TSTP Solution File: GEO197+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO197+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n006.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 07:00:41 EDT 2022
% Result : Theorem 1.61s 1.82s
% Output : Proof 1.61s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : GEO197+2 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : run_zenon %s %d
% 0.14/0.35 % Computer : n006.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jun 18 09:58:25 EDT 2022
% 0.14/0.36 % CPUTime :
% 1.61/1.82 (* PROOF-FOUND *)
% 1.61/1.82 % SZS status Theorem
% 1.61/1.82 (* BEGIN-PROOF *)
% 1.61/1.82 % SZS output start Proof
% 1.61/1.82 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines Z Y)/\((convergent_lines X Z)/\(~(apart_point_and_line (intersection_point X Y) Z)))))->(~(apart_point_and_line (intersection_point Z Y) X)))))).
% 1.61/1.82 Proof.
% 1.61/1.82 assert (zenon_L1_ : forall (zenon_TX_r : zenon_U) (zenon_TY_s : zenon_U) (zenon_TZ_t : zenon_U), (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TZ_t zenon_TY_s) zenon_TX_r)->((distinct_points (intersection_point zenon_TZ_t zenon_TY_s) Z)\/(apart_point_and_line Z zenon_TX_r)))) -> (apart_point_and_line (intersection_point zenon_TZ_t zenon_TY_s) zenon_TX_r) -> (~(distinct_points (intersection_point zenon_TZ_t zenon_TY_s) (intersection_point zenon_TX_r zenon_TY_s))) -> (~(apart_point_and_line (intersection_point zenon_TX_r zenon_TY_s) zenon_TX_r)) -> False).
% 1.61/1.82 do 3 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10.
% 1.61/1.82 generalize (zenon_Hd (intersection_point zenon_TX_r zenon_TY_s)). zenon_intro zenon_H14.
% 1.61/1.82 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ].
% 1.61/1.82 exact (zenon_H16 zenon_He).
% 1.61/1.82 apply (zenon_or_s _ _ zenon_H15); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ].
% 1.61/1.82 exact (zenon_Hf zenon_H18).
% 1.61/1.82 exact (zenon_H10 zenon_H17).
% 1.61/1.82 (* end of lemma zenon_L1_ *)
% 1.61/1.82 assert (zenon_L2_ : forall (zenon_TY_s : zenon_U) (zenon_TZ_t : zenon_U), (apart_point_and_line (intersection_point zenon_TZ_t zenon_TY_s) zenon_TZ_t) -> (convergent_lines zenon_TZ_t zenon_TY_s) -> False).
% 1.61/1.82 do 2 intro. intros zenon_H19 zenon_H1a.
% 1.61/1.82 generalize (con2 zenon_TZ_t). zenon_intro zenon_H1b.
% 1.61/1.82 generalize (zenon_H1b zenon_TY_s). zenon_intro zenon_H1c.
% 1.61/1.82 generalize (apart1 (intersection_point zenon_TZ_t zenon_TY_s)). zenon_intro zenon_H1d.
% 1.61/1.82 generalize (zenon_H1c (intersection_point zenon_TZ_t zenon_TY_s)). zenon_intro zenon_H1e.
% 1.61/1.82 apply (zenon_imply_s _ _ zenon_H1e); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ].
% 1.61/1.82 exact (zenon_H20 zenon_H1a).
% 1.61/1.82 apply (zenon_imply_s _ _ zenon_H1f); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ].
% 1.61/1.82 apply (zenon_notor_s _ _ zenon_H22). zenon_intro zenon_H24. zenon_intro zenon_H23.
% 1.61/1.82 exact (zenon_H24 zenon_H19).
% 1.61/1.82 exact (zenon_H1d zenon_H21).
% 1.61/1.82 (* end of lemma zenon_L2_ *)
% 1.61/1.82 assert (zenon_L3_ : forall (zenon_TZ_t : zenon_U) (zenon_TY_s : zenon_U) (zenon_TX_r : zenon_U), (convergent_lines zenon_TX_r zenon_TY_s) -> (~(apart_point_and_line (intersection_point zenon_TX_r zenon_TY_s) zenon_TZ_t)) -> (distinct_lines zenon_TY_s zenon_TZ_t) -> (apart_point_and_line (intersection_point zenon_TZ_t zenon_TY_s) zenon_TX_r) -> (convergent_lines zenon_TZ_t zenon_TY_s) -> (~(distinct_lines zenon_TZ_t zenon_TZ_t)) -> False).
