TSTP Solution File: LCL674+1.010 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : LCL674+1.010 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n019.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 16:23:48 EDT 2022
% Result : Theorem 0.41s 0.60s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : LCL674+1.010 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.11 % Command : run_zenon %s %d
% 0.12/0.32 % Computer : n019.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Mon Jul 4 02:37:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.41/0.60 (* PROOF-FOUND *)
% 0.41/0.60 % SZS status Theorem
% 0.41/0.60 (* BEGIN-PROOF *)
% 0.41/0.60 % SZS output start Proof
% 0.41/0.60 Theorem main : (~(exists X : zenon_U, (~((~(forall Y : zenon_U, ((~(r1 X Y))\/(p5 Y))))\/(~((forall Y : zenon_U, ((~(r1 X Y))\/((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p11 X))/\((~(p111 X))/\(p110 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p11 X)/\((~(p111 X))/\(p110 X))))))))\/(~((~(p110 Y))/\(p109 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p10 X))/\((~(p110 X))/\(p109 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p10 X)/\((~(p110 X))/\(p109 X))))))))\/(~((~(p109 Y))/\(p108 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p9 X))/\((~(p109 X))/\(p108 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p9 X)/\((~(p109 X))/\(p108 X))))))))\/(~((~(p108 Y))/\(p107 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p8 X))/\((~(p108 X))/\(p107 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p8 X)/\((~(p108 X))/\(p107 X))))))))\/(~((~(p107 Y))/\(p106 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p7 X))/\((~(p107 X))/\(p106 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p7 X)/\((~(p107 X))/\(p106 X))))))))\/(~((~(p106 Y))/\(p105 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p6 X))/\((~(p106 X))/\(p105 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p6 X)/\((~(p106 X))/\(p105 X))))))))\/(~((~(p105 Y))/\(p104 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p5 X))/\((~(p105 X))/\(p104 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p5 X)/\((~(p105 X))/\(p104 X))))))))\/(~((~(p104 Y))/\(p103 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p4 X))/\((~(p104 X))/\(p103 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p4 X)/\((~(p104 X))/\(p103 X))))))))\/(~((~(p103 Y))/\(p102 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p3 X))/\((~(p103 X))/\(p102 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p3 X)/\((~(p103 X))/\(p102 X))))))))\/(~((~(p102 Y))/\(p101 Y))))/\((((~(forall X : zenon_U, ((~(r1 Y X))\/(~((~(p2 X))/\((~(p102 X))/\(p101 X)))))))/\(~(forall X : zenon_U, ((~(r1 Y X))\/(~((p2 X)/\((~(p102 X))/\(p101 X))))))))\/(~((~(p101 Y))/\(p100 Y))))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p11 X))\/(~(p110 X)))))\/(p11 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p11 X)\/(~(p110 X)))))\/(~(p11 Y))))\/(~(p110 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p10 X))\/(~(p109 X)))))\/(p10 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p10 X)\/(~(p109 X)))))\/(~(p10 Y))))\/(~(p109 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p9 X))\/(~(p108 X)))))\/(p9 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p9 X)\/(~(p108 X)))))\/(~(p9 Y))))\/(~(p108 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p8 X))\/(~(p107 X)))))\/(p8 