Washington (CNN) The Republican candidates for president gathered in Las Vegas for their fifth debate Tuesday, and CNN's Reality Check team spent the night putting their statements and assertions to the test.

The team of reporters, researchers and editors across CNN selected key statements and rated them: True; Mostly True; True, but Misleading; False; or It's Complicated.

Ted Cruz, Carly Fiorina, Mike Huckabee

Reality Check: Cruz, Fiorina and Huckabee claim social media checks were prohibited or willfully ignored in visa cases

By Laura Koran, CNN

Sen. Ted Cruz of Texas: "It's not a lack of competence that is preventing the Obama administration from stopping these attacks. It is political correctness. We didn't monitor the Facebook posting of the female San Bernardino terrorist because the Obama DHS thought it would be inappropriate. She made a public call to jihad and they didn't target it."

Former Hewlett-Packard CEO Carly Fiorina: "The bureaucratic processes that have been in place since 9/11 are inadequate, as well. What do we now know? That DHS vets people by going into databases of known or suspected terrorists. And yet, we also know that ISIS is recruiting who are not in those databases. So of course, we're going to miss them. And then we now learn that DHS says, "No, we can't check their social media." For heaven's sake, every parent in America is checking social media and every employer is as well. The government can't do it? The bureaucratic procedures are so far behind."

Former Arkansas Gov. Mike Huckabee: "I just want to make sure that everything we use is going to be effective. We're spending billions of dollars, let's make sure it's effective. Let's use every tool, but let's also check out the Facebook posts, let's look at Twitter accounts. My gosh, we were told we couldn't do it because it might invade somebody's privacy. This lady who came over here and shot up San Bernardino was posting things on Facebook, yet, we were restricted from looking."

CNN Reality Check Team: There is no State Department policy prohibiting social media checks by consular officers, who interview prospective visa recipients and make the final call on whether they qualify for a visa, State Department spokesman John Kirby told reporters Monday.

These consular officers are free to check any and all publicly available information on an applicant, including their social media postings.

That said, they aren't required to do so with every applicant.

The Department of Homeland Security -- which runs background checks on foreign applicants as part of the interagency process -- also allows social media checks, but again, they aren't required. In fact, in recent months the United States has begun to take steps to review social media postings of visa applicants from certain countries.

The value of these social media searches is limited, since terrorist sympathizers can conceal their identities online or use privacy settings to hide their posts.

In fact, San Bernardino shooter Tashfeen Malik obscured her identity when making pro-jihad comments on social media sites and used enhanced security settings, U.S. law enforcement officials told CNN this week.

Some of Malik's postings were only visible to a small group of friends, which runs in direct contrast to Cruz's suggestion that Malik made the statements publicly.

Verdict: False

Chris Christie

Reality Check: Christie on King Hussein of Jordan

By Lisa Rose, CNN

Seeking to highlight his muscular approach to foreign policy, demonstrate his command of Middle East politics and tout his people skills, New Jersey Gov. Chris Christie declared, "When I stand across from King Hussein of Jordan and I say to him, 'You have a friend again, sir, who will stand with you to fight this fight,' he'll change his mind."

Unfortunately, the New Jersey governor's dream meeting is not destined to take place. King Hussein of Jordan has been dead since 1999.

Christie should know. He and his family vacationed in Jordan with King Hussein's son, King Abdullah, three years ago. King Abdullah even treated the Christie family to a $30,000 weekend at a luxury hotel in the desert, according to a New York Times report.

Verdict: False

Rand Paul

Reality Check: Paul says no one in the Middle East is doing anything to address the Syrian refugee crisis

By Laura Koran, CNN

Sen. Rand Paul of Kentucky: "Nobody in the Middle East is doing anything. Saudi Arabia, Qatar, Kuwait. All the Gulf nations are doing nothing. They need to step up and take refugees."

Paul's statement disregards significant commitments by several of Syria's neighbors.

According to the United Nations High Commissioner for Refugees, Turkey has admitted more than 1 million Syrian refugees and "has maintained an emergency response of a consistently high standard."

Lebanon has also admitted over 1 million Syrian refugees, in spite of the fact that Lebanon isn't a party to the 1951 Refugee Convention.

Jordan has taken in hundreds of thousands of Syrian and Iraqi refugees and "continues to demonstrate hospitality, despite the substantial strain on national systems and infrastructure," according to a UNHCR country assessment.

