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I'm trying to find the CNF of the $(p \rightarrow q) \rightarrow p$ and $\lnot (q \wedge (\lnot p \rightarrow q))$, and afterwards proving it's validity. As i'm new to CNF i wanted to ensure i've found the right CNF before trying to move on, so for $(p \rightarrow q) \rightarrow p$:

the normal from is: $p \rightarrow q \wedge q \rightarrow p$

and it's valid?

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    $\begingroup$ The CNF shouldn't contain the "$\rightarrow$" operation $\endgroup$ – HEKTO Dec 3 '18 at 23:03
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Your formula is incorrect as CNF. Conjunctive normal form (CNF) is a normal form like

$$ (a_1 \vee \neg a_2 \vee \dots \vee a_n) \wedge (\neg b_1 \vee \dots \vee b_m) \wedge \dots \wedge (c_1 \vee \dots \vee c_l) $$

therefore a formula in CNF has only literals (i.e. atoms or negated atoms), $\wedge$, and $\vee$. It doesn't have $\to$.

If it's allowed to transform $p \to q$ to its equivalent formula $(\neg p) \vee q$, you can use this for the first step to convert a given formula to a CNF formula.

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