%------------------------------------------------------------------------------
% File     : Zenon---0.7.1
% Problem  : LCL672+1.015 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_zenon %s %d

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Sun Jul 17 16:23:45 EDT 2022

% Result   : Theorem 90.88s 91.13s
% Output   : Proof 90.97s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.14  % Problem  : LCL672+1.015 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14  % Command  : run_zenon %s %d
% 0.14/0.36  % Computer : n021.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Sun Jul  3 12:52:46 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 90.88/91.13  (* PROOF-FOUND *)
% 90.88/91.13  % SZS status Theorem
% 90.88/91.13  (* BEGIN-PROOF *)
% 90.88/91.13  % SZS output start Proof
% 90.88/91.13  Theorem main : (~(exists X : zenon_U, (~(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(p1 Y))))))))/\(p1 Y))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/False))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~(p1 X))))))))/\(p1 X))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 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Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(p1 Y))))))))/\(p1 Y))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/False))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~(p1 X))))))))/\(p1 X))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/False))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(p1 Y))))))))/\(p1 Y))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/False))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))).
% 90.88/91.13  Proof.
% 90.88/91.13  assert (zenon_L1_ : forall (zenon_TX_h : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_j : zenon_U), (r1 zenon_TX_j zenon_TY_i) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TX_h)) -> (r1 zenon_TY_i zenon_TX_h) -> False).
% 90.88/91.13  do 3 intro. intros zenon_H3 zenon_H4 zenon_H5 zenon_H6.
% 90.88/91.13  elim (classic ((~(zenon_TX_j = zenon_TY_i))/\(~(r1 zenon_TX_j zenon_TY_i)))); [ zenon_intro zenon_Ha | zenon_intro zenon_Hb ].
% 90.88/91.13  apply (zenon_and_s _ _ zenon_Ha). zenon_intro zenon_Hd. zenon_intro zenon_Hc.
% 90.88/91.13  exact (zenon_Hc zenon_H3).
% 90.88/91.13  cut ((r1 zenon_TY_i zenon_TX_h) = (r1 zenon_TX_j zenon_TX_h)).
% 90.88/91.13  intro zenon_D_pnotp.
% 90.88/91.13  apply zenon_H5.
% 90.88/91.13  rewrite <- zenon_D_pnotp.
% 90.88/91.13  exact zenon_H6.
% 90.88/91.13  cut ((zenon_TX_h = zenon_TX_h)); [idtac | apply NNPP; zenon_intro zenon_He].
% 90.88/91.13  cut ((zenon_TY_i = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_Hf].
% 90.88/91.13  congruence.
% 90.88/91.13  apply (zenon_notand_s _ _ zenon_Hb); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ].
% 90.88/91.13  apply zenon_H11. zenon_intro zenon_H12.
% 90.88/91.13  elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_i = zenon_TX_j)).
% 90.88/91.13  intro zenon_D_pnotp.
% 90.88/91.13  apply zenon_Hf.
% 90.88/91.13  rewrite <- zenon_D_pnotp.
% 90.88/91.13  exact zenon_H13.
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 90.88/91.13  cut ((zenon_TX_j = zenon_TY_i)); [idtac | apply NNPP; zenon_intro zenon_Hd].
% 90.88/91.13  congruence.
% 90.88/91.13  exact (zenon_Hd zenon_H12).
% 90.88/91.13  apply zenon_H14. apply refl_equal.
% 90.88/91.13  apply zenon_H14. apply refl_equal.
% 90.88/91.13  apply zenon_H10. zenon_intro zenon_H3.
% 90.88/91.13  generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 90.88/91.13  generalize (zenon_H15 zenon_TY_i). zenon_intro zenon_H16.
% 90.88/91.13  generalize (zenon_H16 zenon_TX_h). zenon_intro zenon_H17.
% 90.88/91.13  apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_Hc | zenon_intro zenon_H18 ].
% 90.88/91.13  exact (zenon_Hc zenon_H3).
% 90.88/91.13  apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ].
% 90.88/91.13  exact (zenon_H1a zenon_H6).
% 90.88/91.13  exact (zenon_H5 zenon_H19).
% 90.88/91.13  apply zenon_He. apply refl_equal.
% 90.88/91.13  (* end of lemma zenon_L1_ *)
% 90.88/91.13  assert (zenon_L2_ : forall (zenon_TY_bd : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_j : zenon_U), (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TY_i zenon_TX_h) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TY_bd)) -> (r1 zenon_TX_h zenon_TY_bd) -> False).
% 90.88/91.13  do 4 intro. intros zenon_H3 zenon_H6 zenon_H4 zenon_H1b zenon_H1c.
% 90.88/91.13  elim (classic ((~(zenon_TX_j = zenon_TX_h))/\(~(r1 zenon_TX_j zenon_TX_h)))); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ].
% 90.88/91.13  apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H20. zenon_intro zenon_H5.
% 90.88/91.13  apply (zenon_L1_ zenon_TX_h zenon_TY_i zenon_TX_j); trivial.
% 90.88/91.13  cut ((r1 zenon_TX_h zenon_TY_bd) = (r1 zenon_TX_j zenon_TY_bd)).
% 90.88/91.13  intro zenon_D_pnotp.
% 90.88/91.13  apply zenon_H1b.
% 90.88/91.13  rewrite <- zenon_D_pnotp.
% 90.88/91.13  exact zenon_H1c.
% 90.88/91.13  cut ((zenon_TY_bd = zenon_TY_bd)); [idtac | apply NNPP; zenon_intro zenon_H21].
% 90.88/91.13  cut ((zenon_TX_h = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H22].
% 90.88/91.13  congruence.
% 90.88/91.13  apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ].
% 90.88/91.13  apply zenon_H24. zenon_intro zenon_H25.
% 90.88/91.13  elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_h = zenon_TX_j)).
% 90.88/91.13  intro zenon_D_pnotp.
% 90.88/91.13  apply zenon_H22.
% 90.88/91.13  rewrite <- zenon_D_pnotp.
% 90.88/91.13  exact zenon_H13.
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_h)); [idtac | apply NNPP; zenon_intro zenon_H20].
% 90.88/91.13  congruence.
% 90.88/91.13  exact (zenon_H20 zenon_H25).
% 90.88/91.13  apply zenon_H14. apply refl_equal.
% 90.88/91.13  apply zenon_H14. apply refl_equal.
% 90.88/91.13  apply zenon_H23. zenon_intro zenon_H19.
% 90.88/91.13  generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 90.88/91.13  generalize (zenon_H15 zenon_TX_h). zenon_intro zenon_H26.
% 90.88/91.13  generalize (zenon_H26 zenon_TY_bd). zenon_intro zenon_H27.
% 90.88/91.13  apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H5 | zenon_intro zenon_H28 ].
% 90.88/91.13  exact (zenon_H5 zenon_H19).
% 90.88/91.13  apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 90.88/91.13  exact (zenon_H2a zenon_H1c).
% 90.88/91.13  exact (zenon_H1b zenon_H29).
% 90.88/91.13  apply zenon_H21. apply refl_equal.
% 90.88/91.13  (* end of lemma zenon_L2_ *)
% 90.88/91.13  assert (zenon_L3_ : forall (zenon_TX_bt : zenon_U) (zenon_TY_bd : zenon_U) (zenon_TX_j : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_i : zenon_U), (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TX_h zenon_TY_bd) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TX_bt)) -> (r1 zenon_TY_bd zenon_TX_bt) -> False).
% 90.88/91.13  do 5 intro. intros zenon_H6 zenon_H3 zenon_H1c zenon_H4 zenon_H2b zenon_H2c.
% 90.88/91.13  elim (classic ((~(zenon_TX_j = zenon_TY_bd))/\(~(r1 zenon_TX_j zenon_TY_bd)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ].
% 90.88/91.13  apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H1b.
% 90.88/91.13  apply (zenon_L2_ zenon_TY_bd zenon_TX_h zenon_TY_i zenon_TX_j); trivial.
% 90.88/91.13  cut ((r1 zenon_TY_bd zenon_TX_bt) = (r1 zenon_TX_j zenon_TX_bt)).
% 90.88/91.13  intro zenon_D_pnotp.
% 90.88/91.13  apply zenon_H2b.
% 90.88/91.13  rewrite <- zenon_D_pnotp.
% 90.88/91.13  exact zenon_H2c.
% 90.88/91.13  cut ((zenon_TX_bt = zenon_TX_bt)); [idtac | apply NNPP; zenon_intro zenon_H31].
% 90.88/91.13  cut ((zenon_TY_bd = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H32].
% 90.88/91.13  congruence.
% 90.88/91.13  apply (zenon_notand_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 90.88/91.13  apply zenon_H34. zenon_intro zenon_H35.
% 90.88/91.13  elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_bd = zenon_TX_j)).
% 90.88/91.13  intro zenon_D_pnotp.
