%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL672+1.005 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n010.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 01:32:44 PM UTC 2026 % Result : Theorem 2.43s 2.78s % Output : Proof 2.43s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL672+1.005 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.10/0.36 % Computer : n010.cluster.edu % 0.10/0.36 % Model : x86_64 x86_64 % 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.36 % Memory : 8046.5625MB % 0.10/0.36 % OS : Linux 6.8.0-71-generic % 0.10/0.36 % CPULimit : 300 % 0.10/0.36 % WCLimit : 300 % 0.10/0.36 % DateTime : Fri Sep 4 20:27:23 UTC 2026 % 0.10/0.36 % CPUTime : % 2.43/2.78 (* PROOF-FOUND *) % 2.43/2.78 % SZS status Theorem % 2.43/2.78 (* BEGIN-PROOF *) % 2.43/2.78 % SZS output start Proof % 2.43/2.78 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)))))))))))))))))))))))))))))))))))))))). % 2.43/2.78 Proof. % 2.43/2.78 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). % 2.43/2.78 do 3 intro. intros zenon_H3 zenon_H4 zenon_H5 zenon_H6. % 2.43/2.78 elim (classic ((~(zenon_TY_j = zenon_TX_i))/\(~(r1 zenon_TY_j zenon_TX_i)))); [ zenon_intro zenon_Ha | zenon_intro zenon_Hb ]. % 2.43/2.78 apply (zenon_and_s _ _ zenon_Ha). zenon_intro zenon_Hd. zenon_intro zenon_Hc. % 2.43/2.78 exact (zenon_Hc zenon_H3). % 2.43/2.78 cut ((r1 zenon_TX_i zenon_TY_h) = (r1 zenon_TY_j zenon_TY_h)). % 2.43/2.78 intro zenon_D_pnotp. % 2.43/2.78 apply zenon_H5. % 2.43/2.78 rewrite <- zenon_D_pnotp. % 2.43/2.78 exact zenon_H6. % 2.43/2.78 cut ((zenon_TY_h = zenon_TY_h)); [idtac | apply NNPP; zenon_intro zenon_He]. % 2.43/2.78 cut ((zenon_TX_i = zenon_TY_j)); [idtac | apply NNPP; zenon_intro zenon_Hf]. % 2.43/2.78 congruence. % 2.43/2.78 apply (zenon_notand_s _ _ zenon_Hb); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ]. % 2.43/2.78 apply zenon_H11. zenon_intro zenon_H12. % 2.43/2.78 elim (classic (zenon_TY_j = zenon_TY_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 2.43/2.78 cut ((zenon_TY_j = zenon_TY_j) = (zenon_TX_i = zenon_TY_j)). % 2.43/2.78 intro zenon_D_pnotp. % 2.43/2.78 apply zenon_Hf. % 2.43/2.78 rewrite <- zenon_D_pnotp. % 2.43/2.78 exact zenon_H13. % 2.43/2.78 cut ((zenon_TY_j = zenon_TY_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 2.43/2.78 cut ((zenon_TY_j = zenon_TX_i)); [idtac | apply NNPP; zenon_intro zenon_Hd]. % 2.43/2.78 congruence. % 2.43/2.78 exact (zenon_Hd zenon_H12). % 2.43/2.78 apply zenon_H14. apply refl_equal. % 2.43/2.78 apply zenon_H14. apply refl_equal. % 2.43/2.78 apply zenon_H10. zenon_intro zenon_H3. % 2.43/2.78 generalize (zenon_H4 zenon_TY_j). zenon_intro zenon_H15. % 2.43/2.78 generalize (zenon_H15 zenon_TX_i). zenon_intro zenon_H16. % 2.43/2.78 generalize (zenon_H16 zenon_TY_h). zenon_intro zenon_H17. % 2.43/2.78 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_Hc | zenon_intro zenon_H18 ]. % 2.43/2.78 exact (zenon_Hc zenon_H3). % 2.43/2.78 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ]. % 2.43/2.78 exact (zenon_H1a zenon_H6). % 2.43/2.78 exact (zenon_H5 zenon_H19). % 2.43/2.78 apply zenon_He. apply refl_equal. % 2.43/2.78 (* end of lemma zenon_L1_ *) % 2.43/2.78 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). % 2.43/2.78 do 4 intro. intros zenon_H3 zenon_H6 zenon_H4 zenon_H1b zenon_H1c. % 2.43/2.78 elim (classic ((~(zenon_TY_j = zenon_TY_h))/\(~(r1 zenon_TY_j zenon_TY_h)))); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ]. % 2.43/2.78 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H20. zenon_intro zenon_H5. % 2.43/2.78 apply (zenon_L1_ zenon_TY_h zenon_TX_i zenon_TY_j); trivial. % 2.43/2.78 cut ((r1 zenon_TY_h zenon_TX_bd) = (r1 zenon_TY_j zenon_TX_bd)). % 2.43/2.78 intro zenon_D_pnotp. % 2.43/2.78 apply zenon_H1b. % 2.43/2.78 rewrite <- zenon_D_pnotp. % 2.43/2.78 exact zenon_H1c. % 2.43/2.78 cut ((zenon_TX_bd = zenon_TX_bd)); [idtac | apply NNPP; zenon_intro