Hello,
(last section)
but, I got a counterexample which I think is not correct since both automata are not accepting this counterexample:
I tried to compare automata which presents P1 U p2 and automata which answers 
"no" to everything and I got cycle{P1 & !p2}  as a counterexample.
 attached picture with the code and examples from Ide.
 2. Is there a way to transfer spot automata to LTL?
Regards,
Roi