Looking on the internet deeply has found these results:

to the contrary, is the most popular phrase on the web.

in contrary, 1991,000 results on the web	to the contrary, 154,000,000 results on the web More popular!
Some examples and use cases from the internet:	Some examples and use cases from the internet:
It doesn't look like this phrase is very popular! The search could not find any examples on the internet.	Despite your words to the contrary, clearly you've lost faith in my judgment. Ultimately, despite constant assertions to the contrary, this would, of course, set a precedent. Unless they have evidence to the contrary, Member States shall consider that labels and product information comply with the provisions of this Directive. Until proof to the contrary, I can be your best friend. Your efforts to the contrary, I suppose. But quite to the contrary, Mr. Tuttle's mass seems to have grown larger. We are talking here about women because, until we receive proof to the contrary, men cannot give birth. Despite all the evidence to the contrary, she thought you were the one.

in contrary,

1991,000 results on the web

to the contrary,

154,000,000 results on the web

More popular!

It doesn't look like this phrase is very popular! The search could not find any examples on the internet.

Despite your words to the contrary, clearly you've lost faith in my judgment.
Ultimately, despite constant assertions to the contrary, this would, of course, set a precedent.
Unless they have evidence to the contrary, Member States shall consider that labels and product information comply with the provisions of this Directive.
Until proof to the contrary, I can be your best friend.
Your efforts to the contrary, I suppose.
But quite to the contrary, Mr. Tuttle's mass seems to have grown larger.
We are talking here about women because, until we receive proof to the contrary, men cannot give birth.
Despite all the evidence to the contrary, she thought you were the one.