Lean verification registry · Authored proofs · The Logos Architecture
Written formal sequents verified
Axiom-free: true · 2 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: 2026-10-03T01:36:06.457Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:37:30.044Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: aa7a03fbedd49c6d20e4a22eb6f670eef9d1c06b96d5e57061423a399bcb803b
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 'HunterAuthored.source_identity_rule' does not depend on any axioms
{P, P <-> Q, Q -> R, R -> S, S -> T, 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.
A is A
The explicitly named Identity rule, over every type and element. The remaining prose is not replaced by this witness.
Atheism’s Illogic and the Origin’s Divinity by Maclain Hunter:
Definitions:
God (or “Theos” in Greek): The Origin of Existence.
Divine: God-like or of/from God (Origin)
Origin: The cause of something and reason that it exists.
Reason (or “Logos” in Greek): The Standard of Logic and reasoning. The Rational Fabric of Rationality.
Logic: The Method of Reasoning and means of knowing Reality through coherent Reason and reasoning.
Proof: A demonstration of Truth (coherent with Reason) through valid arguments and evidence.
Evidence: A piece of data or an argument built on facts that demonstrates a/another fact objectively.
Atheism: The position that there is no God or gods; The disbelief in God or any gods.
Theism: The position that there is a God (in monotheism) of gods (in logically incoherent polytheist systems that fail to unify the Universal Cause in their theory as Logic/Cause requires for coherence); The belief in the Divine Logos, or some God or gods.
Monotheism: A theistic system based on the belief or knowledge that the Origin (God) is one (coherent) and cannot be many or incoherent.
Premises (Inputs):
P: Necessarily: Reason is Reason, and no “reasons” (in the particular sense) could exist independent of and without the general/universal existence of Reason. Reason (Logos) is the Reason for Existence (Theos). By definition in the Oxford English Dictionary (OED) the term God refers to the Origin and Ruler of the Cosmos (the Origin or Foundation of Existence and Reality).
Q: Assume that P and Q were not true and that empiricism or anything in existence contradicted Reason (Logic/Logos), A is A form, or P and Q, that would lead to logical incoherence and inconsistency, and to an Origin of Rationality that was irrational - which is logically untenable and reasonable to dismiss as a valid option upon proper consideration.
R: Necessarily: The Logos is the Source (God) of Existence and the atheist position must deny (even) the Logos (the God of Reason) to maintain its identity and be a disbelief in any and all gods or notions of a Divine (Origin-like/God-like) Origin/God. It’s a logical contradiction in fact for the Origin (the Divine) to NOT be Divine (of, from, or aligned with God/Origin), as that would mean the Origin is not itself and/or aligned with itself, which defies Logic and the three traditional Rules of Logic.
S: Necessarily: An atheist couldn’t highlight “logical inconsistencies” if Logos didn’t exist. That would amount to saying something is “incoherent with nothing” (which is logically equivalent to being coherent with anything and everything).
T: To address counter arguments that rely on sowing seemingly “reasonable doubt” (about the Logos - the rationally necessary God of Reason) by pointing to empiricism or the alleged lack of evidence of Order and Logic in Reality (the Logical Order of Nature) in empirical sciences, I merely need to point to evidence of fine-tuning (Perfect Rational Order (Logos) beyond man’s direct influence or power to create) and the necessary logical analysis of any recovered empirical data, as well as the necessary logical coherence of any results, proof, or evidence derived from empiricism and the sciences.
U: Assume that any or all of the set of premises {P, Q, R, S, T} are invalid and false. That leads to logical contradiction and cannot stand. Logically the premises are unassailable, being based in Reason and consistent Logic and remaining coherent with Reason and consistent with Logic without deviation.
Formal Argument (Proof):
{P, P <-> Q, Q -> R, R -> S, S -> T, T <-> U} |= ((P & Q) & (R & S) & T) & U
Conclusion: ((P & Q) & (R & S) & T) & U:
Reason is the Reason for Existence, which is what the term God (the Origin and Ruler of the Cosmos; the Supreme Being; the Moral Authority and Standard) refers to in classical theism and in the Oxford English Dictionary. The fact that logically coherent theism aligns with the Logos while atheism must deny the Logos (God of Reason) and the Divinity (Origin-like nature) of the Origin renders atheism untenable and incoherent.
There is also no lack of empirical support for the Logos and this monotheistic and coherent view. If we assumed that there is no Logos then that leads to contradiction and those who dare challenge that Logic of Reality (Logos - God) by any name are incoherent and are doomed to merely prove the Logos exists by even trying to turn to Logic (Logos) for valid arguments. We need God because we need Reason.
The word Divine means “God-like” and the word God refers to the Origin, so claiming the Origin is not Divine defies Logic (the God-like Origin - the Self-Consistent Logos - the God of Reason). An “Origin that’s not Divine” is a contradiction, like an “irrational logic” is.
We cannot abandon God because we have Reason or vice versa that is incoherent and amounts to saying we need the Rational Foundation and don’t need the Rational Foundation which violates logical rules, particularly the Law of the Excluded Middle (but also Identity and Non-Contradiction).
