TSTP Solution File: GEO212+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO212+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n015.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 : Sat Jul 16 07:00:53 EDT 2022
% Result : Theorem 0.22s 0.61s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO212+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : run_zenon %s %d
% 0.14/0.36 % Computer : n015.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sat Jun 18 00:11:58 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.22/0.61 (* PROOF-FOUND *)
% 0.22/0.61 % SZS status Theorem
% 0.22/0.61 (* BEGIN-PROOF *)
% 0.22/0.61 % SZS output start Proof
% 0.22/0.61 Theorem con : (forall L : zenon_U, (forall M : zenon_U, (forall N : zenon_U, ((unorthogonal_lines L M)->((convergent_lines L N)\/(unorthogonal_lines M N)))))).
% 0.22/0.61 Proof.
% 0.22/0.61 assert (zenon_L1_ : forall (zenon_TM_y : zenon_U), (convergent_lines zenon_TM_y zenon_TM_y) -> False).
% 0.22/0.61 do 1 intro. intros zenon_H17.
% 0.22/0.61 generalize (apart3 zenon_TM_y). zenon_intro zenon_H19.
% 0.22/0.61 exact (zenon_H19 zenon_H17).
% 0.22/0.61 (* end of lemma zenon_L1_ *)
% 0.22/0.61 assert (zenon_L2_ : forall (zenon_TN_bd : zenon_U) (zenon_TM_y : zenon_U), (forall Z : zenon_U, ((convergent_lines zenon_TM_y zenon_TN_bd)->((convergent_lines zenon_TM_y Z)\/(convergent_lines zenon_TN_bd Z)))) -> (convergent_lines zenon_TM_y zenon_TN_bd) -> (~(convergent_lines zenon_TM_y zenon_TM_y)) -> (~(convergent_lines zenon_TN_bd zenon_TM_y)) -> False).
% 0.22/0.61 do 2 intro. intros zenon_H1a zenon_H1b zenon_H19 zenon_H1c.
% 0.22/0.61 generalize (zenon_H1a zenon_TM_y). zenon_intro zenon_H1e.
% 0.22/0.61 apply (zenon_imply_s _ _ zenon_H1e); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ].
% 0.22/0.61 exact (zenon_H20 zenon_H1b).
% 0.22/0.61 apply (zenon_or_s _ _ zenon_H1f); [ zenon_intro zenon_H17 | zenon_intro zenon_H21 ].
% 0.22/0.61 exact (zenon_H19 zenon_H17).
% 0.22/0.61 exact (zenon_H1c zenon_H21).
% 0.22/0.61 (* end of lemma zenon_L2_ *)
% 0.22/0.61 assert (zenon_L3_ : forall (zenon_TL_bm : zenon_U) (zenon_TN_bd : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines zenon_TN_bd Y)->((convergent_lines zenon_TN_bd Z)\/(convergent_lines Y Z))))) -> (~(convergent_lines zenon_TL_bm zenon_TN_bd)) -> (~(convergent_lines zenon_TN_bd zenon_TN_bd)) -> (convergent_lines zenon_TN_bd zenon_TL_bm) -> False).
% 0.22/0.61 do 2 intro. intros zenon_H22 zenon_H23 zenon_H24 zenon_H25.
% 0.22/0.61 generalize (zenon_H22 zenon_TL_bm). zenon_intro zenon_H27.
% 0.22/0.61 generalize (zenon_H27 zenon_TN_bd). zenon_intro zenon_H28.
% 0.22/0.61 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 0.22/0.61 exact (zenon_H2a zenon_H25).
% 0.22/0.61 apply (zenon_or_s _ _ zenon_H29); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ].
% 0.22/0.61 exact (zenon_H24 zenon_H2c).
% 0.22/0.61 exact (zenon_H23 zenon_H2b).
% 0.22/0.61 (* end of lemma zenon_L3_ *)
% 0.22/0.61 assert (zenon_L4_ : forall (zenon_TL_bm : zenon_U) (zenon_TM_y : zenon_U) (zenon_TN_bd : zenon_U), (convergent_lines zenon_TN_bd zenon_TM_y) -> (~(convergent_lines zenon_TL_bm zenon_TN_bd)) -> (~(convergent_lines zenon_TN_bd zenon_TN_bd)) -> (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines zenon_TM_y Y)->((convergent_lines zenon_TM_y Z)\/(convergent_lines Y Z))))) -> (~(convergent_lines zenon_TL_bm zenon_TM_y)) -> (~(convergent_lines zenon_TM_y zenon_TM_y)) -> False).
