Call it “Catch-23.” The lawsuit that a United States Army captain just filed against President Obama, alleging that the war against the Islamic State is illegal, highlights a situation almost as absurd as Joseph Heller’s novel about World War II.

The hero of “Catch-22,” Captain John Yossarian, is on a quest to get out of flying combat missions. He discovers that the only way an officer can get out of flying a bombing mission is if he’s crazy. Yet, by military logic, the fact that Yossarian wants to get out of flying combat is proof he’s sane.

That’s “Catch-22.” It was greeted with great hilarity after World War II, no doubt in part because we won the war.

The latest absurdity isn’t such a bundle of laughs. It’s underscored by that riveting new video showing the ferocity of the combat US forces are engaged in against the Islamic State — for all the president’s repeated claims that we have no ground troops in combat.

The video, turned up by the London Guardian, makes all too real how serious are the questions in a constitutionally absurd situation. Heads up for Donald Trump, Hillary Clinton, or whoever wins the election in November.

The officer suing President Obama, Captain Michael Nathan Smith, isn’t exactly like Yossarian. He’s serving in Operation Inherent Resolve in Kuwait and says he’s gung-ho for the war. Smith told the court he’s suing on a “matter of conscience.” He reckons that the war against the Islamic State is illegal, because it’s been going on for longer than is allowed by the War Powers Act that Congress passed after Vietnam.

For years Mr. Obama has claimed he has all the authority he needs to levy the war against the Islamic State, citing the Authorization to Use Military Force passed after 9/11, and also the 2003 Iraq war resolution. That’s ironica, because Mr. Obama opposed the Iraq war and announced in 2011 that the withdrawal of Yank troops would soon be done. He declared, “after nearly nine years, America’s war in Iraq will be over.”

It may be the worst mistake of his presidency (although the competition is stiff).

By mid-2014, the Islamic State was growing dangerous enough that Mr. Obama sent American GIs back to Iraq, albeit in tiny numbers; there are now reportedly more than 5,000 US military personnel in Iraq. The challenge under the War Powers Act, which limits unauthorized fighting to 60 days, sets up an amazing situation — at least for those of us who covered the Reagan administration.

Back then, left-wing Democrats loved the War Powers Act, because they thought they could use it to stop Reagan’s battle against the Communists in Nicaragua. What Smith really wants, he says, is for a federal court to declare the war illegal absent a new authorization passed by Congress and that if Congress fails to act, withdrawal is required.

Where it starts to get absurd is that Obama, the defendant, seems to agree with him. In February 2015, he asked Congress to pass a resolution authorizing the fight against the Islamic State, even while saying he already has such authority.

But Mr. Obama’s idea of a resolution turns out to be a poison pill. It authorizes only a “limited” war (if we’d bought into limitations in 1941, we’d all be speaking Japanese and German). And its authority would expire after only three years.

Meantime — wait for it — it repeals the indefinite Iraq war authority the president already claims. So the next president could soon be left with no permanent authority to fight this war and an expired authority to fight the Islamic State.

That’s what I call “Catch-23.” Joseph Heller couldn’t have thought of a plot so bizarre — a president who’d rather not get clear authority for the current conflict unless he gets to tie his successors’ hands. Plus, Congress doesn’t really want to do anything, lest it take on ownership of either the war or a retreat. All in all, it’s an issue tailor-made for a Trump-Clinton contest.

The thing to remember in all of this is that there are two ways for America to get into a state of war. We can start it — or the enemy can. In the latter case, we’re at war whether Congress declares it or not.

In my book, that’s “Catch-1.”

This column first appeared in the New York Post.