TSTP Solution File: GEO182+2 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO182+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n015.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 07:00:29 EDT 2022
% Result : Theorem 0.37s 0.54s
% Output : Proof 0.37s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO182+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.14 % Command : run_zenon %s %d
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jun 18 01:14:28 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.37/0.54 (* PROOF-FOUND *)
% 0.37/0.54 % SZS status Theorem
% 0.37/0.54 (* BEGIN-PROOF *)
% 0.37/0.54 % SZS output start Proof
% 0.37/0.54 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, ((distinct_points X Y)->((apart_point_and_line Z (line_connecting X Y))->(apart_point_and_line Z (line_connecting Y X))))))).
% 0.37/0.54 Proof.
% 0.37/0.54 apply NNPP. intro zenon_G.
% 0.37/0.54 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, ((distinct_points X Y)->((apart_point_and_line Z (line_connecting X Y))->(apart_point_and_line Z (line_connecting Y X))))))) zenon_G); [ zenon_intro zenon_Hd; idtac ].
% 0.37/0.54 elim zenon_Hd. zenon_intro zenon_TX_o. zenon_intro zenon_Hf.
% 0.37/0.54 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, ((distinct_points zenon_TX_o Y)->((apart_point_and_line Z (line_connecting zenon_TX_o Y))->(apart_point_and_line Z (line_connecting Y zenon_TX_o)))))) zenon_Hf); [ zenon_intro zenon_H10; idtac ].
% 0.37/0.54 elim zenon_H10. zenon_intro zenon_TY_r. zenon_intro zenon_H12.
% 0.37/0.54 apply (zenon_notallex_s (fun Z : zenon_U => ((distinct_points zenon_TX_o zenon_TY_r)->((apart_point_and_line Z (line_connecting zenon_TX_o zenon_TY_r))->(apart_point_and_line Z (line_connecting zenon_TY_r zenon_TX_o))))) zenon_H12); [ zenon_intro zenon_H13; idtac ].
% 0.37/0.54 elim zenon_H13. zenon_intro zenon_TZ_u. zenon_intro zenon_H15.
% 0.37/0.54 apply (zenon_notimply_s _ _ zenon_H15). zenon_intro zenon_H17. zenon_intro zenon_H16.
% 0.37/0.54 apply (zenon_notimply_s _ _ zenon_H16). zenon_intro zenon_H19. zenon_intro zenon_H18.
% 0.37/0.54 generalize (apart1 zenon_TY_r). zenon_intro zenon_H1a.
% 0.37/0.54 generalize (con1 zenon_TY_r). zenon_intro zenon_H1b.
% 0.37/0.54 generalize (cu1 zenon_TX_o). zenon_intro zenon_H1c.
% 0.37/0.54 generalize (apart4 zenon_TX_o). zenon_intro zenon_H1d.
% 0.37/0.54 generalize (zenon_H1c zenon_TY_r). zenon_intro zenon_H1e.
% 0.37/0.54 generalize (zenon_H1d zenon_TY_r). zenon_intro zenon_H1f.
% 0.37/0.54 generalize (con1 zenon_TX_o). zenon_intro zenon_H20.
% 0.37/0.54 generalize (apart1 zenon_TX_o). zenon_intro zenon_H21.
% 0.37/0.54 generalize (zenon_H20 zenon_TY_r). zenon_intro zenon_H22.
% 0.37/0.54 generalize (zenon_H1b zenon_TX_o). zenon_intro zenon_H23.
% 0.37/0.54 generalize (ceq2 zenon_TZ_u). zenon_intro zenon_H24.
% 0.37/0.54 generalize (zenon_H22 zenon_TY_r). zenon_intro zenon_H25.
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H25); [ zenon_intro zenon_H27 | zenon_intro zenon_H26 ].
% 0.37/0.54 exact (zenon_H27 zenon_H17).
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H26); [ zenon_intro zenon_H29 | zenon_intro zenon_H28 ].
% 0.37/0.54 generalize (zenon_H22 zenon_TX_o). zenon_intro zenon_H2a.
