TSTP Solution File: SWC103+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWC103+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n032.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 22:29:18 EDT 2022
% Result : Theorem 0.14s 0.46s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.10 % Problem : SWC103+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.10 % Command : run_zenon %s %d
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Sun Jun 12 07:17:25 EDT 2022
% 0.10/0.29 % CPUTime :
% 0.14/0.46 (* PROOF-FOUND *)
% 0.14/0.46 % SZS status Theorem
% 0.14/0.46 (* BEGIN-PROOF *)
% 0.14/0.46 % SZS output start Proof
% 0.14/0.46 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))\/((~(neq V (nil)))\/(((~((nil) = W))/\((nil) = X))\/(((neq U (nil))/\(frontsegP V U))\/((neq X (nil))/\((~(neq W (nil)))\/(~(frontsegP X W))))))))))))))))).
% 0.14/0.46 Proof.
% 0.14/0.46 assert (zenon_L1_ : (~((nil) = (nil))) -> False).
% 0.14/0.46 do 0 intro. intros zenon_H60.
% 0.14/0.46 apply zenon_H60. apply refl_equal.
% 0.14/0.46 (* end of lemma zenon_L1_ *)
% 0.14/0.46 assert (zenon_L2_ : forall (zenon_TV_dw : zenon_U) (zenon_TX_dx : zenon_U), (~(neq zenon_TX_dx (nil))) -> (neq zenon_TV_dw (nil)) -> (zenon_TV_dw = zenon_TX_dx) -> False).
% 0.14/0.46 do 2 intro. intros zenon_H61 zenon_H62 zenon_H63.
% 0.14/0.46 cut ((neq zenon_TV_dw (nil)) = (neq zenon_TX_dx (nil))).
% 0.14/0.46 intro zenon_D_pnotp.
% 0.14/0.46 apply zenon_H61.
% 0.14/0.46 rewrite <- zenon_D_pnotp.
% 0.14/0.46 exact zenon_H62.
% 0.14/0.46 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 0.14/0.46 cut ((zenon_TV_dw = zenon_TX_dx)); [idtac | apply NNPP; zenon_intro zenon_H66].
% 0.14/0.46 congruence.
% 0.14/0.46 exact (zenon_H66 zenon_H63).
% 0.14/0.46 apply zenon_H60. apply refl_equal.
% 0.14/0.46 (* end of lemma zenon_L2_ *)
% 0.14/0.46 apply NNPP. intro zenon_G.
% 0.14/0.46 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))\/((~(neq V (nil)))\/(((~((nil) = W))/\((nil) = X))\/(((neq U (nil))/\(frontsegP V U))\/((neq X (nil))/\((~(neq W (nil)))\/(~(frontsegP X W))))))))))))))))) zenon_G); [ zenon_intro zenon_H67; idtac ].
% 0.14/0.46 elim zenon_H67. zenon_intro zenon_TU_ea. zenon_intro zenon_H69.
% 0.14/0.46 apply (zenon_notimply_s _ _ zenon_H69). zenon_intro zenon_H6b. zenon_intro zenon_H6a.
% 0.14/0.46 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_ea = W))\/((~(neq V (nil)))\/(((~((nil) = W))/\((nil) = X))\/(((neq zenon_TU_ea (nil))/\(frontsegP V zenon_TU_ea))\/((neq X (nil))/\((~(neq W (nil)))\/(~(frontsegP X W))))))))))))))) zenon_H6a); [ zenon_intro zenon_H6c; idtac ].
% 0.14/0.46 elim zenon_H6c. zenon_intro zenon_TV_dw. zenon_intro zenon_H6d.
% 0.14/0.46 apply (zenon_notimply_s _ _ zenon_H6d). zenon_intro zenon_H6f. zenon_intro zenon_H6e.
% 0.14/0.46 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(zenon_TV_dw = X))\/((~(zenon_TU_ea = W))\/((~(neq zenon_TV_dw (nil)))\/(((~((nil) = W))/\((nil) = X))\/(((neq zenon_TU_ea (nil))/\(frontsegP zenon_TV_dw zenon_TU_ea))\/((neq X (nil))/\((~(neq W (nil)))\/(~(frontsegP X W))))))))))))) zenon_H6e); [ zenon_intro zenon_H70; idtac ].
% 0.14/0.46 elim zenon_H70. zenon_intro zenon_TW_ej. zenon_intro zenon_H72.
% 0.14/0.46 apply (zenon_notimply_s _ _ zenon_H72). zenon_intro zenon_H74. zenon_intro zenon_H73.
