Let A be a set of animals, let U(x) mean "animal x is a unicorn", and H(x) mean "animal x has a horn". Let Premise 1 be "forall x: U(x) --> H(x)" and let Premise 2 be "forall x: U(x) --> not H(x)". The following is a proof that these two premises imply the statement C, "not exists y: U(y)".

1) Let z be an arbitrary animal.

2) By (rule 1) applied to Premise 1, U(z) --> H(z).

3) By (rule 1) applied to Premise 2, U(z) --> not H(z).

4) Assume U(z). By (rule 2), both H(z) and not H(z) are true.

5) By (rule 3), we can conclude "not U(z)".

6) By (rule 4), we have proved "forall y: not U(y)".

7) By (rule 5), this is equivalent to "not exists y: U(y)".

What are rules 1-5?

Select one:

a. Generalization, Modus Ponens, Vacuous Proof, Specification, Negation of Quantifiersb. Specification, Modus Ponens, Proof by Contradiction, Generalization, Negation of Quantifiersc. Specification, Vacuous Proof, Proof by Contradiction, Instantiation, Negation of Quantifiers.d. Specification, Modus Ponens, Trivial Proof, Negation of Quantifiers, Existence