TSTP Solution File: LCL668+1.001 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : LCL668+1.001 : TPTP v8.1.0. Released v4.0.0.
% 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 : Sun Jul 17 16:23:38 EDT 2022
% Result : Theorem 42.35s 42.51s
% Output : Proof 42.35s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : LCL668+1.001 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : run_zenon %s %d
% 0.14/0.36 % Computer : n013.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 : Sun Jul 3 07:29:14 EDT 2022
% 0.14/0.36 % CPUTime :
% 42.35/42.51 (* PROOF-FOUND *)
% 42.35/42.51 % SZS status Theorem
% 42.35/42.51 (* BEGIN-PROOF *)
% 42.35/42.51 % SZS output start Proof
% 42.35/42.51 Theorem main : (~(exists X : zenon_U, (~((forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((~(p12 X))/\((~(p10 X))/\((~(p8 X))/\((~(p6 X))/\((~(p4 X))/\(~(p2 X)))))))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p7 Y)))\/((~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))))))))))))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p6 X)/\((p5 X)/\((p4 X)/\((p3 X)/\((p2 X)/\(p1 X)))))))))))))))))))))))).
% 42.35/42.51 Proof.
% 42.35/42.51 assert (zenon_L1_ : forall (zenon_TY_e : zenon_U), (~(~(p5 zenon_TY_e))) -> (~(p5 zenon_TY_e)) -> False).
% 42.35/42.51 do 1 intro. intros zenon_H2 zenon_H3.
% 42.35/42.51 exact (zenon_H2 zenon_H3).
% 42.35/42.51 (* end of lemma zenon_L1_ *)
% 42.35/42.51 assert (zenon_L2_ : forall (zenon_TY_e : zenon_U), (~(((~(p1 zenon_TY_e))/\(~(p2 zenon_TY_e)))\/((p2 zenon_TY_e)/\(p1 zenon_TY_e)))) -> (p2 zenon_TY_e) -> (p1 zenon_TY_e) -> False).
% 42.35/42.51 do 1 intro. intros zenon_H5 zenon_H6 zenon_H7.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H5). zenon_intro zenon_H9. zenon_intro zenon_H8.
% 42.35/42.51 apply (zenon_notand_s _ _ zenon_H8); [ zenon_intro zenon_Hb | zenon_intro zenon_Ha ].
% 42.35/42.51 exact (zenon_Hb zenon_H6).
% 42.35/42.51 exact (zenon_Ha zenon_H7).
% 42.35/42.51 (* end of lemma zenon_L2_ *)
% 42.35/42.51 assert (zenon_L3_ : forall (zenon_TY_e : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TY_e X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))) -> (p2 zenon_TY_e) -> (p1 zenon_TY_e) -> False).
% 42.35/42.51 do 1 intro. intros zenon_Hc zenon_H6 zenon_H7.
% 42.35/42.51 generalize (zenon_Hc zenon_TY_e). zenon_intro zenon_Hd.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_Hd); [ zenon_intro zenon_He | zenon_intro zenon_H5 ].
% 42.35/42.51 generalize (reflexivity zenon_TY_e). zenon_intro zenon_Hf.
% 42.35/42.51 exact (zenon_He zenon_Hf).
% 42.35/42.51 apply (zenon_L2_ zenon_TY_e); trivial.
% 42.35/42.51 (* end of lemma zenon_L3_ *)
% 42.35/42.51 assert (zenon_L4_ : forall (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))) -> (r1 zenon_TX_s zenon_TY_e) -> (p2 zenon_TY_e) -> (p1 zenon_TY_e) -> False).
% 42.35/42.51 do 2 intro. intros zenon_H10 zenon_H11 zenon_H6 zenon_H7.
% 42.35/42.51 generalize (zenon_H10 zenon_TY_e). zenon_intro zenon_H13.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H13); [ zenon_intro zenon_H14 | zenon_intro zenon_Hc ].
% 42.35/42.51 exact (zenon_H14 zenon_H11).
% 42.35/42.51 apply (zenon_L3_ zenon_TY_e); trivial.
% 42.35/42.51 (* end of lemma zenon_L4_ *)
% 42.35/42.51 assert (zenon_L5_ : forall (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U), (~(~(forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))) -> (p1 zenon_TY_e) -> (p2 zenon_TY_e) -> (r1 zenon_TX_s zenon_TY_e) -> False).
% 42.35/42.51 do 2 intro. intros zenon_H15 zenon_H7 zenon_H6 zenon_H11.
% 42.35/42.51 apply zenon_H15. zenon_intro zenon_H16.
% 42.35/42.51 generalize (zenon_H16 zenon_TX_s). zenon_intro zenon_H17.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H17); [ zenon_intro zenon_H18 | zenon_intro zenon_H10 ].
% 42.35/42.51 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19.
% 42.35/42.51 exact (zenon_H18 zenon_H19).
% 42.35/42.51 apply (zenon_L4_ zenon_TY_e zenon_TX_s); trivial.
% 42.35/42.51 (* end of lemma zenon_L5_ *)
% 42.35/42.51 assert (zenon_L6_ : forall (zenon_TX_s : zenon_U) (zenon_TY_e : zenon_U), (~(~(p1 zenon_TY_e))) -> (r1 zenon_TX_s zenon_TY_e) -> (p2 zenon_TY_e) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> False).
% 42.35/42.51 do 2 intro. intros zenon_H1a zenon_H11 zenon_H6 zenon_H1b.
