TECHNOLOGY FOCUS - INSTRUMENTATION AND TESTING - Preferred Components: The oxide has a perovskite structure. The carbon monoxide extraction part further includes: a heating part configured to heat the carbon dioxide adsorbing member with exhaust gas, to a one of a first temperature of 200-300 degrees C and a second temperature of 600-700 degrees C; a cooling part configured to cool the carbon dioxide adsorbing member to a room temperature; and a pump configured to evacuate the processing container. The carbon monoxide recycling part includes: a tank configured to retain the carbon monoxide generated by the reduction in the carbon monoxide extraction part; and a carbon monoxide gas adding part configured to add the carbon monoxide in the tank to the fuel gas. The fuel system further comprises a culturing tank configured to be fed with the exhaust gas from the carbon monoxide extraction part, where the exhaust gas includes a remaining portion of the carbon dioxide unreduced in the carbon monoxide extraction part, and to culture algae using the remaining portion of the carbon dioxide as a nutrient. Preferred Method: The method further comprises feeding the carbon monoxide extracted by the reduction as a part of a fuel gas fed to the fuel cell. The carbon dioxide adsorbing member: adsorbs the carbon dioxide molecule by capturing the second oxygen atom of the carbon dioxide molecule with an oxygen deficiency of the carbon dioxide adsorbing member in adsorbing the carbon dioxide molecule; decomposes the carbon dioxide molecule into the second oxygen atom and the carbon monoxide molecule while retaining the second oxygen atom captured with the oxygen deficiency by heating to the second temperature in desorbing the carbon monoxide molecule; and releases the second oxygen atom captured with the oxygen deficiency by heating to the third temperature in desorbing the second oxygen atom. The reduction of the carbon dioxide in the exhaust gas to the carbon monoxide is performed in at least a first system and a second system of the fuel cell system, where the first and second system each includes the carbon dioxide adsorbing member, and when adsorbing the carbon dioxide molecule is performed in the first system, an operation of the second system is changed sequentially from desorbing the carbon monoxide molecule to desorbing the oxygen atom to cooling the carbon dioxide adsorbing member, and when adsorbing the carbon dioxide molecule is performed in the second system, an operation of the first system is changed sequentially from desorbing the carbon monoxide molecule to desorbing the oxygen atom to cooling the carbon dioxide adsorbing member.