TSTP Solution File: LAT356+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : LAT356+1 : TPTP v8.1.0. Released v3.4.0.
% 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 07:24:03 EDT 2022
% Result : Theorem 0.38s 0.59s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : LAT356+1 : TPTP v8.1.0. Released v3.4.0.
% 0.06/0.12 % 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 : Thu Jun 30 09:29:29 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.38/0.59 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 0.38/0.59 (* PROOF-FOUND *)
% 0.38/0.59 % SZS status Theorem
% 0.38/0.59 (* BEGIN-PROOF *)
% 0.38/0.59 % SZS output start Proof
% 0.38/0.59 Theorem t7_waybel34 : (forall A : zenon_U, (((v2_orders_2 A)/\((v3_orders_2 A)/\((v4_orders_2 A)/\((v1_lattice3 A)/\((v2_lattice3 A)/\((v3_lattice3 A)/\(l1_orders_2 A)))))))->(((k1_waybel34 A A (k7_grcat_1 A)) = (k7_grcat_1 A))/\((k2_waybel34 A A (k7_grcat_1 A)) = (k7_grcat_1 A))))).
% 0.38/0.59 Proof.
% 0.38/0.59 assert (zenon_L1_ : forall (zenon_TA_er : zenon_U), (l1_orders_2 zenon_TA_er) -> (~(v1_funct_1 (k7_grcat_1 zenon_TA_er))) -> False).
% 0.38/0.59 do 1 intro. intros zenon_H77 zenon_H78.
% 0.38/0.59 generalize (fc2_waybel_1 zenon_TA_er). zenon_intro zenon_H7a.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_H7a); [ zenon_intro zenon_H7c | zenon_intro zenon_H7b ].
% 0.38/0.59 exact (zenon_H7c zenon_H77).
% 0.38/0.59 apply (zenon_and_s _ _ zenon_H7b). zenon_intro zenon_H7e. zenon_intro zenon_H7d.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_H7d). zenon_intro zenon_H80. zenon_intro zenon_H7f.
% 0.38/0.59 exact (zenon_H78 zenon_H80).
% 0.38/0.59 (* end of lemma zenon_L1_ *)
% 0.38/0.59 assert (zenon_L2_ : forall (zenon_TA_er : zenon_U), (l1_orders_2 zenon_TA_er) -> (~(l1_struct_0 zenon_TA_er)) -> False).
% 0.38/0.59 do 1 intro. intros zenon_H77 zenon_H81.
% 0.38/0.59 generalize (dt_l1_orders_2 zenon_TA_er). zenon_intro zenon_H82.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_H82); [ zenon_intro zenon_H7c | zenon_intro zenon_H83 ].
% 0.38/0.59 exact (zenon_H7c zenon_H77).
% 0.38/0.59 exact (zenon_H81 zenon_H83).
% 0.38/0.59 (* end of lemma zenon_L2_ *)
% 0.38/0.59 assert (zenon_L3_ : forall (zenon_TA_er : zenon_U), (l1_orders_2 zenon_TA_er) -> (~(v1_funct_2 (k7_grcat_1 zenon_TA_er) (u1_struct_0 zenon_TA_er) (u1_struct_0 zenon_TA_er))) -> False).
% 0.38/0.59 do 1 intro. intros zenon_H77 zenon_H84.
% 0.38/0.59 generalize (fc3_waybel10 zenon_TA_er). zenon_intro zenon_H85.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_H85); [ zenon_intro zenon_H81 | zenon_intro zenon_H86 ].
% 0.38/0.59 apply (zenon_L2_ zenon_TA_er); trivial.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_H86). zenon_intro zenon_H7e. zenon_intro zenon_H87.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H80. zenon_intro zenon_H88.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H8a. zenon_intro zenon_H89.
% 0.38/0.59 exact (zenon_H84 zenon_H89).
% 0.38/0.59 (* end of lemma zenon_L3_ *)
% 0.38/0.59 assert (zenon_L4_ : forall (zenon_TA_er : zenon_U), (l1_orders_2 zenon_TA_er) -> (~(m2_relset_1 (k7_grcat_1 zenon_TA_er) (u1_struct_0 zenon_TA_er) (u1_struct_0 zenon_TA_er))) -> False).
% 0.38/0.59 do 1 intro. intros zenon_H77 zenon_H8b.
