TSTP Solution File: GEO203+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO203+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n029.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 0.60s 0.76s
% Output : Proof 0.60s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO203+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : run_zenon %s %d
% 0.13/0.34 % Computer : n029.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 06:21:28 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.60/0.76 (* PROOF-FOUND *)
% 0.60/0.76 % SZS status Theorem
% 0.60/0.76 (* BEGIN-PROOF *)
% 0.60/0.76 % SZS output start Proof
% 0.60/0.76 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)))))).
% 0.60/0.76 Proof.
% 0.60/0.76 assert (zenon_L1_ : forall (zenon_TY_s : zenon_U) (zenon_TX_t : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TX_t Y)->(~(apart_point_and_line (intersection_point zenon_TX_t Y) zenon_TX_t)))) -> (convergent_lines zenon_TX_t zenon_TY_s) -> (apart_point_and_line (intersection_point zenon_TX_t zenon_TY_s) zenon_TX_t) -> False).
% 0.60/0.76 do 2 intro. intros zenon_Hf zenon_H10 zenon_H11.
% 0.60/0.76 generalize (zenon_Hf zenon_TY_s). zenon_intro zenon_H14.
% 0.60/0.76 apply (zenon_imply_s _ _ zenon_H14); [ zenon_intro zenon_H16 | zenon_intro zenon_H15 ].
% 0.60/0.76 exact (zenon_H16 zenon_H10).
% 0.60/0.76 exact (zenon_H15 zenon_H11).
% 0.60/0.76 (* end of lemma zenon_L1_ *)
% 0.60/0.76 assert (zenon_L2_ : forall (zenon_TZ_z : zenon_U) (zenon_TX_t : zenon_U), (forall Y : zenon_U, ((convergent_lines zenon_TX_t Y)->(~(apart_point_and_line (intersection_point zenon_TX_t Y) zenon_TX_t)))) -> (convergent_lines zenon_TX_t zenon_TZ_z) -> (apart_point_and_line (intersection_point zenon_TX_t zenon_TZ_z) zenon_TX_t) -> False).
% 0.60/0.76 do 2 intro. intros zenon_Hf zenon_H17 zenon_H18.
% 0.60/0.76 generalize (zenon_Hf zenon_TZ_z). zenon_intro zenon_H1a.
% 0.60/0.76 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ].
% 0.60/0.76 exact (zenon_H1c zenon_H17).
% 0.60/0.76 exact (zenon_H1b zenon_H18).
% 0.60/0.76 (* end of lemma zenon_L2_ *)
% 0.60/0.76 apply NNPP. intro zenon_G.
% 0.60/0.76 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_H1d; idtac ].
% 0.60/0.76 elim zenon_H1d. zenon_intro zenon_TX_t. zenon_intro zenon_H1e.
% 0.60/0.76 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_t Y)/\((convergent_lines zenon_TX_t Z)/\(distinct_points (intersection_point zenon_TX_t Y) (intersection_point zenon_TX_t Z))))->(~(distinct_lines (line_connecting (intersection_point zenon_TX_t Y) (intersection_point zenon_TX_t Z)) zenon_TX_t))))) zenon_H1e); [ zenon_intro zenon_H1f; idtac ].
% 0.60/0.76 elim zenon_H1f. zenon_intro zenon_TY_s. zenon_intro zenon_H20.
% 0.60/0.76 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_t zenon_TY_s)/\((convergent_lines zenon_TX_t Z)/\(distinct_points (intersection_point zenon_TX_t zenon_TY_s) (intersection_point zenon_TX_t Z))))->(~(distinct_lines (line_connecting (intersection_point zenon_TX_t zenon_TY_s) (intersection_point zenon_TX_t Z)) zenon_TX_t)))) zenon_H20); [ zenon_intro zenon_H21; idtac ].
% 0.60/0.76 elim zenon_H21. zenon_intro zenon_TZ_z. zenon_intro zenon_H22.
% 0.60/0.76 apply (zenon_notimply_s _ _ zenon_H22). zenon_intro zenon_H24. zenon_intro zenon_H23.
% 0.60/0.76 apply zenon_H23. zenon_intro zenon_H25.
% 0.60/0.76 apply (zenon_and_s _ _ zenon_H24). zenon_intro zenon_H10. zenon_intro zenon_H26.
% 0.60/0.76 apply (zenon_and_s _ _ zenon_H26). zenon_intro zenon_H17. zenon_intro zenon_H27.
