TSTP Solution File: SWC127+1 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWC127+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 22:29:25 EDT 2022
% Result : Theorem 0.36s 0.56s
% Output : Proof 0.36s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SWC127+1 : TPTP v8.1.0. Released v2.4.0.
% 0.00/0.07 % Command : run_zenon %s %d
% 0.06/0.26 % Computer : n032.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 600
% 0.06/0.26 % DateTime : Sun Jun 12 15:32:56 EDT 2022
% 0.06/0.26 % CPUTime :
% 0.36/0.56 (* PROOF-FOUND *)
% 0.36/0.56 % SZS status Theorem
% 0.36/0.56 (* BEGIN-PROOF *)
% 0.36/0.56 % SZS output start Proof
% 0.36/0.56 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)))\/((~(segmentP X W))\/(((~(singletonP W))/\(neq X (nil)))\/((neq U (nil))/\(segmentP V U))))))))))))))).
% 0.36/0.56 Proof.
% 0.36/0.56 assert (zenon_L1_ : (~((nil) = (nil))) -> False).
% 0.36/0.56 do 0 intro. intros zenon_H60.
% 0.36/0.56 apply zenon_H60. apply refl_equal.
% 0.36/0.56 (* end of lemma zenon_L1_ *)
% 0.36/0.56 apply NNPP. intro zenon_G.
% 0.36/0.56 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)))\/((~(segmentP X W))\/(((~(singletonP W))/\(neq X (nil)))\/((neq U (nil))/\(segmentP V U))))))))))))))) zenon_G); [ zenon_intro zenon_H61; idtac ].
% 0.36/0.56 elim zenon_H61. zenon_intro zenon_TU_du. zenon_intro zenon_H63.
% 0.36/0.56 apply (zenon_notimply_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64.
% 0.36/0.56 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))\/((~(neq V (nil)))\/((~(segmentP X W))\/(((~(singletonP W))/\(neq X (nil)))\/((neq zenon_TU_du (nil))/\(segmentP V zenon_TU_du))))))))))))) zenon_H64); [ zenon_intro zenon_H66; idtac ].
% 0.36/0.56 elim zenon_H66. zenon_intro zenon_TV_dz. zenon_intro zenon_H68.
% 0.36/0.56 apply (zenon_notimply_s _ _ zenon_H68). zenon_intro zenon_H6a. zenon_intro zenon_H69.
% 0.36/0.56 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(zenon_TV_dz = X))\/((~(zenon_TU_du = W))\/((~(neq zenon_TV_dz (nil)))\/((~(segmentP X W))\/(((~(singletonP W))/\(neq X (nil)))\/((neq zenon_TU_du (nil))/\(segmentP zenon_TV_dz zenon_TU_du))))))))))) zenon_H69); [ zenon_intro zenon_H6b; idtac ].
% 0.36/0.56 elim zenon_H6b. zenon_intro zenon_TW_ee. zenon_intro zenon_H6d.
% 0.36/0.56 apply (zenon_notimply_s _ _ zenon_H6d). zenon_intro zenon_H6f. zenon_intro zenon_H6e.
% 0.36/0.56 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~(zenon_TV_dz = X))\/((~(zenon_TU_du = zenon_TW_ee))\/((~(neq zenon_TV_dz (nil)))\/((~(segmentP X zenon_TW_ee))\/(((~(singletonP zenon_TW_ee))/\(neq X (nil)))\/((neq zenon_TU_du (nil))/\(segmentP zenon_TV_dz zenon_TU_du))))))))) zenon_H6e); [ zenon_intro zenon_H70; idtac ].
% 0.36/0.56 elim zenon_H70. zenon_intro zenon_TX_ej. zenon_intro zenon_H72.
% 0.36/0.56 apply (zenon_notimply_s _ _ zenon_H72). zenon_intro zenon_H74. zenon_intro zenon_H73.
% 0.36/0.56 apply (zenon_notor_s _ _ zenon_H73). zenon_intro zenon_H76. zenon_intro zenon_H75.
% 0.36/0.56 apply (zenon_notor_s _ _ zenon_H75). zenon_intro zenon_H78. zenon_intro zenon_H77.
% 0.36/0.56 apply (zenon_notor_s _ _ zenon_H77). zenon_intro zenon_H7a. zenon_intro zenon_H79.
% 0.36/0.56 apply (zenon_notor_s _ _ zenon_H79). zenon_intro zenon_H7c. zenon_intro zenon_H7b.
% 0.36/0.56 apply (zenon_notor_s _ _ zenon_H7b). zenon_intro zenon_H7e. zenon_intro zenon_H7d.
% 0.36/0.56 apply zenon_H7c. zenon_intro zenon_H7f.
% 0.36/0.56 apply zenon_H7a. zenon_intro zenon_H80.
% 0.36/0.56 apply zenon_H78. zenon_intro zenon_H81.
% 0.36/0.56 apply zenon_H76. zenon_intro zenon_H82.
% 0.36/0.56 apply (zenon_notand_s _ _ zenon_H7e); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ].
% 0.36/0.56 apply zenon_H84. zenon_intro zenon_H85.
% 0.36/0.56 apply (zenon_notand_s _ _ zenon_H7d); [ zenon_intro zenon_H87 | zenon_intro zenon_H86 ].
