%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWC210+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n018.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 22:29:52 EDT 2022 % Result : Theorem 0.75s 0.93s % Output : Proof 0.75s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.13 % Problem : SWC210+1 : TPTP v8.1.0. Released v2.4.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.13/0.35 % Computer : n018.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Sun Jun 12 11:06:11 EDT 2022 % 0.13/0.35 % CPUTime : % 0.75/0.93 (* PROOF-FOUND *) % 0.75/0.93 % SZS status Theorem % 0.75/0.93 (* BEGIN-PROOF *) % 0.75/0.93 % SZS output start Proof % 0.75/0.93 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)))\/((~(singletonP W))\/(neq U (nil))))/\((~(neq V (nil)))\/(neq X (nil)))))))))))))). % 0.75/0.93 Proof. % 0.75/0.93 assert (zenon_L1_ : (~((nil) = (nil))) -> False). % 0.75/0.93 do 0 intro. intros zenon_H60. % 0.75/0.93 apply zenon_H60. apply refl_equal. % 0.75/0.93 (* end of lemma zenon_L1_ *) % 0.75/0.93 apply NNPP. intro zenon_G. % 0.75/0.93 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)))\/((~(singletonP W))\/(neq U (nil))))/\((~(neq V (nil)))\/(neq X (nil)))))))))))))) zenon_G); [ zenon_intro zenon_H61; idtac ]. % 0.75/0.93 elim zenon_H61. zenon_intro zenon_TU_du. zenon_intro zenon_H63. % 0.75/0.93 apply (zenon_notimply_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 0.75/0.93 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)))\/((~(singletonP W))\/(neq zenon_TU_du (nil))))/\((~(neq V (nil)))\/(neq X (nil)))))))))))) zenon_H64); [ zenon_intro zenon_H66; idtac ]. % 0.75/0.93 elim zenon_H66. zenon_intro zenon_TV_dz. zenon_intro zenon_H68. % 0.75/0.93 apply (zenon_notimply_s _ _ zenon_H68). zenon_intro zenon_H6a. zenon_intro zenon_H69. % 0.75/0.93 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)))\/((~(singletonP W))\/(neq zenon_TU_du (nil))))/\((~(neq zenon_TV_dz (nil)))\/(neq X (nil)))))))))) zenon_H69); [ zenon_intro zenon_H6b; idtac ]. % 0.75/0.93 elim zenon_H6b. zenon_intro zenon_TW_ee. zenon_intro zenon_H6d. % 0.75/0.93 apply (zenon_notimply_s _ _ zenon_H6d). zenon_intro zenon_H6f. zenon_intro zenon_H6e. % 0.75/0.93 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)))\/((~(singletonP zenon_TW_ee))\/(neq zenon_TU_du (nil))))/\((~(neq zenon_TV_dz (nil)))\/(neq X (nil)))))))) zenon_H6e); [ zenon_intro zenon_H70; idtac ]. % 0.75/0.93 elim zenon_H70. zenon_intro zenon_TX_ej. zenon_intro zenon_H72. % 0.75/0.93 apply (zenon_notimply_s _ _ zenon_H72). zenon_intro zenon_H74. zenon_intro zenon_H73. % 0.75/0.93 apply (zenon_notor_s _ _ zenon_H73). zenon_intro zenon_H76. zenon_intro zenon_H75. % 0.75/0.93 apply (zenon_notor_s _ _ zenon_H75). zenon_intro zenon_H78. zenon_intro zenon_H77. % 0.75/0.93 apply zenon_H78. zenon_intro zenon_H79. % 0.75/0.93 apply zenon_H76. zenon_intro zenon_H7a. % 0.75/0.93 apply (zenon_notand_s _ _ zenon_H77); [ zenon_intro zenon_H7c | zenon_intro zenon_H7b ]. % 0.75/0.93 apply (zenon_notor_s _ _ zenon_H7c). zenon_intro zenon_H7e. zenon_intro zenon_H7d. % 0.75/0.93 apply (zenon_notor_s _ _ zenon_H7d). zenon_intro zenon_H80. zenon_intro zenon_H7f. % 0.75/0.93 apply zenon_H80. zenon_intro zenon_H81. % 0.75/0.93 cut ((singletonP zenon_TW_ee) = (singletonP (nil))). % 0.75/0.93 intro zenon_D_pnotp. % 0.75/0.93 apply ax39. % 0.75/0.93 