JUST WATCHED On GPS: Inside a refugee's struggle to come to America Replay More Videos ... MUST WATCH On GPS: Inside a refugee's struggle to come to America 12:40

After initially saying "no one in the Middle East is doing anything," Paul then narrows his focus to the Gulf states, calling out Saudi Arabia, Qatar and Kuwait by name.

Those countries have, in fact, come under fire for not taking in more refugees, but leaders in those states argue they have given millions of dollars to the United Nations to help with the international refugee effort.

Saudi Arabia, the largest Gulf state, claims to have provided residency to more than 2 million Syrians since the conflict began. But because the country isn't a signatory to the U.N. refugee convention, there isn't a formal accounting of when these individuals arrived and under what circumstances.

Verdict: False

Marco Rubio

Reality Check: Rubio on oldest, smallest Air Force

By Chip Grabow, CNN

Sen. Marco Rubio of Florida criticized Sen. Ted Cruz's voting record against defense spending bills. Rubio stated that, in any effort to defeat ISIS, "airstrikes are important. But we need to have an Air Force capable of it and because of the budget cuts we are facing in this country, we are going to be left with the oldest and the smallest Air Force we have ever had."

In its 2015 Index of U.S. Military Strength, the Heritage Foundation reported "due to fiscal constraints, the Air Force prioritized capability over capacity. The USAF is on track to reduce the size of its force to the smallest in its history. As of FY 2014, the Air Force has 329,500 active airmen and 7,750 reservists and fields a total of 5,032 aircraft, including 40 combat coded squadrons."

Photos: GOP debates in Las Vegas Photos: GOP debates in Las Vegas Businessman Donald Trump watches U.S. Sen. Ted Cruz speak Tuesday, December 15, during a Republican presidential debate in Las Vegas. Hide Caption 1 of 20 Photos: GOP debates in Las Vegas An overhead view of the stage at the Venetian hotel and casino. Hide Caption 2 of 20 Photos: GOP debates in Las Vegas Trump answers a question at the debate. During the event, the GOP front-runner said it was "very unprofessional" and "very sad" that so many questions directed at other candidates were about him. Hide Caption 3 of 20 Photos: GOP debates in Las Vegas Cruz, the junior U.S. senator from Texas, has been gaining in the polls recently. "We need a President who understands the first obligation of the commander-in-chief is to keep America safe," he said in his opening remarks. "If I am elected President, we will hunt down and kill the terrorists. We will utterly destroy ISIS." Hide Caption 4 of 20 Photos: GOP debates in Las Vegas New Jersey Gov. Chris Christie, center, makes a point between former Florida Gov. Jeb Bush, left, and U.S. Sen. Rand Paul. "I'm a former federal prosecutor," Christie said during the debate. "I've fought terrorists and won, and when we get back in the White House we will fight terrorists and win again and America will be safe." Much of Tuesday night's debates focused on national security and the ISIS terror threat. Hide Caption 5 of 20 Photos: GOP debates in Las Vegas Candidate Ben Carson speaks during the debate. "As a pediatric neurosurgeon, I frequently faced life-and-death situations and had to come up with the right diagnosis, the right plan, and execute that plan frequently with other colleagues," Carson said. "Right now, the United States of America is the patient. And the patient is in critical condition and will not be cured by political correctness and will not be cured by timidity." Hide Caption 6 of 20 Photos: GOP debates in Las Vegas Businesswoman Carly Fiorina, left, responds to a question from debate moderator Wolf Blitzer. In her opening remarks, Fiorina said: "I have been tested. I have beaten breast cancer. I have buried a child. I started as a secretary. I fought my way to the top of corporate America while being called every B-word in the book. I fought my way into this election and on to this debate stage while all the political insiders and the pundits told me it couldn't be done." Hide Caption 7 of 20 Photos: GOP debates in Las Vegas Bush makes a point as Cruz looks on during the debate. Bush clashed with Trump often during the debate, at one point calling him a "chaos candidate." Hide Caption 8 of 20 Photos: GOP debates in Las Vegas U.S. Sen. Marco Rubio answers a question during the debate. "Today you have millions of Americans that feel left out and out of place in their own country, struggling to live paycheck to paycheck, called bigots because they hold on to traditional values," the junior U.S. senator from Florida said. "And around the world, America's influence has declined while this president has destroyed our military, our allies no longer trust us, and our adversaries no longer respect us. And that is why this election is so important." Hide Caption 9 of 20 Photos: GOP debates in Las Vegas Carson and Trump share a laugh on stage. Hide Caption 10 of 20 Photos: GOP debates in Las Vegas Ohio Gov. John Kasich speaks during the debate. "When we think about our country and the big issues that we face in this country -- creating jobs, making sure people can keep their jobs, the need for rising wages, whether our children when they graduate from college can find a job, protecting the homeland, destroying ISIS, rebuilding defense -- these are all the things that we need to focus on," Kasich said. "But we'll never get there if we're divided. We'll never get there if Republicans and Democrats just fight with one another." Hide Caption 11 of 20 Photos: GOP debates in Las Vegas Paul waves as he takes the stage before the start of the debate. "I think we defeat terrorism by showing them that we do not fear them," said the junior U.S. senator from Kentucky. "I think if we ban certain religions, if we censor the Internet, I think that at that point the terrorists will have won." Hide Caption 12 of 20 Photos: GOP debates in Las Vegas The candidates put their hands over the hearts during the national anthem. Hide Caption 13 of 20 Photos: GOP debates in Las Vegas A wide shot of the Venetian theater. Hide Caption 14 of 20 Photos: GOP debates in Las Vegas Four Republican presidential candidates take the stage for the "undercard" debate featuring lower-polling candidates. From left are former New York Gov. George Pataki, former Arkansas Gov. Mike Huckabee, former U.S. Sen. Rick Santorum and U.S. Sen. Lindsey Graham. Hide Caption 15 of 20 Photos: GOP debates in Las Vegas Graham has served South Carolina in Congress since 1995. He continued his tough talk on the threat of terrorism. "If I'm President of the United States, and you join ISIL, you are going to get killed or captured," he said. "And the last thing you are going to hear if I'm President is, 'You've got a right to remain silent.' " Hide Caption 16 of 20 Photos: GOP debates in Las Vegas Huckabee responds to a question. "We've lost confidence in our government," Huckabee said during the first debate. "And when Americans lose confidence in their government, we're in a dangerous place. We're in danger because we have an enemy that is out to kill us, and we have a government that we don't trust any more. This election is about going back to having a government we can trust with leaders who have the courage and conviction to actually lead and not follow." Hide Caption 17 of 20 Photos: GOP debates in Las Vegas Santorum, who served Pennsylvania in the U.S. Senate, also ran for President in 2012. "This is an important time in our country's history," he said in his opening remarks. "We have entered World War III. World War III has begun, and we have a leader who refuses to identify it and be truthful to the American people to the stakes that are involved, in part, because his policies have led us here." Hide Caption 18 of 20 Photos: GOP debates in Las Vegas Former Alaska Gov. Sarah Palin -- Sen. John McCain's running mate in 2008 -- watches the debate from the audience. Hide Caption 19 of 20 Photos: GOP debates in Las Vegas Pataki was New York governor from 1995 to 2006. "Our party needs to nominate a strong leader who will unite us as Republicans, but more importantly, unite us as Americans," he said at the beginning of the first debate. Hide Caption 20 of 20

