WASHINGTON — The plot is intricate, but the math is simple.

The latter requires senators and the public to understand only that "two plus two equals four," Rep. Adam Schiff, D-Calif., the lead House manager in President Donald Trump's Senate impeachment trial, said Wednesday.

That basic math is all it takes, he argued, to conclude that Trump prioritized his own interests over national security by using foreign aid as leverage to force Ukraine into helping his re-election effort. The Ukrainians knew the score — "they're not stupid," Schiff said — and he left unspoken his thoughts on the intellectual capacity of senators who couldn't or wouldn't perform the same addition with the facts in front of them.

Of course, the arithmetic of the eventual Senate vote is nothing like the formula for determining whether the president abused the powers of his office in the ways the Founding Fathers envisioned a chief executive might when they vested Congress with removal authority.

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Trump's defenders — his attorneys and most, if not all, of the 53 Senate Republicans, from whom he needs just 34 votes to remain in office — say he did nothing wrong, that House Democrats rushed to impeach him in a partisan fever without sufficient evidence and that even if he'd done all that is alleged, the bill of particulars would come up short of justifying ejecting him from the Oval Office.

The expectation that Trump will be acquitted is the reason Democratic House managers are appealing to two audiences as they argue the facts. They would like to persuade a handful of Republican senators to vote in favor of articles of impeachment, and they are determined to demonstrate to the public that Trump was rightly impeached by the House.

There were moments of rhetorical flourish Wednesday: Democratic Rep. Hakeem Jeffries described fellow New Yorker Rudy Giuliani as a "cold-blooded political operative for President Trump's re-election campaign" in explaining why Giuliani's role as unofficial head of the Oval Office's Ukraine team pointed to a personal mission for the president rather than a foreign policy agenda for the United States.

And yet Schiff and his fellow House prosecutors also began to lay out labyrinthine details that punched home the thoroughness of the record against a president who appeared to have boasted earlier in the day that he is withholding more evidence from Congress and the public. It was the first time — and, because the prosecutors repeated the facts, the second, third and fourth times — that the full timeline had been presented, along with videotaped testimony from the House's investigation, from end to end.

The evidence was "overwhelming," Carol Lam, a former U.S. attorney for the Southern District of California, said on NBC as the Senate broke for dinner Wednesday night.

The recitation of appendix-like particulars may have sounded arcane, but they were necessary to support the allegations in the two articles of impeachment the House approved last month. They involved initialisms like FMF (foreign military financing), OMB (Office of Management and Budget) and FOIA (Freedom of Information Act); Ukrainian names like Volodymyr Zelenskiy (the president), Yuriy Lutsenko (a former prosecutor) and Oleksandr Danylyuk (a former Cabinet official); and a thicket of legal principles, from the strictures of the Impoundment Control Act to the concepts of the Federalist Papers.

But while Trump and his friends on Capitol Hill are counting on the public to tune out, there's no question that senators are capable of following every twist and turn. Nearly a third of them sit on the Appropriations Committee, whose power of the purse Trump challenged by unilaterally blocking the aid.

Sen. Rob Portman, R-Ohio, the chairman of the Ukraine Caucus and a former director of the OMB, pressed the White House last year for answers on what had happened to the money, and he is intimately familiar with the laws governing how budget officials are supposed to treat appropriated funds. Portman's office did not respond to a request for comment on whether he believes the funds were frozen legally.

Republican senators objected to the repetition of Democratic impeachment managers, and Sen. John Barrasso, R-Wyo., dismissed the trial as an "attempt by the Democrats to take the Senate" by embarrassing moderates up for re-election.

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Trump defense attorney Jay Sekulow said Democrats were leveling new charges when they repeatedly said Wednesday that he offered Ukraine a quid pro quo.

"Notice what's not in the articles of impeachment — allegations or accusations of quid pro quo," Sekulow said. "That's because they didn't exist. So you know there's a lot of things we'll rebut, but we'll do it in an orderly and, I hope, more systematic fashion."

But while the first article of impeachment doesn't use the Latin phrase — which means "something for something" — it charges the president with "conditioning" official acts of the U.S. government on acts by Ukraine. It alleges a quid pro quo in plain English.

The president's defense team will not get a chance to rebut the Democratic case on the Senate floor until Saturday, but the facts themselves will be hard to contradict. Trump privately and publicly solicited foreign assistance in investigating former Vice President Joe Biden, who is leading in national polls for the Democratic nomination to oppose Trump's re-election, as Democrats charged. He went to extraordinary lengths — in violation of budget law, according to the Government Accountability Office — to freeze aid to Ukraine while he was pressing Ukraine to announce investigations into Biden and another matter important to his re-election.

Several of his aides testified, despite his orders that they not appear before Congress, that he conditioned the release of money for Ukraine on the announcement of the investigations. His acting chief of staff, Mick Mulvaney, acknowledged at one point — before backtracking — that the money was held back as leverage to produce one of the inquiries. And Trump showed no interest in the subject of corruption in Ukraine — or, really, anything else about the country — outside of its potential to aid his political fortunes, according to the sworn testimony of administration officials that was replayed Wednesday.

Throughout the day, House prosecutors noted points at which they believed they could have made a stronger case had Trump not ordered administration officials to defy subpoenas and requests for documents and testimony. At a news conference in Europe on Wednesday morning, Trump appeared to brag that he had not been forced to produce more evidence.

"Honestly, we have all the material," he said. "They don't have the material."

But many lawyers believe that House Democrats had more than enough evidence to justify his impeachment and that the case for his removal is strong — whether or not 20 Republicans will eventually cross the partisan aisle to join Democrats to tally the needed two-thirds majority.

"If this isn't impeachable, then you should just take it out of the Constitution, because nothing could be impeachable," Jill Wine-Banks, an MSNBC contributor who was a prosecutor during the Watergate scandal, said Wednesday on "NBC News Now."