%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : LCL668+1.001 : TPTP v9.3.1. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n027.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8046.5625MB % OS : Linux 6.8.0-71-generic % CPULimit : 300s % WCLimit : 300s % DateTime : Mon Sep 7 01:32:42 PM UTC 2026 % Result : Theorem 78.13s 78.41s % Output : Proof 78.13s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : LCL668+1.001 : TPTP v9.3.1. Released v4.0.0. % 0.00/0.04 % Command : run_zenon %s %d % 0.11/0.37 % Computer : n027.cluster.edu % 0.11/0.37 % Model : x86_64 x86_64 % 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.11/0.37 % Memory : 8046.5625MB % 0.11/0.37 % OS : Linux 6.8.0-71-generic % 0.11/0.37 % CPULimit : 300 % 0.11/0.37 % WCLimit : 300 % 0.11/0.37 % DateTime : Sat Sep 5 07:04:58 UTC 2026 % 0.11/0.37 % CPUTime : % 78.13/78.41 (* PROOF-FOUND *) % 78.13/78.41 % SZS status Theorem % 78.13/78.41 (* BEGIN-PROOF *) % 78.13/78.41 % SZS output start Proof % 78.13/78.41 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)))))))))))))))))))))))). % 78.13/78.41 Proof. % 78.13/78.41 assert (zenon_L1_ : forall (zenon_TY_e : zenon_U), (~(~(p5 zenon_TY_e))) -> (~(p5 zenon_TY_e)) -> False). % 78.13/78.41 do 1 intro. intros zenon_H2 zenon_H3. % 78.13/78.41 exact (zenon_H2 zenon_H3). % 78.13/78.41 (* end of lemma zenon_L1_ *) % 78.13/78.41 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). % 78.13/78.41 do 1 intro. intros zenon_H5 zenon_H6 zenon_H7. % 78.13/78.41 apply (zenon_notor_s _ _ zenon_H5). zenon_intro zenon_H9. zenon_intro zenon_H8. % 78.13/78.41 apply (zenon_notand_s _ _ zenon_H8); [ zenon_intro zenon_Hb | zenon_intro zenon_Ha ]. % 78.13/78.41 exact (zenon_Hb zenon_H6). % 78.13/78.41 exact (zenon_Ha zenon_H7). % 78.13/78.41 (* end of lemma zenon_L2_ *) % 78.13/78.41 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). % 78.13/78.41 do 1 intro. intros zenon_Hc zenon_H6 zenon_H7. % 78.13/78.41 generalize (zenon_Hc zenon_TY_e). zenon_intro zenon_Hd. % 78.13/78.41 apply (zenon_or_s _ _ zenon_Hd); [ zenon_intro zenon_He | zenon_intro zenon_H5 ]. % 78.13/78.41 generalize (reflexivity zenon_TY_e). zenon_intro zenon_Hf. % 78.13/78.41 exact (zenon_He zenon_Hf). % 78.13/78.41 apply (zenon_L2_ zenon_TY_e); trivial. % 78.13/78.41 (* end of lemma zenon_L3_ *) % 78.13/78.41 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). % 78.13/78.41 do 2 intro. intros zenon_H10 zenon_H11 zenon_H6 zenon_H7. % 78.13/78.41 generalize (zenon_H10 zenon_TY_e). zenon_intro zenon_H13. % 78.13/78.41 apply (zenon_or_s _ _ zenon_H13); [ zenon_intro zenon_H14 | zenon_intro zenon_Hc ]. % 78.13/78.41 exact (zenon_H14 zenon_H11). % 78.13/78.41 apply (zenon_L3_ zenon_TY_e); trivial. % 78.13/78.42 (* end of lemma zenon_L4_ *) % 78.13/78.42 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). % 78.13/78.42 do 2 intro. intros zenon_H15 zenon_H7 zenon_H6 zenon_H11. % 78.13/78.42 apply zenon_H15. zenon_intro zenon_H16. % 78.13/78.42 generalize (zenon_H16 zenon_TX_s). zenon_intro zenon_H17. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H17); [ zenon_intro zenon_H18 | zenon_intro zenon_H10 ]. % 78.13/78.42 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19. % 78.13/78.42 exact (zenon_H18 zenon_H19). % 78.13/78.42 apply (zenon_L4_ zenon_TY_e zenon_TX_s); trivial. % 78.13/78.42 (* end of lemma zenon_L5_ *) % 78.13/78.42 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). % 78.13/78.42 do 2 intro. intros zenon_H1a zenon_H11 zenon_H6 zenon_H1b. % 78.13/78.42 apply zenon_H1a. zenon_intro zenon_H7. % 78.13/78.42 generalize (zenon_H1b zenon_TX_s). zenon_intro zenon_H1c. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H1c); [ zenon_intro zenon_H18 | zenon_intro zenon_H15 ]. % 78.13/78.42 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19. % 78.13/78.42 exact (zenon_H18 zenon_H19). % 78.13/78.42 apply (zenon_L5_ zenon_TY_e zenon_TX_s); trivial. % 78.13/78.42 (* end of lemma zenon_L6_ *) % 78.13/78.42 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). % 78.13/78.42 do 2 intro. intros zenon_H1d zenon_H3 zenon_H11 zenon_H6 zenon_H1b. % 78.13/78.42 apply (zenon_notor_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e. % 78.13/78.42 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H2 | zenon_intro zenon_H1a ]. % 78.13/78.42 exact (zenon_H2 zenon_H3). % 78.13/78.42 apply (zenon_L6_ zenon_TX_s zenon_TY_e); trivial. % 78.13/78.42 (* end of lemma zenon_L7_ *) % 78.13/78.42 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). % 78.13/78.42 do 2 intro. intros zenon_H20 zenon_H3 zenon_H11 zenon_H6 zenon_H1b. % 78.13/78.42 generalize (zenon_H20 zenon_TY_e). zenon_intro zenon_H21. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H21); [ zenon_intro zenon_He | zenon_intro zenon_H1d ]. % 78.13/78.42 generalize (reflexivity zenon_TY_e). zenon_intro zenon_Hf. % 78.13/78.42 exact (zenon_He zenon_Hf). % 78.13/78.42 apply (zenon_L7_ zenon_TX_s zenon_TY_e); trivial. % 78.13/78.42 (* end of lemma zenon_L8_ *) % 78.13/78.42 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). % 78.13/78.42 do 2 intro. intros zenon_H22 zenon_H11 zenon_H3 zenon_H6 zenon_H1b. % 78.13/78.42 generalize (zenon_H22 zenon_TY_e). zenon_intro zenon_H23. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H23); [ zenon_intro zenon_H14 | zenon_intro zenon_H20 ]. % 78.13/78.42 exact (zenon_H14 zenon_H11). % 78.13/78.42 apply (zenon_L8_ zenon_TX_s zenon_TY_e); trivial. % 78.13/78.42 (* end of lemma zenon_L9_ *) % 78.13/78.42 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). % 78.13/78.42 do 2 intro. intros zenon_H24 zenon_H11 zenon_H3 zenon_H6 zenon_H1b. % 78.13/78.42 generalize (zenon_H24 zenon_TX_s). zenon_intro zenon_H25. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H25); [ zenon_intro zenon_H18 | zenon_intro zenon_H22 ]. % 78.13/78.42 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19. % 78.13/78.42 exact (zenon_H18 zenon_H19). % 78.13/78.42 apply (zenon_L9_ zenon_TY_e zenon_TX_s); trivial. % 78.13/78.42 (* end of lemma zenon_L10_ *) % 78.13/78.42 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). % 78.13/78.42 do 2 intro. intros zenon_H26 zenon_H11 zenon_H3 zenon_H6 zenon_H1b. % 78.13/78.42 generalize (zenon_H26 zenon_TX_s). zenon_intro zenon_H27. