TSTP Solution File: GRP642+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GRP642+1 : TPTP v8.1.0. Released v3.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n025.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 : Sat Jul 16 12:36:34 EDT 2022
% Result : Theorem 32.43s 32.63s
% Output : Proof 32.43s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GRP642+1 : TPTP v8.1.0. Released v3.4.0.
% 0.08/0.14 % Command : run_zenon %s %d
% 0.13/0.35 % Computer : n025.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Mon Jun 13 16:32:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 32.43/32.63 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski
% 32.43/32.63 (* PROOF-FOUND *)
% 32.43/32.63 % SZS status Theorem
% 32.43/32.63 (* BEGIN-PROOF *)
% 32.43/32.63 % SZS output start Proof
% 32.43/32.63 Theorem t20_latsubgr : (forall A : zenon_U, (((~(v3_struct_0 A))/\((v3_group_1 A)/\((v4_group_1 A)/\(l1_group_1 A))))->(forall B : zenon_U, (((v1_group_1 B)/\(m1_group_2 B A))->(~((k1_funct_1 (k1_latsubgr A) B) = (k1_xboole_0))))))).
% 32.43/32.63 Proof.
% 32.43/32.63 assert (zenon_L1_ : forall (zenon_TB_bw : zenon_U), ((~(v3_struct_0 zenon_TB_bw))/\((v3_group_1 zenon_TB_bw)/\(l1_group_1 zenon_TB_bw))) -> (~(l1_group_1 zenon_TB_bw)) -> False).
% 32.43/32.63 do 1 intro. intros zenon_H2e zenon_H2f.
% 32.43/32.63 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H32. zenon_intro zenon_H31.
% 32.43/32.63 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 32.43/32.63 exact (zenon_H2f zenon_H33).
% 32.43/32.63 (* end of lemma zenon_L1_ *)
% 32.43/32.63 assert (zenon_L2_ : forall (zenon_TB_bw : zenon_U) (zenon_TA_cf : zenon_U), (~(v3_struct_0 zenon_TA_cf)) -> (v3_group_1 zenon_TA_cf) -> (l1_group_1 zenon_TA_cf) -> (m1_group_2 zenon_TB_bw zenon_TA_cf) -> (~(l1_group_1 zenon_TB_bw)) -> False).
% 32.43/32.63 do 2 intro. intros zenon_H35 zenon_H36 zenon_H37 zenon_H38 zenon_H2f.
% 32.43/32.63 generalize (dt_m1_group_2 zenon_TA_cf). zenon_intro zenon_H3a.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ].
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ].
% 32.43/32.63 exact (zenon_H3e zenon_H35).
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H3d); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ].
% 32.43/32.63 exact (zenon_H40 zenon_H36).
% 32.43/32.63 exact (zenon_H3f zenon_H37).
% 32.43/32.63 generalize (zenon_H3b zenon_TB_bw). zenon_intro zenon_H41.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H42 | zenon_intro zenon_H2e ].
% 32.43/32.63 exact (zenon_H42 zenon_H38).
% 32.43/32.63 apply (zenon_L1_ zenon_TB_bw); trivial.
% 32.43/32.63 (* end of lemma zenon_L2_ *)
% 32.43/32.63 assert (zenon_L3_ : forall (zenon_TB_bw : zenon_U) (zenon_TA_cf : zenon_U), (~(v3_struct_0 zenon_TA_cf)) -> (v3_group_1 zenon_TA_cf) -> (v4_group_1 zenon_TA_cf) -> (l1_group_1 zenon_TA_cf) -> (~((u1_struct_0 zenon_TB_bw) = (k1_funct_1 (k1_latsubgr zenon_TA_cf) zenon_TB_bw))) -> (m1_group_2 zenon_TB_bw zenon_TA_cf) -> (v1_group_1 zenon_TB_bw) -> False).
% 32.43/32.63 do 2 intro. intros zenon_H35 zenon_H36 zenon_H43 zenon_H37 zenon_H44 zenon_H38 zenon_H45.
