TSTP Solution File: KRS202+1 by Zenon---0.7.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Zenon---0.7.1
% Problem  : KRS202+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_zenon %s %d

% Computer : n028.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 : Sun Jul 17 03:39:45 EDT 2022

% Result   : Theorem 165.40s 165.61s
% Output   : Proof 165.40s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.14  % Problem  : KRS202+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.12/0.14  % Command  : run_zenon %s %d
% 0.14/0.36  % Computer : n028.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 600
% 0.14/0.36  % DateTime : Tue Jun  7 06:54:29 EDT 2022
% 0.14/0.36  % CPUTime  : 
% 165.40/165.61  (* PROOF-FOUND *)
% 165.40/165.61  % SZS status Theorem
% 165.40/165.61  (* BEGIN-PROOF *)
% 165.40/165.61  % SZS output start Proof
% 165.40/165.61  Theorem nota_esa_thm : (nota (esa) (thm)).
% 165.40/165.61  Proof.
% 165.40/165.61  assert (zenon_L1_ : forall (zenon_TC_bl : zenon_U) (zenon_TF_bm : zenon_U), (~(~(status zenon_TF_bm zenon_TC_bl (thm)))) -> (~(status zenon_TF_bm zenon_TC_bl (thm))) -> False).
% 165.40/165.61  do 2 intro. intros zenon_H23 zenon_H24.
% 165.40/165.61  exact (zenon_H23 zenon_H24).
% 165.40/165.61  (* end of lemma zenon_L1_ *)
% 165.40/165.61  assert (zenon_L2_ : forall (zenon_TC_bl : zenon_U) (zenon_TF_bm : zenon_U), (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (esa))/\(~(status Ax C (thm))))))) -> (~(status zenon_TF_bm zenon_TC_bl (thm))) -> (exists I1 : zenon_U, (model I1 zenon_TC_bl)) -> (exists I1 : zenon_U, (model I1 zenon_TF_bm)) -> False).
% 165.40/165.61  do 2 intro. intros zenon_H27 zenon_H24 zenon_H28 zenon_H29.
% 165.40/165.61  apply zenon_H27. exists zenon_TF_bm. apply NNPP. zenon_intro zenon_H2a.
% 165.40/165.61  apply zenon_H2a. exists zenon_TC_bl. apply NNPP. zenon_intro zenon_H2b.
% 165.40/165.61  apply (zenon_notand_s _ _ zenon_H2b); [ zenon_intro zenon_H2c | zenon_intro zenon_H23 ].
% 165.40/165.61  generalize (esa zenon_TF_bm). zenon_intro zenon_H2d.
% 165.40/165.61  generalize (zenon_H2d zenon_TC_bl). zenon_intro zenon_H2e.
% 165.40/165.61  apply (zenon_equiv_s _ _ zenon_H2e); [ zenon_intro zenon_H31; zenon_intro zenon_H2c | zenon_intro zenon_H30; zenon_intro zenon_H2f ].
% 165.40/165.61  apply (zenon_notequiv_s _ _ zenon_H31); [ zenon_intro zenon_H33; zenon_intro zenon_H28 | zenon_intro zenon_H29; zenon_intro zenon_H32 ].
% 165.40/165.61  exact (zenon_H33 zenon_H29).
% 165.40/165.61  exact (zenon_H32 zenon_H28).
% 165.40/165.61  exact (zenon_H2c zenon_H2f).
% 165.40/165.61  exact (zenon_H23 zenon_H24).
% 165.40/165.61  (* end of lemma zenon_L2_ *)
% 165.40/165.61  assert (zenon_L3_ : forall (zenon_TI4_cc : zenon_U) (zenon_TF_bm : zenon_U), (~(exists I4 : zenon_U, (~(model I4 zenon_TF_bm)))) -> (~(model zenon_TI4_cc zenon_TF_bm)) -> False).
% 165.40/165.61  do 2 intro. intros zenon_H34 zenon_H35.
