TSTP Solution File: SYN548+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SYN548+1 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n012.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 : Thu Jul 21 13:54:15 EDT 2022
% Result : Theorem 7.47s 7.69s
% Output : Proof 7.47s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SYN548+1 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Mon Jul 11 22:56:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 7.47/7.69 (* PROOF-FOUND *)
% 7.47/7.69 % SZS status Theorem
% 7.47/7.69 (* BEGIN-PROOF *)
% 7.47/7.69 % SZS output start Proof
% 7.47/7.69 Theorem prove_this : (exists X : zenon_U, ((reachable (initial_world) X)/\(forall Y : zenon_U, ((reachable X Y)->((forall Z : zenon_U, ((reachable Y Z)->((p Z)\/(forall V : zenon_U, ((reachable Z V)->(q V))))))<->((forall W : zenon_U, ((reachable Y W)->(p W)))\/(forall W : zenon_U, ((reachable Y W)->(q W))))))))).
% 7.47/7.69 Proof.
% 7.47/7.69 assert (zenon_L1_ : forall (zenon_TW_h : zenon_U) (zenon_TY_i : zenon_U), (reachable (initial_world) zenon_TY_i) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((reachable x y)->((reachable y z)->(reachable x z)))))) -> (~(reachable (initial_world) zenon_TW_h)) -> (reachable zenon_TY_i zenon_TW_h) -> False).
% 7.47/7.69 do 2 intro. intros zenon_H3 zenon_H4 zenon_H5 zenon_H6.
% 7.47/7.69 elim (classic ((~((initial_world) = zenon_TY_i))/\(~(reachable (initial_world) zenon_TY_i)))); [ zenon_intro zenon_H9 | zenon_intro zenon_Ha ].
% 7.47/7.69 apply (zenon_and_s _ _ zenon_H9). zenon_intro zenon_Hc. zenon_intro zenon_Hb.
% 7.47/7.69 exact (zenon_Hb zenon_H3).
% 7.47/7.69 cut ((reachable zenon_TY_i zenon_TW_h) = (reachable (initial_world) zenon_TW_h)).
% 7.47/7.69 intro zenon_D_pnotp.
% 7.47/7.69 apply zenon_H5.
% 7.47/7.69 rewrite <- zenon_D_pnotp.
% 7.47/7.69 exact zenon_H6.
% 7.47/7.69 cut ((zenon_TW_h = zenon_TW_h)); [idtac | apply NNPP; zenon_intro zenon_Hd].
% 7.47/7.69 cut ((zenon_TY_i = (initial_world))); [idtac | apply NNPP; zenon_intro zenon_He].
% 7.47/7.69 congruence.
% 7.47/7.69 apply (zenon_notand_s _ _ zenon_Ha); [ zenon_intro zenon_H10 | zenon_intro zenon_Hf ].
% 7.47/7.69 apply zenon_H10. zenon_intro zenon_H11.
% 7.47/7.69 elim (classic ((initial_world) = (initial_world))); [ zenon_intro zenon_H12 | zenon_intro zenon_H13 ].
% 7.47/7.69 cut (((initial_world) = (initial_world)) = (zenon_TY_i = (initial_world))).
% 7.47/7.69 intro zenon_D_pnotp.
% 7.47/7.69 apply zenon_He.
% 7.47/7.69 rewrite <- zenon_D_pnotp.
% 7.47/7.69 exact zenon_H12.
% 7.47/7.69 cut (((initial_world) = (initial_world))); [idtac | apply NNPP; zenon_intro zenon_H13].
% 7.47/7.69 cut (((initial_world) = zenon_TY_i)); [idtac | apply NNPP; zenon_intro zenon_Hc].
% 7.47/7.69 congruence.
% 7.47/7.69 exact (zenon_Hc zenon_H11).
% 7.47/7.69 apply zenon_H13. apply refl_equal.
% 7.47/7.69 apply zenon_H13. apply refl_equal.
% 7.47/7.69 apply zenon_Hf. zenon_intro zenon_H3.
% 7.47/7.69 generalize (zenon_H4 (initial_world)). zenon_intro zenon_H14.
% 7.47/7.69 generalize (zenon_H14 zenon_TY_i). zenon_intro zenon_H15.
% 7.47/7.69 generalize (zenon_H15 zenon_TW_h). zenon_intro zenon_H16.
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_H16); [ zenon_intro zenon_Hb | zenon_intro zenon_H17 ].
% 7.47/7.69 exact (zenon_Hb zenon_H3).
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ].
% 7.47/7.69 exact (zenon_H19 zenon_H6).
% 7.47/7.69 exact (zenon_H5 zenon_H18).
% 7.47/7.69 apply zenon_Hd. apply refl_equal.