% 32.43/32.63 generalize (d1_latsubgr zenon_TA_cf). zenon_intro zenon_H46.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ].
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H48); [ zenon_intro zenon_H3e | zenon_intro zenon_H49 ].
% 32.43/32.63 exact (zenon_H3e zenon_H35).
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H49); [ zenon_intro zenon_H40 | zenon_intro zenon_H4a ].
% 32.43/32.63 exact (zenon_H40 zenon_H36).
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H4b | zenon_intro zenon_H3f ].
% 32.43/32.63 exact (zenon_H4b zenon_H43).
% 32.43/32.63 exact (zenon_H3f zenon_H37).
% 32.43/32.63 generalize (zenon_H47 (k1_latsubgr zenon_TA_cf)). zenon_intro zenon_H4c.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ].
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_H50 | zenon_intro zenon_H4f ].
% 32.43/32.63 generalize (dt_k1_latsubgr zenon_TA_cf). zenon_intro zenon_H51.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H48 | zenon_intro zenon_H52 ].
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H48); [ zenon_intro zenon_H3e | zenon_intro zenon_H49 ].
% 32.43/32.63 exact (zenon_H3e zenon_H35).
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H49); [ zenon_intro zenon_H40 | zenon_intro zenon_H4a ].
% 32.43/32.63 exact (zenon_H40 zenon_H36).
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H4b | zenon_intro zenon_H3f ].
% 32.43/32.63 exact (zenon_H4b zenon_H43).
% 32.43/32.63 exact (zenon_H3f zenon_H37).
% 32.43/32.63 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53.
% 32.43/32.63 exact (zenon_H50 zenon_H54).
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H4f); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ].
% 32.43/32.63 generalize (dt_k1_latsubgr zenon_TA_cf). zenon_intro zenon_H51.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H48 | zenon_intro zenon_H52 ].
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H48); [ zenon_intro zenon_H3e | zenon_intro zenon_H49 ].
% 32.43/32.63 exact (zenon_H3e zenon_H35).
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H49); [ zenon_intro zenon_H40 | zenon_intro zenon_H4a ].
% 32.43/32.63 exact (zenon_H40 zenon_H36).
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H4b | zenon_intro zenon_H3f ].
% 32.43/32.63 exact (zenon_H4b zenon_H43).
% 32.43/32.63 exact (zenon_H3f zenon_H37).
% 32.43/32.63 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53.
% 32.43/32.63 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H58. zenon_intro zenon_H57.
% 32.43/32.63 exact (zenon_H56 zenon_H58).
% 32.43/32.63 generalize (redefinition_m2_relset_1 (k1_group_3 zenon_TA_cf)). zenon_intro zenon_H59.
% 32.43/32.63 generalize (zenon_H59 (k1_zfmisc_1 (u1_struct_0 zenon_TA_cf))). zenon_intro zenon_H5a.
% 32.43/32.63 generalize (zenon_H5a (k1_latsubgr zenon_TA_cf)). zenon_intro zenon_H5b.
% 32.43/32.63 apply (zenon_equiv_s _ _ zenon_H5b); [ zenon_intro zenon_H55; zenon_intro zenon_H5d | zenon_intro zenon_H57; zenon_intro zenon_H5c ].
% 32.43/32.63 generalize (dt_k1_latsubgr zenon_TA_cf). zenon_intro zenon_H51.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H48 | zenon_intro zenon_H52 ].
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H48); [ zenon_intro zenon_H3e | zenon_intro zenon_H49 ].
% 32.43/32.63 exact (zenon_H3e zenon_H35).
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H49); [ zenon_intro zenon_H40 | zenon_intro zenon_H4a ].
% 32.43/32.63 exact (zenon_H40 zenon_H36).
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H4b | zenon_intro zenon_H3f ].
% 32.43/32.63 exact (zenon_H4b zenon_H43).
% 32.43/32.63 exact (zenon_H3f zenon_H37).
