%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWC352+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n032.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 22:30:35 EDT 2022 % Result : Theorem 20.89s 21.11s % Output : Proof 20.89s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.09 % Problem : SWC352+1 : TPTP v8.1.0. Released v2.4.0. % 0.00/0.09 % Command : run_zenon %s %d % 0.08/0.28 % Computer : n032.cluster.edu % 0.08/0.28 % Model : x86_64 x86_64 % 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.08/0.28 % Memory : 8042.1875MB % 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64 % 0.08/0.28 % CPULimit : 300 % 0.08/0.28 % WCLimit : 600 % 0.08/0.28 % DateTime : Sat Jun 11 22:48:55 EDT 2022 % 0.08/0.29 % CPUTime : % 20.89/21.11 (* PROOF-FOUND *) % 20.89/21.11 % SZS status Theorem % 20.89/21.11 (* BEGIN-PROOF *) % 20.89/21.11 % SZS output start Proof % 20.89/21.11 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))\/((frontsegP V U)\/(((~((nil) = W))/\((nil) = X))\/((neq X (nil))/\((~(neq W (nil)))\/(~(frontsegP X W)))))))))))))))). % 20.89/21.11 Proof. % 20.89/21.11 assert (zenon_L1_ : forall (zenon_TW_dw : zenon_U) (zenon_TX_dx : zenon_U) (zenon_TU_dy : zenon_U) (zenon_TV_dz : zenon_U), (~(frontsegP zenon_TV_dz zenon_TU_dy)) -> (frontsegP zenon_TX_dx zenon_TW_dw) -> (zenon_TU_dy = zenon_TW_dw) -> (zenon_TV_dz = zenon_TX_dx) -> False). % 20.89/21.11 do 4 intro. intros zenon_H60 zenon_H61 zenon_H62 zenon_H63. % 20.89/21.11 cut ((frontsegP zenon_TX_dx zenon_TW_dw) = (frontsegP zenon_TV_dz zenon_TU_dy)). % 20.89/21.11 intro zenon_D_pnotp. % 20.89/21.11 apply zenon_H60. % 20.89/21.11 rewrite <- zenon_D_pnotp. % 20.89/21.11 exact zenon_H61. % 20.89/21.11 cut ((zenon_TW_dw = zenon_TU_dy)); [idtac | apply NNPP; zenon_intro zenon_H68]. % 20.89/21.11 cut ((zenon_TX_dx = zenon_TV_dz)); [idtac | apply NNPP; zenon_intro zenon_H69]. % 20.89/21.11 congruence. % 20.89/21.11 apply zenon_H69. apply sym_equal. exact zenon_H63. % 20.89/21.11 apply zenon_H68. apply sym_equal. exact zenon_H62. % 20.89/21.11 (* end of lemma zenon_L1_ *) % 20.89/21.11 assert (zenon_L2_ : forall (zenon_TU_dy : zenon_U) (zenon_TV_dz : zenon_U) (zenon_TW_dw : zenon_U) (zenon_TX_dx : zenon_U), (forall W : zenon_U, ((ssList W)->(((frontsegP zenon_TX_dx (nil))/\(frontsegP (nil) W))->(frontsegP zenon_TX_dx W)))) -> (ssList zenon_TW_dw) -> (frontsegP zenon_TX_dx (nil)) -> (frontsegP (nil) zenon_TW_dw) -> (~(frontsegP zenon_TV_dz zenon_TU_dy)) -> (zenon_TU_dy = zenon_TW_dw) -> (zenon_TV_dz = zenon_TX_dx) -> False). % 20.89/21.11 do 4 intro. intros zenon_H6a zenon_H6b zenon_H6c zenon_H6d zenon_H60 zenon_H62 