% 165.40/165.61  apply zenon_H34. exists zenon_TI4_cc. apply NNPP. zenon_intro zenon_H37.
% 165.40/165.61  exact (zenon_H37 zenon_H35).
% 165.40/165.61  (* end of lemma zenon_L3_ *)
% 165.40/165.61  assert (zenon_L4_ : forall (zenon_TI4_cc : zenon_U) (zenon_TC_bl : zenon_U) (zenon_TF_bm : zenon_U), (forall I1 : zenon_U, ((model I1 zenon_TF_bm)->(model I1 zenon_TC_bl))) -> (model zenon_TI4_cc zenon_TF_bm) -> (~(model zenon_TI4_cc zenon_TC_bl)) -> False).
% 165.40/165.61  do 3 intro. intros zenon_H38 zenon_H39 zenon_H3a.
% 165.40/165.61  generalize (zenon_H38 zenon_TI4_cc). zenon_intro zenon_H3b.
% 165.40/165.61  apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H35 | zenon_intro zenon_H3c ].
% 165.40/165.61  exact (zenon_H35 zenon_H39).
% 165.40/165.61  exact (zenon_H3a zenon_H3c).
% 165.40/165.61  (* end of lemma zenon_L4_ *)
% 165.40/165.61  assert (zenon_L5_ : forall (zenon_TC_bl : zenon_U) (zenon_TF_bm : zenon_U) (zenon_TI4_cc : zenon_U), (forall F : zenon_U, (~((model zenon_TI4_cc F)<->(model zenon_TI4_cc (not F))))) -> (~(exists I4 : zenon_U, (~(model I4 zenon_TF_bm)))) -> (forall I1 : zenon_U, ((model I1 zenon_TF_bm)->(model I1 zenon_TC_bl))) -> (~(model zenon_TI4_cc zenon_TC_bl)) -> False).
% 165.40/165.61  do 3 intro. intros zenon_H3d zenon_H34 zenon_H38 zenon_H3a.
% 165.40/165.61  generalize (zenon_H3d zenon_TF_bm). zenon_intro zenon_H3e.
% 165.40/165.61  apply (zenon_notequiv_s _ _ zenon_H3e); [ zenon_intro zenon_H35; zenon_intro zenon_H40 | zenon_intro zenon_H39; zenon_intro zenon_H3f ].
% 165.40/165.61  apply (zenon_L3_ zenon_TI4_cc zenon_TF_bm); trivial.
% 165.40/165.61  apply (zenon_L4_ zenon_TI4_cc zenon_TC_bl zenon_TF_bm); trivial.
% 165.40/165.61  (* end of lemma zenon_L5_ *)
% 165.40/165.61  assert (zenon_L6_ : forall (zenon_TI4_cc : zenon_U) (zenon_TC_bl : zenon_U) (zenon_TF_bm : zenon_U), (forall C : zenon_U, ((forall I1 : zenon_U, ((model I1 zenon_TF_bm)->(model I1 C)))<->(status zenon_TF_bm C (thm)))) -> (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (esa))/\(~(status Ax C (thm))))))) -> (exists I1 : zenon_U, (model I1 zenon_TC_bl)) -> (exists I1 : zenon_U, (model I1 zenon_TF_bm)) -> (forall F : zenon_U, (~((model zenon_TI4_cc F)<->(model zenon_TI4_cc (not F))))) -> (~(exists I4 : zenon_U, (~(model I4 zenon_TF_bm)))) -> (~(model zenon_TI4_cc zenon_TC_bl)) -> False).
% 165.40/165.61  do 3 intro. intros zenon_H41 zenon_H27 zenon_H28 zenon_H29 zenon_H3d zenon_H34 zenon_H3a.
% 165.40/165.61  generalize (zenon_H41 zenon_TC_bl). zenon_intro zenon_H42.
% 165.40/165.61  apply (zenon_equiv_s _ _ zenon_H42); [ zenon_intro zenon_H44; zenon_intro zenon_H24 | zenon_intro zenon_H38; zenon_intro zenon_H43 ].
