Washington (CNN) The Supreme Court held arguments on Wednesday over President Donald Trump's proclamation restricting travel from several majority-Muslim countries. During a lively session that lasted just over an hour, the justices asked an array of questions, some that broadly sought to explore the President's motives, some that looked more narrowly at how the travel restrictions worked.

All of the justices jumped into the fray, except for Clarence Thomas, who typically does not ask questions during oral argument sessions. The most crucial queries may have come from Justice Anthony Kennedy, who is in the middle of this ideologically divided court. Representing the Trump administration was Solicitor General Noel Francisco. Representing the state of Hawaii and other challengers was Neal Katyal.

Here are the key moments:

How the ban was created

Solicitor General Noel Francisco: "After a worldwide multi-agency review, the President's acting Homeland Security Secretary recommended that he adopt entry restrictions on countries that failed to provide the minimum baseline of information needed to vet their nationals."

Francisco opened with this and continued to pound on the point that Trump was not alone in instituting the program: he had the backing of other executive branch officials. It was a thorough, worldwide approach. Francisco returned to the "tailored" nature of the policy and that very few countries were covered.

Justice Anthony Kennedy: "In fact, if you compare this proclamation to the Reagan and the Carter proclamations, which I think were one or two sentences, this is longer than any proclamation that I've seen in this particular area."

At the outset, Kennedy, the key swing justice, appeared open to arguments that the travel order arose from a comprehensive approach. He later asked about safeguards in the system, to prevent discrimination against particular individuals, but he did not voice any broadside to the Trump order.

What if a President is anti-Semitic?

Justice Elena Kagan: "So let's say in some future time, a president gets elected who is a vehement anti-Semite. And says all kinds of denigrating comments about Jews and provokes a lot of resentment and hatred over the course of a campaign and in his presidency. And in the course of that, asks his staff or his Cabinet members to issue recommendations so that he can issue a proclamation of this kind, and they dot all the i's and cross all the t's. And what emerges, and again in the context of this virulent anti-Semitism, what emerges is a proclamation that says "No one shall enter from Israel."

Francisco responds: "Since we don't have the extreme hypothetical that you're suggesting, Your Honor, we do have a multi-agency worldwide review and a Cabinet-level recommendation that applied a neutral baseline. And this wasn't done just by the Cabinet secretaries but by the agencies to every country in the world."

Kagan is offering an extreme example, and she even observes that "this is an out-of-the-box kind of president in my hypothetical." But she will return to a variation of this example later in the questioning, with a more familiar theme of a president targeting Muslims.

Do campaign statements count?

Kagan extended her hypothetical: "You said if at the time the President had said we don't want Muslims coming into this country ... that would undermine the proclamation."

Francisco: "We are very much of the view that campaign statements are made by a private citizen before he takes the oath of office and before, under the Opinions Clause of the Constitution, receives the advice of his Cabinet, and that those are constitutionally significant acts that mark the fundamental transformation from being a private citizen to the embodiment of the executive branch. So that those statements should be out of bounds."

Kagan has brought to the fore precisely the situation at hand and precisely the grounds on which several lower court judges have cast suspicion on the Trump proclamation. Francisco's message here: You must separate private citizen Trump from public President Trump.

Kennedy: "Suppose you have a local mayor and, as a candidate, he makes vituperative hateful statements, and he's elected, and on day two, he takes acts that are consistent with those hateful statements. ... Whatever he said in the campaign is irrelevant?"

Francisco: "I would say yes, because we do think that oath marks a fundamental transformation, but I would also say here it doesn't matter, because, here, the statements that they principally rely on don't actually address the meaning of the proclamation itself. This is not a so-called Muslim ban. If it were, it would be the most ineffective Muslim ban that one could possibly imagine since not only does it exclude the vast majority of the Muslim world, it also omits three Muslim-majority countries that were covered by past orders, including Iraq, Chad, and Sudan."

Kennedy did not follow up. He earlier asked whether individuals might be able to claim religious discrimination in a particular situation, and Francisco said yes. But this was another point that Kennedy seemed to signal general acceptance for the overall order.

Later, Roberts put the issue to Katyal, showing reluctance to have the President's statements used against him for his entire time in the White House

Roberts: "If your argument based on campaign statements, is there a statute of ... limitations on that, or is that a ban from presidential findings for the rest of the administration."

Katyal says the anti-discrimination challenge is grounded in the terms of federal immigration law: "It's purely the text of the proclamation, which is nationality-based discrimination through and through." His message is that the challengers are not relying on Trump's provocative campaign statements.

Katyal's argument

Katyal: "This executive order is unlawful for three reasons: It conflicts with Congress's policy choices. It defies the bar on nationality discrimination. ... And it violates the First Amendment."

Katyal is trying to pound all bases, the last regarding the First Amendment protections against religious discrimination. But then he hits a roadblock in the question from Chief Justice John Roberts about Syria. It is extreme like Kagan's and it similarly draws attention.

National security

Roberts: "Let's suppose the intelligence agencies go to the President and say, we have 100% solid information that on a particular day 20 nationals from Syria are going to enter the United States with chemical and biological weapons. They could kill tens of thousands of Americans. In that situation, could the President ban the entry of Syrian nationals on that one day?"

Roberts cuts to the heart of the national security arguments that the administration has advanced.

Katyal fights the hypothetical and said the president might even have time to get Congress to sign onto such an order. But Roberts says, what if that legislation is blocked.

Katyal: "We understand the President will have residual authority to keep the country safe."

Katyal a few minutes later asserts, "there's nothing in the order that ends it."

Where's Kennedy's head at

Kennedy interjects in a way that continues to indicate which way he might be leaning: "I thought it had to be reexamined every 180 days. ... That indicates there will be a reassessment. ... And the President has continuing discretion."

He poses this as a question but it seems more of an assertion of his belief there are safeguards here.

Is it a Muslim ban?

Alito: Would any reasonable observer reading this proclamation, without taking into account statements, think this was a Muslim ban? ... I think there are 50 predominately Muslim countries in the world. Five countries, five predominately Muslim countries are on this list. The population of the predominately Muslim countries on this list make up about eight percent of the world's Muslim population. ... If you looked at the 10 countries with the most Muslims, exactly one, Iran, would on that list of the top ten, so would a reasonable observer think this was a Muslim ban?

Katyal answers him pointedly: "The fact that the order only encompasses some Muslim countries I don't think means it's not religious discrimination. For example, if I'm an employer and I have 10 African-Americans working for me and I only fire two of them, ... I don't think anyone can say that's not discrimination."

Finally, lest one think Francisco accepted any suggestion that Trump was motivated by religious animus he said in the last seconds of the argument of the President: "He has made crystal clear that Muslims in this country are great Americans and there are many, many Muslim countries who love this country."