%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL672+1.010 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n008.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 12.13s 12.49s % Output : Proof 0.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL672+1.010 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.08/0.36 % Computer : n008.cluster.edu % 0.08/0.36 % Model : x86_64 x86_64 % 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.36 % Memory : 8046.5625MB % 0.08/0.36 % OS : Linux 6.8.0-71-generic % 0.08/0.36 % CPULimit : 300 % 0.08/0.36 % WCLimit : 300 % 0.08/0.36 % DateTime : Fri Sep 4 21:07:23 UTC 2026 % 0.13/0.36 % CPUTime : % 12.13/12.49 (* PROOF-FOUND *) % 12.13/12.49 % SZS status Theorem % 12.13/12.49 (* BEGIN-PROOF *) % 12.13/12.49 % SZS output start Proof % 12.13/12.49 Theorem main : (~(exists X : zenon_U, (~(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~(p1 X))))))))/\(p1 X))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/False))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 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Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall 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((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(p1 Y))))))))/\(p1 Y))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/False))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~(p1 X))))))))/\(p1 X))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(p2 X))))/\((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/False))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(p1 Y))))))))/\(p1 Y))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(((~(forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y))))/\((~(forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/False))))))/\(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). % 12.13/12.49 Proof. % 12.13/12.49 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). % 12.13/12.49 do 3 intro. intros zenon_H3 zenon_H4 zenon_H5 zenon_H6. % 12.13/12.49 elim (classic ((~(zenon_TX_j = zenon_TY_i))/\(~(r1 zenon_TX_j zenon_TY_i)))); [ zenon_intro zenon_Ha | zenon_intro zenon_Hb ]. % 12.13/12.49 apply (zenon_and_s _ _ zenon_Ha). zenon_intro zenon_Hd. zenon_intro zenon_Hc. % 12.13/12.49 exact (zenon_Hc zenon_H3). % 12.13/12.49 cut ((r1 zenon_TY_i zenon_TX_h) = (r1 zenon_TX_j zenon_TX_h)). % 12.13/12.49 intro zenon_D_pnotp. % 12.13/12.49 apply zenon_H5. % 12.13/12.49 rewrite <- zenon_D_pnotp. % 12.13/12.49 exact zenon_H6. % 12.13/12.49 cut ((zenon_TX_h = zenon_TX_h)); [idtac | apply NNPP; zenon_intro zenon_He]. % 12.13/12.49 cut ((zenon_TY_i = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_Hf]. % 12.13/12.49 congruence. % 12.13/12.49 apply (zenon_notand_s _ _ zenon_Hb); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ]. % 12.13/12.49 apply zenon_H11. zenon_intro zenon_H12. % 12.13/12.49 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 12.13/12.49 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_i = zenon_TX_j)). % 12.13/12.49 intro zenon_D_pnotp. % 12.13/12.49 apply zenon_Hf. % 12.13/12.49 rewrite <- zenon_D_pnotp. % 12.13/12.49 exact zenon_H13. % 12.13/12.49 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 12.13/12.49 cut ((zenon_TX_j = zenon_TY_i)); [idtac | apply NNPP; zenon_intro zenon_Hd]. % 12.13/12.49 congruence. % 12.13/12.49 exact (zenon_Hd zenon_H12). % 12.13/12.49 apply zenon_H14. apply refl_equal. % 12.13/12.49 apply zenon_H14. apply refl_equal. % 12.13/12.49 apply zenon_H10. zenon_intro zenon_H3. % 12.13/12.49 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 12.13/12.49 generalize (zenon_H15 zenon_TY_i). zenon_intro zenon_H16. % 12.13/12.49 generalize (zenon_H16 zenon_TX_h). zenon_intro zenon_H17. % 12.13/12.49 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_Hc | zenon_intro zenon_H18 ]. % 12.13/12.49 exact (zenon_Hc zenon_H3). % 12.13/12.49 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ]. % 12.13/12.49 exact (zenon_H1a zenon_H6). % 12.13/12.49 exact (zenon_H5 zenon_H19). % 12.13/12.49 apply zenon_He. apply refl_equal. % 12.13/12.49 (* end of lemma zenon_L1_ *) % 12.13/12.49 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). % 12.13/12.49 do 4 intro. intros zenon_H3 zenon_H6 zenon_H4 zenon_H1b zenon_H1c. % 12.13/12.49 elim (classic ((~(zenon_TX_j = zenon_TX_h))/\(~(r1 zenon_TX_j zenon_TX_h)))); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ]. % 12.13/12.49 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H20. zenon_intro zenon_H5. % 12.13/12.49 apply (zenon_L1_ zenon_TX_h zenon_TY_i zenon_TX_j); trivial. % 12.13/12.49 cut ((r1 zenon_TX_h zenon_TY_bd) = (r1 zenon_TX_j zenon_TY_bd)). % 12.13/12.49 intro zenon_D_pnotp. % 12.13/12.49 apply zenon_H1b. % 12.13/12.49 rewrite <- zenon_D_pnotp. % 12.13/12.49 exact zenon_H1c. % 12.13/12.49 cut ((zenon_TY_bd = zenon_TY_bd)); [idtac | apply NNPP; zenon_intro zenon_H21]. % 12.13/12.49 cut ((zenon_TX_h = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H22]. % 12.13/12.49 congruence. % 12.13/12.49 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ]. % 12.13/12.49 apply zenon_H24. zenon_intro zenon_H25. % 12.13/12.49 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 12.13/12.49 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_h = zenon_TX_j)). % 12.13/12.49 intro zenon_D_pnotp. % 12.13/12.49 apply zenon_H22. % 12.13/12.49 rewrite <- zenon_D_pnotp. % 12.13/12.49 exact zenon_H13. % 12.13/12.49 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 12.13/12.49 cut ((zenon_TX_j = zenon_TX_h)); [idtac | apply NNPP; zenon_intro zenon_H20]. % 12.13/12.49 congruence. % 12.13/12.49 exact (zenon_H20 zenon_H25). % 12.13/12.49 apply zenon_H14. apply refl_equal. % 12.13/12.49 apply zenon_H14. apply refl_equal. % 12.13/12.49 apply zenon_H23. zenon_intro zenon_H19. % 12.13/12.49 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 12.13/12.49 generalize (zenon_H15 zenon_TX_h). zenon_intro zenon_H26. % 12.13/12.49 generalize (zenon_H26 zenon_TY_bd). zenon_intro zenon_H27. % 12.13/12.49 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H5 | zenon_intro zenon_H28 ]. % 12.13/12.49 exact (zenon_H5 zenon_H19). % 12.13/12.49 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 12.13/12.49 exact (zenon_H2a zenon_H1c). % 12.13/12.49 exact (zenon_H1b zenon_H29). % 12.13/12.49 apply zenon_H21. apply refl_equal. % 12.13/12.49 (* end of lemma zenon_L2_ *) % 12.13/12.49 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). % 12.13/12.49 do 5 intro. intros zenon_H6 zenon_H3 zenon_H1c zenon_H4 zenon_H2b zenon_H2c. % 12.13/12.49 elim (classic ((~(zenon_TX_j = zenon_TY_bd))/\(~(r1 zenon_TX_j zenon_TY_bd)))); [ zenon_intro zenon_H2e | zenon_intro zenon_H2f ]. % 12.13/12.49 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H1b. % 12.13/12.49 apply (zenon_L2_ zenon_TY_bd zenon_TX_h zenon_TY_i zenon_TX_j); trivial. % 12.13/12.49 cut ((r1 zenon_TY_bd zenon_TX_bt) = (r1 zenon_TX_j zenon_TX_bt)). % 12.13/12.49 intro zenon_D_pnotp. % 12.13/12.49 apply zenon_H2b. % 12.13/12.49 rewrite <- zenon_D_pnotp. % 12.13/12.49 exact zenon_H2c. % 12.13/12.49 cut ((zenon_TX_bt = zenon_TX_bt)); [idtac | apply NNPP; zenon_intro zenon_H31]. % 12.13/12.49 cut ((zenon_TY_bd = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H32]. % 12.13/12.49 congruence. % 12.13/12.49 apply (zenon_notand_s _ _ zenon_H2f); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 12.13/12.49 apply zenon_H34. zenon_intro zenon_H35. % 12.13/12.49 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 12.13/12.49 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TY_bd = zenon_TX_j)). % 12.13/12.49 intro zenon_D_pnotp. % 12.13/12.49 apply zenon_H32. % 12.13/12.49 rewrite <- zenon_D_pnotp. % 12.13/12.49 exact zenon_H13. % 12.13/12.49 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 12.13/12.49 cut ((zenon_TX_j = zenon_TY_bd)); [idtac | apply NNPP; zenon_intro zenon_H30]. % 12.13/12.49 congruence. % 12.13/12.49 exact (zenon_H30 zenon_H35). % 12.13/12.49 apply zenon_H14. apply refl_equal. % 12.13/12.49 apply zenon_H14. apply refl_equal. % 12.13/12.49 apply zenon_H33. zenon_intro zenon_H29. % 12.13/12.49 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 12.13/12.49 generalize (zenon_H15 zenon_TY_bd). zenon_intro zenon_H36. % 12.13/12.49 generalize (zenon_H36 zenon_TX_bt). zenon_intro zenon_H37. % 12.13/12.49 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H1b | zenon_intro zenon_H38 ]. % 12.13/12.49 exact (zenon_H1b zenon_H29). % 12.13/12.49 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ]. % 12.13/12.49 exact (zenon_H3a zenon_H2c). % 12.13/12.49 exact (zenon_H2b zenon_H39). % 12.13/12.49 apply zenon_H31. apply refl_equal. % 12.13/12.49 (* end of lemma zenon_L3_ *) % 12.13/12.49 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). % 12.13/12.49 do 6 intro. intros zenon_H1c zenon_H3 zenon_H6 zenon_H2c zenon_H4 zenon_H3b zenon_H3c. % 12.13/12.49 elim (classic ((~(zenon_TX_j = zenon_TX_bt))/\(~(r1 zenon_TX_j zenon_TX_bt)))); [ zenon_intro zenon_H3e | zenon_intro zenon_H3f ]. % 12.13/12.49 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H2b. % 12.13/12.49 