TSTP Solution File: LCL672+1.010 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : LCL672+1.010 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n003.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 4.93s 5.17s
% Output : Proof 5.01s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : LCL672+1.010 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 4 03:37:09 EDT 2022
% 0.13/0.34 % CPUTime :
% 4.93/5.17 (* PROOF-FOUND *)
% 4.93/5.17 % SZS status Theorem
% 4.93/5.17 (* BEGIN-PROOF *)
% 4.93/5.17 % SZS output start Proof
% 4.93/5.17 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))\/(~(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 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))\/(~((~(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 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))\/(~(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 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))\/False))))))/\(~(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))\/(~(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))\/(~(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 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 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 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 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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))))))\/(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))\/(~(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))\/(~(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))\/(~(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))\/(~(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))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))).
% 4.93/5.17 Proof.
% 4.93/5.17 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).
% 4.93/5.17 do 3 intro. intros zenon_H3 zenon_H4 zenon_H5 zenon_H6.
% 4.93/5.17 elim (classic ((~(zenon_TX_j = zenon_TY_i))/\(~(r1 zenon_TX_j zenon_TY_i)))); [ zenon_intro zenon_Ha | zenon_intro zenon_Hb ].
% 4.93/5.17 apply (zenon_and_s _ _ zenon_Ha). zenon_intro zenon_Hd. zenon_intro zenon_Hc.
% 4.93/5.17 exact (zenon_Hc zenon_H3).
% 4.93/5.17 cut ((r1 zenon_TY_i zenon_TX_h) = (r1 zenon_TX_j zenon_TX_h)).
% 4.93/5.17 intro zenon_D_pnotp.
% 4.93/5.17 apply zenon_H5.
% 4.93/5.17 rewrite <- zenon_D_pnotp.
% 4.93/5.17 exact zenon_H6.
% 4.93/5.17 cut ((zenon_TX_h = zenon_TX_h)); [idtac | apply NNPP; zenon_intro zenon_He].
% 4.93/5.17 cut ((zenon_TY_i = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_Hf].
% 4.93/5.17 congruence.
% 4.93/5.17 apply (zenon_notand_s _ _ zenon_Hb); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ].
% 4.93/5.17 apply zenon_H11. zenon_intro zenon_H12.
% 4.93/5.17 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 4.93/5.17 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_i = zenon_TX_j)).
% 4.93/5.17 intro zenon_D_pnotp.
% 4.93/5.17 apply zenon_Hf.
% 4.93/5.17 rewrite <- zenon_D_pnotp.
% 4.93/5.17 exact zenon_H13.
% 4.93/5.17 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 4.93/5.17 cut ((zenon_TX_j = zenon_TY_i)); [idtac | apply NNPP; zenon_intro zenon_Hd].
% 4.93/5.17 congruence.
% 4.93/5.17 exact (zenon_Hd zenon_H12).
% 4.93/5.17 apply zenon_H14. apply refl_equal.
% 4.93/5.17 apply zenon_H14. apply refl_equal.
% 4.93/5.17 apply zenon_H10. zenon_intro zenon_H3.
% 4.93/5.17 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 4.93/5.17 generalize (zenon_H15 zenon_TY_i). zenon_intro zenon_H16.
% 4.93/5.17 generalize (zenon_H16 zenon_TX_h). zenon_intro zenon_H17.
% 4.93/5.17 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_Hc | zenon_intro zenon_H18 ].
% 4.93/5.17 exact (zenon_Hc zenon_H3).
% 4.93/5.17 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ].
% 4.93/5.17 exact (zenon_H1a zenon_H6).
% 4.93/5.17 exact (zenon_H5 zenon_H19).
% 4.93/5.17 apply zenon_He. apply refl_equal.
% 4.93/5.17 (* end of lemma zenon_L1_ *)
% 4.93/5.17 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).
% 4.93/5.17 do 4 intro. intros zenon_H3 zenon_H6 zenon_H4 zenon_H1b zenon_H1c.
% 4.93/5.17 elim (classic ((~(zenon_TX_j = zenon_TX_h))/\(~(r1 zenon_TX_j zenon_TX_h)))); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ].
% 4.93/5.17 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H20. zenon_intro zenon_H5.
% 4.93/5.17 apply (zenon_L1_ zenon_TX_h zenon_TY_i zenon_TX_j); trivial.
% 4.93/5.17 cut ((r1 zenon_TX_h zenon_TY_bd) = (r1 zenon_TX_j zenon_TY_bd)).
% 4.93/5.17 intro zenon_D_pnotp.
% 4.93/5.17 apply zenon_H1b.
% 4.93/5.17 rewrite <- zenon_D_pnotp.
% 4.93/5.17 exact zenon_H1c.
% 4.93/5.17 cut ((zenon_TY_bd = zenon_TY_bd)); [idtac | apply NNPP; zenon_intro zenon_H21].
% 4.93/5.17 cut ((zenon_TX_h = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H22].
% 4.93/5.17 congruence.
% 4.93/5.17 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ].
% 4.93/5.17 apply zenon_H24. zenon_intro zenon_H25.
% 4.93/5.17 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 4.93/5.17 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_h = zenon_TX_j)).
