TSTP Solution File: GEO175+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO175+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n017.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 07:00:24 EDT 2022
% Result : Theorem 0.18s 0.52s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO175+3 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n017.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 11:49:57 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.52 (* PROOF-FOUND *)
% 0.18/0.52 % SZS status Theorem
% 0.18/0.52 (* BEGIN-PROOF *)
% 0.18/0.52 % SZS output start Proof
% 0.18/0.52 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((convergent_lines U V)/\(distinct_points X (intersection_point U V))))->((apart_point_and_line X U)\/(apart_point_and_line X V))))))).
% 0.18/0.52 Proof.
% 0.18/0.52 assert (zenon_L1_ : forall (zenon_TV_bn : zenon_U) (zenon_TU_bo : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TU_bo Y)->(~(apart_point_and_line (intersection_point zenon_TU_bo Y) zenon_TU_bo)))) -> (convergent_lines zenon_TU_bo zenon_TV_bn) -> (apart_point_and_line (intersection_point zenon_TU_bo zenon_TV_bn) zenon_TU_bo) -> False).
% 0.18/0.52 do 2 intro. intros zenon_H24 zenon_H25 zenon_H26.
% 0.18/0.52 generalize (zenon_H24 zenon_TV_bn). zenon_intro zenon_H29.
% 0.18/0.52 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 0.18/0.52 exact (zenon_H2b zenon_H25).
% 0.18/0.52 exact (zenon_H2a zenon_H26).
% 0.18/0.52 (* end of lemma zenon_L1_ *)
% 0.18/0.52 apply NNPP. intro zenon_G.
% 0.18/0.52 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((convergent_lines U V)/\(distinct_points X (intersection_point U V))))->((apart_point_and_line X U)\/(apart_point_and_line X V))))))) zenon_G); [ zenon_intro zenon_H2c; idtac ].
% 0.18/0.52 elim zenon_H2c. zenon_intro zenon_TX_bt. zenon_intro zenon_H2e.
% 0.18/0.52 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_bt Y)/\((convergent_lines U V)/\(distinct_points zenon_TX_bt (intersection_point U V))))->((apart_point_and_line zenon_TX_bt U)\/(apart_point_and_line zenon_TX_bt V)))))) zenon_H2e); [ zenon_intro zenon_H2f; idtac ].
% 0.18/0.52 elim zenon_H2f. zenon_intro zenon_TY_bw. zenon_intro zenon_H31.
% 0.18/0.52 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_bt zenon_TY_bw)/\((convergent_lines U V)/\(distinct_points zenon_TX_bt (intersection_point U V))))->((apart_point_and_line zenon_TX_bt U)\/(apart_point_and_line zenon_TX_bt V))))) zenon_H31); [ zenon_intro zenon_H32; idtac ].
% 0.18/0.52 elim zenon_H32. zenon_intro zenon_TU_bo. zenon_intro zenon_H33.
% 0.18/0.52 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_bt zenon_TY_bw)/\((convergent_lines zenon_TU_bo V)/\(distinct_points zenon_TX_bt (intersection_point zenon_TU_bo V))))->((apart_point_and_line zenon_TX_bt zenon_TU_bo)\/(apart_point_and_line zenon_TX_bt V)))) zenon_H33); [ zenon_intro zenon_H34; idtac ].
% 0.18/0.52 elim zenon_H34. zenon_intro zenon_TV_bn. zenon_intro zenon_H35.
% 0.18/0.52 apply (zenon_notimply_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36.
% 0.18/0.52 apply (zenon_notor_s _ _ zenon_H36). zenon_intro zenon_H39. zenon_intro zenon_H38.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H3b. zenon_intro zenon_H3a.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H25. zenon_intro zenon_H3c.
% 0.18/0.52 generalize (ceq3 zenon_TU_bo). zenon_intro zenon_H3d.
% 0.18/0.52 generalize (apart4 zenon_TX_bt). zenon_intro zenon_H3e.
% 0.18/0.52 generalize (zenon_H3d zenon_TV_bn). zenon_intro zenon_H3f.
% 0.18/0.52 generalize (apart1 zenon_TX_bt). zenon_intro zenon_H40.
% 0.18/0.52 generalize (zenon_H3e (intersection_point zenon_TU_bo zenon_TV_bn)). zenon_intro zenon_H41.
% 0.18/0.52 generalize (zenon_H41 zenon_TX_bt). zenon_intro zenon_H42.
% 0.18/0.52 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ].
% 0.18/0.52 exact (zenon_H44 zenon_H3c).
% 0.18/0.52 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ].
% 0.18/0.52 exact (zenon_H40 zenon_H46).
% 0.18/0.52 generalize (cu1 (intersection_point zenon_TU_bo zenon_TV_bn)). zenon_intro zenon_H47.
% 0.18/0.52 generalize (zenon_H47 zenon_TX_bt). zenon_intro zenon_H48.
% 0.18/0.52 generalize (ci3 zenon_TU_bo). zenon_intro zenon_H24.
% 0.18/0.52 generalize (apart3 zenon_TU_bo). zenon_intro zenon_H49.
% 0.18/0.52 generalize (zenon_H3f zenon_TU_bo). zenon_intro zenon_H4a.
% 0.18/0.52 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H2b | zenon_intro zenon_H4b ].
% 0.18/0.52 exact (zenon_H2b zenon_H25).
% 0.18/0.52 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H4d | zenon_intro zenon_H4c ].
% 0.18/0.52 generalize (zenon_H48 zenon_TV_bn). zenon_intro zenon_H4e.
% 0.18/0.52 generalize (zenon_H4e zenon_TU_bo). zenon_intro zenon_H4f.
% 0.18/0.52 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ].
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_H51); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ].
% 0.18/0.52 exact (zenon_H53 zenon_H45).
% 0.18/0.52 exact (zenon_H52 zenon_H4d).
% 0.18/0.52 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ].
% 0.18/0.52 generalize (ci4 zenon_TU_bo). zenon_intro zenon_H56.
% 0.18/0.52 generalize (zenon_H56 zenon_TV_bn). zenon_intro zenon_H57.
% 0.18/0.52 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H2b | zenon_intro zenon_H58 ].
% 0.18/0.52 exact (zenon_H2b zenon_H25).
% 0.18/0.52 exact (zenon_H58 zenon_H55).
% 0.18/0.52 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H26 | zenon_intro zenon_H59 ].
% 0.18/0.52 apply (zenon_L1_ zenon_TV_bn zenon_TU_bo); trivial.
% 0.18/0.52 apply (zenon_or_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ].
% 0.18/0.52 exact (zenon_H38 zenon_H5b).
% 0.18/0.52 exact (zenon_H39 zenon_H5a).
% 0.18/0.52 exact (zenon_H49 zenon_H4c).
% 0.18/0.52 Qed.
% 0.18/0.52 % SZS output end Proof
% 0.18/0.52 (* END-PROOF *)
% 0.18/0.52 nodes searched: 1487
% 0.18/0.52 max branch formulas: 759
% 0.18/0.52 proof nodes created: 151
% 0.18/0.52 formulas created: 6534
% 0.18/0.52
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