TSTP Solution File: SWC349+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWC349+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n022.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 22:30:34 EDT 2022
% Result : Theorem 32.05s 32.27s
% Output : Proof 32.05s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWC349+1 : TPTP v8.1.0. Released v2.4.0.
% 0.06/0.12 % Command : run_zenon %s %d
% 0.13/0.33 % Computer : n022.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 : Sun Jun 12 22:36:03 EDT 2022
% 0.13/0.33 % CPUTime :
% 32.05/32.27 (* PROOF-FOUND *)
% 32.05/32.27 % SZS status Theorem
% 32.05/32.27 (* BEGIN-PROOF *)
% 32.05/32.27 % SZS output start Proof
% 32.05/32.27 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)->((~((nil) = W))\/((~(V = X))\/((~(U = W))\/((~(neq V (nil)))\/(frontsegP V U))))))))))))).
% 32.05/32.27 Proof.
% 32.05/32.27 assert (zenon_L1_ : (~((nil) = (nil))) -> False).
% 32.05/32.27 do 0 intro. intros zenon_H60.
% 32.05/32.27 apply zenon_H60. apply refl_equal.
% 32.05/32.27 (* end of lemma zenon_L1_ *)
% 32.05/32.27 assert (zenon_L2_ : forall (zenon_TW_dw : zenon_U) (zenon_TU_dx : zenon_U), (~((nil) = zenon_TU_dx)) -> ((nil) = zenon_TW_dw) -> (zenon_TU_dx = zenon_TW_dw) -> False).
% 32.05/32.27 do 2 intro. intros zenon_H61 zenon_H62 zenon_H63.
% 32.05/32.27 cut (((nil) = zenon_TW_dw) = ((nil) = zenon_TU_dx)).
% 32.05/32.27 intro zenon_D_pnotp.
% 32.05/32.27 apply zenon_H61.
% 32.05/32.27 rewrite <- zenon_D_pnotp.
% 32.05/32.27 exact zenon_H62.
% 32.05/32.27 cut ((zenon_TW_dw = zenon_TU_dx)); [idtac | apply NNPP; zenon_intro zenon_H66].
% 32.05/32.27 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 32.05/32.27 congruence.
% 32.05/32.27 apply zenon_H60. apply refl_equal.
% 32.05/32.27 apply zenon_H66. apply sym_equal. exact zenon_H63.
% 32.05/32.27 (* end of lemma zenon_L2_ *)
% 32.05/32.27 assert (zenon_L3_ : forall (zenon_TV_eb : zenon_U), (ssList zenon_TV_eb) -> (~(frontsegP zenon_TV_eb (nil))) -> False).
% 32.05/32.27 do 1 intro. intros zenon_H67 zenon_H68.
% 32.05/32.27 generalize (ax45 zenon_TV_eb). zenon_intro zenon_H6a.
% 32.05/32.27 apply (zenon_imply_s _ _ zenon_H6a); [ zenon_intro zenon_H6c | zenon_intro zenon_H6b ].
% 32.05/32.27 exact (zenon_H6c zenon_H67).
% 32.05/32.27 exact (zenon_H68 zenon_H6b).
% 32.05/32.27 (* end of lemma zenon_L3_ *)
% 32.05/32.27 assert (zenon_L4_ : forall (zenon_TU_dx : zenon_U) (zenon_TV_eb : zenon_U), (forall W : zenon_U, ((ssList W)->(((frontsegP zenon_TV_eb (nil))/\(frontsegP (nil) W))->(frontsegP zenon_TV_eb W)))) -> (ssList zenon_TU_dx) -> (frontsegP zenon_TV_eb (nil)) -> (frontsegP (nil) zenon_TU_dx) -> (~(frontsegP zenon_TV_eb zenon_TU_dx)) -> False).
% 32.05/32.27 do 2 intro. intros zenon_H6d zenon_H6e zenon_H6b zenon_H6f zenon_H70.
% 32.05/32.27 generalize (zenon_H6d zenon_TU_dx). zenon_intro zenon_H71.
% 32.05/32.27 apply (zenon_imply_s _ _ zenon_H71); [ zenon_intro zenon_H73 | zenon_intro zenon_H72 ].
% 32.05/32.27 exact (zenon_H73 zenon_H6e).