% 4.93/5.17 intro zenon_D_pnotp.
% 4.93/5.17 apply zenon_H22.
% 4.93/5.17 rewrite <- zenon_D_pnotp.
% 4.93/5.17 exact zenon_H13.
% 4.93/5.17 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 4.93/5.17 cut ((zenon_TX_j = zenon_TX_h)); [idtac | apply NNPP; zenon_intro zenon_H20].
% 4.93/5.17 congruence.
% 4.93/5.17 exact (zenon_H20 zenon_H25).
% 4.93/5.17 apply zenon_H14. apply refl_equal.
% 4.93/5.17 apply zenon_H14. apply refl_equal.
% 4.93/5.17 apply zenon_H23. zenon_intro zenon_H19.
% 4.93/5.17 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 4.93/5.17 generalize (zenon_H15 zenon_TX_h). zenon_intro zenon_H26.
% 4.93/5.17 generalize (zenon_H26 zenon_TY_bd). zenon_intro zenon_H27.
% 4.93/5.17 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H5 | zenon_intro zenon_H28 ].
% 4.93/5.17 exact (zenon_H5 zenon_H19).
% 4.93/5.17 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 4.93/5.17 exact (zenon_H2a zenon_H1c).
% 4.93/5.17 exact (zenon_H1b zenon_H29).
% 4.93/5.17 apply zenon_H21. apply refl_equal.
% 4.93/5.17 (* end of lemma zenon_L2_ *)
% 4.93/5.17 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).
% 4.93/5.17 do 5 intro. intros zenon_H6 zenon_H3 zenon_H1c zenon_H4 zenon_H2b zenon_H2c.
% 4.93/5.17 elim (classic ((~(zenon_TX_j = zenon_TY_bd))/\(~(r1 zenon_TX_j zenon_TY_bd)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ].
% 4.93/5.17 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H1b.
% 4.93/5.17 apply (zenon_L2_ zenon_TY_bd zenon_TX_h zenon_TY_i zenon_TX_j); trivial.
% 4.93/5.17 cut ((r1 zenon_TY_bd zenon_TX_bt) = (r1 zenon_TX_j zenon_TX_bt)).
% 4.93/5.17 intro zenon_D_pnotp.
% 4.93/5.17 apply zenon_H2b.
% 4.93/5.17 rewrite <- zenon_D_pnotp.
% 4.93/5.17 exact zenon_H2c.
% 4.93/5.17 cut ((zenon_TX_bt = zenon_TX_bt)); [idtac | apply NNPP; zenon_intro zenon_H31].
% 4.93/5.17 cut ((zenon_TY_bd = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H32].
% 4.93/5.17 congruence.
% 4.93/5.17 apply (zenon_notand_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 4.93/5.17 apply zenon_H34. zenon_intro zenon_H35.
% 4.93/5.17 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 4.93/5.17 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_bd = zenon_TX_j)).
% 4.93/5.17 intro zenon_D_pnotp.
% 4.93/5.17 apply zenon_H32.
% 4.93/5.17 rewrite <- zenon_D_pnotp.
% 4.93/5.17 exact zenon_H13.
% 4.93/5.17 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 4.93/5.17 cut ((zenon_TX_j = zenon_TY_bd)); [idtac | apply NNPP; zenon_intro zenon_H30].
% 4.93/5.17 congruence.
% 4.93/5.17 exact (zenon_H30 zenon_H35).
% 4.93/5.17 apply zenon_H14. apply refl_equal.
% 4.93/5.17 apply zenon_H14. apply refl_equal.
% 4.93/5.17 apply zenon_H33. zenon_intro zenon_H29.
% 4.93/5.17 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 4.93/5.17 generalize (zenon_H15 zenon_TY_bd). zenon_intro zenon_H36.
% 4.93/5.17 generalize (zenon_H36 zenon_TX_bt). zenon_intro zenon_H37.
% 4.93/5.17 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H1b | zenon_intro zenon_H38 ].
% 4.93/5.17 exact (zenon_H1b zenon_H29).
% 4.93/5.17 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ].
% 4.93/5.17 exact (zenon_H3a zenon_H2c).
% 4.93/5.17 exact (zenon_H2b zenon_H39).
% 4.93/5.17 apply zenon_H31. apply refl_equal.
% 4.93/5.17 (* end of lemma zenon_L3_ *)
% 4.93/5.17 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).
% 4.93/5.18 do 6 intro. intros zenon_H1c zenon_H3 zenon_H6 zenon_H2c zenon_H4 zenon_H3b zenon_H3c.
% 4.93/5.18 elim (classic ((~(zenon_TX_j = zenon_TX_bt))/\(~(r1 zenon_TX_j zenon_TX_bt)))); [ zenon_intro zenon_H3e | zenon_intro zenon_H3f ].
% 4.93/5.18 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H2b.
% 4.93/5.18 apply (zenon_L3_ zenon_TX_bt zenon_TY_bd zenon_TX_j zenon_TX_h zenon_TY_i); trivial.
% 4.93/5.18 cut ((r1 zenon_TX_bt zenon_TY_cj) = (r1 zenon_TX_j zenon_TY_cj)).
% 4.93/5.18 intro zenon_D_pnotp.