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H18 | zenon_intro zenon_H24 ]. % 78.13/78.42 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19. % 78.13/78.42 exact (zenon_H18 zenon_H19). % 78.13/78.42 apply (zenon_L10_ zenon_TY_e zenon_TX_s); trivial. % 78.13/78.42 (* end of lemma zenon_L11_ *) % 78.13/78.42 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). % 78.13/78.42 do 3 intro. intros zenon_H28 zenon_H29 zenon_H11 zenon_H3 zenon_H6 zenon_H1b. % 78.13/78.42 generalize (zenon_H28 zenon_TX_s). zenon_intro zenon_H2b. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H2b); [ zenon_intro zenon_H2c | zenon_intro zenon_H26 ]. % 78.13/78.42 exact (zenon_H2c zenon_H29). % 78.13/78.42 apply (zenon_L11_ zenon_TY_e zenon_TX_s); trivial. % 78.13/78.42 (* end of lemma zenon_L12_ *) % 78.13/78.42 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). % 78.13/78.42 do 3 intro. intros zenon_H2d zenon_H29 zenon_H11 zenon_H3 zenon_H6 zenon_H1b. % 78.13/78.42 generalize (zenon_H2d zenon_TY_bq). zenon_intro zenon_H2e. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H2e); [ zenon_intro zenon_H2f | zenon_intro zenon_H28 ]. % 78.13/78.42 generalize (reflexivity zenon_TY_bq). zenon_intro zenon_H30. % 78.13/78.42 exact (zenon_H2f zenon_H30). % 78.13/78.42 apply (zenon_L12_ zenon_TY_e zenon_TX_s zenon_TY_bq); trivial. % 78.13/78.42 (* end of lemma zenon_L13_ *) % 78.13/78.42 assert (zenon_L14_ : forall (zenon_TY_e : zenon_U), (~(~(p3 zenon_TY_e))) -> (~(p3 zenon_TY_e)) -> False). % 78.13/78.42 do 1 intro. intros zenon_H31 zenon_H32. % 78.13/78.42 exact (zenon_H31 zenon_H32). % 78.13/78.42 (* end of lemma zenon_L14_ *) % 78.13/78.42 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). % 78.13/78.42 do 1 intro. intros zenon_H33 zenon_H32 zenon_H34. % 78.13/78.42 apply (zenon_notor_s _ _ zenon_H33). zenon_intro zenon_H36. zenon_intro zenon_H35. % 78.13/78.42 apply (zenon_notand_s _ _ zenon_H36); [ zenon_intro zenon_H31 | zenon_intro zenon_H37 ]. % 78.13/78.42 exact (zenon_H31 zenon_H32). % 78.13/78.42 exact (zenon_H37 zenon_H34). % 78.13/78.42 (* end of lemma zenon_L15_ *) % 78.13/78.42 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). % 78.13/78.42 do 2 intro. intros zenon_H38 zenon_H11 zenon_H32 zenon_H34. % 78.13/78.42 generalize (zenon_H38 zenon_TY_e). zenon_intro zenon_H39. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H39); [ zenon_intro zenon_H14 | zenon_intro zenon_H33 ]. % 78.13/78.42 exact (zenon_H14 zenon_H11). % 78.13/78.42 apply (zenon_L15_ zenon_TY_e); trivial. % 78.13/78.42 (* end of lemma zenon_L16_ *) % 78.13/78.42 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). % 78.13/78.42 do 2 intro. intros zenon_H3a zenon_H11 zenon_H32 zenon_H34. % 78.13/78.42 generalize (zenon_H3a zenon_TX_s). zenon_intro zenon_H3b. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H18 | zenon_intro zenon_H38 ]. % 78.13/78.42 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19. % 78.13/78.42 exact (zenon_H18 zenon_H19). % 78.13/78.42 apply (zenon_L16_ zenon_TY_e zenon_TX_s); trivial. % 78.13/78.42 (* end of lemma zenon_L17_ *) % 78.13/78.42 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). % 78.13/78.42 do 2 intro. intros zenon_H3c zenon_H11 zenon_H32 zenon_H34. % 78.13/78.42 generalize (zenon_H3c zenon_TX_s). zenon_intro zenon_H3d. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H18 | zenon_intro zenon_H3a ]. % 78.13/78.42 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19. % 78.13/78.42 exact (zenon_H18 zenon_H19). % 78.13/78.42 apply (zenon_L17_ zenon_TY_e zenon_TX_s); trivial. % 78.13/78.42 (* end of lemma zenon_L18_ *) % 78.13/78.42 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). % 78.13/78.42 do 2 intro. intros zenon_H3e zenon_H11 zenon_H32 zenon_H34. % 78.13/78.42 generalize (zenon_H3e zenon_TX_s). zenon_intro zenon_H3f. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H18 | zenon_intro zenon_H3c ]. % 78.13/78.42 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19. % 78.13/78.42 exact (zenon_H18 zenon_H19). % 78.13/78.42 apply (zenon_L18_ zenon_TY_e zenon_TX_s); trivial. % 78.13/78.42 (* end of lemma zenon_L19_ *) % 78.13/78.42 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). % 78.13/78.42 do 2 intro. intros zenon_H2 zenon_H40 zenon_H11 zenon_H32 zenon_H41. % 78.13/78.42 apply zenon_H2. zenon_intro zenon_H42. % 78.13/78.42 apply (zenon_notand_s _ _ zenon_H41); [ zenon_intro zenon_H3 | zenon_intro zenon_H34 ]. % 78.13/78.42 exact (zenon_H3 zenon_H42). % 78.13/78.42 generalize (zenon_H40 zenon_TX_s). zenon_intro zenon_H43. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H18 | zenon_intro zenon_H3e ]. % 78.13/78.42 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19. % 78.13/78.42 exact (zenon_H18 zenon_H19). % 78.13/78.42 apply (zenon_L19_ zenon_TY_e zenon_TX_s); trivial. % 78.13/78.42 (* end of lemma zenon_L20_ *) % 78.13/78.42 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). % 78.13/78.42 do 4 intro. intros zenon_H44 zenon_H45 zenon_H46 zenon_H1b zenon_H6 zenon_H11 zenon_H29 zenon_H40 zenon_H32. % 78.13/78.42 apply (zenon_notor_s _ _ zenon_H44). zenon_intro zenon_H48. zenon_intro zenon_H41. % 78.13/78.42 apply (zenon_notand_s _ _ zenon_H48); [ zenon_intro zenon_H37 | zenon_intro zenon_H2 ]. % 78.13/78.42 apply zenon_H37. zenon_intro zenon_H49. % 78.13/78.42 apply (zenon_notand_s _ _ zenon_H41); [ zenon_intro zenon_H3 | zenon_intro zenon_H34 ]. % 78.13/78.42 generalize (zenon_H45 zenon_TY_bq). zenon_intro zenon_H4a. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 78.13/78.42 exact (zenon_H4c zenon_H46). % 78.13/78.42 apply (zenon_notor_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 78.13/78.42 apply zenon_H4e. zenon_intro zenon_H4f. % 78.13/78.42 generalize (zenon_H4f zenon_TY_bq). zenon_intro zenon_H50. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H2f | zenon_intro zenon_H2d ]. % 78.13/78.42 generalize (reflexivity zenon_TY_bq). zenon_intro zenon_H30. % 78.13/78.42 exact (zenon_H2f zenon_H30). % 78.13/78.42 apply (zenon_L13_ zenon_TY_e zenon_TX_s zenon_TY_bq); trivial. % 78.13/78.42 exact (zenon_H34 zenon_H49). % 78.13/78.42 apply (zenon_L20_ zenon_TX_s zenon_TY_e); trivial. % 78.13/78.42 (* end of lemma zenon_L21_ *) % 78.13/78.42 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). % 78.13/78.42 do 4 intro. intros zenon_H51 zenon_H11 zenon_H45 zenon_H46 zenon_H1b zenon_H6 zenon_H29 zenon_H40 zenon_H32. % 78.13/78.42 generalize (zenon_H51 zenon_TY_e). zenon_intro zenon_H52. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H14 | zenon_intro zenon_H44 ]. % 78.13/78.42 exact (zenon_H14 zenon_H11). % 78.13/78.42 apply (zenon_L21_ zenon_TX_s zenon_TY_bq zenon_TX_ct zenon_TY_e); trivial. % 78.13/78.42 (* end of lemma zenon_L22_ *) % 78.13/78.42 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). % 78.13/78.42 do 4 intro. intros zenon_H53 zenon_H11 zenon_H45 zenon_H46 zenon_H1b zenon_H6 zenon_H29 zenon_H40 zenon_H32. % 78.13/78.42 generalize (zenon_H53 zenon_TX_s). zenon_intro zenon_H54. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H18 | zenon_intro zenon_H51 ]. % 78.13/78.42 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19. % 78.13/78.42 exact (zenon_H18 zenon_H19). % 78.13/78.42 apply (zenon_L22_ zenon_TY_bq zenon_TX_ct zenon_TY_e zenon_TX_s); trivial. % 78.13/78.42 (* end of lemma zenon_L23_ *) % 78.13/78.42 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). % 78.13/78.42 do 4 intro. intros zenon_H55 zenon_H11 zenon_H45 zenon_H46 zenon_H1b zenon_H6 zenon_H29 zenon_H40 zenon_H32. % 78.13/78.42 generalize (zenon_H55 zenon_TX_s). zenon_intro zenon_H56. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H18 | zenon_intro zenon_H53 ]. % 78.13/78.42 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19. % 78.13/78.42 exact (zenon_H18 zenon_H19). % 78.13/78.42 apply (zenon_L23_ zenon_TY_bq zenon_TX_ct zenon_TY_e zenon_TX_s); trivial. % 78.13/78.42 (* end of lemma zenon_L24_ *) % 78.13/78.42 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). % 78.13/78.42 do 4 intro. intros zenon_H57 zenon_H29 zenon_H11 zenon_H45 zenon_H46 zenon_H1b zenon_H6 zenon_H40 zenon_H32. % 78.13/78.42 generalize (zenon_H57 zenon_TX_s). zenon_intro zenon_H58. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H2c | zenon_intro zenon_H55 ]. % 78.13/78.42 exact (zenon_H2c zenon_H29). % 78.13/78.42 apply (zenon_L24_ zenon_TY_bq zenon_TX_ct zenon_TY_e zenon_TX_s); trivial. % 78.13/78.42 (* end of lemma zenon_L25_ *) % 78.13/78.42 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). % 78.13/78.42 do 4 intro. intros zenon_H59 zenon_H46 zenon_H29 zenon_H11 zenon_H45 zenon_H1b zenon_H6 zenon_H40 zenon_H32. % 78.13/78.42 generalize (zenon_H59 zenon_TY_bq). zenon_intro zenon_H5a. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_H4c | zenon_intro zenon_H57 ]. % 78.13/78.42 exact (zenon_H4c zenon_H46). % 78.13/78.42 apply (zenon_L25_ zenon_TX_ct zenon_TY_e zenon_TX_s zenon_TY_bq); trivial. % 78.13/78.42 (* end of lemma zenon_L26_ *) % 78.13/78.42 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). % 78.13/78.42 do 4 intro. intros zenon_H5b zenon_H46 zenon_H29 zenon_H11 zenon_H45 zenon_H1b zenon_H6 zenon_H40 zenon_H32. % 78.13/78.42 apply (zenon_notor_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H5c. % 78.13/78.42 apply zenon_H5d. zenon_intro zenon_H5e. % 78.13/78.42 generalize (zenon_H5e zenon_TX_ct). zenon_intro zenon_H5f. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H5f); [ zenon_intro zenon_H60 | zenon_intro zenon_H59 ]. % 78.13/78.42 generalize (reflexivity zenon_TX_ct). zenon_intro zenon_H61. % 78.13/78.42 exact (zenon_H60 zenon_H61). % 78.13/78.42 apply (zenon_L26_ zenon_TY_e zenon_TX_s zenon_TY_bq zenon_TX_ct); trivial. % 78.13/78.42 (* end of lemma zenon_L27_ *) % 78.13/78.42 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). % 78.13/78.42 do 4 intro. intros zenon_H62 zenon_H32 zenon_H40 zenon_H1b zenon_H45 zenon_H11 zenon_H29 zenon_H46. % 78.13/78.42 apply zenon_H62. zenon_intro zenon_H6. % 78.13/78.42 generalize (zenon_H45 zenon_TX_ct). zenon_intro zenon_H63. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H60 | zenon_intro zenon_H64 ]. % 78.13/78.42 generalize (reflexivity zenon_TX_ct). zenon_intro zenon_H61. % 78.13/78.42 exact (zenon_H60 zenon_H61). % 78.13/78.42 apply (zenon_notor_s _ _ zenon_H64). zenon_intro zenon_H66. zenon_intro zenon_H65. % 78.13/78.42 apply (zenon_notor_s _ _ zenon_H65). zenon_intro zenon_H68. zenon_intro zenon_H67. % 78.13/78.42 apply zenon_H67. zenon_intro zenon_H69. % 78.13/78.42 generalize (zenon_H69 zenon_TX_ct). zenon_intro zenon_H6a. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H6a); [ zenon_intro zenon_H60 | zenon_intro zenon_H5b ]. % 78.13/78.42 generalize (reflexivity zenon_TX_ct). zenon_intro zenon_H61. % 78.13/78.42 exact (zenon_H60 zenon_H61). % 78.13/78.42 apply (zenon_L27_ zenon_TY_e zenon_TX_s zenon_TY_bq zenon_TX_ct); trivial. % 78.13/78.42 (* end of lemma zenon_L28_ *) % 78.13/78.42 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). % 78.13/78.42 do 4 intro. intros zenon_H6b zenon_H32 zenon_H40 zenon_H1b zenon_H45 zenon_H11 zenon_H29 zenon_H46. % 78.13/78.42 apply (zenon_notor_s _ _ zenon_H6b). zenon_intro zenon_H6d. zenon_intro zenon_H6c. % 78.13/78.42 apply (zenon_notand_s _ _ zenon_H6d); [ zenon_intro zenon_H62 | zenon_intro zenon_H31 ]. % 78.13/78.42 apply (zenon_L28_ zenon_TY_bq zenon_TX_ct zenon_TX_s zenon_TY_e); trivial. % 78.13/78.42 exact (zenon_H31 zenon_H32). % 78.13/78.42 (* end of lemma zenon_L29_ *) % 78.13/78.42 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). % 78.13/78.42 do 4 intro. intros zenon_H6e zenon_H32 zenon_H40 zenon_H1b zenon_H45 zenon_H11 zenon_H29 zenon_H46. % 78.13/78.42 generalize (zenon_H6e zenon_TY_e). zenon_intro zenon_H6f. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_He | zenon_intro zenon_H6b ]. % 78.13/78.42 generalize (reflexivity zenon_TY_e). zenon_intro zenon_Hf. % 78.13/78.42 exact (zenon_He zenon_Hf). % 78.13/78.42 apply (zenon_L29_ zenon_TY_bq zenon_TX_ct zenon_TX_s zenon_TY_e); trivial. % 78.13/78.42 (* end of lemma zenon_L30_ *) % 78.13/78.42 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). % 78.13/78.42 do 4 intro. intros zenon_H70 zenon_H32 zenon_H40 zenon_H1b zenon_H45 zenon_H11 zenon_H29 zenon_H46. % 78.13/78.42 generalize (zenon_H70 zenon_TY_e). zenon_intro zenon_H71. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H71); [ zenon_intro zenon_He | zenon_intro zenon_H6e ]. % 78.13/78.42 generalize (reflexivity zenon_TY_e). zenon_intro zenon_Hf. % 78.13/78.42 exact (zenon_He zenon_Hf). % 78.13/78.42 apply (zenon_L30_ zenon_TY_bq zenon_TX_ct zenon_TX_s zenon_TY_e); trivial. % 78.13/78.42 (* end of lemma zenon_L31_ *) % 78.13/78.42 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). % 78.13/78.42 do 4 intro. intros zenon_H72 zenon_H11 zenon_H32 zenon_H40 zenon_H1b zenon_H45 zenon_H29 zenon_H46. % 78.13/78.42 generalize (zenon_H72 zenon_TY_e). zenon_intro zenon_H73. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H73); [ zenon_intro zenon_H14 | zenon_intro zenon_H70 ]. % 78.13/78.42 exact (zenon_H14 zenon_H11). % 78.13/78.42 apply (zenon_L31_ zenon_TY_bq zenon_TX_ct zenon_TX_s zenon_TY_e); trivial. % 78.13/78.42 (* end of lemma zenon_L32_ *) % 78.13/78.42 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). % 78.13/78.42 do 3 intro. intros zenon_H74 zenon_H40 zenon_H45 zenon_H29 zenon_H46. % 78.13/78.42 apply (zenon_notor_s _ _ zenon_H74). zenon_intro zenon_H76. zenon_intro zenon_H75. % 78.13/78.42 apply (zenon_notor_s _ _ zenon_H75). zenon_intro zenon_H78. zenon_intro zenon_H77. % 78.13/78.42 apply zenon_H77. zenon_intro zenon_H1b. % 78.13/78.42 apply zenon_H76. zenon_intro zenon_H79. % 78.13/78.42 apply (zenon_notallex_s (fun Y : zenon_U => ((~(r1 zenon_TX_s Y))\/(p3 Y))) zenon_H78); [ zenon_intro zenon_H7a; idtac ]. % 78.13/78.42 elim zenon_H7a. zenon_intro zenon_TY_e. zenon_intro zenon_H7b. % 78.13/78.42 apply (zenon_notor_s _ _ zenon_H7b). zenon_intro zenon_H7c. zenon_intro zenon_H32. % 78.13/78.42 apply zenon_H7c. zenon_intro zenon_H11. % 78.13/78.42 generalize (zenon_H79 zenon_TX_s). zenon_intro zenon_H7d. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H18 | zenon_intro zenon_H72 ]. % 78.13/78.42 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19. % 78.13/78.42 exact (zenon_H18 zenon_H19). % 78.13/78.42 apply (zenon_L32_ zenon_TY_bq zenon_TX_ct zenon_TY_e zenon_TX_s); trivial. % 78.13/78.42 (* end of lemma zenon_L33_ *) % 78.13/78.42 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). % 78.13/78.42 do 3 intro. intros zenon_H7e zenon_H45 zenon_H29 zenon_H46. % 78.13/78.42 apply (zenon_notor_s _ _ zenon_H7e). zenon_intro zenon_H80. zenon_intro zenon_H7f. % 78.13/78.42 apply (zenon_notor_s _ _ zenon_H7f). zenon_intro zenon_H82. zenon_intro zenon_H81. % 78.13/78.42 apply zenon_H81. zenon_intro zenon_H83. % 78.13/78.42 apply zenon_H80. zenon_intro zenon_H40. % 78.13/78.42 generalize (zenon_H83 zenon_TX_s). zenon_intro zenon_H84. % 78.13/78.42 apply (zenon_or_s _ _ zenon_H84); [ zenon_intro zenon_H18 | zenon_intro zenon_H74 ]. % 78.13/78.42 generalize (reflexivity zenon_TX_s). zenon_intro zenon_H19. % 78.13/78.42 exact (zenon_H18 zenon_H19). % 78.13/78.42 apply (zenon_L33_ zenon_TY_bq zenon_TX_ct zenon_TX_s); trivial. % 78.13/78.42 (* end of lemma zenon_L34_ *) % 78.13/78.42 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). % 78.13/78.44 do 3 intro. intros zenon_H85 zenon_H29 zenon_H46 zenon_H45. % 78.13/78.44 apply (zenon_notor_s _ _ zenon_H85). zenon_intro zenon_H87. zenon_intro zenon_H86. % 78.13/78.44 apply (zenon_notor_s _ _ zenon_H86). zenon_intro zenon_H89. zenon_intro zenon_H88. % 78.13/78.44 apply zenon_H88. zenon_intro zenon_H8a. % 78.13/78.44 generalize (zenon_H8a zenon_TX_s). zenon_intro zenon_H8b. % 78.13/78.44 apply (zenon_or_s _ _ zenon_H8b); [ zenon_intro zenon_H2c | zenon_intro zenon_H7e ]. % 78.13/78.44 exact (zenon_H2c zenon_H29). % 78.13/78.44 apply (zenon_L34_ zenon_TY_bq zenon_TX_ct zenon_TX_s); trivial. % 78.13/78.44 (* end of lemma zenon_L35_ *) % 78.13/78.44 apply NNPP. intro zenon_G. % 78.13/78.44 apply zenon_G. zenon_intro zenon_H8c. % 78.13/78.44 elim zenon_H8c. zenon_intro zenon_TX_ct. zenon_intro zenon_H8d. % 78.13/78.44 apply (zenon_notor_s _ _ zenon_H8d). zenon_intro zenon_H8f. zenon_intro zenon_H8e. % 78.13/78.44 apply (zenon_notor_s _ _ zenon_H8e). zenon_intro zenon_H91. zenon_intro zenon_H90. % 78.13/78.44 apply (zenon_notor_s _ _ zenon_H90). zenon_intro zenon_H93. zenon_intro zenon_H92. % 78.13/78.44 apply zenon_H93. zenon_intro zenon_H45. % 78.13/78.44 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 ]. % 78.13/78.44 elim zenon_H94. zenon_intro zenon_TY_bq. zenon_intro zenon_H95. % 78.13/78.44 apply (zenon_notor_s _ _ zenon_H95). zenon_intro zenon_H97. zenon_intro zenon_H96. % 78.13/78.44 apply zenon_H97. zenon_intro zenon_H46. % 78.13/78.44 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 ]. % 78.13/78.44 elim zenon_H98. zenon_intro zenon_TX_s. zenon_intro zenon_H99. % 78.13/78.44 apply (zenon_notor_s _ _ zenon_H99). zenon_intro zenon_H9b. zenon_intro zenon_H9a. % 78.13/78.44 apply zenon_H9b. zenon_intro zenon_H29. % 78.13/78.44 generalize (zenon_H45 zenon_TY_bq). zenon_intro zenon_H4a. % 78.13/78.44 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 78.13/78.44 exact (zenon_H4c zenon_H46). % 78.13/78.44 apply (zenon_notor_s _ _ zenon_H4b). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 78.13/78.44 apply (zenon_notor_s _ _ zenon_H4d). zenon_intro zenon_H9d. zenon_intro zenon_H9c. % 78.13/78.44 apply zenon_H9c. zenon_intro zenon_H9e. % 78.13/78.44 generalize (zenon_H9e zenon_TY_bq). zenon_intro zenon_H9f. % 78.13/78.44 apply (zenon_or_s _ _ zenon_H9f); [ zenon_intro zenon_H2f | zenon_intro zenon_H85 ]. % 78.13/78.44 generalize (reflexivity zenon_TY_bq). zenon_intro zenon_H30. % 78.13/78.44 exact (zenon_H2f zenon_H30). % 78.13/78.44 apply (zenon_L35_ zenon_TX_ct zenon_TX_s zenon_TY_bq); trivial. % 78.13/78.44 Qed. % 78.13/78.44 % SZS output end Proof % 78.13/78.44 (* END-PROOF *) % 78.13/78.44 nodes searched: 1897342 % 78.13/78.44 max branch formulas: 6169 % 78.13/78.44 proof nodes created: 93586 % 78.13/78.44 formulas created: 5367893 % 78.13/78.44 %------------------------------------------------------------------------------