%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL672+1.015 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n006.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 176.20s 176.55s % Output : Proof 0.12s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL672+1.015 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.08/0.35 % Computer : n006.cluster.edu % 0.08/0.35 % Model : x86_64 x86_64 % 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.35 % Memory : 8046.5625MB % 0.08/0.35 % OS : Linux 6.8.0-71-generic % 0.08/0.35 % CPULimit : 300 % 0.08/0.35 % WCLimit : 300 % 0.08/0.35 % DateTime : Fri Sep 4 20:10:46 UTC 2026 % 0.08/0.35 % CPUTime : % 176.20/176.55 (* PROOF-FOUND *) % 176.20/176.55 % SZS status Theorem % 176.20/176.55 (* BEGIN-PROOF *) % 176.20/176.55 % SZS output start Proof % 176.20/176.55 Theorem main : (~(exists X : zenon_U, (~(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(p1 Y))))))))/\(p1 Y))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : 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((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(p1 Y))))))))/\(p1 Y))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/False))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~(p1 X))))))))/\(p1 X))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/False))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(p1 Y))))))))/\(p1 Y))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/False))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). % 176.20/176.55 Proof. % 176.20/176.55 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). % 176.20/176.55 do 3 intro. intros zenon_H3 zenon_H4 zenon_H5 zenon_H6. % 176.20/176.55 elim (classic ((~(zenon_TX_j = zenon_TY_i))/\(~(r1 zenon_TX_j zenon_TY_i)))); [ zenon_intro zenon_Ha | zenon_intro zenon_Hb ]. % 176.20/176.55 apply (zenon_and_s _ _ zenon_Ha). zenon_intro zenon_Hd. zenon_intro zenon_Hc. % 176.20/176.55 exact (zenon_Hc zenon_H3). % 176.20/176.55 cut ((r1 zenon_TY_i zenon_TX_h) = (r1 zenon_TX_j zenon_TX_h)). % 176.20/176.55 intro zenon_D_pnotp. % 176.20/176.55 apply zenon_H5. % 176.20/176.55 rewrite <- zenon_D_pnotp. % 176.20/176.55 exact zenon_H6. % 176.20/176.55 cut ((zenon_TX_h = zenon_TX_h)); [idtac | apply NNPP; zenon_intro zenon_He]. % 176.20/176.55 cut ((zenon_TY_i = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_Hf]. % 176.20/176.55 congruence. % 176.20/176.55 apply (zenon_notand_s _ _ zenon_Hb); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ]. % 176.20/176.55 apply zenon_H11. zenon_intro zenon_H12. % 176.20/176.55 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_i = zenon_TX_j)). % 176.20/176.55 intro zenon_D_pnotp. % 176.20/176.55 apply zenon_Hf. % 176.20/176.55 rewrite <- zenon_D_pnotp. % 176.20/176.55 exact zenon_H13. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 176.20/176.55 cut ((zenon_TX_j = zenon_TY_i)); [idtac | apply NNPP; zenon_intro zenon_Hd]. % 176.20/176.55 congruence. % 176.20/176.55 exact (zenon_Hd zenon_H12). % 176.20/176.55 apply zenon_H14. apply refl_equal. % 176.20/176.55 apply zenon_H14. apply refl_equal. % 176.20/176.55 apply zenon_H10. zenon_intro zenon_H3. % 176.20/176.55 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 176.20/176.55 generalize (zenon_H15 zenon_TY_i). zenon_intro zenon_H16. % 176.20/176.55 generalize (zenon_H16 zenon_TX_h). zenon_intro zenon_H17. % 176.20/176.55 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_Hc | zenon_intro zenon_H18 ]. % 176.20/176.55 exact (zenon_Hc zenon_H3). % 176.20/176.55 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ]. % 176.20/176.55 exact (zenon_H1a zenon_H6). % 176.20/176.55 exact (zenon_H5 zenon_H19). % 176.20/176.55 apply zenon_He. apply refl_equal. % 176.20/176.55 (* end of lemma zenon_L1_ *) % 176.20/176.55 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). % 176.20/176.55 do 4 intro. intros zenon_H3 zenon_H6 zenon_H4 zenon_H1b zenon_H1c. % 176.20/176.55 elim (classic ((~(zenon_TX_j = zenon_TX_h))/\(~(r1 zenon_TX_j zenon_TX_h)))); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ]. % 176.20/176.55 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H20. zenon_intro zenon_H5. % 176.20/176.55 apply (zenon_L1_ zenon_TX_h zenon_TY_i zenon_TX_j); trivial. % 176.20/176.55 cut ((r1 zenon_TX_h zenon_TY_bd) = (r1 zenon_TX_j zenon_TY_bd)). % 176.20/176.55 intro zenon_D_pnotp. % 176.20/176.55 apply zenon_H1b. % 176.20/176.55 rewrite <- zenon_D_pnotp. % 176.20/176.55 exact zenon_H1c. % 176.20/176.55 cut ((zenon_TY_bd = zenon_TY_bd)); [idtac | apply NNPP; zenon_intro zenon_H21]. % 176.20/176.55 cut ((zenon_TX_h = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H22]. % 176.20/176.55 congruence. % 176.20/176.55 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ]. % 176.20/176.55 apply zenon_H24. zenon_intro zenon_H25. % 176.20/176.55 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_h = zenon_TX_j)). % 176.20/176.55 intro zenon_D_pnotp. % 176.20/176.55 apply zenon_H22. % 176.20/176.55 rewrite <- zenon_D_pnotp. % 176.20/176.55 exact zenon_H13. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_h)); [idtac | apply NNPP; zenon_intro zenon_H20]. % 176.20/176.55 congruence. % 176.20/176.55 exact (zenon_H20 zenon_H25). % 176.20/176.55 apply zenon_H14. apply refl_equal. % 176.20/176.55 apply zenon_H14. apply refl_equal. % 176.20/176.55 apply zenon_H23. zenon_intro zenon_H19. % 176.20/176.55 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 176.20/176.55 generalize (zenon_H15 zenon_TX_h). zenon_intro zenon_H26. % 176.20/176.55 generalize (zenon_H26 zenon_TY_bd). zenon_intro zenon_H27. % 176.20/176.55 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H5 | zenon_intro zenon_H28 ]. % 176.20/176.55 exact (zenon_H5 zenon_H19). % 176.20/176.55 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 176.20/176.55 exact (zenon_H2a zenon_H1c). % 176.20/176.55 exact (zenon_H1b zenon_H29). % 176.20/176.55 apply zenon_H21. apply refl_equal. % 176.20/176.55 (* end of lemma zenon_L2_ *) % 176.20/176.55 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). % 176.20/176.55 do 5 intro. intros zenon_H6 zenon_H3 zenon_H1c zenon_H4 zenon_H2b zenon_H2c. % 176.20/176.55 elim (classic ((~(zenon_TX_j = zenon_TY_bd))/\(~(r1 zenon_TX_j zenon_TY_bd)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 176.20/176.55 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H1b. % 176.20/176.55 apply (zenon_L2_ zenon_TY_bd zenon_TX_h zenon_TY_i zenon_TX_j); trivial. % 176.20/176.55 cut ((r1 zenon_TY_bd zenon_TX_bt) = (r1 zenon_TX_j zenon_TX_bt)). % 176.20/176.55 intro zenon_D_pnotp. % 176.20/176.55 apply zenon_H2b. % 176.20/176.55 rewrite <- zenon_D_pnotp. % 176.20/176.55 exact zenon_H2c. % 176.20/176.55 cut ((zenon_TX_bt = zenon_TX_bt)); [idtac | apply NNPP; zenon_intro zenon_H31]. % 176.20/176.55 cut ((zenon_TY_bd = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H32]. % 176.20/176.55 congruence. % 176.20/176.55 apply (zenon_notand_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 176.20/176.55 apply zenon_H34. zenon_intro zenon_H35. % 176.20/176.55 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_bd = zenon_TX_j)). % 176.20/176.55 intro zenon_D_pnotp. % 176.20/176.55 apply zenon_H32. % 176.20/176.55 rewrite <- zenon_D_pnotp. % 176.20/176.55 exact zenon_H13. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 176.20/176.55 cut ((zenon_TX_j = zenon_TY_bd)); [idtac | apply NNPP; zenon_intro zenon_H30]. % 176.20/176.55 congruence. % 176.20/176.55 exact (zenon_H30 zenon_H35). % 176.20/176.55 apply zenon_H14. apply refl_equal. % 176.20/176.55 apply zenon_H14. apply refl_equal. % 176.20/176.55 apply zenon_H33. zenon_intro zenon_H29. % 176.20/176.55 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 176.20/176.55 generalize (zenon_H15 zenon_TY_bd). zenon_intro zenon_H36. % 176.20/176.55 generalize (zenon_H36 zenon_TX_bt). zenon_intro zenon_H37. % 176.20/176.55 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H1b | zenon_intro zenon_H38 ]. % 176.20/176.55 exact (zenon_H1b zenon_H29). % 176.20/176.55 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 176.20/176.55 exact (zenon_H3a zenon_H2c). % 176.20/176.55 exact (zenon_H2b zenon_H39). % 176.20/176.55 apply zenon_H31. apply refl_equal. % 176.20/176.55 (* end of lemma zenon_L3_ *) % 176.20/176.55 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). % 176.20/176.55 do 6 intro. intros zenon_H1c zenon_H3 zenon_H6 zenon_H2c zenon_H4 zenon_H3b zenon_H3c. % 176.20/176.55 elim (classic ((~(zenon_TX_j = zenon_TX_bt))/\(~(r1 zenon_TX_j zenon_TX_bt)))); [ zenon_intro zenon_H3e | zenon_intro zenon_H3f ]. % 176.20/176.55 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H2b. % 176.20/176.55 apply (zenon_L3_ zenon_TX_bt zenon_TY_bd zenon_TX_j zenon_TX_h zenon_TY_i); trivial. % 176.20/176.55 cut ((r1 zenon_TX_bt zenon_TY_cj) = (r1 zenon_TX_j zenon_TY_cj)). % 176.20/176.55 intro zenon_D_pnotp. % 176.20/176.55 apply zenon_H3b. % 176.20/176.55 rewrite <- zenon_D_pnotp. % 176.20/176.55 exact zenon_H3c. % 176.20/176.55 cut ((zenon_TY_cj = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H41]. % 176.20/176.55 cut ((zenon_TX_bt = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H42]. % 176.20/176.55 congruence. % 176.20/176.55 apply (zenon_notand_s _ _ zenon_H3f); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 176.20/176.55 apply zenon_H44. zenon_intro zenon_H45. % 176.20/176.55 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_bt = zenon_TX_j)). % 176.20/176.55 intro zenon_D_pnotp. % 176.20/176.55 apply zenon_H42. % 176.20/176.55 rewrite <- zenon_D_pnotp. % 176.20/176.55 exact zenon_H13. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_bt)); [idtac | apply NNPP; zenon_intro zenon_H40]. % 176.20/176.55 congruence. % 176.20/176.55 exact (zenon_H40 zenon_H45). % 176.20/176.55 apply zenon_H14. apply refl_equal. % 176.20/176.55 apply zenon_H14. apply refl_equal. % 176.20/176.55 apply zenon_H43. zenon_intro zenon_H39. % 176.20/176.55 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 176.20/176.55 generalize (zenon_H15 zenon_TX_bt). zenon_intro zenon_H46. % 176.20/176.55 generalize (zenon_H46 zenon_TY_cj). zenon_intro zenon_H47. % 176.20/176.55 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H2b | zenon_intro zenon_H48 ]. % 176.20/176.55 exact (zenon_H2b zenon_H39). % 176.20/176.55 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 176.20/176.55 exact (zenon_H4a zenon_H3c). % 176.20/176.55 exact (zenon_H3b zenon_H49). % 176.20/176.55 apply zenon_H41. apply refl_equal. % 176.20/176.55 (* end of lemma zenon_L4_ *) % 176.20/176.55 assert (zenon_L5_ : forall (zenon_TX_cz : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TX_j : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_bt : zenon_U) (zenon_TY_bd : zenon_U), (r1 zenon_TY_bd zenon_TX_bt) -> (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TX_h zenon_TY_bd) -> (r1 zenon_TX_bt zenon_TY_cj) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TX_cz)) -> (r1 zenon_TY_cj zenon_TX_cz) -> False). % 176.20/176.55 do 7 intro. intros zenon_H2c zenon_H6 zenon_H3 zenon_H1c zenon_H3c zenon_H4 zenon_H4b zenon_H4c. % 176.20/176.55 elim (classic ((~(zenon_TX_j = zenon_TY_cj))/\(~(r1 zenon_TX_j zenon_TY_cj)))); [ zenon_intro zenon_H4e | zenon_intro zenon_H4f ]. % 176.20/176.55 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H50. zenon_intro zenon_H3b. % 176.20/176.55 apply (zenon_L4_ zenon_TY_cj zenon_TX_bt zenon_TY_i zenon_TX_j zenon_TY_bd zenon_TX_h); trivial. % 176.20/176.55 cut ((r1 zenon_TY_cj zenon_TX_cz) = (r1 zenon_TX_j zenon_TX_cz)). % 176.20/176.55 intro zenon_D_pnotp. % 176.20/176.55 apply zenon_H4b. % 176.20/176.55 rewrite <- zenon_D_pnotp. % 176.20/176.55 exact zenon_H4c. % 176.20/176.55 cut ((zenon_TX_cz = zenon_TX_cz)); [idtac | apply NNPP; zenon_intro zenon_H51]. % 176.20/176.55 cut ((zenon_TY_cj = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H52]. % 176.20/176.55 congruence. % 176.20/176.55 apply (zenon_notand_s _ _ zenon_H4f); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ]. % 176.20/176.55 apply zenon_H54. zenon_intro zenon_H55. % 176.20/176.55 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_cj = zenon_TX_j)). % 176.20/176.55 intro zenon_D_pnotp. % 176.20/176.55 apply zenon_H52. % 176.20/176.55 rewrite <- zenon_D_pnotp. % 176.20/176.55 exact zenon_H13. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 176.20/176.55 cut ((zenon_TX_j = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H50]. % 176.20/176.55 congruence. % 176.20/176.55 exact (zenon_H50 zenon_H55). % 176.20/176.55 apply zenon_H14. apply refl_equal. % 176.20/176.55 apply zenon_H14. apply refl_equal. % 176.20/176.55 apply zenon_H53. zenon_intro zenon_H49. % 176.20/176.55 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 176.20/176.55 generalize (zenon_H15 zenon_TY_cj). zenon_intro zenon_H56. % 176.20/176.55 generalize (zenon_H56 zenon_TX_cz). zenon_intro zenon_H57. % 176.20/176.55 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H3b | zenon_intro zenon_H58 ]. % 176.20/176.55 exact (zenon_H3b zenon_H49). % 176.20/176.55 apply (zenon_imply_s _ _ zenon_H58); [ zenon_intro zenon_H5a | zenon_intro zenon_H59 ]. % 176.20/176.55 exact (zenon_H5a zenon_H4c). % 176.20/176.55 exact (zenon_H4b zenon_H59). % 176.20/176.55 apply zenon_H51. apply refl_equal. % 176.20/176.55 (* end of lemma zenon_L5_ *) % 176.20/176.55 assert (zenon_L6_ : forall (zenon_TY_dp : zenon_U) (zenon_TX_cz : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_j : zenon_U) (zenon_TY_bd : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TX_bt : zenon_U), (r1 zenon_TX_bt zenon_TY_cj) -> (r1 zenon_TX_h zenon_TY_bd) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TY_bd zenon_TX_bt) -> (r1 zenon_TY_cj zenon_TX_cz) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TY_dp)) -> (r1 zenon_TX_cz zenon_TY_dp) -> False). % 176.20/176.55 do 8 intro. intros zenon_H3c zenon_H1c zenon_H3 zenon_H6 zenon_H2c zenon_H4c zenon_H4 zenon_H5b zenon_H5c. % 176.20/176.55 elim (classic ((~(zenon_TX_j = zenon_TX_cz))/\(~(r1 zenon_TX_j zenon_TX_cz)))); [ zenon_intro zenon_H5e | zenon_intro zenon_H5f ]. % 176.20/176.55 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H60. zenon_intro zenon_H4b. % 176.20/176.55 apply (zenon_L5_ zenon_TX_cz zenon_TY_cj zenon_TX_j zenon_TX_h zenon_TY_i zenon_TX_bt zenon_TY_bd); trivial. % 176.20/176.55 cut ((r1 zenon_TX_cz zenon_TY_dp) = (r1 zenon_TX_j zenon_TY_dp)). % 176.20/176.55 intro zenon_D_pnotp. % 176.20/176.55 apply zenon_H5b. % 176.20/176.55 rewrite <- zenon_D_pnotp. % 176.20/176.55 exact zenon_H5c. % 176.20/176.55 cut ((zenon_TY_dp = zenon_TY_dp)); [idtac | apply NNPP; zenon_intro zenon_H61]. % 176.20/176.55 cut ((zenon_TX_cz = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H62]. % 176.20/176.55 congruence. % 176.20/176.55 apply (zenon_notand_s _ _ zenon_H5f); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ]. % 176.20/176.55 apply zenon_H64. zenon_intro zenon_H65. % 176.20/176.55 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_cz = zenon_TX_j)). % 176.20/176.55 intro zenon_D_pnotp. % 176.20/176.55 apply zenon_H62. % 176.20/176.55 rewrite <- zenon_D_pnotp. % 176.20/176.55 exact zenon_H13. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_cz)); [idtac | apply NNPP; zenon_intro zenon_H60]. % 176.20/176.55 congruence. % 176.20/176.55 exact (zenon_H60 zenon_H65). % 176.20/176.55 apply zenon_H14. apply refl_equal. % 176.20/176.55 apply zenon_H14. apply refl_equal. % 176.20/176.55 apply zenon_H63. zenon_intro zenon_H59. % 176.20/176.55 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 176.20/176.55 generalize (zenon_H15 zenon_TX_cz). zenon_intro zenon_H66. % 176.20/176.55 generalize (zenon_H66 zenon_TY_dp). zenon_intro zenon_H67. % 176.20/176.55 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H4b | zenon_intro zenon_H68 ]. % 176.20/176.55 exact (zenon_H4b zenon_H59). % 176.20/176.55 apply (zenon_imply_s _ _ zenon_H68); [ zenon_intro zenon_H6a | zenon_intro zenon_H69 ]. % 176.20/176.55 exact (zenon_H6a zenon_H5c). % 176.20/176.55 exact (zenon_H5b zenon_H69). % 176.20/176.55 apply zenon_H61. apply refl_equal. % 176.20/176.55 (* end of lemma zenon_L6_ *) % 176.20/176.55 assert (zenon_L7_ : forall (zenon_TX_ef : zenon_U) (zenon_TY_dp : zenon_U) (zenon_TX_j : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_bt : zenon_U) (zenon_TY_bd : zenon_U) (zenon_TX_cz : zenon_U) (zenon_TY_cj : zenon_U), (r1 zenon_TY_cj zenon_TX_cz) -> (r1 zenon_TY_bd zenon_TX_bt) -> (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TX_h zenon_TY_bd) -> (r1 zenon_TX_bt zenon_TY_cj) -> (r1 zenon_TX_cz zenon_TY_dp) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TX_ef)) -> (r1 zenon_TY_dp zenon_TX_ef) -> False). % 176.20/176.55 do 9 intro. intros zenon_H4c zenon_H2c zenon_H6 zenon_H3 zenon_H1c zenon_H3c zenon_H5c zenon_H4 zenon_H6b zenon_H6c. % 176.20/176.55 elim (classic ((~(zenon_TX_j = zenon_TY_dp))/\(~(r1 zenon_TX_j zenon_TY_dp)))); [ zenon_intro zenon_H6e | zenon_intro zenon_H6f ]. % 176.20/176.55 apply (zenon_and_s _ _ zenon_H6e). zenon_intro zenon_H70. zenon_intro zenon_H5b. % 176.20/176.55 apply (zenon_L6_ zenon_TY_dp zenon_TX_cz zenon_TY_i zenon_TX_j zenon_TY_bd zenon_TX_h zenon_TY_cj zenon_TX_bt); trivial. % 176.20/176.55 cut ((r1 zenon_TY_dp zenon_TX_ef) = (r1 zenon_TX_j zenon_TX_ef)). % 176.20/176.55 intro zenon_D_pnotp. % 176.20/176.55 apply zenon_H6b. % 176.20/176.55 rewrite <- zenon_D_pnotp. % 176.20/176.55 exact zenon_H6c. % 176.20/176.55 cut ((zenon_TX_ef = zenon_TX_ef)); [idtac | apply NNPP; zenon_intro zenon_H71]. % 176.20/176.55 cut ((zenon_TY_dp = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H72]. % 176.20/176.55 congruence. % 176.20/176.55 apply (zenon_notand_s _ _ zenon_H6f); [ zenon_intro zenon_H74 | zenon_intro zenon_H73 ]. % 176.20/176.55 apply zenon_H74. zenon_intro zenon_H75. % 176.20/176.55 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_dp = zenon_TX_j)). % 176.20/176.55 intro zenon_D_pnotp. % 176.20/176.55 apply zenon_H72. % 176.20/176.55 rewrite <- zenon_D_pnotp. % 176.20/176.55 exact zenon_H13. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 176.20/176.55 cut ((zenon_TX_j = zenon_TY_dp)); [idtac | apply NNPP; zenon_intro zenon_H70]. % 176.20/176.55 congruence. % 176.20/176.55 exact (zenon_H70 zenon_H75). % 176.20/176.55 apply zenon_H14. apply refl_equal. % 176.20/176.55 apply zenon_H14. apply refl_equal. % 176.20/176.55 apply zenon_H73. zenon_intro zenon_H69. % 176.20/176.55 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 176.20/176.55 generalize (zenon_H15 zenon_TY_dp). zenon_intro zenon_H76. % 176.20/176.55 generalize (zenon_H76 zenon_TX_ef). zenon_intro zenon_H77. % 176.20/176.55 apply (zenon_imply_s _ _ zenon_H77); [ zenon_intro zenon_H5b | zenon_intro zenon_H78 ]. % 176.20/176.55 exact (zenon_H5b zenon_H69). % 176.20/176.55 apply (zenon_imply_s _ _ zenon_H78); [ zenon_intro zenon_H7a | zenon_intro zenon_H79 ]. % 176.20/176.55 exact (zenon_H7a zenon_H6c). % 176.20/176.55 exact (zenon_H6b zenon_H79). % 176.20/176.55 apply zenon_H71. apply refl_equal. % 176.20/176.55 (* end of lemma zenon_L7_ *) % 176.20/176.55 assert (zenon_L8_ : forall (zenon_TY_ev : zenon_U) (zenon_TX_ef : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_j : zenon_U) (zenon_TY_bd : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TX_bt : zenon_U) (zenon_TY_dp : zenon_U) (zenon_TX_cz : zenon_U), (r1 zenon_TX_cz zenon_TY_dp) -> (r1 zenon_TX_bt zenon_TY_cj) -> (r1 zenon_TX_h zenon_TY_bd) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TY_bd zenon_TX_bt) -> (r1 zenon_TY_cj zenon_TX_cz) -> (r1 zenon_TY_dp zenon_TX_ef) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TY_ev)) -> (r1 zenon_TX_ef zenon_TY_ev) -> False). % 176.20/176.55 do 10 intro. intros zenon_H5c zenon_H3c zenon_H1c zenon_H3 zenon_H6 zenon_H2c zenon_H4c zenon_H6c zenon_H4 zenon_H7b zenon_H7c. % 176.20/176.55 elim (classic ((~(zenon_TX_j = zenon_TX_ef))/\(~(r1 zenon_TX_j zenon_TX_ef)))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ]. % 176.20/176.55 apply (zenon_and_s _ _ zenon_H7e). zenon_intro zenon_H80. zenon_intro zenon_H6b. % 176.20/176.55 apply (zenon_L7_ zenon_TX_ef zenon_TY_dp zenon_TX_j zenon_TX_h zenon_TY_i zenon_TX_bt zenon_TY_bd zenon_TX_cz zenon_TY_cj); trivial. % 176.20/176.55 cut ((r1 zenon_TX_ef zenon_TY_ev) = (r1 zenon_TX_j zenon_TY_ev)). % 176.20/176.55 intro zenon_D_pnotp. % 176.20/176.55 apply zenon_H7b. % 176.20/176.55 rewrite <- zenon_D_pnotp. % 176.20/176.55 exact zenon_H7c. % 176.20/176.55 cut ((zenon_TY_ev = zenon_TY_ev)); [idtac | apply NNPP; zenon_intro zenon_H81]. % 176.20/176.55 cut ((zenon_TX_ef = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H82]. % 176.20/176.55 congruence. % 176.20/176.55 apply (zenon_notand_s _ _ zenon_H7f); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ]. % 176.20/176.55 apply zenon_H84. zenon_intro zenon_H85. % 176.20/176.55 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_ef = zenon_TX_j)). % 176.20/176.55 intro zenon_D_pnotp. % 176.20/176.55 apply zenon_H82. % 176.20/176.55 rewrite <- zenon_D_pnotp. % 176.20/176.55 exact zenon_H13. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 176.20/176.55 cut ((zenon_TX_j = zenon_TX_ef)); [idtac | apply NNPP; zenon_intro zenon_H80]. % 176.20/176.55 congruence. % 176.20/176.55 exact (zenon_H80 zenon_H85). % 176.20/176.55 apply zenon_H14. apply refl_equal. % 176.20/176.55 apply zenon_H14. apply refl_equal. % 176.20/176.55 apply zenon_H83. zenon_intro zenon_H79. % 176.20/176.55 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 176.20/176.56 generalize (zenon_H15 zenon_TX_ef). zenon_intro zenon_H86. % 176.20/176.56 generalize (zenon_H86 zenon_TY_ev). zenon_intro zenon_H87. % 176.20/176.56 apply (zenon_imply_s _ _ zenon_H87); [ zenon_intro zenon_H6b | zenon_intro zenon_H88 ]. % 176.20/176.56 exact (zenon_H6b zenon_H79). % 176.20/176.56 apply (zenon_imply_s _ _ zenon_H88); [ zenon_intro zenon_H8a | zenon_intro zenon_H89 ]. % 176.20/176.56 exact (zenon_H8a zenon_H7c). % 176.20/176.56 exact (zenon_H7b zenon_H89). % 176.20/176.56 apply zenon_H81. apply refl_equal. % 176.20/176.56 (* end of lemma zenon_L8_ *) % 176.20/176.56 assert (zenon_L9_ : forall (zenon_TX_fl : zenon_U) (zenon_TY_ev : zenon_U) (zenon_TX_j : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_bt : zenon_U) (zenon_TY_bd : zenon_U) (zenon_TX_cz : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TX_ef : zenon_U) (zenon_TY_dp : zenon_U), (r1 zenon_TY_dp zenon_TX_ef) -> (r1 zenon_TY_cj zenon_TX_cz) -> (r1 zenon_TY_bd zenon_TX_bt) -> (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TX_h zenon_TY_bd) -> (r1 zenon_TX_bt zenon_TY_cj) -> (r1 zenon_TX_cz zenon_TY_dp) -> (r1 zenon_TX_ef zenon_TY_ev) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TX_fl)) -> (r1 zenon_TY_ev