Symbolic Logic, D. Jacquette, Wadsworth, 2001, Chpt. 8, IV(19), p. 436

The argument is put like this:

"Either no multimillionaires are truly happy and satisfied with their lives, or some persons are dissatisfied with their lives. But everyone, at some level, is satisfied with his or her life. Therefore, all multimillionaires are dissatisfied with their lives."

The proof:

1. (x){(Px • Mx) ⊃(y)[(Lyx ⊃ (¬ Hxy • ¬ Sxy)]} ∨(∃x)[Px • (∃y)(Lyx • ¬ Sxy)]
2. (x)[Px ⊃(y)(Lyx ⊃Sxy)]
3. ∴(x)[(Px • Mx) ⊃(y)(Lyx ⊃ ¬ Sxy)]
4. (x){(Px • Mx) ⊃(y)[(Lyx ⊃ (¬ Hxy • ¬ Sxy)]} ∨¬ (x)[Px ⊃(y)(Lyx ⊃Sxy)] ......... 1 QC
5. (x){(Px • Mx) ⊃(y)[(Lyx ⊃ (¬ Hxy • ¬ Sxy)]} ......... 2,4 DS
6. * Px • Mx ......... ACP
7. * * Lyx ......... ACP
8. * * (Px • Mx) ⊃(y)[(Lyx ⊃ (¬ Hxy • ¬ Sxy)] ......... 5 UI x/x
9. * * (y)[(Lyx ⊃ (¬ Hxy • ¬ Sxy)] ......... 6,8 MP
10. * * Lyx ⊃ (¬ Hxy • ¬ Sxy) ......... 9 UI y/y
11. * * ¬ Hxy • ¬ Sxy ......... 7,10 MP
12. * * ¬ Sxy ......... 11 Simp.
13. * Lyx ⊃ ¬ Sxy ......... 7-12 CP
14. * (y)(Lyx ⊃ ¬ Sxy)] ......... 13 UG
15. (Px • Mx) ⊃(y)(Lyx ⊃ ¬ Sxy)] ......... 6-14 CP
16. (x){Px • Mx) ⊃(y)(Lyx ⊃ ¬ Sxy)]} ......... 15 UG