TSTP Solution File: GEO195+3 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO195+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n009.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 07:00:40 EDT 2022
% Result : Theorem 0.54s 0.73s
% Output : Proof 0.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO195+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : run_zenon %s %d
% 0.14/0.34 % Computer : n009.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jun 18 04:46:23 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.54/0.73 (* PROOF-FOUND *)
% 0.54/0.73 % SZS status Theorem
% 0.54/0.73 (* BEGIN-PROOF *)
% 0.54/0.73 % SZS output start Proof
% 0.54/0.73 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines Z Y)/\(convergent_lines X Z)))->((apart_point_and_line (intersection_point X Y) Z)->(apart_point_and_line (intersection_point Y X) Z)))))).
% 0.54/0.73 Proof.
% 0.54/0.73 assert (zenon_L1_ : forall (zenon_TX_bl : zenon_U), (convergent_lines zenon_TX_bl zenon_TX_bl) -> False).
% 0.54/0.73 do 1 intro. intros zenon_H24.
% 0.54/0.73 generalize (apart3 zenon_TX_bl). zenon_intro zenon_H26.
% 0.54/0.73 exact (zenon_H26 zenon_H24).
% 0.54/0.73 (* end of lemma zenon_L1_ *)
% 0.54/0.73 assert (zenon_L2_ : forall (zenon_TY_bq : zenon_U) (zenon_TX_bl : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TX_bl Y)->(~(apart_point_and_line (intersection_point zenon_TX_bl Y) zenon_TX_bl)))) -> (convergent_lines zenon_TX_bl zenon_TY_bq) -> (apart_point_and_line (intersection_point zenon_TX_bl zenon_TY_bq) zenon_TX_bl) -> False).
% 0.54/0.73 do 2 intro. intros zenon_H27 zenon_H28 zenon_H29.
% 0.54/0.73 generalize (zenon_H27 zenon_TY_bq). zenon_intro zenon_H2b.
% 0.54/0.73 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 0.54/0.73 exact (zenon_H2d zenon_H28).
% 0.54/0.73 exact (zenon_H2c zenon_H29).
% 0.54/0.73 (* end of lemma zenon_L2_ *)
% 0.54/0.73 assert (zenon_L3_ : forall (zenon_TY_bq : zenon_U) (zenon_TX_bl : zenon_U), (forall Z : zenon_U, ((convergent_lines zenon_TX_bl zenon_TY_bq)->((convergent_lines zenon_TX_bl Z)\/(convergent_lines zenon_TY_bq Z)))) -> (convergent_lines zenon_TX_bl zenon_TY_bq) -> (~(convergent_lines zenon_TY_bq zenon_TX_bl)) -> False).
% 0.54/0.73 do 2 intro. intros zenon_H2e zenon_H28 zenon_H2f.
% 0.54/0.73 generalize (zenon_H2e zenon_TX_bl). zenon_intro zenon_H30.
% 0.54/0.73 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H2d | zenon_intro zenon_H31 ].
% 0.54/0.73 exact (zenon_H2d zenon_H28).
% 0.54/0.73 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H24 | zenon_intro zenon_H32 ].
% 0.54/0.73 apply (zenon_L1_ zenon_TX_bl); trivial.
% 0.54/0.73 exact (zenon_H2f zenon_H32).
% 0.54/0.73 (* end of lemma zenon_L3_ *)
% 0.54/0.73 assert (zenon_L4_ : forall (zenon_TX_bl : zenon_U) (zenon_TY_bq : zenon_U), (apart_point_and_line (intersection_point zenon_TY_bq zenon_TX_bl) zenon_TX_bl) -> (convergent_lines zenon_TX_bl zenon_TY_bq) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bl zenon_TY_bq)->((convergent_lines zenon_TX_bl Z)\/(convergent_lines zenon_TY_bq Z)))) -> False).
% 0.54/0.73 do 2 intro. intros zenon_H33 zenon_H28 zenon_H2e.
% 0.54/0.73 generalize (ci4 zenon_TY_bq). zenon_intro zenon_H34.
