Discrete Math

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 and clausal form 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 guide me how to prove that "Diana will win the game" , using above clausal forms? Am I following the correct path displaying the above sentences in axioms and in clausal form?


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asked by Arya

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