We present sensitive and high angular-resolution (∼0"2-0"3) (sub)millimeter (230 and 345 GHz) continuum and CO(2-1)/CO(3-2) line archive observations of the disk star system in UX Tauri carried out with the Atacama Large Millimeter/Submillimeter Array. These observations reveal the gas and dusty disk surrounding the young star UX Tauri A with a large signal-to-noise ratio (>400 in the continuum and >50 in the line), and for the first time we detect the molecular gas emission associated with the disk of UX Tauri C (with a size for the disk of <56 au). No (sub)millimeter continuum emission is detected at the 5σ level (0.2 mJy at 0.85 mm) associated with UX Tauri C. For the component UX Tauri C, we estimate a dust disk mass of ≤0.05 M⊕. Additionally, we report a strong tidal disk interaction between both disks, UX Tauri A/C, separated 360 au in projected distance. The CO line observations reveal marked spiral arms in the disk of UX Tauri A and an extended redshifted stream of gas associated with the UX Tauri C disk. No spiral arms are observed in the dust continuum emission of UX Tauri A. Assuming a Keplerian rotation we estimate the enclosed masses (disk+star) from their radial velocities in 1.4 ± 0.6 M⊙ for UX Tauri A, and 70 ± 30/sin I Jupiter masses for UX Tauri C (the latter coincides with the mass upper limit value for a brown dwarf). The observational evidence presented here lead us to propose that UX Tauri C has a close approach of a possible wide, evolving, and eccentric orbit around the disk of UX Tauri A, causing the formation of spiral arms and a stream of molecular gas falling toward UX Tauri C.