rewrite <- zenon_D_pnotp. % 0.75/0.93 exact zenon_H81. % 0.75/0.93 cut ((zenon_TW_ee = (nil))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 0.75/0.93 congruence. % 0.75/0.93 generalize (ax15 zenon_TU_du). zenon_intro zenon_H83. % 0.75/0.93 apply (zenon_imply_s _ _ zenon_H83); [ zenon_intro zenon_H85 | zenon_intro zenon_H84 ]. % 0.75/0.93 exact (zenon_H85 zenon_H65). % 0.75/0.93 elim (classic ((nil) = (nil))); [ zenon_intro zenon_H86 | zenon_intro zenon_H60 ]. % 0.75/0.93 cut (((nil) = (nil)) = (zenon_TW_ee = (nil))). % 0.75/0.93 intro zenon_D_pnotp. % 0.75/0.93 apply zenon_H82. % 0.75/0.93 rewrite <- zenon_D_pnotp. % 0.75/0.93 exact zenon_H86. % 0.75/0.93 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 0.75/0.93 cut (((nil) = zenon_TW_ee)); [idtac | apply NNPP; zenon_intro zenon_H87]. % 0.75/0.93 congruence. % 0.75/0.93 cut ((zenon_TU_du = zenon_TW_ee) = ((nil) = zenon_TW_ee)). % 0.75/0.93 intro zenon_D_pnotp. % 0.75/0.93 apply zenon_H87. % 0.75/0.93 rewrite <- zenon_D_pnotp. % 0.75/0.93 exact zenon_H79. % 0.75/0.93 cut ((zenon_TW_ee = zenon_TW_ee)); [idtac | apply NNPP; zenon_intro zenon_H88]. % 0.75/0.93 cut ((zenon_TU_du = (nil))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 0.75/0.93 congruence. % 0.75/0.93 elim (classic ((nil) = (nil))); [ zenon_intro zenon_H86 | zenon_intro zenon_H60 ]. % 0.75/0.93 cut (((nil) = (nil)) = (zenon_TU_du = (nil))). % 0.75/0.93 intro zenon_D_pnotp. % 0.75/0.93 apply zenon_H89. % 0.75/0.93 rewrite <- zenon_D_pnotp. % 0.75/0.93 exact zenon_H86. % 0.75/0.93 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 0.75/0.93 cut (((nil) = zenon_TU_du)); [idtac | apply NNPP; zenon_intro zenon_H8a]. % 0.75/0.93 congruence. % 0.75/0.93 generalize (zenon_H84 (nil)). zenon_intro zenon_H8b. % 0.75/0.93 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H8d | zenon_intro zenon_H8c ]. % 0.75/0.93 exact (zenon_H8d ax17). % 0.75/0.93 apply (zenon_equiv_s _ _ zenon_H8c); [ zenon_intro zenon_H7f; zenon_intro zenon_H8f | zenon_intro zenon_H8e; zenon_intro zenon_H89 ]. % 0.75/0.93 apply zenon_H8f. zenon_intro zenon_H90. % 0.75/0.93 apply zenon_H8a. apply sym_equal. exact zenon_H90. % 0.75/0.93 exact (zenon_H7f zenon_H8e). % 0.75/0.93 apply zenon_H60. apply refl_equal. % 0.75/0.93 apply zenon_H60. apply refl_equal. % 0.75/0.93 apply zenon_H88. apply refl_equal. % 0.75/0.93 apply zenon_H60. apply refl_equal. % 0.75/0.93 apply zenon_H60. apply refl_equal. % 0.75/0.93 apply (zenon_notor_s _ _ zenon_H7b). zenon_intro zenon_H7e. zenon_intro zenon_H91. % 0.75/0.93 apply zenon_H7e. zenon_intro zenon_H92. % 0.75/0.93 cut ((neq zenon_TV_dz (nil)) = (neq zenon_TX_ej (nil))). % 0.75/0.93 intro zenon_D_pnotp. % 0.75/0.93 apply zenon_H91. % 0.75/0.93 rewrite <- zenon_D_pnotp. % 0.75/0.93 exact zenon_H92. % 0.75/0.93 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 0.75/0.93 cut ((zenon_TV_dz = zenon_TX_ej)); [idtac | apply NNPP; zenon_intro zenon_H93]. % 0.75/0.93 congruence. % 0.75/0.93 exact (zenon_H93 zenon_H7a). % 0.75/0.93 apply zenon_H60. apply refl_equal. % 0.75/0.93 Qed. % 0.75/0.93 % SZS output end Proof % 0.75/0.93 (* END-PROOF *) % 0.75/0.93 nodes searched: 8994 % 0.75/0.93 max branch formulas: 2294 % 0.75/0.93 proof nodes created: 775 % 0.75/0.93 formulas created: 41612 % 0.75/0.93 %------------------------------------------------------------------------------