%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWC205+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n025.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 600s % DateTime : Tue Jul 19 22:29:50 EDT 2022 % Result : Theorem 20.72s 20.96s % Output : Proof 20.72s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SWC205+1 : TPTP v8.1.0. Released v2.4.0. % 0.11/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n025.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Sun Jun 12 21:16:08 EDT 2022 % 0.13/0.34 % CPUTime : % 20.72/20.96 (* PROOF-FOUND *) % 20.72/20.96 % SZS status Theorem % 20.72/20.96 (* BEGIN-PROOF *) % 20.72/20.96 % SZS output start Proof % 20.72/20.96 Theorem co1 : (forall U : zenon_U, ((ssList U)->(forall V : zenon_U, ((ssList V)->(forall W : zenon_U, ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(V = X))\/((~(U = W))\/((~(neq V (nil)))\/((neq U (nil))\/(((~((nil) = X))/\((nil) = W))\/((~((nil) = W))/\((nil) = X))))))))))))))). % 20.72/20.96 Proof. % 20.72/20.96 assert (zenon_L1_ : forall (zenon_TU_dv : zenon_U), ((neq zenon_TU_dv (nil))<->(~(zenon_TU_dv = (nil)))) -> (~(neq zenon_TU_dv (nil))) -> (~((nil) = zenon_TU_dv)) -> False). % 20.72/20.96 do 1 intro. intros zenon_H60 zenon_H61 zenon_H62. % 20.72/20.96 apply (zenon_equiv_s _ _ zenon_H60); [ zenon_intro zenon_H61; zenon_intro zenon_H66 | zenon_intro zenon_H65; zenon_intro zenon_H64 ]. % 20.72/20.96 apply zenon_H66. zenon_intro zenon_H67. % 20.72/20.96 apply zenon_H62. apply sym_equal. exact zenon_H67. % 20.72/20.96 exact (zenon_H61 zenon_H65). % 20.72/20.96 (* end of lemma zenon_L1_ *) % 20.72/20.96 assert (zenon_L2_ : forall (zenon_TU_dv : zenon_U), (forall V : zenon_U, ((ssList V)->((neq zenon_TU_dv V)<->(~(zenon_TU_dv = V))))) -> (~(neq zenon_TU_dv (nil))) -> (~((nil) = zenon_TU_dv)) -> False). % 20.72/20.96 do 1 intro. intros zenon_H68 zenon_H61 zenon_H62. % 20.72/20.96 generalize (zenon_H68 (nil)). zenon_intro zenon_H69. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_H69); [ zenon_intro zenon_H6a | zenon_intro zenon_H60 ]. % 20.72/20.96 exact (zenon_H6a ax17). % 20.72/20.96 apply (zenon_L1_ zenon_TU_dv); trivial. % 20.72/20.96 (* end of lemma zenon_L2_ *) % 20.72/20.96 assert (zenon_L3_ : forall (zenon_TU_dv : zenon_U), (ssList zenon_TU_dv) -> (~(neq zenon_TU_dv (nil))) -> (~((nil) = zenon_TU_dv)) -> False). % 20.72/20.96 do 1 intro. intros zenon_H6b zenon_H61 zenon_H62. % 20.72/20.96 generalize (ax15 zenon_TU_dv). zenon_intro zenon_H6c. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_H6c); [ zenon_intro zenon_H6d | zenon_intro zenon_H68 ]. % 20.72/20.96 exact (zenon_H6d zenon_H6b). % 20.72/20.96 apply (zenon_L2_ zenon_TU_dv); trivial. % 20.72/20.96 (* end of lemma zenon_L3_ *) % 20.72/20.96 assert (zenon_L4_ : forall (zenon_TX_el : zenon_U) (zenon_TU_dv : zenon_U), (forall W : zenon_U, ((ssList W)->(((frontsegP zenon_TU_dv (nil))/\(frontsegP (nil) W))->(frontsegP zenon_TU_dv W)))) -> (ssList zenon_TX_el) -> (frontsegP zenon_TU_dv (nil)) -> (frontsegP (nil) zenon_TX_el) -> (~(frontsegP zenon_TU_dv zenon_TX_el)) -> False). % 20.72/20.96 do 2 intro. intros zenon_H6e zenon_H6f zenon_H70 zenon_H71 zenon_H72. % 20.72/20.96 generalize (zenon_H6e zenon_TX_el). zenon_intro zenon_H74. