TSTP Solution File: SWC369+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWC369+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n015.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 22:30:40 EDT 2022
% Result : Theorem 5.32s 5.50s
% Output : Proof 5.32s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC369+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : run_zenon %s %d
% 0.13/0.33 % Computer : n015.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 20:29:22 EDT 2022
% 0.13/0.33 % CPUTime :
% 5.32/5.50 (* PROOF-FOUND *)
% 5.32/5.50 % SZS status Theorem
% 5.32/5.50 (* BEGIN-PROOF *)
% 5.32/5.50 % SZS output start Proof
% 5.32/5.50 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))\/((segmentP V U)\/(((~((nil) = W))/\((nil) = X))\/((neq X (nil))/\((~(neq W (nil)))\/(~(segmentP X W)))))))))))))))).
% 5.32/5.50 Proof.
% 5.32/5.50 assert (zenon_L1_ : (~((nil) = (nil))) -> False).
% 5.32/5.50 do 0 intro. intros zenon_H60.
% 5.32/5.50 apply zenon_H60. apply refl_equal.
% 5.32/5.50 (* end of lemma zenon_L1_ *)
% 5.32/5.50 assert (zenon_L2_ : forall (zenon_TU_dy : zenon_U) (zenon_TV_dz : zenon_U), (forall W : zenon_U, ((ssList W)->(((segmentP zenon_TV_dz (nil))/\(segmentP (nil) W))->(segmentP zenon_TV_dz W)))) -> (ssList zenon_TU_dy) -> (segmentP zenon_TV_dz (nil)) -> (segmentP (nil) zenon_TU_dy) -> (~(segmentP zenon_TV_dz zenon_TU_dy)) -> False).
% 5.32/5.50 do 2 intro. intros zenon_H61 zenon_H62 zenon_H63 zenon_H64 zenon_H65.
% 5.32/5.50 generalize (zenon_H61 zenon_TU_dy). zenon_intro zenon_H68.
% 5.32/5.50 apply (zenon_imply_s _ _ zenon_H68); [ zenon_intro zenon_H6a | zenon_intro zenon_H69 ].
% 5.32/5.50 exact (zenon_H6a zenon_H62).
% 5.32/5.50 apply (zenon_imply_s _ _ zenon_H69); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ].
% 5.32/5.50 apply (zenon_notand_s _ _ zenon_H6c); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ].
% 5.32/5.50 exact (zenon_H6e zenon_H63).
% 5.32/5.50 exact (zenon_H6d zenon_H64).
% 5.32/5.50 exact (zenon_H65 zenon_H6b).
% 5.32/5.50 (* end of lemma zenon_L2_ *)
% 5.32/5.50 assert (zenon_L3_ : forall (zenon_TX_ek : zenon_U), ((neq zenon_TX_ek (nil))<->(~(zenon_TX_ek = (nil)))) -> (~(neq zenon_TX_ek (nil))) -> (~((nil) = zenon_TX_ek)) -> False).
% 5.32/5.50 do 1 intro. intros zenon_H6f zenon_H70 zenon_H71.
% 5.32/5.50 apply (zenon_equiv_s _ _ zenon_H6f); [ zenon_intro zenon_H70; zenon_intro zenon_H75 | zenon_intro zenon_H74; zenon_intro zenon_H73 ].
% 5.32/5.50 apply zenon_H75. zenon_intro zenon_H76.
% 5.32/5.50 apply zenon_H71. apply sym_equal. exact zenon_H76.
% 5.32/5.50 exact (zenon_H70 zenon_H74).
% 5.32/5.50 (* end of lemma zenon_L3_ *)
% 5.32/5.50 assert (zenon_L4_ : forall (zenon_TW_es : zenon_U) (zenon_TX_ek : zenon_U) (zenon_TU_dy : zenon_U) (zenon_TV_dz : zenon_U), (~(segmentP zenon_TV_dz zenon_TU_dy)) -> (segmentP zenon_TX_ek zenon_TW_es) -> (zenon_TU_dy = zenon_TW_es) -> (zenon_TV_dz = zenon_TX_ek) -> False).
% 5.32/5.50 do 4 intro. intros zenon_H65 zenon_H77 zenon_H78 zenon_H79.
% 5.32/5.50 cut ((segmentP zenon_TX_ek zenon_TW_es) = (segmentP zenon_TV_dz zenon_TU_dy)).
% 5.32/5.50 intro zenon_D_pnotp.
% 5.32/5.50 apply zenon_H65.
% 5.32/5.50 rewrite <- zenon_D_pnotp.
% 5.32/5.50 exact zenon_H77.
% 5.32/5.50 cut ((zenon_TW_es = zenon_TU_dy)); [idtac | apply NNPP; zenon_intro zenon_H7b].
% 5.32/5.50 cut ((zenon_TX_ek = zenon_TV_dz)); [idtac | apply NNPP; zenon_intro zenon_H7c].
