TSTP Solution File: GEO203+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO203+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n010.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 07:00:46 EDT 2022
% Result : Theorem 1.62s 1.80s
% Output : Proof 1.62s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO203+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n010.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 : Fri Jun 17 15:26:08 EDT 2022
% 0.12/0.33 % CPUTime :
% 1.62/1.80 (* PROOF-FOUND *)
% 1.62/1.80 % SZS status Theorem
% 1.62/1.80 (* BEGIN-PROOF *)
% 1.62/1.80 % SZS output start Proof
% 1.62/1.80 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines X Z)/\(distinct_points (intersection_point X Y) (intersection_point X Z))))->(~(distinct_lines (line_connecting (intersection_point X Y) (intersection_point X Z)) X)))))).
% 1.62/1.80 Proof.
% 1.62/1.80 assert (zenon_L1_ : forall (zenon_TY_p : zenon_U) (zenon_TZ_q : zenon_U) (zenon_TX_r : zenon_U), ((distinct_points (intersection_point zenon_TX_r zenon_TZ_q) (intersection_point zenon_TX_r zenon_TY_p))/\(distinct_points (intersection_point zenon_TX_r zenon_TZ_q) (intersection_point zenon_TX_r zenon_TZ_q))) -> (~(distinct_points (intersection_point zenon_TX_r zenon_TZ_q) (intersection_point zenon_TX_r zenon_TZ_q))) -> False).
% 1.62/1.80 do 3 intro. intros zenon_Hd zenon_He.
% 1.62/1.80 apply (zenon_and_s _ _ zenon_Hd). zenon_intro zenon_H13. zenon_intro zenon_H12.
% 1.62/1.80 exact (zenon_He zenon_H12).
% 1.62/1.80 (* end of lemma zenon_L1_ *)
% 1.62/1.80 assert (zenon_L2_ : forall (zenon_TZ_q : zenon_U) (zenon_TY_p : zenon_U) (zenon_TX_r : zenon_U), ((distinct_points (intersection_point zenon_TX_r zenon_TY_p) (intersection_point zenon_TX_r zenon_TY_p))/\(distinct_points (intersection_point zenon_TX_r zenon_TY_p) (intersection_point zenon_TX_r zenon_TZ_q))) -> (~(distinct_points (intersection_point zenon_TX_r zenon_TY_p) (intersection_point zenon_TX_r zenon_TY_p))) -> False).
% 1.62/1.80 do 3 intro. intros zenon_H14 zenon_H15.
% 1.62/1.80 apply (zenon_and_s _ _ zenon_H14). zenon_intro zenon_H17. zenon_intro zenon_H16.
% 1.62/1.80 exact (zenon_H15 zenon_H17).
% 1.62/1.80 (* end of lemma zenon_L2_ *)
% 1.62/1.80 apply NNPP. intro zenon_G.
% 1.62/1.80 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines X Z)/\(distinct_points (intersection_point X Y) (intersection_point X Z))))->(~(distinct_lines (line_connecting (intersection_point X Y) (intersection_point X Z)) X)))))) zenon_G); [ zenon_intro zenon_H18; idtac ].
% 1.62/1.80 elim zenon_H18. zenon_intro zenon_TX_r. zenon_intro zenon_H19.
% 1.62/1.80 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_r Y)/\((convergent_lines zenon_TX_r Z)/\(distinct_points (intersection_point zenon_TX_r Y) (intersection_point zenon_TX_r Z))))->(~(distinct_lines (line_connecting (intersection_point zenon_TX_r Y) (intersection_point zenon_TX_r Z)) zenon_TX_r))))) zenon_H19); [ zenon_intro zenon_H1a; idtac ].
% 1.62/1.80 elim zenon_H1a. zenon_intro zenon_TY_p. zenon_intro zenon_H1b.
% 1.62/1.80 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_r zenon_TY_p)/\((convergent_lines zenon_TX_r Z)/\(distinct_points (intersection_point zenon_TX_r zenon_TY_p) (intersection_point zenon_TX_r Z))))->(~(distinct_lines (line_connecting (intersection_point zenon_TX_r zenon_TY_p) (intersection_point zenon_TX_r Z)) zenon_TX_r)))) zenon_H1b); [ zenon_intro zenon_H1c; idtac ].
% 1.62/1.80 elim zenon_H1c. zenon_intro zenon_TZ_q. zenon_intro zenon_H1d.
% 1.62/1.80 apply (zenon_notimply_s _ _ zenon_H1d). zenon_intro zenon_H1f. zenon_intro zenon_H1e.
% 1.62/1.80 apply zenon_H1e. zenon_intro zenon_H20.
% 1.62/1.80 apply (zenon_and_s _ _ zenon_H1f). zenon_intro zenon_H22. zenon_intro zenon_H21.
