TSTP Solution File: SET768+4 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : SET768+4 : TPTP v8.1.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n013.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 06:38:27 EDT 2022
% Result : Theorem 0.60s 0.78s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET768+4 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12 % Command : run_zenon %s %d
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sun Jul 10 01:23:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.60/0.78 (* PROOF-FOUND *)
% 0.60/0.78 % SZS status Theorem
% 0.60/0.78 (* BEGIN-PROOF *)
% 0.60/0.78 % SZS output start Proof
% 0.60/0.78 Theorem thIII04 : (forall E : zenon_U, (forall R : zenon_U, (forall A : zenon_U, (forall B : zenon_U, (((equivalence R E)/\((member A E)/\(member B E)))->((equal_set (equivalence_class A E R) (equivalence_class B E R))<->(apply R A B))))))).
% 0.60/0.78 Proof.
% 0.60/0.78 assert (zenon_L1_ : forall (zenon_TX_u : zenon_U) (zenon_TR_v : zenon_U) (zenon_TE_w : zenon_U) (zenon_TA_x : zenon_U), (forall X : zenon_U, ((member X (equivalence_class zenon_TA_x zenon_TE_w zenon_TR_v))<->((member X zenon_TE_w)/\(apply zenon_TR_v zenon_TA_x X)))) -> (member zenon_TX_u (equivalence_class zenon_TA_x zenon_TE_w zenon_TR_v)) -> (~(member zenon_TX_u zenon_TE_w)) -> False).
% 0.60/0.78 do 4 intro. intros zenon_H11 zenon_H12 zenon_H13.
% 0.60/0.78 generalize (zenon_H11 zenon_TX_u). zenon_intro zenon_H18.
% 0.60/0.78 apply (zenon_equiv_s _ _ zenon_H18); [ zenon_intro zenon_H1b; zenon_intro zenon_H1a | zenon_intro zenon_H12; zenon_intro zenon_H19 ].
% 0.60/0.78 exact (zenon_H1b zenon_H12).
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H19). zenon_intro zenon_H1d. zenon_intro zenon_H1c.
% 0.60/0.78 exact (zenon_H13 zenon_H1d).
% 0.60/0.78 (* end of lemma zenon_L1_ *)
% 0.60/0.78 assert (zenon_L2_ : forall (zenon_TA_x : zenon_U) (zenon_TX_u : zenon_U) (zenon_TR_v : zenon_U) (zenon_TE_w : zenon_U) (zenon_TB_bl : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, (((member zenon_TB_bl zenon_TE_w)/\((member Y zenon_TE_w)/\(member Z zenon_TE_w)))->(((apply zenon_TR_v zenon_TB_bl Y)/\(apply zenon_TR_v Y Z))->(apply zenon_TR_v zenon_TB_bl Z))))) -> (~(apply zenon_TR_v zenon_TB_bl zenon_TX_u)) -> (member zenon_TX_u (equivalence_class zenon_TA_x zenon_TE_w zenon_TR_v)) -> (forall A : zenon_U, (forall X : zenon_U, ((member X (equivalence_class A zenon_TE_w zenon_TR_v))<->((member X zenon_TE_w)/\(apply zenon_TR_v A X))))) -> (apply zenon_TR_v zenon_TA_x zenon_TB_bl) -> (forall X : zenon_U, (forall Y : zenon_U, (((member X zenon_TE_w)/\(member Y zenon_TE_w))->((apply zenon_TR_v X Y)->(apply zenon_TR_v Y X))))) -> (member zenon_TX_u zenon_TE_w) -> (member zenon_TA_x zenon_TE_w) -> (member zenon_TB_bl zenon_TE_w) -> False).
% 0.60/0.78 do 5 intro. intros zenon_H1e zenon_H1f zenon_H12 zenon_H20 zenon_H21 zenon_H22 zenon_H1d zenon_H23 zenon_H24.
% 0.60/0.78 generalize (zenon_H1e zenon_TA_x). zenon_intro zenon_H26.
% 0.60/0.78 generalize (zenon_H26 zenon_TX_u). zenon_intro zenon_H27.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 0.60/0.78 apply (zenon_notand_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 0.60/0.78 exact (zenon_H2b zenon_H24).