% 0.22/0.61 do 3 intro. intros zenon_H21 zenon_H23 zenon_H24 zenon_H2d zenon_H2e zenon_H19.
% 0.22/0.61 generalize (ax6 zenon_TN_bd). zenon_intro zenon_H22.
% 0.22/0.61 generalize (zenon_H22 zenon_TM_y). zenon_intro zenon_H2f.
% 0.22/0.61 generalize (zenon_H2f zenon_TL_bm). zenon_intro zenon_H30.
% 0.22/0.61 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H1c | zenon_intro zenon_H31 ].
% 0.22/0.61 exact (zenon_H1c zenon_H21).
% 0.22/0.61 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H25 | zenon_intro zenon_H32 ].
% 0.22/0.61 apply (zenon_L3_ zenon_TL_bm zenon_TN_bd); trivial.
% 0.22/0.61 generalize (zenon_H2d zenon_TL_bm). zenon_intro zenon_H33.
% 0.22/0.61 generalize (zenon_H33 zenon_TM_y). zenon_intro zenon_H34.
% 0.22/0.61 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ].
% 0.22/0.61 exact (zenon_H36 zenon_H32).
% 0.22/0.61 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H17 | zenon_intro zenon_H37 ].
% 0.22/0.61 exact (zenon_H19 zenon_H17).
% 0.22/0.61 exact (zenon_H2e zenon_H37).
% 0.22/0.61 (* end of lemma zenon_L4_ *)
% 0.22/0.61 assert (zenon_L5_ : forall (zenon_TL_bm : zenon_U) (zenon_TM_y : zenon_U) (zenon_TN_bd : zenon_U), (~(unorthogonal_lines zenon_TN_bd zenon_TM_y)) -> (~(convergent_lines zenon_TM_y zenon_TM_y)) -> (~(convergent_lines zenon_TL_bm zenon_TM_y)) -> (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines zenon_TM_y Y)->((convergent_lines zenon_TM_y Z)\/(convergent_lines Y Z))))) -> (~(convergent_lines zenon_TN_bd zenon_TN_bd)) -> (~(convergent_lines zenon_TL_bm zenon_TN_bd)) -> False).
% 0.22/0.61 do 3 intro. intros zenon_H38 zenon_H19 zenon_H2e zenon_H2d zenon_H24 zenon_H23.
% 0.22/0.61 generalize (occu1 zenon_TN_bd). zenon_intro zenon_H39.
% 0.22/0.61 generalize (zenon_H39 zenon_TM_y). zenon_intro zenon_H3a.
% 0.22/0.61 apply (zenon_or_s _ _ zenon_H3a); [ zenon_intro zenon_H21 | zenon_intro zenon_H3b ].
% 0.22/0.61 apply (zenon_L4_ zenon_TL_bm zenon_TM_y zenon_TN_bd); trivial.
% 0.22/0.61 exact (zenon_H38 zenon_H3b).
% 0.22/0.61 (* end of lemma zenon_L5_ *)
% 0.22/0.61 assert (zenon_L6_ : forall (zenon_TM_y : zenon_U) (zenon_TN_bd : zenon_U) (zenon_TL_bm : zenon_U), (~(convergent_lines zenon_TL_bm zenon_TN_bd)) -> (~(convergent_lines zenon_TN_bd zenon_TN_bd)) -> (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines zenon_TM_y Y)->((convergent_lines zenon_TM_y Z)\/(convergent_lines Y Z))))) -> (~(convergent_lines zenon_TL_bm zenon_TM_y)) -> (~(convergent_lines zenon_TM_y zenon_TM_y)) -> (convergent_lines zenon_TM_y zenon_TN_bd) -> False).
% 0.22/0.61 do 3 intro. intros zenon_H23 zenon_H24 zenon_H2d zenon_H2e zenon_H19 zenon_H1b.
% 0.22/0.61 generalize (zenon_H2d zenon_TN_bd). zenon_intro zenon_H1a.
% 0.22/0.61 generalize (oac1 zenon_TN_bd). zenon_intro zenon_H3c.
% 0.22/0.61 generalize (zenon_H3c zenon_TM_y). zenon_intro zenon_H3d.
% 0.22/0.61 generalize (zenon_H3d zenon_TM_y). zenon_intro zenon_H3e.
