TSTP Solution File: SWC387+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SWC387+1 : TPTP v8.1.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n018.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 22:30:46 EDT 2022
% Result : Theorem 37.26s 37.46s
% Output : Proof 37.26s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SWC387+1 : TPTP v8.1.0. Released v2.4.0.
% 0.04/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n018.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 11:02:41 EDT 2022
% 0.13/0.34 % CPUTime :
% 37.26/37.46 (* PROOF-FOUND *)
% 37.26/37.46 % SZS status Theorem
% 37.26/37.46 (* BEGIN-PROOF *)
% 37.26/37.46 % SZS output start Proof
% 37.26/37.46 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))\/((exists Y : zenon_U, ((ssItem Y)/\(((cons Y (nil)) = U)/\(memberP V Y))))\/(((~((nil) = W))/\((nil) = X))\/((((nil) = V)/\((nil) = U))\/((forall Z : zenon_U, ((ssItem Z)->((~((cons Z (nil)) = W))\/(~(memberP X Z)))))/\(neq X (nil)))))))))))))))).
% 37.26/37.46 Proof.
% 37.26/37.46 assert (zenon_L1_ : (~((nil) = (nil))) -> False).
% 37.26/37.46 do 0 intro. intros zenon_H60.
% 37.26/37.46 apply zenon_H60. apply refl_equal.
% 37.26/37.46 (* end of lemma zenon_L1_ *)
% 37.26/37.46 assert (zenon_L2_ : forall (zenon_TZ_dw : zenon_U) (zenon_TV_dx : zenon_U), ((memberP zenon_TV_dx zenon_TZ_dw)\/(memberP (nil) zenon_TZ_dw)) -> (~(memberP (nil) zenon_TZ_dw)) -> (~(memberP zenon_TV_dx zenon_TZ_dw)) -> False).
% 37.26/37.46 do 2 intro. intros zenon_H61 zenon_H62 zenon_H63.
% 37.26/37.46 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H67 | zenon_intro zenon_H66 ].
% 37.26/37.46 exact (zenon_H63 zenon_H67).
% 37.26/37.46 exact (zenon_H62 zenon_H66).
% 37.26/37.46 (* end of lemma zenon_L2_ *)
% 37.26/37.46 assert (zenon_L3_ : forall (zenon_TU_eg : zenon_U) (zenon_TV_dx : zenon_U) (zenon_TX_eh : zenon_U) (zenon_TW_ei : zenon_U), (~(forall Z : zenon_U, ((ssItem Z)->((~((cons Z (nil)) = zenon_TW_ei))\/(~(memberP zenon_TX_eh Z)))))) -> (ssList zenon_TX_eh) -> (zenon_TV_dx = zenon_TX_eh) -> (ssList zenon_TV_dx) -> (zenon_TU_eg = zenon_TW_ei) -> (~(exists Y : zenon_U, ((ssItem Y)/\(((cons Y (nil)) = zenon_TU_eg)/\(memberP zenon_TV_dx Y))))) -> False).
% 37.26/37.46 do 4 intro. intros zenon_H68 zenon_H69 zenon_H6a zenon_H6b zenon_H6c zenon_H6d.
% 37.26/37.46 apply (zenon_notallex_s (fun Z : zenon_U => ((ssItem Z)->((~((cons Z (nil)) = zenon_TW_ei))\/(~(memberP zenon_TX_eh Z))))) zenon_H68); [ zenon_intro zenon_H71; idtac ].
% 37.26/37.46 elim zenon_H71. zenon_intro zenon_TZ_dw. zenon_intro zenon_H72.
% 37.26/37.46 apply (zenon_notimply_s _ _ zenon_H72). zenon_intro zenon_H74. zenon_intro zenon_H73.
% 37.26/37.46 apply (zenon_notor_s _ _ zenon_H73). zenon_intro zenon_H76. zenon_intro zenon_H75.
% 37.26/37.46 apply zenon_H75. zenon_intro zenon_H77.
