TSTP Solution File: GEO170+3 by Zenon---0.7.1
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%------------------------------------------------------------------------------
% File : Zenon---0.7.1
% Problem : GEO170+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_zenon %s %d
% Computer : n017.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 07:00:21 EDT 2022
% Result : Theorem 0.21s 0.51s
% Output : Proof 0.21s
% Verified :
% SZS Type : -
% Comments :
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%----WARNING: Could not form TPTP format derivation
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%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO170+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : run_zenon %s %d
% 0.14/0.34 % Computer : n017.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 600
% 0.14/0.34 % DateTime : Sat Jun 18 15:08:57 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.21/0.51 (* PROOF-FOUND *)
% 0.21/0.51 % SZS status Theorem
% 0.21/0.51 (* BEGIN-PROOF *)
% 0.21/0.51 % SZS output start Proof
% 0.21/0.51 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((incident_point_and_line X Z)/\(incident_point_and_line Y Z)))->(equal_lines Z (line_connecting X Y)))))).
% 0.21/0.51 Proof.
% 0.21/0.51 apply NNPP. intro zenon_G.
% 0.21/0.51 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((distinct_points X Y)/\((incident_point_and_line X Z)/\(incident_point_and_line Y Z)))->(equal_lines Z (line_connecting X Y)))))) zenon_G); [ zenon_intro zenon_H24; idtac ].
% 0.21/0.51 elim zenon_H24. zenon_intro zenon_TX_bl. zenon_intro zenon_H26.
% 0.21/0.51 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((distinct_points zenon_TX_bl Y)/\((incident_point_and_line zenon_TX_bl Z)/\(incident_point_and_line Y Z)))->(equal_lines Z (line_connecting zenon_TX_bl Y))))) zenon_H26); [ zenon_intro zenon_H27; idtac ].
% 0.21/0.51 elim zenon_H27. zenon_intro zenon_TY_bo. zenon_intro zenon_H29.
% 0.21/0.51 apply (zenon_notallex_s (fun Z : zenon_U => (((distinct_points zenon_TX_bl zenon_TY_bo)/\((incident_point_and_line zenon_TX_bl Z)/\(incident_point_and_line zenon_TY_bo Z)))->(equal_lines Z (line_connecting zenon_TX_bl zenon_TY_bo)))) zenon_H29); [ zenon_intro zenon_H2a; idtac ].
% 0.21/0.51 elim zenon_H2a. zenon_intro zenon_TZ_br. zenon_intro zenon_H2c.
% 0.21/0.51 apply (zenon_notimply_s _ _ zenon_H2c). zenon_intro zenon_H2e. zenon_intro zenon_H2d.
% 0.21/0.51 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H2f.
% 0.21/0.51 apply (zenon_and_s _ _ zenon_H2f). zenon_intro zenon_H32. zenon_intro zenon_H31.
% 0.21/0.51 generalize (a4 zenon_TX_bl). zenon_intro zenon_H33.
% 0.21/0.51 generalize (zenon_H33 zenon_TZ_br). zenon_intro zenon_H34.
% 0.21/0.51 apply (zenon_equiv_s _ _ zenon_H34); [ zenon_intro zenon_H37; zenon_intro zenon_H36 | zenon_intro zenon_H32; zenon_intro zenon_H35 ].
% 0.21/0.51 exact (zenon_H37 zenon_H32).
% 0.21/0.51 generalize (a4 zenon_TY_bo). zenon_intro zenon_H38.
% 0.21/0.51 generalize (zenon_H38 zenon_TZ_br). zenon_intro zenon_H39.
% 0.21/0.51 apply (zenon_equiv_s _ _ zenon_H39); [ zenon_intro zenon_H3c; zenon_intro zenon_H3b | zenon_intro zenon_H31; zenon_intro zenon_H3a ].
% 0.21/0.51 exact (zenon_H3c zenon_H31).
% 0.21/0.51 generalize (ax2 zenon_TZ_br). zenon_intro zenon_H3d.
% 0.21/0.51 generalize (zenon_H3d (line_connecting zenon_TX_bl zenon_TY_bo)). zenon_intro zenon_H3e.
% 0.21/0.51 apply (zenon_equiv_s _ _ zenon_H3e); [ zenon_intro zenon_H2d; zenon_intro zenon_H41 | zenon_intro zenon_H40; zenon_intro zenon_H3f ].
% 0.21/0.51 apply zenon_H41. zenon_intro zenon_H42.
% 0.21/0.51 generalize (cu1 zenon_TX_bl). zenon_intro zenon_H43.
% 0.21/0.51 generalize (zenon_H43 zenon_TY_bo). zenon_intro zenon_H44.
% 0.21/0.51 generalize (ci1 zenon_TX_bl). zenon_intro zenon_H45.
% 0.21/0.51 generalize (ci2 zenon_TX_bl). zenon_intro zenon_H46.
% 0.21/0.51 generalize (zenon_H45 zenon_TY_bo). zenon_intro zenon_H47.
% 0.21/0.51 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ].
% 0.21/0.51 exact (zenon_H49 zenon_H30).
% 0.21/0.51 generalize (zenon_H46 zenon_TY_bo). zenon_intro zenon_H4a.
% 0.21/0.51 apply (zenon_imply_s _ _ zenon_H4a); [ zenon_intro zenon_H49 | zenon_intro zenon_H4b ].
% 0.21/0.51 exact (zenon_H49 zenon_H30).
% 0.21/0.51 generalize (zenon_H44 zenon_TZ_br). zenon_intro zenon_H4c.
% 0.21/0.51 generalize (zenon_H4c (line_connecting zenon_TX_bl zenon_TY_bo)). zenon_intro zenon_H4d.
% 0.21/0.51 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ].
% 0.21/0.51 apply (zenon_notand_s _ _ zenon_H4f); [ zenon_intro zenon_H49 | zenon_intro zenon_H3f ].
% 0.21/0.51 exact (zenon_H49 zenon_H30).
% 0.21/0.51 exact (zenon_H3f zenon_H42).
% 0.21/0.51 apply (zenon_or_s _ _ zenon_H4e); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ].
% 0.21/0.51 exact (zenon_H35 zenon_H51).
% 0.21/0.51 apply (zenon_or_s _ _ zenon_H50); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ].
% 0.21/0.51 exact (zenon_H48 zenon_H53).
% 0.21/0.51 apply (zenon_or_s _ _ zenon_H52); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ].
% 0.21/0.51 exact (zenon_H3a zenon_H55).
% 0.21/0.51 exact (zenon_H4b zenon_H54).
% 0.21/0.51 exact (zenon_H2d zenon_H40).
% 0.21/0.51 Qed.
% 0.21/0.51 % SZS output end Proof
% 0.21/0.51 (* END-PROOF *)
% 0.21/0.51 nodes searched: 486
% 0.21/0.51 max branch formulas: 400
% 0.21/0.51 proof nodes created: 62
% 0.21/0.51 formulas created: 3182
% 0.21/0.51
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