% 32.43/32.63 apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53.
% 32.43/32.63 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H58. zenon_intro zenon_H57.
% 32.43/32.63 generalize (redefinition_m2_relset_1 (k1_group_3 zenon_TA_cf)). zenon_intro zenon_H59.
% 32.43/32.63 generalize (zenon_H59 (k1_zfmisc_1 (u1_struct_0 zenon_TA_cf))). zenon_intro zenon_H5a.
% 32.43/32.63 generalize (zenon_H5a (k1_latsubgr zenon_TA_cf)). zenon_intro zenon_H5b.
% 32.43/32.63 apply (zenon_equiv_s _ _ zenon_H5b); [ zenon_intro zenon_H55; zenon_intro zenon_H5d | zenon_intro zenon_H57; zenon_intro zenon_H5c ].
% 32.43/32.63 exact (zenon_H55 zenon_H57).
% 32.43/32.63 exact (zenon_H5d zenon_H5c).
% 32.43/32.63 exact (zenon_H55 zenon_H57).
% 32.43/32.63 apply (zenon_equiv_s _ _ zenon_H4d); [ zenon_intro zenon_H61; zenon_intro zenon_H60 | zenon_intro zenon_H5f; zenon_intro zenon_H5e ].
% 32.43/32.63 apply zenon_H61. apply refl_equal.
% 32.43/32.63 generalize (zenon_H5e zenon_TB_bw). zenon_intro zenon_H62.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ].
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H64); [ zenon_intro zenon_H65 | zenon_intro zenon_H42 ].
% 32.43/32.63 exact (zenon_H65 zenon_H45).
% 32.43/32.63 exact (zenon_H42 zenon_H38).
% 32.43/32.63 apply zenon_H44. apply sym_equal. exact zenon_H63.
% 32.43/32.63 (* end of lemma zenon_L3_ *)
% 32.43/32.63 assert (zenon_L4_ : (~((k1_xboole_0) = (k1_xboole_0))) -> False).
% 32.43/32.63 do 0 intro. intros zenon_H66.
% 32.43/32.63 apply zenon_H66. apply refl_equal.
% 32.43/32.63 (* end of lemma zenon_L4_ *)
% 32.43/32.63 assert (zenon_L5_ : forall (zenon_TA_cf : zenon_U) (zenon_TB_bw : zenon_U), (~((g1_group_1 (u1_struct_0 zenon_TB_bw) (u1_group_1 zenon_TB_bw)) = (g1_group_1 (k1_xboole_0) (u1_group_1 zenon_TB_bw)))) -> (~(v3_struct_0 zenon_TA_cf)) -> (v3_group_1 zenon_TA_cf) -> (v4_group_1 zenon_TA_cf) -> (l1_group_1 zenon_TA_cf) -> (m1_group_2 zenon_TB_bw zenon_TA_cf) -> (v1_group_1 zenon_TB_bw) -> ((k1_funct_1 (k1_latsubgr zenon_TA_cf) zenon_TB_bw) = (k1_xboole_0)) -> False).
% 32.43/32.63 do 2 intro. intros zenon_H67 zenon_H35 zenon_H36 zenon_H43 zenon_H37 zenon_H38 zenon_H45 zenon_H68.
% 32.43/32.63 cut (((u1_group_1 zenon_TB_bw) = (u1_group_1 zenon_TB_bw))); [idtac | apply NNPP; zenon_intro zenon_H69].
% 32.43/32.63 cut (((u1_struct_0 zenon_TB_bw) = (k1_xboole_0))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 32.43/32.63 congruence.
% 32.43/32.63 cut (((k1_funct_1 (k1_latsubgr zenon_TA_cf) zenon_TB_bw) = (k1_xboole_0)) = ((u1_struct_0 zenon_TB_bw) = (k1_xboole_0))).
% 32.43/32.63 intro zenon_D_pnotp.
% 32.43/32.63 apply zenon_H6a.
% 32.43/32.63 rewrite <- zenon_D_pnotp.
