TSTP Solution File: LCL640+1.005 by Zenon---0.7.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : LCL640+1.005 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n013.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 16:22:53 EDT 2022
% Result : Theorem 4.56s 4.74s
% Output : Proof 4.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL640+1.005 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n013.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 : Mon Jul 4 23:50:44 EDT 2022
% 0.12/0.33 % CPUTime :
% 4.56/4.74 (* PROOF-FOUND *)
% 4.56/4.74 % SZS status Theorem
% 4.56/4.74 (* BEGIN-PROOF *)
% 4.56/4.74 % SZS output start Proof
% 4.56/4.74 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))\/(((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))\/(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 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 X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 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 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)))\/(~(p1 X)))))))))))\/(~(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))\/(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 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))\/(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)))))))))))))))))).
% 4.56/4.74 Proof.
% 4.56/4.74 assert (zenon_L1_ : forall (zenon_TY_d : zenon_U), (~((forall X : zenon_U, ((~(r1 zenon_TY_d X))\/(p1 X)))\/(~(p1 zenon_TY_d)))) -> (~(p1 zenon_TY_d)) -> False).
% 4.56/4.74 do 1 intro. intros zenon_H1 zenon_H2.
% 4.56/4.74 apply (zenon_notor_s _ _ zenon_H1). zenon_intro zenon_H5. zenon_intro zenon_H4.
% 4.56/4.74 exact (zenon_H4 zenon_H2).
% 4.56/4.74 (* end of lemma zenon_L1_ *)
% 4.56/4.74 assert (zenon_L2_ : forall (zenon_TX_m : zenon_U) (zenon_TY_n : zenon_U), (((forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(p1 X)))\/((~(p1 zenon_TY_n))\/((forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))\/(~(forall X : zenon_U, ((~(r1 zenon_TY_n 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 X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))))))/\(((p1 zenon_TY_n)\/((forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 zenon_TY_n 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_TY_n 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 zenon_TY_n 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 X : zenon_U, ((~(r1 zenon_TY_n 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 zenon_TY_n X))\/(p1 X)))) -> (p1 zenon_TY_n) -> (forall Y : zenon_U, ((~(r1 zenon_TX_m Y))\/(p1 Y))) -> (r1 zenon_TY_n zenon_TX_m) -> (forall X : zenon_U, ((~(r1 zenon_TY_n X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))) -> False).
% 4.56/4.74 do 2 intro. intros zenon_H6 zenon_H7 zenon_H8 zenon_H9 zenon_Ha zenon_Hb.
% 4.56/4.74 apply (zenon_and_s _ _ zenon_H6). zenon_intro zenon_Hf. zenon_intro zenon_He.
% 4.56/4.74 apply (zenon_and_s _ _ zenon_He). zenon_intro zenon_H11. zenon_intro zenon_H10.
% 4.56/4.74 apply (zenon_and_s _ _ zenon_H10). zenon_intro zenon_H13. zenon_intro zenon_H12.
% 4.56/4.74 apply (zenon_or_s _ _ zenon_Hf); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ].
% 4.56/4.74 exact (zenon_H7 zenon_H15).
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H14); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ].
% 4.56/4.74 exact (zenon_H17 zenon_H8).
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H16); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ].
% 4.56/4.74 generalize (zenon_H13 zenon_TX_m). zenon_intro zenon_H1a.
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ].
% 4.56/4.74 exact (zenon_H1c zenon_Ha).
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H1b); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ].
% 4.56/4.74 generalize (zenon_H19 zenon_TX_m). zenon_intro zenon_H1f.
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H1f); [ zenon_intro zenon_H1c | zenon_intro zenon_H20 ].
% 4.56/4.74 exact (zenon_H1c zenon_Ha).
% 4.56/4.74 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_m X))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))\/(~(p1 X))))) zenon_H20); [ zenon_intro zenon_H21; idtac ].
% 4.56/4.74 elim zenon_H21. zenon_intro zenon_TX_bi. zenon_intro zenon_H23.
% 4.56/4.74 apply (zenon_notor_s _ _ zenon_H23). zenon_intro zenon_H25. zenon_intro zenon_H24.
% 4.56/4.74 apply (zenon_notor_s _ _ zenon_H24). zenon_intro zenon_H27. zenon_intro zenon_H26.
% 4.56/4.74 apply zenon_H25. zenon_intro zenon_H28.
% 4.56/4.74 generalize (zenon_H1e zenon_TX_bi). zenon_intro zenon_H29.
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 4.56/4.74 exact (zenon_H2b zenon_H28).
% 4.56/4.74 exact (zenon_H27 zenon_H2a).
% 4.56/4.74 exact (zenon_H1d zenon_H9).