% 4.93/5.18 apply zenon_H3b.
% 4.93/5.18 rewrite <- zenon_D_pnotp.
% 4.93/5.18 exact zenon_H3c.
% 4.93/5.18 cut ((zenon_TY_cj = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H41].
% 4.93/5.18 cut ((zenon_TX_bt = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H42].
% 4.93/5.18 congruence.
% 4.93/5.18 apply (zenon_notand_s _ _ zenon_H3f); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ].
% 4.93/5.18 apply zenon_H44. zenon_intro zenon_H45.
% 4.93/5.18 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 4.93/5.18 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_bt = zenon_TX_j)).
% 4.93/5.18 intro zenon_D_pnotp.
% 4.93/5.18 apply zenon_H42.
% 4.93/5.18 rewrite <- zenon_D_pnotp.
% 4.93/5.18 exact zenon_H13.
% 4.93/5.18 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 4.93/5.18 cut ((zenon_TX_j = zenon_TX_bt)); [idtac | apply NNPP; zenon_intro zenon_H40].
% 4.93/5.18 congruence.
% 4.93/5.18 exact (zenon_H40 zenon_H45).
% 4.93/5.18 apply zenon_H14. apply refl_equal.
% 4.93/5.18 apply zenon_H14. apply refl_equal.
% 4.93/5.18 apply zenon_H43. zenon_intro zenon_H39.
% 4.93/5.18 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 4.93/5.18 generalize (zenon_H15 zenon_TX_bt). zenon_intro zenon_H46.
% 4.93/5.18 generalize (zenon_H46 zenon_TY_cj). zenon_intro zenon_H47.
% 4.93/5.18 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H2b | zenon_intro zenon_H48 ].
% 4.93/5.18 exact (zenon_H2b zenon_H39).
% 4.93/5.18 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ].
% 4.93/5.18 exact (zenon_H4a zenon_H3c).
% 4.93/5.18 exact (zenon_H3b zenon_H49).
% 4.93/5.18 apply zenon_H41. apply refl_equal.
% 4.93/5.18 (* end of lemma zenon_L4_ *)
% 4.93/5.18 assert (zenon_L5_ : forall (zenon_TY_da : zenon_U) (zenon_TX_db : zenon_U) (zenon_TY_cj : zenon_U), (r1 zenon_TY_cj zenon_TX_db) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TY_cj zenon_TY_da)) -> (r1 zenon_TX_db zenon_TY_da) -> False).
% 4.93/5.18 do 3 intro. intros zenon_H4b zenon_H4 zenon_H4c zenon_H4d.
% 4.93/5.18 elim (classic ((~(zenon_TY_cj = zenon_TX_db))/\(~(r1 zenon_TY_cj zenon_TX_db)))); [ zenon_intro zenon_H50 | zenon_intro zenon_H51 ].
% 4.93/5.18 apply (zenon_and_s _ _ zenon_H50). zenon_intro zenon_H53. zenon_intro zenon_H52.
% 4.93/5.18 exact (zenon_H52 zenon_H4b).
% 4.93/5.18 cut ((r1 zenon_TX_db zenon_TY_da) = (r1 zenon_TY_cj zenon_TY_da)).
% 4.93/5.18 intro zenon_D_pnotp.
% 4.93/5.18 apply zenon_H4c.
% 4.93/5.18 rewrite <- zenon_D_pnotp.
% 4.93/5.18 exact zenon_H4d.
% 4.93/5.18 cut ((zenon_TY_da = zenon_TY_da)); [idtac | apply NNPP; zenon_intro zenon_H54].
% 4.93/5.18 cut ((zenon_TX_db = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H55].
% 4.93/5.18 congruence.
% 4.93/5.18 apply (zenon_notand_s _ _ zenon_H51); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ].
% 4.93/5.18 apply zenon_H57. zenon_intro zenon_H58.
% 4.93/5.18 elim (classic (zenon_TY_cj = zenon_TY_cj)); [ zenon_intro zenon_H59 | zenon_intro zenon_H41 ].
% 4.93/5.18 cut ((zenon_TY_cj = zenon_TY_cj) = (zenon_TX_db = zenon_TY_cj)).
% 4.93/5.18 intro zenon_D_pnotp.
% 4.93/5.18 apply zenon_H55.
% 4.93/5.18 rewrite <- zenon_D_pnotp.
% 4.93/5.18 exact zenon_H59.
% 4.93/5.18 cut ((zenon_TY_cj = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H41].
% 4.93/5.18 cut ((zenon_TY_cj = zenon_TX_db)); [idtac | apply NNPP; zenon_intro zenon_H53].
% 4.93/5.18 congruence.
% 4.93/5.18 exact (zenon_H53 zenon_H58).
% 4.93/5.18 apply zenon_H41. apply refl_equal.
% 4.93/5.18 apply zenon_H41. apply refl_equal.
% 4.93/5.18 apply zenon_H56. zenon_intro zenon_H4b.
% 4.93/5.18 generalize (zenon_H4 zenon_TY_cj). zenon_intro zenon_H5a.
% 4.93/5.18 generalize (zenon_H5a zenon_TX_db). zenon_intro zenon_H5b.