zenon_H63. % 20.89/21.11 generalize (zenon_H6a zenon_TW_dw). zenon_intro zenon_H6e. % 20.89/21.11 apply (zenon_imply_s _ _ zenon_H6e); [ zenon_intro zenon_H70 | zenon_intro zenon_H6f ]. % 20.89/21.11 exact (zenon_H70 zenon_H6b). % 20.89/21.11 apply (zenon_imply_s _ _ zenon_H6f); [ zenon_intro zenon_H71 | zenon_intro zenon_H61 ]. % 20.89/21.11 apply (zenon_notand_s _ _ zenon_H71); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ]. % 20.89/21.11 exact (zenon_H73 zenon_H6c). % 20.89/21.11 exact (zenon_H72 zenon_H6d). % 20.89/21.11 apply (zenon_L1_ zenon_TW_dw zenon_TX_dx zenon_TU_dy zenon_TV_dz); trivial. % 20.89/21.11 (* end of lemma zenon_L2_ *) % 20.89/21.11 assert (zenon_L3_ : forall (zenon_TX_dx : zenon_U), (forall V : zenon_U, ((ssList V)->((neq zenon_TX_dx V)<->(~(zenon_TX_dx = V))))) -> (~(neq zenon_TX_dx (nil))) -> (~((nil) = zenon_TX_dx)) -> False). % 20.89/21.11 do 1 intro. intros zenon_H74 zenon_H75 zenon_H76. % 20.89/21.11 generalize (zenon_H74 (nil)). zenon_intro zenon_H77. % 20.89/21.11 apply (zenon_imply_s _ _ zenon_H77); [ zenon_intro zenon_H79 | zenon_intro zenon_H78 ]. % 20.89/21.11 exact (zenon_H79 ax17). % 20.89/21.11 apply (zenon_equiv_s _ _ zenon_H78); [ zenon_intro zenon_H75; zenon_intro zenon_H7c | zenon_intro zenon_H7b; zenon_intro zenon_H7a ]. % 20.89/21.11 apply zenon_H7c. zenon_intro zenon_H7d. % 20.89/21.11 apply zenon_H76. apply sym_equal. exact zenon_H7d. % 20.89/21.11 exact (zenon_H75 zenon_H7b). % 20.89/21.11 (* end of lemma zenon_L3_ *) % 20.89/21.11 assert (zenon_L4_ : forall (zenon_TU_dy : zenon_U) (zenon_TV_dz : zenon_U) (zenon_TX_dx : zenon_U) (zenon_TW_dw : zenon_U), (~((~(neq zenon_TW_dw (nil)))\/(~(frontsegP zenon_TX_dx zenon_TW_dw)))) -> (~(frontsegP zenon_TV_dz zenon_TU_dy)) -> (zenon_TU_dy = zenon_TW_dw) -> (zenon_TV_dz = zenon_TX_dx) -> False). % 20.89/21.11 do 4 intro. intros zenon_H7e zenon_H60 zenon_H62 zenon_H63. % 20.89/21.11 apply (zenon_notor_s _ _ zenon_H7e). zenon_intro zenon_H80. zenon_intro zenon_H7f. % 20.89/21.11 apply zenon_H7f. zenon_intro zenon_H61. % 20.89/21.11 apply (zenon_L1_ zenon_TW_dw zenon_TX_dx zenon_TU_dy zenon_TV_dz); trivial. % 20.89/21.11 (* end of lemma zenon_L4_ *) % 20.89/21.11 assert (zenon_L5_ : forall (zenon_TU_dy : zenon_U) (zenon_TV_dz : zenon_U) (zenon_TW_dw : zenon_U) (zenon_TX_dx : zenon_U), (~((neq zenon_TX_dx (nil))/\((~(neq zenon_TW_dw (nil)))\/(~(frontsegP zenon_TX_dx zenon_TW_dw))))) -> (zenon_TV_dz = zenon_TX_dx) -> (zenon_TU_dy = zenon_TW_dw) -> (~(frontsegP zenon_TV_dz zenon_TU_dy)) -> (~((nil) = zenon_TX_dx)) -> (ssList zenon_TX_dx) -> False). % 20.89/21.11 do 4 intro. intros zenon_H81 zenon_H63 zenon_H62 