TSTP Solution File: GEO194+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO194+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n012.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 07:00:38 EDT 2022
% Result : Theorem 1.69s 1.88s
% Output : Proof 1.69s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO194+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : run_zenon %s %d
% 0.13/0.33 % Computer : n012.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 600
% 0.13/0.33 % DateTime : Sat Jun 18 00:45:53 EDT 2022
% 0.13/0.34 % CPUTime :
% 1.69/1.88 (* PROOF-FOUND *)
% 1.69/1.88 % SZS status Theorem
% 1.69/1.88 (* BEGIN-PROOF *)
% 1.69/1.88 % SZS output start Proof
% 1.69/1.88 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 X Z) Y)))))).
% 1.69/1.88 Proof.
% 1.69/1.88 assert (zenon_L1_ : forall (zenon_TX_o : zenon_U), (convergent_lines zenon_TX_o zenon_TX_o) -> False).
% 1.69/1.88 do 1 intro. intros zenon_Hd.
% 1.69/1.88 generalize (apart3 zenon_TX_o). zenon_intro zenon_Hf.
% 1.69/1.88 exact (zenon_Hf zenon_Hd).
% 1.69/1.88 (* end of lemma zenon_L1_ *)
% 1.69/1.88 assert (zenon_L2_ : forall (zenon_TY_s : zenon_U) (zenon_TX_o : zenon_U), (apart_point_and_line (intersection_point zenon_TX_o zenon_TY_s) zenon_TY_s) -> (convergent_lines zenon_TX_o zenon_TY_s) -> False).
% 1.69/1.88 do 2 intro. intros zenon_H10 zenon_H11.
% 1.69/1.88 generalize (con2 zenon_TX_o). zenon_intro zenon_H13.
% 1.69/1.88 generalize (zenon_H13 zenon_TY_s). zenon_intro zenon_H14.
% 1.69/1.88 generalize (apart1 (intersection_point zenon_TX_o zenon_TY_s)). zenon_intro zenon_H15.
% 1.69/1.88 generalize (zenon_H14 (intersection_point zenon_TX_o zenon_TY_s)). zenon_intro zenon_H16.
% 1.69/1.88 apply (zenon_imply_s _ _ zenon_H16); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ].
% 1.69/1.88 exact (zenon_H18 zenon_H11).
% 1.69/1.88 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ].
% 1.69/1.88 apply (zenon_notor_s _ _ zenon_H1a). zenon_intro zenon_H1c. zenon_intro zenon_H1b.
% 1.69/1.88 exact (zenon_H1b zenon_H10).
% 1.69/1.88 exact (zenon_H15 zenon_H19).
% 1.69/1.88 (* end of lemma zenon_L2_ *)
% 1.69/1.88 assert (zenon_L3_ : forall (zenon_TZ_bk : zenon_U) (zenon_TY_s : zenon_U) (zenon_TX_o : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TX_o zenon_TY_s) Y)->((distinct_lines Y Z)\/(apart_point_and_line (intersection_point zenon_TX_o zenon_TY_s) Z))))) -> (~(distinct_lines zenon_TY_s zenon_TY_s)) -> (convergent_lines zenon_TX_o zenon_TY_s) -> (forall Z : zenon_U, ((apart_point_and_line (intersection_point zenon_TX_o zenon_TY_s) zenon_TZ_bk)->((distinct_points (intersection_point zenon_TX_o zenon_TY_s) Z)\/(apart_point_and_line Z zenon_TZ_bk)))) -> (apart_point_and_line (intersection_point zenon_TX_o zenon_TY_s) zenon_TZ_bk) -> (~(apart_point_and_line (intersection_point zenon_TX_o zenon_TZ_bk) zenon_TY_s)) -> (distinct_lines zenon_TY_s zenon_TX_o) -> (convergent_lines zenon_TX_o zenon_TZ_bk) -> False).
% 1.69/1.88 do 3 intro. intros zenon_H1d zenon_H1e zenon_H11 zenon_H1f zenon_H20 zenon_H21 zenon_H22 zenon_H23.
% 1.69/1.88 generalize (zenon_H1d zenon_TY_s). zenon_intro zenon_H25.
% 1.69/1.88 generalize (zenon_H25 zenon_TY_s). zenon_intro zenon_H26.
% 1.69/1.88 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H1b | zenon_intro zenon_H27 ].
