%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GEO195+1 : TPTP v8.1.0. Released v3.3.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n011.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 07:00:39 EDT 2022 % Result : Theorem 0.35s 0.53s % Output : Proof 0.35s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : GEO195+1 : TPTP v8.1.0. Released v3.3.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n011.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 : Sat Jun 18 05:41:37 EDT 2022 % 0.12/0.33 % CPUTime : % 0.35/0.53 (* PROOF-FOUND *) % 0.35/0.53 % SZS status Theorem % 0.35/0.53 (* BEGIN-PROOF *) % 0.35/0.53 % SZS output start Proof % 0.35/0.53 Theorem con : (forall X : zenon_U, (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines Z Y)/\(convergent_lines X Z)))->((apart_point_and_line (intersection_point X Y) Z)->(apart_point_and_line (intersection_point Y X) Z)))))). % 0.35/0.53 Proof. % 0.35/0.53 assert (zenon_L1_ : forall (zenon_TX_q : zenon_U), (convergent_lines zenon_TX_q zenon_TX_q) -> False). % 0.35/0.53 do 1 intro. intros zenon_Hf. % 0.35/0.53 generalize (apart3 zenon_TX_q). zenon_intro zenon_H11. % 0.35/0.53 exact (zenon_H11 zenon_Hf). % 0.35/0.53 (* end of lemma zenon_L1_ *) % 0.35/0.53 assert (zenon_L2_ : forall (zenon_TY_v : zenon_U) (zenon_TX_q : zenon_U), (forall Z : zenon_U, ((convergent_lines zenon_TX_q zenon_TY_v)->((convergent_lines zenon_TX_q Z)\/(convergent_lines zenon_TY_v Z)))) -> (convergent_lines zenon_TX_q zenon_TY_v) -> (~(convergent_lines zenon_TY_v zenon_TX_q)) -> False). % 0.35/0.53 do 2 intro. intros zenon_H12 zenon_H13 zenon_H14. % 0.35/0.53 generalize (zenon_H12 zenon_TX_q). zenon_intro zenon_H16. % 0.35/0.53 apply (zenon_imply_s _ _ zenon_H16); [ zenon_intro zenon_H18 | zenon_intro zenon_H17 ]. % 0.35/0.53 exact (zenon_H18 zenon_H13). % 0.35/0.53 apply (zenon_or_s _ _ zenon_H17); [ zenon_intro zenon_Hf | zenon_intro zenon_H19 ]. % 0.35/0.53 apply (zenon_L1_ zenon_TX_q); trivial. % 0.35/0.53 exact (zenon_H14 zenon_H19). % 0.35/0.53 (* end of lemma zenon_L2_ *) % 0.35/0.53 assert (zenon_L3_ : forall (zenon_TX_q : zenon_U) (zenon_TY_v : zenon_U), (apart_point_and_line (intersection_point zenon_TY_v zenon_TX_q) zenon_TY_v) -> (convergent_lines zenon_TX_q zenon_TY_v) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_q zenon_TY_v)->((convergent_lines zenon_TX_q Z)\/(convergent_lines zenon_TY_v Z)))) -> False). % 0.35/0.53 do 2 intro. intros zenon_H1a zenon_H13 zenon_H12. % 0.35/0.53 generalize (ci3 zenon_TY_v). zenon_intro zenon_H1b. % 0.35/0.53 generalize (zenon_H1b zenon_TX_q). zenon_intro zenon_H1c. % 0.35/0.53 apply (zenon_imply_s _ _ zenon_H1c); [ zenon_intro zenon_H14 | zenon_intro zenon_H1d ]. % 0.35/0.53 apply (zenon_L2_ zenon_TY_v zenon_TX_q); trivial. % 