Lean verification registry · Authored proofs · The Logos Architecture
Verified sequents with unresolved formal parts
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: 2026-10-03T01:32:03.466Z (not original authorship).
Formalized: 2026-10-03T10:37:05.082Z.
Checked: 2026-10-03T10:42:07.063Z.
Independent timestamp: 2026-10-03T10:42:55.000Z.
Authored source SHA-256: ce242959d2333e6dcedb61d5c33506ff698f04381a311d0b8e2944f6ea479b29
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_2' 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)
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.
Unsupported formal syntax near ">Q"
{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.
The Grand Loop:
{P,P>Q,Q>R, R>S,S>T,T>U,U>P}
|=((P&Q)&(R&S)&T)&U)
{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.
Another Version:
P: If there is no Universal Logic (God), then there would be no consistent and reliable means of reasoning.
Q: We have consistent and reliable means of reasoning, such as propositional logic, which operate under certain basic principles and rules.
R: These principles and rules cannot be arbitrary, as they must apply across all domains and situations to ensure their reliability and consistency.
S: Therefore, there must be a Universal Logic (God) that provides the foundation for these principles and rules, which applies universally across all domains and situations.
Conclusion: Therefore, the Universal Logic (God) exists and is the foundation for all consistent and reliable forms of reasoning.