TSTP Solution File: GEO205+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO205+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n027.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 07:00:48 EDT 2022
% Result : Theorem 0.39s 0.61s
% Output : Proof 0.39s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO205+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : run_zenon %s %d
% 0.12/0.33 % Computer : n027.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 16:17:38 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.39/0.61 (* PROOF-FOUND *)
% 0.39/0.61 % SZS status Theorem
% 0.39/0.61 (* BEGIN-PROOF *)
% 0.39/0.61 % SZS output start Proof
% 0.39/0.61 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\(~(distinct_lines Y Z)))->((convergent_lines X Z)/\(~(distinct_points (intersection_point X Y) (intersection_point X Z)))))))).
% 0.39/0.61 Proof.
% 0.39/0.61 assert (zenon_L1_ : forall (zenon_TZ_s : zenon_U) (zenon_TY_t : zenon_U) (zenon_TX_u : zenon_U), (forall Z : zenon_U, ((convergent_lines zenon_TX_u zenon_TY_t)->((convergent_lines zenon_TX_u Z)\/(convergent_lines zenon_TY_t Z)))) -> (convergent_lines zenon_TX_u zenon_TY_t) -> (~(convergent_lines zenon_TX_u zenon_TZ_s)) -> (forall Y : zenon_U, ((convergent_lines zenon_TY_t Y)->(distinct_lines zenon_TY_t Y))) -> (~(distinct_lines zenon_TY_t zenon_TZ_s)) -> False).
% 0.39/0.61 do 3 intro. intros zenon_Hd zenon_He zenon_Hf zenon_H10 zenon_H11.
% 0.39/0.61 generalize (zenon_Hd zenon_TZ_s). zenon_intro zenon_H15.
% 0.39/0.61 apply (zenon_imply_s _ _ zenon_H15); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ].
% 0.39/0.61 exact (zenon_H17 zenon_He).
% 0.39/0.61 apply (zenon_or_s _ _ zenon_H16); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ].
% 0.39/0.61 exact (zenon_Hf zenon_H19).
% 0.39/0.61 generalize (zenon_H10 zenon_TZ_s). zenon_intro zenon_H1a.
% 0.39/0.61 apply (zenon_imply_s _ _ zenon_H1a); [ zenon_intro zenon_H1c | zenon_intro zenon_H1b ].
% 0.39/0.61 exact (zenon_H1c zenon_H18).
% 0.39/0.61 exact (zenon_H11 zenon_H1b).
% 0.39/0.61 (* end of lemma zenon_L1_ *)
% 0.39/0.61 assert (zenon_L2_ : forall (zenon_TY_t : zenon_U) (zenon_TZ_s : zenon_U), (distinct_lines zenon_TZ_s zenon_TY_t) -> (~(distinct_lines zenon_TY_t zenon_TZ_s)) -> False).
% 0.39/0.61 do 2 intro. intros zenon_H1d zenon_H11.
% 0.39/0.61 generalize (apart5 zenon_TZ_s). zenon_intro zenon_H1e.
% 0.39/0.61 generalize (zenon_H1e zenon_TY_t). zenon_intro zenon_H1f.
% 0.39/0.61 generalize (zenon_H1f zenon_TZ_s). zenon_intro zenon_H20.
% 0.39/0.61 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H22 | zenon_intro zenon_H21 ].
% 0.39/0.61 exact (zenon_H22 zenon_H1d).
% 0.39/0.61 apply (zenon_or_s _ _ zenon_H21); [ zenon_intro zenon_H23 | zenon_intro zenon_H1b ].
% 0.39/0.61 generalize (apart2 zenon_TZ_s). zenon_intro zenon_H24.
% 0.39/0.61 exact (zenon_H24 zenon_H23).
% 0.39/0.61 exact (zenon_H11 zenon_H1b).
% 0.39/0.61 (* end of lemma zenon_L2_ *)
% 0.39/0.61 assert (zenon_L3_ : forall (zenon_TZ_s : zenon_U) (zenon_TY_t : zenon_U) (zenon_TX_u : zenon_U), (apart_point_and_line (intersection_point zenon_TX_u zenon_TY_t) zenon_TZ_s) -> (~(distinct_lines zenon_TY_t zenon_TZ_s)) -> (~(apart_point_and_line (intersection_point zenon_TX_u zenon_TY_t) zenon_TY_t)) -> False).
% 0.39/0.61 do 3 intro. intros zenon_H25 zenon_H11 zenon_H26.
% 0.39/0.61 generalize (ceq2 (intersection_point zenon_TX_u zenon_TY_t)). zenon_intro zenon_H27.
% 0.39/0.61 generalize (zenon_H27 zenon_TZ_s). zenon_intro zenon_H28.
% 0.39/0.61 generalize (zenon_H28 zenon_TY_t). zenon_intro zenon_H29.
