TSTP Solution File: GEO181+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO181+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n021.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 07:00:28 EDT 2022
% Result : Theorem 0.46s 0.64s
% Output : Proof 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO181+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n021.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 10:53:16 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.46/0.64 (* PROOF-FOUND *)
% 0.46/0.64 % SZS status Theorem
% 0.46/0.64 (* BEGIN-PROOF *)
% 0.46/0.64 % SZS output start Proof
% 0.46/0.64 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, ((distinct_points X Y)->((apart_point_and_line Z (line_connecting X Y))->(apart_point_and_line Y (line_connecting X Z))))))).
% 0.46/0.64 Proof.
% 0.46/0.64 assert (zenon_L1_ : forall (zenon_TX_r : zenon_U) (zenon_TZ_s : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((distinct_points zenon_TZ_s Y)->((distinct_points zenon_TZ_s Z)\/(distinct_points Y Z))))) -> (~(distinct_points zenon_TX_r zenon_TZ_s)) -> (~(distinct_points zenon_TZ_s zenon_TZ_s)) -> (distinct_points zenon_TZ_s zenon_TX_r) -> False).
% 0.46/0.64 do 2 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10.
% 0.46/0.64 generalize (zenon_Hd zenon_TX_r). zenon_intro zenon_H13.
% 0.46/0.64 generalize (zenon_H13 zenon_TZ_s). zenon_intro zenon_H14.
% 0.46/0.64 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ].
% 0.46/0.64 exact (zenon_H16 zenon_H10).
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H15); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ].
% 0.46/0.64 exact (zenon_Hf zenon_H18).
% 0.46/0.64 exact (zenon_He zenon_H17).
% 0.46/0.64 (* end of lemma zenon_L1_ *)
% 0.46/0.64 assert (zenon_L2_ : forall (zenon_TY_bi : zenon_U) (zenon_TX_r : zenon_U) (zenon_TZ_s : zenon_U), (distinct_points zenon_TZ_s zenon_TX_r) -> (~(distinct_points zenon_TZ_s zenon_TZ_s)) -> (distinct_points zenon_TX_r zenon_TY_bi) -> (~(apart_point_and_line zenon_TX_r (line_connecting zenon_TX_r zenon_TY_bi))) -> (~(apart_point_and_line zenon_TY_bi (line_connecting zenon_TX_r zenon_TY_bi))) -> (~(apart_point_and_line zenon_TY_bi (line_connecting zenon_TX_r zenon_TZ_s))) -> (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_r zenon_TY_bi)/\(distinct_lines U V))->((apart_point_and_line zenon_TX_r U)\/((apart_point_and_line zenon_TX_r V)\/((apart_point_and_line zenon_TY_bi U)\/(apart_point_and_line zenon_TY_bi V))))))) -> (apart_point_and_line zenon_TZ_s (line_connecting zenon_TX_r zenon_TY_bi)) -> (forall Z : zenon_U, ((apart_point_and_line zenon_TZ_s (line_connecting zenon_TX_r zenon_TY_bi))->((distinct_lines (line_connecting zenon_TX_r zenon_TY_bi) Z)\/(apart_point_and_line zenon_TZ_s Z)))) -> (forall Z : zenon_U, ((distinct_points zenon_TX_r zenon_TZ_s)->((apart_point_and_line Z (line_connecting zenon_TX_r zenon_TZ_s))->((distinct_points Z zenon_TX_r)/\(distinct_points Z zenon_TZ_s))))) -> (~(distinct_points zenon_TX_r zenon_TX_r)) -> False).
% 0.46/0.64 do 3 intro. intros zenon_H10 zenon_Hf zenon_H19 zenon_H1a zenon_H1b zenon_H1c zenon_H1d zenon_H1e zenon_H1f zenon_H20 zenon_H21.
% 0.46/0.64 generalize (zenon_H20 zenon_TX_r). zenon_intro zenon_H23.
% 0.46/0.64 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_He | zenon_intro zenon_H24 ].
% 0.46/0.64 generalize (apart4 zenon_TZ_s). zenon_intro zenon_Hd.
% 0.46/0.64 apply (zenon_L1_ zenon_TX_r zenon_TZ_s); trivial.
% 0.46/0.64 apply (zenon_imply_s _ _ zenon_H24); [ zenon_intro zenon_H26 | zenon_intro zenon_H25 ].
% 0.46/0.64 generalize (apart4 zenon_TZ_s). zenon_intro zenon_Hd.
% 0.46/0.64 generalize (zenon_H20 zenon_TZ_s). zenon_intro zenon_H27.
% 0.46/0.64 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_He | zenon_intro zenon_H28 ].
% 0.46/0.64 apply (zenon_L1_ zenon_TX_r zenon_TZ_s); trivial.
% 0.46/0.64 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 0.46/0.64 generalize (zenon_H1f (line_connecting zenon_TX_r zenon_TZ_s)). zenon_intro zenon_H2b.
% 0.46/0.64 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 0.46/0.64 exact (zenon_H2d zenon_H1e).
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H2c); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ].
% 0.46/0.64 generalize (zenon_H1d (line_connecting zenon_TX_r zenon_TY_bi)). zenon_intro zenon_H30.
% 0.46/0.64 generalize (zenon_H30 (line_connecting zenon_TX_r zenon_TZ_s)). zenon_intro zenon_H31.
% 0.46/0.64 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 0.46/0.64 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ].
% 0.46/0.64 exact (zenon_H35 zenon_H19).
% 0.46/0.64 exact (zenon_H34 zenon_H2f).
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H32); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ].
% 0.46/0.64 exact (zenon_H1a zenon_H37).
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H36); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ].
% 0.46/0.64 exact (zenon_H26 zenon_H39).