% 32.43/32.63 exact zenon_H68.
% 32.43/32.63 cut (((k1_xboole_0) = (k1_xboole_0))); [idtac | apply NNPP; zenon_intro zenon_H66].
% 32.43/32.63 cut (((k1_funct_1 (k1_latsubgr zenon_TA_cf) zenon_TB_bw) = (u1_struct_0 zenon_TB_bw))); [idtac | apply NNPP; zenon_intro zenon_H6b].
% 32.43/32.63 congruence.
% 32.43/32.63 elim (classic ((u1_struct_0 zenon_TB_bw) = (u1_struct_0 zenon_TB_bw))); [ zenon_intro zenon_H6c | zenon_intro zenon_H6d ].
% 32.43/32.63 cut (((u1_struct_0 zenon_TB_bw) = (u1_struct_0 zenon_TB_bw)) = ((k1_funct_1 (k1_latsubgr zenon_TA_cf) zenon_TB_bw) = (u1_struct_0 zenon_TB_bw))).
% 32.43/32.63 intro zenon_D_pnotp.
% 32.43/32.63 apply zenon_H6b.
% 32.43/32.63 rewrite <- zenon_D_pnotp.
% 32.43/32.63 exact zenon_H6c.
% 32.43/32.63 cut (((u1_struct_0 zenon_TB_bw) = (u1_struct_0 zenon_TB_bw))); [idtac | apply NNPP; zenon_intro zenon_H6d].
% 32.43/32.63 cut (((u1_struct_0 zenon_TB_bw) = (k1_funct_1 (k1_latsubgr zenon_TA_cf) zenon_TB_bw))); [idtac | apply NNPP; zenon_intro zenon_H44].
% 32.43/32.63 congruence.
% 32.43/32.63 apply (zenon_L3_ zenon_TB_bw zenon_TA_cf); trivial.
% 32.43/32.63 apply zenon_H6d. apply refl_equal.
% 32.43/32.63 apply zenon_H6d. apply refl_equal.
% 32.43/32.63 apply zenon_H66. apply refl_equal.
% 32.43/32.63 apply zenon_H69. apply refl_equal.
% 32.43/32.63 (* end of lemma zenon_L5_ *)
% 32.43/32.63 assert (zenon_L6_ : forall (zenon_TB_bw : zenon_U), (forall x : zenon_U, (r1_tarski x x)) -> (~(m1_subset_1 (u1_struct_0 zenon_TB_bw) (k1_zfmisc_1 (k1_xboole_0)))) -> ((u1_struct_0 zenon_TB_bw) = (k1_xboole_0)) -> False).
% 32.43/32.63 do 1 intro. intros zenon_H6e zenon_H6f zenon_H70.
% 32.43/32.63 generalize (t3_subset (u1_struct_0 zenon_TB_bw)). zenon_intro zenon_H71.
% 32.43/32.63 generalize (zenon_H71 (k1_xboole_0)). zenon_intro zenon_H72.
% 32.43/32.63 apply (zenon_equiv_s _ _ zenon_H72); [ zenon_intro zenon_H6f; zenon_intro zenon_H75 | zenon_intro zenon_H74; zenon_intro zenon_H73 ].
% 32.43/32.63 generalize (zenon_H6e (u1_struct_0 zenon_TB_bw)). zenon_intro zenon_H76.
% 32.43/32.63 cut ((r1_tarski (u1_struct_0 zenon_TB_bw) (u1_struct_0 zenon_TB_bw)) = (r1_tarski (u1_struct_0 zenon_TB_bw) (k1_xboole_0))).
% 32.43/32.63 intro zenon_D_pnotp.
% 32.43/32.63 apply zenon_H75.
% 32.43/32.63 rewrite <- zenon_D_pnotp.
% 32.43/32.63 exact zenon_H76.
% 32.43/32.63 cut (((u1_struct_0 zenon_TB_bw) = (k1_xboole_0))); [idtac | apply NNPP; zenon_intro zenon_H6a].
