After further investigation Joecaption is correct, there is a 1/4 layer of plywood between the sheet vinyl and the 23/32 subfloor.
Well of course there is, resilient flooring is not installed directly on the subfloor.
So, removed the 1/4" with the flooring still attached in one operation. Prep the old subfloor and install the thickest underlayment you can stand, but no thinner than 3/8". I recommend 1/2" or 5/8". Be sure it's not cheapo CDX sheathing ply, you want B/C underlayment grade with exterior glue bonded plies.
Then the heat mats, self leveling and then Ditra and tiles. What kind of tiles are you planning?