TSTP Solution File: GEO187+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO187+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n007.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 07:00:32 EDT 2022
% Result : Theorem 0.48s 0.73s
% Output : Proof 0.48s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO187+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.13 % Command : run_zenon %s %d
% 0.15/0.35 % Computer : n007.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 600
% 0.15/0.35 % DateTime : Sat Jun 18 16:38:43 EDT 2022
% 0.15/0.35 % CPUTime :
% 0.48/0.73 (* PROOF-FOUND *)
% 0.48/0.73 % SZS status Theorem
% 0.48/0.73 (* BEGIN-PROOF *)
% 0.48/0.73 % SZS output start Proof
% 0.48/0.73 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))))))))).
% 0.48/0.73 Proof.
% 0.48/0.73 assert (zenon_L1_ : forall (zenon_TV_u : zenon_U) (zenon_TU_v : zenon_U) (zenon_TY_w : zenon_U) (zenon_TX_x : zenon_U), (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_x zenon_TY_w)/\(distinct_lines U V))->((apart_point_and_line zenon_TX_x U)\/((apart_point_and_line zenon_TX_x V)\/((apart_point_and_line zenon_TY_w U)\/(apart_point_and_line zenon_TY_w V))))))) -> (~(apart_point_and_line zenon_TY_w (line_connecting zenon_TU_v zenon_TV_u))) -> (~(apart_point_and_line zenon_TY_w (line_connecting zenon_TX_x zenon_TY_w))) -> (~(apart_point_and_line zenon_TX_x (line_connecting zenon_TU_v zenon_TV_u))) -> (~(apart_point_and_line zenon_TX_x (line_connecting zenon_TX_x zenon_TY_w))) -> (distinct_lines (line_connecting zenon_TX_x zenon_TY_w) (line_connecting zenon_TU_v zenon_TV_u)) -> (distinct_points zenon_TX_x zenon_TY_w) -> False).
% 0.48/0.73 do 4 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10 zenon_H11 zenon_H12 zenon_H13.
% 0.48/0.73 generalize (zenon_Hd (line_connecting zenon_TX_x zenon_TY_w)). zenon_intro zenon_H18.
% 0.48/0.73 generalize (zenon_H18 (line_connecting zenon_TU_v zenon_TV_u)). zenon_intro zenon_H19.
% 0.48/0.73 apply (zenon_imply_s _ _ zenon_H19); [ zenon_intro zenon_H1b | zenon_intro zenon_H1a ].
% 0.48/0.73 apply (zenon_notand_s _ _ zenon_H1b); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ].
% 0.48/0.73 exact (zenon_H1d zenon_H13).
% 0.48/0.73 exact (zenon_H1c zenon_H12).
% 0.48/0.73 apply (zenon_or_s _ _ zenon_H1a); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ].
% 0.48/0.73 exact (zenon_H11 zenon_H1f).
% 0.48/0.73 apply (zenon_or_s _ _ zenon_H1e); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ].
% 0.48/0.73 exact (zenon_H10 zenon_H21).
% 0.48/0.73 apply (zenon_or_s _ _ zenon_H20); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ].
% 0.48/0.73 exact (zenon_Hf zenon_H23).
% 0.48/0.73 exact (zenon_He zenon_H22).
% 0.48/0.73 (* end of lemma zenon_L1_ *)
% 0.48/0.73 assert (zenon_L2_ : forall (zenon_TY_w : zenon_U) (zenon_TX_x : zenon_U), ((distinct_points zenon_TX_x zenon_TX_x)/\(distinct_points zenon_TX_x zenon_TY_w)) -> (~(distinct_points zenon_TX_x zenon_TX_x)) -> False).
% 0.48/0.73 do 2 intro. intros zenon_H24 zenon_H25.
% 0.48/0.73 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H26. zenon_intro zenon_H13.
% 0.48/0.73 exact (zenon_H25 zenon_H26).
