Seeing U.S. forces track down and kill the Islamic State's leader wasn't enough for President Donald Trump. He puffed up and told a story about the raid that is unfamiliar to the military leaders who mounted it.

In recent days, Trump also related details from Syria that the Pentagon and diplomats contradicted. When the stock market went up, he took credit — "Enjoy!" — and when it went down, he blamed the impeachment inquiry despite scant evidence the market cares.

A look at some claims and the reality over the past week:

ISLAMIC STATE

TRUMP, on IS leader Abu Bakr al-Baghdadi: "He died whimpering and crying." —interview Thursday with Britain's LBC Radio.

TRUMP: "He died after running into a dead-end tunnel, whimpering and crying and screaming all the way. ...He died like a dog, he died like a coward. He was whimpering, screaming, and crying." — news conference Sunday.

THE FACTS: His top military leaders don't know what Trump is talking about.

Gen. Mark Milley, chairman of the Joint Chiefs of Staff, watched the U.S. military raid with Trump in the Situation Room.

"I don't know what the source of that was," Milley said when asked about whimpering and crying. He offered that Trump might have talked directly to members of the unit, though it is inconceivable that they would not have briefed their commanders, too.

Gen. Frank McKenzie, head of U.S. Central Command who oversaw the U.S. raid on the Islamic State leader, did not support the commander in chief's story.

"He crawled into a hole with two small children and blew himself up while his people stayed on the grounds," McKenzie said of al-Baghdadi at a Pentagon briefing Wednesday. "I'm not able to confirm anything else about his last seconds."

Defense Secretary Mark Esper, who also was in the Situation Room, demurred when asked about Trump's comments. "I don't have those details," he said on ABC's "This Week."

White House officials have declined to say how the president got his information about al-Baghdadi's alleged last moments' meltdown.

Al-Baghdadi died during the raid in Syria after he detonated a suicide vest.

IMMIGRATION

TRUMP ad: "President Trump is changing Washington ... cutting illegal immigration in half ..." — reelection ad shown Wednesday during Game 7 of the World Series.

THE FACTS: That's a distortion. The claim is based on a three-month data snapshot that ignores a spike in border arrests earlier in the year. Border arrests are down only about 10% from President Barack Obama's last month in office.

The ad features shots of Trump shaking hands with Border Patrol agents and cites "Fox News, 9/10/19" as the source for the claim.

In that Fox News interview, Ken Cuccinelli, acting director of the U.S. Citizenship and Immigration Services, said border arrests dropped by more than 50% from May to August, the latest data available at that time.

It's true that arrests and denials of entry along the Mexico border plunged from 144,116 in May to 52,546 in September, a 64% drop. But border arrests had soared to a 13-year monthly high in May. Measuring from Obama's last full month in office, the latest monthly tally in September was down only 10%. December 2016 was a high number for Obama's presidency as people rushed to cross the border before Trump's inauguration.

On top of that, border arrests are a flawed gauge of illegal immigration. It may be impossible to know how many people escaped capture, but the Border Patrol estimates 20% eluded arrest in the 2018 calendar year.

Also, an estimated 40% of people in the country illegally arrived legally and overstayed their visas. Border arrests don't take them into account. So the ad rests on partial accounting and misleading figures.

SYRIA

ROBERT O'BRIEN, Trump's national security adviser, asked about at least 100 captured IS fighters who escaped from prisons in Syria: "I think that's Twitter intel. I've seen that on Twitter as well." — interview Sunday on NBC's "Meet the Press."

TRUMP: "ISIS is under very, very strict lock and key, and the detention facilities are being strongly maintained. There were a few that got out — a small number, relatively speaking — and they've been largely recaptured." — remarks on Syria on Oct. 23.

THE FACTS: The 100 or so captured IS prisoners who were said to have escaped aren't "Twitter intel" and speculation, but an estimate coming from the Defense Department. There's also no evidence those prisoners have been recaptured as Trump stated. The administration has said their whereabouts aren't known.

It's been a hanging question since Turkey's military incursion, which began Oct. 9: Would IS fighters held by U.S.-allied Kurdish fighters known as the Syrian Democratic Forces escape in large numbers? As they push the Kurds out, the Turks are supposed to take control of the prisons.

Esper told CNN on Oct. 22 that of about 11,000 detainees in Syria, "we've only had reports of a little bit more than 100 that have escaped."

