Prompted by the use of a poster who obviously uses supine as a variant for to-infinitive I was really a bit annoyed about such confusion of terms, as supine is a term in Latin grammar for a rare verb form.
So I googled for supine and looked up the word in Oxford Dictionaries. They have nothing about the use of supine /'su:pain/'sju:pain/ as a variant for to-infinitive.
Astonishingly en.wikipedia mentions that supine is sometimes used for to-infinitive, but only when it is used in subject position. I have the impression wikipedia has digged up a term that was last used a hundred years ago. Wikipedia has a preference for rare grammar terms.
As I said this is my impression. But I would like to hear views of members of this forum. The term is not listed in the register of Oxford Guide to English Grammar nor of Longman English Grammar.