TSTP Solution File: GEO213+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO213+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n023.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 07:00:55 EDT 2022
% Result : Theorem 0.18s 0.56s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO213+2 : TPTP v8.1.0. Released v3.3.0.
% 0.10/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 14:14:19 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.18/0.56 (* PROOF-FOUND *)
% 0.18/0.56 % SZS status Theorem
% 0.18/0.56 (* BEGIN-PROOF *)
% 0.18/0.56 % SZS output start Proof
% 0.18/0.56 Theorem con : (forall L : zenon_U, (forall M : zenon_U, (forall N : zenon_U, ((unorthogonal_lines L M)->((distinct_lines L N)\/(unorthogonal_lines M N)))))).
% 0.18/0.56 Proof.
% 0.18/0.56 assert (zenon_L1_ : forall (zenon_TL_z : zenon_U) (zenon_TN_ba : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((distinct_lines zenon_TN_ba Y)->((distinct_lines zenon_TN_ba Z)\/(distinct_lines Y Z))))) -> (~(distinct_lines zenon_TL_z zenon_TN_ba)) -> (~(distinct_lines zenon_TN_ba zenon_TN_ba)) -> (distinct_lines zenon_TN_ba zenon_TL_z) -> False).
% 0.18/0.56 do 2 intro. intros zenon_H15 zenon_H16 zenon_H17 zenon_H18.
% 0.18/0.56 generalize (zenon_H15 zenon_TL_z). zenon_intro zenon_H1b.
% 0.18/0.56 generalize (zenon_H1b zenon_TN_ba). zenon_intro zenon_H1c.
% 0.18/0.56 apply (zenon_imply_s _ _ zenon_H1c); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ].
% 0.18/0.56 exact (zenon_H1e zenon_H18).
% 0.18/0.56 apply (zenon_or_s _ _ zenon_H1d); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ].
% 0.18/0.56 exact (zenon_H17 zenon_H20).
% 0.18/0.56 exact (zenon_H16 zenon_H1f).
% 0.18/0.56 (* end of lemma zenon_L1_ *)
% 0.18/0.56 assert (zenon_L2_ : forall (zenon_TN_ba : zenon_U) (zenon_TL_z : zenon_U) (zenon_TM_bk : zenon_U), (forall M : zenon_U, ((convergent_lines zenon_TM_bk M)\/(unorthogonal_lines zenon_TM_bk M))) -> (~(convergent_lines zenon_TL_z zenon_TM_bk)) -> (~(distinct_lines zenon_TL_z zenon_TN_ba)) -> (~(unorthogonal_lines zenon_TM_bk zenon_TN_ba)) -> False).
% 0.18/0.56 do 3 intro. intros zenon_H21 zenon_H22 zenon_H16 zenon_H23.
% 0.18/0.56 generalize (zenon_H21 zenon_TN_ba). zenon_intro zenon_H25.
% 0.18/0.56 apply (zenon_or_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ].
% 0.18/0.56 generalize (apart3 zenon_TM_bk). zenon_intro zenon_H28.
% 0.18/0.56 generalize (apart2 zenon_TN_ba). zenon_intro zenon_H17.
% 0.18/0.56 generalize (ceq3 zenon_TN_ba). zenon_intro zenon_H29.
% 0.18/0.56 generalize (apart5 zenon_TN_ba). zenon_intro zenon_H15.
% 0.18/0.56 generalize (apart6 zenon_TM_bk). zenon_intro zenon_H2a.
% 0.18/0.56 generalize (zenon_H2a zenon_TN_ba). zenon_intro zenon_H2b.
% 0.18/0.56 generalize (zenon_H2b zenon_TL_z). zenon_intro zenon_H2c.
% 0.18/0.56 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ].
% 0.18/0.56 exact (zenon_H2e zenon_H27).
% 0.18/0.56 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ].
% 0.18/0.56 generalize (zenon_H2a zenon_TL_z). zenon_intro zenon_H31.
% 0.18/0.56 generalize (zenon_H31 zenon_TM_bk). zenon_intro zenon_H32.
% 0.18/0.56 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 0.18/0.56 exact (zenon_H34 zenon_H30).
% 0.18/0.56 apply (zenon_or_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ].
% 0.18/0.56 exact (zenon_H28 zenon_H36).
% 0.18/0.56 exact (zenon_H22 zenon_H35).
% 0.18/0.56 generalize (zenon_H29 zenon_TL_z). zenon_intro zenon_H37.
% 0.18/0.56 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H38 | zenon_intro zenon_H18 ].
