TSTP Solution File: GEO188+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO188+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n029.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 07:00:33 EDT 2022
% Result : Theorem 0.21s 0.58s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO188+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : run_zenon %s %d
% 0.14/0.35 % Computer : n029.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Sat Jun 18 14:12:44 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.21/0.58 (* PROOF-FOUND *)
% 0.21/0.58 % SZS status Theorem
% 0.21/0.58 (* BEGIN-PROOF *)
% 0.21/0.58 % SZS output start Proof
% 0.21/0.58 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((distinct_points X Z)/\((distinct_points Y Z)/\(~(apart_point_and_line Z (line_connecting X Y))))))->(~(apart_point_and_line X (line_connecting Z Y))))))).
% 0.21/0.58 Proof.
% 0.21/0.58 assert (zenon_L1_ : forall (zenon_TZ_r : zenon_U) (zenon_TY_s : zenon_U), (forall Z : zenon_U, ((distinct_points zenon_TY_s zenon_TZ_r)->((distinct_points zenon_TY_s Z)\/(distinct_points zenon_TZ_r Z)))) -> (distinct_points zenon_TY_s zenon_TZ_r) -> (~(distinct_points zenon_TY_s zenon_TY_s)) -> (~(distinct_points zenon_TZ_r zenon_TY_s)) -> False).
% 0.21/0.58 do 2 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10.
% 0.21/0.58 generalize (zenon_Hd zenon_TY_s). zenon_intro zenon_H13.
% 0.21/0.58 apply (zenon_imply_s _ _ zenon_H13); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ].
% 0.21/0.58 exact (zenon_H15 zenon_He).
% 0.21/0.58 apply (zenon_or_s _ _ zenon_H14); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ].
% 0.21/0.58 exact (zenon_Hf zenon_H17).
% 0.21/0.58 exact (zenon_H10 zenon_H16).
% 0.21/0.58 (* end of lemma zenon_L1_ *)
% 0.21/0.58 apply NNPP. intro zenon_G.
% 0.21/0.58 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((distinct_points X Z)/\((distinct_points Y Z)/\(~(apart_point_and_line Z (line_connecting X Y))))))->(~(apart_point_and_line X (line_connecting Z Y))))))) zenon_G); [ zenon_intro zenon_H18; idtac ].
% 0.21/0.58 elim zenon_H18. zenon_intro zenon_TX_z. zenon_intro zenon_H1a.
% 0.21/0.58 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((distinct_points zenon_TX_z Y)/\((distinct_points zenon_TX_z Z)/\((distinct_points Y Z)/\(~(apart_point_and_line Z (line_connecting zenon_TX_z Y))))))->(~(apart_point_and_line zenon_TX_z (line_connecting Z Y)))))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ].
% 0.21/0.58 elim zenon_H1b. zenon_intro zenon_TY_s. zenon_intro zenon_H1c.
% 0.21/0.58 apply (zenon_notallex_s (fun Z : zenon_U => (((distinct_points zenon_TX_z zenon_TY_s)/\((distinct_points zenon_TX_z Z)/\((distinct_points zenon_TY_s Z)/\(~(apart_point_and_line Z (line_connecting zenon_TX_z zenon_TY_s))))))->(~(apart_point_and_line zenon_TX_z (line_connecting Z zenon_TY_s))))) zenon_H1c); [ zenon_intro zenon_H1d; idtac ].
% 0.21/0.58 elim zenon_H1d. zenon_intro zenon_TZ_r. zenon_intro zenon_H1e.
% 0.21/0.58 apply (zenon_notimply_s _ _ zenon_H1e). zenon_intro zenon_H20. zenon_intro zenon_H1f.
% 0.21/0.58 apply zenon_H1f. zenon_intro zenon_H21.
% 0.21/0.58 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_H23. zenon_intro zenon_H22.
% 0.21/0.58 apply (zenon_and_s _ _ zenon_H22). zenon_intro zenon_H25. zenon_intro zenon_H24.
% 0.21/0.58 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_He. zenon_intro zenon_H26.
% 0.21/0.58 generalize (apart1 zenon_TZ_r). zenon_intro zenon_H27.
% 0.21/0.58 generalize (apart1 zenon_TY_s). zenon_intro zenon_Hf.
% 0.21/0.58 generalize (con1 zenon_TZ_r). zenon_intro zenon_H28.
% 0.21/0.58 generalize (apart4 zenon_TY_s). zenon_intro zenon_H29.
% 0.21/0.58 generalize (cu1 zenon_TY_s). zenon_intro zenon_H2a.
% 0.21/0.58 generalize (ceq2 zenon_TX_z). zenon_intro zenon_H2b.
