TSTP Solution File: SET600+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n017.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 06:37:12 EDT 2022
% Result : Theorem 2.55s 2.74s
% Output : Proof 2.55s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET600+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.13 % Command : run_zenon %s %d
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jul 9 22:41:32 EDT 2022
% 0.14/0.34 % CPUTime :
% 2.55/2.74 (* PROOF-FOUND *)
% 2.55/2.74 % SZS status Theorem
% 2.55/2.74 (* BEGIN-PROOF *)
% 2.55/2.74 % SZS output start Proof
% 2.55/2.74 Theorem prove_th59 : (forall B : zenon_U, (forall C : zenon_U, (((union B C) = (empty_set))<->((B = (empty_set))/\(C = (empty_set)))))).
% 2.55/2.74 Proof.
% 2.55/2.74 assert (zenon_L1_ : forall (zenon_TC_n : zenon_U) (zenon_TB_o : zenon_U) (zenon_TD_p : zenon_U), (member zenon_TD_p (union zenon_TB_o zenon_TC_n)) -> (zenon_TC_n = (empty_set)) -> (~(member zenon_TD_p (empty_set))) -> (~(member zenon_TD_p zenon_TB_o)) -> False).
% 2.55/2.74 do 3 intro. intros zenon_H9 zenon_Ha zenon_Hb zenon_Hc.
% 2.55/2.74 generalize (union_defn zenon_TB_o). zenon_intro zenon_H10.
% 2.55/2.74 generalize (zenon_H10 (empty_set)). zenon_intro zenon_H11.
% 2.55/2.74 generalize (zenon_H11 zenon_TD_p). zenon_intro zenon_H12.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H12); [ zenon_intro zenon_H16; zenon_intro zenon_H15 | zenon_intro zenon_H14; zenon_intro zenon_H13 ].
% 2.55/2.74 cut ((member zenon_TD_p (union zenon_TB_o zenon_TC_n)) = (member zenon_TD_p (union zenon_TB_o (empty_set)))).
% 2.55/2.74 intro zenon_D_pnotp.
% 2.55/2.74 apply zenon_H16.
% 2.55/2.74 rewrite <- zenon_D_pnotp.
% 2.55/2.74 exact zenon_H9.
% 2.55/2.74 cut (((union zenon_TB_o zenon_TC_n) = (union zenon_TB_o (empty_set)))); [idtac | apply NNPP; zenon_intro zenon_H17].
% 2.55/2.74 cut ((zenon_TD_p = zenon_TD_p)); [idtac | apply NNPP; zenon_intro zenon_H18].
% 2.55/2.74 congruence.
% 2.55/2.74 apply zenon_H18. apply refl_equal.
% 2.55/2.74 cut ((zenon_TC_n = (empty_set))); [idtac | apply NNPP; zenon_intro zenon_H19].
% 2.55/2.74 cut ((zenon_TB_o = zenon_TB_o)); [idtac | apply NNPP; zenon_intro zenon_H1a].
% 2.55/2.74 congruence.
% 2.55/2.74 apply zenon_H1a. apply refl_equal.
% 2.55/2.74 exact (zenon_H19 zenon_Ha).
% 2.55/2.74 apply (zenon_or_s _ _ zenon_H13); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ].
% 2.55/2.74 exact (zenon_Hc zenon_H1c).
% 2.55/2.74 exact (zenon_Hb zenon_H1b).
% 2.55/2.74 (* end of lemma zenon_L1_ *)
% 2.55/2.74 assert (zenon_L2_ : forall (zenon_TD_p : zenon_U), (member zenon_TD_p (empty_set)) -> False).
% 2.55/2.74 do 1 intro. intros zenon_H1b.
% 2.55/2.74 generalize (empty_set_defn zenon_TD_p). zenon_intro zenon_Hb.
% 2.55/2.74 exact (zenon_Hb zenon_H1b).
% 2.55/2.74 (* end of lemma zenon_L2_ *)
% 2.55/2.74 assert (zenon_L3_ : forall (zenon_TD_be : zenon_U), (member zenon_TD_be (empty_set)) -> False).