% 0.48/0.73 (* end of lemma zenon_L2_ *)
% 0.48/0.73 assert (zenon_L3_ : forall (zenon_TX_x : zenon_U) (zenon_TY_w : zenon_U), ((distinct_points zenon_TY_w zenon_TX_x)/\(distinct_points zenon_TY_w zenon_TY_w)) -> (~(distinct_points zenon_TY_w zenon_TY_w)) -> False).
% 0.48/0.73 do 2 intro. intros zenon_H27 zenon_H28.
% 0.48/0.73 apply (zenon_and_s _ _ zenon_H27). zenon_intro zenon_H2a. zenon_intro zenon_H29.
% 0.48/0.73 exact (zenon_H28 zenon_H29).
% 0.48/0.73 (* end of lemma zenon_L3_ *)
% 0.48/0.73 assert (zenon_L4_ : forall (zenon_TV_u : zenon_U) (zenon_TU_v : zenon_U), ((distinct_points zenon_TU_v zenon_TU_v)/\(distinct_points zenon_TU_v zenon_TV_u)) -> (~(distinct_points zenon_TU_v zenon_TU_v)) -> False).
% 0.48/0.73 do 2 intro. intros zenon_H2b zenon_H2c.
% 0.48/0.73 apply (zenon_and_s _ _ zenon_H2b). zenon_intro zenon_H2e. zenon_intro zenon_H2d.
% 0.48/0.73 exact (zenon_H2c zenon_H2e).
% 0.48/0.73 (* end of lemma zenon_L4_ *)
% 0.48/0.73 assert (zenon_L5_ : forall (zenon_TU_v : zenon_U) (zenon_TV_u : zenon_U), ((distinct_points zenon_TV_u zenon_TU_v)/\(distinct_points zenon_TV_u zenon_TV_u)) -> (~(distinct_points zenon_TV_u zenon_TV_u)) -> False).
% 0.48/0.73 do 2 intro. intros zenon_H2f zenon_H30.
% 0.48/0.73 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H32. zenon_intro zenon_H31.
% 0.48/0.73 exact (zenon_H30 zenon_H31).
% 0.48/0.73 (* end of lemma zenon_L5_ *)
% 0.48/0.73 apply NNPP. intro zenon_G.
% 0.48/0.73 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_H33; idtac ].
% 0.48/0.73 elim zenon_H33. zenon_intro zenon_TX_x. zenon_intro zenon_H34.
% 0.48/0.73 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_x Y)/\((distinct_points U V)/\((~(apart_point_and_line zenon_TX_x (line_connecting U V)))/\(~(apart_point_and_line Y (line_connecting U V))))))->((~(apart_point_and_line U (line_connecting zenon_TX_x Y)))/\(~(apart_point_and_line V (line_connecting zenon_TX_x Y)))))))) zenon_H34); [ zenon_intro zenon_H35; idtac ].
% 0.48/0.73 elim zenon_H35. zenon_intro zenon_TY_w. zenon_intro zenon_H36.
% 0.48/0.73 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_x zenon_TY_w)/\((distinct_points U V)/\((~(apart_point_and_line zenon_TX_x (line_connecting U V)))/\(~(apart_point_and_line zenon_TY_w (line_connecting U V))))))->((~(apart_point_and_line U (line_connecting zenon_TX_x zenon_TY_w)))/\(~(apart_point_and_line V (line_connecting zenon_TX_x zenon_TY_w))))))) zenon_H36); [ zenon_intro zenon_H37; idtac ].
% 0.48/0.73 elim zenon_H37. zenon_intro zenon_TU_v. zenon_intro zenon_H38.
% 0.48/0.73 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_x zenon_TY_w)/\((distinct_points zenon_TU_v V)/\((~(apart_point_and_line zenon_TX_x (line_connecting zenon_TU_v V)))/\(~(apart_point_and_line zenon_TY_w (line_connecting zenon_TU_v V))))))->((~(apart_point_and_line zenon_TU_v (line_connecting zenon_TX_x zenon_TY_w)))/\(~(apart_point_and_line V (line_connecting zenon_TX_x zenon_TY_w)))))) zenon_H38); [ zenon_intro zenon_H39; idtac ].
