Lawyers for the plaintiffs responded that in that case, the owner of the Zyklon-B gas company was found guilty. “Thus, even though it was solely the Nazis who controlled whether gas would be used on prisoners, and solely the Nazis who decided upon the victims, Bruno Tesch, the owner, was hanged,” they argued. “Like Mr. Tesch, defendants had control over assistance to the C.I.A. program, both personally and as the owners of Mitchell, Jessen & Associates. As a matter of law, that is more than sufficient.”

Image John Bruce Jessen, a psychologist and former C.I.A. contractor, is also a defendant in the case.

The defendants had also moved to exclude as hearsay any evidence from the executive summary of the 6,700-page Senate Intelligence Committee Report on Torture. They argued that the summary — published in December 2014 and based on a five-year review of over six million pages of documents, most of them from the C.I.A. itself — was partisan and not trustworthy or reliable. Judge Quackenbush denied their motion, but reserved the right to change his opinion for purposes of the trial.

To get a favorable summary judgment, the lawyers would have needed to prove that the relevant facts were beyond dispute. In recent weeks, each side submitted lengthy filings taking issue with the purported facts offered by the other. They also moved to exclude testimony of medical experts hired by opposing counsel who examined the former detainees for post-traumatic stress disorder.

The American Civil Liberties Union and the Gibbons law firm of Newark brought the lawsuit under the Alien Tort Statute, which allows foreign citizens to seek justice in United States courts for violations of their rights under international law or United States treaties.

The three former detainees included Mohamed Ben Soud, a Libyan who was detained by the C.I.A. in Afghanistan and was locked in small boxes, slammed against a wall and doused with buckets of ice water while naked and shackled; Suleiman Salim, a Tanzanian captured in 2003 and also held by the C.I.A. in Afghanistan, who was beaten, isolated in a dark cell for months, doused with water and deprived of sleep; and Gul Rahman, who died in C.I.A. custody in Afghanistan in 2002, probably of hypothermia, according to a C.I.A. investigation into his death.

While Dr. Jessen has kept a low profile, Dr. Mitchell has offered himself as a public speaker about his association with the C.I.A. program and his insights on “the minds of those trying to destroy America.” His fee is listed as $15,000 to $25,000 on the site of Worldwide Speakers Group, which states: “Dr. Mitchell led the development of the C.I.A.’s enhanced interrogation program after 9/11 and was a primary interrogator from its inception.”