Which of the following proofs are correct derivations in the sequent calculus (note that labels of the rules have been omitted).

Given propositional formula

(¬c) ∧ (a ∨ b ∨ c)  ∧ (d ∨ ¬a) ∧ (e ∨ ¬b) ∧ (¬f ∨ ¬c) ∧ (¬a ∨ ¬b) ∧  (¬d ∨ e) ∧ (¬e ∨ ¬c) ∧ (¬f ∨ ¬c)

Which two clauses given in the list below can be derived with one or more applications of the resolution rule?

(Keep in mind that disjunction is commutative, i.e., the order of literals in a clause is irrelevant).

Which of the following rules are applicable on sequent ¬(a ∧ (¬c ∨ d)), ¬e, a  ⊢ ¬a ∧ b in the next step?