% 0.60/0.78 apply (zenon_notand_s _ _ zenon_H2a); [ zenon_intro zenon_H2c | zenon_intro zenon_H13 ].
% 0.60/0.78 exact (zenon_H2c zenon_H23).
% 0.60/0.78 exact (zenon_H13 zenon_H1d).
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ].
% 0.60/0.78 apply (zenon_notand_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ].
% 0.60/0.78 generalize (zenon_H22 zenon_TA_x). zenon_intro zenon_H31.
% 0.60/0.78 generalize (zenon_H31 zenon_TB_bl). zenon_intro zenon_H32.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 0.60/0.78 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ].
% 0.60/0.78 exact (zenon_H2c zenon_H23).
% 0.60/0.78 exact (zenon_H2b zenon_H24).
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ].
% 0.60/0.78 exact (zenon_H36 zenon_H21).
% 0.60/0.78 exact (zenon_H30 zenon_H35).
% 0.60/0.78 generalize (zenon_H20 zenon_TA_x). zenon_intro zenon_H11.
% 0.60/0.78 generalize (zenon_H11 zenon_TX_u). zenon_intro zenon_H18.
% 0.60/0.78 apply (zenon_equiv_s _ _ zenon_H18); [ zenon_intro zenon_H1b; zenon_intro zenon_H1a | zenon_intro zenon_H12; zenon_intro zenon_H19 ].
% 0.60/0.78 exact (zenon_H1b zenon_H12).
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H19). zenon_intro zenon_H1d. zenon_intro zenon_H1c.
% 0.60/0.78 exact (zenon_H2f zenon_H1c).
% 0.60/0.78 exact (zenon_H1f zenon_H2d).
% 0.60/0.78 (* end of lemma zenon_L2_ *)
% 0.60/0.78 assert (zenon_L3_ : forall (zenon_TX_cg : zenon_U) (zenon_TR_v : zenon_U) (zenon_TE_w : zenon_U) (zenon_TB_bl : zenon_U), (forall X : zenon_U, ((member X (equivalence_class zenon_TB_bl zenon_TE_w zenon_TR_v))<->((member X zenon_TE_w)/\(apply zenon_TR_v zenon_TB_bl X)))) -> (member zenon_TX_cg (equivalence_class zenon_TB_bl zenon_TE_w zenon_TR_v)) -> (~(member zenon_TX_cg zenon_TE_w)) -> False).
% 0.60/0.78 do 4 intro. intros zenon_H37 zenon_H38 zenon_H39.
% 0.60/0.78 generalize (zenon_H37 zenon_TX_cg). zenon_intro zenon_H3b.
% 0.60/0.78 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H3e; zenon_intro zenon_H3d | zenon_intro zenon_H38; zenon_intro zenon_H3c ].
% 0.60/0.78 exact (zenon_H3e zenon_H38).
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H40. zenon_intro zenon_H3f.
% 0.60/0.78 exact (zenon_H39 zenon_H40).
% 0.60/0.78 (* end of lemma zenon_L3_ *)
% 0.60/0.78 assert (zenon_L4_ : forall (zenon_TX_cg : zenon_U) (zenon_TR_v : zenon_U) (zenon_TB_bl : zenon_U) (zenon_TE_w : zenon_U) (zenon_TA_x : zenon_U), (forall Z : zenon_U, (((member zenon_TA_x zenon_TE_w)/\((member zenon_TB_bl zenon_TE_w)/\(member Z zenon_TE_w)))->(((apply zenon_TR_v zenon_TA_x zenon_TB_bl)/\(apply zenon_TR_v zenon_TB_bl Z))->(apply zenon_TR_v zenon_TA_x Z)))) -> (member zenon_TA_x zenon_TE_w) -> (member zenon_TB_bl zenon_TE_w) -> (member zenon_TX_cg zenon_TE_w) -> (apply zenon_TR_v zenon_TA_x zenon_TB_bl) -> (forall A : zenon_U, (forall X : zenon_U, ((member X (equivalence_class A zenon_TE_w zenon_TR_v))<->((member X zenon_TE_w)/\(apply zenon_TR_v A X))))) -> (member zenon_TX_cg (equivalence_class zenon_TB_bl zenon_TE_w zenon_TR_v)) -> (~(apply zenon_TR_v zenon_TA_x zenon_TX_cg)) -> False).
