In some alternate universe, this might actually prove worthwhile. During their opening exchange in today’s House Oversight hearing, chair Jason Chaffetz asked FBI Director James Comey whether his investigation looked into whether Hillary Clinton lied under oath when she testified to Congress that she had neither received or transmitted classified information through her private e-mail system. Shaft seemed stunned when Comey said they hadn’t — and that they would have needed a referral from Congress to investigate it.

“You’ll get one,” Chaffetz promised:

.@jasoninthehouse: Did FBI review statements @HillaryClinton made about emails under oath? https://t.co/YkPMdsoEmE pic.twitter.com/pyQid15rR0

— CBS News (@CBSNews) July 7, 2016

Trey Gowdy tried barking up the same tree:

.@TGowdySC goes over statements @HillaryClinton made about emails; FBI director responds https://t.co/YkPMdsoEmE pic.twitter.com/FqGwyORNTg

— CBS News (@CBSNews) July 7, 2016

It won’t take much effort for the House to produce a referral on the perjury question. The House has a large enough Republican majority to muscle that through. The Department of Justice may or may not be able to tell the FBI to stand down from such a probe. If the DoJ did quash such an inquiry, there might be a political price to pay.

But what if the FBI did start an investigation into potential perjury? It would take months, and might not be concluded before the election. The likelihood of producing a referral for prosecution is about nil.

Perjury isn’t as easy to prove as simply contradicting a sworn statement. One has to prove that the defendant knowingly and intentionally lied about a material point while under oath. Even more so than with 18 USC 793 (f), you have to find intent and materiality. Hillary can simply say that she had no recollection of ever transmitting classified material, and it would require the DoJ to prove that she did recall it and lied purposefully, rather than simply have a concrete but mistaken belief. The burden of proof will be on the prosecutor, not the defendant, to show that difference.

Prosecution of perjury in Congressional testimony is exceedingly rare, both for that reason and because most Congressional hearings involve political considerations. Nine years ago, P.J. Meitl wrote an analysis specific to prosecutions for lying to Congress, and found only a half-dozen attempts in six decades:

Almost no one is prosecuted for lying to Congress; in fact, only six people have been convicted of perjury or related charges in relation to Congress in the last sixty years.6 There are two possible causes for such a result: either almost all – far above 99% – of those who testify to Congress do so truthfully or Congress and prosecutors rarely successfully prosecute the crime of lying to Congress. Logic and history indicate the latter.

Meitl isn’t necessarily happy about it:

The low number of successful prosecutions is indicative of a potentially larger problem – lying to Congress has become accepted. This is due to a number of reasons: the applicable statutes impose considerable hurdles in terms of proof and offer strong defenses, a lack of political will to enforce the law, and an increasing realization on the part of witnesses and the attorneys who represent them that prosecutions for lying to Congress are extremely rare.

There are three potential statutes through which such a prosecution could be offered, but all three require proving willful lying under oath. There is another problem with this, too — the rarity of Congressional demands for enforcement through prosecution. Comey made his case on Tuesday and again today on the fact that “no reasonable prosecutor” would have gone to court with an 18 USC 793(f) case. Comey could simply rely on precedent here as well to shrug off any findings that Hillary may have willfully lied under oath.

So, don’t get your hopes up. Also, don’t expect much to come from the demands for the transcripts of Hillary’s interview with the FBI on Saturday either. Comey made it clear that he doesn’t have any issues with her honesty during the interrogation:

FBI Director James Comey told lawmakers on Thursday that Democratic presidential candidate Hillary Clinton did not lie to the FBI about her handling of emails as secretary of state and did not break the law.

It’s the end of the line, at least in terms of law enforcement.