%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO194+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n024.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 07:00:39 EDT 2022 % Result : Theorem 0.72s 0.92s % Output : Proof 0.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : GEO194+3 : TPTP v8.1.0. Released v4.0.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n024.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Sat Jun 18 06:43:32 EDT 2022 % 0.12/0.34 % CPUTime : % 0.72/0.92 (* PROOF-FOUND *) % 0.72/0.92 % SZS status Theorem % 0.72/0.92 (* BEGIN-PROOF *) % 0.72/0.92 % SZS output start Proof % 0.72/0.92 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines Z Y)/\(convergent_lines X Z)))->((apart_point_and_line (intersection_point X Y) Z)->(apart_point_and_line (intersection_point X Z) Y)))))). % 0.72/0.92 Proof. % 0.72/0.92 assert (zenon_L1_ : forall (zenon_TY_bn : zenon_U) (zenon_TX_bo : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TX_bo Y)->(~(apart_point_and_line (intersection_point zenon_TX_bo Y) zenon_TX_bo)))) -> (convergent_lines zenon_TX_bo zenon_TY_bn) -> (apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) zenon_TX_bo) -> False). % 0.72/0.92 do 2 intro. intros zenon_H24 zenon_H25 zenon_H26. % 0.72/0.92 generalize (zenon_H24 zenon_TY_bn). zenon_intro zenon_H29. % 0.72/0.92 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 0.72/0.92 exact (zenon_H2b zenon_H25). % 0.72/0.92 exact (zenon_H2a zenon_H26). % 0.72/0.92 (* end of lemma zenon_L1_ *) % 0.72/0.92 assert (zenon_L2_ : forall (zenon_TZ_bu : zenon_U) (zenon_TX_bo : zenon_U), (apart_point_and_line (intersection_point zenon_TX_bo zenon_TZ_bu) zenon_TZ_bu) -> (convergent_lines zenon_TX_bo zenon_TZ_bu) -> False). % 0.72/0.92 do 2 intro. intros zenon_H2c zenon_H2d. % 0.72/0.92 generalize (ci4 zenon_TX_bo). zenon_intro zenon_H2f. % 0.72/0.92 generalize (zenon_H2f zenon_TZ_bu). zenon_intro zenon_H30. % 0.72/0.92 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 0.72/0.92 exact (zenon_H32 zenon_H2d). % 0.72/0.92 exact (zenon_H31 zenon_H2c). % 0.72/0.92 (* end of lemma zenon_L2_ *) % 0.72/0.92 assert (zenon_L3_ : forall (zenon_TZ_bu : zenon_U) (zenon_TX_bo : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TX_bo Y)->(~(apart_point_and_line (intersection_point zenon_TX_bo Y) zenon_TX_bo)))) -> (convergent_lines zenon_TX_bo zenon_TZ_bu) -> (apart_point_and_line (intersection_point zenon_TX_bo zenon_TZ_bu) zenon_TX_bo) -> False). % 0.72/0.92 do 2 intro. intros zenon_H24 zenon_H2d zenon_H33. % 0.72/0.92 generalize (zenon_H24 zenon_TZ_bu). zenon_intro zenon_H34. % 0.72/0.92 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H32 | zenon_intro zenon_H35 ]. % 0.72/0.92 exact (zenon_H32 zenon_H2d). % 0.72/0.92 exact (zenon_H35 zenon_H33). % 0.72/0.92 (* end of lemma zenon_L3_ *) % 0.72/0.92 assert (zenon_L4_ : forall (zenon_TY_bn : zenon_U) (zenon_TZ_bu : zenon_U), (apart_point_and_line (intersection_point zenon_TZ_bu zenon_TY_bn) zenon_TY_bn) -> (convergent_lines zenon_TZ_bu zenon_TY_bn) -> False). % 0.72/0.92 do 2 intro. intros zenon_H36 zenon_H37. % 0.72/0.92 generalize (ci4 zenon_TZ_bu). zenon_intro zenon_H38. % 0.72/0.92 generalize (zenon_H38 zenon_TY_bn). zenon_intro zenon_H39. % 0.72/0.92 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ]. % 0.72/0.92 exact (zenon_H3b zenon_H37). % 0.72/0.92 exact (zenon_H3a zenon_H36). % 0.72/0.92 (* end of lemma zenon_L4_ *) % 0.72/0.92 assert (zenon_L5_ : forall (zenon_TZ_bu : zenon_U) (zenon_TX_bo : 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)) -> (distinct_points (intersection_point zenon_TX_bo zenon_TY_bn) (intersection_point zenon_TZ_bu zenon_TY_bn)) -> (convergent_lines zenon_TX_bo zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) zenon_TY_bn)) -> (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TX_bo