%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWC381+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n006.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 22:30:44 EDT 2022 % Result : Theorem 14.41s 14.63s % Output : Proof 14.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.11 % Problem : SWC381+1 : TPTP v8.1.0. Released v2.4.0. % 0.12/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n006.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Sat Jun 11 22:48:12 EDT 2022 % 0.12/0.33 % CPUTime : % 14.41/14.63 (* PROOF-FOUND *) % 14.41/14.63 % SZS status Theorem % 14.41/14.63 (* BEGIN-PROOF *) % 14.41/14.63 % SZS output start Proof % 14.41/14.63 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)/\(((cons Y (nil)) = U)/\(memberP V Y))))\/(forall Z : zenon_U, ((ssItem Z)->((~((cons Z (nil)) = W))\/(~(memberP X Z)))))))/\((~(neq V (nil)))\/(neq X (nil)))))))))))))). % 14.41/14.63 Proof. % 14.41/14.63 assert (zenon_L1_ : forall (zenon_TZ_du : zenon_U) (zenon_TV_dv : zenon_U), ((memberP zenon_TV_dv zenon_TZ_du)\/(memberP zenon_TV_dv zenon_TZ_du)) -> (~(memberP zenon_TV_dv zenon_TZ_du)) -> False). % 14.41/14.63 do 2 intro. intros zenon_H60 zenon_H61. % 14.41/14.63 apply (zenon_or_s _ _ zenon_H60); [ zenon_intro zenon_H64 | zenon_intro zenon_H64 ]. % 14.41/14.63 exact (zenon_H61 zenon_H64). % 14.41/14.63 exact (zenon_H61 zenon_H64). % 14.41/14.63 (* end of lemma zenon_L1_ *) % 14.41/14.63 assert (zenon_L2_ : (~((nil) = (nil))) -> False). % 14.41/14.63 do 0 intro. intros zenon_H65. % 14.41/14.63 apply zenon_H65. apply refl_equal. % 14.41/14.63 (* end of lemma zenon_L2_ *) % 14.41/14.63 apply NNPP. intro zenon_G. % 14.41/14.63 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)/\(((cons Y (nil)) = U)/\(memberP V Y))))\/(forall Z : zenon_U, ((ssItem Z)->((~((cons Z (nil)) = W))\/(~(memberP X Z)))))))/\((~(neq V (nil)))\/(neq X (nil)))))))))))))) zenon_G); [ zenon_intro zenon_H66; idtac ]. % 14.41/14.63 elim zenon_H66. zenon_intro zenon_TU_dz. zenon_intro zenon_H68. % 14.41/14.63 apply (zenon_notimply_s _ _ zenon_H68). zenon_intro zenon_H6a. zenon_intro zenon_H69. % 14.41/14.63 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_dz = W))\/(((~(neq V (nil)))\/((exists Y : zenon_U, ((ssItem Y)/\(((cons Y (nil)) = zenon_TU_dz)/\(memberP V Y))))\/(forall Z : zenon_U, ((ssItem Z)->((~((cons Z (nil)) = W))\/(~(memberP X Z)))))))/\((~(neq V (nil)))\/(neq X (nil)))))))))))) zenon_H69); [ zenon_intro zenon_H6b; idtac ]. % 14.41/14.63 elim zenon_H6b. zenon_intro zenon_TV_dv. zenon_intro zenon_H6c. % 14.41/14.63 apply (zenon_notimply_s _ _ zenon_H6c). zenon_intro zenon_H6e. zenon_intro zenon_H6d. % 14.41/14.63 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(zenon_TV_dv = X))\/((~(zenon_TU_dz = W))\/(((~(neq zenon_TV_dv (nil)))\/((exists Y : zenon_U, ((ssItem Y)/\(((cons Y (nil)) = zenon_TU_dz)/\(memberP zenon_TV_dv Y))))\/(forall Z : zenon_U, ((ssItem Z)->((~((cons Z (nil)) = W))\/(~(memberP X Z)))))))/\((~(neq zenon_TV_dv (nil)))\/(neq X (nil)))))))))) zenon_H6d); [ zenon_intro zenon_H6f; idtac ]. % 14.41/14.63 elim zenon_H6f. zenon_intro zenon_TW_ei. zenon_intro zenon_H71. % 14.41/14.63 apply (zenon_notimply_s _ _ zenon_H71). zenon_intro zenon_H73. zenon_intro zenon_H72. % 14.41/14.63 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~(zenon_TV_dv = X))\/((~(zenon_TU_dz = zenon_TW_ei))\/(((~(neq zenon_TV_dv (nil)))\/((exists Y : zenon_U, ((ssItem Y)/\(((cons Y (nil)) = zenon_TU_dz)/\(memberP zenon_TV_dv Y))))\/(forall Z : zenon_U, ((ssItem Z)->((~((cons Z (nil)) = zenon_TW_ei))\/(~(memberP X Z)))))))/\((~(neq zenon_TV_dv (nil)))\/(neq X (nil)))))))) zenon_H72); [ zenon_intro zenon_H74; idtac ]. % 14.41/14.63 elim zenon_H74. zenon_intro zenon_TX_en. zenon_intro zenon_H76. % 14.41/14.63 apply (zenon_notimply_s _ _ zenon_H76). zenon_intro zenon_H78. zenon_intro zenon_H77. % 14.41/14.63 apply (zenon_notor_s _ _ zenon_H77). zenon_intro zenon_H7a. zenon_intro zenon_H79. % 14.41/14.63 apply (zenon_notor_s _ _ zenon_H79). zenon_intro zenon_H7c. zenon_intro zenon_H7b. % 14.41/14.63 apply zenon_H7c. zenon_intro zenon_H7d. % 14.41/14.63 apply zenon_H7a. zenon_intro zenon_H7e. % 14.41/14.63 apply (zenon_notand_s _ _ zenon_H7b); [ zenon_intro zenon_H80 | zenon_intro zenon_H7f ]. % 14.41/14.63 apply (zenon_notor_s _ _ zenon_H80). zenon_intro zenon_H82. zenon_intro zenon_H81. % 14.41/14.63 apply (zenon_notor_s _ _ zenon_H81). zenon_intro zenon_H84. zenon_intro zenon_H83. % 14.41/14.63 apply (zenon_notallex_s (fun Z : zenon_U => ((ssItem Z)->((~((cons Z (nil)) = zenon_TW_ei))\/(~(memberP zenon_TX_en Z))))) zenon_H83); [ zenon_intro zenon_H85; idtac ]. % 14.41/14.63 elim zenon_H85. zenon_intro zenon_TZ_du. zenon_intro zenon_H86. % 14.41/14.63 apply (zenon_notimply_s _ _ zenon_H86). zenon_intro zenon_H88. zenon_intro zenon_H87. % 14.41/14.63 apply (zenon_notor_s _ _ zenon_H87). zenon_intro zenon_H8a. zenon_intro zenon_H89. % 14.41/14.63 apply zenon_H89. zenon_intro zenon_H8b. % 14.41/14.63 apply zenon_H8a. zenon_intro zenon_H8c. % 14.41/14.63 generalize (ax31 zenon_TZ_du). zenon_intro zenon_H8d. % 14.41/14.63 apply (zenon_imply_s _ _ zenon_H8d); [ zenon_intro zenon_H8f | zenon_intro zenon_H8e ]. % 14.41/14.63 exact (zenon_H8f zenon_H88). % 14.41/14.63 generalize (ax36 zenon_TZ_du). zenon_intro zenon_H90. % 14.41/14.63 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H8f | zenon_intro zenon_H91 ]. % 14.41/14.63 exact (zenon_H8f zenon_H88). % 14.41/14.63 apply zenon_H84. exists zenon_TZ_du. apply NNPP. zenon_intro zenon_H92. % 14.41/14.63 apply (zenon_notand_s _ _ zenon_H92); [ zenon_intro zenon_H8f | zenon_intro zenon_H93 ]. % 14.41/14.63 exact (zenon_H8f zenon_H88). % 14.41/14.63 apply (zenon_notand_s _ _ zenon_H93); [ zenon_intro zenon_H94 | zenon_intro zenon_H61 ]. % 14.41/14.63 cut (((cons zenon_TZ_du (nil)) = zenon_TW_ei) = ((cons zenon_TZ_du (nil)) = zenon_TU_dz)). % 14.41/14.63 intro zenon_D_pnotp. % 14.41/14.63 apply zenon_H94. % 14.41/14.63 rewrite <- zenon_D_pnotp. % 14.41/14.63 exact zenon_H8c. % 14.41/14.63 cut ((zenon_TW_ei = zenon_TU_dz)); [idtac | apply NNPP; zenon_intro zenon_H95]. % 14.41/14.63 cut (((cons zenon_TZ_du (nil)) = (cons zenon_TZ_du (nil)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 14.41/14.63 congruence. % 14.41/14.63 apply zenon_H96. apply refl_equal. % 14.41/14.63 apply zenon_H95. apply sym_equal. exact zenon_H7d. % 14.41/14.63 generalize (ax90 zenon_TZ_du). zenon_intro zenon_H97. % 14.41/14.63 apply (zenon_imply_s _ _ zenon_H97); [ zenon_intro zenon_H8f | zenon_intro zenon_H98 ]. % 14.41/14.63 exact (zenon_H8f zenon_H88). % 14.41/14.63 generalize (zenon_H91 zenon_TV_dv). zenon_intro zenon_H99. % 14.41/14.63 apply (zenon_imply_s _ _ zenon_H99); [ zenon_intro zenon_H9b | zenon_intro zenon_H9a ]. % 14.41/14.63 exact (zenon_H9b zenon_H6e). % 14.41/14.63 generalize (ax93 zenon_TZ_du). zenon_intro zenon_H9c. % 14.41/14.63 apply (zenon_imply_s _ _ zenon_H9c); [ zenon_intro zenon_H8f | zenon_intro zenon_H9d ]. % 14.41/14.63 exact (zenon_H8f zenon_H88). % 14.41/14.63 generalize (zenon_H9a zenon_TV_dv). zenon_intro