IF OR, problem if the reference cell contain formula

Any text string (including null string "") is greater than any number, so the greater than tests both return TRUE. You either need to change the formula in column F so that it returns something other than null string (maybe -1 and suppress the display of the negative number using number formatting), or you need to change the formula in column I to test for the null string case and choose accordingly [maybe IF(F1="","",current formula)].

Will either of those options work?

Maybe try

=IF(OR(D1>1,N(F1)>1),"ok","no")