And in a House hearing the next day, James Jeffrey, the U.S. special envoy for Syria, cited the same figure. "Now over 100," he said. "We do not know where they are."

___

TRUMP, on the conflict between Kurds and Turks: "They're fighting for 1,000 years, they're fighting for centuries. — news conference Oct. 27.

TRUMP: "Let them fight their own wars. They've been fighting for 1,000 years." — remarks on Oct. 16.

THE FACTS: Not true that they've been fighting for a millennium.

There has been a 100-year effort to create a Kurdish state after the fall of the Ottoman Empire, not a conflict extending 1,000 years.

After Turkey's founding in 1923, the state pursued a policy emphasizing Turkish identity, and the Kurd minority staged a string of revolts and insurgencies, prompting bloody reprisals against their push for self-rule and Kurdish identity. Fighting has persisted since then.

Prior to Turkey's creation, the Ottoman Empire — which rose in 1299, or 720 years ago — saw some tension with its Kurdish population and a period in the mid-1800s when some Kurdish chieftains revolted.

IMPEACHMENT

TRUMP: "There was an exact transcript of the meeting. ... The transcript of the, of the call that I had with the Ukrainian President is a perfect and, and totally appropriate document." — interview Thursday with LBC Radio.

THE FACTS: It's not an "exact" or "perfect" document. Lt. Col. Alexander S. Vindman, the top Ukraine expert on the National Security Council, told House investigators this past week that the rough transcript omitted key words and phrases. He tried to add them but was rebuffed.

The memorandum of Trump's July 25 phone call to Ukrainian President Volodymyr Zelenskiy itself makes clear that it does not capture the exact words between the leaders.

The document says it is "not a verbatim transcript" and instead "records the notes and recollections of Situation Room Duty Officers and NSC policy staff assigned to listen and memorialize the conversation in written form as the conversation takes place. A number of factors can affect the accuracy of the record."

NSC refers to the National Security Council.

The House impeachment inquiry is looking into Trump's call, in which he asked Zelenskiy for a "favor" — to investigate Democrats in the 2016 election and Biden, a potential 2020 Democratic rival — as the Trump administration held up military aid for the Eastern European ally confronted by Russia.

___

TRUMP: "The Impeachment Hoax is hurting our Stock Market. The Do Nothing Democrats don't care!" — tweet Thursday.

THE FACTS: He falsely suggests that Thursday's stock market decline was driven primarily by the impeachment inquiry. The stock market has risen overall since the inquiry was announced, and the S&P 500 reached a record high on Friday.

When Trump sent his tweet Thursday morning, the S&P 500 was down about 0.5% as the House convened to vote on the ground rules for its impeachment inquiry, and eventually closed with a decline of 0.3%.

Analysts say the stock market is more concerned with the U.S.-China trade war, the strength of the global and U.S. economies, interest rates and corporate profits than the impeachment inquiry.

For instance, on Thursday, analysts pinned the market's drop largely on a weak report on business activity in the Midwest and worries about the trade war with China that Trump himself began. On Friday, a surprisingly strong report on the jobs market drove the S&P 500 and Nasdaq composite index to records, even as Democrats pushed ahead with the impeachment inquiry.

Since House Speaker Nancy Pelosi, D-Calif., announced an impeachment inquiry Sept. 24, the S&P 500 has risen 3.4%.

It's tough to tease out for certain the impact of the impeachment proceedings given all the moving parts that go into setting stock prices. But many investors on Wall Street see impeachment having only a modest effect at most, and one unlikely to last for long.

That's chiefly because few see a real threat of Trump ultimately getting removed from office by Congress. Even if the House impeaches Trump for asking another country to investigate a political opponent, investors tend to believe the Republican-controlled Senate will acquit him. So they think his lower-tax, less-regulation approach that markets like will last at least until the next election.

AFGHANISTAN vs CHICAGO

TRUMP, on murders in Chicago in recent years: "It's embarrassing to us as a nation. All over the world, they're talking about Chicago. Afghanistan is a safe place by comparison." — remarks Monday to police chiefs in Chicago.

THE FACTS: Afghanistan, at war for more than 40 years, is not safer than Chicago. More people died in violent episodes in a month in Afghanistan than were murdered in Chicago in a year.

Few direct comparisons exist of killings in Afghanistan, with a population of 38 million, and the city of Chicago, which has 2.7 million. It's true that Afghanistan's homicide rate per 100,000 was listed as 7.1 in 2017, lower than Chicago's rate of 20.7 per 100,000 in 2018.