zenon_TX_fl) -> False). % 176.20/176.56 do 11 intro. intros zenon_H6c zenon_H4c zenon_H2c zenon_H6 zenon_H3 zenon_H1c zenon_H3c zenon_H5c zenon_H7c zenon_H4 zenon_H8b zenon_H8c. % 176.20/176.56 elim (classic ((~(zenon_TX_j = zenon_TY_ev))/\(~(r1 zenon_TX_j zenon_TY_ev)))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ]. % 176.20/176.56 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H90. zenon_intro zenon_H7b. % 176.20/176.56 apply (zenon_L8_ zenon_TY_ev zenon_TX_ef zenon_TY_i zenon_TX_j zenon_TY_bd zenon_TX_h zenon_TY_cj zenon_TX_bt zenon_TY_dp zenon_TX_cz); trivial. % 176.20/176.56 cut ((r1 zenon_TY_ev zenon_TX_fl) = (r1 zenon_TX_j zenon_TX_fl)). % 176.20/176.56 intro zenon_D_pnotp. % 176.20/176.56 apply zenon_H8b. % 176.20/176.56 rewrite <- zenon_D_pnotp. % 176.20/176.56 exact zenon_H8c. % 176.20/176.56 cut ((zenon_TX_fl = zenon_TX_fl)); [idtac | apply NNPP; zenon_intro zenon_H91]. % 176.20/176.56 cut ((zenon_TY_ev = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H92]. % 176.20/176.56 congruence. % 176.20/176.56 apply (zenon_notand_s _ _ zenon_H8f); [ zenon_intro zenon_H94 | zenon_intro zenon_H93 ]. % 176.20/176.56 apply zenon_H94. zenon_intro zenon_H95. % 176.20/176.56 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 176.20/176.56 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_ev = zenon_TX_j)). % 176.20/176.56 intro zenon_D_pnotp. % 176.20/176.56 apply zenon_H92. % 176.20/176.56 rewrite <- zenon_D_pnotp. % 176.20/176.56 exact zenon_H13. % 176.20/176.56 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 176.20/176.56 cut ((zenon_TX_j = zenon_TY_ev)); [idtac | apply NNPP; zenon_intro zenon_H90]. % 176.20/176.56 congruence. % 176.20/176.56 exact (zenon_H90 zenon_H95). % 176.20/176.56 apply zenon_H14. apply refl_equal. % 176.20/176.56 apply zenon_H14. apply refl_equal. % 176.20/176.56 apply zenon_H93. zenon_intro zenon_H89. % 176.20/176.56 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 176.20/176.56 generalize (zenon_H15 zenon_TY_ev). zenon_intro zenon_H96. % 176.20/176.56 generalize (zenon_H96 zenon_TX_fl). zenon_intro zenon_H97. % 176.20/176.56 apply (zenon_imply_s _ _ zenon_H97); [ zenon_intro zenon_H7b | zenon_intro zenon_H98 ]. % 176.20/176.56 exact (zenon_H7b zenon_H89). % 176.20/176.56 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H9a | zenon_intro zenon_H99 ]. % 176.20/176.56 exact (zenon_H9a zenon_H8c). % 176.20/176.56 exact (zenon_H8b zenon_H99). % 176.20/176.56 apply zenon_H91. apply refl_equal. % 176.20/176.56 (* end of lemma zenon_L9_ *) % 176.20/176.56 assert (zenon_L10_ : forall (zenon_TY_gb : zenon_U) (zenon_TX_fl : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_j : zenon_U) (zenon_TY_bd : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TX_bt : zenon_U) (zenon_TY_dp : zenon_U) (zenon_TX_cz : zenon_U) (zenon_TY_ev : zenon_U) (zenon_TX_ef : zenon_U), (r1 zenon_TX_ef zenon_TY_ev) -> (r1 zenon_TX_cz zenon_TY_dp) -> (r1 zenon_TX_bt zenon_TY_cj) -> (r1 zenon_TX_h zenon_TY_bd) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TY_bd zenon_TX_bt) -> (r1 zenon_TY_cj zenon_TX_cz) -> (r1 zenon_TY_dp zenon_TX_ef) -> (r1 zenon_TY_ev zenon_TX_fl) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TY_gb)) -> (r1 zenon_TX_fl zenon_TY_gb) -> False). % 176.20/176.56 do 12 intro. intros zenon_H7c zenon_H5c zenon_H3c zenon_H1c zenon_H3 zenon_H6 zenon_H2c zenon_H4c zenon_H6c zenon_H8c zenon_H4 zenon_H9b zenon_H9c. % 176.20/176.56 elim (classic ((~(zenon_TX_j = zenon_TX_fl))/\(~(r1 zenon_TX_j zenon_TX_fl)))); [ zenon_intro zenon_H9e | zenon_intro zenon_H9f ]. % 176.20/176.56 apply (zenon_and_s _ _ zenon_H9e). zenon_intro zenon_Ha0. zenon_intro zenon_H8b. % 176.20/176.56 apply (zenon_L9_ zenon_TX_fl zenon_TY_ev zenon_TX_j zenon_TX_h zenon_TY_i zenon_TX_bt zenon_TY_bd zenon_TX_cz zenon_TY_cj zenon_TX_ef zenon_TY_dp); trivial. % 176.20/176.56 cut ((r1 zenon_TX_fl zenon_TY_gb) = (r1 zenon_TX_j zenon_TY_gb)). % 176.20/176.56 intro zenon_D_pnotp. % 176.20/176.56 apply zenon_H9b. % 176.20/176.56 rewrite <- zenon_D_pnotp. % 176.20/176.56 exact zenon_H9c. % 176.20/176.56 cut ((zenon_TY_gb = zenon_TY_gb)); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 176.20/176.56 cut ((zenon_TX_fl = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 176.20/176.56 congruence. % 176.20/176.56 apply (zenon_notand_s _ _ zenon_H9f); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Ha3 ]. % 176.20/176.56 apply zenon_Ha4. zenon_intro zenon_Ha5. % 176.20/176.56 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 176.20/176.56 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_fl = zenon_TX_j)). % 176.20/176.56 intro zenon_D_pnotp. % 176.20/176.56 apply zenon_Ha2. % 176.20/176.56 rewrite <- zenon_D_pnotp. % 176.20/176.56 exact zenon_H13. % 176.20/176.56 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 176.20/176.56 cut ((zenon_TX_j = zenon_TX_fl)); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 176.20/176.56 congruence. % 176.20/176.56 exact (zenon_Ha0 zenon_Ha5). % 176.20/176.56 apply zenon_H14. apply refl_equal. % 176.20/176.56 apply zenon_H14. apply refl_equal. % 176.20/176.56 apply zenon_Ha3. zenon_intro zenon_H99. % 176.20/176.56 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 176.20/176.56 generalize (zenon_H15 zenon_TX_fl). zenon_intro zenon_Ha6. % 176.20/176.56 generalize (zenon_Ha6 zenon_TY_gb). zenon_intro zenon_Ha7. % 176.20/176.56 apply (zenon_imply_s _ _ zenon_Ha7); [ zenon_intro zenon_H8b | zenon_intro zenon_Ha8 ]. % 176.20/176.56 exact (zenon_H8b zenon_H99). % 176.20/176.56 apply (zenon_imply_s _ _ zenon_Ha8); [ zenon_intro zenon_Haa | zenon_intro zenon_Ha9 ]. % 176.20/176.56 exact (zenon_Haa zenon_H9c). % 176.20/176.56 exact (zenon_H9b zenon_Ha9). % 176.20/176.56 apply zenon_Ha1. apply refl_equal. % 176.20/176.56 (* end of lemma zenon_L10_ *) % 176.20/176.56 assert (zenon_L11_ : forall (zenon_TX_gr : zenon_U) (zenon_TY_gb : zenon_U) (zenon_TX_j : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_bt : zenon_U) (zenon_TY_bd : zenon_U) (zenon_TX_cz : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TX_ef : zenon_U) (zenon_TY_dp : zenon_U) (zenon_TX_fl : zenon_U) (zenon_TY_ev : zenon_U), (r1 zenon_TY_ev zenon_TX_fl) -> (r1 zenon_TY_dp zenon_TX_ef) -> (r1 zenon_TY_cj zenon_TX_cz) -> (r1 zenon_TY_bd zenon_TX_bt) -> (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TX_h zenon_TY_bd) -> (r1 zenon_TX_bt zenon_TY_cj) -> (r1 zenon_TX_cz zenon_TY_dp) -> (r1 zenon_TX_ef zenon_TY_ev) -> (r1 zenon_TX_fl zenon_TY_gb) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TX_gr)) -> (r1 zenon_TY_gb zenon_TX_gr) -> False). % 176.20/176.56 do 13 intro. intros zenon_H8c zenon_H6c zenon_H4c zenon_H2c zenon_H6 zenon_H3 zenon_H1c zenon_H3c zenon_H5c zenon_H7c zenon_H9c zenon_H4 zenon_Hab zenon_Hac. % 176.20/176.56 elim (classic ((~(zenon_TX_j = zenon_TY_gb))/\(~(r1 zenon_TX_j zenon_TY_gb)))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 176.20/176.56 apply (zenon_and_s _ _ zenon_Hae). zenon_intro zenon_Hb0. zenon_intro zenon_H9b. % 176.20/176.56 apply (zenon_L10_ zenon_TY_gb zenon_TX_fl zenon_TY_i zenon_TX_j zenon_TY_bd zenon_TX_h zenon_TY_cj zenon_TX_bt zenon_TY_dp zenon_TX_cz zenon_TY_ev zenon_TX_ef); trivial. % 176.20/176.56 cut ((r1 zenon_TY_gb zenon_TX_gr) = (r1 zenon_TX_j zenon_TX_gr)). % 176.20/176.56 intro zenon_D_pnotp. % 176.20/176.56 apply zenon_Hab. % 176.20/176.56 rewrite <- zenon_D_pnotp. % 176.20/176.56 exact zenon_Hac. % 176.20/176.56 cut ((zenon_TX_gr = zenon_TX_gr)); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 176.20/176.56 cut ((zenon_TY_gb = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 