%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO191+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n021.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 07:00:36 EDT 2022 % Result : Theorem 0.82s 1.07s % Output : Proof 0.82s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.11 % Problem : GEO191+3 : TPTP v8.1.0. Released v4.0.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n021.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 06:00:31 EDT 2022 % 0.12/0.33 % CPUTime : % 0.82/1.07 (* PROOF-FOUND *) % 0.82/1.07 % SZS status Theorem % 0.82/1.07 (* BEGIN-PROOF *) % 0.82/1.07 % SZS output start Proof % 0.82/1.07 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((convergent_lines X Y)/\((convergent_lines U V)/\((apart_point_and_line (intersection_point X Y) U)\/(apart_point_and_line (intersection_point X Y) V))))->((apart_point_and_line (intersection_point U V) X)\/(apart_point_and_line (intersection_point U V) Y))))))). % 0.82/1.07 Proof. % 0.82/1.07 assert (zenon_L1_ : forall (zenon_TY_bn : zenon_U) (zenon_TU_bo : zenon_U), (forall Y : zenon_U, ((distinct_lines zenon_TU_bo Y)->(convergent_lines zenon_TU_bo Y))) -> (distinct_lines zenon_TU_bo zenon_TY_bn) -> (~(convergent_lines zenon_TU_bo zenon_TY_bn)) -> False). % 0.82/1.07 do 2 intro. intros zenon_H24 zenon_H25 zenon_H26. % 0.82/1.07 generalize (zenon_H24 zenon_TY_bn). zenon_intro zenon_H29. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 0.82/1.07 exact (zenon_H2b zenon_H25). % 0.82/1.07 exact (zenon_H26 zenon_H2a). % 0.82/1.07 (* end of lemma zenon_L1_ *) % 0.82/1.07 assert (zenon_L2_ : forall (zenon_TY_bn : zenon_U) (zenon_TX_bu : zenon_U), (apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TY_bn) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> False). % 0.82/1.07 do 2 intro. intros zenon_H2c zenon_H2d. % 0.82/1.07 generalize (ci4 zenon_TX_bu). zenon_intro zenon_H2f. % 0.82/1.07 generalize (zenon_H2f zenon_TY_bn). zenon_intro zenon_H30. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 0.82/1.07 exact (zenon_H32 zenon_H2d). % 0.82/1.07 exact (zenon_H31 zenon_H2c). % 0.82/1.07 (* end of lemma zenon_L2_ *) % 0.82/1.07 assert (zenon_L3_ : forall (zenon_TU_bo : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TX_bu : zenon_U), (convergent_lines zenon_TX_bu zenon_TY_bn) -> (~(convergent_lines zenon_TU_bo zenon_TY_bn)) -> (apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TU_bo) -> False). % 0.82/1.07 do 3 intro. intros zenon_H2d zenon_H26 zenon_H33. % 0.82/1.07 generalize (p1 zenon_TU_bo). zenon_intro zenon_H24. % 0.82/1.07 generalize (ceq2 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_H34. % 0.82/1.07 generalize (zenon_H34 zenon_TU_bo). zenon_intro zenon_H35. % 0.82/1.07 generalize (zenon_H35 zenon_TY_bn). zenon_intro zenon_H36. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.82/1.07 exact (zenon_H38 zenon_H33). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H37); [ zenon_intro zenon_H25 | zenon_intro zenon_H2c ]. % 0.82/1.07 apply (zenon_L1_ zenon_TY_bn zenon_TU_bo); trivial. % 0.82/1.07 apply (zenon_L2_ zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 (* end of lemma zenon_L3_ *) % 0.82/1.07 assert (zenon_L4_ : forall (zenon_TY_bn : zenon_U) (zenon_TV_ch : zenon_U), (~(convergent_lines zenon_TV_ch zenon_TY_bn)) -> (distinct_lines zenon_TV_ch zenon_TY_bn) -> False). % 0.82/1.07 do 2 intro. intros zenon_H39 zenon_H3a. % 0.82/1.07 generalize (p1 zenon_TV_ch). zenon_intro zenon_H3c. % 0.82/1.07 generalize (zenon_H3c zenon_TY_bn). zenon_intro zenon_H3d. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ]. % 0.82/1.07 exact (zenon_H3f zenon_H3a). % 0.82/1.07 exact (zenon_H39 zenon_H3e). % 0.82/1.07 (* end of lemma zenon_L4_ *) % 0.82/1.07 assert (zenon_L5_ : forall (zenon_TV_ch : zenon_U) (zenon_TU_bo : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TU_bo Y)->(~(apart_point_and_line (intersection_point zenon_TU_bo Y) zenon_TU_bo)))) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TU_bo) -> False). % 0.82/1.07 do 2 intro. intros zenon_H40 zenon_H41 zenon_H42. % 0.82/1.07 generalize (zenon_H40 zenon_TV_ch). zenon_intro zenon_H43. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ]. % 0.82/1.07 exact (zenon_H45 zenon_H41). % 0.82/1.07 exact (zenon_H44 zenon_H42). % 0.82/1.07 (* end of lemma zenon_L5_ *) % 0.82/1.07 assert (zenon_L6_ : forall (zenon_TV_ch : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TU_bo : zenon_U), (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TU_bo zenon_TY_bn) (intersection_point zenon_TU_bo zenon_TV_ch))/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) U)\/((apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) V)\/((apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) U)\/(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) V))))))) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (forall Y : zenon_U, ((convergent_lines zenon_TU_bo Y)->(~(apart_point_and_line (intersection_point zenon_TU_bo Y) zenon_TU_bo)))) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TU_bo)) -> (distinct_lines zenon_TU_bo zenon_TY_bn) -> (distinct_points (intersection_point zenon_TU_bo zenon_TY_bn) (intersection_point zenon_TU_bo zenon_TV_ch)) -> False). % 0.82/1.07 do 3 intro. intros zenon_H46 zenon_H47 zenon_H41 zenon_H40 zenon_H48 zenon_H49 zenon_H25 zenon_H4a. % 0.82/1.07 generalize (zenon_H46 zenon_TU_bo). zenon_intro zenon_H4b. % 0.82/1.07 generalize (zenon_H4b zenon_TY_bn). zenon_intro zenon_H4c. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ]. % 0.82/1.07 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_H4f | zenon_intro zenon_H2b ]. % 0.82/1.07 exact (zenon_H4f zenon_H4a). % 0.82/1.07 exact (zenon_H2b zenon_H25). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 0.82/1.07 exact (zenon_H49 zenon_H51). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ]. % 0.82/1.07 exact (zenon_H48 zenon_H53). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H42 | zenon_intro zenon_H54 ]. % 0.82/1.07 apply (zenon_L5_ zenon_TV_ch zenon_TU_bo); trivial. % 0.82/1.07 exact (zenon_H47 zenon_H54). % 0.82/1.07 (* end of lemma zenon_L6_ *) % 0.82/1.07 assert (zenon_L7_ : forall (zenon_TX_bu : zenon_U) (zenon_TV_ch : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TU_bo : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) Y)->((distinct_points (intersection_point zenon_TU_bo zenon_TY_bn) Z)\/(apart_point_and_line Z Y))))) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (distinct_lines zenon_TU_bo zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TU_bo)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TY_bn)) -> (forall Y : zenon_U, ((convergent_lines zenon_TU_bo Y)->(~(apart_point_and_line (intersection_point zenon_TU_bo Y) zenon_TU_bo)))) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TX_bu) -> False). % 0.82/1.07 do 4 intro. intros zenon_H55 zenon_H56 zenon_H25 zenon_H49 zenon_H48 zenon_H40 zenon_H41 zenon_H47 zenon_H57. % 0.82/1.07 generalize (zenon_H55 zenon_TX_bu). zenon_intro zenon_H58. % 0.82/1.07 generalize (zenon_H58 (intersection_point zenon_TU_bo zenon_TV_ch)). zenon_intro zenon_H59. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 0.82/1.07 exact (zenon_H5b zenon_H57). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4a | zenon_intro zenon_H5c ]. % 0.82/1.07 generalize (cu1 (intersection_point zenon_TU_bo zenon_TY_bn)). zenon_intro zenon_H5d. % 0.82/1.07 generalize (zenon_H5d (intersection_point zenon_TU_bo zenon_TV_ch)). zenon_intro zenon_H46. % 0.82/1.07 apply (zenon_L6_ zenon_TV_ch zenon_TY_bn zenon_TU_bo); trivial. % 0.82/1.07 exact (zenon_H56 zenon_H5c). % 0.82/1.07 (* end of lemma zenon_L7_ *) % 0.82/1.07 assert (zenon_L8_ : forall (zenon_TV_ch : zenon_U) (zenon_TX_bu : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TU_bo : zenon_U), (apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TX_bu) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (forall Y : zenon_U, ((convergent_lines zenon_TU_bo Y)->(~(apart_point_and_line (intersection_point zenon_TU_bo Y) zenon_TU_bo)))) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TU_bo)) -> (distinct_lines zenon_TU_bo zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> False). % 0.82/1.07 do 4 intro. intros zenon_H57 zenon_H47 zenon_H41 zenon_H40 zenon_H48 zenon_H49 zenon_H25 zenon_H56. % 0.82/1.07 generalize (ceq1 (intersection_point zenon_TU_bo zenon_TY_bn)). zenon_intro zenon_H55. % 0.82/1.07 apply (zenon_L7_ zenon_TX_bu zenon_TV_ch zenon_TY_bn zenon_TU_bo); trivial. % 0.82/1.07 (* end of lemma zenon_L8_ *) % 0.82/1.07 assert (zenon_L9_ : forall (zenon_TV_ch : zenon_U) (zenon_TU_bo : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TX_bu : zenon_U), (forall V : zenon_U, (((distinct_points (intersection_point zenon_TX_bu zenon_TY_bn) (intersection_point zenon_TU_bo zenon_TY_bn))/\(distinct_lines zenon_TX_bu V))->((apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TX_bu)\/((apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) V)\/((apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TX_bu)\/(apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) V)))))) -> (distinct_points (intersection_point zenon_TX_bu zenon_TY_bn) (intersection_point zenon_TU_bo zenon_TY_bn)) -> (distinct_lines zenon_TX_bu zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TX_bu)) -> (~(apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (forall Y : zenon_U, ((convergent_lines zenon_TU_bo Y)->(~(apart_point_and_line (intersection_point zenon_TU_bo Y) zenon_TU_bo)))) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TU_bo)) -> (distinct_lines zenon_TU_bo zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> False). % 0.82/1.07 do 4 intro. intros zenon_H5e zenon_H5f zenon_H60 zenon_H61 zenon_H31 zenon_H47 zenon_H41 zenon_H40 zenon_H48 zenon_H49 zenon_H25 zenon_H56. % 0.82/1.07 generalize (zenon_H5e zenon_TY_bn). zenon_intro zenon_H62. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ]. % 0.82/1.07 apply (zenon_notand_s _ _ zenon_H64); [ zenon_intro zenon_H66 | zenon_intro zenon_H65 ]. % 0.82/1.07 exact (zenon_H66 zenon_H5f). % 0.82/1.07 exact (zenon_H65 zenon_H60). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H68 | zenon_intro zenon_H67 ]. % 0.82/1.07 exact (zenon_H61 zenon_H68). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H67); [ zenon_intro zenon_H2c | zenon_intro zenon_H69 ]. % 0.82/1.07 exact (zenon_H31 zenon_H2c). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H57 | zenon_intro zenon_H53 ]. % 0.82/1.07 apply (zenon_L8_ zenon_TV_ch zenon_TX_bu zenon_TY_bn zenon_TU_bo); trivial. % 0.82/1.07 exact (zenon_H48 zenon_H53). % 0.82/1.07 (* end of lemma zenon_L9_ *) % 0.82/1.07 assert (zenon_L10_ : forall (zenon_TY_bn : zenon_U) (zenon_TX_bu : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TX_bu Y)->(~(apart_point_and_line (intersection_point zenon_TX_bu Y) zenon_TX_bu)))) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> (apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TX_bu) -> False). % 0.82/1.07 do 2 intro. intros zenon_H6a zenon_H2d zenon_H68. % 0.82/1.07 generalize (zenon_H6a zenon_TY_bn). zenon_intro zenon_H6b. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H6b); [ zenon_intro zenon_H32 | zenon_intro zenon_H61 ]. % 0.82/1.07 exact (zenon_H32 zenon_H2d). % 0.82/1.07 exact (zenon_H61 zenon_H68). % 0.82/1.07 (* end of lemma zenon_L10_ *) % 0.82/1.07 assert (zenon_L11_ : forall (zenon_TX_bu : zenon_U), (convergent_lines zenon_TX_bu zenon_TX_bu) -> False). % 0.82/1.07 do 1 intro. intros zenon_H6c. % 0.82/1.07 generalize (apart3 zenon_TX_bu). zenon_intro zenon_H6d. % 0.82/1.07 exact (zenon_H6d zenon_H6c). % 0.82/1.07 (* end of lemma zenon_L11_ *) % 0.82/1.07 assert (zenon_L12_ : forall (zenon_TY_bn : zenon_U) (zenon_TU_bo : zenon_U), (apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TY_bn) -> (convergent_lines zenon_TU_bo zenon_TY_bn) -> False). % 0.82/1.07 do 2 intro. intros zenon_H53 zenon_H2a. % 0.82/1.07 generalize (ci4 zenon_TU_bo). zenon_intro zenon_H6e. % 0.82/1.07 generalize (zenon_H6e zenon_TY_bn). zenon_intro zenon_H6f. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H6f); [ zenon_intro zenon_H26 | zenon_intro zenon_H48 ]. % 0.82/1.07 exact (zenon_H26 zenon_H2a). % 0.82/1.07 exact (zenon_H48 zenon_H53). % 0.82/1.07 (* end of lemma zenon_L12_ *) % 0.82/1.07 assert (zenon_L13_ : forall (zenon_TX_bu : zenon_U) (zenon_TV_ch : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TU_bo : zenon_U), (apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TV_ch) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bu zenon_TY_bn)->((distinct_lines zenon_TY_bn Z)\/(convergent_lines zenon_TX_bu Z)))) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (forall Y : zenon_U, ((convergent_lines zenon_TU_bo Y)->(~(apart_point_and_line (intersection_point zenon_TU_bo Y) zenon_TU_bo)))) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TU_bo)) -> (distinct_lines zenon_TU_bo zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (~(apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TV_ch)) -> (~(distinct_lines zenon_TY_bn zenon_TY_bn)) -> (convergent_lines zenon_TU_bo zenon_TY_bn) -> False). % 0.82/1.07 do 4 intro. intros zenon_H70 zenon_H71 zenon_H2d zenon_H47 zenon_H41 zenon_H40 zenon_H49 zenon_H25 zenon_H56 zenon_H31 zenon_H72 zenon_H73 zenon_H2a. % 0.82/1.07 generalize (ceq2 (intersection_point zenon_TU_bo zenon_TY_bn)). zenon_intro zenon_H74. % 0.82/1.07 generalize (zenon_H74 zenon_TY_bn). zenon_intro zenon_H75. % 0.82/1.07 generalize (zenon_H75 zenon_TY_bn). zenon_intro zenon_H76. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H76); [ zenon_intro zenon_H48 | zenon_intro zenon_H77 ]. % 0.82/1.07 generalize (ceq1 (intersection_point zenon_TU_bo zenon_TY_bn)). zenon_intro zenon_H55. % 0.82/1.07 generalize (zenon_H55 zenon_TV_ch). zenon_intro zenon_H78. % 0.82/1.07 generalize (zenon_H78 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_H79. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H79); [ zenon_intro zenon_H7b | zenon_intro zenon_H7a ]. % 0.82/1.07 exact (zenon_H7b zenon_H70). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H7a); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ]. % 0.82/1.07 generalize (cu1 (intersection_point zenon_TU_bo zenon_TY_bn)). zenon_intro zenon_H5d. % 0.82/1.07 generalize (zenon_H5d (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_H7e. % 0.82/1.07 generalize (zenon_H71 zenon_TX_bu). zenon_intro zenon_H7f. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H7f); [ zenon_intro zenon_H32 | zenon_intro zenon_H80 ]. % 0.82/1.07 exact (zenon_H32 zenon_H2d). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H80); [ zenon_intro zenon_H81 | zenon_intro zenon_H6c ]. % 0.82/1.07 generalize (ci3 zenon_TX_bu). zenon_intro zenon_H6a. % 0.82/1.07 generalize (zenon_H7e zenon_TY_bn). zenon_intro zenon_H82. % 0.82/1.07 generalize (zenon_H82 zenon_TX_bu). zenon_intro zenon_H83. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H83); [ zenon_intro zenon_H85 | zenon_intro zenon_H84 ]. % 0.82/1.07 apply (zenon_notand_s _ _ zenon_H85); [ zenon_intro zenon_H87 | zenon_intro zenon_H86 ]. % 0.82/1.07 exact (zenon_H87 zenon_H7d). % 0.82/1.07 exact (zenon_H86 zenon_H81). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H53 | zenon_intro zenon_H88 ]. % 0.82/1.07 exact (zenon_H48 zenon_H53). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H88); [ zenon_intro zenon_H57 | zenon_intro zenon_H89 ]. % 0.82/1.07 apply (zenon_L8_ zenon_TV_ch zenon_TX_bu zenon_TY_bn zenon_TU_bo); trivial. % 0.82/1.07 apply (zenon_or_s _ _ zenon_H89); [ zenon_intro zenon_H2c | zenon_intro zenon_H68 ]. % 0.82/1.07 exact (zenon_H31 zenon_H2c). % 0.82/1.07 apply (zenon_L10_ zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 apply (zenon_L11_ zenon_TX_bu); trivial. % 0.82/1.07 exact (zenon_H72 zenon_H7c). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H8a | zenon_intro zenon_H53 ]. % 0.82/1.07 exact (zenon_H73 zenon_H8a). % 0.82/1.07 apply (zenon_L12_ zenon_TY_bn zenon_TU_bo); trivial. % 0.82/1.07 (* end of lemma zenon_L13_ *) % 0.82/1.07 assert (zenon_L14_ : forall (zenon_TV_ch : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TX_bu : zenon_U), ((apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TV_ch)->((distinct_lines zenon_TV_ch zenon_TY_bn)\/(apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TY_bn))) -> (apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TV_ch) -> (~(convergent_lines zenon_TV_ch zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TY_bn)) -> False). % 0.82/1.07 do 3 intro. intros zenon_H8b zenon_H7c zenon_H39 zenon_H31. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H72 | zenon_intro zenon_H8c ]. % 0.82/1.07 exact (zenon_H72 zenon_H7c). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H3a | zenon_intro zenon_H2c ]. % 0.82/1.07 apply (zenon_L4_ zenon_TY_bn zenon_TV_ch); trivial. % 0.82/1.07 exact (zenon_H31 zenon_H2c). % 0.82/1.07 (* end of lemma zenon_L14_ *) % 0.82/1.07 assert (zenon_L15_ : forall (zenon_TV_ch : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TX_bu : zenon_U), (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TV_ch)->((distinct_lines zenon_TV_ch Z)\/(apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) Z)))) -> (apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TV_ch) -> (~(convergent_lines zenon_TV_ch zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TY_bn)) -> False). % 0.82/1.07 do 3 intro. intros zenon_H8d zenon_H7c zenon_H39 zenon_H31. % 0.82/1.07 generalize (zenon_H8d zenon_TY_bn). zenon_intro zenon_H8b. % 0.82/1.07 apply (zenon_L14_ zenon_TV_ch zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 (* end of lemma zenon_L15_ *) % 0.82/1.07 assert (zenon_L16_ : forall (zenon_TV_ch : zenon_U) (zenon_TU_bo : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TX_bu : zenon_U), (forall Z : zenon_U, ((convergent_lines zenon_TX_bu zenon_TY_bn)->((distinct_lines zenon_TY_bn Z)\/(convergent_lines zenon_TX_bu Z)))) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> (forall V : zenon_U, (((distinct_points (intersection_point zenon_TX_bu zenon_TY_bn) (intersection_point zenon_TU_bo zenon_TV_ch))/\(distinct_lines zenon_TY_bn V))->((apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TY_bn)\/((apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) V)\/((apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)\/(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) V)))))) -> (distinct_points (intersection_point zenon_TX_bu zenon_TY_bn) (intersection_point zenon_TU_bo zenon_TV_ch)) -> (forall Y : zenon_U, ((convergent_lines zenon_TX_bu Y)->(~(apart_point_and_line (intersection_point zenon_TX_bu Y) zenon_TX_bu)))) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (~(convergent_lines zenon_TX_bu zenon_TX_bu)) -> False). % 0.82/1.07 do 4 intro. intros zenon_H71 zenon_H2d zenon_H8e zenon_H8f zenon_H6a zenon_H47 zenon_H56 zenon_H6d. % 0.82/1.07 generalize (zenon_H71 zenon_TX_bu). zenon_intro zenon_H7f. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H7f); [ zenon_intro zenon_H32 | zenon_intro zenon_H80 ]. % 0.82/1.07 exact (zenon_H32 zenon_H2d). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H80); [ zenon_intro zenon_H81 | zenon_intro zenon_H6c ]. % 0.82/1.07 generalize (zenon_H8e zenon_TX_bu). zenon_intro zenon_H90. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H92 | zenon_intro zenon_H91 ]. % 0.82/1.07 apply (zenon_notand_s _ _ zenon_H92); [ zenon_intro zenon_H93 | zenon_intro zenon_H86 ]. % 0.82/1.07 exact (zenon_H93 zenon_H8f). % 0.82/1.07 exact (zenon_H86 zenon_H81). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H2c | zenon_intro zenon_H94 ]. % 0.82/1.07 apply (zenon_L2_ zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H68 | zenon_intro zenon_H95 ]. % 0.82/1.07 apply (zenon_L10_ zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H54 | zenon_intro zenon_H5c ]. % 0.82/1.07 exact (zenon_H47 zenon_H54). % 0.82/1.07 exact (zenon_H56 zenon_H5c). % 0.82/1.07 exact (zenon_H6d zenon_H6c). % 0.82/1.07 (* end of lemma zenon_L16_ *) % 0.82/1.07 assert (zenon_L17_ : forall (zenon_TV_ch : zenon_U) (zenon_TU_bo : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TX_bu : zenon_U), (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TX_bu zenon_TY_bn) Y)/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) U)\/((apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) V)\/((apart_point_and_line Y U)\/(apart_point_and_line Y V)))))))) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bu zenon_TY_bn)->((distinct_lines zenon_TY_bn Z)\/(convergent_lines zenon_TX_bu Z)))) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> (distinct_points (intersection_point zenon_TX_bu zenon_TY_bn) (intersection_point zenon_TU_bo zenon_TV_ch)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> False). % 0.82/1.07 do 4 intro. intros zenon_H96 zenon_H71 zenon_H2d zenon_H8f zenon_H47 zenon_H56. % 0.82/1.07 generalize (zenon_H96 (intersection_point zenon_TU_bo zenon_TV_ch)). zenon_intro zenon_H97. % 0.82/1.07 generalize (ci3 zenon_TX_bu). zenon_intro zenon_H6a. % 0.82/1.07 generalize (zenon_H97 zenon_TY_bn). zenon_intro zenon_H8e. % 0.82/1.07 generalize (apart3 zenon_TX_bu). zenon_intro zenon_H6d. % 0.82/1.07 apply (zenon_L16_ zenon_TV_ch zenon_TU_bo zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 (* end of lemma zenon_L17_ *) % 0.82/1.07 assert (zenon_L18_ : forall (zenon_TY_bn : zenon_U) (zenon_TX_bu : zenon_U) (zenon_TV_ch : zenon_U) (zenon_TU_bo : zenon_U), (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (distinct_points (intersection_point zenon_TX_bu zenon_TY_bn) (intersection_point zenon_TU_bo zenon_TV_ch)) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bu zenon_TY_bn)->((distinct_lines zenon_TY_bn Z)\/(convergent_lines zenon_TX_bu Z)))) -> False). % 0.82/1.07 do 4 intro. intros zenon_H56 zenon_H47 zenon_H8f zenon_H2d zenon_H71. % 0.82/1.07 generalize (cu1 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_H96. % 0.82/1.07 apply (zenon_L17_ zenon_TV_ch zenon_TU_bo zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 (* end of lemma zenon_L18_ *) % 0.82/1.07 assert (zenon_L19_ : forall (zenon_TV_ch : zenon_U) (zenon_TU_bo : zenon_U), (apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TV_ch) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> False). % 0.82/1.07 do 2 intro. intros zenon_H98 zenon_H41. % 0.82/1.07 generalize (ci4 zenon_TU_bo). zenon_intro zenon_H6e. % 0.82/1.07 generalize (zenon_H6e zenon_TV_ch). zenon_intro zenon_H99. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H45 | zenon_intro zenon_H9a ]. % 0.82/1.07 exact (zenon_H45 zenon_H41). % 0.82/1.07 exact (zenon_H9a zenon_H98). % 0.82/1.07 (* end of lemma zenon_L19_ *) % 0.82/1.07 assert (zenon_L20_ : forall (zenon_TU_bo : zenon_U) (zenon_TX_bu : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TV_ch : zenon_U), (apart_point_and_line (intersection_point zenon_TV_ch zenon_TY_bn) zenon_TX_bu) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (~(apart_point_and_line (intersection_point zenon_TV_ch zenon_TY_bn) zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TV_ch zenon_TY_bn) zenon_TV_ch)) -> (distinct_lines zenon_TV_ch zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> False). % 0.82/1.07 do 4 intro. intros zenon_H9b zenon_H47 zenon_H41 zenon_H9c zenon_H9d zenon_H3a zenon_H56. % 0.82/1.07 generalize (ceq1 (intersection_point zenon_TV_ch zenon_TY_bn)). zenon_intro zenon_H9e. % 0.82/1.07 generalize (zenon_H9e zenon_TX_bu). zenon_intro zenon_H9f. % 0.82/1.07 generalize (zenon_H9f (intersection_point zenon_TU_bo zenon_TV_ch)). zenon_intro zenon_Ha0. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Ha0); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha1 ]. % 0.82/1.07 exact (zenon_Ha2 zenon_H9b). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Ha1); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H5c ]. % 0.82/1.07 generalize (cu1 (intersection_point zenon_TV_ch zenon_TY_bn)). zenon_intro zenon_Ha4. % 0.82/1.07 generalize (zenon_Ha4 (intersection_point zenon_TU_bo zenon_TV_ch)). zenon_intro zenon_Ha5. % 0.82/1.07 generalize (zenon_Ha5 zenon_TV_ch). zenon_intro zenon_Ha6. % 0.82/1.07 generalize (zenon_Ha6 zenon_TY_bn). zenon_intro zenon_Ha7. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Ha7); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Ha8 ]. % 0.82/1.07 apply (zenon_notand_s _ _ zenon_Ha9); [ zenon_intro zenon_Haa | zenon_intro zenon_H3f ]. % 0.82/1.07 exact (zenon_Haa zenon_Ha3). % 0.82/1.07 exact (zenon_H3f zenon_H3a). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Ha8); [ zenon_intro zenon_Hac | zenon_intro zenon_Hab ]. % 0.82/1.07 exact (zenon_H9d zenon_Hac). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hab); [ zenon_intro zenon_Hae | zenon_intro zenon_Had ]. % 0.82/1.07 exact (zenon_H9c zenon_Hae). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Had); [ zenon_intro zenon_H98 | zenon_intro zenon_H54 ]. % 0.82/1.07 apply (zenon_L19_ zenon_TV_ch zenon_TU_bo); trivial. % 0.82/1.07 exact (zenon_H47 zenon_H54). % 0.82/1.07 exact (zenon_H56 zenon_H5c). % 0.82/1.07 (* end of lemma zenon_L20_ *) % 0.82/1.07 assert (zenon_L21_ : forall (zenon_TY_bn : zenon_U) (zenon_TV_ch : zenon_U), (apart_point_and_line (intersection_point zenon_TV_ch zenon_TY_bn) zenon_TY_bn) -> (convergent_lines zenon_TV_ch zenon_TY_bn) -> False). % 0.82/1.07 do 2 intro. intros zenon_Hae zenon_H3e. % 0.82/1.07 generalize (ci4 zenon_TV_ch). zenon_intro zenon_Haf. % 0.82/1.07 generalize (zenon_Haf zenon_TY_bn). zenon_intro zenon_Hb0. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hb0); [ zenon_intro zenon_H39 | zenon_intro zenon_H9c ]. % 0.82/1.07 exact (zenon_H39 zenon_H3e). % 0.82/1.07 exact (zenon_H9c zenon_Hae). % 0.82/1.07 (* end of lemma zenon_L21_ *) % 0.82/1.07 assert (zenon_L22_ : forall (zenon_TU_bo : zenon_U) (zenon_TX_bu : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TV_ch : zenon_U), (apart_point_and_line (intersection_point zenon_TV_ch zenon_TY_bn) zenon_TX_bu) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (~(apart_point_and_line (intersection_point zenon_TV_ch zenon_TY_bn) zenon_TV_ch)) -> (distinct_lines zenon_TV_ch zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (~(distinct_lines zenon_TY_bn zenon_TY_bn)) -> (convergent_lines zenon_TV_ch zenon_TY_bn) -> False). % 0.82/1.07 do 4 intro. intros zenon_H9b zenon_H47 zenon_H41 zenon_H9d zenon_H3a zenon_H56 zenon_H73 zenon_H3e. % 0.82/1.07 generalize (ceq2 (intersection_point zenon_TV_ch zenon_TY_bn)). zenon_intro zenon_Hb1. % 0.82/1.07 generalize (zenon_Hb1 zenon_TY_bn). zenon_intro zenon_Hb2. % 0.82/1.07 generalize (zenon_Hb2 zenon_TY_bn). zenon_intro zenon_Hb3. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hb3); [ zenon_intro zenon_H9c | zenon_intro zenon_Hb4 ]. % 0.82/1.07 apply (zenon_L20_ zenon_TU_bo zenon_TX_bu zenon_TY_bn zenon_TV_ch); trivial. % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hb4); [ zenon_intro zenon_H8a | zenon_intro zenon_Hae ]. % 0.82/1.07 exact (zenon_H73 zenon_H8a). % 0.82/1.07 apply (zenon_L21_ zenon_TY_bn zenon_TV_ch); trivial. % 0.82/1.07 (* end of lemma zenon_L22_ *) % 0.82/1.07 assert (zenon_L23_ : forall (zenon_TU_bo : zenon_U) (zenon_TV_ch : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TX_bu : zenon_U), (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TX_bu zenon_TY_bn) (intersection_point zenon_TV_ch zenon_TY_bn))/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) U)\/((apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) V)\/((apart_point_and_line (intersection_point zenon_TV_ch zenon_TY_bn) U)\/(apart_point_and_line (intersection_point zenon_TV_ch zenon_TY_bn) V))))))) -> (convergent_lines zenon_TV_ch zenon_TY_bn) -> (~(distinct_lines zenon_TY_bn zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (distinct_lines zenon_TV_ch zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TV_ch zenon_TY_bn) zenon_TV_ch)) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TX_bu)) -> (distinct_lines zenon_TX_bu zenon_TY_bn) -> (distinct_points (intersection_point zenon_TX_bu zenon_TY_bn) (intersection_point zenon_TV_ch zenon_TY_bn)) -> False). % 0.82/1.07 do 4 intro. intros zenon_Hb5 zenon_H3e zenon_H73 zenon_H56 zenon_H3a zenon_H9d zenon_H41 zenon_H47 zenon_H31 zenon_H61 zenon_H60 zenon_Hb6. % 0.82/1.07 generalize (zenon_Hb5 zenon_TX_bu). zenon_intro zenon_Hb7. % 0.82/1.07 generalize (zenon_Hb7 zenon_TY_bn). zenon_intro zenon_Hb8. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hb8); [ zenon_intro zenon_Hba | zenon_intro zenon_Hb9 ]. % 0.82/1.07 apply (zenon_notand_s _ _ zenon_Hba); [ zenon_intro zenon_Hbb | zenon_intro zenon_H65 ]. % 0.82/1.07 exact (zenon_Hbb zenon_Hb6). % 0.82/1.07 exact (zenon_H65 zenon_H60). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hb9); [ zenon_intro zenon_H68 | zenon_intro zenon_Hbc ]. % 0.82/1.07 exact (zenon_H61 zenon_H68). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_H2c | zenon_intro zenon_Hbd ]. % 0.82/1.07 exact (zenon_H31 zenon_H2c). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hbd); [ zenon_intro zenon_H9b | zenon_intro zenon_Hae ]. % 0.82/1.07 apply (zenon_L22_ zenon_TU_bo zenon_TX_bu zenon_TY_bn zenon_TV_ch); trivial. % 0.82/1.07 apply (zenon_L21_ zenon_TY_bn zenon_TV_ch); trivial. % 0.82/1.07 (* end of lemma zenon_L23_ *) % 0.82/1.07 assert (zenon_L24_ : forall (zenon_TU_bo : zenon_U) (zenon_TV_ch : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TX_bu : zenon_U), (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TX_bu)->((distinct_points (intersection_point zenon_TX_bu zenon_TY_bn) Z)\/(apart_point_and_line Z zenon_TX_bu)))) -> (convergent_lines zenon_TV_ch zenon_TY_bn) -> (~(distinct_lines zenon_TY_bn zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (distinct_lines zenon_TV_ch zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TV_ch zenon_TY_bn) zenon_TV_ch)) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TY_bn)) -> (distinct_lines zenon_TX_bu zenon_TY_bn) -> (distinct_points (intersection_point zenon_TX_bu zenon_TY_bn) (intersection_point zenon_TV_ch zenon_TY_bn)) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> (forall Y : zenon_U, ((convergent_lines zenon_TX_bu Y)->(~(apart_point_and_line (intersection_point zenon_TX_bu Y) zenon_TX_bu)))) -> False). % 0.82/1.07 do 4 intro. intros zenon_Hbe zenon_H3e zenon_H73 zenon_H56 zenon_H3a zenon_H9d zenon_H41 zenon_H47 zenon_H31 zenon_H60 zenon_Hb6 zenon_H2d zenon_H6a. % 0.82/1.07 generalize (zenon_Hbe (intersection_point zenon_TU_bo zenon_TV_ch)). zenon_intro zenon_Hbf. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hbf); [ zenon_intro zenon_H61 | zenon_intro zenon_Hc0 ]. % 0.82/1.07 generalize (cu1 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_H96. % 0.82/1.07 generalize (zenon_H96 (intersection_point zenon_TV_ch zenon_TY_bn)). zenon_intro zenon_Hb5. % 0.82/1.07 apply (zenon_L23_ zenon_TU_bo zenon_TV_ch zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_H8f | zenon_intro zenon_H5c ]. % 0.82/1.07 generalize (cu1 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_H96. % 0.82/1.07 generalize (zenon_H96 (intersection_point zenon_TU_bo zenon_TV_ch)). zenon_intro zenon_H97. % 0.82/1.07 generalize (zenon_H97 zenon_TX_bu). zenon_intro zenon_Hc1. % 0.82/1.07 generalize (zenon_Hc1 zenon_TY_bn). zenon_intro zenon_Hc2. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hc3 ]. % 0.82/1.07 apply (zenon_notand_s _ _ zenon_Hc4); [ zenon_intro zenon_H93 | zenon_intro zenon_H65 ]. % 0.82/1.07 exact (zenon_H93 zenon_H8f). % 0.82/1.07 exact (zenon_H65 zenon_H60). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_H68 | zenon_intro zenon_Hc5 ]. % 0.82/1.07 apply (zenon_L10_ zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_H2c | zenon_intro zenon_Hc6 ]. % 0.82/1.07 exact (zenon_H31 zenon_H2c). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_H5c | zenon_intro zenon_H54 ]. % 0.82/1.07 exact (zenon_H56 zenon_H5c). % 0.82/1.07 exact (zenon_H47 zenon_H54). % 0.82/1.07 exact (zenon_H56 zenon_H5c). % 0.82/1.07 (* end of lemma zenon_L24_ *) % 0.82/1.07 assert (zenon_L25_ : forall (zenon_TU_bo : zenon_U) (zenon_TV_ch : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TX_bu : zenon_U), (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TY_bn)->((distinct_lines zenon_TY_bn Z)\/(apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) Z)))) -> (apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TV_ch) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bu zenon_TY_bn)->((distinct_lines zenon_TY_bn Z)\/(convergent_lines zenon_TX_bu Z)))) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> (forall Y : zenon_U, (forall Z : zenon_U, ((distinct_lines zenon_TY_bn Y)->((distinct_lines zenon_TY_bn Z)\/(distinct_lines Y Z))))) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (~(apart_point_and_line (intersection_point zenon_TV_ch zenon_TY_bn) zenon_TV_ch)) -> (distinct_lines zenon_TV_ch zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (convergent_lines zenon_TV_ch zenon_TY_bn) -> (~(distinct_lines zenon_TY_bn zenon_TY_bn)) -> False). % 0.82/1.07 do 4 intro. intros zenon_Hc7 zenon_H7c zenon_H71 zenon_H2d zenon_Hc8 zenon_H47 zenon_H41 zenon_H9d zenon_H3a zenon_H56 zenon_H3e zenon_H73. % 0.82/1.07 generalize (zenon_Hc7 zenon_TY_bn). zenon_intro zenon_Hc9. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hc9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hca ]. % 0.82/1.07 generalize (ceq1 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_Hcb. % 0.82/1.07 generalize (zenon_Hcb zenon_TV_ch). zenon_intro zenon_Hcc. % 0.82/1.07 generalize (zenon_Hcc (intersection_point zenon_TV_ch zenon_TY_bn)). zenon_intro zenon_Hcd. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hcd); [ zenon_intro zenon_H72 | zenon_intro zenon_Hce ]. % 0.82/1.07 exact (zenon_H72 zenon_H7c). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hce); [ zenon_intro zenon_Hb6 | zenon_intro zenon_Hac ]. % 0.82/1.07 generalize (zenon_H71 zenon_TX_bu). zenon_intro zenon_H7f. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H7f); [ zenon_intro zenon_H32 | zenon_intro zenon_H80 ]. % 0.82/1.07 exact (zenon_H32 zenon_H2d). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H80); [ zenon_intro zenon_H81 | zenon_intro zenon_H6c ]. % 0.82/1.07 generalize (zenon_Hc8 zenon_TX_bu). zenon_intro zenon_Hcf. % 0.82/1.07 generalize (zenon_Hcf zenon_TY_bn). zenon_intro zenon_Hd0. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hd0); [ zenon_intro zenon_H86 | zenon_intro zenon_Hd1 ]. % 0.82/1.07 exact (zenon_H86 zenon_H81). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_H8a | zenon_intro zenon_H60 ]. % 0.82/1.07 exact (zenon_H73 zenon_H8a). % 0.82/1.07 generalize (zenon_Hcb zenon_TX_bu). zenon_intro zenon_Hbe. % 0.82/1.07 generalize (ci3 zenon_TX_bu). zenon_intro zenon_H6a. % 0.82/1.07 apply (zenon_L24_ zenon_TU_bo zenon_TV_ch zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 apply (zenon_L11_ zenon_TX_bu); trivial. % 0.82/1.07 exact (zenon_H9d zenon_Hac). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H8a | zenon_intro zenon_H2c ]. % 0.82/1.07 exact (zenon_H73 zenon_H8a). % 0.82/1.07 apply (zenon_L2_ zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 (* end of lemma zenon_L25_ *) % 0.82/1.07 assert (zenon_L26_ : forall (zenon_TU_bo : zenon_U) (zenon_TV_ch : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TX_bu : zenon_U), (apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TV_ch) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bu zenon_TY_bn)->((distinct_lines zenon_TY_bn Z)\/(convergent_lines zenon_TX_bu Z)))) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (~(apart_point_and_line (intersection_point zenon_TV_ch zenon_TY_bn) zenon_TV_ch)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (~(convergent_lines zenon_TY_bn zenon_TY_bn)) -> (convergent_lines zenon_TY_bn zenon_TV_ch) -> False). % 0.82/1.07 do 4 intro. intros zenon_H7c zenon_H71 zenon_H2d zenon_H47 zenon_H41 zenon_H9d zenon_H56 zenon_Hd2 zenon_Hd3. % 0.82/1.07 generalize (apart5 zenon_TY_bn). zenon_intro zenon_Hc8. % 0.82/1.07 generalize (ax6 zenon_TY_bn). zenon_intro zenon_Hd4. % 0.82/1.07 generalize (zenon_Hd4 zenon_TV_ch). zenon_intro zenon_Hd5. % 0.82/1.07 generalize (zenon_Hd5 zenon_TY_bn). zenon_intro zenon_Hd6. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hd6); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hd7 ]. % 0.82/1.07 exact (zenon_Hd8 zenon_Hd3). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_Hd9 | zenon_intro zenon_H3e ]. % 0.82/1.07 exact (zenon_Hd2 zenon_Hd9). % 0.82/1.07 generalize (ceq3 zenon_TY_bn). zenon_intro zenon_Hda. % 0.82/1.07 generalize (zenon_Hda zenon_TV_ch). zenon_intro zenon_Hdb. % 0.82/1.07 generalize (zenon_Hdb zenon_TY_bn). zenon_intro zenon_Hdc. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hdc); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hdd ]. % 0.82/1.07 exact (zenon_Hd8 zenon_Hd3). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd9 ]. % 0.82/1.07 generalize (ceq2 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_H34. % 0.82/1.07 generalize (zenon_H34 zenon_TY_bn). zenon_intro zenon_Hc7. % 0.82/1.07 generalize (apart2 zenon_TY_bn). zenon_intro zenon_H73. % 0.82/1.07 apply (zenon_L25_ zenon_TU_bo zenon_TV_ch zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 exact (zenon_Hd2 zenon_Hd9). % 0.82/1.07 (* end of lemma zenon_L26_ *) % 0.82/1.07 assert (zenon_L27_ : forall (zenon_TU_bo : zenon_U) (zenon_TX_bu : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TV_ch : zenon_U), (forall Z : zenon_U, ((convergent_lines zenon_TV_ch zenon_TY_bn)->((convergent_lines zenon_TV_ch Z)\/(convergent_lines zenon_TY_bn Z)))) -> (convergent_lines zenon_TV_ch zenon_TY_bn) -> (~(convergent_lines zenon_TV_ch zenon_TV_ch)) -> (apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TV_ch) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bu zenon_TY_bn)->((distinct_lines zenon_TY_bn Z)\/(convergent_lines zenon_TX_bu Z)))) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (~(apart_point_and_line (intersection_point zenon_TV_ch zenon_TY_bn) zenon_TV_ch)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (~(convergent_lines zenon_TY_bn zenon_TY_bn)) -> False). % 0.82/1.07 do 4 intro. intros zenon_Hde zenon_H3e zenon_Hdf zenon_H7c zenon_H71 zenon_H2d zenon_H47 zenon_H41 zenon_H9d zenon_H56 zenon_Hd2. % 0.82/1.07 generalize (zenon_Hde zenon_TV_ch). zenon_intro zenon_He0. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_He0); [ zenon_intro zenon_H39 | zenon_intro zenon_He1 ]. % 0.82/1.07 exact (zenon_H39 zenon_H3e). % 0.82/1.07 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_He2 | zenon_intro zenon_Hd3 ]. % 0.82/1.07 exact (zenon_Hdf zenon_He2). % 0.82/1.07 apply (zenon_L26_ zenon_TU_bo zenon_TV_ch zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 (* end of lemma zenon_L27_ *) % 0.82/1.07 assert (zenon_L28_ : forall (zenon_TV_ch : zenon_U) (zenon_TU_bo : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TX_bu : zenon_U), (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TY_bn)->((distinct_points (intersection_point zenon_TX_bu zenon_TY_bn) Z)\/(apart_point_and_line Z zenon_TY_bn)))) -> (~(convergent_lines zenon_TY_bn zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (~(apart_point_and_line (intersection_point zenon_TV_ch zenon_TY_bn) zenon_TV_ch)) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bu zenon_TY_bn)->((distinct_lines zenon_TY_bn Z)\/(convergent_lines zenon_TX_bu Z)))) -> (~(convergent_lines zenon_TV_ch zenon_TV_ch)) -> (apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TV_ch) -> (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TV_ch)->((distinct_lines zenon_TV_ch Z)\/(apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) Z)))) -> False). % 0.82/1.07 do 4 intro. intros zenon_He3 zenon_Hd2 zenon_H56 zenon_H9d zenon_H41 zenon_H47 zenon_H2d zenon_H71 zenon_Hdf zenon_H7c zenon_H8d. % 0.82/1.07 generalize (zenon_He3 (intersection_point zenon_TU_bo zenon_TV_ch)). zenon_intro zenon_He4. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_He4); [ zenon_intro zenon_H31 | zenon_intro zenon_He5 ]. % 0.82/1.07 generalize (ax6 zenon_TV_ch). zenon_intro zenon_He6. % 0.82/1.07 generalize (zenon_H8d zenon_TY_bn). zenon_intro zenon_H8b. % 0.82/1.07 generalize (zenon_He6 zenon_TY_bn). zenon_intro zenon_Hde. % 0.82/1.07 generalize (zenon_Hde zenon_TY_bn). zenon_intro zenon_He7. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_He7); [ zenon_intro zenon_H39 | zenon_intro zenon_He8 ]. % 0.82/1.07 apply (zenon_L14_ zenon_TV_ch zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3e | zenon_intro zenon_Hd9 ]. % 0.82/1.07 apply (zenon_L27_ zenon_TU_bo zenon_TX_bu zenon_TY_bn zenon_TV_ch); trivial. % 0.82/1.07 exact (zenon_Hd2 zenon_Hd9). % 0.82/1.07 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_H8f | zenon_intro zenon_H54 ]. % 0.82/1.07 apply (zenon_L18_ zenon_TY_bn zenon_TX_bu zenon_TV_ch zenon_TU_bo); trivial. % 0.82/1.07 exact (zenon_H47 zenon_H54). % 0.82/1.07 (* end of lemma zenon_L28_ *) % 0.82/1.07 assert (zenon_L29_ : forall (zenon_TU_bo : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TX_bu : zenon_U) (zenon_TV_ch : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TV_ch Y)->(~(apart_point_and_line (intersection_point zenon_TV_ch Y) zenon_TV_ch)))) -> (apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TV_ch) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> False). % 0.82/1.07 do 4 intro. intros zenon_He9 zenon_H7c zenon_H56 zenon_H47 zenon_H2d zenon_H41. % 0.82/1.07 generalize (apart3 zenon_TV_ch). zenon_intro zenon_Hdf. % 0.82/1.07 generalize (apart3 zenon_TY_bn). zenon_intro zenon_Hd2. % 0.82/1.07 generalize (zenon_He9 zenon_TY_bn). zenon_intro zenon_Hea. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hea); [ zenon_intro zenon_H39 | zenon_intro zenon_H9d ]. % 0.82/1.07 generalize (ceq3 zenon_TX_bu). zenon_intro zenon_Heb. % 0.82/1.07 generalize (zenon_Heb zenon_TY_bn). zenon_intro zenon_H71. % 0.82/1.07 generalize (ceq2 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_H34. % 0.82/1.07 generalize (zenon_H34 zenon_TV_ch). zenon_intro zenon_H8d. % 0.82/1.07 generalize (ceq1 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_Hcb. % 0.82/1.07 generalize (zenon_Hcb zenon_TY_bn). zenon_intro zenon_He3. % 0.82/1.07 generalize (zenon_He3 (intersection_point zenon_TU_bo zenon_TV_ch)). zenon_intro zenon_He4. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_He4); [ zenon_intro zenon_H31 | zenon_intro zenon_He5 ]. % 0.82/1.07 apply (zenon_L15_ zenon_TV_ch zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_H8f | zenon_intro zenon_H54 ]. % 0.82/1.07 apply (zenon_L18_ zenon_TY_bn zenon_TX_bu zenon_TV_ch zenon_TU_bo); trivial. % 0.82/1.07 exact (zenon_H47 zenon_H54). % 0.82/1.07 generalize (ceq3 zenon_TX_bu). zenon_intro zenon_Heb. % 0.82/1.07 generalize (zenon_Heb zenon_TY_bn). zenon_intro zenon_H71. % 0.82/1.07 generalize (ceq2 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_H34. % 0.82/1.07 generalize (zenon_H34 zenon_TV_ch). zenon_intro zenon_H8d. % 0.82/1.07 generalize (ceq1 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_Hcb. % 0.82/1.07 generalize (zenon_Hcb zenon_TY_bn). zenon_intro zenon_He3. % 0.82/1.07 apply (zenon_L28_ zenon_TV_ch zenon_TU_bo zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 (* end of lemma zenon_L29_ *) % 0.82/1.07 assert (zenon_L30_ : forall (zenon_TX_bu : zenon_U) (zenon_TV_ch : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TU_bo : zenon_U), (convergent_lines zenon_TU_bo zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TU_bo)) -> (forall Y : zenon_U, ((convergent_lines zenon_TU_bo Y)->(~(apart_point_and_line (intersection_point zenon_TU_bo Y) zenon_TU_bo)))) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bu zenon_TY_bn)->((distinct_lines zenon_TY_bn Z)\/(convergent_lines zenon_TX_bu Z)))) -> (distinct_lines zenon_TV_ch zenon_TY_bn) -> (forall Y : zenon_U, ((convergent_lines zenon_TV_ch Y)->(~(apart_point_and_line (intersection_point zenon_TV_ch Y) zenon_TV_ch)))) -> (apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TU_bo) -> False). % 0.82/1.07 do 4 intro. intros zenon_H2a zenon_H56 zenon_H49 zenon_H40 zenon_H41 zenon_H47 zenon_H2d zenon_H71 zenon_H3a zenon_He9 zenon_H33. % 0.82/1.07 generalize (apart2 zenon_TY_bn). zenon_intro zenon_H73. % 0.82/1.07 generalize (ceq2 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_H34. % 0.82/1.07 generalize (zenon_H34 zenon_TU_bo). zenon_intro zenon_H35. % 0.82/1.07 generalize (zenon_H34 zenon_TV_ch). zenon_intro zenon_H8d. % 0.82/1.07 generalize (zenon_H34 zenon_TY_bn). zenon_intro zenon_Hc7. % 0.82/1.07 generalize (zenon_H35 zenon_TY_bn). zenon_intro zenon_H36. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 0.82/1.07 exact (zenon_H38 zenon_H33). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H37); [ zenon_intro zenon_H25 | zenon_intro zenon_H2c ]. % 0.82/1.07 generalize (zenon_Hc7 zenon_TY_bn). zenon_intro zenon_Hc9. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hc9); [ zenon_intro zenon_H31 | zenon_intro zenon_Hca ]. % 0.82/1.07 generalize (apart2 zenon_TV_ch). zenon_intro zenon_Hec. % 0.82/1.07 generalize (zenon_H8d zenon_TV_ch). zenon_intro zenon_Hed. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hed); [ zenon_intro zenon_H72 | zenon_intro zenon_Hee ]. % 0.82/1.07 generalize (ceq1 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_Hcb. % 0.82/1.07 generalize (zenon_Hcb zenon_TU_bo). zenon_intro zenon_Hef. % 0.82/1.07 generalize (zenon_Hef (intersection_point zenon_TU_bo zenon_TY_bn)). zenon_intro zenon_Hf0. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hf0); [ zenon_intro zenon_H38 | zenon_intro zenon_Hf1 ]. % 0.82/1.07 exact (zenon_H38 zenon_H33). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H5f | zenon_intro zenon_H51 ]. % 0.82/1.07 generalize (cu1 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_H96. % 0.82/1.07 generalize (zenon_H96 (intersection_point zenon_TU_bo zenon_TY_bn)). zenon_intro zenon_Hf2. % 0.82/1.07 generalize (zenon_Hf2 zenon_TV_ch). zenon_intro zenon_Hf3. % 0.82/1.07 generalize (zenon_Hf3 zenon_TY_bn). zenon_intro zenon_Hf4. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hf4); [ zenon_intro zenon_Hf6 | zenon_intro zenon_Hf5 ]. % 0.82/1.07 apply (zenon_notand_s _ _ zenon_Hf6); [ zenon_intro zenon_H66 | zenon_intro zenon_H3f ]. % 0.82/1.07 exact (zenon_H66 zenon_H5f). % 0.82/1.07 exact (zenon_H3f zenon_H3a). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_H7c | zenon_intro zenon_Hf7 ]. % 0.82/1.07 exact (zenon_H72 zenon_H7c). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hf7); [ zenon_intro zenon_H2c | zenon_intro zenon_Hf8 ]. % 0.82/1.07 exact (zenon_H31 zenon_H2c). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H70 | zenon_intro zenon_H53 ]. % 0.82/1.07 apply (zenon_L13_ zenon_TX_bu zenon_TV_ch zenon_TY_bn zenon_TU_bo); trivial. % 0.82/1.07 apply (zenon_L12_ zenon_TY_bn zenon_TU_bo); trivial. % 0.82/1.07 exact (zenon_H49 zenon_H51). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_Hf9 | zenon_intro zenon_H7c ]. % 0.82/1.07 exact (zenon_Hec zenon_Hf9). % 0.82/1.07 apply (zenon_L29_ zenon_TU_bo zenon_TY_bn zenon_TX_bu zenon_TV_ch); trivial. % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H8a | zenon_intro zenon_H2c ]. % 0.82/1.07 exact (zenon_H73 zenon_H8a). % 0.82/1.07 apply (zenon_L2_ zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 apply (zenon_L2_ zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 (* end of lemma zenon_L30_ *) % 0.82/1.07 assert (zenon_L31_ : forall (zenon_TX_bu : zenon_U) (zenon_TV_ch : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TU_bo : zenon_U), (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TV_ch)->((distinct_lines zenon_TV_ch Z)\/(apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) Z)))) -> (apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TV_ch) -> (convergent_lines zenon_TU_bo zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TU_bo)) -> (forall Y : zenon_U, ((convergent_lines zenon_TU_bo Y)->(~(apart_point_and_line (intersection_point zenon_TU_bo Y) zenon_TU_bo)))) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bu zenon_TY_bn)->((distinct_lines zenon_TY_bn Z)\/(convergent_lines zenon_TX_bu Z)))) -> (forall Y : zenon_U, ((convergent_lines zenon_TV_ch Y)->(~(apart_point_and_line (intersection_point zenon_TV_ch Y) zenon_TV_ch)))) -> (apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TU_bo) -> False). % 0.82/1.07 do 4 intro. intros zenon_Hfa zenon_H70 zenon_H2a zenon_H56 zenon_H49 zenon_H40 zenon_H41 zenon_H47 zenon_H2d zenon_H71 zenon_He9 zenon_H33. % 0.82/1.07 generalize (zenon_Hfa zenon_TY_bn). zenon_intro zenon_Hfb. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hfb); [ zenon_intro zenon_H7b | zenon_intro zenon_Hfc ]. % 0.82/1.07 exact (zenon_H7b zenon_H70). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H3a | zenon_intro zenon_H53 ]. % 0.82/1.07 apply (zenon_L30_ zenon_TX_bu zenon_TV_ch zenon_TY_bn zenon_TU_bo); trivial. % 0.82/1.07 apply (zenon_L12_ zenon_TY_bn zenon_TU_bo); trivial. % 0.82/1.07 (* end of lemma zenon_L31_ *) % 0.82/1.07 assert (zenon_L32_ : forall (zenon_TV_ch : zenon_U) (zenon_TU_bo : zenon_U) (zenon_TX_bu : zenon_U) (zenon_TY_bn : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines zenon_TY_bn Y)->((distinct_lines Y Z)\/(convergent_lines zenon_TY_bn Z))))) -> (~(convergent_lines zenon_TY_bn zenon_TY_bn)) -> (apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TU_bo) -> (forall Y : zenon_U, ((convergent_lines zenon_TV_ch Y)->(~(apart_point_and_line (intersection_point zenon_TV_ch Y) zenon_TV_ch)))) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bu zenon_TY_bn)->((distinct_lines zenon_TY_bn Z)\/(convergent_lines zenon_TX_bu Z)))) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (forall Y : zenon_U, ((convergent_lines zenon_TU_bo Y)->(~(apart_point_and_line (intersection_point zenon_TU_bo Y) zenon_TU_bo)))) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TU_bo)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (convergent_lines zenon_TU_bo zenon_TY_bn) -> (convergent_lines zenon_TY_bn zenon_TV_ch) -> False). % 0.82/1.07 do 4 intro. intros zenon_Hda zenon_Hd2 zenon_H33 zenon_He9 zenon_H71 zenon_H2d zenon_H47 zenon_H41 zenon_H40 zenon_H49 zenon_H56 zenon_H2a zenon_Hd3. % 0.82/1.07 generalize (zenon_Hda zenon_TV_ch). zenon_intro zenon_Hdb. % 0.82/1.07 generalize (zenon_Hdb zenon_TY_bn). zenon_intro zenon_Hdc. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hdc); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hdd ]. % 0.82/1.07 exact (zenon_Hd8 zenon_Hd3). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hdd); [ zenon_intro zenon_H3a | zenon_intro zenon_Hd9 ]. % 0.82/1.07 apply (zenon_L30_ zenon_TX_bu zenon_TV_ch zenon_TY_bn zenon_TU_bo); trivial. % 0.82/1.07 exact (zenon_Hd2 zenon_Hd9). % 0.82/1.07 (* end of lemma zenon_L32_ *) % 0.82/1.07 assert (zenon_L33_ : forall (zenon_TV_ch : zenon_U) (zenon_TX_bu : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TU_bo : zenon_U), ((convergent_lines zenon_TU_bo zenon_TY_bn)->((convergent_lines zenon_TU_bo zenon_TY_bn)\/(convergent_lines zenon_TY_bn zenon_TY_bn))) -> (apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TU_bo) -> (forall Y : zenon_U, ((convergent_lines zenon_TV_ch Y)->(~(apart_point_and_line (intersection_point zenon_TV_ch Y) zenon_TV_ch)))) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bu zenon_TY_bn)->((distinct_lines zenon_TY_bn Z)\/(convergent_lines zenon_TX_bu Z)))) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (forall Y : zenon_U, ((convergent_lines zenon_TU_bo Y)->(~(apart_point_and_line (intersection_point zenon_TU_bo Y) zenon_TU_bo)))) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TU_bo)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (convergent_lines zenon_TY_bn zenon_TV_ch) -> (~(convergent_lines zenon_TY_bn zenon_TY_bn)) -> False). % 0.82/1.07 do 4 intro. intros zenon_Hfd zenon_H33 zenon_He9 zenon_H71 zenon_H2d zenon_H47 zenon_H41 zenon_H40 zenon_H49 zenon_H56 zenon_Hd3 zenon_Hd2. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hfd); [ zenon_intro zenon_H26 | zenon_intro zenon_Hfe ]. % 0.82/1.07 apply (zenon_L3_ zenon_TU_bo zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2a | zenon_intro zenon_Hd9 ]. % 0.82/1.07 generalize (ceq3 zenon_TY_bn). zenon_intro zenon_Hda. % 0.82/1.07 apply (zenon_L32_ zenon_TV_ch zenon_TU_bo zenon_TX_bu zenon_TY_bn); trivial. % 0.82/1.07 exact (zenon_Hd2 zenon_Hd9). % 0.82/1.07 (* end of lemma zenon_L33_ *) % 0.82/1.07 assert (zenon_L34_ : forall (zenon_TX_bu : zenon_U) (zenon_TU_bo : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TV_ch : zenon_U), (forall Z : zenon_U, ((convergent_lines zenon_TV_ch zenon_TY_bn)->((convergent_lines zenon_TV_ch Z)\/(convergent_lines zenon_TY_bn Z)))) -> (convergent_lines zenon_TV_ch zenon_TY_bn) -> (~(convergent_lines zenon_TV_ch zenon_TV_ch)) -> ((convergent_lines zenon_TU_bo zenon_TY_bn)->((convergent_lines zenon_TU_bo zenon_TY_bn)\/(convergent_lines zenon_TY_bn zenon_TY_bn))) -> (~(convergent_lines zenon_TY_bn zenon_TY_bn)) -> (forall Y : zenon_U, ((convergent_lines zenon_TV_ch Y)->(~(apart_point_and_line (intersection_point zenon_TV_ch Y) zenon_TV_ch)))) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bu zenon_TY_bn)->((distinct_lines zenon_TY_bn Z)\/(convergent_lines zenon_TX_bu Z)))) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (convergent_lines zenon_TU_bo zenon_TV_ch) -> (forall Y : zenon_U, ((convergent_lines zenon_TU_bo Y)->(~(apart_point_and_line (intersection_point zenon_TU_bo Y) zenon_TU_bo)))) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TY_bn) zenon_TU_bo)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TU_bo) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> False). % 0.82/1.07 do 4 intro. intros zenon_Hde zenon_H3e zenon_Hdf zenon_Hfd zenon_Hd2 zenon_He9 zenon_H71 zenon_H47 zenon_H41 zenon_H40 zenon_H49 zenon_H56 zenon_H33 zenon_H2d. % 0.82/1.07 generalize (zenon_Hde zenon_TV_ch). zenon_intro zenon_He0. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_He0); [ zenon_intro zenon_H39 | zenon_intro zenon_He1 ]. % 0.82/1.07 exact (zenon_H39 zenon_H3e). % 0.82/1.07 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_He2 | zenon_intro zenon_Hd3 ]. % 0.82/1.07 exact (zenon_Hdf zenon_He2). % 0.82/1.07 apply (zenon_L33_ zenon_TV_ch zenon_TX_bu zenon_TY_bn zenon_TU_bo); trivial. % 0.82/1.07 (* end of lemma zenon_L34_ *) % 0.82/1.07 assert (zenon_L35_ : forall (zenon_TY_bn : zenon_U) (zenon_TX_bu : zenon_U) (zenon_TV_ch : zenon_U) (zenon_TU_bo : zenon_U), (convergent_lines zenon_TU_bo zenon_TV_ch) -> (convergent_lines zenon_TX_bu zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_ch) zenon_TX_bu)) -> (apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TV_ch) -> False). % 0.82/1.07 do 4 intro. intros zenon_H41 zenon_H2d zenon_H47 zenon_H56 zenon_H7c. % 0.82/1.07 generalize (ci3 zenon_TV_ch). zenon_intro zenon_He9. % 0.82/1.07 apply (zenon_L29_ zenon_TU_bo zenon_TY_bn zenon_TX_bu zenon_TV_ch); trivial. % 0.82/1.07 (* end of lemma zenon_L35_ *) % 0.82/1.07 apply NNPP. intro zenon_G. % 0.82/1.07 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((convergent_lines X Y)/\((convergent_lines U V)/\((apart_point_and_line (intersection_point X Y) U)\/(apart_point_and_line (intersection_point X Y) V))))->((apart_point_and_line (intersection_point U V) X)\/(apart_point_and_line (intersection_point U V) Y))))))) zenon_G); [ zenon_intro zenon_Hff; idtac ]. % 0.82/1.07 elim zenon_Hff. zenon_intro zenon_TX_bu. zenon_intro zenon_H100. % 0.82/1.07 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((convergent_lines zenon_TX_bu Y)/\((convergent_lines U V)/\((apart_point_and_line (intersection_point zenon_TX_bu Y) U)\/(apart_point_and_line (intersection_point zenon_TX_bu Y) V))))->((apart_point_and_line (intersection_point U V) zenon_TX_bu)\/(apart_point_and_line (intersection_point U V) Y)))))) zenon_H100); [ zenon_intro zenon_H101; idtac ]. % 0.82/1.07 elim zenon_H101. zenon_intro zenon_TY_bn. zenon_intro zenon_H102. % 0.82/1.07 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((convergent_lines zenon_TX_bu zenon_TY_bn)/\((convergent_lines U V)/\((apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) U)\/(apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) V))))->((apart_point_and_line (intersection_point U V) zenon_TX_bu)\/(apart_point_and_line (intersection_point U V) zenon_TY_bn))))) zenon_H102); [ zenon_intro zenon_H103; idtac ]. % 0.82/1.07 elim zenon_H103. zenon_intro zenon_TU_bo. zenon_intro zenon_H104. % 0.82/1.07 apply (zenon_notallex_s (fun V : zenon_U => (((convergent_lines zenon_TX_bu zenon_TY_bn)/\((convergent_lines zenon_TU_bo V)/\((apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) zenon_TU_bo)\/(apart_point_and_line (intersection_point zenon_TX_bu zenon_TY_bn) V))))->((apart_point_and_line (intersection_point zenon_TU_bo V) zenon_TX_bu)\/(apart_point_and_line (intersection_point zenon_TU_bo V) zenon_TY_bn)))) zenon_H104); [ zenon_intro zenon_H105; idtac ]. % 0.82/1.07 elim zenon_H105. zenon_intro zenon_TV_ch. zenon_intro zenon_H106. % 0.82/1.07 apply (zenon_notimply_s _ _ zenon_H106). zenon_intro zenon_H108. zenon_intro zenon_H107. % 0.82/1.07 apply (zenon_notor_s _ _ zenon_H107). zenon_intro zenon_H56. zenon_intro zenon_H47. % 0.82/1.07 apply (zenon_and_s _ _ zenon_H108). zenon_intro zenon_H2d. zenon_intro zenon_H109. % 0.82/1.07 apply (zenon_and_s _ _ zenon_H109). zenon_intro zenon_H41. zenon_intro zenon_H10a. % 0.82/1.07 apply (zenon_or_s _ _ zenon_H10a); [ zenon_intro zenon_H33 | zenon_intro zenon_H7c ]. % 0.82/1.07 generalize (ci3 zenon_TU_bo). zenon_intro zenon_H40. % 0.82/1.07 generalize (apart3 zenon_TV_ch). zenon_intro zenon_Hdf. % 0.82/1.07 generalize (apart3 zenon_TY_bn). zenon_intro zenon_Hd2. % 0.82/1.07 generalize (zenon_H40 zenon_TY_bn). zenon_intro zenon_H10b. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H10b); [ zenon_intro zenon_H26 | zenon_intro zenon_H49 ]. % 0.82/1.07 apply (zenon_L3_ zenon_TU_bo zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 generalize (ceq3 zenon_TX_bu). zenon_intro zenon_Heb. % 0.82/1.07 generalize (ax6 zenon_TU_bo). zenon_intro zenon_H10c. % 0.82/1.07 generalize (ci3 zenon_TV_ch). zenon_intro zenon_He9. % 0.82/1.07 generalize (ax6 zenon_TX_bu). zenon_intro zenon_H10d. % 0.82/1.07 generalize (zenon_Heb zenon_TV_ch). zenon_intro zenon_H10e. % 0.82/1.07 generalize (zenon_Heb zenon_TY_bn). zenon_intro zenon_H71. % 0.82/1.07 generalize (zenon_H10d zenon_TY_bn). zenon_intro zenon_H10f. % 0.82/1.07 generalize (zenon_H10c zenon_TV_ch). zenon_intro zenon_H110. % 0.82/1.07 generalize (zenon_H10f zenon_TV_ch). zenon_intro zenon_H111. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H111); [ zenon_intro zenon_H32 | zenon_intro zenon_H112 ]. % 0.82/1.07 exact (zenon_H32 zenon_H2d). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H112); [ zenon_intro zenon_H113 | zenon_intro zenon_Hd3 ]. % 0.82/1.07 generalize (zenon_H10c zenon_TY_bn). zenon_intro zenon_H114. % 0.82/1.07 generalize (zenon_H110 zenon_TY_bn). zenon_intro zenon_H115. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H115); [ zenon_intro zenon_H45 | zenon_intro zenon_H116 ]. % 0.82/1.07 exact (zenon_H45 zenon_H41). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H116); [ zenon_intro zenon_H2a | zenon_intro zenon_H3e ]. % 0.82/1.07 generalize (zenon_H114 zenon_TY_bn). zenon_intro zenon_Hfd. % 0.82/1.07 generalize (ceq2 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_H34. % 0.82/1.07 generalize (zenon_H34 zenon_TV_ch). zenon_intro zenon_H8d. % 0.82/1.07 generalize (ceq1 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_Hcb. % 0.82/1.07 generalize (zenon_Hcb zenon_TU_bo). zenon_intro zenon_Hef. % 0.82/1.07 generalize (zenon_Hcb zenon_TY_bn). zenon_intro zenon_He3. % 0.82/1.07 generalize (zenon_Hef (intersection_point zenon_TU_bo zenon_TY_bn)). zenon_intro zenon_Hf0. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hf0); [ zenon_intro zenon_H38 | zenon_intro zenon_Hf1 ]. % 0.82/1.07 exact (zenon_H38 zenon_H33). % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_H5f | zenon_intro zenon_H51 ]. % 0.82/1.07 generalize (zenon_He3 (intersection_point zenon_TU_bo zenon_TV_ch)). zenon_intro zenon_He4. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_He4); [ zenon_intro zenon_H31 | zenon_intro zenon_He5 ]. % 0.82/1.07 generalize (cu1 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_H96. % 0.82/1.07 generalize (cup1 (intersection_point zenon_TX_bu zenon_TY_bn)). zenon_intro zenon_H117. % 0.82/1.07 generalize (zenon_H96 (intersection_point zenon_TU_bo zenon_TY_bn)). zenon_intro zenon_Hf2. % 0.82/1.07 generalize (ci3 zenon_TX_bu). zenon_intro zenon_H6a. % 0.82/1.07 generalize (apart3 zenon_TU_bo). zenon_intro zenon_H118. % 0.82/1.07 generalize (zenon_H114 zenon_TU_bo). zenon_intro zenon_H119. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H119); [ zenon_intro zenon_H26 | zenon_intro zenon_H11a ]. % 0.82/1.07 exact (zenon_H26 zenon_H2a). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H11c | zenon_intro zenon_H11b ]. % 0.82/1.07 exact (zenon_H118 zenon_H11c). % 0.82/1.07 generalize (apart5 zenon_TV_ch). zenon_intro zenon_H11d. % 0.82/1.07 generalize (ceq3 zenon_TY_bn). zenon_intro zenon_Hda. % 0.82/1.07 generalize (ax6 zenon_TY_bn). zenon_intro zenon_Hd4. % 0.82/1.07 generalize (ax6 zenon_TV_ch). zenon_intro zenon_He6. % 0.82/1.07 generalize (zenon_Hda zenon_TU_bo). zenon_intro zenon_H11e. % 0.82/1.07 generalize (zenon_H11e zenon_TY_bn). zenon_intro zenon_H11f. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H11f); [ zenon_intro zenon_H121 | zenon_intro zenon_H120 ]. % 0.82/1.07 exact (zenon_H121 zenon_H11b). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H120); [ zenon_intro zenon_H25 | zenon_intro zenon_Hd9 ]. % 0.82/1.07 generalize (zenon_He6 zenon_TY_bn). zenon_intro zenon_Hde. % 0.82/1.07 generalize (zenon_Hde zenon_TY_bn). zenon_intro zenon_He7. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_He7); [ zenon_intro zenon_H39 | zenon_intro zenon_He8 ]. % 0.82/1.07 generalize (zenon_H8d zenon_TY_bn). zenon_intro zenon_H8b. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H72 | zenon_intro zenon_H8c ]. % 0.82/1.07 generalize (zenon_H117 zenon_TY_bn). zenon_intro zenon_H122. % 0.82/1.07 generalize (zenon_Hd4 zenon_TV_ch). zenon_intro zenon_Hd5. % 0.82/1.07 generalize (zenon_Hd5 zenon_TY_bn). zenon_intro zenon_Hd6. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_Hd6); [ zenon_intro zenon_Hd8 | zenon_intro zenon_Hd7 ]. % 0.82/1.07 generalize (zenon_H10e zenon_TX_bu). zenon_intro zenon_H123. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H123); [ zenon_intro zenon_H125 | zenon_intro zenon_H124 ]. % 0.82/1.07 exact (zenon_H125 zenon_H113). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H126 | zenon_intro zenon_H6c ]. % 0.82/1.07 generalize (apart2 zenon_TX_bu). zenon_intro zenon_H127. % 0.82/1.07 generalize (zenon_H11d zenon_TX_bu). zenon_intro zenon_H128. % 0.82/1.07 generalize (zenon_H128 zenon_TY_bn). zenon_intro zenon_H129. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H129); [ zenon_intro zenon_H12b | zenon_intro zenon_H12a ]. % 0.82/1.07 exact (zenon_H12b zenon_H126). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H3a | zenon_intro zenon_H60 ]. % 0.82/1.07 apply (zenon_L4_ zenon_TY_bn zenon_TV_ch); trivial. % 0.82/1.07 generalize (zenon_Hf2 zenon_TX_bu). zenon_intro zenon_H5e. % 0.82/1.07 generalize (zenon_H34 zenon_TX_bu). zenon_intro zenon_H12c. % 0.82/1.07 generalize (zenon_H12c zenon_TX_bu). zenon_intro zenon_H12d. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H12d); [ zenon_intro zenon_H61 | zenon_intro zenon_H12e ]. % 0.82/1.07 generalize (ceq2 (intersection_point zenon_TU_bo zenon_TY_bn)). zenon_intro zenon_H74. % 0.82/1.07 generalize (zenon_H74 zenon_TY_bn). zenon_intro zenon_H75. % 0.82/1.07 generalize (zenon_H74 zenon_TV_ch). zenon_intro zenon_Hfa. % 0.82/1.07 generalize (zenon_H75 zenon_TV_ch). zenon_intro zenon_H12f. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H12f); [ zenon_intro zenon_H48 | zenon_intro zenon_H130 ]. % 0.82/1.07 apply (zenon_L9_ zenon_TV_ch zenon_TU_bo zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H131 | zenon_intro zenon_H70 ]. % 0.82/1.07 generalize (zenon_H122 zenon_TV_ch). zenon_intro zenon_H132. % 0.82/1.07 apply (zenon_imply_s _ _ zenon_H132); [ zenon_intro zenon_H134 | zenon_intro zenon_H133 ]. % 0.82/1.07 exact (zenon_H134 zenon_H131). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H2c | zenon_intro zenon_H135 ]. % 0.82/1.07 exact (zenon_H31 zenon_H2c). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_H7c | zenon_intro zenon_Hd3 ]. % 0.82/1.07 exact (zenon_H72 zenon_H7c). % 0.82/1.07 exact (zenon_Hd8 zenon_Hd3). % 0.82/1.07 apply (zenon_L31_ zenon_TX_bu zenon_TV_ch zenon_TY_bn zenon_TU_bo); trivial. % 0.82/1.07 apply (zenon_or_s _ _ zenon_H12e); [ zenon_intro zenon_H136 | zenon_intro zenon_H68 ]. % 0.82/1.07 exact (zenon_H127 zenon_H136). % 0.82/1.07 apply (zenon_L10_ zenon_TY_bn zenon_TX_bu); trivial. % 0.82/1.07 apply (zenon_L11_ zenon_TX_bu); trivial. % 0.82/1.07 apply (zenon_or_s _ _ zenon_Hd7); [ zenon_intro zenon_Hd9 | zenon_intro zenon_H3e ]. % 0.82/1.07 exact (zenon_Hd2 zenon_Hd9). % 0.82/1.07 exact (zenon_H39 zenon_H3e). % 0.82/1.07 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H3a | zenon_intro zenon_H2c ]. % 0.82/1.07 apply (zenon_L4_ zenon_TY_bn zenon_TV_ch); trivial. % 0.82/1.07 exact (zenon_H31 zenon_H2c). % 0.82/1.07 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_H3e | zenon_intro zenon_Hd9 ]. % 0.82/1.07 apply (zenon_L34_ zenon_TX_bu zenon_TU_bo zenon_TY_bn zenon_TV_ch); trivial. % 0.82/1.07 exact (zenon_Hd2 zenon_Hd9). % 0.82/1.07 exact (zenon_Hd2 zenon_Hd9). % 0.82/1.07 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_H8f | zenon_intro zenon_H54 ]. % 0.82/1.07 apply (zenon_L18_ zenon_TY_bn zenon_TX_bu zenon_TV_ch zenon_TU_bo); trivial. % 0.82/1.07 exact (zenon_H47 zenon_H54). % 0.82/1.07 exact (zenon_H49 zenon_H51). % 0.82/1.07 generalize (zenon_H114 zenon_TY_bn). zenon_intro zenon_Hfd. % 0.82/1.07 generalize (ax6 zenon_TV_ch). zenon_intro zenon_He6. % 0.82/1.07 generalize (zenon_He6 zenon_TY_bn). zenon_intro zenon_Hde. % 0.82/1.07 apply (zenon_L34_ zenon_TX_bu zenon_TU_bo zenon_TY_bn zenon_TV_ch); trivial. % 0.82/1.07 generalize (zenon_H10c zenon_TY_bn). zenon_intro zenon_H114. % 0.82/1.07 generalize (zenon_H114 zenon_TY_bn). zenon_intro zenon_Hfd. % 0.82/1.07 apply (zenon_L33_ zenon_TV_ch zenon_TX_bu zenon_TY_bn zenon_TU_bo); trivial. % 0.82/1.07 apply (zenon_L35_ zenon_TY_bn zenon_TX_bu zenon_TV_ch zenon_TU_bo); trivial. % 0.82/1.07 Qed. % 0.82/1.07 % SZS output end Proof % 0.82/1.07 (* END-PROOF *) % 0.82/1.07 nodes searched: 47874 % 0.82/1.07 max branch formulas: 2934 % 0.82/1.07 proof nodes created: 3350 % 0.82/1.07 formulas created: 110035 % 0.82/1.07 %------------------------------------------------------------------------------