zenon_TY_bn) Y)/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) U)\/((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) V)\/((apart_point_and_line Y U)\/(apart_point_and_line Y V)))))))) -> (convergent_lines zenon_TX_bo zenon_TZ_bu) -> (~(apart_point_and_line (intersection_point zenon_TX_bo zenon_TZ_bu) zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TZ_bu zenon_TY_bn) zenon_TZ_bu)) -> (distinct_lines zenon_TY_bn zenon_TZ_bu) -> (~(distinct_lines zenon_TY_bn zenon_TY_bn)) -> (convergent_lines zenon_TZ_bu zenon_TY_bn) -> (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) Y)->((distinct_lines Y Z)\/(apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) Z))))) -> (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TX_bo zenon_TY_bn) (intersection_point zenon_TZ_bu zenon_TY_bn))/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) U)\/((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) V)\/((apart_point_and_line (intersection_point zenon_TZ_bu zenon_TY_bn) U)\/(apart_point_and_line (intersection_point zenon_TZ_bu zenon_TY_bn) V))))))) -> (convergent_lines zenon_TY_bn zenon_TX_bo) -> False). % 0.72/0.92 do 3 intro. intros zenon_H3c zenon_H3d zenon_H3e zenon_H25 zenon_H3f zenon_H40 zenon_H2d zenon_H41 zenon_H42 zenon_H43 zenon_H44 zenon_H37 zenon_H45 zenon_H46 zenon_H47. % 0.72/0.92 generalize (zenon_H3c zenon_TX_bo). zenon_intro zenon_H48. % 0.72/0.92 generalize (zenon_H48 zenon_TY_bn). zenon_intro zenon_H49. % 0.72/0.92 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ]. % 0.72/0.92 exact (zenon_H4b zenon_H47). % 0.72/0.92 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4d | zenon_intro zenon_H4c ]. % 0.72/0.92 generalize (zenon_H46 zenon_TX_bo). zenon_intro zenon_H4e. % 0.72/0.92 generalize (zenon_H4e zenon_TY_bn). zenon_intro zenon_H4f. % 0.72/0.92 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 0.72/0.92 apply (zenon_notand_s _ _ zenon_H51); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ]. % 0.72/0.92 exact (zenon_H53 zenon_H3e). % 0.72/0.92 exact (zenon_H52 zenon_H4d). % 0.72/0.92 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H26 | zenon_intro zenon_H54 ]. % 0.72/0.92 generalize (ci3 zenon_TX_bo). zenon_intro zenon_H24. % 0.72/0.92 apply (zenon_L1_ zenon_TY_bn zenon_TX_bo); trivial. % 0.72/0.92 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ]. % 0.72/0.92 exact (zenon_H3f zenon_H56). % 0.72/0.92 apply (zenon_or_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H36 ]. % 0.72/0.92 generalize (ci3 zenon_TX_bo). zenon_intro zenon_H24. % 0.72/0.92 generalize (zenon_H45 zenon_TX_bo). zenon_intro zenon_H58. % 0.72/0.92 generalize (ceq2 (intersection_point zenon_TZ_bu zenon_TY_bn)). zenon_intro zenon_H59. % 0.72/0.92 generalize (zenon_H59 zenon_TY_bn). zenon_intro zenon_H5a. % 0.72/0.92 generalize (zenon_H5a zenon_TY_bn). zenon_intro zenon_H5b. % 0.72/0.92 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H3a | zenon_intro zenon_H5c ]. % 0.72/0.92 generalize (zenon_H58 zenon_TX_bo). zenon_intro zenon_H5d. % 0.72/0.92 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H2a | zenon_intro zenon_H5e ]. % 0.72/0.92 generalize (ceq1 (intersection_point zenon_TZ_bu zenon_TY_bn)). zenon_intro zenon_H5f. % 0.72/0.92 generalize (zenon_H5f zenon_TX_bo). zenon_intro zenon_H60. % 0.72/0.92 generalize (zenon_H60 (intersection_point zenon_TX_bo zenon_TY_bn)). zenon_intro zenon_H61. % 0.72/0.92 apply (zenon_imply_s _ _ zenon_H61); [ zenon_intro zenon_H63 | zenon_intro zenon_H62 ]. % 0.72/0.92 exact (zenon_H63 zenon_H57). % 0.72/0.92 apply (zenon_or_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H26 ]. % 0.72/0.92 generalize (apart4 (intersection_point zenon_TZ_bu zenon_TY_bn)). zenon_intro zenon_H65. % 0.72/0.92 generalize (cu1 (intersection_point zenon_TZ_bu zenon_TY_bn)). zenon_intro zenon_H66. % 0.72/0.92 generalize (zenon_H65 (intersection_point zenon_TX_bo zenon_TY_bn)). zenon_intro zenon_H67. % 0.72/0.92 generalize (zenon_H67 (intersection_point zenon_TX_bo zenon_TZ_bu)). zenon_intro zenon_H68. % 0.72/0.92 apply (zenon_imply_s _ _ zenon_H68); [ zenon_intro zenon_H6a | zenon_intro zenon_H69 ]. % 0.72/0.92 exact (zenon_H6a zenon_H64). % 0.72/0.92 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ]. % 0.72/0.92 generalize (zenon_H66 (intersection_point zenon_TX_bo zenon_TZ_bu)). zenon_intro zenon_H6d. % 0.72/0.92 generalize (zenon_H6d zenon_TY_bn). zenon_intro zenon_H6e. % 0.72/0.92 generalize (zenon_H6e zenon_TZ_bu). zenon_intro zenon_H6f. % 0.72/0.92 apply (zenon_imply_s _ _ zenon_H6f); [ zenon_intro zenon_H71 | zenon_intro zenon_H70 ]. % 0.72/0.92 apply (zenon_notand_s _ _ zenon_H71); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ]. % 0.72/0.92 exact (zenon_H73 zenon_H6c). % 0.72/0.92 exact (zenon_H72 zenon_H43). % 0.72/0.92 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H36 | zenon_intro zenon_H74 ]. % 0.72/0.92 exact (zenon_H3a zenon_H36). % 0.72/0.92 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H76 | zenon_intro zenon_H75 ]. % 0.72/0.92 exact (zenon_H42 zenon_H76). % 0.72/0.92 apply (zenon_or_s _ _ zenon_H75); [ zenon_intro zenon_H77 | zenon_intro zenon_H2c ]. % 0.72/0.92 exact (zenon_H41 zenon_H77). % 0.72/0.92 apply (zenon_L2_ zenon_TZ_bu zenon_TX_bo); trivial. % 0.72/0.92 generalize (zenon_H40 (intersection_point zenon_TX_bo zenon_TZ_bu)). zenon_intro zenon_H78. % 0.72/0.92 generalize (zenon_H78 zenon_TX_bo). zenon_intro zenon_H79. % 0.72/0.92 generalize (zenon_H79 zenon_TY_bn). zenon_intro zenon_H7a. % 0.72/0.92 apply (zenon_imply_s _ _ zenon_H7a); [ zenon_intro zenon_H7c | zenon_intro zenon_H7b ]. % 0.72/0.92 apply (zenon_notand_s _ _ zenon_H7c); [ zenon_intro zenon_H7d | zenon_intro zenon_H52 ]. % 0.72/0.92 exact (zenon_H7d zenon_H6b). % 0.72/0.92 exact (zenon_H52 zenon_H4d). % 0.72/0.92 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H26 | zenon_intro zenon_H7e ]. % 0.72/0.92 exact (zenon_H2a zenon_H26). % 0.72/0.92 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H56 | zenon_intro zenon_H7f ]. % 0.72/0.92 exact (zenon_H3f zenon_H56). % 0.72/0.92 apply (zenon_or_s _ _ zenon_H7f); [ zenon_intro zenon_H33 | zenon_intro zenon_H77 ]. % 0.72/0.92 apply (zenon_L3_ zenon_TZ_bu zenon_TX_bo); trivial. % 0.72/0.92 exact (zenon_H41 zenon_H77). % 0.72/0.92 exact (zenon_H2a zenon_H26). % 0.72/0.92 apply (zenon_or_s _ _ zenon_H5e); [ zenon_intro zenon_H80 | zenon_intro zenon_H26 ]. % 0.72/0.92 generalize (apart2 zenon_TX_bo). zenon_intro zenon_H81. % 0.72/0.92 exact (zenon_H81 zenon_H80). % 0.72/0.92 apply (zenon_L1_ zenon_TY_bn zenon_TX_bo); trivial. % 0.72/0.92 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H82 | zenon_intro zenon_H36 ]. % 0.72/0.92 exact (zenon_H44 zenon_H82). % 0.72/0.92 apply (zenon_L4_ zenon_TY_bn zenon_TZ_bu); trivial. % 0.72/0.92 apply (zenon_L4_ zenon_TY_bn zenon_TZ_bu); trivial. % 0.72/0.92 exact (zenon_H3d zenon_H4c). % 0.72/0.92 (* end of lemma zenon_L5_ *) % 0.72/0.92 assert (zenon_L6_ : forall (zenon_TZ_bu : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TX_bo : zenon_U), (forall Z : zenon_U, ((convergent_lines zenon_TX_bo zenon_TY_bn)->((distinct_lines zenon_TY_bn Z)\/(convergent_lines zenon_TX_bo Z)))) -> (convergent_lines zenon_TX_bo zenon_TY_bn) -> (forall Z : zenon_U, ((distinct_lines zenon_TY_bn Z)->((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) zenon_TY_bn)\/((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) Z)\/(convergent_lines zenon_TY_bn Z))))) -> (~(apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) zenon_TY_bn)) -> (forall Y : zenon_U, ((convergent_lines zenon_TX_bo Y)->(~(apart_point_and_line (intersection_point zenon_TX_bo Y) zenon_TX_bo)))) -> (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)) -> (distinct_points (intersection_point zenon_TX_bo zenon_TY_bn) (intersection_point zenon_TZ_bu zenon_TY_bn)) -> (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TX_bo