% 42.35/42.51 apply zenon_H1a. zenon_intro zenon_H7.
% 42.35/42.51 generalize (zenon_H1b zenon_TX_s). zenon_intro zenon_H1c.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H1c); [ zenon_intro zenon_H18 | zenon_intro zenon_H15 ].
% 42.35/42.51 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19.
% 42.35/42.51 exact (zenon_H18 zenon_H19).
% 42.35/42.51 apply (zenon_L5_ zenon_TY_e zenon_TX_s); trivial.
% 42.35/42.51 (* end of lemma zenon_L6_ *)
% 42.35/42.51 assert (zenon_L7_ : forall (zenon_TX_s : zenon_U) (zenon_TY_e : zenon_U), (~(((~(p5 zenon_TY_e))/\(~(p1 zenon_TY_e)))\/((p1 zenon_TY_e)/\(p5 zenon_TY_e)))) -> (~(p5 zenon_TY_e)) -> (r1 zenon_TX_s zenon_TY_e) -> (p2 zenon_TY_e) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> False).
% 42.35/42.51 do 2 intro. intros zenon_H1d zenon_H3 zenon_H11 zenon_H6 zenon_H1b.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e.
% 42.35/42.51 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H2 | zenon_intro zenon_H1a ].
% 42.35/42.51 exact (zenon_H2 zenon_H3).
% 42.35/42.51 apply (zenon_L6_ zenon_TX_s zenon_TY_e); trivial.
% 42.35/42.51 (* end of lemma zenon_L7_ *)
% 42.35/42.51 assert (zenon_L8_ : forall (zenon_TX_s : zenon_U) (zenon_TY_e : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TY_e X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))) -> (~(p5 zenon_TY_e)) -> (r1 zenon_TX_s zenon_TY_e) -> (p2 zenon_TY_e) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> False).
% 42.35/42.51 do 2 intro. intros zenon_H20 zenon_H3 zenon_H11 zenon_H6 zenon_H1b.
% 42.35/42.51 generalize (zenon_H20 zenon_TY_e). zenon_intro zenon_H21.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H21); [ zenon_intro zenon_He | zenon_intro zenon_H1d ].
% 42.35/42.51 generalize (reflexivity zenon_TY_e). zenon_intro zenon_Hf.
% 42.35/42.51 exact (zenon_He zenon_Hf).
% 42.35/42.51 apply (zenon_L7_ zenon_TX_s zenon_TY_e); trivial.
% 42.35/42.51 (* end of lemma zenon_L8_ *)
% 42.35/42.51 assert (zenon_L9_ : forall (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))) -> (r1 zenon_TX_s zenon_TY_e) -> (~(p5 zenon_TY_e)) -> (p2 zenon_TY_e) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> False).
% 42.35/42.51 do 2 intro. intros zenon_H22 zenon_H11 zenon_H3 zenon_H6 zenon_H1b.
% 42.35/42.51 generalize (zenon_H22 zenon_TY_e). zenon_intro zenon_H23.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H23); [ zenon_intro zenon_H14 | zenon_intro zenon_H20 ].
% 42.35/42.51 exact (zenon_H14 zenon_H11).
% 42.35/42.51 apply (zenon_L8_ zenon_TX_s zenon_TY_e); trivial.
% 42.35/42.51 (* end of lemma zenon_L9_ *)
% 42.35/42.51 assert (zenon_L10_ : forall (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))) -> (r1 zenon_TX_s zenon_TY_e) -> (~(p5 zenon_TY_e)) -> (p2 zenon_TY_e) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> False).
% 42.35/42.51 do 2 intro. intros zenon_H24 zenon_H11 zenon_H3 zenon_H6 zenon_H1b.
% 42.35/42.51 generalize (zenon_H24 zenon_TX_s). zenon_intro zenon_H25.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H25); [ zenon_intro zenon_H18 | zenon_intro zenon_H22 ].
% 42.35/42.51 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19.
% 42.35/42.51 exact (zenon_H18 zenon_H19).
% 42.35/42.51 apply (zenon_L9_ zenon_TY_e zenon_TX_s); trivial.
% 42.35/42.51 (* end of lemma zenon_L10_ *)
% 42.35/42.51 assert (zenon_L11_ : forall (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))) -> (r1 zenon_TX_s zenon_TY_e) -> (~(p5 zenon_TY_e)) -> (p2 zenon_TY_e) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> False).
% 42.35/42.51 do 2 intro. intros zenon_H26 zenon_H11 zenon_H3 zenon_H6 zenon_H1b.
% 42.35/42.51 generalize (zenon_H26 zenon_TX_s). zenon_intro zenon_H27.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H18 | zenon_intro zenon_H24 ].
% 42.35/42.51 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19.
% 42.35/42.51 exact (zenon_H18 zenon_H19).
% 42.35/42.51 apply (zenon_L10_ zenon_TY_e zenon_TX_s); trivial.
% 42.35/42.51 (* end of lemma zenon_L11_ *)
% 42.35/42.51 assert (zenon_L12_ : forall (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U) (zenon_TY_bq : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TY_bq X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))) -> (r1 zenon_TY_bq zenon_TX_s) -> (r1 zenon_TX_s zenon_TY_e) -> (~(p5 zenon_TY_e)) -> (p2 zenon_TY_e) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> False).
