TSTP Solution File: SWC367+1 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWC367+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n009.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 44.54s 44.80s
% Output : Proof 44.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : SWC367+1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.09 % Command : run_zenon %s %d
% 0.08/0.28 % Computer : n009.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Sun Jun 12 12:41:38 EDT 2022
% 0.08/0.28 % CPUTime :
% 44.54/44.80 (* PROOF-FOUND *)
% 44.54/44.80 % SZS status Theorem
% 44.54/44.80 (* BEGIN-PROOF *)
% 44.54/44.80 % SZS output start Proof
% 44.54/44.80 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))\/((rearsegP V U)\/(((~((nil) = X))\/(~((nil) = W)))/\((~(neq W (nil)))\/(~(rearsegP X W))))))))))))))).
% 44.54/44.80 Proof.
% 44.54/44.80 assert (zenon_L1_ : (~((nil) = (nil))) -> False).
% 44.54/44.80 do 0 intro. intros zenon_H60.
% 44.54/44.80 apply zenon_H60. apply refl_equal.
% 44.54/44.80 (* end of lemma zenon_L1_ *)
% 44.54/44.80 assert (zenon_L2_ : forall (zenon_TU_dy : zenon_U) (zenon_TV_dz : zenon_U), (forall W : zenon_U, ((ssList W)->(((rearsegP zenon_TV_dz (nil))/\(rearsegP (nil) W))->(rearsegP zenon_TV_dz W)))) -> (ssList zenon_TU_dy) -> (rearsegP zenon_TV_dz (nil)) -> (rearsegP (nil) zenon_TU_dy) -> (~(rearsegP zenon_TV_dz zenon_TU_dy)) -> False).
% 44.54/44.80 do 2 intro. intros zenon_H61 zenon_H62 zenon_H63 zenon_H64 zenon_H65.
% 44.54/44.80 generalize (zenon_H61 zenon_TU_dy). zenon_intro zenon_H68.
% 44.54/44.80 apply (zenon_imply_s _ _ zenon_H68); [ zenon_intro zenon_H6a | zenon_intro zenon_H69 ].
% 44.54/44.80 exact (zenon_H6a zenon_H62).
% 44.54/44.80 apply (zenon_imply_s _ _ zenon_H69); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ].
% 44.54/44.80 apply (zenon_notand_s _ _ zenon_H6c); [ zenon_intro zenon_H6e | zenon_intro zenon_H6d ].
% 44.54/44.80 exact (zenon_H6e zenon_H63).
% 44.54/44.80 exact (zenon_H6d zenon_H64).
% 44.54/44.80 exact (zenon_H65 zenon_H6b).
% 44.54/44.80 (* end of lemma zenon_L2_ *)
% 44.54/44.80 assert (zenon_L3_ : forall (zenon_TW_ek : zenon_U) (zenon_TX_el : zenon_U) (zenon_TU_dy : zenon_U) (zenon_TV_dz : zenon_U), (~(rearsegP zenon_TV_dz zenon_TU_dy)) -> (rearsegP zenon_TX_el zenon_TW_ek) -> (zenon_TU_dy = zenon_TW_ek) -> (zenon_TV_dz = zenon_TX_el) -> False).
% 44.54/44.80 do 4 intro. intros zenon_H65 zenon_H6f zenon_H70 zenon_H71.
% 44.54/44.80 cut ((rearsegP zenon_TX_el zenon_TW_ek) = (rearsegP zenon_TV_dz zenon_TU_dy)).
% 44.54/44.80 intro zenon_D_pnotp.
% 44.54/44.80 apply zenon_H65.
% 44.54/44.80 rewrite <- zenon_D_pnotp.
% 44.54/44.80 exact zenon_H6f.
% 44.54/44.80 cut ((zenon_TW_ek = zenon_TU_dy)); [idtac | apply NNPP; zenon_intro zenon_H74].
% 44.54/44.80 cut ((zenon_TX_el = zenon_TV_dz)); [idtac | apply NNPP; zenon_intro zenon_H75].
% 44.54/44.80 congruence.
% 44.54/44.80 apply zenon_H75. apply sym_equal. exact zenon_H71.
% 44.54/44.80 apply zenon_H74. apply sym_equal. exact zenon_H70.
% 44.54/44.80 (* end of lemma zenon_L3_ *)
% 44.54/44.80 apply NNPP. intro zenon_G.
% 44.54/44.80 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))\/((rearsegP V U)\/(((~((nil) = X))\/(~((nil) = W)))/\((~(neq W (nil)))\/(~(rearsegP X W))))))))))))))) zenon_G); [ zenon_intro zenon_H76; idtac ].
% 44.54/44.80 elim zenon_H76. zenon_intro zenon_TU_dy. zenon_intro zenon_H77.
% 44.54/44.80 apply (zenon_notimply_s _ _ zenon_H77). zenon_intro zenon_H62. zenon_intro zenon_H78.
% 44.54/44.80 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))\/((rearsegP V zenon_TU_dy)\/(((~((nil) = X))\/(~((nil) = W)))/\((~(neq W (nil)))\/(~(rearsegP X W))))))))))))) zenon_H78); [ zenon_intro zenon_H79; idtac ].
% 44.54/44.80 elim zenon_H79. zenon_intro zenon_TV_dz. zenon_intro zenon_H7a.
% 44.54/44.80 apply (zenon_notimply_s _ _ zenon_H7a). zenon_intro zenon_H7c. zenon_intro zenon_H7b.