zenon_TY_bn) Y)/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) U)\/((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) V)\/((apart_point_and_line Y U)\/(apart_point_and_line Y V)))))))) -> (convergent_lines zenon_TX_bo zenon_TZ_bu) -> (~(apart_point_and_line (intersection_point zenon_TX_bo zenon_TZ_bu) zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TZ_bu zenon_TY_bn) zenon_TZ_bu)) -> (distinct_lines zenon_TY_bn zenon_TZ_bu) -> (~(distinct_lines zenon_TY_bn zenon_TY_bn)) -> (convergent_lines zenon_TZ_bu zenon_TY_bn) -> (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) Y)->((distinct_lines Y Z)\/(apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) Z))))) -> (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TX_bo zenon_TY_bn) (intersection_point zenon_TZ_bu zenon_TY_bn))/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) U)\/((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) V)\/((apart_point_and_line (intersection_point zenon_TZ_bu zenon_TY_bn) U)\/(apart_point_and_line (intersection_point zenon_TZ_bu zenon_TY_bn) V))))))) -> (~(convergent_lines zenon_TX_bo zenon_TX_bo)) -> False). % 0.72/0.92 do 3 intro. intros zenon_H83 zenon_H25 zenon_H84 zenon_H3f zenon_H24 zenon_H3c zenon_H3d zenon_H3e zenon_H40 zenon_H2d zenon_H41 zenon_H42 zenon_H43 zenon_H44 zenon_H37 zenon_H45 zenon_H46 zenon_H85. % 0.72/0.92 generalize (zenon_H83 zenon_TX_bo). zenon_intro zenon_H86. % 0.72/0.92 apply (zenon_imply_s _ _ zenon_H86); [ zenon_intro zenon_H2b | zenon_intro zenon_H87 ]. % 0.72/0.92 exact (zenon_H2b zenon_H25). % 0.72/0.92 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H89 | zenon_intro zenon_H88 ]. % 0.72/0.92 generalize (zenon_H84 zenon_TX_bo). zenon_intro zenon_H8a. % 0.72/0.92 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H8c | zenon_intro zenon_H8b ]. % 0.72/0.92 exact (zenon_H8c zenon_H89). % 0.72/0.92 apply (zenon_or_s _ _ zenon_H8b); [ zenon_intro zenon_H56 | zenon_intro zenon_H8d ]. % 0.72/0.92 exact (zenon_H3f zenon_H56). % 0.72/0.92 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H26 | zenon_intro zenon_H47 ]. % 0.72/0.92 apply (zenon_L1_ zenon_TY_bn zenon_TX_bo); trivial. % 0.72/0.92 apply (zenon_L5_ zenon_TZ_bu zenon_TX_bo zenon_TY_bn); trivial. % 0.72/0.92 exact (zenon_H85 zenon_H88). % 0.72/0.92 (* end of lemma zenon_L6_ *) % 0.72/0.92 assert (zenon_L7_ : forall (zenon_TY_bn : zenon_U) (zenon_TX_bo : zenon_U), ((convergent_lines zenon_TX_bo zenon_TY_bn)/\(unorthogonal_lines zenon_TX_bo zenon_TY_bn)) -> (~(unorthogonal_lines zenon_TX_bo zenon_TY_bn)) -> False). % 0.72/0.92 do 2 intro. intros zenon_H8e zenon_H8f. % 0.72/0.92 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H25. zenon_intro zenon_H90. % 0.72/0.92 exact (zenon_H8f zenon_H90). % 0.72/0.92 (* end of lemma zenon_L7_ *) % 0.72/0.92 assert (zenon_L8_ : forall (zenon_TZ_bu : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TX_bo : zenon_U), (forall M : zenon_U, (forall N : zenon_U, (((convergent_lines zenon_TX_bo M)/\(unorthogonal_lines zenon_TX_bo M))->(((convergent_lines zenon_TX_bo N)/\(unorthogonal_lines zenon_TX_bo N))\/((convergent_lines M N)/\(unorthogonal_lines M N)))))) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bo zenon_TY_bn)->((distinct_lines zenon_TY_bn Z)\/(convergent_lines zenon_TX_bo Z)))) -> (convergent_lines zenon_TX_bo zenon_TY_bn) -> (forall Z : zenon_U, ((distinct_lines zenon_TY_bn Z)->((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) zenon_TY_bn)\/((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) Z)\/(convergent_lines zenon_TY_bn Z))))) -> (~(apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) zenon_TY_bn)) -> (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)) -> (distinct_points (intersection_point zenon_TX_bo zenon_TY_bn) (intersection_point zenon_TZ_bu zenon_TY_bn)) -> (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TX_bo