2.
1. G-> (H&-K) (P)
2. H <-> (L&I) (P)
3. -IvK
(P)
4. G
(Negation of conclusion)
5. H&-K
(1,4)
6. H
(5)
7. -K
(5)
8. L&I
(2,6)
9. I
(8)
10. -I
(3,7)
11. I&-I
(9,10)
3.
1. F->(-GvH) (P)
2. F->G
(P)
3. -(HvI)
(P)
4. -(F->J)
(Negation of conclusion)
5. F
(4)
6. -J
(4)
7. -GvH
(1,5)
8. G
(2,5)
9. H
(7,8)
10. -H
(3)
11. H&-H
(9,10)
4.
1. FvH
(P)
2. -H<->(LvG)
(P)
3. (G&B)v[G&(K->G)] (P)
4. -F
(Negation of conclusion)
5. H
(1,4)
6. -(LvG)
(2,5)
7. -G
(6)
8. G&B
(3,7)
9. G
(8)
10. -G&G
(7,9)
5.
1. (-HvJ)vK
(P)
2. K-> -I
(P)
3. -[(H&I)->J]
(Negation of conclusion)
4. H&I
(3)
5. -J
(3)
6. H
(4)
7. I
(4)
8. -K
(2,7)
9. -HvJ
(1,8)
10. -H
(5,9)
11. H&-H
(6,10)
6.
1. (Av-B)v-C
(P)
2. (DvG)vC
(P)
3. -{-A -> [B->(GvD)]}
(Negation of conclusion)
4. -A
(3)
5. -[B->(GvD)]
(3)
6. B
(5)
7. -(GvD)
(5)
8. C
(2,7)
9. Av-B
(1,8)
10. -B
(4,9)
11. B&-B
(6,10)
7.
1. G&(A&N)
(P)
2. (A<-> -M)&(N->M)
(P)
3. -F
(Negation of conclusion)
4. G
(1)
5. A
(1)
6. N
(1)
7. -M
(2,5)
8. -N
(2,7)
9. N&-N
(6,8)