Context: Infrared dark clouds are the coldest and densest portions of giant molecular clouds. The most massive ones represent some of the most likely birthplaces for the next generation of massive stars in the Milky Way. Because a strong mid-IR background is needed to make them appear in absorption, they are usually assumed to be nearby. Aims: We use THz absorption spectroscopy to solve the distance ambiguity associated with kinematic distances for the IR-dark clouds in the TOP100 ATLASGAL sample, a flux-limited selection of massive clumps in different evolutionary phases of star formation. Methods: The para-H2O ground state transition at 1113.343 GHz, observed with Herschel/HIFI, was used to investigate the occurrence of foreground absorption along the line of sight directly towards infrared-dark clouds. Additional consistency checks were performed using MALT90 and HiGAL archival data and targeted Mopra and APEX spectroscopic observations. Results: We report the first discovery of five IRDCs in the TOP100 lying conclusively at the far kinematic distance, showing that the mere presence of low-contrast mid-IR absorption is not sufficient to unequivocally resolve the near/far ambiguity in favour of the former. All IRDCs are massive and actively forming high-mass stars; four of them also show infall signatures. Conclusions: We give a first estimate of the fraction of dark sources at the far distance (~11% in the TOP100) and describe their appearance and properties. The assumption that all dark clouds lie at the near distance may lead, in some cases, to underestimating masses, sizes, and luminosities, possibly causing clouds to be missed that will form very massive stars and clusters.
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