zenon_TY_bn) Y)/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) U)\/((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) V)\/((apart_point_and_line Y U)\/(apart_point_and_line Y V)))))))) -> (convergent_lines zenon_TX_bo zenon_TZ_bu) -> (~(apart_point_and_line (intersection_point zenon_TX_bo zenon_TZ_bu) zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TZ_bu zenon_TY_bn) zenon_TZ_bu)) -> (distinct_lines zenon_TY_bn zenon_TZ_bu) -> (~(distinct_lines zenon_TY_bn zenon_TY_bn)) -> (convergent_lines zenon_TZ_bu zenon_TY_bn) -> (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) Y)->((distinct_lines Y Z)\/(apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) Z))))) -> (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TX_bo zenon_TY_bn) (intersection_point zenon_TZ_bu zenon_TY_bn))/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) U)\/((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) V)\/((apart_point_and_line (intersection_point zenon_TZ_bu zenon_TY_bn) U)\/(apart_point_and_line (intersection_point zenon_TZ_bu zenon_TY_bn) V))))))) -> (unorthogonal_lines zenon_TX_bo zenon_TX_bo) -> (~(unorthogonal_lines zenon_TX_bo zenon_TY_bn)) -> False). % 0.72/0.92 do 3 intro. intros zenon_H91 zenon_H83 zenon_H25 zenon_H84 zenon_H3f zenon_H3c zenon_H3d zenon_H3e zenon_H40 zenon_H2d zenon_H41 zenon_H42 zenon_H43 zenon_H44 zenon_H37 zenon_H45 zenon_H46 zenon_H92 zenon_H8f. % 0.72/0.92 generalize (zenon_H91 zenon_TX_bo). zenon_intro zenon_H93. % 0.72/0.92 generalize (ci3 zenon_TX_bo). zenon_intro zenon_H24. % 0.72/0.92 generalize (zenon_H93 zenon_TY_bn). zenon_intro zenon_H94. % 0.72/0.92 apply (zenon_imply_s _ _ zenon_H94); [ zenon_intro zenon_H96 | zenon_intro zenon_H95 ]. % 0.72/0.92 apply (zenon_notand_s _ _ zenon_H96); [ zenon_intro zenon_H85 | zenon_intro zenon_H97 ]. % 0.72/0.92 apply (zenon_L6_ zenon_TZ_bu zenon_TY_bn zenon_TX_bo); trivial. % 0.72/0.92 exact (zenon_H97 zenon_H92). % 0.72/0.92 apply (zenon_or_s _ _ zenon_H95); [ zenon_intro zenon_H8e | zenon_intro zenon_H8e ]. % 0.72/0.92 apply (zenon_L7_ zenon_TY_bn zenon_TX_bo); trivial. % 0.72/0.92 apply (zenon_L7_ zenon_TY_bn zenon_TX_bo); trivial. % 0.72/0.92 (* end of lemma zenon_L8_ *) % 0.72/0.92 assert (zenon_L9_ : forall (zenon_TY_bn : zenon_U), (~((~(convergent_lines zenon_TY_bn zenon_TY_bn))\/(~(unorthogonal_lines zenon_TY_bn zenon_TY_bn)))) -> (~(convergent_lines zenon_TY_bn zenon_TY_bn)) -> False). % 0.72/0.92 do 1 intro. intros zenon_H98 zenon_H3d. % 0.72/0.92 apply (zenon_notor_s _ _ zenon_H98). zenon_intro zenon_H9a. zenon_intro zenon_H99. % 0.72/0.92 exact (zenon_H9a zenon_H3d). % 0.72/0.92 (* end of lemma zenon_L9_ *) % 0.72/0.92 assert (zenon_L10_ : forall (zenon_TZ_bu : zenon_U) (zenon_TX_bo : 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)) -> (distinct_points (intersection_point zenon_TX_bo zenon_TY_bn) (intersection_point zenon_TZ_bu zenon_TY_bn)) -> (convergent_lines zenon_TX_bo zenon_TY_bn) -> (~(apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) zenon_TY_bn)) -> (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TX_bo zenon_TY_bn) Y)/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) U)\/((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) V)\/((apart_point_and_line Y U)\/(apart_point_and_line Y V)))))))) -> (convergent_lines zenon_TX_bo zenon_TZ_bu) -> (~(apart_point_and_line (intersection_point zenon_TX_bo zenon_TZ_bu) zenon_TY_bn)) -> (~(apart_point_and_line (intersection_point zenon_TZ_bu zenon_TY_bn) zenon_TZ_bu)) -> (distinct_lines zenon_TY_bn zenon_TZ_bu) -> (~(distinct_lines zenon_TY_bn zenon_TY_bn)) -> (convergent_lines zenon_TZ_bu zenon_TY_bn) -> (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) Y)->((distinct_lines Y Z)\/(apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) Z))))) -> (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TX_bo zenon_TY_bn) (intersection_point