TSTP Solution File: GEO179+2 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO179+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n003.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 07:00:26 EDT 2022
% Result : Theorem 0.60s 0.78s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO179+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n003.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 : Sat Jun 18 00:58:42 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.60/0.78 (* PROOF-FOUND *)
% 0.60/0.78 % SZS status Theorem
% 0.60/0.78 (* BEGIN-PROOF *)
% 0.60/0.78 % SZS output start Proof
% 0.60/0.78 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\(apart_point_and_line Z (line_connecting X Y)))->((distinct_lines (line_connecting X Y) (line_connecting Z X))/\(distinct_lines (line_connecting X Y) (line_connecting Z Y))))))).
% 0.60/0.78 Proof.
% 0.60/0.78 assert (zenon_L1_ : forall (zenon_TX_u : zenon_U) (zenon_TY_v : zenon_U), (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TY_v zenon_TX_u)/\(distinct_lines U V))->((apart_point_and_line zenon_TY_v U)\/((apart_point_and_line zenon_TY_v V)\/((apart_point_and_line zenon_TX_u U)\/(apart_point_and_line zenon_TX_u V))))))) -> (~(apart_point_and_line zenon_TX_u (line_connecting zenon_TY_v zenon_TX_u))) -> (~(apart_point_and_line zenon_TX_u (line_connecting zenon_TX_u zenon_TY_v))) -> (~(apart_point_and_line zenon_TY_v (line_connecting zenon_TY_v zenon_TX_u))) -> (~(apart_point_and_line zenon_TY_v (line_connecting zenon_TX_u zenon_TY_v))) -> (distinct_lines (line_connecting zenon_TX_u zenon_TY_v) (line_connecting zenon_TY_v zenon_TX_u)) -> (distinct_points zenon_TY_v zenon_TX_u) -> False).
% 0.60/0.78 do 2 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10 zenon_H11 zenon_H12 zenon_H13.
% 0.60/0.78 generalize (zenon_Hd (line_connecting zenon_TX_u zenon_TY_v)). zenon_intro zenon_H16.
% 0.60/0.78 generalize (zenon_H16 (line_connecting zenon_TY_v zenon_TX_u)). zenon_intro zenon_H17.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ].
% 0.60/0.78 apply (zenon_notand_s _ _ zenon_H19); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ].
% 0.60/0.78 exact (zenon_H1b zenon_H13).
% 0.60/0.78 exact (zenon_H1a zenon_H12).
% 0.60/0.78 apply (zenon_or_s _ _ zenon_H18); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ].
% 0.60/0.78 exact (zenon_H11 zenon_H1d).
% 0.60/0.78 apply (zenon_or_s _ _ zenon_H1c); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ].
% 0.60/0.78 exact (zenon_H10 zenon_H1f).
% 0.60/0.78 apply (zenon_or_s _ _ zenon_H1e); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ].
% 0.60/0.78 exact (zenon_Hf zenon_H21).
% 0.60/0.78 exact (zenon_He zenon_H20).
% 0.60/0.78 (* end of lemma zenon_L1_ *)
% 0.60/0.78 assert (zenon_L2_ : forall (zenon_TZ_bl : zenon_U) (zenon_TX_u : zenon_U) (zenon_TY_v : zenon_U), (forall Z : zenon_U, ((distinct_points zenon_TY_v zenon_TX_u)->((apart_point_and_line Z (line_connecting zenon_TY_v zenon_TX_u))->((distinct_points Z zenon_TY_v)/\(distinct_points Z zenon_TX_u))))) -> (distinct_points zenon_TY_v zenon_TX_u) -> (apart_point_and_line zenon_TZ_bl (line_connecting zenon_TY_v zenon_TX_u)) -> (~(distinct_points zenon_TZ_bl zenon_TX_u)) -> False).
% 0.60/0.78 do 3 intro. intros zenon_H22 zenon_H13 zenon_H23 zenon_H24.
% 0.60/0.78 generalize (zenon_H22 zenon_TZ_bl). zenon_intro zenon_H26.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H1b | zenon_intro zenon_H27 ].
% 0.60/0.78 exact (zenon_H1b zenon_H13).
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 0.60/0.78 exact (zenon_H29 zenon_H23).
