Deduction, Daniel Bonevac, Blackwell Publishing 2003, 2nd edition, 8.3, problem 2, p. 238

The argument goes:

Everything other than God had a creator. So, given any two things, at least one had a creator.

We can choose the level of detail we want our predicates to capture in symbolizing this argument. I've opted for the more complete translation here. Glossary: Cxy - x created y, g - God. The proof follows.

1. (x)[¬(x=g) ⊃(∃y)(Cyx • ¬ Cyg)]
2. ∴(x)(y)[¬ (x=y) ⊃(∃z)(Czx ∨Czy)]
3. * ¬ (x)(y)[¬ (x=y) ⊃(∃z)(Czx ∨Czy)] ......... AIP
4. * (∃x)(∃y)[ ¬ (x=y) • (z)(¬Czx • ¬ Czy)] ......... 3CQ
5. * (∃y)[ ¬ (a=y) • (z)(¬Cza • ¬ Czy)] ......... 4EI x/a
6. * ¬ (a=m) • (z)(¬Cza • ¬ Czm) ......... 5EI y/m
7. * ¬ (a=m) ......... 6Simp.
8. * (z)(¬Cza • ¬ Czm) ......... 6Simp.
9. * ¬(a=g) ⊃(∃y)(Cya • ¬ Cyg) ......... 1UI x/a
10. * ¬Cya • ¬ Cym ......... 8UI z/y
11. * ¬Cya ......... 10Simp.
12. * ¬Cya ∨Cyg ......... 11Add.
13. * (y)(¬Cya ∨Cyg) ......... 12UG
14. * (y)¬ (Cya • ¬ Cyg) ......... 13DeM
15. * ¬ (∃y)(Cya • ¬ Cyg) ......... 14CQ
16. * a = g ......... 15,9MT
17. * ¬ (g = m) ......... 16,7Id
18. * ¬ (m = g) ......... 17Comm.
19. * ¬(m=g) ⊃(∃y)(Cym • ¬ Cyg) ......... 1UI x/m
20. * (∃y)(Cym • ¬ Cyg) ......... 18,19MP
21. * Crm • ¬ Crg ......... 20EI y/r
22. * Crm ......... 21Simp.
23. * ¬Cra • ¬ Crm ......... 8UI z/r
24. * ¬ Crm ......... 23Simp.
25. * Crm • ¬ Crm ......... 22,24Conj.
26. ¬ ¬ (x)(y)[¬ (x=y) ⊃(∃z)(Czx ∨Czy)] ......... 3-25IP
27. (x)(y)[¬ (x=y) ⊃(∃z)(Czx ∨Czy)] ......... 26DN