But that statistic doesn't capture the danger of living in Afghanistan. It does not, for example, count the dead from war.

Afghanistan has no well-trained police force to investigate in a consistent way if a death was a homicide, accident or a mistake. Many other killings might not be recorded at all and in most areas of Afghanistan. Outside the major cities, no statistics of homicides are even compiled.

Danger comes from all directions and in many guises in Afghanistan.

In recent weeks, for instance, an attack believed to have been carried out by an Islamic State affiliate killed 62 people and wounded more than 100 who were assaulted as they prayed; the Taliban stormed a checkpoint in northern Afghanistan, killing at least 15 policemen in the latest attack by insurgents; a Taliban suicide attack targeted a convoy carrying officials from the country's intelligence service, killing five people including a child in eastern Nangarhar province; and Pakistani mortar and rocket fire into Afghanistan killed three women in eastern Kunar province.

At the peak of Afghanistan's most recent war that began with the U.S.-led invasion to topple the Taliban in 2001, more than 150,000 soldiers battled an insurgent force that today holds sway in roughly half the country and is at its strongest since 2001. Adding to the dangers is the growth of a brutal Islamic State affiliate that is expanding its footprint and drawing fighters driven from Syria and Iraq.

In addition to murders from crimes unrelated to war, the BBC this year found 2,307 people died in Afghanistan in 611 violent "security incidents" such as armed clashes, air strikes and explosions, in August alone. Those 2,307 deaths in one month — probably an undercount — are far higher than the number of homicides in Chicago for an entire year.

In 2016, Chicago recorded more than 760 homicides, its worst year in nearly two decades. Last year, homicides claimed more than 560 people.

ECONOMY

TRUMP: "It was just announced, as I was getting off the plane, that the S&P has hit an all-time high -- the highest in the history of our country. And that's not for rich people; that's for everybody." — remarks Monday to police chiefs.

THE FACTS: Actually, stock market gains disproportionately benefit the wealthy.

The problem with the president claiming the stock market has helped "everybody" is that the richest 10% of the country controls 84% of stock market value, according to a Federal Reserve survey.

Because they hold more stocks, wealthier Americans have inherently benefited more from the 20% gain in the Standard & Poor's index of 500 stocks so far this year. Only about half of U.S. families even hold stocks, so plenty of people are getting little to no benefit from the stock market gains.

Trump often portrays policies that have comparatively favored the wealthy as helping everyone equally if not better.

For example, the president promised in 2017 that his tax cuts would be a "middle-class miracle." But much of the magic went to millionaires.

People earning more than $1 million received a combined total tax cut last year of $36 billion, or $64,428 per filer, according to the Joint Committee on Taxation. Those earning between $50,000 to $75,000 — a solidly middle-class income — got back a combined $22.4 billion, or $819 per filer.

AUTOS

TRUMP, on some automakers siding with the Trump administration in a lawsuit over whether California has the right to set its own fuel economy standards: "Thank you ... for standing with us for Better, Cheaper, Safer Cars for Americans." — tweet Wednesday.

THE FACTS: His statement is based on inflated projected cost savings to consumers under his proposal to freeze Obama-era fuel mileage standards at 2021 levels. He also may be exaggerating the safety benefits.

California is seeking to set its own, tougher emissions standards.

General Motors, Fiat Chrysler, Toyota and 10 smaller automakers are backing the Trump administration in the lawsuit filed by the Environmental Defense Fund.

The Trump administration puts the cost of meeting Obama-era requirements at around $2,700 per vehicle. It claims buyers would save that much by 2025, over standards in place in 2016. But that number is disputed by environmental groups and is more than double the estimates from the Obama administration.

Trump is also ignoring money that consumers would save at the gas pump if cars get better mileage. A study released in August by Consumer Reports found that the owner of a 2026 vehicle will pay over $3,300 more for gasoline during the life of a vehicle if the standards are frozen at 2021 levels.

Trump's assertion that cars would be substantially safer also is in dispute. His administration argues that cheaper vehicles would allow more people to buy new ones that are safer, cutting roadway deaths by 12,700 through the 2029 model year. But Consumer Reports says any safety impact from changes in fuel mileage standards are small and won't vary much from zero.

Associated Press writers Elliot Spagat, Kathy Gannon, Stan Choe, Alex Veiga, Tom Krisher, Robert Burns and Lolita C. Baldor contributed to this report.