TSTP Solution File: GEO202+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO202+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n024.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 07:00:45 EDT 2022
% Result : Theorem 0.38s 0.55s
% Output : Proof 0.40s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO202+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.12/0.34 % Computer : n024.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 : Fri Jun 17 21:06:17 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.38/0.55 (* PROOF-FOUND *)
% 0.38/0.55 % SZS status Theorem
% 0.38/0.55 (* BEGIN-PROOF *)
% 0.38/0.55 % SZS output start Proof
% 0.38/0.55 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((distinct_points X Z)/\(convergent_lines (line_connecting X Y) (line_connecting X Z))))->(~(distinct_points (intersection_point (line_connecting X Y) (line_connecting X Z)) X)))))).
% 0.38/0.55 Proof.
% 0.38/0.55 assert (zenon_L1_ : forall (zenon_TZ_u : zenon_U) (zenon_TY_v : zenon_U) (zenon_TX_w : zenon_U), (distinct_points (intersection_point (line_connecting zenon_TX_w zenon_TY_v) (line_connecting zenon_TX_w zenon_TZ_u)) zenon_TX_w) -> (convergent_lines (line_connecting zenon_TX_w zenon_TY_v) (line_connecting zenon_TX_w zenon_TZ_u)) -> (apart_point_and_line zenon_TZ_u (line_connecting zenon_TX_w zenon_TY_v)) -> (distinct_points zenon_TX_w zenon_TZ_u) -> (distinct_points zenon_TX_w zenon_TY_v) -> False).
% 0.38/0.55 do 3 intro. intros zenon_Hf zenon_H10 zenon_H11 zenon_H12 zenon_H13.
% 0.38/0.55 generalize (ci1 zenon_TX_w). zenon_intro zenon_H17.
% 0.38/0.55 generalize (ceq2 zenon_TZ_u). zenon_intro zenon_H18.
% 0.40/0.55 generalize (ci2 zenon_TX_w). zenon_intro zenon_H19.
% 0.40/0.55 generalize (zenon_H17 zenon_TY_v). zenon_intro zenon_H1a.
% 0.40/0.55 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ].
% 0.40/0.55 exact (zenon_H1c zenon_H13).
% 0.40/0.55 generalize (zenon_H17 zenon_TZ_u). zenon_intro zenon_H1d.
% 0.40/0.55 apply (zenon_imply_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ].
% 0.40/0.55 exact (zenon_H1f zenon_H12).
% 0.40/0.55 generalize (zenon_H19 zenon_TZ_u). zenon_intro zenon_H20.
% 0.40/0.55 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H1f | zenon_intro zenon_H21 ].
% 0.40/0.55 exact (zenon_H1f zenon_H12).
% 0.40/0.55 generalize (cu1 (intersection_point (line_connecting zenon_TX_w zenon_TY_v) (line_connecting zenon_TX_w zenon_TZ_u))). zenon_intro zenon_H22.
% 0.40/0.55 generalize (zenon_H22 zenon_TX_w). zenon_intro zenon_H23.
% 0.40/0.55 generalize (ci3 (line_connecting zenon_TX_w zenon_TY_v)). zenon_intro zenon_H24.
% 0.40/0.55 generalize (zenon_H18 (line_connecting zenon_TX_w zenon_TY_v)). zenon_intro zenon_H25.
% 0.40/0.55 generalize (zenon_H25 (line_connecting zenon_TX_w zenon_TZ_u)). zenon_intro zenon_H26.
% 0.40/0.55 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ].
% 0.40/0.55 exact (zenon_H28 zenon_H11).
% 0.40/0.55 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 0.40/0.55 generalize (zenon_H23 (line_connecting zenon_TX_w zenon_TY_v)). zenon_intro zenon_H2b.
% 0.40/0.55 generalize (zenon_H2b (line_connecting zenon_TX_w zenon_TZ_u)). zenon_intro zenon_H2c.
% 0.40/0.55 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ].
% 0.40/0.55 apply (zenon_notand_s _ _ zenon_H2e); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ].
% 0.40/0.55 exact (zenon_H30 zenon_Hf).
% 0.40/0.55 exact (zenon_H2f zenon_H2a).
% 0.40/0.55 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ].
% 0.40/0.55 generalize (zenon_H24 (line_connecting zenon_TX_w zenon_TZ_u)). zenon_intro zenon_H33.
% 0.40/0.55 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ].
% 0.40/0.55 exact (zenon_H35 zenon_H10).
% 0.40/0.55 exact (zenon_H34 zenon_H32).