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2b. zenon_intro zenon_H2a.
% 0.60/0.78 exact (zenon_H24 zenon_H2a).
% 0.60/0.78 (* end of lemma zenon_L2_ *)
% 0.60/0.78 assert (zenon_L3_ : forall (zenon_TY_v : zenon_U) (zenon_TX_u : zenon_U) (zenon_TZ_bl : zenon_U), (forall Z : zenon_U, ((apart_point_and_line zenon_TZ_bl (line_connecting zenon_TX_u zenon_TY_v))->((distinct_lines (line_connecting zenon_TX_u zenon_TY_v) Z)\/(apart_point_and_line zenon_TZ_bl Z)))) -> (apart_point_and_line zenon_TZ_bl (line_connecting zenon_TX_u zenon_TY_v)) -> (~(distinct_lines (line_connecting zenon_TX_u zenon_TY_v) (line_connecting zenon_TZ_bl zenon_TX_u))) -> (~(apart_point_and_line zenon_TZ_bl (line_connecting zenon_TZ_bl zenon_TX_u))) -> False).
% 0.60/0.78 do 3 intro. intros zenon_H2c zenon_H2d zenon_H2e zenon_H2f.
% 0.60/0.78 generalize (zenon_H2c (line_connecting zenon_TZ_bl zenon_TX_u)). zenon_intro zenon_H30.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ].
% 0.60/0.78 exact (zenon_H32 zenon_H2d).
% 0.60/0.78 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 0.60/0.78 exact (zenon_H2e zenon_H34).
% 0.60/0.78 exact (zenon_H2f zenon_H33).
% 0.60/0.78 (* end of lemma zenon_L3_ *)
% 0.60/0.78 assert (zenon_L4_ : forall (zenon_TX_u : zenon_U) (zenon_TZ_bl : zenon_U), ((distinct_points zenon_TZ_bl zenon_TZ_bl)/\(distinct_points zenon_TZ_bl zenon_TX_u)) -> (~(distinct_points zenon_TZ_bl zenon_TZ_bl)) -> False).
% 0.60/0.78 do 2 intro. intros zenon_H35 zenon_H36.
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H2a.
% 0.60/0.78 exact (zenon_H36 zenon_H37).
% 0.60/0.78 (* end of lemma zenon_L4_ *)
% 0.60/0.78 assert (zenon_L5_ : forall (zenon_TY_v : zenon_U) (zenon_TX_u : zenon_U), ((distinct_points zenon_TX_u zenon_TY_v)/\(distinct_points zenon_TX_u zenon_TX_u)) -> (~(distinct_points zenon_TX_u zenon_TX_u)) -> False).
% 0.60/0.78 do 2 intro. intros zenon_H38 zenon_H39.
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H38). zenon_intro zenon_H3b. zenon_intro zenon_H3a.
% 0.60/0.78 exact (zenon_H39 zenon_H3a).
% 0.60/0.78 (* end of lemma zenon_L5_ *)
% 0.60/0.78 assert (zenon_L6_ : forall (zenon_TX_u : zenon_U) (zenon_TY_v : zenon_U), ((distinct_points zenon_TY_v zenon_TY_v)/\(distinct_points zenon_TY_v zenon_TX_u)) -> (~(distinct_points zenon_TY_v zenon_TY_v)) -> False).
% 0.60/0.78 do 2 intro. intros zenon_H3c zenon_H3d.
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H3e. zenon_intro zenon_H13.
% 0.60/0.78 exact (zenon_H3d zenon_H3e).
% 0.60/0.78 (* end of lemma zenon_L6_ *)
% 0.60/0.78 assert (zenon_L7_ : forall (zenon_TY_v : zenon_U) (zenon_TX_u : zenon_U), ((distinct_points zenon_TX_u zenon_TX_u)/\(distinct_points zenon_TX_u zenon_TY_v)) -> (~(distinct_points zenon_TX_u zenon_TX_u)) -> False).
% 0.60/0.78 do 2 intro. intros zenon_H3f zenon_H39.
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H3a. zenon_intro zenon_H3b.
% 0.60/0.78 exact (zenon_H39 zenon_H3a).
