| $T \rightarrow B$ |
| $B \rightarrow ( \sim\ P \rightarrow\ \sim\ Q)$ |
| $\sim\ P\ \&\ \sim\ R$ |
| $T$ |
| $\therefore\sim\ Q\ v\ X$ |
| $(1)\ T\ \rightarrow\ B$ | $P$ |
| $(2)\ B\ \rightarrow\ (\sim\ P\ \rightarrow\ \sim\ Q)$ | $P$ |
| $(3)\ \sim\ P\ \&\ \sim\ R$ | $P$ |
| $(4)\ T$ | $P/ \therefore\ \sim\ Q\ v\ X$ |
| $(5)\ B$ | $1, 4, MP$ |
| $(6)\ \sim\ P\ \rightarrow\ \sim\ Q$ | $2, 5, MP$ |
| $(7)\ \sim\ P$ | $3,$ Simp. |
| $(8)\ \sim\ Q$ | $6, 7, MP$ |
| $(9)\ \sim\ Q\ v\ X$ | $8,$ Add. |
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| $N \ \&\ M$ |
| $\sim S\ (T \ \&\ W)$ |
| $(P \ \&\ R)\ v\ \sim S$ |
| $(N \ \&\ M) \rightarrow \sim (T \ \&\ W)$ |
| $(R \ \&\ N)\ v\ S$ |
| (G $\rightarrow$ H) $\rightarrow$ (I $\leftrightarrow$ J) |
| K v ~(L $\rightarrow$ M) |
| (G $\rightarrow$ H) v ~ K |
| N $\rightarrow$ (L $\rightarrow$ M) |
| ~ (I J) |
| $\therefore$~ N & ~ K |
| $A \rightarrow B$ |
| $B \rightarrow S$ |
| $A\ \&\ T$ |
| $\therefore S\ \&\ T$ |
| $A \rightarrow B$ |
| $C \rightarrow B$ |
| $(\sim\ A\ \&\ \sim \ C)\ \rightarrow\ (D\ \rightarrow\ E)$ |
| $(E\ \rightarrow\ G)\ \&\ (D\ v\ E)$ |
| $E\ v\ G$ |