% 0.38/0.59 generalize (redefinition_m2_relset_1 (u1_struct_0 zenon_TA_er)). zenon_intro zenon_H8c.
% 0.38/0.59 generalize (zenon_H8c (u1_struct_0 zenon_TA_er)). zenon_intro zenon_H8d.
% 0.38/0.59 generalize (zenon_H8d (k7_grcat_1 zenon_TA_er)). zenon_intro zenon_H8e.
% 0.38/0.59 apply (zenon_equiv_s _ _ zenon_H8e); [ zenon_intro zenon_H8b; zenon_intro zenon_H91 | zenon_intro zenon_H90; zenon_intro zenon_H8f ].
% 0.38/0.59 generalize (dt_k7_grcat_1 zenon_TA_er). zenon_intro zenon_H92.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_H92); [ zenon_intro zenon_H81 | zenon_intro zenon_H93 ].
% 0.38/0.59 apply (zenon_L2_ zenon_TA_er); trivial.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_H93). zenon_intro zenon_H80. zenon_intro zenon_H94.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_H94). zenon_intro zenon_H89. zenon_intro zenon_H90.
% 0.38/0.59 generalize (redefinition_m2_relset_1 (u1_struct_0 zenon_TA_er)). zenon_intro zenon_H8c.
% 0.38/0.59 generalize (zenon_H8c (u1_struct_0 zenon_TA_er)). zenon_intro zenon_H8d.
% 0.38/0.59 generalize (zenon_H8d (k7_grcat_1 zenon_TA_er)). zenon_intro zenon_H8e.
% 0.38/0.59 apply (zenon_equiv_s _ _ zenon_H8e); [ zenon_intro zenon_H8b; zenon_intro zenon_H91 | zenon_intro zenon_H90; zenon_intro zenon_H8f ].
% 0.38/0.59 exact (zenon_H8b zenon_H90).
% 0.38/0.59 exact (zenon_H91 zenon_H8f).
% 0.38/0.59 exact (zenon_H8b zenon_H90).
% 0.38/0.59 (* end of lemma zenon_L4_ *)
% 0.38/0.59 assert (zenon_L5_ : forall (zenon_TA_er : zenon_U), (l1_orders_2 zenon_TA_er) -> (v1_lattice3 zenon_TA_er) -> (v3_struct_0 zenon_TA_er) -> False).
% 0.38/0.59 do 1 intro. intros zenon_H77 zenon_H95 zenon_H96.
% 0.38/0.59 generalize (cc1_lattice3 zenon_TA_er). zenon_intro zenon_H97.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_H97); [ zenon_intro zenon_H7c | zenon_intro zenon_H98 ].
% 0.38/0.59 exact (zenon_H7c zenon_H77).
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H9a | zenon_intro zenon_H99 ].
% 0.38/0.59 exact (zenon_H9a zenon_H95).
% 0.38/0.59 exact (zenon_H99 zenon_H96).
% 0.38/0.59 (* end of lemma zenon_L5_ *)
% 0.38/0.59 apply NNPP. intro zenon_G.
% 0.38/0.59 apply (zenon_notallex_s (fun A : zenon_U => (((v2_orders_2 A)/\((v3_orders_2 A)/\((v4_orders_2 A)/\((v1_lattice3 A)/\((v2_lattice3 A)/\((v3_lattice3 A)/\(l1_orders_2 A)))))))->(((k1_waybel34 A A (k7_grcat_1 A)) = (k7_grcat_1 A))/\((k2_waybel34 A A (k7_grcat_1 A)) = (k7_grcat_1 A))))) zenon_G); [ zenon_intro zenon_H9b; idtac ].
% 0.38/0.59 elim zenon_H9b. zenon_intro zenon_TA_er. zenon_intro zenon_H9c.
% 0.38/0.59 apply (zenon_notimply_s _ _ zenon_H9c). zenon_intro zenon_H9e. zenon_intro zenon_H9d.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_H9e). zenon_intro zenon_Ha0. zenon_intro zenon_H9f.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_H9f). zenon_intro zenon_Ha2. zenon_intro zenon_Ha1.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Ha1). zenon_intro zenon_Ha4. zenon_intro zenon_Ha3.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Ha3). zenon_intro zenon_H95. zenon_intro zenon_Ha5.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Ha5). zenon_intro zenon_Ha7. zenon_intro zenon_Ha6.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Ha6). zenon_intro zenon_Ha8. zenon_intro zenon_H77.
