Did Classical Music influence Prog?

Strange as it may seem, I believe so. If we examine: the long forms, changing sections, form structure of establishing themes, solos, theme illusion and recapitulation and reiteration of theme; they all seem to be inherent in the very best that prog has to offer. Look at Close To The Edge, Gates Of Delirium, Karn Evil 9, Dogs, Suppers Ready, The Colony Of Slippermen, Thick as A Brick. All of them have the many qualities of classical music that was created by the masters.

Yes, of course Prog is influenced by Classical.  So many prog artists have had classical training, and there are significant differences in the prog approach to rock than in the blues approach - structure, tonality, etc.   This is not to say that Classical is the only influence, though.  Rock, at its core, is blues, and we see plenty of that in Prog, notably in Heavy-Prog and Proto-Prog bands.  There is also a Jazz influence, and a Raga influence, and a Celtic influence, etc. as well.  At the same time, let's acknowledge that Classical is a broad category.  Beethoven is not the same as Stravinsky.  To run down specific instances of influence would be a matter of identifying the influences of individual musicians in Prog.  Is the Classical influence seen everywhere?  Probably not.  Is it seen in many prominent artists?  Most certainly.