The report went on, saying, "The Air Force's capacity in terms of number of aircraft has been on a constant downward slope since 1952. Unlike the other services, the Air Force did not grow during the post-9/11 buildup. The reduction in capacity is expected to continue in the future due to continued budgetary pressure. Under sequestration, the Air Force will shrink to 26 tactical aircraft (TACAIR) squadrons."

As far as the Air Force being the "oldest and smallest," that is likely referring to the age and total inventory of aircraft in the fleet. An April 2014 study by the Center for Strategic and Budgetary Assessments described Air Force aircraft as "the smallest and oldest the service has ever fielded." The study noted that in 2014, the average age of an Air Force fighter jet was 24 years, and that of a bomber was 38 years. The inventory of fighters was 2,010, down from 7,456 in 1955. The U.S. Air Force was formally created in 1947, following World War II, when it was still part of the Army.

Verdict: True

Reality Check: Rubio on a weaker NSA

By Jose Pagliery, CNNMoney

Sen. Marco Rubio warned that new limits on National Security Agency spying has made it slow at getting phone records to keep track of terrorism suspects.

"This metadata program is actually more strict than what a regular law enforcement agency has now. If a regular law enforcement agency wants your phone records, all they have to do is issue a subpoena."

"But now the intelligence agency is not able to quickly gather records and look at them to see who these terrorists are calling."

That's incorrect. The FBI and NSA can still quickly acquire call records, and in an emergency, they can do so immediately without any court approval.

Rubio is referring to the USA Freedom Act, which passed this summer. That law revamped the controversial NSA bulk phone record collection program.

Previously, a secret federal court granted NSA ongoing access to phone company customer records. Those phone records were kept at NSA for a long period of time.