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H27 | zenon_intro zenon_H2b ].
% 0.37/0.54 exact (zenon_H27 zenon_H17).
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ].
% 0.37/0.54 generalize (zenon_H1f zenon_TX_o). zenon_intro zenon_H2e.
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H27 | zenon_intro zenon_H2f ].
% 0.37/0.54 exact (zenon_H27 zenon_H17).
% 0.37/0.54 apply (zenon_or_s _ _ zenon_H2f); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ].
% 0.37/0.54 exact (zenon_H21 zenon_H31).
% 0.37/0.54 generalize (zenon_H23 zenon_TY_r). zenon_intro zenon_H32.
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ].
% 0.37/0.54 exact (zenon_H34 zenon_H30).
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H36 | zenon_intro zenon_H35 ].
% 0.37/0.54 generalize (zenon_H23 zenon_TX_o). zenon_intro zenon_H37.
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H37); [ zenon_intro zenon_H34 | zenon_intro zenon_H38 ].
% 0.37/0.54 exact (zenon_H34 zenon_H30).
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H3a | zenon_intro zenon_H39 ].
% 0.37/0.54 generalize (zenon_H24 (line_connecting zenon_TX_o zenon_TY_r)). zenon_intro zenon_H3b.
% 0.37/0.54 generalize (zenon_H3b (line_connecting zenon_TY_r zenon_TX_o)). zenon_intro zenon_H3c.
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ].
% 0.37/0.54 exact (zenon_H3e zenon_H19).
% 0.37/0.54 apply (zenon_or_s _ _ zenon_H3d); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ].
% 0.37/0.54 generalize (zenon_H1e (line_connecting zenon_TX_o zenon_TY_r)). zenon_intro zenon_H41.
% 0.37/0.54 generalize (zenon_H41 (line_connecting zenon_TY_r zenon_TX_o)). zenon_intro zenon_H42.
% 0.37/0.54 apply (zenon_imply_s _ _ zenon_H42); [ zenon_intro zenon_H44 | zenon_intro zenon_H43 ].
% 0.37/0.54 apply (zenon_notand_s _ _ zenon_H44); [ zenon_intro zenon_H27 | zenon_intro zenon_H45 ].
% 0.37/0.54 exact (zenon_H27 zenon_H17).
% 0.37/0.54 exact (zenon_H45 zenon_H40).
% 0.37/0.54 apply (zenon_or_s _ _ zenon_H43); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ].
% 0.37/0.54 exact (zenon_H2d zenon_H47).
% 0.37/0.54 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ].
% 0.37/0.54 exact (zenon_H3a zenon_H49).
% 0.37/0.54 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ].
% 0.37/0.54 exact (zenon_H29 zenon_H4b).
% 0.37/0.54 exact (zenon_H36 zenon_H4a).
% 0.37/0.54 exact (zenon_H18 zenon_H3f).
% 0.37/0.54 apply (zenon_and_s _ _ zenon_H39). zenon_intro zenon_H17. zenon_intro zenon_H31.
% 0.37/0.54 exact (zenon_H21 zenon_H31).
% 0.37/0.54 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H4c. zenon_intro zenon_H30.
% 0.37/0.54 exact (zenon_H1a zenon_H4c).
% 0.37/0.54 apply (zenon_and_s _ _ zenon_H2c). zenon_intro zenon_H31. zenon_intro zenon_H17.
% 0.37/0.54 exact (zenon_H21 zenon_H31).
% 0.37/0.54 apply (zenon_and_s _ _ zenon_H28). zenon_intro zenon_H30. zenon_intro zenon_H4c.
% 0.37/0.54 exact (zenon_H1a zenon_H4c).
% 0.37/0.54 Qed.
% 0.37/0.54 % SZS output end Proof
% 0.37/0.54 (* END-PROOF *)
% 0.37/0.54 nodes searched: 615
% 0.37/0.54 max branch formulas: 350
% 0.37/0.54 proof nodes created: 111
% 0.37/0.54 formulas created: 2936
% 0.37/0.54
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