% 4.93/5.18 generalize (zenon_H5b zenon_TY_da). zenon_intro zenon_H5c.
% 4.93/5.18 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H52 | zenon_intro zenon_H5d ].
% 4.93/5.18 exact (zenon_H52 zenon_H4b).
% 4.93/5.18 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ].
% 4.93/5.18 exact (zenon_H5f zenon_H4d).
% 4.93/5.18 exact (zenon_H4c zenon_H5e).
% 4.93/5.18 apply zenon_H54. apply refl_equal.
% 4.93/5.18 (* end of lemma zenon_L5_ *)
% 4.93/5.18 assert (zenon_L6_ : forall (zenon_TY_dv : zenon_U) (zenon_TX_dw : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TY_da : zenon_U) (zenon_TX_db : zenon_U), (r1 zenon_TX_db zenon_TY_da) -> (r1 zenon_TY_cj zenon_TX_db) -> (r1 zenon_TY_da zenon_TX_dw) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TY_cj zenon_TY_dv)) -> (r1 zenon_TX_dw zenon_TY_dv) -> False).
% 4.93/5.18 do 5 intro. intros zenon_H4d zenon_H4b zenon_H60 zenon_H4 zenon_H61 zenon_H62.
% 4.93/5.18 elim (classic ((~(zenon_TY_cj = zenon_TX_dw))/\(~(r1 zenon_TY_cj zenon_TX_dw)))); [ zenon_intro zenon_H65 | zenon_intro zenon_H66 ].
% 4.93/5.18 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H68. zenon_intro zenon_H67.
% 4.93/5.18 elim (classic ((~(zenon_TY_cj = zenon_TY_da))/\(~(r1 zenon_TY_cj zenon_TY_da)))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ].
% 4.93/5.18 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H6b. zenon_intro zenon_H4c.
% 4.93/5.18 apply (zenon_L5_ zenon_TY_da zenon_TX_db zenon_TY_cj); trivial.
% 4.93/5.18 cut ((r1 zenon_TY_da zenon_TX_dw) = (r1 zenon_TY_cj zenon_TX_dw)).
% 4.93/5.18 intro zenon_D_pnotp.
% 4.93/5.18 apply zenon_H67.
% 4.93/5.18 rewrite <- zenon_D_pnotp.
% 4.93/5.18 exact zenon_H60.
% 4.93/5.18 cut ((zenon_TX_dw = zenon_TX_dw)); [idtac | apply NNPP; zenon_intro zenon_H6c].
% 4.93/5.18 cut ((zenon_TY_da = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H6d].
% 4.93/5.18 congruence.
% 4.93/5.18 apply (zenon_notand_s _ _ zenon_H6a); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ].
% 4.93/5.18 apply zenon_H6f. zenon_intro zenon_H70.
% 4.93/5.18 elim (classic (zenon_TY_cj = zenon_TY_cj)); [ zenon_intro zenon_H59 | zenon_intro zenon_H41 ].
% 4.93/5.18 cut ((zenon_TY_cj = zenon_TY_cj) = (zenon_TY_da = zenon_TY_cj)).
% 4.93/5.18 intro zenon_D_pnotp.
% 4.93/5.18 apply zenon_H6d.
% 4.93/5.18 rewrite <- zenon_D_pnotp.
% 4.93/5.18 exact zenon_H59.
% 4.93/5.18 cut ((zenon_TY_cj = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H41].
% 4.93/5.18 cut ((zenon_TY_cj = zenon_TY_da)); [idtac | apply NNPP; zenon_intro zenon_H6b].
% 4.93/5.18 congruence.
% 4.93/5.18 exact (zenon_H6b zenon_H70).
% 4.93/5.18 apply zenon_H41. apply refl_equal.
% 4.93/5.18 apply zenon_H41. apply refl_equal.
% 4.93/5.18 apply zenon_H6e. zenon_intro zenon_H5e.
% 4.93/5.18 generalize (zenon_H4 zenon_TY_cj). zenon_intro zenon_H5a.
% 4.93/5.18 generalize (zenon_H5a zenon_TY_da). zenon_intro zenon_H71.
% 4.93/5.18 generalize (zenon_H71 zenon_TX_dw). zenon_intro zenon_H72.
% 4.93/5.18 apply (zenon_imply_s _ _ zenon_H72); [ zenon_intro zenon_H4c | zenon_intro zenon_H73 ].
% 4.93/5.18 exact (zenon_H4c zenon_H5e).
% 4.93/5.18 apply (zenon_imply_s _ _ zenon_H73); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ].
% 4.93/5.18 exact (zenon_H75 zenon_H60).
% 4.93/5.18 exact (zenon_H67 zenon_H74).
% 4.93/5.18 apply zenon_H6c. apply refl_equal.
% 4.93/5.18 cut ((r1 zenon_TX_dw zenon_TY_dv) = (r1 zenon_TY_cj zenon_TY_dv)).
% 4.93/5.18 intro zenon_D_pnotp.
% 4.93/5.18 apply zenon_H61.
% 4.93/5.18 rewrite <- zenon_D_pnotp.
% 4.93/5.18 exact zenon_H62.