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p8 X)\/(~(p107 X)))))\/(~(p8 Y))))\/(~(p107 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p7 X))\/(~(p106 X)))))\/(p7 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p7 X)\/(~(p106 X)))))\/(~(p7 Y))))\/(~(p106 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p6 X))\/(~(p105 X)))))\/(p6 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p6 X)\/(~(p105 X)))))\/(~(p6 Y))))\/(~(p105 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p5 X))\/(~(p104 X)))))\/(p5 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p5 X)\/(~(p104 X)))))\/(~(p5 Y))))\/(~(p104 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p4 X))\/(~(p103 X)))))\/(p4 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p4 X)\/(~(p103 X)))))\/(~(p4 Y))))\/(~(p103 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p3 X))\/(~(p102 X)))))\/(p3 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p3 X)\/(~(p102 X)))))\/(~(p3 Y))))\/(~(p102 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p2 X))\/(~(p101 X)))))\/(p2 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p2 X)\/(~(p101 X)))))\/(~(p2 Y))))\/(~(p101 Y)))/\(((((forall X : zenon_U, ((~(r1 Y X))\/((~(p1 X))\/(~(p100 X)))))\/(p1 Y))/\((forall X : zenon_U, ((~(r1 Y X))\/((p1 X)\/(~(p100 X)))))\/(~(p1 Y))))\/(~(p100 Y)))/\(((p110 Y)\/(~(p111 Y)))/\(((p109 Y)\/(~(p110 Y)))/\(((p108 Y)\/(~(p109 Y)))/\(((p107 Y)\/(~(p108 Y)))/\(((p106 Y)\/(~(p107 Y)))/\(((p105 Y)\/(~(p106 Y)))/\(((p104 Y)\/(~(p105 Y)))/\(((p103 Y)\/(~(p104 Y)))/\(((p102 Y)\/(~(p103 Y)))/\(((p101 Y)\/(~(p102 Y)))/\((p100 Y)\/(~(p101 Y))))))))))))))))))))))))))))))))))))/\((~(p101 X))/\(p100 X)))))))).
% 0.41/0.60 Proof.
% 0.41/0.60 assert (zenon_L1_ : forall (zenon_TX_h : zenon_U) (zenon_TX_i : zenon_U) (zenon_TX_j : zenon_U), (r1 zenon_TX_j zenon_TX_i) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TX_h)) -> (r1 zenon_TX_i zenon_TX_h) -> False).
% 0.41/0.60 do 3 intro. intros zenon_H3 zenon_H4 zenon_H5 zenon_H6.
% 0.41/0.60 elim (classic ((~(zenon_TX_j = zenon_TX_i))/\(~(r1 zenon_TX_j zenon_TX_i)))); [ zenon_intro zenon_Ha | zenon_intro zenon_Hb ].
% 0.41/0.60 apply (zenon_and_s _ _ zenon_Ha). zenon_intro zenon_Hd. zenon_intro zenon_Hc.
% 0.41/0.60 exact (zenon_Hc zenon_H3).
% 0.41/0.60 cut ((r1 zenon_TX_i zenon_TX_h) = (r1 zenon_TX_j zenon_TX_h)).
% 0.41/0.60 intro zenon_D_pnotp.
% 0.41/0.60 apply zenon_H5.
% 0.41/0.60 rewrite <- zenon_D_pnotp.
% 0.41/0.60 exact zenon_H6.
% 0.41/0.60 cut ((zenon_TX_h = zenon_TX_h)); [idtac | apply NNPP; zenon_intro zenon_He].
% 0.41/0.60 cut ((zenon_TX_i = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_Hf].
% 0.41/0.60 congruence.
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_Hb); [ zenon_intro zenon_H11 | zenon_intro zenon_H10 ].
% 0.41/0.60 apply zenon_H11. zenon_intro zenon_H12.
% 0.41/0.60 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 0.41/0.60 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_i = zenon_TX_j)).
% 0.41/0.60 intro zenon_D_pnotp.
% 0.41/0.60 apply zenon_Hf.
% 0.41/0.60 rewrite <- zenon_D_pnotp.
% 0.41/0.60 exact zenon_H13.
% 0.41/0.60 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 0.41/0.60 cut ((zenon_TX_j = zenon_TX_i)); [idtac | apply NNPP; zenon_intro zenon_Hd].
% 0.41/0.60 congruence.
% 0.41/0.60 exact (zenon_Hd zenon_H12).
% 0.41/0.60 apply zenon_H14. apply refl_equal.
% 0.41/0.60 apply zenon_H14. apply refl_equal.
