TSTP Solution File: LCL640+1.010 by Zenon---0.7.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : LCL640+1.010 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sun Jul 17 16:22:54 EDT 2022
% Result : Theorem 13.94s 14.16s
% Output : Proof 14.00s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : LCL640+1.010 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n015.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sun Jul 3 16:19:15 EDT 2022
% 0.12/0.33 % CPUTime :
% 13.94/14.16 (* PROOF-FOUND *)
% 13.94/14.16 % SZS status Theorem
% 13.94/14.16 (* BEGIN-PROOF *)
% 13.94/14.16 % SZS output start Proof
% 13.94/14.16 Theorem main : (~(exists X : zenon_U, (~((~(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))\/(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))\/(forall Y : zenon_U, ((~(r1 X Y))\/(((p1 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))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 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))\/(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))\/(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))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 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))\/(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))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 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))\/(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))\/(forall X : zenon_U, ((~(r1 Y X))\/(((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/((~(p1 X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))))))))\/(~((~(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))\/(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 Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))))))/\((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))\/(forall Y : zenon_U, ((~(r1 X Y))\/(((p1 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))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 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))\/(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))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 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))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 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))\/(forall X : zenon_U, ((~(r1 Y X))\/(((p1 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 Y : zenon_U, ((~(r1 X Y))\/(((p1 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))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 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))))))))))))))))))))))).
% 13.94/14.16 Proof.
% 13.94/14.16 assert (zenon_L1_ : forall (zenon_TX_d : zenon_U), (~((forall Y : zenon_U, ((~(r1 zenon_TX_d Y))\/(p1 Y)))\/(~(p1 zenon_TX_d)))) -> (~(p1 zenon_TX_d)) -> False).
% 13.94/14.16 do 1 intro. intros zenon_H1 zenon_H2.
% 13.94/14.16 apply (zenon_notor_s _ _ zenon_H1). zenon_intro zenon_H5. zenon_intro zenon_H4.
% 13.94/14.16 exact (zenon_H4 zenon_H2).
% 13.94/14.16 (* end of lemma zenon_L1_ *)
% 13.94/14.16 assert (zenon_L2_ : forall (zenon_TY_m : zenon_U) (zenon_TX_n : zenon_U), (((forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))\/((~(p1 zenon_TX_n))\/((forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 zenon_TX_n)\/((forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))/\((forall X : zenon_U, ((~(r1 zenon_TX_n 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 zenon_TX_n Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (p1 zenon_TX_n) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (r1 zenon_TX_n zenon_TY_m) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> False).
% 13.94/14.16 do 2 intro. intros zenon_H6 zenon_H7 zenon_H8 zenon_H9 zenon_Ha zenon_Hb.
% 13.94/14.16 apply (zenon_and_s _ _ zenon_H6). zenon_intro zenon_Hf. zenon_intro zenon_He.
% 13.94/14.16 apply (zenon_and_s _ _ zenon_He). zenon_intro zenon_H11. zenon_intro zenon_H10.
% 13.94/14.16 apply (zenon_and_s _ _ zenon_H10). zenon_intro zenon_H13. zenon_intro zenon_H12.
% 13.94/14.16 apply (zenon_or_s _ _ zenon_Hf); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ].
% 13.94/14.16 exact (zenon_H7 zenon_H15).
% 13.94/14.16 apply (zenon_or_s _ _ zenon_H14); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ].
% 13.94/14.16 exact (zenon_H17 zenon_H8).
% 13.94/14.16 apply (zenon_or_s _ _ zenon_H16); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ].
% 13.94/14.16 generalize (zenon_H13 zenon_TY_m). zenon_intro zenon_H1a.
% 13.94/14.16 apply (zenon_or_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ].
% 13.94/14.16 exact (zenon_H1c zenon_Ha).
% 13.94/14.16 apply (zenon_or_s _ _ zenon_H1b); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ].
