKA software.