% 165.40/165.61  apply (zenon_L2_ zenon_TC_bl zenon_TF_bm); trivial.
% 165.40/165.61  apply (zenon_L5_ zenon_TC_bl zenon_TF_bm zenon_TI4_cc); trivial.
% 165.40/165.61  (* end of lemma zenon_L6_ *)
% 165.40/165.61  assert (zenon_L7_ : forall (zenon_TF_bm : zenon_U), (exists I4 : zenon_U, (~(model I4 zenon_TF_bm))) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> False).
% 165.40/165.61  do 1 intro. intros zenon_H45 zenon_H46.
% 165.40/165.61  elim zenon_H45. zenon_intro zenon_TI4_ct. zenon_intro zenon_H48.
% 165.40/165.61  generalize (zenon_H46 zenon_TI4_ct). zenon_intro zenon_H49.
% 165.40/165.61  exact (zenon_H48 zenon_H49).
% 165.40/165.61  (* end of lemma zenon_L7_ *)
% 165.40/165.61  assert (zenon_L8_ : forall (zenon_TF_bm : zenon_U), (~(forall I : zenon_U, (model I zenon_TF_bm))) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> False).
% 165.40/165.61  do 1 intro. intros zenon_H4a zenon_H46.
% 165.40/165.61  exact (zenon_H4a zenon_H46).
% 165.40/165.61  (* end of lemma zenon_L8_ *)
% 165.40/165.61  assert (zenon_L9_ : forall (zenon_TC_bl : zenon_U) (zenon_TI4_cc : zenon_U) (zenon_TF_bm : zenon_U), (forall C : zenon_U, (((exists I1 : zenon_U, (model I1 zenon_TF_bm))/\((exists I4 : zenon_U, (~(model I4 zenon_TF_bm)))/\(forall I2 : zenon_U, (model I2 C))))<->(status zenon_TF_bm C (wtc)))) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> (~(model zenon_TI4_cc zenon_TC_bl)) -> (exists I1 : zenon_U, (model I1 zenon_TC_bl)) -> (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (esa))/\(~(status Ax C (thm))))))) -> (exists I1 : zenon_U, (model I1 zenon_TF_bm)) -> False).
% 165.40/165.61  do 3 intro. intros zenon_H4b zenon_H46 zenon_H3a zenon_H28 zenon_H27 zenon_H29.
% 165.40/165.61  generalize (thm zenon_TF_bm). zenon_intro zenon_H41.
% 165.40/165.61  generalize (completeness zenon_TI4_cc). zenon_intro zenon_H3d.
% 165.40/165.61  generalize (zenon_H4b zenon_TF_bm). zenon_intro zenon_H4c.
% 165.40/165.61  apply (zenon_equiv_s _ _ zenon_H4c); [ zenon_intro zenon_H50; zenon_intro zenon_H4f | zenon_intro zenon_H4e; zenon_intro zenon_H4d ].
% 165.40/165.61  apply (zenon_notand_s _ _ zenon_H50); [ zenon_intro zenon_H33 | zenon_intro zenon_H51 ].
% 165.40/165.61  exact (zenon_H33 zenon_H29).
% 165.40/165.61  apply (zenon_notand_s _ _ zenon_H51); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ].
% 165.40/165.61  apply (zenon_L6_ zenon_TI4_cc zenon_TC_bl zenon_TF_bm); trivial.
% 165.40/165.61  exact (zenon_H4a zenon_H46).
% 165.40/165.61  apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H29. zenon_intro zenon_H52.
% 165.40/165.61  apply (zenon_and_s _ _ zenon_H52). zenon_intro zenon_H45. zenon_intro zenon_H46.
% 165.40/165.61  apply (zenon_L7_ zenon_TF_bm); trivial.
% 165.40/165.61  (* end of lemma zenon_L9_ *)
% 165.40/165.61  assert (zenon_L10_ : forall (zenon_TI1_dg : zenon_U) (zenon_TF_bm : zenon_U), (forall I : zenon_U, (model I zenon_TF_bm)) -> (~(model zenon_TI1_dg zenon_TF_bm)) -> False).
