Although they are spelled and pronounced almost identically and they are somewhat similar, to contemn something is not the same as to condemn it. To contemn something is to despise it. You might condemn something that you contemn, but this is not automatic.
One word that is more closely related is contempt. Both words come from the Latin contemnere meaning to (intensely) despise. The intensifier "con-" is the same one that makes its appearance in "condemn", but in that case it is intensifying damnare, which means "to sentence" (rather than temnere, "to despise").
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