% 0.54/0.73 generalize (zenon_H34 zenon_TX_bl). zenon_intro zenon_H35.
% 0.54/0.73 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H2f | zenon_intro zenon_H36 ].
% 0.54/0.73 apply (zenon_L3_ zenon_TY_bq zenon_TX_bl); trivial.
% 0.54/0.73 exact (zenon_H36 zenon_H33).
% 0.54/0.73 (* end of lemma zenon_L4_ *)
% 0.54/0.73 assert (zenon_L5_ : forall (zenon_TX_bl : zenon_U) (zenon_TY_bq : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TY_bq Y)->(~(apart_point_and_line (intersection_point zenon_TY_bq Y) zenon_TY_bq)))) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bl zenon_TY_bq)->((convergent_lines zenon_TX_bl Z)\/(convergent_lines zenon_TY_bq Z)))) -> (convergent_lines zenon_TX_bl zenon_TY_bq) -> (apart_point_and_line (intersection_point zenon_TY_bq zenon_TX_bl) zenon_TY_bq) -> False).
% 0.54/0.73 do 2 intro. intros zenon_H37 zenon_H2e zenon_H28 zenon_H38.
% 0.54/0.73 generalize (zenon_H37 zenon_TX_bl). zenon_intro zenon_H39.
% 0.54/0.73 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H2f | zenon_intro zenon_H3a ].
% 0.54/0.73 apply (zenon_L3_ zenon_TY_bq zenon_TX_bl); trivial.
% 0.54/0.73 exact (zenon_H3a zenon_H38).
% 0.54/0.73 (* end of lemma zenon_L5_ *)
% 0.54/0.73 assert (zenon_L6_ : forall (zenon_TY_bq : zenon_U) (zenon_TX_bl : zenon_U), (forall U : zenon_U, (forall V : zenon_U, (((distinct_points (intersection_point zenon_TX_bl zenon_TY_bq) (intersection_point zenon_TY_bq zenon_TX_bl))/\(distinct_lines U V))->((apart_point_and_line (intersection_point zenon_TX_bl zenon_TY_bq) U)\/((apart_point_and_line (intersection_point zenon_TX_bl zenon_TY_bq) V)\/((apart_point_and_line (intersection_point zenon_TY_bq zenon_TX_bl) U)\/(apart_point_and_line (intersection_point zenon_TY_bq zenon_TX_bl) V))))))) -> (forall Y : zenon_U, ((convergent_lines zenon_TY_bq Y)->(~(apart_point_and_line (intersection_point zenon_TY_bq Y) zenon_TY_bq)))) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_bl zenon_TY_bq)->((convergent_lines zenon_TX_bl Z)\/(convergent_lines zenon_TY_bq Z)))) -> (~(apart_point_and_line (intersection_point zenon_TX_bl zenon_TY_bq) zenon_TY_bq)) -> (convergent_lines zenon_TX_bl zenon_TY_bq) -> (forall Y : zenon_U, ((convergent_lines zenon_TX_bl Y)->(~(apart_point_and_line (intersection_point zenon_TX_bl Y) zenon_TX_bl)))) -> (distinct_lines zenon_TX_bl zenon_TY_bq) -> (distinct_points (intersection_point zenon_TX_bl zenon_TY_bq) (intersection_point zenon_TY_bq zenon_TX_bl)) -> False).
% 0.54/0.73 do 2 intro. intros zenon_H3b zenon_H37 zenon_H2e zenon_H3c zenon_H28 zenon_H27 zenon_H3d zenon_H3e.
% 0.54/0.73 generalize (zenon_H3b zenon_TX_bl). zenon_intro zenon_H3f.
% 0.54/0.73 generalize (zenon_H3f zenon_TY_bq). zenon_intro zenon_H40.
% 0.54/0.73 apply (zenon_imply_s _ _ zenon_H40); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ].
% 0.54/0.73 apply (zenon_notand_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ].
% 0.54/0.73 exact (zenon_H44 zenon_H3e).
% 0.54/0.73 exact (zenon_H43 zenon_H3d).
% 0.54/0.73 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H29 | zenon_intro zenon_H45 ].
