%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWC367+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n009.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 22:30:40 EDT 2022 % Result : Theorem 44.54s 44.80s % Output : Proof 44.54s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.08 % Problem : SWC367+1 : TPTP v8.1.0. Released v2.4.0. % 0.04/0.09 % Command : run_zenon %s %d % 0.08/0.28 % Computer : n009.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 : Sun Jun 12 12:41:38 EDT 2022 % 0.08/0.28 % CPUTime : % 44.54/44.80 (* PROOF-FOUND *) % 44.54/44.80 % SZS status Theorem % 44.54/44.80 (* BEGIN-PROOF *) % 44.54/44.80 % SZS output start Proof % 44.54/44.80 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))\/((rearsegP V U)\/(((~((nil) = X))\/(~((nil) = W)))/\((~(neq W (nil)))\/(~(rearsegP X W))))))))))))))). % 44.54/44.80 Proof. % 44.54/44.80 assert (zenon_L1_ : (~((nil) = (nil))) -> False). % 44.54/44.80 do 0 intro. intros zenon_H60. % 44.54/44.80 apply zenon_H60. apply refl_equal. % 44.54/44.80 (* end of lemma zenon_L1_ *) % 44.54/44.80 assert (zenon_L2_ : forall (zenon_TU_dy : zenon_U) (zenon_TV_dz : zenon_U), (forall W : zenon_U, ((ssList W)->(((rearsegP zenon_TV_dz (nil))/\(rearsegP (nil) W))->(rearsegP zenon_TV_dz W)))) -> (ssList zenon_TU_dy) -> (rearsegP zenon_TV_dz (nil)) -> (rearsegP (nil) zenon_TU_dy) -> (~(rearsegP zenon_TV_dz zenon_TU_dy)) -> False). % 44.54/44.80 do 2 intro. intros zenon_H61 zenon_H62 zenon_H63 zenon_H64 zenon_H65. % 44.54/44.80 generalize (zenon_H61 zenon_TU_dy). zenon_intro zenon_H68. % 44.54/44.80 apply (zenon_imply_s _ _ zenon_H68); [ zenon_intro zenon_H6a | zenon_intro zenon_H69 ]. % 44.54/44.80 exact (zenon_H6a zenon_H62). % 44.54/44.80 apply (zenon_imply_s _ _ zenon_H69); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ]. % 44.54/44.80 apply (zenon_notand_s _ _ zenon_H6c); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ]. % 44.54/44.80 exact (zenon_H6e zenon_H63). % 44.54/44.80 exact (zenon_H6d zenon_H64). % 44.54/44.80 exact (zenon_H65 zenon_H6b). % 44.54/44.80 (* end of lemma zenon_L2_ *) % 44.54/44.80 assert (zenon_L3_ : forall (zenon_TW_ek : zenon_U) (zenon_TX_el : zenon_U) (zenon_TU_dy : zenon_U) (zenon_TV_dz : zenon_U), (~(rearsegP zenon_TV_dz zenon_TU_dy)) -> (rearsegP zenon_TX_el zenon_TW_ek) -> (zenon_TU_dy = zenon_TW_ek) -> (zenon_TV_dz = zenon_TX_el) -> False). % 44.54/44.80 do 4 intro. intros zenon_H65 zenon_H6f zenon_H70 zenon_H71. % 44.54/44.80 cut ((rearsegP zenon_TX_el zenon_TW_ek) = (rearsegP zenon_TV_dz zenon_TU_dy)). % 44.54/44.80 intro zenon_D_pnotp. % 44.54/44.80 apply zenon_H65. % 44.54/44.80 rewrite <- zenon_D_pnotp. % 44.54/44.80 exact zenon_H6f. % 44.54/44.80 cut ((zenon_TW_ek = zenon_TU_dy)); [idtac | apply NNPP; zenon_intro zenon_H74]. % 44.54/44.80 cut ((zenon_TX_el = zenon_TV_dz)); [idtac | apply NNPP; zenon_intro zenon_H75]. % 44.54/44.80 congruence. % 44.54/44.80 apply zenon_H75. apply sym_equal. exact zenon_H71. % 44.54/44.80 apply zenon_H74. apply sym_equal. exact zenon_H70. % 44.54/44.80 (* end of lemma zenon_L3_ *) % 44.54/44.80 apply NNPP. intro zenon_G. % 44.54/44.80 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))\/((rearsegP V U)\/(((~((nil) = X))\/(~((nil) = W)))/\((~(neq W (nil)))\/(~(rearsegP X W))))))))))))))) zenon_G); [ zenon_intro zenon_H76; idtac ]. % 44.54/44.80 elim zenon_H76. zenon_intro zenon_TU_dy. zenon_intro zenon_H77. % 44.54/44.80 apply (zenon_notimply_s _ _ zenon_H77). zenon_intro zenon_H62. zenon_intro zenon_H78. % 44.54/44.80 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))\/((rearsegP V zenon_TU_dy)\/(((~((nil) = X))\/(~((nil) = W)))/\((~(neq W (nil)))\/(~(rearsegP X W))))))))))))) zenon_H78); [ zenon_intro zenon_H79; idtac ]. % 44.54/44.80 elim zenon_H79. zenon_intro zenon_TV_dz. zenon_intro zenon_H7a. % 