Now, they're kept at phone companies. But companies decide how long to keep them. And NSA can still access them, but it must first get a judge's approval from the special Foreign Intelligence Surveillance Court.

JUST WATCHED NSA stops collecting your phone data ... for now Replay More Videos ... MUST WATCH NSA stops collecting your phone data ... for now 05:26

But there's a lot of leeway here. NSA can claim "exigent circumstances" and tap into the "emergency provisions" under Section 215 of the Patriot Act. The agency can demand records directly from phone companies, quickly get them, then get court approval later.

Notably, Rubio also mentioned that investigators should have had access to the phone records of the San Bernardino mass shooter, Syed Rizwan Farook.

"The terrorist that attacked us in San Bernardino was an American citizen, born and raised in this country. And I bet you we wish we had access to five years of his records, so we could see who he was working with before they carry out another attack," he said.

Actually, the FBI and NSA might still have access to the terrorists' past phone call records. They have to ask whatever phone carrier the shooters used.

The question now is whether the company kept 18 months of records or more. And given that the shooters already committed a crime, any judge would approve it.

In conclusion, Rubio is wrong.

Verdict: False

John Kasich

Reality Check: Kasich on encryption

By Kate Grise, CNN

Ohio Gov. John Kasich said, "The people in San Bernardino were communicating with people who the FBI had been watching, but because their phone was encrypted, because the intelligence officials could not see who they were talking to, it was lost. We have to solve the encryption problem."

Tashfeen Malik advocated jihad in messages on social media, but her comments were made under a pseudonym and with strict privacy settings that did not allow people outside a small group of friends to see them, U.S. law enforcement officials told CNN on Monday

A U.S. official told CNN that the United States only recently began reviewing the social media activity of visa applicants from certain countries. The date that these types of reviews began is not clear, but it was after Malik's application was considered, the source said.

FBI Director James Comey did not specify if encrypted communications played a role in the San Bernardino massacre when speaking to the Senate Judiciary Committee last week. However, Comey seemed to be in agreement with Kasich that encryption can be an obstacle and urged the tech industry to allow decryption of data under a court order.

Some in the tech industry insist that encryption is necessary to protect people who use their products. "We believe very strongly in end-to-end encryption and no backdoors," Apple CEO Tim Cook said in an interview with the London Daily Telegraph. "We don't think people want us to read their messages. We don't feel we have the right to read their emails."

Encryption is not the reason the couples' posts were not being monitored. Rather, they were private communications, both by phone and social media, and the U.S. government was not monitoring them because they had no reason to. The couple were not on any terrorist watchlists, and Malik made her comments under a fake name behind many privacy settings that would have required a warrant to access them.

Verdict: False

Donald Trump

Reality Check: Trump wants to shut down the Internet in Iraq and Syria to help stem terrorism

By Tami Luhby, Jose Pagliery and David Goldman, CNNMoney

"We're not talking about closing the Internet. I'm talking about parts of Syria, parts of Iraq. Where ISIS is. Now, you could close it," businessman Donald Trump said.

It actually is possible to shut down the Internet. Governments can take out servers, cell phone antennas and space satellites to restrict access. North Korea already does it on the ground there. Egypt limited access during the 2011 Arab Spring uprising.

JUST WATCHED Donald Trump clarifies Internet comments Replay More Videos ... MUST WATCH Donald Trump clarifies Internet comments 01:41

But for America to shut down the Internet in Iraq and Syria would be a very complicated task. The United States does not control the global Internet or servers on foreign soil.

So foreign Internet infrastructure would need to be disrupted or shut down to turn off service in certain areas -- a tricky task made even harder if the countries and companies controlling those servers and cell towers don't cooperate.

If those countries didn't comply, America would have to take out the servers and towers through the use of force, possibly involving ground troops to find and destroy this infrastructure. The U.S. would have to jam all space satellites -- or demand satellite operators not provide service to Iraq and Syria.

Another complication: Shutting down the Internet in Iraq and Syria would eliminate intelligence gathering from phone calls, emails and other electronic communication coming from Syria and Iraq, rendering the National Security Agency effectively blind and deaf.

Verdict: True, but not likely to happen.

Reality Check: Trump on $150 billion in unfrozen Iranian assets

By Eve Bower, CNN

Businessman Donald Trump criticized the Iranian nuclear deal, calling it "that horrible, disgusting, absolutely incompetent deal with Iran where they get $150 billion."

