Iet U: Universe of Discourse or Domain.

Universal Instantiation

$12$

Universal Goneralization

:$.\frac{P(c)\text{f}\text{o}\text{r}\text{a}\text{n}\text{y}\text{a}\text{r}\text{b}\text{i}\text{r}\text{a}\text{r}\text{y}\text{c}\text{i}\text{n}\text{U}}{\text{A}\text{A}\text{x}\text{P}(x)}$

Existential Instantiation

:$.\frac{\text{E}\text{E}\text{x}\text{P}(x)}{P(c)\text{f}\text{o}\text{r}\text{s}\text{o}\text{m}\text{e}\text{e}\text{l}\text{e}\text{m}\text{e}\text{n}\text{t}\text{c}\text{i}\text{n}\text{U}}$

Existential Generalization

:$.\frac{P(c)\text{f}\text{o}\text{r}\text{s}\text{o}\text{m}\text{e}\text{e}\text{l}\text{e}\text{m}\text{e}\text{n}\text{t}\text{c}\text{i}\text{n}\text{U}}{\text{E}\text{E}\text{x}\text{P}(x)}$

Show that the premises lead to the conclusion:

"All lions are fierce. Some lions do not drink coffee.

Therefore, Some fierce creatures do not drink coffee."

Let $L(x)$ be $"x$ is a lion," $F(x)$ be $"x$ is fierce," and $C(x)$ be $"x$ drinks coffee."