% 0.41/0.60 apply zenon_H10. zenon_intro zenon_H3.
% 0.41/0.60 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 0.41/0.60 generalize (zenon_H15 zenon_TX_i). zenon_intro zenon_H16.
% 0.41/0.60 generalize (zenon_H16 zenon_TX_h). zenon_intro zenon_H17.
% 0.41/0.60 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_Hc | zenon_intro zenon_H18 ].
% 0.41/0.60 exact (zenon_Hc zenon_H3).
% 0.41/0.60 apply (zenon_imply_s _ _ zenon_H18); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ].
% 0.41/0.60 exact (zenon_H1a zenon_H6).
% 0.41/0.60 exact (zenon_H5 zenon_H19).
% 0.41/0.60 apply zenon_He. apply refl_equal.
% 0.41/0.60 (* end of lemma zenon_L1_ *)
% 0.41/0.60 assert (zenon_L2_ : forall (zenon_TX_bd : zenon_U) (zenon_TX_h : zenon_U) (zenon_TX_i : zenon_U) (zenon_TX_j : zenon_U), (r1 zenon_TX_j zenon_TX_i) -> (r1 zenon_TX_i zenon_TX_h) -> (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z)))))) -> (~(r1 zenon_TX_j zenon_TX_bd)) -> (r1 zenon_TX_h zenon_TX_bd) -> False).
% 0.41/0.60 do 4 intro. intros zenon_H3 zenon_H6 zenon_H4 zenon_H1b zenon_H1c.
% 0.41/0.60 elim (classic ((~(zenon_TX_j = zenon_TX_h))/\(~(r1 zenon_TX_j zenon_TX_h)))); [ zenon_intro zenon_H1e | zenon_intro zenon_H1f ].
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H20. zenon_intro zenon_H5.
% 0.41/0.60 apply (zenon_L1_ zenon_TX_h zenon_TX_i zenon_TX_j); trivial.
% 0.41/0.60 cut ((r1 zenon_TX_h zenon_TX_bd) = (r1 zenon_TX_j zenon_TX_bd)).
% 0.41/0.60 intro zenon_D_pnotp.
% 0.41/0.60 apply zenon_H1b.
% 0.41/0.60 rewrite <- zenon_D_pnotp.
% 0.41/0.60 exact zenon_H1c.
% 0.41/0.60 cut ((zenon_TX_bd = zenon_TX_bd)); [idtac | apply NNPP; zenon_intro zenon_H21].
% 0.41/0.60 cut ((zenon_TX_h = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H22].
% 0.41/0.60 congruence.
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_H24 | zenon_intro zenon_H23 ].
% 0.41/0.60 apply zenon_H24. zenon_intro zenon_H25.
% 0.41/0.60 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 0.41/0.60 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_h = zenon_TX_j)).
% 0.41/0.60 intro zenon_D_pnotp.
% 0.41/0.60 apply zenon_H22.
% 0.41/0.60 rewrite <- zenon_D_pnotp.
% 0.41/0.60 exact zenon_H13.
% 0.41/0.60 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 0.41/0.60 cut ((zenon_TX_j = zenon_TX_h)); [idtac | apply NNPP; zenon_intro zenon_H20].
% 0.41/0.60 congruence.
% 0.41/0.60 exact (zenon_H20 zenon_H25).
% 0.41/0.60 apply zenon_H14. apply refl_equal.
% 0.41/0.60 apply zenon_H14. apply refl_equal.
% 0.41/0.60 apply zenon_H23. zenon_intro zenon_H19.
% 0.41/0.60 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 0.41/0.60 generalize (zenon_H15 zenon_TX_h). zenon_intro zenon_H26.
% 0.41/0.60 generalize (zenon_H26 zenon_TX_bd). zenon_intro zenon_H27.
% 0.41/0.60 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H5 | zenon_intro zenon_H28 ].