% 32.43/32.63 cut (((u1_struct_0 zenon_TB_bw) = (u1_struct_0 zenon_TB_bw))); [idtac | apply NNPP; zenon_intro zenon_H6d].
% 32.43/32.63 congruence.
% 32.43/32.63 apply zenon_H6d. apply refl_equal.
% 32.43/32.63 exact (zenon_H6a zenon_H70).
% 32.43/32.63 exact (zenon_H6f zenon_H74).
% 32.43/32.63 (* end of lemma zenon_L6_ *)
% 32.43/32.63 assert (zenon_L7_ : forall (zenon_TB_bw : zenon_U), (forall x : zenon_U, (r1_tarski x x)) -> (~(v1_xboole_0 (u1_struct_0 zenon_TB_bw))) -> ((u1_struct_0 zenon_TB_bw) = (k1_xboole_0)) -> False).
% 32.43/32.63 do 1 intro. intros zenon_H6e zenon_H77 zenon_H70.
% 32.43/32.63 generalize (existence_m1_subset_1 (u1_struct_0 zenon_TB_bw)). zenon_intro zenon_H78.
% 32.43/32.63 elim zenon_H78. zenon_intro zenon_TB_er. zenon_intro zenon_H7a.
% 32.43/32.63 generalize (t2_subset zenon_TB_er). zenon_intro zenon_H7b.
% 32.43/32.63 generalize (t5_subset zenon_TB_er). zenon_intro zenon_H7c.
% 32.43/32.63 generalize (zenon_H7b (u1_struct_0 zenon_TB_bw)). zenon_intro zenon_H7d.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_H7d); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ].
% 32.43/32.63 exact (zenon_H7f zenon_H7a).
% 32.43/32.63 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H81 | zenon_intro zenon_H80 ].
% 32.43/32.63 exact (zenon_H77 zenon_H81).
% 32.43/32.63 generalize (zenon_H7c (u1_struct_0 zenon_TB_bw)). zenon_intro zenon_H82.
% 32.43/32.63 generalize (zenon_H82 (k1_xboole_0)). zenon_intro zenon_H83.
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H83); [ zenon_intro zenon_H85 | zenon_intro zenon_H84 ].
% 32.43/32.63 exact (zenon_H85 zenon_H80).
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H84); [ zenon_intro zenon_H6f | zenon_intro zenon_H86 ].
% 32.43/32.63 apply (zenon_L6_ zenon_TB_bw); trivial.
% 32.43/32.63 exact (zenon_H86 fc1_xboole_0).
% 32.43/32.63 (* end of lemma zenon_L7_ *)
% 32.43/32.63 assert (zenon_L8_ : forall (zenon_TB_bw : zenon_U), ((~(v3_struct_0 zenon_TB_bw))/\((v3_group_1 zenon_TB_bw)/\(l1_group_1 zenon_TB_bw))) -> (v3_struct_0 zenon_TB_bw) -> False).
% 32.43/32.63 do 1 intro. intros zenon_H2e zenon_H87.
% 32.43/32.63 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H32. zenon_intro zenon_H31.
% 32.43/32.63 exact (zenon_H32 zenon_H87).
% 32.43/32.63 (* end of lemma zenon_L8_ *)
% 32.43/32.63 apply NNPP. intro zenon_G.
% 32.43/32.63 elim (classic (forall x : zenon_U, (r1_tarski x x))); [ zenon_intro zenon_H6e | zenon_intro zenon_H88 ].
% 32.43/32.63 apply (zenon_notallex_s (fun A : zenon_U => (((~(v3_struct_0 A))/\((v3_group_1 A)/\((v4_group_1 A)/\(l1_group_1 A))))->(forall B : zenon_U, (((v1_group_1 B)/\(m1_group_2 B A))->(~((k1_funct_1 (k1_latsubgr A) B) = (k1_xboole_0))))))) zenon_G); [ zenon_intro zenon_H89; idtac ].
