Infinite Regresses, Infinite Beliefs

One way of mapping part of the domain of epistemology is
to represent various theories as responses to the following
argument:
(I) A belief (strictly, a token state of belief) is
justified only if a justified belief is a reason for it.
(Premiss.)
(II) There are justified beliefs. (Premiss.)
(III) The proper ancestral of the reason-relation
is irreflexive. (Premiss.)
(IV) There is an infinite sequence (strictly, a
sequence with infinite range) of justified beliefs
each of which is a reason for its predecessor,
if any. (From (I) to (III).)
(V) There is no such sequence. (Premiss.)
(VI) There both is and is not such a sequence.
(From (IV) and (V).)
(VII) Not-(I) / not-(II) / not-(III) / not-(V). (Reductio.)