How is first-order logic complete but not decidable?

Why doesn't completeness imply decidability for first-order logic? First order logic is complete, which means (I think) given a set of sentences A and a sentence B, then either B or ~B can be arrived at through the rules of inference being applied to A. If B is arrived at, then A implies B in every interpretation. If ~B is arrived at, then A implies ~B in every interpretation. First order logic is undecidable, which means (again, I think) that given a set of sentences A and a sentence B, there is no procedure for determining whether A implies B (i.e. it's not the case that A are true and B is false) in all interpretations. Why doesn't this work: Enumerate all strings x. If x encodes the valid derivation of B from A, accept. If x encodes the valid derivation of ~B from A, reject. Because of completeness, eventually this process will stumble across an x which is either a proof of B or ~B from A. If B, then A implies B in all interpretations. If ~B, then it is not the case that A implies B in all interpretations. So FOL is decidable. But it's not, so I must have the wrong definition of either completeness or decidability.