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Lenny Hochstein Files for Divorce from Real Housewives of Miami Star Wife Lisa Hochstein

Lisa Hochstein and Lenny Hochstein
Lisa Hochstein and Lenny Hochstein

Alexander Tamargo/Getty

It's official: Lenny Hochstein has filed for divorce from his Real Housewives of Miami star wife, Lisa Hochstein.

The pair confirmed their split on May 16. Now the formal paperwork filed by Lenny, 55, on Monday cites "irreconcilable differences" as the reason why he and and Lisa, 39, have split after 12 years of marriage.

Other details in the filing, which was obtained by Page Six, include that the "marriage is irretrievably broken and there is no present hope for a meaningful reconciliation." Lenny and Lisa signed a prenuptial agreement before they wed in 2009, and, per the terms, Lenny will pay spousal support to Lisa.

The couple share two children (who were welcomed via surrogate while RHOM was off air): Logan, 6, and Elle, 2. Lenny also stated in the filing that he will "fully provide for all of the children's needs" and added he'd like "frequent time-sharing" of the children.

RELATED: Real Housewives of Miami's Lisa Hochstein Calls Husband Lenny's Divorce Announcement 'Reckless'

Lisa Hochstein and Lenny Hochstein
Lisa Hochstein and Lenny Hochstein

Alexander Tamargo/Getty

Through a spokesperson, Lisa told PEOPLE las week that she was "blindsided" by Lenny's public announcement.

"With two young children involved, as a mom I'm going to focus all of my energy and time on them," she said, criticizing her estranged husband's "reckless handling of the situation."

RELATED: Real Housewives of Miami Star Lisa Hochstein Defiant After Getting Slammed for Photo of Evacuating Irma on Private Jet

Lenny confirmed the divorce to PEOPLE as well, noting that the reason for the split would "be kept private." At the time, he said lawyers were drafting the official divorce paperwork.

Hochstein told PEOPLE he is in a new relationship with model Katharina Mazepa.

"Nothing happened between [Katharina and I] until [Lisa and I] decided on the divorce," he said, "and Lisa was aware of my plans before anything happened between Katharina and myself."