Question: I have to prove the following:

```
PREMISSES:

1. A IMPLIES ¬C
2. ¬ (B AND ¬A)
3. A OR B

CONCLUSION: ¬C

```

I've done the following so far:

```
^   AND
v   OR
¬   NEG
->  IMP

4. C              H
5. |  A           H
6. |  | ¬C        E-> 1,5
7. |  |  C        Reit 4
8. | ¬A           I¬ 5,6,7
9. |  B           H
10.|  |  B ^ ¬A   I^ 8,9
11.|  | ¬(B^¬A)   Reit 2
12.|  ¬B          I¬ 9,10,11
. . .

N. ¬C

```

I'm stuck at this point. I don't know how to continue and get an A or a B to get ¬C.

Answer: 
Combine the $\neg B$ with premise 3 to get $A$, which with premise 1 gives you $\neg C$, and thus the contradiction with $C$ you are looking for.
$\def\fitch#1#2{\quad\begin{array}{|l}#1\\\hline#2\end{array}}$
Always keep your mind on the goal.

You are attempting to deduce $\neg C$ using a subproof with an assumption of $C$. The goal of this subproof is a contradiction. 

The means of achieving that goal is using the third premise and $\vee$-elimination. 
$$\fitch{~~1.~A\to\neg C\\~~2.~\neg (B\wedge\neg A)\\~~3.~A\vee B}{\fitch{~~4.~C\hspace{12ex}\textsf{H}}{\fitch{~~5.~A\hspace{8.5ex}\textsf{H}}{~~6.~\neg C\hspace{7ex}{\to}\textsf{E}~1,8\\~~7.~\bot\hspace{8.5ex}\neg\textsf{E}~~4,6}\\~~8.~\neg A\hspace{11ex}\neg\textsf{I}~~5{-}7\\\fitch{~~9.~B\hspace{9.5ex}\textsf{H}}{10.~B\wedge\neg A\hspace{3ex}\wedge\textsf{I}~~8,9\\11.~\bot\hspace{9.5ex}\neg\textsf{E}~~10,2}\\12.~\bot\hspace{12ex}\vee\textsf{E}~~3,5{-}7,9{-}11}\\13.~\neg C\hspace{14ex}\neg\textsf{I}~4{-}12}$$