% 0.18/0.56 exact (zenon_H38 zenon_H2f).
% 0.18/0.56 apply (zenon_L1_ zenon_TL_z zenon_TN_ba); trivial.
% 0.18/0.56 exact (zenon_H23 zenon_H26).
% 0.18/0.56 (* end of lemma zenon_L2_ *)
% 0.18/0.56 assert (zenon_L3_ : forall (zenon_TN_ba : zenon_U) (zenon_TL_z : zenon_U), (~(distinct_lines zenon_TL_z zenon_TN_ba)) -> (convergent_lines zenon_TL_z zenon_TN_ba) -> False).
% 0.18/0.56 do 2 intro. intros zenon_H16 zenon_H39.
% 0.18/0.56 generalize (ceq3 zenon_TL_z). zenon_intro zenon_H3a.
% 0.18/0.56 generalize (zenon_H3a zenon_TN_ba). zenon_intro zenon_H3b.
% 0.18/0.56 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H3c | zenon_intro zenon_H1f ].
% 0.18/0.56 exact (zenon_H3c zenon_H39).
% 0.18/0.56 exact (zenon_H16 zenon_H1f).
% 0.18/0.56 (* end of lemma zenon_L3_ *)
% 0.18/0.56 apply NNPP. intro zenon_G.
% 0.18/0.56 apply (zenon_notallex_s (fun L : zenon_U => (forall M : zenon_U, (forall N : zenon_U, ((unorthogonal_lines L M)->((distinct_lines L N)\/(unorthogonal_lines M N)))))) zenon_G); [ zenon_intro zenon_H3d; idtac ].
% 0.18/0.56 elim zenon_H3d. zenon_intro zenon_TL_z. zenon_intro zenon_H3e.
% 0.18/0.56 apply (zenon_notallex_s (fun M : zenon_U => (forall N : zenon_U, ((unorthogonal_lines zenon_TL_z M)->((distinct_lines zenon_TL_z N)\/(unorthogonal_lines M N))))) zenon_H3e); [ zenon_intro zenon_H3f; idtac ].
% 0.18/0.56 elim zenon_H3f. zenon_intro zenon_TM_bk. zenon_intro zenon_H40.
% 0.18/0.56 apply (zenon_notallex_s (fun N : zenon_U => ((unorthogonal_lines zenon_TL_z zenon_TM_bk)->((distinct_lines zenon_TL_z N)\/(unorthogonal_lines zenon_TM_bk N)))) zenon_H40); [ zenon_intro zenon_H41; idtac ].
% 0.18/0.56 elim zenon_H41. zenon_intro zenon_TN_ba. zenon_intro zenon_H42.
% 0.18/0.56 apply (zenon_notimply_s _ _ zenon_H42). zenon_intro zenon_H44. zenon_intro zenon_H43.
% 0.18/0.56 apply (zenon_notor_s _ _ zenon_H43). zenon_intro zenon_H16. zenon_intro zenon_H23.
% 0.18/0.56 generalize (oac1 zenon_TL_z). zenon_intro zenon_H45.
% 0.18/0.56 generalize (zenon_H45 zenon_TM_bk). zenon_intro zenon_H46.
% 0.18/0.56 generalize (occu1 zenon_TM_bk). zenon_intro zenon_H21.
% 0.18/0.56 generalize (zenon_H46 zenon_TN_ba). zenon_intro zenon_H47.
% 0.18/0.56 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ].
% 0.18/0.56 apply (zenon_notand_s _ _ zenon_H49); [ zenon_intro zenon_H22 | zenon_intro zenon_H4a ].
% 0.18/0.56 apply (zenon_L2_ zenon_TN_ba zenon_TL_z zenon_TM_bk); trivial.
% 0.18/0.56 exact (zenon_H4a zenon_H44).
% 0.18/0.56 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ].
% 0.18/0.56 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H39. zenon_intro zenon_H4d.
% 0.18/0.56 apply (zenon_L3_ zenon_TN_ba zenon_TL_z); trivial.
% 0.18/0.56 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H27. zenon_intro zenon_H26.
% 0.18/0.56 exact (zenon_H23 zenon_H26).
% 0.18/0.56 Qed.
% 0.18/0.56 % SZS output end Proof
% 0.18/0.56 (* END-PROOF *)
% 0.18/0.56 nodes searched: 2810
% 0.18/0.56 max branch formulas: 709
% 0.18/0.56 proof nodes created: 295
% 0.18/0.56 formulas created: 8914
% 0.18/0.56
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