% 0.48/0.73 elim zenon_H39. zenon_intro zenon_TV_u. zenon_intro zenon_H3a.
% 0.48/0.73 apply (zenon_notimply_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b.
% 0.48/0.73 apply (zenon_and_s _ _ zenon_H3c). zenon_intro zenon_H13. zenon_intro zenon_H3d.
% 0.48/0.73 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H2d. zenon_intro zenon_H3e.
% 0.48/0.73 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H10. zenon_intro zenon_He.
% 0.48/0.73 apply (zenon_notand_s _ _ zenon_H3b); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ].
% 0.48/0.73 apply zenon_H40. zenon_intro zenon_H41.
% 0.48/0.73 generalize (apart1 zenon_TY_w). zenon_intro zenon_H28.
% 0.48/0.73 generalize (cu1 zenon_TX_x). zenon_intro zenon_H42.
% 0.48/0.73 generalize (con1 zenon_TU_v). zenon_intro zenon_H43.
% 0.48/0.73 generalize (con1 zenon_TX_x). zenon_intro zenon_H44.
% 0.48/0.73 generalize (zenon_H42 zenon_TY_w). zenon_intro zenon_Hd.
% 0.48/0.73 generalize (zenon_H43 zenon_TV_u). zenon_intro zenon_H45.
% 0.48/0.73 generalize (zenon_H44 zenon_TY_w). zenon_intro zenon_H46.
% 0.48/0.73 generalize (apart1 zenon_TU_v). zenon_intro zenon_H2c.
% 0.48/0.73 generalize (apart1 zenon_TX_x). zenon_intro zenon_H25.
% 0.48/0.73 generalize (ceq2 zenon_TU_v). zenon_intro zenon_H47.
% 0.48/0.73 generalize (zenon_H45 zenon_TU_v). zenon_intro zenon_H48.
% 0.48/0.73 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ].
% 0.48/0.73 exact (zenon_H4a zenon_H2d).
% 0.48/0.73 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4b | zenon_intro zenon_H2b ].
% 0.48/0.73 generalize (zenon_H46 zenon_TY_w). zenon_intro zenon_H4c.
% 0.48/0.73 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H1d | zenon_intro zenon_H4d ].
% 0.48/0.73 exact (zenon_H1d zenon_H13).
% 0.48/0.73 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_Hf | zenon_intro zenon_H27 ].
% 0.48/0.73 generalize (zenon_H46 zenon_TX_x). zenon_intro zenon_H4e.
% 0.48/0.73 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H1d | zenon_intro zenon_H4f ].
% 0.48/0.73 exact (zenon_H1d zenon_H13).
% 0.48/0.73 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H11 | zenon_intro zenon_H24 ].
% 0.48/0.73 generalize (zenon_H47 (line_connecting zenon_TX_x zenon_TY_w)). zenon_intro zenon_H50.
% 0.48/0.73 generalize (zenon_H50 (line_connecting zenon_TU_v zenon_TV_u)). zenon_intro zenon_H51.
% 0.48/0.73 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ].
% 0.48/0.73 exact (zenon_H53 zenon_H41).
% 0.48/0.73 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H12 | zenon_intro zenon_H54 ].
% 0.48/0.73 apply (zenon_L1_ zenon_TV_u zenon_TU_v zenon_TY_w zenon_TX_x); trivial.
% 0.48/0.73 exact (zenon_H4b zenon_H54).
% 0.48/0.73 apply (zenon_L2_ zenon_TY_w zenon_TX_x); trivial.
% 0.48/0.73 apply (zenon_L3_ zenon_TX_x zenon_TY_w); trivial.