% 90.88/91.13  apply zenon_H32.
% 90.88/91.13  rewrite <- zenon_D_pnotp.
% 90.88/91.13  exact zenon_H13.
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 90.88/91.13  cut ((zenon_TX_j = zenon_TY_bd)); [idtac | apply NNPP; zenon_intro zenon_H30].
% 90.88/91.13  congruence.
% 90.88/91.13  exact (zenon_H30 zenon_H35).
% 90.88/91.13  apply zenon_H14. apply refl_equal.
% 90.88/91.13  apply zenon_H14. apply refl_equal.
% 90.88/91.13  apply zenon_H33. zenon_intro zenon_H29.
% 90.88/91.13  generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 90.88/91.13  generalize (zenon_H15 zenon_TY_bd). zenon_intro zenon_H36.
% 90.88/91.13  generalize (zenon_H36 zenon_TX_bt). zenon_intro zenon_H37.
% 90.88/91.13  apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H1b | zenon_intro zenon_H38 ].
% 90.88/91.13  exact (zenon_H1b zenon_H29).
% 90.88/91.13  apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ].
% 90.88/91.13  exact (zenon_H3a zenon_H2c).
% 90.88/91.13  exact (zenon_H2b zenon_H39).
% 90.88/91.13  apply zenon_H31. apply refl_equal.
% 90.88/91.13  (* end of lemma zenon_L3_ *)
% 90.88/91.13  assert (zenon_L4_ : forall (zenon_TY_cj : zenon_U) (zenon_TX_bt : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_j : zenon_U) (zenon_TY_bd : zenon_U) (zenon_TX_h : zenon_U), (r1 zenon_TX_h zenon_TY_bd) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TY_bd zenon_TX_bt) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TY_cj)) -> (r1 zenon_TX_bt zenon_TY_cj) -> False).
% 90.88/91.13  do 6 intro. intros zenon_H1c zenon_H3 zenon_H6 zenon_H2c zenon_H4 zenon_H3b zenon_H3c.
% 90.88/91.13  elim (classic ((~(zenon_TX_j = zenon_TX_bt))/\(~(r1 zenon_TX_j zenon_TX_bt)))); [ zenon_intro zenon_H3e | zenon_intro zenon_H3f ].
% 90.88/91.13  apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H2b.
% 90.88/91.13  apply (zenon_L3_ zenon_TX_bt zenon_TY_bd zenon_TX_j zenon_TX_h zenon_TY_i); trivial.
% 90.88/91.13  cut ((r1 zenon_TX_bt zenon_TY_cj) = (r1 zenon_TX_j zenon_TY_cj)).
% 90.88/91.13  intro zenon_D_pnotp.
% 90.88/91.13  apply zenon_H3b.
% 90.88/91.13  rewrite <- zenon_D_pnotp.
% 90.88/91.13  exact zenon_H3c.
% 90.88/91.13  cut ((zenon_TY_cj = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H41].
% 90.88/91.13  cut ((zenon_TX_bt = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H42].
% 90.88/91.13  congruence.
% 90.88/91.13  apply (zenon_notand_s _ _ zenon_H3f); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ].
% 90.88/91.13  apply zenon_H44. zenon_intro zenon_H45.
% 90.88/91.13  elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_bt = zenon_TX_j)).
% 90.88/91.13  intro zenon_D_pnotp.
% 90.88/91.13  apply zenon_H42.
% 90.88/91.13  rewrite <- zenon_D_pnotp.
% 90.88/91.13  exact zenon_H13.
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_bt)); [idtac | apply NNPP; zenon_intro zenon_H40].
% 90.88/91.13  congruence.
% 90.88/91.13  exact (zenon_H40 zenon_H45).
% 90.88/91.13  apply zenon_H14. apply refl_equal.
% 90.88/91.13  apply zenon_H14. apply refl_equal.
% 90.88/91.13  apply zenon_H43. zenon_intro zenon_H39.
% 90.88/91.13  generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 90.88/91.13  generalize (zenon_H15 zenon_TX_bt). zenon_intro zenon_H46.
% 90.88/91.13  generalize (zenon_H46 zenon_TY_cj). zenon_intro zenon_H47.
% 90.88/91.13  apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H2b | zenon_intro zenon_H48 ].
% 90.88/91.13  exact (zenon_H2b zenon_H39).
% 90.88/91.13  apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ].
% 90.88/91.13  exact (zenon_H4a zenon_H3c).
% 90.88/91.13  exact (zenon_H3b zenon_H49).
% 90.88/91.13  apply zenon_H41. apply refl_equal.
% 90.88/91.13  (* end of lemma zenon_L4_ *)
% 90.88/91.13  assert (zenon_L5_ : forall (zenon_TX_cz : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TX_j : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_bt : zenon_U) (zenon_TY_bd : zenon_U), (r1 zenon_TY_bd zenon_TX_bt) -> (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TX_h zenon_TY_bd) -> (r1 zenon_TX_bt zenon_TY_cj) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TX_cz)) -> (r1 zenon_TY_cj zenon_TX_cz) -> False).
% 90.88/91.13  do 7 intro. intros zenon_H2c zenon_H6 zenon_H3 zenon_H1c zenon_H3c zenon_H4 zenon_H4b zenon_H4c.
% 90.88/91.13  elim (classic ((~(zenon_TX_j = zenon_TY_cj))/\(~(r1 zenon_TX_j zenon_TY_cj)))); [ zenon_intro zenon_H4e | zenon_intro zenon_H4f ].
% 90.88/91.13  apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H50. zenon_intro zenon_H3b.
% 90.88/91.13  apply (zenon_L4_ zenon_TY_cj zenon_TX_bt zenon_TY_i zenon_TX_j zenon_TY_bd zenon_TX_h); trivial.
% 90.88/91.13  cut ((r1 zenon_TY_cj zenon_TX_cz) = (r1 zenon_TX_j zenon_TX_cz)).
% 90.88/91.13  intro zenon_D_pnotp.
% 90.88/91.13  apply zenon_H4b.
% 90.88/91.13  rewrite <- zenon_D_pnotp.
% 90.88/91.13  exact zenon_H4c.
% 90.88/91.13  cut ((zenon_TX_cz = zenon_TX_cz)); [idtac | apply NNPP; zenon_intro zenon_H51].
% 90.88/91.13  cut ((zenon_TY_cj = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H52].
% 90.88/91.13  congruence.
% 90.88/91.13  apply (zenon_notand_s _ _ zenon_H4f); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ].
% 90.88/91.13  apply zenon_H54. zenon_intro zenon_H55.
% 90.88/91.13  elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_cj = zenon_TX_j)).
% 90.88/91.13  intro zenon_D_pnotp.
% 90.88/91.13  apply zenon_H52.
% 90.88/91.13  rewrite <- zenon_D_pnotp.
% 90.88/91.13  exact zenon_H13.
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 90.88/91.13  cut ((zenon_TX_j = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H50].
% 90.88/91.13  congruence.
% 90.88/91.13  exact (zenon_H50 zenon_H55).
% 90.88/91.13  apply zenon_H14. apply refl_equal.
% 90.88/91.13  apply zenon_H14. apply refl_equal.
% 90.88/91.13  apply zenon_H53. zenon_intro zenon_H49.
% 90.88/91.13  generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 90.88/91.13  generalize (zenon_H15 zenon_TY_cj). zenon_intro zenon_H56.
% 90.88/91.13  generalize (zenon_H56 zenon_TX_cz). zenon_intro zenon_H57.
% 90.88/91.13  apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H3b | zenon_intro zenon_H58 ].
% 90.88/91.13  exact (zenon_H3b zenon_H49).
% 90.88/91.13  apply (zenon_imply_s _ _ zenon_H58); [ zenon_intro zenon_H5a | zenon_intro zenon_H59 ].
% 90.88/91.13  exact (zenon_H5a zenon_H4c).
% 90.88/91.13  exact (zenon_H4b zenon_H59).
% 90.88/91.13  apply zenon_H51. apply refl_equal.
% 90.88/91.13  (* end of lemma zenon_L5_ *)
% 90.88/91.13  assert (zenon_L6_ : forall (zenon_TY_dp : zenon_U) (zenon_TX_cz : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_j : zenon_U) (zenon_TY_bd : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TX_bt : zenon_U), (r1 zenon_TX_bt zenon_TY_cj) -> (r1 zenon_TX_h zenon_TY_bd) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TY_bd zenon_TX_bt) -> (r1 zenon_TY_cj zenon_TX_cz) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TY_dp)) -> (r1 zenon_TX_cz zenon_TY_dp) -> False).
% 90.88/91.13  do 8 intro. intros zenon_H3c zenon_H1c zenon_H3 zenon_H6 zenon_H2c zenon_H4c zenon_H4 zenon_H5b zenon_H5c.