% 44.54/44.80 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(zenon_TV_dz = X))\/((~(zenon_TU_dy = W))\/((rearsegP zenon_TV_dz zenon_TU_dy)\/(((~((nil) = X))\/(~((nil) = W)))/\((~(neq W (nil)))\/(~(rearsegP X W))))))))))) zenon_H7b); [ zenon_intro zenon_H7d; idtac ].
% 44.54/44.80 elim zenon_H7d. zenon_intro zenon_TW_ek. zenon_intro zenon_H7e.
% 44.54/44.80 apply (zenon_notimply_s _ _ zenon_H7e). zenon_intro zenon_H80. zenon_intro zenon_H7f.
% 44.54/44.80 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~(zenon_TV_dz = X))\/((~(zenon_TU_dy = zenon_TW_ek))\/((rearsegP zenon_TV_dz zenon_TU_dy)\/(((~((nil) = X))\/(~((nil) = zenon_TW_ek)))/\((~(neq zenon_TW_ek (nil)))\/(~(rearsegP X zenon_TW_ek))))))))) zenon_H7f); [ zenon_intro zenon_H81; idtac ].
% 44.54/44.80 elim zenon_H81. zenon_intro zenon_TX_el. zenon_intro zenon_H82.
% 44.54/44.80 apply (zenon_notimply_s _ _ zenon_H82). zenon_intro zenon_H84. zenon_intro zenon_H83.
% 44.54/44.80 apply (zenon_notor_s _ _ zenon_H83). zenon_intro zenon_H86. zenon_intro zenon_H85.
% 44.54/44.81 apply (zenon_notor_s _ _ zenon_H85). zenon_intro zenon_H88. zenon_intro zenon_H87.
% 44.54/44.81 apply (zenon_notor_s _ _ zenon_H87). zenon_intro zenon_H65. zenon_intro zenon_H89.
% 44.54/44.81 apply zenon_H88. zenon_intro zenon_H70.
% 44.54/44.81 apply zenon_H86. zenon_intro zenon_H71.
% 44.54/44.81 apply (zenon_notand_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8a ].
% 44.54/44.81 apply (zenon_notor_s _ _ zenon_H8b). zenon_intro zenon_H8d. zenon_intro zenon_H8c.
% 44.54/44.81 apply zenon_H8c. zenon_intro zenon_H8e.
% 44.54/44.81 generalize (ax52 zenon_TU_dy). zenon_intro zenon_H8f.
% 44.54/44.81 apply (zenon_imply_s _ _ zenon_H8f); [ zenon_intro zenon_H6a | zenon_intro zenon_H90 ].
% 44.54/44.81 exact (zenon_H6a zenon_H62).
% 44.54/44.81 apply (zenon_equiv_s _ _ zenon_H90); [ zenon_intro zenon_H6d; zenon_intro zenon_H92 | zenon_intro zenon_H64; zenon_intro zenon_H91 ].
% 44.54/44.81 cut (((nil) = zenon_TW_ek) = ((nil) = zenon_TU_dy)).
% 44.54/44.81 intro zenon_D_pnotp.
% 44.54/44.81 apply zenon_H92.
% 44.54/44.81 rewrite <- zenon_D_pnotp.
% 44.54/44.81 exact zenon_H8e.
% 44.54/44.81 cut ((zenon_TW_ek = zenon_TU_dy)); [idtac | apply NNPP; zenon_intro zenon_H74].
% 44.54/44.81 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 44.54/44.81 congruence.
% 44.54/44.81 apply zenon_H60. apply refl_equal.
% 44.54/44.81 apply zenon_H74. apply sym_equal. exact zenon_H70.
% 44.54/44.81 generalize (ax47 zenon_TV_dz). zenon_intro zenon_H93.
% 44.54/44.81 apply (zenon_imply_s _ _ zenon_H93); [ zenon_intro zenon_H95 | zenon_intro zenon_H94 ].
% 44.54/44.81 exact (zenon_H95 zenon_H7c).
% 44.54/44.81 generalize (zenon_H94 (nil)). zenon_intro zenon_H96.
% 44.54/44.81 apply (zenon_imply_s _ _ zenon_H96); [ zenon_intro zenon_H97 | zenon_intro zenon_H61 ].
% 44.54/44.81 exact (zenon_H97 ax17).
% 44.54/44.81 generalize (ax51 zenon_TV_dz). zenon_intro zenon_H98.
% 44.54/44.81 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H95 | zenon_intro zenon_H63 ].
% 44.54/44.81 exact (zenon_H95 zenon_H7c).
% 44.54/44.81 apply (zenon_L2_ zenon_TU_dy zenon_TV_dz); trivial.
% 44.54/44.81 apply (zenon_notor_s _ _ zenon_H8a). zenon_intro zenon_H9a. zenon_intro zenon_H99.
% 44.54/44.81 apply zenon_H99. zenon_intro zenon_H6f.
% 44.54/44.81 apply (zenon_L3_ zenon_TW_ek zenon_TX_el zenon_TU_dy zenon_TV_dz); trivial.
% 44.54/44.81 Qed.
% 44.54/44.81 % SZS output end Proof
% 44.54/44.81 (* END-PROOF *)
% 44.54/44.81 nodes searched: 408599
% 44.54/44.81 max branch formulas: 15173
% 44.54/44.81 proof nodes created: 27188
% 44.54/44.81 formulas created: 2116118
% 44.54/44.81
%------------------------------------------------------------------------------