% 0.48/0.73 apply (zenon_L4_ zenon_TV_u zenon_TU_v); trivial.
% 0.48/0.73 apply zenon_H3f. zenon_intro zenon_H55.
% 0.48/0.73 generalize (apart1 zenon_TV_u). zenon_intro zenon_H30.
% 0.48/0.73 generalize (apart1 zenon_TY_w). zenon_intro zenon_H28.
% 0.48/0.73 generalize (cu1 zenon_TX_x). zenon_intro zenon_H42.
% 0.48/0.73 generalize (con1 zenon_TU_v). zenon_intro zenon_H43.
% 0.48/0.73 generalize (con1 zenon_TX_x). zenon_intro zenon_H44.
% 0.48/0.73 generalize (zenon_H42 zenon_TY_w). zenon_intro zenon_Hd.
% 0.48/0.73 generalize (zenon_H43 zenon_TV_u). zenon_intro zenon_H45.
% 0.48/0.73 generalize (zenon_H45 zenon_TV_u). zenon_intro zenon_H56.
% 0.48/0.73 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H4a | zenon_intro zenon_H57 ].
% 0.48/0.73 exact (zenon_H4a zenon_H2d).
% 0.48/0.73 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H58 | zenon_intro zenon_H2f ].
% 0.48/0.73 generalize (zenon_H44 zenon_TY_w). zenon_intro zenon_H46.
% 0.48/0.73 generalize (apart1 zenon_TX_x). zenon_intro zenon_H25.
% 0.48/0.73 generalize (ceq2 zenon_TV_u). zenon_intro zenon_H59.
% 0.48/0.73 generalize (zenon_H46 zenon_TY_w). zenon_intro zenon_H4c.
% 0.48/0.73 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H1d | zenon_intro zenon_H4d ].
% 0.48/0.73 exact (zenon_H1d zenon_H13).
% 0.48/0.73 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_Hf | zenon_intro zenon_H27 ].
% 0.48/0.73 generalize (zenon_H46 zenon_TX_x). zenon_intro zenon_H4e.
% 0.48/0.73 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H1d | zenon_intro zenon_H4f ].
% 0.48/0.73 exact (zenon_H1d zenon_H13).
% 0.48/0.73 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H11 | zenon_intro zenon_H24 ].
% 0.48/0.73 generalize (zenon_H59 (line_connecting zenon_TX_x zenon_TY_w)). zenon_intro zenon_H5a.
% 0.48/0.73 generalize (zenon_H5a (line_connecting zenon_TU_v zenon_TV_u)). zenon_intro zenon_H5b.
% 0.48/0.73 apply (zenon_imply_s _ _ zenon_H5b); [ zenon_intro zenon_H5d | zenon_intro zenon_H5c ].
% 0.48/0.73 exact (zenon_H5d zenon_H55).
% 0.48/0.73 apply (zenon_or_s _ _ zenon_H5c); [ zenon_intro zenon_H12 | zenon_intro zenon_H5e ].
% 0.48/0.73 apply (zenon_L1_ zenon_TV_u zenon_TU_v zenon_TY_w zenon_TX_x); trivial.
% 0.48/0.73 exact (zenon_H58 zenon_H5e).
% 0.48/0.73 apply (zenon_L2_ zenon_TY_w zenon_TX_x); trivial.
% 0.48/0.73 apply (zenon_L3_ zenon_TX_x zenon_TY_w); trivial.
% 0.48/0.73 apply (zenon_L5_ zenon_TU_v zenon_TV_u); trivial.
% 0.48/0.73 Qed.
% 0.48/0.73 % SZS output end Proof
% 0.48/0.73 (* END-PROOF *)
% 0.48/0.73 nodes searched: 13014
% 0.48/0.73 max branch formulas: 1682
% 0.48/0.73 proof nodes created: 1239
% 0.48/0.73 formulas created: 25564
% 0.48/0.73
%------------------------------------------------------------------------------