% 165.40/165.61  do 2 intro. intros zenon_H46 zenon_H53.
% 165.40/165.61  generalize (zenon_H46 zenon_TI1_dg). zenon_intro zenon_H55.
% 165.40/165.61  exact (zenon_H53 zenon_H55).
% 165.40/165.61  (* end of lemma zenon_L10_ *)
% 165.40/165.61  assert (zenon_L11_ : forall (zenon_TI4_cc : zenon_U) (zenon_TF_bm : zenon_U) (zenon_TAx_dk : zenon_U), (forall I1 : zenon_U, ((model I1 zenon_TAx_dk)/\(model I1 zenon_TF_bm))) -> (~(model zenon_TI4_cc zenon_TAx_dk)) -> False).
% 165.40/165.61  do 3 intro. intros zenon_H56 zenon_H57.
% 165.40/165.61  generalize (zenon_H56 zenon_TI4_cc). zenon_intro zenon_H59.
% 165.40/165.61  apply (zenon_and_s _ _ zenon_H59). zenon_intro zenon_H5a. zenon_intro zenon_H39.
% 165.40/165.61  exact (zenon_H57 zenon_H5a).
% 165.40/165.61  (* end of lemma zenon_L11_ *)
% 165.40/165.61  assert (zenon_L12_ : forall (zenon_TI4_cc : zenon_U) (zenon_TF_bm : zenon_U) (zenon_TC_bl : zenon_U) (zenon_TAx_dk : zenon_U), (forall I1 : zenon_U, ((model I1 zenon_TAx_dk)->(model I1 zenon_TC_bl))) -> (forall C : zenon_U, ((forall I1 : zenon_U, ((model I1 zenon_TAx_dk)/\(model I1 C)))<->(status zenon_TAx_dk C (tau)))) -> (forall C : zenon_U, ((forall I1 : zenon_U, ((model I1 zenon_TF_bm)->(model I1 C)))<->(status zenon_TF_bm C (thm)))) -> (~(exists I1 : zenon_U, (model I1 zenon_TF_bm))) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> (~(model zenon_TI4_cc zenon_TC_bl)) -> False).
% 165.40/165.61  do 4 intro. intros zenon_H5b zenon_H5c zenon_H41 zenon_H33 zenon_H46 zenon_H3a.
% 165.40/165.61  generalize (zenon_H5b zenon_TI4_cc). zenon_intro zenon_H5d.
% 165.40/165.61  apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H57 | zenon_intro zenon_H3c ].
% 165.40/165.61  generalize (zenon_H5c zenon_TF_bm). zenon_intro zenon_H5e.
% 165.40/165.61  apply (zenon_equiv_s _ _ zenon_H5e); [ zenon_intro zenon_H61; zenon_intro zenon_H60 | zenon_intro zenon_H56; zenon_intro zenon_H5f ].
% 165.40/165.61  apply (zenon_notallex_s (fun I1 : zenon_U => ((model I1 zenon_TAx_dk)/\(model I1 zenon_TF_bm))) zenon_H61); [ zenon_intro zenon_H62; idtac ].
% 165.40/165.61  elim zenon_H62. zenon_intro zenon_TI1_dg. zenon_intro zenon_H63.
% 165.40/165.61  apply (zenon_notand_s _ _ zenon_H63); [ zenon_intro zenon_H64 | zenon_intro zenon_H53 ].
% 165.40/165.61  generalize (zenon_H41 zenon_TAx_dk). zenon_intro zenon_H65.
% 165.40/165.61  apply (zenon_equiv_s _ _ zenon_H65); [ zenon_intro zenon_H69; zenon_intro zenon_H68 | zenon_intro zenon_H67; zenon_intro zenon_H66 ].