% 4.56/4.74 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_n 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 X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y)))))))))))) zenon_H18); [ zenon_intro zenon_H2c; idtac ].
% 4.56/4.74 elim zenon_H2c. zenon_intro zenon_TX_bt. zenon_intro zenon_H2e.
% 4.56/4.74 apply (zenon_notor_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H2f.
% 4.56/4.74 apply (zenon_notor_s _ _ zenon_H2f). zenon_intro zenon_H32. zenon_intro zenon_H31.
% 4.56/4.74 apply (zenon_notor_s _ _ zenon_H31). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 4.56/4.74 apply zenon_H33. zenon_intro zenon_H35.
% 4.56/4.74 apply zenon_H30. zenon_intro zenon_H36.
% 4.56/4.74 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_bt Y))\/(p1 Y))) zenon_H32); [ zenon_intro zenon_H37; idtac ].
% 4.56/4.74 elim zenon_H37. zenon_intro zenon_TY_d. zenon_intro zenon_H38.
% 4.56/4.74 apply (zenon_notor_s _ _ zenon_H38). zenon_intro zenon_H39. zenon_intro zenon_H2.
% 4.56/4.74 apply zenon_H39. zenon_intro zenon_H3a.
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H12); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ].
% 4.56/4.74 generalize (zenon_H35 zenon_TY_d). zenon_intro zenon_H3d.
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ].
% 4.56/4.74 exact (zenon_H3f zenon_H3a).
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H1 ].
% 4.56/4.74 generalize (zenon_H3c zenon_TX_bt). zenon_intro zenon_H41.
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ].
% 4.56/4.74 exact (zenon_H43 zenon_H36).
% 4.56/4.74 generalize (zenon_H42 zenon_TY_d). zenon_intro zenon_H44.
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H3f | zenon_intro zenon_H45 ].
% 4.56/4.74 exact (zenon_H3f zenon_H3a).
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 4.56/4.74 exact (zenon_H2 zenon_H47).
% 4.56/4.74 exact (zenon_H46 zenon_H40).
% 4.56/4.74 apply (zenon_L1_ zenon_TY_d); trivial.
% 4.56/4.74 exact (zenon_H3b zenon_Hb).
% 4.56/4.74 (* end of lemma zenon_L2_ *)
% 4.56/4.74 assert (zenon_L3_ : forall (zenon_TX_m : zenon_U) (zenon_TY_n : zenon_U) (zenon_TX_cw : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_cw 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 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 X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 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 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)))\/(~(p1 X)))))))))))\/(~(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)))))))))))))))) -> (r1 zenon_TX_cw zenon_TY_n) -> (~(forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(p1 X)))) -> (p1 zenon_TY_n) -> (r1 zenon_TY_n zenon_TX_m) -> (forall Y : zenon_U, ((~(r1 zenon_TX_m Y))\/(p1 Y))) -> (forall X : zenon_U, ((~(r1 zenon_TY_n X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))) -> False).
% 4.56/4.74 do 3 intro. intros zenon_H48 zenon_H49 zenon_H7 zenon_H8 zenon_Ha zenon_H9 zenon_Hb.
% 4.56/4.74 generalize (zenon_H48 zenon_TY_n). zenon_intro zenon_H4b.
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H4c | zenon_intro zenon_H6 ].
% 4.56/4.74 exact (zenon_H4c zenon_H49).
% 4.56/4.74 apply (zenon_L2_ zenon_TX_m zenon_TY_n); trivial.
% 4.56/4.74 (* end of lemma zenon_L3_ *)
% 4.56/4.74 assert (zenon_L4_ : forall (zenon_TX_dd : zenon_U) (zenon_TY_de : zenon_U) (zenon_TX_cw : zenon_U) (zenon_TX_m : zenon_U) (zenon_TY_n : zenon_U), ((p1 zenon_TY_n)\/((forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 zenon_TY_n 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_m Y))\/(p1 Y))) -> (r1 zenon_TY_n zenon_TX_m) -> (~(forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(p1 X)))) -> (r1 zenon_TX_cw zenon_TY_n) -> (r1 zenon_TY_de zenon_TX_cw) -> (r1 zenon_TX_dd zenon_TY_de) -> (forall Y : zenon_U, ((~(r1 zenon_TX_dd 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 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 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 X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 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 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)))\/(~(p1 X)))))))))))\/(~(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 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) -> (forall X : zenon_U, ((~(r1 zenon_TY_n X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))) -> False).
% 4.56/4.74 do 5 intro. intros zenon_H11 zenon_H9 zenon_Ha zenon_H7 zenon_H49 zenon_H4d zenon_H4e zenon_H4f zenon_H50 zenon_Hb.