% 7.47/7.69 (* end of lemma zenon_L1_ *)
% 7.47/7.69 assert (zenon_L2_ : forall (zenon_TW_be : zenon_U) (zenon_TY_bf : zenon_U) (zenon_TW_bg : zenon_U), (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((reachable x y)->((reachable y z)->(reachable x z)))))) -> (forall V : zenon_U, ((reachable zenon_TW_bg V)->(q V))) -> (reachable zenon_TY_bf zenon_TW_be) -> (reachable zenon_TW_bg zenon_TY_bf) -> (~(q zenon_TW_be)) -> False).
% 7.47/7.69 do 3 intro. intros zenon_H4 zenon_H1a zenon_H1b zenon_H1c zenon_H1d.
% 7.47/7.69 generalize (zenon_H1a zenon_TW_be). zenon_intro zenon_H21.
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ].
% 7.47/7.69 elim (classic ((~(zenon_TW_bg = zenon_TY_bf))/\(~(reachable zenon_TW_bg zenon_TY_bf)))); [ zenon_intro zenon_H24 | zenon_intro zenon_H25 ].
% 7.47/7.69 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H27. zenon_intro zenon_H26.
% 7.47/7.69 exact (zenon_H26 zenon_H1c).
% 7.47/7.69 cut ((reachable zenon_TY_bf zenon_TW_be) = (reachable zenon_TW_bg zenon_TW_be)).
% 7.47/7.69 intro zenon_D_pnotp.
% 7.47/7.69 apply zenon_H23.
% 7.47/7.69 rewrite <- zenon_D_pnotp.
% 7.47/7.69 exact zenon_H1b.
% 7.47/7.69 cut ((zenon_TW_be = zenon_TW_be)); [idtac | apply NNPP; zenon_intro zenon_H28].
% 7.47/7.69 cut ((zenon_TY_bf = zenon_TW_bg)); [idtac | apply NNPP; zenon_intro zenon_H29].
% 7.47/7.69 congruence.
% 7.47/7.69 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 7.47/7.69 apply zenon_H2b. zenon_intro zenon_H2c.
% 7.47/7.69 elim (classic (zenon_TW_bg = zenon_TW_bg)); [ zenon_intro zenon_H2d | zenon_intro zenon_H2e ].
% 7.47/7.69 cut ((zenon_TW_bg = zenon_TW_bg) = (zenon_TY_bf = zenon_TW_bg)).
% 7.47/7.69 intro zenon_D_pnotp.
% 7.47/7.69 apply zenon_H29.
% 7.47/7.69 rewrite <- zenon_D_pnotp.
% 7.47/7.69 exact zenon_H2d.
% 7.47/7.69 cut ((zenon_TW_bg = zenon_TW_bg)); [idtac | apply NNPP; zenon_intro zenon_H2e].
% 7.47/7.69 cut ((zenon_TW_bg = zenon_TY_bf)); [idtac | apply NNPP; zenon_intro zenon_H27].
% 7.47/7.69 congruence.
% 7.47/7.69 exact (zenon_H27 zenon_H2c).
% 7.47/7.69 apply zenon_H2e. apply refl_equal.
% 7.47/7.69 apply zenon_H2e. apply refl_equal.
% 7.47/7.69 apply zenon_H2a. zenon_intro zenon_H1c.
% 7.47/7.69 generalize (zenon_H4 zenon_TW_bg). zenon_intro zenon_H2f.
% 7.47/7.69 generalize (zenon_H2f zenon_TY_bf). zenon_intro zenon_H30.
% 7.47/7.69 generalize (zenon_H30 zenon_TW_be). zenon_intro zenon_H31.
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H26 | zenon_intro zenon_H32 ].
% 7.47/7.69 exact (zenon_H26 zenon_H1c).
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 7.47/7.69 exact (zenon_H34 zenon_H1b).
% 7.47/7.69 exact (zenon_H23 zenon_H33).
% 7.47/7.69 apply zenon_H28. apply refl_equal.
% 7.47/7.69 exact (zenon_H1d zenon_H22).
% 7.47/7.69 (* end of lemma zenon_L2_ *)
% 7.47/7.69 apply NNPP. intro zenon_G.
% 7.47/7.69 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((reachable x y)->((reachable y z)->(reachable x z))))))); [ zenon_intro zenon_H4 | zenon_intro zenon_H35 ].
% 7.47/7.69 apply zenon_G. exists (initial_world). apply NNPP. zenon_intro zenon_H36.
% 7.47/7.69 apply (zenon_notand_s _ _ zenon_H36); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ].
% 7.47/7.69 generalize (reflexivity_of_reachable (initial_world)). zenon_intro zenon_H39.
% 7.47/7.69 exact (zenon_H38 zenon_H39).
% 7.47/7.69 apply (zenon_notallex_s (fun Y : zenon_U => ((reachable (initial_world) Y)->((forall Z : zenon_U, ((reachable Y Z)->((p Z)\/(forall V : zenon_U, ((reachable Z V)->(q V))))))<->((forall W : zenon_U, ((reachable Y W)->(p W)))\/(forall W : zenon_U, ((reachable Y W)->(q W))))))) zenon_H37); [ zenon_intro zenon_H3a; idtac ].