% 0.41/0.60 exact (zenon_H5 zenon_H19).
% 0.41/0.60 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 0.41/0.60 exact (zenon_H2a zenon_H1c).
% 0.41/0.60 exact (zenon_H1b zenon_H29).
% 0.41/0.60 apply zenon_H21. apply refl_equal.
% 0.41/0.60 (* end of lemma zenon_L2_ *)
% 0.41/0.60 apply NNPP. intro zenon_G.
% 0.41/0.60 elim (classic (forall x : zenon_U, (forall y : zenon_U, (forall z : zenon_U, ((r1 x y)->((r1 y z)->(r1 x z))))))); [ zenon_intro zenon_H4 | zenon_intro zenon_H2b ].
% 0.41/0.60 apply zenon_G. zenon_intro zenon_H2c.
% 0.41/0.60 elim zenon_H2c. zenon_intro zenon_TX_j. zenon_intro zenon_H2d.
% 0.41/0.60 apply (zenon_notor_s _ _ zenon_H2d). zenon_intro zenon_H2f. zenon_intro zenon_H2e.
% 0.41/0.60 apply zenon_H2e. zenon_intro zenon_H30.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 0.41/0.60 apply zenon_H2f. zenon_intro zenon_H35.
% 0.41/0.60 generalize (zenon_H32 zenon_TX_j). zenon_intro zenon_H36.
% 0.41/0.60 apply (zenon_or_s _ _ zenon_H36); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ].
% 0.41/0.60 generalize (reflexivity zenon_TX_j). zenon_intro zenon_H39.
% 0.41/0.60 exact (zenon_H38 zenon_H39).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H3b. zenon_intro zenon_H3a.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3d. zenon_intro zenon_H3c.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H3f. zenon_intro zenon_H3e.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H41. zenon_intro zenon_H40.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H43. zenon_intro zenon_H42.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H45. zenon_intro zenon_H44.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H47. zenon_intro zenon_H46.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H46). zenon_intro zenon_H49. zenon_intro zenon_H48.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H48). zenon_intro zenon_H4b. zenon_intro zenon_H4a.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H4a). zenon_intro zenon_H4d. zenon_intro zenon_H4c.
% 0.41/0.60 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ].
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H4f). zenon_intro zenon_H51. zenon_intro zenon_H50.
% 0.41/0.60 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_j X))\/(~((~(p2 X))/\((~(p102 X))/\(p101 X)))))) zenon_H51); [ zenon_intro zenon_H52; idtac ].
% 0.41/0.60 elim zenon_H52. zenon_intro zenon_TX_i. zenon_intro zenon_H53.
% 0.41/0.60 apply (zenon_notor_s _ _ zenon_H53). zenon_intro zenon_H10. zenon_intro zenon_H54.
% 0.41/0.60 apply zenon_H54. zenon_intro zenon_H55.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H57. zenon_intro zenon_H56.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H56). zenon_intro zenon_H59. zenon_intro zenon_H58.
% 0.41/0.60 apply zenon_H10. zenon_intro zenon_H3.
% 0.41/0.60 generalize (zenon_H32 zenon_TX_i). zenon_intro zenon_H5a.
% 0.41/0.60 apply (zenon_or_s _ _ zenon_H5a); [ zenon_intro zenon_Hc | zenon_intro zenon_H5b ].
% 0.41/0.60 exact (zenon_Hc zenon_H3).
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H5d. zenon_intro zenon_H5c.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H5c). zenon_intro zenon_H5f. zenon_intro zenon_H5e.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H61. zenon_intro zenon_H60.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H60). zenon_intro zenon_H63. zenon_intro zenon_H62.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H62). zenon_intro zenon_H65. zenon_intro zenon_H64.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H67. zenon_intro zenon_H66.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H66). zenon_intro zenon_H69. zenon_intro zenon_H68.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H68). zenon_intro zenon_H6b. zenon_intro zenon_H6a.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H6a). zenon_intro zenon_H6d. zenon_intro zenon_H6c.