% 42.35/42.51 do 3 intro. intros zenon_H28 zenon_H29 zenon_H11 zenon_H3 zenon_H6 zenon_H1b.
% 42.35/42.51 generalize (zenon_H28 zenon_TX_s). zenon_intro zenon_H2b.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H2b); [ zenon_intro zenon_H2c | zenon_intro zenon_H26 ].
% 42.35/42.51 exact (zenon_H2c zenon_H29).
% 42.35/42.51 apply (zenon_L11_ zenon_TY_e zenon_TX_s); trivial.
% 42.35/42.51 (* end of lemma zenon_L12_ *)
% 42.35/42.51 assert (zenon_L13_ : forall (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U) (zenon_TY_bq : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TY_bq Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))))) -> (r1 zenon_TY_bq zenon_TX_s) -> (r1 zenon_TX_s zenon_TY_e) -> (~(p5 zenon_TY_e)) -> (p2 zenon_TY_e) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> False).
% 42.35/42.51 do 3 intro. intros zenon_H2d zenon_H29 zenon_H11 zenon_H3 zenon_H6 zenon_H1b.
% 42.35/42.51 generalize (zenon_H2d zenon_TY_bq). zenon_intro zenon_H2e.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H2e); [ zenon_intro zenon_H2f | zenon_intro zenon_H28 ].
% 42.35/42.51 generalize (reflexivity zenon_TY_bq). zenon_intro zenon_H30.
% 42.35/42.51 exact (zenon_H2f zenon_H30).
% 42.35/42.51 apply (zenon_L12_ zenon_TY_e zenon_TX_s zenon_TY_bq); trivial.
% 42.35/42.51 (* end of lemma zenon_L13_ *)
% 42.35/42.51 assert (zenon_L14_ : forall (zenon_TY_e : zenon_U), (~(~(p3 zenon_TY_e))) -> (~(p3 zenon_TY_e)) -> False).
% 42.35/42.51 do 1 intro. intros zenon_H31 zenon_H32.
% 42.35/42.51 exact (zenon_H31 zenon_H32).
% 42.35/42.51 (* end of lemma zenon_L14_ *)
% 42.35/42.51 assert (zenon_L15_ : forall (zenon_TY_e : zenon_U), (~(((~(p3 zenon_TY_e))/\(~(p4 zenon_TY_e)))\/((p4 zenon_TY_e)/\(p3 zenon_TY_e)))) -> (~(p3 zenon_TY_e)) -> (~(p4 zenon_TY_e)) -> False).
% 42.35/42.51 do 1 intro. intros zenon_H33 zenon_H32 zenon_H34.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H33). zenon_intro zenon_H36. zenon_intro zenon_H35.
% 42.35/42.51 apply (zenon_notand_s _ _ zenon_H36); [ zenon_intro zenon_H31 | zenon_intro zenon_H37 ].
% 42.35/42.51 exact (zenon_H31 zenon_H32).
% 42.35/42.51 exact (zenon_H37 zenon_H34).
% 42.35/42.51 (* end of lemma zenon_L15_ *)
% 42.35/42.51 assert (zenon_L16_ : forall (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))) -> (r1 zenon_TX_s zenon_TY_e) -> (~(p3 zenon_TY_e)) -> (~(p4 zenon_TY_e)) -> False).
% 42.35/42.51 do 2 intro. intros zenon_H38 zenon_H11 zenon_H32 zenon_H34.
% 42.35/42.51 generalize (zenon_H38 zenon_TY_e). zenon_intro zenon_H39.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H39); [ zenon_intro zenon_H14 | zenon_intro zenon_H33 ].
% 42.35/42.51 exact (zenon_H14 zenon_H11).
% 42.35/42.51 apply (zenon_L15_ zenon_TY_e); trivial.
% 42.35/42.51 (* end of lemma zenon_L16_ *)
% 42.35/42.51 assert (zenon_L17_ : forall (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))) -> (r1 zenon_TX_s zenon_TY_e) -> (~(p3 zenon_TY_e)) -> (~(p4 zenon_TY_e)) -> False).
% 42.35/42.51 do 2 intro. intros zenon_H3a zenon_H11 zenon_H32 zenon_H34.
% 42.35/42.51 generalize (zenon_H3a zenon_TX_s). zenon_intro zenon_H3b.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H18 | zenon_intro zenon_H38 ].
% 42.35/42.51 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19.
% 42.35/42.51 exact (zenon_H18 zenon_H19).
% 42.35/42.51 apply (zenon_L16_ zenon_TY_e zenon_TX_s); trivial.
% 42.35/42.51 (* end of lemma zenon_L17_ *)
% 42.35/42.51 assert (zenon_L18_ : forall (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))) -> (r1 zenon_TX_s zenon_TY_e) -> (~(p3 zenon_TY_e)) -> (~(p4 zenon_TY_e)) -> False).
% 42.35/42.51 do 2 intro. intros zenon_H3c zenon_H11 zenon_H32 zenon_H34.
% 42.35/42.51 generalize (zenon_H3c zenon_TX_s). zenon_intro zenon_H3d.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H18 | zenon_intro zenon_H3a ].
% 42.35/42.51 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19.
% 42.35/42.51 exact (zenon_H18 zenon_H19).
% 42.35/42.51 apply (zenon_L17_ zenon_TY_e zenon_TX_s); trivial.
