Washington (CNN) President Donald Trump was asked Wednesday if he is "okay" with Turkish President Recep Tayyip Erdogan saying Tuesday that "we will never declare a ceasefire" in Syria.

Trump's response: "He didn't say that at all."

While we can't know what Erdogan might have told US officials in private, his public comments were unequivocal.

Trump's inaccurate denial was one of at least 12 false claims he made to reporters during an Oval Office meeting and subsequent joint press conference with Italian President Sergio Mattarella.

Here's what we found:

The troops and Syria, part 1

Touting his decision to remove troops from northern Syria, Trump said, "We're bringing our soldiers back home, and we've done a great job."

Facts First: The soldiers are not being brought "home," at least not yet. Trump : The soldiers are not being brought "home," at least not yet. Trump announced Monday that "United States troops coming out of Syria will now redeploy and remain in the region to monitor the situation and prevent a repeat of 2014, when the neglected threat of ISIS raged across Syria and Iraq." He also announced last week that 1,800 more troops would be deployed to Saudi Arabia.

The troops and Syria, part 2

Trump said that the US military deployment to Syria was initially supposed to last just "one month."

Facts First: There was never any specific timeline for the US military's involvement in Syria, much less a timeline of a mere 30 days.

"There was never a 30-day timetable on the US presence in Syria," said Syria expert Steven Heydemann, a professor of government and director of the Middle East Studies program at Smith College. "The previous administration, and officials serving in this administration, have never offered a fixed timetable for the US mission. Official statements have emphasized that the presence of US forces would be short, limited in scope, and small. But beyond general comments along those lines, there has been no statement indicating it would end after 30 days."

The Ukraine conspiracy

Trump repeated his debunked allegations about a Ukrainian conspiracy related to the Democratic National Committee computer servers that were hacked in 2016.

"Where is the server? I want to see the server. Let's see what's on the server. So the server, they say, is held by a company whose primary ownership individual is from Ukraine. I'd like to see the server," he said.

Facts First: Trump appeared to be referring to : Trump appeared to be referring to CrowdStrike , a publicly traded cybersecurity firm that was hired to investigate the hack of DNC servers in 2016. The company was co-founded by Dmitri Alperovitch, an American citizen who was born in Russia, not Ukraine . There is no evidence that any physical DNC server is currently being "held" by CrowdStrike; such companies do not typically take possession of the actual servers to conduct their analysis.

CrowdStrike -- which, like former special counsel Robert Mueller, attributed the hack to Russia -- said in a previous statement: "With regards to our investigation of the DNC hack in 2016, we provided all forensic evidence and analysis to the FBI. As we've stated before, we stand by our findings and conclusions that have been fully supported by the US Intelligence community."

The company has been hired by Republicans as well as Democrats. It has been paid during Trump's presidency by the National Republican Congressional Committee and National Republican Senatorial Committee, public records show.

The whistleblower

Trump claimed again that the whistleblower who filed a complaint about his July call with Ukrainian President Volodymyr Zelensky was inaccurate, saying, "The whistleblower's report was totally wrong. The whistleblower didn't know what he was talking about or was given false information or was even worse than that."

Facts First: As we've : As we've explained repeatedly, the whistleblower's account of the call was proven highly accurate by the rough transcript released by the White House.

Stock market ownership

"If you look at people's stocks, their 401(k)s, if you look at anything you want to look at, they're far better off now than they probably ever have been in this country. Record stock markets. And don't forget, stock market is not just rich people. It's all people. Because all people own in the stock markets," Trump said.

Facts First: Trump was right that it's not only rich people who own stocks, but it's not true that "all" people own stocks. Roughly : Trump was right that it's not only rich people who own stocks, but it's not true that "all" people own stocks. Roughly half of Americans owned stocks as of 2017, according to academic studies and polls.

Wealthy people own a disproportionate share of stocks. A 2017 paper by New York University economist Edward Wolff found that the top 10% of households owned 84% of stocks in 2016.

The Soviet Union's "downsizing"

Warning of the perils of getting involved in unwinnable wars, Trump said, "You know, Russia was involved in Afghanistan. It used to be called the Soviet Union -- now it's called Russia for a reason. Because they lost so much money in Afghanistan that they had to downsize. A very big downsizing."

Facts First: This was an exaggeration. Experts say the Soviet Union's failed war in Afghanistan was far from the only reason for its collapse, though it did contribute to it. (We'll ignore Trump's use of the term "downsizing" to describe the dissolution of the Soviet Union.) You can read a longer fact check : This was an exaggeration. Experts say the Soviet Union's failed war in Afghanistan was far from the only reason for its collapse, though it did contribute to it. (We'll ignore Trump's use of the term "downsizing" to describe the dissolution of the Soviet Union.) You can read a longer fact check here

"Corruption"

Trump recited his usual complaints about how he was treated by US intelligence officials involved in investigating his campaign's relationship with Russia, including former FBI Director James Comey and former deputy director Andrew McCabe. This time, he accused former President Barack Obama of being involved in the supposed "corruption."

"There was a lot of corruption. Maybe it goes right up to President Obama. I happen to think it does," Trump said.