% 37.26/37.46 apply zenon_H76. zenon_intro zenon_H78.
% 37.26/37.46 generalize (ax31 zenon_TZ_dw). zenon_intro zenon_H79.
% 37.26/37.46 apply (zenon_imply_s _ _ zenon_H79); [ zenon_intro zenon_H7b | zenon_intro zenon_H7a ].
% 37.26/37.46 exact (zenon_H7b zenon_H74).
% 37.26/37.46 generalize (ax36 zenon_TZ_dw). zenon_intro zenon_H7c.
% 37.26/37.46 apply (zenon_imply_s _ _ zenon_H7c); [ zenon_intro zenon_H7b | zenon_intro zenon_H7d ].
% 37.26/37.46 exact (zenon_H7b zenon_H74).
% 37.26/37.46 apply zenon_H6d. exists zenon_TZ_dw. apply NNPP. zenon_intro zenon_H7e.
% 37.26/37.46 apply (zenon_notand_s _ _ zenon_H7e); [ zenon_intro zenon_H7b | zenon_intro zenon_H7f ].
% 37.26/37.46 exact (zenon_H7b zenon_H74).
% 37.26/37.46 apply (zenon_notand_s _ _ zenon_H7f); [ zenon_intro zenon_H80 | zenon_intro zenon_H63 ].
% 37.26/37.46 cut (((cons zenon_TZ_dw (nil)) = zenon_TW_ei) = ((cons zenon_TZ_dw (nil)) = zenon_TU_eg)).
% 37.26/37.46 intro zenon_D_pnotp.
% 37.26/37.46 apply zenon_H80.
% 37.26/37.46 rewrite <- zenon_D_pnotp.
% 37.26/37.46 exact zenon_H78.
% 37.26/37.46 cut ((zenon_TW_ei = zenon_TU_eg)); [idtac | apply NNPP; zenon_intro zenon_H81].
% 37.26/37.46 cut (((cons zenon_TZ_dw (nil)) = (cons zenon_TZ_dw (nil)))); [idtac | apply NNPP; zenon_intro zenon_H82].
% 37.26/37.46 congruence.
% 37.26/37.46 apply zenon_H82. apply refl_equal.
% 37.26/37.46 apply zenon_H81. apply sym_equal. exact zenon_H6c.
% 37.26/37.46 generalize (ax38 zenon_TZ_dw). zenon_intro zenon_H83.
% 37.26/37.46 apply (zenon_imply_s _ _ zenon_H83); [ zenon_intro zenon_H7b | zenon_intro zenon_H62 ].
% 37.26/37.46 exact (zenon_H7b zenon_H74).
% 37.26/37.46 generalize (zenon_H7d zenon_TV_dx). zenon_intro zenon_H84.
% 37.26/37.46 apply (zenon_imply_s _ _ zenon_H84); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ].
% 37.26/37.46 exact (zenon_H86 zenon_H6b).
% 37.26/37.46 generalize (ax90 zenon_TZ_dw). zenon_intro zenon_H87.
% 37.26/37.46 apply (zenon_imply_s _ _ zenon_H87); [ zenon_intro zenon_H7b | zenon_intro zenon_H88 ].
% 37.26/37.46 exact (zenon_H7b zenon_H74).
% 37.26/37.46 generalize (ax93 zenon_TZ_dw). zenon_intro zenon_H89.
% 37.26/37.46 apply (zenon_imply_s _ _ zenon_H89); [ zenon_intro zenon_H7b | zenon_intro zenon_H8a ].
% 37.26/37.46 exact (zenon_H7b zenon_H74).
% 37.26/37.46 generalize (zenon_H85 (nil)). zenon_intro zenon_H8b.
% 37.26/37.46 apply (zenon_imply_s _ _ zenon_H8b); [ zenon_intro zenon_H8d | zenon_intro zenon_H8c ].
% 37.26/37.46 exact (zenon_H8d ax17).
% 37.26/37.46 apply (zenon_equiv_s _ _ zenon_H8c); [ zenon_intro zenon_H90; zenon_intro zenon_H8f | zenon_intro zenon_H8e; zenon_intro zenon_H61 ].