% 0.60/0.78 (* end of lemma zenon_L7_ *)
% 0.60/0.78 assert (zenon_L8_ : forall (zenon_TX_u : zenon_U) (zenon_TY_v : zenon_U), ((distinct_points zenon_TY_v zenon_TX_u)/\(distinct_points zenon_TY_v zenon_TY_v)) -> (~(distinct_points zenon_TY_v zenon_TY_v)) -> False).
% 0.60/0.78 do 2 intro. intros zenon_H40 zenon_H3d.
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H13. zenon_intro zenon_H3e.
% 0.60/0.78 exact (zenon_H3d zenon_H3e).
% 0.60/0.78 (* end of lemma zenon_L8_ *)
% 0.60/0.78 assert (zenon_L9_ : forall (zenon_TZ_bl : zenon_U) (zenon_TX_u : zenon_U) (zenon_TY_v : zenon_U), (forall Z : zenon_U, ((distinct_points zenon_TY_v zenon_TX_u)->((apart_point_and_line Z (line_connecting zenon_TY_v zenon_TX_u))->((distinct_points Z zenon_TY_v)/\(distinct_points Z zenon_TX_u))))) -> (distinct_points zenon_TY_v zenon_TX_u) -> (apart_point_and_line zenon_TZ_bl (line_connecting zenon_TY_v zenon_TX_u)) -> (~(distinct_points zenon_TZ_bl zenon_TY_v)) -> False).
% 0.60/0.78 do 3 intro. intros zenon_H22 zenon_H13 zenon_H23 zenon_H41.
% 0.60/0.78 generalize (zenon_H22 zenon_TZ_bl). zenon_intro zenon_H26.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H1b | zenon_intro zenon_H27 ].
% 0.60/0.78 exact (zenon_H1b zenon_H13).
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 0.60/0.78 exact (zenon_H29 zenon_H23).
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H2b. zenon_intro zenon_H2a.
% 0.60/0.78 exact (zenon_H41 zenon_H2b).
% 0.60/0.78 (* end of lemma zenon_L9_ *)
% 0.60/0.78 assert (zenon_L10_ : forall (zenon_TY_v : zenon_U) (zenon_TZ_bl : zenon_U), ((distinct_points zenon_TZ_bl zenon_TZ_bl)/\(distinct_points zenon_TZ_bl zenon_TY_v)) -> (~(distinct_points zenon_TZ_bl zenon_TZ_bl)) -> False).
% 0.60/0.78 do 2 intro. intros zenon_H42 zenon_H36.
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H37. zenon_intro zenon_H2b.
% 0.60/0.78 exact (zenon_H36 zenon_H37).
% 0.60/0.78 (* end of lemma zenon_L10_ *)
% 0.60/0.78 assert (zenon_L11_ : forall (zenon_TZ_bl : zenon_U) (zenon_TY_v : zenon_U) (zenon_TX_u : zenon_U), (~(distinct_lines (line_connecting zenon_TX_u zenon_TY_v) (line_connecting zenon_TZ_bl zenon_TY_v))) -> (apart_point_and_line zenon_TZ_bl (line_connecting zenon_TX_u zenon_TY_v)) -> (forall Z : zenon_U, ((apart_point_and_line zenon_TZ_bl (line_connecting zenon_TX_u zenon_TY_v))->((distinct_lines (line_connecting zenon_TX_u zenon_TY_v) Z)\/(apart_point_and_line zenon_TZ_bl Z)))) -> (apart_point_and_line zenon_TZ_bl (line_connecting zenon_TY_v zenon_TX_u)) -> (distinct_points zenon_TY_v zenon_TX_u) -> (forall Z : zenon_U, ((distinct_points zenon_TY_v zenon_TX_u)->((apart_point_and_line Z (line_connecting zenon_TY_v zenon_TX_u))->((distinct_points Z zenon_TY_v)/\(distinct_points Z zenon_TX_u))))) -> False).
% 0.60/0.78 do 3 intro. intros zenon_H43 zenon_H2d zenon_H2c zenon_H23 zenon_H13 zenon_H22.
% 0.60/0.78 generalize (con1 zenon_TZ_bl). zenon_intro zenon_H44.
