Here is a 'KQRR vs krrp' mate in 3 chess problem generated autonomously by the program, Chesthetica, using the approach known as the DSNS from the sub-field of AI, computational creativity. Depending on the type and complexity of the problem desired, a single instance of Chesthetica running on a desktop computer can probably generate anywhere between one and ten problems per hour. The position below contains 8 pieces which means it simply could not have been derived even from an existing endgame tablebase which is presently limited to 7 pieces.
White to Play and Mate in 3
Chesthetica v11.32 (Selangor, Malaysia)
Generated on 30 Aug 2019 at 11:55:33 PM
Some of the earliest chess problems by humans are over 10 centuries old but original ones by computer are very recent. Now, let's see what else there is to say. Give me a moment. Try to solve this as quickly as you can. If you like it, please share with your friends. Note that not all the chess problems are like this. They cover quite the spectrum of solving ability and there are thousands published already.
A Similar Chess Problem by Chesthetica: 02510
Solution
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