% 37.26/37.46 generalize (zenon_H8a zenon_TZ_dw). zenon_intro zenon_H91.
% 37.26/37.46 apply (zenon_imply_s _ _ zenon_H91); [ zenon_intro zenon_H7b | zenon_intro zenon_H92 ].
% 37.26/37.46 exact (zenon_H7b zenon_H74).
% 37.26/37.46 apply (zenon_equiv_s _ _ zenon_H92); [ zenon_intro zenon_H88; zenon_intro zenon_H95 | zenon_intro zenon_H94; zenon_intro zenon_H93 ].
% 37.26/37.46 apply (zenon_notand_s _ _ zenon_H95); [ zenon_intro zenon_H97 | zenon_intro zenon_H96 ].
% 37.26/37.46 generalize (zenon_H7d zenon_TX_eh). zenon_intro zenon_H98.
% 37.26/37.46 apply (zenon_imply_s _ _ zenon_H98); [ zenon_intro zenon_H9a | zenon_intro zenon_H99 ].
% 37.26/37.46 exact (zenon_H9a zenon_H69).
% 37.26/37.46 generalize (zenon_H99 (nil)). zenon_intro zenon_H9b.
% 37.26/37.46 apply (zenon_imply_s _ _ zenon_H9b); [ zenon_intro zenon_H8d | zenon_intro zenon_H9c ].
% 37.26/37.46 exact (zenon_H8d ax17).
% 37.26/37.46 apply (zenon_equiv_s _ _ zenon_H9c); [ zenon_intro zenon_Ha0; zenon_intro zenon_H9f | zenon_intro zenon_H9e; zenon_intro zenon_H9d ].
% 37.26/37.46 apply (zenon_notor_s _ _ zenon_H9f). zenon_intro zenon_Ha1. zenon_intro zenon_H62.
% 37.26/37.46 exact (zenon_Ha1 zenon_H77).
% 37.26/37.46 cut ((memberP (app zenon_TX_eh (nil)) zenon_TZ_dw) = (memberP (app zenon_TV_dx (nil)) zenon_TZ_dw)).
% 37.26/37.46 intro zenon_D_pnotp.
% 37.26/37.46 apply zenon_H90.
% 37.26/37.46 rewrite <- zenon_D_pnotp.
% 37.26/37.46 exact zenon_H9e.
% 37.26/37.46 cut ((zenon_TZ_dw = zenon_TZ_dw)); [idtac | apply NNPP; zenon_intro zenon_Ha2].
% 37.26/37.46 cut (((app zenon_TX_eh (nil)) = (app zenon_TV_dx (nil)))); [idtac | apply NNPP; zenon_intro zenon_Ha3].
% 37.26/37.46 congruence.
% 37.26/37.46 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 37.26/37.46 cut ((zenon_TX_eh = zenon_TV_dx)); [idtac | apply NNPP; zenon_intro zenon_Ha4].
% 37.26/37.46 congruence.
% 37.26/37.46 apply zenon_Ha4. apply sym_equal. exact zenon_H6a.
% 37.26/37.46 apply zenon_H60. apply refl_equal.
% 37.26/37.46 exact (zenon_H97 zenon_Ha2).
% 37.26/37.46 exact (zenon_H96 zenon_H7a).
% 37.26/37.46 exact (zenon_H88 zenon_H94).
% 37.26/37.46 apply (zenon_L2_ zenon_TZ_dw zenon_TV_dx); trivial.
% 37.26/37.46 (* end of lemma zenon_L3_ *)
% 37.26/37.46 assert (zenon_L4_ : forall (zenon_TX_eh : zenon_U), ((neq zenon_TX_eh (nil))<->(~(zenon_TX_eh = (nil)))) -> (~(neq zenon_TX_eh (nil))) -> (~(zenon_TX_eh = (nil))) -> False).
