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I wanted to confirm, Is the below solution correct?. I am trying to violate S1 as S2 is always true.
You are right. The second formula is always true. The first formula needs to be not satisfied. This can be done by having a path that (from the third step on) shows both a at some point and ¬a at some other point. Alternating between these two states is an option.
See also task 8a in https://es.cs.uni-kl.de/teaching/vrs/exams/2018.08.21.vrs/2018.08.21.vrs.solutions.pdf