TSTP Solution File: LCL672+1.005 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : LCL672+1.005 : 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 16:23:44 EDT 2022
% Result : Theorem 1.30s 1.46s
% Output : Proof 1.30s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : LCL672+1.005 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.12 % Command : run_zenon %s %d
% 0.13/0.32 % Computer : n003.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 600
% 0.13/0.32 % DateTime : Sun Jul 3 06:52:09 EDT 2022
% 0.13/0.32 % CPUTime :
% 1.30/1.46 (* PROOF-FOUND *)
% 1.30/1.46 % SZS status Theorem
% 1.30/1.46 (* BEGIN-PROOF *)
% 1.30/1.46 % SZS output start Proof
% 1.30/1.46 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))\/(~(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 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 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 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 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 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 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 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 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 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 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))\/(~(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))\/(~(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))\/(~(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)))))))))))))))))))))))))))))))))))))))).
% 1.30/1.46 Proof.
% 1.30/1.46 assert (zenon_L1_ : forall (zenon_TY_h : zenon_U) (zenon_TX_i : zenon_U) (zenon_TY_j : zenon_U), (r1 zenon_TY_j zenon_TX_i) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TY_j zenon_TY_h)) -> (r1 zenon_TX_i zenon_TY_h) -> False).
% 1.30/1.46 do 3 intro. intros zenon_H3 zenon_H4 zenon_H5 zenon_H6.
% 1.30/1.46 elim (classic ((~(zenon_TY_j = zenon_TX_i))/\(~(r1 zenon_TY_j zenon_TX_i)))); [ zenon_intro zenon_Ha | zenon_intro zenon_Hb ].
% 1.30/1.46 apply (zenon_and_s _ _ zenon_Ha). zenon_intro zenon_Hd. zenon_intro zenon_Hc.
% 1.30/1.46 exact (zenon_Hc zenon_H3).
% 1.30/1.46 cut ((r1 zenon_TX_i zenon_TY_h) = (r1 zenon_TY_j zenon_TY_h)).
% 1.30/1.46 intro zenon_D_pnotp.
% 1.30/1.46 apply zenon_H5.
% 1.30/1.46 rewrite <- zenon_D_pnotp.
% 1.30/1.46 exact zenon_H6.
% 1.30/1.46 cut ((zenon_TY_h = zenon_TY_h)); [idtac | apply NNPP; zenon_intro zenon_He].
% 1.30/1.46 cut ((zenon_TX_i = zenon_TY_j)); [idtac | apply NNPP; zenon_intro zenon_Hf].
% 1.30/1.46 congruence.
% 1.30/1.46 apply (zenon_notand_s _ _ zenon_Hb); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ].
% 1.30/1.46 apply zenon_H11. zenon_intro zenon_H12.
% 1.30/1.46 elim (classic (zenon_TY_j = zenon_TY_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 1.30/1.46 cut ((zenon_TY_j = zenon_TY_j) = (zenon_TX_i = zenon_TY_j)).
% 1.30/1.46 intro zenon_D_pnotp.
% 1.30/1.46 apply zenon_Hf.
% 1.30/1.46 rewrite <- zenon_D_pnotp.
% 1.30/1.46 exact zenon_H13.
% 1.30/1.46 cut ((zenon_TY_j = zenon_TY_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 1.30/1.46 cut ((zenon_TY_j = zenon_TX_i)); [idtac | apply NNPP; zenon_intro zenon_Hd].
% 1.30/1.46 congruence.
% 1.30/1.46 exact (zenon_Hd zenon_H12).
% 1.30/1.46 apply zenon_H14. apply refl_equal.
% 1.30/1.46 apply zenon_H14. apply refl_equal.
% 1.30/1.46 apply zenon_H10. zenon_intro zenon_H3.
% 1.30/1.46 generalize (zenon_H4 zenon_TY_j). zenon_intro zenon_H15.
% 1.30/1.46 generalize (zenon_H15 zenon_TX_i). zenon_intro zenon_H16.
% 1.30/1.46 generalize (zenon_H16 zenon_TY_h). zenon_intro zenon_H17.
