President Putin will be striving to claim, as he began doing today, victory at Ukraine’s city of Bakhmut. It’s Europe’s largest battle since World War II. Bakhmut, though, while potentially Russia’s first victory in nearly one year, would be a Pyrrhic one.

Russia’s military, as Russia itself braces for Ukraine’s expected summer counteroffensive, has been weakened by months of severe losses in the Eastern Ukrainian city. Since Russia first attacked Bakhmut last summer, Western estimates reckon that 100,000 soldiers have been killed or wounded — most of them Russian. 

That would be twice the number of Americans killed in the entire Vietnam war. NATO estimates that five Russian attackers were killed for each Ukrainian defender. The leader of Russia’s Wagner mercenaries, Yevgheny Prigozhin, called it “the Bakhmut meat grinder.”

Realizing that Bakhmut was key to decimating Russia’s military, Ukrainian leaders adopted the slogan last winter: “Hold Bakhmut.” A provincial city of negligible strategic value, Bakhmut sucked in soldiers from across Russia’s 620-mile front. Two months ago, President Zelenskyy made a risky, morale boosting visit to Bakhmut, a bombed out shell that looked like a World War II landscape.

Sunday, at a meeting of the G-7 at Hiroshima, Japan, Mr. Zelensky mourned: “There is nothing. They destroyed everything. There are no buildings… It’s a pity, it’s a tragedy, but” — and here Mr. Zelensky articulated the tragedy in words that will be uttered for years to come  —“for today,” he said, “Bakhmut is only in our hearts.” 

At Kyiv, officials hastened to say that Ukrainian soldiers continue to hold fringes of the urban center of Bakhmut. Two weeks ago, Ukrainian units made their biggest advance in six months. They took advantage of a rotation of Wagner troops for Russian regular soldiers to reclaim 12 square miles of the suburban land north and south of the city.

This advance reportedly has not been reversed. Ukraine’s deputy defense minister, Hanna Maliar, wrote Sunday on Telegram: “Our forces have put the city in a semi-encirclement, which gives us the opportunity to destroy the enemy.” 

Indeed, this weekend’s claims and counterclaims might have less to do with the end of Ukraine’s longest battle and more to do with Russian military politics. Divisions are clear among the estimated 200,000 Russian troops entrenched along the front line.

On Saturday, Mr. Prigozhin of the Wagner mercenaries recorded a video in front of Bakhmut’s rail station. Mr. Prigozhin claimed that his forces had finally taken the city, which had a pre-war population of 70,000.  “Today, at 12 noon, Bakhmut was completely taken,” Prigozhin said.

The Wagner leader was filmed in combat fatigues and standing in front of his fighters, holding Russian flags and Wagner banners. Then, though, he charged that due to the “whims” of Defense Minister Sergei Shoigu and Chief of Staff Valery Gerasimov, “five times more guys died than they should have.”

The mercenary leader then profusely thanked President Putin saying, “he gave us this chance and great honor to defend our motherland.” Mr. Prigozhin then announced that he will withdraw his troops from the city by Friday. In Russian eyes, Prigozin gets public credit for the “victory.”

“As a result of offensive actions by Wagner assault units, supported by artillery and aviation of the Southern Group of Forces, the liberation of Artyomovsk has been completed,” the Russian Defense Ministry said, referring to the city by its Soviet-era name.  The Kremlin said Sunday: “All who distinguished themselves will be put forward for state awards.”

In civilian politics, Mr. Putin has stayed in power for almost a quarter century by playing rival groups against each other. In war, he seems to follow the same strategy. He allows rivalries to play out in public between the Defense establishment and the Wagner Group and Ramzan Kadyrov, leader of Chechnya, a major supplier of fighters of Ukraine.

A London-based Russian analyst, Mark Galeotti, also speculates that Russia’s president may also want to create ample daylight between himself and his military brass — in case Russia’s army fares poorly in the steppes of Eastern Ukraine this summer.