TSTP Solution File: LAT346+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : LAT346+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n007.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 07:23:52 EDT 2022
% Result : Theorem 9.26s 9.45s
% Output : Proof 9.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LAT346+1 : TPTP v8.1.0. Released v3.4.0.
% 0.12/0.13 % Command : run_zenon %s %d
% 0.12/0.34 % Computer : n007.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Thu Jun 30 10:08:38 EDT 2022
% 0.12/0.34 % CPUTime :
% 9.26/9.45 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 9.26/9.45 (* PROOF-FOUND *)
% 9.26/9.45 % SZS status Theorem
% 9.26/9.45 (* BEGIN-PROOF *)
% 9.26/9.45 % SZS output start Proof
% 9.26/9.45 Theorem t22_conlat_2 : (forall A : zenon_U, (((~(v3_conlat_1 A))/\(l2_conlat_1 A))->(r1_filter_1 (k11_conlat_1 (k7_conlat_2 A)) (k1_lattice2 (k11_conlat_1 A))))).
% 9.26/9.45 Proof.
% 9.26/9.45 assert (zenon_L1_ : forall (zenon_TA_ds : zenon_U), (~(v3_conlat_1 zenon_TA_ds)) -> (l2_conlat_1 zenon_TA_ds) -> (~(l3_lattices (k11_conlat_1 zenon_TA_ds))) -> False).
% 9.26/9.45 do 1 intro. intros zenon_H5d zenon_H5e zenon_H5f.
% 9.26/9.45 generalize (dt_k11_conlat_1 zenon_TA_ds). zenon_intro zenon_H61.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_H61); [ zenon_intro zenon_H63 | zenon_intro zenon_H62 ].
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ].
% 9.26/9.45 exact (zenon_H65 zenon_H5d).
% 9.26/9.45 exact (zenon_H64 zenon_H5e).
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H67. zenon_intro zenon_H66.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H66). zenon_intro zenon_H69. zenon_intro zenon_H68.
% 9.26/9.45 exact (zenon_H5f zenon_H68).
% 9.26/9.45 (* end of lemma zenon_L1_ *)
% 9.26/9.45 assert (zenon_L2_ : forall (zenon_TA_ds : zenon_U), (~(v3_conlat_1 zenon_TA_ds)) -> (l2_conlat_1 zenon_TA_ds) -> (~(l3_lattices (k1_lattice2 (k11_conlat_1 zenon_TA_ds)))) -> False).
% 9.26/9.45 do 1 intro. intros zenon_H5d zenon_H5e zenon_H6a.
% 9.26/9.45 generalize (dt_k1_lattice2 (k11_conlat_1 zenon_TA_ds)). zenon_intro zenon_H6b.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_H6b); [ zenon_intro zenon_H5f | zenon_intro zenon_H6c ].
% 9.26/9.45 apply (zenon_L1_ zenon_TA_ds); trivial.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H6c). zenon_intro zenon_H6e. zenon_intro zenon_H6d.
% 9.26/9.45 exact (zenon_H6a zenon_H6d).
% 9.26/9.45 (* end of lemma zenon_L2_ *)
% 9.26/9.45 assert (zenon_L3_ : forall (zenon_TA_ds : zenon_U), (~(v3_conlat_1 zenon_TA_ds)) -> (l2_conlat_1 zenon_TA_ds) -> (v3_conlat_1 (k7_conlat_2 zenon_TA_ds)) -> False).
% 9.26/9.45 do 1 intro. intros zenon_H5d zenon_H5e zenon_H6f.
% 9.26/9.45 generalize (dt_k7_conlat_2 zenon_TA_ds). zenon_intro zenon_H70.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H63 | zenon_intro zenon_H71 ].
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ].
% 9.26/9.45 exact (zenon_H65 zenon_H5d).
% 9.26/9.45 exact (zenon_H64 zenon_H5e).
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H73. zenon_intro zenon_H72.
% 9.26/9.45 exact (zenon_H73 zenon_H6f).
% 9.26/9.45 (* end of lemma zenon_L3_ *)
% 9.26/9.45 assert (zenon_L4_ : forall (zenon_TA_ds : zenon_U), (~(v3_conlat_1 zenon_TA_ds)) -> (l2_conlat_1 zenon_TA_ds) -> (~(l2_conlat_1 (k7_conlat_2 zenon_TA_ds))) -> False).
% 9.26/9.45 do 1 intro. intros zenon_H5d zenon_H5e zenon_H74.
% 9.26/9.45 generalize (dt_k7_conlat_2 zenon_TA_ds). zenon_intro zenon_H70.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H63 | zenon_intro zenon_H71 ].