% 0.41/0.60 apply (zenon_or_s _ _ zenon_H6d); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ].
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H6f). zenon_intro zenon_H71. zenon_intro zenon_H70.
% 0.41/0.60 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_i X))\/(~((p3 X)/\((~(p103 X))/\(p102 X)))))) zenon_H70); [ zenon_intro zenon_H72; idtac ].
% 0.41/0.60 elim zenon_H72. zenon_intro zenon_TX_h. zenon_intro zenon_H73.
% 0.41/0.60 apply (zenon_notor_s _ _ zenon_H73). zenon_intro zenon_H75. zenon_intro zenon_H74.
% 0.41/0.60 apply zenon_H74. zenon_intro zenon_H76.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H76). zenon_intro zenon_H78. zenon_intro zenon_H77.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H77). zenon_intro zenon_H7a. zenon_intro zenon_H79.
% 0.41/0.60 apply zenon_H75. zenon_intro zenon_H6.
% 0.41/0.60 generalize (zenon_H32 zenon_TX_h). zenon_intro zenon_H7b.
% 0.41/0.60 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H5 | zenon_intro zenon_H7c ].
% 0.41/0.60 apply (zenon_L1_ zenon_TX_h zenon_TX_i zenon_TX_j); trivial.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H7c). zenon_intro zenon_H7e. zenon_intro zenon_H7d.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H7d). zenon_intro zenon_H80. zenon_intro zenon_H7f.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H7f). zenon_intro zenon_H82. zenon_intro zenon_H81.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H81). zenon_intro zenon_H84. zenon_intro zenon_H83.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H83). zenon_intro zenon_H86. zenon_intro zenon_H85.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H85). zenon_intro zenon_H88. zenon_intro zenon_H87.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H87). zenon_intro zenon_H8a. zenon_intro zenon_H89.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H8c. zenon_intro zenon_H8b.
% 0.41/0.60 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H8e | zenon_intro zenon_H8d ].
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H8e). zenon_intro zenon_H90. zenon_intro zenon_H8f.
% 0.41/0.60 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_h X))\/(~((~(p4 X))/\((~(p104 X))/\(p103 X)))))) zenon_H90); [ zenon_intro zenon_H91; idtac ].
% 0.41/0.60 elim zenon_H91. zenon_intro zenon_TX_bd. zenon_intro zenon_H92.
% 0.41/0.60 apply (zenon_notor_s _ _ zenon_H92). zenon_intro zenon_H94. zenon_intro zenon_H93.
% 0.41/0.60 apply zenon_H93. zenon_intro zenon_H95.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H95). zenon_intro zenon_H97. zenon_intro zenon_H96.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H96). zenon_intro zenon_H99. zenon_intro zenon_H98.
% 0.41/0.60 apply zenon_H94. zenon_intro zenon_H1c.
% 0.41/0.60 generalize (zenon_H32 zenon_TX_bd). zenon_intro zenon_H9a.
% 0.41/0.60 apply (zenon_or_s _ _ zenon_H9a); [ zenon_intro zenon_H1b | zenon_intro zenon_H9b ].
% 0.41/0.60 apply (zenon_L2_ zenon_TX_bd zenon_TX_h zenon_TX_i zenon_TX_j); trivial.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H9b). zenon_intro zenon_H9d. zenon_intro zenon_H9c.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H9c). zenon_intro zenon_H9f. zenon_intro zenon_H9e.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_H9e). zenon_intro zenon_Ha1. zenon_intro zenon_Ha0.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_Ha0). zenon_intro zenon_Ha3. zenon_intro zenon_Ha2.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_Ha2). zenon_intro zenon_Ha5. zenon_intro zenon_Ha4.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_Ha4). zenon_intro zenon_Ha7. zenon_intro zenon_Ha6.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_Ha6). zenon_intro zenon_Ha9. zenon_intro zenon_Ha8.