% 0.54/0.73 apply (zenon_L2_ zenon_TY_bq zenon_TX_bl); trivial.
% 0.54/0.73 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 0.54/0.73 exact (zenon_H3c zenon_H47).
% 0.54/0.73 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H33 | zenon_intro zenon_H38 ].
% 0.54/0.73 apply (zenon_L4_ zenon_TX_bl zenon_TY_bq); trivial.
% 0.54/0.73 apply (zenon_L5_ zenon_TX_bl zenon_TY_bq); trivial.
% 0.54/0.73 (* end of lemma zenon_L6_ *)
% 0.54/0.73 apply NNPP. intro zenon_G.
% 0.54/0.73 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines Z Y)/\(convergent_lines X Z)))->((apart_point_and_line (intersection_point X Y) Z)->(apart_point_and_line (intersection_point Y X) Z)))))) zenon_G); [ zenon_intro zenon_H48; idtac ].
% 0.54/0.73 elim zenon_H48. zenon_intro zenon_TX_bl. zenon_intro zenon_H49.
% 0.54/0.73 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_bl Y)/\((convergent_lines Z Y)/\(convergent_lines zenon_TX_bl Z)))->((apart_point_and_line (intersection_point zenon_TX_bl Y) Z)->(apart_point_and_line (intersection_point Y zenon_TX_bl) Z))))) zenon_H49); [ zenon_intro zenon_H4a; idtac ].
% 0.54/0.73 elim zenon_H4a. zenon_intro zenon_TY_bq. zenon_intro zenon_H4b.
% 0.54/0.73 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_bl zenon_TY_bq)/\((convergent_lines Z zenon_TY_bq)/\(convergent_lines zenon_TX_bl Z)))->((apart_point_and_line (intersection_point zenon_TX_bl zenon_TY_bq) Z)->(apart_point_and_line (intersection_point zenon_TY_bq zenon_TX_bl) Z)))) zenon_H4b); [ zenon_intro zenon_H4c; idtac ].
% 0.54/0.73 elim zenon_H4c. zenon_intro zenon_TZ_cz. zenon_intro zenon_H4e.
% 0.54/0.73 apply (zenon_notimply_s _ _ zenon_H4e). zenon_intro zenon_H50. zenon_intro zenon_H4f.
% 0.54/0.73 apply (zenon_notimply_s _ _ zenon_H4f). zenon_intro zenon_H52. zenon_intro zenon_H51.
% 0.54/0.73 apply (zenon_and_s _ _ zenon_H50). zenon_intro zenon_H28. zenon_intro zenon_H53.
% 0.54/0.73 generalize (apart3 zenon_TY_bq). zenon_intro zenon_H54.
% 0.54/0.73 generalize (ax6 zenon_TX_bl). zenon_intro zenon_H55.
% 0.54/0.73 generalize (ci3 zenon_TY_bq). zenon_intro zenon_H37.
% 0.54/0.73 generalize (zenon_H55 zenon_TY_bq). zenon_intro zenon_H2e.
% 0.54/0.73 generalize (ceq3 zenon_TY_bq). zenon_intro zenon_H56.
% 0.54/0.73 generalize (ceq2 (intersection_point zenon_TX_bl zenon_TY_bq)). zenon_intro zenon_H57.
% 0.54/0.73 generalize (zenon_H57 zenon_TY_bq). zenon_intro zenon_H58.
% 0.54/0.73 generalize (ceq1 (intersection_point zenon_TX_bl zenon_TY_bq)). zenon_intro zenon_H59.
% 0.54/0.73 generalize (zenon_H59 zenon_TZ_cz). zenon_intro zenon_H5a.
% 0.54/0.73 generalize (zenon_H5a (intersection_point zenon_TY_bq zenon_TX_bl)). zenon_intro zenon_H5b.
% 0.54/0.73 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ].
% 0.54/0.73 exact (zenon_H5d zenon_H52).
% 0.54/0.73 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H3e | zenon_intro zenon_H5e ].
% 0.54/0.73 generalize (cu1 (intersection_point zenon_TX_bl zenon_TY_bq)). zenon_intro zenon_H5f.
