%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWC044+1 : TPTP v8.1.0. Released v2.4.0. % 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 : Tue Jul 19 22:29:01 EDT 2022 % Result : Theorem 30.50s 30.71s % Output : Proof 30.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SWC044+1 : TPTP v8.1.0. Released v2.4.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n024.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 05:11:34 EDT 2022 % 0.13/0.34 % CPUTime : % 30.50/30.71 (* PROOF-FOUND *) % 30.50/30.71 % SZS status Theorem % 30.50/30.71 (* BEGIN-PROOF *) % 30.50/30.71 % SZS output start Proof % 30.50/30.71 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)->((~((nil) = V))\/((~(V = X))\/((~(U = W))\/((~(rearsegP X W))\/((nil) = U))))))))))))). % 30.50/30.71 Proof. % 30.50/30.71 assert (zenon_L1_ : (~((nil) = (nil))) -> False). % 30.50/30.71 do 0 intro. intros zenon_H60. % 30.50/30.71 apply zenon_H60. apply refl_equal. % 30.50/30.71 (* end of lemma zenon_L1_ *) % 30.50/30.71 assert (zenon_L2_ : forall (zenon_TW_dv : zenon_U), (ssList zenon_TW_dv) -> (~(rearsegP zenon_TW_dv (nil))) -> False). % 30.50/30.71 do 1 intro. intros zenon_H61 zenon_H62. % 30.50/30.71 generalize (ax51 zenon_TW_dv). zenon_intro zenon_H64. % 30.50/30.71 apply (zenon_imply_s _ _ zenon_H64); [ zenon_intro zenon_H66 | zenon_intro zenon_H65 ]. % 30.50/30.71 exact (zenon_H66 zenon_H61). % 30.50/30.71 exact (zenon_H62 zenon_H65). % 30.50/30.71 (* end of lemma zenon_L2_ *) % 30.50/30.71 assert (zenon_L3_ : forall (zenon_TW_dv : zenon_U) (zenon_TX_ed : zenon_U), (ssList zenon_TX_ed) -> (~(rearsegP (nil) zenon_TW_dv)) -> (rearsegP zenon_TX_ed zenon_TW_dv) -> (ssList zenon_TW_dv) -> ((nil) = zenon_TX_ed) -> False). % 30.50/30.71 do 2 intro. intros zenon_H67 zenon_H68 zenon_H69 zenon_H61 zenon_H6a. % 30.50/30.71 generalize (ax52 zenon_TX_ed). zenon_intro zenon_H6c. % 30.50/30.71 apply (zenon_imply_s _ _ zenon_H6c); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 30.50/30.71 exact (zenon_H6e zenon_H67). % 30.50/30.71 apply (zenon_equiv_s _ _ zenon_H6d); [ zenon_intro zenon_H71; zenon_intro zenon_H70 | zenon_intro zenon_H6f; zenon_intro zenon_H6a ]. % 30.50/30.71 exact (zenon_H70 zenon_H6a). % 30.50/30.71 generalize (ax47 (nil)). zenon_intro zenon_H72. % 30.50/30.71 apply (zenon_imply_s _ _ zenon_H72); [ zenon_intro zenon_H74 | zenon_intro zenon_H73 ]. % 30.50/30.71 exact (zenon_H74 ax17). % 30.50/30.71 generalize (zenon_H73 zenon_TX_ed). zenon_intro zenon_H75. % 30.50/30.71 apply (zenon_imply_s _ _ zenon_H75); [ zenon_intro zenon_H6e | zenon_intro zenon_H76 ]. % 30.50/30.71 exact (zenon_H6e zenon_H67). % 30.50/30.71 generalize (zenon_H76 zenon_TW_dv). zenon_intro zenon_H77. % 30.50/30.71 apply (zenon_imply_s _ _ zenon_H77); [ zenon_intro zenon_H66 | zenon_intro zenon_H78 ]. % 30.50/30.71 exact (zenon_H66 zenon_H61). % 30.50/30.71 apply (zenon_imply_s _ _ zenon_H78); [ zenon_intro zenon_H7a | zenon_intro zenon_H79 ]. % 30.50/30.71 apply (zenon_notand_s _ _ zenon_H7a); [ zenon_intro zenon_H71 | zenon_intro zenon_H7b ]. % 30.50/30.71 