%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWC349+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 22:30:34 EDT 2022 % Result : Theorem 32.05s 32.27s % Output : Proof 32.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SWC349+1 : TPTP v8.1.0. Released v2.4.0. % 0.06/0.12 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n022.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 600 % 0.13/0.33 % DateTime : Sun Jun 12 22:36:03 EDT 2022 % 0.13/0.33 % CPUTime : % 32.05/32.27 (* PROOF-FOUND *) % 32.05/32.27 % SZS status Theorem % 32.05/32.27 (* BEGIN-PROOF *) % 32.05/32.27 % SZS output start Proof % 32.05/32.27 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) = W))\/((~(V = X))\/((~(U = W))\/((~(neq V (nil)))\/(frontsegP V U))))))))))))). % 32.05/32.27 Proof. % 32.05/32.27 assert (zenon_L1_ : (~((nil) = (nil))) -> False). % 32.05/32.27 do 0 intro. intros zenon_H60. % 32.05/32.27 apply zenon_H60. apply refl_equal. % 32.05/32.27 (* end of lemma zenon_L1_ *) % 32.05/32.27 assert (zenon_L2_ : forall (zenon_TW_dw : zenon_U) (zenon_TU_dx : zenon_U), (~((nil) = zenon_TU_dx)) -> ((nil) = zenon_TW_dw) -> (zenon_TU_dx = zenon_TW_dw) -> False). % 32.05/32.27 do 2 intro. intros zenon_H61 zenon_H62 zenon_H63. % 32.05/32.27 cut (((nil) = zenon_TW_dw) = ((nil) = zenon_TU_dx)). % 32.05/32.27 intro zenon_D_pnotp. % 32.05/32.27 apply zenon_H61. % 32.05/32.27 rewrite <- zenon_D_pnotp. % 32.05/32.27 exact zenon_H62. % 32.05/32.27 cut ((zenon_TW_dw = zenon_TU_dx)); [idtac | apply NNPP; zenon_intro zenon_H66]. % 32.05/32.27 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 32.05/32.27 congruence. % 32.05/32.27 apply zenon_H60. apply refl_equal. % 32.05/32.27 apply zenon_H66. apply sym_equal. exact zenon_H63. % 32.05/32.27 (* end of lemma zenon_L2_ *) % 32.05/32.27 assert (zenon_L3_ : forall (zenon_TV_eb : zenon_U), (ssList zenon_TV_eb) -> (~(frontsegP zenon_TV_eb (nil))) -> False). % 32.05/32.27 do 1 intro. intros zenon_H67 zenon_H68. % 32.05/32.27 generalize (ax45 zenon_TV_eb). zenon_intro zenon_H6a. % 32.05/32.27 apply (zenon_imply_s _ _ zenon_H6a); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ]. % 32.05/32.27 exact (zenon_H6c zenon_H67). % 32.05/32.27 exact (zenon_H68 zenon_H6b). % 32.05/32.27 (* end of lemma zenon_L3_ *) % 32.05/32.27 assert (zenon_L4_ : forall (zenon_TU_dx : zenon_U) (zenon_TV_eb : zenon_U), (forall W : zenon_U, ((ssList W)->(((frontsegP zenon_TV_eb (nil))/\(frontsegP (nil) W))->(frontsegP zenon_TV_eb W)))) -> (ssList zenon_TU_dx) -> (frontsegP zenon_TV_eb (nil)) -> (frontsegP (nil) zenon_TU_dx) -> (~(frontsegP zenon_TV_eb zenon_TU_dx)) -> False). % 32.05/32.27 do 2 intro. intros zenon_H6d zenon_H6e zenon_H6b zenon_H6f zenon_H70. % 32.05/32.27 generalize (zenon_H6d zenon_TU_dx). zenon_intro zenon_H71. % 32.05/32.27 apply (zenon_imply_s _ _ zenon_H71); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ]. % 32.05/32.27 exact (zenon_H73 zenon_H6e). % 32.05/32.27 apply (zenon_imply_s _ _ zenon_H72); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ]. % 32.05/32.27 apply (zenon_notand_s _ _ zenon_H75); [ zenon_intro zenon_H68 | zenon_intro zenon_H76 ]. % 32.05/32.27 exact (zenon_H68 zenon_H6b). % 32.05/32.27 exact (zenon_H76 zenon_H6f). % 32.05/32.27 exact (zenon_H70 zenon_H74). % 32.05/32.27 (* end of lemma zenon_L4_ *) % 32.05/32.27 assert (zenon_L5_ : forall (zenon_TU_dx : zenon_U) (zenon_TV_eb : zenon_U), ((ssList (nil))->(forall W : zenon_U, ((ssList W)->(((frontsegP zenon_TV_eb (nil))/\(frontsegP (nil) W))->(frontsegP zenon_TV_eb W))))) -> (~(frontsegP zenon_TV_eb zenon_TU_dx)) -> (frontsegP (nil) zenon_TU_dx) -> (frontsegP zenon_TV_eb (nil)) -> (ssList zenon_TU_dx) -> False). % 32.05/32.27 do 2 intro. intros zenon_H77 zenon_H70 zenon_H6f zenon_H6b zenon_H6e. % 32.05/32.27 apply (zenon_imply_s _ _ zenon_H77); [ zenon_intro zenon_H78 | zenon_intro zenon_H6d ]. % 32.05/32.27 exact (zenon_H78 ax17). % 32.05/32.27 apply (zenon_L4_ zenon_TU_dx zenon_TV_eb); trivial. % 32.05/32.27 (* end of lemma zenon_L5_ *) % 32.05/32.27 assert (zenon_L6_ : forall (zenon_TU_dx : zenon_U) (zenon_TV_eb : zenon_U), (ssList zenon_TV_eb) -> (~(frontsegP zenon_TV_eb zenon_TU_dx)) -> (frontsegP (nil) zenon_TU_dx) -> (ssList zenon_TU_dx) -> (forall V : zenon_U, ((ssList V)->((frontsegP zenon_TV_eb V)<->(exists W : zenon_U, ((ssList W)/\((app V W) = zenon_TV_eb)))))) -> False). % 32.05/32.27 do 2 intro. intros zenon_H67 zenon_H70 zenon_H6f zenon_H6e zenon_H79. % 32.05/32.27 generalize (ax40 zenon_TV_eb). zenon_intro zenon_H7a. % 32.05/32.27 apply (zenon_imply_s _ _ zenon_H7a); [ zenon_intro zenon_H6c | zenon_intro zenon_H7b ]. % 32.05/32.27 exact (zenon_H6c zenon_H67). % 32.05/32.27 generalize (zenon_H7b (nil)). zenon_intro zenon_H77. % 32.05/32.27 generalize (zenon_H79 (nil)). zenon_intro zenon_H7c. % 32.05/32.27 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H78 | zenon_intro zenon_H7d ]. % 32.05/32.27 exact (zenon_H78 ax17). % 32.05/32.27 apply (zenon_equiv_s _ _ zenon_H7d); [ zenon_intro zenon_H68; zenon_intro zenon_H7f | zenon_intro zenon_H6b; zenon_intro zenon_H7e ]. % 32.05/32.27 apply (zenon_L3_ zenon_TV_eb); trivial. % 32.05/32.27 apply (zenon_L5_ zenon_TU_dx zenon_TV_eb); trivial. % 32.05/32.27 (* end of lemma zenon_L6_ *) % 32.05/32.27 apply NNPP. intro zenon_G. % 32.05/32.27 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) = W))\/((~(V = X))\/((~(U = W))\/((~(neq V (nil)))\/(frontsegP V U))))))))))))) zenon_G); [ zenon_intro zenon_H80; idtac ]. % 32.05/32.28 elim zenon_H80. zenon_intro zenon_TU_dx. zenon_intro zenon_H81. % 32.05/32.28 apply (zenon_notimply_s _ _ zenon_H81). zenon_intro zenon_H6e. zenon_intro zenon_H82. % 32.05/32.28 apply (zenon_notallex_s (fun V : zenon_U => ((ssList V)->(forall W : zenon_U, ((ssList W)->(forall X : zenon_U, ((ssList X)->((~((nil) = W))\/((~(V = X))\/((~(zenon_TU_dx = W))\/((~(neq V (nil)))\/(frontsegP V zenon_TU_dx))))))))))) zenon_H82); [ zenon_intro zenon_H83; idtac ]. % 32.05/32.28 elim zenon_H83. zenon_intro zenon_TV_eb. zenon_intro zenon_H84. % 32.05/32.28 apply (zenon_notimply_s _ _ zenon_H84). zenon_intro zenon_H67. zenon_intro zenon_H85. % 32.05/32.28 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~((nil) = W))\/((~(zenon_TV_eb = X))\/((~(zenon_TU_dx = W))\/((~(neq zenon_TV_eb (nil)))\/(frontsegP zenon_TV_eb zenon_TU_dx))))))))) zenon_H85); [ zenon_intro zenon_H86; idtac ]. % 32.05/32.28 elim zenon_H86. zenon_intro zenon_TW_dw. zenon_intro zenon_H87. % 32.05/32.28 apply (zenon_notimply_s _ _ zenon_H87). zenon_intro zenon_H89. zenon_intro zenon_H88. % 32.05/32.28 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~((nil) = zenon_TW_dw))\/((~(zenon_TV_eb = X))\/((~(zenon_TU_dx = zenon_TW_dw))\/((~(neq zenon_TV_eb (nil)))\/(frontsegP zenon_TV_eb zenon_TU_dx))))))) zenon_H88); [ zenon_intro zenon_H8a; idtac ]. % 32.05/32.28 elim zenon_H8a. zenon_intro zenon_TX_fj. zenon_intro zenon_H8c. % 32.05/32.28 apply (zenon_notimply_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 32.05/32.28 apply (zenon_notor_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f. % 32.05/32.28 apply (zenon_notor_s _ _ zenon_H8f). zenon_intro zenon_H92. zenon_intro zenon_H91. % 32.05/32.28 apply (zenon_notor_s _ _ zenon_H91). zenon_intro zenon_H94. zenon_intro zenon_H93. % 32.05/32.28 apply (zenon_notor_s _ _ zenon_H93). zenon_intro zenon_H95. zenon_intro zenon_H70. % 32.05/32.28 apply zenon_H94. zenon_intro zenon_H63. % 32.05/32.28 apply zenon_H90. zenon_intro zenon_H62. % 32.05/32.28 generalize (ax5 zenon_TV_eb). zenon_intro zenon_H96. % 32.05/32.28 apply (zenon_imply_s _ _ zenon_H96); [ zenon_intro zenon_H6c | zenon_intro zenon_H79 ]. % 32.05/32.28 exact (zenon_H6c zenon_H67). % 32.05/32.28 generalize (ax46 zenon_TU_dx). zenon_intro zenon_H97. % 32.05/32.28 apply (zenon_imply_s _ _ zenon_H97); [ zenon_intro zenon_H73 | zenon_intro zenon_H98 ]. % 32.05/32.28 exact (zenon_H73 zenon_H6e). % 32.05/32.28 apply (zenon_equiv_s _ _ zenon_H98); [ zenon_intro zenon_H76; zenon_intro zenon_H61 | zenon_intro zenon_H6f; zenon_intro zenon_H99 ]. % 32.05/32.28 apply (zenon_L2_ zenon_TW_dw zenon_TU_dx); trivial. % 32.05/32.28 apply (zenon_L6_ zenon_TU_dx zenon_TV_eb); trivial. % 32.05/32.28 Qed. % 32.05/32.28 % SZS output end Proof % 32.05/32.28 (* END-PROOF *) % 32.05/32.28 nodes searched: 459860 % 32.05/32.28 max branch formulas: 10575 % 32.05/32.28 proof nodes created: 38087 % 32.05/32.28 formulas created: 2031329 % 32.05/32.28 %------------------------------------------------------------------------------