zenon_H60 zenon_H76 zenon_H82. % 20.89/21.11 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H75 | zenon_intro zenon_H7e ]. % 20.89/21.11 generalize (ax15 zenon_TX_dx). zenon_intro zenon_H83. % 20.89/21.11 apply (zenon_imply_s _ _ zenon_H83); [ zenon_intro zenon_H84 | zenon_intro zenon_H74 ]. % 20.89/21.11 exact (zenon_H84 zenon_H82). % 20.89/21.11 apply (zenon_L3_ zenon_TX_dx); trivial. % 20.89/21.11 apply (zenon_L4_ zenon_TU_dy zenon_TV_dz zenon_TX_dx zenon_TW_dw); trivial. % 20.89/21.11 (* end of lemma zenon_L5_ *) % 20.89/21.11 apply NNPP. intro zenon_G. % 20.89/21.11 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))\/((frontsegP V U)\/(((~((nil) = W))/\((nil) = X))\/((neq X (nil))/\((~(neq W (nil)))\/(~(frontsegP X W)))))))))))))))) zenon_G); [ zenon_intro zenon_H85; idtac ]. % 20.89/21.11 elim zenon_H85. zenon_intro zenon_TU_dy. zenon_intro zenon_H86. % 20.89/21.11 apply (zenon_notimply_s _ _ zenon_H86). zenon_intro zenon_H88. zenon_intro zenon_H87. % 20.89/21.11 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_dy = W))\/((frontsegP V zenon_TU_dy)\/(((~((nil) = W))/\((nil) = X))\/((neq X (nil))/\((~(neq W (nil)))\/(~(frontsegP X W)))))))))))))) zenon_H87); [ zenon_intro zenon_H89; idtac ]. % 20.89/21.11 elim zenon_H89. zenon_intro zenon_TV_dz. zenon_intro zenon_H8a. % 20.89/21.11 apply (zenon_notimply_s _ _ zenon_H8a). zenon_intro zenon_H8c. zenon_intro zenon_H8b. % 20.89/21.11 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(zenon_TV_dz = X))\/((~(zenon_TU_dy = W))\/((frontsegP zenon_TV_dz zenon_TU_dy)\/(((~((nil) = W))/\((nil) = X))\/((neq X (nil))/\((~(neq W (nil)))\/(~(frontsegP X W)))))))))))) zenon_H8b); [ zenon_intro zenon_H8d; idtac ]. % 20.89/21.11 elim zenon_H8d. zenon_intro zenon_TW_dw. zenon_intro zenon_H8e. % 20.89/21.11 apply (zenon_notimply_s _ _ zenon_H8e). zenon_intro zenon_H6b. zenon_intro zenon_H8f. % 20.89/21.11 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~(zenon_TV_dz = X))\/((~(zenon_TU_dy = zenon_TW_dw))\/((frontsegP zenon_TV_dz zenon_TU_dy)\/(((~((nil) = zenon_TW_dw))/\((nil) = X))\/((neq X (nil))/\((~(neq zenon_TW_dw (nil)))\/(~(frontsegP X zenon_TW_dw)))))))))) zenon_H8f); [ zenon_intro zenon_H90; idtac ]. % 20.89/21.11 elim zenon_H90. zenon_intro zenon_TX_dx. zenon_intro zenon_H91. % 20.89/21.11 apply (zenon_notimply_s _ _ zenon_H91). zenon_intro zenon_H82. zenon_intro zenon_H92. % 20.89/21.11 apply (zenon_notor_s _ _ zenon_H92). zenon_intro zenon_H94. zenon_intro zenon_H93. % 20.89/21.11 apply (zenon_notor_s _ _ zenon_H93). zenon_intro zenon_H96. zenon_intro zenon_H95. % 20.89/21.11 apply (zenon_notor_s _ _ zenon_H95). zenon_intro