In 2011 and 2012, the United States and Europe imposed sanctions on Iran that included freezing some Iranian assets overseas. With the announcement of a nuclear deal in 2015, those same assets stand to be released, creating a pool of money that will be newly available to the Iranian government. The total amount of those assets is not known, but as a deal with Iran seemed imminent, some estimated that the number was as high as $150 billion.

In late July, at a Senate Foreign Relations Committee hearing on the deal, House Speaker John Boehner and others claimed that "more than $100 billion" in unfrozen assets would be available to Iran.

Both the Department of the Treasury and the White House have disputed these estimates.

In Treasury Secretary Jacob Lew's July testimony to the Senate, he estimated that, after sanctions relief, Iran will only be able to access "about $50 billion" in unfrozen assets. He noted that another large portion -- about $20 billion -- was tied up in projects with China, and "tens of billions" comprise nonperforming loans to Iranian energy and banking interests.

In a detailed statement on the deal, the White House later called the $150 billion estimate "entirely off base."

Because none of the parties with access to the assets have substantiated an estimate anywhere close to the figure Trump suggests, this assertion is deemed False.

Reality Check: Trump on San Bernardino shooters

By Jamie Crawford, CNN

Speaking about the attack in San Bernardino, California, Donald Trump claimed "numerous people, including the mother, knew what was going on. They saw a pipe bomb sitting all over the floor. They saw ammunition all over the place. They knew exactly what was going on."

It is true that the apartment of the shooters, Syed Rizwan Farook and Tashfeen Malik, contained a large amount of firepower and weapons. In a briefing with reporters after the attack, San Bernardino Police Chief Jarrod Burguan spoke about hundreds of rounds of ammunition being found in the SUV used by the shooters as well as in their apartment. Authorities also found 12 pipe bombs in the apartment and hundreds of tools that "could be used to construct IEDs or pipe bombs," Burguan said.

There were 19 devices in all that were found, some that were not finished.

JUST WATCHED FBI: No clues found in San Bernardino lake Replay More Videos ... MUST WATCH FBI: No clues found in San Bernardino lake 02:31

David Chesley, an attorney representing the family of Farook in California, said Farook's mother lived in an isolated part of the residence the couple rented. On the day of the attack, the couple left their baby with her. But U.S. officials have yet to come to a conclusion about the extent of what Farook's mother knew or was aware of, and it is a still a matter of investigation. "Obviously, it's something that we're looking at very, very closely," U.S. Attorney General Loretta Lynch said on NBC's "Meet the Press" earlier this month.

To date, no law enforcement official at this point has said that Farook's mother was aware of the arsenal that Farook and Malik were amassing in the home they shared with Farook's mother.

Verdict: False

Carly Fiorina

Reality Check: Fiorina on generals retiring early

By Lisa Rose, CNN

While describing the steps she would take to confront ISIS overseas, Carly Fiorina said that she would call in former military leaders including Gen. Stanley McChrystal and Gen. David Petraeus, both of whom "retired early because they told President Obama things that he didn't want to hear."

Although McChrystal and Petraeus may have said things the President didn't want to hear, their early departures were not prompted by contentious conversations with Obama.

McChrystal resigned in 2010 after Rolling Stone published a profile in which he mocked members of the Obama administration, including Vice President Joe Biden and then-Afghanistan adviser Richard Holbrooke.

Petraeus resigned as CIA director in 2012 after an FBI investigation revealed that he was having an affair with Paula Broadwell, a woman who was writing a book about him. He pleaded guilty to sharing classified information with Broadwell and was sentenced to two years of probation.

Verdict: False

Reality Check: Fiorina on tech companies cooperating with FBI

By Jose Pagliery, CNNMoney

Former Hewlett-Packard CEO Carly Fiorina was asked whether tech companies should be forced to cooperate with the FBI to expose terrorists' communications.

Fiorina said: "They do not need to be forced. They need to be asked ... they have not been asked."

That's not true. The FBI has indeed asked all major tech companies -- Apple, Google, Microsoft, and others -- to help them spy on terrorists.

But so far, the only proposal the FBI has made would turn the modern world upside down. According to many experts in the field, it would undermine the safety of all communications.

That's because terrorists are using encryption -- the same thing that protects your email and banking from hackers.

The FBI wants tech companies to give law enforcement an extra set of keys to locked communications.

JUST WATCHED Carly Fiorina's career history Replay More Videos ... MUST WATCH Carly Fiorina's career history 02:29

But encryption only works because it keeps everyone out. If Apple creates iPhones that have a "back door," hackers can get in, too. If a company keeps an extra set of keys lying around to spy on employees, Chinese hackers can grab them to break into company data.