% 0.36/0.56 cut ((singletonP zenon_TW_ee) = (singletonP (nil))).
% 0.36/0.56 intro zenon_D_pnotp.
% 0.36/0.56 apply ax39.
% 0.36/0.56 rewrite <- zenon_D_pnotp.
% 0.36/0.56 exact zenon_H85.
% 0.36/0.56 cut ((zenon_TW_ee = (nil))); [idtac | apply NNPP; zenon_intro zenon_H88].
% 0.36/0.56 congruence.
% 0.36/0.56 generalize (ax15 zenon_TU_du). zenon_intro zenon_H89.
% 0.36/0.56 apply (zenon_imply_s _ _ zenon_H89); [ zenon_intro zenon_H8b | zenon_intro zenon_H8a ].
% 0.36/0.56 exact (zenon_H8b zenon_H65).
% 0.36/0.56 generalize (zenon_H8a (nil)). zenon_intro zenon_H8c.
% 0.36/0.56 apply (zenon_imply_s _ _ zenon_H8c); [ zenon_intro zenon_H8e | zenon_intro zenon_H8d ].
% 0.36/0.56 exact (zenon_H8e ax17).
% 0.36/0.56 apply (zenon_equiv_s _ _ zenon_H8d); [ zenon_intro zenon_H87; zenon_intro zenon_H91 | zenon_intro zenon_H90; zenon_intro zenon_H8f ].
% 0.36/0.56 apply zenon_H91. zenon_intro zenon_H92.
% 0.36/0.56 elim (classic ((nil) = (nil))); [ zenon_intro zenon_H93 | zenon_intro zenon_H60 ].
% 0.36/0.56 cut (((nil) = (nil)) = (zenon_TW_ee = (nil))).
% 0.36/0.56 intro zenon_D_pnotp.
% 0.36/0.56 apply zenon_H88.
% 0.36/0.56 rewrite <- zenon_D_pnotp.
% 0.36/0.56 exact zenon_H93.
% 0.36/0.56 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 0.36/0.56 cut (((nil) = zenon_TW_ee)); [idtac | apply NNPP; zenon_intro zenon_H94].
% 0.36/0.56 congruence.
% 0.36/0.56 cut ((zenon_TU_du = zenon_TW_ee) = ((nil) = zenon_TW_ee)).
% 0.36/0.56 intro zenon_D_pnotp.
% 0.36/0.56 apply zenon_H94.
% 0.36/0.56 rewrite <- zenon_D_pnotp.
% 0.36/0.56 exact zenon_H81.
% 0.36/0.56 cut ((zenon_TW_ee = zenon_TW_ee)); [idtac | apply NNPP; zenon_intro zenon_H95].
% 0.36/0.56 cut ((zenon_TU_du = (nil))); [idtac | apply NNPP; zenon_intro zenon_H8f].
% 0.36/0.56 congruence.
% 0.36/0.56 exact (zenon_H8f zenon_H92).
% 0.36/0.56 apply zenon_H95. apply refl_equal.
% 0.36/0.56 apply zenon_H60. apply refl_equal.
% 0.36/0.56 apply zenon_H60. apply refl_equal.
% 0.36/0.56 exact (zenon_H87 zenon_H90).
% 0.36/0.56 cut ((segmentP zenon_TX_ej zenon_TW_ee) = (segmentP zenon_TV_dz zenon_TU_du)).
% 0.36/0.56 intro zenon_D_pnotp.
% 0.36/0.56 apply zenon_H86.
% 0.36/0.56 rewrite <- zenon_D_pnotp.
% 0.36/0.56 exact zenon_H7f.
% 0.36/0.56 cut ((zenon_TW_ee = zenon_TU_du)); [idtac | apply NNPP; zenon_intro zenon_H96].
% 0.36/0.56 cut ((zenon_TX_ej = zenon_TV_dz)); [idtac | apply NNPP; zenon_intro zenon_H97].
% 0.36/0.56 congruence.
% 0.36/0.56 apply zenon_H97. apply sym_equal. exact zenon_H82.
% 0.36/0.56 apply zenon_H96. apply sym_equal. exact zenon_H81.
% 0.36/0.56 cut ((neq zenon_TV_dz (nil)) = (neq zenon_TX_ej (nil))).
% 0.36/0.56 intro zenon_D_pnotp.
% 0.36/0.56 apply zenon_H83.
% 0.36/0.56 rewrite <- zenon_D_pnotp.
% 0.36/0.56 exact zenon_H80.
% 0.36/0.56 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 0.36/0.56 cut ((zenon_TV_dz = zenon_TX_ej)); [idtac | apply NNPP; zenon_intro zenon_H98].
% 0.36/0.56 congruence.
% 0.36/0.56 exact (zenon_H98 zenon_H82).
% 0.36/0.56 apply zenon_H60. apply refl_equal.
% 0.36/0.56 Qed.
% 0.36/0.56 % SZS output end Proof
% 0.36/0.56 (* END-PROOF *)
% 0.36/0.56 nodes searched: 5852
% 0.36/0.56 max branch formulas: 2141
% 0.36/0.56 proof nodes created: 426
% 0.36/0.56 formulas created: 33194
% 0.36/0.56
%------------------------------------------------------------------------------