TSTP Solution File: SWC026+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWC026+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 22:28:55 EDT 2022
% Result : Theorem 0.38s 0.55s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SWC026+1 : TPTP v8.1.0. Released v2.4.0.
% 0.07/0.12 % Command : run_zenon %s %d
% 0.13/0.33 % Computer : n012.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 : Sat Jun 11 23:40:56 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.38/0.55 (* PROOF-FOUND *)
% 0.38/0.55 % SZS status Theorem
% 0.38/0.55 (* BEGIN-PROOF *)
% 0.38/0.55 % SZS output start Proof
% 0.38/0.55 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))\/(((~((nil) = X))/\((nil) = W))\/(((~((nil) = W))/\((nil) = X))\/(((~((nil) = V))\/((nil) = U))/\((~((nil) = U))\/((nil) = V))))))))))))))).
% 0.38/0.55 Proof.
% 0.38/0.55 assert (zenon_L1_ : (~((nil) = (nil))) -> False).
% 0.38/0.55 do 0 intro. intros zenon_H60.
% 0.38/0.55 apply zenon_H60. apply refl_equal.
% 0.38/0.55 (* end of lemma zenon_L1_ *)
% 0.38/0.55 apply NNPP. intro zenon_G.
% 0.38/0.55 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))\/(((~((nil) = X))/\((nil) = W))\/(((~((nil) = W))/\((nil) = X))\/(((~((nil) = V))\/((nil) = U))/\((~((nil) = U))\/((nil) = V))))))))))))))) zenon_G); [ zenon_intro zenon_H61; idtac ].
% 0.38/0.55 elim zenon_H61. zenon_intro zenon_TU_du. zenon_intro zenon_H63.
% 0.38/0.55 apply (zenon_notimply_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64.
% 0.38/0.55 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_du = W))\/(((~((nil) = X))/\((nil) = W))\/(((~((nil) = W))/\((nil) = X))\/(((~((nil) = V))\/((nil) = zenon_TU_du))/\((~((nil) = zenon_TU_du))\/((nil) = V))))))))))))) zenon_H64); [ zenon_intro zenon_H66; idtac ].
% 0.38/0.55 elim zenon_H66. zenon_intro zenon_TV_dz. zenon_intro zenon_H68.
% 0.38/0.55 apply (zenon_notimply_s _ _ zenon_H68). zenon_intro zenon_H6a. zenon_intro zenon_H69.
% 0.38/0.55 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(zenon_TV_dz = X))\/((~(zenon_TU_du = W))\/(((~((nil) = X))/\((nil) = W))\/(((~((nil) = W))/\((nil) = X))\/(((~((nil) = zenon_TV_dz))\/((nil) = zenon_TU_du))/\((~((nil) = zenon_TU_du))\/((nil) = zenon_TV_dz))))))))))) zenon_H69); [ zenon_intro zenon_H6b; idtac ].
% 0.38/0.55 elim zenon_H6b. zenon_intro zenon_TW_ee. zenon_intro zenon_H6d.
% 0.38/0.55 apply (zenon_notimply_s _ _ zenon_H6d). zenon_intro zenon_H6f. zenon_intro zenon_H6e.
% 0.38/0.55 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~(zenon_TV_dz = X))\/((~(zenon_TU_du = zenon_TW_ee))\/(((~((nil) = X))/\((nil) = zenon_TW_ee))\/(((~((nil) = zenon_TW_ee))/\((nil) = X))\/(((~((nil) = zenon_TV_dz))\/((nil) = zenon_TU_du))/\((~((nil) = zenon_TU_du))\/((nil) = zenon_TV_dz))))))))) zenon_H6e); [ zenon_intro zenon_H70; idtac ].
% 0.38/0.55 elim zenon_H70. zenon_intro zenon_TX_ej. zenon_intro zenon_H72.