zenon_H21]. % 2.43/2.78 cut ((zenon_TY_h = zenon_TY_j)); [idtac | apply NNPP; zenon_intro zenon_H22]. % 2.43/2.78 congruence. % 2.43/2.78 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ]. % 2.43/2.78 apply zenon_H24. zenon_intro zenon_H25. % 2.43/2.78 elim (classic (zenon_TY_j = zenon_TY_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 2.43/2.78 cut ((zenon_TY_j = zenon_TY_j) = (zenon_TY_h = zenon_TY_j)). % 2.43/2.78 intro zenon_D_pnotp. % 2.43/2.78 apply zenon_H22. % 2.43/2.78 rewrite <- zenon_D_pnotp. % 2.43/2.78 exact zenon_H13. % 2.43/2.78 cut ((zenon_TY_j = zenon_TY_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 2.43/2.78 cut ((zenon_TY_j = zenon_TY_h)); [idtac | apply NNPP; zenon_intro zenon_H20]. % 2.43/2.78 congruence. % 2.43/2.78 exact (zenon_H20 zenon_H25). % 2.43/2.78 apply zenon_H14. apply refl_equal. % 2.43/2.78 apply zenon_H14. apply refl_equal. % 2.43/2.78 apply zenon_H23. zenon_intro zenon_H19. % 2.43/2.78 generalize (zenon_H4 zenon_TY_j). zenon_intro zenon_H15. % 2.43/2.78 generalize (zenon_H15 zenon_TY_h). zenon_intro zenon_H26. % 2.43/2.78 generalize (zenon_H26 zenon_TX_bd). zenon_intro zenon_H27. % 2.43/2.78 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H5 | zenon_intro zenon_H28 ]. % 2.43/2.78 exact (zenon_H5 zenon_H19). % 2.43/2.78 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 2.43/2.78 exact (zenon_H2a zenon_H1c). % 2.43/2.78 exact (zenon_H1b zenon_H29). % 2.43/2.78 apply zenon_H21. apply refl_equal. % 2.43/2.78 (* end of lemma zenon_L2_ *) % 2.43/2.78 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). % 2.43/2.78 do 5 intro. intros zenon_H6 zenon_H3 zenon_H1c zenon_H4 zenon_H2b zenon_H2c. % 2.43/2.78 elim (classic ((~(zenon_TY_j = zenon_TX_bd))/\(~(r1 zenon_TY_j zenon_TX_bd)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 2.43/2.78 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H1b. % 2.43/2.78 apply (zenon_L2_ zenon_TX_bd zenon_TY_h zenon_TX_i zenon_TY_j); trivial. % 2.43/2.78 cut ((r1 zenon_TX_bd zenon_TY_bt) = (r1 zenon_TY_j zenon_TY_bt)). % 2.43/2.78 intro zenon_D_pnotp. % 2.43/2.78 apply zenon_H2b. % 2.43/2.78 rewrite <- zenon_D_pnotp. % 2.43/2.78 exact zenon_H2c. % 2.43/2.78 cut ((zenon_TY_bt = zenon_TY_bt)); [idtac | apply NNPP; zenon_intro zenon_H31]. % 2.43/2.78 cut ((zenon_TX_bd = zenon_TY_j)); [idtac | apply NNPP; zenon_intro zenon_H32]. % 2.43/2.78 congruence. % 2.43/2.78 apply (zenon_notand_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 2.43/2.78 apply zenon_H34. zenon_intro zenon_H35. % 2.43/2.78 elim (classic (zenon_TY_j = zenon_TY_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 2.43/2.78 cut ((zenon_TY_j = zenon_TY_j) = (zenon_TX_bd = zenon_TY_j)). % 2.43/2.78 intro zenon_D_pnotp. % 2.43/2.78 apply zenon_H32. % 2.43/2.78 rewrite <- zenon_D_pnotp. % 2.43/2.78 exact zenon_H13. % 2.43/2.78 cut ((zenon_TY_j = zenon_TY_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 2.43/2.78 cut ((zenon_TY_j = zenon_TX_bd)); [idtac | apply NNPP; zenon_intro zenon_H30]. % 2.43/2.78 congruence. % 2.43/2.78 exact (zenon_H30 zenon_H35). % 2.43/2.78 apply zenon_H14. apply refl_equal. % 2.43/2.78 apply zenon_H14. apply refl_equal. % 2.43/2.78 apply zenon_H33. zenon_intro zenon_H29. % 2.43/2.78 generalize (zenon_H4 zenon_TY_j). zenon_intro zenon_H15. % 2.43/2.78 generalize (zenon_H15 zenon_TX_bd). zenon_intro zenon_H36. % 2.43/2.78 generalize (zenon_H36 zenon_TY_bt). zenon_intro zenon_H37. % 2.43/2.78 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H1b | zenon_intro zenon_H38 ]. % 2.43/2.78 exact (zenon_H1b zenon_H29). % 2.43/2.78 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 2.43/2.78 exact (zenon_H3a zenon_H2c). % 2.43/2.78 exact (zenon_H2b zenon_H39). % 2.43/2.78 apply zenon_H31. apply refl_equal. % 2.43/2.78 (* end of lemma zenon_L3_ *) % 2.43/2.78 apply NNPP. intro zenon_G. % 2.43/2.78 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 ]. % 2.43/2.78 apply zenon_G. zenon_intro zenon_H3c. % 2.43/2.78 elim zenon_H3c. zenon_intro zenon_TX_cj. zenon_intro zenon_H3e. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H3f. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H3f). zenon_intro zenon_H42. zenon_intro zenon_H41. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H41). zenon_intro zenon_H44. zenon_intro zenon_H43. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H45). zenon_intro zenon_H48. zenon_intro zenon_H47. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H47). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H4d). zenon_intro zenon_H50. zenon_intro zenon_H4f. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H51). zenon_intro zenon_H54. zenon_intro zenon_H53. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H53). zenon_intro zenon_H48. zenon_intro zenon_H55. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H55). zenon_intro zenon_H4a. zenon_intro zenon_H56. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H56). zenon_intro zenon_H4c. zenon_intro zenon_H57. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H57). zenon_intro zenon_H59. zenon_intro zenon_H58. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H58). zenon_intro zenon_H5b. zenon_intro zenon_H5a. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H5a). zenon_intro zenon_H5d. zenon_intro zenon_H5c. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H5c). zenon_intro zenon_H5f. zenon_intro zenon_H5e. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H5e). zenon_intro zenon_H48. zenon_intro zenon_H60. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H60). zenon_intro zenon_H4a. zenon_intro zenon_H61. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H61). zenon_intro zenon_H4c. zenon_intro zenon_H62. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H62). zenon_intro zenon_H64. zenon_intro zenon_H63. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H63). zenon_intro zenon_H66. zenon_intro zenon_H65. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H65). zenon_intro zenon_H68. zenon_intro zenon_H67. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H67). zenon_intro zenon_H6a. zenon_intro zenon_H69. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H69). zenon_intro zenon_H48. zenon_intro zenon_H6b. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H6b). zenon_intro zenon_H4a. zenon_intro zenon_H6c. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H6c). zenon_intro zenon_H4c. zenon_intro zenon_H6d. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H6d). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H6e). zenon_intro zenon_H71. zenon_intro zenon_H70. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H70). zenon_intro zenon_H73. zenon_intro zenon_H72. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H72). zenon_intro zenon_H75. zenon_intro zenon_H74. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H74). zenon_intro zenon_H48. zenon_intro zenon_H76. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H76). zenon_intro zenon_H4a. zenon_intro zenon_H4c. % 2.43/2.78 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 ]. % 2.43/2.78 elim zenon_H77. zenon_intro zenon_TY_j. zenon_intro zenon_H78. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H78). zenon_intro zenon_H7a. zenon_intro zenon_H79. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H79). zenon_intro zenon_H7c. zenon_intro zenon_H7b. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H7b). zenon_intro zenon_H7e. zenon_intro zenon_H7d. % 2.43/2.78 apply zenon_H7a. zenon_intro zenon_H7f. % 2.43/2.78 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 ]. % 2.43/2.78 elim zenon_H80. zenon_intro zenon_TX_i. zenon_intro zenon_H81. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H81). zenon_intro zenon_H10. zenon_intro zenon_H82. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H82). zenon_intro zenon_H84. zenon_intro zenon_H83. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H83). zenon_intro zenon_H86. zenon_intro zenon_H85. % 2.43/2.78 apply zenon_H10. zenon_intro zenon_H3. % 2.43/2.78 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 ]. % 2.43/2.78 elim zenon_H87. zenon_intro zenon_TY_h. zenon_intro zenon_H88. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H88). zenon_intro zenon_H8a. zenon_intro zenon_H89. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H89). zenon_intro zenon_H8c. zenon_intro zenon_H8b. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H8b). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 2.43/2.78 apply zenon_H8a. zenon_intro zenon_H6. % 2.43/2.78 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 ]. % 2.43/2.78 elim zenon_H8f. zenon_intro zenon_TX_bd. zenon_intro zenon_H90. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H90). zenon_intro zenon_H92. zenon_intro zenon_H91. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H91). zenon_intro zenon_H94. zenon_intro zenon_H93. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H93). zenon_intro zenon_H96. zenon_intro zenon_H95. % 2.43/2.78 apply zenon_H92. zenon_intro zenon_H1c. % 2.43/2.78 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 ]. % 2.43/2.78 elim zenon_H97. zenon_intro zenon_TY_bt. zenon_intro zenon_H98. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H98). zenon_intro zenon_H9a. zenon_intro zenon_H99. % 2.43/2.78 apply (zenon_notor_s _ _ zenon_H99). zenon_intro zenon_H9c. zenon_intro zenon_H9b. % 2.43/2.78 apply zenon_H9a. zenon_intro zenon_H2c. % 2.43/2.78 apply (zenon_notand_s _ _ zenon_H71); [ zenon_intro zenon_H9e | zenon_intro zenon_H9d ]. % 2.43/2.78 exact (zenon_H9e zenon_H48). % 2.43/2.78 apply (zenon_notand_s _ _ zenon_H9d); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H9f ]. % 2.43/2.78 apply zenon_Ha0. zenon_intro zenon_Ha1. % 2.43/2.78 generalize (zenon_Ha1 zenon_TY_j). zenon_intro zenon_Ha2. % 2.43/2.78 apply (zenon_or_s _ _ zenon_Ha2); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha3 ]. % 2.43/2.78 exact (zenon_Ha4 zenon_H7f). % 2.43/2.78 generalize (zenon_Ha3 zenon_TY_bt). zenon_intro zenon_Ha5. % 2.43/2.78 apply (zenon_or_s _ _ zenon_Ha5); [ zenon_intro zenon_H2b | zenon_intro zenon_Ha6 ]. % 2.43/2.78 apply (zenon_L3_ zenon_TY_bt zenon_TX_bd zenon_TY_j zenon_TY_h zenon_TX_i); trivial. % 2.43/2.78 apply (zenon_notand_s _ _ zenon_Ha6); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Ha7 ]. % 2.43/2.78 exact (zenon_Ha8 zenon_H9c). % 2.43/2.78 exact (zenon_Ha7 zenon_H9b). % 2.43/2.78 exact (zenon_H9f zenon_H4c). % 2.43/2.78 apply zenon_H3b. zenon_intro zenon_Tx_gn. apply NNPP. zenon_intro zenon_Haa. % 2.43/2.78 apply zenon_Haa. zenon_intro zenon_Ty_gp. apply NNPP. zenon_intro zenon_Hac. % 2.43/2.78 apply zenon_Hac. zenon_intro zenon_Tz_gr. apply NNPP. zenon_intro zenon_Hae. % 2.43/2.78 apply (zenon_notimply_s _ _ zenon_Hae). zenon_intro zenon_Hb0. zenon_intro zenon_Haf. % 2.43/2.78 apply (zenon_notimply_s _ _ zenon_Haf). zenon_intro zenon_Hb2. zenon_intro zenon_Hb1. % 2.43/2.78 generalize (transitivity zenon_Tx_gn). zenon_intro zenon_Hb3. % 2.43/2.78 generalize (zenon_Hb3 zenon_Ty_gp). zenon_intro zenon_Hb4. % 2.43/2.78 generalize (zenon_Hb4 zenon_Tz_gr). zenon_intro zenon_Hb5. % 2.43/2.78 apply (zenon_imply_s _ _ zenon_Hb5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hb6 ]. % 2.43/2.78 apply (zenon_notand_s _ _ zenon_Hb7); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ]. % 2.43/2.78 exact (zenon_Hb9 zenon_Hb0). % 2.43/2.78 exact (zenon_Hb8 zenon_Hb2). % 2.43/2.78 exact (zenon_Hb1 zenon_Hb6). % 2.43/2.78 Qed. % 2.43/2.78 % SZS output end Proof % 2.43/2.78 (* END-PROOF *) % 2.43/2.78 nodes searched: 47946 % 2.43/2.78 max branch formulas: 6956 % 2.43/2.78 proof nodes created: 5351 % 2.43/2.78 formulas created: 136200 % 2.43/2.78 %------------------------------------------------------------------------------