%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : NUM404+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n016.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 : Mon Jul 18 15:55:23 EDT 2022 % Result : Theorem 0.45s 0.64s % Output : Proof 0.45s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.08/0.12 % Problem : NUM404+1 : TPTP v8.1.0. Released v3.2.0. % 0.08/0.13 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n016.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 : Wed Jul 6 08:41:50 EDT 2022 % 0.12/0.33 % CPUTime : % 0.45/0.64 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.45/0.64 (* PROOF-FOUND *) % 0.45/0.64 % SZS status Theorem % 0.45/0.64 (* BEGIN-PROOF *) % 0.45/0.64 % SZS output start Proof % 0.45/0.64 Theorem t37_ordinal1 : (forall A : zenon_U, (~(forall B : zenon_U, ((in B A)<->(ordinal B))))). % 0.45/0.64 Proof. % 0.45/0.64 assert (zenon_L1_ : forall (zenon_TB_br : zenon_U), ((epsilon_transitive zenon_TB_br)/\(epsilon_connected zenon_TB_br)) -> (~(ordinal zenon_TB_br)) -> False). % 0.45/0.64 do 1 intro. intros zenon_H29 zenon_H2a. % 0.45/0.64 generalize (d4_ordinal1 zenon_TB_br). zenon_intro zenon_H2c. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H2c); [ zenon_intro zenon_H2a; zenon_intro zenon_H2e | zenon_intro zenon_H2d; zenon_intro zenon_H29 ]. % 0.45/0.64 exact (zenon_H2e zenon_H29). % 0.45/0.64 exact (zenon_H2a zenon_H2d). % 0.45/0.64 (* end of lemma zenon_L1_ *) % 0.45/0.64 assert (zenon_L2_ : forall (zenon_TC_bx : zenon_U), (ordinal zenon_TC_bx) -> (~(forall B : zenon_U, ((in B zenon_TC_bx)->(subset B zenon_TC_bx)))) -> False). % 0.45/0.64 do 1 intro. intros zenon_H2f zenon_H30. % 0.45/0.64 generalize (d4_ordinal1 zenon_TC_bx). zenon_intro zenon_H32. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H35; zenon_intro zenon_H34 | zenon_intro zenon_H2f; zenon_intro zenon_H33 ]. % 0.45/0.64 exact (zenon_H35 zenon_H2f). % 0.45/0.64 apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_H37. zenon_intro zenon_H36. % 0.45/0.64 generalize (d2_ordinal1 zenon_TC_bx). zenon_intro zenon_H38. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H38); [ zenon_intro zenon_H3a; zenon_intro zenon_H30 | zenon_intro zenon_H37; zenon_intro zenon_H39 ]. % 0.45/0.64 exact (zenon_H3a zenon_H37). % 0.45/0.64 exact (zenon_H30 zenon_H39). % 0.45/0.64 (* end of lemma zenon_L2_ *) % 0.45/0.64 assert (zenon_L3_ : forall (zenon_TC_bx : zenon_U), (ordinal zenon_TC_bx) -> (~(forall B : zenon_U, (forall C : zenon_U, (~((in B zenon_TC_bx)/\((in C zenon_TC_bx)/\((~(in B C))/\((~(B = C))/\(~(in C B)))))))))) -> False). % 0.45/0.64 do 1 intro. intros zenon_H2f zenon_H3b. % 0.45/0.64 generalize (d4_ordinal1 zenon_TC_bx). zenon_intro zenon_H32. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H35; zenon_intro zenon_H34 | zenon_intro zenon_H2f; zenon_intro zenon_H33 ]. % 0.45/0.64 exact (zenon_H35 zenon_H2f). % 0.45/0.64 apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_H37. zenon_intro zenon_H36. % 0.45/0.64 generalize (d3_ordinal1 zenon_TC_bx). zenon_intro zenon_H3c. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H3e; zenon_intro zenon_H3b | zenon_intro zenon_H36; zenon_intro zenon_H3d ]. % 0.45/0.64 exact (zenon_H3e zenon_H36). % 0.45/0.64 exact (zenon_H3b zenon_H3d). % 0.45/0.64 (* end of lemma zenon_L3_ *) % 0.45/0.64 assert (zenon_L4_ : forall (zenon_TC_bx : zenon_U) (zenon_TB_br : zenon_U) (zenon_TA_co : zenon_U), (forall B : zenon_U, ((in B zenon_TA_co)<->(ordinal B))) -> ((epsilon_transitive zenon_TB_br)/\(epsilon_connected zenon_TB_br)) -> (in zenon_TC_bx zenon_TB_br) -> (~(in zenon_TC_bx zenon_TA_co)) -> False). % 0.45/0.64 do 3 intro. intros zenon_H3f zenon_H29 zenon_H40 zenon_H41. % 0.45/0.64 generalize (zenon_H3f zenon_TC_bx). zenon_intro zenon_H43. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H43); [ zenon_intro zenon_H41; zenon_intro zenon_H35 | zenon_intro zenon_H44; zenon_intro zenon_H2f ]. % 0.45/0.64 generalize (d4_ordinal1 zenon_TC_bx). zenon_intro zenon_H32. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H35; zenon_intro zenon_H34 | zenon_intro zenon_H2f; zenon_intro zenon_H33 ]. % 0.45/0.64 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H3a | zenon_intro zenon_H3e ]. % 0.45/0.64 generalize (d2_ordinal1 zenon_TC_bx). zenon_intro zenon_H38. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H38); [ zenon_intro zenon_H3a; zenon_intro zenon_H30 | zenon_intro zenon_H37; zenon_intro zenon_H39 ]. % 0.45/0.64 generalize (t23_ordinal1 zenon_TC_bx). zenon_intro zenon_H45. % 0.45/0.64 generalize (zenon_H45 zenon_TB_br). zenon_intro zenon_H46. % 0.45/0.64 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H2a | zenon_intro zenon_H47 ]. % 0.45/0.64 apply (zenon_L1_ zenon_TB_br); trivial. % 0.45/0.64 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H48 | zenon_intro zenon_H2f ]. % 0.45/0.64 exact (zenon_H48 zenon_H40). % 0.45/0.64 apply (zenon_L2_ zenon_TC_bx); trivial. % 0.45/0.64 exact (zenon_H3a zenon_H37). % 0.45/0.64 generalize (d3_ordinal1 zenon_TC_bx). zenon_intro zenon_H3c. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H3e; zenon_intro zenon_H3b | zenon_intro zenon_H36; zenon_intro zenon_H3d ]. % 0.45/0.64 generalize (t23_ordinal1 zenon_TC_bx). zenon_intro zenon_H45. % 0.45/0.64 generalize (zenon_H45 zenon_TB_br). zenon_intro zenon_H46. % 0.45/0.64 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H2a | zenon_intro zenon_H47 ]. % 0.45/0.64 apply (zenon_L1_ zenon_TB_br); trivial. % 0.45/0.64 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H48 | zenon_intro zenon_H2f ]. % 0.45/0.64 exact (zenon_H48 zenon_H40). % 0.45/0.64 apply (zenon_L3_ zenon_TC_bx); trivial. % 0.45/0.64 exact (zenon_H3e zenon_H36). % 0.45/0.64 exact (zenon_H35 zenon_H2f). % 0.45/0.64 exact (zenon_H41 zenon_H44). % 0.45/0.64 (* end of lemma zenon_L4_ *) % 0.45/0.64 assert (zenon_L5_ : forall (zenon_TC_bx : zenon_U) (zenon_TA_co : zenon_U) (zenon_TB_br : zenon_U), (ordinal zenon_TB_br) -> (forall B : zenon_U, ((in B zenon_TA_co)<->(ordinal B))) -> (in zenon_TC_bx zenon_TB_br) -> (~(in zenon_TC_bx zenon_TA_co)) -> False). % 0.45/0.64 do 3 intro. intros zenon_H2d zenon_H3f zenon_H40 zenon_H41. % 0.45/0.64 generalize (d4_ordinal1 zenon_TB_br). zenon_intro zenon_H2c. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H2c); [ zenon_intro zenon_H2a; zenon_intro zenon_H2e | zenon_intro zenon_H2d; zenon_intro zenon_H29 ]. % 0.45/0.64 exact (zenon_H2a zenon_H2d). % 0.45/0.64 apply (zenon_L4_ zenon_TC_bx zenon_TB_br zenon_TA_co); trivial. % 0.45/0.64 (* end of lemma zenon_L5_ *) % 0.45/0.64 assert (zenon_L6_ : forall (zenon_TB_cx : zenon_U), (ordinal zenon_TB_cx) -> (~(forall B : zenon_U, ((in B zenon_TB_cx)->(subset B zenon_TB_cx)))) -> False). % 0.45/0.64 do 1 intro. intros zenon_H49 zenon_H4a. % 0.45/0.64 generalize (d4_ordinal1 zenon_TB_cx). zenon_intro zenon_H4c. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H4f; zenon_intro zenon_H4e | zenon_intro zenon_H49; zenon_intro zenon_H4d ]. % 0.45/0.64 exact (zenon_H4f zenon_H49). % 0.45/0.64 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H51. zenon_intro zenon_H50. % 0.45/0.64 generalize (d2_ordinal1 zenon_TB_cx). zenon_intro zenon_H52. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H52); [ zenon_intro zenon_H54; zenon_intro zenon_H4a | zenon_intro zenon_H51; zenon_intro zenon_H53 ]. % 0.45/0.64 exact (zenon_H54 zenon_H51). % 0.45/0.64 exact (zenon_H4a zenon_H53). % 0.45/0.64 (* end of lemma zenon_L6_ *) % 0.45/0.64 assert (zenon_L7_ : forall (zenon_TB_cx : zenon_U), (ordinal zenon_TB_cx) -> (~(forall B : zenon_U, (forall C : zenon_U, (~((in B zenon_TB_cx)/\((in C zenon_TB_cx)/\((~(in B C))/\((~(B = C))/\(~(in C B)))))))))) -> False). % 0.45/0.64 do 1 intro. intros zenon_H49 zenon_H55. % 0.45/0.64 generalize (d4_ordinal1 zenon_TB_cx). zenon_intro zenon_H4c. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H4f; zenon_intro zenon_H4e | zenon_intro zenon_H49; zenon_intro zenon_H4d ]. % 0.45/0.64 exact (zenon_H4f zenon_H49). % 0.45/0.64 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H51. zenon_intro zenon_H50. % 0.45/0.64 generalize (d3_ordinal1 zenon_TB_cx). zenon_intro zenon_H56. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H56); [ zenon_intro zenon_H58; zenon_intro zenon_H55 | zenon_intro zenon_H50; zenon_intro zenon_H57 ]. % 0.45/0.64 exact (zenon_H58 zenon_H50). % 0.45/0.64 exact (zenon_H55 zenon_H57). % 0.45/0.64 (* end of lemma zenon_L7_ *) % 0.45/0.64 assert (zenon_L8_ : forall (zenon_TB_cx : zenon_U) (zenon_TC_dq : zenon_U), (ordinal zenon_TC_dq) -> (forall B : zenon_U, ((ordinal B)->(~((~(in zenon_TB_cx B))/\((~(zenon_TB_cx = B))/\(~(in B zenon_TB_cx))))))) -> (~(in zenon_TB_cx zenon_TC_dq)) -> (~(zenon_TB_cx = zenon_TC_dq)) -> (~(in zenon_TC_dq zenon_TB_cx)) -> False). % 0.45/0.64 do 2 intro. intros zenon_H59 zenon_H5a zenon_H5b zenon_H5c zenon_H5d. % 0.45/0.64 generalize (d4_ordinal1 zenon_TC_dq). zenon_intro zenon_H5f. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H5f); [ zenon_intro zenon_H62; zenon_intro zenon_H61 | zenon_intro zenon_H59; zenon_intro zenon_H60 ]. % 0.45/0.64 exact (zenon_H62 zenon_H59). % 0.45/0.64 generalize (zenon_H5a zenon_TC_dq). zenon_intro zenon_H63. % 0.45/0.64 apply (zenon_imply_s _ _ zenon_H63); [ zenon_intro zenon_H62 | zenon_intro zenon_H64 ]. % 0.45/0.64 generalize (d4_ordinal1 zenon_TC_dq). zenon_intro zenon_H5f. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H5f); [ zenon_intro zenon_H62; zenon_intro zenon_H61 | zenon_intro zenon_H59; zenon_intro zenon_H60 ]. % 0.45/0.64 exact (zenon_H61 zenon_H60). % 0.45/0.64 exact (zenon_H62 zenon_H59). % 0.45/0.64 apply (zenon_notand_s _ _ zenon_H64); [ zenon_intro zenon_H66 | zenon_intro zenon_H65 ]. % 0.45/0.64 exact (zenon_H66 zenon_H5b). % 0.45/0.64 apply (zenon_notand_s _ _ zenon_H65); [ zenon_intro zenon_H68 | zenon_intro zenon_H67 ]. % 0.45/0.64 exact (zenon_H68 zenon_H5c). % 0.45/0.64 exact (zenon_H67 zenon_H5d). % 0.45/0.64 (* end of lemma zenon_L8_ *) % 0.45/0.64 assert (zenon_L9_ : forall (zenon_TA_co : zenon_U), (forall B : zenon_U, ((in B zenon_TA_co)<->(ordinal B))) -> ((epsilon_transitive zenon_TA_co)/\(epsilon_connected zenon_TA_co)) -> False). % 0.45/0.64 do 1 intro. intros zenon_H3f zenon_H69. % 0.45/0.64 generalize (zenon_H3f zenon_TA_co). zenon_intro zenon_H6a. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H6a); [ zenon_intro zenon_H6e; zenon_intro zenon_H6d | zenon_intro zenon_H6c; zenon_intro zenon_H6b ]. % 0.45/0.64 generalize (d4_ordinal1 zenon_TA_co). zenon_intro zenon_H6f. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H6f); [ zenon_intro zenon_H6d; zenon_intro zenon_H70 | zenon_intro zenon_H6b; zenon_intro zenon_H69 ]. % 0.45/0.64 exact (zenon_H70 zenon_H69). % 0.45/0.64 exact (zenon_H6d zenon_H6b). % 0.45/0.64 generalize (antisymmetry_r2_hidden zenon_TA_co). zenon_intro zenon_H71. % 0.45/0.64 generalize (zenon_H71 zenon_TA_co). zenon_intro zenon_H72. % 0.45/0.64 apply (zenon_imply_s _ _ zenon_H72); [ zenon_intro zenon_H6e | zenon_intro zenon_H6e ]. % 0.45/0.64 exact (zenon_H6e zenon_H6c). % 0.45/0.64 exact (zenon_H6e zenon_H6c). % 0.45/0.64 (* end of lemma zenon_L9_ *) % 0.45/0.64 assert (zenon_L10_ : forall (zenon_TA_co : zenon_U), (ordinal zenon_TA_co) -> (forall B : zenon_U, ((in B zenon_TA_co)<->(ordinal B))) -> False). % 0.45/0.64 do 1 intro. intros zenon_H6b zenon_H3f. % 0.45/0.64 generalize (d4_ordinal1 zenon_TA_co). zenon_intro zenon_H6f. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H6f); [ zenon_intro zenon_H6d; zenon_intro zenon_H70 | zenon_intro zenon_H6b; zenon_intro zenon_H69 ]. % 0.45/0.64 exact (zenon_H6d zenon_H6b). % 0.45/0.64 apply (zenon_L9_ zenon_TA_co); trivial. % 0.45/0.64 (* end of lemma zenon_L10_ *) % 0.45/0.64 apply NNPP. intro zenon_G. % 0.45/0.64 apply (zenon_notallex_s (fun A : zenon_U => (~(forall B : zenon_U, ((in B A)<->(ordinal B))))) zenon_G); [ zenon_intro zenon_H73; idtac ]. % 0.45/0.64 elim zenon_H73. zenon_intro zenon_TA_co. zenon_intro zenon_H74. % 0.45/0.64 apply zenon_H74. zenon_intro zenon_H3f. % 0.45/0.64 generalize (cc2_ordinal1 zenon_TA_co). zenon_intro zenon_H75. % 0.45/0.64 apply (zenon_imply_s _ _ zenon_H75); [ zenon_intro zenon_H70 | zenon_intro zenon_H6b ]. % 0.45/0.64 apply (zenon_notand_s _ _ zenon_H70); [ zenon_intro zenon_H77 | zenon_intro zenon_H76 ]. % 0.45/0.64 generalize (d2_ordinal1 zenon_TA_co). zenon_intro zenon_H78. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H78); [ zenon_intro zenon_H77; zenon_intro zenon_H7b | zenon_intro zenon_H7a; zenon_intro zenon_H79 ]. % 0.45/0.64 apply (zenon_notallex_s (fun B : zenon_U => ((in B zenon_TA_co)->(subset B zenon_TA_co))) zenon_H7b); [ zenon_intro zenon_H7c; idtac ]. % 0.45/0.64 elim zenon_H7c. zenon_intro zenon_TB_br. zenon_intro zenon_H7d. % 0.45/0.64 apply (zenon_notimply_s _ _ zenon_H7d). zenon_intro zenon_H7f. zenon_intro zenon_H7e. % 0.45/0.64 generalize (d3_tarski zenon_TB_br). zenon_intro zenon_H80. % 0.45/0.64 generalize (zenon_H80 zenon_TA_co). zenon_intro zenon_H81. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H81); [ zenon_intro zenon_H7e; zenon_intro zenon_H84 | zenon_intro zenon_H83; zenon_intro zenon_H82 ]. % 0.45/0.64 apply (zenon_notallex_s (fun C : zenon_U => ((in C zenon_TB_br)->(in C zenon_TA_co))) zenon_H84); [ zenon_intro zenon_H85; idtac ]. % 0.45/0.64 elim zenon_H85. zenon_intro zenon_TC_bx. zenon_intro zenon_H86. % 0.45/0.64 apply (zenon_notimply_s _ _ zenon_H86). zenon_intro zenon_H40. zenon_intro zenon_H41. % 0.45/0.64 generalize (zenon_H3f zenon_TB_br). zenon_intro zenon_H87. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H87); [ zenon_intro zenon_H88; zenon_intro zenon_H2a | zenon_intro zenon_H7f; zenon_intro zenon_H2d ]. % 0.45/0.64 exact (zenon_H88 zenon_H7f). % 0.45/0.64 apply (zenon_L5_ zenon_TC_bx zenon_TA_co zenon_TB_br); trivial. % 0.45/0.64 exact (zenon_H7e zenon_H83). % 0.45/0.64 exact (zenon_H77 zenon_H7a). % 0.45/0.64 generalize (d3_ordinal1 zenon_TA_co). zenon_intro zenon_H89. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H89); [ zenon_intro zenon_H76; zenon_intro zenon_H8c | zenon_intro zenon_H8b; zenon_intro zenon_H8a ]. % 0.45/0.64 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (~((in B zenon_TA_co)/\((in C zenon_TA_co)/\((~(in B C))/\((~(B = C))/\(~(in C B))))))))) zenon_H8c); [ zenon_intro zenon_H8d; idtac ]. % 0.45/0.64 elim zenon_H8d. zenon_intro zenon_TB_cx. zenon_intro zenon_H8e. % 0.45/0.64 apply (zenon_notallex_s (fun C : zenon_U => (~((in zenon_TB_cx zenon_TA_co)/\((in C zenon_TA_co)/\((~(in zenon_TB_cx C))/\((~(zenon_TB_cx = C))/\(~(in C zenon_TB_cx)))))))) zenon_H8e); [ zenon_intro zenon_H8f; idtac ]. % 0.45/0.64 elim zenon_H8f. zenon_intro zenon_TC_dq. zenon_intro zenon_H90. % 0.45/0.64 apply zenon_H90. zenon_intro zenon_H91. % 0.45/0.64 apply (zenon_and_s _ _ zenon_H91). zenon_intro zenon_H93. zenon_intro zenon_H92. % 0.45/0.64 apply (zenon_and_s _ _ zenon_H92). zenon_intro zenon_H95. zenon_intro zenon_H94. % 0.45/0.64 apply (zenon_and_s _ _ zenon_H94). zenon_intro zenon_H5b. zenon_intro zenon_H96. % 0.45/0.64 apply (zenon_and_s _ _ zenon_H96). zenon_intro zenon_H5c. zenon_intro zenon_H5d. % 0.45/0.64 generalize (t24_ordinal1 zenon_TB_cx). zenon_intro zenon_H97. % 0.45/0.64 apply (zenon_imply_s _ _ zenon_H97); [ zenon_intro zenon_H4f | zenon_intro zenon_H5a ]. % 0.45/0.64 generalize (d4_ordinal1 zenon_TB_cx). zenon_intro zenon_H4c. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H4f; zenon_intro zenon_H4e | zenon_intro zenon_H49; zenon_intro zenon_H4d ]. % 0.45/0.64 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_H54 | zenon_intro zenon_H58 ]. % 0.45/0.64 generalize (d2_ordinal1 zenon_TB_cx). zenon_intro zenon_H52. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H52); [ zenon_intro zenon_H54; zenon_intro zenon_H4a | zenon_intro zenon_H51; zenon_intro zenon_H53 ]. % 0.45/0.64 generalize (zenon_H3f zenon_TB_cx). zenon_intro zenon_H98. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H98); [ zenon_intro zenon_H99; zenon_intro zenon_H4f | zenon_intro zenon_H93; zenon_intro zenon_H49 ]. % 0.45/0.64 exact (zenon_H99 zenon_H93). % 0.45/0.64 apply (zenon_L6_ zenon_TB_cx); trivial. % 0.45/0.64 exact (zenon_H54 zenon_H51). % 0.45/0.64 generalize (d3_ordinal1 zenon_TB_cx). zenon_intro zenon_H56. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H56); [ zenon_intro zenon_H58; zenon_intro zenon_H55 | zenon_intro zenon_H50; zenon_intro zenon_H57 ]. % 0.45/0.64 generalize (zenon_H3f zenon_TB_cx). zenon_intro zenon_H98. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H98); [ zenon_intro zenon_H99; zenon_intro zenon_H4f | zenon_intro zenon_H93; zenon_intro zenon_H49 ]. % 0.45/0.64 exact (zenon_H99 zenon_H93). % 0.45/0.64 apply (zenon_L7_ zenon_TB_cx); trivial. % 0.45/0.64 exact (zenon_H58 zenon_H50). % 0.45/0.64 exact (zenon_H4f zenon_H49). % 0.45/0.64 generalize (zenon_H3f zenon_TC_dq). zenon_intro zenon_H9a. % 0.45/0.64 apply (zenon_equiv_s _ _ zenon_H9a); [ zenon_intro zenon_H9b; zenon_intro zenon_H62 | zenon_intro zenon_H95; zenon_intro zenon_H59 ]. % 0.45/0.64 exact (zenon_H9b zenon_H95). % 0.45/0.64 apply (zenon_L8_ zenon_TB_cx zenon_TC_dq); trivial. % 0.45/0.64 exact (zenon_H76 zenon_H8b). % 0.45/0.64 apply (zenon_L10_ zenon_TA_co); trivial. % 0.45/0.64 Qed. % 0.45/0.64 % SZS output end Proof % 0.45/0.64 (* END-PROOF *) % 0.45/0.64 nodes searched: 8307 % 0.45/0.64 max branch formulas: 1400 % 0.45/0.64 proof nodes created: 551 % 0.45/0.64 formulas created: 41062 % 0.45/0.64 %------------------------------------------------------------------------------