% 1.62/1.80 apply (zenon_and_s _ _ zenon_H21). zenon_intro zenon_H23. zenon_intro zenon_H16.
% 1.62/1.80 generalize (con2 zenon_TX_r). zenon_intro zenon_H24.
% 1.62/1.80 generalize (zenon_H24 zenon_TZ_q). zenon_intro zenon_H25.
% 1.62/1.80 generalize (cu1 (intersection_point zenon_TX_r zenon_TY_p)). zenon_intro zenon_H26.
% 1.62/1.80 generalize (zenon_H26 (intersection_point zenon_TX_r zenon_TZ_q)). zenon_intro zenon_H27.
% 1.62/1.80 generalize (apart1 (intersection_point zenon_TX_r zenon_TZ_q)). zenon_intro zenon_He.
% 1.62/1.80 generalize (zenon_H25 (intersection_point zenon_TX_r zenon_TZ_q)). zenon_intro zenon_H28.
% 1.62/1.80 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 1.62/1.80 exact (zenon_H2a zenon_H23).
% 1.62/1.80 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H12 ].
% 1.62/1.80 apply (zenon_notor_s _ _ zenon_H2b). zenon_intro zenon_H2d. zenon_intro zenon_H2c.
% 1.62/1.80 generalize (con1 (intersection_point zenon_TX_r zenon_TY_p)). zenon_intro zenon_H2e.
% 1.62/1.80 generalize (zenon_H24 zenon_TY_p). zenon_intro zenon_H2f.
% 1.62/1.80 generalize (apart1 (intersection_point zenon_TX_r zenon_TY_p)). zenon_intro zenon_H15.
% 1.62/1.80 generalize (zenon_H2e (intersection_point zenon_TX_r zenon_TZ_q)). zenon_intro zenon_H30.
% 1.62/1.80 generalize (zenon_H2f (intersection_point zenon_TX_r zenon_TY_p)). zenon_intro zenon_H31.
% 1.62/1.80 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 1.62/1.80 exact (zenon_H33 zenon_H22).
% 1.62/1.80 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H17 ].
% 1.62/1.80 apply (zenon_notor_s _ _ zenon_H34). zenon_intro zenon_H36. zenon_intro zenon_H35.
% 1.62/1.80 generalize (zenon_H30 (intersection_point zenon_TX_r zenon_TY_p)). zenon_intro zenon_H37.
% 1.62/1.80 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ].
% 1.62/1.80 exact (zenon_H39 zenon_H16).
% 1.62/1.80 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H14 ].
% 1.62/1.80 generalize (zenon_H30 (intersection_point zenon_TX_r zenon_TZ_q)). zenon_intro zenon_H3b.
% 1.62/1.80 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H39 | zenon_intro zenon_H3c ].
% 1.62/1.80 exact (zenon_H39 zenon_H16).
% 1.62/1.80 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_H3d | zenon_intro zenon_Hd ].
% 1.62/1.80 generalize (zenon_H27 (line_connecting (intersection_point zenon_TX_r zenon_TY_p) (intersection_point zenon_TX_r zenon_TZ_q))). zenon_intro zenon_H3e.
% 1.62/1.80 generalize (zenon_H3e zenon_TX_r). zenon_intro zenon_H3f.
% 1.62/1.80 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ].
% 1.62/1.80 apply (zenon_notand_s _ _ zenon_H41); [ zenon_intro zenon_H39 | zenon_intro zenon_H42 ].
% 1.62/1.80 exact (zenon_H39 zenon_H16).
% 1.62/1.80 exact (zenon_H42 zenon_H20).
% 1.62/1.80 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ].
% 1.62/1.80 exact (zenon_H3a zenon_H44).
% 1.62/1.80 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ].
% 1.62/1.80 exact (zenon_H36 zenon_H46).
% 1.62/1.80 apply (zenon_or_s _ _ zenon_H45); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ].
% 1.62/1.80 exact (zenon_H3d zenon_H48).
% 1.62/1.80 exact (zenon_H2d zenon_H47).
% 1.62/1.80 apply (zenon_L1_ zenon_TY_p zenon_TZ_q zenon_TX_r); trivial.
% 1.62/1.80 apply (zenon_L2_ zenon_TZ_q zenon_TY_p zenon_TX_r); trivial.
% 1.62/1.80 exact (zenon_H15 zenon_H17).
% 1.62/1.80 exact (zenon_He zenon_H12).
% 1.62/1.80 Qed.
% 1.62/1.80 % SZS output end Proof
% 1.62/1.80 (* END-PROOF *)
% 1.62/1.80 nodes searched: 162760
% 1.62/1.80 max branch formulas: 7649
% 1.62/1.80 proof nodes created: 7388
% 1.62/1.80 formulas created: 294905
% 1.62/1.80
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