% 0.38/0.55 apply (zenon_notimply_s _ _ zenon_H72). zenon_intro zenon_H74. zenon_intro zenon_H73.
% 0.38/0.55 apply (zenon_notor_s _ _ zenon_H73). zenon_intro zenon_H76. zenon_intro zenon_H75.
% 0.38/0.55 apply (zenon_notor_s _ _ zenon_H75). zenon_intro zenon_H78. zenon_intro zenon_H77.
% 0.38/0.55 apply (zenon_notor_s _ _ zenon_H77). zenon_intro zenon_H7a. zenon_intro zenon_H79.
% 0.38/0.55 apply (zenon_notor_s _ _ zenon_H79). zenon_intro zenon_H7c. zenon_intro zenon_H7b.
% 0.38/0.55 apply zenon_H78. zenon_intro zenon_H7d.
% 0.38/0.55 apply zenon_H76. zenon_intro zenon_H7e.
% 0.38/0.55 apply (zenon_notand_s _ _ zenon_H7a); [ zenon_intro zenon_H80 | zenon_intro zenon_H7f ].
% 0.38/0.55 apply zenon_H80. zenon_intro zenon_H81.
% 0.38/0.55 apply (zenon_notand_s _ _ zenon_H7c); [ zenon_intro zenon_H83 | zenon_intro zenon_H82 ].
% 0.38/0.55 apply zenon_H83. zenon_intro zenon_H84.
% 0.38/0.55 apply (zenon_notand_s _ _ zenon_H7b); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ].
% 0.38/0.55 apply (zenon_notor_s _ _ zenon_H86). zenon_intro zenon_H88. zenon_intro zenon_H87.
% 0.38/0.55 cut (((nil) = zenon_TW_ee) = ((nil) = zenon_TU_du)).
% 0.38/0.55 intro zenon_D_pnotp.
% 0.38/0.55 apply zenon_H87.
% 0.38/0.55 rewrite <- zenon_D_pnotp.
% 0.38/0.55 exact zenon_H84.
% 0.38/0.55 cut ((zenon_TW_ee = zenon_TU_du)); [idtac | apply NNPP; zenon_intro zenon_H89].
% 0.38/0.55 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 0.38/0.55 congruence.
% 0.38/0.55 apply zenon_H60. apply refl_equal.
% 0.38/0.55 apply zenon_H89. apply sym_equal. exact zenon_H7d.
% 0.38/0.55 apply (zenon_notor_s _ _ zenon_H85). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 0.38/0.55 cut (((nil) = zenon_TX_ej) = ((nil) = zenon_TV_dz)).
% 0.38/0.55 intro zenon_D_pnotp.
% 0.38/0.55 apply zenon_H8a.
% 0.38/0.55 rewrite <- zenon_D_pnotp.
% 0.38/0.55 exact zenon_H81.
% 0.38/0.55 cut ((zenon_TX_ej = zenon_TV_dz)); [idtac | apply NNPP; zenon_intro zenon_H8c].
% 0.38/0.55 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 0.38/0.55 congruence.
% 0.38/0.55 apply zenon_H60. apply refl_equal.
% 0.38/0.55 apply zenon_H8c. apply sym_equal. exact zenon_H7e.
% 0.38/0.55 exact (zenon_H82 zenon_H81).
% 0.38/0.55 apply (zenon_notand_s _ _ zenon_H7c); [ zenon_intro zenon_H83 | zenon_intro zenon_H82 ].
% 0.38/0.55 exact (zenon_H83 zenon_H7f).
% 0.38/0.55 apply (zenon_notand_s _ _ zenon_H7b); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ].
% 0.38/0.55 apply (zenon_notor_s _ _ zenon_H86). zenon_intro zenon_H88. zenon_intro zenon_H87.
% 0.38/0.55 apply zenon_H88. zenon_intro zenon_H8d.
% 0.38/0.55 cut ((zenon_TV_dz = zenon_TX_ej) = ((nil) = zenon_TX_ej)).