% 42.35/42.51 (* end of lemma zenon_L18_ *)
% 42.35/42.51 assert (zenon_L19_ : forall (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))) -> (r1 zenon_TX_s zenon_TY_e) -> (~(p3 zenon_TY_e)) -> (~(p4 zenon_TY_e)) -> False).
% 42.35/42.51 do 2 intro. intros zenon_H3e zenon_H11 zenon_H32 zenon_H34.
% 42.35/42.51 generalize (zenon_H3e zenon_TX_s). zenon_intro zenon_H3f.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H18 | zenon_intro zenon_H3c ].
% 42.35/42.51 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19.
% 42.35/42.51 exact (zenon_H18 zenon_H19).
% 42.35/42.51 apply (zenon_L18_ zenon_TY_e zenon_TX_s); trivial.
% 42.35/42.51 (* end of lemma zenon_L19_ *)
% 42.35/42.51 assert (zenon_L20_ : forall (zenon_TX_s : zenon_U) (zenon_TY_e : zenon_U), (~(~(p5 zenon_TY_e))) -> (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))) -> (r1 zenon_TX_s zenon_TY_e) -> (~(p3 zenon_TY_e)) -> (~((p5 zenon_TY_e)/\(p4 zenon_TY_e))) -> False).
% 42.35/42.51 do 2 intro. intros zenon_H2 zenon_H40 zenon_H11 zenon_H32 zenon_H41.
% 42.35/42.51 apply zenon_H2. zenon_intro zenon_H42.
% 42.35/42.51 apply (zenon_notand_s _ _ zenon_H41); [ zenon_intro zenon_H3 | zenon_intro zenon_H34 ].
% 42.35/42.51 exact (zenon_H3 zenon_H42).
% 42.35/42.51 generalize (zenon_H40 zenon_TX_s). zenon_intro zenon_H43.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H18 | zenon_intro zenon_H3e ].
% 42.35/42.51 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19.
% 42.35/42.51 exact (zenon_H18 zenon_H19).
% 42.35/42.51 apply (zenon_L19_ zenon_TY_e zenon_TX_s); trivial.
% 42.35/42.51 (* end of lemma zenon_L20_ *)
% 42.35/42.51 assert (zenon_L21_ : forall (zenon_TX_s : zenon_U) (zenon_TY_bq : zenon_U) (zenon_TX_ct : zenon_U) (zenon_TY_e : zenon_U), (~(((~(p4 zenon_TY_e))/\(~(p5 zenon_TY_e)))\/((p5 zenon_TY_e)/\(p4 zenon_TY_e)))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))))))))))) -> (r1 zenon_TX_ct zenon_TY_bq) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> (p2 zenon_TY_e) -> (r1 zenon_TX_s zenon_TY_e) -> (r1 zenon_TY_bq zenon_TX_s) -> (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))) -> (~(p3 zenon_TY_e)) -> False).
% 42.35/42.51 do 4 intro. intros zenon_H44 zenon_H45 zenon_H46 zenon_H1b zenon_H6 zenon_H11 zenon_H29 zenon_H40 zenon_H32.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H44). zenon_intro zenon_H48. zenon_intro zenon_H41.
% 42.35/42.51 apply (zenon_notand_s _ _ zenon_H48); [ zenon_intro zenon_H37 | zenon_intro zenon_H2 ].
% 42.35/42.51 apply zenon_H37. zenon_intro zenon_H49.
% 42.35/42.51 apply (zenon_notand_s _ _ zenon_H41); [ zenon_intro zenon_H3 | zenon_intro zenon_H34 ].
% 42.35/42.51 generalize (zenon_H45 zenon_TY_bq). zenon_intro zenon_H4a.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ].
% 42.35/42.51 exact (zenon_H4c zenon_H46).
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d.
% 42.35/42.51 apply zenon_H4e. zenon_intro zenon_H4f.
% 42.35/42.51 generalize (zenon_H4f zenon_TY_bq). zenon_intro zenon_H50.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H2f | zenon_intro zenon_H2d ].
% 42.35/42.51 generalize (reflexivity zenon_TY_bq). zenon_intro zenon_H30.
% 42.35/42.51 exact (zenon_H2f zenon_H30).
% 42.35/42.51 apply (zenon_L13_ zenon_TY_e zenon_TX_s zenon_TY_bq); trivial.
% 42.35/42.51 exact (zenon_H34 zenon_H49).
% 42.35/42.51 apply (zenon_L20_ zenon_TX_s zenon_TY_e); trivial.
% 42.35/42.51 (* end of lemma zenon_L21_ *)
% 42.35/42.51 assert (zenon_L22_ : forall (zenon_TY_bq : zenon_U) (zenon_TX_ct : zenon_U) (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))) -> (r1 zenon_TX_s zenon_TY_e) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))))))))))) -> (r1 zenon_TX_ct zenon_TY_bq) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> (p2 zenon_TY_e) -> (r1 zenon_TY_bq zenon_TX_s) -> (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))) -> (~(p3 zenon_TY_e)) -> False).
% 42.35/42.51 do 4 intro. intros zenon_H51 zenon_H11 zenon_H45 zenon_H46 zenon_H1b zenon_H6 zenon_H29 zenon_H40 zenon_H32.
% 42.35/42.51 generalize (zenon_H51 zenon_TY_e). zenon_intro zenon_H52.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H14 | zenon_intro zenon_H44 ].
% 42.35/42.51 exact (zenon_H14 zenon_H11).