% 5.32/5.50 congruence.
% 5.32/5.50 apply zenon_H7c. apply sym_equal. exact zenon_H79.
% 5.32/5.50 apply zenon_H7b. apply sym_equal. exact zenon_H78.
% 5.32/5.50 (* end of lemma zenon_L4_ *)
% 5.32/5.50 assert (zenon_L5_ : forall (zenon_TU_dy : zenon_U) (zenon_TV_dz : zenon_U) (zenon_TX_ek : zenon_U) (zenon_TW_es : zenon_U), (~((~(neq zenon_TW_es (nil)))\/(~(segmentP zenon_TX_ek zenon_TW_es)))) -> (~(segmentP zenon_TV_dz zenon_TU_dy)) -> (zenon_TU_dy = zenon_TW_es) -> (zenon_TV_dz = zenon_TX_ek) -> False).
% 5.32/5.50 do 4 intro. intros zenon_H7d zenon_H65 zenon_H78 zenon_H79.
% 5.32/5.50 apply (zenon_notor_s _ _ zenon_H7d). zenon_intro zenon_H7f. zenon_intro zenon_H7e.
% 5.32/5.50 apply zenon_H7e. zenon_intro zenon_H77.
% 5.32/5.50 apply (zenon_L4_ zenon_TW_es zenon_TX_ek zenon_TU_dy zenon_TV_dz); trivial.
% 5.32/5.50 (* end of lemma zenon_L5_ *)
% 5.32/5.50 apply NNPP. intro zenon_G.
% 5.32/5.50 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))\/((segmentP V U)\/(((~((nil) = W))/\((nil) = X))\/((neq X (nil))/\((~(neq W (nil)))\/(~(segmentP X W)))))))))))))))) zenon_G); [ zenon_intro zenon_H80; idtac ].
% 5.32/5.50 elim zenon_H80. zenon_intro zenon_TU_dy. zenon_intro zenon_H81.
% 5.32/5.50 apply (zenon_notimply_s _ _ zenon_H81). zenon_intro zenon_H62. zenon_intro zenon_H82.
% 5.32/5.50 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_dy = W))\/((segmentP V zenon_TU_dy)\/(((~((nil) = W))/\((nil) = X))\/((neq X (nil))/\((~(neq W (nil)))\/(~(segmentP X W)))))))))))))) zenon_H82); [ zenon_intro zenon_H83; idtac ].
% 5.32/5.50 elim zenon_H83. zenon_intro zenon_TV_dz. zenon_intro zenon_H84.
% 5.32/5.50 apply (zenon_notimply_s _ _ zenon_H84). zenon_intro zenon_H86. zenon_intro zenon_H85.
% 5.32/5.50 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(zenon_TV_dz = X))\/((~(zenon_TU_dy = W))\/((segmentP zenon_TV_dz zenon_TU_dy)\/(((~((nil) = W))/\((nil) = X))\/((neq X (nil))/\((~(neq W (nil)))\/(~(segmentP X W)))))))))))) zenon_H85); [ zenon_intro zenon_H87; idtac ].
% 5.32/5.50 elim zenon_H87. zenon_intro zenon_TW_es. zenon_intro zenon_H88.
% 5.32/5.50 apply (zenon_notimply_s _ _ zenon_H88). zenon_intro zenon_H8a. zenon_intro zenon_H89.
% 5.32/5.50 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~(zenon_TV_dz = X))\/((~(zenon_TU_dy = zenon_TW_es))\/((segmentP zenon_TV_dz zenon_TU_dy)\/(((~((nil) = zenon_TW_es))/\((nil) = X))\/((neq X (nil))/\((~(neq zenon_TW_es (nil)))\/(~(segmentP X zenon_TW_es)))))))))) zenon_H89); [ zenon_intro zenon_H8b; idtac ].
% 5.32/5.50 elim zenon_H8b. zenon_intro zenon_TX_ek. zenon_intro zenon_H8c.
% 5.32/5.50 apply (zenon_notimply_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 5.32/5.50 apply (zenon_notor_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 5.32/5.50 apply (zenon_notor_s _ _ zenon_H8f). zenon_intro zenon_H92. zenon_intro zenon_H91.
% 5.32/5.50 apply (zenon_notor_s _ _ zenon_H91). zenon_intro zenon_H65. zenon_intro zenon_H93.
% 5.32/5.50 apply (zenon_notor_s _ _ zenon_H93). zenon_intro zenon_H95. zenon_intro zenon_H94.
% 5.32/5.50 apply zenon_H92. zenon_intro zenon_H78.
% 5.32/5.50 apply zenon_H90. zenon_intro zenon_H79.
% 5.32/5.50 apply (zenon_notand_s _ _ zenon_H95); [ zenon_intro zenon_H96 | zenon_intro zenon_H71 ].