% 0.40/0.55 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ].
% 0.40/0.55 generalize (ci4 (line_connecting zenon_TX_w zenon_TY_v)). zenon_intro zenon_H38.
% 0.40/0.55 generalize (zenon_H38 (line_connecting zenon_TX_w zenon_TZ_u)). zenon_intro zenon_H39.
% 0.40/0.55 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H35 | zenon_intro zenon_H3a ].
% 0.40/0.55 exact (zenon_H35 zenon_H10).
% 0.40/0.55 exact (zenon_H3a zenon_H37).
% 0.40/0.55 apply (zenon_or_s _ _ zenon_H36); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ].
% 0.40/0.55 exact (zenon_H1b zenon_H3c).
% 0.40/0.55 exact (zenon_H1e zenon_H3b).
% 0.40/0.55 exact (zenon_H21 zenon_H29).
% 0.40/0.55 (* end of lemma zenon_L1_ *)
% 0.40/0.55 assert (zenon_L2_ : forall (zenon_TY_v : zenon_U) (zenon_TX_w : zenon_U), (forall Y : zenon_U, ((distinct_points zenon_TX_w Y)->(~(apart_point_and_line zenon_TX_w (line_connecting zenon_TX_w Y))))) -> (distinct_points zenon_TX_w zenon_TY_v) -> (apart_point_and_line zenon_TX_w (line_connecting zenon_TX_w zenon_TY_v)) -> False).
% 0.40/0.55 do 2 intro. intros zenon_H17 zenon_H13 zenon_H3c.
% 0.40/0.55 generalize (zenon_H17 zenon_TY_v). zenon_intro zenon_H1a.
% 0.40/0.55 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ].
% 0.40/0.55 exact (zenon_H1c zenon_H13).
% 0.40/0.55 exact (zenon_H1b zenon_H3c).
% 0.40/0.55 (* end of lemma zenon_L2_ *)
% 0.40/0.55 assert (zenon_L3_ : forall (zenon_TY_v : zenon_U) (zenon_TX_w : zenon_U), (apart_point_and_line zenon_TX_w (line_connecting zenon_TX_w zenon_TY_v)) -> (distinct_points zenon_TX_w zenon_TY_v) -> False).
% 0.40/0.55 do 2 intro. intros zenon_H3c zenon_H13.
% 0.40/0.55 generalize (ci1 zenon_TX_w). zenon_intro zenon_H17.
% 0.40/0.55 apply (zenon_L2_ zenon_TY_v zenon_TX_w); trivial.
% 0.40/0.55 (* end of lemma zenon_L3_ *)
% 0.40/0.55 apply NNPP. intro zenon_G.
% 0.40/0.55 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((distinct_points X Z)/\(convergent_lines (line_connecting X Y) (line_connecting X Z))))->(~(distinct_points (intersection_point (line_connecting X Y) (line_connecting X Z)) X)))))) zenon_G); [ zenon_intro zenon_H3d; idtac ].
% 0.40/0.55 elim zenon_H3d. zenon_intro zenon_TX_w. zenon_intro zenon_H3e.
% 0.40/0.55 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((distinct_points zenon_TX_w Y)/\((distinct_points zenon_TX_w Z)/\(convergent_lines (line_connecting zenon_TX_w Y) (line_connecting zenon_TX_w Z))))->(~(distinct_points (intersection_point (line_connecting zenon_TX_w Y) (line_connecting zenon_TX_w Z)) zenon_TX_w))))) zenon_H3e); [ zenon_intro zenon_H3f; idtac ].
% 0.40/0.55 elim zenon_H3f. zenon_intro zenon_TY_v. zenon_intro zenon_H40.
% 0.40/0.55 apply (zenon_notallex_s (fun Z : zenon_U => (((distinct_points zenon_TX_w zenon_TY_v)/\((distinct_points zenon_TX_w Z)/\(convergent_lines (line_connecting zenon_TX_w zenon_TY_v) (line_connecting zenon_TX_w Z))))->(~(distinct_points (intersection_point (line_connecting zenon_TX_w zenon_TY_v) (line_connecting zenon_TX_w Z)) zenon_TX_w)))) zenon_H40); [ zenon_intro zenon_H41; idtac ].
% 0.40/0.55 elim zenon_H41. zenon_intro zenon_TZ_u. zenon_intro zenon_H42.
% 0.40/0.55 apply (zenon_notimply_s _ _ zenon_H42). zenon_intro zenon_H44. zenon_intro zenon_H43.