% 42.35/42.51 apply (zenon_L21_ zenon_TX_s zenon_TY_bq zenon_TX_ct zenon_TY_e); trivial.
% 42.35/42.51 (* end of lemma zenon_L22_ *)
% 42.35/42.51 assert (zenon_L23_ : forall (zenon_TY_bq : zenon_U) (zenon_TX_ct : zenon_U) (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))) -> (r1 zenon_TX_s zenon_TY_e) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))))))))))) -> (r1 zenon_TX_ct zenon_TY_bq) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> (p2 zenon_TY_e) -> (r1 zenon_TY_bq zenon_TX_s) -> (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))) -> (~(p3 zenon_TY_e)) -> False).
% 42.35/42.51 do 4 intro. intros zenon_H53 zenon_H11 zenon_H45 zenon_H46 zenon_H1b zenon_H6 zenon_H29 zenon_H40 zenon_H32.
% 42.35/42.51 generalize (zenon_H53 zenon_TX_s). zenon_intro zenon_H54.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H18 | zenon_intro zenon_H51 ].
% 42.35/42.51 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19.
% 42.35/42.51 exact (zenon_H18 zenon_H19).
% 42.35/42.51 apply (zenon_L22_ zenon_TY_bq zenon_TX_ct zenon_TY_e zenon_TX_s); trivial.
% 42.35/42.51 (* end of lemma zenon_L23_ *)
% 42.35/42.51 assert (zenon_L24_ : forall (zenon_TY_bq : zenon_U) (zenon_TX_ct : zenon_U) (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))) -> (r1 zenon_TX_s zenon_TY_e) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))))))))))) -> (r1 zenon_TX_ct zenon_TY_bq) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> (p2 zenon_TY_e) -> (r1 zenon_TY_bq zenon_TX_s) -> (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))) -> (~(p3 zenon_TY_e)) -> False).
% 42.35/42.51 do 4 intro. intros zenon_H55 zenon_H11 zenon_H45 zenon_H46 zenon_H1b zenon_H6 zenon_H29 zenon_H40 zenon_H32.
% 42.35/42.51 generalize (zenon_H55 zenon_TX_s). zenon_intro zenon_H56.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H18 | zenon_intro zenon_H53 ].
% 42.35/42.51 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19.
% 42.35/42.51 exact (zenon_H18 zenon_H19).
% 42.35/42.51 apply (zenon_L23_ zenon_TY_bq zenon_TX_ct zenon_TY_e zenon_TX_s); trivial.
% 42.35/42.51 (* end of lemma zenon_L24_ *)
% 42.35/42.51 assert (zenon_L25_ : forall (zenon_TX_ct : zenon_U) (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U) (zenon_TY_bq : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TY_bq Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))) -> (r1 zenon_TY_bq zenon_TX_s) -> (r1 zenon_TX_s zenon_TY_e) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))))))))))) -> (r1 zenon_TX_ct zenon_TY_bq) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> (p2 zenon_TY_e) -> (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))) -> (~(p3 zenon_TY_e)) -> False).
% 42.35/42.51 do 4 intro. intros zenon_H57 zenon_H29 zenon_H11 zenon_H45 zenon_H46 zenon_H1b zenon_H6 zenon_H40 zenon_H32.
% 42.35/42.51 generalize (zenon_H57 zenon_TX_s). zenon_intro zenon_H58.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H2c | zenon_intro zenon_H55 ].
% 42.35/42.51 exact (zenon_H2c zenon_H29).
% 42.35/42.51 apply (zenon_L24_ zenon_TY_bq zenon_TX_ct zenon_TY_e zenon_TX_s); trivial.
% 42.35/42.51 (* end of lemma zenon_L25_ *)
% 42.35/42.51 assert (zenon_L26_ : forall (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U) (zenon_TY_bq : zenon_U) (zenon_TX_ct : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TX_ct X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))) -> (r1 zenon_TX_ct zenon_TY_bq) -> (r1 zenon_TY_bq zenon_TX_s) -> (r1 zenon_TX_s zenon_TY_e) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))))))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> (p2 zenon_TY_e) -> (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))) -> (~(p3 zenon_TY_e)) -> False).
% 42.35/42.51 do 4 intro. intros zenon_H59 zenon_H46 zenon_H29 zenon_H11 zenon_H45 zenon_H1b zenon_H6 zenon_H40 zenon_H32.
% 42.35/42.51 generalize (zenon_H59 zenon_TY_bq). zenon_intro zenon_H5a.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4c | zenon_intro zenon_H57 ].
% 42.35/42.51 exact (zenon_H4c zenon_H46).
% 42.35/42.51 apply (zenon_L25_ zenon_TX_ct zenon_TY_e zenon_TX_s zenon_TY_bq); trivial.
% 42.35/42.51 (* end of lemma zenon_L26_ *)
% 42.35/42.51 assert (zenon_L27_ : forall (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U) (zenon_TY_bq : zenon_U) (zenon_TX_ct : zenon_U), (~((~(forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))) -> (r1 zenon_TX_ct zenon_TY_bq) -> (r1 zenon_TY_bq zenon_TX_s) -> (r1 zenon_TX_s zenon_TY_e) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))))))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> (p2 zenon_TY_e) -> (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))) -> (~(p3 zenon_TY_e)) -> False).
% 42.35/42.51 do 4 intro. intros zenon_H5b zenon_H46 zenon_H29 zenon_H11 zenon_H45 zenon_H1b zenon_H6 zenon_H40 zenon_H32.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H5c.