% 165.40/165.61  apply (zenon_notallex_s (fun I1 : zenon_U => ((model I1 zenon_TF_bm)->(model I1 zenon_TAx_dk))) zenon_H69); [ zenon_intro zenon_H6a; idtac ].
% 165.40/165.61  elim zenon_H6a. zenon_intro zenon_TI1_ed. zenon_intro zenon_H6c.
% 165.40/165.61  apply (zenon_notimply_s _ _ zenon_H6c). zenon_intro zenon_H6e. zenon_intro zenon_H6d.
% 165.40/165.61  apply zenon_H33. exists zenon_TI1_ed. apply NNPP. zenon_intro zenon_H6f.
% 165.40/165.61  exact (zenon_H6f zenon_H6e).
% 165.40/165.61  generalize (zenon_H67 zenon_TI1_dg). zenon_intro zenon_H70.
% 165.40/165.61  apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H53 | zenon_intro zenon_H71 ].
% 165.40/165.61  apply (zenon_L10_ zenon_TI1_dg zenon_TF_bm); trivial.
% 165.40/165.61  exact (zenon_H64 zenon_H71).
% 165.40/165.61  apply (zenon_L10_ zenon_TI1_dg zenon_TF_bm); trivial.
% 165.40/165.61  apply (zenon_L11_ zenon_TI4_cc zenon_TF_bm zenon_TAx_dk); trivial.
% 165.40/165.61  exact (zenon_H3a zenon_H3c).
% 165.40/165.61  (* end of lemma zenon_L12_ *)
% 165.40/165.61  assert (zenon_L13_ : forall (zenon_TI4_cc : zenon_U) (zenon_TF_bm : zenon_U) (zenon_TC_bl : zenon_U) (zenon_TAx_dk : zenon_U), (forall I1 : zenon_U, ((model I1 zenon_TAx_dk)->(model I1 zenon_TC_bl))) -> (~(exists I1 : zenon_U, (model I1 zenon_TF_bm))) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> (~(model zenon_TI4_cc zenon_TC_bl)) -> False).
% 165.40/165.61  do 4 intro. intros zenon_H5b zenon_H33 zenon_H46 zenon_H3a.
% 165.40/165.61  generalize (thm zenon_TF_bm). zenon_intro zenon_H41.
% 165.40/165.61  generalize (tau zenon_TAx_dk). zenon_intro zenon_H5c.
% 165.40/165.61  apply (zenon_L12_ zenon_TI4_cc zenon_TF_bm zenon_TC_bl zenon_TAx_dk); trivial.
% 165.40/165.61  (* end of lemma zenon_L13_ *)
% 165.40/165.61  assert (zenon_L14_ : forall (zenon_TAx_dk : zenon_U) (zenon_TF_bm : zenon_U) (zenon_TI4_cc : zenon_U) (zenon_TC_bl : zenon_U), (~(exists Ax : zenon_U, (exists C : zenon_U, ((status Ax C (esa))/\(~(status Ax C (thm))))))) -> (exists I1 : zenon_U, (model I1 zenon_TC_bl)) -> (~(model zenon_TI4_cc zenon_TC_bl)) -> (forall I : zenon_U, (model I zenon_TF_bm)) -> (forall I1 : zenon_U, ((model I1 zenon_TAx_dk)->(model I1 zenon_TC_bl))) -> False).
% 165.40/165.61  do 4 intro. intros zenon_H27 zenon_H28 zenon_H3a zenon_H46 zenon_H5b.
% 165.40/165.61  generalize (wtc zenon_TF_bm). zenon_intro zenon_H4b.
% 165.40/165.61  generalize (cax zenon_TF_bm). zenon_intro zenon_H0.
% 165.40/165.61  generalize (zenon_H0 zenon_E). zenon_intro zenon_H72.
% 165.40/165.61  apply (zenon_equiv_s _ _ zenon_H72); [ zenon_intro zenon_H75; zenon_intro zenon_H74 | zenon_intro zenon_H33; zenon_intro zenon_H73 ].