% 0.14/0.46 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~(zenon_TV_dw = X))\/((~(zenon_TU_ea = zenon_TW_ej))\/((~(neq zenon_TV_dw (nil)))\/(((~((nil) = zenon_TW_ej))/\((nil) = X))\/(((neq zenon_TU_ea (nil))/\(frontsegP zenon_TV_dw zenon_TU_ea))\/((neq X (nil))/\((~(neq zenon_TW_ej (nil)))\/(~(frontsegP X zenon_TW_ej))))))))))) zenon_H73); [ zenon_intro zenon_H75; idtac ].
% 0.14/0.46 elim zenon_H75. zenon_intro zenon_TX_dx. zenon_intro zenon_H76.
% 0.14/0.46 apply (zenon_notimply_s _ _ zenon_H76). zenon_intro zenon_H78. zenon_intro zenon_H77.
% 0.14/0.46 apply (zenon_notor_s _ _ zenon_H77). zenon_intro zenon_H7a. zenon_intro zenon_H79.
% 0.14/0.46 apply (zenon_notor_s _ _ zenon_H79). zenon_intro zenon_H7c. zenon_intro zenon_H7b.
% 0.14/0.46 apply (zenon_notor_s _ _ zenon_H7b). zenon_intro zenon_H7e. zenon_intro zenon_H7d.
% 0.14/0.46 apply (zenon_notor_s _ _ zenon_H7d). zenon_intro zenon_H80. zenon_intro zenon_H7f.
% 0.14/0.46 apply (zenon_notor_s _ _ zenon_H7f). zenon_intro zenon_H82. zenon_intro zenon_H81.
% 0.14/0.46 apply zenon_H7e. zenon_intro zenon_H62.
% 0.14/0.46 apply zenon_H7c. zenon_intro zenon_H83.
% 0.14/0.46 apply zenon_H7a. zenon_intro zenon_H63.
% 0.14/0.46 apply (zenon_notand_s _ _ zenon_H82); [ zenon_intro zenon_H85 | zenon_intro zenon_H84 ].
% 0.14/0.46 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H61 | zenon_intro zenon_H86 ].
% 0.14/0.46 apply (zenon_L2_ zenon_TV_dw zenon_TX_dx); trivial.
% 0.14/0.46 apply (zenon_notor_s _ _ zenon_H86). zenon_intro zenon_H88. zenon_intro zenon_H87.
% 0.14/0.46 apply zenon_H88. zenon_intro zenon_H89.
% 0.14/0.46 cut ((neq zenon_TW_ej (nil)) = (neq zenon_TU_ea (nil))).
% 0.14/0.46 intro zenon_D_pnotp.
% 0.14/0.46 apply zenon_H85.
% 0.14/0.46 rewrite <- zenon_D_pnotp.
% 0.14/0.46 exact zenon_H89.
% 0.14/0.46 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 0.14/0.46 cut ((zenon_TW_ej = zenon_TU_ea)); [idtac | apply NNPP; zenon_intro zenon_H8a].
% 0.14/0.46 congruence.
% 0.14/0.46 apply zenon_H8a. apply sym_equal. exact zenon_H83.
% 0.14/0.46 apply zenon_H60. apply refl_equal.
% 0.14/0.46 apply (zenon_notand_s _ _ zenon_H81); [ zenon_intro zenon_H61 | zenon_intro zenon_H86 ].
% 0.14/0.46 apply (zenon_L2_ zenon_TV_dw zenon_TX_dx); trivial.
% 0.14/0.46 apply (zenon_notor_s _ _ zenon_H86). zenon_intro zenon_H88. zenon_intro zenon_H87.
% 0.14/0.46 apply zenon_H87. zenon_intro zenon_H8b.
% 0.14/0.46 cut ((frontsegP zenon_TX_dx zenon_TW_ej) = (frontsegP zenon_TV_dw zenon_TU_ea)).
% 0.14/0.46 intro zenon_D_pnotp.
% 0.14/0.46 apply zenon_H84.
% 0.14/0.46 rewrite <- zenon_D_pnotp.
% 0.14/0.46 exact zenon_H8b.
% 0.14/0.46 cut ((zenon_TW_ej = zenon_TU_ea)); [idtac | apply NNPP; zenon_intro zenon_H8a].
% 0.14/0.46 cut ((zenon_TX_dx = zenon_TV_dw)); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 0.14/0.46 congruence.
% 0.14/0.46 apply zenon_H8c. apply sym_equal. exact zenon_H63.
% 0.14/0.46 apply zenon_H8a. apply sym_equal. exact zenon_H83.
% 0.14/0.46 Qed.
% 0.14/0.46 % SZS output end Proof
% 0.14/0.46 (* END-PROOF *)
% 0.14/0.46 nodes searched: 2737
% 0.14/0.46 max branch formulas: 993
% 0.14/0.46 proof nodes created: 56
% 0.14/0.46 formulas created: 14700
% 0.14/0.46
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