zenon_H9e. % 14.41/14.63 apply (zenon_imply_s _ _ zenon_H9e); [ zenon_intro zenon_H9b | zenon_intro zenon_H9f ]. % 14.41/14.63 exact (zenon_H9b zenon_H6e). % 14.41/14.63 apply (zenon_equiv_s _ _ zenon_H9f); [ zenon_intro zenon_Ha2; zenon_intro zenon_Ha1 | zenon_intro zenon_Ha0; zenon_intro zenon_H60 ]. % 14.41/14.63 generalize (zenon_H9d zenon_TZ_du). zenon_intro zenon_Ha3. % 14.41/14.63 apply (zenon_imply_s _ _ zenon_Ha3); [ zenon_intro zenon_H8f | zenon_intro zenon_Ha4 ]. % 14.41/14.63 exact (zenon_H8f zenon_H88). % 14.41/14.63 apply (zenon_equiv_s _ _ zenon_Ha4); [ zenon_intro zenon_H98; zenon_intro zenon_Ha7 | zenon_intro zenon_Ha6; zenon_intro zenon_Ha5 ]. % 14.41/14.63 apply (zenon_notand_s _ _ zenon_Ha7); [ zenon_intro zenon_Ha9 | zenon_intro zenon_Ha8 ]. % 14.41/14.63 generalize (zenon_H91 zenon_TX_en). zenon_intro zenon_Haa. % 14.41/14.63 apply (zenon_imply_s _ _ zenon_Haa); [ zenon_intro zenon_Hac | zenon_intro zenon_Hab ]. % 14.41/14.63 exact (zenon_Hac zenon_H78). % 14.41/14.63 generalize (zenon_Hab zenon_TV_dv). zenon_intro zenon_Had. % 14.41/14.63 apply (zenon_imply_s _ _ zenon_Had); [ zenon_intro zenon_H9b | zenon_intro zenon_Hae ]. % 14.41/14.63 exact (zenon_H9b zenon_H6e). % 14.41/14.63 apply (zenon_equiv_s _ _ zenon_Hae); [ zenon_intro zenon_Hb2; zenon_intro zenon_Hb1 | zenon_intro zenon_Hb0; zenon_intro zenon_Haf ]. % 14.41/14.63 apply (zenon_notor_s _ _ zenon_Hb1). zenon_intro zenon_Hb3. zenon_intro zenon_H61. % 14.41/14.63 exact (zenon_Hb3 zenon_H8b). % 14.41/14.63 cut ((memberP (app zenon_TX_en zenon_TV_dv) zenon_TZ_du) = (memberP (app zenon_TV_dv zenon_TV_dv) zenon_TZ_du)). % 14.41/14.63 intro zenon_D_pnotp. % 14.41/14.63 apply zenon_Ha2. % 14.41/14.63 rewrite <- zenon_D_pnotp. % 14.41/14.63 exact zenon_Hb0. % 14.41/14.63 cut ((zenon_TZ_du = zenon_TZ_du)); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 14.41/14.63 cut (((app zenon_TX_en zenon_TV_dv) = (app zenon_TV_dv zenon_TV_dv))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 14.41/14.63 congruence. % 14.41/14.63 cut ((zenon_TV_dv = zenon_TV_dv)); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 14.41/14.63 cut ((zenon_TX_en = zenon_TV_dv)); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 14.41/14.63 congruence. % 14.41/14.63 apply zenon_Hb7. apply sym_equal. exact zenon_H7e. % 14.41/14.63 apply zenon_Hb6. apply refl_equal. % 14.41/14.63 exact (zenon_Ha9 zenon_Hb4). % 14.41/14.63 exact (zenon_Ha8 zenon_H8e). % 14.41/14.63 exact (zenon_H98 zenon_Ha6). % 14.41/14.63 apply (zenon_L1_ zenon_TZ_du zenon_TV_dv); trivial. % 14.41/14.63 apply (zenon_notor_s _ _ zenon_H7f). zenon_intro zenon_H82. zenon_intro zenon_Hb8. % 14.41/14.64 apply zenon_H82. zenon_intro zenon_Hb9. % 14.41/14.64 cut ((neq zenon_TV_dv (nil)) = (neq zenon_TX_en (nil))). % 14.41/14.64 intro zenon_D_pnotp. % 14.41/14.64 apply zenon_Hb8. % 14.41/14.64 rewrite <- zenon_D_pnotp. % 14.41/14.64 exact zenon_Hb9. % 14.41/14.64 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 14.41/14.64 cut ((zenon_TV_dv = zenon_TX_en)); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 14.41/14.64 congruence. % 14.41/14.64 exact (zenon_Hba zenon_H7e). % 14.41/14.64 apply zenon_H65. apply refl_equal. % 14.41/14.64 Qed. % 14.41/14.64 % SZS output end Proof % 14.41/14.64 (* END-PROOF *) % 14.41/14.64 nodes searched: 208634 % 14.41/14.64 max branch formulas: 18122 % 14.41/14.64 proof nodes created: 14475 % 14.41/14.64 formulas created: 795900 % 14.41/14.64 %------------------------------------------------------------------------------