| $(A\ \rightarrow\ B)\ \&\ (D\ \rightarrow\ E)$ |
| $(B\ \rightarrow\ T)\ \&\ (E\ \rightarrow\ A)$ |
| $\sim\ T$ |
| $\therefore\ \sim\ D\ \&\ \sim\ T$ |
| $(1)\ (A\ \rightarrow\ B)\ \&\ (D\ \rightarrow\ E)$ | $P$ |
| $(2)\ (B\ \rightarrow\ T)\ \&\ (E\ \rightarrow\ A)$ | $P$ |
| $(3)\ \sim\ T$ | $P/\ \therefore\ \sim\ D\ \&\ \sim\ T$ |
| $(4)\ B\ \rightarrow\ T$ | $2,$ Simp. |
| $(5)\ \sim \ B$ | $4, 3, MT$ |
| $(6)\ A\ \rightarrow\ B$ | $1,$ Simp. |
| $(7)\ \sim\ A$ | $6, 5, MT$ |
| $(8)\ E\ \rightarrow\ A$ | $2,$ Simp. |
| $(9)\ \sim\ E$ | $8, 7, MT$ |
| $(10)\ D\ \rightarrow\ E$ | $1,$ Simp. |
| $(11)\ \sim\ D$ | $10, 9, MT$ |
| $(12)\ \sim\ D\ \&\ \sim\ T$ | $11, 3,$ Conj. |
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| $A \rightarrow B$ |
| $C \rightarrow D$ |
| $\sim B\ \&\ \sim D$ |
| $(\sim A\ \&\ \sim C)\ v\ P$ |
| $(M\ v\ N)\ \&\ K$ |
| $[M\ v\ N)\ v\ L] \rightarrow H$ |
| $[( M\ v\ N)\ \&\ H] \rightarrow Z$ |
| $\therefore Z$ |
| (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 |
| $A \rightarrow B$ |
| $B \rightarrow S$ |
| $A\ \&\ T$ |
| $\therefore S\ \&\ T$ |