% 90.88/91.13  elim (classic ((~(zenon_TX_j = zenon_TX_cz))/\(~(r1 zenon_TX_j zenon_TX_cz)))); [ zenon_intro zenon_H5e | zenon_intro zenon_H5f ].
% 90.88/91.13  apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H60. zenon_intro zenon_H4b.
% 90.88/91.13  apply (zenon_L5_ zenon_TX_cz zenon_TY_cj zenon_TX_j zenon_TX_h zenon_TY_i zenon_TX_bt zenon_TY_bd); trivial.
% 90.88/91.13  cut ((r1 zenon_TX_cz zenon_TY_dp) = (r1 zenon_TX_j zenon_TY_dp)).
% 90.88/91.13  intro zenon_D_pnotp.
% 90.88/91.13  apply zenon_H5b.
% 90.88/91.13  rewrite <- zenon_D_pnotp.
% 90.88/91.13  exact zenon_H5c.
% 90.88/91.13  cut ((zenon_TY_dp = zenon_TY_dp)); [idtac | apply NNPP; zenon_intro zenon_H61].
% 90.88/91.13  cut ((zenon_TX_cz = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H62].
% 90.88/91.13  congruence.
% 90.88/91.13  apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ].
% 90.88/91.13  apply zenon_H64. zenon_intro zenon_H65.
% 90.88/91.13  elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_cz = zenon_TX_j)).
% 90.88/91.13  intro zenon_D_pnotp.
% 90.88/91.13  apply zenon_H62.
% 90.88/91.13  rewrite <- zenon_D_pnotp.
% 90.88/91.13  exact zenon_H13.
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_cz)); [idtac | apply NNPP; zenon_intro zenon_H60].
% 90.88/91.13  congruence.
% 90.88/91.13  exact (zenon_H60 zenon_H65).
% 90.88/91.13  apply zenon_H14. apply refl_equal.
% 90.88/91.13  apply zenon_H14. apply refl_equal.
% 90.88/91.13  apply zenon_H63. zenon_intro zenon_H59.
% 90.88/91.13  generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 90.88/91.13  generalize (zenon_H15 zenon_TX_cz). zenon_intro zenon_H66.
% 90.88/91.13  generalize (zenon_H66 zenon_TY_dp). zenon_intro zenon_H67.
% 90.88/91.13  apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H4b | zenon_intro zenon_H68 ].
% 90.88/91.13  exact (zenon_H4b zenon_H59).
% 90.88/91.13  apply (zenon_imply_s _ _ zenon_H68); [ zenon_intro zenon_H6a | zenon_intro zenon_H69 ].
% 90.88/91.13  exact (zenon_H6a zenon_H5c).
% 90.88/91.13  exact (zenon_H5b zenon_H69).
% 90.88/91.13  apply zenon_H61. apply refl_equal.
% 90.88/91.13  (* end of lemma zenon_L6_ *)
% 90.88/91.13  assert (zenon_L7_ : forall (zenon_TX_ef : zenon_U) (zenon_TY_dp : zenon_U) (zenon_TX_j : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_bt : zenon_U) (zenon_TY_bd : zenon_U) (zenon_TX_cz : zenon_U) (zenon_TY_cj : zenon_U), (r1 zenon_TY_cj zenon_TX_cz) -> (r1 zenon_TY_bd zenon_TX_bt) -> (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TX_h zenon_TY_bd) -> (r1 zenon_TX_bt zenon_TY_cj) -> (r1 zenon_TX_cz zenon_TY_dp) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TX_ef)) -> (r1 zenon_TY_dp zenon_TX_ef) -> False).
% 90.88/91.13  do 9 intro. intros zenon_H4c zenon_H2c zenon_H6 zenon_H3 zenon_H1c zenon_H3c zenon_H5c zenon_H4 zenon_H6b zenon_H6c.
% 90.88/91.13  elim (classic ((~(zenon_TX_j = zenon_TY_dp))/\(~(r1 zenon_TX_j zenon_TY_dp)))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ].
% 90.88/91.13  apply (zenon_and_s _ _ zenon_H6e). zenon_intro zenon_H70. zenon_intro zenon_H5b.
% 90.88/91.13  apply (zenon_L6_ zenon_TY_dp zenon_TX_cz zenon_TY_i zenon_TX_j zenon_TY_bd zenon_TX_h zenon_TY_cj zenon_TX_bt); trivial.
% 90.88/91.13  cut ((r1 zenon_TY_dp zenon_TX_ef) = (r1 zenon_TX_j zenon_TX_ef)).
% 90.88/91.13  intro zenon_D_pnotp.
% 90.88/91.13  apply zenon_H6b.
% 90.88/91.13  rewrite <- zenon_D_pnotp.
% 90.88/91.13  exact zenon_H6c.
% 90.88/91.13  cut ((zenon_TX_ef = zenon_TX_ef)); [idtac | apply NNPP; zenon_intro zenon_H71].
% 90.88/91.13  cut ((zenon_TY_dp = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H72].
% 90.88/91.13  congruence.
% 90.88/91.13  apply (zenon_notand_s _ _ zenon_H6f); [ zenon_intro zenon_H74 | zenon_intro zenon_H73 ].
% 90.88/91.13  apply zenon_H74. zenon_intro zenon_H75.
% 90.88/91.13  elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_dp = zenon_TX_j)).
% 90.88/91.13  intro zenon_D_pnotp.
% 90.88/91.13  apply zenon_H72.
% 90.88/91.13  rewrite <- zenon_D_pnotp.
% 90.88/91.13  exact zenon_H13.
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 90.88/91.13  cut ((zenon_TX_j = zenon_TY_dp)); [idtac | apply NNPP; zenon_intro zenon_H70].
% 90.88/91.13  congruence.
% 90.88/91.13  exact (zenon_H70 zenon_H75).
% 90.88/91.13  apply zenon_H14. apply refl_equal.
% 90.88/91.13  apply zenon_H14. apply refl_equal.
% 90.88/91.13  apply zenon_H73. zenon_intro zenon_H69.
% 90.88/91.13  generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 90.88/91.13  generalize (zenon_H15 zenon_TY_dp). zenon_intro zenon_H76.
% 90.88/91.13  generalize (zenon_H76 zenon_TX_ef). zenon_intro zenon_H77.
% 90.88/91.13  apply (zenon_imply_s _ _ zenon_H77); [ zenon_intro zenon_H5b | zenon_intro zenon_H78 ].
% 90.88/91.13  exact (zenon_H5b zenon_H69).
% 90.88/91.13  apply (zenon_imply_s _ _ zenon_H78); [ zenon_intro zenon_H7a | zenon_intro zenon_H79 ].
% 90.88/91.13  exact (zenon_H7a zenon_H6c).
% 90.88/91.13  exact (zenon_H6b zenon_H79).
% 90.88/91.13  apply zenon_H71. apply refl_equal.
% 90.88/91.13  (* end of lemma zenon_L7_ *)
% 90.88/91.13  assert (zenon_L8_ : forall (zenon_TY_ev : zenon_U) (zenon_TX_ef : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_j : zenon_U) (zenon_TY_bd : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TX_bt : zenon_U) (zenon_TY_dp : zenon_U) (zenon_TX_cz : zenon_U), (r1 zenon_TX_cz zenon_TY_dp) -> (r1 zenon_TX_bt zenon_TY_cj) -> (r1 zenon_TX_h zenon_TY_bd) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TY_bd zenon_TX_bt) -> (r1 zenon_TY_cj zenon_TX_cz) -> (r1 zenon_TY_dp zenon_TX_ef) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TY_ev)) -> (r1 zenon_TX_ef zenon_TY_ev) -> False).
% 90.88/91.13  do 10 intro. intros zenon_H5c zenon_H3c zenon_H1c zenon_H3 zenon_H6 zenon_H2c zenon_H4c zenon_H6c zenon_H4 zenon_H7b zenon_H7c.
% 90.88/91.13  elim (classic ((~(zenon_TX_j = zenon_TX_ef))/\(~(r1 zenon_TX_j zenon_TX_ef)))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ].
% 90.88/91.13  apply (zenon_and_s _ _ zenon_H7e). zenon_intro zenon_H80. zenon_intro zenon_H6b.
% 90.88/91.13  apply (zenon_L7_ zenon_TX_ef zenon_TY_dp zenon_TX_j zenon_TX_h zenon_TY_i zenon_TX_bt zenon_TY_bd zenon_TX_cz zenon_TY_cj); trivial.
% 90.88/91.13  cut ((r1 zenon_TX_ef zenon_TY_ev) = (r1 zenon_TX_j zenon_TY_ev)).
% 90.88/91.13  intro zenon_D_pnotp.
% 90.88/91.13  apply zenon_H7b.
% 90.88/91.13  rewrite <- zenon_D_pnotp.
% 90.88/91.13  exact zenon_H7c.
% 90.88/91.13  cut ((zenon_TY_ev = zenon_TY_ev)); [idtac | apply NNPP; zenon_intro zenon_H81].