% 0.22/0.61 apply (zenon_imply_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ].
% 0.22/0.61 apply (zenon_notand_s _ _ zenon_H40); [ zenon_intro zenon_H1c | zenon_intro zenon_H38 ].
% 0.22/0.61 apply (zenon_L2_ zenon_TN_bd zenon_TM_y); trivial.
% 0.22/0.61 apply (zenon_L5_ zenon_TL_bm zenon_TM_y zenon_TN_bd); trivial.
% 0.22/0.61 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ].
% 0.22/0.61 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H21. zenon_intro zenon_H3b.
% 0.22/0.61 apply (zenon_L4_ zenon_TL_bm zenon_TM_y zenon_TN_bd); trivial.
% 0.22/0.61 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H17. zenon_intro zenon_H43.
% 0.22/0.61 exact (zenon_H19 zenon_H17).
% 0.22/0.61 (* end of lemma zenon_L6_ *)
% 0.22/0.61 assert (zenon_L7_ : forall (zenon_TN_bd : zenon_U) (zenon_TM_y : zenon_U), ((convergent_lines zenon_TM_y zenon_TN_bd)/\(unorthogonal_lines zenon_TM_y zenon_TN_bd)) -> (~(unorthogonal_lines zenon_TM_y zenon_TN_bd)) -> False).
% 0.22/0.61 do 2 intro. intros zenon_H44 zenon_H45.
% 0.22/0.61 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H1b. zenon_intro zenon_H46.
% 0.22/0.61 exact (zenon_H45 zenon_H46).
% 0.22/0.61 (* end of lemma zenon_L7_ *)
% 0.22/0.61 assert (zenon_L8_ : forall (zenon_TL_bm : zenon_U) (zenon_TN_bd : zenon_U) (zenon_TM_y : zenon_U), (forall M : zenon_U, ((convergent_lines zenon_TM_y M)\/(unorthogonal_lines zenon_TM_y M))) -> (~(unorthogonal_lines zenon_TM_y zenon_TN_bd)) -> (~(convergent_lines zenon_TL_bm zenon_TM_y)) -> (~(convergent_lines zenon_TN_bd zenon_TN_bd)) -> (~(convergent_lines zenon_TL_bm zenon_TN_bd)) -> False).
% 0.22/0.61 do 3 intro. intros zenon_H47 zenon_H45 zenon_H2e zenon_H24 zenon_H23.
% 0.22/0.61 generalize (zenon_H47 zenon_TN_bd). zenon_intro zenon_H48.
% 0.22/0.61 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H1b | zenon_intro zenon_H46 ].
% 0.22/0.61 generalize (zenon_H47 zenon_TM_y). zenon_intro zenon_H49.
% 0.22/0.61 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H17 | zenon_intro zenon_H43 ].
% 0.22/0.61 apply (zenon_L1_ zenon_TM_y); trivial.
% 0.22/0.61 generalize (oac1 zenon_TM_y). zenon_intro zenon_H4a.
% 0.22/0.61 generalize (zenon_H4a zenon_TM_y). zenon_intro zenon_H4b.
% 0.22/0.61 generalize (ax6 zenon_TM_y). zenon_intro zenon_H2d.
% 0.22/0.61 generalize (zenon_H4b zenon_TN_bd). zenon_intro zenon_H4c.
% 0.22/0.61 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ].
% 0.22/0.61 apply (zenon_notand_s _ _ zenon_H4e); [ zenon_intro zenon_H19 | zenon_intro zenon_H4f ].
% 0.22/0.61 apply (zenon_L6_ zenon_TM_y zenon_TN_bd zenon_TL_bm); trivial.
% 0.22/0.61 exact (zenon_H4f zenon_H43).
% 0.22/0.61 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H44 | zenon_intro zenon_H44 ].
% 0.22/0.61 apply (zenon_L7_ zenon_TN_bd zenon_TM_y); trivial.
% 0.22/0.61 apply (zenon_L7_ zenon_TN_bd zenon_TM_y); trivial.
% 0.22/0.61 exact (zenon_H45 zenon_H46).
% 0.22/0.61 (* end of lemma zenon_L8_ *)
% 0.22/0.61 apply NNPP. intro zenon_G.
% 0.22/0.61 apply (zenon_notallex_s (fun L : zenon_U => (forall M : zenon_U, (forall N : zenon_U, ((unorthogonal_lines L M)->((convergent_lines L N)\/(unorthogonal_lines M N)))))) zenon_G); [ zenon_intro zenon_H50; idtac ].
