TSTP Solution File: GEO198+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO198+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 07:00:42 EDT 2022
% Result : Theorem 2.12s 2.35s
% Output : Proof 2.12s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO198+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : run_zenon %s %d
% 0.12/0.34 % Computer : n023.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 07:32:34 EDT 2022
% 0.12/0.34 % CPUTime :
% 2.12/2.35 (* PROOF-FOUND *)
% 2.12/2.35 % SZS status Theorem
% 2.12/2.35 (* BEGIN-PROOF *)
% 2.12/2.35 % SZS output start Proof
% 2.12/2.35 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 X Z) Y)))))).
% 2.12/2.35 Proof.
% 2.12/2.35 assert (zenon_L1_ : forall (zenon_TY_u : zenon_U) (zenon_TZ_v : zenon_U) (zenon_TX_w : zenon_U), (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TX_w zenon_TZ_v) zenon_TY_u)->((distinct_points (intersection_point zenon_TX_w zenon_TZ_v) Z)\/(apart_point_and_line Z zenon_TY_u)))) -> (apart_point_and_line (intersection_point zenon_TX_w zenon_TZ_v) zenon_TY_u) -> (distinct_lines zenon_TZ_v zenon_TX_w) -> (~(apart_point_and_line (intersection_point zenon_TX_w zenon_TY_u) zenon_TZ_v)) -> (~(apart_point_and_line (intersection_point zenon_TX_w zenon_TZ_v) zenon_TZ_v)) -> (convergent_lines zenon_TX_w zenon_TZ_v) -> (convergent_lines zenon_TX_w zenon_TY_u) -> False).
% 2.12/2.35 do 3 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10 zenon_H11 zenon_H12 zenon_H13.
% 2.12/2.35 generalize (con2 zenon_TX_w). zenon_intro zenon_H17.
% 2.12/2.35 generalize (zenon_H17 zenon_TY_u). zenon_intro zenon_H18.
% 2.12/2.35 generalize (apart1 (intersection_point zenon_TX_w zenon_TY_u)). zenon_intro zenon_H19.
% 2.12/2.35 generalize (zenon_H18 (intersection_point zenon_TX_w zenon_TY_u)). zenon_intro zenon_H1a.
% 2.12/2.35 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ].
% 2.12/2.35 exact (zenon_H1c zenon_H13).
% 2.12/2.35 apply (zenon_imply_s _ _ zenon_H1b); [ zenon_intro zenon_H1e | zenon_intro zenon_H1d ].
% 2.12/2.35 apply (zenon_notor_s _ _ zenon_H1e). zenon_intro zenon_H20. zenon_intro zenon_H1f.
% 2.12/2.35 generalize (zenon_H17 zenon_TZ_v). zenon_intro zenon_H21.
% 2.12/2.35 generalize (apart1 (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H22.
% 2.12/2.35 generalize (zenon_Hd (intersection_point zenon_TX_w zenon_TY_u)). zenon_intro zenon_H23.
% 2.12/2.35 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ].
% 2.12/2.35 exact (zenon_H25 zenon_He).
% 2.12/2.35 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ].
% 2.12/2.35 generalize (apart4 (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H28.
% 2.12/2.35 generalize (zenon_H21 (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H29.
% 2.12/2.35 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 2.12/2.35 exact (zenon_H2b zenon_H12).
% 2.12/2.35 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 2.12/2.35 apply (zenon_notor_s _ _ zenon_H2d). zenon_intro zenon_H2e. zenon_intro zenon_H11.
% 2.12/2.35 generalize (zenon_H28 (intersection_point zenon_TX_w zenon_TY_u)). zenon_intro zenon_H2f.
% 2.12/2.35 generalize (zenon_H2f (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H30.
% 2.12/2.35 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ].
% 2.12/2.35 exact (zenon_H32 zenon_H27).
% 2.12/2.35 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H2c | zenon_intro zenon_H33 ].
% 2.12/2.35 exact (zenon_H22 zenon_H2c).