% 0.60/0.78 do 5 intro. intros zenon_H41 zenon_H23 zenon_H24 zenon_H40 zenon_H21 zenon_H20 zenon_H38 zenon_H42.
% 0.60/0.78 generalize (zenon_H41 zenon_TX_cg). zenon_intro zenon_H43.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ].
% 0.60/0.78 apply (zenon_notand_s _ _ zenon_H45); [ zenon_intro zenon_H2c | zenon_intro zenon_H46 ].
% 0.60/0.78 exact (zenon_H2c zenon_H23).
% 0.60/0.78 apply (zenon_notand_s _ _ zenon_H46); [ zenon_intro zenon_H2b | zenon_intro zenon_H39 ].
% 0.60/0.78 exact (zenon_H2b zenon_H24).
% 0.60/0.78 exact (zenon_H39 zenon_H40).
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ].
% 0.60/0.78 apply (zenon_notand_s _ _ zenon_H48); [ zenon_intro zenon_H36 | zenon_intro zenon_H49 ].
% 0.60/0.78 exact (zenon_H36 zenon_H21).
% 0.60/0.78 generalize (zenon_H20 zenon_TB_bl). zenon_intro zenon_H37.
% 0.60/0.78 generalize (zenon_H37 zenon_TX_cg). zenon_intro zenon_H3b.
% 0.60/0.78 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H3e; zenon_intro zenon_H3d | zenon_intro zenon_H38; zenon_intro zenon_H3c ].
% 0.60/0.78 exact (zenon_H3e zenon_H38).
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H40. zenon_intro zenon_H3f.
% 0.60/0.78 exact (zenon_H49 zenon_H3f).
% 0.60/0.78 exact (zenon_H42 zenon_H47).
% 0.60/0.78 (* end of lemma zenon_L4_ *)
% 0.60/0.78 apply NNPP. intro zenon_G.
% 0.60/0.78 apply (zenon_notallex_s (fun E : zenon_U => (forall R : zenon_U, (forall A : zenon_U, (forall B : zenon_U, (((equivalence R E)/\((member A E)/\(member B E)))->((equal_set (equivalence_class A E R) (equivalence_class B E R))<->(apply R A B))))))) zenon_G); [ zenon_intro zenon_H4a; idtac ].
% 0.60/0.78 elim zenon_H4a. zenon_intro zenon_TE_w. zenon_intro zenon_H4b.
% 0.60/0.78 apply (zenon_notallex_s (fun R : zenon_U => (forall A : zenon_U, (forall B : zenon_U, (((equivalence R zenon_TE_w)/\((member A zenon_TE_w)/\(member B zenon_TE_w)))->((equal_set (equivalence_class A zenon_TE_w R) (equivalence_class B zenon_TE_w R))<->(apply R A B)))))) zenon_H4b); [ zenon_intro zenon_H4c; idtac ].
% 0.60/0.78 elim zenon_H4c. zenon_intro zenon_TR_v. zenon_intro zenon_H4d.
% 0.60/0.78 apply (zenon_notallex_s (fun A : zenon_U => (forall B : zenon_U, (((equivalence zenon_TR_v zenon_TE_w)/\((member A zenon_TE_w)/\(member B zenon_TE_w)))->((equal_set (equivalence_class A zenon_TE_w zenon_TR_v) (equivalence_class B zenon_TE_w zenon_TR_v))<->(apply zenon_TR_v A B))))) zenon_H4d); [ zenon_intro zenon_H4e; idtac ].
% 0.60/0.78 elim zenon_H4e. zenon_intro zenon_TA_x. zenon_intro zenon_H4f.
% 0.60/0.78 apply (zenon_notallex_s (fun B : zenon_U => (((equivalence zenon_TR_v zenon_TE_w)/\((member zenon_TA_x zenon_TE_w)/\(member B zenon_TE_w)))->((equal_set (equivalence_class zenon_TA_x zenon_TE_w zenon_TR_v) (equivalence_class B zenon_TE_w zenon_TR_v))<->(apply zenon_TR_v zenon_TA_x B)))) zenon_H4f); [ zenon_intro zenon_H50; idtac ].
