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Resources :

Z3 site has got some very good examples to test concepts out, Usually we we wont write Z3 SMTLIB format directly but use some APIs/bindings available in scala, C++ or Python. Dafny uses Hoare Logic Structure. The "Loop Invariants" part has a nice explanation on what are the problems with loop unrolling. Dafny is based on Boogie which happens to be an IVL.

Examples & Links :