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H11); [ zenon_intro zenon_H8 | zenon_intro zenon_H53 ].
% 4.56/4.74 generalize (zenon_H4f zenon_TY_de). zenon_intro zenon_H54.
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ].
% 4.56/4.74 exact (zenon_H56 zenon_H4e).
% 4.56/4.74 generalize (zenon_H55 zenon_TX_cw). zenon_intro zenon_H57.
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H57); [ zenon_intro zenon_H58 | zenon_intro zenon_H48 ].
% 4.56/4.74 exact (zenon_H58 zenon_H4d).
% 4.56/4.74 apply (zenon_L3_ zenon_TX_m zenon_TY_n zenon_TX_cw); trivial.
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H59 | zenon_intro zenon_H3b ].
% 4.56/4.74 exact (zenon_H50 zenon_H59).
% 4.56/4.74 exact (zenon_H3b zenon_Hb).
% 4.56/4.74 (* end of lemma zenon_L4_ *)
% 4.56/4.74 assert (zenon_L5_ : forall (zenon_TX_dd : zenon_U) (zenon_TY_de : zenon_U) (zenon_TX_cw : zenon_U) (zenon_TX_m : zenon_U) (zenon_TY_n : zenon_U), (((forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(p1 X)))\/((~(p1 zenon_TY_n))\/((forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))\/(~(forall X : zenon_U, ((~(r1 zenon_TY_n 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 X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))))))))))/\(((p1 zenon_TY_n)\/((forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))\/(~(forall X : zenon_U, ((~(r1 zenon_TY_n 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_TY_n 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 zenon_TY_n 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 X : zenon_U, ((~(r1 zenon_TY_n 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_m Y))\/(p1 Y))) -> (r1 zenon_TY_n zenon_TX_m) -> (~(forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(p1 X)))) -> (r1 zenon_TX_cw zenon_TY_n) -> (r1 zenon_TY_de zenon_TX_cw) -> (r1 zenon_TX_dd zenon_TY_de) -> (forall Y : zenon_U, ((~(r1 zenon_TX_dd 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 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 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 X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 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 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)))\/(~(p1 X)))))))))))\/(~(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 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) -> (forall X : zenon_U, ((~(r1 zenon_TY_n X))\/((p1 X)\/(~(forall Y : zenon_U, ((~(r1 X Y))\/((forall X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 Y))))))))) -> False).
% 4.56/4.74 do 5 intro. intros zenon_H6 zenon_H9 zenon_Ha zenon_H7 zenon_H49 zenon_H4d zenon_H4e zenon_H4f zenon_H50 zenon_Hb.
% 4.56/4.74 apply (zenon_and_s _ _ zenon_H6). zenon_intro zenon_Hf. zenon_intro zenon_He.
% 4.56/4.74 apply (zenon_and_s _ _ zenon_He). zenon_intro zenon_H11. zenon_intro zenon_H10.
% 4.56/4.74 apply (zenon_L4_ zenon_TX_dd zenon_TY_de zenon_TX_cw zenon_TX_m zenon_TY_n); trivial.
% 4.56/4.74 (* end of lemma zenon_L5_ *)
% 4.56/4.74 assert (zenon_L6_ : forall (zenon_TX_m : zenon_U) (zenon_TY_de : zenon_U) (zenon_TX_dd : zenon_U) (zenon_TY_n : zenon_U) (zenon_TX_cw : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_cw 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 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 X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 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 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)))\/(~(p1 X)))))))))))\/(~(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)))))))))))))))) -> (r1 zenon_TX_cw zenon_TY_n) -> (forall Y : zenon_U, ((~(r1 zenon_TX_dd 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 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 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 X : zenon_U, ((~(r1 Y X))\/(p1 X)))\/(~(p1 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 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)))\/(~(p1 X)))))))))))\/(~(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)))))))))))))))))))) -> (r1 zenon_TX_dd zenon_TY_de) -> (r1 zenon_TY_de zenon_TX_cw) -> (~(forall X : zenon_U, ((~(r1 zenon_TY_n X))\/(p1 X)))) -> (r1 zenon_TY_n zenon_TX_m) -> (forall Y : zenon_U, ((~(r1 zenon_TX_m Y))\/(p1 Y))) -> (forall X : zenon_U, ((~(r1 zenon_TY_n 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 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y))))))) -> False).
% 4.56/4.74 do 5 intro. intros zenon_H48 zenon_H49 zenon_H4f zenon_H4e zenon_H4d zenon_H7 zenon_Ha zenon_H9 zenon_Hb zenon_H50.
% 4.56/4.74 generalize (zenon_H48 zenon_TY_n). zenon_intro zenon_H4b.
