TRANSDUCTIVE SCIENCESCIENCE AFTER HUMANS / 001ED. 01 / 2026
W57 / Verification

Automated theorem proving

Search for proofs is conflated with independently establishing that a theorem statement was proved.

01 / Source of departure [W57] ↗

What the reference describes.

Automated theorem proving (ATP), also known as automated deduction, is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major motivating factor for the development of computer science.
Shortened extract from “Automated theorem proving”, English Wikipedia contributors, revision 1380246457; original text licensed CC BY-SA 4.0. Excerpt shortened, line breaks normalized. For full article references and edit history, open the fixed source revision. The independent critique below is not Wikipedia text.
02 / Inherited constraint

What the process still cannot guarantee.

Search for proofs is conflated with independently establishing that a theorem statement was proved.

That is a design criticism of how this research operation may be used, not a claim that the encyclopedia endorses the limitation. In this domain, the general redesign question is: mathematical, computational and semantic validation are separated into independent trust layers.

03 / Machine-native reconstruction

Replace the mechanism.

Separate conjecture generation, trusted kernel checking and semantic alignment with natural-language claims.

Implementation requires a typed scientific claim, explicit operational definitions, controlled access to evidence, an immutable record of relevant transformations, and independent checking appropriate to the kind of assertion. An AI-generated interpretation without those checks would reproduce the underlying failure at greater speed.

04 / Adversarial acceptance test

What would demonstrate improvement?

Feed altered formal statements to independent semantic auditors and measure misalignment detection.

Compare with a defined baseline under matched resources, keep evaluation cases independent of the system under test, and measure both false alarms and undetected errors. Publish any negative or inconclusive result as part of the same investigation record.

Unresolved requirement. These are proposed experiments, not completed demonstrations. Better generated explanations are not proof of better scientific inference.
05 / Adjacent evidence

Continue across concepts.

Each related title has its own revision-specific Wikipedia source and a separate critical dossier. Crosslinks are exploratory; they do not imply the encyclopedia articles support the proposed replacement.

06 / Verification & provenance

No single authority.

The reference article establishes the historical and methodological subject under examination. The proposed criticism and replacement must earn their own support through reproducible tests and independent validation. Record disagreements instead of silently overwriting them.

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