% 90.88/91.13  cut ((zenon_TX_ef = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H82].
% 90.88/91.13  congruence.
% 90.88/91.13  apply (zenon_notand_s _ _ zenon_H7f); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ].
% 90.88/91.13  apply zenon_H84. zenon_intro zenon_H85.
% 90.88/91.13  elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_ef = zenon_TX_j)).
% 90.88/91.13  intro zenon_D_pnotp.
% 90.88/91.13  apply zenon_H82.
% 90.88/91.13  rewrite <- zenon_D_pnotp.
% 90.88/91.13  exact zenon_H13.
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 90.88/91.13  cut ((zenon_TX_j = zenon_TX_ef)); [idtac | apply NNPP; zenon_intro zenon_H80].
% 90.88/91.13  congruence.
% 90.88/91.13  exact (zenon_H80 zenon_H85).
% 90.88/91.13  apply zenon_H14. apply refl_equal.
% 90.88/91.13  apply zenon_H14. apply refl_equal.
% 90.88/91.13  apply zenon_H83. zenon_intro zenon_H79.
% 90.88/91.13  generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 90.88/91.13  generalize (zenon_H15 zenon_TX_ef). zenon_intro zenon_H86.
% 90.88/91.13  generalize (zenon_H86 zenon_TY_ev). zenon_intro zenon_H87.
% 90.88/91.13  apply (zenon_imply_s _ _ zenon_H87); [ zenon_intro zenon_H6b | zenon_intro zenon_H88 ].
% 90.88/91.13  exact (zenon_H6b zenon_H79).
% 90.88/91.13  apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H8a | zenon_intro zenon_H89 ].
% 90.88/91.13  exact (zenon_H8a zenon_H7c).
% 90.88/91.13  exact (zenon_H7b zenon_H89).
% 90.88/91.13  apply zenon_H81. apply refl_equal.
% 90.88/91.13  (* end of lemma zenon_L8_ *)
% 90.88/91.13  assert (zenon_L9_ : forall (zenon_TX_fl : zenon_U) (zenon_TY_ev : zenon_U) (zenon_TX_j : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_bt : zenon_U) (zenon_TY_bd : zenon_U) (zenon_TX_cz : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TX_ef : zenon_U) (zenon_TY_dp : zenon_U), (r1 zenon_TY_dp zenon_TX_ef) -> (r1 zenon_TY_cj zenon_TX_cz) -> (r1 zenon_TY_bd zenon_TX_bt) -> (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TX_h zenon_TY_bd) -> (r1 zenon_TX_bt zenon_TY_cj) -> (r1 zenon_TX_cz zenon_TY_dp) -> (r1 zenon_TX_ef zenon_TY_ev) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TX_fl)) -> (r1 zenon_TY_ev zenon_TX_fl) -> False).
% 90.88/91.13  do 11 intro. intros zenon_H6c zenon_H4c zenon_H2c zenon_H6 zenon_H3 zenon_H1c zenon_H3c zenon_H5c zenon_H7c zenon_H4 zenon_H8b zenon_H8c.
% 90.88/91.13  elim (classic ((~(zenon_TX_j = zenon_TY_ev))/\(~(r1 zenon_TX_j zenon_TY_ev)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ].
% 90.88/91.13  apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H90. zenon_intro zenon_H7b.
% 90.88/91.13  apply (zenon_L8_ zenon_TY_ev zenon_TX_ef zenon_TY_i zenon_TX_j zenon_TY_bd zenon_TX_h zenon_TY_cj zenon_TX_bt zenon_TY_dp zenon_TX_cz); trivial.
% 90.88/91.13  cut ((r1 zenon_TY_ev zenon_TX_fl) = (r1 zenon_TX_j zenon_TX_fl)).
% 90.88/91.13  intro zenon_D_pnotp.
% 90.88/91.13  apply zenon_H8b.
% 90.88/91.13  rewrite <- zenon_D_pnotp.
% 90.88/91.13  exact zenon_H8c.
% 90.88/91.13  cut ((zenon_TX_fl = zenon_TX_fl)); [idtac | apply NNPP; zenon_intro zenon_H91].
% 90.88/91.13  cut ((zenon_TY_ev = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H92].
% 90.88/91.13  congruence.
% 90.88/91.13  apply (zenon_notand_s _ _ zenon_H8f); [ zenon_intro zenon_H94 | zenon_intro zenon_H93 ].
% 90.88/91.14  apply zenon_H94. zenon_intro zenon_H95.
% 90.88/91.14  elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 90.88/91.14  cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_ev = zenon_TX_j)).
% 90.88/91.14  intro zenon_D_pnotp.
% 90.88/91.14  apply zenon_H92.
% 90.88/91.14  rewrite <- zenon_D_pnotp.
% 90.88/91.14  exact zenon_H13.
% 90.88/91.14  cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 90.88/91.14  cut ((zenon_TX_j = zenon_TY_ev)); [idtac | apply NNPP; zenon_intro zenon_H90].
% 90.88/91.14  congruence.
% 90.88/91.14  exact (zenon_H90 zenon_H95).
% 90.88/91.14  apply zenon_H14. apply refl_equal.
% 90.88/91.14  apply zenon_H14. apply refl_equal.
% 90.88/91.14  apply zenon_H93. zenon_intro zenon_H89.
% 90.88/91.14  generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 90.88/91.14  generalize (zenon_H15 zenon_TY_ev). zenon_intro zenon_H96.
% 90.88/91.14  generalize (zenon_H96 zenon_TX_fl). zenon_intro zenon_H97.
% 90.88/91.14  apply (zenon_imply_s _ _ zenon_H97); [ zenon_intro zenon_H7b | zenon_intro zenon_H98 ].
% 90.88/91.14  exact (zenon_H7b zenon_H89).
% 90.88/91.14  apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H9a | zenon_intro zenon_H99 ].
% 90.88/91.14  exact (zenon_H9a zenon_H8c).
% 90.88/91.14  exact (zenon_H8b zenon_H99).
% 90.88/91.14  apply zenon_H91. apply refl_equal.
% 90.88/91.14  (* end of lemma zenon_L9_ *)
% 90.88/91.14  assert (zenon_L10_ : forall (zenon_TY_gb : zenon_U) (zenon_TX_fl : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_j : zenon_U) (zenon_TY_bd : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TX_bt : zenon_U) (zenon_TY_dp : zenon_U) (zenon_TX_cz : zenon_U) (zenon_TY_ev : zenon_U) (zenon_TX_ef : zenon_U), (r1 zenon_TX_ef zenon_TY_ev) -> (r1 zenon_TX_cz zenon_TY_dp) -> (r1 zenon_TX_bt zenon_TY_cj) -> (r1 zenon_TX_h zenon_TY_bd) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TY_bd zenon_TX_bt) -> (r1 zenon_TY_cj zenon_TX_cz) -> (r1 zenon_TY_dp zenon_TX_ef) -> (r1 zenon_TY_ev zenon_TX_fl) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TY_gb)) -> (r1 zenon_TX_fl zenon_TY_gb) -> False).
% 90.88/91.14  do 12 intro. intros zenon_H7c zenon_H5c zenon_H3c zenon_H1c zenon_H3 zenon_H6 zenon_H2c zenon_H4c zenon_H6c zenon_H8c zenon_H4 zenon_H9b zenon_H9c.
% 90.88/91.14  elim (classic ((~(zenon_TX_j = zenon_TX_fl))/\(~(r1 zenon_TX_j zenon_TX_fl)))); [ zenon_intro zenon_H9e | zenon_intro zenon_H9f ].
% 90.88/91.14  apply (zenon_and_s _ _ zenon_H9e). zenon_intro zenon_Ha0. zenon_intro zenon_H8b.
% 90.88/91.14  apply (zenon_L9_ zenon_TX_fl zenon_TY_ev zenon_TX_j zenon_TX_h zenon_TY_i zenon_TX_bt zenon_TY_bd zenon_TX_cz zenon_TY_cj zenon_TX_ef zenon_TY_dp); trivial.
% 90.88/91.14  cut ((r1 zenon_TX_fl zenon_TY_gb) = (r1 zenon_TX_j zenon_TY_gb)).
% 90.88/91.14  intro zenon_D_pnotp.
% 90.88/91.14  apply zenon_H9b.
% 90.88/91.14  rewrite <- zenon_D_pnotp.
% 90.88/91.14  exact zenon_H9c.
% 90.88/91.14  cut ((zenon_TY_gb = zenon_TY_gb)); [idtac | apply NNPP; zenon_intro zenon_Ha1].
% 90.88/91.14  cut ((zenon_TX_fl = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_Ha2].
% 90.88/91.14  congruence.
% 90.88/91.14  apply (zenon_notand_s _ _ zenon_H9f); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha3 ].
