TSTP Solution File: GEO187+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO187+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n014.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 07:00:32 EDT 2022
% Result : Theorem 0.44s 0.63s
% Output : Proof 0.44s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GEO187+1 : TPTP v8.1.0. Released v3.3.0.
% 0.08/0.14 % Command : run_zenon %s %d
% 0.14/0.36 % Computer : n014.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Fri Jun 17 20:47:04 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.44/0.63 (* PROOF-FOUND *)
% 0.44/0.63 % SZS status Theorem
% 0.44/0.63 (* BEGIN-PROOF *)
% 0.44/0.63 % SZS output start Proof
% 0.44/0.63 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((distinct_points U V)/\((~(apart_point_and_line X (line_connecting U V)))/\(~(apart_point_and_line Y (line_connecting U V))))))->((~(apart_point_and_line U (line_connecting X Y)))/\(~(apart_point_and_line V (line_connecting X Y))))))))).
% 0.44/0.63 Proof.
% 0.44/0.63 assert (zenon_L1_ : forall (zenon_TY_t : zenon_U) (zenon_TX_u : zenon_U), (forall Z : zenon_U, ((distinct_points zenon_TX_u zenon_TY_t)->((distinct_points zenon_TX_u Z)\/(distinct_points zenon_TY_t Z)))) -> (distinct_points zenon_TX_u zenon_TY_t) -> (~(distinct_points zenon_TX_u zenon_TX_u)) -> (~(distinct_points zenon_TY_t zenon_TX_u)) -> False).
% 0.44/0.63 do 2 intro. intros zenon_Hf zenon_H10 zenon_H11 zenon_H12.
% 0.44/0.63 generalize (zenon_Hf zenon_TX_u). zenon_intro zenon_H15.
% 0.44/0.63 apply (zenon_imply_s _ _ zenon_H15); [ zenon_intro zenon_H17 | zenon_intro zenon_H16 ].
% 0.44/0.63 exact (zenon_H17 zenon_H10).
% 0.44/0.63 apply (zenon_or_s _ _ zenon_H16); [ zenon_intro zenon_H19 | zenon_intro zenon_H18 ].
% 0.44/0.63 exact (zenon_H11 zenon_H19).
% 0.44/0.63 exact (zenon_H12 zenon_H18).
% 0.44/0.63 (* end of lemma zenon_L1_ *)
% 0.44/0.63 assert (zenon_L2_ : forall (zenon_TV_bg : zenon_U) (zenon_TU_bh : zenon_U) (zenon_TX_u : zenon_U) (zenon_TY_t : zenon_U), (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TY_t zenon_TX_u)/\(distinct_lines U V))->((apart_point_and_line zenon_TY_t U)\/((apart_point_and_line zenon_TY_t V)\/((apart_point_and_line zenon_TX_u U)\/(apart_point_and_line zenon_TX_u V))))))) -> (~(apart_point_and_line zenon_TX_u (line_connecting zenon_TU_bh zenon_TV_bg))) -> (~(apart_point_and_line zenon_TX_u (line_connecting zenon_TX_u zenon_TY_t))) -> (~(apart_point_and_line zenon_TY_t (line_connecting zenon_TU_bh zenon_TV_bg))) -> (~(apart_point_and_line zenon_TY_t (line_connecting zenon_TX_u zenon_TY_t))) -> (distinct_lines (line_connecting zenon_TX_u zenon_TY_t) (line_connecting zenon_TU_bh zenon_TV_bg)) -> (distinct_points zenon_TY_t zenon_TX_u) -> False).
% 0.44/0.63 do 4 intro. intros zenon_H1a zenon_H1b zenon_H1c zenon_H1d zenon_H1e zenon_H1f zenon_H18.
% 0.44/0.63 generalize (zenon_H1a (line_connecting zenon_TX_u zenon_TY_t)). zenon_intro zenon_H22.
% 0.44/0.63 generalize (zenon_H22 (line_connecting zenon_TU_bh zenon_TV_bg)). zenon_intro zenon_H23.
% 0.44/0.63 apply (zenon_imply_s _ _ zenon_H23); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ].
% 0.44/0.63 apply (zenon_notand_s _ _ zenon_H25); [ zenon_intro zenon_H12 | zenon_intro zenon_H26 ].
% 0.44/0.63 exact (zenon_H12 zenon_H18).
% 0.44/0.63 exact (zenon_H26 zenon_H1f).
% 0.44/0.63 apply (zenon_or_s _ _ zenon_H24); [ zenon_intro zenon_H28 | zenon_intro zenon_H27 ].
% 0.44/0.63 exact (zenon_H1e zenon_H28).
% 0.44/0.63 apply (zenon_or_s _ _ zenon_H27); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ].
% 0.44/0.63 exact (zenon_H1d zenon_H2a).
% 0.44/0.63 apply (zenon_or_s _ _ zenon_H29); [ zenon_intro zenon_H2c | zenon_intro zenon_H2b ].
% 0.44/0.63 exact (zenon_H1c zenon_H2c).
% 0.44/0.63 exact (zenon_H1b zenon_H2b).