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_H74); [ zenon_intro zenon_H76 | zenon_intro zenon_H75 ]. % 20.72/20.96 exact (zenon_H76 zenon_H6f). % 20.72/20.96 apply (zenon_imply_s _ _ zenon_H75); [ zenon_intro zenon_H78 | zenon_intro zenon_H77 ]. % 20.72/20.96 apply (zenon_notand_s _ _ zenon_H78); [ zenon_intro zenon_H7a | zenon_intro zenon_H79 ]. % 20.72/20.96 exact (zenon_H7a zenon_H70). % 20.72/20.96 exact (zenon_H79 zenon_H71). % 20.72/20.96 exact (zenon_H72 zenon_H77). % 20.72/20.96 (* end of lemma zenon_L4_ *) % 20.72/20.96 assert (zenon_L5_ : forall (zenon_TX_el : zenon_U) (zenon_TU_dv : zenon_U), (forall V : zenon_U, ((ssList V)->(forall W : zenon_U, ((ssList W)->(((frontsegP zenon_TU_dv V)/\(frontsegP V W))->(frontsegP zenon_TU_dv W)))))) -> (ssList zenon_TX_el) -> (frontsegP zenon_TU_dv (nil)) -> (frontsegP (nil) zenon_TX_el) -> (~(frontsegP zenon_TU_dv zenon_TX_el)) -> False). % 20.72/20.96 do 2 intro. intros zenon_H7b zenon_H6f zenon_H70 zenon_H71 zenon_H72. % 20.72/20.96 generalize (zenon_H7b (nil)). zenon_intro zenon_H7c. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H6a | zenon_intro zenon_H6e ]. % 20.72/20.96 exact (zenon_H6a ax17). % 20.72/20.96 apply (zenon_L4_ zenon_TX_el zenon_TU_dv); trivial. % 20.72/20.96 (* end of lemma zenon_L5_ *) % 20.72/20.96 assert (zenon_L6_ : forall (zenon_TX_el : zenon_U) (zenon_TU_dv : zenon_U), (ssList zenon_TU_dv) -> (~(frontsegP zenon_TU_dv zenon_TX_el)) -> (frontsegP (nil) zenon_TX_el) -> (ssList zenon_TX_el) -> False). % 20.72/20.96 do 2 intro. intros zenon_H6b zenon_H72 zenon_H71 zenon_H6f. % 20.72/20.96 generalize (ax5 zenon_TU_dv). zenon_intro zenon_H7d. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_H7d); [ zenon_intro zenon_H6d | zenon_intro zenon_H7e ]. % 20.72/20.96 exact (zenon_H6d zenon_H6b). % 20.72/20.96 generalize (ax40 zenon_TU_dv). zenon_intro zenon_H7f. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_H7f); [ zenon_intro zenon_H6d | zenon_intro zenon_H7b ]. % 20.72/20.96 exact (zenon_H6d zenon_H6b). % 20.72/20.96 generalize (zenon_H7e (nil)). zenon_intro zenon_H80. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_H80); [ zenon_intro zenon_H6a | zenon_intro zenon_H81 ]. % 20.72/20.96 exact (zenon_H6a ax17). % 20.72/20.96 apply (zenon_equiv_s _ _ zenon_H81); [ zenon_intro zenon_H7a; zenon_intro zenon_H83 | zenon_intro zenon_H70; zenon_intro zenon_H82 ]. % 20.72/20.96 generalize (ax45 zenon_TU_dv). zenon_intro zenon_H84. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_H84); [ zenon_intro zenon_H6d | zenon_intro zenon_H70 ]. % 20.72/20.96 exact (zenon_H6d zenon_H6b). % 20.72/20.96 exact (zenon_H7a zenon_H70). % 20.72/20.96 apply (zenon_L5_ zenon_TX_el zenon_TU_dv); trivial. % 20.72/20.96 (* end of lemma zenon_L6_ *) % 20.72/20.96 assert (zenon_L7_ : forall (zenon_TX_el : zenon_U), (ssList zenon_TX_el) -> (~(frontsegP zenon_TX_el (nil))) -> False). % 20.72/20.96 do 1 intro. intros zenon_H6f zenon_H85. % 20.72/20.96 generalize (ax45 zenon_TX_el). zenon_intro zenon_H86. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_H86); [ zenon_intro zenon_H76 | zenon_intro zenon_H87 ]. % 20.72/20.96 exact (zenon_H76 zenon_H6f). % 20.72/20.96 exact (zenon_H85 zenon_H87). % 20.72/20.96 (* end of lemma zenon_L7_ *) % 20.72/20.96 assert (zenon_L8_ : forall (zenon_TU_dv : zenon_U) (zenon_TX_el : zenon_U), (forall W : zenon_U, ((ssList W)->(((frontsegP zenon_TX_el (nil))/\(frontsegP (nil) W))->(frontsegP zenon_TX_el W)))) -> (ssList zenon_TU_dv) -> (frontsegP zenon_TX_el (nil)) -> (frontsegP (nil) zenon_TU_dv) -> (~(frontsegP zenon_TX_el zenon_TU_dv)) -> False). % 20.72/20.96 do 2 intro. intros zenon_H88 zenon_H6b zenon_H87 zenon_H89 zenon_H8a. % 20.72/20.96 generalize (zenon_H88 zenon_TU_dv). zenon_intro zenon_H8b. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H6d | zenon_intro zenon_H8c ]. % 20.72/20.96 exact (zenon_H6d zenon_H6b). % 20.72/20.96 apply (zenon_imply_s _ _ zenon_H8c); [ zenon_intro zenon_H8e | zenon_intro zenon_H8d ]. % 20.72/20.96 apply (zenon_notand_s _ _ zenon_H8e); [ zenon_intro zenon_H85 | zenon_intro zenon_H8f ]. % 20.72/20.96 exact (zenon_H85 zenon_H87). % 20.72/20.96 exact (zenon_H8f zenon_H89). % 20.72/20.96 exact (zenon_H8a zenon_H8d). % 20.72/20.96 (* end of lemma zenon_L8_ *) % 20.72/20.96 assert (zenon_L9_ : (~((nil) = (nil))) -> False). % 20.72/20.96 do 0 intro. intros zenon_H90. % 20.72/20.96 apply zenon_H90. apply refl_equal. % 20.72/20.96 (* end of lemma zenon_L9_ *) % 20.72/20.96 apply NNPP. intro zenon_G. % 20.72/20.96 apply (zenon_notallex_s (fun U : zenon_U => ((ssList U)->(forall V : zenon_U, ((ssList V)->(forall W : zenon_U, ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(V = X))\/((~(U = W))\/((~(neq V (nil)))\/((neq U (nil))\/(((~((nil) = X))/\((nil) = W))\/((~((nil) = W))/\((nil) = X))))))))))))))) zenon_G); [ zenon_intro zenon_H91; idtac ]. % 20.72/20.96 elim zenon_H91. zenon_intro zenon_TU_dv. zenon_intro zenon_H92. % 20.72/20.96 apply (zenon_notimply_s _ _ zenon_H92). zenon_intro zenon_H6b. zenon_intro zenon_H93. % 20.72/20.96 apply (zenon_notallex_s (fun V : zenon_U => ((ssList V)->(forall W : zenon_U, ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(V = X))\/((~(zenon_TU_dv = W))\/((~(neq V (nil)))\/((neq zenon_TU_dv (nil))\/(((~((nil) = X))/\((nil) = W))\/((~((nil) = W))/\((nil) = X))))))))))))) zenon_H93); [ zenon_intro zenon_H94; idtac ]. % 20.72/20.96 elim zenon_H94. zenon_intro zenon_TV_ft. zenon_intro zenon_H96. % 20.72/20.96 apply (zenon_notimply_s _ _ zenon_H96). zenon_intro zenon_H98. zenon_intro zenon_H97. % 20.72/20.96 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(zenon_TV_ft = X))\/((~(zenon_TU_dv = W))\/((~(neq zenon_TV_ft (nil)))\/((neq zenon_TU_dv (nil))\/(((~((nil) = X))/\((nil) = W))\/((~((nil) = W))/\((nil) = X))))))))))) zenon_H97); [ zenon_intro zenon_H99; idtac ]. % 20.72/20.96 elim zenon_H99. zenon_intro zenon_TW_fy. zenon_intro zenon_H9b. % 20.72/20.96 apply (zenon_notimply_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 20.72/20.96 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~(zenon_TV_ft = X))\/((~(zenon_TU_dv = zenon_TW_fy))\/((~(neq zenon_TV_ft (nil)))\/((neq