% 90.88/91.14  apply zenon_Ha4. zenon_intro zenon_Ha5.
% 90.88/91.14  elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 90.88/91.14  cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_fl = zenon_TX_j)).
% 90.88/91.14  intro zenon_D_pnotp.
% 90.88/91.14  apply zenon_Ha2.
% 90.88/91.14  rewrite <- zenon_D_pnotp.
% 90.88/91.14  exact zenon_H13.
% 90.88/91.14  cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 90.88/91.14  cut ((zenon_TX_j = zenon_TX_fl)); [idtac | apply NNPP; zenon_intro zenon_Ha0].
% 90.88/91.14  congruence.
% 90.88/91.14  exact (zenon_Ha0 zenon_Ha5).
% 90.88/91.14  apply zenon_H14. apply refl_equal.
% 90.88/91.14  apply zenon_H14. apply refl_equal.
% 90.88/91.14  apply zenon_Ha3. zenon_intro zenon_H99.
% 90.88/91.14  generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 90.88/91.14  generalize (zenon_H15 zenon_TX_fl). zenon_intro zenon_Ha6.
% 90.88/91.14  generalize (zenon_Ha6 zenon_TY_gb). zenon_intro zenon_Ha7.
% 90.88/91.14  apply (zenon_imply_s _ _ zenon_Ha7); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ].
% 90.88/91.14  exact (zenon_H8b zenon_H99).
% 90.88/91.14  apply (zenon_imply_s _ _ zenon_Ha8); [ zenon_intro zenon_Haa | zenon_intro zenon_Ha9 ].
% 90.88/91.14  exact (zenon_Haa zenon_H9c).
% 90.88/91.14  exact (zenon_H9b zenon_Ha9).
% 90.88/91.14  apply zenon_Ha1. apply refl_equal.
% 90.88/91.14  (* end of lemma zenon_L10_ *)
% 90.88/91.14  assert (zenon_L11_ : forall (zenon_TX_gr : zenon_U) (zenon_TY_gb : zenon_U) (zenon_TX_j : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_bt : zenon_U) (zenon_TY_bd : zenon_U) (zenon_TX_cz : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TX_ef : zenon_U) (zenon_TY_dp : zenon_U) (zenon_TX_fl : zenon_U) (zenon_TY_ev : zenon_U), (r1 zenon_TY_ev zenon_TX_fl) -> (r1 zenon_TY_dp zenon_TX_ef) -> (r1 zenon_TY_cj zenon_TX_cz) -> (r1 zenon_TY_bd zenon_TX_bt) -> (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TX_h zenon_TY_bd) -> (r1 zenon_TX_bt zenon_TY_cj) -> (r1 zenon_TX_cz zenon_TY_dp) -> (r1 zenon_TX_ef zenon_TY_ev) -> (r1 zenon_TX_fl zenon_TY_gb) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TX_gr)) -> (r1 zenon_TY_gb zenon_TX_gr) -> False).
% 90.88/91.14  do 13 intro. intros zenon_H8c zenon_H6c zenon_H4c zenon_H2c zenon_H6 zenon_H3 zenon_H1c zenon_H3c zenon_H5c zenon_H7c zenon_H9c zenon_H4 zenon_Hab zenon_Hac.
% 90.88/91.14  elim (classic ((~(zenon_TX_j = zenon_TY_gb))/\(~(r1 zenon_TX_j zenon_TY_gb)))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ].
% 90.88/91.14  apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Hb0. zenon_intro zenon_H9b.
% 90.88/91.14  apply (zenon_L10_ zenon_TY_gb zenon_TX_fl zenon_TY_i zenon_TX_j zenon_TY_bd zenon_TX_h zenon_TY_cj zenon_TX_bt zenon_TY_dp zenon_TX_cz zenon_TY_ev zenon_TX_ef); trivial.
% 90.88/91.14  cut ((r1 zenon_TY_gb zenon_TX_gr) = (r1 zenon_TX_j zenon_TX_gr)).
% 90.88/91.14  intro zenon_D_pnotp.
% 90.88/91.14  apply zenon_Hab.
% 90.88/91.14  rewrite <- zenon_D_pnotp.
% 90.88/91.14  exact zenon_Hac.
% 90.88/91.14  cut ((zenon_TX_gr = zenon_TX_gr)); [idtac | apply NNPP; zenon_intro zenon_Hb1].
% 90.88/91.14  cut ((zenon_TY_gb = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_Hb2].
% 90.88/91.14  congruence.
% 90.88/91.14  apply (zenon_notand_s _ _ zenon_Haf); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ].
% 90.88/91.14  apply zenon_Hb4. zenon_intro zenon_Hb5.
% 90.88/91.14  elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 90.88/91.14  cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_gb = zenon_TX_j)).
% 90.88/91.14  intro zenon_D_pnotp.
% 90.88/91.14  apply zenon_Hb2.
% 90.88/91.14  rewrite <- zenon_D_pnotp.
% 90.88/91.14  exact zenon_H13.
% 90.88/91.14  cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 90.88/91.14  cut ((zenon_TX_j = zenon_TY_gb)); [idtac | apply NNPP; zenon_intro zenon_Hb0].
% 90.88/91.14  congruence.
% 90.88/91.14  exact (zenon_Hb0 zenon_Hb5).
% 90.88/91.14  apply zenon_H14. apply refl_equal.
% 90.88/91.14  apply zenon_H14. apply refl_equal.
% 90.88/91.14  apply zenon_Hb3. zenon_intro zenon_Ha9.
% 90.88/91.14  generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 90.88/91.14  generalize (zenon_H15 zenon_TY_gb). zenon_intro zenon_Hb6.
% 90.88/91.14  generalize (zenon_Hb6 zenon_TX_gr). zenon_intro zenon_Hb7.
% 90.88/91.14  apply (zenon_imply_s _ _ zenon_Hb7); [ zenon_intro zenon_H9b | zenon_intro zenon_Hb8 ].
% 90.88/91.14  exact (zenon_H9b zenon_Ha9).
% 90.88/91.14  apply (zenon_imply_s _ _ zenon_Hb8); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ].
% 90.88/91.14  exact (zenon_Hba zenon_Hac).
% 90.88/91.14  exact (zenon_Hab zenon_Hb9).
% 90.88/91.14  apply zenon_Hb1. apply refl_equal.
% 90.88/91.14  (* end of lemma zenon_L11_ *)
% 90.88/91.14  assert (zenon_L12_ : forall (zenon_TY_hh : zenon_U) (zenon_TX_gr : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_j : zenon_U) (zenon_TY_bd : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TX_bt : zenon_U) (zenon_TY_dp : zenon_U) (zenon_TX_cz : zenon_U) (zenon_TY_ev : zenon_U) (zenon_TX_ef : zenon_U) (zenon_TY_gb : zenon_U) (zenon_TX_fl : zenon_U), (r1 zenon_TX_fl zenon_TY_gb) -> (r1 zenon_TX_ef zenon_TY_ev) -> (r1 zenon_TX_cz zenon_TY_dp) -> (r1 zenon_TX_bt zenon_TY_cj) -> (r1 zenon_TX_h zenon_TY_bd) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TY_bd zenon_TX_bt) -> (r1 zenon_TY_cj zenon_TX_cz) -> (r1 zenon_TY_dp zenon_TX_ef) -> (r1 zenon_TY_ev zenon_TX_fl) -> (r1 zenon_TY_gb zenon_TX_gr) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TY_hh)) -> (r1 zenon_TX_gr zenon_TY_hh) -> False).
% 90.88/91.14  do 14 intro. intros zenon_H9c zenon_H7c zenon_H5c zenon_H3c zenon_H1c zenon_H3 zenon_H6 zenon_H2c zenon_H4c zenon_H6c zenon_H8c zenon_Hac zenon_H4 zenon_Hbb zenon_Hbc.
% 90.88/91.14  elim (classic ((~(zenon_TX_j = zenon_TX_gr))/\(~(r1 zenon_TX_j zenon_TX_gr)))); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hbf ].
% 90.88/91.14  apply (zenon_and_s _ _ zenon_Hbe). zenon_intro zenon_Hc0. zenon_intro zenon_Hab.
% 90.88/91.14  apply (zenon_L11_ zenon_TX_gr zenon_TY_gb zenon_TX_j zenon_TX_h zenon_TY_i zenon_TX_bt zenon_TY_bd zenon_TX_cz zenon_TY_cj zenon_TX_ef zenon_TY_dp zenon_TX_fl zenon_TY_ev); trivial.
% 90.88/91.14  cut ((r1 zenon_TX_gr zenon_TY_hh) = (r1 zenon_TX_j zenon_TY_hh)).
% 90.88/91.14  intro zenon_D_pnotp.
% 90.88/91.14  apply zenon_Hbb.
% 90.88/91.14  rewrite <- zenon_D_pnotp.
% 90.88/91.14  exact zenon_Hbc.
