%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWC208+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n011.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 22:29:51 EDT 2022 % Result : Theorem 16.37s 16.56s % Output : Proof 16.37s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SWC208+1 : TPTP v8.1.0. Released v2.4.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n011.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sun Jun 12 04:56:02 EDT 2022 % 0.13/0.33 % CPUTime : % 16.37/16.56 (* PROOF-FOUND *) % 16.37/16.56 % SZS status Theorem % 16.37/16.56 (* BEGIN-PROOF *) % 16.37/16.56 % SZS output start Proof % 16.37/16.56 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)))/\((~(neq W (nil)))\/(~(frontsegP X W)))))))))))))))). % 16.37/16.56 Proof. % 16.37/16.56 assert (zenon_L1_ : 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). % 16.37/16.56 do 1 intro. intros zenon_H60 zenon_H61 zenon_H62. % 16.37/16.56 generalize (zenon_H60 (nil)). zenon_intro zenon_H64. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_H64); [ zenon_intro zenon_H66 | zenon_intro zenon_H65 ]. % 16.37/16.56 exact (zenon_H66 ax17). % 16.37/16.56 apply (zenon_equiv_s _ _ zenon_H65); [ zenon_intro zenon_H61; zenon_intro zenon_H69 | zenon_intro zenon_H68; zenon_intro zenon_H67 ]. % 16.37/16.56 apply zenon_H69. zenon_intro zenon_H6a. % 16.37/16.56 apply zenon_H62. apply sym_equal. exact zenon_H6a. % 16.37/16.56 exact (zenon_H61 zenon_H68). % 16.37/16.56 (* end of lemma zenon_L1_ *) % 16.37/16.56 assert (zenon_L2_ : forall (zenon_TX_ei : 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_ei) -> (frontsegP zenon_TU_dv (nil)) -> (frontsegP (nil) zenon_TX_ei) -> (~(frontsegP zenon_TU_dv zenon_TX_ei)) -> False). % 16.37/16.56 do 2 intro. intros zenon_H6b zenon_H6c zenon_H6d zenon_H6e zenon_H6f. % 16.37/16.56 generalize (zenon_H6b zenon_TX_ei). zenon_intro zenon_H71. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_H71); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ]. % 16.37/16.56 exact (zenon_H73 zenon_H6c). % 16.37/16.56 apply (zenon_imply_s _ _ zenon_H72); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ]. % 16.37/16.56 apply (zenon_notand_s _ _ zenon_H75); [ zenon_intro zenon_H77 | zenon_intro zenon_H76 ]. % 16.37/16.56 exact (zenon_H77 zenon_H6d). % 16.37/16.56 exact (zenon_H76 zenon_H6e). % 16.37/16.56 exact (zenon_H6f zenon_H74). % 16.37/16.56 (* end of lemma zenon_L2_ *) % 16.37/16.56 assert (zenon_L3_ : forall (zenon_TX_ei : 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_ei) -> (frontsegP zenon_TU_dv (nil)) -> (frontsegP (nil) zenon_TX_ei) -> (~(frontsegP zenon_TU_dv zenon_TX_ei)) -> False). % 16.37/16.56 do 2 intro. intros zenon_H78 zenon_H6c zenon_H6d zenon_H6e zenon_H6f. % 16.37/16.56 generalize (zenon_H78 (nil)). zenon_intro zenon_H79. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_H79); [ zenon_intro zenon_H66 | zenon_intro zenon_H6b ]. % 16.37/16.56 exact (zenon_H66 ax17). % 16.37/16.56 apply (zenon_L2_ zenon_TX_ei zenon_TU_dv); trivial. % 16.37/16.56 (* end of lemma zenon_L3_ *) % 16.37/16.56 assert (zenon_L4_ : forall (zenon_TX_ei : zenon_U) (zenon_TU_dv : zenon_U), (ssList zenon_TU_dv) -> (~(frontsegP zenon_TU_dv zenon_TX_ei)) -> (frontsegP (nil) zenon_TX_ei) -> (ssList zenon_TX_ei) -> False). % 16.37/16.56 do 2 intro. intros zenon_H7a zenon_H6f zenon_H6e zenon_H6c. % 16.37/16.56 generalize (ax5 zenon_TU_dv). zenon_intro zenon_H7b. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_H7b); [ zenon_intro zenon_H7d | zenon_intro zenon_H7c ]. % 16.37/16.56 exact (zenon_H7d zenon_H7a). % 16.37/16.56 generalize (ax40 zenon_TU_dv). zenon_intro zenon_H7e. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_H7e); [ zenon_intro zenon_H7d | zenon_intro zenon_H78 ]. % 16.37/16.56 exact (zenon_H7d zenon_H7a). % 16.37/16.56 generalize (zenon_H7c (nil)). zenon_intro zenon_H7f. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_H7f); [ zenon_intro zenon_H66 | zenon_intro zenon_H80 ]. % 16.37/16.56 exact (zenon_H66 ax17). % 16.37/16.56 apply (zenon_equiv_s _ _ zenon_H80); [ zenon_intro zenon_H77; zenon_intro zenon_H82 | zenon_intro zenon_H6d; zenon_intro zenon_H81 ]. % 16.37/16.56 generalize (ax45 zenon_TU_dv). zenon_intro zenon_H83. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_H83); [ zenon_intro zenon_H7d | zenon_intro zenon_H6d ]. % 16.37/16.56 exact (zenon_H7d zenon_H7a). % 16.37/16.56 exact (zenon_H77 zenon_H6d). % 16.37/16.56 apply (zenon_L3_ zenon_TX_ei zenon_TU_dv); trivial. % 16.37/16.56 (* end of lemma zenon_L4_ *) % 16.37/16.56 assert (zenon_L5_ : forall (zenon_TX_ei : zenon_U), (ssList zenon_TX_ei) -> (~(frontsegP zenon_TX_ei (nil))) -> False). % 16.37/16.56 do 1 intro. intros zenon_H6c zenon_H84. % 16.37/16.56 generalize (ax45 zenon_TX_ei). zenon_intro zenon_H85. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_H85); [ zenon_intro zenon_H73 | zenon_intro zenon_H86 ]. % 16.37/16.56 exact (zenon_H73 zenon_H6c). % 16.37/16.56 exact (zenon_H84 zenon_H86). % 16.37/16.56 (* end of lemma zenon_L5_ *) % 16.37/16.56 assert (zenon_L6_ : forall (zenon_TU_dv : zenon_U) (zenon_TX_ei : zenon_U), (forall W : zenon_U, ((ssList W)->(((frontsegP zenon_TX_ei (nil))/\(frontsegP (nil) W))->(frontsegP zenon_TX_ei W)))) -> (ssList zenon_TU_dv) -> (frontsegP zenon_TX_ei (nil)) -> (frontsegP (nil) zenon_TU_dv) -> (~(frontsegP zenon_TX_ei zenon_TU_dv)) -> False). % 16.37/16.56 do 2 intro. intros zenon_H87 zenon_H7a zenon_H86 zenon_H88 zenon_H89. % 16.37/16.56 generalize (zenon_H87 zenon_TU_dv). zenon_intro zenon_H8a. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_H8a); [ zenon_intro zenon_H7d | zenon_intro zenon_H8b ]. % 16.37/16.56 exact (zenon_H7d zenon_H7a). % 16.37/16.56 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H8d | zenon_intro zenon_H8c ]. % 16.37/16.56 apply (zenon_notand_s _ _ zenon_H8d); [ zenon_intro zenon_H84 | zenon_intro zenon_H8e ]. % 16.37/16.56 exact (zenon_H84 zenon_H86). % 16.37/16.56 exact (zenon_H8e zenon_H88). % 16.37/16.56 exact (zenon_H89 zenon_H8c). % 16.37/16.56 (* end of lemma zenon_L6_ *) % 16.37/16.56 assert (zenon_L7_ : (~((nil) = (nil))) -> False). % 16.37/16.56 do 0 intro. intros zenon_H8f. % 16.37/16.56 apply zenon_H8f. apply refl_equal. % 16.37/16.56 (* end of lemma zenon_L7_ *) % 16.37/16.56 apply NNPP. intro zenon_G. % 16.37/16.56 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)))/\((~(neq W (nil)))\/(~(frontsegP X W)))))))))))))))) zenon_G); [ zenon_intro zenon_H90; idtac ]. % 16.37/16.56 elim zenon_H90. zenon_intro zenon_TU_dv. zenon_intro zenon_H91. % 16.37/16.56 apply (zenon_notimply_s _ _ zenon_H91). zenon_intro zenon_H7a. zenon_intro zenon_H92. % 16.37/16.56 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)))/\((~(neq W (nil)))\/(~(frontsegP X W)))))))))))))) zenon_H92); [ zenon_intro zenon_H93; idtac ]. % 16.37/16.56 