% 32.05/32.27 apply (zenon_imply_s _ _ zenon_H72); [ zenon_intro zenon_H75 | zenon_intro zenon_H74 ].
% 32.05/32.27 apply (zenon_notand_s _ _ zenon_H75); [ zenon_intro zenon_H68 | zenon_intro zenon_H76 ].
% 32.05/32.27 exact (zenon_H68 zenon_H6b).
% 32.05/32.27 exact (zenon_H76 zenon_H6f).
% 32.05/32.27 exact (zenon_H70 zenon_H74).
% 32.05/32.27 (* end of lemma zenon_L4_ *)
% 32.05/32.27 assert (zenon_L5_ : forall (zenon_TU_dx : zenon_U) (zenon_TV_eb : zenon_U), ((ssList (nil))->(forall W : zenon_U, ((ssList W)->(((frontsegP zenon_TV_eb (nil))/\(frontsegP (nil) W))->(frontsegP zenon_TV_eb W))))) -> (~(frontsegP zenon_TV_eb zenon_TU_dx)) -> (frontsegP (nil) zenon_TU_dx) -> (frontsegP zenon_TV_eb (nil)) -> (ssList zenon_TU_dx) -> False).
% 32.05/32.27 do 2 intro. intros zenon_H77 zenon_H70 zenon_H6f zenon_H6b zenon_H6e.
% 32.05/32.27 apply (zenon_imply_s _ _ zenon_H77); [ zenon_intro zenon_H78 | zenon_intro zenon_H6d ].
% 32.05/32.27 exact (zenon_H78 ax17).
% 32.05/32.27 apply (zenon_L4_ zenon_TU_dx zenon_TV_eb); trivial.
% 32.05/32.27 (* end of lemma zenon_L5_ *)
% 32.05/32.27 assert (zenon_L6_ : forall (zenon_TU_dx : zenon_U) (zenon_TV_eb : zenon_U), (ssList zenon_TV_eb) -> (~(frontsegP zenon_TV_eb zenon_TU_dx)) -> (frontsegP (nil) zenon_TU_dx) -> (ssList zenon_TU_dx) -> (forall V : zenon_U, ((ssList V)->((frontsegP zenon_TV_eb V)<->(exists W : zenon_U, ((ssList W)/\((app V W) = zenon_TV_eb)))))) -> False).
% 32.05/32.27 do 2 intro. intros zenon_H67 zenon_H70 zenon_H6f zenon_H6e zenon_H79.
% 32.05/32.27 generalize (ax40 zenon_TV_eb). zenon_intro zenon_H7a.
% 32.05/32.27 apply (zenon_imply_s _ _ zenon_H7a); [ zenon_intro zenon_H6c | zenon_intro zenon_H7b ].
% 32.05/32.27 exact (zenon_H6c zenon_H67).
% 32.05/32.27 generalize (zenon_H7b (nil)). zenon_intro zenon_H77.
% 32.05/32.27 generalize (zenon_H79 (nil)). zenon_intro zenon_H7c.
% 32.05/32.27 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H78 | zenon_intro zenon_H7d ].
% 32.05/32.27 exact (zenon_H78 ax17).
% 32.05/32.27 apply (zenon_equiv_s _ _ zenon_H7d); [ zenon_intro zenon_H68; zenon_intro zenon_H7f | zenon_intro zenon_H6b; zenon_intro zenon_H7e ].
% 32.05/32.27 apply (zenon_L3_ zenon_TV_eb); trivial.
% 32.05/32.27 apply (zenon_L5_ zenon_TU_dx zenon_TV_eb); trivial.
% 32.05/32.27 (* end of lemma zenon_L6_ *)
% 32.05/32.27 apply NNPP. intro zenon_G.
% 32.05/32.27 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)->((~((nil) = W))\/((~(V = X))\/((~(U = W))\/((~(neq V (nil)))\/(frontsegP V U))))))))))))) zenon_G); [ zenon_intro zenon_H80; idtac ].
% 32.05/32.28 elim zenon_H80. zenon_intro zenon_TU_dx. zenon_intro zenon_H81.
% 32.05/32.28 apply (zenon_notimply_s _ _ zenon_H81). zenon_intro zenon_H6e. zenon_intro zenon_H82.