% 0.39/0.61 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ].
% 0.39/0.61 exact (zenon_H2b zenon_H25).
% 0.39/0.61 apply (zenon_or_s _ _ zenon_H2a); [ zenon_intro zenon_H1d | zenon_intro zenon_H2c ].
% 0.39/0.61 apply (zenon_L2_ zenon_TY_t zenon_TZ_s); trivial.
% 0.39/0.61 exact (zenon_H26 zenon_H2c).
% 0.39/0.61 (* end of lemma zenon_L3_ *)
% 0.39/0.61 apply NNPP. intro zenon_G.
% 0.39/0.61 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\(~(distinct_lines Y Z)))->((convergent_lines X Z)/\(~(distinct_points (intersection_point X Y) (intersection_point X Z)))))))) zenon_G); [ zenon_intro zenon_H2d; idtac ].
% 0.39/0.61 elim zenon_H2d. zenon_intro zenon_TX_u. zenon_intro zenon_H2e.
% 0.39/0.61 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_u Y)/\(~(distinct_lines Y Z)))->((convergent_lines zenon_TX_u Z)/\(~(distinct_points (intersection_point zenon_TX_u Y) (intersection_point zenon_TX_u Z))))))) zenon_H2e); [ zenon_intro zenon_H2f; idtac ].
% 0.39/0.61 elim zenon_H2f. zenon_intro zenon_TY_t. zenon_intro zenon_H30.
% 0.39/0.61 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_u zenon_TY_t)/\(~(distinct_lines zenon_TY_t Z)))->((convergent_lines zenon_TX_u Z)/\(~(distinct_points (intersection_point zenon_TX_u zenon_TY_t) (intersection_point zenon_TX_u Z)))))) zenon_H30); [ zenon_intro zenon_H31; idtac ].
% 0.39/0.61 elim zenon_H31. zenon_intro zenon_TZ_s. zenon_intro zenon_H32.
% 0.39/0.61 apply (zenon_notimply_s _ _ zenon_H32). zenon_intro zenon_H34. zenon_intro zenon_H33.
% 0.39/0.61 apply (zenon_and_s _ _ zenon_H34). zenon_intro zenon_He. zenon_intro zenon_H11.
% 0.39/0.61 apply (zenon_notand_s _ _ zenon_H33); [ zenon_intro zenon_Hf | zenon_intro zenon_H35 ].
% 0.39/0.61 generalize (apart6 zenon_TX_u). zenon_intro zenon_H36.
% 0.39/0.61 generalize (ceq3 zenon_TY_t). zenon_intro zenon_H10.
% 0.39/0.61 generalize (zenon_H36 zenon_TY_t). zenon_intro zenon_Hd.
% 0.39/0.61 apply (zenon_L1_ zenon_TZ_s zenon_TY_t zenon_TX_u); trivial.
% 0.39/0.61 apply zenon_H35. zenon_intro zenon_H37.
% 0.39/0.61 generalize (apart2 zenon_TY_t). zenon_intro zenon_H38.
% 0.39/0.61 generalize (ceq3 zenon_TY_t). zenon_intro zenon_H10.
% 0.39/0.61 generalize (apart6 zenon_TX_u). zenon_intro zenon_H36.
% 0.39/0.61 generalize (zenon_H36 zenon_TY_t). zenon_intro zenon_Hd.
% 0.39/0.61 generalize (con2 zenon_TX_u). zenon_intro zenon_H39.
% 0.39/0.61 generalize (zenon_H39 zenon_TZ_s). zenon_intro zenon_H3a.
% 0.39/0.61 generalize (apart4 (intersection_point zenon_TX_u zenon_TY_t)). zenon_intro zenon_H3b.
% 0.39/0.61 generalize (apart1 (intersection_point zenon_TX_u zenon_TZ_s)). zenon_intro zenon_H3c.
% 0.39/0.61 generalize (zenon_H3b (intersection_point zenon_TX_u zenon_TZ_s)). zenon_intro zenon_H3d.
% 0.39/0.61 generalize (zenon_H3a (intersection_point zenon_TX_u zenon_TZ_s)). zenon_intro zenon_H3e.
% 0.39/0.61 apply (zenon_imply_s _ _ zenon_H3e); [ zenon_intro zenon_Hf | zenon_intro zenon_H3f ].
% 0.39/0.61 apply (zenon_L1_ zenon_TZ_s zenon_TY_t zenon_TX_u); trivial.
% 0.39/0.61 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ].
% 0.39/0.61 apply (zenon_notor_s _ _ zenon_H41). zenon_intro zenon_H43. zenon_intro zenon_H42.
% 0.39/0.61 generalize (apart1 (intersection_point zenon_TX_u zenon_TY_t)). zenon_intro zenon_H44.
