%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWC040+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n020.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 22:29:00 EDT 2022 % Result : Theorem 0.36s 0.54s % Output : Proof 0.36s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SWC040+1 : TPTP v8.1.0. Released v2.4.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n020.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 : Sun Jun 12 02:00:50 EDT 2022 % 0.12/0.33 % CPUTime : % 0.36/0.54 (* PROOF-FOUND *) % 0.36/0.54 % SZS status Theorem % 0.36/0.54 (* BEGIN-PROOF *) % 0.36/0.54 % SZS output start Proof % 0.36/0.54 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)->((~((nil) = V))\/((~(V = X))\/((~(U = W))\/(((nil) = U)\/(((~((nil) = W))/\((nil) = X))\/((forall Y : zenon_U, ((ssItem Y)->(forall Z : zenon_U, ((ssList Z)->((~((app (cons Y (nil)) Z) = W))\/(~((app Z (cons Y (nil))) = X)))))))/\(neq X (nil)))))))))))))))). % 0.36/0.54 Proof. % 0.36/0.54 apply NNPP. intro zenon_G. % 0.36/0.54 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)->((~((nil) = V))\/((~(V = X))\/((~(U = W))\/(((nil) = U)\/(((~((nil) = W))/\((nil) = X))\/((forall Y : zenon_U, ((ssItem Y)->(forall Z : zenon_U, ((ssList Z)->((~((app (cons Y (nil)) Z) = W))\/(~((app Z (cons Y (nil))) = X)))))))/\(neq X (nil)))))))))))))))) zenon_G); [ zenon_intro zenon_H60; idtac ]. % 0.36/0.54 elim zenon_H60. zenon_intro zenon_TU_dt. zenon_intro zenon_H62. % 0.36/0.54 apply (zenon_notimply_s _ _ zenon_H62). zenon_intro zenon_H64. zenon_intro zenon_H63. % 0.36/0.54 apply (zenon_notallex_s (fun V : zenon_U => ((ssList V)->(forall W : zenon_U, ((ssList W)->(forall X : zenon_U, ((ssList X)->((~((nil) = V))\/((~(V = X))\/((~(zenon_TU_dt = W))\/(((nil) = zenon_TU_dt)\/(((~((nil) = W))/\((nil) = X))\/((forall Y : zenon_U, ((ssItem Y)->(forall Z : zenon_U, ((ssList Z)->((~((app (cons Y (nil)) Z) = W))\/(~((app Z (cons Y (nil))) = X)))))))/\(neq X (nil)))))))))))))) zenon_H63); [ zenon_intro zenon_H65; idtac ]. % 0.36/0.54 elim zenon_H65. zenon_intro zenon_TV_dy. zenon_intro zenon_H67. % 0.36/0.54 apply (zenon_notimply_s _ _ zenon_H67). zenon_intro zenon_H69. zenon_intro zenon_H68. % 0.36/0.54 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~((nil) = zenon_TV_dy))\/((~(zenon_TV_dy = X))\/((~(zenon_TU_dt = W))\/(((nil) = zenon_TU_dt)\/(((~((nil) = W))/\((nil) = X))\/((forall Y : zenon_U, ((ssItem Y)->(forall Z : zenon_U, ((ssList Z)->((~((app (cons Y (nil)) Z) = W))\/(~((app Z (cons Y (nil))) = X)))))))/\(neq X (nil)))))))))))) zenon_H68); [ zenon_intro zenon_H6a; idtac ]. % 0.36/0.54 elim zenon_H6a. zenon_intro zenon_TW_ed. zenon_intro zenon_H6c. % 0.36/0.54 apply (zenon_notimply_s _ _ zenon_H6c). zenon_intro zenon_H6e. zenon_intro zenon_H6d. % 0.36/0.54 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~((nil) = zenon_TV_dy))\/((~(zenon_TV_dy = X))\/((~(zenon_TU_dt = zenon_TW_ed))\/(((nil) = zenon_TU_dt)\/(((~((nil) = zenon_TW_ed))/\((nil) = X))\/((forall Y : zenon_U, ((ssItem Y)->(forall Z : zenon_U, ((ssList Z)->((~((app (cons Y (nil)) Z) = zenon_TW_ed))\/(~((app Z (cons Y (nil))) = X)))))))/\(neq X (nil)))))))))) zenon_H6d); [ zenon_intro zenon_H6f; idtac ]. % 0.36/0.54 elim zenon_H6f. zenon_intro zenon_TX_ei. zenon_intro zenon_H71. % 0.36/0.54 apply (zenon_notimply_s _ _ zenon_H71). zenon_intro zenon_H73. zenon_intro zenon_H72. % 0.36/0.54 apply (zenon_notor_s _ _ zenon_H72). zenon_intro zenon_H75. zenon_intro zenon_H74. % 0.36/0.54 apply (zenon_notor_s _ _ zenon_H74). zenon_intro zenon_H77. zenon_intro zenon_H76. % 0.36/0.54 apply (zenon_notor_s _ _ zenon_H76). zenon_intro zenon_H79. zenon_intro zenon_H78. % 0.36/0.54 apply (zenon_notor_s _ _ zenon_H78). zenon_intro zenon_H7b. zenon_intro zenon_H7a. % 0.36/0.54 apply (zenon_notor_s _ _ zenon_H7a). zenon_intro zenon_H7d. zenon_intro zenon_H7c. % 0.36/0.54 apply zenon_H79. zenon_intro zenon_H7e. % 0.36/0.54 apply zenon_H77. zenon_intro zenon_H7f. % 0.36/0.54 apply zenon_H75. zenon_intro zenon_H80. % 0.36/0.54 apply (zenon_notand_s _ _ zenon_H7d); [ zenon_intro zenon_H82 | zenon_intro zenon_H81 ]. % 0.36/0.54 apply zenon_H82. zenon_intro zenon_H83. % 0.36/0.54 elim (classic (zenon_TU_dt = zenon_TU_dt)); [ zenon_intro zenon_H84 | zenon_intro zenon_H85 ]. % 0.36/0.54 cut ((zenon_TU_dt = zenon_TU_dt) = ((nil) = zenon_TU_dt)). % 0.36/0.54 intro zenon_D_pnotp. % 0.36/0.54 apply zenon_H7b. % 0.36/0.54 rewrite <- zenon_D_pnotp. % 0.36/0.54 exact zenon_H84. % 0.36/0.54 cut ((zenon_TU_dt = zenon_TU_dt)); [idtac | apply NNPP; zenon_intro zenon_H85]. % 0.36/0.54 cut ((zenon_TU_dt = (nil))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 0.36/0.54 congruence. % 0.36/0.54 cut ((zenon_TU_dt = zenon_TW_ed) = (zenon_TU_dt = (nil))). % 0.36/0.54 intro zenon_D_pnotp. % 0.36/0.54 apply zenon_H86. % 0.36/0.54 rewrite <- zenon_D_pnotp. % 0.36/0.54 exact zenon_H7e. % 0.36/0.54 cut ((zenon_TW_ed = (nil))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 0.36/0.54 cut ((zenon_TU_dt = zenon_TU_dt)); [idtac | apply NNPP; zenon_intro zenon_H85]. % 0.36/0.54 congruence. % 0.36/0.54 apply zenon_H85. apply refl_equal. % 0.36/0.54 apply zenon_H87. apply sym_equal. exact zenon_H83. % 0.36/0.54 apply zenon_H85. apply refl_equal. % 0.36/0.54 apply zenon_H85. apply refl_equal. % 0.36/0.54 cut (((nil) = zenon_TV_dy) = ((nil) = zenon_TX_ei)). % 0.36/0.54 intro zenon_D_pnotp. % 0.36/0.54 apply zenon_H81. % 0.36/0.54 rewrite <- zenon_D_pnotp. % 0.36/0.54 exact zenon_H80. % 0.36/0.54 cut ((zenon_TV_dy = zenon_TX_ei)); [idtac | apply NNPP; zenon_intro zenon_H88]. % 0.36/0.54 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 0.36/0.54 congruence. % 0.36/0.54 apply zenon_H89. apply refl_equal. % 0.36/0.54 exact (zenon_H88 zenon_H7f). % 0.36/0.54 Qed. % 0.36/0.54 % SZS output end Proof % 0.36/0.54 (* END-PROOF *) % 0.36/0.54 nodes searched: 1313 % 0.36/0.54 max branch formulas: 809 % 0.36/0.54 proof nodes created: 19 % 0.36/0.54 formulas created: 10391 % 0.36/0.54 %------------------------------------------------------------------------------