% 2.55/2.74 do 1 intro. intros zenon_H1d.
% 2.55/2.74 generalize (empty_set_defn zenon_TD_be). zenon_intro zenon_H1f.
% 2.55/2.74 exact (zenon_H1f zenon_H1d).
% 2.55/2.74 (* end of lemma zenon_L3_ *)
% 2.55/2.74 assert (zenon_L4_ : forall (zenon_TC_n : zenon_U) (zenon_TB_o : zenon_U) (zenon_TD_be : zenon_U), (~((member zenon_TD_be zenon_TB_o)\/(member zenon_TD_be zenon_TC_n))) -> (member zenon_TD_be zenon_TC_n) -> False).
% 2.55/2.74 do 3 intro. intros zenon_H20 zenon_H21.
% 2.55/2.74 apply (zenon_notor_s _ _ zenon_H20). zenon_intro zenon_H23. zenon_intro zenon_H22.
% 2.55/2.74 exact (zenon_H22 zenon_H21).
% 2.55/2.74 (* end of lemma zenon_L4_ *)
% 2.55/2.74 assert (zenon_L5_ : forall (zenon_TB_o : zenon_U) (zenon_TC_n : zenon_U), (~(forall D : zenon_U, ((member D zenon_TC_n)<->(member D (empty_set))))) -> ((union zenon_TB_o zenon_TC_n) = (empty_set)) -> False).
% 2.55/2.74 do 2 intro. intros zenon_H24 zenon_H25.
% 2.55/2.74 apply (zenon_notallex_s (fun D : zenon_U => ((member D zenon_TC_n)<->(member D (empty_set)))) zenon_H24); [ zenon_intro zenon_H26; idtac ].
% 2.55/2.74 elim zenon_H26. zenon_intro zenon_TD_be. zenon_intro zenon_H27.
% 2.55/2.74 apply (zenon_notequiv_s _ _ zenon_H27); [ zenon_intro zenon_H22; zenon_intro zenon_H1d | zenon_intro zenon_H21; zenon_intro zenon_H1f ].
% 2.55/2.74 apply (zenon_L3_ zenon_TD_be); trivial.
% 2.55/2.74 generalize (equal_defn (union zenon_TB_o zenon_TC_n)). zenon_intro zenon_H28.
% 2.55/2.74 generalize (zenon_H28 (empty_set)). zenon_intro zenon_H29.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H29); [ zenon_intro zenon_H2c; zenon_intro zenon_H2b | zenon_intro zenon_H25; zenon_intro zenon_H2a ].
% 2.55/2.74 exact (zenon_H2c zenon_H25).
% 2.55/2.74 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H2e. zenon_intro zenon_H2d.
% 2.55/2.74 generalize (subset_defn (union zenon_TB_o zenon_TC_n)). zenon_intro zenon_H2f.
% 2.55/2.74 generalize (zenon_H2f (empty_set)). zenon_intro zenon_H30.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H30); [ zenon_intro zenon_H33; zenon_intro zenon_H32 | zenon_intro zenon_H2e; zenon_intro zenon_H31 ].
% 2.55/2.74 exact (zenon_H33 zenon_H2e).
% 2.55/2.74 generalize (union_defn zenon_TB_o). zenon_intro zenon_H10.
% 2.55/2.74 generalize (zenon_H31 zenon_TD_be). zenon_intro zenon_H34.
% 2.55/2.74 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H35 | zenon_intro zenon_H1d ].
% 2.55/2.74 generalize (zenon_H10 zenon_TC_n). zenon_intro zenon_H36.
% 2.55/2.74 generalize (zenon_H36 zenon_TD_be). zenon_intro zenon_H37.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H37); [ zenon_intro zenon_H35; zenon_intro zenon_H20 | zenon_intro zenon_H39; zenon_intro zenon_H38 ].
% 2.55/2.74 apply (zenon_L4_ zenon_TC_n zenon_TB_o zenon_TD_be); trivial.
% 2.55/2.74 exact (zenon_H35 zenon_H39).