% 0.60/0.78 generalize (apart1 zenon_TZ_bl). zenon_intro zenon_H36.
% 0.60/0.78 generalize (zenon_H44 zenon_TY_v). zenon_intro zenon_H45.
% 0.60/0.78 generalize (zenon_H45 zenon_TZ_bl). zenon_intro zenon_H46.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H41 | zenon_intro zenon_H47 ].
% 0.60/0.78 apply (zenon_L9_ zenon_TZ_bl zenon_TX_u zenon_TY_v); trivial.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H48 | zenon_intro zenon_H42 ].
% 0.60/0.78 generalize (zenon_H2c (line_connecting zenon_TZ_bl zenon_TY_v)). zenon_intro zenon_H49.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H32 | zenon_intro zenon_H4a ].
% 0.60/0.78 exact (zenon_H32 zenon_H2d).
% 0.60/0.78 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ].
% 0.60/0.78 exact (zenon_H43 zenon_H4c).
% 0.60/0.78 exact (zenon_H48 zenon_H4b).
% 0.60/0.78 apply (zenon_L10_ zenon_TY_v zenon_TZ_bl); trivial.
% 0.60/0.78 (* end of lemma zenon_L11_ *)
% 0.60/0.78 apply NNPP. intro zenon_G.
% 0.60/0.78 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\(apart_point_and_line Z (line_connecting X Y)))->((distinct_lines (line_connecting X Y) (line_connecting Z X))/\(distinct_lines (line_connecting X Y) (line_connecting Z Y))))))) zenon_G); [ zenon_intro zenon_H4d; idtac ].
% 0.60/0.78 elim zenon_H4d. zenon_intro zenon_TX_u. zenon_intro zenon_H4e.
% 0.60/0.78 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((distinct_points zenon_TX_u Y)/\(apart_point_and_line Z (line_connecting zenon_TX_u Y)))->((distinct_lines (line_connecting zenon_TX_u Y) (line_connecting Z zenon_TX_u))/\(distinct_lines (line_connecting zenon_TX_u Y) (line_connecting Z Y)))))) zenon_H4e); [ zenon_intro zenon_H4f; idtac ].
% 0.60/0.78 elim zenon_H4f. zenon_intro zenon_TY_v. zenon_intro zenon_H50.
% 0.60/0.78 apply (zenon_notallex_s (fun Z : zenon_U => (((distinct_points zenon_TX_u zenon_TY_v)/\(apart_point_and_line Z (line_connecting zenon_TX_u zenon_TY_v)))->((distinct_lines (line_connecting zenon_TX_u zenon_TY_v) (line_connecting Z zenon_TX_u))/\(distinct_lines (line_connecting zenon_TX_u zenon_TY_v) (line_connecting Z zenon_TY_v))))) zenon_H50); [ zenon_intro zenon_H51; idtac ].
% 0.60/0.78 elim zenon_H51. zenon_intro zenon_TZ_bl. zenon_intro zenon_H52.
% 0.60/0.78 apply (zenon_notimply_s _ _ zenon_H52). zenon_intro zenon_H54. zenon_intro zenon_H53.
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H3b. zenon_intro zenon_H2d.
% 0.60/0.78 apply (zenon_notand_s _ _ zenon_H53); [ zenon_intro zenon_H2e | zenon_intro zenon_H43 ].
% 0.60/0.78 generalize (apart1 zenon_TY_v). zenon_intro zenon_H3d.
% 0.60/0.78 generalize (con1 zenon_TY_v). zenon_intro zenon_H55.
% 0.60/0.78 generalize (apart4 zenon_TX_u). zenon_intro zenon_H56.
% 0.60/0.78 generalize (zenon_H56 zenon_TY_v). zenon_intro zenon_H57.
% 0.60/0.78 generalize (con1 zenon_TX_u). zenon_intro zenon_H58.
% 0.60/0.78 generalize (apart1 zenon_TX_u). zenon_intro zenon_H39.
% 0.60/0.78 generalize (zenon_H58 zenon_TY_v). zenon_intro zenon_H59.
% 0.60/0.78 generalize (zenon_H55 zenon_TX_u). zenon_intro zenon_H22.
% 0.60/0.78 generalize (ceq2 zenon_TZ_bl). zenon_intro zenon_H5a.