% 32.05/32.28 apply (zenon_notallex_s (fun V : zenon_U => ((ssList V)->(forall W : zenon_U, ((ssList W)->(forall X : zenon_U, ((ssList X)->((~((nil) = W))\/((~(V = X))\/((~(zenon_TU_dx = W))\/((~(neq V (nil)))\/(frontsegP V zenon_TU_dx))))))))))) zenon_H82); [ zenon_intro zenon_H83; idtac ].
% 32.05/32.28 elim zenon_H83. zenon_intro zenon_TV_eb. zenon_intro zenon_H84.
% 32.05/32.28 apply (zenon_notimply_s _ _ zenon_H84). zenon_intro zenon_H67. zenon_intro zenon_H85.
% 32.05/32.28 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~((nil) = W))\/((~(zenon_TV_eb = X))\/((~(zenon_TU_dx = W))\/((~(neq zenon_TV_eb (nil)))\/(frontsegP zenon_TV_eb zenon_TU_dx))))))))) zenon_H85); [ zenon_intro zenon_H86; idtac ].
% 32.05/32.28 elim zenon_H86. zenon_intro zenon_TW_dw. zenon_intro zenon_H87.
% 32.05/32.28 apply (zenon_notimply_s _ _ zenon_H87). zenon_intro zenon_H89. zenon_intro zenon_H88.
% 32.05/32.28 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~((nil) = zenon_TW_dw))\/((~(zenon_TV_eb = X))\/((~(zenon_TU_dx = zenon_TW_dw))\/((~(neq zenon_TV_eb (nil)))\/(frontsegP zenon_TV_eb zenon_TU_dx))))))) zenon_H88); [ zenon_intro zenon_H8a; idtac ].
% 32.05/32.28 elim zenon_H8a. zenon_intro zenon_TX_fj. zenon_intro zenon_H8c.
% 32.05/32.28 apply (zenon_notimply_s _ _ zenon_H8c). zenon_intro zenon_H8e. zenon_intro zenon_H8d.
% 32.05/32.28 apply (zenon_notor_s _ _ zenon_H8d). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 32.05/32.28 apply (zenon_notor_s _ _ zenon_H8f). zenon_intro zenon_H92. zenon_intro zenon_H91.
% 32.05/32.28 apply (zenon_notor_s _ _ zenon_H91). zenon_intro zenon_H94. zenon_intro zenon_H93.
% 32.05/32.28 apply (zenon_notor_s _ _ zenon_H93). zenon_intro zenon_H95. zenon_intro zenon_H70.
% 32.05/32.28 apply zenon_H94. zenon_intro zenon_H63.
% 32.05/32.28 apply zenon_H90. zenon_intro zenon_H62.
% 32.05/32.28 generalize (ax5 zenon_TV_eb). zenon_intro zenon_H96.
% 32.05/32.28 apply (zenon_imply_s _ _ zenon_H96); [ zenon_intro zenon_H6c | zenon_intro zenon_H79 ].
% 32.05/32.28 exact (zenon_H6c zenon_H67).
% 32.05/32.28 generalize (ax46 zenon_TU_dx). zenon_intro zenon_H97.
% 32.05/32.28 apply (zenon_imply_s _ _ zenon_H97); [ zenon_intro zenon_H73 | zenon_intro zenon_H98 ].
% 32.05/32.28 exact (zenon_H73 zenon_H6e).
% 32.05/32.28 apply (zenon_equiv_s _ _ zenon_H98); [ zenon_intro zenon_H76; zenon_intro zenon_H61 | zenon_intro zenon_H6f; zenon_intro zenon_H99 ].
% 32.05/32.28 apply (zenon_L2_ zenon_TW_dw zenon_TU_dx); trivial.
% 32.05/32.28 apply (zenon_L6_ zenon_TU_dx zenon_TV_eb); trivial.
% 32.05/32.28 Qed.
% 32.05/32.28 % SZS output end Proof
% 32.05/32.28 (* END-PROOF *)
% 32.05/32.28 nodes searched: 459860
% 32.05/32.28 max branch formulas: 10575
% 32.05/32.28 proof nodes created: 38087
% 32.05/32.28 formulas created: 2031329
% 32.05/32.28
%------------------------------------------------------------------------------