% 0.60/0.76 generalize (apart2 zenon_TX_t). zenon_intro zenon_H28.
% 0.60/0.76 generalize (cu1 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H29.
% 0.60/0.76 generalize (zenon_H29 (intersection_point zenon_TX_t zenon_TZ_z)). zenon_intro zenon_H2a.
% 0.60/0.76 generalize (ceq2 (intersection_point zenon_TX_t zenon_TZ_z)). zenon_intro zenon_H2b.
% 0.60/0.76 generalize (ci3 zenon_TX_t). zenon_intro zenon_Hf.
% 0.60/0.76 generalize (zenon_H2b zenon_TX_t). zenon_intro zenon_H2c.
% 0.60/0.76 generalize (zenon_H2c zenon_TX_t). zenon_intro zenon_H2d.
% 0.60/0.76 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H1b | zenon_intro zenon_H2e ].
% 0.60/0.76 generalize (ceq2 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H2f.
% 0.60/0.76 generalize (zenon_H2f zenon_TX_t). zenon_intro zenon_H30.
% 0.60/0.76 generalize (zenon_H30 zenon_TX_t). zenon_intro zenon_H31.
% 0.60/0.76 apply (zenon_imply_s _ _ zenon_H31); [ zenon_intro zenon_H15 | zenon_intro zenon_H32 ].
% 0.60/0.77 generalize (zenon_H2a (line_connecting (intersection_point zenon_TX_t zenon_TY_s) (intersection_point zenon_TX_t zenon_TZ_z))). zenon_intro zenon_H33.
% 0.60/0.77 generalize (zenon_H33 zenon_TX_t). zenon_intro zenon_H34.
% 0.60/0.77 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ].
% 0.60/0.77 apply (zenon_notand_s _ _ zenon_H36); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ].
% 0.60/0.77 exact (zenon_H38 zenon_H27).
% 0.60/0.77 exact (zenon_H37 zenon_H25).
% 0.60/0.77 apply (zenon_or_s _ _ zenon_H35); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ].
% 0.60/0.77 generalize (ci1 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H3b.
% 0.60/0.77 generalize (zenon_H3b (intersection_point zenon_TX_t zenon_TZ_z)). zenon_intro zenon_H3c.
% 0.60/0.77 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_H38 | zenon_intro zenon_H3d ].
% 0.60/0.77 exact (zenon_H38 zenon_H27).
% 0.60/0.77 exact (zenon_H3d zenon_H3a).
% 0.60/0.77 apply (zenon_or_s _ _ zenon_H39); [ zenon_intro zenon_H11 | zenon_intro zenon_H3e ].
% 0.60/0.77 exact (zenon_H15 zenon_H11).
% 0.60/0.77 apply (zenon_or_s _ _ zenon_H3e); [ zenon_intro zenon_H3f | zenon_intro zenon_H18 ].
% 0.60/0.77 generalize (ci2 (intersection_point zenon_TX_t zenon_TY_s)). zenon_intro zenon_H40.
% 0.60/0.77 generalize (zenon_H40 (intersection_point zenon_TX_t zenon_TZ_z)). zenon_intro zenon_H41.
% 0.60/0.77 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H38 | zenon_intro zenon_H42 ].
% 0.60/0.77 exact (zenon_H38 zenon_H27).
% 0.60/0.77 exact (zenon_H42 zenon_H3f).
% 0.60/0.77 exact (zenon_H1b zenon_H18).
% 0.60/0.77 apply (zenon_or_s _ _ zenon_H32); [ zenon_intro zenon_H43 | zenon_intro zenon_H11 ].
% 0.60/0.77 exact (zenon_H28 zenon_H43).
% 0.60/0.77 apply (zenon_L1_ zenon_TY_s zenon_TX_t); trivial.
% 0.60/0.77 apply (zenon_or_s _ _ zenon_H2e); [ zenon_intro zenon_H43 | zenon_intro zenon_H18 ].
% 0.60/0.77 exact (zenon_H28 zenon_H43).
% 0.60/0.77 apply (zenon_L2_ zenon_TZ_z zenon_TX_t); trivial.
% 0.60/0.77 Qed.
% 0.60/0.77 % SZS output end Proof
% 0.60/0.77 (* END-PROOF *)
% 0.60/0.77 nodes searched: 19207
% 0.60/0.77 max branch formulas: 3137
% 0.60/0.77 proof nodes created: 938
% 0.60/0.77 formulas created: 52907
% 0.60/0.77
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