User blog comment:Boboris02/MBOT/@comment-24920136-20161219043958

I honestly thought this blog post was some sort of very elaborate prank. I apologize for laughing while skimming the body  of text, now that  it seems boboris did in fact intend to be serious on this.

To chip in, that "long chain" U operator doesn't work, it reduces to "next step" operator, but it doesn't nest the "inside of"  part, so in fact PHI can't even reach f_w(n) level using a finite amount of words, Let alone fw^w(n) level

What you seem to believe is your source of strength is actually your greatest weakness, let me quote your post: "Since their definitions aren't well-defind that leaves them open for any definition that you can set,respecting the conditions above.This makes Phi systems particularly strong,since we do not need a new symbol for ...."

This makes phi systems weak, because it requires ad-hoc definitions at each step, which makes it impossible to employ diagonalization when working with PHI