% 90.88/91.14  cut ((zenon_TY_hh = zenon_TY_hh)); [idtac | apply NNPP; zenon_intro zenon_Hc1].
% 90.88/91.14  cut ((zenon_TX_gr = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_Hc2].
% 90.88/91.14  congruence.
% 90.88/91.14  apply (zenon_notand_s _ _ zenon_Hbf); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ].
% 90.88/91.14  apply zenon_Hc4. zenon_intro zenon_Hc5.
% 90.88/91.14  elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 90.88/91.14  cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_gr = zenon_TX_j)).
% 90.88/91.14  intro zenon_D_pnotp.
% 90.88/91.14  apply zenon_Hc2.
% 90.88/91.14  rewrite <- zenon_D_pnotp.
% 90.88/91.14  exact zenon_H13.
% 90.88/91.14  cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 90.88/91.14  cut ((zenon_TX_j = zenon_TX_gr)); [idtac | apply NNPP; zenon_intro zenon_Hc0].
% 90.88/91.14  congruence.
% 90.88/91.14  exact (zenon_Hc0 zenon_Hc5).
% 90.88/91.14  apply zenon_H14. apply refl_equal.
% 90.88/91.14  apply zenon_H14. apply refl_equal.
% 90.88/91.14  apply zenon_Hc3. zenon_intro zenon_Hb9.
% 90.88/91.14  generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 90.88/91.14  generalize (zenon_H15 zenon_TX_gr). zenon_intro zenon_Hc6.
% 90.88/91.14  generalize (zenon_Hc6 zenon_TY_hh). zenon_intro zenon_Hc7.
% 90.88/91.14  apply (zenon_imply_s _ _ zenon_Hc7); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc8 ].
% 90.88/91.14  exact (zenon_Hab zenon_Hb9).
% 90.88/91.14  apply (zenon_imply_s _ _ zenon_Hc8); [ zenon_intro zenon_Hca | zenon_intro zenon_Hc9 ].
% 90.88/91.14  exact (zenon_Hca zenon_Hbc).
% 90.88/91.14  exact (zenon_Hbb zenon_Hc9).
% 90.88/91.14  apply zenon_Hc1. apply refl_equal.
% 90.88/91.14  (* end of lemma zenon_L12_ *)
% 90.88/91.14  apply NNPP. intro zenon_G.
% 90.88/91.14  elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z))))))); [ zenon_intro zenon_H4 | zenon_intro zenon_Hcb ].
% 90.88/91.14  apply zenon_G. zenon_intro zenon_Hcc.
% 90.88/91.14  elim zenon_Hcc. zenon_intro zenon_TX_j. zenon_intro zenon_Hcd.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hcd). zenon_intro zenon_Hcf. zenon_intro zenon_Hce.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hce). zenon_intro zenon_Hd1. zenon_intro zenon_Hd0.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hd0). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hd2). zenon_intro zenon_Hd5. zenon_intro zenon_Hd4.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hd4). zenon_intro zenon_Hd7. zenon_intro zenon_Hd6.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hd6). zenon_intro zenon_Hd9. zenon_intro zenon_Hd8.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hd8). zenon_intro zenon_Hdb. zenon_intro zenon_Hda.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hda). zenon_intro zenon_Hdd. zenon_intro zenon_Hdc.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hdc). zenon_intro zenon_Hdf. zenon_intro zenon_Hde.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hde). zenon_intro zenon_He1. zenon_intro zenon_He0.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_He0). zenon_intro zenon_He3. zenon_intro zenon_He2.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_He2). zenon_intro zenon_Hd7. zenon_intro zenon_He4.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_He4). zenon_intro zenon_Hd9. zenon_intro zenon_He5.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_He5). zenon_intro zenon_Hdb. zenon_intro zenon_He6.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_He6). zenon_intro zenon_He8. zenon_intro zenon_He7.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_He7). zenon_intro zenon_Hea. zenon_intro zenon_He9.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_He9). zenon_intro zenon_Hec. zenon_intro zenon_Heb.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Heb). zenon_intro zenon_Hee. zenon_intro zenon_Hed.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hed). zenon_intro zenon_Hd7. zenon_intro zenon_Hef.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hef). zenon_intro zenon_Hd9. zenon_intro zenon_Hf0.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hf0). zenon_intro zenon_Hdb. zenon_intro zenon_Hf1.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hf1). zenon_intro zenon_Hf3. zenon_intro zenon_Hf2.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hf2). zenon_intro zenon_Hf5. zenon_intro zenon_Hf4.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hf4). zenon_intro zenon_Hf7. zenon_intro zenon_Hf6.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hf6). zenon_intro zenon_Hf9. zenon_intro zenon_Hf8.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hf8). zenon_intro zenon_Hd7. zenon_intro zenon_Hfa.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hfa). zenon_intro zenon_Hd9. zenon_intro zenon_Hfb.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hfb). zenon_intro zenon_Hdb. zenon_intro zenon_Hfc.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hfc). zenon_intro zenon_Hfe. zenon_intro zenon_Hfd.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hfd). zenon_intro zenon_H100. zenon_intro zenon_Hff.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_Hff). zenon_intro zenon_H102. zenon_intro zenon_H101.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H101). zenon_intro zenon_H104. zenon_intro zenon_H103.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H103). zenon_intro zenon_Hd7. zenon_intro zenon_H105.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H105). zenon_intro zenon_Hd9. zenon_intro zenon_H106.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H106). zenon_intro zenon_Hdb. zenon_intro zenon_H107.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H107). zenon_intro zenon_H109. zenon_intro zenon_H108.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H108). zenon_intro zenon_H10b. zenon_intro zenon_H10a.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H10a). zenon_intro zenon_H10d. zenon_intro zenon_H10c.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H10c). zenon_intro zenon_H10f. zenon_intro zenon_H10e.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H10e). zenon_intro zenon_Hd7. zenon_intro zenon_H110.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H110). zenon_intro zenon_Hd9. zenon_intro zenon_H111.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H111). zenon_intro zenon_Hdb. zenon_intro zenon_H112.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H112). zenon_intro zenon_H114. zenon_intro zenon_H113.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H113). zenon_intro zenon_H116. zenon_intro zenon_H115.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H115). zenon_intro zenon_H118. zenon_intro zenon_H117.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H117). zenon_intro zenon_H11a. zenon_intro zenon_H119.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H119). zenon_intro zenon_Hd7. zenon_intro zenon_H11b.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H11b). zenon_intro zenon_Hd9. zenon_intro zenon_H11c.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H11c). zenon_intro zenon_Hdb. zenon_intro zenon_H11d.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H11d). zenon_intro zenon_H11f. zenon_intro zenon_H11e.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H11e). zenon_intro zenon_H121. zenon_intro zenon_H120.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H120). zenon_intro zenon_H123. zenon_intro zenon_H122.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H122). zenon_intro zenon_H125. zenon_intro zenon_H124.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H124). zenon_intro zenon_Hd7. zenon_intro zenon_H126.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H126). zenon_intro zenon_Hd9. zenon_intro zenon_H127.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H127). zenon_intro zenon_Hdb. zenon_intro zenon_H128.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H128). zenon_intro zenon_H12a. zenon_intro zenon_H129.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H129). zenon_intro zenon_H12c. zenon_intro zenon_H12b.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H12b). zenon_intro zenon_H12e. zenon_intro zenon_H12d.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H12d). zenon_intro zenon_H130. zenon_intro zenon_H12f.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H12f). zenon_intro zenon_Hd7. zenon_intro zenon_H131.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H131). zenon_intro zenon_Hd9. zenon_intro zenon_H132.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H132). zenon_intro zenon_Hdb. zenon_intro zenon_H133.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H133). zenon_intro zenon_H135. zenon_intro zenon_H134.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H134). zenon_intro zenon_H137. zenon_intro zenon_H136.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H136). zenon_intro zenon_H139. zenon_intro zenon_H138.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H138). zenon_intro zenon_H13b. zenon_intro zenon_H13a.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H13a). zenon_intro zenon_Hd7. zenon_intro zenon_H13c.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H13c). zenon_intro zenon_Hd9. zenon_intro zenon_H13d.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H13d). zenon_intro zenon_Hdb. zenon_intro zenon_H13e.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H13e). zenon_intro zenon_H140. zenon_intro zenon_H13f.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H13f). zenon_intro zenon_H142. zenon_intro zenon_H141.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H143). zenon_intro zenon_H146. zenon_intro zenon_H145.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H145). zenon_intro zenon_Hd7. zenon_intro zenon_H147.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H147). zenon_intro zenon_Hd9. zenon_intro zenon_H148.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H148). zenon_intro zenon_Hdb. zenon_intro zenon_H149.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H149). zenon_intro zenon_H14b. zenon_intro zenon_H14a.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H14a). zenon_intro zenon_H14d. zenon_intro zenon_H14c.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H14c). zenon_intro zenon_H14f. zenon_intro zenon_H14e.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H14e). zenon_intro zenon_H151. zenon_intro zenon_H150.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H150). zenon_intro zenon_Hd7. zenon_intro zenon_H152.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H152). zenon_intro zenon_Hd9. zenon_intro zenon_H153.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H153). zenon_intro zenon_Hdb. zenon_intro zenon_H154.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H154). zenon_intro zenon_H156. zenon_intro zenon_H155.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H155). zenon_intro zenon_H158. zenon_intro zenon_H157.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H157). zenon_intro zenon_H15a. zenon_intro zenon_H159.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H159). zenon_intro zenon_H15c. zenon_intro zenon_H15b.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H15b). zenon_intro zenon_Hd7. zenon_intro zenon_H15d.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H15d). zenon_intro zenon_Hd9. zenon_intro zenon_H15e.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H15e). zenon_intro zenon_Hdb. zenon_intro zenon_H15f.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H15f). zenon_intro zenon_H161. zenon_intro zenon_H160.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H160). zenon_intro zenon_H163. zenon_intro zenon_H162.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H162). zenon_intro zenon_H165. zenon_intro zenon_H164.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H164). zenon_intro zenon_H167. zenon_intro zenon_H166.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H166). zenon_intro zenon_Hd7. zenon_intro zenon_H168.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H168). zenon_intro zenon_Hd9. zenon_intro zenon_H169.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H169). zenon_intro zenon_Hdb. zenon_intro zenon_H16a.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H16a). zenon_intro zenon_H16c. zenon_intro zenon_H16b.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H16b). zenon_intro zenon_H16e. zenon_intro zenon_H16d.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H16d). zenon_intro zenon_H170. zenon_intro zenon_H16f.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H16f). zenon_intro zenon_H172. zenon_intro zenon_H171.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H171). zenon_intro zenon_Hd7. zenon_intro zenon_H173.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H173). zenon_intro zenon_Hd9. zenon_intro zenon_Hdb.