% 0.41/0.60 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_Hab | zenon_intro zenon_Haa ].
% 0.41/0.60 apply (zenon_and_s _ _ zenon_Hab). zenon_intro zenon_Had. zenon_intro zenon_Hac.
% 0.41/0.60 apply (zenon_notallex_s (fun X : zenon_U => ((~(r1 zenon_TX_bd X))\/(~((~(p5 X))/\((~(p105 X))/\(p104 X)))))) zenon_Had); [ zenon_intro zenon_Hae; idtac ].
% 0.41/0.60 elim zenon_Hae. zenon_intro zenon_TX_gt. zenon_intro zenon_Hb0.
% 0.41/0.60 apply (zenon_notor_s _ _ zenon_Hb0). zenon_intro zenon_Hb2. zenon_intro zenon_Hb1.
% 0.41/0.60 apply zenon_Hb1. zenon_intro zenon_Hb3.
% 0.41/0.60 apply (zenon_and_s _ _ zenon_Hb3). zenon_intro zenon_Hb5. zenon_intro zenon_Hb4.
% 0.41/0.60 apply zenon_Hb2. zenon_intro zenon_Hb6.
% 0.41/0.60 generalize (zenon_H35 zenon_TX_gt). zenon_intro zenon_Hb7.
% 0.41/0.60 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hb8 ].
% 0.41/0.60 elim (classic ((~(zenon_TX_j = zenon_TX_bd))/\(~(r1 zenon_TX_j zenon_TX_bd)))); [ zenon_intro zenon_Hba | zenon_intro zenon_Hbb ].
% 0.41/0.60 apply (zenon_and_s _ _ zenon_Hba). zenon_intro zenon_Hbc. zenon_intro zenon_H1b.
% 0.41/0.60 apply (zenon_L2_ zenon_TX_bd zenon_TX_h zenon_TX_i zenon_TX_j); trivial.
% 0.41/0.60 cut ((r1 zenon_TX_bd zenon_TX_gt) = (r1 zenon_TX_j zenon_TX_gt)).
% 0.41/0.60 intro zenon_D_pnotp.
% 0.41/0.60 apply zenon_Hb9.
% 0.41/0.60 rewrite <- zenon_D_pnotp.
% 0.41/0.60 exact zenon_Hb6.
% 0.41/0.60 cut ((zenon_TX_gt = zenon_TX_gt)); [idtac | apply NNPP; zenon_intro zenon_Hbd].
% 0.41/0.60 cut ((zenon_TX_bd = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_Hbe].
% 0.41/0.60 congruence.
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_Hbb); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hbf ].
% 0.41/0.60 apply zenon_Hc0. zenon_intro zenon_Hc1.
% 0.41/0.60 elim (classic (zenon_TX_j = zenon_TX_j)); [ zenon_intro zenon_H13 | zenon_intro zenon_H14 ].
% 0.41/0.60 cut ((zenon_TX_j = zenon_TX_j) = (zenon_TX_bd = zenon_TX_j)).
% 0.41/0.60 intro zenon_D_pnotp.
% 0.41/0.60 apply zenon_Hbe.
% 0.41/0.60 rewrite <- zenon_D_pnotp.
% 0.41/0.60 exact zenon_H13.
% 0.41/0.60 cut ((zenon_TX_j = zenon_TX_j)); [idtac | apply NNPP; zenon_intro zenon_H14].
% 0.41/0.60 cut ((zenon_TX_j = zenon_TX_bd)); [idtac | apply NNPP; zenon_intro zenon_Hbc].
% 0.41/0.60 congruence.
% 0.41/0.60 exact (zenon_Hbc zenon_Hc1).
% 0.41/0.60 apply zenon_H14. apply refl_equal.
% 0.41/0.60 apply zenon_H14. apply refl_equal.