elim zenon_H93. zenon_intro zenon_TV_fs. zenon_intro zenon_H95. % 16.37/16.56 apply (zenon_notimply_s _ _ zenon_H95). zenon_intro zenon_H97. zenon_intro zenon_H96. % 16.37/16.56 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(zenon_TV_fs = X))\/((~(zenon_TU_dv = W))\/((~(neq zenon_TV_fs (nil)))\/((neq zenon_TU_dv (nil))\/(((~((nil) = X))\/(~((nil) = W)))/\((~(neq W (nil)))\/(~(frontsegP X W)))))))))))) zenon_H96); [ zenon_intro zenon_H98; idtac ]. % 16.37/16.56 elim zenon_H98. zenon_intro zenon_TW_fx. zenon_intro zenon_H9a. % 16.37/16.56 apply (zenon_notimply_s _ _ zenon_H9a). zenon_intro zenon_H9c. zenon_intro zenon_H9b. % 16.37/16.56 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~(zenon_TV_fs = X))\/((~(zenon_TU_dv = zenon_TW_fx))\/((~(neq zenon_TV_fs (nil)))\/((neq zenon_TU_dv (nil))\/(((~((nil) = X))\/(~((nil) = zenon_TW_fx)))/\((~(neq zenon_TW_fx (nil)))\/(~(frontsegP X zenon_TW_fx)))))))))) zenon_H9b); [ zenon_intro zenon_H9d; idtac ]. % 16.37/16.56 elim zenon_H9d. zenon_intro zenon_TX_ei. zenon_intro zenon_H9e. % 16.37/16.56 apply (zenon_notimply_s _ _ zenon_H9e). zenon_intro zenon_H6c. zenon_intro zenon_H9f. % 16.37/16.56 apply (zenon_notor_s _ _ zenon_H9f). zenon_intro zenon_Ha1. zenon_intro zenon_Ha0. % 16.37/16.56 apply (zenon_notor_s _ _ zenon_Ha0). zenon_intro zenon_Ha3. zenon_intro zenon_Ha2. % 16.37/16.56 apply (zenon_notor_s _ _ zenon_Ha2). zenon_intro zenon_Ha5. zenon_intro zenon_Ha4. % 16.37/16.56 apply (zenon_notor_s _ _ zenon_Ha4). zenon_intro zenon_H61. zenon_intro zenon_Ha6. % 16.37/16.56 apply zenon_Ha5. zenon_intro zenon_Ha7. % 16.37/16.56 apply zenon_Ha3. zenon_intro zenon_Ha8. % 16.37/16.56 apply zenon_Ha1. zenon_intro zenon_Ha9. % 16.37/16.56 apply (zenon_notand_s _ _ zenon_Ha6); [ zenon_intro zenon_Hab | zenon_intro zenon_Haa ]. % 16.37/16.56 apply (zenon_notor_s _ _ zenon_Hab). zenon_intro zenon_Had. zenon_intro zenon_Hac. % 16.37/16.56 apply zenon_Had. zenon_intro zenon_Hae. % 16.37/16.56 cut ((neq zenon_TV_fs (nil)) = (neq zenon_TU_dv (nil))). % 16.37/16.56 intro zenon_D_pnotp. % 16.37/16.56 apply zenon_H61. % 16.37/16.56 rewrite <- zenon_D_pnotp. % 16.37/16.56 exact zenon_Ha7. % 16.37/16.56 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 16.37/16.56 cut ((zenon_TV_fs = zenon_TU_dv)); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 16.37/16.56 congruence. % 16.37/16.56 generalize (ax46 zenon_TX_ei). zenon_intro zenon_Hb0. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_Hb0); [ zenon_intro zenon_H73 | zenon_intro zenon_Hb1 ]. % 16.37/16.56 exact (zenon_H73 zenon_H6c). % 16.37/16.56 apply (zenon_equiv_s _ _ zenon_Hb1); [ zenon_intro zenon_H76; zenon_intro zenon_Hb2 | zenon_intro zenon_H6e; zenon_intro zenon_Hae ]. % 16.37/16.56 exact (zenon_Hb2 zenon_Hae). % 16.37/16.56 generalize (ax41 zenon_TU_dv). zenon_intro zenon_Hb3. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_Hb3); [ zenon_intro zenon_H7d | zenon_intro zenon_Hb4 ]. % 16.37/16.56 exact (zenon_H7d zenon_H7a). % 16.37/16.56 generalize (ax15 zenon_TU_dv). zenon_intro zenon_Hb5. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_Hb5); [ zenon_intro zenon_H7d | zenon_intro zenon_H60 ]. % 16.37/16.56 exact (zenon_H7d zenon_H7a). % 16.37/16.56 generalize (ax46 zenon_TU_dv). zenon_intro zenon_Hb6. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_Hb6); [ zenon_intro zenon_H7d | zenon_intro zenon_Hb7 ]. % 16.37/16.56 exact (zenon_H7d zenon_H7a). % 16.37/16.56 apply (zenon_equiv_s _ _ zenon_Hb7); [ zenon_intro zenon_H8e; zenon_intro zenon_H62 | zenon_intro zenon_H88; zenon_intro zenon_Hb8 ]. % 16.37/16.56 apply (zenon_L1_ zenon_TU_dv); trivial. % 16.37/16.56 generalize (ax40 zenon_TX_ei). zenon_intro zenon_Hb9. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_Hb9); [ zenon_intro zenon_H73 | zenon_intro zenon_Hba ]. % 16.37/16.56 exact (zenon_H73 zenon_H6c). % 16.37/16.56 cut ((zenon_TV_fs = zenon_TX_ei) = (zenon_TV_fs = zenon_TU_dv)). % 16.37/16.56 intro zenon_D_pnotp. % 16.37/16.56 apply zenon_Haf. % 16.37/16.56 rewrite <- zenon_D_pnotp. % 16.37/16.56 exact zenon_Ha9. % 16.37/16.56 cut ((zenon_TX_ei = zenon_TU_dv)); [idtac | apply NNPP; zenon_intro zenon_Hbb]. % 16.37/16.56 cut ((zenon_TV_fs = zenon_TV_fs)); [idtac | apply NNPP; zenon_intro zenon_Hbc]. % 16.37/16.56 congruence. % 16.37/16.56 apply zenon_Hbc. apply refl_equal. % 16.37/16.56 generalize (ax5 zenon_TX_ei). zenon_intro zenon_Hbd. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_Hbd); [ zenon_intro zenon_H73 | zenon_intro zenon_Hbe ]. % 16.37/16.56 exact (zenon_H73 zenon_H6c). % 16.37/16.56 generalize (zenon_Hb4 zenon_TX_ei). zenon_intro zenon_Hbf. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_Hbf); [ zenon_intro zenon_H73 | zenon_intro zenon_Hc0 ]. % 16.37/16.56 exact (zenon_H73 zenon_H6c). % 16.37/16.56 apply (zenon_imply_s _ _ zenon_Hc0); [ zenon_intro zenon_Hc2 | zenon_intro zenon_Hc1 ]. % 16.37/16.56 apply (zenon_notand_s _ _ zenon_Hc2); [ zenon_intro zenon_H6f | zenon_intro zenon_H89 ]. % 16.37/16.56 apply (zenon_L4_ zenon_TX_ei zenon_TU_dv); trivial. % 16.37/16.56 generalize (zenon_Hba (nil)). zenon_intro zenon_Hc3. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_Hc3); [ zenon_intro zenon_H66 | zenon_intro zenon_H87 ]. % 16.37/16.56 exact (zenon_H66 ax17). % 16.37/16.56 generalize (zenon_Hbe (nil)). zenon_intro zenon_Hc4. % 16.37/16.56 apply (zenon_imply_s _ _ zenon_Hc4); [ zenon_intro zenon_H66 | zenon_intro zenon_Hc5 ]. % 16.37/16.56 exact (zenon_H66 ax17). % 16.37/16.56 apply (zenon_equiv_s _ _ zenon_Hc5); [ zenon_intro zenon_H84; zenon_intro zenon_Hc7 | zenon_intro zenon_H86; zenon_intro zenon_Hc6 ]. % 16.37/16.56 apply (zenon_L5_ zenon_TX_ei); trivial. % 16.37/16.56 apply (zenon_L6_ zenon_TU_dv zenon_TX_ei); trivial. % 16.37/16.56 apply zenon_Hbb. apply sym_equal. exact zenon_Hc1. % 16.37/16.56 apply zenon_H8f. apply refl_equal. % 16.37/16.56 apply (zenon_notor_s _ _ zenon_Haa). zenon_intro zenon_Hc9. zenon_intro zenon_Hc8. % 16.37/16.56 apply zenon_Hc9. zenon_intro zenon_Hca. % 16.37/16.56 cut ((neq zenon_TW_fx (nil)) = (neq zenon_TU_dv (nil))). % 16.37/16.56 intro zenon_D_pnotp. % 16.37/16.56 apply zenon_H61. % 16.37/16.56 rewrite <- zenon_D_pnotp. % 16.37/16.56 exact zenon_Hca. % 16.37/16.56 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 16.37/16.56 cut ((zenon_TW_fx = zenon_TU_dv)); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 16.37/16.56 congruence. % 16.37/16.56 apply zenon_Hcb. apply sym_equal. exact zenon_Ha8. % 16.37/16.56 apply zenon_H8f. apply refl_equal. % 16.37/16.56 Qed. % 16.37/16.56 % SZS output end Proof % 16.37/16.56 (* END-PROOF *) % 16.37/16.56 nodes searched: 250276 % 16.37/16.56 max branch formulas: 8369 % 16.37/16.56 proof nodes created: 21894 % 16.37/16.56 formulas created: 1102345 % 16.37/16.56 %------------------------------------------------------------------------------