exact (zenon_H71 zenon_H6f). % 30.50/30.71 exact (zenon_H7b zenon_H69). % 30.50/30.71 exact (zenon_H68 zenon_H79). % 30.50/30.71 (* end of lemma zenon_L3_ *) % 30.50/30.71 assert (zenon_L4_ : forall (zenon_TX_ed : zenon_U) (zenon_TW_dv : zenon_U), (forall V : zenon_U, ((ssList V)->(((rearsegP zenon_TW_dv V)/\(rearsegP V zenon_TW_dv))->(zenon_TW_dv = V)))) -> (ssList zenon_TW_dv) -> (ssList zenon_TX_ed) -> (rearsegP zenon_TX_ed zenon_TW_dv) -> ((nil) = zenon_TX_ed) -> (~(zenon_TW_dv = (nil))) -> False). % 30.50/30.71 do 2 intro. intros zenon_H7c zenon_H61 zenon_H67 zenon_H69 zenon_H6a zenon_H7d. % 30.50/30.71 generalize (zenon_H7c (nil)). zenon_intro zenon_H7e. % 30.50/30.71 apply (zenon_imply_s _ _ zenon_H7e); [ zenon_intro zenon_H74 | zenon_intro zenon_H7f ]. % 30.50/30.71 exact (zenon_H74 ax17). % 30.50/30.71 apply (zenon_imply_s _ _ zenon_H7f); [ zenon_intro zenon_H81 | zenon_intro zenon_H80 ]. % 30.50/30.71 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H62 | zenon_intro zenon_H68 ]. % 30.50/30.71 apply (zenon_L2_ zenon_TW_dv); trivial. % 30.50/30.71 apply (zenon_L3_ zenon_TW_dv zenon_TX_ed); trivial. % 30.50/30.71 exact (zenon_H7d zenon_H80). % 30.50/30.71 (* end of lemma zenon_L4_ *) % 30.50/30.71 apply NNPP. intro zenon_G. % 30.50/30.71 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)->((~((nil) = V))\/((~(V = X))\/((~(U = W))\/((~(rearsegP X W))\/((nil) = U))))))))))))) zenon_G); [ zenon_intro zenon_H82; idtac ]. % 30.50/30.71 elim zenon_H82. zenon_intro zenon_TU_fb. zenon_intro zenon_H84. % 30.50/30.71 apply (zenon_notimply_s _ _ zenon_H84). zenon_intro zenon_H86. zenon_intro zenon_H85. % 30.50/30.71 apply (zenon_notallex_s (fun V : zenon_U => ((ssList V)->(forall W : zenon_U, ((ssList W)->(forall X : zenon_U, ((ssList X)->((~((nil) = V))\/((~(V = X))\/((~(zenon_TU_fb = W))\/((~(rearsegP X W))\/((nil) = zenon_TU_fb))))))))))) zenon_H85); [ zenon_intro zenon_H87; idtac ]. % 30.50/30.71 elim zenon_H87. zenon_intro zenon_TV_fg. zenon_intro zenon_H89. % 30.50/30.71 apply (zenon_notimply_s _ _ zenon_H89). zenon_intro zenon_H8b. zenon_intro zenon_H8a. % 30.50/30.71 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~((nil) = zenon_TV_fg))\/((~(zenon_TV_fg = X))\/((~(zenon_TU_fb = W))\/((~(rearsegP X W))\/((nil) = zenon_TU_fb))))))))) zenon_H8a); [ zenon_intro zenon_H8c; idtac ]. % 30.50/30.71 elim zenon_H8c. zenon_intro zenon_TW_dv. zenon_intro zenon_H8d. % 30.50/30.71 apply (zenon_notimply_s _ _ zenon_H8d). zenon_intro zenon_H61. zenon_intro zenon_H8e. % 30.50/30.71 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~((nil) = zenon_TV_fg))\/((~(zenon_TV_fg = X))\/((~(zenon_TU_fb = zenon_TW_dv))\/((~(rearsegP X zenon_TW_dv))\/((nil) = zenon_TU_fb))))))) zenon_H8e); [ zenon_intro zenon_H8f; idtac ]. % 30.50/30.71 elim zenon_H8f. zenon_intro zenon_TX_ed. zenon_intro zenon_H90. % 30.50/30.71 apply (zenon_notimply_s _ _ zenon_H90). zenon_intro zenon_H67. zenon_intro zenon_H91. % 30.50/30.71 apply (zenon_notor_s _ _ zenon_H91). zenon_intro zenon_H93. zenon_intro zenon_H92. % 30.50/30.71 apply (zenon_notor_s _ _ zenon_H92). zenon_intro zenon_H95. zenon_intro zenon_H94. % 30.50/30.71 apply (zenon_notor_s _ _ zenon_H94). zenon_intro zenon_H97. zenon_intro zenon_H96. % 30.50/30.71 apply (zenon_notor_s _ _ zenon_H96). zenon_intro zenon_H99. zenon_intro zenon_H98. % 30.50/30.71 apply zenon_H99. zenon_intro zenon_H69. % 30.50/30.71 apply zenon_H97. zenon_intro zenon_H9a. % 30.50/30.71 apply zenon_H95. zenon_intro zenon_H9b. % 30.50/30.71 apply zenon_H93. zenon_intro zenon_H9c. % 30.50/30.71 elim (classic (zenon_TU_fb = zenon_TU_fb)); [ zenon_intro zenon_H9d | zenon_intro zenon_H9e ]. % 30.50/30.71 cut ((zenon_TU_fb = zenon_TU_fb) = ((nil) = zenon_TU_fb)). % 30.50/30.71 intro zenon_D_pnotp. % 30.50/30.71 apply zenon_H98. % 30.50/30.71 rewrite <- zenon_D_pnotp. % 30.50/30.71 exact zenon_H9d. % 30.50/30.71 cut ((zenon_TU_fb = zenon_TU_fb)); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 30.50/30.71 cut ((zenon_TU_fb = (nil))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 30.50/30.71 congruence. % 30.50/30.71 cut ((zenon_TU_fb = zenon_TW_dv) = (zenon_TU_fb = (nil))). % 30.50/30.71 intro zenon_D_pnotp. % 30.50/30.71 apply zenon_H9f. % 30.50/30.71 rewrite <- zenon_D_pnotp. % 30.50/30.71 exact zenon_H9a. % 30.50/30.71 cut ((zenon_TW_dv = (nil))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 30.50/30.71 cut ((zenon_TU_fb = zenon_TU_fb)); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 30.50/30.71 congruence. % 30.50/30.71 apply zenon_H9e. apply refl_equal. % 30.50/30.71 generalize (ax48 zenon_TW_dv). zenon_intro zenon_Ha0. % 30.50/30.71 apply (zenon_imply_s _ _ zenon_Ha0); [ zenon_intro zenon_H66 | zenon_intro zenon_H7c ]. % 30.50/30.71 exact (zenon_H66 zenon_H61). % 30.50/30.71 generalize (ax46 zenon_TX_ed). zenon_intro zenon_Ha1. % 30.50/30.71 apply (zenon_imply_s _ _ zenon_Ha1); [ zenon_intro zenon_H6e | zenon_intro zenon_Ha2 ]. % 30.50/30.71 exact (zenon_H6e zenon_H67). % 30.50/30.71 apply (zenon_equiv_s _ _ zenon_Ha2); [ zenon_intro zenon_Ha4; zenon_intro zenon_H70 | zenon_intro zenon_Ha3; zenon_intro zenon_H6a ]. % 30.50/30.71 cut (((nil) = zenon_TV_fg) = ((nil) = zenon_TX_ed)). % 30.50/30.71 intro zenon_D_pnotp. % 30.50/30.71 apply zenon_H70. % 30.50/30.71 rewrite <- zenon_D_pnotp. % 30.50/30.71 exact zenon_H9c. % 30.50/30.71 cut ((zenon_TV_fg = zenon_TX_ed)); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 30.50/30.71 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 30.50/30.71 congruence. % 30.50/30.71 apply zenon_H60. apply refl_equal. % 30.50/30.71 exact (zenon_Ha5 zenon_H9b). % 30.50/30.71 apply (zenon_L4_ zenon_TX_ed zenon_TW_dv); trivial. % 30.50/30.71 apply zenon_H9e. apply refl_equal. % 30.50/30.71 apply zenon_H9e. apply refl_equal. % 30.50/30.71 Qed. % 30.50/30.71 % SZS output end Proof % 30.50/30.71 (* END-PROOF *) % 30.50/30.71 nodes searched: 373427 % 30.50/30.71 max branch formulas: 10963 % 30.50/30.71 proof nodes created: 30127 % 30.50/30.71 formulas created: 1756040 % 30.50/30.71 %------------------------------------------------------------------------------