NOVELTY - The method comprises: performing high-temperature electrolysis of water and carbon dioxide in an electrolysis reactor housed in a sealed chamber; maintaining the chamber under a given pressure; supplying water vapor and carbon dioxide to a cathode of the reactor under the given pressure; performing catalytic conversion of water vapor in reaction zone that is radially arranged to the same reactor under pressure and contains a solid catalyst (80); injecting carbon dioxide into a gap between the electrolysis reactor and the reaction zone; and recovering a product combustible gas.    USE - The method is useful for obtaining a combustible gas including methane, methanol, dimethyl ether or diesel by heterogeneous catalysis (claimed).    ADVANTAGE - The method is capable of economically obtaining the combustible gas with less energy consumption.    DETAILED DESCRIPTION - The method comprises: performing high-temperature electrolysis of water and carbon dioxide in an electrolysis reactor housed in a sealed chamber; maintaining the chamber under a given pressure; supplying water vapor and carbon dioxide to a cathode of the reactor under the given pressure; performing catalytic conversion of water vapor in reaction zone that is radially arranged to the same reactor under pressure and contains a solid catalyst (80); injecting carbon dioxide into a gap between the electrolysis reactor and the reaction zone; and recovering a product combustible gas in the gap between reaction zone and a radial wall of the chamber and/or unconverted water vapor produced in the electrolysis step. The catalytic conversion step is carried out using hydrogen produced in the electrolysis step. The reaction zone is further concentrically arranged around the reactor. The electrolysis step is carried out at a temperature of 600-1000 degrees C and at a pressure of 0-100 bars. The wall of the chamber is cooled at a temperature below a saturation temperature of water at the given pressure of the chamber so that the recovered combustible gas is cooled within the chamber. The combustible gas is separated and cooled with water by gravity on a bottom of the chamber. The method further comprises a methanation process. The reactor is maintained at a pressure of 30-25 bars and at a temperature of 800 degrees C. The reaction zone is maintained at a temperature of 400 degrees C. The wall of the chamber is maintained at a temperature less than 230 degrees C. INDEPENDENT CLAIMS are included for:    (1) a reactor;    (2) a system for obtaining a combustible gas; and    (3) a method for operating a reactor.    DESCRIPTION OF DRAWING(S) - The figure shows a schematic partial perspective view of a reactor.    Primary support (9)    Secondary support (10)    Heat exchanger (12)    Lid (70)    Catalyst. (80)