Froggy Problem Validation of Conclusion
This is the Validation of Conclusion for Lewis Carroll's Froggy problem using the Dictionary given by Lewis Carroll.
We assume the negative of the conclusion viz E & ~a & ~b & d and show this leads to a contradiction:
Original Premisses:
01.   ~s ⇒ r
02.   ~m & h ⇒ ~d
03.   E ⇒ a & ~k
04.   l & n ⇒ v
05.   z & m ⇒ ~c
06.   t ⇒ A
07.   ~s & ~n & c ⇒ ~r
08.   z & v ⇒ m
09.   E ⇒ w
10.   v & k & m ⇒ t
11.   E ⇒ s & c & ~n
12.   A ⇒ ~B
13.   k & ~h ⇒ n
14.   r ⇒ c
15.   ~v & ~a & ~h ⇒ l
16.   w & ~t & s ⇒ n
17.   d ⇒ e & k
18.   s & n & ~b ⇒ B
19.   w & e ⇒ z
20.   ~t & ~A & ~r & ~c ⇒ ~n

HE & ~a & ~b & dHypothesis
21 E ⇒ w By 9
22 w ⇒ z ∨ ~e By 19
23 d ⇒ eBy 17
24eBy H, 23
25 w ⇒ z By 22, 24
26 z ⇒ ~c ∨ ~m By 5
27 E ⇒ cBy 11
28cBy H, 27
29 z ⇒ ~mBy 26, 28
30 E ⇒ ~m By 21, 25, 29
31~mBy H, 30
32 E ⇒ z By 21, 25
33zBy H, 32
34 ~m ⇒ ~z ∨ ~v By 8
35 ~v By 31, 33, 34
36 ~v ⇒ ~l ∨ ~n By 4
37~l ∨ ~nBy 35, 36
38 ~l ⇒ v ∨ a ∨ hBy 15
39~aBy H
40 ~l ⇒ h So by 35,38,39
41 h ⇒ ~d ∨ m By 2
42 dBy H
43 ~h By 31, 42, 41
44 l By 40
45 ~v ⇒ ~nBy 36,44
46 ~n By 35, 45
47 ~n ⇒ ~k ∨ hBy 13
48kBy 42, 17
49~n ⇒ h By 47, 48
50 ~n ⇒ ~d ∨ m By 49, 41
51 d&~m By 31, 42
52nBy 50, 51
53Contradiction46, 52
54~(E & ~a & ~b & d)By H, 53
Note that the attribute b is not used in this derivation and therefore the broader conclusion ~(E & ~a & d) holds, as explained in the notes on the solution by method of trees
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