How to determine a set of conclusions that can be derived from a set of premises? Considering the following three premises.
How is it possible to determine the set of conclusions that can be derived from the given set of premises.
P1 ⟺ A → (B → C)
P2 ⟺ A ∨ ((B ∧ C) ∨ (¬B ∧ ¬C))
P3 ⟺ B → C

 A: Figured it out.  
At first the CNF of all premises has to be derived 
(in my case I am using a truth-table to do so).
| ABC | B→C | A→P_3 | B∧C | ¬B∧¬C | A∨E∨F | CNF(P_1)       | CNF(P_2)       | CNF(P_3)       |
|---- |---- |------ |---- |------ |------ |--------------- |--------------- |--------------- |
|     | P_3 |  P_1  |  E  |   F   |  P_2  |                |                |                |
| 000 |  1  |   1   |  0  |   1   |   1   |                |                |                |
| 001 |  1  |   1   |  0  |   0   |  (0)  |                | (A ∨ B ∨ ¬C) ∧ |                |
| 010 | (0) |   1   |  0  |   0   |  (0)  |                | (A ∨ ¬B ∨ C)   | (A ∨ ¬B ∨ C) ∧ |
| 011 |  1  |   1   |  1  |   0   |   1   |                |                |                |
| 100 |  1  |   1   |  0  |   1   |   1   |                |                |                |
| 101 |  1  |   1   |  0  |   0   |   1   |                |                |                |
| 110 | (0) |  (0)  |  0  |   0   |   1   | (¬A ∨ ¬B ∨ C)  |                | (¬A ∨ ¬B ∨ C)  |
| 111 |  1  |   1   |  1  |   0   |   1   |                |                |                |

Than linking the three CNFs into one general CNF.
CNF(P_1) = (¬A ∨ ¬B ∨ C)
CNF(P_2) = (A ∨ B ∨ ¬C) ∧ (A ∨ ¬B ∨ C)  
CNF(P_3) = (A ∨ ¬B ∨ C) ∧ (¬A ∨ ¬B ∨ C)
CNF = (P_1) ∧ (P_2) ∧ (P_3)
CNF = (¬A ∨ ¬B ∨ C) ∧ (A ∨ B ∨ ¬C) ∧ (A ∨ ¬B ∨ C)  

Finally derive the set of conclusions C from the general CNF:
C_1 = (¬A ∨ ¬B ∨ C)
C_2 = (A ∨ B ∨ ¬C)
C_3 = (A ∨ ¬B ∨ C)
C_4 = (¬A ∨ ¬B ∨ C) ∧ (A ∨ B ∨ ¬C)
C_5 = (¬A ∨ ¬B ∨ C) ∧ (A ∨ ¬B ∨ C)
C_6 = (A ∨ B ∨ ¬C) ∧ (A ∨ ¬B ∨ C)
C_7 = (¬A ∨ ¬B ∨ C) ∧ (A ∨ B ∨ ¬C) ∧ (A ∨ ¬B ∨ C)  

C = {C_1, C_2, C_3, C_4, C_5, C_6, C_7}