% 7.47/7.69 elim zenon_H3a. zenon_intro zenon_TY_i. zenon_intro zenon_H3b.
% 7.47/7.69 apply (zenon_notimply_s _ _ zenon_H3b). zenon_intro zenon_H3. zenon_intro zenon_H3c.
% 7.47/7.69 apply (zenon_notequiv_s _ _ zenon_H3c); [ zenon_intro zenon_H40; zenon_intro zenon_H3f | zenon_intro zenon_H3e; zenon_intro zenon_H3d ].
% 7.47/7.69 apply (zenon_notallex_s (fun Z : zenon_U => ((reachable zenon_TY_i Z)->((p Z)\/(forall V : zenon_U, ((reachable Z V)->(q V)))))) zenon_H40); [ zenon_intro zenon_H41; idtac ].
% 7.47/7.69 elim zenon_H41. zenon_intro zenon_TZ_co. zenon_intro zenon_H43.
% 7.47/7.69 apply (zenon_notimply_s _ _ zenon_H43). zenon_intro zenon_H45. zenon_intro zenon_H44.
% 7.47/7.69 apply (zenon_notor_s _ _ zenon_H44). zenon_intro zenon_H47. zenon_intro zenon_H46.
% 7.47/7.69 apply (zenon_notallex_s (fun V : zenon_U => ((reachable zenon_TZ_co V)->(q V))) zenon_H46); [ zenon_intro zenon_H48; idtac ].
% 7.47/7.69 elim zenon_H48. zenon_intro zenon_TV_cv. zenon_intro zenon_H4a.
% 7.47/7.69 apply (zenon_notimply_s _ _ zenon_H4a). zenon_intro zenon_H4c. zenon_intro zenon_H4b.
% 7.47/7.69 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ].
% 7.47/7.69 generalize (zenon_H4e zenon_TZ_co). zenon_intro zenon_H4f.
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ].
% 7.47/7.69 exact (zenon_H51 zenon_H45).
% 7.47/7.69 exact (zenon_H47 zenon_H50).
% 7.47/7.69 generalize (zenon_H4d zenon_TV_cv). zenon_intro zenon_H52.
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ].
% 7.47/7.69 elim (classic ((~(zenon_TY_i = zenon_TZ_co))/\(~(reachable zenon_TY_i zenon_TZ_co)))); [ zenon_intro zenon_H55 | zenon_intro zenon_H56 ].
% 7.47/7.69 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H57. zenon_intro zenon_H51.
% 7.47/7.69 exact (zenon_H51 zenon_H45).
% 7.47/7.69 cut ((reachable zenon_TZ_co zenon_TV_cv) = (reachable zenon_TY_i zenon_TV_cv)).
% 7.47/7.69 intro zenon_D_pnotp.
% 7.47/7.69 apply zenon_H54.
% 7.47/7.69 rewrite <- zenon_D_pnotp.
% 7.47/7.69 exact zenon_H4c.
% 7.47/7.69 cut ((zenon_TV_cv = zenon_TV_cv)); [idtac | apply NNPP; zenon_intro zenon_H58].
% 7.47/7.69 cut ((zenon_TZ_co = zenon_TY_i)); [idtac | apply NNPP; zenon_intro zenon_H59].
% 7.47/7.69 congruence.
% 7.47/7.69 apply (zenon_notand_s _ _ zenon_H56); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ].
% 7.47/7.69 apply zenon_H5b. zenon_intro zenon_H5c.
% 7.47/7.69 elim (classic (zenon_TY_i = zenon_TY_i)); [ zenon_intro zenon_H5d | zenon_intro zenon_H5e ].
% 7.47/7.69 cut ((zenon_TY_i = zenon_TY_i) = (zenon_TZ_co = zenon_TY_i)).
% 7.47/7.69 intro zenon_D_pnotp.
% 7.47/7.69 apply zenon_H59.
% 7.47/7.69 rewrite <- zenon_D_pnotp.
% 7.47/7.69 exact zenon_H5d.
% 7.47/7.69 cut ((zenon_TY_i = zenon_TY_i)); [idtac | apply NNPP; zenon_intro zenon_H5e].
% 7.47/7.69 cut ((zenon_TY_i = zenon_TZ_co)); [idtac | apply NNPP; zenon_intro zenon_H57].
% 7.47/7.69 congruence.
% 7.47/7.69 exact (zenon_H57 zenon_H5c).
% 7.47/7.69 apply zenon_H5e. apply refl_equal.
% 7.47/7.69 apply zenon_H5e. apply refl_equal.
% 7.47/7.69 apply zenon_H5a. zenon_intro zenon_H45.
% 7.47/7.69 generalize (zenon_H4 zenon_TY_i). zenon_intro zenon_H5f.
% 7.47/7.69 generalize (zenon_H5f zenon_TZ_co). zenon_intro zenon_H60.
% 7.47/7.69 generalize (zenon_H60 zenon_TV_cv). zenon_intro zenon_H61.
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_H61); [ zenon_intro zenon_H51 | zenon_intro zenon_H62 ].