% 4.93/5.18 cut ((zenon_TY_dv = zenon_TY_dv)); [idtac | apply NNPP; zenon_intro zenon_H76].
% 4.93/5.18 cut ((zenon_TX_dw = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H77].
% 4.93/5.18 congruence.
% 4.93/5.18 apply (zenon_notand_s _ _ zenon_H66); [ zenon_intro zenon_H79 | zenon_intro zenon_H78 ].
% 4.93/5.18 apply zenon_H79. zenon_intro zenon_H7a.
% 4.93/5.18 elim (classic (zenon_TY_cj = zenon_TY_cj)); [ zenon_intro zenon_H59 | zenon_intro zenon_H41 ].
% 4.93/5.18 cut ((zenon_TY_cj = zenon_TY_cj) = (zenon_TX_dw = zenon_TY_cj)).
% 4.93/5.18 intro zenon_D_pnotp.
% 4.93/5.18 apply zenon_H77.
% 4.93/5.18 rewrite <- zenon_D_pnotp.
% 4.93/5.18 exact zenon_H59.
% 4.93/5.18 cut ((zenon_TY_cj = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H41].
% 4.93/5.18 cut ((zenon_TY_cj = zenon_TX_dw)); [idtac | apply NNPP; zenon_intro zenon_H68].
% 4.93/5.18 congruence.
% 4.93/5.18 exact (zenon_H68 zenon_H7a).
% 4.93/5.18 apply zenon_H41. apply refl_equal.
% 4.93/5.18 apply zenon_H41. apply refl_equal.
% 4.93/5.18 apply zenon_H78. zenon_intro zenon_H74.
% 4.93/5.18 generalize (zenon_H4 zenon_TY_cj). zenon_intro zenon_H5a.
% 4.93/5.18 generalize (zenon_H5a zenon_TX_dw). zenon_intro zenon_H7b.
% 4.93/5.18 generalize (zenon_H7b zenon_TY_dv). zenon_intro zenon_H7c.
% 4.93/5.18 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H67 | zenon_intro zenon_H7d ].
% 4.93/5.18 exact (zenon_H67 zenon_H74).
% 4.93/5.18 apply (zenon_imply_s _ _ zenon_H7d); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ].
% 4.93/5.18 exact (zenon_H7f zenon_H62).
% 4.93/5.18 exact (zenon_H61 zenon_H7e).
% 4.93/5.18 apply zenon_H76. apply refl_equal.
% 4.93/5.18 (* end of lemma zenon_L6_ *)
% 4.93/5.18 apply NNPP. intro zenon_G.
% 4.93/5.18 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_H80 ].
% 4.93/5.18 apply zenon_G. zenon_intro zenon_H81.
% 4.93/5.18 elim zenon_H81. zenon_intro zenon_TX_j. zenon_intro zenon_H82.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H82). zenon_intro zenon_H84. zenon_intro zenon_H83.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H83). zenon_intro zenon_H86. zenon_intro zenon_H85.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H85). zenon_intro zenon_H88. zenon_intro zenon_H87.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H87). zenon_intro zenon_H8a. zenon_intro zenon_H89.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H89). zenon_intro zenon_H8c. zenon_intro zenon_H8b.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H8b). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H8f). zenon_intro zenon_H92. zenon_intro zenon_H91.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H91). zenon_intro zenon_H94. zenon_intro zenon_H93.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H93). zenon_intro zenon_H96. zenon_intro zenon_H95.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H95). zenon_intro zenon_H98. zenon_intro zenon_H97.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H97). zenon_intro zenon_H8c. zenon_intro zenon_H99.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H99). zenon_intro zenon_H8e. zenon_intro zenon_H9a.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H9a). zenon_intro zenon_H90. zenon_intro zenon_H9b.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H9c). zenon_intro zenon_H9f. zenon_intro zenon_H9e.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H9e). zenon_intro zenon_Ha1. zenon_intro zenon_Ha0.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Ha0). zenon_intro zenon_Ha3. zenon_intro zenon_Ha2.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Ha2). zenon_intro zenon_H8c. zenon_intro zenon_Ha4.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Ha4). zenon_intro zenon_H8e. zenon_intro zenon_Ha5.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Ha5). zenon_intro zenon_H90. zenon_intro zenon_Ha6.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Ha6). zenon_intro zenon_Ha8. zenon_intro zenon_Ha7.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Ha7). zenon_intro zenon_Haa. zenon_intro zenon_Ha9.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Ha9). zenon_intro zenon_Hac. zenon_intro zenon_Hab.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hab). zenon_intro zenon_Hae. zenon_intro zenon_Had.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Had). zenon_intro zenon_H8c. zenon_intro zenon_Haf.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Haf). zenon_intro zenon_H8e. zenon_intro zenon_Hb0.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hb0). zenon_intro zenon_H90. zenon_intro zenon_Hb1.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hb1). zenon_intro zenon_Hb3. zenon_intro zenon_Hb2.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hb2). zenon_intro zenon_Hb5. zenon_intro zenon_Hb4.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hb4). zenon_intro zenon_Hb7. zenon_intro zenon_Hb6.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hb6). zenon_intro zenon_Hb9. zenon_intro zenon_Hb8.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hb8). zenon_intro zenon_H8c. zenon_intro zenon_Hba.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hba). zenon_intro zenon_H8e. zenon_intro zenon_Hbb.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hbb). zenon_intro zenon_H90. zenon_intro zenon_Hbc.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hbd). zenon_intro zenon_Hc0. zenon_intro zenon_Hbf.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hbf). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hc1). zenon_intro zenon_Hc4. zenon_intro zenon_Hc3.