% 37.26/37.46 do 1 intro. intros zenon_Ha5 zenon_Ha6 zenon_Ha7.
% 37.26/37.46 apply (zenon_equiv_s _ _ zenon_Ha5); [ zenon_intro zenon_Ha6; zenon_intro zenon_Ha9 | zenon_intro zenon_Ha8; zenon_intro zenon_Ha7 ].
% 37.26/37.46 exact (zenon_Ha9 zenon_Ha7).
% 37.26/37.46 exact (zenon_Ha6 zenon_Ha8).
% 37.26/37.46 (* end of lemma zenon_L4_ *)
% 37.26/37.46 assert (zenon_L5_ : forall (zenon_TX_eh : zenon_U), ((neq zenon_TX_eh (nil))<->(~(zenon_TX_eh = (nil)))) -> (~(neq zenon_TX_eh (nil))) -> (~((nil) = zenon_TX_eh)) -> False).
% 37.26/37.46 do 1 intro. intros zenon_Ha5 zenon_Ha6 zenon_Haa.
% 37.26/37.46 apply (zenon_equiv_s _ _ zenon_Ha5); [ zenon_intro zenon_Ha6; zenon_intro zenon_Ha9 | zenon_intro zenon_Ha8; zenon_intro zenon_Ha7 ].
% 37.26/37.46 apply zenon_Ha9. zenon_intro zenon_Hab.
% 37.26/37.46 apply zenon_Haa. apply sym_equal. exact zenon_Hab.
% 37.26/37.46 exact (zenon_Ha6 zenon_Ha8).
% 37.26/37.46 (* end of lemma zenon_L5_ *)
% 37.26/37.46 apply NNPP. intro zenon_G.
% 37.26/37.46 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))\/((exists Y : zenon_U, ((ssItem Y)/\(((cons Y (nil)) = U)/\(memberP V Y))))\/(((~((nil) = W))/\((nil) = X))\/((((nil) = V)/\((nil) = U))\/((forall Z : zenon_U, ((ssItem Z)->((~((cons Z (nil)) = W))\/(~(memberP X Z)))))/\(neq X (nil)))))))))))))))) zenon_G); [ zenon_intro zenon_Hac; idtac ].
% 37.26/37.46 elim zenon_Hac. zenon_intro zenon_TU_eg. zenon_intro zenon_Had.
% 37.26/37.46 apply (zenon_notimply_s _ _ zenon_Had). zenon_intro zenon_Haf. zenon_intro zenon_Hae.
% 37.26/37.46 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_eg = W))\/((exists Y : zenon_U, ((ssItem Y)/\(((cons Y (nil)) = zenon_TU_eg)/\(memberP V Y))))\/(((~((nil) = W))/\((nil) = X))\/((((nil) = V)/\((nil) = zenon_TU_eg))\/((forall Z : zenon_U, ((ssItem Z)->((~((cons Z (nil)) = W))\/(~(memberP X Z)))))/\(neq X (nil)))))))))))))) zenon_Hae); [ zenon_intro zenon_Hb0; idtac ].
% 37.26/37.46 elim zenon_Hb0. zenon_intro zenon_TV_dx. zenon_intro zenon_Hb1.
% 37.26/37.46 apply (zenon_notimply_s _ _ zenon_Hb1). zenon_intro zenon_H6b. zenon_intro zenon_Hb2.
% 37.26/37.46 apply (zenon_notallex_s (fun W : zenon_U => ((ssList W)->(forall X : zenon_U, ((ssList X)->((~(zenon_TV_dx = X))\/((~(zenon_TU_eg = W))\/((exists Y : zenon_U, ((ssItem Y)/\(((cons Y (nil)) = zenon_TU_eg)/\(memberP zenon_TV_dx Y))))\/(((~((nil) = W))/\((nil) = X))\/((((nil) = zenon_TV_dx)/\((nil) = zenon_TU_eg))\/((forall Z : zenon_U, ((ssItem Z)->((~((cons Z (nil)) = W))\/(~(memberP X Z)))))/\(neq X (nil)))))))))))) zenon_Hb2); [ zenon_intro zenon_Hb3; idtac ].
