%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWC116+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n022.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 22:29:22 EDT 2022 % Result : Theorem 1.22s 1.42s % Output : Proof 1.22s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWC116+1 : TPTP v8.1.0. Released v2.4.0. % 0.00/0.12 % Command : run_zenon %s %d % 0.11/0.33 % Computer : n022.cluster.edu % 0.11/0.33 % Model : x86_64 x86_64 % 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.33 % Memory : 8042.1875MB % 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.11/0.33 % CPULimit : 300 % 0.11/0.33 % WCLimit : 600 % 0.11/0.33 % DateTime : Sun Jun 12 07:48:48 EDT 2022 % 0.11/0.33 % CPUTime : % 1.22/1.42 (* PROOF-FOUND *) % 1.22/1.42 % SZS status Theorem % 1.22/1.42 (* BEGIN-PROOF *) % 1.22/1.42 % SZS output start Proof % 1.22/1.42 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))\/(((~((nil) = W))/\((nil) = X))\/((((nil) = V)/\((nil) = U))\/(((neq U (nil))/\(segmentP V U))\/((neq X (nil))/\((~(neq W (nil)))\/(~(segmentP X W))))))))))))))))). % 1.22/1.42 Proof. % 1.22/1.42 assert (zenon_L1_ : forall (zenon_TX_dw : zenon_U) (zenon_TV_dx : zenon_U), (zenon_TV_dx = zenon_TX_dw) -> (ssList zenon_TX_dw) -> (~(neq zenon_TX_dw (nil))) -> (~((nil) = zenon_TV_dx)) -> False). % 1.22/1.42 do 2 intro. intros zenon_H60 zenon_H61 zenon_H62 zenon_H63. % 1.22/1.42 elim (classic (zenon_TV_dx = zenon_TV_dx)); [ zenon_intro zenon_H66 | zenon_intro zenon_H67 ]. % 1.22/1.42 cut ((zenon_TV_dx = zenon_TV_dx) = ((nil) = zenon_TV_dx)). % 1.22/1.42 intro zenon_D_pnotp. % 1.22/1.42 apply zenon_H63. % 1.22/1.42 rewrite <- zenon_D_pnotp. % 1.22/1.42 exact zenon_H66. % 1.22/1.42 cut ((zenon_TV_dx = zenon_TV_dx)); [idtac | apply NNPP; zenon_intro zenon_H67]. % 1.22/1.42 cut ((zenon_TV_dx = (nil))); [idtac | apply NNPP; zenon_intro zenon_H68]. % 1.22/1.42 congruence. % 1.22/1.42 cut ((zenon_TV_dx = zenon_TX_dw) = (zenon_TV_dx = (nil))). % 1.22/1.42 intro zenon_D_pnotp. % 1.22/1.42 apply zenon_H68. % 1.22/1.42 rewrite <- zenon_D_pnotp. % 1.22/1.42 exact zenon_H60. % 1.22/1.42 cut ((zenon_TX_dw = (nil))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 1.22/1.42 cut ((zenon_TV_dx = zenon_TV_dx)); [idtac | apply NNPP; zenon_intro zenon_H67]. % 1.22/1.42 congruence. % 1.22/1.42 apply zenon_H67. apply refl_equal. % 1.22/1.42 generalize (ax15 zenon_TX_dw). zenon_intro zenon_H6a. % 1.22/1.42 apply (zenon_imply_s _ _ zenon_H6a); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ]. % 1.22/1.42 exact (zenon_H6c zenon_H61). % 1.22/1.42 generalize (zenon_H6b (nil)). zenon_intro zenon_H6d. % 1.22/1.42 apply (zenon_imply_s _ _ zenon_H6d); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ]. % 1.22/1.42 exact (zenon_H6f ax17). % 1.22/1.42 apply (zenon_equiv_s _ _ zenon_H6e); [ zenon_intro zenon_H62; zenon_intro zenon_H71 | zenon_intro zenon_H70; zenon_intro zenon_H69 ]. % 1.22/1.42 