Here is an analysis of some of the claims made in the second presidential debate.

DONALD TRUMP

On women linked to Bill Clinton sexually: “Hillary Clinton attacked those same women and attacked them viciously.”

THE FACTS:

There is no clear, independent evidence that Hillary Clinton “viciously” attacked women who alleged or confirmed sexual contact with her husband.

To be sure, in the 1992 Democratic primaries, she was deeply involved in the Clinton campaign’s effort to discredit one accuser, actress Gennifer Flowers, who alleged she had a long-running affair with Bill Clinton. Both Clintons acknowledged past troubles in their marriage but sought to undermine Ms Flowers’ claims. Bill Clinton later acknowledged in a 1998 court deposition that he had a sexual encounter with Ms Flowers.

Hillary Clinton was also quoted over the years making disparaging comments about other women linked with her husband, but what is lacking is proof that she engineered efforts to smear their reputation.

Diane Blair, a political science professor and long-time Hillary Clinton friend who died in 2000, left behind an account of private interviews with Mrs Clinton in which she told her during the Monica Lewinsky affair that she considered the former White House intern a “narcissistic loony toon”.

DONALD TRUMP

On Mrs Clinton’s behaviour when, as a young defence lawyer, she was assigned to represent an accused child rapist: “She’s seen on two separate occasions, laughing at the girl who was raped. Kathy Shelton, that young woman, is here with us tonight.”

THE FACTS:

At no point was Mrs Clinton seen laughing at the victim.

In 1975, at the age of 12, Ms Shelton was sexually assaulted in north-west Arkansas. Mrs Clinton was asked by a judge overseeing the case to represent her alleged attacker. After the prosecution lost key evidence, Mrs Clinton’s client entered a plea to a lesser charge.

In an interview a decade later, Mrs Clinton expressed horror at the crime, but was recorded on tape laughing about procedural details of the case. The audio has been seized on by conservative groups looking to attack her presidential candidacy but does not convey mirth at the girl’s fate.

DONALD TRUMP

On Bill Clinton: “He lost his licence. He had to pay an 850,000-dollar fine.”

THE FACTS:

Mr Trump’s facts are, at best, jumbled. In 1998, lawyers for Bill Clinton settled with former Arkansas state employee Paul Jones for 850,000 dollars in her four-year lawsuit alleging sexual harassment. It was not a fine and there was no finding or admission of wrongdoing.

Mr Trump erred in describing the legal consequences of that case. In a related case before the Arkansas State Supreme Court, Mr Clinton was fined 25,000 dollars and his Arkansas law licence was suspended for five years. Mr Clinton also faced disbarment before the US Supreme Court but opted to resign from the court’s practice instead of facing any penalties.

HILLARY CLINTON

In response to a question about her saying that politicians need to have “both a public and a private position” in a 2013 paid speech, said: “As I recall, that was something I said about Abraham Lincoln after having seen the wonderful Steven Spielberg movie called Lincoln. It was a master class watching President Lincoln get the Congress to approve the 13th Amendment.”

DONALD TRUMP replied: “She lied. Now she’s blaming the lie on the late, great Abraham Lincoln.”

THE FACTS:

Mrs Clinton’s recollection is correct.

She invoked the movie Lincoln and the deal-making that went into passage of the 13th Amendment, which outlawed slavery, in an April 2013 speech to the National Multifamily Housing Council.

According to excerpts of the speech included in hacked emails published last week by WikiLeaks, Mrs Clinton said politicians must balance “both a public and a private position” while making deals, a process she said was like making sausage.

“It is unsavoury, and it always has been that way, but we usually end up where we need to be,” she said according to the excerpts.

“But if everybody’s watching, you know, all of the back-room discussions and the deals, you know, then people get a little nervous to say the least. So, you need both a public and a private position.”

DONALD TRUMP

Asked whether the predatory behaviour with women that he described in a 2005 video amounted to sexual assault, said: “No, I didn’t say that at all.”

THE FACTS:

He certainly didn’t own up to sexual assault in his boastful remarks in 2005. But he clearly described groping and kissing women without their permission, using his celebrity status to impose himself on them.

“I don’t even wait,” he bragged in the video. “And when you’re a star, they let you do it. You can do anything.”

He described a specific sexual advance toward a married woman, saying: “I moved on her like a bitch. But I couldn’t get there.”

No court has considered whether that is sexual assault, but some of the Republicans who abandoned support for his candidacy, as well as Democrats and activists, say that sounds like that to them.

HILLARY CLINTON

“I do think … the use of (US and coalition) enablers and trainers in Iraq, which has had some positive effect, are very much in our interest.”

THE FACTS:

She is right about the positive effect, at least on the Iraqi military. After losing the city of Ramadi to the Islamic State group again in May 2015, the hundreds of US military trainers and advisers have made some gains.

It took more than a year, but the programme Mrs Clinton cited has produced a more competent Iraqi military and set the stage for an Iraqi campaign to retake the northern city of Mosul. That city has been the Islamic State militants’ main stronghold since it swept into Iraq in 2014, almost unopposed by the Iraqi army.

As Mrs Clinton’s characterisation of the programme suggests, it has not been an unqualified success and is expected to require years of additional effort to ensure that the Iraqi military does not collapse as it did in 2014.