% 0.54/0.73 generalize (zenon_H58 zenon_TY_bq). zenon_intro zenon_H60.
% 0.54/0.73 apply (zenon_imply_s _ _ zenon_H60); [ zenon_intro zenon_H3c | zenon_intro zenon_H61 ].
% 0.54/0.73 generalize (zenon_H5f (intersection_point zenon_TY_bq zenon_TX_bl)). zenon_intro zenon_H3b.
% 0.54/0.73 generalize (ci3 zenon_TX_bl). zenon_intro zenon_H27.
% 0.54/0.73 generalize (apart2 zenon_TY_bq). zenon_intro zenon_H62.
% 0.54/0.73 generalize (apart5 zenon_TX_bl). zenon_intro zenon_H63.
% 0.54/0.73 generalize (zenon_H63 zenon_TY_bq). zenon_intro zenon_H64.
% 0.54/0.73 generalize (zenon_H64 zenon_TY_bq). zenon_intro zenon_H65.
% 0.54/0.73 apply (zenon_imply_s _ _ zenon_H65); [ zenon_intro zenon_H43 | zenon_intro zenon_H66 ].
% 0.54/0.73 generalize (zenon_H2e zenon_TX_bl). zenon_intro zenon_H30.
% 0.54/0.73 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H2d | zenon_intro zenon_H31 ].
% 0.54/0.73 exact (zenon_H2d zenon_H28).
% 0.54/0.73 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H24 | zenon_intro zenon_H32 ].
% 0.54/0.73 apply (zenon_L1_ zenon_TX_bl); trivial.
% 0.54/0.73 generalize (zenon_H56 zenon_TX_bl). zenon_intro zenon_H67.
% 0.54/0.73 generalize (zenon_H67 zenon_TY_bq). zenon_intro zenon_H68.
% 0.54/0.73 apply (zenon_imply_s _ _ zenon_H68); [ zenon_intro zenon_H2f | zenon_intro zenon_H69 ].
% 0.54/0.73 exact (zenon_H2f zenon_H32).
% 0.54/0.73 apply (zenon_or_s _ _ zenon_H69); [ zenon_intro zenon_H3d | zenon_intro zenon_H6a ].
% 0.54/0.73 exact (zenon_H43 zenon_H3d).
% 0.54/0.73 exact (zenon_H54 zenon_H6a).
% 0.54/0.73 apply (zenon_or_s _ _ zenon_H66); [ zenon_intro zenon_H3d | zenon_intro zenon_H6b ].
% 0.54/0.73 apply (zenon_L6_ zenon_TY_bq zenon_TX_bl); trivial.
% 0.54/0.73 exact (zenon_H62 zenon_H6b).
% 0.54/0.73 apply (zenon_or_s _ _ zenon_H61); [ zenon_intro zenon_H6b | zenon_intro zenon_H47 ].
% 0.54/0.73 generalize (apart2 zenon_TY_bq). zenon_intro zenon_H62.
% 0.54/0.73 exact (zenon_H62 zenon_H6b).
% 0.54/0.73 generalize (ci4 zenon_TX_bl). zenon_intro zenon_H6c.
% 0.54/0.73 generalize (zenon_H6c zenon_TY_bq). zenon_intro zenon_H6d.
% 0.54/0.73 apply (zenon_imply_s _ _ zenon_H6d); [ zenon_intro zenon_H2d | zenon_intro zenon_H3c ].
% 0.54/0.73 exact (zenon_H2d zenon_H28).
% 0.54/0.73 exact (zenon_H3c zenon_H47).
% 0.54/0.73 exact (zenon_H51 zenon_H5e).
% 0.54/0.73 Qed.
% 0.54/0.73 % SZS output end Proof
% 0.54/0.73 (* END-PROOF *)
% 0.54/0.73 nodes searched: 10791
% 0.54/0.73 max branch formulas: 1926
% 0.54/0.73 proof nodes created: 644
% 0.54/0.73 formulas created: 33973
% 0.54/0.73
%------------------------------------------------------------------------------