Suppose a person testifies, under oath, on two different occasions, as to certain events. The two sworn testimonies are in direct and clear contradiction to each other. For example, one time Jane Doe testifies that Joe Smith was present at a crime scene, and the next testimony is that he was not (ever) present.
There is no independent way to determine which statement is true, and which is false.
Nevertheless, one of the statements must be false. Can a charge of perjury be laid against Jane Doe in such a case, without specifying which actual testimony? If a charge of perjury is impossible, are there other false statement charges that could be brought?