Encryption is math. Cryptographers are its mathematicians. They all agree that any extra access is dangerous to everyone.

The world's top cryptographers issued a joint statement in July, calling the FBI's attempts "mandating insecurity." They describe this in binary terms: either data is secured against everyone, or it's not.

"This is a trade-off ... law enforcement cannot be guaranteed access without creating serious risk that criminal intruders will gain the same access," they said.

At least 48 major companies and 37 civil society groups take a similar stand.

In conclusion, so far, law enforcement has only given U.S. tech companies a devastating choice.

Verdict: False, but it's complicated.

Ted Cruz

Reality Check: Cruz on legalization and amnesty

By Sonam Vashi, CNN

Sen. Marco Rubio said, "Ted Cruz supported a 500% increase in the number of H-1B visas, the guest workers that are allowed in this country, and supports doubling the number of green cards."

In response, Cruz said, "I led the fight against (Rubio's) legalization and amnesty bill. ... I have never supported legalization and do not intend to support legalization."

Cruz has been consistently against a pathway for citizenship for undocumented immigrants , and he has previously criticized plans for types of amnesty, but his statements Tuesday night are some of the clearest indications of his views on the issue.

In 2013, Cruz filed additional amendments to immigration legislation that would have increased legal immigration. Although the amendments were ultimately unsuccessful, his amendments would have increased the H-1B visa cap from 65,000 to 325,000 (actually a 400% increase, but it's 500%, or five times, of the original. We'll chalk up the difference to a math mistake). It would also have doubled the worldwide green card caps from 675,000 visas annually to 1.35 million annually. Green cards allow foreign nationals to permanently live and work in the United States. However, another of those amendments specifically called for the bill not to give a path to citizenship for undocumented immigrants.

Last month, Cruz flipped, and said he no longer supported an increase in legal immigration.

Cruz has been pretty consistent in his views toward undocumented immigrants, so we rate this claim as True. And likewise, we rate Rubio's claim True.

Reality Check: Cruz on Syrian refugees

By Sonam Vashi, CNN

In response to a question about Donald Trump's policy on Muslim travel to the U.S., Sen. Ted Cruz said, "Even worse, President Obama and Hillary Clinton are proposing tens of thousands of Syrian refugees to this country when the head of the FBI has told Congress they cannot vet those refugees."

Let's take a look:

Since the start of the Syrian civil war in 2011, fewer than 2,500 Syrian refugees have been admitted to the U.S. More than half of those refugees are children, according to senior administration officials.

In September, the White House announced it planned to admit 10,000 Syrian refugees this fiscal year. Shortly after that, Secretary of State John Kerry announced that the U.S. would increase the total number of migrants accepted from any country to 100,000 in 2017. Many of those additional migrants would likely be Syrian refugees, but it's unclear how many Syrian refugees over 10,000 the U.S. would accept.

As for the FBI's inability to vet Syrian refugees: In October, FBI Director James Comey told Congress that Syrian refugees will be more difficult to check than those from many other countries, especially because the U.S. hasn't been regularly exchanging information with Syria. "If someone has never made a ripple in the pond in Syria in a way that would get their identity or their interest reflected in our database, we can query our database until the cows come home, but there will be nothing showing up because we have no record of them," Comey said at the hearing

JUST WATCHED Marco Rubio attacks Ted Cruz's voting record Replay More Videos ... MUST WATCH Marco Rubio attacks Ted Cruz's voting record 02:38

However, it's incorrect to imply that the FBI said that it can't vet Syrian refugees. Refugees that come to the U.S. undergo several screenings, such as biographic checks and in-person interviews, which involve multiple federal intelligence and security agencies. Syrian refugees in particular go through additional screening, called the Syria Enhanced Review process. That process uses biographical information collected from the U.N. refugee agency to determine whether an applicant needs to go through a fraud or national security unit, which then conducts individualized research on each applicant's story and records. Syrian refugee applications can take much longer to process than the average case processing time of 18 to 24 months . Mark Toner, a deputy State Department spokesman, recently called the refugee vetting process, "the most stringent security process for anyone entering the United States."

Cruz said "tens of thousands" of Syrian refugees will come to this country, but it's unclear how much more than 10,000 refugees the U.S. plans to accept. The FBI has admitted that there are serious challenges in screening Syrian refugees that come to the U.S., but refugees are vetted across multiple agencies in a process that is being constantly refined, according to senior State department officials.