% 1.30/1.46 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_Hc | zenon_intro zenon_H18 ].
% 1.30/1.46 exact (zenon_Hc zenon_H3).
% 1.30/1.46 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ].
% 1.30/1.46 exact (zenon_H1a zenon_H6).
% 1.30/1.46 exact (zenon_H5 zenon_H19).
% 1.30/1.46 apply zenon_He. apply refl_equal.
% 1.30/1.46 (* end of lemma zenon_L1_ *)
% 1.30/1.46 assert (zenon_L2_ : forall (zenon_TX_bd : zenon_U) (zenon_TY_h : zenon_U) (zenon_TX_i : zenon_U) (zenon_TY_j : zenon_U), (r1 zenon_TY_j zenon_TX_i) -> (r1 zenon_TX_i zenon_TY_h) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TY_j zenon_TX_bd)) -> (r1 zenon_TY_h zenon_TX_bd) -> False).
% 1.30/1.46 do 4 intro. intros zenon_H3 zenon_H6 zenon_H4 zenon_H1b zenon_H1c.
% 1.30/1.46 elim (classic ((~(zenon_TY_j = zenon_TY_h))/\(~(r1 zenon_TY_j zenon_TY_h)))); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ].
% 1.30/1.46 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H20. zenon_intro zenon_H5.
% 1.30/1.46 apply (zenon_L1_ zenon_TY_h zenon_TX_i zenon_TY_j); trivial.
% 1.30/1.46 cut ((r1 zenon_TY_h zenon_TX_bd) = (r1 zenon_TY_j zenon_TX_bd)).
% 1.30/1.46 intro zenon_D_pnotp.
% 1.30/1.46 apply zenon_H1b.
% 1.30/1.46 rewrite <- zenon_D_pnotp.
% 1.30/1.46 exact zenon_H1c.
% 1.30/1.46 cut ((zenon_TX_bd = zenon_TX_bd)); [idtac | apply NNPP; zenon_intro zenon_H21].
% 1.30/1.46 cut ((zenon_TY_h = zenon_TY_j)); [idtac | apply NNPP; zenon_intro zenon_H22].
% 1.30/1.46 congruence.
% 1.30/1.46 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ].
% 1.30/1.46 apply zenon_H24. zenon_intro zenon_H25.
% 1.30/1.46 elim (classic (zenon_TY_j = zenon_TY_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 1.30/1.46 cut ((zenon_TY_j = zenon_TY_j) = (zenon_TY_h = zenon_TY_j)).
% 1.30/1.46 intro zenon_D_pnotp.
% 1.30/1.46 apply zenon_H22.
% 1.30/1.46 rewrite <- zenon_D_pnotp.
% 1.30/1.46 exact zenon_H13.
% 1.30/1.46 cut ((zenon_TY_j = zenon_TY_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 1.30/1.46 cut ((zenon_TY_j = zenon_TY_h)); [idtac | apply NNPP; zenon_intro zenon_H20].
% 1.30/1.46 congruence.
% 1.30/1.46 exact (zenon_H20 zenon_H25).
% 1.30/1.46 apply zenon_H14. apply refl_equal.
% 1.30/1.46 apply zenon_H14. apply refl_equal.
% 1.30/1.46 apply zenon_H23. zenon_intro zenon_H19.
% 1.30/1.46 generalize (zenon_H4 zenon_TY_j). zenon_intro zenon_H15.
% 1.30/1.46 generalize (zenon_H15 zenon_TY_h). zenon_intro zenon_H26.
% 1.30/1.46 generalize (zenon_H26 zenon_TX_bd). zenon_intro zenon_H27.
% 1.30/1.46 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H5 | zenon_intro zenon_H28 ].
% 1.30/1.46 exact (zenon_H5 zenon_H19).
% 1.30/1.46 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 1.30/1.46 exact (zenon_H2a zenon_H1c).
% 1.30/1.46 exact (zenon_H1b zenon_H29).
% 1.30/1.46 apply zenon_H21. apply refl_equal.
