TSTP Solution File: GEO192+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO192+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n018.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 07:00:37 EDT 2022
% Result : Theorem 0.38s 0.57s
% Output : Proof 0.38s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO192+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.12/0.34 % Computer : n018.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 18:21:03 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.38/0.57 (* PROOF-FOUND *)
% 0.38/0.57 % SZS status Theorem
% 0.38/0.57 (* BEGIN-PROOF *)
% 0.38/0.57 % SZS output start Proof
% 0.38/0.57 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines X Y)->((apart_point_and_line (intersection_point X Y) Z)->((distinct_lines X Z)/\(distinct_lines Y Z))))))).
% 0.38/0.57 Proof.
% 0.38/0.57 assert (zenon_L1_ : forall (zenon_TY_bn : zenon_U) (zenon_TX_bo : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TX_bo Y)->(~(apart_point_and_line (intersection_point zenon_TX_bo Y) zenon_TX_bo)))) -> (convergent_lines zenon_TX_bo zenon_TY_bn) -> (apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) zenon_TX_bo) -> False).
% 0.38/0.57 do 2 intro. intros zenon_H24 zenon_H25 zenon_H26.
% 0.38/0.57 generalize (zenon_H24 zenon_TY_bn). zenon_intro zenon_H29.
% 0.38/0.57 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 0.38/0.57 exact (zenon_H2b zenon_H25).
% 0.38/0.57 exact (zenon_H2a zenon_H26).
% 0.38/0.57 (* end of lemma zenon_L1_ *)
% 0.38/0.57 apply NNPP. intro zenon_G.
% 0.38/0.57 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, ((convergent_lines X Y)->((apart_point_and_line (intersection_point X Y) Z)->((distinct_lines X Z)/\(distinct_lines Y Z))))))) zenon_G); [ zenon_intro zenon_H2c; idtac ].
% 0.38/0.57 elim zenon_H2c. zenon_intro zenon_TX_bo. zenon_intro zenon_H2d.
% 0.38/0.57 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, ((convergent_lines zenon_TX_bo Y)->((apart_point_and_line (intersection_point zenon_TX_bo Y) Z)->((distinct_lines zenon_TX_bo Z)/\(distinct_lines Y Z)))))) zenon_H2d); [ zenon_intro zenon_H2e; idtac ].
% 0.38/0.57 elim zenon_H2e. zenon_intro zenon_TY_bn. zenon_intro zenon_H2f.
% 0.38/0.57 apply (zenon_notallex_s (fun Z : zenon_U => ((convergent_lines zenon_TX_bo zenon_TY_bn)->((apart_point_and_line (intersection_point zenon_TX_bo zenon_TY_bn) Z)->((distinct_lines zenon_TX_bo Z)/\(distinct_lines zenon_TY_bn Z))))) zenon_H2f); [ zenon_intro zenon_H30; idtac ].
% 0.38/0.57 elim zenon_H30. zenon_intro zenon_TZ_bx. zenon_intro zenon_H32.
% 0.38/0.57 apply (zenon_notimply_s _ _ zenon_H32). zenon_intro zenon_H25. zenon_intro zenon_H33.
% 0.38/0.57 apply (zenon_notimply_s _ _ zenon_H33). zenon_intro zenon_H35. zenon_intro zenon_H34.
% 0.38/0.57 apply (zenon_notand_s _ _ zenon_H34); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ].
% 0.38/0.57 generalize (ceq2 (intersection_point zenon_TX_bo zenon_TY_bn)). zenon_intro zenon_H38.
% 0.38/0.57 generalize (zenon_H38 zenon_TZ_bx). zenon_intro zenon_H39.
% 0.38/0.57 generalize (ci3 zenon_TX_bo). zenon_intro zenon_H24.
% 0.38/0.57 generalize (zenon_H39 zenon_TX_bo). zenon_intro zenon_H3a.
% 0.38/0.57 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H3c | zenon_intro zenon_H3b ].
