TSTP Solution File: GEO204+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO204+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n025.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 07:00:47 EDT 2022
% Result : Theorem 0.37s 0.54s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO204+2 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n025.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 05:39:43 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.37/0.54 (* PROOF-FOUND *)
% 0.37/0.54 % SZS status Theorem
% 0.37/0.54 (* BEGIN-PROOF *)
% 0.37/0.54 % SZS output start Proof
% 0.37/0.54 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\(~(distinct_points Y Z)))->((distinct_points X Z)/\(~(distinct_lines (line_connecting X Y) (line_connecting X Z)))))))).
% 0.37/0.54 Proof.
% 0.37/0.54 assert (zenon_L1_ : forall (zenon_TZ_r : zenon_U) (zenon_TY_s : zenon_U) (zenon_TX_t : zenon_U), (forall Z : zenon_U, ((distinct_points zenon_TX_t zenon_TY_s)->((distinct_points zenon_TX_t Z)\/(distinct_points zenon_TY_s Z)))) -> (distinct_points zenon_TX_t zenon_TY_s) -> (~(distinct_points zenon_TX_t zenon_TZ_r)) -> (~(distinct_points zenon_TY_s zenon_TZ_r)) -> False).
% 0.37/0.54 do 3 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10.
% 0.37/0.54 generalize (zenon_Hd zenon_TZ_r). zenon_intro zenon_H14.
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ].
% 0.37/0.54 exact (zenon_H16 zenon_He).
% 0.37/0.54 apply (zenon_or_s _ _ zenon_H15); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ].
% 0.37/0.54 exact (zenon_Hf zenon_H18).
% 0.37/0.54 exact (zenon_H10 zenon_H17).
% 0.37/0.54 (* end of lemma zenon_L1_ *)
% 0.37/0.54 apply NNPP. intro zenon_G.
% 0.37/0.54 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\(~(distinct_points Y Z)))->((distinct_points X Z)/\(~(distinct_lines (line_connecting X Y) (line_connecting X Z)))))))) zenon_G); [ zenon_intro zenon_H19; idtac ].
% 0.37/0.54 elim zenon_H19. zenon_intro zenon_TX_t. zenon_intro zenon_H1a.
% 0.37/0.54 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((distinct_points zenon_TX_t Y)/\(~(distinct_points Y Z)))->((distinct_points zenon_TX_t Z)/\(~(distinct_lines (line_connecting zenon_TX_t Y) (line_connecting zenon_TX_t Z))))))) zenon_H1a); [ zenon_intro zenon_H1b; idtac ].
% 0.37/0.54 elim zenon_H1b. zenon_intro zenon_TY_s. zenon_intro zenon_H1c.
% 0.37/0.54 apply (zenon_notallex_s (fun Z : zenon_U => (((distinct_points zenon_TX_t zenon_TY_s)/\(~(distinct_points zenon_TY_s Z)))->((distinct_points zenon_TX_t Z)/\(~(distinct_lines (line_connecting zenon_TX_t zenon_TY_s) (line_connecting zenon_TX_t Z)))))) zenon_H1c); [ zenon_intro zenon_H1d; idtac ].
% 0.37/0.54 elim zenon_H1d. zenon_intro zenon_TZ_r. zenon_intro zenon_H1e.
% 0.37/0.54 apply (zenon_notimply_s _ _ zenon_H1e). zenon_intro zenon_H20. zenon_intro zenon_H1f.
% 0.37/0.54 apply (zenon_and_s _ _ zenon_H20). zenon_intro zenon_He. zenon_intro zenon_H10.
% 0.37/0.54 apply (zenon_notand_s _ _ zenon_H1f); [ zenon_intro zenon_Hf | zenon_intro zenon_H21 ].
% 0.37/0.54 generalize (apart4 zenon_TX_t). zenon_intro zenon_H22.
% 0.37/0.54 generalize (zenon_H22 zenon_TY_s). zenon_intro zenon_Hd.
% 0.37/0.54 apply (zenon_L1_ zenon_TZ_r zenon_TY_s zenon_TX_t); trivial.
% 0.37/0.54 apply zenon_H21. zenon_intro zenon_H23.
% 0.37/0.54 generalize (apart1 zenon_TY_s). zenon_intro zenon_H24.
% 0.37/0.54 generalize (cu1 zenon_TX_t). zenon_intro zenon_H25.
% 0.37/0.54 generalize (apart4 zenon_TX_t). zenon_intro zenon_H22.
