TSTP Solution File: GEO170+1 by Zenon---0.7.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO170+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n013.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 07:00:20 EDT 2022
% Result : Theorem 0.20s 0.50s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO170+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n013.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 08:11:29 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.50 (* PROOF-FOUND *)
% 0.20/0.50 % SZS status Theorem
% 0.20/0.50 (* BEGIN-PROOF *)
% 0.20/0.50 % SZS output start Proof
% 0.20/0.50 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((~(apart_point_and_line X Z))/\(~(apart_point_and_line Y Z))))->(~(distinct_lines Z (line_connecting X Y))))))).
% 0.20/0.50 Proof.
% 0.20/0.50 assert (zenon_L1_ : forall (zenon_TX_r : zenon_U) (zenon_TY_s : zenon_U), (apart_point_and_line zenon_TY_s (line_connecting zenon_TX_r zenon_TY_s)) -> (distinct_points zenon_TX_r zenon_TY_s) -> False).
% 0.20/0.50 do 2 intro. intros zenon_Hf zenon_H10.
% 0.20/0.50 generalize (ci2 zenon_TX_r). zenon_intro zenon_H13.
% 0.20/0.50 generalize (zenon_H13 zenon_TY_s). zenon_intro zenon_H14.
% 0.20/0.50 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ].
% 0.20/0.50 exact (zenon_H16 zenon_H10).
% 0.20/0.50 exact (zenon_H15 zenon_Hf).
% 0.20/0.50 (* end of lemma zenon_L1_ *)
% 0.20/0.50 apply NNPP. intro zenon_G.
% 0.20/0.50 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((~(apart_point_and_line X Z))/\(~(apart_point_and_line Y Z))))->(~(distinct_lines Z (line_connecting X Y))))))) zenon_G); [ zenon_intro zenon_H17; idtac ].
% 0.20/0.50 elim zenon_H17. zenon_intro zenon_TX_r. zenon_intro zenon_H18.
% 0.20/0.50 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((distinct_points zenon_TX_r Y)/\((~(apart_point_and_line zenon_TX_r Z))/\(~(apart_point_and_line Y Z))))->(~(distinct_lines Z (line_connecting zenon_TX_r Y)))))) zenon_H18); [ zenon_intro zenon_H19; idtac ].
% 0.20/0.50 elim zenon_H19. zenon_intro zenon_TY_s. zenon_intro zenon_H1a.
% 0.20/0.50 apply (zenon_notallex_s (fun Z : zenon_U => (((distinct_points zenon_TX_r zenon_TY_s)/\((~(apart_point_and_line zenon_TX_r Z))/\(~(apart_point_and_line zenon_TY_s Z))))->(~(distinct_lines Z (line_connecting zenon_TX_r zenon_TY_s))))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ].
% 0.20/0.50 elim zenon_H1b. zenon_intro zenon_TZ_bc. zenon_intro zenon_H1d.
% 0.20/0.50 apply (zenon_notimply_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e.
% 0.20/0.50 apply zenon_H1e. zenon_intro zenon_H20.
% 0.20/0.50 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_H10. zenon_intro zenon_H21.
% 0.20/0.50 apply (zenon_and_s _ _ zenon_H21). zenon_intro zenon_H23. zenon_intro zenon_H22.
% 0.20/0.50 generalize (cu1 zenon_TX_r). zenon_intro zenon_H24.
% 0.20/0.50 generalize (zenon_H24 zenon_TY_s). zenon_intro zenon_H25.
% 0.20/0.50 generalize (zenon_H25 zenon_TZ_bc). zenon_intro zenon_H26.
% 0.20/0.50 generalize (zenon_H26 (line_connecting zenon_TX_r zenon_TY_s)). zenon_intro zenon_H27.
% 0.20/0.50 apply (zenon_imply_s _ _ zenon_H27); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 0.20/0.50 apply (zenon_notand_s _ _ zenon_H29); [ zenon_intro zenon_H16 | zenon_intro zenon_H2a ].
% 0.20/0.50 exact (zenon_H16 zenon_H10).
% 0.20/0.50 exact (zenon_H2a zenon_H20).
% 0.20/0.50 apply (zenon_or_s _ _ zenon_H28); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ].
% 0.20/0.50 exact (zenon_H23 zenon_H2c).
% 0.20/0.50 apply (zenon_or_s _ _ zenon_H2b); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ].
% 0.20/0.50 generalize (ci1 zenon_TX_r). zenon_intro zenon_H2f.
% 0.20/0.50 generalize (zenon_H2f zenon_TY_s). zenon_intro zenon_H30.
% 0.20/0.50 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H16 | zenon_intro zenon_H31 ].
% 0.20/0.50 exact (zenon_H16 zenon_H10).
% 0.20/0.50 exact (zenon_H31 zenon_H2e).
% 0.20/0.50 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H32 | zenon_intro zenon_Hf ].
% 0.20/0.50 exact (zenon_H22 zenon_H32).
% 0.20/0.50 apply (zenon_L1_ zenon_TX_r zenon_TY_s); trivial.
% 0.20/0.50 Qed.
% 0.20/0.50 % SZS output end Proof
% 0.20/0.50 (* END-PROOF *)
% 0.20/0.50 nodes searched: 184
% 0.20/0.50 max branch formulas: 151
% 0.20/0.50 proof nodes created: 30
% 0.20/0.50 formulas created: 1123
% 0.20/0.50
%------------------------------------------------------------------------------