% 90.88/91.14  apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_j Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_Hd9); [ zenon_intro zenon_H174; idtac ].
% 90.88/91.14  elim zenon_H174. zenon_intro zenon_TY_i. zenon_intro zenon_H175.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H175). zenon_intro zenon_H10. zenon_intro zenon_H176.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H176). zenon_intro zenon_H178. zenon_intro zenon_H177.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H177). zenon_intro zenon_H17a. zenon_intro zenon_H179.
% 90.88/91.14  apply zenon_H10. zenon_intro zenon_H3.
% 90.88/91.14  apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_i X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_H17a); [ zenon_intro zenon_H17b; idtac ].
% 90.88/91.14  elim zenon_H17b. zenon_intro zenon_TX_h. zenon_intro zenon_H17c.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H17c). zenon_intro zenon_H17e. zenon_intro zenon_H17d.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H17d). zenon_intro zenon_H180. zenon_intro zenon_H17f.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H17f). zenon_intro zenon_H182. zenon_intro zenon_H181.
% 90.88/91.14  apply zenon_H17e. zenon_intro zenon_H6.
% 90.88/91.14  apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_h Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H182); [ zenon_intro zenon_H183; idtac ].
% 90.88/91.14  elim zenon_H183. zenon_intro zenon_TY_bd. zenon_intro zenon_H184.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H184). zenon_intro zenon_H186. zenon_intro zenon_H185.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H185). zenon_intro zenon_H188. zenon_intro zenon_H187.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H187). zenon_intro zenon_H18a. zenon_intro zenon_H189.
% 90.88/91.14  apply zenon_H186. zenon_intro zenon_H1c.
% 90.88/91.14  apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_bd X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_H18a); [ zenon_intro zenon_H18b; idtac ].
% 90.88/91.14  elim zenon_H18b. zenon_intro zenon_TX_bt. zenon_intro zenon_H18c.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H18c). zenon_intro zenon_H18e. zenon_intro zenon_H18d.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H18d). zenon_intro zenon_H190. zenon_intro zenon_H18f.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H18f). zenon_intro zenon_H192. zenon_intro zenon_H191.
% 90.88/91.14  apply zenon_H18e. zenon_intro zenon_H2c.
% 90.88/91.14  apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_bt Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H192); [ zenon_intro zenon_H193; idtac ].
% 90.88/91.14  elim zenon_H193. zenon_intro zenon_TY_cj. zenon_intro zenon_H194.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H194). zenon_intro zenon_H196. zenon_intro zenon_H195.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H195). zenon_intro zenon_H198. zenon_intro zenon_H197.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H197). zenon_intro zenon_H19a. zenon_intro zenon_H199.
% 90.88/91.14  apply zenon_H196. zenon_intro zenon_H3c.
% 90.88/91.14  apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_cj X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_H19a); [ zenon_intro zenon_H19b; idtac ].
% 90.88/91.14  elim zenon_H19b. zenon_intro zenon_TX_cz. zenon_intro zenon_H19c.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H19c). zenon_intro zenon_H19e. zenon_intro zenon_H19d.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H19d). zenon_intro zenon_H1a0. zenon_intro zenon_H19f.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H19f). zenon_intro zenon_H1a2. zenon_intro zenon_H1a1.
% 90.88/91.14  apply zenon_H19e. zenon_intro zenon_H4c.
% 90.88/91.14  apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_cz Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H1a2); [ zenon_intro zenon_H1a3; idtac ].
% 90.88/91.14  elim zenon_H1a3. zenon_intro zenon_TY_dp. zenon_intro zenon_H1a4.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1a4). zenon_intro zenon_H1a6. zenon_intro zenon_H1a5.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1a5). zenon_intro zenon_H1a8. zenon_intro zenon_H1a7.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1a7). zenon_intro zenon_H1aa. zenon_intro zenon_H1a9.
% 90.88/91.14  apply zenon_H1a6. zenon_intro zenon_H5c.
% 90.88/91.14  apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_dp X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_H1aa); [ zenon_intro zenon_H1ab; idtac ].
% 90.88/91.14  elim zenon_H1ab. zenon_intro zenon_TX_ef. zenon_intro zenon_H1ac.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1ac). zenon_intro zenon_H1ae. zenon_intro zenon_H1ad.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1ad). zenon_intro zenon_H1b0. zenon_intro zenon_H1af.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1af). zenon_intro zenon_H1b2. zenon_intro zenon_H1b1.
% 90.88/91.14  apply zenon_H1ae. zenon_intro zenon_H6c.
% 90.88/91.14  apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_ef Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H1b2); [ zenon_intro zenon_H1b3; idtac ].
% 90.88/91.14  elim zenon_H1b3. zenon_intro zenon_TY_ev. zenon_intro zenon_H1b4.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1b4). zenon_intro zenon_H1b6. zenon_intro zenon_H1b5.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1b5). zenon_intro zenon_H1b8. zenon_intro zenon_H1b7.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1b7). zenon_intro zenon_H1ba. zenon_intro zenon_H1b9.
% 90.88/91.14  apply zenon_H1b6. zenon_intro zenon_H7c.
% 90.88/91.14  apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_ev X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_H1ba); [ zenon_intro zenon_H1bb; idtac ].
% 90.88/91.14  elim zenon_H1bb. zenon_intro zenon_TX_fl. zenon_intro zenon_H1bc.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1bc). zenon_intro zenon_H1be. zenon_intro zenon_H1bd.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1bd). zenon_intro zenon_H1c0. zenon_intro zenon_H1bf.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1bf). zenon_intro zenon_H1c2. zenon_intro zenon_H1c1.
% 90.88/91.14  apply zenon_H1be. zenon_intro zenon_H8c.
% 90.88/91.14  apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_fl Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H1c2); [ zenon_intro zenon_H1c3; idtac ].
% 90.88/91.14  elim zenon_H1c3. zenon_intro zenon_TY_gb. zenon_intro zenon_H1c4.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1c4). zenon_intro zenon_H1c6. zenon_intro zenon_H1c5.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1c5). zenon_intro zenon_H1c8. zenon_intro zenon_H1c7.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1c7). zenon_intro zenon_H1ca. zenon_intro zenon_H1c9.
% 90.88/91.14  apply zenon_H1c6. zenon_intro zenon_H9c.
% 90.88/91.14  apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_gb X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_H1ca); [ zenon_intro zenon_H1cb; idtac ].
% 90.88/91.14  elim zenon_H1cb. zenon_intro zenon_TX_gr. zenon_intro zenon_H1cc.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1cc). zenon_intro zenon_H1ce. zenon_intro zenon_H1cd.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1cd). zenon_intro zenon_H1d0. zenon_intro zenon_H1cf.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1cf). zenon_intro zenon_H1d2. zenon_intro zenon_H1d1.
% 90.88/91.14  apply zenon_H1ce. zenon_intro zenon_Hac.
% 90.88/91.14  apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_gr Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H1d2); [ zenon_intro zenon_H1d3; idtac ].