176.20/176.56 congruence. % 176.20/176.56 apply (zenon_notand_s _ _ zenon_Haf); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ]. % 176.20/176.56 apply zenon_Hb4. zenon_intro zenon_Hb5. % 176.20/176.56 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 176.20/176.56 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_gb = zenon_TX_j)). % 176.20/176.56 intro zenon_D_pnotp. % 176.20/176.56 apply zenon_Hb2. % 176.20/176.56 rewrite <- zenon_D_pnotp. % 176.20/176.56 exact zenon_H13. % 176.20/176.56 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 176.20/176.56 cut ((zenon_TX_j = zenon_TY_gb)); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 176.20/176.56 congruence. % 176.20/176.56 exact (zenon_Hb0 zenon_Hb5). % 176.20/176.56 apply zenon_H14. apply refl_equal. % 176.20/176.56 apply zenon_H14. apply refl_equal. % 176.20/176.56 apply zenon_Hb3. zenon_intro zenon_Ha9. % 176.20/176.56 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 176.20/176.56 generalize (zenon_H15 zenon_TY_gb). zenon_intro zenon_Hb6. % 176.20/176.56 generalize (zenon_Hb6 zenon_TX_gr). zenon_intro zenon_Hb7. % 176.20/176.56 apply (zenon_imply_s _ _ zenon_Hb7); [ zenon_intro zenon_H9b | zenon_intro zenon_Hb8 ]. % 176.20/176.56 exact (zenon_H9b zenon_Ha9). % 176.20/176.56 apply (zenon_imply_s _ _ zenon_Hb8); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 176.20/176.56 exact (zenon_Hba zenon_Hac). % 176.20/176.56 exact (zenon_Hab zenon_Hb9). % 176.20/176.56 apply zenon_Hb1. apply refl_equal. % 176.20/176.56 (* end of lemma zenon_L11_ *) % 176.20/176.56 assert (zenon_L12_ : forall (zenon_TY_hh : zenon_U) (zenon_TX_gr : zenon_U) (zenon_TY_i : zenon_U) (zenon_TX_j : zenon_U) (zenon_TY_bd : zenon_U) (zenon_TX_h : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TX_bt : zenon_U) (zenon_TY_dp : zenon_U) (zenon_TX_cz : zenon_U) (zenon_TY_ev : zenon_U) (zenon_TX_ef : zenon_U) (zenon_TY_gb : zenon_U) (zenon_TX_fl : zenon_U), (r1 zenon_TX_fl zenon_TY_gb) -> (r1 zenon_TX_ef zenon_TY_ev) -> (r1 zenon_TX_cz zenon_TY_dp) -> (r1 zenon_TX_bt zenon_TY_cj) -> (r1 zenon_TX_h zenon_TY_bd) -> (r1 zenon_TX_j zenon_TY_i) -> (r1 zenon_TY_i zenon_TX_h) -> (r1 zenon_TY_bd zenon_TX_bt) -> (r1 zenon_TY_cj zenon_TX_cz) -> (r1 zenon_TY_dp zenon_TX_ef) -> (r1 zenon_TY_ev zenon_TX_fl) -> (r1 zenon_TY_gb zenon_TX_gr) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TY_hh)) -> (r1 zenon_TX_gr zenon_TY_hh) -> False). % 176.20/176.56 do 14 intro. intros zenon_H9c zenon_H7c zenon_H5c zenon_H3c zenon_H1c zenon_H3 zenon_H6 zenon_H2c zenon_H4c zenon_H6c zenon_H8c zenon_Hac zenon_H4 zenon_Hbb zenon_Hbc. % 176.20/176.56 elim (classic ((~(zenon_TX_j = zenon_TX_gr))/\(~(r1 zenon_TX_j zenon_TX_gr)))); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hbf ]. % 176.20/176.56 apply (zenon_and_s _ _ zenon_Hbe). zenon_intro zenon_Hc0. zenon_intro zenon_Hab. % 176.20/176.56 apply (zenon_L11_ zenon_TX_gr zenon_TY_gb zenon_TX_j zenon_TX_h zenon_TY_i zenon_TX_bt zenon_TY_bd zenon_TX_cz zenon_TY_cj zenon_TX_ef zenon_TY_dp zenon_TX_fl zenon_TY_ev); trivial. % 176.20/176.56 cut ((r1 zenon_TX_gr zenon_TY_hh) = (r1 zenon_TX_j zenon_TY_hh)). % 176.20/176.56 intro zenon_D_pnotp. % 176.20/176.56 apply zenon_Hbb. % 176.20/176.56 rewrite <- zenon_D_pnotp. % 176.20/176.56 exact zenon_Hbc. % 176.20/176.56 cut ((zenon_TY_hh = zenon_TY_hh)); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 176.20/176.56 cut ((zenon_TX_gr = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_Hc2]. % 176.20/176.56 congruence. % 176.20/176.56 apply (zenon_notand_s _ _ zenon_Hbf); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 176.20/176.56 apply zenon_Hc4. zenon_intro zenon_Hc5. % 176.20/176.56 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 176.20/176.56 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_gr = zenon_TX_j)). % 176.20/176.56 intro zenon_D_pnotp. % 176.20/176.56 apply zenon_Hc2. % 176.20/176.56 rewrite <- zenon_D_pnotp. % 176.20/176.56 exact zenon_H13. % 176.20/176.56 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 176.20/176.56 cut ((zenon_TX_j = zenon_TX_gr)); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 176.20/176.56 congruence. % 176.20/176.56 exact (zenon_Hc0 zenon_Hc5). % 176.20/176.56 apply zenon_H14. apply refl_equal. % 176.20/176.56 apply zenon_H14. apply refl_equal. % 176.20/176.56 apply zenon_Hc3. zenon_intro zenon_Hb9. % 176.20/176.56 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 176.20/176.56 generalize (zenon_H15 zenon_TX_gr). zenon_intro zenon_Hc6. % 176.20/176.56 generalize (zenon_Hc6 zenon_TY_hh). zenon_intro zenon_Hc7. % 176.20/176.56 apply (zenon_imply_s _ _ zenon_Hc7); [ zenon_intro zenon_Hab | zenon_intro zenon_Hc8 ]. % 176.20/176.56 exact (zenon_Hab zenon_Hb9). % 176.20/176.56 apply (zenon_imply_s _ _ zenon_Hc8); [ zenon_intro zenon_Hca | zenon_intro zenon_Hc9 ]. % 176.20/176.56 exact (zenon_Hca zenon_Hbc). % 176.20/176.56 exact (zenon_Hbb zenon_Hc9). % 176.20/176.56 apply zenon_Hc1. apply refl_equal. % 176.20/176.56 (* end of lemma zenon_L12_ *) % 176.20/176.56 apply NNPP. intro zenon_G. % 176.20/176.56 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z))))))); [ zenon_intro zenon_H4 | zenon_intro zenon_Hcb ]. % 176.20/176.56 apply zenon_G. zenon_intro zenon_Hcc. % 176.20/176.56 elim zenon_Hcc. zenon_intro zenon_TX_j. zenon_intro zenon_Hcd. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hcd). zenon_intro zenon_Hcf. zenon_intro zenon_Hce. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hce). zenon_intro zenon_Hd1. zenon_intro zenon_Hd0. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hd0). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hd2). zenon_intro zenon_Hd5. zenon_intro zenon_Hd4. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hd4). zenon_intro zenon_Hd7. zenon_intro zenon_Hd6. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hd6). zenon_intro zenon_Hd9. zenon_intro zenon_Hd8. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hd8). zenon_intro zenon_Hdb. zenon_intro zenon_Hda. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hda). zenon_intro zenon_Hdd. zenon_intro zenon_Hdc. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hdc). zenon_intro zenon_Hdf. zenon_intro zenon_Hde. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hde). zenon_intro zenon_He1. zenon_intro zenon_He0. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_He0). zenon_intro zenon_He3. zenon_intro zenon_He2. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_He2). zenon_intro zenon_Hd7. zenon_intro zenon_He4. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_He4). zenon_intro zenon_Hd9. zenon_intro zenon_He5. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_He5). zenon_intro zenon_Hdb. zenon_intro zenon_He6. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_He6). zenon_intro zenon_He8. zenon_intro zenon_He7. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_He7). zenon_intro zenon_Hea. zenon_intro zenon_He9. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_He9). zenon_intro zenon_Hec. zenon_intro zenon_Heb. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Heb). zenon_intro zenon_Hee. zenon_intro zenon_Hed. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hed). zenon_intro zenon_Hd7. zenon_intro zenon_Hef. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hef). zenon_intro zenon_Hd9. zenon_intro zenon_Hf0. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hf0). zenon_intro zenon_Hdb. zenon_intro zenon_Hf1. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hf1). zenon_intro zenon_Hf3. zenon_intro zenon_Hf2. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hf2). zenon_intro zenon_Hf5. zenon_intro zenon_Hf4. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hf4). zenon_intro zenon_Hf7. zenon_intro zenon_Hf6. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hf6). zenon_intro zenon_Hf9. zenon_intro zenon_Hf8. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hf8). zenon_intro zenon_Hd7. zenon_intro zenon_Hfa. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hfa). zenon_intro zenon_Hd9. zenon_intro zenon_Hfb. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hfb). zenon_intro zenon_Hdb. zenon_intro zenon_Hfc. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hfc). zenon_intro zenon_Hfe. zenon_intro zenon_Hfd. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hfd). zenon_intro zenon_H100. zenon_intro zenon_Hff. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_Hff). zenon_intro zenon_H102. zenon_intro zenon_H101. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H101). zenon_intro zenon_H104. zenon_intro zenon_H103. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H103). zenon_intro zenon_Hd7. zenon_intro zenon_H105. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H105). zenon_intro zenon_Hd9. zenon_intro zenon_H106. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H106). zenon_intro zenon_Hdb. zenon_intro zenon_H107. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H107). zenon_intro zenon_H109. zenon_intro zenon_H108. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H108). zenon_intro zenon_H10b. zenon_intro zenon_H10a. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H10a). zenon_intro zenon_H10d. zenon_intro zenon_H10c. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H10c). zenon_intro zenon_H10f. zenon_intro zenon_H10e. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H10e). zenon_intro zenon_Hd7. zenon_intro zenon_H110. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H110). zenon_intro zenon_Hd9. zenon_intro zenon_H111. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H111). zenon_intro zenon_Hdb. zenon_intro zenon_H112. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H112). zenon_intro zenon_H114. zenon_intro zenon_H113. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H113). zenon_intro zenon_H116. zenon_intro zenon_H115. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H115). zenon_intro zenon_H118. zenon_intro zenon_H117. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H117). zenon_intro zenon_H11a. zenon_intro zenon_H119. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H119). zenon_intro zenon_Hd7. zenon_intro zenon_H11b. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H11b). zenon_intro zenon_Hd9. zenon_intro zenon_H11c. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H11c). zenon_intro zenon_Hdb. zenon_intro zenon_H11d. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H11d). zenon_intro zenon_H11f. zenon_intro zenon_H11e. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H11e). zenon_intro zenon_H121. zenon_intro zenon_H120. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H120). zenon_intro zenon_H123. zenon_intro zenon_H122. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H122). zenon_intro zenon_H125. zenon_intro zenon_H124. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H124). zenon_intro zenon_Hd7. zenon_intro zenon_H126. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H126). zenon_intro zenon_Hd9. zenon_intro zenon_H127. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H127). zenon_intro zenon_Hdb. zenon_intro zenon_H128. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H128). zenon_intro zenon_H12a. zenon_intro zenon_H129. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H129). zenon_intro zenon_H12c. zenon_intro zenon_H12b. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H12b). zenon_intro zenon_H12e. zenon_intro zenon_H12d. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H12d). zenon_intro zenon_H130. zenon_intro zenon_H12f. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H12f). zenon_intro zenon_Hd7. zenon_intro zenon_H131. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H131). zenon_intro zenon_Hd9. zenon_intro zenon_H132. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H132). zenon_intro zenon_Hdb. zenon_intro zenon_H133. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H133). zenon_intro zenon_H135. zenon_intro zenon_H134. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H134). zenon_intro zenon_H137. zenon_intro zenon_H136. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H136). zenon_intro zenon_H139. zenon_intro zenon_H138. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H138). zenon_intro zenon_H13b. zenon_intro zenon_H13a. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H13a). zenon_intro zenon_Hd7. zenon_intro zenon_H13c. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H13c). zenon_intro zenon_Hd9. zenon_intro zenon_H13d. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H13d). zenon_intro zenon_Hdb. zenon_intro zenon_H13e. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H13e). zenon_intro zenon_H140. zenon_intro zenon_H13f. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H13f). zenon_intro zenon_H142. zenon_intro zenon_H141. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H141). zenon_intro zenon_H144. zenon_intro zenon_H143. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H143). zenon_intro zenon_H146. zenon_intro zenon_H145. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H145). zenon_intro zenon_Hd7. zenon_intro zenon_H147. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H147). zenon_intro zenon_Hd9. zenon_intro zenon_H148. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H148). zenon_intro zenon_Hdb. zenon_intro zenon_H149. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H149). zenon_intro zenon_H14b. zenon_intro zenon_H14a. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H14a). zenon_intro zenon_H14d. zenon_intro zenon_H14c. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H14c). zenon_intro zenon_H14f. zenon_intro zenon_H14e. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H14e). zenon_intro zenon_H151. zenon_intro zenon_H150. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H150). zenon_intro zenon_Hd7. zenon_intro zenon_H152. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H152). zenon_intro zenon_Hd9. zenon_intro zenon_H153. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H153). zenon_intro zenon_Hdb. zenon_intro zenon_H154. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H154). zenon_intro zenon_H156. zenon_intro zenon_H155. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H155). zenon_intro zenon_H158. zenon_intro zenon_H157. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H157). zenon_intro zenon_H15a. zenon_intro zenon_H159. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H159). zenon_intro zenon_H15c. zenon_intro zenon_H15b. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H15b). zenon_intro zenon_Hd7. zenon_intro zenon_H15d. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H15d). zenon_intro zenon_Hd9. zenon_intro zenon_H15e. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H15e). zenon_intro zenon_Hdb. zenon_intro zenon_H15f. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H15f). zenon_intro zenon_H161. zenon_intro zenon_H160. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H160). zenon_intro zenon_H163. zenon_intro zenon_H162. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H162). zenon_intro zenon_H165. zenon_intro zenon_H164. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H164). zenon_intro zenon_H167. zenon_intro zenon_H166. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H166). zenon_intro zenon_Hd7. zenon_intro zenon_H168. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H168). zenon_intro zenon_Hd9. zenon_intro zenon_H169. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H169). zenon_intro zenon_Hdb. zenon_intro zenon_H16a. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H16a). zenon_intro zenon_H16c. zenon_intro zenon_H16b. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H16b). zenon_intro zenon_H16e. zenon_intro zenon_H16d. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H16d). zenon_intro zenon_H170. zenon_intro zenon_H16f. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H16f). zenon_intro zenon_H172. zenon_intro zenon_H171. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H171). zenon_intro zenon_Hd7. zenon_intro zenon_H173. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H173). zenon_intro zenon_Hd9. zenon_intro zenon_Hdb. % 176.20/176.56 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_j Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_Hd9); [ zenon_intro zenon_H174; idtac ]. % 176.20/176.56 elim zenon_H174. zenon_intro zenon_TY_i. zenon_intro zenon_H175. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H175). zenon_intro zenon_H10. zenon_intro zenon_H176. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H176). zenon_intro zenon_H178. zenon_intro zenon_H177. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H177). zenon_intro zenon_H17a. zenon_intro zenon_H179. % 176.20/176.56 apply zenon_H10. zenon_intro zenon_H3. % 176.20/176.56 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_i X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_H17a); [ zenon_intro zenon_H17b; idtac ]. % 176.20/176.56 elim zenon_H17b. zenon_intro zenon_TX_h. zenon_intro zenon_H17c. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H17c). zenon_intro zenon_H17e. zenon_intro zenon_H17d. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H17d). zenon_intro zenon_H180. zenon_intro zenon_H17f. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H17f). zenon_intro zenon_H182. zenon_intro zenon_H181. % 176.20/176.56 apply zenon_H17e. zenon_intro zenon_H6. % 176.20/176.56 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_h Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H182); [ zenon_intro zenon_H183; idtac ]. % 176.20/176.56 elim zenon_H183. zenon_intro zenon_TY_bd. zenon_intro zenon_H184. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H184). zenon_intro zenon_H186. zenon_intro zenon_H185. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H185). zenon_intro zenon_H188. zenon_intro zenon_H187. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H187). zenon_intro zenon_H18a. zenon_intro zenon_H189. % 176.20/176.56 apply zenon_H186. zenon_intro zenon_H1c. % 176.20/176.56 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_bd X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_H18a); [ zenon_intro zenon_H18b; idtac ]. % 176.20/176.56 elim zenon_H18b. zenon_intro zenon_TX_bt. zenon_intro zenon_H18c. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H18c). zenon_intro zenon_H18e. zenon_intro zenon_H18d. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H18d). zenon_intro zenon_H190. zenon_intro zenon_H18f. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H18f). zenon_intro zenon_H192. zenon_intro zenon_H191. % 176.20/176.56 apply zenon_H18e. zenon_intro zenon_H2c. % 176.20/176.56 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_bt Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H192); [ zenon_intro zenon_H193; idtac ]. % 176.20/176.56 elim zenon_H193. zenon_intro zenon_TY_cj. zenon_intro zenon_H194. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H194). zenon_intro zenon_H196. zenon_intro zenon_H195. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H195). zenon_intro zenon_H198. zenon_intro zenon_H197. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H197). zenon_intro zenon_H19a. zenon_intro zenon_H199. % 176.20/176.56 apply zenon_H196. zenon_intro zenon_H3c. % 176.20/176.56 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_cj X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_H19a); [ zenon_intro zenon_H19b; idtac ]. % 176.20/176.56 elim zenon_H19b. zenon_intro zenon_TX_cz. zenon_intro zenon_H19c. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H19c). zenon_intro zenon_H19e. zenon_intro zenon_H19d. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H19d). zenon_intro zenon_H1a0. zenon_intro zenon_H19f. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H19f). zenon_intro zenon_H1a2. zenon_intro zenon_H1a1. % 176.20/176.56 apply zenon_H19e. zenon_intro zenon_H4c. % 176.20/176.56 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_cz Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H1a2); [ zenon_intro zenon_H1a3; idtac ]. % 176.20/176.56 elim zenon_H1a3. zenon_intro zenon_TY_dp. zenon_intro zenon_H1a4. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1a4). zenon_intro zenon_H1a6. zenon_intro zenon_H1a5. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1a5). zenon_intro zenon_H1a8. zenon_intro zenon_H1a7. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1a7). zenon_intro zenon_H1aa. zenon_intro zenon_H1a9. % 176.20/176.56 apply zenon_H1a6. zenon_intro zenon_H5c. % 176.20/176.56 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_dp X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_H1aa); [ zenon_intro zenon_H1ab; idtac ]. % 176.20/176.56 elim zenon_H1ab. zenon_intro zenon_TX_ef. zenon_intro zenon_H1ac. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1ac). zenon_intro zenon_H1ae. zenon_intro zenon_H1ad. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1ad). zenon_intro zenon_H1b0. zenon_intro zenon_H1af. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1af). zenon_intro zenon_H1b2. zenon_intro zenon_H1b1. % 176.20/176.56 apply zenon_H1ae. zenon_intro zenon_H6c. % 176.20/176.56 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_ef Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H1b2); [ zenon_intro zenon_H1b3; idtac ]. % 176.20/176.56 elim zenon_H1b3. zenon_intro zenon_TY_ev. zenon_intro zenon_H1b4. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1b4). zenon_intro zenon_H1b6. zenon_intro zenon_H1b5. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1b5). zenon_intro zenon_H1b8. zenon_intro zenon_H1b7. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1b7). zenon_intro zenon_H1ba. zenon_intro zenon_H1b9. % 176.20/176.56 apply zenon_H1b6. zenon_intro zenon_H7c. % 176.20/176.56 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_ev X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_H1ba); [ zenon_intro zenon_H1bb; idtac ]. % 176.20/176.56 elim zenon_H1bb. zenon_intro zenon_TX_fl. zenon_intro zenon_H1bc. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1bc). zenon_intro zenon_H1be. zenon_intro zenon_H1bd. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1bd). zenon_intro zenon_H1c0. zenon_intro zenon_H1bf. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1bf). zenon_intro zenon_H1c2. zenon_intro zenon_H1c1. % 176.20/176.56 apply zenon_H1be. zenon_intro zenon_H8c. % 176.20/176.56 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_fl Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H1c2); [ zenon_intro zenon_H1c3; idtac ]. % 176.20/176.56 elim zenon_H1c3. zenon_intro zenon_TY_gb. zenon_intro zenon_H1c4. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1c4). zenon_intro zenon_H1c6. zenon_intro zenon_H1c5. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1c5). zenon_intro zenon_H1c8. zenon_intro zenon_H1c7. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1c7). zenon_intro zenon_H1ca. zenon_intro zenon_H1c9. % 176.20/176.56 apply zenon_H1c6. zenon_intro zenon_H9c. % 176.20/176.56 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_gb X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_H1ca); [ zenon_intro zenon_H1cb; idtac ]. % 176.20/176.56 elim zenon_H1cb. zenon_intro zenon_TX_gr. zenon_intro zenon_H1cc. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1cc). zenon_intro zenon_H1ce. zenon_intro zenon_H1cd. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1cd). zenon_intro zenon_H1d0. zenon_intro zenon_H1cf. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1cf). zenon_intro zenon_H1d2. zenon_intro zenon_H1d1. % 176.20/176.56 apply zenon_H1ce. zenon_intro zenon_Hac. % 176.20/176.56 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_gr Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H1d2); [ zenon_intro zenon_H1d3; idtac ]. % 176.20/176.56 elim zenon_H1d3. zenon_intro zenon_TY_hh. zenon_intro zenon_H1d4. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1d4). zenon_intro zenon_H1d6. zenon_intro zenon_H1d5. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1d5). zenon_intro zenon_H1d8. zenon_intro zenon_H1d7. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1d7). zenon_intro zenon_H1da. zenon_intro zenon_H1d9. % 176.20/176.56 apply zenon_H1d6. zenon_intro zenon_Hbc. % 176.20/176.56 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_hh X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_H1da); [ zenon_intro zenon_H1db; idtac ]. % 176.20/176.56 elim zenon_H1db. zenon_intro zenon_TX_si. zenon_intro zenon_H1dd. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1dd). zenon_intro zenon_H1df. zenon_intro zenon_H1de. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1de). zenon_intro zenon_H1e1. zenon_intro zenon_H1e0. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1e0). zenon_intro zenon_H1e3. zenon_intro zenon_H1e2. % 176.20/176.56 apply zenon_H1df. zenon_intro zenon_H1e4. % 176.20/176.56 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_si Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))) zenon_H1e3); [ zenon_intro zenon_H1e5; idtac ]. % 176.20/176.56 elim zenon_H1e5. zenon_intro zenon_TY_ss. zenon_intro zenon_H1e7. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1e7). zenon_intro zenon_H1e9. zenon_intro zenon_H1e8. % 176.20/176.56 apply (zenon_notor_s _ _ zenon_H1e8). zenon_intro zenon_H1eb. zenon_intro zenon_H1ea. % 176.20/176.56 apply zenon_H1e9. zenon_intro zenon_H1ec. % 176.20/176.56 apply (zenon_notand_s _ _ zenon_H16e); [ zenon_intro zenon_H1ee | zenon_intro zenon_H1ed ]. % 176.20/176.56 exact (zenon_H1ee zenon_Hd7). % 176.20/176.56 apply (zenon_notand_s _ _ zenon_H1ed); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1ef ]. % 176.20/176.56 apply zenon_H1f0. zenon_intro zenon_H1f1. % 176.20/176.56 generalize (zenon_H1f1 zenon_TY_hh). zenon_intro zenon_H1f2. % 176.20/176.56 apply (zenon_or_s _ _ zenon_H1f2); [ zenon_intro zenon_Hbb | zenon_intro zenon_H1f3 ]. % 176.20/176.56 apply (zenon_L12_ zenon_TY_hh zenon_TX_gr zenon_TY_i zenon_TX_j zenon_TY_bd zenon_TX_h zenon_TY_cj zenon_TX_bt zenon_TY_dp zenon_TX_cz zenon_TY_ev zenon_TX_ef zenon_TY_gb zenon_TX_fl); trivial. % 176.20/176.56 generalize (zenon_H1f3 zenon_TY_ss). zenon_intro zenon_H1f4. % 176.20/176.56 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f6 | zenon_intro zenon_H1f5 ]. % 176.20/176.56 elim (classic ((~(zenon_TY_hh = zenon_TX_si))/\(~(r1 zenon_TY_hh zenon_TX_si)))); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H1f8 ]. % 176.20/176.56 apply (zenon_and_s _ _ zenon_H1f7). zenon_intro zenon_H1fa. zenon_intro zenon_H1f9. % 176.20/176.56 exact (zenon_H1f9 zenon_H1e4). % 176.20/176.56 cut ((r1 zenon_TX_si zenon_TY_ss) = (r1 zenon_TY_hh zenon_TY_ss)). % 176.20/176.56 intro zenon_D_pnotp. % 176.20/176.56 apply zenon_H1f6. % 176.20/176.56 rewrite <- zenon_D_pnotp. % 176.20/176.56 exact zenon_H1ec. % 176.20/176.56 cut ((zenon_TY_ss = zenon_TY_ss)); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 0.12/176.78 cut ((zenon_TX_si = zenon_TY_hh)); [idtac | apply NNPP; zenon_intro zenon_H1fc]. % 0.12/176.78 congruence. % 0.12/176.78 apply (zenon_notand_s _ _ zenon_H1f8); [ zenon_intro zenon_H1fd | zenon_intro zenon_H1df ]. % 0.12/176.78 apply zenon_H1fd. zenon_intro zenon_H1fe. % 0.12/176.78 elim (classic (zenon_TY_hh = zenon_TY_hh)); [ zenon_intro zenon_H1ff | zenon_intro zenon_Hc1 ]. % 0.12/176.78 cut ((zenon_TY_hh = zenon_TY_hh) = (zenon_TX_si = zenon_TY_hh)). % 0.12/176.78 intro zenon_D_pnotp. % 0.12/176.78 apply zenon_H1fc. % 0.12/176.78 rewrite <- zenon_D_pnotp. % 0.12/176.78 exact zenon_H1ff. % 0.12/176.78 cut ((zenon_TY_hh = zenon_TY_hh)); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 0.12/176.78 cut ((zenon_TY_hh = zenon_TX_si)); [idtac | apply NNPP; zenon_intro zenon_H1fa]. % 0.12/176.78 congruence. % 0.12/176.78 exact (zenon_H1fa zenon_H1fe). % 0.12/176.78 apply zenon_Hc1. apply refl_equal. % 0.12/176.78 apply zenon_Hc1. apply refl_equal. % 0.12/176.78 apply zenon_H1df. zenon_intro zenon_H1e4. % 0.12/176.78 generalize (zenon_H4 zenon_TY_hh). zenon_intro zenon_H200. % 0.12/176.78 generalize (zenon_H200 zenon_TX_si). zenon_intro zenon_H201. % 0.12/176.78 generalize (zenon_H201 zenon_TY_ss). zenon_intro zenon_H202. % 0.12/176.78 apply (zenon_imply_s _ _ zenon_H202); [ zenon_intro zenon_H1f9 | zenon_intro zenon_H203 ]. % 0.12/176.78 exact (zenon_H1f9 zenon_H1e4). % 0.12/176.78 apply (zenon_imply_s _ _ zenon_H203); [ zenon_intro zenon_H205 | zenon_intro zenon_H204 ]. % 0.12/176.78 exact (zenon_H205 zenon_H1ec). % 0.12/176.78 exact (zenon_H1f6 zenon_H204). % 0.12/176.78 apply zenon_H1fb. apply refl_equal. % 0.12/176.78 apply (zenon_notand_s _ _ zenon_H1f5); [ zenon_intro zenon_H207 | zenon_intro zenon_H206 ]. % 0.12/176.78 exact (zenon_H207 zenon_H1eb). % 0.12/176.78 exact (zenon_H206 zenon_H1ea). % 0.12/176.78 exact (zenon_H1ef zenon_Hdb). % 0.12/176.78 apply zenon_Hcb. zenon_intro zenon_Tx_ua. apply NNPP. zenon_intro zenon_H209. % 0.12/176.78 apply zenon_H209. zenon_intro zenon_Ty_uc. apply NNPP. zenon_intro zenon_H20b. % 0.12/176.78 apply zenon_H20b. zenon_intro zenon_Tz_ue. apply NNPP. zenon_intro zenon_H20d. % 0.12/176.78 apply (zenon_notimply_s _ _ zenon_H20d). zenon_intro zenon_H20f. zenon_intro zenon_H20e. % 0.12/176.78 apply (zenon_notimply_s _ _ zenon_H20e). zenon_intro zenon_H211. zenon_intro zenon_H210. % 0.12/176.78 generalize (transitivity zenon_Tx_ua). zenon_intro zenon_H212. % 0.12/176.78 generalize (zenon_H212 zenon_Ty_uc). zenon_intro zenon_H213. % 0.12/176.78 generalize (zenon_H213 zenon_Tz_ue). zenon_intro zenon_H214. % 0.12/176.78 apply (zenon_imply_s _ _ zenon_H214); [ zenon_intro zenon_H216 | zenon_intro zenon_H215 ]. % 0.12/176.78 apply (zenon_notand_s _ _ zenon_H216); [ zenon_intro zenon_H218 | zenon_intro zenon_H217 ]. % 0.12/176.78 exact (zenon_H218 zenon_H20f). % 0.12/176.78 exact (zenon_H217 zenon_H211). % 0.12/176.78 exact (zenon_H210 zenon_H215). % 0.12/176.78 Qed. % 0.12/176.78 % SZS output end Proof % 0.12/176.78 (* END-PROOF *) % 0.12/176.78 nodes searched: 1668975 % 0.12/176.78 max branch formulas: 165388 % 0.12/176.78 proof nodes created: 137573 % 0.12/176.78 formulas created: 4287387 % 0.12/176.78 %------------------------------------------------------------------------------