% 32.43/32.63 elim zenon_H89. zenon_intro zenon_TA_cf. zenon_intro zenon_H8a.
% 32.43/32.63 apply (zenon_notimply_s _ _ zenon_H8a). zenon_intro zenon_H8c. zenon_intro zenon_H8b.
% 32.43/32.63 apply (zenon_and_s _ _ zenon_H8c). zenon_intro zenon_H35. zenon_intro zenon_H8d.
% 32.43/32.63 apply (zenon_and_s _ _ zenon_H8d). zenon_intro zenon_H36. zenon_intro zenon_H8e.
% 32.43/32.63 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H43. zenon_intro zenon_H37.
% 32.43/32.63 apply (zenon_notallex_s (fun B : zenon_U => (((v1_group_1 B)/\(m1_group_2 B zenon_TA_cf))->(~((k1_funct_1 (k1_latsubgr zenon_TA_cf) B) = (k1_xboole_0))))) zenon_H8b); [ zenon_intro zenon_H8f; idtac ].
% 32.43/32.63 elim zenon_H8f. zenon_intro zenon_TB_bw. zenon_intro zenon_H90.
% 32.43/32.63 apply (zenon_notimply_s _ _ zenon_H90). zenon_intro zenon_H92. zenon_intro zenon_H91.
% 32.43/32.63 apply zenon_H91. zenon_intro zenon_H68.
% 32.43/32.63 apply (zenon_and_s _ _ zenon_H92). zenon_intro zenon_H45. zenon_intro zenon_H38.
% 32.43/32.63 generalize (t6_boole (u1_struct_0 zenon_TB_bw)). zenon_intro zenon_H93.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_H93); [ zenon_intro zenon_H77 | zenon_intro zenon_H70 ].
% 32.43/32.63 generalize (free_g1_group_1 (u1_struct_0 zenon_TB_bw)). zenon_intro zenon_H94.
% 32.43/32.63 generalize (zenon_H94 (u1_group_1 zenon_TB_bw)). zenon_intro zenon_H95.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H97 | zenon_intro zenon_H96 ].
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H97); [ zenon_intro zenon_H99 | zenon_intro zenon_H98 ].
% 32.43/32.63 generalize (dt_u1_group_1 zenon_TB_bw). zenon_intro zenon_H9a.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_H9a); [ zenon_intro zenon_H2f | zenon_intro zenon_H9b ].
% 32.43/32.63 apply (zenon_L2_ zenon_TB_bw zenon_TA_cf); trivial.
% 32.43/32.63 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c.
% 32.43/32.63 exact (zenon_H99 zenon_H9d).
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H98); [ zenon_intro zenon_H9f | zenon_intro zenon_H9e ].
% 32.43/32.63 generalize (dt_u1_group_1 zenon_TB_bw). zenon_intro zenon_H9a.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_H9a); [ zenon_intro zenon_H2f | zenon_intro zenon_H9b ].
% 32.43/32.63 apply (zenon_L2_ zenon_TB_bw zenon_TA_cf); trivial.
% 32.43/32.63 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c.
% 32.43/32.63 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_Ha1. zenon_intro zenon_Ha0.
% 32.43/32.63 exact (zenon_H9f zenon_Ha1).
% 32.43/32.63 generalize (dt_u1_group_1 zenon_TB_bw). zenon_intro zenon_H9a.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_H9a); [ zenon_intro zenon_H2f | zenon_intro zenon_H9b ].
% 32.43/32.63 apply (zenon_L2_ zenon_TB_bw zenon_TA_cf); trivial.
% 32.43/32.63 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c.
% 32.43/32.63 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_Ha1. zenon_intro zenon_Ha0.
% 32.43/32.63 generalize (redefinition_m2_relset_1 (k2_zfmisc_1 (u1_struct_0 zenon_TB_bw) (u1_struct_0 zenon_TB_bw))). zenon_intro zenon_Ha2.
