Current Status: Trying to learn a new thing.
I think they called it Coq because it's hard.. (Sorry 
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Also, QF SMT solvers by themselves don't know anything about complete proves of temporal properties. You can use techniques like k-induction with SMT solvers, but they are very limited. Stuff like IC3 is better but also has massive limitations.
With an SMT solver that excepts quantified SMT formulas you can express most temporal properties easily, but except for the most trivial problems the SMT solver will either not finish before the heat death of the universe, or it will return UNKNOWN.
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thanks, I didn't know that SMT solvers had such limitations
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