% 13.94/14.16 generalize (zenon_H19 zenon_TY_m). zenon_intro zenon_H1f.
% 13.94/14.16 apply (zenon_or_s _ _ zenon_H1f); [ zenon_intro zenon_H1c | zenon_intro zenon_H20 ].
% 13.94/14.16 exact (zenon_H1c zenon_Ha).
% 13.94/14.16 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TY_m Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))) zenon_H20); [ zenon_intro zenon_H21; idtac ].
% 13.94/14.16 elim zenon_H21. zenon_intro zenon_TY_bi. zenon_intro zenon_H23.
% 13.94/14.16 apply (zenon_notor_s _ _ zenon_H23). zenon_intro zenon_H25. zenon_intro zenon_H24.
% 13.94/14.16 apply (zenon_notor_s _ _ zenon_H24). zenon_intro zenon_H27. zenon_intro zenon_H26.
% 13.94/14.16 apply zenon_H25. zenon_intro zenon_H28.
% 13.94/14.16 generalize (zenon_H1e zenon_TY_bi). zenon_intro zenon_H29.
% 13.94/14.16 apply (zenon_or_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 13.94/14.16 exact (zenon_H2b zenon_H28).
% 13.94/14.16 exact (zenon_H27 zenon_H2a).
% 13.94/14.16 exact (zenon_H1d zenon_H9).
% 13.94/14.16 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_n Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))) zenon_H18); [ zenon_intro zenon_H2c; idtac ].
% 13.94/14.16 elim zenon_H2c. zenon_intro zenon_TY_bt. zenon_intro zenon_H2e.
% 13.94/14.16 apply (zenon_notor_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H2f.
% 13.94/14.16 apply (zenon_notor_s _ _ zenon_H2f). zenon_intro zenon_H32. zenon_intro zenon_H31.
% 13.94/14.16 apply (zenon_notor_s _ _ zenon_H31). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 13.94/14.16 apply zenon_H33. zenon_intro zenon_H35.
% 13.94/14.16 apply zenon_H30. zenon_intro zenon_H36.
% 13.94/14.16 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_bt X))\/(p1 X))) zenon_H32); [ zenon_intro zenon_H37; idtac ].
% 13.94/14.16 elim zenon_H37. zenon_intro zenon_TX_d. zenon_intro zenon_H38.
% 13.94/14.16 apply (zenon_notor_s _ _ zenon_H38). zenon_intro zenon_H39. zenon_intro zenon_H2.
% 13.94/14.16 apply zenon_H39. zenon_intro zenon_H3a.
% 13.94/14.16 apply (zenon_or_s _ _ zenon_H12); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ].
% 13.94/14.16 generalize (zenon_H35 zenon_TX_d). zenon_intro zenon_H3d.
% 13.94/14.16 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ].
% 13.94/14.16 exact (zenon_H3f zenon_H3a).
% 13.94/14.16 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H1 ].
% 13.94/14.16 generalize (zenon_H3c zenon_TY_bt). zenon_intro zenon_H41.
% 13.94/14.16 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ].
% 13.94/14.16 exact (zenon_H43 zenon_H36).
% 13.94/14.16 generalize (zenon_H42 zenon_TX_d). zenon_intro zenon_H44.
% 13.94/14.16 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3f | zenon_intro zenon_H45 ].
% 13.94/14.16 exact (zenon_H3f zenon_H3a).
% 13.94/14.16 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 13.94/14.16 exact (zenon_H2 zenon_H47).
% 13.94/14.16 exact (zenon_H46 zenon_H40).
% 13.94/14.16 apply (zenon_L1_ zenon_TX_d); trivial.
% 13.94/14.16 exact (zenon_H3b zenon_Hb).