% 90.88/91.14  elim zenon_H1d3. zenon_intro zenon_TY_hh. zenon_intro zenon_H1d4.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1d4). zenon_intro zenon_H1d6. zenon_intro zenon_H1d5.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1d5). zenon_intro zenon_H1d8. zenon_intro zenon_H1d7.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1d7). zenon_intro zenon_H1da. zenon_intro zenon_H1d9.
% 90.88/91.14  apply zenon_H1d6. zenon_intro zenon_Hbc.
% 90.88/91.14  apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_hh X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_H1da); [ zenon_intro zenon_H1db; idtac ].
% 90.88/91.14  elim zenon_H1db. zenon_intro zenon_TX_si. zenon_intro zenon_H1dd.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1dd). zenon_intro zenon_H1df. zenon_intro zenon_H1de.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1de). zenon_intro zenon_H1e1. zenon_intro zenon_H1e0.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1e0). zenon_intro zenon_H1e3. zenon_intro zenon_H1e2.
% 90.88/91.14  apply zenon_H1df. zenon_intro zenon_H1e4.
% 90.88/91.14  apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_si Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))) zenon_H1e3); [ zenon_intro zenon_H1e5; idtac ].
% 90.88/91.14  elim zenon_H1e5. zenon_intro zenon_TY_ss. zenon_intro zenon_H1e7.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1e7). zenon_intro zenon_H1e9. zenon_intro zenon_H1e8.
% 90.88/91.14  apply (zenon_notor_s _ _ zenon_H1e8). zenon_intro zenon_H1eb. zenon_intro zenon_H1ea.
% 90.88/91.14  apply zenon_H1e9. zenon_intro zenon_H1ec.
% 90.88/91.14  apply (zenon_notand_s _ _ zenon_H16e); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1ed ].
% 90.88/91.14  exact (zenon_H1ee zenon_Hd7).
% 90.88/91.14  apply (zenon_notand_s _ _ zenon_H1ed); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1ef ].
% 90.88/91.14  apply zenon_H1f0. zenon_intro zenon_H1f1.
% 90.88/91.14  generalize (zenon_H1f1 zenon_TY_hh). zenon_intro zenon_H1f2.
% 90.88/91.14  apply (zenon_or_s _ _ zenon_H1f2); [ zenon_intro zenon_Hbb | zenon_intro zenon_H1f3 ].
% 90.88/91.14  apply (zenon_L12_ zenon_TY_hh zenon_TX_gr zenon_TY_i zenon_TX_j zenon_TY_bd zenon_TX_h zenon_TY_cj zenon_TX_bt zenon_TY_dp zenon_TX_cz zenon_TY_ev zenon_TX_ef zenon_TY_gb zenon_TX_fl); trivial.
% 90.88/91.14  generalize (zenon_H1f3 zenon_TY_ss). zenon_intro zenon_H1f4.
% 90.88/91.14  apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f6 | zenon_intro zenon_H1f5 ].
% 90.88/91.14  elim (classic ((~(zenon_TY_hh = zenon_TX_si))/\(~(r1 zenon_TY_hh zenon_TX_si)))); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H1f8 ].
% 90.88/91.14  apply (zenon_and_s _ _ zenon_H1f7). zenon_intro zenon_H1fa. zenon_intro zenon_H1f9.
% 90.88/91.14  exact (zenon_H1f9 zenon_H1e4).
% 90.88/91.14  cut ((r1 zenon_TX_si zenon_TY_ss) = (r1 zenon_TY_hh zenon_TY_ss)).
% 90.88/91.14  intro zenon_D_pnotp.
% 90.88/91.14  apply zenon_H1f6.
% 90.88/91.14  rewrite <- zenon_D_pnotp.
% 90.88/91.14  exact zenon_H1ec.
% 90.88/91.14  cut ((zenon_TY_ss = zenon_TY_ss)); [idtac | apply NNPP; zenon_intro zenon_H1fb].
% 90.97/91.17  cut ((zenon_TX_si = zenon_TY_hh)); [idtac | apply NNPP; zenon_intro zenon_H1fc].
% 90.97/91.17  congruence.
% 90.97/91.17  apply (zenon_notand_s _ _ zenon_H1f8); [ zenon_intro zenon_H1fd | zenon_intro zenon_H1df ].
% 90.97/91.17  apply zenon_H1fd. zenon_intro zenon_H1fe.
% 90.97/91.17  elim (classic (zenon_TY_hh = zenon_TY_hh)); [ zenon_intro zenon_H1ff | zenon_intro zenon_Hc1 ].
% 90.97/91.17  cut ((zenon_TY_hh = zenon_TY_hh) = (zenon_TX_si = zenon_TY_hh)).
% 90.97/91.17  intro zenon_D_pnotp.
% 90.97/91.17  apply zenon_H1fc.
% 90.97/91.17  rewrite <- zenon_D_pnotp.
% 90.97/91.17  exact zenon_H1ff.
% 90.97/91.17  cut ((zenon_TY_hh = zenon_TY_hh)); [idtac | apply NNPP; zenon_intro zenon_Hc1].
% 90.97/91.17  cut ((zenon_TY_hh = zenon_TX_si)); [idtac | apply NNPP; zenon_intro zenon_H1fa].
% 90.97/91.17  congruence.
% 90.97/91.17  exact (zenon_H1fa zenon_H1fe).
% 90.97/91.17  apply zenon_Hc1. apply refl_equal.
% 90.97/91.17  apply zenon_Hc1. apply refl_equal.
% 90.97/91.17  apply zenon_H1df. zenon_intro zenon_H1e4.
% 90.97/91.17  generalize (zenon_H4 zenon_TY_hh). zenon_intro zenon_H200.
% 90.97/91.17  generalize (zenon_H200 zenon_TX_si). zenon_intro zenon_H201.
% 90.97/91.17  generalize (zenon_H201 zenon_TY_ss). zenon_intro zenon_H202.
% 90.97/91.17  apply (zenon_imply_s _ _ zenon_H202); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H203 ].
% 90.97/91.17  exact (zenon_H1f9 zenon_H1e4).
% 90.97/91.17  apply (zenon_imply_s _ _ zenon_H203); [ zenon_intro zenon_H205 | zenon_intro zenon_H204 ].
% 90.97/91.17  exact (zenon_H205 zenon_H1ec).
% 90.97/91.17  exact (zenon_H1f6 zenon_H204).
% 90.97/91.17  apply zenon_H1fb. apply refl_equal.
% 90.97/91.17  apply (zenon_notand_s _ _ zenon_H1f5); [ zenon_intro zenon_H207 | zenon_intro zenon_H206 ].
% 90.97/91.17  exact (zenon_H207 zenon_H1eb).
% 90.97/91.17  exact (zenon_H206 zenon_H1ea).
% 90.97/91.17  exact (zenon_H1ef zenon_Hdb).
% 90.97/91.17  apply zenon_Hcb. zenon_intro zenon_Tx_ua. apply NNPP. zenon_intro zenon_H209.
% 90.97/91.17  apply zenon_H209. zenon_intro zenon_Ty_uc. apply NNPP. zenon_intro zenon_H20b.
% 90.97/91.17  apply zenon_H20b. zenon_intro zenon_Tz_ue. apply NNPP. zenon_intro zenon_H20d.
% 90.97/91.17  apply (zenon_notimply_s _ _ zenon_H20d). zenon_intro zenon_H20f. zenon_intro zenon_H20e.
% 90.97/91.17  apply (zenon_notimply_s _ _ zenon_H20e). zenon_intro zenon_H211. zenon_intro zenon_H210.
% 90.97/91.17  generalize (transitivity zenon_Tx_ua). zenon_intro zenon_H212.
% 90.97/91.17  generalize (zenon_H212 zenon_Ty_uc). zenon_intro zenon_H213.
% 90.97/91.17  generalize (zenon_H213 zenon_Tz_ue). zenon_intro zenon_H214.
% 90.97/91.17  apply (zenon_imply_s _ _ zenon_H214); [ zenon_intro zenon_H216 | zenon_intro zenon_H215 ].
% 90.97/91.17  apply (zenon_notand_s _ _ zenon_H216); [ zenon_intro zenon_H218 | zenon_intro zenon_H217 ].
% 90.97/91.17  exact (zenon_H218 zenon_H20f).
% 90.97/91.17  exact (zenon_H217 zenon_H211).
% 90.97/91.17  exact (zenon_H210 zenon_H215).
% 90.97/91.17  Qed.
% 90.97/91.17  % SZS output end Proof
% 90.97/91.17  (* END-PROOF *)
% 90.97/91.17  nodes searched: 1668975
% 90.97/91.17  max branch formulas: 165388
% 90.97/91.17  proof nodes created: 137573
% 90.97/91.17  formulas created: 4248565
% 90.97/91.17  
%------------------------------------------------------------------------------