Plagiarism software will not detect assignments that use Spinbot or other paraphrasing software. How do you prove a student is doing so?
I think you would need to know the particular source text that you believe it was modified from. In that case, demonstrating identical structure ought to be sufficient: a sentence-by-sentence comparison ought to show convincingly that the exact same ideas have been used in the same order. This absolutely falls under the definition of plagiarism (whether or not it was done in an automated way by a spinbot), and provided the text is of a decent length, it would be unreasonable for the student to claim that they happened upon the same structure by coincidence.
If you don't have the original text, I'm not aware of any tools you could use to search for it - that would seem to be a very complex (though maybe not insurmountable) AI problem. But if you don't know the source text, how would you suspect it in the first place (unless you'd caught the student in the act)?
You don't need to prove it. A mechanical paraphrase is no different from a paraphrase written by the student. What makes plagiarism is the absence of a citation. I've found that it is generally luminously clear when (undergraduate) students have copied without citation, whether paraphrased or not.
If you can recognize the original source, then paraphrase without citation is clear. If not, asking the student for more detail about the idea that the student claims as his own will generally demonstrate the misconduct. Whether you can take formal action in the latter case depends on the rules and culture of your institution.
Well, a good clue would be sentences that don't actually make sense, like the classic:
“I could hear the charlatan of the ducks in the distance,” and other examples stolen from:
Unfortunately, the only way I can think of to identify this automatically would require custom-written software, and a decent amount of work. Essentially, you could take chunks of text, throw it into a spinbot repeatedly, and then see if you turn up matches. This seems like a computationally difficult problem, since you have to test (number of synonyms)^(sentence length) options - you could only do this for short sentences. Maybe it's possible to cut that down by going to more-common synonyms first. Sounds a little like a problem where testing a proposed match is a lot faster than actually finding the match. Maybe you could get some interest from folks on https://cs.stackexchange.com/ to see if defeating spinbot plagiarism is NP-Complete!
A method that might be useful is contextual analysis. A statement that used jargon that seems out of place, or whose meaning doesn’t tie into the larger narrative lends weight to the possibility that the words were not the authors own.
If you ever do in person reviews of papers, you can cross examine the author on his or her knowledge and intent of including the statements.
If they are able to defend themselves, then the possibility shifts from suspected plagiarism to authentic knowledge.
If not, then you’ll know.
Nevertheless, it will be up to you to determine how much time resources you want to devote to authenticating the work of your students.
Could you tell us more about your assignments, your suspicions, your students, and your grading scheme? For my answer, I'll make a simple assumption but please straighten me out if this is wrong.
I'll assume that the plagiarism problem comes up primarily because you are assigning some standard homework problems for which other students have posted solutions online. Example: http://www.amandalscott.com/wp-content/uploads/2016/02/Amanda-Scott-PRL-102-Final-Fall-2015.pdf. This is a homework assignment that a student submitted for a class two years ago and then uploaded to the web. Who knows why!
The assignment comes from a standard textbook. This very same assignment is given to large numbers of students across the country every semester.
If this is the type of situation you're facing, as an instructor... I think the solution lies in modifying the assignment. Then if the work submitted doesn't hang together, you grade it accordingly. Let's suppose your student tried to cobble something together based on a homework submission someone else turned in and posted on the web, for the homework problem as it appears in the textbook, which is a slightly different assignment than the one you gave. If your student learned something from the submission s/he found on the web, and then did a good job of cobbling; OR if your student did not do a very good job of cobbling -- in both cases, just grade the work the way you would normally do. Does the prose have good structure and readability? Do the ideas flow with good logic? Does the document hit the important points? Not too short, not too wordy? Etc.