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To accurately answer your question the tires will bulge up or down in the middle based on the air pressure - but they will bulge.
Keep it off the street and you'll be fine.
Take it on the street and they will wear funny no matter what pressure you run. Not to mention if you buying the tires new, you'll void the warranty completely*.
I am unaware of any tire manufacturer approving a rim width of less than 8.0 inches for a 12.50 tire, so this will hold true regardless of the on or off road use.
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