% 2.55/2.74 exact (zenon_H1f zenon_H1d).
% 2.55/2.74 (* end of lemma zenon_L5_ *)
% 2.55/2.74 assert (zenon_L6_ : forall (zenon_TB_o : zenon_U) (zenon_TC_n : zenon_U), (forall C : zenon_U, ((zenon_TC_n = C)<->(forall D : zenon_U, ((member D zenon_TC_n)<->(member D C))))) -> ((union zenon_TB_o zenon_TC_n) = (empty_set)) -> (~((empty_set) = zenon_TC_n)) -> False).
% 2.55/2.74 do 2 intro. intros zenon_H3a zenon_H25 zenon_H3b.
% 2.55/2.74 generalize (zenon_H3a (empty_set)). zenon_intro zenon_H3c.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H19; zenon_intro zenon_H24 | zenon_intro zenon_Ha; zenon_intro zenon_H3d ].
% 2.55/2.74 apply (zenon_L5_ zenon_TB_o zenon_TC_n); trivial.
% 2.55/2.74 apply zenon_H3b. apply sym_equal. exact zenon_Ha.
% 2.55/2.74 (* end of lemma zenon_L6_ *)
% 2.55/2.74 assert (zenon_L7_ : forall (zenon_TC_n : zenon_U) (zenon_TB_o : zenon_U), (~((union zenon_TB_o (empty_set)) = (union zenon_TB_o zenon_TC_n))) -> ((empty_set) = zenon_TC_n) -> False).
% 2.55/2.74 do 2 intro. intros zenon_H3e zenon_H3f.
% 2.55/2.74 cut (((empty_set) = zenon_TC_n)); [idtac | apply NNPP; zenon_intro zenon_H3b].
% 2.55/2.74 cut ((zenon_TB_o = zenon_TB_o)); [idtac | apply NNPP; zenon_intro zenon_H1a].
% 2.55/2.74 congruence.
% 2.55/2.74 apply zenon_H1a. apply refl_equal.
% 2.55/2.74 exact (zenon_H3b zenon_H3f).
% 2.55/2.74 (* end of lemma zenon_L7_ *)
% 2.55/2.74 assert (zenon_L8_ : forall (zenon_TD_cn : zenon_U), (member zenon_TD_cn (empty_set)) -> False).
% 2.55/2.74 do 1 intro. intros zenon_H40.
% 2.55/2.74 generalize (empty_set_defn zenon_TD_cn). zenon_intro zenon_H42.
% 2.55/2.74 exact (zenon_H42 zenon_H40).
% 2.55/2.74 (* end of lemma zenon_L8_ *)
% 2.55/2.74 assert (zenon_L9_ : forall (zenon_TB_o : zenon_U) (zenon_TC_n : zenon_U), (forall C : zenon_U, ((zenon_TC_n = C)<->(forall D : zenon_U, ((member D zenon_TC_n)<->(member D C))))) -> ((union zenon_TB_o zenon_TC_n) = (empty_set)) -> (~(zenon_TC_n = (empty_set))) -> False).
% 2.55/2.74 do 2 intro. intros zenon_H3a zenon_H25 zenon_H19.
% 2.55/2.74 generalize (zenon_H3a (empty_set)). zenon_intro zenon_H3c.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H3c); [ zenon_intro zenon_H19; zenon_intro zenon_H24 | zenon_intro zenon_Ha; zenon_intro zenon_H3d ].
% 2.55/2.74 apply (zenon_L5_ zenon_TB_o zenon_TC_n); trivial.
% 2.55/2.74 exact (zenon_H19 zenon_Ha).
% 2.55/2.74 (* end of lemma zenon_L9_ *)
% 2.55/2.74 assert (zenon_L10_ : forall (zenon_TB_o : zenon_U) (zenon_TC_n : zenon_U), (~(zenon_TC_n = (empty_set))) -> ((union zenon_TB_o zenon_TC_n) = (empty_set)) -> False).
% 2.55/2.74 do 2 intro. intros zenon_H19 zenon_H25.