% 32.43/32.63 generalize (zenon_Ha2 (u1_struct_0 zenon_TB_bw)). zenon_intro zenon_Ha3.
% 32.43/32.63 generalize (zenon_Ha3 (u1_group_1 zenon_TB_bw)). zenon_intro zenon_Ha4.
% 32.43/32.63 apply (zenon_equiv_s _ _ zenon_Ha4); [ zenon_intro zenon_Ha6; zenon_intro zenon_H9e | zenon_intro zenon_Ha0; zenon_intro zenon_Ha5 ].
% 32.43/32.63 exact (zenon_Ha6 zenon_Ha0).
% 32.43/32.63 exact (zenon_H9e zenon_Ha5).
% 32.43/32.63 generalize (zenon_H96 (k1_xboole_0)). zenon_intro zenon_Ha7.
% 32.43/32.63 generalize (zenon_Ha7 (u1_group_1 zenon_TB_bw)). zenon_intro zenon_Ha8.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_Ha8); [ zenon_intro zenon_H67 | zenon_intro zenon_Ha9 ].
% 32.43/32.63 apply (zenon_L5_ zenon_TA_cf zenon_TB_bw); trivial.
% 32.43/32.63 apply (zenon_and_s _ _ zenon_Ha9). zenon_intro zenon_H70. zenon_intro zenon_Haa.
% 32.43/32.63 apply (zenon_L7_ zenon_TB_bw); trivial.
% 32.43/32.63 generalize (fc1_struct_0 zenon_TB_bw). zenon_intro zenon_Hab.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_Hab); [ zenon_intro zenon_Hac | zenon_intro zenon_H77 ].
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_Hac); [ zenon_intro zenon_Hae | zenon_intro zenon_Had ].
% 32.43/32.63 apply zenon_Hae. zenon_intro zenon_H87.
% 32.43/32.63 generalize (dt_m1_group_2 zenon_TA_cf). zenon_intro zenon_H3a.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ].
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ].
% 32.43/32.63 exact (zenon_H3e zenon_H35).
% 32.43/32.63 apply (zenon_notand_s _ _ zenon_H3d); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ].
% 32.43/32.63 exact (zenon_H40 zenon_H36).
% 32.43/32.63 exact (zenon_H3f zenon_H37).
% 32.43/32.63 generalize (zenon_H3b zenon_TB_bw). zenon_intro zenon_H41.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H42 | zenon_intro zenon_H2e ].
% 32.43/32.63 exact (zenon_H42 zenon_H38).
% 32.43/32.63 apply (zenon_L8_ zenon_TB_bw); trivial.
% 32.43/32.63 generalize (dt_l1_group_1 zenon_TB_bw). zenon_intro zenon_Haf.
% 32.43/32.63 apply (zenon_imply_s _ _ zenon_Haf); [ zenon_intro zenon_H2f | zenon_intro zenon_Hb0 ].
% 32.43/32.63 apply (zenon_L2_ zenon_TB_bw zenon_TA_cf); trivial.
% 32.43/32.63 exact (zenon_Had zenon_Hb0).
% 32.43/32.63 apply (zenon_L7_ zenon_TB_bw); trivial.
% 32.43/32.63 apply zenon_H88. zenon_intro zenon_Tx_gv. apply NNPP. zenon_intro zenon_Hb2.
% 32.43/32.63 generalize (reflexivity_r1_tarski zenon_Tx_gv). zenon_intro zenon_H0.
% 32.43/32.63 generalize (zenon_H0 zenon_E). zenon_intro zenon_Hb3.
% 32.43/32.63 exact (zenon_Hb2 zenon_Hb3).
% 32.43/32.63 Qed.
% 32.43/32.63 % SZS output end Proof
% 32.43/32.63 (* END-PROOF *)
% 32.43/32.63 nodes searched: 279013
% 32.43/32.63 max branch formulas: 6112
% 32.43/32.63 proof nodes created: 5631
% 32.43/32.63 formulas created: 1621114
% 32.43/32.63
%------------------------------------------------------------------------------