This paper is intended to construct a decidable first-order logic for appropriately expressing medical reasoning which may require to express not only time-dependency, paraconsistency, constructiveness, resource-sensitivity, but also order-sensitivity. A first-order temporal paraconsistent non-commutative logic is introduced as a Gentzen-type sequent calculus. This logic has no structural rules and has some bounded temporal operators and a paraconsistent negation connective. This logic is shown to be decidable and cut-eliminable.