The seller says this is the guitar a man infamously bought at a charity auction for $4,000 and then proceeded to smash with a hammer in a video that's gone viral on social media.

The eBay listing says the man donated the guitar back to the Texas nonprofit he originally bought it from, the Ellis County Wild Game Dinner, and the sale proceeds will be put towards supporting agricultural education for local youth.

While the seller claims Taylor signed the guitar herself, that claim is being denied by a source close to Taylor's merchandise company ... who tells us Taylor did NOT sign that guitar.

The source adds ... the guitar is NOT an official Taylor Swift guitar and her merch company did NOT send a certificate of authenticity.

However, photos from the eBay listing appear to show a signature on the guitar, which is decorated with images from Taylor's "Eras" tour.

What's more, the certificate of authenticity from the original auction sale, obtained by TMZ, claims "the guitar has been personally signed by Taylor Swift and is guaranteed to be authentic."

Thing is ... the certificate of authenticity does NOT have a seal, which is something that's typically present on such documents.