zenon_TU_dv (nil))\/(((~((nil) = X))/\((nil) = zenon_TW_fy))\/((~((nil) = zenon_TW_fy))/\((nil) = X))))))))) zenon_H9c); [ zenon_intro zenon_H9e; idtac ]. % 20.72/20.96 elim zenon_H9e. zenon_intro zenon_TX_el. zenon_intro zenon_H9f. % 20.72/20.96 apply (zenon_notimply_s _ _ zenon_H9f). zenon_intro zenon_H6f. zenon_intro zenon_Ha0. % 20.72/20.96 apply (zenon_notor_s _ _ zenon_Ha0). zenon_intro zenon_Ha2. zenon_intro zenon_Ha1. % 20.72/20.96 apply (zenon_notor_s _ _ zenon_Ha1). zenon_intro zenon_Ha4. zenon_intro zenon_Ha3. % 20.72/20.96 apply (zenon_notor_s _ _ zenon_Ha3). zenon_intro zenon_Ha6. zenon_intro zenon_Ha5. % 20.72/20.96 apply (zenon_notor_s _ _ zenon_Ha5). zenon_intro zenon_H61. zenon_intro zenon_Ha7. % 20.72/20.96 apply (zenon_notor_s _ _ zenon_Ha7). zenon_intro zenon_Ha9. zenon_intro zenon_Ha8. % 20.72/20.96 apply zenon_Ha6. zenon_intro zenon_Haa. % 20.72/20.96 apply zenon_Ha4. zenon_intro zenon_Hab. % 20.72/20.96 apply zenon_Ha2. zenon_intro zenon_Hac. % 20.72/20.96 apply (zenon_notand_s _ _ zenon_Ha9); [ zenon_intro zenon_Hae | zenon_intro zenon_Had ]. % 20.72/20.96 apply zenon_Hae. zenon_intro zenon_Haf. % 20.72/20.96 cut ((neq zenon_TV_ft (nil)) = (neq zenon_TU_dv (nil))). % 20.72/20.96 intro zenon_D_pnotp. % 20.72/20.96 apply zenon_H61. % 20.72/20.96 rewrite <- zenon_D_pnotp. % 20.72/20.96 exact zenon_Haa. % 20.72/20.96 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H90]. % 20.72/20.96 cut ((zenon_TV_ft = zenon_TU_dv)); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 20.72/20.96 congruence. % 20.72/20.96 generalize (ax46 zenon_TX_el). zenon_intro zenon_Hb1. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_Hb1); [ zenon_intro zenon_H76 | zenon_intro zenon_Hb2 ]. % 20.72/20.96 exact (zenon_H76 zenon_H6f). % 20.72/20.96 apply (zenon_equiv_s _ _ zenon_Hb2); [ zenon_intro zenon_H79; zenon_intro zenon_Hb3 | zenon_intro zenon_H71; zenon_intro zenon_Haf ]. % 20.72/20.96 exact (zenon_Hb3 zenon_Haf). % 20.72/20.96 generalize (ax41 zenon_TU_dv). zenon_intro zenon_Hb4. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_Hb4); [ zenon_intro zenon_H6d | zenon_intro zenon_Hb5 ]. % 20.72/20.96 exact (zenon_H6d zenon_H6b). % 20.72/20.96 generalize (ax46 zenon_TU_dv). zenon_intro zenon_Hb6. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_Hb6); [ zenon_intro zenon_H6d | zenon_intro zenon_Hb7 ]. % 20.72/20.96 exact (zenon_H6d zenon_H6b). % 20.72/20.96 apply (zenon_equiv_s _ _ zenon_Hb7); [ zenon_intro zenon_H8f; zenon_intro zenon_H62 | zenon_intro zenon_H89; zenon_intro zenon_Hb8 ]. % 20.72/20.96 apply (zenon_L3_ zenon_TU_dv); trivial. % 20.72/20.96 generalize (ax40 zenon_TX_el). zenon_intro zenon_Hb9. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_Hb9); [ zenon_intro zenon_H76 | zenon_intro zenon_Hba ]. % 20.72/20.96 exact (zenon_H76 zenon_H6f). % 20.72/20.96 cut ((zenon_TV_ft = zenon_TX_el) = (zenon_TV_ft = zenon_TU_dv)). % 20.72/20.96 intro zenon_D_pnotp. % 20.72/20.96 apply zenon_Hb0. % 20.72/20.96 rewrite <- zenon_D_pnotp. % 20.72/20.96 exact zenon_Hac. % 20.72/20.96 cut ((zenon_TX_el = zenon_TU_dv)); [idtac | apply NNPP; zenon_intro zenon_Hbb]. % 20.72/20.96 cut ((zenon_TV_ft = zenon_TV_ft)); [idtac | apply NNPP; zenon_intro zenon_Hbc]. % 20.72/20.96 congruence. % 20.72/20.96 apply zenon_Hbc. apply refl_equal. % 20.72/20.96 generalize (ax5 zenon_TX_el). zenon_intro zenon_Hbd. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_Hbd); [ zenon_intro zenon_H76 | zenon_intro zenon_Hbe ]. % 20.72/20.96 exact (zenon_H76 zenon_H6f). % 20.72/20.96 generalize (zenon_Hb5 zenon_TX_el). zenon_intro zenon_Hbf. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_Hbf); [ zenon_intro zenon_H76 | zenon_intro zenon_Hc0 ]. % 20.72/20.96 exact (zenon_H76 zenon_H6f). % 20.72/20.96 apply (zenon_imply_s _ _ zenon_Hc0); [ zenon_intro zenon_Hc2 | zenon_intro zenon_Hc1 ]. % 20.72/20.96 apply (zenon_notand_s _ _ zenon_Hc2); [ zenon_intro zenon_H72 | zenon_intro zenon_H8a ]. % 20.72/20.96 apply (zenon_L6_ zenon_TX_el zenon_TU_dv); trivial. % 20.72/20.96 generalize (zenon_Hba (nil)). zenon_intro zenon_Hc3. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_Hc3); [ zenon_intro zenon_H6a | zenon_intro zenon_H88 ]. % 20.72/20.96 exact (zenon_H6a ax17). % 20.72/20.96 generalize (zenon_Hbe (nil)). zenon_intro zenon_Hc4. % 20.72/20.96 apply (zenon_imply_s _ _ zenon_Hc4); [ zenon_intro zenon_H6a | zenon_intro zenon_Hc5 ]. % 20.72/20.96 exact (zenon_H6a ax17). % 20.72/20.96 apply (zenon_equiv_s _ _ zenon_Hc5); [ zenon_intro zenon_H85; zenon_intro zenon_Hc7 | zenon_intro zenon_H87; zenon_intro zenon_Hc6 ]. % 20.72/20.96 apply (zenon_L7_ zenon_TX_el); trivial. % 20.72/20.96 apply (zenon_L8_ zenon_TU_dv zenon_TX_el); trivial. % 20.72/20.96 apply zenon_Hbb. apply sym_equal. exact zenon_Hc1. % 20.72/20.96 apply zenon_H90. apply refl_equal. % 20.72/20.96 cut ((zenon_TU_dv = zenon_TW_fy) = ((nil) = zenon_TW_fy)). % 20.72/20.96 intro zenon_D_pnotp. % 20.72/20.96 apply zenon_Had. % 20.72/20.96 rewrite <- zenon_D_pnotp. % 20.72/20.96 exact zenon_Hab. % 20.72/20.96 cut ((zenon_TW_fy = zenon_TW_fy)); [idtac | apply NNPP; zenon_intro zenon_Hc8]. % 20.72/20.96 cut ((zenon_TU_dv = (nil))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 20.72/20.96 congruence. % 20.72/20.96 elim (classic ((nil) = (nil))); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H90 ]. % 20.72/20.96 cut (((nil) = (nil)) = (zenon_TU_dv = (nil))). % 20.72/20.96 intro zenon_D_pnotp. % 20.72/20.96 apply zenon_H64. % 20.72/20.96 rewrite <- zenon_D_pnotp. % 20.72/20.96 exact zenon_Hc9. % 20.72/20.96 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H90]. % 20.72/20.96 cut (((nil) = zenon_TU_dv)); [idtac | apply NNPP; zenon_intro zenon_H62]. % 20.72/20.96 congruence. % 20.72/20.96 apply (zenon_L3_ zenon_TU_dv); trivial. % 20.72/20.96 apply zenon_H90. apply refl_equal. % 20.72/20.96 apply zenon_H90. apply refl_equal. % 20.72/20.96 apply zenon_Hc8. apply refl_equal. % 20.72/20.96 Qed. % 20.72/20.96 % SZS output end Proof % 20.72/20.96 (* END-PROOF *) % 20.72/20.96 nodes searched: 259446 % 20.72/20.96 max branch formulas: 8369 % 20.72/20.96 proof nodes created: 22819 % 20.72/20.96 formulas created: 1253976 % 20.72/20.96 %------------------------------------------------------------------------------