% 37.26/37.46 elim zenon_Hb3. zenon_intro zenon_TW_ei. zenon_intro zenon_Hb4.
% 37.26/37.46 apply (zenon_notimply_s _ _ zenon_Hb4). zenon_intro zenon_Hb6. zenon_intro zenon_Hb5.
% 37.26/37.46 apply (zenon_notallex_s (fun X : zenon_U => ((ssList X)->((~(zenon_TV_dx = X))\/((~(zenon_TU_eg = zenon_TW_ei))\/((exists Y : zenon_U, ((ssItem Y)/\(((cons Y (nil)) = zenon_TU_eg)/\(memberP zenon_TV_dx Y))))\/(((~((nil) = zenon_TW_ei))/\((nil) = X))\/((((nil) = zenon_TV_dx)/\((nil) = zenon_TU_eg))\/((forall Z : zenon_U, ((ssItem Z)->((~((cons Z (nil)) = zenon_TW_ei))\/(~(memberP X Z)))))/\(neq X (nil)))))))))) zenon_Hb5); [ zenon_intro zenon_Hb7; idtac ].
% 37.26/37.46 elim zenon_Hb7. zenon_intro zenon_TX_eh. zenon_intro zenon_Hb8.
% 37.26/37.46 apply (zenon_notimply_s _ _ zenon_Hb8). zenon_intro zenon_H69. zenon_intro zenon_Hb9.
% 37.26/37.46 apply (zenon_notor_s _ _ zenon_Hb9). zenon_intro zenon_Hbb. zenon_intro zenon_Hba.
% 37.26/37.46 apply (zenon_notor_s _ _ zenon_Hba). zenon_intro zenon_Hbd. zenon_intro zenon_Hbc.
% 37.26/37.46 apply (zenon_notor_s _ _ zenon_Hbc). zenon_intro zenon_H6d. zenon_intro zenon_Hbe.
% 37.26/37.46 apply (zenon_notor_s _ _ zenon_Hbe). zenon_intro zenon_Hc0. zenon_intro zenon_Hbf.
% 37.26/37.46 apply (zenon_notor_s _ _ zenon_Hbf). zenon_intro zenon_Hc2. zenon_intro zenon_Hc1.
% 37.26/37.46 apply zenon_Hbd. zenon_intro zenon_H6c.
% 37.26/37.46 apply zenon_Hbb. zenon_intro zenon_H6a.
% 37.26/37.46 apply (zenon_notand_s _ _ zenon_Hc0); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Haa ].
% 37.26/37.46 apply zenon_Hc3. zenon_intro zenon_Hc4.
% 37.26/37.46 apply (zenon_notand_s _ _ zenon_Hc2); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hc5 ].
% 37.26/37.46 apply (zenon_notand_s _ _ zenon_Hc1); [ zenon_intro zenon_H68 | zenon_intro zenon_Ha6 ].
% 37.26/37.46 apply (zenon_L3_ zenon_TU_eg zenon_TV_dx zenon_TX_eh zenon_TW_ei); trivial.
% 37.26/37.46 elim (classic (zenon_TV_dx = zenon_TV_dx)); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hc8 ].
% 37.26/37.46 cut ((zenon_TV_dx = zenon_TV_dx) = ((nil) = zenon_TV_dx)).
% 37.26/37.46 intro zenon_D_pnotp.
% 37.26/37.46 apply zenon_Hc6.
% 37.26/37.46 rewrite <- zenon_D_pnotp.
% 37.26/37.46 exact zenon_Hc7.
% 37.26/37.46 cut ((zenon_TV_dx = zenon_TV_dx)); [idtac | apply NNPP; zenon_intro zenon_Hc8].
% 37.26/37.46 cut ((zenon_TV_dx = (nil))); [idtac | apply NNPP; zenon_intro zenon_Hc9].
% 37.26/37.46 congruence.
