-- Maclain Hunter: Necessary Entailment by Maclain Hunter
-- Exact authored source SHA-256: 7e101488b48dd99fff8e338b62c9bb1063d1a010bcb693cfe3635a8de298b990
-- Machine formalization by Replit Agent; authority below Logic/Logos/God.
import Lean
namespace HunterAuthored

theorem inference_1 (v0 v1 v2 : Bool) :
    ((!((((v1 && (v1 == v2)) && (v2 == v0)) && (v0 == v0)) && v0)) || (((v1 == v2) && (v1 && v2)) && v0)) = true := by
  cases v0 <;> cases v1 <;> cases v2 <;> decide
#print axioms inference_1

theorem inference_2 (v0 v1 v2 v3 v4 v5 : Bool) :
    ((!(((((((((((((((((v3 && (v3 == v5)) && (v3 == v2)) && (v5 == v4)) && (v2 == v4)) && (v2 == v5)) && (v3 == v4)) && (v3 == v5)) && (v5 == v0)) && (v3 == v0)) && (v0 == v1)) && (v1 == v1)) && v3) && v2) && v5) && v4) && v0) && v1)) || ((((v3 && v5) && (v2 && v4)) && v0) && v1)) = true := by
  cases v0 <;> cases v1 <;> cases v2 <;> cases v3 <;> cases v4 <;> cases v5 <;> decide
#print axioms inference_2

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

end HunterAuthored