1. Kevin seems to have forgotten the appointment.

2. Kevin seems to have forgot the appointment.
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Which one is right? Do we have to use 'forgot' or 'forgotten'?

#1 is correct; #2 is not.

The principal parts of the verb "to forget" are forget, forgot, forgotten ~

~ "forget"is used for present tense and with certain auxiliary/helping verbs to form future and conditional tenses, too.

~ "forgot" is used for the simple past tense, no helping verbs at all

~ "forgotten" (past participle) is used as a verbal adjective and with different helping verbs to form perfect tenses and others.