TSTP Solution File: GEO218+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO218+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n016.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 07:00:59 EDT 2022
% Result : Theorem 0.21s 0.57s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO218+3 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14 % Command : run_zenon %s %d
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 600
% 0.13/0.36 % DateTime : Sat Jun 18 04:44:51 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.21/0.57 (* PROOF-FOUND *)
% 0.21/0.57 % SZS status Theorem
% 0.21/0.57 (* BEGIN-PROOF *)
% 0.21/0.57 % SZS output start Proof
% 0.21/0.57 Theorem con : (forall L : zenon_U, (forall M : zenon_U, (forall N : zenon_U, (((parallel_lines L M)/\(orthogonal_lines L N))->(orthogonal_lines M N))))).
% 0.21/0.57 Proof.
% 0.21/0.57 assert (zenon_L1_ : forall (zenon_TN_bp : zenon_U) (zenon_TM_bq : zenon_U) (zenon_TL_br : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines zenon_TL_br Y)->((convergent_lines zenon_TL_br Z)\/(convergent_lines Y Z))))) -> (~(convergent_lines zenon_TM_bq zenon_TN_bp)) -> (~(convergent_lines zenon_TN_bp zenon_TN_bp)) -> (~(convergent_lines zenon_TL_br zenon_TM_bq)) -> (convergent_lines zenon_TL_br zenon_TN_bp) -> False).
% 0.21/0.57 do 3 intro. intros zenon_H24 zenon_H25 zenon_H26 zenon_H27 zenon_H28.
% 0.21/0.57 generalize (zenon_H24 zenon_TN_bp). zenon_intro zenon_H2c.
% 0.21/0.57 generalize (zenon_H2c zenon_TM_bq). zenon_intro zenon_H2d.
% 0.21/0.57 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ].
% 0.21/0.57 exact (zenon_H2f zenon_H28).
% 0.21/0.57 apply (zenon_or_s _ _ zenon_H2e); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ].
% 0.21/0.57 exact (zenon_H27 zenon_H31).
% 0.21/0.57 generalize (ax6 zenon_TN_bp). zenon_intro zenon_H32.
% 0.21/0.57 generalize (zenon_H32 zenon_TM_bq). zenon_intro zenon_H33.
% 0.21/0.57 generalize (zenon_H33 zenon_TN_bp). zenon_intro zenon_H34.
% 0.21/0.57 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ].
% 0.21/0.57 exact (zenon_H36 zenon_H30).
% 0.21/0.57 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ].
% 0.21/0.57 exact (zenon_H26 zenon_H38).
% 0.21/0.57 exact (zenon_H25 zenon_H37).
% 0.21/0.57 (* end of lemma zenon_L1_ *)
% 0.21/0.57 assert (zenon_L2_ : forall (zenon_TL_br : zenon_U) (zenon_TN_bp : zenon_U) (zenon_TM_bq : zenon_U), (~(convergent_lines zenon_TM_bq zenon_TN_bp)) -> (~(convergent_lines zenon_TL_br zenon_TM_bq)) -> (convergent_lines zenon_TL_br zenon_TN_bp) -> False).
% 0.21/0.57 do 3 intro. intros zenon_H25 zenon_H27 zenon_H28.
% 0.21/0.57 generalize (apart3 zenon_TN_bp). zenon_intro zenon_H26.
% 0.21/0.57 generalize (ax6 zenon_TL_br). zenon_intro zenon_H24.
% 0.21/0.57 apply (zenon_L1_ zenon_TN_bp zenon_TM_bq zenon_TL_br); trivial.
% 0.21/0.57 (* end of lemma zenon_L2_ *)
% 0.21/0.57 assert (zenon_L3_ : forall (zenon_TN_bp : zenon_U) (zenon_TL_br : zenon_U), (~(~(unorthogonal_lines zenon_TL_br zenon_TN_bp))) -> (~(unorthogonal_lines zenon_TL_br zenon_TN_bp)) -> False).
% 0.21/0.57 do 2 intro. intros zenon_H39 zenon_H3a.
% 0.21/0.57 exact (zenon_H39 zenon_H3a).
% 0.21/0.57 (* end of lemma zenon_L3_ *)
% 0.21/0.57 apply NNPP. intro zenon_G.
% 0.21/0.57 apply (zenon_notallex_s (fun L : zenon_U => (forall M : zenon_U, (forall N : zenon_U, (((parallel_lines L M)/\(orthogonal_lines L N))->(orthogonal_lines M N))))) zenon_G); [ zenon_intro zenon_H3b; idtac ].
% 0.21/0.57 elim zenon_H3b. zenon_intro zenon_TL_br. zenon_intro zenon_H3c.
% 0.21/0.57 apply (zenon_notallex_s (fun M : zenon_U => (forall N : zenon_U, (((parallel_lines zenon_TL_br M)/\(orthogonal_lines zenon_TL_br N))->(orthogonal_lines M N)))) zenon_H3c); [ zenon_intro zenon_H3d; idtac ].
% 0.21/0.57 elim zenon_H3d. zenon_intro zenon_TM_bq. zenon_intro zenon_H3e.
% 0.21/0.57 apply (zenon_notallex_s (fun N : zenon_U => (((parallel_lines zenon_TL_br zenon_TM_bq)/\(orthogonal_lines zenon_TL_br N))->(orthogonal_lines zenon_TM_bq N))) zenon_H3e); [ zenon_intro zenon_H3f; idtac ].
