%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SWC328+1 : TPTP v8.1.0. Released v2.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n013.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 22:30:27 EDT 2022 % Result : Theorem 40.69s 40.87s % Output : Proof 40.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SWC328+1 : TPTP v8.1.0. Released v2.4.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n013.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 09:30:43 EDT 2022 % 0.12/0.34 % CPUTime : % 40.69/40.87 (* PROOF-FOUND *) % 40.69/40.87 % SZS status Theorem % 40.69/40.87 (* BEGIN-PROOF *) % 40.69/40.87 % SZS output start Proof % 40.69/40.87 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))\/((segmentP V U)/\(equalelemsP U))))))))))))). % 40.69/40.87 Proof. % 40.69/40.87 assert (zenon_L1_ : (~((nil) = (nil))) -> False). % 40.69/40.87 do 0 intro. intros zenon_H60. % 40.69/40.87 apply zenon_H60. apply refl_equal. % 40.69/40.87 (* end of lemma zenon_L1_ *) % 40.69/40.87 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). % 40.69/40.87 do 2 intro. intros zenon_H61 zenon_H62 zenon_H63. % 40.69/40.87 cut (((nil) = zenon_TW_dw) = ((nil) = zenon_TU_dx)). % 40.69/40.87 intro zenon_D_pnotp. % 40.69/40.87 apply zenon_H61. % 40.69/40.87 rewrite <- zenon_D_pnotp. % 40.69/40.87 exact zenon_H62. % 40.69/40.87 cut ((zenon_TW_dw = zenon_TU_dx)); [idtac | apply NNPP; zenon_intro zenon_H66]. % 40.69/40.87 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 40.69/40.87 congruence. % 40.69/40.87 apply zenon_H60. apply refl_equal. % 40.69/40.87 apply zenon_H66. apply sym_equal. exact zenon_H63. % 40.69/40.87 (* end of lemma zenon_L2_ *) % 40.69/40.87 assert (zenon_L3_ : forall (zenon_TV_eb : zenon_U), (ssList zenon_TV_eb) -> (~(segmentP zenon_TV_eb (nil))) -> False). % 40.69/40.87 do 1 intro. intros zenon_H67 zenon_H68. % 40.69/40.87 generalize (ax57 zenon_TV_eb). zenon_intro zenon_H6a. % 40.69/40.87 apply (zenon_imply_s _ _ zenon_H6a); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ]. % 40.69/40.87 exact (zenon_H6c zenon_H67). % 40.69/40.87 exact (zenon_H68 zenon_H6b). % 40.69/40.87 (* end of lemma zenon_L3_ *) % 40.69/40.87 assert (zenon_L4_ : forall (zenon_TU_dx : zenon_U) (zenon_TV_eb : zenon_U), (forall W : zenon_U, ((ssList W)->(((segmentP zenon_TV_eb (nil))/\(segmentP (nil) W))->(segmentP zenon_TV_eb W)))) -> (ssList zenon_TU_dx) -> (segmentP zenon_TV_eb (nil)) -> (segmentP (nil) zenon_TU_dx) -> (~(segmentP zenon_TV_eb zenon_TU_dx)) -> False). % 40.69/40.87 do 2 intro. intros zenon_H6d zenon_H6e zenon_H6b zenon_H6f zenon_H70. % 40.69/40.87 generalize (zenon_H6d zenon_TU_dx). zenon_intro zenon_H71. % 40.69/40.87 apply (zenon_imply_s _ _ zenon_H71); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ]. % 40.69/40.87 exact (zenon_H73 zenon_H6e). % 40.69/40.87 apply (zenon_imply_s _ _ zenon_H72); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ]. % 40.69/40.87 apply (zenon_notand_s _ _ zenon_H75); [ zenon_intro zenon_H68 | zenon_intro zenon_H76 ]. % 40.69/40.87 exact (zenon_H68 zenon_H6b). % 40.69/40.87 exact (zenon_H76 zenon_H6f). % 40.69/40.87 exact (zenon_H70 zenon_H74). % 40.69/40.87 (* end of lemma zenon_L4_ *) % 40.69/40.87 assert (zenon_L5_ : forall (zenon_TU_dx : zenon_U) (zenon_TV_eb : zenon_U), (forall V : zenon_U, ((ssList V)->(forall W : zenon_U, ((ssList W)->(((segmentP zenon_TV_eb V)/\(segmentP V W))->(segmentP zenon_TV_eb W)))))) -> (ssList zenon_TU_dx) -> (segmentP zenon_TV_eb (nil)) -> (segmentP (nil) zenon_TU_dx) -> (~(segmentP zenon_TV_eb zenon_TU_dx)) -> False). % 40.69/40.87 do 2 intro. intros zenon_H77 zenon_H6e zenon_H6b zenon_H6f zenon_H70. % 40.69/40.87 generalize (zenon_H77 (nil)). zenon_intro zenon_H78. % 40.69/40.87 apply (zenon_imply_s _ _ zenon_H78); [ zenon_intro zenon_H79 | zenon_intro zenon_H6d ]. % 40.69/40.87 exact (zenon_H79 ax17). % 40.69/40.87 apply (zenon_L4_ zenon_TU_dx zenon_TV_eb); trivial. % 40.69/40.87 (* end of lemma zenon_L5_ *) % 40.69/40.87 apply NNPP. intro zenon_G. % 40.69/40.87 