%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWC097+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 22:29:16 EDT 2022 % Result : Theorem 0.73s 0.92s % Output : Proof 0.73s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : SWC097+1 : TPTP v8.1.0. Released v2.4.0. % 0.12/0.14 % Command : run_zenon %s %d % 0.14/0.35 % Computer : n025.cluster.edu % 0.14/0.35 % Model : x86_64 x86_64 % 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.14/0.35 % Memory : 8042.1875MB % 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.14/0.35 % CPULimit : 300 % 0.14/0.35 % WCLimit : 600 % 0.14/0.35 % DateTime : Sun Jun 12 23:57:23 EDT 2022 % 0.14/0.35 % CPUTime : % 0.73/0.92 (* PROOF-FOUND *) % 0.73/0.92 % SZS status Theorem % 0.73/0.92 (* BEGIN-PROOF *) % 0.73/0.92 % SZS output start Proof % 0.73/0.92 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)))\/((exists Y : zenon_U, ((ssItem Y)/\((app U (cons Y (nil))) = V)))\/(forall Z : zenon_U, ((ssItem Z)->(~((app W (cons Z (nil))) = X))))))/\((~(neq V (nil)))\/(neq X (nil)))))))))))))). % 0.73/0.92 Proof. % 0.73/0.92 assert (zenon_L1_ : (~((nil) = (nil))) -> False). % 0.73/0.92 do 0 intro. intros zenon_H60. % 0.73/0.92 apply zenon_H60. apply refl_equal. % 0.73/0.92 (* end of lemma zenon_L1_ *) % 0.73/0.92 apply NNPP. intro zenon_G. % 0.73/0.92 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)))\/((exists Y : zenon_U, ((ssItem Y)/\((app U (cons Y (nil))) = V)))\/(forall Z : zenon_U, ((ssItem Z)->(~((app W (cons Z (nil))) = X))))))/\((~(neq V (nil)))\/(neq X (nil)))))))))))))) zenon_G); [ zenon_intro zenon_H61; idtac ]. % 0.73/0.92 elim zenon_H61. zenon_intro zenon_TU_du. zenon_intro zenon_H63. % 0.73/0.92 apply (zenon_notimply_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 0.73/0.92 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_du = W))\/(((~(neq V (nil)))\/((exists Y : zenon_U, ((ssItem Y)/\((app zenon_TU_du (cons Y (nil))) = V)))\/(forall Z : zenon_U, ((ssItem Z)->(~((app W (cons Z (nil))) = X))))))/\((~(neq V (nil)))\/(neq X (nil)))))))))))) zenon_H64); [ zenon_intro zenon_H66; idtac ]. % 0.73/0.92 elim zenon_H66. zenon_intro zenon_TV_dz. zenon_intro zenon_H68. % 0.73/0.92 apply (zenon_notimply_s _ _ zenon_H68). zenon_intro zenon_H6a. zenon_intro zenon_H69. % 0.73/0.92 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(zenon_TV_dz = X))\/((~(zenon_TU_du = W))\/(((~(neq zenon_TV_dz (nil)))\/((exists Y : zenon_U, ((ssItem Y)/\((app zenon_TU_du (cons Y (nil))) = zenon_TV_dz)))\/(forall Z : zenon_U, ((ssItem Z)->(~((app W (cons Z (nil))) = X))))))/\((~(neq zenon_TV_dz (nil)))\/(neq X (nil)))))))))) zenon_H69); [ zenon_intro zenon_H6b; idtac ]. % 0.73/0.92 elim zenon_H6b. zenon_intro zenon_TW_ee. zenon_intro zenon_H6d. % 0.73/0.92 apply (zenon_notimply_s _ _ zenon_H6d). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 0.73/0.92 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~(zenon_TV_dz = X))\/((~(zenon_TU_du = zenon_TW_ee))\/(((~(neq zenon_TV_dz (nil)))\/((exists Y : zenon_U, ((ssItem Y)/\((app zenon_TU_du (cons Y (nil))) = zenon_TV_dz)))\/(forall Z : zenon_U, ((ssItem Z)->(~((app zenon_TW_ee (cons Z (nil))) = X))))))/\((~(neq zenon_TV_dz (nil)))\/(neq X (nil)))))))) zenon_H6e); [ zenon_intro zenon_H70; idtac ]. % 0.73/0.92 elim zenon_H70. zenon_intro zenon_TX_ej. zenon_intro zenon_H72. % 0.73/0.92 apply (zenon_notimply_s _ _ zenon_H72). zenon_intro zenon_H74. zenon_intro zenon_H73. % 0.73/0.92 apply (zenon_notor_s _ _ zenon_H73). zenon_intro zenon_H76. zenon_intro zenon_H75. % 0.73/0.92 apply (zenon_notor_s _ _ zenon_H75). zenon_intro zenon_H78. zenon_intro zenon_H77. % 0.73/0.92 apply zenon_H78. zenon_intro zenon_H79. % 0.73/0.92 apply zenon_H76. zenon_intro