%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO176+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 07:00:24 EDT 2022 % Result : Theorem 1.95s 2.14s % Output : Proof 1.95s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : GEO176+3 : TPTP v8.1.0. Released v4.0.0. % 0.11/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n017.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Fri Jun 17 22:00:42 EDT 2022 % 0.12/0.34 % CPUTime : % 1.95/2.14 (* PROOF-FOUND *) % 1.95/2.14 % SZS status Theorem % 1.95/2.14 (* BEGIN-PROOF *) % 1.95/2.14 % SZS output start Proof % 1.95/2.14 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((convergent_lines U V)/\((apart_point_and_line X U)\/(apart_point_and_line X V))))->(distinct_points X (intersection_point U V))))))). % 1.95/2.14 Proof. % 1.95/2.14 assert (zenon_L1_ : forall (zenon_TV_bo : zenon_U) (zenon_TU_bp : zenon_U) (zenon_TX_bq : zenon_U), (forall Y : zenon_U, (forall Z : zenon_U, ((apart_point_and_line zenon_TX_bq Y)->((distinct_points zenon_TX_bq Z)\/(apart_point_and_line Z Y))))) -> (convergent_lines zenon_TU_bp zenon_TV_bo) -> (apart_point_and_line zenon_TX_bq zenon_TV_bo) -> (~(distinct_points zenon_TX_bq (intersection_point zenon_TU_bp zenon_TV_bo))) -> False). % 1.95/2.14 do 3 intro. intros zenon_H24 zenon_H25 zenon_H26 zenon_H27. % 1.95/2.14 generalize (zenon_H24 zenon_TV_bo). zenon_intro zenon_H2b. % 1.95/2.14 generalize (ci4 zenon_TU_bp). zenon_intro zenon_H2c. % 1.95/2.14 generalize (zenon_H2c zenon_TV_bo). zenon_intro zenon_H2d. % 1.95/2.14 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H2f | zenon_intro zenon_H2e ]. % 1.95/2.14 exact (zenon_H2f zenon_H25). % 1.95/2.14 generalize (zenon_H2b (intersection_point zenon_TU_bp zenon_TV_bo)). zenon_intro zenon_H30. % 1.95/2.14 apply (zenon_imply_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 1.95/2.14 exact (zenon_H32 zenon_H26). % 1.95/2.14 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H34 | zenon_intro zenon_H33 ]. % 1.95/2.14 exact (zenon_H27 zenon_H34). % 1.95/2.14 exact (zenon_H2e zenon_H33). % 1.95/2.14 (* end of lemma zenon_L1_ *) % 1.95/2.14 apply NNPP. intro zenon_G. % 1.95/2.14 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall U : zenon_U, (forall V : zenon_U, (((distinct_points X Y)/\((convergent_lines U V)/\((apart_point_and_line X U)\/(apart_point_and_line X V))))->(distinct_points X (intersection_point U V))))))) zenon_G); [ zenon_intro zenon_H35; idtac ]. % 1.95/2.14 elim zenon_H35. zenon_intro zenon_TX_bq. zenon_intro zenon_H36. % 1.95/2.14 apply (zenon_notallex_s (fun Y : zenon_U => (forall U : zenon_U, (forall V : zenon_U, (((distinct_points zenon_TX_bq Y)/\((convergent_lines U V)/\((apart_point_and_line zenon_TX_bq U)\/(apart_point_and_line zenon_TX_bq V))))->(distinct_points zenon_TX_bq (intersection_point U V)))))) zenon_H36); [ zenon_intro zenon_H37; idtac ]. % 1.95/2.14 elim zenon_H37. zenon_intro zenon_TY_ce. zenon_intro zenon_H39. % 1.95/2.14 apply (zenon_notallex_s (fun U : zenon_U => (forall V : zenon_U, (((distinct_points zenon_TX_bq zenon_TY_ce)/\((convergent_lines U V)/\((apart_point_and_line zenon_TX_bq U)\/(apart_point_and_line zenon_TX_bq V))))->(distinct_points zenon_TX_bq (intersection_point U V))))) zenon_H39); [ zenon_intro zenon_H3a; idtac ]. % 1.95/2.14 elim zenon_H3a. zenon_intro zenon_TU_bp. zenon_intro zenon_H3b. % 1.95/2.14 apply (zenon_notallex_s (fun V : zenon_U => (((distinct_points zenon_TX_bq zenon_TY_ce)/\((convergent_lines zenon_TU_bp V)/\((apart_point_and_line zenon_TX_bq zenon_TU_bp)\/(apart_point_and_line zenon_TX_bq V))))->(distinct_points zenon_TX_bq (intersection_point zenon_TU_bp V)))) zenon_H3b); [ zenon_intro zenon_H3c; idtac ]. % 1.95/2.14 elim zenon_H3c. zenon_intro zenon_TV_bo. zenon_intro zenon_H3d. % 1.95/2.14 apply (zenon_notimply_s _ _ zenon_H3d). zenon_intro zenon_H3e. zenon_intro zenon_H27. % 1.95/2.14 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H3f. % 1.95/2.14 apply (zenon_and_s _ _ zenon_H3f). zenon_intro zenon_H25. zenon_intro zenon_H41. % 1.95/2.14 apply (zenon_or_s _ _ zenon_H41); [ zenon_intro zenon_H42 | zenon_intro zenon_H26 ]. % 1.95/2.14 generalize (ci3 zenon_TU_bp). zenon_intro zenon_H43. % 1.95/2.14 generalize (ceq1 zenon_TX_bq). zenon_intro zenon_H24. % 1.95/2.14 generalize (zenon_H24 zenon_TU_bp). zenon_intro zenon_H44. % 1.95/2.14 generalize (zenon_H43 zenon_TV_bo). zenon_intro zenon_H45. % 1.95/2.14 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H2f | zenon_intro zenon_H46 ]. % 1.95/2.14 exact (zenon_H2f zenon_H25). % 1.95/2.14 generalize (zenon_H44 (intersection_point zenon_TU_bp zenon_TV_bo)). zenon_intro zenon_H47. % 1.95/2.14 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ]. % 1.95/2.14 exact (zenon_H49 zenon_H42). % 1.95/2.14 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H34 | zenon_intro zenon_H4a ]. % 1.95/2.14 exact (zenon_H27 zenon_H34). % 1.95/2.14 exact (zenon_H46 zenon_H4a). % 1.95/2.14 generalize (ceq1 zenon_TX_bq). zenon_intro zenon_H24. % 1.95/2.14 apply (zenon_L1_ zenon_TV_bo zenon_TU_bp zenon_TX_bq); trivial. % 1.95/2.14 Qed. % 1.95/2.14 % SZS output end Proof % 1.95/2.14 (* END-PROOF *) % 1.95/2.14 nodes searched: 164070 % 1.95/2.14 max branch formulas: 7394 % 1.95/2.14 proof nodes created: 5059 % 1.95/2.14 formulas created: 340627 % 1.95/2.14 %------------------------------------------------------------------------------