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ].
% 9.26/9.45 exact (zenon_H65 zenon_H5d).
% 9.26/9.45 exact (zenon_H64 zenon_H5e).
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H73. zenon_intro zenon_H72.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H72). zenon_intro zenon_H76. zenon_intro zenon_H75.
% 9.26/9.45 exact (zenon_H74 zenon_H75).
% 9.26/9.45 (* end of lemma zenon_L4_ *)
% 9.26/9.45 apply NNPP. intro zenon_G.
% 9.26/9.45 apply (zenon_notallex_s (fun A : zenon_U => (((~(v3_conlat_1 A))/\(l2_conlat_1 A))->(r1_filter_1 (k11_conlat_1 (k7_conlat_2 A)) (k1_lattice2 (k11_conlat_1 A))))) zenon_G); [ zenon_intro zenon_H77; idtac ].
% 9.26/9.45 elim zenon_H77. zenon_intro zenon_TA_ds. zenon_intro zenon_H78.
% 9.26/9.45 apply (zenon_notimply_s _ _ zenon_H78). zenon_intro zenon_H7a. zenon_intro zenon_H79.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H7a). zenon_intro zenon_H5d. zenon_intro zenon_H5e.
% 9.26/9.45 generalize (fc2_conlat_2 (k11_conlat_1 zenon_TA_ds)). zenon_intro zenon_H7b.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_H7b); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ].
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_H7d); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ].
% 9.26/9.45 apply zenon_H7f. zenon_intro zenon_H80.
% 9.26/9.45 generalize (dt_k11_conlat_1 zenon_TA_ds). zenon_intro zenon_H61.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_H61); [ zenon_intro zenon_H63 | zenon_intro zenon_H62 ].
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ].
% 9.26/9.45 exact (zenon_H65 zenon_H5d).
% 9.26/9.45 exact (zenon_H64 zenon_H5e).
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H67. zenon_intro zenon_H66.
% 9.26/9.45 exact (zenon_H67 zenon_H80).
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_H7e); [ zenon_intro zenon_H82 | zenon_intro zenon_H81 ].
% 9.26/9.45 generalize (fc1_conlat_2 zenon_TA_ds). zenon_intro zenon_H83.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_H83); [ zenon_intro zenon_H63 | zenon_intro zenon_H84 ].
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ].
% 9.26/9.45 exact (zenon_H65 zenon_H5d).
% 9.26/9.45 exact (zenon_H64 zenon_H5e).
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H84). zenon_intro zenon_H67. zenon_intro zenon_H85.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H85). zenon_intro zenon_H69. zenon_intro zenon_H86.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H86). zenon_intro zenon_H88. zenon_intro zenon_H87.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H8a. zenon_intro zenon_H89.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8c. zenon_intro zenon_H8b.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H8b). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H92. zenon_intro zenon_H91.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H91). zenon_intro zenon_H94. zenon_intro zenon_H93.
% 9.26/9.45 exact (zenon_H82 zenon_H94).
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H95 | zenon_intro zenon_H5f ].
% 9.26/9.45 generalize (fc1_conlat_2 zenon_TA_ds). zenon_intro zenon_H83.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_H83); [ zenon_intro zenon_H63 | zenon_intro zenon_H84 ].
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ].
% 9.26/9.45 exact (zenon_H65 zenon_H5d).
% 9.26/9.45 exact (zenon_H64 zenon_H5e).
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H84). zenon_intro zenon_H67. zenon_intro zenon_H85.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H85). zenon_intro zenon_H69. zenon_intro zenon_H86.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H86). zenon_intro zenon_H88. zenon_intro zenon_H87.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H8a. zenon_intro zenon_H89.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8c. zenon_intro zenon_H8b.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H8b). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H8f). zenon_intro zenon_H92. zenon_intro zenon_H91.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H91). zenon_intro zenon_H94. zenon_intro zenon_H93.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H93). zenon_intro zenon_H97. zenon_intro zenon_H96.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H96). zenon_intro zenon_H99. zenon_intro zenon_H98.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H98). zenon_intro zenon_H9b. zenon_intro zenon_H9a.
% 9.26/9.45 exact (zenon_H95 zenon_H9a).
