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Carbon is an essential element for life on Earth, and the relative abundances of major carbon species (CO _2 , CO, and CH _4 ) in the atmosphere exert fundamental controls on planetary climate and biogeochemistry. Here we employed a theoretical model of atmospheric chemistry to investigate diversity in the atmospheric abundances of CO _2 , CO, and CH _4 on Earth-like lifeless planets orbiting Sun-like (F-, G-, and K-type) stars. We focused on the conditions for the formation of a CO-rich atmosphere, which would be favorable for the origin of life. Results demonstrated that elevated atmospheric CO _2 levels trigger photochemical instability of the CO budget in the atmosphere (i.e., CO runaway) owing to enhanced CO _2 photolysis relative to H _2 O photolysis. Higher volcanic outgassing fluxes of reduced C (CO and CH _4 ) also tend to initiate CO runaway. Our systematic examinations revealed that anoxic atmospheres of Earth-like lifeless planets could be classified in the phase space of CH _4 /CO _2 versus CO/CO _2 , where a distinct gap in atmospheric carbon chemistry is expected to be observed. Our findings indicate that the gap structure is a general feature of Earth-like lifeless planets with reducing atmospheres orbiting Sun-like (F-, G-, and K-type) stars.