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