Truth Table:
valid
↓ ↓ ↓ ↓ ↓ ↓ ↓
PQRSTU⎪P P↔Q Q→R R→S S→T T↔U╞((P&Q)&(R&S)&T)&U
―――――――――――――――――――――――――――――――――――――――――――――――
TTTTTT⎪T TTT TTT TTT TTT TTT TTT T TTT TT TT
TTTTTF⎪T TTT TTT TTT TTT TFF TTT T TTT TT FF
TTTTFT⎪T TTT TTT TTT TFF FFT TTT T TTT FF TT
TTTTFF⎪T TTT TTT TTT TFF FTF TTT T TTT FF FF
TTTFTT⎪T TTT TTT TFF FTT TTT TTT F TFF FT FT
TTTFTF⎪T TTT TTT TFF FTT TFF TTT F TFF FT FF
TTTFFT⎪T TTT TTT TFF FTF FFT TTT F TFF FF FT
TTTFFF⎪T TTT TTT TFF FTF FTF TTT F TFF FF FF
TTFTTT⎪T TTT TFF FTT TTT TTT TTT F FFT FT FT
TTFTTF⎪T TTT TFF FTT TTT TFF TTT F FFT FT FF
TTFTFT⎪T TTT TFF FTT TFF FFT TTT F FFT FF FT
TTFTFF⎪T TTT TFF FTT TFF FTF TTT F FFT FF FF
TTFFTT⎪T TTT TFF FTF FTT TTT TTT F FFF FT FT
TTFFTF⎪T TTT TFF FTF FTT TFF TTT F FFF FT FF
TTFFFT⎪T TTT TFF FTF FTF FFT TTT F FFF FF FT
TTFFFF⎪T TTT TFF FTF FTF FTF TTT F FFF FF FF
TFTTTT⎪T TFF FTT TTT TTT TTT TFF F TTT TT FT
TFTTTF⎪T TFF FTT TTT TTT TFF TFF F TTT TT FF
TFTTFT⎪T TFF FTT TTT TFF FFT TFF F TTT FF FT
TFTTFF⎪T TFF FTT TTT TFF FTF TFF F TTT FF FF
TFTFTT⎪T TFF FTT TFF FTT TTT TFF F TFF FT FT
TFTFTF⎪T TFF FTT TFF FTT TFF TFF F TFF FT FF
TFTFFT⎪T TFF FTT TFF FTF FFT TFF F TFF FF FT
TFTFFF⎪T TFF FTT TFF FTF FTF TFF F TFF FF FF
TFFTTT⎪T TFF FTF FTT TTT TTT TFF F FFT FT FT
TFFTTF⎪T TFF FTF FTT TTT TFF TFF F FFT FT FF
TFFTFT⎪T TFF FTF FTT TFF FFT TFF F FFT FF FT
TFFTFF⎪T TFF FTF FTT TFF FTF TFF F FFT FF FF
TFFFTT⎪T TFF FTF FTF FTT TTT TFF F FFF FT FT
TFFFTF⎪T TFF FTF FTF FTT TFF TFF F FFF FT FF
TFFFFT⎪T TFF FTF FTF FTF FFT TFF F FFF FF FT
TFFFFF⎪T TFF FTF FTF FTF FTF TFF F FFF FF FF
FTTTTT⎪F FFT TTT TTT TTT TTT FFT F TTT TT FT
FTTTTF⎪F FFT TTT TTT TTT TFF FFT F TTT TT FF
FTTTFT⎪F FFT TTT TTT TFF FFT FFT F TTT FF FT
FTTTFF⎪F FFT TTT TTT TFF FTF FFT F TTT FF FF
FTTFTT⎪F FFT TTT TFF FTT TTT FFT F TFF FT FT
FTTFTF⎪F FFT TTT TFF FTT TFF FFT F TFF FT FF
FTTFFT⎪F FFT TTT TFF FTF FFT FFT F TFF FF FT
FTTFFF⎪F FFT TTT TFF FTF FTF FFT F TFF FF FF
FTFTTT⎪F FFT TFF FTT TTT TTT FFT F FFT FT FT
FTFTTF⎪F FFT TFF FTT TTT TFF FFT F FFT FT FF
FTFTFT⎪F FFT TFF FTT TFF FFT FFT F FFT FF FT
FTFTFF⎪F FFT TFF FTT TFF FTF FFT F FFT FF FF
FTFFTT⎪F FFT TFF FTF FTT TTT FFT F FFF FT FT
FTFFTF⎪F FFT TFF FTF FTT TFF FFT F FFF FT FF
FTFFFT⎪F FFT TFF FTF FTF FFT FFT F FFF FF FT
FTFFFF⎪F FFT TFF FTF FTF FTF FFT F FFF FF FF
FFTTTT⎪F FTF FTT TTT TTT TTT FFF F TTT TT FT
FFTTTF⎪F FTF FTT TTT TTT TFF FFF F TTT TT FF
FFTTFT⎪F FTF FTT TTT TFF FFT FFF F TTT FF FT
FFTTFF⎪F FTF FTT TTT TFF FTF FFF F TTT FF FF
FFTFTT⎪F FTF FTT TFF FTT TTT FFF F TFF FT FT
FFTFTF⎪F FTF FTT TFF FTT TFF FFF F TFF FT FF
FFTFFT⎪F FTF FTT TFF FTF FFT FFF F TFF FF FT
FFTFFF⎪F FTF FTT TFF FTF FTF FFF F TFF FF FF
FFFTTT⎪F FTF FTF FTT TTT TTT FFF F FFT FT FT
FFFTTF⎪F FTF FTF FTT TTT TFF FFF F FFT FT FF
FFFTFT⎪F FTF FTF FTT TFF FFT FFF F FFT FF FT
FFFTFF⎪F FTF FTF FTT TFF FTF FFF F FFT FF FF
FFFFTT⎪F FTF FTF FTF FTT TTT FFF F FFF FT FT
FFFFTF⎪F FTF FTF FTF FTT TFF FFF F FFF FT FF
FFFFFT⎪F FTF FTF FTF FTF FFT FFF F FFF FF FT
FFFFFF⎪F FTF FTF FTF FTF FTF FFF F FFF FF FF