% 13.94/14.16 (* end of lemma zenon_L2_ *)
% 13.94/14.16 assert (zenon_L3_ : forall (zenon_TY_m : zenon_U) (zenon_TX_n : zenon_U) (zenon_TY_cw : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TY_cw X))\/(((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/((~(p1 X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))) -> (r1 zenon_TY_cw zenon_TX_n) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (p1 zenon_TX_n) -> (r1 zenon_TX_n zenon_TY_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> False).
% 13.94/14.16 do 3 intro. intros zenon_H48 zenon_H49 zenon_H7 zenon_H8 zenon_Ha zenon_H9 zenon_Hb.
% 13.94/14.16 generalize (zenon_H48 zenon_TX_n). zenon_intro zenon_H4b.
% 13.94/14.16 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H4c | zenon_intro zenon_H6 ].
% 13.94/14.16 exact (zenon_H4c zenon_H49).
% 13.94/14.16 apply (zenon_L2_ zenon_TY_m zenon_TX_n); trivial.
% 13.94/14.16 (* end of lemma zenon_L3_ *)
% 13.94/14.16 assert (zenon_L4_ : forall (zenon_TY_m : zenon_U) (zenon_TX_n : zenon_U) (zenon_TY_cw : zenon_U) (zenon_TX_db : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_db Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/((~(p1 X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))) -> (r1 zenon_TX_db zenon_TY_cw) -> (r1 zenon_TY_cw zenon_TX_n) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (p1 zenon_TX_n) -> (r1 zenon_TX_n zenon_TY_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> False).
% 13.94/14.16 do 4 intro. intros zenon_H4d zenon_H4e zenon_H49 zenon_H7 zenon_H8 zenon_Ha zenon_H9 zenon_Hb.
% 13.94/14.16 generalize (zenon_H4d zenon_TY_cw). zenon_intro zenon_H50.
% 13.94/14.16 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H51 | zenon_intro zenon_H48 ].
% 13.94/14.16 exact (zenon_H51 zenon_H4e).
% 13.94/14.16 apply (zenon_L3_ zenon_TY_m zenon_TX_n zenon_TY_cw); trivial.
% 13.94/14.16 (* end of lemma zenon_L4_ *)
% 13.94/14.16 assert (zenon_L5_ : forall (zenon_TY_m : zenon_U) (zenon_TX_n : zenon_U) (zenon_TY_cw : zenon_U) (zenon_TX_db : zenon_U) (zenon_TY_dg : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TY_dg X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/((~(p1 X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))) -> (r1 zenon_TY_dg zenon_TX_db) -> (r1 zenon_TX_db zenon_TY_cw) -> (r1 zenon_TY_cw zenon_TX_n) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (p1 zenon_TX_n) -> (r1 zenon_TX_n zenon_TY_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> False).
% 13.94/14.17 do 5 intro. intros zenon_H52 zenon_H53 zenon_H4e zenon_H49 zenon_H7 zenon_H8 zenon_Ha zenon_H9 zenon_Hb.
% 13.94/14.17 generalize (zenon_H52 zenon_TX_db). zenon_intro zenon_H55.
% 13.94/14.17 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H56 | zenon_intro zenon_H4d ].
% 13.94/14.17 exact (zenon_H56 zenon_H53).
% 13.94/14.17 apply (zenon_L4_ zenon_TY_m zenon_TX_n zenon_TY_cw zenon_TX_db); trivial.
% 13.94/14.17 (* end of lemma zenon_L5_ *)
% 13.94/14.17 assert (zenon_L6_ : forall (zenon_TY_m : zenon_U) (zenon_TX_n : zenon_U) (zenon_TY_cw : zenon_U) (zenon_TX_db : zenon_U) (zenon_TY_dg : zenon_U) (zenon_TX_dl : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_dl Y))\/(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)))\/((~(p1 X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))) -> (r1 zenon_TX_dl zenon_TY_dg) -> (r1 zenon_TY_dg zenon_TX_db) -> (r1 zenon_TX_db zenon_TY_cw) -> (r1 zenon_TY_cw zenon_TX_n) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (p1 zenon_TX_n) -> (r1 zenon_TX_n zenon_TY_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> False).
