TSTP Solution File: GEO181+1 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO181+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n004.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 0.19s 0.53s
% Output : Proof 0.19s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO181+1 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n004.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 12:37:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.53 (* PROOF-FOUND *)
% 0.19/0.53 % SZS status Theorem
% 0.19/0.53 (* BEGIN-PROOF *)
% 0.19/0.53 % SZS output start Proof
% 0.19/0.53 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))))))).
% 0.19/0.53 Proof.
% 0.19/0.53 assert (zenon_L1_ : forall (zenon_TX_s : zenon_U) (zenon_TZ_t : zenon_U), (forall Z : zenon_U, ((distinct_points zenon_TZ_t zenon_TX_s)->((distinct_points zenon_TZ_t Z)\/(distinct_points zenon_TX_s Z)))) -> (distinct_points zenon_TZ_t zenon_TX_s) -> (~(distinct_points zenon_TX_s zenon_TZ_t)) -> False).
% 0.19/0.53 do 2 intro. intros zenon_Hf zenon_H10 zenon_H11.
% 0.19/0.53 generalize (zenon_Hf zenon_TZ_t). zenon_intro zenon_H14.
% 0.19/0.53 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ].
% 0.19/0.53 exact (zenon_H16 zenon_H10).
% 0.19/0.53 apply (zenon_or_s _ _ zenon_H15); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ].
% 0.19/0.53 generalize (apart1 zenon_TZ_t). zenon_intro zenon_H19.
% 0.19/0.53 exact (zenon_H19 zenon_H18).
% 0.19/0.53 exact (zenon_H11 zenon_H17).
% 0.19/0.53 (* end of lemma zenon_L1_ *)
% 0.19/0.53 assert (zenon_L2_ : forall (zenon_TY_bj : zenon_U) (zenon_TX_s : zenon_U) (zenon_TZ_t : zenon_U), (forall Z : zenon_U, ((apart_point_and_line zenon_TZ_t (line_connecting zenon_TX_s zenon_TY_bj))->((distinct_lines (line_connecting zenon_TX_s zenon_TY_bj) Z)\/(apart_point_and_line zenon_TZ_t Z)))) -> (apart_point_and_line zenon_TZ_t (line_connecting zenon_TX_s zenon_TY_bj)) -> (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_s zenon_TY_bj)/\(distinct_lines U V))->((apart_point_and_line zenon_TX_s U)\/((apart_point_and_line zenon_TX_s V)\/((apart_point_and_line zenon_TY_bj U)\/(apart_point_and_line zenon_TY_bj V))))))) -> (~(apart_point_and_line zenon_TY_bj (line_connecting zenon_TX_s zenon_TZ_t))) -> (~(apart_point_and_line zenon_TY_bj (line_connecting zenon_TX_s zenon_TY_bj))) -> (~(apart_point_and_line zenon_TX_s (line_connecting zenon_TX_s zenon_TZ_t))) -> (~(apart_point_and_line zenon_TX_s (line_connecting zenon_TX_s zenon_TY_bj))) -> (distinct_points zenon_TX_s zenon_TY_bj) -> (~(apart_point_and_line zenon_TZ_t (line_connecting zenon_TX_s zenon_TZ_t))) -> False).
% 0.19/0.53 do 3 intro. intros zenon_H1a zenon_H1b zenon_H1c zenon_H1d zenon_H1e zenon_H1f zenon_H20 zenon_H21 zenon_H22.
% 0.19/0.53 generalize (zenon_H1a (line_connecting zenon_TX_s zenon_TZ_t)). zenon_intro zenon_H24.
% 0.19/0.53 apply (zenon_imply_s _ _ zenon_H24); [ zenon_intro zenon_H26 | zenon_intro zenon_H25 ].
% 0.19/0.53 exact (zenon_H26 zenon_H1b).
% 0.19/0.53 apply (zenon_or_s _ _ zenon_H25); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ].
% 0.19/0.53 generalize (zenon_H1c (line_connecting zenon_TX_s zenon_TY_bj)). zenon_intro zenon_H29.
% 0.19/0.53 generalize (zenon_H29 (line_connecting zenon_TX_s zenon_TZ_t)). zenon_intro zenon_H2a.
% 0.19/0.53 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ].
% 0.19/0.53 apply (zenon_notand_s _ _ zenon_H2c); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ].
% 0.19/0.53 exact (zenon_H2e zenon_H21).
% 0.19/0.53 exact (zenon_H2d zenon_H28).
% 0.19/0.53 apply (zenon_or_s _ _ zenon_H2b); [ zenon_intro zenon_H30 | zenon_intro zenon_H2f ].
% 0.19/0.53 exact (zenon_H20 zenon_H30).
% 0.19/0.53 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ].
% 0.19/0.53 exact (zenon_H1f zenon_H32).
% 0.19/0.53 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 0.19/0.53 exact (zenon_H1e zenon_H34).
% 0.19/0.53 exact (zenon_H1d zenon_H33).
% 0.19/0.53 exact (zenon_H22 zenon_H27).
% 0.19/0.53 (* end of lemma zenon_L2_ *)
% 0.19/0.53 apply NNPP. intro zenon_G.
% 0.19/0.53 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_H35; idtac ].