% 1.69/1.88 generalize (apart1 (intersection_point zenon_TX_o zenon_TZ_bk)). zenon_intro zenon_H28.
% 1.69/1.88 generalize (con2 zenon_TX_o). zenon_intro zenon_H13.
% 1.69/1.88 generalize (zenon_H13 zenon_TZ_bk). zenon_intro zenon_H29.
% 1.69/1.88 generalize (apart1 (intersection_point zenon_TX_o zenon_TY_s)). zenon_intro zenon_H15.
% 1.69/1.88 generalize (zenon_H13 zenon_TY_s). zenon_intro zenon_H14.
% 1.69/1.88 generalize (zenon_H14 (intersection_point zenon_TX_o zenon_TY_s)). zenon_intro zenon_H16.
% 1.69/1.88 apply (zenon_imply_s _ _ zenon_H16); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ].
% 1.69/1.88 exact (zenon_H18 zenon_H11).
% 1.69/1.88 apply (zenon_imply_s _ _ zenon_H17); [ zenon_intro zenon_H1a | zenon_intro zenon_H19 ].
% 1.69/1.88 apply (zenon_notor_s _ _ zenon_H1a). zenon_intro zenon_H1c. zenon_intro zenon_H1b.
% 1.69/1.88 generalize (zenon_H29 (intersection_point zenon_TX_o zenon_TZ_bk)). zenon_intro zenon_H2a.
% 1.69/1.88 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ].
% 1.69/1.88 exact (zenon_H2c zenon_H23).
% 1.69/1.88 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H2e | zenon_intro zenon_H2d ].
% 1.69/1.88 apply (zenon_notor_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H2f.
% 1.69/1.88 generalize (zenon_H1f (intersection_point zenon_TX_o zenon_TZ_bk)). zenon_intro zenon_H31.
% 1.69/1.88 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H33 | zenon_intro zenon_H32 ].
% 1.69/1.88 exact (zenon_H33 zenon_H20).
% 1.69/1.88 apply (zenon_or_s _ _ zenon_H32); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ].
% 1.69/1.88 generalize (cu1 (intersection_point zenon_TX_o zenon_TY_s)). zenon_intro zenon_H36.
% 1.69/1.88 generalize (zenon_H36 (intersection_point zenon_TX_o zenon_TZ_bk)). zenon_intro zenon_H37.
% 1.69/1.88 generalize (zenon_H37 zenon_TY_s). zenon_intro zenon_H38.
% 1.69/1.88 generalize (zenon_H38 zenon_TX_o). zenon_intro zenon_H39.
% 1.69/1.88 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ].
% 1.69/1.88 apply (zenon_notand_s _ _ zenon_H3b); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ].
% 1.69/1.88 exact (zenon_H3d zenon_H35).
% 1.69/1.88 exact (zenon_H3c zenon_H22).
% 1.69/1.88 apply (zenon_or_s _ _ zenon_H3a); [ zenon_intro zenon_H10 | zenon_intro zenon_H3e ].
% 1.69/1.88 exact (zenon_H1b zenon_H10).
% 1.69/1.88 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ].
% 1.69/1.88 exact (zenon_H1c zenon_H40).
% 1.69/1.88 apply (zenon_or_s _ _ zenon_H3f); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ].
% 1.69/1.88 exact (zenon_H21 zenon_H42).
% 1.69/1.88 exact (zenon_H30 zenon_H41).
% 1.69/1.88 exact (zenon_H2f zenon_H34).
% 1.69/1.88 exact (zenon_H28 zenon_H2d).
% 1.69/1.88 exact (zenon_H15 zenon_H19).
% 1.69/1.88 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H43 | zenon_intro zenon_H10 ].
% 1.69/1.88 exact (zenon_H1e zenon_H43).
% 1.69/1.88 apply (zenon_L2_ zenon_TY_s zenon_TX_o); trivial.
% 1.69/1.88 (* end of lemma zenon_L3_ *)
% 1.69/1.88 apply NNPP. intro zenon_G.
% 1.69/1.88 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 X Z) Y)))))) zenon_G); [ zenon_intro zenon_H44; idtac ].
% 1.69/1.88 elim zenon_H44. zenon_intro zenon_TX_o. zenon_intro zenon_H45.