% 0.37/0.54 generalize (apart1 zenon_TZ_r). zenon_intro zenon_H26.
% 0.37/0.54 generalize (zenon_H25 zenon_TY_s). zenon_intro zenon_H27.
% 0.37/0.54 generalize (zenon_H22 zenon_TZ_r). zenon_intro zenon_H28.
% 0.37/0.54 generalize (zenon_H22 zenon_TY_s). zenon_intro zenon_Hd.
% 0.37/0.54 generalize (zenon_H28 zenon_TZ_r). zenon_intro zenon_H29.
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_Hf | zenon_intro zenon_H2a ].
% 0.37/0.54 apply (zenon_L1_ zenon_TZ_r zenon_TY_s zenon_TX_t); trivial.
% 0.37/0.54 apply (zenon_or_s _ _ zenon_H2a); [ zenon_intro zenon_H18 | zenon_intro zenon_H2b ].
% 0.37/0.54 generalize (con1 zenon_TX_t). zenon_intro zenon_H2c.
% 0.37/0.54 generalize (apart1 zenon_TX_t). zenon_intro zenon_H2d.
% 0.37/0.54 generalize (zenon_H2c zenon_TY_s). zenon_intro zenon_H2e.
% 0.37/0.54 generalize (zenon_H2c zenon_TZ_r). zenon_intro zenon_H2f.
% 0.37/0.54 generalize (zenon_H2e zenon_TX_t). zenon_intro zenon_H30.
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H16 | zenon_intro zenon_H31 ].
% 0.37/0.54 exact (zenon_H16 zenon_He).
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 0.37/0.54 generalize (zenon_H2e zenon_TY_s). zenon_intro zenon_H34.
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H16 | zenon_intro zenon_H35 ].
% 0.37/0.54 exact (zenon_H16 zenon_He).
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ].
% 0.37/0.54 generalize (zenon_H2f zenon_TY_s). zenon_intro zenon_H38.
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_Hf | zenon_intro zenon_H39 ].
% 0.37/0.54 exact (zenon_Hf zenon_H18).
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ].
% 0.37/0.54 generalize (zenon_H2f zenon_TX_t). zenon_intro zenon_H3c.
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_Hf | zenon_intro zenon_H3d ].
% 0.37/0.54 exact (zenon_Hf zenon_H18).
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ].
% 0.37/0.54 generalize (zenon_H27 (line_connecting zenon_TX_t zenon_TY_s)). zenon_intro zenon_H40.
% 0.37/0.54 generalize (zenon_H40 (line_connecting zenon_TX_t zenon_TZ_r)). zenon_intro zenon_H41.
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ].
% 0.37/0.54 apply (zenon_notand_s _ _ zenon_H43); [ zenon_intro zenon_H16 | zenon_intro zenon_H44 ].
% 0.37/0.54 exact (zenon_H16 zenon_He).
% 0.37/0.54 exact (zenon_H44 zenon_H23).
% 0.37/0.54 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ].
% 0.37/0.54 exact (zenon_H33 zenon_H46).
% 0.37/0.54 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ].
% 0.37/0.54 exact (zenon_H3f zenon_H48).
% 0.37/0.54 apply (zenon_or_s _ _ zenon_H47); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ].
% 0.37/0.54 exact (zenon_H37 zenon_H4a).
% 0.37/0.54 exact (zenon_H3b zenon_H49).
% 0.37/0.54 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H4b. zenon_intro zenon_H18.
% 0.37/0.54 exact (zenon_H2d zenon_H4b).
% 0.37/0.54 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H4c. zenon_intro zenon_H17.
% 0.37/0.54 exact (zenon_H10 zenon_H17).
% 0.37/0.54 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H4c. zenon_intro zenon_H4d.
% 0.37/0.54 exact (zenon_H24 zenon_H4d).
% 0.37/0.54 apply (zenon_and_s _ _ zenon_H32). zenon_intro zenon_H4b. zenon_intro zenon_He.
% 0.37/0.54 exact (zenon_H2d zenon_H4b).
% 0.37/0.54 exact (zenon_H26 zenon_H2b).
% 0.37/0.54 Qed.
% 0.37/0.54 % SZS output end Proof
% 0.37/0.54 (* END-PROOF *)
% 0.37/0.54 nodes searched: 1562
% 0.37/0.54 max branch formulas: 497
% 0.37/0.54 proof nodes created: 216
% 0.37/0.54 formulas created: 4826
% 0.37/0.54
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