Symbolic Logic, Dale Jacquette, Wadsworth, 2001, Chpt. 8, IV(5), p.435

Prove:

Everything is either an unconscious or immaterial entity. All sentient beings, if they are physically embodied, are material entities. Hence, no sentient physically embodied beings are conscious.

The argument looks daunting, but in fact isn't. It is a good example, perhaps, of how the shape and sound of words stand in the way of our seeing the message. Once we get past the symbolisation, we can practically walk through to the conclusion.

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