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_H9d); [ zenon_intro zenon_Haa | zenon_intro zenon_Ha9 ].
% 0.38/0.59 generalize (d1_waybel34 zenon_TA_er). zenon_intro zenon_Hab.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_Hab); [ zenon_intro zenon_Had | zenon_intro zenon_Hac ].
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Had); [ zenon_intro zenon_Haf | zenon_intro zenon_Hae ].
% 0.38/0.59 exact (zenon_Haf zenon_Ha0).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hae); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb0 ].
% 0.38/0.59 exact (zenon_Hb1 zenon_Ha2).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hb0); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hb2 ].
% 0.38/0.59 exact (zenon_Hb3 zenon_Ha4).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hb2); [ zenon_intro zenon_H9a | zenon_intro zenon_Hb4 ].
% 0.38/0.59 exact (zenon_H9a zenon_H95).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hb4); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H7c ].
% 0.38/0.59 exact (zenon_Hb5 zenon_Ha7).
% 0.38/0.59 exact (zenon_H7c zenon_H77).
% 0.38/0.59 generalize (zenon_Hac zenon_TA_er). zenon_intro zenon_Hb6.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_Hb6); [ zenon_intro zenon_Had | zenon_intro zenon_Hb7 ].
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Had); [ zenon_intro zenon_Haf | zenon_intro zenon_Hae ].
% 0.38/0.59 exact (zenon_Haf zenon_Ha0).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hae); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb0 ].
% 0.38/0.59 exact (zenon_Hb1 zenon_Ha2).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hb0); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hb2 ].
% 0.38/0.59 exact (zenon_Hb3 zenon_Ha4).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hb2); [ zenon_intro zenon_H9a | zenon_intro zenon_Hb4 ].
% 0.38/0.59 exact (zenon_H9a zenon_H95).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hb4); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H7c ].
% 0.38/0.59 exact (zenon_Hb5 zenon_Ha7).
% 0.38/0.59 exact (zenon_H7c zenon_H77).
% 0.38/0.59 generalize (zenon_Hb7 (k7_grcat_1 zenon_TA_er)). zenon_intro zenon_Hb8.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_Hb8); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ].
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hba); [ zenon_intro zenon_H78 | zenon_intro zenon_Hbb ].
% 0.38/0.59 apply (zenon_L1_ zenon_TA_er); trivial.
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hbb); [ zenon_intro zenon_H84 | zenon_intro zenon_H8b ].
% 0.38/0.59 apply (zenon_L3_ zenon_TA_er); trivial.
% 0.38/0.59 apply (zenon_L4_ zenon_TA_er); trivial.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_Hb9); [ zenon_intro zenon_Hbd | zenon_intro zenon_Hbc ].
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hbd); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hbe ].
% 0.38/0.59 exact (zenon_Hbf zenon_Ha8).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hbe); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hc0 ].
% 0.38/0.59 exact (zenon_Hbf zenon_Ha8).
% 0.38/0.59 generalize (fc4_waybel10 zenon_TA_er). zenon_intro zenon_Hc1.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc2 ].
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hc3); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hc4 ].
% 0.38/0.59 apply zenon_Hc5. zenon_intro zenon_H96.
% 0.38/0.59 apply (zenon_L5_ zenon_TA_er); trivial.
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hc4); [ zenon_intro zenon_Haf | zenon_intro zenon_H7c ].
% 0.38/0.59 exact (zenon_Haf zenon_Ha0).
% 0.38/0.59 exact (zenon_H7c zenon_H77).
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H7e. zenon_intro zenon_Hc6.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_H80. zenon_intro zenon_Hc7.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_H8a. zenon_intro zenon_Hc8.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H89. zenon_intro zenon_Hcb.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Hcd. zenon_intro zenon_Hcc.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_Hcf. zenon_intro zenon_Hce.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_Hd1. zenon_intro zenon_Hd0.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hd0). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2.
% 0.38/0.59 exact (zenon_Hc0 zenon_Hd3).
% 0.38/0.59 generalize (t6_waybel34 zenon_TA_er). zenon_intro zenon_Hd4.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_Hd4); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd5 ].
