The Logic Book, M. Bergmann, J. Moor, J. Nelson, McGraw Hill, 2004, 10.4E, 6(f), p. 557

The following set of sentences is inconsistent. Prove.

1. ¬ (∃y)Jy ......... Assumption
2. ¬ (∃x)¬ Hx ......... Assumption
3. (z)(Jz ∨¬ Hz) ......... Assumption
4. (y) ¬ Jy ......... 1 QC
5. (x) ¬ ¬ Hx ......... 2 QC
6. (x)Hx ......... 5 DN
7. Jz ∨¬ Hz ......... 3 UI z/z
8. ¬ Jz ......... 4 UI y/z
9. Hz ......... 6 UI x/z
10. ¬ Hz ......... 7,8 DS
11. Hz • ¬ Hz ......... 9,10 Conj.