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))\/((segmentP V U)/\(equalelemsP U))))))))))))) zenon_G); [ zenon_intro zenon_H7a; idtac ]. % 40.69/40.87 elim zenon_H7a. zenon_intro zenon_TU_dx. zenon_intro zenon_H7b. % 40.69/40.87 apply (zenon_notimply_s _ _ zenon_H7b). zenon_intro zenon_H6e. zenon_intro zenon_H7c. % 40.69/40.87 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))\/((segmentP V zenon_TU_dx)/\(equalelemsP zenon_TU_dx))))))))))) zenon_H7c); [ zenon_intro zenon_H7d; idtac ]. % 40.69/40.87 elim zenon_H7d. zenon_intro zenon_TV_eb. zenon_intro zenon_H7e. % 40.69/40.87 apply (zenon_notimply_s _ _ zenon_H7e). zenon_intro zenon_H67. zenon_intro zenon_H7f. % 40.69/40.87 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))\/((segmentP zenon_TV_eb zenon_TU_dx)/\(equalelemsP zenon_TU_dx))))))))) zenon_H7f); [ zenon_intro zenon_H80; idtac ]. % 40.69/40.88 elim zenon_H80. zenon_intro zenon_TW_dw. zenon_intro zenon_H81. % 40.69/40.88 apply (zenon_notimply_s _ _ zenon_H81). zenon_intro zenon_H83. zenon_intro zenon_H82. % 40.69/40.88 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~((nil) = zenon_TW_dw))\/((~(zenon_TV_eb = X))\/((~(zenon_TU_dx = zenon_TW_dw))\/((segmentP zenon_TV_eb zenon_TU_dx)/\(equalelemsP zenon_TU_dx))))))) zenon_H82); [ zenon_intro zenon_H84; idtac ]. % 40.69/40.88 elim zenon_H84. zenon_intro zenon_TX_fd. zenon_intro zenon_H86. % 40.69/40.88 apply (zenon_notimply_s _ _ zenon_H86). zenon_intro zenon_H88. zenon_intro zenon_H87. % 40.69/40.88 apply (zenon_notor_s _ _ zenon_H87). zenon_intro zenon_H8a. zenon_intro zenon_H89. % 40.69/40.88 apply (zenon_notor_s _ _ zenon_H89). zenon_intro zenon_H8c. zenon_intro zenon_H8b. % 40.69/40.88 apply (zenon_notor_s _ _ zenon_H8b). zenon_intro zenon_H8e. zenon_intro zenon_H8d. % 40.69/40.88 apply zenon_H8e. zenon_intro zenon_H63. % 40.69/40.88 apply zenon_H8a. zenon_intro zenon_H62. % 40.69/40.88 apply (zenon_notand_s _ _ zenon_H8d); [ zenon_intro zenon_H70 | zenon_intro zenon_H8f ]. % 40.69/40.88 generalize (ax7 zenon_TV_eb). zenon_intro zenon_H90. % 40.69/40.88 apply (zenon_imply_s _ _ zenon_H90); [ zenon_intro zenon_H6c | zenon_intro zenon_H91 ]. % 40.69/40.88 exact (zenon_H6c zenon_H67). % 40.69/40.88 generalize (ax58 zenon_TU_dx). zenon_intro zenon_H92. % 40.69/40.88 apply (zenon_imply_s _ _ zenon_H92); [ zenon_intro zenon_H73 | zenon_intro zenon_H93 ]. % 40.69/40.88 exact (zenon_H73 zenon_H6e). % 40.69/40.88 apply (zenon_equiv_s _ _ zenon_H93); [ zenon_intro zenon_H76; zenon_intro zenon_H61 | zenon_intro zenon_H6f; zenon_intro zenon_H94 ]. % 40.69/40.88 apply (zenon_L2_ zenon_TW_dw zenon_TU_dx); trivial. % 40.69/40.88 generalize (ax53 zenon_TV_eb). zenon_intro zenon_H95. % 40.69/40.88 apply (zenon_imply_s _ _ zenon_H95); [ zenon_intro zenon_H6c | zenon_intro zenon_H77 ]. % 40.69/40.88 exact (zenon_H6c zenon_H67). % 40.69/40.88 generalize (zenon_H91 (nil)). zenon_intro zenon_H96. % 40.69/40.88 apply (zenon_imply_s _ _ zenon_H96); [ zenon_intro zenon_H79 | zenon_intro zenon_H97 ]. % 40.69/40.88 exact (zenon_H79 ax17). % 40.69/40.88 apply (zenon_equiv_s _ _ zenon_H97); [ zenon_intro zenon_H68; zenon_intro zenon_H99 | zenon_intro zenon_H6b; zenon_intro zenon_H98 ]. % 40.69/40.88 apply (zenon_L3_ zenon_TV_eb); trivial. % 40.69/40.88 apply (zenon_L5_ zenon_TU_dx zenon_TV_eb); trivial. % 40.69/40.88 cut ((equalelemsP (nil)) = (equalelemsP zenon_TU_dx)). % 40.69/40.88 intro zenon_D_pnotp. % 40.69/40.88 apply zenon_H8f. % 40.69/40.88 rewrite <- zenon_D_pnotp. % 40.69/40.88 exact ax74. % 40.69/40.88 cut (((nil) = zenon_TU_dx)); [idtac | apply NNPP; zenon_intro zenon_H61]. % 40.69/40.88 congruence. % 40.69/40.88 apply (zenon_L2_ zenon_TW_dw zenon_TU_dx); trivial. % 40.69/40.88 Qed. % 40.69/40.88 % SZS output end Proof % 40.69/40.88 (* END-PROOF *) % 40.69/40.88 nodes searched: 494143 % 40.69/40.88 max branch formulas: 14926 % 40.69/40.88 proof nodes created: 35970 % 40.69/40.88 formulas created: 2424754 % 40.69/40.88 %------------------------------------------------------------------------------