Verdict: False

Reality Check: Cruz on deportation records

By Kevin Liptak, CNN

Demanding tougher enforcement of immigration laws, Sen. Ted Cruz cited the deportation records of previous presidents.

"You enforce the law," Cruz said. "That means you stop the Obama administration's policy of releasing criminal illegal aliens. You know how many illegal aliens Bill Clinton deported? Twelve million. You know how many illegal aliens George W. Bush deported? Ten million."

Those numbers are tricky, since "deportation" isn't an official law enforcement term used by the U.S. government. There are two types of ways that detained undocumented immigrants are forced to leave the country: "removals," which require a court order, and "returns," which occur when immigrants apprehended near the Mexican or Canadian border are told to turn back.

When counting both "removals" and "returns," 12.3 million undocumented immigrants were forced to leave the country under Clinton. The figure for Bush is close to 10 million, according to Homeland Security records.

From the years 2009-2013 -- the years Obama has been in office where data is available -- 3.8 million undocumented immigrants were either "removed" or "returned."

Breaking down those statistics, Obama has relied far more heavily on "removals," and is outpacing any previous commander-in-chief.

Cruz is suggesting in his statement that Obama has been weaker on deportation than his two predecessors -- an assertion that doesn't stand up to figures showing Obama "removing" far more people than Clinton or Bush.

But under his administration, there have been fewer "returns" since there have been fewer Mexicans or Canadians attempting to cross the southern or northern borders.

Verdict: True, but misleading

George Pataki

Reality Check: Pataki on Trump's Muslim ban for U.S. soldiers

By Eve Bower, CNN

Former New York Gov. George Pataki implied that Donald Trump had called for Muslim-American soldiers to be barred from re-entering the United States, saying, "To target a religion and say that regardless of whether you're an American soldier [...] simply because of your religion we are going to ban you is un-American, it is unconstitutional, and it is wrong."

This is a mischaracterization of the policy as Trump presented it.

JUST WATCHED Fierce backlash over Trump's plan to ban Muslims Replay More Videos ... MUST WATCH Fierce backlash over Trump's plan to ban Muslims 02:11

In a formal statement released on December 7, Trump called for a "total and complete shutdown of Muslims entering the United States."

Later that evening, while speaking to Fox News, Trump was specifically asked how his policy would apply to Muslim members of the U.S. military. He said, "They will come home," and, "We have to take care of the Muslims that are living here. But we have to be vigilant."

Verdict: False

Reality Check: Pataki on Muslim surveillance preventing "dozens" of attacks

By Lisa Rose, CNN

Former New York Gov. George Pataki declared that the New York Police Department's surveillance program that monitored Muslim communities in New York and New Jersey "stopped and prevented dozens and dozens of attacks in New York."

The program, which dispatched undercover police officers to spy on mosques and Muslim-owned businesses, ended in April 2014.

Contrary to Pataki's claim, the program didn't stop any attacks in New York , according to the head of the NYPD's intelligence division.

There were some successes, however, including the 2010 bust of two New Jersey men who tried to travel overseas to join the terrorist group Al-Shabaab in Somalia. The men were not plotting domestic attacks.

Authorities have thwarted two attacks in New York. In 2004, two men were charged with attempting to set off explosives in the Herald Square subway station. In 2010, a man tried to detonate a car bomb in Times Square. According to the NYPD, the surveillance program did not help stop either of those attacks.

Verdict: False

Rick Santorum

Reality Check: Santorum on the NSA's canceled phone record spying

By Jose Pagliery, CNNMoney

Congress recently ended the National Security Agency's controversial phone record spying program.

Former Sen. Rick Santorum of Pennsylvania said the United States should bring it back. He said: "This metadata collection is not collecting people's phone calls, their voices. They're not collecting information that's personal. There's no names attached to these numbers."

He also described this information as "anonymous."

Santorum is right. This NSA program was limited.

For a decade, the NSA collected phone records in bulk from major American companies like AT&T and Verizon. It was granted this ability by Section 215 of the Patriot Act.

Santorum correctly described the limitations of the NSA program. According to declassified intelligence court documents, it only allowed the NSA to collect phone numbers, a cell network identifier, the time and duration of calls. This information -- called telephone metadata -- does not include names.

However, this information was not anonymous. There are two dimensions to this.

First, it's easy for the NSA to identify those phone numbers on the back end. Intelligence officials regularly demand customer data from companies in secret, using something called a "National Security Letter."

Second, phone metadata allows the NSA to map our entire personal networks.