% 2.55/2.74 generalize (equal_member_defn zenon_TC_n). zenon_intro zenon_H3a.
% 2.55/2.74 apply (zenon_L9_ zenon_TB_o zenon_TC_n); trivial.
% 2.55/2.74 (* end of lemma zenon_L10_ *)
% 2.55/2.74 apply NNPP. intro zenon_G.
% 2.55/2.74 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((union B C) = (empty_set))<->((B = (empty_set))/\(C = (empty_set)))))) zenon_G); [ zenon_intro zenon_H43; idtac ].
% 2.55/2.74 elim zenon_H43. zenon_intro zenon_TB_o. zenon_intro zenon_H44.
% 2.55/2.74 apply (zenon_notallex_s (fun C : zenon_U => (((union zenon_TB_o C) = (empty_set))<->((zenon_TB_o = (empty_set))/\(C = (empty_set))))) zenon_H44); [ zenon_intro zenon_H45; idtac ].
% 2.55/2.74 elim zenon_H45. zenon_intro zenon_TC_n. zenon_intro zenon_H46.
% 2.55/2.74 apply (zenon_notequiv_s _ _ zenon_H46); [ zenon_intro zenon_H2c; zenon_intro zenon_H48 | zenon_intro zenon_H25; zenon_intro zenon_H47 ].
% 2.55/2.74 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H49. zenon_intro zenon_Ha.
% 2.55/2.74 generalize (equal_member_defn (empty_set)). zenon_intro zenon_H4a.
% 2.55/2.74 generalize (equal_defn zenon_TB_o). zenon_intro zenon_H4b.
% 2.55/2.74 generalize (zenon_H4b (empty_set)). zenon_intro zenon_H4c.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H4f; zenon_intro zenon_H4e | zenon_intro zenon_H49; zenon_intro zenon_H4d ].
% 2.55/2.74 exact (zenon_H4f zenon_H49).
% 2.55/2.74 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H51. zenon_intro zenon_H50.
% 2.55/2.74 generalize (subset_defn zenon_TB_o). zenon_intro zenon_H52.
% 2.55/2.74 generalize (zenon_H52 (empty_set)). zenon_intro zenon_H53.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H53); [ zenon_intro zenon_H56; zenon_intro zenon_H55 | zenon_intro zenon_H51; zenon_intro zenon_H54 ].
% 2.55/2.74 exact (zenon_H56 zenon_H51).
% 2.55/2.74 generalize (zenon_H4a (union zenon_TB_o zenon_TC_n)). zenon_intro zenon_H57.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H57); [ zenon_intro zenon_H5b; zenon_intro zenon_H5a | zenon_intro zenon_H59; zenon_intro zenon_H58 ].
% 2.55/2.74 apply (zenon_notallex_s (fun D : zenon_U => ((member D (empty_set))<->(member D (union zenon_TB_o zenon_TC_n)))) zenon_H5a); [ zenon_intro zenon_H5c; idtac ].
% 2.55/2.74 elim zenon_H5c. zenon_intro zenon_TD_p. zenon_intro zenon_H5d.
% 2.55/2.74 apply (zenon_notequiv_s _ _ zenon_H5d); [ zenon_intro zenon_Hb; zenon_intro zenon_H9 | zenon_intro zenon_H1b; zenon_intro zenon_H5e ].
% 2.55/2.74 generalize (zenon_H54 zenon_TD_p). zenon_intro zenon_H5f.
% 2.55/2.74 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_Hc | zenon_intro zenon_H1b ].
% 2.55/2.74 apply (zenon_L1_ zenon_TC_n zenon_TB_o zenon_TD_p); trivial.
% 2.55/2.74 exact (zenon_Hb zenon_H1b).
% 2.55/2.74 apply (zenon_L2_ zenon_TD_p); trivial.
% 2.55/2.74 apply zenon_H2c. apply sym_equal. exact zenon_H59.
% 2.55/2.74 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H4f | zenon_intro zenon_H19 ].
% 2.55/2.74 generalize (equal_member_defn (empty_set)). zenon_intro zenon_H4a.