% 1.61/1.82 do 3 intro. intros zenon_H25 zenon_H26 zenon_H27 zenon_He zenon_H1a zenon_H28.
% 1.61/1.82 generalize (ceq2 (intersection_point zenon_TZ_t zenon_TY_s)). zenon_intro zenon_H29.
% 1.61/1.82 generalize (ceq1 (intersection_point zenon_TZ_t zenon_TY_s)). zenon_intro zenon_H2a.
% 1.61/1.82 generalize (zenon_H2a zenon_TX_r). zenon_intro zenon_Hd.
% 1.61/1.82 generalize (zenon_H29 zenon_TZ_t). zenon_intro zenon_H2b.
% 1.61/1.82 generalize (zenon_H2b zenon_TZ_t). zenon_intro zenon_H2c.
% 1.61/1.82 apply (zenon_imply_s _ _ zenon_H2c); [ zenon_intro zenon_H24 | zenon_intro zenon_H2d ].
% 1.61/1.82 generalize (con2 zenon_TZ_t). zenon_intro zenon_H1b.
% 1.61/1.82 generalize (zenon_H1b zenon_TY_s). zenon_intro zenon_H1c.
% 1.61/1.82 generalize (apart1 (intersection_point zenon_TZ_t zenon_TY_s)). zenon_intro zenon_H1d.
% 1.61/1.82 generalize (zenon_H1c (intersection_point zenon_TZ_t zenon_TY_s)). zenon_intro zenon_H1e.
% 1.61/1.82 apply (zenon_imply_s _ _ zenon_H1e); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ].
% 1.61/1.82 exact (zenon_H20 zenon_H1a).
% 1.61/1.82 apply (zenon_imply_s _ _ zenon_H1f); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ].
% 1.61/1.82 apply (zenon_notor_s _ _ zenon_H22). zenon_intro zenon_H24. zenon_intro zenon_H23.
% 1.61/1.82 generalize (cu1 (intersection_point zenon_TZ_t zenon_TY_s)). zenon_intro zenon_H2e.
% 1.61/1.82 generalize (apart1 (intersection_point zenon_TX_r zenon_TY_s)). zenon_intro zenon_H2f.
% 1.61/1.82 generalize (con2 zenon_TX_r). zenon_intro zenon_H30.
% 1.61/1.82 generalize (zenon_H30 zenon_TY_s). zenon_intro zenon_H31.
% 1.61/1.82 generalize (zenon_H31 (intersection_point zenon_TX_r zenon_TY_s)). zenon_intro zenon_H32.
% 1.61/1.82 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 1.61/1.82 exact (zenon_H34 zenon_H25).
% 1.61/1.82 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ].
% 1.61/1.82 apply (zenon_notor_s _ _ zenon_H36). zenon_intro zenon_H10. zenon_intro zenon_H37.
% 1.61/1.82 generalize (zenon_H2e (intersection_point zenon_TX_r zenon_TY_s)). zenon_intro zenon_H38.
% 1.61/1.82 generalize (zenon_H38 zenon_TY_s). zenon_intro zenon_H39.
% 1.61/1.82 generalize (zenon_H39 zenon_TZ_t). zenon_intro zenon_H3a.
% 1.61/1.82 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ].
% 1.61/1.82 apply (zenon_notand_s _ _ zenon_H3c); [ zenon_intro zenon_Hf | zenon_intro zenon_H3d ].
% 1.61/1.82 apply (zenon_L1_ zenon_TX_r zenon_TY_s zenon_TZ_t); trivial.
% 1.61/1.82 exact (zenon_H3d zenon_H27).
% 1.61/1.82 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ].
% 1.61/1.82 exact (zenon_H23 zenon_H3f).
% 1.61/1.82 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H19 | zenon_intro zenon_H40 ].
% 1.61/1.82 exact (zenon_H24 zenon_H19).
% 1.61/1.82 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ].
% 1.61/1.82 exact (zenon_H37 zenon_H42).
% 1.61/1.82 exact (zenon_H26 zenon_H41).
% 1.61/1.82 exact (zenon_H2f zenon_H35).