zenon_H7a. % 0.73/0.92 apply (zenon_notand_s _ _ zenon_H77); [ zenon_intro zenon_H7c | zenon_intro zenon_H7b ]. % 0.73/0.92 apply (zenon_notor_s _ _ zenon_H7c). zenon_intro zenon_H7e. zenon_intro zenon_H7d. % 0.73/0.92 apply (zenon_notor_s _ _ zenon_H7d). zenon_intro zenon_H80. zenon_intro zenon_H7f. % 0.73/0.92 apply (zenon_notallex_s (fun Z : zenon_U => ((ssItem Z)->(~((app zenon_TW_ee (cons Z (nil))) = zenon_TX_ej)))) zenon_H7f); [ zenon_intro zenon_H81; idtac ]. % 0.73/0.92 elim zenon_H81. zenon_intro zenon_TZ_fa. zenon_intro zenon_H83. % 0.73/0.92 apply (zenon_notimply_s _ _ zenon_H83). zenon_intro zenon_H85. zenon_intro zenon_H84. % 0.73/0.92 apply zenon_H84. zenon_intro zenon_H86. % 0.73/0.92 apply zenon_H80. exists zenon_TZ_fa. apply NNPP. zenon_intro zenon_H87. % 0.73/0.92 apply (zenon_notand_s _ _ zenon_H87); [ zenon_intro zenon_H89 | zenon_intro zenon_H88 ]. % 0.73/0.92 exact (zenon_H89 zenon_H85). % 0.73/0.92 cut (((app zenon_TW_ee (cons zenon_TZ_fa (nil))) = zenon_TX_ej) = ((app zenon_TU_du (cons zenon_TZ_fa (nil))) = zenon_TV_dz)). % 0.73/0.92 intro zenon_D_pnotp. % 0.73/0.92 apply zenon_H88. % 0.73/0.92 rewrite <- zenon_D_pnotp. % 0.73/0.92 exact zenon_H86. % 0.73/0.92 cut ((zenon_TX_ej = zenon_TV_dz)); [idtac | apply NNPP; zenon_intro zenon_H8a]. % 0.73/0.92 cut (((app zenon_TW_ee (cons zenon_TZ_fa (nil))) = (app zenon_TU_du (cons zenon_TZ_fa (nil))))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 0.73/0.92 congruence. % 0.73/0.92 elim (classic ((app zenon_TU_du (cons zenon_TZ_fa (nil))) = (app zenon_TU_du (cons zenon_TZ_fa (nil))))); [ zenon_intro zenon_H8c | zenon_intro zenon_H8d ]. % 0.73/0.92 cut (((app zenon_TU_du (cons zenon_TZ_fa (nil))) = (app zenon_TU_du (cons zenon_TZ_fa (nil)))) = ((app zenon_TW_ee (cons zenon_TZ_fa (nil))) = (app zenon_TU_du (cons zenon_TZ_fa (nil))))). % 0.73/0.92 intro zenon_D_pnotp. % 0.73/0.92 apply zenon_H8b. % 0.73/0.92 rewrite <- zenon_D_pnotp. % 0.73/0.92 exact zenon_H8c. % 0.73/0.92 cut (((app zenon_TU_du (cons zenon_TZ_fa (nil))) = (app zenon_TU_du (cons zenon_TZ_fa (nil))))); [idtac | apply NNPP; zenon_intro zenon_H8d]. % 0.73/0.92 cut (((app zenon_TU_du (cons zenon_TZ_fa (nil))) = (app zenon_TW_ee (cons zenon_TZ_fa (nil))))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 0.73/0.92 congruence. % 0.73/0.92 cut (((cons zenon_TZ_fa (nil)) = (cons zenon_TZ_fa (nil)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 0.73/0.92 cut ((zenon_TU_du = zenon_TW_ee)); [idtac | apply NNPP; zenon_intro zenon_H90]. % 0.73/0.92 congruence. % 0.73/0.92 exact (zenon_H90 zenon_H79). % 0.73/0.92 apply zenon_H8f. apply refl_equal. % 0.73/0.92 apply zenon_H8d. apply refl_equal. % 0.73/0.92 apply zenon_H8d. apply refl_equal. % 0.73/0.92 apply zenon_H8a. apply sym_equal. exact zenon_H7a. % 0.73/0.92 apply (zenon_notor_s _ _ zenon_H7b). zenon_intro zenon_H7e. zenon_intro zenon_H91. % 0.73/0.92 apply zenon_H7e. zenon_intro zenon_H92. % 0.73/0.92 cut ((neq zenon_TV_dz (nil)) = (neq zenon_TX_ej (nil))). % 0.73/0.92 intro zenon_D_pnotp. % 0.73/0.92 apply zenon_H91. % 0.73/0.92 rewrite <- zenon_D_pnotp. % 0.73/0.92 exact zenon_H92. % 0.73/0.92 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 0.73/0.92 cut ((zenon_TV_dz = zenon_TX_ej)); [idtac | apply NNPP; zenon_intro zenon_H93]. % 0.73/0.92 congruence. % 0.73/0.92 exact (zenon_H93 zenon_H7a). % 0.73/0.92 apply zenon_H60. apply refl_equal. % 0.73/0.92 Qed. % 0.73/0.92 % SZS output end Proof % 0.73/0.92 (* END-PROOF *) % 0.73/0.92 nodes searched: 5905 % 0.73/0.92 max branch formulas: 3248 % 0.73/0.92 proof nodes created: 442 % 0.73/0.92 formulas created: 47094 % 0.73/0.92 %------------------------------------------------------------------------------