% 0.21/0.58 generalize (zenon_H28 zenon_TY_s). zenon_intro zenon_H2c.
% 0.21/0.58 generalize (zenon_H2a zenon_TZ_r). zenon_intro zenon_H2d.
% 0.21/0.58 generalize (con1 zenon_TX_z). zenon_intro zenon_H2e.
% 0.21/0.58 generalize (zenon_H29 zenon_TZ_r). zenon_intro zenon_Hd.
% 0.21/0.58 generalize (zenon_H2c zenon_TY_s). zenon_intro zenon_H2f.
% 0.21/0.58 apply (zenon_imply_s _ _ zenon_H2f); [ zenon_intro zenon_H10 | zenon_intro zenon_H30 ].
% 0.21/0.58 apply (zenon_L1_ zenon_TZ_r zenon_TY_s); trivial.
% 0.21/0.58 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ].
% 0.21/0.58 generalize (apart1 zenon_TX_z). zenon_intro zenon_H33.
% 0.21/0.58 generalize (zenon_H2c zenon_TZ_r). zenon_intro zenon_H34.
% 0.21/0.58 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H10 | zenon_intro zenon_H35 ].
% 0.21/0.58 apply (zenon_L1_ zenon_TZ_r zenon_TY_s); trivial.
% 0.21/0.58 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ].
% 0.21/0.58 generalize (zenon_H2e zenon_TY_s). zenon_intro zenon_H38.
% 0.21/0.58 generalize (zenon_H38 zenon_TX_z). zenon_intro zenon_H39.
% 0.21/0.58 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ].
% 0.21/0.58 exact (zenon_H3b zenon_H23).
% 0.21/0.58 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ].
% 0.21/0.58 generalize (zenon_H38 zenon_TY_s). zenon_intro zenon_H3e.
% 0.21/0.58 apply (zenon_imply_s _ _ zenon_H3e); [ zenon_intro zenon_H3b | zenon_intro zenon_H3f ].
% 0.21/0.58 exact (zenon_H3b zenon_H23).
% 0.21/0.58 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ].
% 0.21/0.58 generalize (zenon_H2b (line_connecting zenon_TZ_r zenon_TY_s)). zenon_intro zenon_H42.
% 0.21/0.58 generalize (zenon_H42 (line_connecting zenon_TX_z zenon_TY_s)). zenon_intro zenon_H43.
% 0.21/0.58 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ].
% 0.21/0.58 exact (zenon_H45 zenon_H21).
% 0.21/0.58 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 0.21/0.58 generalize (zenon_H2d (line_connecting zenon_TZ_r zenon_TY_s)). zenon_intro zenon_H48.
% 0.21/0.58 generalize (zenon_H48 (line_connecting zenon_TX_z zenon_TY_s)). zenon_intro zenon_H49.
% 0.21/0.58 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ].
% 0.21/0.58 apply (zenon_notand_s _ _ zenon_H4b); [ zenon_intro zenon_H15 | zenon_intro zenon_H4c ].
% 0.21/0.58 exact (zenon_H15 zenon_He).
% 0.21/0.58 exact (zenon_H4c zenon_H47).
% 0.21/0.58 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ].
% 0.21/0.58 exact (zenon_H32 zenon_H4e).
% 0.21/0.58 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H50 | zenon_intro zenon_H4f ].
% 0.21/0.58 exact (zenon_H41 zenon_H50).
% 0.21/0.58 apply (zenon_or_s _ _ zenon_H4f); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ].
% 0.21/0.58 exact (zenon_H37 zenon_H52).
% 0.21/0.58 exact (zenon_H26 zenon_H51).
% 0.21/0.58 exact (zenon_H3d zenon_H46).
% 0.21/0.58 apply (zenon_and_s _ _ zenon_H40). zenon_intro zenon_H53. zenon_intro zenon_H17.
% 0.21/0.58 exact (zenon_Hf zenon_H17).
% 0.21/0.58 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H54. zenon_intro zenon_H23.
% 0.21/0.58 exact (zenon_H33 zenon_H54).
% 0.21/0.58 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H55. zenon_intro zenon_H16.
% 0.21/0.58 exact (zenon_H27 zenon_H55).
% 0.21/0.58 apply (zenon_and_s _ _ zenon_H31). zenon_intro zenon_He. zenon_intro zenon_H17.
% 0.21/0.58 exact (zenon_Hf zenon_H17).
% 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: 2166
% 0.21/0.58 max branch formulas: 793
% 0.21/0.58 proof nodes created: 248
% 0.21/0.58 formulas created: 7130
% 0.21/0.58
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