%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO224+3 : TPTP v8.1.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n018.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 07:01:04 EDT 2022 % Result : Theorem 8.10s 8.30s % Output : Proof 8.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : GEO224+3 : TPTP v8.1.0. Released v4.0.0. % 0.06/0.13 % Command : run_zenon %s %d % 0.13/0.33 % Computer : n018.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 600 % 0.13/0.34 % DateTime : Fri Jun 17 15:28:32 EDT 2022 % 0.13/0.34 % CPUTime : % 8.10/8.30 (* PROOF-FOUND *) % 8.10/8.30 % SZS status Theorem % 8.10/8.30 (* BEGIN-PROOF *) % 8.10/8.30 % SZS output start Proof % 8.10/8.30 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (((point X)/\(line Y))->(exists Z : zenon_U, ((point Z)/\(incident_point_and_line Z Y)))))). % 8.10/8.30 Proof. % 8.10/8.30 assert (zenon_L1_ : forall (zenon_TY_bm : zenon_U) (zenon_TX_bn : zenon_U), (forall Y : zenon_U, (~(apart_point_and_line zenon_TX_bn (parallel_through_point Y zenon_TX_bn)))) -> (apart_point_and_line zenon_TX_bn (parallel_through_point zenon_TY_bm zenon_TX_bn)) -> False). % 8.10/8.30 do 2 intro. intros zenon_H24 zenon_H25. % 8.10/8.30 generalize (zenon_H24 zenon_TY_bm). zenon_intro zenon_H28. % 8.10/8.30 exact (zenon_H28 zenon_H25). % 8.10/8.30 (* end of lemma zenon_L1_ *) % 8.10/8.30 apply NNPP. intro zenon_G. % 8.10/8.30 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (((point X)/\(line Y))->(exists Z : zenon_U, ((point Z)/\(incident_point_and_line Z Y)))))) zenon_G); [ zenon_intro zenon_H29; idtac ]. % 8.10/8.30 elim zenon_H29. zenon_intro zenon_TX_bn. zenon_intro zenon_H2a. % 8.10/8.30 apply (zenon_notallex_s (fun Y : zenon_U => (((point zenon_TX_bn)/\(line Y))->(exists Z : zenon_U, ((point Z)/\(incident_point_and_line Z Y))))) zenon_H2a); [ zenon_intro zenon_H2b; idtac ]. % 8.10/8.30 elim zenon_H2b. zenon_intro zenon_TY_bm. zenon_intro zenon_H2c. % 8.10/8.30 apply (zenon_notimply_s _ _ zenon_H2c). zenon_intro zenon_H2e. zenon_intro zenon_H2d. % 8.10/8.30 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 8.10/8.30 generalize (ceq2 zenon_TX_bn). zenon_intro zenon_H31. % 8.10/8.30 generalize (zenon_H31 zenon_TY_bm). zenon_intro zenon_H32. % 8.10/8.30 generalize (zenon_H32 zenon_TY_bm). zenon_intro zenon_H33. % 8.10/8.30 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 8.10/8.30 apply zenon_H2d. exists zenon_TX_bn. apply NNPP. zenon_intro zenon_H36. % 8.10/8.30 apply (zenon_notand_s _ _ zenon_H36); [ zenon_intro zenon_H38 | zenon_intro zenon_H37 ]. % 8.10/8.30 exact (zenon_H38 zenon_H30). % 8.10/8.30 generalize (a4 zenon_TX_bn). zenon_intro zenon_H39. % 8.10/8.30 generalize (zenon_H39 zenon_TY_bm). zenon_intro zenon_H3a. % 8.10/8.30 apply (zenon_equiv_s _ _ zenon_H3a); [ zenon_intro zenon_H37; zenon_intro zenon_H3c | zenon_intro zenon_H3b; zenon_intro zenon_H35 ]. % 8.10/8.30 exact (zenon_H3c zenon_H35). % 8.10/8.30 exact (zenon_H37 zenon_H3b). % 8.10/8.30 apply (zenon_or_s _ _ zenon_H34); [ zenon_intro zenon_H3e | zenon_intro zenon_H3d ]. % 8.10/8.30 generalize (apart2 zenon_TY_bm). zenon_intro zenon_H3f. % 8.10/8.30 exact (zenon_H3f zenon_H3e). % 8.10/8.30 generalize (apart2 zenon_TY_bm). zenon_intro zenon_H3f. % 8.10/8.30 generalize (apart5 zenon_TY_bm). zenon_intro zenon_H40. % 8.10/8.30 generalize (cp2 zenon_TX_bn). zenon_intro zenon_H24. % 8.10/8.30 generalize (cp1 zenon_TX_bn). zenon_intro zenon_H41. % 8.10/8.30 generalize (zenon_H41 zenon_TY_bm). zenon_intro zenon_H42. % 8.10/8.30 generalize (p1 (parallel_through_point zenon_TY_bm zenon_TX_bn)). zenon_intro zenon_H43. % 8.10/8.30 generalize (zenon_H43 zenon_TY_bm). zenon_intro zenon_H44. % 8.10/8.30 apply (zenon_imply_s _ _ zenon_H44); [ zenon_intro zenon_H46 | zenon_intro zenon_H45 ]. % 8.10/8.30 generalize (zenon_H32 (parallel_through_point zenon_TY_bm zenon_TX_bn)). zenon_intro zenon_H47. % 8.10/8.30 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H35 | zenon_intro zenon_H48 ]. % 8.10/8.30 exact (zenon_H35 zenon_H3d). % 8.10/8.30 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H49 | zenon_intro zenon_H25 ]. % 8.10/8.30 generalize (zenon_H40 (parallel_through_point zenon_TY_bm zenon_TX_bn)). zenon_intro zenon_H4a. % 8.10/8.30 generalize (zenon_H4a zenon_TY_bm). zenon_intro zenon_H4b. % 8.10/8.30 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H4d | zenon_intro zenon_H4c ]. % 8.10/8.30 exact (zenon_H4d zenon_H49). % 8.10/8.30 apply (zenon_or_s _ _ zenon_H4c); [ zenon_intro zenon_H3e | zenon_intro zenon_H4e ]. % 8.10/8.30 exact (zenon_H3f zenon_H3e). % 8.10/8.30 exact (zenon_H46 zenon_H4e). % 8.10/8.30 apply (zenon_L1_ zenon_TY_bm zenon_TX_bn); trivial. % 8.10/8.30 exact (zenon_H42 zenon_H45). % 8.10/8.30 Qed. % 8.10/8.30 % SZS output end Proof % 8.10/8.30 (* END-PROOF *) % 8.10/8.30 nodes searched: 1307080 % 8.10/8.30 max branch formulas: 34432 % 8.10/8.30 proof nodes created: 10260 % 8.10/8.30 formulas created: 1675651 % 8.10/8.30 %------------------------------------------------------------------------------