% 42.35/42.51 apply zenon_H5d. zenon_intro zenon_H5e.
% 42.35/42.51 generalize (zenon_H5e zenon_TX_ct). zenon_intro zenon_H5f.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H5f); [ zenon_intro zenon_H60 | zenon_intro zenon_H59 ].
% 42.35/42.51 generalize (reflexivity zenon_TX_ct). zenon_intro zenon_H61.
% 42.35/42.51 exact (zenon_H60 zenon_H61).
% 42.35/42.51 apply (zenon_L26_ zenon_TY_e zenon_TX_s zenon_TY_bq zenon_TX_ct); trivial.
% 42.35/42.51 (* end of lemma zenon_L27_ *)
% 42.35/42.51 assert (zenon_L28_ : forall (zenon_TY_bq : zenon_U) (zenon_TX_ct : zenon_U) (zenon_TX_s : zenon_U) (zenon_TY_e : zenon_U), (~(~(p2 zenon_TY_e))) -> (~(p3 zenon_TY_e)) -> (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))))))))))) -> (r1 zenon_TX_s zenon_TY_e) -> (r1 zenon_TY_bq zenon_TX_s) -> (r1 zenon_TX_ct zenon_TY_bq) -> False).
% 42.35/42.51 do 4 intro. intros zenon_H62 zenon_H32 zenon_H40 zenon_H1b zenon_H45 zenon_H11 zenon_H29 zenon_H46.
% 42.35/42.51 apply zenon_H62. zenon_intro zenon_H6.
% 42.35/42.51 generalize (zenon_H45 zenon_TX_ct). zenon_intro zenon_H63.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H60 | zenon_intro zenon_H64 ].
% 42.35/42.51 generalize (reflexivity zenon_TX_ct). zenon_intro zenon_H61.
% 42.35/42.51 exact (zenon_H60 zenon_H61).
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H65.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H65). zenon_intro zenon_H68. zenon_intro zenon_H67.
% 42.35/42.51 apply zenon_H67. zenon_intro zenon_H69.
% 42.35/42.51 generalize (zenon_H69 zenon_TX_ct). zenon_intro zenon_H6a.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H60 | zenon_intro zenon_H5b ].
% 42.35/42.51 generalize (reflexivity zenon_TX_ct). zenon_intro zenon_H61.
% 42.35/42.51 exact (zenon_H60 zenon_H61).
% 42.35/42.51 apply (zenon_L27_ zenon_TY_e zenon_TX_s zenon_TY_bq zenon_TX_ct); trivial.
% 42.35/42.51 (* end of lemma zenon_L28_ *)
% 42.35/42.51 assert (zenon_L29_ : forall (zenon_TY_bq : zenon_U) (zenon_TX_ct : zenon_U) (zenon_TX_s : zenon_U) (zenon_TY_e : zenon_U), (~(((~(p2 zenon_TY_e))/\(~(p3 zenon_TY_e)))\/((p3 zenon_TY_e)/\(p2 zenon_TY_e)))) -> (~(p3 zenon_TY_e)) -> (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))))))))))) -> (r1 zenon_TX_s zenon_TY_e) -> (r1 zenon_TY_bq zenon_TX_s) -> (r1 zenon_TX_ct zenon_TY_bq) -> False).
% 42.35/42.51 do 4 intro. intros zenon_H6b zenon_H32 zenon_H40 zenon_H1b zenon_H45 zenon_H11 zenon_H29 zenon_H46.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H6b). zenon_intro zenon_H6d. zenon_intro zenon_H6c.
% 42.35/42.51 apply (zenon_notand_s _ _ zenon_H6d); [ zenon_intro zenon_H62 | zenon_intro zenon_H31 ].
% 42.35/42.51 apply (zenon_L28_ zenon_TY_bq zenon_TX_ct zenon_TX_s zenon_TY_e); trivial.
% 42.35/42.51 exact (zenon_H31 zenon_H32).
% 42.35/42.51 (* end of lemma zenon_L29_ *)
% 42.35/42.51 assert (zenon_L30_ : forall (zenon_TY_bq : zenon_U) (zenon_TX_ct : zenon_U) (zenon_TX_s : zenon_U) (zenon_TY_e : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TY_e X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))) -> (~(p3 zenon_TY_e)) -> (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))))))))))) -> (r1 zenon_TX_s zenon_TY_e) -> (r1 zenon_TY_bq zenon_TX_s) -> (r1 zenon_TX_ct zenon_TY_bq) -> False).
% 42.35/42.51 do 4 intro. intros zenon_H6e zenon_H32 zenon_H40 zenon_H1b zenon_H45 zenon_H11 zenon_H29 zenon_H46.
% 42.35/42.51 generalize (zenon_H6e zenon_TY_e). zenon_intro zenon_H6f.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_He | zenon_intro zenon_H6b ].
% 42.35/42.51 generalize (reflexivity zenon_TY_e). zenon_intro zenon_Hf.
% 42.35/42.51 exact (zenon_He zenon_Hf).
% 42.35/42.51 apply (zenon_L29_ zenon_TY_bq zenon_TX_ct zenon_TX_s zenon_TY_e); trivial.
