I have made a little bit more research on this and found out this topic from X forum.
It's the exact same problem I have on a same setup. X theme, multisite and w3 total cache.
Once I disable W3 Total Cache plugin, error disappeared. I will discuss the issue with W3 Total Cache support too.
However it is still so strange that in whole internet there are only 3 instances regarding "wp-content/themes/index.php/style.css" (which is really strange directory path due to /index.php/style.css) and all related to X theme.
Anyway, I will try to solve this by myself.
However, could you please respond my other issue regarding auto update problem of X Pro theme. Since day 1 I have this problem. I can auto update all other plugins and themes except X Pro! I don't get any notification to my dashboard at all. I know I can update manually, but I would like to solve the problem instead of workaround.
Could you please assist me on this. Thanks in advance.