% 0.41/0.60 apply zenon_Hbf. zenon_intro zenon_H29.
% 0.41/0.60 generalize (zenon_H4 zenon_TX_j). zenon_intro zenon_H15.
% 0.41/0.60 generalize (zenon_H15 zenon_TX_bd). zenon_intro zenon_Hc2.
% 0.41/0.60 generalize (zenon_Hc2 zenon_TX_gt). zenon_intro zenon_Hc3.
% 0.41/0.60 apply (zenon_imply_s _ _ zenon_Hc3); [ zenon_intro zenon_H1b | zenon_intro zenon_Hc4 ].
% 0.41/0.60 exact (zenon_H1b zenon_H29).
% 0.41/0.60 apply (zenon_imply_s _ _ zenon_Hc4); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hc5 ].
% 0.41/0.60 exact (zenon_Hc6 zenon_Hb6).
% 0.41/0.60 exact (zenon_Hb9 zenon_Hc5).
% 0.41/0.60 apply zenon_Hbd. apply refl_equal.
% 0.41/0.60 exact (zenon_Hb5 zenon_Hb8).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_Haa); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hc7 ].
% 0.41/0.60 exact (zenon_Hc8 zenon_H99).
% 0.41/0.60 exact (zenon_Hc7 zenon_H98).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H8d); [ zenon_intro zenon_Hca | zenon_intro zenon_Hc9 ].
% 0.41/0.60 exact (zenon_Hca zenon_H7a).
% 0.41/0.60 exact (zenon_Hc9 zenon_H79).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H6e); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hcb ].
% 0.41/0.60 exact (zenon_Hcc zenon_H59).
% 0.41/0.60 exact (zenon_Hcb zenon_H58).
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcd ].
% 0.41/0.60 exact (zenon_Hce zenon_H34).
% 0.41/0.60 exact (zenon_Hcd zenon_H33).
% 0.41/0.60 apply zenon_H2b. zenon_intro zenon_Tx_hz. apply NNPP. zenon_intro zenon_Hd0.
% 0.41/0.60 apply zenon_Hd0. zenon_intro zenon_Ty_ib. apply NNPP. zenon_intro zenon_Hd2.
% 0.41/0.60 apply zenon_Hd2. zenon_intro zenon_Tz_id. apply NNPP. zenon_intro zenon_Hd4.
% 0.41/0.60 apply (zenon_notimply_s _ _ zenon_Hd4). zenon_intro zenon_Hd6. zenon_intro zenon_Hd5.
% 0.41/0.60 apply (zenon_notimply_s _ _ zenon_Hd5). zenon_intro zenon_Hd8. zenon_intro zenon_Hd7.
% 0.41/0.60 generalize (transitivity zenon_Tx_hz). zenon_intro zenon_Hd9.
% 0.41/0.60 generalize (zenon_Hd9 zenon_Ty_ib). zenon_intro zenon_Hda.
% 0.41/0.60 generalize (zenon_Hda zenon_Tz_id). zenon_intro zenon_Hdb.
% 0.41/0.60 apply (zenon_imply_s _ _ zenon_Hdb); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hdc ].
% 0.41/0.60 apply (zenon_notand_s _ _ zenon_Hdd); [ zenon_intro zenon_Hdf | zenon_intro zenon_Hde ].
% 0.41/0.60 exact (zenon_Hdf zenon_Hd6).
% 0.41/0.60 exact (zenon_Hde zenon_Hd8).
% 0.41/0.60 exact (zenon_Hd7 zenon_Hdc).
% 0.41/0.60 Qed.
% 0.41/0.60 % SZS output end Proof
% 0.41/0.60 (* END-PROOF *)
% 0.41/0.60 nodes searched: 4862
% 0.41/0.60 max branch formulas: 2450
% 0.41/0.60 proof nodes created: 546
% 0.41/0.60 formulas created: 21836
% 0.41/0.60
%------------------------------------------------------------------------------