% 42.35/42.51 (* end of lemma zenon_L30_ *)
% 42.35/42.51 assert (zenon_L31_ : forall (zenon_TY_bq : zenon_U) (zenon_TX_ct : zenon_U) (zenon_TX_s : zenon_U) (zenon_TY_e : zenon_U), (forall Y : zenon_U, ((~(r1 zenon_TY_e Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))) -> (~(p3 zenon_TY_e)) -> (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))))))))))) -> (r1 zenon_TX_s zenon_TY_e) -> (r1 zenon_TY_bq zenon_TX_s) -> (r1 zenon_TX_ct zenon_TY_bq) -> False).
% 42.35/42.51 do 4 intro. intros zenon_H70 zenon_H32 zenon_H40 zenon_H1b zenon_H45 zenon_H11 zenon_H29 zenon_H46.
% 42.35/42.51 generalize (zenon_H70 zenon_TY_e). zenon_intro zenon_H71.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H71); [ zenon_intro zenon_He | zenon_intro zenon_H6e ].
% 42.35/42.51 generalize (reflexivity zenon_TY_e). zenon_intro zenon_Hf.
% 42.35/42.51 exact (zenon_He zenon_Hf).
% 42.35/42.51 apply (zenon_L30_ zenon_TY_bq zenon_TX_ct zenon_TX_s zenon_TY_e); trivial.
% 42.35/42.51 (* end of lemma zenon_L31_ *)
% 42.35/42.51 assert (zenon_L32_ : forall (zenon_TY_bq : zenon_U) (zenon_TX_ct : zenon_U) (zenon_TY_e : zenon_U) (zenon_TX_s : zenon_U), (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))) -> (r1 zenon_TX_s zenon_TY_e) -> (~(p3 zenon_TY_e)) -> (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))))))))))) -> (r1 zenon_TY_bq zenon_TX_s) -> (r1 zenon_TX_ct zenon_TY_bq) -> False).
% 42.35/42.51 do 4 intro. intros zenon_H72 zenon_H11 zenon_H32 zenon_H40 zenon_H1b zenon_H45 zenon_H29 zenon_H46.
% 42.35/42.51 generalize (zenon_H72 zenon_TY_e). zenon_intro zenon_H73.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H73); [ zenon_intro zenon_H14 | zenon_intro zenon_H70 ].
% 42.35/42.51 exact (zenon_H14 zenon_H11).
% 42.35/42.51 apply (zenon_L31_ zenon_TY_bq zenon_TX_ct zenon_TX_s zenon_TY_e); trivial.
% 42.35/42.51 (* end of lemma zenon_L32_ *)
% 42.35/42.51 assert (zenon_L33_ : forall (zenon_TY_bq : zenon_U) (zenon_TX_ct : zenon_U) (zenon_TX_s : zenon_U), (~((~(forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 zenon_TX_s Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))) -> (forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))))))))))) -> (r1 zenon_TY_bq zenon_TX_s) -> (r1 zenon_TX_ct zenon_TY_bq) -> False).
% 42.35/42.51 do 3 intro. intros zenon_H74 zenon_H40 zenon_H45 zenon_H29 zenon_H46.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H74). zenon_intro zenon_H76. zenon_intro zenon_H75.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H75). zenon_intro zenon_H78. zenon_intro zenon_H77.
% 42.35/42.51 apply zenon_H77. zenon_intro zenon_H1b.
% 42.35/42.51 apply zenon_H76. zenon_intro zenon_H79.
% 42.35/42.51 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_s Y))\/(p3 Y))) zenon_H78); [ zenon_intro zenon_H7a; idtac ].
% 42.35/42.51 elim zenon_H7a. zenon_intro zenon_TY_e. zenon_intro zenon_H7b.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H7b). zenon_intro zenon_H7c. zenon_intro zenon_H32.
% 42.35/42.51 apply zenon_H7c. zenon_intro zenon_H11.
% 42.35/42.51 generalize (zenon_H79 zenon_TX_s). zenon_intro zenon_H7d.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H18 | zenon_intro zenon_H72 ].
% 42.35/42.51 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19.
% 42.35/42.51 exact (zenon_H18 zenon_H19).
% 42.35/42.51 apply (zenon_L32_ zenon_TY_bq zenon_TX_ct zenon_TY_e zenon_TX_s); trivial.
% 42.35/42.51 (* end of lemma zenon_L33_ *)
% 42.35/42.51 assert (zenon_L34_ : forall (zenon_TY_bq : zenon_U) (zenon_TX_ct : zenon_U) (zenon_TX_s : zenon_U), (~((~(forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 zenon_TX_s X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))))))))))) -> (r1 zenon_TY_bq zenon_TX_s) -> (r1 zenon_TX_ct zenon_TY_bq) -> False).
% 42.35/42.51 do 3 intro. intros zenon_H7e zenon_H45 zenon_H29 zenon_H46.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H7e). zenon_intro zenon_H80. zenon_intro zenon_H7f.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H7f). zenon_intro zenon_H82. zenon_intro zenon_H81.
% 42.35/42.51 apply zenon_H81. zenon_intro zenon_H83.
% 42.35/42.51 apply zenon_H80. zenon_intro zenon_H40.
% 42.35/42.51 generalize (zenon_H83 zenon_TX_s). zenon_intro zenon_H84.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H18 | zenon_intro zenon_H74 ].
% 42.35/42.51 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19.
% 42.35/42.51 exact (zenon_H18 zenon_H19).
% 42.35/42.51 apply (zenon_L33_ zenon_TY_bq zenon_TX_ct zenon_TX_s); trivial.