"The NSA could tell that you called your pastor, or a suicide hotline," said American Civil Liberties Union lawyer Neema Singh Guliani.

That's why Sen. Mike Lee of Utah has described this as the "bulk collection of personal data."

In short, the NSA's bulk phone collection didn't give the agency people's names -- but it gave the government a major first step in identifying everyone's personal networks.

Verdict: True, but misleading

Lindsey Graham

Reality Check: Graham on ISIS in nine countries

By Kate Grise, CNN

Sen. Lindsey Graham of South Carolina said: "I want to find out what do we need militarily to keep them contained and eventually destroy them in Libya? They're in nine countries. You want to deal with Libya. Go to Iraq or Syria. You want to prevent another 9/11, take the caliphate headquarters away from ISIL."

ISIS and its affiliates have carried out attacks in 11 countries in addition to their terror in Iraq and Syria. The group has carried out attacks in France, Tunisia, Libya, Egypt, Turkey, Saudi Arabia, Yemen, Afghanistan, Bangladesh, Kuwait, and Lebanon.

The November terror attacks in Paris were the sole incident in Europe. The group has hit Bangladesh, Afghanistan, Lebanon and Kuwait once each. ISIS and its affiliates are believed to have carried out multiple attacks in Libya, Egypt, Tunisia, Yemen, Turkey, and Saudi Arabia.

In reality, Graham is slightly underestimating ISIS's reach. It has taken control of territory or carried out organized terror attacks in at least 13 countries. But the substance of what Graham is saying is accurate.

Verdict: True

Mike Huckabee

Reality Check: Huckabee on surveillance of religious institutions

By Sonam Vashi, CNN

Former Arkansas Gov. Mike Huckabee said: "You can go to any church in America. It's a public place ... So if it's a public place and people are invited to come, how does it violate anybody's First Amendment rights if somebody shows up because they might want to listen in and see, is there something that is a little nefarious? And if there is, then you take the second step, getting a search warrant. You do what you have to do. That's all protected under the Constitution."

There's no clear-cut answer here, but the FBI and other law enforcement organizations have legally monitored mosques in the past.Last year, a federal judge threw out a case regarding the New York City Police Department's secret surveillance program , which included monitoring mosques, Muslim businesses, and other organizations. The court found that the NYPD program did not violate the Constitution, since it had been focused on anti-terrorism, not anti-Muslim, activities.

Based on prior surveillance programs and the legal limbo of the NYPD program, which could determine the constitutionality of such monitoring, we rate Huckabee's claim as Mostly True.

Reality Check: Huckabee on military size

By Kevin Liptak, CNN

Former Arkansas Gov. Mike Huckabee claimed that the country's "biggest mistake we've made militarily is letting Barack Obama cut our defense forces by 25% and leaving us at the least prepared position we've been in since before World War II."

Huckabee's claims that Obama has cut military forces by a quarter don't match enrollment figures provided by the Department of Defense. In 2008, the year before Obama took office, the total number of people enlisted in the U.S. military -- across all branches -- stood at 1,401,757.

Data for the latest year, 2014, show the number has decreased to 1,338,487 -- a 4% decrease.

Obama has overseen declines in defense spending, spurred partly by his decision to withdraw U.S. troops from Iraq and Afghanistan, but also by mandatory, across-the-board spending cuts that went into effect in 2011 when Congress failed to arrive at a budget deal.

Estimates on exactly how much that spending has decreased vary based on what's included in the calculation, and range anywhere from 15% to 25%.

Obama has sought to replace sequestration, those forced cuts, which he insists puts the U.S. in a weakened position militarily. And he recently proposed a budget plan increasing military spending by almost 8%.

While Huckabee is correct that the military has shrunk under Obama, his assertion that defense forces have been slashed by 25% doesn't stand up to scrutiny.

Verdict: False

Reality Check: Huckabee asserts movie "Casablanca" ends with walk into sunset

By Richard T. Griffiths, CNN

In making an assertion about trusting Russian President Vladimir Putin, former Arkansas Gov. Mike Huckabee compares the relationship to the close of the movie "Casablanca," suggesting Rick, played by Humphrey Bogart, and the police captain, played by Claude Rains, walk off into the sunset.

"Do I think we can hug Putin and have a wonderful relationship with the Russians and go off into the sunset like the end of 'Casablanca?' No, I don't," Huckabee said.

Huckabee needs to watch the movie again on his next cross-country flight. He asserts they walk off into the sunset. They do not. They walk off into a thick fog.

Verdict: False