% 0.46/0.64 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ].
% 0.46/0.64 exact (zenon_H1b zenon_H3b).
% 0.46/0.64 exact (zenon_H1c zenon_H3a).
% 0.46/0.64 exact (zenon_H2a zenon_H2e).
% 0.46/0.64 apply (zenon_and_s _ _ zenon_H29). zenon_intro zenon_H10. zenon_intro zenon_H18.
% 0.46/0.64 exact (zenon_Hf zenon_H18).
% 0.46/0.64 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H3c. zenon_intro zenon_H17.
% 0.46/0.64 exact (zenon_H21 zenon_H3c).
% 0.46/0.64 (* end of lemma zenon_L2_ *)
% 0.46/0.64 apply NNPP. intro zenon_G.
% 0.46/0.64 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, ((distinct_points X Y)->((apart_point_and_line Z (line_connecting X Y))->(apart_point_and_line Y (line_connecting X Z))))))) zenon_G); [ zenon_intro zenon_H3d; idtac ].
% 0.46/0.64 elim zenon_H3d. zenon_intro zenon_TX_r. zenon_intro zenon_H3e.
% 0.46/0.64 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, ((distinct_points zenon_TX_r Y)->((apart_point_and_line Z (line_connecting zenon_TX_r Y))->(apart_point_and_line Y (line_connecting zenon_TX_r Z)))))) zenon_H3e); [ zenon_intro zenon_H3f; idtac ].
% 0.46/0.64 elim zenon_H3f. zenon_intro zenon_TY_bi. zenon_intro zenon_H40.
% 0.46/0.64 apply (zenon_notallex_s (fun Z : zenon_U => ((distinct_points zenon_TX_r zenon_TY_bi)->((apart_point_and_line Z (line_connecting zenon_TX_r zenon_TY_bi))->(apart_point_and_line zenon_TY_bi (line_connecting zenon_TX_r Z))))) zenon_H40); [ zenon_intro zenon_H41; idtac ].
% 0.46/0.64 elim zenon_H41. zenon_intro zenon_TZ_s. zenon_intro zenon_H42.
% 0.46/0.64 apply (zenon_notimply_s _ _ zenon_H42). zenon_intro zenon_H19. zenon_intro zenon_H43.
% 0.46/0.64 apply (zenon_notimply_s _ _ zenon_H43). zenon_intro zenon_H1e. zenon_intro zenon_H1c.
% 0.46/0.64 generalize (apart1 zenon_TY_bi). zenon_intro zenon_H44.
% 0.46/0.64 generalize (cu1 zenon_TX_r). zenon_intro zenon_H45.
% 0.46/0.64 generalize (zenon_H45 zenon_TY_bi). zenon_intro zenon_H1d.
% 0.46/0.64 generalize (con1 zenon_TX_r). zenon_intro zenon_H46.
% 0.46/0.64 generalize (apart1 zenon_TX_r). zenon_intro zenon_H21.
% 0.46/0.64 generalize (zenon_H46 zenon_TY_bi). zenon_intro zenon_H47.
% 0.46/0.64 generalize (ceq2 zenon_TZ_s). zenon_intro zenon_H48.
% 0.46/0.64 generalize (zenon_H47 zenon_TY_bi). zenon_intro zenon_H49.
% 0.46/0.64 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H35 | zenon_intro zenon_H4a ].
% 0.46/0.64 exact (zenon_H35 zenon_H19).
% 0.46/0.64 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H1b | zenon_intro zenon_H4b ].
% 0.46/0.64 generalize (zenon_H47 zenon_TX_r). zenon_intro zenon_H4c.
% 0.46/0.64 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H35 | zenon_intro zenon_H4d ].
% 0.46/0.64 exact (zenon_H35 zenon_H19).
% 0.46/0.64 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H1a | zenon_intro zenon_H4e ].
% 0.46/0.64 generalize (zenon_H48 (line_connecting zenon_TX_r zenon_TY_bi)). zenon_intro zenon_H1f.
% 0.46/0.64 generalize (apart1 zenon_TZ_s). zenon_intro zenon_Hf.
% 0.46/0.64 generalize (zenon_H46 zenon_TZ_s). zenon_intro zenon_H20.
% 0.46/0.64 generalize (zenon_H47 zenon_TZ_s). zenon_intro zenon_H4f.
% 0.46/0.64 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H35 | zenon_intro zenon_H50 ].
% 0.46/0.64 exact (zenon_H35 zenon_H19).
% 0.46/0.64 apply (zenon_imply_s _ _ zenon_H50); [ zenon_intro zenon_H2d | zenon_intro zenon_H51 ].
% 0.46/0.64 exact (zenon_H2d zenon_H1e).
% 0.46/0.64 apply (zenon_and_s _ _ zenon_H51). zenon_intro zenon_H10. zenon_intro zenon_H52.
% 0.46/0.64 apply (zenon_L2_ zenon_TY_bi zenon_TX_r zenon_TZ_s); trivial.
% 0.46/0.64 apply (zenon_and_s _ _ zenon_H4e). zenon_intro zenon_H3c. zenon_intro zenon_H19.
% 0.46/0.64 exact (zenon_H21 zenon_H3c).
% 0.46/0.64 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H54. zenon_intro zenon_H53.
% 0.46/0.64 exact (zenon_H44 zenon_H53).
% 0.46/0.64 Qed.
% 0.46/0.64 % SZS output end Proof
% 0.46/0.64 (* END-PROOF *)
% 0.46/0.64 nodes searched: 6802
% 0.46/0.64 max branch formulas: 1461
% 0.46/0.64 proof nodes created: 672
% 0.46/0.64 formulas created: 17440
% 0.46/0.64
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