TSTP Solution File: GEO177+1 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO177+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n016.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 07:00:25 EDT 2022
% Result : Theorem 0.19s 0.57s
% Output : Proof 0.41s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO177+1 : TPTP v8.1.0. Released v3.3.0.
% 0.12/0.13 % Command : run_zenon %s %d
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Fri Jun 17 23:47:36 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.57 (* PROOF-FOUND *)
% 0.19/0.57 % SZS status Theorem
% 0.19/0.57 (* BEGIN-PROOF *)
% 0.19/0.57 % SZS output start Proof
% 0.19/0.57 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))))))))).
% 0.19/0.57 Proof.
% 0.19/0.57 assert (zenon_L1_ : forall (zenon_TY_w : zenon_U) (zenon_TX_x : zenon_U) (zenon_TV_y : zenon_U) (zenon_TU_z : zenon_U), (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TU_z zenon_TV_y)/\(distinct_lines U V))->((apart_point_and_line zenon_TU_z U)\/((apart_point_and_line zenon_TU_z V)\/((apart_point_and_line zenon_TV_y U)\/(apart_point_and_line zenon_TV_y V))))))) -> (~(apart_point_and_line zenon_TV_y (line_connecting zenon_TX_x zenon_TY_w))) -> (~(apart_point_and_line zenon_TV_y (line_connecting zenon_TU_z zenon_TV_y))) -> (~(apart_point_and_line zenon_TU_z (line_connecting zenon_TX_x zenon_TY_w))) -> (~(apart_point_and_line zenon_TU_z (line_connecting zenon_TU_z zenon_TV_y))) -> (distinct_lines (line_connecting zenon_TU_z zenon_TV_y) (line_connecting zenon_TX_x zenon_TY_w)) -> (distinct_points zenon_TU_z zenon_TV_y) -> False).
% 0.19/0.57 do 4 intro. intros zenon_Hf zenon_H10 zenon_H11 zenon_H12 zenon_H13 zenon_H14 zenon_H15.
% 0.19/0.57 generalize (zenon_Hf (line_connecting zenon_TU_z zenon_TV_y)). zenon_intro zenon_H1a.
% 0.19/0.57 generalize (zenon_H1a (line_connecting zenon_TX_x zenon_TY_w)). zenon_intro zenon_H1b.
% 0.19/0.57 apply (zenon_imply_s _ _ zenon_H1b); [ zenon_intro zenon_H1d | zenon_intro zenon_H1c ].
% 0.19/0.57 apply (zenon_notand_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ].
% 0.19/0.57 exact (zenon_H1f zenon_H15).
% 0.19/0.57 exact (zenon_H1e zenon_H14).
% 0.19/0.57 apply (zenon_or_s _ _ zenon_H1c); [ zenon_intro zenon_H21 | zenon_intro zenon_H20 ].
% 0.19/0.57 exact (zenon_H13 zenon_H21).
% 0.19/0.57 apply (zenon_or_s _ _ zenon_H20); [ zenon_intro zenon_H23 | zenon_intro zenon_H22 ].
% 0.19/0.57 exact (zenon_H12 zenon_H23).
% 0.19/0.57 apply (zenon_or_s _ _ zenon_H22); [ zenon_intro zenon_H25 | zenon_intro zenon_H24 ].
% 0.19/0.57 exact (zenon_H11 zenon_H25).
% 0.19/0.57 exact (zenon_H10 zenon_H24).
% 0.19/0.57 (* end of lemma zenon_L1_ *)
% 0.19/0.57 apply NNPP. intro zenon_G.
% 0.19/0.57 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_H26; idtac ].
% 0.19/0.57 elim zenon_H26. zenon_intro zenon_TX_x. zenon_intro zenon_H27.
% 0.19/0.57 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_x Y)/\(distinct_points U V))->(((apart_point_and_line zenon_TX_x (line_connecting U V))\/(apart_point_and_line Y (line_connecting U V)))->((apart_point_and_line U (line_connecting zenon_TX_x Y))\/(apart_point_and_line V (line_connecting zenon_TX_x Y)))))))) zenon_H27); [ zenon_intro zenon_H28; idtac ].
% 0.19/0.57 elim zenon_H28. zenon_intro zenon_TY_w. zenon_intro zenon_H29.
% 0.19/0.57 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_x zenon_TY_w)/\(distinct_points U V))->(((apart_point_and_line zenon_TX_x (line_connecting U V))\/(apart_point_and_line zenon_TY_w (line_connecting U V)))->((apart_point_and_line U (line_connecting zenon_TX_x zenon_TY_w))\/(apart_point_and_line V (line_connecting zenon_TX_x zenon_TY_w))))))) zenon_H29); [ zenon_intro zenon_H2a; idtac ].
% 0.19/0.57 elim zenon_H2a. zenon_intro zenon_TU_z. zenon_intro zenon_H2b.
% 0.19/0.57 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_x zenon_TY_w)/\(distinct_points zenon_TU_z V))->(((apart_point_and_line zenon_TX_x (line_connecting zenon_TU_z V))\/(apart_point_and_line zenon_TY_w (line_connecting zenon_TU_z V)))->((apart_point_and_line zenon_TU_z (line_connecting zenon_TX_x zenon_TY_w))\/(apart_point_and_line V (line_connecting zenon_TX_x zenon_TY_w)))))) zenon_H2b); [ zenon_intro zenon_H2c; idtac ].
% 0.19/0.58 elim zenon_H2c. zenon_intro zenon_TV_y. zenon_intro zenon_H2d.
