We apply time-dependent R-matrix theory to study inner-shell ionization of C atoms in ultrashort highfrequency light fields with a photon energy between 170 and 245 eV. At an intensity of 10 17 W/cm 2 , ionization is dominated by single-photon emission of a 2 electron, with two-photon emission of a 1s electron accounting for about 2-3% of all emission processes, and two-photon emission of 2 contributing about 0.5-1%. Three-photon emission of a 1s electron is estimated to contribute about 0.01-0.03%. Around a photon energy of 225 eV, two-photon emission of a 1s electron, leaving C + in either 1s2s2p 3 or 1s2p 4 , is resonantly enhanced by intermediate 1s2s 2 2p 3 states. The results demonstrate the capability of time-dependent R-matrix theory to describe inner-shell ionization processes including rearrangement of the outer electrons.