He’s widely considered the most powerful politician in Illinois, but there’s no proof that House Speaker Mike Madigan uses his numerous roles to influence Democrats throughout the state.

Nor that he mixes government and politics.

At least that’s what lawyers for the head of the state Democratic Party argue in their latest federal court filing, seeking to knock down a lawsuit accusing Madigan of using his vast power to rig elections and punish enemies. Madigan’s lawyers produced the lengthy reply on Monday in their quest to resolve the lawsuit before it could head to a trial.

An unsuccessful 2016 Democratic primary challenger to Madigan, Jason Gonzales, contends Madigan planted fake candidates in the race to split the Hispanic vote in his Southwest Side district. Lawyers have worked hard to dissect Madigan’s political operations in the matter.

“Defendants dispute that Defendant Madigan uses the numerous roles he holds to influence Democrats at all levels of government,” Madigan’s lawyers wrote. “The evidence cited does not support this statement, nor does the record otherwise support a statement.”

His lawyers also wrote that they “object to the word ‘influence’ as unreasonably vague, and ambiguous.”

And the latest filing did confirm some tidbits, including that Madigan personally told Tim Mapes — his former chief of staff and executive director of the Illinois Democratic Party — to resign amid allegations of harassment. It also revealed that Madigan personally “terminated” Kevin Quinn, another longtime political aide who was fired the day before political consultant Alaina Hampton went public with accusations that Quinn stalked her with barrages of unwanted text messages and phone calls in pursuit of a romantic and sexual relationship.

Gonzales’ attorneys had claimed that Mapes’ resignation was the result of “Madigan’s power and influence.”

“Defendant Madigan testified only that he ‘told him [Mr. Mapes] to submit his resignation,’ and that he accepted his resignation,” Madigan’s attorneys wrote.

The filing also alleges there’s no evidence to prove that Shaw Decremer, an ousted former Madigan political operative and lobbyist, “advocates ‘on behalf of his clients to the same individuals he dealt with while working for the Office of he Speaker or on political campaigns.’”

Gonzales’ attorneys contend that Decremer filed the nominating petitions for the two alleged sham candidates, but in his deposition, Decremer said he only took the documents to Springfield, but did not actually file them himself.

Madigan’s attorneys said Decremer notarized Madigan’s statement of candidacy and loyalty oath and brought his nominating petitions to the Illinois State Board of Elections in the 2016 primary election.

Lawyers for Gonzales have also argued that “the offices and personnel used by Michael Madigan by governmental and political functions is distinguishable as to who pays for the offices and office supplies and time of the year or time of the day.” They tried to prove that point by inspecting Madigan’s offices at 6500 S. Pulaski and the 13th Ward Democratic Organization offices at 6014 S. Central Ave in October — a demand Madigan’s lawyers called a violation of the First Amendment and “a political fishing expedition.”

During his deposition in the case, Madigan testified that “there are certain legal requirements on separation and that’s what I would abide by” and “I’m not going to engage in any inappropriate or illegal activity in terms of blending.”

Madigan’s attorneys also argue that having other candidates on the ballot didn’t affect the outcome of the election, claiming an expert testified that “even if all the votes cast for them were given to Gonzales, Gonzales would not have beaten Madigan.”

Madigan beat Gonzales 65.2% to 27.1%. Grasiela Rodriguez got 5.8% and Joe Barbosa 2%.

The latest filing also states that Ald. Silvana Tabares (23rd), who is also a defendant in the case, said she voted for Madigan as speaker when she served as a state representative but that he “did not promise her anything in return for the support/vote.” Tabares was asked by Ald. Marty Quinn (13th) — brother of Kevin Quinn — to help with Madigan’s 2016 campaign, the filing says, including canvassing, phone banking and passing out fliers on Election Day for Madigan.

Madigan lawyers, however, admit that Madigan privately supported Tabares’ appointment as alderman, not challenging Gonzales’ attorneys’ claim that “Michael Madigan spoke with Mayor Rahm Emanuel about having Silvana Tabares appointed to the 23rd Ward Aldermanic position.”

During Tabares’ deposition she stated she asked Madigan for some help to go door-to-door in her district and that “Speaker Madigan sent Alaina Hampton to help her.”

Madigan’s lawyers in another filing say Gonzales, whom they call a “disappointed primary candidate,” failed to prove a reasonable likelihood that the defendants changed the outcome of the election.

“Because Gonzales failed to find any evidence to support this showing, Defendants are entitled to summary judgment on this claim,” the filing says.