% 4.56/4.74 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H4c | zenon_intro zenon_H6 ].
% 4.56/4.74 exact (zenon_H4c zenon_H49).
% 4.56/4.74 apply (zenon_L5_ zenon_TX_dd zenon_TY_de zenon_TX_cw zenon_TX_m zenon_TY_n); trivial.
% 4.56/4.74 (* end of lemma zenon_L6_ *)
% 4.56/4.74 apply NNPP. intro zenon_G.
% 4.56/4.74 apply zenon_G. zenon_intro zenon_H5a.
% 4.56/4.74 elim zenon_H5a. zenon_intro zenon_TX_dd. zenon_intro zenon_H5b.
% 4.56/4.74 apply (zenon_notor_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H5c.
% 4.56/4.74 apply (zenon_notor_s _ _ zenon_H5c). zenon_intro zenon_H5f. zenon_intro zenon_H5e.
% 4.56/4.74 apply zenon_H5e. zenon_intro zenon_H60.
% 4.56/4.74 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H62. zenon_intro zenon_H61.
% 4.56/4.74 apply zenon_H5f. zenon_intro zenon_H4f.
% 4.56/4.74 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_dd 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 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)))))))))))))))))) zenon_H62); [ zenon_intro zenon_H63; idtac ].
% 4.56/4.74 elim zenon_H63. zenon_intro zenon_TY_de. zenon_intro zenon_H64.
% 4.56/4.74 apply (zenon_notor_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H65.
% 4.56/4.74 apply zenon_H66. zenon_intro zenon_H4e.
% 4.56/4.74 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_de 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 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)))))))))))))))) zenon_H65); [ zenon_intro zenon_H67; idtac ].
% 4.56/4.74 elim zenon_H67. zenon_intro zenon_TX_cw. zenon_intro zenon_H68.
% 4.56/4.74 apply (zenon_notor_s _ _ zenon_H68). zenon_intro zenon_H6a. zenon_intro zenon_H69.
% 4.56/4.74 apply zenon_H6a. zenon_intro zenon_H4d.
% 4.56/4.74 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_cw 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 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)))))))))))))) zenon_H69); [ zenon_intro zenon_H6b; idtac ].
% 4.56/4.74 elim zenon_H6b. zenon_intro zenon_TY_n. zenon_intro zenon_H6c.
% 4.56/4.74 apply (zenon_notor_s _ _ zenon_H6c). zenon_intro zenon_H6e. zenon_intro zenon_H6d.
% 4.56/4.74 apply (zenon_notor_s _ _ zenon_H6d). zenon_intro zenon_H7. zenon_intro zenon_H6f.
% 4.56/4.74 apply (zenon_notor_s _ _ zenon_H6f). zenon_intro zenon_H50. zenon_intro zenon_H70.
% 4.56/4.74 apply zenon_H70. zenon_intro zenon_Hb.
% 4.56/4.74 apply zenon_H6e. zenon_intro zenon_H49.
% 4.56/4.74 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_n X))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(p1 Y)))))) zenon_H50); [ zenon_intro zenon_H71; idtac ].
% 4.56/4.74 elim zenon_H71. zenon_intro zenon_TX_m. zenon_intro zenon_H72.
% 4.56/4.75 apply (zenon_notor_s _ _ zenon_H72). zenon_intro zenon_H74. zenon_intro zenon_H73.
% 4.56/4.75 apply zenon_H74. zenon_intro zenon_Ha.
% 4.56/4.75 apply zenon_H73. zenon_intro zenon_H9.
% 4.56/4.75 generalize (zenon_H4f zenon_TY_de). zenon_intro zenon_H54.
% 4.56/4.75 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ].
% 4.56/4.75 exact (zenon_H56 zenon_H4e).
% 4.56/4.75 generalize (zenon_H55 zenon_TX_cw). zenon_intro zenon_H57.
% 4.56/4.75 apply (zenon_or_s _ _ zenon_H57); [ zenon_intro zenon_H58 | zenon_intro zenon_H48 ].
% 4.56/4.75 exact (zenon_H58 zenon_H4d).
% 4.56/4.75 apply (zenon_L6_ zenon_TX_m zenon_TY_de zenon_TX_dd zenon_TY_n zenon_TX_cw); trivial.
% 4.56/4.75 Qed.
% 4.56/4.75 % SZS output end Proof
% 4.56/4.75 (* END-PROOF *)
% 4.56/4.75 nodes searched: 118259
% 4.56/4.75 max branch formulas: 36809
% 4.56/4.75 proof nodes created: 3805
% 4.56/4.75 formulas created: 897632
% 4.56/4.75
%------------------------------------------------------------------------------