$S,C,D,O$ are statements.
Then $((\neg S\rightarrow C)\wedge(C\rightarrow\neg D)\wedge(D\vee O)\wedge \neg O)\rightarrow S$ is a tautology.
This can be checked by a truth table or by the following.
(1) $\neg S\rightarrow C$
(2) $C\rightarrow\neg D$
(3) $D\vee O$
(4) $\neg O$
((1),(2),(3),(4) are premises.)
(5) $D$ ((3),(4)$\implies$(5))
(6) $\neg C$ ((2),(5)$\implies$(6))
(7) $S$ ((1),(6)$\implies$(7))
I don't understand why the above process, (1)-(7) verifies $((\neg S\rightarrow C)\wedge(C\rightarrow\neg D)\wedge(D\vee O)\wedge \neg O)\rightarrow S$ is a tautology.