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hc3). zenon_intro zenon_H8c. zenon_intro zenon_Hc5.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hc5). zenon_intro zenon_H8e. zenon_intro zenon_Hc6.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hc6). zenon_intro zenon_H90. zenon_intro zenon_Hc7.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hc7). zenon_intro zenon_Hc9. zenon_intro zenon_Hc8.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hc8). zenon_intro zenon_Hcb. zenon_intro zenon_Hca.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hca). zenon_intro zenon_Hcd. zenon_intro zenon_Hcc.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hcc). zenon_intro zenon_Hcf. zenon_intro zenon_Hce.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hce). zenon_intro zenon_H8c. zenon_intro zenon_Hd0.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hd0). zenon_intro zenon_H8e. zenon_intro zenon_Hd1.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hd1). zenon_intro zenon_H90. zenon_intro zenon_Hd2.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hd2). zenon_intro zenon_Hd4. zenon_intro zenon_Hd3.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hd3). zenon_intro zenon_Hd6. zenon_intro zenon_Hd5.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hd5). zenon_intro zenon_Hd8. zenon_intro zenon_Hd7.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hd7). zenon_intro zenon_Hda. zenon_intro zenon_Hd9.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hd9). zenon_intro zenon_H8c. zenon_intro zenon_Hdb.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hdb). zenon_intro zenon_H8e. zenon_intro zenon_Hdc.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hdc). zenon_intro zenon_H90. zenon_intro zenon_Hdd.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hdd). zenon_intro zenon_Hdf. zenon_intro zenon_Hde.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hde). zenon_intro zenon_He1. zenon_intro zenon_He0.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_He0). zenon_intro zenon_He3. zenon_intro zenon_He2.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_He2). zenon_intro zenon_He5. zenon_intro zenon_He4.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_He4). zenon_intro zenon_H8c. zenon_intro zenon_He6.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_He6). zenon_intro zenon_H8e. zenon_intro zenon_He7.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_He7). zenon_intro zenon_H90. zenon_intro zenon_He8.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_He8). zenon_intro zenon_Hea. zenon_intro zenon_He9.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_He9). zenon_intro zenon_Hec. zenon_intro zenon_Heb.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Heb). zenon_intro zenon_Hee. zenon_intro zenon_Hed.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hed). zenon_intro zenon_Hf0. zenon_intro zenon_Hef.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hef). zenon_intro zenon_H8c. zenon_intro zenon_Hf1.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hf1). zenon_intro zenon_H8e. zenon_intro zenon_H90.
% 4.93/5.18 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))\/(~(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_H8e); [ zenon_intro zenon_Hf2; idtac ].
% 4.93/5.18 elim zenon_Hf2. zenon_intro zenon_TY_i. zenon_intro zenon_Hf3.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hf3). zenon_intro zenon_H10. zenon_intro zenon_Hf4.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hf4). zenon_intro zenon_Hf6. zenon_intro zenon_Hf5.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hf5). zenon_intro zenon_Hf8. zenon_intro zenon_Hf7.
% 4.93/5.18 apply zenon_H10. zenon_intro zenon_H3.
% 4.93/5.18 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))\/(~(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_Hf8); [ zenon_intro zenon_Hf9; idtac ].
% 4.93/5.18 elim zenon_Hf9. zenon_intro zenon_TX_h. zenon_intro zenon_Hfa.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hfa). zenon_intro zenon_Hfc. zenon_intro zenon_Hfb.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hfb). zenon_intro zenon_Hfe. zenon_intro zenon_Hfd.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_Hfd). zenon_intro zenon_H100. zenon_intro zenon_Hff.
% 4.93/5.18 apply zenon_Hfc. zenon_intro zenon_H6.
% 4.93/5.18 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))\/(~(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_H100); [ zenon_intro zenon_H101; idtac ].
% 4.93/5.18 elim zenon_H101. zenon_intro zenon_TY_bd. zenon_intro zenon_H102.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H102). zenon_intro zenon_H104. zenon_intro zenon_H103.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H103). zenon_intro zenon_H106. zenon_intro zenon_H105.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H105). zenon_intro zenon_H108. zenon_intro zenon_H107.
% 4.93/5.18 apply zenon_H104. zenon_intro zenon_H1c.
% 4.93/5.18 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))\/(~(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_H108); [ zenon_intro zenon_H109; idtac ].
% 4.93/5.18 elim zenon_H109. zenon_intro zenon_TX_bt. zenon_intro zenon_H10a.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H10a). zenon_intro zenon_H10c. zenon_intro zenon_H10b.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H10b). zenon_intro zenon_H10e. zenon_intro zenon_H10d.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H10d). zenon_intro zenon_H110. zenon_intro zenon_H10f.
% 4.93/5.18 apply zenon_H10c. zenon_intro zenon_H2c.