exact (zenon_H71 zenon_H69). % 1.22/1.42 exact (zenon_H62 zenon_H70). % 1.22/1.42 apply zenon_H67. apply refl_equal. % 1.22/1.42 apply zenon_H67. apply refl_equal. % 1.22/1.42 (* end of lemma zenon_L1_ *) % 1.22/1.42 assert (zenon_L2_ : (~((nil) = (nil))) -> False). % 1.22/1.42 do 0 intro. intros zenon_H72. % 1.22/1.42 apply zenon_H72. apply refl_equal. % 1.22/1.42 (* end of lemma zenon_L2_ *) % 1.22/1.42 assert (zenon_L3_ : forall (zenon_TU_eo : zenon_U) (zenon_TX_dw : zenon_U) (zenon_TW_ep : zenon_U), (~((~(neq zenon_TW_ep (nil)))\/(~(segmentP zenon_TX_dw zenon_TW_ep)))) -> (~(neq zenon_TU_eo (nil))) -> (zenon_TU_eo = zenon_TW_ep) -> False). % 1.22/1.42 do 3 intro. intros zenon_H73 zenon_H74 zenon_H75. % 1.22/1.42 apply (zenon_notor_s _ _ zenon_H73). zenon_intro zenon_H79. zenon_intro zenon_H78. % 1.22/1.42 apply zenon_H79. zenon_intro zenon_H7a. % 1.22/1.42 cut ((neq zenon_TW_ep (nil)) = (neq zenon_TU_eo (nil))). % 1.22/1.42 intro zenon_D_pnotp. % 1.22/1.42 apply zenon_H74. % 1.22/1.42 rewrite <- zenon_D_pnotp. % 1.22/1.42 exact zenon_H7a. % 1.22/1.42 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 1.22/1.42 cut ((zenon_TW_ep = zenon_TU_eo)); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 1.22/1.42 congruence. % 1.22/1.42 apply zenon_H7b. apply sym_equal. exact zenon_H75. % 1.22/1.42 apply zenon_H72. apply refl_equal. % 1.22/1.42 (* end of lemma zenon_L3_ *) % 1.22/1.42 assert (zenon_L4_ : forall (zenon_TU_eo : zenon_U) (zenon_TV_dx : zenon_U) (zenon_TX_dw : zenon_U) (zenon_TW_ep : zenon_U), (~((~(neq zenon_TW_ep (nil)))\/(~(segmentP zenon_TX_dw zenon_TW_ep)))) -> (~(segmentP zenon_TV_dx zenon_TU_eo)) -> (zenon_TU_eo = zenon_TW_ep) -> (zenon_TV_dx = zenon_TX_dw) -> False). % 1.22/1.42 do 4 intro. intros zenon_H73 zenon_H7c zenon_H75 zenon_H60. % 1.22/1.42 apply (zenon_notor_s _ _ zenon_H73). zenon_intro zenon_H79. zenon_intro zenon_H78. % 1.22/1.42 apply zenon_H78. zenon_intro zenon_H7d. % 1.22/1.42 cut ((segmentP zenon_TX_dw zenon_TW_ep) = (segmentP zenon_TV_dx zenon_TU_eo)). % 1.22/1.42 intro zenon_D_pnotp. % 1.22/1.42 apply zenon_H7c. % 1.22/1.42 rewrite <- zenon_D_pnotp. % 1.22/1.42 exact zenon_H7d. % 1.22/1.42 cut ((zenon_TW_ep = zenon_TU_eo)); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 1.22/1.42 cut ((zenon_TX_dw = zenon_TV_dx)); [idtac | apply NNPP; zenon_intro zenon_H7e]. % 1.22/1.42 congruence. % 1.22/1.42 apply zenon_H7e. apply sym_equal. exact zenon_H60. % 1.22/1.42 apply zenon_H7b. apply sym_equal. exact zenon_H75. % 1.22/1.42 (* end of lemma zenon_L4_ *) % 1.22/1.42 assert (zenon_L5_ : forall (zenon_TX_dw : zenon_U), ((neq zenon_TX_dw (nil))<->(~(zenon_TX_dw = (nil)))) -> (~(neq zenon_TX_dw (nil))) -> (~((nil) = zenon_TX_dw)) -> False). % 1.22/1.42 do 1 intro. intros zenon_H6e zenon_H62 zenon_H7f. % 1.22/1.42 apply (zenon_equiv_s _ _ zenon_H6e); [ zenon_intro zenon_H62; zenon_intro zenon_H71 | zenon_intro zenon_H70; zenon_intro