% 2.12/2.35 generalize (cu1 (intersection_point zenon_TX_w zenon_TY_u)). zenon_intro zenon_H34.
% 2.12/2.35 generalize (zenon_H34 (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H35.
% 2.12/2.35 generalize (zenon_H35 zenon_TZ_v). zenon_intro zenon_H36.
% 2.12/2.35 generalize (zenon_H36 zenon_TX_w). zenon_intro zenon_H37.
% 2.12/2.35 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ].
% 2.12/2.35 apply (zenon_notand_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ].
% 2.12/2.35 exact (zenon_H3b zenon_H33).
% 2.12/2.35 exact (zenon_H3a zenon_Hf).
% 2.12/2.35 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ].
% 2.12/2.35 exact (zenon_H10 zenon_H3d).
% 2.12/2.35 apply (zenon_or_s _ _ zenon_H3c); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ].
% 2.12/2.35 exact (zenon_H20 zenon_H3f).
% 2.12/2.35 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ].
% 2.12/2.35 exact (zenon_H11 zenon_H41).
% 2.12/2.35 exact (zenon_H2e zenon_H40).
% 2.12/2.35 exact (zenon_H22 zenon_H2c).
% 2.12/2.35 exact (zenon_H1f zenon_H26).
% 2.12/2.35 exact (zenon_H19 zenon_H1d).
% 2.12/2.35 (* end of lemma zenon_L1_ *)
% 2.12/2.35 assert (zenon_L2_ : forall (zenon_TX_w : zenon_U), (distinct_lines zenon_TX_w zenon_TX_w) -> False).
% 2.12/2.35 do 1 intro. intros zenon_H42.
% 2.12/2.35 generalize (apart2 zenon_TX_w). zenon_intro zenon_H43.
% 2.12/2.35 exact (zenon_H43 zenon_H42).
% 2.12/2.35 (* end of lemma zenon_L2_ *)
% 2.12/2.35 assert (zenon_L3_ : forall (zenon_TZ_v : zenon_U) (zenon_TX_w : zenon_U), (apart_point_and_line (intersection_point zenon_TX_w zenon_TZ_v) zenon_TZ_v) -> (convergent_lines zenon_TX_w zenon_TZ_v) -> False).
% 2.12/2.35 do 2 intro. intros zenon_H41 zenon_H12.
% 2.12/2.35 generalize (con2 zenon_TX_w). zenon_intro zenon_H17.
% 2.12/2.35 generalize (apart1 (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H22.
% 2.12/2.35 generalize (zenon_H17 zenon_TZ_v). zenon_intro zenon_H21.
% 2.12/2.35 generalize (zenon_H21 (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H29.
% 2.12/2.35 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 2.12/2.35 exact (zenon_H2b zenon_H12).
% 2.12/2.35 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 2.12/2.35 apply (zenon_notor_s _ _ zenon_H2d). zenon_intro zenon_H2e. zenon_intro zenon_H11.
% 2.12/2.35 exact (zenon_H11 zenon_H41).
% 2.12/2.35 exact (zenon_H22 zenon_H2c).
% 2.12/2.35 (* end of lemma zenon_L3_ *)
% 2.12/2.35 apply NNPP. intro zenon_G.
% 2.12/2.35 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 X Z) Y)))))) zenon_G); [ zenon_intro zenon_H44; idtac ].
% 2.12/2.35 elim zenon_H44. zenon_intro zenon_TX_w. zenon_intro zenon_H45.
% 2.12/2.35 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_w Y)/\((convergent_lines Z Y)/\((convergent_lines zenon_TX_w Z)/\(~(apart_point_and_line (intersection_point zenon_TX_w Y) Z)))))->(~(apart_point_and_line (intersection_point zenon_TX_w Z) Y))))) zenon_H45); [ zenon_intro zenon_H46; idtac ].
% 2.12/2.35 elim zenon_H46. zenon_intro zenon_TY_u. zenon_intro zenon_H47.