% 0.60/0.78 elim zenon_H50. zenon_intro zenon_TB_bl. zenon_intro zenon_H51.
% 0.60/0.78 apply (zenon_notimply_s _ _ zenon_H51). zenon_intro zenon_H53. zenon_intro zenon_H52.
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H55. zenon_intro zenon_H54.
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H54). zenon_intro zenon_H23. zenon_intro zenon_H24.
% 0.60/0.78 generalize (equivalence zenon_TE_w). zenon_intro zenon_H56.
% 0.60/0.78 generalize (zenon_H56 zenon_TR_v). zenon_intro zenon_H57.
% 0.60/0.78 apply (zenon_equiv_s _ _ zenon_H57); [ zenon_intro zenon_H5a; zenon_intro zenon_H59 | zenon_intro zenon_H55; zenon_intro zenon_H58 ].
% 0.60/0.78 exact (zenon_H5a zenon_H55).
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5c. zenon_intro zenon_H5b.
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H22. zenon_intro zenon_H5d.
% 0.60/0.78 apply (zenon_notequiv_s _ _ zenon_H52); [ zenon_intro zenon_H5f; zenon_intro zenon_H21 | zenon_intro zenon_H5e; zenon_intro zenon_H36 ].
% 0.60/0.78 generalize (equal_set (equivalence_class zenon_TA_x zenon_TE_w zenon_TR_v)). zenon_intro zenon_H60.
% 0.60/0.78 generalize (zenon_H60 (equivalence_class zenon_TB_bl zenon_TE_w zenon_TR_v)). zenon_intro zenon_H61.
% 0.60/0.78 apply (zenon_equiv_s _ _ zenon_H61); [ zenon_intro zenon_H5f; zenon_intro zenon_H63 | zenon_intro zenon_H5e; zenon_intro zenon_H62 ].
% 0.60/0.78 apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H65 | zenon_intro zenon_H64 ].
% 0.60/0.78 generalize (subset (equivalence_class zenon_TA_x zenon_TE_w zenon_TR_v)). zenon_intro zenon_H66.
% 0.60/0.78 generalize (zenon_H66 (equivalence_class zenon_TB_bl zenon_TE_w zenon_TR_v)). zenon_intro zenon_H67.
% 0.60/0.78 apply (zenon_equiv_s _ _ zenon_H67); [ zenon_intro zenon_H65; zenon_intro zenon_H6a | zenon_intro zenon_H69; zenon_intro zenon_H68 ].
% 0.60/0.78 apply (zenon_notallex_s (fun X : zenon_U => ((member X (equivalence_class zenon_TA_x zenon_TE_w zenon_TR_v))->(member X (equivalence_class zenon_TB_bl zenon_TE_w zenon_TR_v)))) zenon_H6a); [ zenon_intro zenon_H6b; idtac ].
% 0.60/0.78 elim zenon_H6b. zenon_intro zenon_TX_u. zenon_intro zenon_H6c.
% 0.60/0.78 apply (zenon_notimply_s _ _ zenon_H6c). zenon_intro zenon_H12. zenon_intro zenon_H6d.
% 0.60/0.78 generalize (equivalence_class zenon_TR_v). zenon_intro zenon_H6e.
% 0.60/0.78 generalize (zenon_H6e zenon_TE_w). zenon_intro zenon_H20.
% 0.60/0.78 generalize (zenon_H20 zenon_TB_bl). zenon_intro zenon_H37.
% 0.60/0.78 generalize (zenon_H37 zenon_TX_u). zenon_intro zenon_H6f.
% 0.60/0.78 apply (zenon_equiv_s _ _ zenon_H6f); [ zenon_intro zenon_H6d; zenon_intro zenon_H72 | zenon_intro zenon_H71; zenon_intro zenon_H70 ].
% 0.60/0.78 apply (zenon_notand_s _ _ zenon_H72); [ zenon_intro zenon_H13 | zenon_intro zenon_H1f ].
% 0.60/0.78 generalize (zenon_H20 zenon_TA_x). zenon_intro zenon_H11.
% 0.60/0.78 apply (zenon_L1_ zenon_TX_u zenon_TR_v zenon_TE_w zenon_TA_x); trivial.
% 0.60/0.78 generalize (zenon_H20 zenon_TA_x). zenon_intro zenon_H11.