% 2.55/2.74 generalize (equal_member_defn zenon_TC_n). zenon_intro zenon_H3a.
% 2.55/2.74 generalize (zenon_H4a zenon_TC_n). zenon_intro zenon_H60.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H60); [ zenon_intro zenon_H3b; zenon_intro zenon_H62 | zenon_intro zenon_H3f; zenon_intro zenon_H61 ].
% 2.55/2.74 apply (zenon_L6_ zenon_TB_o zenon_TC_n); trivial.
% 2.55/2.74 generalize (zenon_H4a (union zenon_TB_o zenon_TC_n)). zenon_intro zenon_H57.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H57); [ zenon_intro zenon_H5b; zenon_intro zenon_H5a | zenon_intro zenon_H59; zenon_intro zenon_H58 ].
% 2.55/2.74 apply zenon_H5b. apply sym_equal. exact zenon_H25.
% 2.55/2.74 generalize (union_defn zenon_TB_o). zenon_intro zenon_H10.
% 2.55/2.74 generalize (zenon_H10 (empty_set)). zenon_intro zenon_H11.
% 2.55/2.74 generalize (equal_defn (union zenon_TB_o (empty_set))). zenon_intro zenon_H63.
% 2.55/2.74 generalize (zenon_H63 (empty_set)). zenon_intro zenon_H64.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H64); [ zenon_intro zenon_H68; zenon_intro zenon_H67 | zenon_intro zenon_H66; zenon_intro zenon_H65 ].
% 2.55/2.74 apply (zenon_notand_s _ _ zenon_H67); [ zenon_intro zenon_H6a | zenon_intro zenon_H69 ].
% 2.55/2.74 generalize (subset_defn (union zenon_TB_o (empty_set))). zenon_intro zenon_H6b.
% 2.55/2.74 generalize (zenon_H6b (empty_set)). zenon_intro zenon_H6c.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H6c); [ zenon_intro zenon_H6a; zenon_intro zenon_H6f | zenon_intro zenon_H6e; zenon_intro zenon_H6d ].
% 2.55/2.74 apply (zenon_notallex_s (fun D : zenon_U => ((member D (union zenon_TB_o (empty_set)))->(member D (empty_set)))) zenon_H6f); [ zenon_intro zenon_H70; idtac ].
% 2.55/2.74 elim zenon_H70. zenon_intro zenon_TD_ej. zenon_intro zenon_H72.
% 2.55/2.74 apply (zenon_notimply_s _ _ zenon_H72). zenon_intro zenon_H74. zenon_intro zenon_H73.
% 2.55/2.74 generalize (zenon_H58 zenon_TD_ej). zenon_intro zenon_H75.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H75); [ zenon_intro zenon_H73; zenon_intro zenon_H78 | zenon_intro zenon_H77; zenon_intro zenon_H76 ].
% 2.55/2.74 cut ((member zenon_TD_ej (union zenon_TB_o (empty_set))) = (member zenon_TD_ej (union zenon_TB_o zenon_TC_n))).
% 2.55/2.74 intro zenon_D_pnotp.
% 2.55/2.74 apply zenon_H78.
% 2.55/2.74 rewrite <- zenon_D_pnotp.
% 2.55/2.74 exact zenon_H74.
% 2.55/2.74 cut (((union zenon_TB_o (empty_set)) = (union zenon_TB_o zenon_TC_n))); [idtac | apply NNPP; zenon_intro zenon_H3e].
% 2.55/2.74 cut ((zenon_TD_ej = zenon_TD_ej)); [idtac | apply NNPP; zenon_intro zenon_H79].
% 2.55/2.74 congruence.
% 2.55/2.74 apply zenon_H79. apply refl_equal.
% 2.55/2.74 apply (zenon_L7_ zenon_TC_n zenon_TB_o); trivial.
% 2.55/2.74 exact (zenon_H73 zenon_H77).
% 2.55/2.74 exact (zenon_H6a zenon_H6e).
% 2.55/2.74 generalize (subset_defn (empty_set)). zenon_intro zenon_H7a.