% 0.44/0.63 (* end of lemma zenon_L2_ *)
% 0.44/0.63 apply NNPP. intro zenon_G.
% 0.44/0.63 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((distinct_points U V)/\((~(apart_point_and_line X (line_connecting U V)))/\(~(apart_point_and_line Y (line_connecting U V))))))->((~(apart_point_and_line U (line_connecting X Y)))/\(~(apart_point_and_line V (line_connecting X Y))))))))) zenon_G); [ zenon_intro zenon_H2d; idtac ].
% 0.44/0.63 elim zenon_H2d. zenon_intro zenon_TX_u. zenon_intro zenon_H2e.
% 0.44/0.63 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_u Y)/\((distinct_points U V)/\((~(apart_point_and_line zenon_TX_u (line_connecting U V)))/\(~(apart_point_and_line Y (line_connecting U V))))))->((~(apart_point_and_line U (line_connecting zenon_TX_u Y)))/\(~(apart_point_and_line V (line_connecting zenon_TX_u Y)))))))) zenon_H2e); [ zenon_intro zenon_H2f; idtac ].
% 0.44/0.63 elim zenon_H2f. zenon_intro zenon_TY_t. zenon_intro zenon_H30.
% 0.44/0.63 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_u zenon_TY_t)/\((distinct_points U V)/\((~(apart_point_and_line zenon_TX_u (line_connecting U V)))/\(~(apart_point_and_line zenon_TY_t (line_connecting U V))))))->((~(apart_point_and_line U (line_connecting zenon_TX_u zenon_TY_t)))/\(~(apart_point_and_line V (line_connecting zenon_TX_u zenon_TY_t))))))) zenon_H30); [ zenon_intro zenon_H31; idtac ].
% 0.44/0.63 elim zenon_H31. zenon_intro zenon_TU_bh. zenon_intro zenon_H32.
% 0.44/0.63 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_u zenon_TY_t)/\((distinct_points zenon_TU_bh V)/\((~(apart_point_and_line zenon_TX_u (line_connecting zenon_TU_bh V)))/\(~(apart_point_and_line zenon_TY_t (line_connecting zenon_TU_bh V))))))->((~(apart_point_and_line zenon_TU_bh (line_connecting zenon_TX_u zenon_TY_t)))/\(~(apart_point_and_line V (line_connecting zenon_TX_u zenon_TY_t)))))) zenon_H32); [ zenon_intro zenon_H33; idtac ].
% 0.44/0.63 elim zenon_H33. zenon_intro zenon_TV_bg. zenon_intro zenon_H34.
% 0.44/0.63 apply (zenon_notimply_s _ _ zenon_H34). zenon_intro zenon_H36. zenon_intro zenon_H35.
% 0.44/0.63 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H10. zenon_intro zenon_H37.
% 0.44/0.63 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H39. zenon_intro zenon_H38.
% 0.44/0.63 apply (zenon_and_s _ _ zenon_H38). zenon_intro zenon_H1b. zenon_intro zenon_H1d.
% 0.44/0.63 apply (zenon_notand_s _ _ zenon_H35); [ zenon_intro zenon_H3b | zenon_intro zenon_H3a ].
% 0.44/0.63 apply zenon_H3b. zenon_intro zenon_H3c.
% 0.44/0.63 generalize (apart4 zenon_TX_u). zenon_intro zenon_H3d.
% 0.44/0.63 generalize (ci1 zenon_TX_u). zenon_intro zenon_H3e.
% 0.44/0.63 generalize (zenon_H3d zenon_TY_t). zenon_intro zenon_Hf.
% 0.44/0.63 generalize (cu1 zenon_TY_t). zenon_intro zenon_H3f.
% 0.44/0.63 generalize (apart4 zenon_TY_t). zenon_intro zenon_H40.
% 0.44/0.63 generalize (ci2 zenon_TX_u). zenon_intro zenon_H41.
% 0.44/0.63 generalize (zenon_H3e zenon_TY_t). zenon_intro zenon_H42.
% 0.44/0.63 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H17 | zenon_intro zenon_H1c ].
% 0.44/0.63 exact (zenon_H17 zenon_H10).
% 0.44/0.63 generalize (zenon_H41 zenon_TY_t). zenon_intro zenon_H43.
% 0.44/0.63 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H17 | zenon_intro zenon_H1e ].
% 0.44/0.63 exact (zenon_H17 zenon_H10).
% 0.44/0.63 generalize (apart1 zenon_TX_u). zenon_intro zenon_H11.
% 0.44/0.63 generalize (zenon_H3f zenon_TX_u). zenon_intro zenon_H1a.
% 0.44/0.63 generalize (zenon_H40 zenon_TX_u). zenon_intro zenon_H44.
% 0.44/0.63 generalize (zenon_H44 zenon_TX_u). zenon_intro zenon_H45.
% 0.44/0.63 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H12 | zenon_intro zenon_H46 ].
% 0.44/0.63 apply (zenon_L1_ zenon_TY_t zenon_TX_u); trivial.
