Understanding Symbolic Logic, Virginia Klenk Prentice Hall, 2008, 5th edition, Unit 20, 1(m), p. 381

The premise is notable for the use of a superlative, but unlike the examples commonly used in logic textbooks, it does not single out a named individual to whom the given quality is attributed. Here, 'a dog', rather than, say, Rover or Fido, is a class of animals that answers to the description of 'canine'. We need to adjust our translation to fit the message which the statement conveys.

The fastest animal on the track is a dog. Therefore, any animal on the track that isn't a dog can be outrun by some dog.

1. (x)(y){[Ax • Tx • Ay • Ty • Dy • ¬ (x = y)] ⊃Fyx} • (∃y)(Ay • Ty • Dy)
2. ∴(x)[(Ax • Tx • ¬ Dx) ⊃(∃y)(Dy • Fyx)]
3. * ¬ (x)[(Ax • Tx • ¬ Dx) ⊃(∃y)(Dy • Fyx)] ......... AIP
4. * (∃x)[Ax • Tx • ¬ Dx • (y)(Dy ⊃ ¬ Fyx)] ......... 3QC
5. * Aa • Ta • ¬ Da • (y)(Dy ⊃ ¬ Fya) ......... 4 EI x/a
6. * (∃y)(Ay • Ty • Dy) ......... 1 Simp.
7. * Am • Tm • Dm ......... 6 EI y/m
8. * ¬ Da ......... 5 Simp.
9. * Dm ......... 7 Simp.
10. * ¬ (a = m) ......... 8,9 Id
11. * (y){[Aa • Ta • Ay • Ty • Dy • ¬ (a = y)] ⊃Fya} ......... 1 UI x/a
12. * [Aa • Ta • Am • Tm • Dm • ¬ (a = m)] ⊃Fma ......... 11 UI y/m
13. * Aa • Ta ......... 5 Simp.
14. * Aa • Ta • Am • Tm • Dm • ¬ (a = m) ......... 13,7,10 Conj.
15. * Fma ......... 14,12 MP
16. * (y)(Dy ⊃ ¬ Fya) ......... 5 Simp.
17. * Dm ⊃ ¬ Fma ......... 16 UI y/m
18. * ¬ Fma ......... 9,17 MP
19. * Fma • ¬ Fma ......... 15,18 Conj.
20. ¬ ¬ (x)[(Ax • Tx • ¬ Dx) ⊃(∃y)(Dy • Fyx) ......... 3-19 IP
21. (x)[(Ax • Tx • ¬ Dx) ⊃(∃y)(Dy • Fyx) ......... 20 DN