% 0.38/0.55 intro zenon_D_pnotp.
% 0.38/0.55 apply zenon_H82.
% 0.38/0.55 rewrite <- zenon_D_pnotp.
% 0.38/0.55 exact zenon_H7e.
% 0.38/0.55 cut ((zenon_TX_ej = zenon_TX_ej)); [idtac | apply NNPP; zenon_intro zenon_H8e].
% 0.38/0.55 cut ((zenon_TV_dz = (nil))); [idtac | apply NNPP; zenon_intro zenon_H8f].
% 0.38/0.55 congruence.
% 0.38/0.55 elim (classic ((nil) = (nil))); [ zenon_intro zenon_H90 | zenon_intro zenon_H60 ].
% 0.38/0.55 cut (((nil) = (nil)) = (zenon_TV_dz = (nil))).
% 0.38/0.55 intro zenon_D_pnotp.
% 0.38/0.55 apply zenon_H8f.
% 0.38/0.55 rewrite <- zenon_D_pnotp.
% 0.38/0.55 exact zenon_H90.
% 0.38/0.55 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 0.38/0.55 cut (((nil) = zenon_TV_dz)); [idtac | apply NNPP; zenon_intro zenon_H8a].
% 0.38/0.55 congruence.
% 0.38/0.55 exact (zenon_H8a zenon_H8d).
% 0.38/0.55 apply zenon_H60. apply refl_equal.
% 0.38/0.55 apply zenon_H60. apply refl_equal.
% 0.38/0.55 apply zenon_H8e. apply refl_equal.
% 0.38/0.55 apply (zenon_notor_s _ _ zenon_H85). zenon_intro zenon_H8b. zenon_intro zenon_H8a.
% 0.38/0.55 apply zenon_H8b. zenon_intro zenon_H91.
% 0.38/0.55 cut ((zenon_TU_du = zenon_TW_ee) = ((nil) = zenon_TW_ee)).
% 0.38/0.55 intro zenon_D_pnotp.
% 0.38/0.55 apply zenon_H7f.
% 0.38/0.55 rewrite <- zenon_D_pnotp.
% 0.38/0.55 exact zenon_H7d.
% 0.38/0.55 cut ((zenon_TW_ee = zenon_TW_ee)); [idtac | apply NNPP; zenon_intro zenon_H92].
% 0.38/0.55 cut ((zenon_TU_du = (nil))); [idtac | apply NNPP; zenon_intro zenon_H93].
% 0.38/0.55 congruence.
% 0.38/0.55 elim (classic ((nil) = (nil))); [ zenon_intro zenon_H90 | zenon_intro zenon_H60 ].
% 0.38/0.55 cut (((nil) = (nil)) = (zenon_TU_du = (nil))).
% 0.38/0.55 intro zenon_D_pnotp.
% 0.38/0.55 apply zenon_H93.
% 0.38/0.55 rewrite <- zenon_D_pnotp.
% 0.38/0.55 exact zenon_H90.
% 0.38/0.55 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 0.38/0.55 cut (((nil) = zenon_TU_du)); [idtac | apply NNPP; zenon_intro zenon_H87].
% 0.38/0.55 congruence.
% 0.38/0.55 exact (zenon_H87 zenon_H91).
% 0.38/0.55 apply zenon_H60. apply refl_equal.
% 0.38/0.55 apply zenon_H60. apply refl_equal.
% 0.38/0.55 apply zenon_H92. apply refl_equal.
% 0.38/0.55 Qed.
% 0.38/0.55 % SZS output end Proof
% 0.38/0.55 (* END-PROOF *)
% 0.38/0.55 nodes searched: 2607
% 0.38/0.55 max branch formulas: 811
% 0.38/0.55 proof nodes created: 39
% 0.38/0.55 formulas created: 16169
% 0.38/0.55
%------------------------------------------------------------------------------