% 5.32/5.50 apply zenon_H96. zenon_intro zenon_H97.
% 5.32/5.50 generalize (ax58 zenon_TU_dy). zenon_intro zenon_H98.
% 5.32/5.50 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H6a | zenon_intro zenon_H99 ].
% 5.32/5.50 exact (zenon_H6a zenon_H62).
% 5.32/5.50 apply (zenon_equiv_s _ _ zenon_H99); [ zenon_intro zenon_H6d; zenon_intro zenon_H9b | zenon_intro zenon_H64; zenon_intro zenon_H9a ].
% 5.32/5.50 cut (((nil) = zenon_TW_es) = ((nil) = zenon_TU_dy)).
% 5.32/5.50 intro zenon_D_pnotp.
% 5.32/5.50 apply zenon_H9b.
% 5.32/5.50 rewrite <- zenon_D_pnotp.
% 5.32/5.50 exact zenon_H97.
% 5.32/5.50 cut ((zenon_TW_es = zenon_TU_dy)); [idtac | apply NNPP; zenon_intro zenon_H7b].
% 5.32/5.50 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 5.32/5.50 congruence.
% 5.32/5.50 apply zenon_H60. apply refl_equal.
% 5.32/5.50 apply zenon_H7b. apply sym_equal. exact zenon_H78.
% 5.32/5.50 generalize (ax7 zenon_TV_dz). zenon_intro zenon_H9c.
% 5.32/5.50 apply (zenon_imply_s _ _ zenon_H9c); [ zenon_intro zenon_H9e | zenon_intro zenon_H9d ].
% 5.32/5.50 exact (zenon_H9e zenon_H86).
% 5.32/5.50 generalize (ax53 zenon_TV_dz). zenon_intro zenon_H9f.
% 5.32/5.50 apply (zenon_imply_s _ _ zenon_H9f); [ zenon_intro zenon_H9e | zenon_intro zenon_Ha0 ].
% 5.32/5.50 exact (zenon_H9e zenon_H86).
% 5.32/5.50 generalize (zenon_Ha0 (nil)). zenon_intro zenon_Ha1.
% 5.32/5.50 apply (zenon_imply_s _ _ zenon_Ha1); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H61 ].
% 5.32/5.50 exact (zenon_Ha2 ax17).
% 5.32/5.50 generalize (zenon_H9d (nil)). zenon_intro zenon_Ha3.
% 5.32/5.50 apply (zenon_imply_s _ _ zenon_Ha3); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha4 ].
% 5.32/5.50 exact (zenon_Ha2 ax17).
% 5.32/5.50 apply (zenon_equiv_s _ _ zenon_Ha4); [ zenon_intro zenon_H6e; zenon_intro zenon_Ha6 | zenon_intro zenon_H63; zenon_intro zenon_Ha5 ].
% 5.32/5.50 generalize (ax57 zenon_TV_dz). zenon_intro zenon_Ha7.
% 5.32/5.50 apply (zenon_imply_s _ _ zenon_Ha7); [ zenon_intro zenon_H9e | zenon_intro zenon_H63 ].
% 5.32/5.50 exact (zenon_H9e zenon_H86).
% 5.32/5.50 exact (zenon_H6e zenon_H63).
% 5.32/5.50 apply (zenon_L2_ zenon_TU_dy zenon_TV_dz); trivial.
% 5.32/5.50 apply (zenon_notand_s _ _ zenon_H94); [ zenon_intro zenon_H70 | zenon_intro zenon_H7d ].
% 5.32/5.50 generalize (ax15 zenon_TX_ek). zenon_intro zenon_Ha8.
% 5.32/5.50 apply (zenon_imply_s _ _ zenon_Ha8); [ zenon_intro zenon_Haa | zenon_intro zenon_Ha9 ].
% 5.32/5.50 exact (zenon_Haa zenon_H8e).
% 5.32/5.50 generalize (zenon_Ha9 (nil)). zenon_intro zenon_Hab.
% 5.32/5.50 apply (zenon_imply_s _ _ zenon_Hab); [ zenon_intro zenon_Ha2 | zenon_intro zenon_H6f ].
% 5.32/5.50 exact (zenon_Ha2 ax17).
% 5.32/5.50 apply (zenon_L3_ zenon_TX_ek); trivial.
% 5.32/5.50 apply (zenon_L5_ zenon_TU_dy zenon_TV_dz zenon_TX_ek zenon_TW_es); trivial.
% 5.32/5.50 Qed.
% 5.32/5.50 % SZS output end Proof
% 5.32/5.50 (* END-PROOF *)
% 5.32/5.50 nodes searched: 76670
% 5.32/5.50 max branch formulas: 7817
% 5.32/5.50 proof nodes created: 6615
% 5.32/5.50 formulas created: 363334
% 5.32/5.50
%------------------------------------------------------------------------------