Strictly speaking, cows emit CH4 by belching, not farting ... and they don't have to be home ... which as good an answer your posting deserves .
And all the CH4 that the cows can make aren't going to fog your film either.
You can change the conditions of the experience all you want to ... and each change will change the results ... that's well known in science and one of the most important jobs of the peer-review team of any reputable scientific publication ...
What change in conditions? Other than eliminating visible light. The counters, walls, and floors of the dark room are still warmer than the air in the room and are therefore radiating...maybe you are saying that CO2 can only back radiate outside but absorbs and emits differently? You have warmer surfaces radiating into the air...you have an even higher concentration of CO2 inside than you have outside...the conditions are essentially the same...but no back radiation fogging the film...just as there is no back radiation fogging the film outside...the only difference is that you have completely eliminated light...and viola....no more fogging film.
You will believe what you want to believe and it is highly doubtful that you could be convinced otherwise...never mind empirical evidence...you have a terribly flawed mathematical model and belief....which trumps all...
you're not going to try this, because you know I'm right ...
There is no point, because I know that you are wrong....it isn't dark just because the moon isn't out...starlight...or ambient light reflected from clouds is enough to fog film...any trace of light is enough to fog film. I have spent plenty of time in the darkroom, where there is plenty of radiation emitting from the solid surfaces, and plenty of CO2 to back radiate and fog film if such a thing were possible...but what do you know...it never happens...never ever...no matter how much your mathematical model says so.
This is part of your "my eyes are closed and you can't make me open them" religious philosophy, like you think murderous glaciers are cool or something ... "all hail intelligent photons, they're smarter than me so they must be smarter than you" ...
Sorry guy...you are the one closing your eyes to empirical evidence...unless you care to explain why a higher concentration of CO2 inside would refuse to fog the film while the lower concentration outside would be more than obliging.
And intelligent photons? Are you another one who believes that everything must possess intelligence in order to obey the laws of physics? All hail smart rocks that know to fall down when dropped...and smart air which knows that it can not rush into the punctured tire to fill it up...and smart water which knows that it must flow downhill.
The film fogs ... I've done something similar (on accident) ... just because you can't explain why doesn't mean I can't ... ah, you've covered your ears now, such a shame, the third part is covering your mouth, remember? ...
Of course the film fogs outside.....it is because it is never truly dark outside...not the sort of dark you can create in a dark room....And your film fogs because of that...not because you wish it were back radiation from CO2...or CH4...or any other absorbing gas you care to name...