Quantifiers/Axiom to Clausal form

Question

Question :

Consider the following sentences and prove that "Diana will win the game"

1.All Players are clever.

2.Anyone who is clever and dedicated can play the game well.

3.Anyone who is playing the game well will win his/her game.

4.Diana is a dedicated player.

So my first attempt was representing the using axioms as follows(Please note that I'll be using the following notations as follows:

VX - For all X(Universal quantifier)

EX - For some X(Existential quantifier)

Let P(X) be X is a player

C(X) be X is clever

D(X) be X is dedicated

G(X) be X can play the game well

W(X) be X will win his/her game

Axiom Form :

1. VX [P(X) --> C(X) ]

2. [ ( C(X) ^ D(X) ) --> G(X) ]

3. VX [ G(X) --> W(X) ]

4. P(Diana) --> D(X)

Clausal Form :

1. ~P(X) v C(X)

2. ~C(X) v ~D(X) v G(X)

3. ~G(X) v W(X)

4. ~P(Diana) v D(X)

Can anyone please explain how to prove that "Diana will win the game" , using above clausal forms.

Thanks!

Answer 1

Every player is clever, C

every player who is dedicated and clever plays well. D & C will play Well

Diana is dedicated. and clever, since all players are clever, so Diana plays well

Any player who plays well wins. Diana plays well, so she will win.