% 13.94/14.17 do 6 intro. intros zenon_H57 zenon_H58 zenon_H53 zenon_H4e zenon_H49 zenon_H7 zenon_H8 zenon_Ha zenon_H9 zenon_Hb.
% 13.94/14.17 generalize (zenon_H57 zenon_TY_dg). zenon_intro zenon_H5a.
% 13.94/14.17 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H5b | zenon_intro zenon_H52 ].
% 13.94/14.17 exact (zenon_H5b zenon_H58).
% 13.94/14.17 apply (zenon_L5_ zenon_TY_m zenon_TX_n zenon_TY_cw zenon_TX_db zenon_TY_dg); trivial.
% 13.94/14.17 (* end of lemma zenon_L6_ *)
% 13.94/14.17 assert (zenon_L7_ : forall (zenon_TX_ds : zenon_U) (zenon_TY_dt : zenon_U) (zenon_TX_dl : zenon_U) (zenon_TY_dg : zenon_U) (zenon_TX_db : zenon_U) (zenon_TY_cw : zenon_U) (zenon_TY_m : zenon_U) (zenon_TX_n : zenon_U), ((p1 zenon_TX_n)\/((forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (r1 zenon_TX_n zenon_TY_m) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (r1 zenon_TY_cw zenon_TX_n) -> (r1 zenon_TX_db zenon_TY_cw) -> (r1 zenon_TY_dg zenon_TX_db) -> (r1 zenon_TX_dl zenon_TY_dg) -> (r1 zenon_TY_dt zenon_TX_dl) -> (r1 zenon_TX_ds zenon_TY_dt) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ds Y))\/(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))\/(forall X : zenon_U, ((~(r1 Y X))\/(((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/((~(p1 X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))))))) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> False).
% 13.94/14.17 do 8 intro. intros zenon_H11 zenon_H9 zenon_Ha zenon_H7 zenon_H49 zenon_H4e zenon_H53 zenon_H58 zenon_H5c zenon_H5d zenon_H5e zenon_H5f zenon_Hb.
% 13.94/14.17 apply (zenon_or_s _ _ zenon_H11); [ zenon_intro zenon_H8 | zenon_intro zenon_H62 ].
% 13.94/14.17 generalize (zenon_H5e zenon_TY_dt). zenon_intro zenon_H63.
% 13.94/14.17 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ].
% 13.94/14.17 exact (zenon_H65 zenon_H5d).
% 13.94/14.17 generalize (zenon_H64 zenon_TX_dl). zenon_intro zenon_H66.
% 13.94/14.17 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H67 | zenon_intro zenon_H57 ].
% 13.94/14.17 exact (zenon_H67 zenon_H5c).
% 13.94/14.17 apply (zenon_L6_ zenon_TY_m zenon_TX_n zenon_TY_cw zenon_TX_db zenon_TY_dg zenon_TX_dl); trivial.
% 13.94/14.17 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H68 | zenon_intro zenon_H3b ].
% 13.94/14.17 exact (zenon_H5f zenon_H68).
% 13.94/14.17 exact (zenon_H3b zenon_Hb).
% 13.94/14.17 (* end of lemma zenon_L7_ *)
% 13.94/14.17 assert (zenon_L8_ : forall (zenon_TX_ds : zenon_U) (zenon_TY_dt : zenon_U) (zenon_TX_dl : zenon_U) (zenon_TY_dg : zenon_U) (zenon_TX_db : zenon_U) (zenon_TY_cw : zenon_U) (zenon_TY_m : zenon_U) (zenon_TX_n : zenon_U), (((forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))\/((~(p1 zenon_TX_n))\/((forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 zenon_TX_n)\/((forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))/\((forall X : zenon_U, ((~(r1 zenon_TX_n 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 zenon_TX_n Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (r1 zenon_TX_n zenon_TY_m) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (r1 zenon_TY_cw zenon_TX_n) -> (r1 zenon_TX_db zenon_TY_cw) -> (r1 zenon_TY_dg zenon_TX_db) -> (r1 zenon_TX_dl zenon_TY_dg) -> (r1 zenon_TY_dt zenon_TX_dl) -> (r1 zenon_TX_ds zenon_TY_dt) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ds Y))\/(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))\/(forall X : zenon_U, ((~(r1 Y X))\/(((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/((~(p1 X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))))))) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> False).
