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Yes. In Classical Logic Syllogism: (A -> B, B -> ~C) -> (A -> ~C) is provable. However I found an interpretation that makes the premises true and the conclusion false: take A = "Are mortal", B = "All men" and C = "are dogs", "~" = not. Thus it does not semantically follow.
I didn't know A -> B needs to be the whole truth.
I found an interpretation that makes the premises true and the conclusion false
If I read the OP correctly, it states that all mortals are men, which is false; and all men are not dogs, which is true. Using Boolean representation we have 0 x 1 = 0, so the conclusion is false.