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hd6); [ zenon_intro zenon_Hc5 | zenon_intro zenon_H7c ].
% 0.38/0.59 apply zenon_Hc5. zenon_intro zenon_H96.
% 0.38/0.59 apply (zenon_L5_ zenon_TA_er); trivial.
% 0.38/0.59 exact (zenon_H7c zenon_H77).
% 0.38/0.59 generalize (zenon_Hbc (k7_grcat_1 zenon_TA_er)). zenon_intro zenon_Hd7.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_Hd7); [ zenon_intro zenon_Hba | zenon_intro zenon_Hd8 ].
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hba); [ zenon_intro zenon_H78 | zenon_intro zenon_Hbb ].
% 0.38/0.59 apply (zenon_L1_ zenon_TA_er); trivial.
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hbb); [ zenon_intro zenon_H84 | zenon_intro zenon_H8b ].
% 0.38/0.59 apply (zenon_L3_ zenon_TA_er); trivial.
% 0.38/0.59 apply (zenon_L4_ zenon_TA_er); trivial.
% 0.38/0.59 apply (zenon_equiv_s _ _ zenon_Hd8); [ zenon_intro zenon_Hdb; zenon_intro zenon_Hda | zenon_intro zenon_Hd9; zenon_intro zenon_Hd5 ].
% 0.38/0.59 exact (zenon_Hda zenon_Hd5).
% 0.38/0.59 apply zenon_Haa. apply sym_equal. exact zenon_Hd9.
% 0.38/0.59 generalize (d2_waybel34 zenon_TA_er). zenon_intro zenon_Hdc.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_Hdc); [ zenon_intro zenon_Had | zenon_intro zenon_Hdd ].
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Had); [ zenon_intro zenon_Haf | zenon_intro zenon_Hae ].
% 0.38/0.59 exact (zenon_Haf zenon_Ha0).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hae); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb0 ].
% 0.38/0.59 exact (zenon_Hb1 zenon_Ha2).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hb0); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hb2 ].
% 0.38/0.59 exact (zenon_Hb3 zenon_Ha4).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hb2); [ zenon_intro zenon_H9a | zenon_intro zenon_Hb4 ].
% 0.38/0.59 exact (zenon_H9a zenon_H95).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hb4); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H7c ].
% 0.38/0.59 exact (zenon_Hb5 zenon_Ha7).
% 0.38/0.59 exact (zenon_H7c zenon_H77).
% 0.38/0.59 generalize (zenon_Hdd zenon_TA_er). zenon_intro zenon_Hde.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_Hde); [ zenon_intro zenon_Had | zenon_intro zenon_Hdf ].
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Had); [ zenon_intro zenon_Haf | zenon_intro zenon_Hae ].
% 0.38/0.59 exact (zenon_Haf zenon_Ha0).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hae); [ zenon_intro zenon_Hb1 | zenon_intro zenon_Hb0 ].
% 0.38/0.59 exact (zenon_Hb1 zenon_Ha2).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hb0); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hb2 ].
% 0.38/0.59 exact (zenon_Hb3 zenon_Ha4).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hb2); [ zenon_intro zenon_H9a | zenon_intro zenon_Hb4 ].
% 0.38/0.59 exact (zenon_H9a zenon_H95).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hb4); [ zenon_intro zenon_Hb5 | zenon_intro zenon_H7c ].
% 0.38/0.59 exact (zenon_Hb5 zenon_Ha7).
% 0.38/0.59 exact (zenon_H7c zenon_H77).
% 0.38/0.59 generalize (zenon_Hdf (k7_grcat_1 zenon_TA_er)). zenon_intro zenon_He0.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_He0); [ zenon_intro zenon_Hba | zenon_intro zenon_He1 ].
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hba); [ zenon_intro zenon_H78 | zenon_intro zenon_Hbb ].
% 0.38/0.59 apply (zenon_L1_ zenon_TA_er); trivial.
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hbb); [ zenon_intro zenon_H84 | zenon_intro zenon_H8b ].
% 0.38/0.59 apply (zenon_L3_ zenon_TA_er); trivial.
% 0.38/0.59 apply (zenon_L4_ zenon_TA_er); trivial.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_He1); [ zenon_intro zenon_He3 | zenon_intro zenon_He2 ].
