This document discusses various logical formulas and rules of inference. It contains propositional logic formulas in conjunctive normal form and Horn clauses. It also shows rules like modus ponens and hypothetical syllogism being applied to conditional statements with variables.

1. Δ {¬A} Δ {A} - Δ
CNF
╞A ├A
{q ( p r), p (q r), q r, q}
. HORN
A B, C→A ├ ( D→B) → (D C)
p q, (r s)→ q ╞ (p→s) →
(s r)
x x(A→B) ╞ xA→B
B-