%------------------------------------------------------------------------------ % 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 %------------------------------------------------------------------------------