Now that I'm looking at this on the computer instead of my phone I believe I see a "7,85" in the markings under the barrel. That's your bore size (7.85mm or 0.309"). The Mauser I had with a 7,85 bore was also marked "8,2" for the groove diameter (which would be 0.323").

According to folks on this board smarter than me, the "156,14" is a gauge diameter indicating a 7.87mm bore at the time of proof (though that gauge number is not intended to be exact).

So I think you have an 8x57IS.