% 165.40/165.61  apply zenon_H75. zenon_intro zenon_H29.
% 165.40/165.61  apply (zenon_L9_ zenon_TC_bl zenon_TI4_cc zenon_TF_bm); trivial.
% 165.40/165.61  apply (zenon_L13_ zenon_TI4_cc zenon_TF_bm zenon_TC_bl zenon_TAx_dk); trivial.
% 165.40/165.61  (* end of lemma zenon_L14_ *)
% 165.40/165.61  assert (zenon_L15_ : forall (zenon_TI3_ep : zenon_U) (zenon_TC_bl : zenon_U), (~(exists I1 : zenon_U, (model I1 zenon_TC_bl))) -> (model zenon_TI3_ep zenon_TC_bl) -> False).
% 165.40/165.61  do 2 intro. intros zenon_H32 zenon_H76.
% 165.40/165.61  apply zenon_H32. exists zenon_TI3_ep. apply NNPP. zenon_intro zenon_H78.
% 165.40/165.61  exact (zenon_H78 zenon_H76).
% 165.40/165.61  (* end of lemma zenon_L15_ *)
% 165.40/165.61  apply NNPP. intro zenon_G.
% 165.40/165.61  elim tautology. zenon_intro zenon_TF_bm. zenon_intro zenon_H46.
% 165.40/165.61  elim mixed_pair. zenon_intro zenon_TAx_dk. zenon_intro zenon_H79.
% 165.40/165.61  elim zenon_H79. zenon_intro zenon_TC_bl. zenon_intro zenon_H7a.
% 165.40/165.61  apply (zenon_and_s _ _ zenon_H7a). zenon_intro zenon_H7c. zenon_intro zenon_H7b.
% 165.40/165.61  apply (zenon_and_s _ _ zenon_H7b). zenon_intro zenon_H5b. zenon_intro zenon_H7d.
% 165.40/165.61  apply (zenon_and_s _ _ zenon_H7d). zenon_intro zenon_H7f. zenon_intro zenon_H7e.
% 165.40/165.61  elim zenon_H7f. zenon_intro zenon_TI3_ep. zenon_intro zenon_H80.
% 165.40/165.61  apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H81. zenon_intro zenon_H76.
% 165.40/165.61  elim zenon_H7e. zenon_intro zenon_TI4_cc. zenon_intro zenon_H3a.
% 165.40/165.61  generalize (nota (esa)). zenon_intro zenon_H82.
% 165.40/165.61  generalize (zenon_H82 (thm)). zenon_intro zenon_H83.
% 165.40/165.61  apply (zenon_equiv_s _ _ zenon_H83); [ zenon_intro zenon_H27; zenon_intro zenon_G | zenon_intro zenon_H85; zenon_intro zenon_H84 ].
% 165.40/165.62  generalize (cax zenon_TC_bl). zenon_intro zenon_H1.
% 165.40/165.62  generalize (zenon_H1 zenon_E). zenon_intro zenon_H86.
% 165.40/165.62  apply (zenon_equiv_s _ _ zenon_H86); [ zenon_intro zenon_H89; zenon_intro zenon_H88 | zenon_intro zenon_H32; zenon_intro zenon_H87 ].
% 165.40/165.62  apply zenon_H89. zenon_intro zenon_H28.
% 165.40/165.62  apply (zenon_L14_ zenon_TAx_dk zenon_TF_bm zenon_TI4_cc zenon_TC_bl); trivial.
% 165.40/165.62  apply (zenon_L15_ zenon_TI3_ep zenon_TC_bl); trivial.
% 165.40/165.62  exact (zenon_G zenon_H84).
% 165.40/165.62  Qed.
% 165.40/165.62  % SZS output end Proof
% 165.40/165.62  (* END-PROOF *)
% 165.40/165.62  nodes searched: 7884492
% 165.40/165.62  max branch formulas: 25923
% 165.40/165.62  proof nodes created: 490335
% 165.40/165.62  formulas created: 19112971
% 165.40/165.62  
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