TSTP Solution File: SWC131+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWC131+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n012.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 22:29:27 EDT 2022
% Result : Theorem 1.15s 1.31s
% Output : Proof 1.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWC131+1 : TPTP v8.1.0. Released v2.4.0.
% 0.03/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n012.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sun Jun 12 19:44:11 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.15/1.31 (* PROOF-FOUND *)
% 1.15/1.31 % SZS status Theorem
% 1.15/1.31 (* BEGIN-PROOF *)
% 1.15/1.31 % SZS output start Proof
% 1.15/1.31 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 X (nil))\/(cyclefreeP V)))))))))))).
% 1.15/1.31 Proof.
% 1.15/1.31 assert (zenon_L1_ : forall (zenon_TX_dv : zenon_U), ((neq zenon_TX_dv (nil))<->(~(zenon_TX_dv = (nil)))) -> (~(neq zenon_TX_dv (nil))) -> (~(zenon_TX_dv = (nil))) -> False).
% 1.15/1.31 do 1 intro. intros zenon_H60 zenon_H61 zenon_H62.
% 1.15/1.31 apply (zenon_equiv_s _ _ zenon_H60); [ zenon_intro zenon_H61; zenon_intro zenon_H65 | zenon_intro zenon_H64; zenon_intro zenon_H62 ].
% 1.15/1.31 exact (zenon_H65 zenon_H62).
% 1.15/1.31 exact (zenon_H61 zenon_H64).
% 1.15/1.31 (* end of lemma zenon_L1_ *)
% 1.15/1.31 assert (zenon_L2_ : forall (zenon_TX_dv : zenon_U), (ssList zenon_TX_dv) -> (~(neq zenon_TX_dv (nil))) -> (~(zenon_TX_dv = (nil))) -> False).
% 1.15/1.31 do 1 intro. intros zenon_H66 zenon_H61 zenon_H62.
% 1.15/1.31 generalize (ax15 zenon_TX_dv). zenon_intro zenon_H67.
% 1.15/1.31 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ].
% 1.15/1.31 exact (zenon_H69 zenon_H66).
% 1.15/1.31 generalize (zenon_H68 (nil)). zenon_intro zenon_H6a.
% 1.15/1.31 apply (zenon_imply_s _ _ zenon_H6a); [ zenon_intro zenon_H6b | zenon_intro zenon_H60 ].
% 1.15/1.31 exact (zenon_H6b ax17).
% 1.15/1.31 apply (zenon_L1_ zenon_TX_dv); trivial.
% 1.15/1.31 (* end of lemma zenon_L2_ *)
% 1.15/1.31 apply NNPP. intro zenon_G.
% 1.15/1.31 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 X (nil))\/(cyclefreeP V)))))))))))) zenon_G); [ zenon_intro zenon_H6c; idtac ].
% 1.15/1.31 elim zenon_H6c. zenon_intro zenon_TU_ef. zenon_intro zenon_H6e.
% 1.15/1.31 apply (zenon_notimply_s _ _ zenon_H6e). zenon_intro zenon_H70. zenon_intro zenon_H6f.
% 1.15/1.31 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_ef = W))\/((neq X (nil))\/(cyclefreeP V)))))))))) zenon_H6f); [ zenon_intro zenon_H71; idtac ].
% 1.15/1.31 elim zenon_H71. zenon_intro zenon_TV_ek. zenon_intro zenon_H73.
% 1.15/1.31 apply (zenon_notimply_s _ _ zenon_H73). zenon_intro zenon_H75. zenon_intro zenon_H74.
% 1.15/1.31 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(zenon_TV_ek = X))\/((~(zenon_TU_ef = W))\/((neq X (nil))\/(cyclefreeP zenon_TV_ek)))))))) zenon_H74); [ zenon_intro zenon_H76; idtac ].
% 1.15/1.31 elim zenon_H76. zenon_intro zenon_TW_ep. zenon_intro zenon_H78.