% 0.44/0.63 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H18 | zenon_intro zenon_H19 ].
% 0.44/0.63 generalize (ceq2 zenon_TU_bh). zenon_intro zenon_H47.
% 0.44/0.63 generalize (zenon_H47 (line_connecting zenon_TX_u zenon_TY_t)). zenon_intro zenon_H48.
% 0.44/0.63 generalize (ci1 zenon_TU_bh). zenon_intro zenon_H49.
% 0.44/0.63 generalize (zenon_H49 zenon_TV_bg). zenon_intro zenon_H4a.
% 0.44/0.63 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ].
% 0.44/0.63 exact (zenon_H4c zenon_H39).
% 0.44/0.63 generalize (zenon_H48 (line_connecting zenon_TU_bh zenon_TV_bg)). zenon_intro zenon_H4d.
% 0.44/0.63 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ].
% 0.44/0.63 exact (zenon_H4f zenon_H3c).
% 0.44/0.63 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H1f | zenon_intro zenon_H50 ].
% 0.44/0.63 apply (zenon_L2_ zenon_TV_bg zenon_TU_bh zenon_TX_u zenon_TY_t); trivial.
% 0.44/0.63 exact (zenon_H4b zenon_H50).
% 0.44/0.63 exact (zenon_H11 zenon_H19).
% 0.44/0.63 apply zenon_H3a. zenon_intro zenon_H51.
% 0.44/0.63 generalize (apart4 zenon_TX_u). zenon_intro zenon_H3d.
% 0.44/0.63 generalize (ci1 zenon_TX_u). zenon_intro zenon_H3e.
% 0.44/0.63 generalize (zenon_H3d zenon_TY_t). zenon_intro zenon_Hf.
% 0.44/0.63 generalize (cu1 zenon_TY_t). zenon_intro zenon_H3f.
% 0.44/0.63 generalize (apart4 zenon_TY_t). zenon_intro zenon_H40.
% 0.44/0.63 generalize (ci2 zenon_TX_u). zenon_intro zenon_H41.
% 0.44/0.63 generalize (zenon_H3e zenon_TY_t). zenon_intro zenon_H42.
% 0.44/0.63 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H17 | zenon_intro zenon_H1c ].
% 0.44/0.63 exact (zenon_H17 zenon_H10).
% 0.44/0.63 generalize (zenon_H41 zenon_TY_t). zenon_intro zenon_H43.
% 0.44/0.63 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H17 | zenon_intro zenon_H1e ].
% 0.44/0.63 exact (zenon_H17 zenon_H10).
% 0.44/0.63 generalize (apart1 zenon_TX_u). zenon_intro zenon_H11.
% 0.44/0.63 generalize (zenon_H3f zenon_TX_u). zenon_intro zenon_H1a.
% 0.44/0.63 generalize (zenon_H40 zenon_TX_u). zenon_intro zenon_H44.
% 0.44/0.63 generalize (zenon_H44 zenon_TX_u). zenon_intro zenon_H45.
% 0.44/0.63 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H12 | zenon_intro zenon_H46 ].
% 0.44/0.63 apply (zenon_L1_ zenon_TY_t zenon_TX_u); trivial.
% 0.44/0.63 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H18 | zenon_intro zenon_H19 ].
% 0.44/0.63 generalize (ceq2 zenon_TV_bg). zenon_intro zenon_H52.
% 0.44/0.63 generalize (zenon_H52 (line_connecting zenon_TX_u zenon_TY_t)). zenon_intro zenon_H53.
% 0.44/0.63 generalize (ci2 zenon_TU_bh). zenon_intro zenon_H54.
% 0.44/0.63 generalize (zenon_H54 zenon_TV_bg). zenon_intro zenon_H55.
% 0.44/0.63 apply (zenon_imply_s _ _ zenon_H55); [ zenon_intro zenon_H4c | zenon_intro zenon_H56 ].
% 0.44/0.63 exact (zenon_H4c zenon_H39).
% 0.44/0.63 generalize (zenon_H53 (line_connecting zenon_TU_bh zenon_TV_bg)). zenon_intro zenon_H57.
% 0.44/0.63 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H59 | zenon_intro zenon_H58 ].
% 0.44/0.63 exact (zenon_H59 zenon_H51).
% 0.44/0.63 apply (zenon_or_s _ _ zenon_H58); [ zenon_intro zenon_H1f | zenon_intro zenon_H5a ].
% 0.44/0.63 apply (zenon_L2_ zenon_TV_bg zenon_TU_bh zenon_TX_u zenon_TY_t); trivial.
% 0.44/0.63 exact (zenon_H56 zenon_H5a).
% 0.44/0.63 exact (zenon_H11 zenon_H19).
% 0.44/0.63 Qed.
% 0.44/0.63 % SZS output end Proof
% 0.44/0.63 (* END-PROOF *)
% 0.44/0.63 nodes searched: 3524
% 0.44/0.63 max branch formulas: 1045
% 0.44/0.63 proof nodes created: 303
% 0.44/0.63 formulas created: 10995
% 0.44/0.63
%------------------------------------------------------------------------------