% 7.47/7.69 exact (zenon_H51 zenon_H45).
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ].
% 7.47/7.69 exact (zenon_H64 zenon_H4c).
% 7.47/7.69 exact (zenon_H54 zenon_H63).
% 7.47/7.69 apply zenon_H58. apply refl_equal.
% 7.47/7.69 exact (zenon_H4b zenon_H53).
% 7.47/7.69 apply (zenon_notor_s _ _ zenon_H3d). zenon_intro zenon_H66. zenon_intro zenon_H65.
% 7.47/7.69 apply (zenon_notallex_s (fun W : zenon_U => ((reachable zenon_TY_i W)->(q W))) zenon_H65); [ zenon_intro zenon_H67; idtac ].
% 7.47/7.69 elim zenon_H67. zenon_intro zenon_TW_h. zenon_intro zenon_H68.
% 7.47/7.69 apply (zenon_notimply_s _ _ zenon_H68). zenon_intro zenon_H6. zenon_intro zenon_H69.
% 7.47/7.69 apply zenon_G. exists zenon_TW_h. apply NNPP. zenon_intro zenon_H6a.
% 7.47/7.69 apply (zenon_notand_s _ _ zenon_H6a); [ zenon_intro zenon_H5 | zenon_intro zenon_H6b ].
% 7.47/7.69 apply (zenon_L1_ zenon_TW_h zenon_TY_i); trivial.
% 7.47/7.69 apply (zenon_notallex_s (fun Y : zenon_U => ((reachable zenon_TW_h Y)->((forall Z : zenon_U, ((reachable Y Z)->((p Z)\/(forall V : zenon_U, ((reachable Z V)->(q V))))))<->((forall W : zenon_U, ((reachable Y W)->(p W)))\/(forall W : zenon_U, ((reachable Y W)->(q W))))))) zenon_H6b); [ zenon_intro zenon_H6c; idtac ].
% 7.47/7.69 elim zenon_H6c. zenon_intro zenon_TY_ef. zenon_intro zenon_H6e.
% 7.47/7.69 apply (zenon_notimply_s _ _ zenon_H6e). zenon_intro zenon_H70. zenon_intro zenon_H6f.
% 7.47/7.69 apply (zenon_notequiv_s _ _ zenon_H6f); [ zenon_intro zenon_H74; zenon_intro zenon_H73 | zenon_intro zenon_H72; zenon_intro zenon_H71 ].
% 7.47/7.69 apply (zenon_notallex_s (fun Z : zenon_U => ((reachable zenon_TY_ef Z)->((p Z)\/(forall V : zenon_U, ((reachable Z V)->(q V)))))) zenon_H74); [ zenon_intro zenon_H75; idtac ].
% 7.47/7.69 elim zenon_H75. zenon_intro zenon_TZ_eo. zenon_intro zenon_H77.
% 7.47/7.69 apply (zenon_notimply_s _ _ zenon_H77). zenon_intro zenon_H79. zenon_intro zenon_H78.
% 7.47/7.69 apply (zenon_notor_s _ _ zenon_H78). zenon_intro zenon_H7b. zenon_intro zenon_H7a.
% 7.47/7.69 apply (zenon_notallex_s (fun V : zenon_U => ((reachable zenon_TZ_eo V)->(q V))) zenon_H7a); [ zenon_intro zenon_H7c; idtac ].
% 7.47/7.69 elim zenon_H7c. zenon_intro zenon_TV_ev. zenon_intro zenon_H7e.
% 7.47/7.69 apply (zenon_notimply_s _ _ zenon_H7e). zenon_intro zenon_H80. zenon_intro zenon_H7f.
% 7.47/7.69 apply (zenon_or_s _ _ zenon_H73); [ zenon_intro zenon_H82 | zenon_intro zenon_H81 ].
% 7.47/7.69 generalize (zenon_H82 zenon_TZ_eo). zenon_intro zenon_H83.
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_H83); [ zenon_intro zenon_H85 | zenon_intro zenon_H84 ].
% 7.47/7.69 exact (zenon_H85 zenon_H79).
% 7.47/7.69 exact (zenon_H7b zenon_H84).
% 7.47/7.69 generalize (zenon_H81 zenon_TV_ev). zenon_intro zenon_H86.
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_H86); [ zenon_intro zenon_H88 | zenon_intro zenon_H87 ].
% 7.47/7.69 elim (classic ((~(zenon_TY_ef = zenon_TZ_eo))/\(~(reachable zenon_TY_ef zenon_TZ_eo)))); [ zenon_intro zenon_H89 | zenon_intro zenon_H8a ].
% 7.47/7.69 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H85.
% 7.47/7.69 exact (zenon_H85 zenon_H79).
% 7.47/7.69 cut ((reachable zenon_TZ_eo zenon_TV_ev) = (reachable zenon_TY_ef zenon_TV_ev)).
% 7.47/7.69 intro zenon_D_pnotp.
% 7.47/7.69 apply zenon_H88.