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_He3); [ zenon_intro zenon_Hbf | zenon_intro zenon_He4 ].
% 0.38/0.59 exact (zenon_Hbf zenon_Ha8).
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_He4); [ zenon_intro zenon_Hbf | zenon_intro zenon_He5 ].
% 0.38/0.59 exact (zenon_Hbf zenon_Ha8).
% 0.38/0.59 generalize (fc4_waybel10 zenon_TA_er). zenon_intro zenon_Hc1.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_Hc1); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc2 ].
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hc3); [ zenon_intro zenon_Hc5 | zenon_intro zenon_Hc4 ].
% 0.38/0.59 apply zenon_Hc5. zenon_intro zenon_H96.
% 0.38/0.59 apply (zenon_L5_ zenon_TA_er); trivial.
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hc4); [ zenon_intro zenon_Haf | zenon_intro zenon_H7c ].
% 0.38/0.59 exact (zenon_Haf zenon_Ha0).
% 0.38/0.59 exact (zenon_H7c zenon_H77).
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hc2). zenon_intro zenon_H7e. zenon_intro zenon_Hc6.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hc6). zenon_intro zenon_H80. zenon_intro zenon_Hc7.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hc7). zenon_intro zenon_H8a. zenon_intro zenon_Hc8.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hc8). zenon_intro zenon_Hca. zenon_intro zenon_Hc9.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hc9). zenon_intro zenon_H89. zenon_intro zenon_Hcb.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hcb). zenon_intro zenon_Hcd. zenon_intro zenon_Hcc.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hcc). zenon_intro zenon_Hcf. zenon_intro zenon_Hce.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hce). zenon_intro zenon_Hd1. zenon_intro zenon_Hd0.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hd0). zenon_intro zenon_Hd3. zenon_intro zenon_Hd2.
% 0.38/0.59 apply (zenon_and_s _ _ zenon_Hd2). zenon_intro zenon_He7. zenon_intro zenon_He6.
% 0.38/0.59 exact (zenon_He5 zenon_He7).
% 0.38/0.59 generalize (t6_waybel34 zenon_TA_er). zenon_intro zenon_Hd4.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_Hd4); [ zenon_intro zenon_Hd6 | zenon_intro zenon_Hd5 ].
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hd6); [ zenon_intro zenon_Hc5 | zenon_intro zenon_H7c ].
% 0.38/0.59 apply zenon_Hc5. zenon_intro zenon_H96.
% 0.38/0.59 apply (zenon_L5_ zenon_TA_er); trivial.
% 0.38/0.59 exact (zenon_H7c zenon_H77).
% 0.38/0.59 generalize (zenon_He2 (k7_grcat_1 zenon_TA_er)). zenon_intro zenon_He8.
% 0.38/0.59 apply (zenon_imply_s _ _ zenon_He8); [ zenon_intro zenon_Hba | zenon_intro zenon_He9 ].
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hba); [ zenon_intro zenon_H78 | zenon_intro zenon_Hbb ].
% 0.38/0.59 apply (zenon_L1_ zenon_TA_er); trivial.
% 0.38/0.59 apply (zenon_notand_s _ _ zenon_Hbb); [ zenon_intro zenon_H84 | zenon_intro zenon_H8b ].
% 0.38/0.59 apply (zenon_L3_ zenon_TA_er); trivial.
% 0.38/0.59 apply (zenon_L4_ zenon_TA_er); trivial.
% 0.38/0.59 apply (zenon_equiv_s _ _ zenon_He9); [ zenon_intro zenon_Heb; zenon_intro zenon_Hda | zenon_intro zenon_Hea; zenon_intro zenon_Hd5 ].
% 0.38/0.59 exact (zenon_Hda zenon_Hd5).
% 0.38/0.59 apply zenon_Ha9. apply sym_equal. exact zenon_Hea.
% 0.38/0.59 Qed.
% 0.38/0.59 % SZS output end Proof
% 0.38/0.59 (* END-PROOF *)
% 0.38/0.59 nodes searched: 3122
% 0.38/0.59 max branch formulas: 1317
% 0.38/0.59 proof nodes created: 375
% 0.38/0.59 formulas created: 15702
% 0.38/0.59
%------------------------------------------------------------------------------