Inorder to or In order to?

Well, there are many constructions where either is correct, i.e.

Alicia wasn't able to prove that she wasn't at the party.

Alicia brought photos in order to prove that she was at the party. (Now in this case, you could use "to prove" also and be grammatically correct.)

"In order to" is an expression used to invoke the purpose for which something was done and is usually followed by a verb in infinitive form.