% 1.61/1.82 exact (zenon_H1d zenon_H21).
% 1.61/1.82 apply (zenon_or_s _ _ zenon_H2d); [ zenon_intro zenon_H43 | zenon_intro zenon_H19 ].
% 1.61/1.82 exact (zenon_H28 zenon_H43).
% 1.61/1.82 apply (zenon_L2_ zenon_TY_s zenon_TZ_t); trivial.
% 1.61/1.82 (* end of lemma zenon_L3_ *)
% 1.61/1.82 apply NNPP. intro zenon_G.
% 1.61/1.82 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines Z Y)/\((convergent_lines X Z)/\(~(apart_point_and_line (intersection_point X Y) Z)))))->(~(apart_point_and_line (intersection_point Z Y) X)))))) zenon_G); [ zenon_intro zenon_H44; idtac ].
% 1.61/1.82 elim zenon_H44. zenon_intro zenon_TX_r. zenon_intro zenon_H45.
% 1.61/1.82 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_r Y)/\((convergent_lines Z Y)/\((convergent_lines zenon_TX_r Z)/\(~(apart_point_and_line (intersection_point zenon_TX_r Y) Z)))))->(~(apart_point_and_line (intersection_point Z Y) zenon_TX_r))))) zenon_H45); [ zenon_intro zenon_H46; idtac ].
% 1.61/1.82 elim zenon_H46. zenon_intro zenon_TY_s. zenon_intro zenon_H47.
% 1.61/1.82 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_r zenon_TY_s)/\((convergent_lines Z zenon_TY_s)/\((convergent_lines zenon_TX_r Z)/\(~(apart_point_and_line (intersection_point zenon_TX_r zenon_TY_s) Z)))))->(~(apart_point_and_line (intersection_point Z zenon_TY_s) zenon_TX_r)))) zenon_H47); [ zenon_intro zenon_H48; idtac ].
% 1.61/1.82 elim zenon_H48. zenon_intro zenon_TZ_t. zenon_intro zenon_H49.
% 1.61/1.82 apply (zenon_notimply_s _ _ zenon_H49). zenon_intro zenon_H4b. zenon_intro zenon_H4a.
% 1.61/1.82 apply zenon_H4a. zenon_intro zenon_He.
% 1.61/1.82 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H25. zenon_intro zenon_H4c.
% 1.61/1.82 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H1a. zenon_intro zenon_H4d.
% 1.61/1.82 apply (zenon_and_s _ _ zenon_H4d). zenon_intro zenon_H4e. zenon_intro zenon_H26.
% 1.61/1.82 generalize (apart3 zenon_TZ_t). zenon_intro zenon_H4f.
% 1.61/1.82 generalize (apart2 zenon_TZ_t). zenon_intro zenon_H28.
% 1.61/1.82 generalize (apart6 zenon_TZ_t). zenon_intro zenon_H50.
% 1.61/1.82 generalize (ceq3 zenon_TY_s). zenon_intro zenon_H51.
% 1.61/1.82 generalize (zenon_H50 zenon_TY_s). zenon_intro zenon_H52.
% 1.61/1.82 generalize (zenon_H52 zenon_TZ_t). zenon_intro zenon_H53.
% 1.61/1.82 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H20 | zenon_intro zenon_H54 ].
% 1.61/1.82 exact (zenon_H20 zenon_H1a).
% 1.61/1.82 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H56 | zenon_intro zenon_H55 ].
% 1.61/1.82 exact (zenon_H4f zenon_H56).
% 1.61/1.82 generalize (zenon_H51 zenon_TZ_t). zenon_intro zenon_H57.
% 1.61/1.82 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H58 | zenon_intro zenon_H27 ].
% 1.61/1.82 exact (zenon_H58 zenon_H55).
% 1.61/1.82 apply (zenon_L3_ zenon_TZ_t zenon_TY_s zenon_TX_r); trivial.
% 1.61/1.82 Qed.
% 1.61/1.82 % SZS output end Proof
% 1.61/1.82 (* END-PROOF *)
% 1.61/1.82 nodes searched: 138566
% 1.61/1.82 max branch formulas: 3265
% 1.61/1.82 proof nodes created: 3711
% 1.61/1.82 formulas created: 199469
% 1.61/1.82
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