% 2.55/2.74 generalize (zenon_H7a (union zenon_TB_o (empty_set))). zenon_intro zenon_H7b.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H7b); [ zenon_intro zenon_H69; zenon_intro zenon_H7e | zenon_intro zenon_H7d; zenon_intro zenon_H7c ].
% 2.55/2.74 apply (zenon_notallex_s (fun D : zenon_U => ((member D (empty_set))->(member D (union zenon_TB_o (empty_set))))) zenon_H7e); [ zenon_intro zenon_H7f; idtac ].
% 2.55/2.74 elim zenon_H7f. zenon_intro zenon_TD_ey. zenon_intro zenon_H81.
% 2.55/2.74 apply (zenon_notimply_s _ _ zenon_H81). zenon_intro zenon_H83. zenon_intro zenon_H82.
% 2.55/2.74 generalize (empty_set_defn zenon_TD_ey). zenon_intro zenon_H84.
% 2.55/2.74 exact (zenon_H84 zenon_H83).
% 2.55/2.74 exact (zenon_H69 zenon_H7d).
% 2.55/2.74 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H6e. zenon_intro zenon_H7d.
% 2.55/2.74 generalize (subset_defn (union zenon_TB_o (empty_set))). zenon_intro zenon_H6b.
% 2.55/2.74 generalize (zenon_H6b (empty_set)). zenon_intro zenon_H6c.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H6c); [ zenon_intro zenon_H6a; zenon_intro zenon_H6f | zenon_intro zenon_H6e; zenon_intro zenon_H6d ].
% 2.55/2.74 exact (zenon_H6a zenon_H6e).
% 2.55/2.74 generalize (zenon_H4a zenon_TB_o). zenon_intro zenon_H85.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H85); [ zenon_intro zenon_H89; zenon_intro zenon_H88 | zenon_intro zenon_H87; zenon_intro zenon_H86 ].
% 2.55/2.74 apply (zenon_notallex_s (fun D : zenon_U => ((member D (empty_set))<->(member D zenon_TB_o))) zenon_H88); [ zenon_intro zenon_H8a; idtac ].
% 2.55/2.74 elim zenon_H8a. zenon_intro zenon_TD_cn. zenon_intro zenon_H8b.
% 2.55/2.74 apply (zenon_notequiv_s _ _ zenon_H8b); [ zenon_intro zenon_H42; zenon_intro zenon_H8d | zenon_intro zenon_H40; zenon_intro zenon_H8c ].
% 2.55/2.74 generalize (zenon_H6d zenon_TD_cn). zenon_intro zenon_H8e.
% 2.55/2.74 apply (zenon_imply_s _ _ zenon_H8e); [ zenon_intro zenon_H8f | zenon_intro zenon_H40 ].
% 2.55/2.74 generalize (zenon_H11 zenon_TD_cn). zenon_intro zenon_H90.
% 2.55/2.74 apply (zenon_equiv_s _ _ zenon_H90); [ zenon_intro zenon_H8f; zenon_intro zenon_H93 | zenon_intro zenon_H92; zenon_intro zenon_H91 ].
% 2.55/2.74 apply (zenon_notor_s _ _ zenon_H93). zenon_intro zenon_H8c. zenon_intro zenon_H42.
% 2.55/2.74 exact (zenon_H8c zenon_H8d).
% 2.55/2.74 exact (zenon_H8f zenon_H92).
% 2.55/2.74 exact (zenon_H42 zenon_H40).
% 2.55/2.74 apply (zenon_L8_ zenon_TD_cn); trivial.
% 2.55/2.74 apply zenon_H4f. apply sym_equal. exact zenon_H87.
% 2.55/2.74 apply (zenon_L10_ zenon_TB_o zenon_TC_n); trivial.
% 2.55/2.74 Qed.
% 2.55/2.74 % SZS output end Proof
% 2.55/2.74 (* END-PROOF *)
% 2.55/2.74 nodes searched: 119965
% 2.55/2.74 max branch formulas: 2292
% 2.55/2.74 proof nodes created: 7658
% 2.55/2.74 formulas created: 214312
% 2.55/2.74
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