% 13.94/14.17 do 8 intro. intros zenon_H6 zenon_H9 zenon_Ha zenon_H7 zenon_H49 zenon_H4e zenon_H53 zenon_H58 zenon_H5c zenon_H5d zenon_H5e zenon_H5f zenon_Hb.
% 13.94/14.17 apply (zenon_and_s _ _ zenon_H6). zenon_intro zenon_Hf. zenon_intro zenon_He.
% 13.94/14.17 apply (zenon_and_s _ _ zenon_He). zenon_intro zenon_H11. zenon_intro zenon_H10.
% 13.94/14.17 apply (zenon_L7_ zenon_TX_ds zenon_TY_dt zenon_TX_dl zenon_TY_dg zenon_TX_db zenon_TY_cw zenon_TY_m zenon_TX_n); trivial.
% 13.94/14.17 (* end of lemma zenon_L8_ *)
% 13.94/14.17 assert (zenon_L9_ : forall (zenon_TY_m : zenon_U) (zenon_TX_db : zenon_U) (zenon_TY_dg : zenon_U) (zenon_TX_dl : zenon_U) (zenon_TY_dt : zenon_U) (zenon_TX_ds : zenon_U) (zenon_TX_n : zenon_U) (zenon_TY_cw : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TY_cw X))\/(((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/((~(p1 X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))) -> (r1 zenon_TY_cw zenon_TX_n) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ds Y))\/(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))\/(forall X : zenon_U, ((~(r1 Y X))\/(((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/((~(p1 X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))))))) -> (r1 zenon_TX_ds zenon_TY_dt) -> (r1 zenon_TY_dt zenon_TX_dl) -> (r1 zenon_TX_dl zenon_TY_dg) -> (r1 zenon_TY_dg zenon_TX_db) -> (r1 zenon_TX_db zenon_TY_cw) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (r1 zenon_TX_n zenon_TY_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) -> False).
% 13.94/14.17 do 8 intro. intros zenon_H48 zenon_H49 zenon_H5e zenon_H5d zenon_H5c zenon_H58 zenon_H53 zenon_H4e zenon_H7 zenon_Ha zenon_H9 zenon_Hb zenon_H5f.
% 13.94/14.17 generalize (zenon_H48 zenon_TX_n). zenon_intro zenon_H4b.
% 13.94/14.17 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H4c | zenon_intro zenon_H6 ].
% 13.94/14.17 exact (zenon_H4c zenon_H49).
% 13.94/14.17 apply (zenon_L8_ zenon_TX_ds zenon_TY_dt zenon_TX_dl zenon_TY_dg zenon_TX_db zenon_TY_cw zenon_TY_m zenon_TX_n); trivial.
% 13.94/14.17 (* end of lemma zenon_L9_ *)
% 13.94/14.17 assert (zenon_L10_ : forall (zenon_TY_m : zenon_U) (zenon_TY_dg : zenon_U) (zenon_TX_dl : zenon_U) (zenon_TY_dt : zenon_U) (zenon_TX_ds : zenon_U) (zenon_TX_n : zenon_U) (zenon_TY_cw : zenon_U) (zenon_TX_db : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_db Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/((~(p1 X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))) -> (r1 zenon_TX_db zenon_TY_cw) -> (r1 zenon_TY_cw zenon_TX_n) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ds Y))\/(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))\/(forall X : zenon_U, ((~(r1 Y X))\/(((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/((~(p1 X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))))))) -> (r1 zenon_TX_ds zenon_TY_dt) -> (r1 zenon_TY_dt zenon_TX_dl) -> (r1 zenon_TX_dl zenon_TY_dg) -> (r1 zenon_TY_dg zenon_TX_db) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (r1 zenon_TX_n zenon_TY_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) -> False).
