Would the same equilibrium concentration of carbon dioxide, carbon monoxide and oxygen always result for a given initial atomic carbon fraction?

**Question:** Starting with a gas mixture of some combination of gases containing carbon and oxygen with a total carbon atomic fraction $f$, would it always reach the same equilibrium proportions of $\ce{CO2 + O2 + CO}$?


For example if I had an equal number of $\ce{CO2}$ and $\ce{O2}$ molecules then $f=0.2$, but so would two molecules of $\ce{CO2}$ for every three molecules of $\ce{O2}$. If I started with either mixture in this example, would I end up with the same equilibrium mixture of $\ce{CO2}$ and $\ce{CO}$ and $\ce{O2}$?


**Simplifying assumptions:** Assume $\pu{273K}$ and $\pu{610Pa}$ if necessary, the answer may be as simple as "yes it would" or "no it wouldn't, because...", a supply of ionizing radiation from space (hard UV and energetic cosmic ray particles) and a billion years, and ignore transmutation of elements by those particles.




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Background and motivation is from my Space Exploration SE question [Are Mars' atmospheric CO₂, O₂ and CO in equilibrium? Are sunlight or chemical reactions involved?](https://space.stackexchange.com/q/41094/12102), which begins:



> 
> According to the NASA JPL video linked below the top five gases comprising the martian atmosphere include $\ce{CO₂, O₂}$ and $\ce{CO}$. Do the proportions reflect some chemical equilibrium? Are sunlight or chemical reactions involved in maintaining these proportions?
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```
Component     Fraction
   CO2          95.9%
   Ar            2.0%
   N2            1.9%
   O2            0.14%
   CO            0.06%

```


> 
> The NASA JPL video **[Crazy Engineering: Making Oxygen on Mars with MOXIE](https://youtu.be/7rzu7TTkIMA)** is linked in [How many square meters of solar panel to power a MOXIE-like oxygen source per person?](https://space.stackexchange.com/q/41091/12102).
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