I think it should be 'without fail'. It's an English idiom meaning for certain; absolutely. 'fail' here is a noun. Example: -I'll be there at noon without fail. -The plane leaves on time every day without fail. Hope this answers your question? Falling Angel

After thinking for a while, I agree with Falling Angel :)

d. neglect

you know now that i look at it because there is no "A" after "doubt" i think i could be "without fail"

A. is the most logical answer and yes it should be "without a doubt"