% 0.60/0.78 generalize (zenon_H59 zenon_TY_v). zenon_intro zenon_H5b.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ].
% 0.60/0.78 exact (zenon_H5d zenon_H3b).
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H11 | zenon_intro zenon_H40 ].
% 0.60/0.78 generalize (zenon_H59 zenon_TX_u). zenon_intro zenon_H5e.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H5d | zenon_intro zenon_H5f ].
% 0.60/0.78 exact (zenon_H5d zenon_H3b).
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_Hf | zenon_intro zenon_H3f ].
% 0.60/0.78 generalize (zenon_H57 zenon_TX_u). zenon_intro zenon_H60.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H60); [ zenon_intro zenon_H5d | zenon_intro zenon_H61 ].
% 0.60/0.78 exact (zenon_H5d zenon_H3b).
% 0.60/0.78 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H3a | zenon_intro zenon_H13 ].
% 0.60/0.78 exact (zenon_H39 zenon_H3a).
% 0.60/0.78 generalize (zenon_H22 zenon_TY_v). zenon_intro zenon_H62.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H1b | zenon_intro zenon_H63 ].
% 0.60/0.78 exact (zenon_H1b zenon_H13).
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H63); [ zenon_intro zenon_H10 | zenon_intro zenon_H3c ].
% 0.60/0.78 generalize (cu1 zenon_TY_v). zenon_intro zenon_H64.
% 0.60/0.78 generalize (zenon_H22 zenon_TX_u). zenon_intro zenon_H65.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H65); [ zenon_intro zenon_H1b | zenon_intro zenon_H66 ].
% 0.60/0.78 exact (zenon_H1b zenon_H13).
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_He | zenon_intro zenon_H38 ].
% 0.60/0.78 generalize (zenon_H64 zenon_TX_u). zenon_intro zenon_Hd.
% 0.60/0.78 generalize (zenon_H5a (line_connecting zenon_TX_u zenon_TY_v)). zenon_intro zenon_H2c.
% 0.60/0.78 generalize (zenon_H2c (line_connecting zenon_TY_v zenon_TX_u)). zenon_intro zenon_H67.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H32 | zenon_intro zenon_H68 ].
% 0.60/0.78 exact (zenon_H32 zenon_H2d).
% 0.60/0.78 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H12 | zenon_intro zenon_H23 ].
% 0.60/0.78 apply (zenon_L1_ zenon_TX_u zenon_TY_v); trivial.
% 0.60/0.78 generalize (con1 zenon_TZ_bl). zenon_intro zenon_H44.
% 0.60/0.78 generalize (apart1 zenon_TZ_bl). zenon_intro zenon_H36.
% 0.60/0.78 generalize (zenon_H44 zenon_TX_u). zenon_intro zenon_H69.
% 0.60/0.78 generalize (zenon_H69 zenon_TZ_bl). zenon_intro zenon_H6a.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H6a); [ zenon_intro zenon_H24 | zenon_intro zenon_H6b ].
% 0.60/0.78 apply (zenon_L2_ zenon_TZ_bl zenon_TX_u zenon_TY_v); trivial.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H6b); [ zenon_intro zenon_H2f | zenon_intro zenon_H35 ].
% 0.60/0.78 apply (zenon_L3_ zenon_TY_v zenon_TX_u zenon_TZ_bl); trivial.
% 0.60/0.78 apply (zenon_L4_ zenon_TX_u zenon_TZ_bl); trivial.
% 0.60/0.78 apply (zenon_L5_ zenon_TY_v zenon_TX_u); trivial.
% 0.60/0.78 apply (zenon_L6_ zenon_TX_u zenon_TY_v); trivial.
% 0.60/0.78 apply (zenon_L7_ zenon_TY_v zenon_TX_u); trivial.
% 0.60/0.78 apply (zenon_L8_ zenon_TX_u zenon_TY_v); trivial.
% 0.60/0.78 generalize (apart1 zenon_TY_v). zenon_intro zenon_H3d.
% 0.60/0.78 generalize (con1 zenon_TY_v). zenon_intro zenon_H55.
% 0.60/0.78 generalize (apart4 zenon_TX_u). zenon_intro zenon_H56.