44.54/44.80 apply (zenon_notimply_s _ _ zenon_H7a). zenon_intro zenon_H7c. zenon_intro zenon_H7b. % 44.54/44.80 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(zenon_TV_dz = X))\/((~(zenon_TU_dy = W))\/((rearsegP zenon_TV_dz zenon_TU_dy)\/(((~((nil) = X))\/(~((nil) = W)))/\((~(neq W (nil)))\/(~(rearsegP X W))))))))))) zenon_H7b); [ zenon_intro zenon_H7d; idtac ]. % 44.54/44.80 elim zenon_H7d. zenon_intro zenon_TW_ek. zenon_intro zenon_H7e. % 44.54/44.80 apply (zenon_notimply_s _ _ zenon_H7e). zenon_intro zenon_H80. zenon_intro zenon_H7f. % 44.54/44.80 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~(zenon_TV_dz = X))\/((~(zenon_TU_dy = zenon_TW_ek))\/((rearsegP zenon_TV_dz zenon_TU_dy)\/(((~((nil) = X))\/(~((nil) = zenon_TW_ek)))/\((~(neq zenon_TW_ek (nil)))\/(~(rearsegP X zenon_TW_ek))))))))) zenon_H7f); [ zenon_intro zenon_H81; idtac ]. % 44.54/44.80 elim zenon_H81. zenon_intro zenon_TX_el. zenon_intro zenon_H82. % 44.54/44.80 apply (zenon_notimply_s _ _ zenon_H82). zenon_intro zenon_H84. zenon_intro zenon_H83. % 44.54/44.80 apply (zenon_notor_s _ _ zenon_H83). zenon_intro zenon_H86. zenon_intro zenon_H85. % 44.54/44.81 apply (zenon_notor_s _ _ zenon_H85). zenon_intro zenon_H88. zenon_intro zenon_H87. % 44.54/44.81 apply (zenon_notor_s _ _ zenon_H87). zenon_intro zenon_H65. zenon_intro zenon_H89. % 44.54/44.81 apply zenon_H88. zenon_intro zenon_H70. % 44.54/44.81 apply zenon_H86. zenon_intro zenon_H71. % 44.54/44.81 apply (zenon_notand_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8a ]. % 44.54/44.81 apply (zenon_notor_s _ _ zenon_H8b). zenon_intro zenon_H8d. zenon_intro zenon_H8c. % 44.54/44.81 apply zenon_H8c. zenon_intro zenon_H8e. % 44.54/44.81 generalize (ax52 zenon_TU_dy). zenon_intro zenon_H8f. % 44.54/44.81 apply (zenon_imply_s _ _ zenon_H8f); [ zenon_intro zenon_H6a | zenon_intro zenon_H90 ]. % 44.54/44.81 exact (zenon_H6a zenon_H62). % 44.54/44.81 apply (zenon_equiv_s _ _ zenon_H90); [ zenon_intro zenon_H6d; zenon_intro zenon_H92 | zenon_intro zenon_H64; zenon_intro zenon_H91 ]. % 44.54/44.81 cut (((nil) = zenon_TW_ek) = ((nil) = zenon_TU_dy)). % 44.54/44.81 intro zenon_D_pnotp. % 44.54/44.81 apply zenon_H92. % 44.54/44.81 rewrite <- zenon_D_pnotp. % 44.54/44.81 exact zenon_H8e. % 44.54/44.81 cut ((zenon_TW_ek = zenon_TU_dy)); [idtac | apply NNPP; zenon_intro zenon_H74]. % 44.54/44.81 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 44.54/44.81 congruence. % 44.54/44.81 apply zenon_H60. apply refl_equal. % 44.54/44.81 apply zenon_H74. apply sym_equal. exact zenon_H70. % 44.54/44.81 generalize (ax47 zenon_TV_dz). zenon_intro zenon_H93. % 44.54/44.81 apply (zenon_imply_s _ _ zenon_H93); [ zenon_intro zenon_H95 | zenon_intro zenon_H94 ]. % 44.54/44.81 exact (zenon_H95 zenon_H7c). % 44.54/44.81 generalize (zenon_H94 (nil)). zenon_intro zenon_H96. % 44.54/44.81 apply (zenon_imply_s _ _ zenon_H96); [ zenon_intro zenon_H97 | zenon_intro zenon_H61 ]. % 44.54/44.81 exact (zenon_H97 ax17). % 44.54/44.81 generalize (ax51 zenon_TV_dz). zenon_intro zenon_H98. % 44.54/44.81 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H95 | zenon_intro zenon_H63 ]. % 44.54/44.81 exact (zenon_H95 zenon_H7c). % 44.54/44.81 apply (zenon_L2_ zenon_TU_dy zenon_TV_dz); trivial. % 44.54/44.81 apply (zenon_notor_s _ _ zenon_H8a). zenon_intro zenon_H9a. zenon_intro zenon_H99. % 44.54/44.81 apply zenon_H99. zenon_intro zenon_H6f. % 44.54/44.81 apply (zenon_L3_ zenon_TW_ek zenon_TX_el zenon_TU_dy zenon_TV_dz); trivial. % 44.54/44.81 Qed. % 44.54/44.81 % SZS output end Proof % 44.54/44.81 (* END-PROOF *) % 44.54/44.81 nodes searched: 408599 % 44.54/44.81 max branch formulas: 15173 % 44.54/44.81 proof nodes created: 27188 % 44.54/44.81 formulas created: 2116118 % 44.54/44.81 %------------------------------------------------------------------------------