% 13.94/14.17 do 8 intro. intros zenon_H4d zenon_H4e zenon_H49 zenon_H5e zenon_H5d zenon_H5c zenon_H58 zenon_H53 zenon_H7 zenon_Ha zenon_H9 zenon_Hb zenon_H5f.
% 13.94/14.17 generalize (zenon_H4d zenon_TY_cw). zenon_intro zenon_H50.
% 13.94/14.17 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H51 | zenon_intro zenon_H48 ].
% 13.94/14.17 exact (zenon_H51 zenon_H4e).
% 13.94/14.17 apply (zenon_L9_ zenon_TY_m zenon_TX_db zenon_TY_dg zenon_TX_dl zenon_TY_dt zenon_TX_ds zenon_TX_n zenon_TY_cw); trivial.
% 13.94/14.17 (* end of lemma zenon_L10_ *)
% 13.94/14.17 assert (zenon_L11_ : forall (zenon_TY_m : zenon_U) (zenon_TX_dl : zenon_U) (zenon_TY_dt : zenon_U) (zenon_TX_ds : zenon_U) (zenon_TX_n : zenon_U) (zenon_TY_cw : zenon_U) (zenon_TX_db : zenon_U) (zenon_TY_dg : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TY_dg X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/((~(p1 X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))) -> (r1 zenon_TY_dg zenon_TX_db) -> (r1 zenon_TX_db zenon_TY_cw) -> (r1 zenon_TY_cw zenon_TX_n) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ds Y))\/(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))\/(forall X : zenon_U, ((~(r1 Y X))\/(((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/((~(p1 X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))))))) -> (r1 zenon_TX_ds zenon_TY_dt) -> (r1 zenon_TY_dt zenon_TX_dl) -> (r1 zenon_TX_dl zenon_TY_dg) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (r1 zenon_TX_n zenon_TY_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) -> False).
% 13.94/14.17 do 8 intro. intros zenon_H52 zenon_H53 zenon_H4e zenon_H49 zenon_H5e zenon_H5d zenon_H5c zenon_H58 zenon_H7 zenon_Ha zenon_H9 zenon_Hb zenon_H5f.
% 13.94/14.17 generalize (zenon_H52 zenon_TX_db). zenon_intro zenon_H55.
% 13.94/14.17 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H56 | zenon_intro zenon_H4d ].
% 13.94/14.17 exact (zenon_H56 zenon_H53).
% 13.94/14.17 apply (zenon_L10_ zenon_TY_m zenon_TY_dg zenon_TX_dl zenon_TY_dt zenon_TX_ds zenon_TX_n zenon_TY_cw zenon_TX_db); trivial.
% 13.94/14.17 (* end of lemma zenon_L11_ *)
% 13.94/14.17 assert (zenon_L12_ : forall (zenon_TY_m : zenon_U) (zenon_TY_dt : zenon_U) (zenon_TX_ds : zenon_U) (zenon_TX_n : zenon_U) (zenon_TY_cw : zenon_U) (zenon_TX_db : zenon_U) (zenon_TY_dg : zenon_U) (zenon_TX_dl : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_dl Y))\/(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)))\/((~(p1 X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))) -> (r1 zenon_TX_dl zenon_TY_dg) -> (r1 zenon_TY_dg zenon_TX_db) -> (r1 zenon_TX_db zenon_TY_cw) -> (r1 zenon_TY_cw zenon_TX_n) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ds Y))\/(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))\/(forall X : zenon_U, ((~(r1 Y X))\/(((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/((~(p1 X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/((~(p1 Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))))))))))/\(((p1 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))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 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 Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))))))) -> (r1 zenon_TX_ds zenon_TY_dt) -> (r1 zenon_TY_dt zenon_TX_dl) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(p1 Y)))) -> (r1 zenon_TX_n zenon_TY_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_m X))\/(p1 X))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))))))) -> (~(forall Y : zenon_U, ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X))))))) -> False).
