TSTP Solution File: GEO173+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO173+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n005.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 07:00:23 EDT 2022
% Result : Theorem 0.18s 0.52s
% Output : Proof 0.18s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GEO173+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : run_zenon %s %d
% 0.11/0.33 % Computer : n005.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sat Jun 18 10:18:23 EDT 2022
% 0.11/0.33 % 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_lines U (line_connecting X Y))))->((apart_point_and_line X U)\/(apart_point_and_line Y U))))))).
% 0.18/0.52 Proof.
% 0.18/0.52 assert (zenon_L1_ : forall (zenon_TX_bm : zenon_U) (zenon_TY_bn : zenon_U), (apart_point_and_line zenon_TY_bn (line_connecting zenon_TX_bm zenon_TY_bn)) -> (distinct_points zenon_TX_bm zenon_TY_bn) -> False).
% 0.18/0.52 do 2 intro. intros zenon_H24 zenon_H25.
% 0.18/0.52 generalize (ci2 zenon_TX_bm). zenon_intro zenon_H28.
% 0.18/0.52 generalize (zenon_H28 zenon_TY_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_H24).
% 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_lines U (line_connecting X Y))))->((apart_point_and_line X U)\/(apart_point_and_line Y U))))))) zenon_G); [ zenon_intro zenon_H2c; idtac ].
% 0.18/0.52 elim zenon_H2c. zenon_intro zenon_TX_bm. zenon_intro zenon_H2d.
% 0.18/0.52 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_bm Y)/\((convergent_lines U V)/\(distinct_lines U (line_connecting zenon_TX_bm Y))))->((apart_point_and_line zenon_TX_bm U)\/(apart_point_and_line Y U)))))) zenon_H2d); [ zenon_intro zenon_H2e; idtac ].
% 0.18/0.52 elim zenon_H2e. zenon_intro zenon_TY_bn. zenon_intro zenon_H2f.
% 0.18/0.52 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_bm zenon_TY_bn)/\((convergent_lines U V)/\(distinct_lines U (line_connecting zenon_TX_bm zenon_TY_bn))))->((apart_point_and_line zenon_TX_bm U)\/(apart_point_and_line zenon_TY_bn U))))) zenon_H2f); [ zenon_intro zenon_H30; idtac ].
% 0.18/0.52 elim zenon_H30. zenon_intro zenon_TU_bx. zenon_intro zenon_H32.
% 0.18/0.52 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_bm zenon_TY_bn)/\((convergent_lines zenon_TU_bx V)/\(distinct_lines zenon_TU_bx (line_connecting zenon_TX_bm zenon_TY_bn))))->((apart_point_and_line zenon_TX_bm zenon_TU_bx)\/(apart_point_and_line zenon_TY_bn zenon_TU_bx)))) zenon_H32); [ zenon_intro zenon_H33; idtac ].
% 0.18/0.52 elim zenon_H33. zenon_intro zenon_TV_ca. 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_H25. zenon_intro zenon_H3a.
% 0.18/0.52 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3c. zenon_intro zenon_H3b.
% 0.18/0.52 generalize (cu1 zenon_TX_bm). zenon_intro zenon_H3d.
% 0.18/0.52 generalize (zenon_H3d zenon_TY_bn). zenon_intro zenon_H3e.
% 0.18/0.52 generalize (apart5 zenon_TU_bx). zenon_intro zenon_H3f.
% 0.18/0.52 generalize (zenon_H3f (line_connecting zenon_TX_bm zenon_TY_bn)). zenon_intro zenon_H40.
% 0.18/0.52 generalize (apart2 zenon_TU_bx). zenon_intro zenon_H41.
% 0.18/0.52 generalize (zenon_H40 zenon_TU_bx). 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_H3b).
% 0.18/0.52 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ].
% 0.18/0.52 exact (zenon_H41 zenon_H46).
% 0.18/0.52 generalize (zenon_H3e (line_connecting zenon_TX_bm zenon_TY_bn)). zenon_intro zenon_H47.
% 0.18/0.52 generalize (zenon_H47 zenon_TU_bx). zenon_intro zenon_H48.
% 0.18/0.52 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ].
% 0.18/0.52 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H2b | zenon_intro zenon_H4b ].
% 0.18/0.52 exact (zenon_H2b zenon_H25).
% 0.18/0.52 exact (zenon_H4b zenon_H45).
% 0.18/0.52 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H4d | zenon_intro zenon_H4c ].
% 0.18/0.52 generalize (ci1 zenon_TX_bm). zenon_intro zenon_H4e.
% 0.18/0.52 generalize (zenon_H4e zenon_TY_bn). zenon_intro zenon_H4f.
% 0.18/0.52 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H2b | zenon_intro zenon_H50 ].
% 0.18/0.52 exact (zenon_H2b zenon_H25).
% 0.18/0.52 exact (zenon_H50 zenon_H4d).
% 0.18/0.52 apply (zenon_or_s _ _ zenon_H4c); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ].
% 0.18/0.52 exact (zenon_H39 zenon_H52).
% 0.18/0.52 apply (zenon_or_s _ _ zenon_H51); [ zenon_intro zenon_H24 | zenon_intro zenon_H53 ].
% 0.18/0.52 apply (zenon_L1_ zenon_TX_bm zenon_TY_bn); trivial.
% 0.18/0.52 exact (zenon_H38 zenon_H53).
% 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: 1179
% 0.18/0.52 max branch formulas: 715
% 0.18/0.52 proof nodes created: 121
% 0.18/0.52 formulas created: 5939
% 0.18/0.52
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