% 9.26/9.45 apply (zenon_L1_ zenon_TA_ds); trivial.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H7c). zenon_intro zenon_H9d. zenon_intro zenon_H9c.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H6e. zenon_intro zenon_H9e.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H9e). zenon_intro zenon_Ha0. zenon_intro zenon_H9f.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_H9f). zenon_intro zenon_Ha2. zenon_intro zenon_Ha1.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Ha1). zenon_intro zenon_Ha4. zenon_intro zenon_Ha3.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Ha3). zenon_intro zenon_Ha6. zenon_intro zenon_Ha5.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Ha5). zenon_intro zenon_Ha8. zenon_intro zenon_Ha7.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Ha7). zenon_intro zenon_Haa. zenon_intro zenon_Ha9.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Ha9). zenon_intro zenon_Hac. zenon_intro zenon_Hab.
% 9.26/9.45 generalize (symmetry_r1_filter_1 (k1_lattice2 (k11_conlat_1 zenon_TA_ds))). zenon_intro zenon_Had.
% 9.26/9.45 generalize (zenon_Had (k11_conlat_1 (k7_conlat_2 zenon_TA_ds))). zenon_intro zenon_Hae.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_Hae); [ zenon_intro zenon_Hb0 | zenon_intro zenon_Haf ].
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_Hb0); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hb1 ].
% 9.26/9.45 exact (zenon_Hb2 zenon_H9d).
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_Hb1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_Hb3 ].
% 9.26/9.45 exact (zenon_Hb4 zenon_Hac).
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_Hb3); [ zenon_intro zenon_H6a | zenon_intro zenon_Hb5 ].
% 9.26/9.45 apply (zenon_L2_ zenon_TA_ds); trivial.
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_Hb5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hb6 ].
% 9.26/9.45 apply zenon_Hb7. zenon_intro zenon_Hb8.
% 9.26/9.45 generalize (dt_k11_conlat_1 (k7_conlat_2 zenon_TA_ds)). zenon_intro zenon_Hb9.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_Hb9); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ].
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_Hbb); [ zenon_intro zenon_Hbc | zenon_intro zenon_H74 ].
% 9.26/9.45 apply zenon_Hbc. zenon_intro zenon_H6f.
% 9.26/9.45 apply (zenon_L3_ zenon_TA_ds); trivial.
% 9.26/9.45 apply (zenon_L4_ zenon_TA_ds); trivial.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hba). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd.
% 9.26/9.45 exact (zenon_Hbe zenon_Hb8).
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_Hb6); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hbf ].
% 9.26/9.45 generalize (fc1_conlat_2 (k7_conlat_2 zenon_TA_ds)). zenon_intro zenon_Hc1.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc2 ].
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_Hbb); [ zenon_intro zenon_Hbc | zenon_intro zenon_H74 ].
% 9.26/9.45 apply zenon_Hbc. zenon_intro zenon_H6f.
% 9.26/9.45 apply (zenon_L3_ zenon_TA_ds); trivial.
% 9.26/9.45 apply (zenon_L4_ zenon_TA_ds); trivial.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_Hbe. zenon_intro zenon_Hc3.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_Hc5. zenon_intro zenon_Hc4.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_Hc7. zenon_intro zenon_Hc6.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc9. zenon_intro zenon_Hc8.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hcb. zenon_intro zenon_Hca.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_Hcd. zenon_intro zenon_Hcc.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_Hcf. zenon_intro zenon_Hce.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_Hd1. zenon_intro zenon_Hd0.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hd0). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2.
% 9.26/9.45 exact (zenon_Hc0 zenon_Hd3).
% 9.26/9.45 generalize (dt_k11_conlat_1 (k7_conlat_2 zenon_TA_ds)). zenon_intro zenon_Hb9.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_Hb9); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ].
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_Hbb); [ zenon_intro zenon_Hbc | zenon_intro zenon_H74 ].
% 9.26/9.45 apply zenon_Hbc. zenon_intro zenon_H6f.
% 9.26/9.45 apply (zenon_L3_ zenon_TA_ds); trivial.
% 9.26/9.45 apply (zenon_L4_ zenon_TA_ds); trivial.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hba). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hc5. zenon_intro zenon_Hd4.
% 9.26/9.45 exact (zenon_Hbf zenon_Hd4).
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_Haf); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd5 ].
% 9.26/9.45 generalize (dt_k11_conlat_1 (k7_conlat_2 zenon_TA_ds)). zenon_intro zenon_Hb9.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_Hb9); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hba ].
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_Hbb); [ zenon_intro zenon_Hbc | zenon_intro zenon_H74 ].
% 9.26/9.45 apply zenon_Hbc. zenon_intro zenon_H6f.
% 9.26/9.45 apply (zenon_L3_ zenon_TA_ds); trivial.
% 9.26/9.45 apply (zenon_L4_ zenon_TA_ds); trivial.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hba). zenon_intro zenon_Hbe. zenon_intro zenon_Hbd.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hbd). zenon_intro zenon_Hc5. zenon_intro zenon_Hd4.