% 42.35/42.51 (* end of lemma zenon_L34_ *)
% 42.35/42.51 assert (zenon_L35_ : forall (zenon_TX_ct : zenon_U) (zenon_TX_s : zenon_U) (zenon_TY_bq : zenon_U), (~((~(forall Y : zenon_U, ((~(r1 zenon_TY_bq Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 zenon_TY_bq Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 zenon_TY_bq Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))) -> (r1 zenon_TY_bq zenon_TX_s) -> (r1 zenon_TX_ct zenon_TY_bq) -> (forall Y : zenon_U, ((~(r1 zenon_TX_ct Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p5 X))/\(~(p1 X)))\/((p1 X)/\(p5 X)))))))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p6 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p4 X))/\(~(p5 X)))\/((p5 X)/\(p4 X)))))))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~((~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p3 X))/\(~(p4 X)))\/((p4 X)/\(p3 X)))))))))))))))\/((forall X : zenon_U, ((~(r1 Y X))\/(p4 X)))\/(~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p2 X))/\(~(p3 X)))\/((p3 X)/\(p2 X)))))))))))))\/((forall Y : zenon_U, ((~(r1 X Y))\/(p3 Y)))\/(~(forall Y : zenon_U, ((~(r1 X Y))\/(~(~(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(~(((~(p1 X))/\(~(p2 X)))\/((p2 X)/\(p1 X)))))))))))))))))))))))))))))))))))))) -> False).
% 42.35/42.51 do 3 intro. intros zenon_H85 zenon_H29 zenon_H46 zenon_H45.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H85). zenon_intro zenon_H87. zenon_intro zenon_H86.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H86). zenon_intro zenon_H89. zenon_intro zenon_H88.
% 42.35/42.51 apply zenon_H88. zenon_intro zenon_H8a.
% 42.35/42.51 generalize (zenon_H8a zenon_TX_s). zenon_intro zenon_H8b.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H8b); [ zenon_intro zenon_H2c | zenon_intro zenon_H7e ].
% 42.35/42.51 exact (zenon_H2c zenon_H29).
% 42.35/42.51 apply (zenon_L34_ zenon_TY_bq zenon_TX_ct zenon_TX_s); trivial.
% 42.35/42.51 (* end of lemma zenon_L35_ *)
% 42.35/42.51 apply NNPP. intro zenon_G.
% 42.35/42.51 apply zenon_G. zenon_intro zenon_H8c.
% 42.35/42.51 elim zenon_H8c. zenon_intro zenon_TX_ct. zenon_intro zenon_H8d.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H8d). zenon_intro zenon_H8f. zenon_intro zenon_H8e.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H90). zenon_intro zenon_H93. zenon_intro zenon_H92.
% 42.35/42.51 apply zenon_H93. zenon_intro zenon_H45.
% 42.35/42.51 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_ct Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p6 X)/\((p5 X)/\((p4 X)/\((p3 X)/\((p2 X)/\(p1 X)))))))))))))))))) zenon_H92); [ zenon_intro zenon_H94; idtac ].
% 42.35/42.51 elim zenon_H94. zenon_intro zenon_TY_bq. zenon_intro zenon_H95.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H95). zenon_intro zenon_H97. zenon_intro zenon_H96.
% 42.35/42.51 apply zenon_H97. zenon_intro zenon_H46.
% 42.35/42.51 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TY_bq X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/(forall Y : zenon_U, ((~(r1 X Y))\/(forall X : zenon_U, ((~(r1 Y X))\/((p6 X)/\((p5 X)/\((p4 X)/\((p3 X)/\((p2 X)/\(p1 X)))))))))))))))) zenon_H96); [ zenon_intro zenon_H98; idtac ].
% 42.35/42.51 elim zenon_H98. zenon_intro zenon_TX_s. zenon_intro zenon_H99.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H99). zenon_intro zenon_H9b. zenon_intro zenon_H9a.
% 42.35/42.51 apply zenon_H9b. zenon_intro zenon_H29.
% 42.35/42.51 generalize (zenon_H45 zenon_TY_bq). zenon_intro zenon_H4a.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ].
% 42.35/42.51 exact (zenon_H4c zenon_H46).
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d.
% 42.35/42.51 apply (zenon_notor_s _ _ zenon_H4d). zenon_intro zenon_H9d. zenon_intro zenon_H9c.
% 42.35/42.51 apply zenon_H9c. zenon_intro zenon_H9e.
% 42.35/42.51 generalize (zenon_H9e zenon_TY_bq). zenon_intro zenon_H9f.
% 42.35/42.51 apply (zenon_or_s _ _ zenon_H9f); [ zenon_intro zenon_H2f | zenon_intro zenon_H85 ].
% 42.35/42.51 generalize (reflexivity zenon_TY_bq). zenon_intro zenon_H30.
% 42.35/42.51 exact (zenon_H2f zenon_H30).
% 42.35/42.51 apply (zenon_L35_ zenon_TX_ct zenon_TX_s zenon_TY_bq); trivial.
% 42.35/42.51 Qed.
% 42.35/42.51 % SZS output end Proof
% 42.35/42.51 (* END-PROOF *)
% 42.35/42.51 nodes searched: 1897342
% 42.35/42.51 max branch formulas: 6169
% 42.35/42.51 proof nodes created: 93586
% 42.35/42.51 formulas created: 5351125
% 42.35/42.51
%------------------------------------------------------------------------------