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: 2026-10-02T16:57:33.584Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:38:41.358Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: 288d3e726bcb02ef352ebdff481057b50f84c908006522b511dbe27442a8f0d6
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.
God’s Rational Existence and Definition by Maclain Hunter:
Premises:
P: My God & The God: the Origin of Existence; the Logos; the Pure Validity and Universal Coherence of the Universe that, through its tautological nature is the “Universal Mind” (coherent Reason and reasoning in and as the non-dual Reality);The Coherent Origin of the Cosmos found in the Coherence of Reality, Logic, and Coherence itself.
Q: Undefined God(s): if God’s (or a set of gods’) definition and nature remains undefined and ambiguous, rather that being a matter of Pure Reason and alignment (of God and the theory/understanding of God) with Coherence itself, then this God or gods’ existence(s) necessarily remains logically contingent (until terms are defined rationally and God is understood coherently).
R: No God: if God is defined as nothing then God would not exist, as nothing is nothing and nonexistence (nothing) cannot exist, however this definition of God could not then coherently also be defined as the Origin of the Universe or Logos since God in that traditional sense (reflected in foundational English dictionaries like the OED and Webster’s).
S: Illogical God or Origin: if God (or the Origin of Logic and Existence) is defined as nonsense or something illogical (including but not limited to mythological gods) then God would not coherently exist, as illogic is not coherent and nonsense (or what is illogical) cannot exist as a logically sound Foundation (God) for the Cosmos, however this incoherent type of definition of God could not then coherently also be defined as the Origin of the Universe or Logos since God in that traditional sense (reflected in foundational English dictionaries like the OED and Webster’s).
T: Assume the negation of the premises P, Q, R & S. This leads to logical contradiction and inconsistency where we either negate the rational necessity of Coherence in all things, including and especially the First Cause, or question or waver on it, as if it is uncertain when logically speaking it cannot be uncertain or any other way. Accepting the premises as rational and true is logically consistent and allows us to avoid the inconsistency that arises from the assumption of the negation of the premises.
U: Addressing potential counterarguments and common arguments against God. For an atheist or critic of theism or God to argue with this God as if it is the True God defined in (or like) P would be a fallacious straw man argument, and this can be common in theological debates, along with defining God as nonsense and then arguing with that “God” instead of the God reflected in P and the Origin of Order (Logos- God) reflected in the Cosmos.
Logical Argument:
{P, P <-> Q, Q <-> R, R <-> S, S <-> T, T <-> U} |= ((P & Q) & (R & S) & T) & U
Conclusion: {P, Q, R, S, T, U}:
God is God, and what God is defined as determines what God is and whether God exists in a rational way or as the “actual Source of Reality”, but when God is defined coherently (in a manner aligned with or literally defined as “Logic”) and as the actual Source of Reality then it becomes evident and even self-evident (tautological) that God is the Source of Reality and that both are coherent with and one with/as Logic, the Validator of Concepts and Pure Validity itself - the strongest feasible Foundation for anything, especially the Cosmos and the Foundation of the Cosmos (Logic - God) itself.
Defining God as nothing (or nonsense) and deriving the nonexistence (or logical inconsistency) of this God LOGICALLY from that algebra serves as evidence of the consistency and existence of the Logic and Pure Validity that the Cosmos is necessarily based on that coherent notions and definitions of God as the First Cause must align with. It does not undermine the True God, it actually reinforces and underlines the fact that A is A and rational notions of concepts lead to real understanding of the nature of Reality and it’s “Ontological Ground” (the True God).
Truth Table Analysis:
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 FFT TTT TTT F TFF FT FT
TTTFTF⎪T TTT TTT TFF FFT 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 FFT TTT TTT TTT F FFT FT FT
TTFTTF⎪T TTT TFF FFT TTT TFF TTT F FFT FT FF
TTFTFT⎪T TTT TFF FFT TFF FFT TTT F FFT FF FT
TTFTFF⎪T TTT TFF FFT TFF FTF TTT F FFT FF FF
TTFFTT⎪T TTT TFF FTF FFT TTT TTT F FFF FT FT
TTFFTF⎪T TTT TFF FTF FFT 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 FFT TTT TTT TTT TFF F TTT TT FT
TFTTTF⎪T TFF FFT TTT TTT TFF TFF F TTT TT FF
TFTTFT⎪T TFF FFT TTT TFF FFT TFF F TTT FF FT
TFTTFF⎪T TFF FFT TTT TFF FTF TFF F TTT FF FF
TFTFTT⎪T TFF FFT TFF FFT TTT TFF F TFF FT FT
TFTFTF⎪T TFF FFT TFF FFT TFF TFF F TFF FT FF
TFTFFT⎪T TFF FFT TFF FTF FFT TFF F TFF FF FT
TFTFFF⎪T TFF FFT TFF FTF FTF TFF F TFF FF FF
TFFTTT⎪T TFF FTF FFT TTT TTT TFF F FFT FT FT
TFFTTF⎪T TFF FTF FFT TTT TFF TFF F FFT FT FF
TFFTFT⎪T TFF FTF FFT TFF FFT TFF F FFT FF FT
TFFTFF⎪T TFF FTF FFT TFF FTF TFF F FFT FF FF
TFFFTT⎪T TFF FTF FTF FFT TTT TFF F FFF FT FT
TFFFTF⎪T TFF FTF FTF FFT 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 FFT TTT FFT F TFF FT FT
FTTFTF⎪F FFT TTT TFF FFT 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 FFT TTT TTT FFT F FFT FT FT
FTFTTF⎪F FFT TFF FFT TTT TFF FFT F FFT FT FF
FTFTFT⎪F FFT TFF FFT TFF FFT FFT F FFT FF FT
FTFTFF⎪F FFT TFF FFT TFF FTF FFT F FFT FF FF
FTFFTT⎪F FFT TFF FTF FFT TTT FFT F FFF FT FT
FTFFTF⎪F FFT TFF FTF FFT 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 FFT TTT TTT TTT FFF F TTT TT FT
FFTTTF⎪F FTF FFT TTT TTT TFF FFF F TTT TT FF
FFTTFT⎪F FTF FFT TTT TFF FFT FFF F TTT FF FT
FFTTFF⎪F FTF FFT TTT TFF FTF FFF F TTT FF FF
FFTFTT⎪F FTF FFT TFF FFT TTT FFF F TFF FT FT
FFTFTF⎪F FTF FFT TFF FFT TFF FFF F TFF FT FF
FFTFFT⎪F FTF FFT TFF FTF FFT FFF F TFF FF FT
FFTFFF⎪F FTF FFT TFF FTF FTF FFF F TFF FF FF
FFFTTT⎪F FTF FTF FFT TTT TTT FFF F FFT FT FT
FFFTTF⎪F FTF FTF FFT TTT TFF FFF F FFT FT FF
FFFTFT⎪F FTF FTF FFT TFF FFT FFF F FFT FF FT
FFFTFF⎪F FTF FTF FFT TFF FTF FFF F FFT FF FF
FFFFTT⎪F FTF FTF FTF FFT TTT FFF F FFF FT FT
FFFFTF⎪F FTF FTF FTF FFT 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
Q.E.D.