Facts First: There is simply no evidence of Obama corruption.

Military spending

Trump said, "I spent $2.5 trillion over the last almost three years rebuilding our military."

Facts First: Trump was exaggerating. As noted by Todd Harrison, director of defense budget analysis at the Center for Strategic and International Studies, total defense spending for fiscal years 2017, 2018 and 2019 was $2.05 trillion -- and that includes more than three-and-a-half months of Obama's tenure, since the 2017 fiscal year began in October 2016.

Harrison said he thinks Trump must have been including military funding for the 2020 fiscal year to get to "$2.5 trillion" figure -- but the 2020 fiscal year has just started, and "the actual appropriations bills for FY20 are still pending in Congress."

The nuclear arsenal

Trump said of the US nuclear arsenal: "Our nuclear has been totally updated and in some cases new."

Facts First: Experts say that Trump has not yet implemented significant changes to the US nuclear arsenal. "I am not aware that Trump can claim to have done anything for the state of the nuclear arsenal -- but nothing urgent needed to be done anyway," said Scott Kemp, director of the Massachusetts Institute of Technology Laboratory for Nuclear Security and Policy, who served as a State Department adviser on arms control early in the Obama administration.

You can read a longer fact check here

NATO contributions

Trump took credit for NATO member states increasing their defense spending, saying that Secretary General Jens Stoltenberg is "going around saying that President Trump was able to raise over $100 billion last year, which is true."

Facts First: This is at least a slight exaggeration -- and one Stoltenberg gently tried to correct when he met with Trump in April. Though Stoltenberg has indeed given Trump credit for pressuring NATO countries into boosting spending, he has said, to Trump and in other forums, that the extra $100 billion the countries will spend on their own militaries will come : This is at least a slight exaggeration -- and one Stoltenberg gently tried to correct when he met with Trump in April. Though Stoltenberg has indeed given Trump credit for pressuring NATO countries into boosting spending, he has said, to Trump and in other forums, that the extra $100 billion the countries will spend on their own militaries will come by the end of 2020 , not that it happened "last year."

Democrats and borders

As usual, Trump claimed of Democrats, "They want open borders."

Facts First: Even 2020 Democratic presidential candidates who advocate the decriminalization of the act of illegally entering the country, such as Massachusetts Sen. Elizabeth Warren and former Housing and Urban Development Secretary Julián Castro, do not support completely unrestricted migration, as Trump suggests.

Here are some claims we can't definitively call false at the moment but are either dubious or require more context:

Facebook and the election

Trump appeared to refer to a flawed study that dubiously alleged that Google bias was sufficiently bad to have shifted at least 2.6 million votes away from Trump in the 2016 presidential election -- except he said somebody had found he lost two million votes or more "because of Facebook."

Facts First: The study in question was about Google in particular. While the author, Robert Epstein, did criticize Facebook in congressional The study in question was about Google in particular. While the author, Robert Epstein, did criticize Facebook in congressional testimony in July, he did not find that Facebook cost Trump 2 million votes.

Trump was vague here, saying that "somebody" said he had lost 2 million votes or more, so it is possible he was referring to something else. Regardless, there is no evidence for Trump's repeated claim that he was robbed of millions of votes in some manner or another.

The Kurds and ISIS prisoners

Trump expressed his hope that ISIS prisoners in Syria will continue to be guarded, accusing the Kurds of having "opened up a couple doors to make us look as bad as possible" and to "create more havoc."

Facts First: US officials : US officials told CNN last week that the Kurds have not intentionally released ISIS prisoners to embarrass the US. In a statement to Foreign Policy, the political wing of the Syrian Democratic Forces also denied having done so.

The SDF has had to remove troops guarding prisons and camps holding ISIS fighters and those displaced by the fight against ISIS.

"We already did not have professional jails or professional prisons to keep those prisoners in," SDF spokesman Mustafa Bali said. "The Turkish invasion to our region is going to leave a huge space, because we are forced to pull out some of our troops from the prisons and from the (displaced people) camps to the border to protect our people."

Since it's at least possible Trump was referring to intelligence information not known to the public, we won't flatly declare that the claim isn't true. But no evidence has emerged to suggest it is.

Ammunition levels

Trump repeated a story he has been telling over the last week about the condition of the military early in his presidency.

"When I was thinking about having to do something," he said, "one of our generals came in to see me and said, 'Sir, we don't have ammunition.' I said, 'That's a terrible thing you just said.' He said, 'We don't have ammunition.'"

Facts First: We can't be sure what a general might have privately told Trump, so we'll give Trump leeway to recount this supposed story without repeating the claim in his own words, but it's clearly not true that the world's most powerful military didn't have ammunition, period, when he was inaugurated in January 2017.

However, there are some real facts underlying the dubious tale. The US did have a shortage of certain precision-guided bombs at the time, according to military officials. You can read our full fact check here

The WTO decision

Trump took credit for a World Trade Organization decision to give the US permission to impose $7.5 billion in tariffs on European products in response to European subsidies to airplane manufacturer Airbus.

"Nobody else but me would have gotten that $7.5 billion back for the taxpayers of the United States," Trump said.