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: 2026-10-02T20:42:29.527Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:40:51.161Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: c0b446fa430b1da250beb17d7ba4e6b123c13dcaa2d106eff50e735a72c8a144
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 <-> ((S <-> R) & (Q <-> P))
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.
Our Proofs Stand by Maclain Hunter
Premises:
P: Coherent Acknowledgment: Logic is God, and God is Logic, as there must be Coherence between Reality and the Ontological and Epistemological Ground (God and Logic).
Q: Lack of Refutation: Indeed, no one has ever formally refuted any proof for God without Logic and thus without contradiction (using God to try to refute God’s existence/rationality, as if Logic isn’t God).
R: Observation of Peculiarity: If Logic is not God, and “nothing” or something deviating from Logic is then Logic would have to be readjusted to be coherent with that alternative First Cause to be coherent and capable of providing knowledge and proof, which is both absurd and leaves things ultimately unchanged once that adjustment was made - making it a distinction without a difference couched within an absurd and logically impossible hypothetical.
S: Reductio Ad Absurdum: Assume that the premises (P, Q, and R) are false/illogical. This leads to logical contradiction where we are both denying and presupposing the existence and supremacy of Logic - which violates the Law of Non-Contradiction by affirming A and denying A in the same sense and context at once. This cannot be, and Logic must logically be understood as supreme (and thus the Supreme Entity or God) to avoid contradiction and absurdity, affirming and aligning with the truth of the previously stated premises (P, Q, and R).
T: Self-Referencing Proof: The combination of the premises, including this one, are a coherent display of self-reference and tautological circularity in Logic and logical reasoning (or logical proof). The way that premise S uses the previous premises to prove their point and the way this premise T points out how premise S has succeeded in using proof for the contradiction to prove the argument of the set of premises makes this a self-supporting logical argument (proof) that needs and relies on nothing beyond Logic, language, logical interpretation, and itself - things reasonably granted in logical discourse and rigorous academic works.
Formal Reasoning:
{P, P -> Q, Q -> R, R <-> S, S -> T} |= T <-> ((S <-> R) & (Q <-> P))
Conclusion: {P, Q, R, S, T}:
Logic is God and no one has been able to or will be able to refute that Objective Truth (or Logic, or God). The logicians (ie - Aristotle, Leibniz, Gödel, Hunter) that have proven God exists have collectively proven that God exists as Logic and have done so with Logic. This is internally, logically, and universally consistent while its alternative is an absurdity - using Logic to prove that Logic is less than or not equal to the Supreme Entity, Moral Authority, and Lawgiver of the Cosmos (or “God” by definition in the English language).
If it were possible to disprove a proof for God logically without using Logic, which is a blatant contradiction, then someone could have done it by now - but no one has (which is solid evidence in itself of Logic as God and the coherent Universal Order). The opposite is the case - that thousands of proofs exist for God or Reason as God and not one exists to the opposite effect without, in contradictory fashion, leaning on Logic.
Trying to logically disprove the Universal Order (Logic - God) is a fools errand and proof of the attempter’s ignorance and illogic, little more.
If Logic isn’t known as God then it opens the door to unreason and the notion that logical incoherence is meaningless, since Logic isn’t one with and locked logically to the Foundation of Reality (God - Logos), which is itself logically incoherent.
It would also then be consistent with that sort of atheistic illogic that theists would not need to prove God logically or rationally for God to be considered proven or meaningful - still deflating atheistic denials and demands for proof for God from theists (which atheists often hide behind while they ignore the proofs that have been produced and that exist as a matter of public record).
As premise T helps reveal, the structure of this proof models the Logic of Reality (God) - relying on nothing but itself (Logic) and aspects of itself. To see this proof (which cannot be separated from its logical structure without incoherence) is to see God - who cannot be coherently divorced from Logic and the being of Logic (or Logical Existence).
The proof shows that any denial of Logic as God is a contradiction. Since contradiction is forbidden in Logic, denial (of God or Logic) is logically forbidden. No illogical, atheistic, or agnostic alternative is coherent or capable of generating true knowledge.
Logic is God, Logic affirms. There is no higher logical authority to appeal to. The proof for God stands (both here and in general).
Truth Table Analysis:
PQRST⎪P P→Q Q→R R↔S S→T╞T↔((S↔R)&(Q↔P))
TTTTT⎪T TTT TTT TTT TTT TT TTT T TTT
TTTTF⎪T TTT TTT TTT TFF FF TTT T TTT
TTTFT⎪T TTT TTT TFF FTT TF FFT F TTT
TTTFF⎪T TTT TTT TFF FTF FT FFT F TTT
TTFTT⎪T TTT TFF FFT TTT TF TFF F TTT
TTFTF⎪T TTT TFF FFT TFF FT TFF F TTT
TTFFT⎪T TTT TFF FTF FTT TT FTF T TTT
TTFFF⎪T TTT TFF FTF FTF FF FTF T TTT
TFTTT⎪T TFF FTT TTT TTT TF TTT F FFT
TFTTF⎪T TFF FTT TTT TFF FT TTT F FFT
TFTFT⎪T TFF FTT TFF FTT TF FFT F FFT
TFTFF⎪T TFF FTT TFF FTF FT FFT F FFT
TFFTT⎪T TFF FTF FFT TTT TF TFF F FFT
TFFTF⎪T TFF FTF FFT TFF FT TFF F FFT
TFFFT⎪T TFF FTF FTF FTT TF FTF F FFT
TFFFF⎪T TFF FTF FTF FTF FT FTF F FFT
FTTTT⎪F FTT TTT TTT TTT TF TTT F TFF
FTTTF⎪F FTT TTT TTT TFF FT TTT F TFF
FTTFT⎪F FTT TTT TFF FTT TF FFT F TFF
FTTFF⎪F FTT TTT TFF FTF FT FFT F TFF
FTFTT⎪F FTT TFF FFT TTT TF TFF F TFF
FTFTF⎪F FTT TFF FFT TFF FT TFF F TFF
FTFFT⎪F FTT TFF FTF FTT TF FTF F TFF
FTFFF⎪F FTT TFF FTF FTF FT FTF F TFF
FFTTT⎪F FTF FTT TTT TTT TT TTT T FTF
FFTTF⎪F FTF FTT TTT TFF FF TTT T FTF
FFTFT⎪F FTF FTT TFF FTT TF FFT F FTF
FFTFF⎪F FTF FTT TFF FTF FT FFT F FTF
FFFTT⎪F FTF FTF FFT TTT TF TFF F FTF
FFFTF⎪F FTF FTF FFT TFF FT TFF F FTF
FFFFT⎪F FTF FTF FTF FTT TT FTF T FTF
FFFFF⎪F FTF FTF FTF FTF FF FTF T FTF
(Valid)
Q.E.D.