[bigwally]

They are here in one block and Cecil One's posts are quite explicit:

I'm uncertain about how these fit together or separate.
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The "actively" is something that is not a normal move while performing his/her duties in the batter's box. Attempting to strike the pitch is part of the duties of a batter and that includes the entire swing, from start to finish.
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The batter is permitted to swing at the ball and in most cases there is a follow-through associated with that swing. Unless you observe the batter do something out of the norm with that follow through, there is no violation.
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In USA Softball, Rule 7-4-I and Rule Supplement 24 says that if a batter swings and misses the pitch, and then on his/her follow-through hits the ball, or hits the ball after it bounces off the catcher or his/her mitt, then the ball is dead and runners cannot advance.
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I guess the natural duties
of the batter theory would not apply in that case and seems that it may not, in fact, apply when the batters follow through knocks the ball out of the catchers glove when there is a steal being attempted according to your quotes of the other rule sets.
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And this one from Cecil One:

I am still finding I a bit ambiguous about the swing follow through hitting ball or catcher being INT and any natural part of the swing not being INT.

"In USA Softball, Rule 7-4-I and Rule Supplement 24 says that if a batter swings and misses the pitch, and then on his/her follow-through hits the ball, or hits the ball after it bounces off the catcher or his/her mitt, then the ball is dead and runners cannot advance. "

AND

"So a normal hitting action and a normal follow thru are not interference"





And this post from Manny:

Need to read the rules on this for the various alphabets.

In USA Softball, Rule 7-4-I and Rule Supplement 24 says that if a batter swings and misses the pitch, and then on his/her follow-through hits the ball, or hits the ball after it bounces off the catcher or his/her mitt, then the ball is dead and runners cannot advance. If this happens on Strike 3, then the batter has interfered with a dropped third strike and she's out.