% 0.19/0.58 apply (zenon_notimply_s _ _ zenon_H2d). zenon_intro zenon_H2f. zenon_intro zenon_H2e.
% 0.19/0.58 apply (zenon_notimply_s _ _ zenon_H2e). zenon_intro zenon_H31. zenon_intro zenon_H30.
% 0.19/0.58 apply (zenon_notor_s _ _ zenon_H30). zenon_intro zenon_H12. zenon_intro zenon_H10.
% 0.19/0.58 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H32. zenon_intro zenon_H15.
% 0.19/0.58 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 0.19/0.58 generalize (cu1 zenon_TU_z). zenon_intro zenon_H35.
% 0.19/0.58 generalize (ci1 zenon_TU_z). zenon_intro zenon_H36.
% 0.19/0.58 generalize (zenon_H35 zenon_TV_y). zenon_intro zenon_Hf.
% 0.19/0.58 generalize (ci2 zenon_TU_z). zenon_intro zenon_H37.
% 0.19/0.58 generalize (zenon_H36 zenon_TV_y). zenon_intro zenon_H38.
% 0.19/0.58 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H1f | zenon_intro zenon_H13 ].
% 0.19/0.58 exact (zenon_H1f zenon_H15).
% 0.19/0.58 generalize (zenon_H37 zenon_TV_y). zenon_intro zenon_H39.
% 0.19/0.58 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H1f | zenon_intro zenon_H11 ].
% 0.19/0.58 exact (zenon_H1f zenon_H15).
% 0.19/0.58 generalize (ceq2 zenon_TX_x). zenon_intro zenon_H3a.
% 0.19/0.58 generalize (zenon_H3a (line_connecting zenon_TU_z zenon_TV_y)). zenon_intro zenon_H3b.
% 0.19/0.58 generalize (ci1 zenon_TX_x). zenon_intro zenon_H3c.
% 0.19/0.58 generalize (zenon_H3c zenon_TY_w). zenon_intro zenon_H3d.
% 0.19/0.58 apply (zenon_imply_s _ _ zenon_H3d); [ zenon_intro zenon_H3f | zenon_intro zenon_H3e ].
% 0.19/0.58 exact (zenon_H3f zenon_H32).
% 0.19/0.58 generalize (zenon_H3b (line_connecting zenon_TX_x zenon_TY_w)). zenon_intro zenon_H40.
% 0.19/0.58 apply (zenon_imply_s _ _ zenon_H40); [ zenon_intro zenon_H42 | zenon_intro zenon_H41 ].
% 0.19/0.58 exact (zenon_H42 zenon_H34).
% 0.19/0.58 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H14 | zenon_intro zenon_H43 ].
% 0.19/0.58 apply (zenon_L1_ zenon_TY_w zenon_TX_x zenon_TV_y zenon_TU_z); trivial.
% 0.19/0.58 exact (zenon_H3e zenon_H43).
% 0.19/0.58 generalize (cu1 zenon_TU_z). zenon_intro zenon_H35.
% 0.19/0.58 generalize (ci1 zenon_TU_z). zenon_intro zenon_H36.
% 0.19/0.58 generalize (zenon_H35 zenon_TV_y). zenon_intro zenon_Hf.
% 0.19/0.58 generalize (ci2 zenon_TU_z). zenon_intro zenon_H37.
% 0.19/0.58 generalize (zenon_H36 zenon_TV_y). zenon_intro zenon_H38.
% 0.41/0.58 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H1f | zenon_intro zenon_H13 ].
% 0.41/0.58 exact (zenon_H1f zenon_H15).
% 0.41/0.58 generalize (zenon_H37 zenon_TV_y). zenon_intro zenon_H39.
% 0.41/0.58 apply (zenon_imply_s _ _ zenon_H39); [ zenon_intro zenon_H1f | zenon_intro zenon_H11 ].
% 0.41/0.58 exact (zenon_H1f zenon_H15).
% 0.41/0.58 generalize (ceq2 zenon_TY_w). zenon_intro zenon_H44.
% 0.41/0.58 generalize (zenon_H44 (line_connecting zenon_TU_z zenon_TV_y)). zenon_intro zenon_H45.
% 0.41/0.58 generalize (ci2 zenon_TX_x). zenon_intro zenon_H46.
% 0.41/0.58 generalize (zenon_H46 zenon_TY_w). zenon_intro zenon_H47.
% 0.41/0.58 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H3f | zenon_intro zenon_H48 ].
% 0.41/0.58 exact (zenon_H3f zenon_H32).
% 0.41/0.58 generalize (zenon_H45 (line_connecting zenon_TX_x zenon_TY_w)). zenon_intro zenon_H49.
% 0.41/0.58 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ].
% 0.41/0.58 exact (zenon_H4b zenon_H33).
% 0.41/0.58 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H14 | zenon_intro zenon_H4c ].
% 0.41/0.58 apply (zenon_L1_ zenon_TY_w zenon_TX_x zenon_TV_y zenon_TU_z); trivial.
% 0.41/0.58 exact (zenon_H48 zenon_H4c).
% 0.41/0.58 Qed.
% 0.41/0.58 % SZS output end Proof
% 0.41/0.58 (* END-PROOF *)
% 0.41/0.58 nodes searched: 3038
% 0.41/0.58 max branch formulas: 936
% 0.41/0.58 proof nodes created: 266
% 0.41/0.58 formulas created: 9454
% 0.41/0.58
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