Amtex Chemical Company makes silicone caulk removal products. One observation-that floor looks like ceramic tile, and solvents may force dissolved caulk into the porous grout, in which case, you're hosed. If it's embossed sheet goods, I'd try the solvent in a hidden spot first to make sure the vinyl isn't damaged by it.
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There ain't nothin' more powerful than the odor of mendacity -Big Daddy
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