$\{1\}$ | (1) $(W \vee P) \rightarrow I$ | Premise |
$\{2\}$ | (2) $I \rightarrow C \vee S$ | Premise |
$\{3\}$ | (3) $S \rightarrow U$ | Premise |
$\{4\}$ | (4) $\neg C \wedge \neg U$ | Premise |
$\{4\}$ | (5) $\neg U \wedge \neg C$ | 4 T Commutative Law of $\wedge$ |
$\{4\}$ | (6) $\neg C$ | 4 T Law of Simplification |
$\{4\}$ | (7) $\neg U$ | 5 T Law of Simplification |
$\{3\}$ | (8) $\neg U \rightarrow \neg S$ | 3 T Law of Contraposition |
$\{3,4\}$ | (9) $\neg S$ | 7 8 T Law of Detachment |
$\{2\}$ | (10) $\neg(C \vee S) \rightarrow \neg I$ | 2 T Law of Contraposition |
$\{1\}$ | (11) $\neg I \rightarrow \neg (W \vee P)$ | 1 T Law of Contraposition |
$\{1,2\}$ | (12) $\neg (C \vee S) \rightarrow \neg (W \vee P)$ | 10 11 T Law of Hypothetical Syllogism |
$\{3,4\}$ | (13) $\neg C \wedge \neg S$ | 6 9 T Law of Adjunction |
$\{3,4\}$ | (14) $\neg (C \vee S)$ | 13 T DeMorgan's Law |
$\{1,2,3,4\}$ | (15) $\neg(W \vee P)$ | 12 14 T Law of Detachment |
$\{1,2,3,4\}$ | (16) $\neg W \wedge \neg P$ | 15 T DeMorgan's Law |
$\{1,2,3,4\}$ | (17) $\neg W$ | 16 T Law of Simplification |
$\{1\}$ | (1) $D \vee \neg L$ | Premise |
$\{2\}$ | (2) $M \rightarrow \neg D$ | Premise |
$\{1\}$ | (3) $\neg L \vee D$ | 1 T Commutative Law of $\vee$ |
$\{1\}$ | (4) $L \rightarrow D$ | 3 T Law of Equivalence of Implication and Disjunction |
$\{2\}$ | (5) $\neg (\neg D) \rightarrow \neg M$ | 2 T Law of Contraposition |
$\{6\}$ | (6) $D$ | Premise |
$\{6\}$ | (7) $\neg(\neg D)$ | 6 T Law of Double Negation |
$\{2,6\}$ | (8) $\neg M$ | 5 7 T Law of Detachment |
$\{2\}$ | (9) $D \rightarrow \neg M$ | 6 8 C.P. |
$\{1,2\}$ | (10) $L \rightarrow \neg M$ | 4 9 Law of Hypothetical Syllogism |
$\{1\}$ | (1) $J \rightarrow \neg N$ | Premise |
$\{2\}$ | (2) $\neg J \rightarrow \neg D$ | Premise |
$\{3\}$ | (3) $\neg D \rightarrow A$ | Premise |
$\{4\}$ | (4) $R \rightarrow N$ | Premise |
$\{1\}$ | (5) $\neg (\neg N) \rightarrow \neg J$ | 1 T Law of Contraposition |
$\{6\}$ | (6) $N$ | Premise |
$\{6\}$ | (7) $\neg (\neg N)$ | 6 T Law of Double Negation |
$\{1,6\}$ | (8) $\neg J$ | 5 7 T Law of Detachment |
$\{1\}$ | (9) $N \rightarrow \neg J$ | 6 8 C.P. |
$\{1,4\}$ | (10) $R \rightarrow \neg J$ | 4 9 T Law of Hypothetical Syllogism |
$\{1,2,4\}$ | (11) $R \rightarrow \neg D$ | 2 10 T Law of Hypothetical Syllogism |
$\{1,2,3,4\}$ | (12) $R \rightarrow A$ | 3 11 T Law of Hypothetical Syllogism |
$\{1,2,3,4\}$ | (13) $\neg R \vee A$ | 12 T Law of Equivalence of Implication and Disjunction |
$\{1\}$ | (1) $S \vee O$ | Premise |
$\{2\}$ | (2) $S \rightarrow \neg E$ | Premise |
$\{3\}$ | (3) $O \rightarrow M$ | Premise |
$\{2\}$ | (4) $\neg(\neg E) \rightarrow \neg S$ | 2 T Law of Contraposition |
$\{5\}$ | (5) $E$ | Premise |
$\{5\}$ | (6) $\neg (\neg E)$ | 5 T Law of Double Negation |
$\{2,5\}$ | (7) $\neg S$ | 4 6 T Law of Detachment |
$\{2\}$ | (8) $E \rightarrow \neg S$ | 5 7 C.P. |
$\{9\}$ | (9) $\neg S$ | Premise |
$\{1,9\}$ | (10) $O$ | 1 9 T Modus tollendo tollens |
$\{1\}$ | (11) $\neg S \rightarrow O$ | 9 10 C.P. |
$\{1,2\}$ | (12) $E \rightarrow O$ | 8 11 T Law of Hypothetical Syllogism |
$\{1,2,3\}$ | (13) $E \rightarrow M$ | 3 12 T Law of Hypothetical Syllogism |
$\{1,2,3\}$ | (14) $\neg E \vee M$ | 13 T Law of Equivalence of Implication and Disjunction |