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Unfortunately, I can't think of any stories that follow your strict requirement on excluding anything that "is able to reproduce". The closest I could come is Ray Bradbury's short story, "There W...
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#3: Attribution notice added
Source: https://writers.stackexchange.com/a/2991 License name: CC BY-SA 3.0 License URL: https://creativecommons.org/licenses/by-sa/3.0/
#2: Initial revision
Unfortunately, I can't think of any stories that follow your strict requirement on excluding anything that "is able to reproduce". The closest I could come is Ray Bradbury's short story, "[There Will Come Soft Rains](http://www.jerrywbrown.com/datafile/datafile/110/ThereWillComeSoftRains_Bradbury.pdf)" (note: link goes to a PDF file). Unfortunately, there are some animals in it, and humans are referred to. Also, as Lynn noted regarding the sun, you could argue that the house is a character. The question does arise, however: with absolutely no characters, or reference to living things, what story is there to tell? There would be no room for character development, and I can't imagine much conflict arising from such a story, either.