% 4.93/5.18 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))\/(~(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_H110); [ zenon_intro zenon_H111; idtac ].
% 4.93/5.18 elim zenon_H111. zenon_intro zenon_TY_cj. zenon_intro zenon_H112.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H112). zenon_intro zenon_H114. zenon_intro zenon_H113.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H113). zenon_intro zenon_H116. zenon_intro zenon_H115.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H115). zenon_intro zenon_H118. zenon_intro zenon_H117.
% 4.93/5.18 apply zenon_H114. zenon_intro zenon_H3c.
% 4.93/5.18 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))\/(~(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_H118); [ zenon_intro zenon_H119; idtac ].
% 4.93/5.18 elim zenon_H119. zenon_intro zenon_TX_db. zenon_intro zenon_H11a.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H11a). zenon_intro zenon_H56. zenon_intro zenon_H11b.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H11b). zenon_intro zenon_H11d. zenon_intro zenon_H11c.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H11c). zenon_intro zenon_H11f. zenon_intro zenon_H11e.
% 4.93/5.18 apply zenon_H56. zenon_intro zenon_H4b.
% 4.93/5.18 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_db 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))))))\/(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_H11f); [ zenon_intro zenon_H120; idtac ].
% 4.93/5.18 elim zenon_H120. zenon_intro zenon_TY_da. zenon_intro zenon_H121.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H121). zenon_intro zenon_H123. zenon_intro zenon_H122.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H122). zenon_intro zenon_H125. zenon_intro zenon_H124.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H124). zenon_intro zenon_H127. zenon_intro zenon_H126.
% 4.93/5.18 apply zenon_H123. zenon_intro zenon_H4d.
% 4.93/5.18 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_da 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))))))\/(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_H127); [ zenon_intro zenon_H128; idtac ].
% 4.93/5.18 elim zenon_H128. zenon_intro zenon_TX_dw. zenon_intro zenon_H129.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H129). zenon_intro zenon_H12b. zenon_intro zenon_H12a.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H12a). zenon_intro zenon_H12d. zenon_intro zenon_H12c.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H12c). zenon_intro zenon_H12f. zenon_intro zenon_H12e.
% 4.93/5.18 apply zenon_H12b. zenon_intro zenon_H60.
% 4.93/5.18 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_dw 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))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H12f); [ zenon_intro zenon_H130; idtac ].
% 4.93/5.18 elim zenon_H130. zenon_intro zenon_TY_dv. zenon_intro zenon_H131.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H131). zenon_intro zenon_H133. zenon_intro zenon_H132.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H132). zenon_intro zenon_H135. zenon_intro zenon_H134.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H134). zenon_intro zenon_H137. zenon_intro zenon_H136.
% 4.93/5.18 apply zenon_H133. zenon_intro zenon_H62.
% 4.93/5.18 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_dv 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)))))) zenon_H137); [ zenon_intro zenon_H138; idtac ].
% 4.93/5.18 elim zenon_H138. zenon_intro zenon_TX_mb. zenon_intro zenon_H13a.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H13a). zenon_intro zenon_H13c. zenon_intro zenon_H13b.
% 4.93/5.18 apply (zenon_notor_s _ _ zenon_H13b). zenon_intro zenon_H13e. zenon_intro zenon_H13d.
% 4.93/5.18 apply zenon_H13c. zenon_intro zenon_H13f.
% 4.93/5.18 apply (zenon_notand_s _ _ zenon_Hec); [ zenon_intro zenon_H141 | zenon_intro zenon_H140 ].
% 4.93/5.18 exact (zenon_H141 zenon_H8c).
% 4.93/5.18 apply (zenon_notand_s _ _ zenon_H140); [ zenon_intro zenon_H143 | zenon_intro zenon_H142 ].
% 4.93/5.18 apply zenon_H143. zenon_intro zenon_H144.
% 4.93/5.18 generalize (zenon_H144 zenon_TY_cj). zenon_intro zenon_H145.
% 4.93/5.18 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H3b | zenon_intro zenon_H146 ].
% 4.93/5.18 apply (zenon_L4_ zenon_TY_cj zenon_TX_bt zenon_TY_i zenon_TX_j zenon_TY_bd zenon_TX_h); trivial.
% 4.93/5.18 generalize (zenon_H146 zenon_TX_mb). zenon_intro zenon_H147.
% 4.93/5.18 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ].
% 4.93/5.18 elim (classic ((~(zenon_TY_cj = zenon_TY_dv))/\(~(r1 zenon_TY_cj zenon_TY_dv)))); [ zenon_intro zenon_H14a | zenon_intro zenon_H14b ].
% 4.93/5.18 apply (zenon_and_s _ _ zenon_H14a). zenon_intro zenon_H14c. zenon_intro zenon_H61.
% 4.93/5.18 apply (zenon_L6_ zenon_TY_dv zenon_TX_dw zenon_TY_cj zenon_TY_da zenon_TX_db); trivial.
% 4.93/5.18 cut ((r1 zenon_TY_dv zenon_TX_mb) = (r1 zenon_TY_cj zenon_TX_mb)).
% 4.93/5.18 intro zenon_D_pnotp.