% 7.47/7.69 rewrite <- zenon_D_pnotp.
% 7.47/7.69 exact zenon_H80.
% 7.47/7.69 cut ((zenon_TV_ev = zenon_TV_ev)); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 7.47/7.69 cut ((zenon_TZ_eo = zenon_TY_ef)); [idtac | apply NNPP; zenon_intro zenon_H8d].
% 7.47/7.69 congruence.
% 7.47/7.69 apply (zenon_notand_s _ _ zenon_H8a); [ zenon_intro zenon_H8f | zenon_intro zenon_H8e ].
% 7.47/7.69 apply zenon_H8f. zenon_intro zenon_H90.
% 7.47/7.69 elim (classic (zenon_TY_ef = zenon_TY_ef)); [ zenon_intro zenon_H91 | zenon_intro zenon_H92 ].
% 7.47/7.69 cut ((zenon_TY_ef = zenon_TY_ef) = (zenon_TZ_eo = zenon_TY_ef)).
% 7.47/7.69 intro zenon_D_pnotp.
% 7.47/7.69 apply zenon_H8d.
% 7.47/7.69 rewrite <- zenon_D_pnotp.
% 7.47/7.69 exact zenon_H91.
% 7.47/7.69 cut ((zenon_TY_ef = zenon_TY_ef)); [idtac | apply NNPP; zenon_intro zenon_H92].
% 7.47/7.69 cut ((zenon_TY_ef = zenon_TZ_eo)); [idtac | apply NNPP; zenon_intro zenon_H8b].
% 7.47/7.69 congruence.
% 7.47/7.69 exact (zenon_H8b zenon_H90).
% 7.47/7.69 apply zenon_H92. apply refl_equal.
% 7.47/7.69 apply zenon_H92. apply refl_equal.
% 7.47/7.69 apply zenon_H8e. zenon_intro zenon_H79.
% 7.47/7.69 generalize (zenon_H4 zenon_TY_ef). zenon_intro zenon_H93.
% 7.47/7.69 generalize (zenon_H93 zenon_TZ_eo). zenon_intro zenon_H94.
% 7.47/7.69 generalize (zenon_H94 zenon_TV_ev). zenon_intro zenon_H95.
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H85 | zenon_intro zenon_H96 ].
% 7.47/7.69 exact (zenon_H85 zenon_H79).
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_H96); [ zenon_intro zenon_H98 | zenon_intro zenon_H97 ].
% 7.47/7.69 exact (zenon_H98 zenon_H80).
% 7.47/7.69 exact (zenon_H88 zenon_H97).
% 7.47/7.69 apply zenon_H8c. apply refl_equal.
% 7.47/7.69 exact (zenon_H7f zenon_H87).
% 7.47/7.69 apply (zenon_notor_s _ _ zenon_H71). zenon_intro zenon_H9a. zenon_intro zenon_H99.
% 7.47/7.69 apply (zenon_notallex_s (fun W : zenon_U => ((reachable zenon_TY_ef W)->(p W))) zenon_H9a); [ zenon_intro zenon_H9b; idtac ].
% 7.47/7.69 elim zenon_H9b. zenon_intro zenon_TW_bg. zenon_intro zenon_H9c.
% 7.47/7.69 apply (zenon_notimply_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H9d.
% 7.47/7.69 apply zenon_G. exists zenon_TW_bg. apply NNPP. zenon_intro zenon_H9f.
% 7.47/7.69 apply (zenon_notand_s _ _ zenon_H9f); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha0 ].
% 7.47/7.69 elim (classic ((~((initial_world) = zenon_TY_ef))/\(~(reachable (initial_world) zenon_TY_ef)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ].
% 7.47/7.69 apply (zenon_and_s _ _ zenon_Ha2). zenon_intro zenon_Ha5. zenon_intro zenon_Ha4.
% 7.47/7.69 elim (classic ((~((initial_world) = zenon_TW_h))/\(~(reachable (initial_world) zenon_TW_h)))); [ zenon_intro zenon_Ha6 | zenon_intro zenon_Ha7 ].
% 7.47/7.69 apply (zenon_and_s _ _ zenon_Ha6). zenon_intro zenon_Ha8. zenon_intro zenon_H5.
% 7.47/7.69 apply (zenon_L1_ zenon_TW_h zenon_TY_i); trivial.
% 7.47/7.69 cut ((reachable zenon_TW_h zenon_TY_ef) = (reachable (initial_world) zenon_TY_ef)).
% 7.47/7.69 intro zenon_D_pnotp.
% 7.47/7.69 apply zenon_Ha4.
% 7.47/7.69 rewrite <- zenon_D_pnotp.
% 7.47/7.69 exact zenon_H70.
% 7.47/7.69 cut ((zenon_TY_ef = zenon_TY_ef)); [idtac | apply NNPP; zenon_intro zenon_H92].
% 7.47/7.69 cut ((zenon_TW_h = (initial_world))); [idtac | apply NNPP; zenon_intro zenon_Ha9].