zenon_TZ_bu zenon_TY_bn))/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) U)\/((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) V)\/((apart_point_and_line (intersection_point zenon_TZ_bu zenon_TY_bn) U)\/(apart_point_and_line (intersection_point zenon_TZ_bu zenon_TY_bn) V))))))) -> (unorthogonal_lines zenon_TX_bo zenon_TY_bn) -> False). % 0.72/0.92 do 3 intro. intros zenon_H3c zenon_H3d zenon_H3e zenon_H25 zenon_H3f zenon_H40 zenon_H2d zenon_H41 zenon_H42 zenon_H43 zenon_H44 zenon_H37 zenon_H45 zenon_H46 zenon_H90. % 0.72/0.92 generalize (cotno1 zenon_TY_bn). zenon_intro zenon_H9b. % 0.72/0.92 generalize (zenon_H9b zenon_TX_bo). zenon_intro zenon_H9c. % 0.72/0.92 generalize (zenon_H9c zenon_TY_bn). zenon_intro zenon_H9d. % 0.72/0.92 apply (zenon_imply_s _ _ zenon_H9d); [ zenon_intro zenon_H9f | zenon_intro zenon_H9e ]. % 0.72/0.92 apply (zenon_notand_s _ _ zenon_H9f); [ zenon_intro zenon_Ha0 | zenon_intro zenon_H98 ]. % 0.72/0.92 apply (zenon_notor_s _ _ zenon_Ha0). zenon_intro zenon_Ha2. zenon_intro zenon_Ha1. % 0.72/0.92 apply zenon_Ha2. zenon_intro zenon_H47. % 0.72/0.92 apply (zenon_L5_ zenon_TZ_bu zenon_TX_bo zenon_TY_bn); trivial. % 0.72/0.92 apply (zenon_L9_ zenon_TY_bn); trivial. % 0.72/0.92 apply (zenon_or_s _ _ zenon_H9e); [ zenon_intro zenon_H2b | zenon_intro zenon_H8f ]. % 0.72/0.92 exact (zenon_H2b zenon_H25). % 0.72/0.92 exact (zenon_H8f zenon_H90). % 0.72/0.92 (* end of lemma zenon_L10_ *) % 0.72/0.92 assert (zenon_L11_ : forall (zenon_TZ_bu : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TX_bo : zenon_U), ((convergent_lines zenon_TX_bo zenon_TY_bn)/\(unorthogonal_lines zenon_TX_bo zenon_TY_bn)) -> (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TX_bo zenon_TY_bn) (intersection_point zenon_TZ_bu zenon_TY_bn))/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) U)\/((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) V)\/((apart_point_and_line (intersection_point zenon_TZ_bu zenon_TY_bn) U)\/(apart_point_and_line (intersection_point zenon_TZ_bu zenon_TY_bn) V))))))) -> (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) Y)->((distinct_lines Y Z)\/(apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) Z))))) -> (convergent_lines zenon_TZ_bu zenon_TY_bn) -> (~(distinct_lines zenon_TY_bn zenon_TY_bn)) -> (distinct_lines zenon_TY_bn zenon_TZ_bu) -> (~(apart_point_and_line (intersection_point zenon_TZ_bu zenon_TY_bn) zenon_TZ_bu)) -> (~(apart_point_and_line (intersection_point zenon_TX_bo zenon_TZ_bu) zenon_TY_bn)) -> (convergent_lines zenon_TX_bo zenon_TZ_bu) -> (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TX_bo zenon_TY_bn) Y)/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) U)\/((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) V)\/((apart_point_and_line Y U)\/(apart_point_and_line Y V)))))))) -> (~(apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) zenon_TY_bn)) -> (convergent_lines zenon_TX_bo zenon_TY_bn) -> (distinct_points (intersection_point zenon_TX_bo zenon_TY_bn) (intersection_point zenon_TZ_bu zenon_TY_bn)) -> (~(convergent_lines zenon_TY_bn zenon_TY_bn)) -> (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines zenon_TY_bn Y)->((distinct_lines Y Z)\/(convergent_lines zenon_TY_bn Z))))) -> False). % 0.72/0.92 do 3 intro. intros zenon_H8e zenon_H46 zenon_H45 zenon_H37 zenon_H44 zenon_H43 zenon_H42 zenon_H41 zenon_H2d zenon_H40 zenon_H3f zenon_H25 zenon_H3e zenon_H3d zenon_H3c. % 0.72/0.92 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H25. zenon_intro zenon_H90. % 0.72/0.92 apply (zenon_L10_ zenon_TZ_bu zenon_TX_bo zenon_TY_bn); trivial. % 0.72/0.92 (* end of lemma zenon_L11_ *) % 0.72/0.92 assert (zenon_L12_ : forall (zenon_TY_bn : zenon_U), ((convergent_lines zenon_TY_bn zenon_TY_bn)/\(unorthogonal_lines zenon_TY_bn zenon_TY_bn)) -> (~(convergent_lines zenon_TY_bn zenon_TY_bn)) -> False). % 0.72/0.92 do 1 intro. intros zenon_Ha3 