0.35/0.53 exact (zenon_H1d zenon_H1a). % 0.35/0.53 (* end of lemma zenon_L3_ *) % 0.35/0.53 assert (zenon_L4_ : forall (zenon_TX_q : zenon_U) (zenon_TY_v : zenon_U), (apart_point_and_line (intersection_point zenon_TY_v zenon_TX_q) zenon_TX_q) -> (convergent_lines zenon_TX_q zenon_TY_v) -> (forall Z : zenon_U, ((convergent_lines zenon_TX_q zenon_TY_v)->((convergent_lines zenon_TX_q Z)\/(convergent_lines zenon_TY_v Z)))) -> False). % 0.35/0.53 do 2 intro. intros zenon_H1e zenon_H13 zenon_H12. % 0.35/0.53 generalize (ci4 zenon_TY_v). zenon_intro zenon_H1f. % 0.35/0.53 generalize (zenon_H1f zenon_TX_q). zenon_intro zenon_H20. % 0.35/0.53 apply (zenon_imply_s _ _ zenon_H20); [ zenon_intro zenon_H14 | zenon_intro zenon_H21 ]. % 0.35/0.53 apply (zenon_L2_ zenon_TY_v zenon_TX_q); trivial. % 0.35/0.53 exact (zenon_H21 zenon_H1e). % 0.35/0.53 (* end of lemma zenon_L4_ *) % 0.35/0.53 apply NNPP. intro zenon_G. % 0.35/0.53 apply (zenon_notallex_s (fun X : zenon_U => (forall Y : zenon_U, (forall Z : zenon_U, (((convergent_lines X Y)/\((convergent_lines Z Y)/\(convergent_lines X Z)))->((apart_point_and_line (intersection_point X Y) Z)->(apart_point_and_line (intersection_point Y X) Z)))))) zenon_G); [ zenon_intro zenon_H22; idtac ]. % 0.35/0.53 elim zenon_H22. zenon_intro zenon_TX_q. zenon_intro zenon_H23. % 0.35/0.53 apply (zenon_notallex_s (fun Y : zenon_U => (forall Z : zenon_U, (((convergent_lines zenon_TX_q Y)/\((convergent_lines Z Y)/\(convergent_lines zenon_TX_q Z)))->((apart_point_and_line (intersection_point zenon_TX_q Y) Z)->(apart_point_and_line (intersection_point Y zenon_TX_q) Z))))) zenon_H23); [ zenon_intro zenon_H24; idtac ]. % 0.35/0.53 elim zenon_H24. zenon_intro zenon_TY_v. zenon_intro zenon_H25. % 0.35/0.53 apply (zenon_notallex_s (fun Z : zenon_U => (((convergent_lines zenon_TX_q zenon_TY_v)/\((convergent_lines Z zenon_TY_v)/\(convergent_lines zenon_TX_q Z)))->((apart_point_and_line (intersection_point zenon_TX_q zenon_TY_v) Z)->(apart_point_and_line (intersection_point zenon_TY_v zenon_TX_q) Z)))) zenon_H25); [ zenon_intro zenon_H26; idtac ]. % 0.35/0.53 elim zenon_H26. zenon_intro zenon_TZ_bn. zenon_intro zenon_H28. % 0.35/0.53 apply (zenon_notimply_s _ _ zenon_H28). zenon_intro zenon_H2a. zenon_intro zenon_H29. % 0.35/0.53 apply (zenon_notimply_s _ _ zenon_H29). zenon_intro zenon_H2c. zenon_intro zenon_H2b. % 0.35/0.53 apply (zenon_and_s _ _ zenon_H2a). zenon_intro zenon_H13. zenon_intro zenon_H2d. % 0.35/0.53 generalize (ax6 zenon_TX_q). zenon_intro zenon_H2e. % 0.35/0.53 generalize (ceq3 zenon_TX_q). zenon_intro zenon_H2f. % 0.35/0.53 generalize (zenon_H2e zenon_TY_v). zenon_intro zenon_H12. % 0.35/0.53 generalize (zenon_H2f zenon_TY_v). zenon_intro zenon_H30. % 0.35/0.53 generalize (ceq1 (intersection_point zenon_TX_q