What is wrong with my character comparison conditional?

I have a simple subroutine here that takes in a char array and returns a boolean value.

There is something wrong with my conditional. I tested it by passing a single character string "A", and so check_char = 97 and using short-circuit the conditional should give false for check_char != 'a'. The subroutine should return 1. But it always returns 0. Why is this? Something wrong here that I'm just not noticing?

/*
 * Checks string of characters and returns 1 if string is a valid DNA sequence and
 * returns 0 if string is not a valid DNA sequence.
 */
int is_valid_dna(char *sequence){
        int i;
        for( i = 0; i < ( sizeof(sequence) / sizeof(sequence[0]) ); i++ ){
                int check_char = tolower(sequence[i]);
                if( check_char != 'a' || check_char != 'c'   
                        || check_char != 'g' || check_char != 't' ){
                        return 0;
                }
        }
        /* If the subroutine made it this far, then the sequence is a valid DNA sequence */
        return 1;
}