% 1.30/1.46 (* end of lemma zenon_L2_ *)
% 1.30/1.46 assert (zenon_L3_ : forall (zenon_TY_bt : zenon_U) (zenon_TX_bd : zenon_U) (zenon_TY_j : zenon_U) (zenon_TY_h : zenon_U) (zenon_TX_i : zenon_U), (r1 zenon_TX_i zenon_TY_h) -> (r1 zenon_TY_j zenon_TX_i) -> (r1 zenon_TY_h zenon_TX_bd) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TY_j zenon_TY_bt)) -> (r1 zenon_TX_bd zenon_TY_bt) -> False).
% 1.30/1.46 do 5 intro. intros zenon_H6 zenon_H3 zenon_H1c zenon_H4 zenon_H2b zenon_H2c.
% 1.30/1.46 elim (classic ((~(zenon_TY_j = zenon_TX_bd))/\(~(r1 zenon_TY_j zenon_TX_bd)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ].
% 1.30/1.46 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H1b.
% 1.30/1.46 apply (zenon_L2_ zenon_TX_bd zenon_TY_h zenon_TX_i zenon_TY_j); trivial.
% 1.30/1.46 cut ((r1 zenon_TX_bd zenon_TY_bt) = (r1 zenon_TY_j zenon_TY_bt)).
% 1.30/1.46 intro zenon_D_pnotp.
% 1.30/1.46 apply zenon_H2b.
% 1.30/1.46 rewrite <- zenon_D_pnotp.
% 1.30/1.46 exact zenon_H2c.
% 1.30/1.46 cut ((zenon_TY_bt = zenon_TY_bt)); [idtac | apply NNPP; zenon_intro zenon_H31].
% 1.30/1.46 cut ((zenon_TX_bd = zenon_TY_j)); [idtac | apply NNPP; zenon_intro zenon_H32].
% 1.30/1.46 congruence.
% 1.30/1.46 apply (zenon_notand_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 1.30/1.46 apply zenon_H34. zenon_intro zenon_H35.
% 1.30/1.46 elim (classic (zenon_TY_j = zenon_TY_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 1.30/1.46 cut ((zenon_TY_j = zenon_TY_j) = (zenon_TX_bd = zenon_TY_j)).
% 1.30/1.46 intro zenon_D_pnotp.
% 1.30/1.46 apply zenon_H32.
% 1.30/1.46 rewrite <- zenon_D_pnotp.
% 1.30/1.46 exact zenon_H13.
% 1.30/1.46 cut ((zenon_TY_j = zenon_TY_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 1.30/1.46 cut ((zenon_TY_j = zenon_TX_bd)); [idtac | apply NNPP; zenon_intro zenon_H30].
% 1.30/1.46 congruence.
% 1.30/1.46 exact (zenon_H30 zenon_H35).
% 1.30/1.46 apply zenon_H14. apply refl_equal.
% 1.30/1.46 apply zenon_H14. apply refl_equal.
% 1.30/1.46 apply zenon_H33. zenon_intro zenon_H29.
% 1.30/1.46 generalize (zenon_H4 zenon_TY_j). zenon_intro zenon_H15.
% 1.30/1.46 generalize (zenon_H15 zenon_TX_bd). zenon_intro zenon_H36.
% 1.30/1.46 generalize (zenon_H36 zenon_TY_bt). zenon_intro zenon_H37.
% 1.30/1.46 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H1b | zenon_intro zenon_H38 ].
% 1.30/1.46 exact (zenon_H1b zenon_H29).
% 1.30/1.46 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ].
% 1.30/1.46 exact (zenon_H3a zenon_H2c).
% 1.30/1.46 exact (zenon_H2b zenon_H39).
% 1.30/1.46 apply zenon_H31. apply refl_equal.
% 1.30/1.46 (* end of lemma zenon_L3_ *)
% 1.30/1.46 apply NNPP. intro zenon_G.
% 1.30/1.46 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_H3b ].
% 1.30/1.46 apply zenon_G. zenon_intro zenon_H3c.