% 9.26/9.45 generalize (fc1_conlat_2 (k7_conlat_2 zenon_TA_ds)). zenon_intro zenon_Hc1.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hc2 ].
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_Hbb); [ zenon_intro zenon_Hbc | zenon_intro zenon_H74 ].
% 9.26/9.45 apply zenon_Hbc. zenon_intro zenon_H6f.
% 9.26/9.45 apply (zenon_L3_ zenon_TA_ds); trivial.
% 9.26/9.45 apply (zenon_L4_ zenon_TA_ds); trivial.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_Hbe. zenon_intro zenon_Hc3.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hc3). zenon_intro zenon_Hc5. zenon_intro zenon_Hc4.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hc4). zenon_intro zenon_Hc7. zenon_intro zenon_Hc6.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_Hc9. zenon_intro zenon_Hc8.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hcb. zenon_intro zenon_Hca.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hca). zenon_intro zenon_Hcd. zenon_intro zenon_Hcc.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_Hcf. zenon_intro zenon_Hce.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_Hd1. zenon_intro zenon_Hd0.
% 9.26/9.45 apply (zenon_and_s _ _ zenon_Hd0). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2.
% 9.26/9.45 generalize (d5_lattice4 (k1_lattice2 (k11_conlat_1 zenon_TA_ds))). zenon_intro zenon_Hd7.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_Hd7); [ zenon_intro zenon_Hd9 | zenon_intro zenon_Hd8 ].
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_Hd9); [ zenon_intro zenon_Hb2 | zenon_intro zenon_Hda ].
% 9.26/9.45 exact (zenon_Hb2 zenon_H9d).
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_Hda); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H6a ].
% 9.26/9.45 exact (zenon_Hb4 zenon_Hac).
% 9.26/9.45 apply (zenon_L2_ zenon_TA_ds); trivial.
% 9.26/9.45 generalize (zenon_Hd8 (k11_conlat_1 (k7_conlat_2 zenon_TA_ds))). zenon_intro zenon_Hdb.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_Hdb); [ zenon_intro zenon_Hb5 | zenon_intro zenon_Hdc ].
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_Hb5); [ zenon_intro zenon_Hb7 | zenon_intro zenon_Hb6 ].
% 9.26/9.45 exact (zenon_Hb7 zenon_Hbe).
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_Hb6); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hbf ].
% 9.26/9.45 exact (zenon_Hc0 zenon_Hd3).
% 9.26/9.45 exact (zenon_Hbf zenon_Hd4).
% 9.26/9.45 apply (zenon_equiv_s _ _ zenon_Hdc); [ zenon_intro zenon_Hd6; zenon_intro zenon_Hdf | zenon_intro zenon_Hde; zenon_intro zenon_Hdd ].
% 9.26/9.45 generalize (t21_conlat_2 zenon_TA_ds). zenon_intro zenon_He0.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_He0); [ zenon_intro zenon_H63 | zenon_intro zenon_He1 ].
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ].
% 9.26/9.45 exact (zenon_H65 zenon_H5d).
% 9.26/9.45 exact (zenon_H64 zenon_H5e).
% 9.26/9.45 apply zenon_Hdf. exists (k10_conlat_2 zenon_TA_ds). apply NNPP. zenon_intro zenon_He2.
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_He2); [ zenon_intro zenon_He4 | zenon_intro zenon_He3 ].
% 9.26/9.45 generalize (dt_k10_conlat_2 zenon_TA_ds). zenon_intro zenon_He5.
% 9.26/9.45 apply (zenon_imply_s _ _ zenon_He5); [ zenon_intro zenon_H63 | zenon_intro zenon_He6 ].
% 9.26/9.45 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ].
% 9.26/9.45 exact (zenon_H65 zenon_H5d).
% 9.26/9.45 exact (zenon_H64 zenon_H5e).
% 9.26/9.45 exact (zenon_He4 zenon_He6).
% 9.26/9.45 exact (zenon_He3 zenon_He1).
% 9.26/9.45 exact (zenon_Hd6 zenon_Hde).
% 9.26/9.45 exact (zenon_H79 zenon_Hd5).
% 9.26/9.45 Qed.
% 9.26/9.45 % SZS output end Proof
% 9.26/9.45 (* END-PROOF *)
% 9.26/9.45 nodes searched: 44712
% 9.26/9.45 max branch formulas: 6203
% 9.26/9.45 proof nodes created: 545
% 9.26/9.45 formulas created: 556933
% 9.26/9.45
%------------------------------------------------------------------------------