Disgraced “academic” Mark Regnerus slid yet further into ignominy on Wednesday after defenders of Utah’s doomed gay marriage ban expunged all references to his debunked study in their brief. The state, which is currently defending the invalidated ban before the Tenth Circuit, had cited Regnerus in two footnotes in a previously filed brief, and structured much of its argument around the conclusions of Regnerus’ work, which asserts that gay couples make inferior parents. Now the state is asking the Tenth Circuit to pretend those footnotes don’t exist, a last-minute revision made “in response to recent press reports and analysis of the study by Professor Mark Regnerus.”

Euphemistic excuses aside, everyone knows that Utah dropped the Regnerus study in direct response to a Michigan federal judge’s complete and total dismissal of Regnerus’ work, after he denounced it as “entirely unbelievable and not worthy of serious consideration.” That searing condemnation seems to have put an end to Regnerus’ shameless, pseudoscientific gay-bashing crusade. This mainstream rejection of Regnerus is long overdue: Many in his own field have repudiated his findings, and the journal that published his original study performed an audit concluding that it had “serious flaws and distortions” and never should have been published. (The most breathtaking flaw of all: Regnerus didn’t even include a valid sample of children raised by same-sex parents.) No one, except perhaps Regnerus’ anti-gay conservative funders, could seriously argue that the Regnerus study actually proves what he—and same-sex marriage opponents—claims it proves. In fact, the study is so methodologically mangled that it’s hard to say it proves much at all.

Utah, then, was wise to slice the footnotes out of its brief, even if the ex post facto maneuver is largely symbolic. But by doing so, the state has accidentally invited a bigger problem: Their remaining arguments are reduced to gibberish. No longer able to make the argument that gay people make inferior parents, Utah is now simply claiming that straight people make superior parents. This argument is so painfully specious that it doesn’t even deserve to be called an argument. If straight parents are superior, then it obviously follows that gay parents are less superior—inferior, you might say, if only doing so didn’t clearly contradict copious, meticulous scholarly research to the contrary.

It’s hard to imagine that the Tenth Circuit will actually buy into Utah’s blizzard of fallacies, which have always relied on Regnerus’ work to anchor them to some semblance of legitimacy. But honestly, it’s hard to imagine Utah winning this case with or without Regnerus. It seems undeniable by this point that Windsor can’t lose in the courts, no matter how convincingly states dress up their anti-gay animus in the garb of protecting children. The entire Regnerus affair merely illustrates how hollow these arguments were at their core all along—and sadly for Utah, they were pretty much the only arguments against gay marriage that anybody still found palatable. The state may have thrown Regnerus overboard, but the anti-gay ship started sinking long ago.