% 7.47/7.69 congruence.
% 7.47/7.69 apply (zenon_notand_s _ _ zenon_Ha7); [ zenon_intro zenon_Hab | zenon_intro zenon_Haa ].
% 7.47/7.69 apply zenon_Hab. zenon_intro zenon_Hac.
% 7.47/7.69 elim (classic ((initial_world) = (initial_world))); [ zenon_intro zenon_H12 | zenon_intro zenon_H13 ].
% 7.47/7.69 cut (((initial_world) = (initial_world)) = (zenon_TW_h = (initial_world))).
% 7.47/7.69 intro zenon_D_pnotp.
% 7.47/7.69 apply zenon_Ha9.
% 7.47/7.69 rewrite <- zenon_D_pnotp.
% 7.47/7.69 exact zenon_H12.
% 7.47/7.69 cut (((initial_world) = (initial_world))); [idtac | apply NNPP; zenon_intro zenon_H13].
% 7.47/7.69 cut (((initial_world) = zenon_TW_h)); [idtac | apply NNPP; zenon_intro zenon_Ha8].
% 7.47/7.69 congruence.
% 7.47/7.69 exact (zenon_Ha8 zenon_Hac).
% 7.47/7.69 apply zenon_H13. apply refl_equal.
% 7.47/7.69 apply zenon_H13. apply refl_equal.
% 7.47/7.69 apply zenon_Haa. zenon_intro zenon_H18.
% 7.47/7.69 generalize (zenon_H4 (initial_world)). zenon_intro zenon_H14.
% 7.47/7.69 generalize (zenon_H14 zenon_TW_h). zenon_intro zenon_Had.
% 7.47/7.69 generalize (zenon_Had zenon_TY_ef). zenon_intro zenon_Hae.
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_Hae); [ zenon_intro zenon_H5 | zenon_intro zenon_Haf ].
% 7.47/7.69 exact (zenon_H5 zenon_H18).
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_Haf); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb0 ].
% 7.47/7.69 exact (zenon_Hb1 zenon_H70).
% 7.47/7.69 exact (zenon_Ha4 zenon_Hb0).
% 7.47/7.69 apply zenon_H92. apply refl_equal.
% 7.47/7.69 cut ((reachable zenon_TY_ef zenon_TW_bg) = (reachable (initial_world) zenon_TW_bg)).
% 7.47/7.69 intro zenon_D_pnotp.
% 7.47/7.69 apply zenon_Ha1.
% 7.47/7.69 rewrite <- zenon_D_pnotp.
% 7.47/7.69 exact zenon_H9e.
% 7.47/7.69 cut ((zenon_TW_bg = zenon_TW_bg)); [idtac | apply NNPP; zenon_intro zenon_H2e].
% 7.47/7.69 cut ((zenon_TY_ef = (initial_world))); [idtac | apply NNPP; zenon_intro zenon_Hb2].
% 7.47/7.69 congruence.
% 7.47/7.69 apply (zenon_notand_s _ _ zenon_Ha3); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ].
% 7.47/7.69 apply zenon_Hb4. zenon_intro zenon_Hb5.
% 7.47/7.69 elim (classic ((initial_world) = (initial_world))); [ zenon_intro zenon_H12 | zenon_intro zenon_H13 ].
% 7.47/7.69 cut (((initial_world) = (initial_world)) = (zenon_TY_ef = (initial_world))).
% 7.47/7.69 intro zenon_D_pnotp.
% 7.47/7.69 apply zenon_Hb2.
% 7.47/7.69 rewrite <- zenon_D_pnotp.
% 7.47/7.69 exact zenon_H12.
% 7.47/7.69 cut (((initial_world) = (initial_world))); [idtac | apply NNPP; zenon_intro zenon_H13].
% 7.47/7.69 cut (((initial_world) = zenon_TY_ef)); [idtac | apply NNPP; zenon_intro zenon_Ha5].
% 7.47/7.69 congruence.
% 7.47/7.69 exact (zenon_Ha5 zenon_Hb5).
% 7.47/7.69 apply zenon_H13. apply refl_equal.
% 7.47/7.69 apply zenon_H13. apply refl_equal.
% 7.47/7.69 apply zenon_Hb3. zenon_intro zenon_Hb0.
% 7.47/7.69 generalize (zenon_H4 (initial_world)). zenon_intro zenon_H14.
% 7.47/7.69 generalize (zenon_H14 zenon_TY_ef). zenon_intro zenon_Hb6.
% 7.47/7.69 generalize (zenon_Hb6 zenon_TW_bg). zenon_intro zenon_Hb7.
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_Hb7); [ zenon_intro zenon_Ha4 | zenon_intro zenon_Hb8 ].
% 7.47/7.69 exact (zenon_Ha4 zenon_Hb0).
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_Hb8); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ].
% 7.47/7.69 exact (zenon_Hba zenon_H9e).
% 7.47/7.69 exact (zenon_Ha1 zenon_Hb9).