% 0.22/0.61 elim zenon_H50. zenon_intro zenon_TL_bm. zenon_intro zenon_H51.
% 0.22/0.61 apply (zenon_notallex_s (fun M : zenon_U => (forall N : zenon_U, ((unorthogonal_lines zenon_TL_bm M)->((convergent_lines zenon_TL_bm N)\/(unorthogonal_lines M N))))) zenon_H51); [ zenon_intro zenon_H52; idtac ].
% 0.22/0.61 elim zenon_H52. zenon_intro zenon_TM_y. zenon_intro zenon_H53.
% 0.22/0.61 apply (zenon_notallex_s (fun N : zenon_U => ((unorthogonal_lines zenon_TL_bm zenon_TM_y)->((convergent_lines zenon_TL_bm N)\/(unorthogonal_lines zenon_TM_y N)))) zenon_H53); [ zenon_intro zenon_H54; idtac ].
% 0.22/0.61 elim zenon_H54. zenon_intro zenon_TN_bd. zenon_intro zenon_H55.
% 0.22/0.61 apply (zenon_notimply_s _ _ zenon_H55). zenon_intro zenon_H57. zenon_intro zenon_H56.
% 0.22/0.61 apply (zenon_notor_s _ _ zenon_H56). zenon_intro zenon_H23. zenon_intro zenon_H45.
% 0.22/0.61 generalize (oac1 zenon_TL_bm). zenon_intro zenon_H58.
% 0.22/0.61 generalize (apart3 zenon_TN_bd). zenon_intro zenon_H24.
% 0.22/0.61 generalize (zenon_H58 zenon_TM_y). zenon_intro zenon_H59.
% 0.22/0.61 generalize (occu1 zenon_TM_y). zenon_intro zenon_H47.
% 0.22/0.61 generalize (zenon_H59 zenon_TM_y). zenon_intro zenon_H5a.
% 0.22/0.61 apply (zenon_imply_s _ _ zenon_H5a); [ zenon_intro zenon_H5c | zenon_intro zenon_H5b ].
% 0.22/0.61 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H2e | zenon_intro zenon_H5d ].
% 0.22/0.61 apply (zenon_L8_ zenon_TL_bm zenon_TN_bd zenon_TM_y); trivial.
% 0.22/0.61 exact (zenon_H5d zenon_H57).
% 0.22/0.61 apply (zenon_or_s _ _ zenon_H5b); [ zenon_intro zenon_H5e | zenon_intro zenon_H41 ].
% 0.22/0.61 apply (zenon_and_s _ _ zenon_H5e). zenon_intro zenon_H37. zenon_intro zenon_H57.
% 0.22/0.61 generalize (zenon_H59 zenon_TN_bd). zenon_intro zenon_H5f.
% 0.22/0.61 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H5c | zenon_intro zenon_H60 ].
% 0.22/0.61 apply (zenon_notand_s _ _ zenon_H5c); [ zenon_intro zenon_H2e | zenon_intro zenon_H5d ].
% 0.22/0.61 exact (zenon_H2e zenon_H37).
% 0.22/0.61 exact (zenon_H5d zenon_H57).
% 0.22/0.61 apply (zenon_or_s _ _ zenon_H60); [ zenon_intro zenon_H61 | zenon_intro zenon_H44 ].
% 0.22/0.61 apply (zenon_and_s _ _ zenon_H61). zenon_intro zenon_H2b. zenon_intro zenon_H62.
% 0.22/0.61 exact (zenon_H23 zenon_H2b).
% 0.22/0.61 apply (zenon_L7_ zenon_TN_bd zenon_TM_y); trivial.
% 0.22/0.61 apply (zenon_and_s _ _ zenon_H41). zenon_intro zenon_H17. zenon_intro zenon_H43.
% 0.22/0.61 apply (zenon_L1_ zenon_TM_y); trivial.
% 0.22/0.61 Qed.
% 0.22/0.61 % SZS output end Proof
% 0.22/0.61 (* END-PROOF *)
% 0.22/0.61 nodes searched: 3505
% 0.22/0.61 max branch formulas: 1198
% 0.22/0.61 proof nodes created: 263
% 0.22/0.61 formulas created: 12268
% 0.22/0.61
%------------------------------------------------------------------------------