% 0.60/0.78 generalize (zenon_H5d zenon_TB_bl). zenon_intro zenon_H1e.
% 0.60/0.78 generalize (zenon_H11 zenon_TX_u). zenon_intro zenon_H18.
% 0.60/0.78 apply (zenon_equiv_s _ _ zenon_H18); [ zenon_intro zenon_H1b; zenon_intro zenon_H1a | zenon_intro zenon_H12; zenon_intro zenon_H19 ].
% 0.60/0.78 exact (zenon_H1b zenon_H12).
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H19). zenon_intro zenon_H1d. zenon_intro zenon_H1c.
% 0.60/0.78 apply (zenon_L2_ zenon_TA_x zenon_TX_u zenon_TR_v zenon_TE_w zenon_TB_bl); trivial.
% 0.60/0.78 exact (zenon_H6d zenon_H71).
% 0.60/0.78 exact (zenon_H65 zenon_H69).
% 0.60/0.78 generalize (subset (equivalence_class zenon_TB_bl zenon_TE_w zenon_TR_v)). zenon_intro zenon_H73.
% 0.60/0.78 generalize (zenon_H73 (equivalence_class zenon_TA_x zenon_TE_w zenon_TR_v)). zenon_intro zenon_H74.
% 0.60/0.78 apply (zenon_equiv_s _ _ zenon_H74); [ zenon_intro zenon_H64; zenon_intro zenon_H77 | zenon_intro zenon_H76; zenon_intro zenon_H75 ].
% 0.60/0.78 apply (zenon_notallex_s (fun X : zenon_U => ((member X (equivalence_class zenon_TB_bl zenon_TE_w zenon_TR_v))->(member X (equivalence_class zenon_TA_x zenon_TE_w zenon_TR_v)))) zenon_H77); [ zenon_intro zenon_H78; idtac ].
% 0.60/0.78 elim zenon_H78. zenon_intro zenon_TX_cg. zenon_intro zenon_H79.
% 0.60/0.78 apply (zenon_notimply_s _ _ zenon_H79). zenon_intro zenon_H38. zenon_intro zenon_H7a.
% 0.60/0.78 generalize (equivalence_class zenon_TR_v). zenon_intro zenon_H6e.
% 0.60/0.78 generalize (zenon_H6e zenon_TE_w). zenon_intro zenon_H20.
% 0.60/0.78 generalize (zenon_H20 zenon_TA_x). zenon_intro zenon_H11.
% 0.60/0.78 generalize (zenon_H11 zenon_TX_cg). zenon_intro zenon_H7b.
% 0.60/0.78 apply (zenon_equiv_s _ _ zenon_H7b); [ zenon_intro zenon_H7a; zenon_intro zenon_H7e | zenon_intro zenon_H7d; zenon_intro zenon_H7c ].
% 0.60/0.78 apply (zenon_notand_s _ _ zenon_H7e); [ zenon_intro zenon_H39 | zenon_intro zenon_H42 ].
% 0.60/0.78 generalize (zenon_H20 zenon_TB_bl). zenon_intro zenon_H37.
% 0.60/0.78 apply (zenon_L3_ zenon_TX_cg zenon_TR_v zenon_TE_w zenon_TB_bl); trivial.
% 0.60/0.78 generalize (zenon_H20 zenon_TB_bl). zenon_intro zenon_H37.
% 0.60/0.78 generalize (zenon_H5d zenon_TA_x). zenon_intro zenon_H7f.
% 0.60/0.78 generalize (zenon_H7f zenon_TB_bl). zenon_intro zenon_H41.
% 0.60/0.78 generalize (zenon_H37 zenon_TX_cg). zenon_intro zenon_H3b.
% 0.60/0.78 apply (zenon_equiv_s _ _ zenon_H3b); [ zenon_intro zenon_H3e; zenon_intro zenon_H3d | zenon_intro zenon_H38; zenon_intro zenon_H3c ].
% 0.60/0.78 exact (zenon_H3e zenon_H38).
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H40. zenon_intro zenon_H3f.
% 0.60/0.78 apply (zenon_L4_ zenon_TX_cg zenon_TR_v zenon_TB_bl zenon_TE_w zenon_TA_x); trivial.