zenon_H69 ]. % 1.22/1.42 apply zenon_H71. zenon_intro zenon_H80. % 1.22/1.42 apply zenon_H7f. apply sym_equal. exact zenon_H80. % 1.22/1.42 exact (zenon_H62 zenon_H70). % 1.22/1.42 (* end of lemma zenon_L5_ *) % 1.22/1.42 assert (zenon_L6_ : forall (zenon_TX_dw : zenon_U), (ssList zenon_TX_dw) -> (~(neq zenon_TX_dw (nil))) -> (~((nil) = zenon_TX_dw)) -> False). % 1.22/1.42 do 1 intro. intros zenon_H61 zenon_H62 zenon_H7f. % 1.22/1.42 generalize (ax15 zenon_TX_dw). zenon_intro zenon_H6a. % 1.22/1.42 apply (zenon_imply_s _ _ zenon_H6a); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ]. % 1.22/1.42 exact (zenon_H6c zenon_H61). % 1.22/1.42 generalize (zenon_H6b (nil)). zenon_intro zenon_H6d. % 1.22/1.42 apply (zenon_imply_s _ _ zenon_H6d); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ]. % 1.22/1.42 exact (zenon_H6f ax17). % 1.22/1.42 apply (zenon_L5_ zenon_TX_dw); trivial. % 1.22/1.42 (* end of lemma zenon_L6_ *) % 1.22/1.42 apply NNPP. intro zenon_G. % 1.22/1.42 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))\/(((~((nil) = W))/\((nil) = X))\/((((nil) = V)/\((nil) = U))\/(((neq U (nil))/\(segmentP V U))\/((neq X (nil))/\((~(neq W (nil)))\/(~(segmentP X W))))))))))))))))) zenon_G); [ zenon_intro zenon_H81; idtac ]. % 1.22/1.42 elim zenon_H81. zenon_intro zenon_TU_eo. zenon_intro zenon_H82. % 1.22/1.42 apply (zenon_notimply_s _ _ zenon_H82). zenon_intro zenon_H84. zenon_intro zenon_H83. % 1.22/1.42 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_eo = W))\/(((~((nil) = W))/\((nil) = X))\/((((nil) = V)/\((nil) = zenon_TU_eo))\/(((neq zenon_TU_eo (nil))/\(segmentP V zenon_TU_eo))\/((neq X (nil))/\((~(neq W (nil)))\/(~(segmentP X W))))))))))))))) zenon_H83); [ zenon_intro zenon_H85; idtac ]. % 1.22/1.42 elim zenon_H85. zenon_intro zenon_TV_dx. zenon_intro zenon_H86. % 1.22/1.42 apply (zenon_notimply_s _ _ zenon_H86). zenon_intro zenon_H88. zenon_intro zenon_H87. % 1.22/1.42 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(zenon_TV_dx = X))\/((~(zenon_TU_eo = W))\/(((~((nil) = W))/\((nil) = X))\/((((nil) = zenon_TV_dx)/\((nil) = zenon_TU_eo))\/(((neq zenon_TU_eo (nil))/\(segmentP zenon_TV_dx zenon_TU_eo))\/((neq X (nil))/\((~(neq W (nil)))\/(~(segmentP X W))))))))))))) zenon_H87); [ zenon_intro zenon_H89; idtac ]. % 1.22/1.42 elim zenon_H89. zenon_intro zenon_TW_ep. zenon_intro zenon_H8a. % 1.22/1.42 apply (zenon_notimply_s _ _ zenon_H8a). zenon_intro zenon_H8c. zenon_intro zenon_H8b. % 1.22/1.42 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~(zenon_TV_dx = X))\/((~(zenon_TU_eo = zenon_TW_ep))\/(((~((nil) = zenon_TW_ep))/\((nil) = X))\/((((nil) = zenon_TV_dx)/\((nil) = zenon_TU_eo))\/(((neq zenon_TU_eo (nil))/\(segmentP zenon_TV_dx zenon_TU_eo))\/((neq X (nil))/\((~(neq zenon_TW_ep (nil)))\/(~(segmentP X zenon_TW_ep))))))))))) zenon_H8b); [ zenon_intro zenon_H8d; idtac ]. % 1.22/1.42 elim zenon_H8d. zenon_intro zenon_TX_dw. zenon_intro