-- Maclain Hunter: Negation, Identity, and Logos by Maclain Hunter
-- Exact authored source SHA-256: 5df940f97f0269418a4c17f0c1de664ac22380fa19f0adc70470d110e22d84fd
-- Machine formalization by Replit Agent; authority below Logic/Logos/God.
import Lean
namespace HunterAuthored

theorem inference_1 (v0 : Bool) :
    ((!v0) || v0) = true := by
  cases v0 <;> decide
#print axioms inference_1

theorem inference_2 (v0 v1 v2 : Bool) :
    ((!((v2 && v0) && v1)) || ((v2 == v0) && v1)) = true := by
  cases v0 <;> cases v1 <;> cases v2 <;> decide
#print axioms inference_2

theorem inference_3 (v0 v1 v2 v3 : Bool) :
    ((!(((v3 && v1) && v2) && v0)) || ((v3 == v1) == (v1 == v0))) = true := by
  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> decide
#print axioms inference_3

theorem inference_4 (v0 v1 : Bool) :
    ((!(v0 == v1)) || (v0 == v1)) = true := by
  cases v0 <;> cases v1 <;> decide
#print axioms inference_4

theorem inference_5 (v0 v1 v2 v3 v4 v5 : Bool) :
    ((!(((((v0 && v1) && v2) && v3) && v4) && v5)) || (((((v0 && v1) && v2) && v3) && v4) && v5)) = true := by
  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> cases v4 <;> cases v5 <;> decide
#print axioms inference_5

theorem inference_6 (v0 v1 : Bool) :
    ((!(v0 && ((!v0) || v1))) || (v0 == v1)) = true := by
  cases v0 <;> cases v1 <;> decide
#print axioms inference_6

theorem source_identity_rule (α : Type) (a : α) : a = a := rfl
#print axioms source_identity_rule

end HunterAuthored