% 37.26/37.46 cut ((zenon_TV_dx = zenon_TX_eh) = (zenon_TV_dx = (nil))).
% 37.26/37.46 intro zenon_D_pnotp.
% 37.26/37.46 apply zenon_Hc9.
% 37.26/37.46 rewrite <- zenon_D_pnotp.
% 37.26/37.46 exact zenon_H6a.
% 37.26/37.46 cut ((zenon_TX_eh = (nil))); [idtac | apply NNPP; zenon_intro zenon_Ha7].
% 37.26/37.46 cut ((zenon_TV_dx = zenon_TV_dx)); [idtac | apply NNPP; zenon_intro zenon_Hc8].
% 37.26/37.46 congruence.
% 37.26/37.46 apply zenon_Hc8. apply refl_equal.
% 37.26/37.46 generalize (ax15 zenon_TX_eh). zenon_intro zenon_Hca.
% 37.26/37.46 apply (zenon_imply_s _ _ zenon_Hca); [ zenon_intro zenon_H9a | zenon_intro zenon_Hcb ].
% 37.26/37.46 exact (zenon_H9a zenon_H69).
% 37.26/37.46 generalize (zenon_Hcb (nil)). zenon_intro zenon_Hcc.
% 37.26/37.46 apply (zenon_imply_s _ _ zenon_Hcc); [ zenon_intro zenon_H8d | zenon_intro zenon_Ha5 ].
% 37.26/37.46 exact (zenon_H8d ax17).
% 37.26/37.46 apply (zenon_L4_ zenon_TX_eh); trivial.
% 37.26/37.46 apply zenon_Hc8. apply refl_equal.
% 37.26/37.46 apply zenon_Hc8. apply refl_equal.
% 37.26/37.46 cut (((nil) = zenon_TW_ei) = ((nil) = zenon_TU_eg)).
% 37.26/37.46 intro zenon_D_pnotp.
% 37.26/37.46 apply zenon_Hc5.
% 37.26/37.46 rewrite <- zenon_D_pnotp.
% 37.26/37.46 exact zenon_Hc4.
% 37.26/37.46 cut ((zenon_TW_ei = zenon_TU_eg)); [idtac | apply NNPP; zenon_intro zenon_H81].
% 37.26/37.46 cut (((nil) = (nil))); [idtac | apply NNPP; zenon_intro zenon_H60].
% 37.26/37.46 congruence.
% 37.26/37.46 apply zenon_H60. apply refl_equal.
% 37.26/37.46 apply zenon_H81. apply sym_equal. exact zenon_H6c.
% 37.26/37.46 apply (zenon_notand_s _ _ zenon_Hc1); [ zenon_intro zenon_H68 | zenon_intro zenon_Ha6 ].
% 37.26/37.46 apply (zenon_L3_ zenon_TU_eg zenon_TV_dx zenon_TX_eh zenon_TW_ei); trivial.
% 37.26/37.46 generalize (ax15 zenon_TX_eh). zenon_intro zenon_Hca.
% 37.26/37.46 apply (zenon_imply_s _ _ zenon_Hca); [ zenon_intro zenon_H9a | zenon_intro zenon_Hcb ].
% 37.26/37.46 exact (zenon_H9a zenon_H69).
% 37.26/37.46 generalize (zenon_Hcb (nil)). zenon_intro zenon_Hcc.
% 37.26/37.46 apply (zenon_imply_s _ _ zenon_Hcc); [ zenon_intro zenon_H8d | zenon_intro zenon_Ha5 ].
% 37.26/37.48 exact (zenon_H8d ax17).
% 37.26/37.48 apply (zenon_L5_ zenon_TX_eh); trivial.
% 37.26/37.48 Qed.
% 37.26/37.48 % SZS output end Proof
% 37.26/37.48 (* END-PROOF *)
% 37.26/37.48 nodes searched: 357598
% 37.26/37.48 max branch formulas: 32875
% 37.26/37.48 proof nodes created: 22009
% 37.26/37.48 formulas created: 1963035
% 37.26/37.48
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