% 1.69/1.88 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_o Y)/\((convergent_lines Z Y)/\(convergent_lines zenon_TX_o Z)))->((apart_point_and_line (intersection_point zenon_TX_o Y) Z)->(apart_point_and_line (intersection_point zenon_TX_o Z) Y))))) zenon_H45); [ zenon_intro zenon_H46; idtac ].
% 1.69/1.88 elim zenon_H46. zenon_intro zenon_TY_s. zenon_intro zenon_H47.
% 1.69/1.88 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_o zenon_TY_s)/\((convergent_lines Z zenon_TY_s)/\(convergent_lines zenon_TX_o Z)))->((apart_point_and_line (intersection_point zenon_TX_o zenon_TY_s) Z)->(apart_point_and_line (intersection_point zenon_TX_o Z) zenon_TY_s)))) zenon_H47); [ zenon_intro zenon_H48; idtac ].
% 1.69/1.88 elim zenon_H48. zenon_intro zenon_TZ_bk. zenon_intro zenon_H49.
% 1.69/1.88 apply (zenon_notimply_s _ _ zenon_H49). zenon_intro zenon_H4b. zenon_intro zenon_H4a.
% 1.69/1.88 apply (zenon_notimply_s _ _ zenon_H4a). zenon_intro zenon_H20. zenon_intro zenon_H21.
% 1.69/1.88 apply (zenon_and_s _ _ zenon_H4b). zenon_intro zenon_H11. zenon_intro zenon_H4c.
% 1.69/1.88 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4d. zenon_intro zenon_H23.
% 1.69/1.88 generalize (apart2 zenon_TY_s). zenon_intro zenon_H1e.
% 1.69/1.88 generalize (apart6 zenon_TX_o). zenon_intro zenon_H4e.
% 1.69/1.88 generalize (zenon_H4e zenon_TY_s). zenon_intro zenon_H4f.
% 1.69/1.88 generalize (ceq3 zenon_TY_s). zenon_intro zenon_H50.
% 1.69/1.88 generalize (apart5 zenon_TY_s). zenon_intro zenon_H51.
% 1.69/1.88 generalize (ceq2 (intersection_point zenon_TX_o zenon_TY_s)). zenon_intro zenon_H1d.
% 1.69/1.88 generalize (ceq1 (intersection_point zenon_TX_o zenon_TY_s)). zenon_intro zenon_H52.
% 1.69/1.88 generalize (zenon_H52 zenon_TZ_bk). zenon_intro zenon_H1f.
% 1.69/1.88 generalize (apart2 zenon_TX_o). zenon_intro zenon_H53.
% 1.69/1.88 generalize (zenon_H51 zenon_TX_o). zenon_intro zenon_H54.
% 1.69/1.88 generalize (zenon_H4f zenon_TX_o). zenon_intro zenon_H55.
% 1.69/1.88 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H18 | zenon_intro zenon_H56 ].
% 1.69/1.88 exact (zenon_H18 zenon_H11).
% 1.69/1.88 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_Hd | zenon_intro zenon_H57 ].
% 1.69/1.88 apply (zenon_L1_ zenon_TX_o); trivial.
% 1.69/1.88 generalize (zenon_H54 zenon_TX_o). zenon_intro zenon_H58.
% 1.69/1.88 apply (zenon_imply_s _ _ zenon_H58); [ zenon_intro zenon_H3c | zenon_intro zenon_H59 ].
% 1.69/1.88 generalize (zenon_H50 zenon_TX_o). zenon_intro zenon_H5a.
% 1.69/1.88 apply (zenon_imply_s _ _ zenon_H5a); [ zenon_intro zenon_H5b | zenon_intro zenon_H22 ].
% 1.69/1.88 exact (zenon_H5b zenon_H57).
% 1.69/1.88 exact (zenon_H3c zenon_H22).
% 1.69/1.88 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H22 | zenon_intro zenon_H5c ].
% 1.69/1.88 apply (zenon_L3_ zenon_TZ_bk zenon_TY_s zenon_TX_o); trivial.
% 1.69/1.88 exact (zenon_H53 zenon_H5c).
% 1.69/1.88 Qed.
% 1.69/1.88 % SZS output end Proof
% 1.69/1.88 (* END-PROOF *)
% 1.69/1.88 nodes searched: 192423
% 1.69/1.88 max branch formulas: 3840
% 1.69/1.88 proof nodes created: 3482
% 1.69/1.88 formulas created: 218515
% 1.69/1.88
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