apply (zenon_L3_ zenon_TX_bt zenon_TY_bd zenon_TX_j zenon_TX_h zenon_TY_i); trivial. % 12.13/12.49 cut ((r1 zenon_TX_bt zenon_TY_cj) = (r1 zenon_TX_j zenon_TY_cj)). % 12.13/12.49 intro zenon_D_pnotp. % 12.13/12.49 apply zenon_H3b. % 12.13/12.49 rewrite <- zenon_D_pnotp. % 12.13/12.49 exact zenon_H3c. % 12.13/12.49 cut ((zenon_TY_cj = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H41]. % 12.13/12.49 cut ((zenon_TX_bt = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H42]. % 12.13/12.49 congruence. % 12.13/12.49 apply (zenon_notand_s _ _ zenon_H3f); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ]. % 12.13/12.49 apply zenon_H44. zenon_intro zenon_H45. % 12.13/12.49 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ]. % 12.13/12.49 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_bt = zenon_TX_j)). % 12.13/12.49 intro zenon_D_pnotp. % 12.13/12.49 apply zenon_H42. % 12.13/12.49 rewrite <- zenon_D_pnotp. % 12.13/12.49 exact zenon_H13. % 12.13/12.49 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14]. % 12.13/12.49 cut ((zenon_TX_j = zenon_TX_bt)); [idtac | apply NNPP; zenon_intro zenon_H40]. % 12.13/12.49 congruence. % 12.13/12.49 exact (zenon_H40 zenon_H45). % 12.13/12.49 apply zenon_H14. apply refl_equal. % 12.13/12.49 apply zenon_H14. apply refl_equal. % 12.13/12.49 apply zenon_H43. zenon_intro zenon_H39. % 12.13/12.49 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15. % 12.13/12.49 generalize (zenon_H15 zenon_TX_bt). zenon_intro zenon_H46. % 12.13/12.49 generalize (zenon_H46 zenon_TY_cj). zenon_intro zenon_H47. % 12.13/12.49 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H2b | zenon_intro zenon_H48 ]. % 12.13/12.49 exact (zenon_H2b zenon_H39). % 12.13/12.49 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 12.13/12.49 exact (zenon_H4a zenon_H3c). % 12.13/12.49 exact (zenon_H3b zenon_H49). % 12.13/12.49 apply zenon_H41. apply refl_equal. % 12.13/12.49 (* end of lemma zenon_L4_ *) % 12.13/12.49 assert (zenon_L5_ : forall (zenon_TY_da : zenon_U) (zenon_TX_db : zenon_U) (zenon_TY_cj : zenon_U), (r1 zenon_TY_cj zenon_TX_db) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TY_cj zenon_TY_da)) -> (r1 zenon_TX_db zenon_TY_da) -> False). % 12.13/12.49 do 3 intro. intros zenon_H4b zenon_H4 zenon_H4c zenon_H4d. % 12.13/12.49 elim (classic ((~(zenon_TY_cj = zenon_TX_db))/\(~(r1 zenon_TY_cj zenon_TX_db)))); [ zenon_intro zenon_H50 | zenon_intro zenon_H51 ]. % 12.13/12.49 apply (zenon_and_s _ _ zenon_H50). zenon_intro zenon_H53. zenon_intro zenon_H52. % 12.13/12.49 exact (zenon_H52 zenon_H4b). % 12.13/12.49 cut ((r1 zenon_TX_db zenon_TY_da) = (r1 zenon_TY_cj zenon_TY_da)). % 12.13/12.49 intro zenon_D_pnotp. % 12.13/12.49 apply zenon_H4c. % 12.13/12.49 rewrite <- zenon_D_pnotp. % 12.13/12.49 exact zenon_H4d. % 12.13/12.49 cut ((zenon_TY_da = zenon_TY_da)); [idtac | apply NNPP; zenon_intro zenon_H54]. % 12.13/12.49 cut ((zenon_TX_db = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H55]. % 12.13/12.49 congruence. % 12.13/12.49 apply (zenon_notand_s _ _ zenon_H51); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ]. % 12.13/12.49 apply zenon_H57. zenon_intro zenon_H58. % 12.13/12.49 elim (classic (zenon_TY_cj = zenon_TY_cj)); [ zenon_intro zenon_H59 | zenon_intro zenon_H41 ]. % 12.13/12.49 cut ((zenon_TY_cj = zenon_TY_cj) = (zenon_TX_db = zenon_TY_cj)). % 12.13/12.49 intro zenon_D_pnotp. % 12.13/12.49 apply zenon_H55. % 12.13/12.49 rewrite <- zenon_D_pnotp. % 12.13/12.49 exact zenon_H59. % 12.13/12.49 cut ((zenon_TY_cj = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H41]. % 12.13/12.49 cut ((zenon_TY_cj = zenon_TX_db)); [idtac | apply NNPP; zenon_intro zenon_H53]. % 12.13/12.49 congruence. % 12.13/12.49 exact (zenon_H53 zenon_H58). % 12.13/12.49 apply zenon_H41. apply refl_equal. % 12.13/12.49 apply zenon_H41. apply refl_equal. % 12.13/12.49 apply zenon_H56. zenon_intro zenon_H4b. % 12.13/12.49 generalize (zenon_H4 zenon_TY_cj). zenon_intro zenon_H5a. % 12.13/12.49 generalize (zenon_H5a zenon_TX_db). zenon_intro zenon_H5b. % 12.13/12.49 generalize (zenon_H5b zenon_TY_da). zenon_intro zenon_H5c. % 12.13/12.49 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H52 | zenon_intro zenon_H5d ]. % 12.13/12.49 exact (zenon_H52 zenon_H4b). % 12.13/12.49 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 12.13/12.49 exact (zenon_H5f zenon_H4d). % 12.13/12.49 exact (zenon_H4c zenon_H5e). % 12.13/12.49 apply zenon_H54. apply refl_equal. % 12.13/12.49 (* end of lemma zenon_L5_ *) % 12.13/12.49 assert (zenon_L6_ : forall (zenon_TY_dv : zenon_U) (zenon_TX_dw : zenon_U) (zenon_TY_cj : zenon_U) (zenon_TY_da : zenon_U) (zenon_TX_db : zenon_U), (r1 zenon_TX_db zenon_TY_da) -> (r1 zenon_TY_cj zenon_TX_db) -> (r1 zenon_TY_da zenon_TX_dw) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TY_cj zenon_TY_dv)) -> (r1 zenon_TX_dw zenon_TY_dv) -> False). % 12.13/12.49 do 5 intro. intros zenon_H4d zenon_H4b zenon_H60 zenon_H4 zenon_H61 zenon_H62. % 12.13/12.49 elim (classic ((~(zenon_TY_cj = zenon_TX_dw))/\(~(r1 zenon_TY_cj zenon_TX_dw)))); [ zenon_intro zenon_H65 | zenon_intro zenon_H66 ]. % 12.13/12.49 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H68. zenon_intro zenon_H67. % 12.13/12.49 elim (classic ((~(zenon_TY_cj = zenon_TY_da))/\(~(r1 zenon_TY_cj zenon_TY_da)))); [ zenon_intro zenon_H69 | zenon_intro zenon_H6a ]. % 12.13/12.49 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H6b. zenon_intro zenon_H4c. % 12.13/12.49 apply (zenon_L5_ zenon_TY_da zenon_TX_db zenon_TY_cj); trivial. % 12.13/12.49 cut ((r1 zenon_TY_da zenon_TX_dw) = (r1 zenon_TY_cj zenon_TX_dw)). % 12.13/12.49 intro zenon_D_pnotp. % 12.13/12.49 apply zenon_H67. % 12.13/12.49 rewrite <- zenon_D_pnotp. % 12.13/12.49 exact zenon_H60. % 12.13/12.49 cut ((zenon_TX_dw = zenon_TX_dw)); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 12.13/12.49 cut ((zenon_TY_da = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 12.13/12.49 congruence. % 12.13/12.49 apply (zenon_notand_s _ _ zenon_H6a); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ]. % 12.13/12.49 apply zenon_H6f. zenon_intro zenon_H70. % 12.13/12.49 elim (classic (zenon_TY_cj = zenon_TY_cj)); [ zenon_intro zenon_H59 | zenon_intro zenon_H41 ]. % 12.13/12.49 cut ((zenon_TY_cj = zenon_TY_cj) = (zenon_TY_da = zenon_TY_cj)). % 12.13/12.49 intro zenon_D_pnotp. % 12.13/12.49 apply zenon_H6d. % 12.13/12.49 rewrite <- zenon_D_pnotp. % 12.13/12.49 exact zenon_H59. % 12.13/12.49 cut ((zenon_TY_cj = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H41]. % 12.13/12.49 cut ((zenon_TY_cj = zenon_TY_da)); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 12.13/12.49 congruence. % 12.13/12.49 exact (zenon_H6b zenon_H70). % 12.13/12.49 apply zenon_H41. apply refl_equal. % 12.13/12.49 apply zenon_H41. apply refl_equal. % 12.13/12.49 apply zenon_H6e. zenon_intro zenon_H5e. % 12.13/12.49 generalize (zenon_H4 zenon_TY_cj). zenon_intro zenon_H5a. % 12.13/12.49 generalize (zenon_H5a zenon_TY_da). zenon_intro zenon_H71. % 12.13/12.49 generalize (zenon_H71 zenon_TX_dw). zenon_intro zenon_H72. % 12.13/12.49 apply (zenon_imply_s _ _ zenon_H72); [ zenon_intro zenon_H4c | zenon_intro zenon_H73 ]. % 12.13/12.49 exact (zenon_H4c zenon_H5e). % 12.13/12.49 apply (zenon_imply_s _ _ zenon_H73); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ]. % 12.13/12.49 exact (zenon_H75 zenon_H60). % 12.13/12.49 exact (zenon_H67 zenon_H74). % 12.13/12.49 apply zenon_H6c. apply refl_equal. % 12.13/12.49 cut ((r1 zenon_TX_dw zenon_TY_dv) = (r1 zenon_TY_cj zenon_TY_dv)). % 12.13/12.49 intro zenon_D_pnotp. % 12.13/12.49 apply zenon_H61. % 12.13/12.49 rewrite <- zenon_D_pnotp. % 12.13/12.49 exact zenon_H62. % 12.13/12.49 cut ((zenon_TY_dv = zenon_TY_dv)); [idtac | apply NNPP; zenon_intro zenon_H76]. % 12.13/12.49 cut ((zenon_TX_dw = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H77]. % 12.13/12.49 congruence. % 12.13/12.49 apply (zenon_notand_s _ _ zenon_H66); [ zenon_intro zenon_H79 | zenon_intro zenon_H78 ]. % 12.13/12.49 apply zenon_H79. zenon_intro zenon_H7a. % 12.13/12.49 elim (classic (zenon_TY_cj = zenon_TY_cj)); [ zenon_intro zenon_H59 | zenon_intro zenon_H41 ]. % 12.13/12.49 cut ((zenon_TY_cj = zenon_TY_cj) = (zenon_TX_dw = zenon_TY_cj)). % 12.13/12.49 intro zenon_D_pnotp. % 12.13/12.49 apply zenon_H77. % 12.13/12.49 rewrite <- zenon_D_pnotp. % 12.13/12.49 exact zenon_H59. % 12.13/12.49 cut ((zenon_TY_cj = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H41]. % 12.13/12.49 cut ((zenon_TY_cj = zenon_TX_dw)); [idtac | apply NNPP; zenon_intro zenon_H68]. % 12.13/12.49 congruence. % 12.13/12.49 exact (zenon_H68 zenon_H7a). % 12.13/12.49 apply zenon_H41. apply refl_equal. % 12.13/12.49 apply zenon_H41. apply refl_equal. % 12.13/12.49 apply zenon_H78. zenon_intro zenon_H74. % 12.13/12.49 generalize (zenon_H4 zenon_TY_cj). zenon_intro zenon_H5a. % 12.13/12.49 generalize (zenon_H5a zenon_TX_dw). zenon_intro zenon_H7b. % 12.13/12.49 generalize (zenon_H7b zenon_TY_dv). zenon_intro zenon_H7c. % 12.13/12.49 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H67 | zenon_intro zenon_H7d ]. % 12.13/12.49 exact (zenon_H67 zenon_H74). % 12.13/12.49 apply (zenon_imply_s _ _ zenon_H7d); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 12.13/12.49 exact (zenon_H7f zenon_H62). % 12.13/12.49 exact (zenon_H61 zenon_H7e). % 12.13/12.49 apply zenon_H76. apply refl_equal. % 12.13/12.49 (* end of lemma zenon_L6_ *) % 12.13/12.49 apply NNPP. intro zenon_G. % 12.13/12.49 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z))))))); [ zenon_intro zenon_H4 | zenon_intro zenon_H80 ]. % 12.13/12.49 apply zenon_G. zenon_intro zenon_H81. % 12.13/12.49 elim zenon_H81. zenon_intro zenon_TX_j. zenon_intro zenon_H82. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H82). zenon_intro zenon_H84. zenon_intro zenon_H83. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H83). zenon_intro zenon_H86. zenon_intro zenon_H85. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H85). zenon_intro zenon_H88. zenon_intro zenon_H87. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H87). zenon_intro zenon_H8a. zenon_intro zenon_H89. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H89). zenon_intro zenon_H8c. zenon_intro zenon_H8b. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H8b). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H8f). zenon_intro zenon_H92. zenon_intro zenon_H91. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H91). zenon_intro zenon_H94. zenon_intro zenon_H93. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H93). zenon_intro zenon_H96. zenon_intro zenon_H95. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H95). zenon_intro zenon_H98. zenon_intro zenon_H97. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H97). zenon_intro zenon_H8c. zenon_intro zenon_H99. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H99). zenon_intro zenon_H8e. zenon_intro zenon_H9a. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H9a). zenon_intro zenon_H90. zenon_intro zenon_H9b. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H9c). zenon_intro zenon_H9f. zenon_intro zenon_H9e. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H9e). zenon_intro zenon_Ha1. zenon_intro zenon_Ha0. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Ha0). zenon_intro zenon_Ha3. zenon_intro zenon_Ha2. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Ha2). zenon_intro zenon_H8c. zenon_intro zenon_Ha4. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Ha4). zenon_intro zenon_H8e. zenon_intro zenon_Ha5. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Ha5). zenon_intro zenon_H90. zenon_intro zenon_Ha6. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Ha6). zenon_intro zenon_Ha8. zenon_intro zenon_Ha7. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Ha7). zenon_intro zenon_Haa. zenon_intro zenon_Ha9. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Ha9). zenon_intro zenon_Hac. zenon_intro zenon_Hab. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hab). zenon_intro zenon_Hae. zenon_intro zenon_Had. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Had). zenon_intro zenon_H8c. zenon_intro zenon_Haf. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Haf). zenon_intro zenon_H8e. zenon_intro zenon_Hb0. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hb0). zenon_intro zenon_H90. zenon_intro zenon_Hb1. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hb1). zenon_intro zenon_Hb3. zenon_intro zenon_Hb2. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hb2). zenon_intro zenon_Hb5. zenon_intro zenon_Hb4. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hb4). zenon_intro zenon_Hb7. zenon_intro zenon_Hb6. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hb6). zenon_intro zenon_Hb9. zenon_intro zenon_Hb8. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hb8). zenon_intro zenon_H8c. zenon_intro zenon_Hba. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hba). zenon_intro zenon_H8e. zenon_intro zenon_Hbb. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hbb). zenon_intro zenon_H90. zenon_intro zenon_Hbc. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hbc). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hbd). zenon_intro zenon_Hc0. zenon_intro zenon_Hbf. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hbf). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hc1). zenon_intro zenon_Hc4. zenon_intro zenon_Hc3. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hc3). zenon_intro zenon_H8c. zenon_intro zenon_Hc5. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hc5). zenon_intro zenon_H8e. zenon_intro zenon_Hc6. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hc6). zenon_intro zenon_H90. zenon_intro zenon_Hc7. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hc7). zenon_intro zenon_Hc9. zenon_intro zenon_Hc8. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hc8). zenon_intro zenon_Hcb. zenon_intro zenon_Hca. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hca). zenon_intro zenon_Hcd. zenon_intro zenon_Hcc. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hcc). zenon_intro zenon_Hcf. zenon_intro zenon_Hce. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hce). zenon_intro zenon_H8c. zenon_intro zenon_Hd0. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hd0). zenon_intro zenon_H8e. zenon_intro zenon_Hd1. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hd1). zenon_intro zenon_H90. zenon_intro zenon_Hd2. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hd2). zenon_intro zenon_Hd4. zenon_intro zenon_Hd3. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hd3). zenon_intro zenon_Hd6. zenon_intro zenon_Hd5. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hd5). zenon_intro zenon_Hd8. zenon_intro zenon_Hd7. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hd7). zenon_intro zenon_Hda. zenon_intro zenon_Hd9. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hd9). zenon_intro zenon_H8c. zenon_intro zenon_Hdb. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hdb). zenon_intro zenon_H8e. zenon_intro zenon_Hdc. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hdc). zenon_intro zenon_H90. zenon_intro zenon_Hdd. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hdd). zenon_intro zenon_Hdf. zenon_intro zenon_Hde. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hde). zenon_intro zenon_He1. zenon_intro zenon_He0. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_He0). zenon_intro zenon_He3. zenon_intro zenon_He2. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_He2). zenon_intro zenon_He5. zenon_intro zenon_He4. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_He4). zenon_intro zenon_H8c. zenon_intro zenon_He6. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_He6). zenon_intro zenon_H8e. zenon_intro zenon_He7. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_He7). zenon_intro zenon_H90. zenon_intro zenon_He8. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_He8). zenon_intro zenon_Hea. zenon_intro zenon_He9. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_He9). zenon_intro zenon_Hec. zenon_intro zenon_Heb. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Heb). zenon_intro zenon_Hee. zenon_intro zenon_Hed. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hed). zenon_intro zenon_Hf0. zenon_intro zenon_Hef. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hef). zenon_intro zenon_H8c. zenon_intro zenon_Hf1. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hf1). zenon_intro zenon_H8e. zenon_intro zenon_H90. % 12.13/12.49 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_j Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H8e); [ zenon_intro zenon_Hf2; idtac ]. % 12.13/12.49 elim zenon_Hf2. zenon_intro zenon_TY_i. zenon_intro zenon_Hf3. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hf3). zenon_intro zenon_H10. zenon_intro zenon_Hf4. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hf4). zenon_intro zenon_Hf6. zenon_intro zenon_Hf5. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hf5). zenon_intro zenon_Hf8. zenon_intro zenon_Hf7. % 12.13/12.49 apply zenon_H10. zenon_intro zenon_H3. % 12.13/12.49 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_i X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_Hf8); [ zenon_intro zenon_Hf9; idtac ]. % 12.13/12.49 elim zenon_Hf9. zenon_intro zenon_TX_h. zenon_intro zenon_Hfa. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hfa). zenon_intro zenon_Hfc. zenon_intro zenon_Hfb. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hfb). zenon_intro zenon_Hfe. zenon_intro zenon_Hfd. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_Hfd). zenon_intro zenon_H100. zenon_intro zenon_Hff. % 12.13/12.49 apply zenon_Hfc. zenon_intro zenon_H6. % 12.13/12.49 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_h Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H100); [ zenon_intro zenon_H101; idtac ]. % 12.13/12.49 elim zenon_H101. zenon_intro zenon_TY_bd. zenon_intro zenon_H102. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H102). zenon_intro zenon_H104. zenon_intro zenon_H103. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H103). zenon_intro zenon_H106. zenon_intro zenon_H105. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H105). zenon_intro zenon_H108. zenon_intro zenon_H107. % 12.13/12.49 apply zenon_H104. zenon_intro zenon_H1c. % 12.13/12.49 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_bd X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_H108); [ zenon_intro zenon_H109; idtac ]. % 12.13/12.49 elim zenon_H109. zenon_intro zenon_TX_bt. zenon_intro zenon_H10a. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H10a). zenon_intro zenon_H10c. zenon_intro zenon_H10b. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H10b). zenon_intro zenon_H10e. zenon_intro zenon_H10d. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H10d). zenon_intro zenon_H110. zenon_intro zenon_H10f. % 12.13/12.49 apply zenon_H10c. zenon_intro zenon_H2c. % 12.13/12.49 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_bt Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H110); [ zenon_intro zenon_H111; idtac ]. % 12.13/12.49 elim zenon_H111. zenon_intro zenon_TY_cj. zenon_intro zenon_H112. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H112). zenon_intro zenon_H114. zenon_intro zenon_H113. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H113). zenon_intro zenon_H116. zenon_intro zenon_H115. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H115). zenon_intro zenon_H118. zenon_intro zenon_H117. % 12.13/12.49 apply zenon_H114. zenon_intro zenon_H3c. % 12.13/12.49 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_cj X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_H118); [ zenon_intro zenon_H119; idtac ]. % 12.13/12.49 elim zenon_H119. zenon_intro zenon_TX_db. zenon_intro zenon_H11a. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H11a). zenon_intro zenon_H56. zenon_intro zenon_H11b. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H11b). zenon_intro zenon_H11d. zenon_intro zenon_H11c. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H11c). zenon_intro zenon_H11f. zenon_intro zenon_H11e. % 12.13/12.49 apply zenon_H56. zenon_intro zenon_H4b. % 12.13/12.49 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_db Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H11f); [ zenon_intro zenon_H120; idtac ]. % 12.13/12.49 elim zenon_H120. zenon_intro zenon_TY_da. zenon_intro zenon_H121. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H121). zenon_intro zenon_H123. zenon_intro zenon_H122. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H122). zenon_intro zenon_H125. zenon_intro zenon_H124. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H124). zenon_intro zenon_H127. zenon_intro zenon_H126. % 12.13/12.49 apply zenon_H123. zenon_intro zenon_H4d. % 12.13/12.49 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_da X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p2 Y)))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) zenon_H127); [ zenon_intro zenon_H128; idtac ]. % 12.13/12.49 elim zenon_H128. zenon_intro zenon_TX_dw. zenon_intro zenon_H129. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H129). zenon_intro zenon_H12b. zenon_intro zenon_H12a. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H12a). zenon_intro zenon_H12d. zenon_intro zenon_H12c. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H12c). zenon_intro zenon_H12f. zenon_intro zenon_H12e. % 12.13/12.49 apply zenon_H12b. zenon_intro zenon_H60. % 12.13/12.49 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_dw Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p2 X)))\/((forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) zenon_H12f); [ zenon_intro zenon_H130; idtac ]. % 12.13/12.49 elim zenon_H130. zenon_intro zenon_TY_dv. zenon_intro zenon_H131. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H131). zenon_intro zenon_H133. zenon_intro zenon_H132. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H132). zenon_intro zenon_H135. zenon_intro zenon_H134. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H134). zenon_intro zenon_H137. zenon_intro zenon_H136. % 12.13/12.49 apply zenon_H133. zenon_intro zenon_H62. % 12.13/12.49 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_dv X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))) zenon_H137); [ zenon_intro zenon_H138; idtac ]. % 12.13/12.49 elim zenon_H138. zenon_intro zenon_TX_mb. zenon_intro zenon_H13a. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H13a). zenon_intro zenon_H13c. zenon_intro zenon_H13b. % 12.13/12.49 apply (zenon_notor_s _ _ zenon_H13b). zenon_intro zenon_H13e. zenon_intro zenon_H13d. % 12.13/12.49 apply zenon_H13c. zenon_intro zenon_H13f. % 12.13/12.49 apply (zenon_notand_s _ _ zenon_Hec); [ zenon_intro zenon_H141 | zenon_intro zenon_H140 ]. % 12.13/12.49 exact (zenon_H141 zenon_H8c). % 12.13/12.49 apply (zenon_notand_s _ _ zenon_H140); [ zenon_intro zenon_H143 | zenon_intro zenon_H142 ]. % 12.13/12.49 apply zenon_H143. zenon_intro zenon_H144. % 12.13/12.49 generalize (zenon_H144 zenon_TY_cj). zenon_intro zenon_H145. % 12.13/12.49 apply (zenon_or_s _ _ zenon_H145); [ zenon_intro zenon_H3b | zenon_intro zenon_H146 ]. % 12.13/12.49 apply (zenon_L4_ zenon_TY_cj zenon_TX_bt zenon_TY_i zenon_TX_j zenon_TY_bd zenon_TX_h); trivial. % 12.13/12.49 generalize (zenon_H146 zenon_TX_mb). zenon_intro zenon_H147. % 12.13/12.49 apply (zenon_or_s _ _ zenon_H147); [ zenon_intro zenon_H149 | zenon_intro zenon_H148 ]. % 12.13/12.49 elim (classic ((~(zenon_TY_cj = zenon_TY_dv))/\(~(r1 zenon_TY_cj zenon_TY_dv)))); [ zenon_intro zenon_H14a | zenon_intro zenon_H14b ]. % 12.13/12.49 apply (zenon_and_s _ _ zenon_H14a). zenon_intro zenon_H14c. zenon_intro zenon_H61. % 12.13/12.49 apply (zenon_L6_ zenon_TY_dv zenon_TX_dw zenon_TY_cj zenon_TY_da zenon_TX_db); trivial. % 12.13/12.49 cut ((r1 zenon_TY_dv zenon_TX_mb) = (r1 zenon_TY_cj zenon_TX_mb)). % 12.13/12.49 intro zenon_D_pnotp. % 12.13/12.49 apply zenon_H149. % 12.13/12.49 rewrite <- zenon_D_pnotp. % 12.13/12.49 exact zenon_H13f. % 12.13/12.49 cut ((zenon_TX_mb = zenon_TX_mb)); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 12.13/12.49 cut ((zenon_TY_dv = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H14e]. % 12.13/12.49 congruence. % 12.13/12.49 apply (zenon_notand_s _ _ zenon_H14b); [ zenon_intro zenon_H150 | zenon_intro zenon_H14f ]. % 12.13/12.49 apply zenon_H150. zenon_intro zenon_H151. % 12.13/12.49 elim (classic (zenon_TY_cj = zenon_TY_cj)); [ zenon_intro zenon_H59 | zenon_intro zenon_H41 ]. % 12.13/12.49 cut ((zenon_TY_cj = zenon_TY_cj) = (zenon_TY_dv = zenon_TY_cj)). % 12.13/12.49 intro zenon_D_pnotp. % 12.13/12.49 apply zenon_H14e. % 12.13/12.49 rewrite <- zenon_D_pnotp. % 12.13/12.49 exact zenon_H59. % 12.13/12.49 cut ((zenon_TY_cj = zenon_TY_cj)); [idtac | apply NNPP; zenon_intro zenon_H41]. % 0.13/12.51 cut ((zenon_TY_cj = zenon_TY_dv)); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 0.13/12.51 congruence. % 0.13/12.51 exact (zenon_H14c zenon_H151). % 0.13/12.51 apply zenon_H41. apply refl_equal. % 0.13/12.51 apply zenon_H41. apply refl_equal. % 0.13/12.51 apply zenon_H14f. zenon_intro zenon_H7e. % 0.13/12.51 generalize (zenon_H4 zenon_TY_cj). zenon_intro zenon_H5a. % 0.13/12.51 generalize (zenon_H5a zenon_TY_dv). zenon_intro zenon_H152. % 0.13/12.51 generalize (zenon_H152 zenon_TX_mb). zenon_intro zenon_H153. % 0.13/12.51 apply (zenon_imply_s _ _ zenon_H153); [ zenon_intro zenon_H61 | zenon_intro zenon_H154 ]. % 0.13/12.51 exact (zenon_H61 zenon_H7e). % 0.13/12.51 apply (zenon_imply_s _ _ zenon_H154); [ zenon_intro zenon_H156 | zenon_intro zenon_H155 ]. % 0.13/12.51 exact (zenon_H156 zenon_H13f). % 0.13/12.51 exact (zenon_H149 zenon_H155). % 0.13/12.51 apply zenon_H14d. apply refl_equal. % 0.13/12.51 apply (zenon_notand_s _ _ zenon_H148); [ zenon_intro zenon_H158 | zenon_intro zenon_H157 ]. % 0.13/12.51 exact (zenon_H158 zenon_H13e). % 0.13/12.51 exact (zenon_H157 zenon_H13d). % 0.13/12.51 exact (zenon_H142 zenon_H90). % 0.13/12.51 apply zenon_H80. zenon_intro zenon_Tx_nh. apply NNPP. zenon_intro zenon_H15a. % 0.13/12.51 apply zenon_H15a. zenon_intro zenon_Ty_nj. apply NNPP. zenon_intro zenon_H15c. % 0.13/12.51 apply zenon_H15c. zenon_intro zenon_Tz_nl. apply NNPP. zenon_intro zenon_H15e. % 0.13/12.51 apply (zenon_notimply_s _ _ zenon_H15e). zenon_intro zenon_H160. zenon_intro zenon_H15f. % 0.13/12.51 apply (zenon_notimply_s _ _ zenon_H15f). zenon_intro zenon_H162. zenon_intro zenon_H161. % 0.13/12.51 generalize (transitivity zenon_Tx_nh). zenon_intro zenon_H163. % 0.13/12.51 generalize (zenon_H163 zenon_Ty_nj). zenon_intro zenon_H164. % 0.13/12.51 generalize (zenon_H164 zenon_Tz_nl). zenon_intro zenon_H165. % 0.13/12.51 apply (zenon_imply_s _ _ zenon_H165); [ zenon_intro zenon_H167 | zenon_intro zenon_H166 ]. % 0.13/12.51 apply (zenon_notand_s _ _ zenon_H167); [ zenon_intro zenon_H169 | zenon_intro zenon_H168 ]. % 0.13/12.51 exact (zenon_H169 zenon_H160). % 0.13/12.51 exact (zenon_H168 zenon_H162). % 0.13/12.51 exact (zenon_H161 zenon_H166). % 0.13/12.51 Qed. % 0.13/12.51 % SZS output end Proof % 0.13/12.51 (* END-PROOF *) % 0.13/12.51 nodes searched: 170301 % 0.13/12.51 max branch formulas: 31939 % 0.13/12.51 proof nodes created: 15110 % 0.13/12.51 formulas created: 546909 % 0.13/12.51 %------------------------------------------------------------------------------