% 0.38/0.57 exact (zenon_H3c zenon_H35).
% 0.38/0.57 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H3d | zenon_intro zenon_H26 ].
% 0.38/0.57 generalize (apart2 zenon_TZ_bx). zenon_intro zenon_H3e.
% 0.38/0.57 generalize (apart5 zenon_TZ_bx). zenon_intro zenon_H3f.
% 0.38/0.57 generalize (zenon_H3f zenon_TX_bo). zenon_intro zenon_H40.
% 0.38/0.57 generalize (zenon_H40 zenon_TZ_bx). zenon_intro zenon_H41.
% 0.38/0.57 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ].
% 0.38/0.57 exact (zenon_H43 zenon_H3d).
% 0.38/0.57 apply (zenon_or_s _ _ zenon_H42); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ].
% 0.38/0.57 exact (zenon_H3e zenon_H45).
% 0.38/0.57 exact (zenon_H37 zenon_H44).
% 0.38/0.57 apply (zenon_L1_ zenon_TY_bn zenon_TX_bo); trivial.
% 0.38/0.57 generalize (ceq2 (intersection_point zenon_TX_bo zenon_TY_bn)). zenon_intro zenon_H38.
% 0.38/0.57 generalize (zenon_H38 zenon_TZ_bx). zenon_intro zenon_H39.
% 0.38/0.57 generalize (zenon_H38 zenon_TY_bn). zenon_intro zenon_H46.
% 0.38/0.57 generalize (apart2 zenon_TY_bn). zenon_intro zenon_H47.
% 0.38/0.57 generalize (zenon_H46 zenon_TY_bn). zenon_intro zenon_H48.
% 0.38/0.57 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ].
% 0.38/0.57 generalize (zenon_H39 zenon_TY_bn). zenon_intro zenon_H4b.
% 0.38/0.57 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H3c | zenon_intro zenon_H4c ].
% 0.38/0.57 exact (zenon_H3c zenon_H35).
% 0.38/0.57 apply (zenon_or_s _ _ zenon_H4c); [ zenon_intro zenon_H4e | zenon_intro zenon_H4d ].
% 0.38/0.57 generalize (apart5 zenon_TZ_bx). zenon_intro zenon_H3f.
% 0.38/0.57 generalize (zenon_H3f zenon_TY_bn). zenon_intro zenon_H4f.
% 0.38/0.57 generalize (zenon_H4f zenon_TZ_bx). zenon_intro zenon_H50.
% 0.38/0.57 apply (zenon_imply_s _ _ zenon_H50); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ].
% 0.38/0.57 exact (zenon_H52 zenon_H4e).
% 0.38/0.57 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H45 | zenon_intro zenon_H53 ].
% 0.38/0.57 generalize (apart2 zenon_TZ_bx). zenon_intro zenon_H3e.
% 0.38/0.57 exact (zenon_H3e zenon_H45).
% 0.38/0.57 exact (zenon_H36 zenon_H53).
% 0.38/0.57 exact (zenon_H4a zenon_H4d).
% 0.38/0.57 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H54 | zenon_intro zenon_H4d ].
% 0.38/0.57 exact (zenon_H47 zenon_H54).
% 0.38/0.57 generalize (ci4 zenon_TX_bo). zenon_intro zenon_H55.
% 0.38/0.57 generalize (zenon_H55 zenon_TY_bn). zenon_intro zenon_H56.
% 0.38/0.57 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H2b | zenon_intro zenon_H4a ].
% 0.38/0.57 exact (zenon_H2b zenon_H25).
% 0.38/0.57 exact (zenon_H4a zenon_H4d).
% 0.38/0.57 Qed.
% 0.38/0.57 % SZS output end Proof
% 0.38/0.57 (* END-PROOF *)
% 0.38/0.57 nodes searched: 3646
% 0.38/0.57 max branch formulas: 974
% 0.38/0.57 proof nodes created: 390
% 0.38/0.57 formulas created: 12544
% 0.38/0.57
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