% 0.60/0.78 exact (zenon_H7a zenon_H7d).
% 0.60/0.78 exact (zenon_H64 zenon_H76).
% 0.60/0.78 exact (zenon_H5f zenon_H5e).
% 0.60/0.78 generalize (equal_set (equivalence_class zenon_TA_x zenon_TE_w zenon_TR_v)). zenon_intro zenon_H60.
% 0.60/0.78 generalize (zenon_H60 (equivalence_class zenon_TB_bl zenon_TE_w zenon_TR_v)). zenon_intro zenon_H61.
% 0.60/0.78 apply (zenon_equiv_s _ _ zenon_H61); [ zenon_intro zenon_H5f; zenon_intro zenon_H63 | zenon_intro zenon_H5e; zenon_intro zenon_H62 ].
% 0.60/0.78 exact (zenon_H5f zenon_H5e).
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H69. zenon_intro zenon_H76.
% 0.60/0.78 generalize (subset (equivalence_class zenon_TB_bl zenon_TE_w zenon_TR_v)). zenon_intro zenon_H73.
% 0.60/0.78 generalize (zenon_H73 (equivalence_class zenon_TA_x zenon_TE_w zenon_TR_v)). zenon_intro zenon_H74.
% 0.60/0.78 apply (zenon_equiv_s _ _ zenon_H74); [ zenon_intro zenon_H64; zenon_intro zenon_H77 | zenon_intro zenon_H76; zenon_intro zenon_H75 ].
% 0.60/0.78 exact (zenon_H64 zenon_H76).
% 0.60/0.78 generalize (zenon_H5c zenon_TB_bl). zenon_intro zenon_H80.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H80); [ zenon_intro zenon_H2b | zenon_intro zenon_H81 ].
% 0.60/0.78 exact (zenon_H2b zenon_H24).
% 0.60/0.78 generalize (equivalence_class zenon_TR_v). zenon_intro zenon_H6e.
% 0.60/0.78 generalize (zenon_H6e zenon_TE_w). zenon_intro zenon_H20.
% 0.60/0.78 generalize (zenon_H20 zenon_TB_bl). zenon_intro zenon_H37.
% 0.60/0.78 generalize (zenon_H20 zenon_TA_x). zenon_intro zenon_H11.
% 0.60/0.78 generalize (zenon_H11 zenon_TB_bl). zenon_intro zenon_H82.
% 0.60/0.78 apply (zenon_equiv_s _ _ zenon_H82); [ zenon_intro zenon_H86; zenon_intro zenon_H85 | zenon_intro zenon_H84; zenon_intro zenon_H83 ].
% 0.60/0.78 generalize (zenon_H75 zenon_TB_bl). zenon_intro zenon_H87.
% 0.60/0.78 apply (zenon_imply_s _ _ zenon_H87); [ zenon_intro zenon_H88 | zenon_intro zenon_H84 ].
% 0.60/0.78 generalize (zenon_H37 zenon_TB_bl). zenon_intro zenon_H89.
% 0.60/0.78 apply (zenon_equiv_s _ _ zenon_H89); [ zenon_intro zenon_H88; zenon_intro zenon_H8c | zenon_intro zenon_H8b; zenon_intro zenon_H8a ].
% 0.60/0.78 apply (zenon_notand_s _ _ zenon_H8c); [ zenon_intro zenon_H2b | zenon_intro zenon_H8d ].
% 0.60/0.78 exact (zenon_H2b zenon_H24).
% 0.60/0.78 exact (zenon_H8d zenon_H81).
% 0.60/0.78 exact (zenon_H88 zenon_H8b).
% 0.60/0.78 exact (zenon_H86 zenon_H84).
% 0.60/0.78 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H24. zenon_intro zenon_H21.
% 0.60/0.78 exact (zenon_H36 zenon_H21).
% 0.60/0.78 Qed.
% 0.60/0.78 % SZS output end Proof
% 0.60/0.78 (* END-PROOF *)
% 0.60/0.78 nodes searched: 10831
% 0.60/0.78 max branch formulas: 1396
% 0.60/0.78 proof nodes created: 734
% 0.60/0.78 formulas created: 46414
% 0.60/0.78
%------------------------------------------------------------------------------