argument to be demonstrated:

$A ∨ (B ∧ C)$

$B → D$

$C → E$

$D ∧ E → A ∨ C$

$¬A$

$∴ C$

My attempt at this mathematical demonstration was as follows:

$A ∨ (B ∧ C)$

$≡ (A ∨ B) ∧ (A ∨ C)$

$≡ (A ∨ A) ∧ (B ∨ C)$

$≡ A ∧ (B ∨ C)$

$≡ (A ∧ B) ∨ (A ∧ C)$