% 7.47/7.69 apply zenon_H2e. apply refl_equal.
% 7.47/7.69 apply (zenon_notallex_s (fun Y : zenon_U => ((reachable zenon_TW_bg Y)->((forall Z : zenon_U, ((reachable Y Z)->((p Z)\/(forall V : zenon_U, ((reachable Z V)->(q V))))))<->((forall W : zenon_U, ((reachable Y W)->(p W)))\/(forall W : zenon_U, ((reachable Y W)->(q W))))))) zenon_Ha0); [ zenon_intro zenon_Hbb; idtac ].
% 7.47/7.69 elim zenon_Hbb. zenon_intro zenon_TY_bf. zenon_intro zenon_Hbc.
% 7.47/7.69 apply (zenon_notimply_s _ _ zenon_Hbc). zenon_intro zenon_H1c. zenon_intro zenon_Hbd.
% 7.47/7.69 apply (zenon_notequiv_s _ _ zenon_Hbd); [ zenon_intro zenon_Hc1; zenon_intro zenon_Hc0 | zenon_intro zenon_Hbf; zenon_intro zenon_Hbe ].
% 7.47/7.69 apply (zenon_notallex_s (fun Z : zenon_U => ((reachable zenon_TY_bf Z)->((p Z)\/(forall V : zenon_U, ((reachable Z V)->(q V)))))) zenon_Hc1); [ zenon_intro zenon_Hc2; idtac ].
% 7.47/7.69 elim zenon_Hc2. zenon_intro zenon_TZ_hn. zenon_intro zenon_Hc4.
% 7.47/7.69 apply (zenon_notimply_s _ _ zenon_Hc4). zenon_intro zenon_Hc6. zenon_intro zenon_Hc5.
% 7.47/7.69 apply (zenon_notor_s _ _ zenon_Hc5). zenon_intro zenon_Hc8. zenon_intro zenon_Hc7.
% 7.47/7.69 apply (zenon_notallex_s (fun V : zenon_U => ((reachable zenon_TZ_hn V)->(q V))) zenon_Hc7); [ zenon_intro zenon_Hc9; idtac ].
% 7.47/7.69 elim zenon_Hc9. zenon_intro zenon_TV_hu. zenon_intro zenon_Hcb.
% 7.47/7.69 apply (zenon_notimply_s _ _ zenon_Hcb). zenon_intro zenon_Hcd. zenon_intro zenon_Hcc.
% 7.47/7.69 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Hcf | zenon_intro zenon_Hce ].
% 7.47/7.69 generalize (zenon_Hcf zenon_TZ_hn). zenon_intro zenon_Hd0.
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_Hd0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd1 ].
% 7.47/7.69 exact (zenon_Hd2 zenon_Hc6).
% 7.47/7.69 exact (zenon_Hc8 zenon_Hd1).
% 7.47/7.69 generalize (zenon_Hce zenon_TV_hu). zenon_intro zenon_Hd3.
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_Hd3); [ zenon_intro zenon_Hd5 | zenon_intro zenon_Hd4 ].
% 7.47/7.69 elim (classic ((~(zenon_TY_bf = zenon_TZ_hn))/\(~(reachable zenon_TY_bf zenon_TZ_hn)))); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd7 ].
% 7.47/7.69 apply (zenon_and_s _ _ zenon_Hd6). zenon_intro zenon_Hd8. zenon_intro zenon_Hd2.
% 7.47/7.69 exact (zenon_Hd2 zenon_Hc6).
% 7.47/7.69 cut ((reachable zenon_TZ_hn zenon_TV_hu) = (reachable zenon_TY_bf zenon_TV_hu)).
% 7.47/7.69 intro zenon_D_pnotp.
% 7.47/7.69 apply zenon_Hd5.
% 7.47/7.69 rewrite <- zenon_D_pnotp.
% 7.47/7.69 exact zenon_Hcd.
% 7.47/7.69 cut ((zenon_TV_hu = zenon_TV_hu)); [idtac | apply NNPP; zenon_intro zenon_Hd9].
% 7.47/7.69 cut ((zenon_TZ_hn = zenon_TY_bf)); [idtac | apply NNPP; zenon_intro zenon_Hda].
% 7.47/7.69 congruence.
% 7.47/7.69 apply (zenon_notand_s _ _ zenon_Hd7); [ zenon_intro zenon_Hdc | zenon_intro zenon_Hdb ].
% 7.47/7.69 apply zenon_Hdc. zenon_intro zenon_Hdd.
% 7.47/7.69 elim (classic (zenon_TY_bf = zenon_TY_bf)); [ zenon_intro zenon_Hde | zenon_intro zenon_Hdf ].
% 7.47/7.69 cut ((zenon_TY_bf = zenon_TY_bf) = (zenon_TZ_hn = zenon_TY_bf)).
% 7.47/7.69 intro zenon_D_pnotp.
% 7.47/7.69 apply zenon_Hda.
% 7.47/7.69 rewrite <- zenon_D_pnotp.
% 7.47/7.69 exact zenon_Hde.
