Oral title: AGN feedback does not destroy cold molecular gas in local luminous Seyfert galaxies Oral abstract: I will report on a controlled study of CO in a complete sample of the most luminous nearby Seyfert galaxies from the LLAMA survey, the most advanced to date. Using constraints on gas fractions and star-formation efficiencies over the inner kpc, we test for the influence of the AGN on the very raw material of star-formation. We find no difference between AGN and inactive galaxies; the star-formation efficiencies in the centres of Seyferts are consistent with their larger-scale discs. Our results highlight the resilience of star-forming molecular gas to the effects of AGN feedback.