zenon_H8e. % 1.22/1.42 apply (zenon_notimply_s _ _ zenon_H8e). zenon_intro zenon_H61. zenon_intro zenon_H8f. % 1.22/1.42 apply (zenon_notor_s _ _ zenon_H8f). zenon_intro zenon_H91. zenon_intro zenon_H90. % 1.22/1.42 apply (zenon_notor_s _ _ zenon_H90). zenon_intro zenon_H93. zenon_intro zenon_H92. % 1.22/1.42 apply (zenon_notor_s _ _ zenon_H92). zenon_intro zenon_H95. zenon_intro zenon_H94. % 1.22/1.42 apply (zenon_notor_s _ _ zenon_H94). zenon_intro zenon_H97. zenon_intro zenon_H96. % 1.22/1.42 apply (zenon_notor_s _ _ zenon_H96). zenon_intro zenon_H99. zenon_intro zenon_H98. % 1.22/1.42 apply zenon_H93. zenon_intro zenon_H75. % 1.22/1.42 apply zenon_H91. zenon_intro zenon_H60. % 1.22/1.42 apply (zenon_notand_s _ _ zenon_H95); [ zenon_intro zenon_H9a | zenon_intro zenon_H7f ]. % 1.22/1.42 apply zenon_H9a. zenon_intro zenon_H9b. % 1.22/1.42 apply (zenon_notand_s _ _ zenon_H97); [ zenon_intro zenon_H63 | zenon_intro zenon_H9c ]. % 1.22/1.42 apply (zenon_notand_s _ _ zenon_H99); [ zenon_intro zenon_H74 | zenon_intro zenon_H7c ]. % 1.22/1.42 apply (zenon_notand_s _ _ zenon_H98); [ zenon_intro zenon_H62 | zenon_intro zenon_H73 ]. % 1.22/1.42 apply (zenon_L1_ zenon_TX_dw zenon_TV_dx); trivial. % 1.22/1.42 apply (zenon_L3_ zenon_TU_eo zenon_TX_dw zenon_TW_ep); trivial. % 1.22/1.42 apply (zenon_notand_s _ _ zenon_H98); [ zenon_intro zenon_H62 | zenon_intro zenon_H73 ]. % 1.22/1.42 apply (zenon_L1_ zenon_TX_dw zenon_TV_dx); trivial. % 1.22/1.42 apply (zenon_L4_ zenon_TU_eo zenon_TV_dx zenon_TX_dw zenon_TW_ep); trivial. % 1.22/1.42 cut (((nil) = zenon_TW_ep) = ((nil) = zenon_TU_eo)). % 1.22/1.42 intro zenon_D_pnotp. % 1.22/1.42 apply zenon_H9c. % 1.22/1.42 rewrite <- zenon_D_pnotp. % 1.22/1.42 exact zenon_H9b. % 1.22/1.42 cut ((zenon_TW_ep = zenon_TU_eo)); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 1.22/1.42 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 1.22/1.42 congruence. % 1.22/1.42 apply zenon_H72. apply refl_equal. % 1.22/1.42 apply zenon_H7b. apply sym_equal. exact zenon_H75. % 1.22/1.42 apply (zenon_notand_s _ _ zenon_H99); [ zenon_intro zenon_H74 | zenon_intro zenon_H7c ]. % 1.22/1.42 apply (zenon_notand_s _ _ zenon_H98); [ zenon_intro zenon_H62 | zenon_intro zenon_H73 ]. % 1.22/1.42 apply (zenon_L6_ zenon_TX_dw); trivial. % 1.22/1.42 apply (zenon_L3_ zenon_TU_eo zenon_TX_dw zenon_TW_ep); trivial. % 1.22/1.42 apply (zenon_notand_s _ _ zenon_H98); [ zenon_intro zenon_H62 | zenon_intro zenon_H73 ]. % 1.22/1.42 apply (zenon_L6_ zenon_TX_dw); trivial. % 1.22/1.42 apply (zenon_L4_ zenon_TU_eo zenon_TV_dx zenon_TX_dw zenon_TW_ep); trivial. % 1.22/1.42 Qed. % 1.22/1.42 % SZS output end Proof % 1.22/1.42 (* END-PROOF *) % 1.22/1.42 nodes searched: 20619 % 1.22/1.42 max branch formulas: 3529 % 1.22/1.42 proof nodes created: 1658 % 1.22/1.42 formulas created: 112048 % 1.22/1.42 %------------------------------------------------------------------------------