[2] viXra:1808.0090 [pdf] submitted on 2018-08-07 15:06:59
Authors: Colin James III
Comments: 1 Page. Copyright © 2018 by Colin James III All rights reserved. Respond to this author's email address: info@ersatz-systems dot com. (We instruct troll Mikko at Disqus to read the entire article twice before she starts typing.)
These examples were found not tautologous: (∀x,px→r)↔(∃x,px)→r; (∃x,px→r)↔(∀x,px)→r; (∃x,r→px)↔(r→∃x,px).
Hence Lean prover from Microsoft is not bivalent and refuted.
Category: Set Theory and Logic
[1] viXra:1808.0047 [pdf] submitted on 2018-08-03 22:08:52
Authors: Colin James III
Comments: 4 Pages. Copyright © 2018 by Colin James III All rights reserved. Note that comments on Disqus are not forwarded or read, so respond to this author's email address: info@ersatz-systems dot com .
The nine Zermelo-Fraenkel (ZF) axioms evaluated are not tautologous.
Category: Set Theory and Logic