% 1.30/1.46 elim zenon_H3c. zenon_intro zenon_TX_cj. zenon_intro zenon_H3e.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H3f.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H3f). zenon_intro zenon_H42. zenon_intro zenon_H41.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H41). zenon_intro zenon_H44. zenon_intro zenon_H43.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H53). zenon_intro zenon_H48. zenon_intro zenon_H55.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H55). zenon_intro zenon_H4a. zenon_intro zenon_H56.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H56). zenon_intro zenon_H4c. zenon_intro zenon_H57.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H57). zenon_intro zenon_H59. zenon_intro zenon_H58.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H58). zenon_intro zenon_H5b. zenon_intro zenon_H5a.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H5a). zenon_intro zenon_H5d. zenon_intro zenon_H5c.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H5c). zenon_intro zenon_H5f. zenon_intro zenon_H5e.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H5e). zenon_intro zenon_H48. zenon_intro zenon_H60.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H60). zenon_intro zenon_H4a. zenon_intro zenon_H61.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H61). zenon_intro zenon_H4c. zenon_intro zenon_H62.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H62). zenon_intro zenon_H64. zenon_intro zenon_H63.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H63). zenon_intro zenon_H66. zenon_intro zenon_H65.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H65). zenon_intro zenon_H68. zenon_intro zenon_H67.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H67). zenon_intro zenon_H6a. zenon_intro zenon_H69.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H69). zenon_intro zenon_H48. zenon_intro zenon_H6b.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H6b). zenon_intro zenon_H4a. zenon_intro zenon_H6c.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H6c). zenon_intro zenon_H4c. zenon_intro zenon_H6d.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H6d). zenon_intro zenon_H6f. zenon_intro zenon_H6e.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H6e). zenon_intro zenon_H71. zenon_intro zenon_H70.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H70). zenon_intro zenon_H73. zenon_intro zenon_H72.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H72). zenon_intro zenon_H75. zenon_intro zenon_H74.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H74). zenon_intro zenon_H48. zenon_intro zenon_H76.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H76). zenon_intro zenon_H4a. zenon_intro zenon_H4c.
% 1.30/1.46 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_cj 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_H4a); [ zenon_intro zenon_H77; idtac ].
% 1.30/1.46 elim zenon_H77. zenon_intro zenon_TY_j. zenon_intro zenon_H78.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H78). zenon_intro zenon_H7a. zenon_intro zenon_H79.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H79). zenon_intro zenon_H7c. zenon_intro zenon_H7b.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H7b). zenon_intro zenon_H7e. zenon_intro zenon_H7d.
% 1.30/1.46 apply zenon_H7a. zenon_intro zenon_H7f.
% 1.30/1.46 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_j 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_H7e); [ zenon_intro zenon_H80; idtac ].
% 1.30/1.46 elim zenon_H80. zenon_intro zenon_TX_i. zenon_intro zenon_H81.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H81). zenon_intro zenon_H10. zenon_intro zenon_H82.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H82). zenon_intro zenon_H84. zenon_intro zenon_H83.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H83). zenon_intro zenon_H86. zenon_intro zenon_H85.
% 1.30/1.46 apply zenon_H10. zenon_intro zenon_H3.
% 1.30/1.46 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_i 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_H86); [ zenon_intro zenon_H87; idtac ].
% 1.30/1.46 elim zenon_H87. zenon_intro zenon_TY_h. zenon_intro zenon_H88.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H88). zenon_intro zenon_H8a. zenon_intro zenon_H89.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H89). zenon_intro zenon_H8c. zenon_intro zenon_H8b.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H8b). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 1.30/1.46 apply zenon_H8a. zenon_intro zenon_H6.
% 1.30/1.46 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_h 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_H8e); [ zenon_intro zenon_H8f; idtac ].
% 1.30/1.46 elim zenon_H8f. zenon_intro zenon_TX_bd. zenon_intro zenon_H90.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H90). zenon_intro zenon_H92. zenon_intro zenon_H91.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H91). zenon_intro zenon_H94. zenon_intro zenon_H93.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H93). zenon_intro zenon_H96. zenon_intro zenon_H95.