% 0.19/0.53 elim zenon_H35. zenon_intro zenon_TX_s. zenon_intro zenon_H36.
% 0.19/0.53 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, ((distinct_points zenon_TX_s Y)->((apart_point_and_line Z (line_connecting zenon_TX_s Y))->(apart_point_and_line Y (line_connecting zenon_TX_s Z)))))) zenon_H36); [ zenon_intro zenon_H37; idtac ].
% 0.19/0.53 elim zenon_H37. zenon_intro zenon_TY_bj. zenon_intro zenon_H38.
% 0.19/0.53 apply (zenon_notallex_s (fun Z : zenon_U => ((distinct_points zenon_TX_s zenon_TY_bj)->((apart_point_and_line Z (line_connecting zenon_TX_s zenon_TY_bj))->(apart_point_and_line zenon_TY_bj (line_connecting zenon_TX_s Z))))) zenon_H38); [ zenon_intro zenon_H39; idtac ].
% 0.19/0.53 elim zenon_H39. zenon_intro zenon_TZ_t. zenon_intro zenon_H3a.
% 0.19/0.53 apply (zenon_notimply_s _ _ zenon_H3a). zenon_intro zenon_H21. zenon_intro zenon_H3b.
% 0.19/0.53 apply (zenon_notimply_s _ _ zenon_H3b). zenon_intro zenon_H1b. zenon_intro zenon_H1d.
% 0.19/0.53 generalize (ci1 zenon_TX_s). zenon_intro zenon_H3c.
% 0.19/0.53 generalize (cu1 zenon_TX_s). zenon_intro zenon_H3d.
% 0.19/0.53 generalize (zenon_H3d zenon_TY_bj). zenon_intro zenon_H1c.
% 0.19/0.53 generalize (ceq2 zenon_TZ_t). zenon_intro zenon_H3e.
% 0.19/0.53 generalize (ci2 zenon_TX_s). zenon_intro zenon_H3f.
% 0.19/0.53 generalize (zenon_H3c zenon_TY_bj). zenon_intro zenon_H40.
% 0.19/0.53 apply (zenon_imply_s _ _ zenon_H40); [ zenon_intro zenon_H2e | zenon_intro zenon_H20 ].
% 0.19/0.53 exact (zenon_H2e zenon_H21).
% 0.19/0.53 generalize (zenon_H3f zenon_TY_bj). zenon_intro zenon_H41.
% 0.19/0.53 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H2e | zenon_intro zenon_H1e ].
% 0.19/0.53 exact (zenon_H2e zenon_H21).
% 0.19/0.53 generalize (apart1 zenon_TX_s). zenon_intro zenon_H42.
% 0.19/0.53 generalize (zenon_H3e (line_connecting zenon_TX_s zenon_TY_bj)). zenon_intro zenon_H1a.
% 0.19/0.53 generalize (apart4 zenon_TZ_t). zenon_intro zenon_H43.
% 0.19/0.53 generalize (zenon_H43 zenon_TX_s). zenon_intro zenon_Hf.
% 0.19/0.53 generalize (zenon_Hf zenon_TX_s). zenon_intro zenon_H44.
% 0.19/0.53 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H16 | zenon_intro zenon_H45 ].
% 0.19/0.53 generalize (ceq1 zenon_TZ_t). zenon_intro zenon_H46.
% 0.19/0.53 generalize (zenon_H46 (line_connecting zenon_TX_s zenon_TY_bj)). zenon_intro zenon_H47.
% 0.19/0.53 generalize (zenon_H47 zenon_TX_s). zenon_intro zenon_H48.
% 0.19/0.53 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H26 | zenon_intro zenon_H49 ].
% 0.19/0.53 exact (zenon_H26 zenon_H1b).
% 0.19/0.53 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H10 | zenon_intro zenon_H30 ].
% 0.19/0.53 exact (zenon_H16 zenon_H10).
% 0.19/0.53 exact (zenon_H20 zenon_H30).
% 0.19/0.53 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H10 | zenon_intro zenon_H4a ].
% 0.19/0.53 generalize (zenon_H3f zenon_TZ_t). zenon_intro zenon_H4b.
% 0.19/0.53 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H11 | zenon_intro zenon_H22 ].
% 0.19/0.53 apply (zenon_L1_ zenon_TX_s zenon_TZ_t); trivial.
% 0.19/0.53 generalize (zenon_H3c zenon_TZ_t). zenon_intro zenon_H4c.
% 0.19/0.53 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H11 | zenon_intro zenon_H1f ].
% 0.19/0.53 apply (zenon_L1_ zenon_TX_s zenon_TZ_t); trivial.
% 0.19/0.53 apply (zenon_L2_ zenon_TY_bj zenon_TX_s zenon_TZ_t); trivial.
% 0.19/0.53 exact (zenon_H42 zenon_H4a).
% 0.19/0.53 Qed.
% 0.19/0.53 % SZS output end Proof
% 0.19/0.53 (* END-PROOF *)
% 0.19/0.53 nodes searched: 1277
% 0.19/0.53 max branch formulas: 550
% 0.19/0.53 proof nodes created: 169
% 0.19/0.53 formulas created: 4901
% 0.19/0.53
%------------------------------------------------------------------------------