zenon_H3d. % 0.72/0.92 apply (zenon_and_s _ _ zenon_Ha3). zenon_intro zenon_H4c. zenon_intro zenon_Ha4. % 0.72/0.92 exact (zenon_H3d zenon_H4c). % 0.72/0.92 (* end of lemma zenon_L12_ *) % 0.72/0.92 assert (zenon_L13_ : forall (zenon_TZ_bu : zenon_U) (zenon_TY_bn : zenon_U) (zenon_TX_bo : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) Y)->((distinct_lines Y Z)\/(apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) Z))))) -> (convergent_lines zenon_TZ_bu zenon_TY_bn) -> (distinct_lines zenon_TY_bn zenon_TZ_bu) -> (~(apart_point_and_line (intersection_point zenon_TZ_bu zenon_TY_bn) zenon_TZ_bu)) -> (~(apart_point_and_line (intersection_point zenon_TX_bo zenon_TZ_bu) zenon_TY_bn)) -> (convergent_lines zenon_TX_bo zenon_TZ_bu) -> (distinct_points (intersection_point zenon_TX_bo zenon_TY_bn) (intersection_point zenon_TZ_bu zenon_TY_bn)) -> (~(convergent_lines zenon_TY_bn zenon_TY_bn)) -> (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines zenon_TY_bn Y)->((distinct_lines Y Z)\/(convergent_lines zenon_TY_bn Z))))) -> (~(apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) zenon_TY_bn)) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bo zenon_TY_bn)->((distinct_lines zenon_TY_bn Z)\/(convergent_lines zenon_TX_bo Z)))) -> (convergent_lines zenon_TX_bo zenon_TY_bn) -> False). % 0.72/0.93 do 3 intro. intros zenon_H45 zenon_H37 zenon_H43 zenon_H42 zenon_H41 zenon_H2d zenon_H3e zenon_H3d zenon_H3c zenon_H3f zenon_H83 zenon_H25. % 0.72/0.93 generalize (cup1 (intersection_point zenon_TX_bo zenon_TY_bn)). zenon_intro zenon_Ha5. % 0.72/0.93 generalize (zenon_Ha5 zenon_TY_bn). zenon_intro zenon_H84. % 0.72/0.93 generalize (cu1 (intersection_point zenon_TX_bo zenon_TY_bn)). zenon_intro zenon_H40. % 0.72/0.93 generalize (zenon_H40 (intersection_point zenon_TZ_bu zenon_TY_bn)). zenon_intro zenon_H46. % 0.72/0.93 generalize (apart2 zenon_TY_bn). zenon_intro zenon_H44. % 0.72/0.93 generalize (couo1 zenon_TX_bo). zenon_intro zenon_Ha6. % 0.72/0.93 generalize (zenon_Ha6 zenon_TX_bo). zenon_intro zenon_Ha7. % 0.72/0.93 generalize (zenon_Ha7 zenon_TY_bn). zenon_intro zenon_Ha8. % 0.72/0.93 apply (zenon_imply_s _ _ zenon_Ha8); [ zenon_intro zenon_Ha9 | zenon_intro zenon_H2b ]. % 0.72/0.93 apply (zenon_notand_s _ _ zenon_Ha9); [ zenon_intro zenon_Hab | zenon_intro zenon_Haa ]. % 0.72/0.93 apply zenon_Hab. zenon_intro zenon_H92. % 0.72/0.93 generalize (oac1 zenon_TX_bo). zenon_intro zenon_H91. % 0.72/0.93 generalize (zenon_H91 zenon_TY_bn). zenon_intro zenon_Hac. % 0.72/0.93 generalize (zenon_Hac zenon_TY_bn). zenon_intro zenon_Had. % 0.72/0.93 apply (zenon_imply_s _ _ zenon_Had); [ zenon_intro zenon_Haf | zenon_intro zenon_Hae ]. % 0.72/0.93 apply (zenon_notand_s _ _ zenon_Haf); [ zenon_intro zenon_H2b | zenon_intro zenon_H8f ]. % 0.72/0.93 exact (zenon_H2b zenon_H25). % 0.72/0.93 apply (zenon_L8_ zenon_TZ_bu zenon_TY_bn zenon_TX_bo); trivial. % 0.72/0.93 apply (zenon_or_s _ _ zenon_Hae); [ zenon_intro zenon_H8e | zenon_intro zenon_Ha3 ]. % 0.72/0.93 apply (zenon_L11_ zenon_TZ_bu zenon_TY_bn zenon_TX_bo); trivial. % 0.72/0.93 apply (zenon_L12_ zenon_TY_bn); trivial. % 0.72/0.93 apply zenon_Haa. zenon_intro zenon_H90. % 0.72/0.93 apply (zenon_L10_ zenon_TZ_bu zenon_TX_bo zenon_TY_bn); trivial. % 0.72/0.93 exact (zenon_H2b zenon_H25). % 0.72/0.93 (* end of lemma zenon_L13_ *) % 0.72/0.93 apply NNPP. intro zenon_G. % 0.72/0.93 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines Z Y)/\(convergent_lines X Z)))->((apart_point_and_line (intersection_point X Y) Z)->(apart_point_and_line (intersection_point X Z) Y)))))) zenon_G); [ zenon_intro zenon_Hb0; idtac ]. % 0.72/0.93 elim zenon_Hb0. zenon_intro zenon_TX_bo. zenon_intro zenon_Hb1. % 0.72/0.93 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_bo Y)/\((convergent_lines Z Y)/\(convergent_lines zenon_TX_bo Z)))->((apart_point_and_line (intersection_point zenon_TX_bo