Can't fit 650x23C tire into 559x17 rim!

[athletic]

I've been trying to fit my new Conti GP4000S II tires (650x23C) into my Mavic 317 rims (559x17) for almost an hour but couldn't achieve it!
I tried both inflating the tube, deflating it as well, used my both hands but it keeps popping off from the rim wall.

I had checked Sheldon Brown's size chart and knew that these tires would be equal to 26x1" (ish) tires but I've been frustrated with the fitting.
I know some new foldable tires may give you hard time for the first time but this seems like the diameter is larger. It's not 700C for sure, nor 27.5" (and there is no option with this width for 27.5" wheels). The width is okay, but the diameter seems tad larger than my 26" rims, or I just need to take it to my local bike shop.

What do you think? Any experience in this?

EDIT : I just found out on its package that it was 23-571 (instead of 559), probably that was the difference but does it mean that these tires are made for another type of rims? I know only 26"-27.5"-29" and 700C rims take place in mtb and road bikes. 650C tires were made once for old triathlon bikes (which my gf previously owned), I thought those bikes had 26" narrow rims.

What should I do now :S

[basilic]

You answered your own question, no? just buy the right size tires. Schwalbe durano or kojak are slicks that come in ISO 559, Conti gatorskins too, there must be others.