% 13.94/14.17 do 8 intro. intros zenon_H57 zenon_H58 zenon_H53 zenon_H4e zenon_H49 zenon_H5e zenon_H5d zenon_H5c zenon_H7 zenon_Ha zenon_H9 zenon_Hb zenon_H5f.
% 13.94/14.17 generalize (zenon_H57 zenon_TY_dg). zenon_intro zenon_H5a.
% 13.94/14.17 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H5b | zenon_intro zenon_H52 ].
% 13.94/14.17 exact (zenon_H5b zenon_H58).
% 13.94/14.17 apply (zenon_L11_ zenon_TY_m zenon_TX_dl zenon_TY_dt zenon_TX_ds zenon_TX_n zenon_TY_cw zenon_TX_db zenon_TY_dg); trivial.
% 13.94/14.17 (* end of lemma zenon_L12_ *)
% 13.94/14.17 apply NNPP. intro zenon_G.
% 13.94/14.17 apply zenon_G. zenon_intro zenon_H69.
% 13.94/14.17 elim zenon_H69. zenon_intro zenon_TX_ds. zenon_intro zenon_H6a.
% 13.94/14.17 apply (zenon_notor_s _ _ zenon_H6a). zenon_intro zenon_H6c. zenon_intro zenon_H6b.
% 13.94/14.17 apply (zenon_notor_s _ _ zenon_H6b). zenon_intro zenon_H6e. zenon_intro zenon_H6d.
% 13.94/14.17 apply (zenon_notor_s _ _ zenon_H6d). zenon_intro zenon_H70. zenon_intro zenon_H6f.
% 13.94/14.17 apply (zenon_notor_s _ _ zenon_H6f). zenon_intro zenon_H72. zenon_intro zenon_H71.
% 13.94/14.17 apply zenon_H71. zenon_intro zenon_H73.
% 13.94/14.17 apply (zenon_and_s _ _ zenon_H73). zenon_intro zenon_H75. zenon_intro zenon_H74.
% 13.94/14.17 apply zenon_H72. zenon_intro zenon_H5e.
% 13.94/14.17 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_ds Y))\/(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))\/(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 Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))))) zenon_H75); [ zenon_intro zenon_H76; idtac ].
% 13.94/14.17 elim zenon_H76. zenon_intro zenon_TY_dt. zenon_intro zenon_H77.
% 13.94/14.17 apply (zenon_notor_s _ _ zenon_H77). zenon_intro zenon_H79. zenon_intro zenon_H78.
% 13.94/14.17 apply zenon_H79. zenon_intro zenon_H5d.
% 13.94/14.17 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_dt X))\/(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))\/((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 Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))))) zenon_H78); [ zenon_intro zenon_H7a; idtac ].
% 13.94/14.17 elim zenon_H7a. zenon_intro zenon_TX_dl. zenon_intro zenon_H7b.
% 13.94/14.17 apply (zenon_notor_s _ _ zenon_H7b). zenon_intro zenon_H7d. zenon_intro zenon_H7c.
% 13.94/14.17 apply zenon_H7d. zenon_intro zenon_H5c.
% 13.94/14.17 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_dl Y))\/(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 Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))))) zenon_H7c); [ zenon_intro zenon_H7e; idtac ].
% 13.94/14.17 elim zenon_H7e. zenon_intro zenon_TY_dg. zenon_intro zenon_H7f.
