Don't resign, but also don't follow the orders. And don't say no. Just delay, make excuses, make mistakes
You sound like someone with experience in this. I've seen similar sentiments among disgruntled military members. Rather than quit, or give an easy excuse to discharge you.... give them excuses... from other people. "Oh no, Captain, I didn't get around to those particular duties because Private ShitBoot lost the equipment and I had to request more." Suddenly, you're not the problem- it's Private ShitBoot who will get chewed out. The shit rolls downhill, as we say.
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