% 0.60/0.78 generalize (zenon_H56 zenon_TY_v). zenon_intro zenon_H57.
% 0.60/0.78 generalize (con1 zenon_TX_u). zenon_intro zenon_H58.
% 0.60/0.78 generalize (apart1 zenon_TX_u). zenon_intro zenon_H39.
% 0.60/0.78 generalize (zenon_H58 zenon_TY_v). zenon_intro zenon_H59.
% 0.60/0.78 generalize (zenon_H55 zenon_TX_u). zenon_intro zenon_H22.
% 0.60/0.78 generalize (ceq2 zenon_TZ_bl). zenon_intro zenon_H5a.
% 0.60/0.78 generalize (zenon_H59 zenon_TY_v). zenon_intro zenon_H5b.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ].
% 0.60/0.78 exact (zenon_H5d zenon_H3b).
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H11 | zenon_intro zenon_H40 ].
% 0.60/0.78 generalize (zenon_H59 zenon_TX_u). zenon_intro zenon_H5e.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H5d | zenon_intro zenon_H5f ].
% 0.60/0.78 exact (zenon_H5d zenon_H3b).
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_Hf | zenon_intro zenon_H3f ].
% 0.60/0.78 generalize (zenon_H57 zenon_TX_u). zenon_intro zenon_H60.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H60); [ zenon_intro zenon_H5d | zenon_intro zenon_H61 ].
% 0.60/0.78 exact (zenon_H5d zenon_H3b).
% 0.60/0.78 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H3a | zenon_intro zenon_H13 ].
% 0.60/0.78 exact (zenon_H39 zenon_H3a).
% 0.60/0.78 generalize (zenon_H22 zenon_TY_v). zenon_intro zenon_H62.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H1b | zenon_intro zenon_H63 ].
% 0.60/0.78 exact (zenon_H1b zenon_H13).
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H63); [ zenon_intro zenon_H10 | zenon_intro zenon_H3c ].
% 0.60/0.78 generalize (cu1 zenon_TY_v). zenon_intro zenon_H64.
% 0.60/0.78 generalize (zenon_H22 zenon_TX_u). zenon_intro zenon_H65.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H65); [ zenon_intro zenon_H1b | zenon_intro zenon_H66 ].
% 0.60/0.78 exact (zenon_H1b zenon_H13).
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H66); [ zenon_intro zenon_He | zenon_intro zenon_H38 ].
% 0.60/0.78 generalize (zenon_H64 zenon_TX_u). zenon_intro zenon_Hd.
% 0.60/0.78 generalize (zenon_H5a (line_connecting zenon_TX_u zenon_TY_v)). zenon_intro zenon_H2c.
% 0.60/0.78 generalize (zenon_H2c (line_connecting zenon_TY_v zenon_TX_u)). zenon_intro zenon_H67.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H32 | zenon_intro zenon_H68 ].
% 0.60/0.78 exact (zenon_H32 zenon_H2d).
% 0.60/0.78 apply (zenon_or_s _ _ zenon_H68); [ zenon_intro zenon_H12 | zenon_intro zenon_H23 ].
% 0.60/0.78 apply (zenon_L1_ zenon_TX_u zenon_TY_v); trivial.
% 0.60/0.78 apply (zenon_L11_ zenon_TZ_bl zenon_TY_v zenon_TX_u); trivial.
% 0.60/0.78 apply (zenon_L5_ zenon_TY_v zenon_TX_u); trivial.
% 0.60/0.78 apply (zenon_L6_ zenon_TX_u zenon_TY_v); trivial.
% 0.60/0.78 apply (zenon_L7_ zenon_TY_v zenon_TX_u); trivial.
% 0.60/0.78 apply (zenon_L8_ zenon_TX_u zenon_TY_v); trivial.
% 0.60/0.78 Qed.
% 0.60/0.78 % SZS output end Proof
% 0.60/0.78 (* END-PROOF *)
% 0.60/0.78 nodes searched: 19034
% 0.60/0.78 max branch formulas: 1557
% 0.60/0.78 proof nodes created: 1664
% 0.60/0.78 formulas created: 32381
% 0.60/0.78
%------------------------------------------------------------------------------