% 13.94/14.17 apply (zenon_notor_s _ _ zenon_H7f). zenon_intro zenon_H81. zenon_intro zenon_H80.
% 13.94/14.17 apply zenon_H81. zenon_intro zenon_H58.
% 13.94/14.17 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_dg 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 Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))))) zenon_H80); [ zenon_intro zenon_H82; idtac ].
% 13.94/14.17 elim zenon_H82. zenon_intro zenon_TX_db. zenon_intro zenon_H83.
% 13.94/14.17 apply (zenon_notor_s _ _ zenon_H83). zenon_intro zenon_H85. zenon_intro zenon_H84.
% 14.00/14.18 apply zenon_H85. zenon_intro zenon_H53.
% 14.00/14.18 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_db 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 Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))))) zenon_H84); [ zenon_intro zenon_H86; idtac ].
% 14.00/14.18 elim zenon_H86. zenon_intro zenon_TY_cw. zenon_intro zenon_H87.
% 14.00/14.18 apply (zenon_notor_s _ _ zenon_H87). zenon_intro zenon_H89. zenon_intro zenon_H88.
% 14.00/14.18 apply zenon_H89. zenon_intro zenon_H4e.
% 14.00/14.18 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_cw 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 Y : zenon_U, ((~(r1 X Y))\/((p1 Y)\/(~(forall X : zenon_U, ((~(r1 Y X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X)))))))))))))) zenon_H88); [ zenon_intro zenon_H8a; idtac ].
% 14.00/14.18 elim zenon_H8a. zenon_intro zenon_TX_n. zenon_intro zenon_H8b.
% 14.00/14.18 apply (zenon_notor_s _ _ zenon_H8b). zenon_intro zenon_H8d. zenon_intro zenon_H8c.
% 14.00/14.18 apply (zenon_notor_s _ _ zenon_H8c). zenon_intro zenon_H7. zenon_intro zenon_H8e.
% 14.00/14.18 apply (zenon_notor_s _ _ zenon_H8e). zenon_intro zenon_H5f. zenon_intro zenon_H8f.
% 14.00/14.18 apply zenon_H8f. zenon_intro zenon_Hb.
% 14.00/14.18 apply zenon_H8d. zenon_intro zenon_H49.
% 14.00/14.18 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_n Y))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))))) zenon_H5f); [ zenon_intro zenon_H90; idtac ].
% 14.00/14.18 elim zenon_H90. zenon_intro zenon_TY_m. zenon_intro zenon_H91.
% 14.00/14.18 apply (zenon_notor_s _ _ zenon_H91). zenon_intro zenon_H93. zenon_intro zenon_H92.
% 14.00/14.18 apply zenon_H93. zenon_intro zenon_Ha.
% 14.00/14.18 apply zenon_H92. zenon_intro zenon_H9.
% 14.00/14.18 generalize (zenon_H5e zenon_TY_dt). zenon_intro zenon_H63.
% 14.00/14.18 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ].
% 14.00/14.18 exact (zenon_H65 zenon_H5d).
% 14.00/14.18 generalize (zenon_H64 zenon_TX_dl). zenon_intro zenon_H66.
% 14.00/14.18 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H67 | zenon_intro zenon_H57 ].
% 14.00/14.18 exact (zenon_H67 zenon_H5c).
% 14.00/14.18 apply (zenon_L12_ zenon_TY_m zenon_TY_dt zenon_TX_ds zenon_TX_n zenon_TY_cw zenon_TX_db zenon_TY_dg zenon_TX_dl); trivial.
% 14.00/14.18 Qed.
% 14.00/14.18 % SZS output end Proof
% 14.00/14.18 (* END-PROOF *)
% 14.00/14.18 nodes searched: 225545
% 14.00/14.18 max branch formulas: 57572
% 14.00/14.18 proof nodes created: 12637
% 14.00/14.18 formulas created: 1617320
% 14.00/14.18
%------------------------------------------------------------------------------