TSTP Solution File: GEO177+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO177+3 : TPTP v8.1.0. Released v4.0.0.
% 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 07:00:25 EDT 2022
% Result : Theorem 0.37s 0.55s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GEO177+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n021.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 03:23:01 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.37/0.55 (* PROOF-FOUND *)
% 0.37/0.55 % SZS status Theorem
% 0.37/0.55 (* BEGIN-PROOF *)
% 0.37/0.55 % SZS output start Proof
% 0.37/0.55 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\(distinct_points U V))->(((apart_point_and_line X (line_connecting U V))\/(apart_point_and_line Y (line_connecting U V)))->((apart_point_and_line U (line_connecting X Y))\/(apart_point_and_line V (line_connecting X Y))))))))).
% 0.37/0.55 Proof.
% 0.37/0.55 assert (zenon_L1_ : forall (zenon_TY_br : zenon_U) (zenon_TX_bs : zenon_U) (zenon_TV_bt : zenon_U) (zenon_TU_bu : zenon_U), (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TU_bu zenon_TV_bt)/\(distinct_lines U V))->((apart_point_and_line zenon_TU_bu U)\/((apart_point_and_line zenon_TU_bu V)\/((apart_point_and_line zenon_TV_bt U)\/(apart_point_and_line zenon_TV_bt V))))))) -> (~(apart_point_and_line zenon_TV_bt (line_connecting zenon_TX_bs zenon_TY_br))) -> (~(apart_point_and_line zenon_TV_bt (line_connecting zenon_TU_bu zenon_TV_bt))) -> (~(apart_point_and_line zenon_TU_bu (line_connecting zenon_TX_bs zenon_TY_br))) -> (~(apart_point_and_line zenon_TU_bu (line_connecting zenon_TU_bu zenon_TV_bt))) -> (distinct_lines (line_connecting zenon_TU_bu zenon_TV_bt) (line_connecting zenon_TX_bs zenon_TY_br)) -> (distinct_points zenon_TU_bu zenon_TV_bt) -> False).
% 0.37/0.55 do 4 intro. intros zenon_H24 zenon_H25 zenon_H26 zenon_H27 zenon_H28 zenon_H29 zenon_H2a.
% 0.37/0.55 generalize (zenon_H24 (line_connecting zenon_TU_bu zenon_TV_bt)). zenon_intro zenon_H2f.
% 0.37/0.55 generalize (zenon_H2f (line_connecting zenon_TX_bs zenon_TY_br)). zenon_intro zenon_H30.
% 0.37/0.55 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ].
% 0.37/0.55 apply (zenon_notand_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 0.37/0.55 exact (zenon_H34 zenon_H2a).
% 0.37/0.55 exact (zenon_H33 zenon_H29).
% 0.37/0.55 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ].
% 0.37/0.55 exact (zenon_H28 zenon_H36).
% 0.37/0.55 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ].
% 0.37/0.55 exact (zenon_H27 zenon_H38).
% 0.37/0.55 apply (zenon_or_s _ _ zenon_H37); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ].
% 0.37/0.55 exact (zenon_H26 zenon_H3a).
% 0.37/0.55 exact (zenon_H25 zenon_H39).
% 0.37/0.55 (* end of lemma zenon_L1_ *)
% 0.37/0.55 apply NNPP. intro zenon_G.
% 0.37/0.55 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\(distinct_points U V))->(((apart_point_and_line X (line_connecting U V))\/(apart_point_and_line Y (line_connecting U V)))->((apart_point_and_line U (line_connecting X Y))\/(apart_point_and_line V (line_connecting X Y))))))))) zenon_G); [ zenon_intro zenon_H3b; idtac ].
% 0.37/0.55 elim zenon_H3b. zenon_intro zenon_TX_bs. zenon_intro zenon_H3c.
% 0.37/0.55 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_bs Y)/\(distinct_points U V))->(((apart_point_and_line zenon_TX_bs (line_connecting U V))\/(apart_point_and_line Y (line_connecting U V)))->((apart_point_and_line U (line_connecting zenon_TX_bs Y))\/(apart_point_and_line V (line_connecting zenon_TX_bs Y)))))))) zenon_H3c); [ zenon_intro zenon_H3d; idtac ].
% 0.37/0.55 elim zenon_H3d. zenon_intro zenon_TY_br. zenon_intro zenon_H3e.
% 0.37/0.55 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_bs zenon_TY_br)/\(distinct_points U V))->(((apart_point_and_line zenon_TX_bs (line_connecting U V))\/(apart_point_and_line zenon_TY_br (line_connecting U V)))->((apart_point_and_line U (line_connecting zenon_TX_bs zenon_TY_br))\/(apart_point_and_line V (line_connecting zenon_TX_bs zenon_TY_br))))))) zenon_H3e); [ zenon_intro zenon_H3f; idtac ].
% 0.37/0.55 elim zenon_H3f. zenon_intro zenon_TU_bu. zenon_intro zenon_H40.
% 0.37/0.55 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_bs zenon_TY_br)/\(distinct_points zenon_TU_bu V))->(((apart_point_and_line zenon_TX_bs (line_connecting zenon_TU_bu V))\/(apart_point_and_line zenon_TY_br (line_connecting zenon_TU_bu V)))->((apart_point_and_line zenon_TU_bu (line_connecting zenon_TX_bs zenon_TY_br))\/(apart_point_and_line V (line_connecting zenon_TX_bs zenon_TY_br)))))) zenon_H40); [ zenon_intro zenon_H41; idtac ].
