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  1. This sequent is not provable, counter example: \\
  2. $\mathcal{M} : p = T, q = F, r = F$ \\
  3. $\mathcal{M} \models (\lnot p \implies q) \land (q \implies r), \lnot r$ \\
  4. $\mathcal{M} \nmodels \lnot \lnot \lnot r \land \lnot p$