Y) Z)->(apart_point_and_line (intersection_point zenon_TX_bo Z) Y))))) zenon_Hb1); [ zenon_intro zenon_Hb2; idtac ]. % 0.72/0.93 elim zenon_Hb2. zenon_intro zenon_TY_bn. zenon_intro zenon_Hb3. % 0.72/0.93 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_bo zenon_TY_bn)/\((convergent_lines Z zenon_TY_bn)/\(convergent_lines zenon_TX_bo Z)))->((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) Z)->(apart_point_and_line (intersection_point zenon_TX_bo Z) zenon_TY_bn)))) zenon_Hb3); [ zenon_intro zenon_Hb4; idtac ]. % 0.72/0.93 elim zenon_Hb4. zenon_intro zenon_TZ_bu. zenon_intro zenon_Hb5. % 0.72/0.93 apply (zenon_notimply_s _ _ zenon_Hb5). zenon_intro zenon_Hb7. zenon_intro zenon_Hb6. % 0.72/0.93 apply (zenon_notimply_s _ _ zenon_Hb6). zenon_intro zenon_Hb8. zenon_intro zenon_H41. % 0.72/0.93 apply (zenon_and_s _ _ zenon_Hb7). zenon_intro zenon_H25. zenon_intro zenon_Hb9. % 0.72/0.93 apply (zenon_and_s _ _ zenon_Hb9). zenon_intro zenon_H37. zenon_intro zenon_H2d. % 0.72/0.93 generalize (ci3 zenon_TZ_bu). zenon_intro zenon_Hba. % 0.72/0.93 generalize (apart3 zenon_TZ_bu). zenon_intro zenon_Hbb. % 0.72/0.93 generalize (apart3 zenon_TY_bn). zenon_intro zenon_H3d. % 0.72/0.93 generalize (zenon_Hba zenon_TY_bn). zenon_intro zenon_Hbc. % 0.72/0.93 apply (zenon_imply_s _ _ zenon_Hbc); [ zenon_intro zenon_H3b | zenon_intro zenon_H42 ]. % 0.72/0.93 exact (zenon_H3b zenon_H37). % 0.72/0.93 generalize (ceq3 zenon_TX_bo). zenon_intro zenon_Hbd. % 0.72/0.93 generalize (ceq3 zenon_TZ_bu). zenon_intro zenon_Hbe. % 0.72/0.93 generalize (zenon_Hbd zenon_TY_bn). zenon_intro zenon_H83. % 0.72/0.93 generalize (zenon_Hbe zenon_TY_bn). zenon_intro zenon_Hbf. % 0.72/0.93 generalize (zenon_Hbf zenon_TZ_bu). zenon_intro zenon_Hc0. % 0.72/0.93 apply (zenon_imply_s _ _ zenon_Hc0); [ zenon_intro zenon_H3b | zenon_intro zenon_Hc1 ]. % 0.72/0.93 exact (zenon_H3b zenon_H37). % 0.72/0.93 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H43 | zenon_intro zenon_Hc2 ]. % 0.72/0.93 generalize (ceq3 zenon_TY_bn). zenon_intro zenon_H3c. % 0.72/0.93 generalize (ceq1 (intersection_point zenon_TX_bo zenon_TY_bn)). zenon_intro zenon_Hc3. % 0.72/0.93 generalize (zenon_Hc3 zenon_TZ_bu). zenon_intro zenon_Hc4. % 0.72/0.93 generalize (ceq2 (intersection_point zenon_TX_bo zenon_TY_bn)). zenon_intro zenon_H45. % 0.72/0.93 generalize (zenon_H45 zenon_TY_bn). zenon_intro zenon_Hc5. % 0.72/0.93 generalize (zenon_Hc4 (intersection_point zenon_TZ_bu zenon_TY_bn)). zenon_intro zenon_Hc6. % 0.72/0.93 apply (zenon_imply_s _ _ zenon_Hc6); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hc7 ]. % 0.72/0.93 exact (zenon_Hc8 zenon_Hb8). % 0.72/0.93 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_H3e | zenon_intro zenon_H76 ]. % 0.72/0.93 generalize (zenon_Hc5 zenon_TY_bn). zenon_intro zenon_Hc9. % 0.72/0.93 apply (zenon_imply_s _ _ zenon_Hc9); [ zenon_intro zenon_H3f | zenon_intro zenon_Hca ]. % 0.72/0.93 apply (zenon_L13_ zenon_TZ_bu zenon_TY_bn zenon_TX_bo); trivial. % 0.72/0.93 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_H82 | zenon_intro zenon_H56 ]. % 0.72/0.93 generalize (apart2 zenon_TY_bn). zenon_intro zenon_H44. % 0.72/0.93 exact (zenon_H44 zenon_H82). % 0.72/0.93 generalize (ci4 zenon_TX_bo). zenon_intro zenon_H2f. % 0.72/0.93 generalize (zenon_H2f zenon_TY_bn). zenon_intro zenon_Hcb. % 0.72/0.93 apply (zenon_imply_s _ _ zenon_Hcb); [ zenon_intro zenon_H2b | zenon_intro zenon_H3f ]. % 0.72/0.93 exact (zenon_H2b zenon_H25). % 0.72/0.93 exact (zenon_H3f zenon_H56). % 0.72/0.93 exact (zenon_H42 zenon_H76). % 0.72/0.93 exact (zenon_Hbb zenon_Hc2). % 0.72/0.93 Qed. % 0.72/0.93 % SZS output end Proof % 0.72/0.93 (* END-PROOF *) % 0.72/0.93 nodes searched: 28132 % 0.72/0.93 max branch formulas: 2977 % 0.72/0.93 proof nodes created: 1521 % 0.72/0.93 formulas created: 70578 % 0.72/0.93 %------------------------------------------------------------------------------