<p>It makes no sense to use a semicolon with a coordinating conjunction like “but.” They both accomplish the same effect: binding two independent clauses together. It is almost redundant to use both a semicolon and “but.” You only use one when the other is not present. Using a semicolon with “but” implies that you can start a sentence with “but,” which may be permissible, but not in this context or case.</p>