% 1.15/1.31 apply (zenon_notimply_s _ _ zenon_H78). zenon_intro zenon_H7a. zenon_intro zenon_H79.
% 1.15/1.31 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~(zenon_TV_ek = X))\/((~(zenon_TU_ef = zenon_TW_ep))\/((neq X (nil))\/(cyclefreeP zenon_TV_ek)))))) zenon_H79); [ zenon_intro zenon_H7b; idtac ].
% 1.15/1.31 elim zenon_H7b. zenon_intro zenon_TX_dv. zenon_intro zenon_H7c.
% 1.15/1.31 apply (zenon_notimply_s _ _ zenon_H7c). zenon_intro zenon_H66. zenon_intro zenon_H7d.
% 1.15/1.31 apply (zenon_notor_s _ _ zenon_H7d). zenon_intro zenon_H7f. zenon_intro zenon_H7e.
% 1.15/1.31 apply (zenon_notor_s _ _ zenon_H7e). zenon_intro zenon_H81. zenon_intro zenon_H80.
% 1.15/1.31 apply (zenon_notor_s _ _ zenon_H80). zenon_intro zenon_H61. zenon_intro zenon_H82.
% 1.15/1.31 apply zenon_H7f. zenon_intro zenon_H83.
% 1.15/1.31 cut ((cyclefreeP (nil)) = (cyclefreeP zenon_TV_ek)).
% 1.15/1.31 intro zenon_D_pnotp.
% 1.15/1.31 apply zenon_H82.
% 1.15/1.31 rewrite <- zenon_D_pnotp.
% 1.15/1.31 exact ax60.
% 1.15/1.31 cut (((nil) = zenon_TV_ek)); [idtac | apply NNPP; zenon_intro zenon_H84].
% 1.15/1.31 congruence.
% 1.15/1.31 elim (classic (zenon_TV_ek = zenon_TV_ek)); [ zenon_intro zenon_H85 | zenon_intro zenon_H86 ].
% 1.15/1.31 cut ((zenon_TV_ek = zenon_TV_ek) = ((nil) = zenon_TV_ek)).
% 1.15/1.31 intro zenon_D_pnotp.
% 1.15/1.31 apply zenon_H84.
% 1.15/1.31 rewrite <- zenon_D_pnotp.
% 1.15/1.31 exact zenon_H85.
% 1.15/1.31 cut ((zenon_TV_ek = zenon_TV_ek)); [idtac | apply NNPP; zenon_intro zenon_H86].
% 1.15/1.31 cut ((zenon_TV_ek = (nil))); [idtac | apply NNPP; zenon_intro zenon_H87].
% 1.15/1.31 congruence.
% 1.15/1.31 cut ((zenon_TV_ek = zenon_TX_dv) = (zenon_TV_ek = (nil))).
% 1.15/1.31 intro zenon_D_pnotp.
% 1.15/1.31 apply zenon_H87.
% 1.15/1.31 rewrite <- zenon_D_pnotp.
% 1.15/1.31 exact zenon_H83.
% 1.15/1.31 cut ((zenon_TX_dv = (nil))); [idtac | apply NNPP; zenon_intro zenon_H62].
% 1.15/1.31 cut ((zenon_TV_ek = zenon_TV_ek)); [idtac | apply NNPP; zenon_intro zenon_H86].
% 1.15/1.31 congruence.
% 1.15/1.31 apply zenon_H86. apply refl_equal.
% 1.15/1.31 apply (zenon_L2_ zenon_TX_dv); trivial.
% 1.15/1.31 apply zenon_H86. apply refl_equal.
% 1.15/1.31 apply zenon_H86. apply refl_equal.
% 1.15/1.31 Qed.
% 1.15/1.31 % SZS output end Proof
% 1.15/1.31 (* END-PROOF *)
% 1.15/1.31 nodes searched: 13172
% 1.15/1.31 max branch formulas: 4972
% 1.15/1.31 proof nodes created: 1179
% 1.15/1.31 formulas created: 84014
% 1.15/1.31
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