NAFILs are non-associative finite invertible loops. These loops form a class that includes IP, Moufang, and Bol loops. This paper deals with the computer generation and determination of all non-isomorphic NAFILs of order n = 5 , 6 , 7. Results show that the number I_n of non-isomorphic NAFILs of order n are: I₅ = 1, I₆ = 33, and I₇ = 2333.