% 4.93/5.18 apply zenon_H149.
% 4.93/5.18 rewrite <- zenon_D_pnotp.
% 4.93/5.18 exact zenon_H13f.
% 4.93/5.18 cut ((zenon_TX_mb = zenon_TX_mb)); [idtac | apply NNPP; zenon_intro zenon_H14d].
% 4.93/5.18 cut ((zenon_TY_dv = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H14e].
% 4.93/5.18 congruence.
% 4.93/5.18 apply (zenon_notand_s _ _ zenon_H14b); [ zenon_intro zenon_H150 | zenon_intro zenon_H14f ].
% 4.93/5.18 apply zenon_H150. zenon_intro zenon_H151.
% 4.93/5.18 elim (classic (zenon_TY_cj = zenon_TY_cj)); [ zenon_intro zenon_H59 | zenon_intro zenon_H41 ].
% 4.93/5.18 cut ((zenon_TY_cj = zenon_TY_cj) = (zenon_TY_dv = zenon_TY_cj)).
% 4.93/5.18 intro zenon_D_pnotp.
% 4.93/5.18 apply zenon_H14e.
% 4.93/5.18 rewrite <- zenon_D_pnotp.
% 4.93/5.18 exact zenon_H59.
% 4.93/5.18 cut ((zenon_TY_cj = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H41].
% 5.01/5.18 cut ((zenon_TY_cj = zenon_TY_dv)); [idtac | apply NNPP; zenon_intro zenon_H14c].
% 5.01/5.18 congruence.
% 5.01/5.18 exact (zenon_H14c zenon_H151).
% 5.01/5.18 apply zenon_H41. apply refl_equal.
% 5.01/5.18 apply zenon_H41. apply refl_equal.
% 5.01/5.18 apply zenon_H14f. zenon_intro zenon_H7e.
% 5.01/5.18 generalize (zenon_H4 zenon_TY_cj). zenon_intro zenon_H5a.
% 5.01/5.18 generalize (zenon_H5a zenon_TY_dv). zenon_intro zenon_H152.
% 5.01/5.18 generalize (zenon_H152 zenon_TX_mb). zenon_intro zenon_H153.
% 5.01/5.18 apply (zenon_imply_s _ _ zenon_H153); [ zenon_intro zenon_H61 | zenon_intro zenon_H154 ].
% 5.01/5.18 exact (zenon_H61 zenon_H7e).
% 5.01/5.18 apply (zenon_imply_s _ _ zenon_H154); [ zenon_intro zenon_H156 | zenon_intro zenon_H155 ].
% 5.01/5.18 exact (zenon_H156 zenon_H13f).
% 5.01/5.18 exact (zenon_H149 zenon_H155).
% 5.01/5.18 apply zenon_H14d. apply refl_equal.
% 5.01/5.18 apply (zenon_notand_s _ _ zenon_H148); [ zenon_intro zenon_H158 | zenon_intro zenon_H157 ].
% 5.01/5.18 exact (zenon_H158 zenon_H13e).
% 5.01/5.18 exact (zenon_H157 zenon_H13d).
% 5.01/5.18 exact (zenon_H142 zenon_H90).
% 5.01/5.18 apply zenon_H80. zenon_intro zenon_Tx_nh. apply NNPP. zenon_intro zenon_H15a.
% 5.01/5.18 apply zenon_H15a. zenon_intro zenon_Ty_nj. apply NNPP. zenon_intro zenon_H15c.
% 5.01/5.18 apply zenon_H15c. zenon_intro zenon_Tz_nl. apply NNPP. zenon_intro zenon_H15e.
% 5.01/5.18 apply (zenon_notimply_s _ _ zenon_H15e). zenon_intro zenon_H160. zenon_intro zenon_H15f.
% 5.01/5.18 apply (zenon_notimply_s _ _ zenon_H15f). zenon_intro zenon_H162. zenon_intro zenon_H161.
% 5.01/5.18 generalize (transitivity zenon_Tx_nh). zenon_intro zenon_H163.
% 5.01/5.18 generalize (zenon_H163 zenon_Ty_nj). zenon_intro zenon_H164.
% 5.01/5.18 generalize (zenon_H164 zenon_Tz_nl). zenon_intro zenon_H165.
% 5.01/5.18 apply (zenon_imply_s _ _ zenon_H165); [ zenon_intro zenon_H167 | zenon_intro zenon_H166 ].
% 5.01/5.18 apply (zenon_notand_s _ _ zenon_H167); [ zenon_intro zenon_H169 | zenon_intro zenon_H168 ].
% 5.01/5.18 exact (zenon_H169 zenon_H160).
% 5.01/5.18 exact (zenon_H168 zenon_H162).
% 5.01/5.18 exact (zenon_H161 zenon_H166).
% 5.01/5.18 Qed.
% 5.01/5.18 % SZS output end Proof
% 5.01/5.18 (* END-PROOF *)
% 5.01/5.18 nodes searched: 170301
% 5.01/5.18 max branch formulas: 31939
% 5.01/5.18 proof nodes created: 15110
% 5.01/5.18 formulas created: 529850
% 5.01/5.18
%------------------------------------------------------------------------------