% 0.39/0.61 generalize (zenon_H39 zenon_TY_t). zenon_intro zenon_H45.
% 0.39/0.61 generalize (zenon_H3d (intersection_point zenon_TX_u zenon_TY_t)). zenon_intro zenon_H46.
% 0.39/0.61 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ].
% 0.39/0.61 exact (zenon_H48 zenon_H37).
% 0.39/0.61 apply (zenon_or_s _ _ zenon_H47); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ].
% 0.39/0.61 exact (zenon_H44 zenon_H4a).
% 0.39/0.61 generalize (cu1 (intersection_point zenon_TX_u zenon_TZ_s)). zenon_intro zenon_H4b.
% 0.39/0.61 generalize (zenon_H45 (intersection_point zenon_TX_u zenon_TY_t)). zenon_intro zenon_H4c.
% 0.39/0.61 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H17 | zenon_intro zenon_H4d ].
% 0.39/0.61 exact (zenon_H17 zenon_He).
% 0.39/0.61 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H4e | zenon_intro zenon_H4a ].
% 0.39/0.61 apply (zenon_notor_s _ _ zenon_H4e). zenon_intro zenon_H4f. zenon_intro zenon_H26.
% 0.39/0.61 generalize (zenon_H4b (intersection_point zenon_TX_u zenon_TY_t)). zenon_intro zenon_H50.
% 0.39/0.61 generalize (apart5 zenon_TX_u). zenon_intro zenon_H51.
% 0.39/0.61 generalize (zenon_H51 zenon_TY_t). zenon_intro zenon_H52.
% 0.39/0.61 generalize (zenon_H52 zenon_TY_t). zenon_intro zenon_H53.
% 0.39/0.61 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ].
% 0.39/0.61 generalize (ceq3 zenon_TX_u). zenon_intro zenon_H56.
% 0.39/0.61 generalize (zenon_H56 zenon_TY_t). zenon_intro zenon_H57.
% 0.39/0.61 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H17 | zenon_intro zenon_H58 ].
% 0.39/0.61 exact (zenon_H17 zenon_He).
% 0.39/0.61 exact (zenon_H55 zenon_H58).
% 0.39/0.61 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H58 | zenon_intro zenon_H59 ].
% 0.39/0.61 generalize (zenon_H52 zenon_TZ_s). zenon_intro zenon_H5a.
% 0.39/0.61 apply (zenon_imply_s _ _ zenon_H5a); [ zenon_intro zenon_H55 | zenon_intro zenon_H5b ].
% 0.39/0.61 exact (zenon_H55 zenon_H58).
% 0.39/0.61 apply (zenon_or_s _ _ zenon_H5b); [ zenon_intro zenon_H5c | zenon_intro zenon_H1b ].
% 0.39/0.61 generalize (zenon_H50 zenon_TX_u). zenon_intro zenon_H5d.
% 0.39/0.61 generalize (zenon_H5d zenon_TZ_s). zenon_intro zenon_H5e.
% 0.39/0.61 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H60 | zenon_intro zenon_H5f ].
% 0.39/0.61 apply (zenon_notand_s _ _ zenon_H60); [ zenon_intro zenon_H62 | zenon_intro zenon_H61 ].
% 0.39/0.61 exact (zenon_H62 zenon_H49).
% 0.39/0.61 exact (zenon_H61 zenon_H5c).
% 0.39/0.61 apply (zenon_or_s _ _ zenon_H5f); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ].
% 0.39/0.61 exact (zenon_H43 zenon_H64).
% 0.39/0.61 apply (zenon_or_s _ _ zenon_H63); [ zenon_intro zenon_H66 | zenon_intro zenon_H65 ].
% 0.39/0.61 exact (zenon_H42 zenon_H66).
% 0.39/0.61 apply (zenon_or_s _ _ zenon_H65); [ zenon_intro zenon_H67 | zenon_intro zenon_H25 ].
% 0.39/0.61 exact (zenon_H4f zenon_H67).
% 0.39/0.61 apply (zenon_L3_ zenon_TZ_s zenon_TY_t zenon_TX_u); trivial.
% 0.39/0.61 exact (zenon_H11 zenon_H1b).
% 0.39/0.61 exact (zenon_H38 zenon_H59).
% 0.39/0.61 exact (zenon_H44 zenon_H4a).
% 0.39/0.61 exact (zenon_H3c zenon_H40).
% 0.39/0.61 Qed.
% 0.39/0.61 % SZS output end Proof
% 0.39/0.61 (* END-PROOF *)
% 0.39/0.61 nodes searched: 8917
% 0.39/0.61 max branch formulas: 1527
% 0.39/0.61 proof nodes created: 831
% 0.39/0.61 formulas created: 24286
% 0.39/0.61
%------------------------------------------------------------------------------