% 7.47/7.69 cut ((zenon_TY_bf = zenon_TY_bf)); [idtac | apply NNPP; zenon_intro zenon_Hdf].
% 7.47/7.69 cut ((zenon_TY_bf = zenon_TZ_hn)); [idtac | apply NNPP; zenon_intro zenon_Hd8].
% 7.47/7.69 congruence.
% 7.47/7.69 exact (zenon_Hd8 zenon_Hdd).
% 7.47/7.69 apply zenon_Hdf. apply refl_equal.
% 7.47/7.69 apply zenon_Hdf. apply refl_equal.
% 7.47/7.69 apply zenon_Hdb. zenon_intro zenon_Hc6.
% 7.47/7.69 generalize (zenon_H4 zenon_TY_bf). zenon_intro zenon_He0.
% 7.47/7.69 generalize (zenon_He0 zenon_TZ_hn). zenon_intro zenon_He1.
% 7.47/7.69 generalize (zenon_He1 zenon_TV_hu). zenon_intro zenon_He2.
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_He2); [ zenon_intro zenon_Hd2 | zenon_intro zenon_He3 ].
% 7.47/7.69 exact (zenon_Hd2 zenon_Hc6).
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_He3); [ zenon_intro zenon_He5 | zenon_intro zenon_He4 ].
% 7.47/7.69 exact (zenon_He5 zenon_Hcd).
% 7.47/7.69 exact (zenon_Hd5 zenon_He4).
% 7.47/7.69 apply zenon_Hd9. apply refl_equal.
% 7.47/7.69 exact (zenon_Hcc zenon_Hd4).
% 7.47/7.69 apply (zenon_notor_s _ _ zenon_Hbe). zenon_intro zenon_He7. zenon_intro zenon_He6.
% 7.47/7.69 apply (zenon_notallex_s (fun W : zenon_U => ((reachable zenon_TY_bf W)->(q W))) zenon_He6); [ zenon_intro zenon_He8; idtac ].
% 7.47/7.69 elim zenon_He8. zenon_intro zenon_TW_be. zenon_intro zenon_He9.
% 7.47/7.69 apply (zenon_notimply_s _ _ zenon_He9). zenon_intro zenon_H1b. zenon_intro zenon_H1d.
% 7.47/7.69 generalize (zenon_H72 zenon_TW_bg). zenon_intro zenon_Hea.
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_Hea); [ zenon_intro zenon_Hba | zenon_intro zenon_Heb ].
% 7.47/7.69 exact (zenon_Hba zenon_H9e).
% 7.47/7.69 apply (zenon_or_s _ _ zenon_Heb); [ zenon_intro zenon_Hec | zenon_intro zenon_H1a ].
% 7.47/7.69 exact (zenon_H9d zenon_Hec).
% 7.47/7.69 apply (zenon_L2_ zenon_TW_be zenon_TY_bf zenon_TW_bg); trivial.
% 7.47/7.69 apply zenon_H35. zenon_intro zenon_Tx_jd. apply NNPP. zenon_intro zenon_Hee.
% 7.47/7.69 apply zenon_Hee. zenon_intro zenon_Ty_jf. apply NNPP. zenon_intro zenon_Hf0.
% 7.47/7.69 apply zenon_Hf0. zenon_intro zenon_Tz_jh. apply NNPP. zenon_intro zenon_Hf2.
% 7.47/7.69 apply (zenon_notimply_s _ _ zenon_Hf2). zenon_intro zenon_Hf4. zenon_intro zenon_Hf3.
% 7.47/7.69 apply (zenon_notimply_s _ _ zenon_Hf3). zenon_intro zenon_Hf6. zenon_intro zenon_Hf5.
% 7.47/7.69 generalize (transitivity_of_reachable zenon_Tx_jd). zenon_intro zenon_Hf7.
% 7.47/7.69 generalize (zenon_Hf7 zenon_Ty_jf). zenon_intro zenon_Hf8.
% 7.47/7.69 generalize (zenon_Hf8 zenon_Tz_jh). zenon_intro zenon_Hf9.
% 7.47/7.69 apply (zenon_imply_s _ _ zenon_Hf9); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hfa ].
% 7.47/7.69 apply (zenon_notand_s _ _ zenon_Hfb); [ zenon_intro zenon_Hfd | zenon_intro zenon_Hfc ].
% 7.47/7.69 exact (zenon_Hfd zenon_Hf4).
% 7.47/7.69 exact (zenon_Hfc zenon_Hf6).
% 7.47/7.69 exact (zenon_Hf5 zenon_Hfa).
% 7.47/7.69 Qed.
% 7.47/7.69 % SZS output end Proof
% 7.47/7.69 (* END-PROOF *)
% 7.47/7.69 nodes searched: 80030
% 7.47/7.69 max branch formulas: 12854
% 7.47/7.69 proof nodes created: 8137
% 7.47/7.69 formulas created: 269800
% 7.47/7.69
%------------------------------------------------------------------------------