How to eliminate rows that do not meet certain criteria in MySQL

Question

I have database that is used to manage sport academy. Now I have table for players, class and class_player (that join the other two tables). What I want to do is when enrolling players to classA, the players which are enrolled to classB (which intersect with classA time) are removed from the result-set of the select statement

Player Table:         class Table               class_player Table
ID INT                ID INT                    classID INT
                      timeFrom TIME             playerID INT
                      timeTo TIME
                      days BIT(7)

In "class" Table: timeFrom: is the begining of the class time
timeTo: is the end of the class time
days: holds the days that the class is teached,
ex: 0x000001 -> one of the seven days will include this class

The select statement I use to get the players:

(
SELECT `players`.`ID`
FROM `players` JOIN `class_player` ON `players`.`ID` = `class_player`.`playerID`
JOIN `classes` ON `class_player`.`classID` = `classes`.`ID`
WHERE (
    -- Get all player with no day intersection
    -- 1 is a variable of the entered day ex: 0x00100100
    NOT (`classes`.`days` & 1)

    -- Time Intersection
    OR (
            -- Entered "FROM" != Existing "FROM"
            '10:00:00' != `timeFrom` 

            -- Entered "TO" != Existing "TO"
            AND '13:00:00' != `timeTo`

            -- Entered "FROM" Not Between Existing (FROM, TO)
            AND NOT ('10:00:00' > `timeFrom` AND  '10:00:00' < `timeTo`)
            -- AND '10:00:00' NOT BETWEEN `timeFrom` AND `timeTo`

            -- Entered "TO" Not Between Existing (FROM, TO)
            AND NOT ('13:00:00' < `timeTo` AND '13:00:00' > `timeFrom`)
            -- AND '13:00:00' NOT BETWEEN `timeFrom` AND `timeTo` 

            -- Entered "FROM" Not Less than Existing "FROM"
            -- Entered "TO" Not Bigger than Existing "TO"
            AND NOT ('10:00:00' < `timeFrom` AND  '13:00:00' > `timeTo` )

        )
    )
)
UNION
(
    -- Players who don't have any classes
    SELECT `players`.`ID`
    FROM `players`
    WHERE `players`.`ID` NOT IN (SELECT `playerID` FROM `class_player`)
);

The problem is when a player have two classes one that does and one that doesn't intersect with classA time, this player is shown in the result-set!!

Answer 1

First: thanks to wojciechz for his efforts, the solution was in his second answer but i didn't understand it until my friend told me a similar solution.

Second: The solution in the SQL will be:
1. get all the players who are busy
2. then search for the player who are not in this list

SELECT DISTINCT `ID` FROM `players` WHERE `ID` NOT IN (
    (
        SELECT `players`.`ID`
        FROM `players` JOIN `class_player` ON `players`.`ID` = `class_player`.`playerID`
        JOIN `classes` ON `class_player`.`classID` = `classes`.`ID`
        WHERE (
            -- Get all player with no day intersection
            -- 1 is a variable of the entered day ex: 0x00100100
            (`classes`.`days` & 1)

            -- Time Intersection
            AND (
                    -- Entered "FROM" != Existed "FROM"
                    '10:00:00' = `timeFrom` 

                    -- Entered "TO" != Existed "TO"
                    OR '13:00:00' = `timeTo`

                    -- Entered "FROM" Not Between Existing (FROM, TO)
                    OR ('10:00:00' > `timeFrom` AND  '10:00:00' < `timeTo`)
                    -- AND '10:00:00' NOT BETWEEN `timeFrom` AND `timeTo`

                    -- Entered "TO" Not Between Existing (FROM, TO)
                    OR ('13:00:00' < `timeTo` AND '13:00:00' > `timeFrom`)
                    -- AND '13:00:00' NOT BETWEEN `timeFrom` AND `timeTo` 

                    -- Entered "FROM" Not Less than Existing "FROM"
                    -- Entered "TO" Not Bigger than Existing "TO"
                    OR ('10:00:00' < `timeFrom` AND  '13:00:00' > `timeTo` )

            )
        )
    )
    UNION
    (
        -- ANOTHER DATE AND TIME
    )
)