We report the first Atacama large millimeter/submillimeter array observations of MCG-03-58-007, a local ($z=0.03236pm0.00002$, this work) AGN ($L_{AGN}sim10^{45}~rm erg~s^{-1}$), hosting a powerful X-ray ultra-fast ($v=0.1c$) outflow (UFO). The CO(1-0) line emission is observed across $sim18,$kpc scales with a resolution of $sim 1,rm kpc$. About 78% of the CO(1-0) luminosity traces a galaxy-size rotating disk. However, after subtracting the emission due to such rotating disk, we detect with a S/N=20 a residual emission in the central $sim 4,$kpc. Such residuals may trace a low velocity ($v_{LOS}=170,rm km,s^{-1}$) outflow. We compare the momentum rate and kinetic power of such putative molecular outflow with that of the X-ray UFO and find $dot{P}_{out}/dot{P}_{UFO}=0.3pm0.2$ and $dot{E}_{mol}/dot{E}_{UFO}sim4cdot10^{-3}$. This result is at odds with the energy-conserving scenario suggested by the large momentum boosts measured in some other molecular outflows. An alternative interpretation of the residual CO emission would be a compact rotating structure, distinct from the main disk, which would be a factor of $sim10-100$ more extended and massive than typical circumnuclear disks revealed in Seyferts. However, in both scenarios, our results rule out the hypothesis of a momentum-boosted molecular outflow in this AGN, despite the presence of a powerful X-ray UFO. [Abridged]
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