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It has been said in Cliff's TOEFL book that negative sentences of gerund & to-infinite are formed by adding 'not' particle just before gerund & to-infinite. From that angle, following sentence 1 is supposed to be correct. But sentence 2 sounds good to me. Pls help to straighten it out.

1. I will stop not watching movies in future.

2. I will not stop watching movies in future.
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Anonymous1. I will stop not watching movies in future.
I have the habit of not watching movies. I will discontinue this habit and begin to watch movies in the future.
Anonymous2. I will not stop watching movies in future.
I have the habit of watching movies. I will not discontinue this habit and will continue to watch movies in the future.

CJ
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We have a modal verb (will) here, and the negative marker is usually put after the auxiliary/modal verb to make the sentence negative.

I will stop watching movies in the future. --> I will not stop watching movies in the future.

When we don't have an auxiliary, the negative marker is put before the gerund/infinitive phrase:

I prefer not to go to the movies tonight.
I prefer not going to the movies tonight.
But:
I do not prefer to go/going to the movies tonight.
Anonymous1. I will stop not watching movies in future.
This sentence is unnatural; it should be rewritten as:
I will start watching movies in the future. As you see, its meaning is different from I will not stop watching movies in the future.

[X post with CJ]