The premises are as follow:

```
1. A
2. A > ~B
3. B
4. C

```

The conclusion is `(A & B) & \~C`

My teacher proceed to use solve it using Indirect Proof.

```
5. ~[(A & B) & ~C ]      AP
6. ~B                    1,2 MP
7. B & ~B                3,6 Conj
8. (A & B) & ~C          5-7 IP

```

If such proof is valid, that means if there are premises with contradiction, I can create any sort of conclusion with IP, even false argument like `A & ~A`. If so, would that make IP not very strict/complete system?

Is there any rule that required AP must be used within the skeleton of IP that result in the reaching the IP conclusion? I think this can prevent creating false argument.