% 1.30/1.46 apply zenon_H92. zenon_intro zenon_H1c.
% 1.30/1.46 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_bd 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_H96); [ zenon_intro zenon_H97; idtac ].
% 1.30/1.46 elim zenon_H97. zenon_intro zenon_TY_bt. zenon_intro zenon_H98.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H98). zenon_intro zenon_H9a. zenon_intro zenon_H99.
% 1.30/1.46 apply (zenon_notor_s _ _ zenon_H99). zenon_intro zenon_H9c. zenon_intro zenon_H9b.
% 1.30/1.46 apply zenon_H9a. zenon_intro zenon_H2c.
% 1.30/1.46 apply (zenon_notand_s _ _ zenon_H71); [ zenon_intro zenon_H9e | zenon_intro zenon_H9d ].
% 1.30/1.46 exact (zenon_H9e zenon_H48).
% 1.30/1.46 apply (zenon_notand_s _ _ zenon_H9d); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H9f ].
% 1.30/1.46 apply zenon_Ha0. zenon_intro zenon_Ha1.
% 1.30/1.46 generalize (zenon_Ha1 zenon_TY_j). zenon_intro zenon_Ha2.
% 1.30/1.46 apply (zenon_or_s _ _ zenon_Ha2); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha3 ].
% 1.30/1.46 exact (zenon_Ha4 zenon_H7f).
% 1.30/1.46 generalize (zenon_Ha3 zenon_TY_bt). zenon_intro zenon_Ha5.
% 1.30/1.46 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H2b | zenon_intro zenon_Ha6 ].
% 1.30/1.46 apply (zenon_L3_ zenon_TY_bt zenon_TX_bd zenon_TY_j zenon_TY_h zenon_TX_i); trivial.
% 1.30/1.46 apply (zenon_notand_s _ _ zenon_Ha6); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ].
% 1.30/1.46 exact (zenon_Ha8 zenon_H9c).
% 1.30/1.46 exact (zenon_Ha7 zenon_H9b).
% 1.30/1.46 exact (zenon_H9f zenon_H4c).
% 1.30/1.46 apply zenon_H3b. zenon_intro zenon_Tx_gn. apply NNPP. zenon_intro zenon_Haa.
% 1.30/1.46 apply zenon_Haa. zenon_intro zenon_Ty_gp. apply NNPP. zenon_intro zenon_Hac.
% 1.30/1.46 apply zenon_Hac. zenon_intro zenon_Tz_gr. apply NNPP. zenon_intro zenon_Hae.
% 1.30/1.46 apply (zenon_notimply_s _ _ zenon_Hae). zenon_intro zenon_Hb0. zenon_intro zenon_Haf.
% 1.30/1.46 apply (zenon_notimply_s _ _ zenon_Haf). zenon_intro zenon_Hb2. zenon_intro zenon_Hb1.
% 1.30/1.46 generalize (transitivity zenon_Tx_gn). zenon_intro zenon_Hb3.
% 1.30/1.46 generalize (zenon_Hb3 zenon_Ty_gp). zenon_intro zenon_Hb4.
% 1.30/1.46 generalize (zenon_Hb4 zenon_Tz_gr). zenon_intro zenon_Hb5.
% 1.30/1.46 apply (zenon_imply_s _ _ zenon_Hb5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hb6 ].
% 1.30/1.46 apply (zenon_notand_s _ _ zenon_Hb7); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ].
% 1.30/1.46 exact (zenon_Hb9 zenon_Hb0).
% 1.30/1.46 exact (zenon_Hb8 zenon_Hb2).
% 1.30/1.46 exact (zenon_Hb1 zenon_Hb6).
% 1.30/1.46 Qed.
% 1.30/1.46 % SZS output end Proof
% 1.30/1.46 (* END-PROOF *)
% 1.30/1.46 nodes searched: 47946
% 1.30/1.46 max branch formulas: 6956
% 1.30/1.46 proof nodes created: 5351
% 1.30/1.46 formulas created: 136200
% 1.30/1.46
%------------------------------------------------------------------------------