WASHINGTON (AP) — Republican presidential contenders hurled insults again Thursday night but not at each other — rather, at the facts.

Bruises were inflicted on the reality of life for Muslim women, the shape of education standards and the reasoning behind U.S. military and foreign policy.

Ted Cruz, Marco Rubio, John Kasich and Donald Trump  arrive for the start of the CNN, Salem Media Group, The Washington Times Republican Presidential Primary Debate on Thursday. (Getty Images/Joe Raedle)

From left, Sen. Marco Rubio (Fla.), Donald Trump, Sen. Ted Cruz (Texas) and Ohio Gov. John Kasich arrive for the start of the CNN Republican presidential debate Thursday. (Getty Images/Joe Raedle)

Some of the claims in the latest Republican presidential debate:

DONALD TRUMP: “Islam treats women horribly.”

THE FACTS: No such generalization is supported by the diverse circumstances for women in the Muslim world. The United States has yet to see a woman as president, many years after Muslim women achieved national leadership in other countries, most prominently Pakistani Prime Minister Benazir Bhutto back in the late 1980s and in the 1990s.

Some Muslim societies are indeed repressive by Western standards, enforcing or pressing for norms such as clothing that covers all but their eyes or faces; bans on driving, voting and education; and restrictions on interacting with the other sex.

But in other Muslim countries, women wear Western clothes, graduate from universities, interact with men, work as Western women do, hold senior government posts and take part in competitive sports.

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TRUMP: “GDP was essentially zero percent in the last few quarters. … Our jobs are gone, our businesses are being taken out of the country.”

THE FACTS: He meant to say there’s been essentially no growth in the gross domestic product — not that there is no GDP at all. But what he meant to say isn’t right, either.

In the past three quarters, the GDP, the broadest measure of the economy’s output, grew at an annual rate of 1 percent, 2 percent and a robust 3.9 percent. The quarter before that it grew just 0.6 percent, but economists considered that a fluke, caused partly by harsh winter weather. For all of 2015, the economy expanded 2.4 percent. That’s not a case of “essentially” no growth.

As for his claim that “jobs are gone,” employers added 2.7 million jobs in 2015 and more than 3 million in the previous year, the two best years for hiring since 1998-99.

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TED CRUZ: “We’re gonna end welfare benefits for anyone who is here illegally.”

THE FACTS: It’s unclear what benefits Cruz could take away. Immigrants living in the country illegally generally are not eligible for federal welfare benefits already.

To be sure, the U.S.-citizen children and spouses of immigrants who are in the country illegally are entitled to federal benefits, including food stamps and housing programs. Public hospitals are required to provide emergency medical care regardless of immigration status.

And children are also legally entitled to a free public education, regardless of their immigration status. But that’s because of a 1982 Supreme Court ruling, not something a president can merely end through executive action or legislation.

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TRUMP on why he opposes Common Core: “Education through Washington, D.C. …. It’s all been taken over now by the bureaucrats in Washington.”

THE FACTS: Common Core is not a federal program at all, but a set of standards developed primarily by governors and education leaders in states. The standards spell out certain skills that students should grasp, while leaving how those skills are mastered up to local school districts and states.

There was no federal mandate that states adopt the Common Core State Standards. However, the federal government did encourage them, through its Race to the Top education grants that were given to states that adopted rigorous academic standards. The flip side of rewarding states that take certain steps is that it punishes states that don’t.

That’s the root of complaints about Washington having a heavy hand in local education. But it’s a far cry from the picture painted by Trump and some other Common Core critics of a local system “taken over” by Washington.

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TRUMP, when asked if he’s created a tone that encourages violence against protesters at his rallies: “I hope not. I truly hope not.”

THE FACTS: Trump has at times appeared to goad his supporters when protesters have emerged at his rallies, a common occurrence.

“You know what they used to do to guys like that when they were in a place like this?” he asked as a protester was removed from a Las Vegas rally. “They’d be carried out on a stretcher, folks.” As the audience cheered, he added: “I’d like to punch him in the face.”

Audiences usually hear an announcement before his rallies start telling them not to harm protesters. Instead his supporters are asked to chant “Trump, Trump, Trump” when a protest begins. This helps steer authorities to the demonstrators in a large crowd, while also focusing the audience’s attention — sometimes its anger — at the protesters.

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MARCO RUBIO on the idea of closing the new U.S. Embassy in Cuba: “The embassy is the former consulate. It’s the same building. So it could just go back to being called a consulate.”

THE FACTS: It was never a consulate. What the U.S. had in Cuba before President Barack Obama restored relations was an “interests section,” a smaller office that is standard in countries with which the United States has no diplomatic relations.

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TRUMP: Says the U.S. is getting nothing in return for its defense partnership with Saudi Arabia. “Saudi Arabia was making a billion dollars a day and we were getting virtually nothing to protect them.”

THE FACTS: The U.S. has no such treaty commitment to defend Saudi Arabia, but rather a decades-long alliance. It has no troops based in the kingdom other than advisers. And it’s not so that the U.S. gets nothing from the alliance: U.S. companies have received tens of billions of dollars from arms sales to the Saudis.

The U.S. did send troops to the kingdom in 1990 after Iraq’s Saddam Hussein invaded neighboring Kuwait. But the Saudis reimbursed the U.S. about $16 billion for that troop presence.

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TRUMP on U.S. military tactics against the Islamic State: “We’re not knocking out the oil because they don’t want to create environmental pollution up in the air.”

THE FACTS: Caution about attacking IS-controlled oil wells and infrastructure in Syria is not about the U.S. armed forces going green.

U.S. military commanders say it would be a mistake to destroy an energy resource that could be preserved for whatever government emerges from the civil war. They also have acknowledged wanting to limit unnecessary side effects such as pollution.

The U.S. has conducted many airstrikes against key elements of that oil infrastructure, including oil collection facilities and distribution networks. This gradual approach has been criticized by many as being too slow, but the Pentagon contends that it has greatly reduced the militants’ income.