% 0.40/0.55 apply zenon_H43. zenon_intro zenon_Hf.
% 0.40/0.55 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H13. zenon_intro zenon_H45.
% 0.40/0.55 apply (zenon_and_s _ _ zenon_H45). zenon_intro zenon_H12. zenon_intro zenon_H10.
% 0.40/0.55 generalize (apart4 zenon_TX_w). zenon_intro zenon_H46.
% 0.40/0.55 generalize (apart1 zenon_TX_w). zenon_intro zenon_H47.
% 0.40/0.55 generalize (zenon_H46 zenon_TZ_u). zenon_intro zenon_H48.
% 0.40/0.55 generalize (zenon_H48 zenon_TX_w). zenon_intro zenon_H49.
% 0.40/0.55 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H1f | zenon_intro zenon_H4a ].
% 0.40/0.55 exact (zenon_H1f zenon_H12).
% 0.40/0.55 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ].
% 0.40/0.55 exact (zenon_H47 zenon_H4c).
% 0.40/0.55 generalize (cu1 zenon_TZ_u). zenon_intro zenon_H4d.
% 0.40/0.55 generalize (zenon_H4d zenon_TX_w). zenon_intro zenon_H4e.
% 0.40/0.55 generalize (ceq3 (line_connecting zenon_TX_w zenon_TY_v)). zenon_intro zenon_H4f.
% 0.40/0.55 generalize (zenon_H4f (line_connecting zenon_TX_w zenon_TZ_u)). zenon_intro zenon_H50.
% 0.40/0.55 generalize (apart3 (line_connecting zenon_TX_w zenon_TY_v)). zenon_intro zenon_H51.
% 0.40/0.55 generalize (zenon_H50 (line_connecting zenon_TX_w zenon_TY_v)). zenon_intro zenon_H52.
% 0.40/0.55 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H35 | zenon_intro zenon_H53 ].
% 0.40/0.55 exact (zenon_H35 zenon_H10).
% 0.40/0.55 apply (zenon_or_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ].
% 0.40/0.55 generalize (zenon_H4e (line_connecting zenon_TX_w zenon_TZ_u)). zenon_intro zenon_H56.
% 0.40/0.55 generalize (zenon_H56 (line_connecting zenon_TX_w zenon_TY_v)). zenon_intro zenon_H57.
% 0.40/0.55 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H59 | zenon_intro zenon_H58 ].
% 0.40/0.55 apply (zenon_notand_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ].
% 0.40/0.55 exact (zenon_H5b zenon_H4b).
% 0.40/0.55 exact (zenon_H5a zenon_H55).
% 0.40/0.55 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H29 | zenon_intro zenon_H5c ].
% 0.40/0.55 generalize (ci2 zenon_TX_w). zenon_intro zenon_H19.
% 0.40/0.55 generalize (zenon_H19 zenon_TZ_u). zenon_intro zenon_H20.
% 0.40/0.55 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H1f | zenon_intro zenon_H21 ].
% 0.40/0.55 exact (zenon_H1f zenon_H12).
% 0.40/0.55 exact (zenon_H21 zenon_H29).
% 0.40/0.55 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H11 | zenon_intro zenon_H5d ].
% 0.40/0.55 apply (zenon_L1_ zenon_TZ_u zenon_TY_v zenon_TX_w); trivial.
% 0.40/0.55 apply (zenon_or_s _ _ zenon_H5d); [ zenon_intro zenon_H3b | zenon_intro zenon_H3c ].
% 0.40/0.55 generalize (ci1 zenon_TX_w). zenon_intro zenon_H17.
% 0.40/0.55 generalize (zenon_H17 zenon_TZ_u). zenon_intro zenon_H1d.
% 0.40/0.55 apply (zenon_imply_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ].
% 0.40/0.55 exact (zenon_H1f zenon_H12).
% 0.40/0.55 exact (zenon_H1e zenon_H3b).
% 0.40/0.55 apply (zenon_L3_ zenon_TY_v zenon_TX_w); trivial.
% 0.40/0.55 exact (zenon_H51 zenon_H54).
% 0.40/0.55 Qed.
% 0.40/0.55 % SZS output end Proof
% 0.40/0.55 (* END-PROOF *)
% 0.40/0.55 nodes searched: 1790
% 0.40/0.55 max branch formulas: 789
% 0.40/0.55 proof nodes created: 198
% 0.40/0.55 formulas created: 6999
% 0.40/0.55
%------------------------------------------------------------------------------