zenon_TY_v)). zenon_intro zenon_H31. % 0.35/0.53 generalize (zenon_H31 zenon_TZ_bn). zenon_intro zenon_H32. % 0.35/0.53 generalize (zenon_H32 (intersection_point zenon_TY_v zenon_TX_q)). zenon_intro zenon_H33. % 0.35/0.53 apply (zenon_imply_s _ _ zenon_H33); [ zenon_intro zenon_H35 | zenon_intro zenon_H34 ]. % 0.35/0.53 exact (zenon_H35 zenon_H2c). % 0.35/0.53 apply (zenon_or_s _ _ zenon_H34); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 0.35/0.53 generalize (cu1 (intersection_point zenon_TX_q zenon_TY_v)). zenon_intro zenon_H38. % 0.35/0.53 generalize (zenon_H38 (intersection_point zenon_TY_v zenon_TX_q)). zenon_intro zenon_H39. % 0.35/0.53 generalize (zenon_H30 zenon_TX_q). zenon_intro zenon_H3a. % 0.35/0.53 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H18 | zenon_intro zenon_H3b ]. % 0.35/0.53 exact (zenon_H18 zenon_H13). % 0.35/0.53 apply (zenon_or_s _ _ zenon_H3b); [ zenon_intro zenon_H3c | zenon_intro zenon_Hf ]. % 0.35/0.53 generalize (zenon_H39 zenon_TY_v). zenon_intro zenon_H3d. % 0.35/0.53 generalize (ci3 zenon_TX_q). zenon_intro zenon_H3e. % 0.35/0.53 generalize (zenon_H3d zenon_TX_q). zenon_intro zenon_H3f. % 0.35/0.53 apply (zenon_imply_s _ _ zenon_H3f); [ zenon_intro zenon_H41 | zenon_intro zenon_H40 ]. % 0.35/0.53 apply (zenon_notand_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 0.35/0.53 exact (zenon_H43 zenon_H37). % 0.35/0.53 exact (zenon_H42 zenon_H3c). % 0.35/0.53 apply (zenon_or_s _ _ zenon_H40); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ]. % 0.35/0.53 generalize (ci4 zenon_TX_q). zenon_intro zenon_H46. % 0.35/0.53 generalize (zenon_H46 zenon_TY_v). zenon_intro zenon_H47. % 0.35/0.53 apply (zenon_imply_s _ _ zenon_H47); [ zenon_intro zenon_H18 | zenon_intro zenon_H48 ]. % 0.35/0.53 exact (zenon_H18 zenon_H13). % 0.35/0.53 exact (zenon_H48 zenon_H45). % 0.35/0.53 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 0.35/0.53 generalize (zenon_H3e zenon_TY_v). zenon_intro zenon_H4b. % 0.35/0.53 apply (zenon_imply_s _ _ zenon_H4b); [ zenon_intro zenon_H18 | zenon_intro zenon_H4c ]. % 0.35/0.53 exact (zenon_H18 zenon_H13). % 0.35/0.53 exact (zenon_H4c zenon_H4a). % 0.35/0.53 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H1a | zenon_intro zenon_H1e ]. % 0.35/0.53 apply (zenon_L3_ zenon_TX_q zenon_TY_v); trivial. % 0.35/0.53 apply (zenon_L4_ zenon_TX_q zenon_TY_v); trivial. % 0.35/0.53 apply (zenon_L1_ zenon_TX_q); trivial. % 0.35/0.53 exact (zenon_H2b zenon_H36). % 0.35/0.53 Qed. % 0.35/0.53 % SZS output end Proof % 0.35/0.53 (* END-PROOF *) % 0.35/0.53 nodes searched: 1680 % 0.35/0.53 max branch formulas: 679 % 0.35/0.53 proof nodes created: 189 % 0.35/0.53 formulas created: 6662 % 0.35/0.53 %------------------------------------------------------------------------------