% 0.21/0.57 elim zenon_H3f. zenon_intro zenon_TN_bp. zenon_intro zenon_H40.
% 0.21/0.57 apply (zenon_notimply_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H41.
% 0.21/0.57 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H44. zenon_intro zenon_H43.
% 0.21/0.57 generalize (a3 zenon_TL_br). zenon_intro zenon_H45.
% 0.21/0.57 generalize (zenon_H45 zenon_TM_bq). zenon_intro zenon_H46.
% 0.21/0.57 apply (zenon_equiv_s _ _ zenon_H46); [ zenon_intro zenon_H48; zenon_intro zenon_H47 | zenon_intro zenon_H44; zenon_intro zenon_H27 ].
% 0.21/0.57 exact (zenon_H48 zenon_H44).
% 0.21/0.57 generalize (a5 zenon_TL_br). zenon_intro zenon_H49.
% 0.21/0.57 generalize (zenon_H49 zenon_TN_bp). zenon_intro zenon_H4a.
% 0.21/0.57 apply (zenon_equiv_s _ _ zenon_H4a); [ zenon_intro zenon_H4b; zenon_intro zenon_H39 | zenon_intro zenon_H43; zenon_intro zenon_H3a ].
% 0.21/0.57 exact (zenon_H4b zenon_H43).
% 0.21/0.57 generalize (a5 zenon_TM_bq). zenon_intro zenon_H4c.
% 0.21/0.57 generalize (zenon_H4c zenon_TN_bp). zenon_intro zenon_H4d.
% 0.21/0.57 apply (zenon_equiv_s _ _ zenon_H4d); [ zenon_intro zenon_H41; zenon_intro zenon_H50 | zenon_intro zenon_H4f; zenon_intro zenon_H4e ].
% 0.21/0.58 apply zenon_H50. zenon_intro zenon_H51.
% 0.21/0.58 generalize (coipo1 zenon_TL_br). zenon_intro zenon_H52.
% 0.21/0.58 generalize (oac1 zenon_TM_bq). zenon_intro zenon_H53.
% 0.21/0.58 generalize (apart3 zenon_TM_bq). zenon_intro zenon_H54.
% 0.21/0.58 generalize (zenon_H52 zenon_TN_bp). zenon_intro zenon_H55.
% 0.21/0.58 apply (zenon_notand_s _ _ zenon_H55); [ zenon_intro zenon_H56 | zenon_intro zenon_H39 ].
% 0.21/0.58 apply zenon_H56. zenon_intro zenon_H28.
% 0.21/0.58 generalize (zenon_H53 zenon_TN_bp). zenon_intro zenon_H57.
% 0.21/0.58 generalize (zenon_H57 zenon_TM_bq). zenon_intro zenon_H58.
% 0.21/0.58 apply (zenon_imply_s _ _ zenon_H58); [ zenon_intro zenon_H5a | zenon_intro zenon_H59 ].
% 0.21/0.58 apply (zenon_notand_s _ _ zenon_H5a); [ zenon_intro zenon_H25 | zenon_intro zenon_H4e ].
% 0.21/0.58 apply (zenon_L2_ zenon_TL_br zenon_TN_bp zenon_TM_bq); trivial.
% 0.21/0.58 exact (zenon_H4e zenon_H51).
% 0.21/0.58 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H5c | zenon_intro zenon_H5b ].
% 0.21/0.58 apply (zenon_and_s _ _ zenon_H5c). zenon_intro zenon_H5e. zenon_intro zenon_H5d.
% 0.21/0.58 exact (zenon_H54 zenon_H5e).
% 0.21/0.58 apply (zenon_and_s _ _ zenon_H5b). zenon_intro zenon_H30. zenon_intro zenon_H5f.
% 0.21/0.58 generalize (cotno1 zenon_TL_br). zenon_intro zenon_H60.
% 0.21/0.58 generalize (zenon_H60 zenon_TN_bp). zenon_intro zenon_H61.
% 0.21/0.58 generalize (zenon_H61 zenon_TM_bq). zenon_intro zenon_H62.
% 0.21/0.58 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ].
% 0.21/0.58 apply (zenon_notand_s _ _ zenon_H64); [ zenon_intro zenon_H66 | zenon_intro zenon_H65 ].
% 0.21/0.58 apply (zenon_notor_s _ _ zenon_H66). zenon_intro zenon_H56. zenon_intro zenon_H39.
% 0.21/0.58 exact (zenon_H39 zenon_H3a).
% 0.21/0.58 apply (zenon_notor_s _ _ zenon_H65). zenon_intro zenon_H47. zenon_intro zenon_H67.
% 0.21/0.58 exact (zenon_H47 zenon_H27).
% 0.21/0.58 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H36 | zenon_intro zenon_H68 ].
% 0.21/0.58 exact (zenon_H36 zenon_H30).
% 0.21/0.58 exact (zenon_H68 zenon_H5f).
% 0.21/0.58 exact (zenon_H39 zenon_H3a).
% 0.21/0.58 exact (zenon_H41 zenon_H4f).
% 0.21/0.58 Qed.
% 0.21/0.58 % SZS output end Proof
% 0.21/0.58 (* END-PROOF *)
% 0.21/0.58 nodes searched: 1693
% 0.21/0.58 max branch formulas: 724
% 0.21/0.58 proof nodes created: 183
% 0.21/0.58 formulas created: 7682
% 0.21/0.58
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