% 0.37/0.55 elim zenon_H41. zenon_intro zenon_TV_bt. zenon_intro zenon_H42.
% 0.37/0.55 apply (zenon_notimply_s _ _ zenon_H42). zenon_intro zenon_H44. zenon_intro zenon_H43.
% 0.37/0.55 apply (zenon_notimply_s _ _ zenon_H43). zenon_intro zenon_H46. zenon_intro zenon_H45.
% 0.37/0.55 apply (zenon_notor_s _ _ zenon_H45). zenon_intro zenon_H27. zenon_intro zenon_H25.
% 0.37/0.55 apply (zenon_and_s _ _ zenon_H44). zenon_intro zenon_H47. zenon_intro zenon_H2a.
% 0.37/0.55 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ].
% 0.37/0.55 generalize (cu1 zenon_TU_bu). zenon_intro zenon_H4a.
% 0.37/0.55 generalize (ci1 zenon_TU_bu). zenon_intro zenon_H4b.
% 0.37/0.55 generalize (zenon_H4a zenon_TV_bt). zenon_intro zenon_H24.
% 0.37/0.55 generalize (ci2 zenon_TU_bu). zenon_intro zenon_H4c.
% 0.37/0.55 generalize (zenon_H4b zenon_TV_bt). zenon_intro zenon_H4d.
% 0.37/0.55 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H34 | zenon_intro zenon_H28 ].
% 0.37/0.55 exact (zenon_H34 zenon_H2a).
% 0.37/0.55 generalize (zenon_H4c zenon_TV_bt). zenon_intro zenon_H4e.
% 0.37/0.55 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H34 | zenon_intro zenon_H26 ].
% 0.37/0.55 exact (zenon_H34 zenon_H2a).
% 0.37/0.55 generalize (ceq2 zenon_TX_bs). zenon_intro zenon_H4f.
% 0.37/0.55 generalize (zenon_H4f (line_connecting zenon_TU_bu zenon_TV_bt)). zenon_intro zenon_H50.
% 0.37/0.55 generalize (ci1 zenon_TX_bs). zenon_intro zenon_H51.
% 0.37/0.55 generalize (zenon_H51 zenon_TY_br). zenon_intro zenon_H52.
% 0.37/0.55 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ].
% 0.37/0.55 exact (zenon_H54 zenon_H47).
% 0.37/0.55 generalize (zenon_H50 (line_connecting zenon_TX_bs zenon_TY_br)). zenon_intro zenon_H55.
% 0.37/0.55 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ].
% 0.37/0.55 exact (zenon_H57 zenon_H49).
% 0.37/0.55 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H29 | zenon_intro zenon_H58 ].
% 0.37/0.55 apply (zenon_L1_ zenon_TY_br zenon_TX_bs zenon_TV_bt zenon_TU_bu); trivial.
% 0.37/0.55 exact (zenon_H53 zenon_H58).
% 0.37/0.55 generalize (cu1 zenon_TU_bu). zenon_intro zenon_H4a.
% 0.37/0.55 generalize (ci1 zenon_TU_bu). zenon_intro zenon_H4b.
% 0.37/0.55 generalize (zenon_H4a zenon_TV_bt). zenon_intro zenon_H24.
% 0.37/0.55 generalize (ci2 zenon_TU_bu). zenon_intro zenon_H4c.
% 0.37/0.55 generalize (zenon_H4b zenon_TV_bt). zenon_intro zenon_H4d.
% 0.37/0.55 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H34 | zenon_intro zenon_H28 ].
% 0.37/0.55 exact (zenon_H34 zenon_H2a).
% 0.37/0.55 generalize (zenon_H4c zenon_TV_bt). zenon_intro zenon_H4e.
% 0.37/0.55 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H34 | zenon_intro zenon_H26 ].
% 0.37/0.55 exact (zenon_H34 zenon_H2a).
% 0.37/0.55 generalize (ceq2 zenon_TY_br). zenon_intro zenon_H59.
% 0.37/0.55 generalize (zenon_H59 (line_connecting zenon_TU_bu zenon_TV_bt)). zenon_intro zenon_H5a.
% 0.37/0.55 generalize (ci2 zenon_TX_bs). zenon_intro zenon_H5b.
% 0.37/0.55 generalize (zenon_H5b zenon_TY_br). zenon_intro zenon_H5c.
% 0.37/0.55 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H54 | zenon_intro zenon_H5d ].
% 0.37/0.55 exact (zenon_H54 zenon_H47).
% 0.37/0.55 generalize (zenon_H5a (line_connecting zenon_TX_bs zenon_TY_br)). zenon_intro zenon_H5e.
% 0.37/0.55 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ].
% 0.37/0.55 exact (zenon_H60 zenon_H48).
% 0.37/0.55 apply (zenon_or_s _ _ zenon_H5f); [ zenon_intro zenon_H29 | zenon_intro zenon_H61 ].
% 0.37/0.55 apply (zenon_L1_ zenon_TY_br zenon_TX_bs zenon_TV_bt zenon_TU_bu); trivial.
% 0.37/0.55 exact (zenon_H5d zenon_H61).
% 0.37/0.55 Qed.
% 0.37/0.55 % SZS output end Proof
% 0.37/0.55 (* END-PROOF *)
% 0.37/0.55 nodes searched: 3941
% 0.37/0.55 max branch formulas: 1303
% 0.37/0.55 proof nodes created: 311
% 0.37/0.55 formulas created: 13324
% 0.37/0.55
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