% 2.12/2.35 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_w zenon_TY_u)/\((convergent_lines Z zenon_TY_u)/\((convergent_lines zenon_TX_w Z)/\(~(apart_point_and_line (intersection_point zenon_TX_w zenon_TY_u) Z)))))->(~(apart_point_and_line (intersection_point zenon_TX_w Z) zenon_TY_u)))) zenon_H47); [ zenon_intro zenon_H48; idtac ].
% 2.12/2.35 elim zenon_H48. zenon_intro zenon_TZ_v. zenon_intro zenon_H49.
% 2.12/2.35 apply (zenon_notimply_s _ _ zenon_H49). zenon_intro zenon_H4b. zenon_intro zenon_H4a.
% 2.12/2.35 apply zenon_H4a. zenon_intro zenon_He.
% 2.12/2.35 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H13. zenon_intro zenon_H4c.
% 2.12/2.35 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4e. zenon_intro zenon_H4d.
% 2.12/2.35 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H12. zenon_intro zenon_H10.
% 2.12/2.35 generalize (apart2 zenon_TZ_v). zenon_intro zenon_H4f.
% 2.12/2.35 generalize (apart6 zenon_TX_w). zenon_intro zenon_H50.
% 2.12/2.35 generalize (ceq3 zenon_TZ_v). zenon_intro zenon_H51.
% 2.12/2.35 generalize (zenon_H50 zenon_TZ_v). zenon_intro zenon_H52.
% 2.12/2.35 generalize (ceq2 (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H53.
% 2.12/2.35 generalize (ceq1 (intersection_point zenon_TX_w zenon_TZ_v)). zenon_intro zenon_H54.
% 2.12/2.35 generalize (zenon_H54 zenon_TY_u). zenon_intro zenon_Hd.
% 2.12/2.35 generalize (ceq3 zenon_TX_w). zenon_intro zenon_H55.
% 2.12/2.35 generalize (zenon_H53 zenon_TZ_v). zenon_intro zenon_H56.
% 2.12/2.35 generalize (zenon_H56 zenon_TZ_v). zenon_intro zenon_H57.
% 2.12/2.35 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H11 | zenon_intro zenon_H58 ].
% 2.12/2.35 generalize (zenon_H55 zenon_TX_w). zenon_intro zenon_H59.
% 2.12/2.35 apply (zenon_imply_s _ _ zenon_H59); [ zenon_intro zenon_H5a | zenon_intro zenon_H42 ].
% 2.12/2.35 generalize (zenon_H51 zenon_TX_w). zenon_intro zenon_H5b.
% 2.12/2.35 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H5c | zenon_intro zenon_Hf ].
% 2.12/2.35 generalize (zenon_H52 zenon_TX_w). zenon_intro zenon_H5d.
% 2.12/2.35 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H2b | zenon_intro zenon_H5e ].
% 2.12/2.35 exact (zenon_H2b zenon_H12).
% 2.12/2.35 apply (zenon_or_s _ _ zenon_H5e); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ].
% 2.12/2.35 exact (zenon_H5a zenon_H60).
% 2.12/2.35 exact (zenon_H5c zenon_H5f).
% 2.12/2.35 apply (zenon_L1_ zenon_TY_u zenon_TZ_v zenon_TX_w); trivial.
% 2.12/2.35 apply (zenon_L2_ zenon_TX_w); trivial.
% 2.12/2.35 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H61 | zenon_intro zenon_H41 ].
% 2.12/2.35 exact (zenon_H4f zenon_H61).
% 2.12/2.35 apply (zenon_L3_ zenon_TZ_v zenon_TX_w); trivial.
% 2.12/2.35 Qed.
% 2.12/2.35 % SZS output end Proof
% 2.12/2.35 (* END-PROOF *)
% 2.12/2.35 nodes searched: 214783
% 2.12/2.35 max branch formulas: 4717
% 2.12/2.35 proof nodes created: 4379
% 2.12/2.35 formulas created: 224151
% 2.12/2.35
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