zenon_H60. zenon_intro zenon_H97. % 20.89/21.11 apply (zenon_notor_s _ _ zenon_H97). zenon_intro zenon_H98. zenon_intro zenon_H81. % 20.89/21.11 apply zenon_H96. zenon_intro zenon_H62. % 20.89/21.11 apply zenon_H94. zenon_intro zenon_H63. % 20.89/21.11 apply (zenon_notand_s _ _ zenon_H98); [ zenon_intro zenon_H99 | zenon_intro zenon_H76 ]. % 20.89/21.11 apply zenon_H99. zenon_intro zenon_H9a. % 20.89/21.11 generalize (ax46 zenon_TW_dw). zenon_intro zenon_H9b. % 20.89/21.11 apply (zenon_imply_s _ _ zenon_H9b); [ zenon_intro zenon_H70 | zenon_intro zenon_H9c ]. % 20.89/21.11 exact (zenon_H70 zenon_H6b). % 20.89/21.11 apply (zenon_equiv_s _ _ zenon_H9c); [ zenon_intro zenon_H72; zenon_intro zenon_H9d | zenon_intro zenon_H6d; zenon_intro zenon_H9a ]. % 20.89/21.11 exact (zenon_H9d zenon_H9a). % 20.89/21.11 generalize (ax40 zenon_TX_dx). zenon_intro zenon_H9e. % 20.89/21.11 apply (zenon_imply_s _ _ zenon_H9e); [ zenon_intro zenon_H84 | zenon_intro zenon_H9f ]. % 20.89/21.11 exact (zenon_H84 zenon_H82). % 20.89/21.11 generalize (zenon_H9f (nil)). zenon_intro zenon_Ha0. % 20.89/21.11 apply (zenon_imply_s _ _ zenon_Ha0); [ zenon_intro zenon_H79 | zenon_intro zenon_H6a ]. % 20.89/21.11 exact (zenon_H79 ax17). % 20.89/21.11 generalize (ax42 (nil)). zenon_intro zenon_Ha1. % 20.89/21.11 apply (zenon_imply_s _ _ zenon_Ha1); [ zenon_intro zenon_H79 | zenon_intro zenon_Ha2 ]. % 20.89/21.11 exact (zenon_H79 ax17). % 20.89/21.11 generalize (zenon_H6a (nil)). zenon_intro zenon_Ha3. % 20.89/21.11 apply (zenon_imply_s _ _ zenon_Ha3); [ zenon_intro zenon_H79 | zenon_intro zenon_Ha4 ]. % 20.89/21.11 exact (zenon_H79 ax17). % 20.89/21.11 apply (zenon_imply_s _ _ zenon_Ha4); [ zenon_intro zenon_Ha5 | zenon_intro zenon_H6c ]. % 20.89/21.11 apply (zenon_notand_s _ _ zenon_Ha5); [ zenon_intro zenon_H73 | zenon_intro zenon_Ha6 ]. % 20.89/21.11 generalize (ax45 zenon_TX_dx). zenon_intro zenon_Ha7. % 20.89/21.11 apply (zenon_imply_s _ _ zenon_Ha7); [ zenon_intro zenon_H84 | zenon_intro zenon_H6c ]. % 20.89/21.11 exact (zenon_H84 zenon_H82). % 20.89/21.11 exact (zenon_H73 zenon_H6c). % 20.89/21.11 exact (zenon_Ha6 zenon_Ha2). % 20.89/21.11 apply (zenon_L2_ zenon_TU_dy zenon_TV_dz zenon_TW_dw zenon_TX_dx); trivial. % 20.89/21.11 apply (zenon_L5_ zenon_TU_dy zenon_TV_dz zenon_TW_dw zenon_TX_dx); trivial. % 20.89/21.11 Qed. % 20.89/21.11 % SZS output end Proof % 20.89/21.11 (* END-PROOF *) % 20.89/21.11 nodes searched: 310058 % 20.89/21.11 max branch formulas: 9303 % 20.89/21.11 proof nodes created: 25193 % 20.89/21.11 formulas created: 1392916 % 20.89/21.11 %------------------------------------------------------------------------------