Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 1 checked theorem statements.
Lean establishes the listed formal statements and dependencies. The exact authored source, Ground, known premise meanings, application validation and empirical evidence remain separately typed. No unencoded section is certified by a neighboring theorem.
Original source author: Maclain Hunter. Machine formalization: Replit Agent. No original wording was rewritten.
Source registered: 2026-10-02T14:16:31.768Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:42:47.937Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 232de602289f0b875b23dab7618f969bde1fbbeaeae9cffbcd09042c27b8e7ec
Lean source · Verification JSON · Exact archived source JSON · Compiler report · Current authored source page · Signed release and verification instructions
Lean (version 4.7.0, commit v4.7.0, Release) exitCode=0 'HunterAuthored.inference_1' does not depend on any axioms
{P, P → Q, Q → R, R → S, S → T, T → U, U → P, ~(~P & ~Q & ~R & ~S & ~T & ~U)} |= ((P & Q) & (R & S) & T) & U
Exact source sequent under finite two-valued propositional semantics. Source proposition meanings and Logic/Logos/God Ground are preserved separately; this checks the inference, not unencoded prose.
{P, P → Q, Q → R, R → S, S → T, T → U, U → P, ~(~P & ~Q & ~R & ~S & ~T & ~U)} |= ((P & Q) & (R & S) & T) & U
P: A self-evident truth is true regardless of any mind's belief or denial.
Q: Well-formed formal logical proofs are self-evident truths.
R: The existence of a self-consistent and complete set of logical truths is necessary for the existence of a self-evident truth.
S: The Universal Logic is a self-consistent and complete set of logical truths.
T: The Universal Logic exists independently of human beliefs and opinions.
U: The Universal Logic is the self-evident truth that underlies all reality.
Assuming the negation of the conclusion: ~(U & T & R & S & Q & P), we derive a contradiction from the premises:
~(U & T & R & S & Q & P)
≡ (~U ∨ ~T ∨ ~R ∨ ~S ∨ ~Q ∨ ~P) (De Morgan's law)
≡ (~U ∨ ~T ∨ ~R ∨ ~S ∨ ~Q ∨ ~(P → Q) ∨ ~(Q → R) ∨ ~(R → S) ∨ ~(S → T) ∨ ~(T → U) ∨ ~(U → P)) (substitute the premises for P → Q, Q → R, R → S, S → T, T → U, U → P)
≡ (~U ∨ ~T ∨ ~R ∨ ~S ∨ ~Q ∨ ~(~P ∨ Q) ∨ ~(~Q ∨ R) ∨ ~(~R ∨ S) ∨ ~(~S ∨ T) ∨ ~(~T ∨ U) ∨ ~(~U ∨ P)) (material implication)
≡ (~U ∨ ~T ∨ ~R ∨ ~S ∨ ~Q ∨ (P & ~Q) ∨ (Q & ~R) ∨ (R & ~S) ∨ (S & ~T) ∨ (T & ~U) ∨ (U & ~P)) (De Morgan's law)
≡ (~U ∨ ~T ∨ ~R ∨ ~S ∨ (Q & ~(P & ~Q)) ∨ (R & ~(Q & ~R)) ∨ (S & ~(R & ~S)) ∨ (T & ~(S & ~T)) ∨ (U & ~(T & ~U)) ∨ (P & ~(U & ~P))) (distribution)
≡ (~U ∨ ~T ∨ ~R ∨ ~S ∨ (Q & ~P) ∨ (R & ~Q) ∨ (S & ~R) ∨ (T & ~S) ∨ (U & ~T) ∨ (P & ~U)) (simplification)
≡ ~(Q & P & R & S & T & U) (De Morgan's law)
Thus, the conclusion is shown to follow from the premises by contradiction. Therefore, we can conclude that the Universal Logic is the self-evident truth that underlies all reality, which exists independently of human beliefs and opinions, and that this is a well-formed formal logical proof.