%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET654+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n022.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 : Tue Jul 19 06:37:46 EDT 2022 % Result : Theorem 0.47s 0.66s % Output : Proof 0.47s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SET654+3 : TPTP v8.1.0. Released v2.2.0. % 0.07/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n022.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 Jul 9 16:04:40 EDT 2022 % 0.12/0.33 % CPUTime : % 0.47/0.66 (* PROOF-FOUND *) % 0.47/0.66 % SZS status Theorem % 0.47/0.66 (* BEGIN-PROOF *) % 0.47/0.66 % SZS output start Proof % 0.47/0.66 Theorem prove_relset_1_16 : (forall B : zenon_U, ((ilf_type B (set_type))->(forall C : zenon_U, ((ilf_type C (set_type))->(forall D : zenon_U, ((ilf_type D (set_type))->(forall E : zenon_U, ((ilf_type E (relation_type D B))->((subset B C)->(ilf_type E (relation_type D C))))))))))). % 0.47/0.66 Proof. % 0.47/0.66 assert (zenon_L1_ : forall (zenon_TE_ba : zenon_U) (zenon_TB_bb : zenon_U) (zenon_TD_bc : zenon_U), (forall D : zenon_U, ((ilf_type D (relation_type zenon_TD_bc zenon_TB_bb))->((subset (domain_of D) zenon_TD_bc)/\(subset (range_of D) zenon_TB_bb)))) -> (ilf_type zenon_TE_ba (relation_type zenon_TD_bc zenon_TB_bb)) -> (~(subset (range_of zenon_TE_ba) zenon_TB_bb)) -> False). % 0.47/0.66 do 3 intro. intros zenon_H17 zenon_H18 zenon_H19. % 0.47/0.66 generalize (zenon_H17 zenon_TE_ba). zenon_intro zenon_H1d. % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 0.47/0.66 exact (zenon_H1f zenon_H18). % 0.47/0.66 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H21. zenon_intro zenon_H20. % 0.47/0.66 exact (zenon_H19 zenon_H20). % 0.47/0.66 (* end of lemma zenon_L1_ *) % 0.47/0.66 assert (zenon_L2_ : forall (zenon_TB_bb : zenon_U) (zenon_TC_bn : zenon_U) (zenon_TE_ba : zenon_U), (forall C : zenon_U, ((ilf_type C (set_type))->((subset (range_of zenon_TE_ba) C)<->(forall D : zenon_U, ((ilf_type D (set_type))->((member D (range_of zenon_TE_ba))->(member D C))))))) -> (ilf_type zenon_TC_bn (set_type)) -> (~(subset (range_of zenon_TE_ba) zenon_TC_bn)) -> (forall D : zenon_U, ((ilf_type D (set_type))->((member D (range_of zenon_TE_ba))->(member D zenon_TB_bb)))) -> (forall D : zenon_U, ((ilf_type D (set_type))->((member D zenon_TB_bb)->(member D zenon_TC_bn)))) -> False). % 0.47/0.66 do 3 intro. intros zenon_H22 zenon_H23 zenon_H24 zenon_H25 zenon_H26. % 0.47/0.66 generalize (zenon_H22 zenon_TC_bn). zenon_intro zenon_H28. % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H28); [ zenon_intro zenon_H2a | zenon_intro zenon_H29 ]. % 0.47/0.66 exact (zenon_H2a zenon_H23). % 0.47/0.66 apply (zenon_equiv_s _ _ zenon_H29); [ zenon_intro zenon_H24; zenon_intro zenon_H2d | zenon_intro zenon_H2c; zenon_intro zenon_H2b ]. % 0.47/0.66 apply (zenon_notallex_s (fun D : zenon_U => ((ilf_type D (set_type))->((member D (range_of zenon_TE_ba))->(member D zenon_TC_bn)))) zenon_H2d); [ zenon_intro zenon_H2e; idtac ]. % 0.47/0.66 elim zenon_H2e. zenon_intro zenon_TD_bv. zenon_intro zenon_H30. % 0.47/0.66 apply (zenon_notimply_s _ _ zenon_H30). zenon_intro zenon_H32. zenon_intro zenon_H31. % 0.47/0.66 apply (zenon_notimply_s _ _ zenon_H31). zenon_intro zenon_H34. zenon_intro zenon_H33. % 0.47/0.66 generalize (zenon_H26 zenon_TD_bv). zenon_intro zenon_H35. % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H35); [ zenon_intro zenon_H37 | zenon_intro zenon_H36 ]. % 0.47/0.66 exact (zenon_H37 zenon_H32). % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H36); [ zenon_intro zenon_H39 | zenon_intro zenon_H38 ]. % 0.47/0.66 generalize (zenon_H25 zenon_TD_bv). zenon_intro zenon_H3a. % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H37 | zenon_intro zenon_H3b ]. % 0.47/0.66 exact (zenon_H37 zenon_H32). % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H3b); [ zenon_intro zenon_H3d | zenon_intro zenon_H3c ]. % 0.47/0.66 exact (zenon_H3d zenon_H34). % 0.47/0.66 exact (zenon_H39 zenon_H3c). % 0.47/0.66 exact (zenon_H33 zenon_H38). % 0.47/0.66 exact (zenon_H24 zenon_H2c). % 0.47/0.66 (* end of lemma zenon_L2_ *) % 0.47/0.66 apply NNPP. intro zenon_G. % 0.47/0.66 apply (zenon_notallex_s (fun B : zenon_U => ((ilf_type B (set_type))->(forall C : zenon_U, ((ilf_type C (set_type))->(forall D : zenon_U, ((ilf_type D (set_type))->(forall E : zenon_U, ((ilf_type E (relation_type D B))->((subset B C)->(ilf_type E (relation_type D C))))))))))) zenon_G); [ zenon_intro zenon_H3e; idtac ]. % 0.47/0.66 elim zenon_H3e. zenon_intro zenon_TB_bb. zenon_intro zenon_H3f. % 0.47/0.66 apply (zenon_notimply_s _ _ zenon_H3f). zenon_intro zenon_H41. zenon_intro zenon_H40. % 0.47/0.66 apply (zenon_notallex_s (fun C : zenon_U => ((ilf_type C (set_type))->(forall D : zenon_U, ((ilf_type D (set_type))->(forall E : zenon_U, ((ilf_type E (relation_type D zenon_TB_bb))->((subset zenon_TB_bb C)->(ilf_type E (relation_type D C))))))))) zenon_H40); [ zenon_intro zenon_H42; idtac ]. % 0.47/0.66 elim zenon_H42. zenon_intro zenon_TC_bn. zenon_intro zenon_H43. % 0.47/0.66 apply (zenon_notimply_s _ _ zenon_H43). zenon_intro zenon_H23. zenon_intro zenon_H44. % 0.47/0.66 apply (zenon_notallex_s (fun D : zenon_U => ((ilf_type D (set_type))->(forall E : zenon_U, ((ilf_type E (relation_type D zenon_TB_bb))->((subset zenon_TB_bb zenon_TC_bn)->(ilf_type E (relation_type D zenon_TC_bn))))))) zenon_H44); [ zenon_intro zenon_H45; idtac ]. % 0.47/0.66 elim zenon_H45. zenon_intro zenon_TD_bc. zenon_intro zenon_H46. % 0.47/0.66 apply (zenon_notimply_s _ _ zenon_H46). zenon_intro zenon_H48. zenon_intro zenon_H47. % 0.47/0.66 apply (zenon_notallex_s (fun E : zenon_U => ((ilf_type E (relation_type zenon_TD_bc zenon_TB_bb))->((subset zenon_TB_bb zenon_TC_bn)->(ilf_type E (relation_type zenon_TD_bc zenon_TC_bn))))) zenon_H47); [ zenon_intro zenon_H49; idtac ]. % 0.47/0.66 elim zenon_H49. zenon_intro zenon_TE_ba. zenon_intro zenon_H4a. % 0.47/0.66 apply (zenon_notimply_s _ _ zenon_H4a). zenon_intro zenon_H18. zenon_intro zenon_H4b. % 0.47/0.66 apply (zenon_notimply_s _ _ zenon_H4b). zenon_intro zenon_H4d. zenon_intro zenon_H4c. % 0.47/0.66 generalize (p3 zenon_TB_bb). zenon_intro zenon_H4e. % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H50 | zenon_intro zenon_H4f ]. % 0.47/0.66 exact (zenon_H50 zenon_H41). % 0.47/0.66 generalize (zenon_H4f zenon_TC_bn). zenon_intro zenon_H51. % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H51); [ zenon_intro zenon_H2a | zenon_intro zenon_H52 ]. % 0.47/0.66 exact (zenon_H2a zenon_H23). % 0.47/0.66 generalize (zenon_H52 zenon_TD_bc). zenon_intro zenon_H53. % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H53); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 0.47/0.66 exact (zenon_H55 zenon_H48). % 0.47/0.66 generalize (zenon_H54 zenon_TE_ba). zenon_intro zenon_H56. % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H1f | zenon_intro zenon_H57 ]. % 0.47/0.66 exact (zenon_H1f zenon_H18). % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H24 | zenon_intro zenon_H58 ]. % 0.47/0.66 generalize (p6 (range_of zenon_TE_ba)). zenon_intro zenon_H59. % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H59); [ zenon_intro zenon_H5a | zenon_intro zenon_H22 ]. % 0.47/0.66 generalize (p22 (range_of zenon_TE_ba)). zenon_intro zenon_H5b. % 0.47/0.66 exact (zenon_H5a zenon_H5b). % 0.47/0.66 generalize (zenon_H22 zenon_TB_bb). zenon_intro zenon_H5c. % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H50 | zenon_intro zenon_H5d ]. % 0.47/0.66 exact (zenon_H50 zenon_H41). % 0.47/0.66 apply (zenon_equiv_s _ _ zenon_H5d); [ zenon_intro zenon_H19; zenon_intro zenon_H5e | zenon_intro zenon_H20; zenon_intro zenon_H25 ]. % 0.47/0.66 generalize (p2 zenon_TD_bc). zenon_intro zenon_H5f. % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H5f); [ zenon_intro zenon_H55 | zenon_intro zenon_H60 ]. % 0.47/0.66 exact (zenon_H55 zenon_H48). % 0.47/0.66 generalize (zenon_H60 zenon_TB_bb). zenon_intro zenon_H61. % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H61); [ zenon_intro zenon_H50 | zenon_intro zenon_H17 ]. % 0.47/0.66 exact (zenon_H50 zenon_H41). % 0.47/0.66 apply (zenon_L1_ zenon_TE_ba zenon_TB_bb zenon_TD_bc); trivial. % 0.47/0.66 generalize (p13 zenon_TB_bb). zenon_intro zenon_H62. % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H50 | zenon_intro zenon_H63 ]. % 0.47/0.66 exact (zenon_H50 zenon_H41). % 0.47/0.66 generalize (zenon_H63 zenon_TC_bn). zenon_intro zenon_H64. % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H64); [ zenon_intro zenon_H2a | zenon_intro zenon_H65 ]. % 0.47/0.66 exact (zenon_H2a zenon_H23). % 0.47/0.66 apply (zenon_equiv_s _ _ zenon_H65); [ zenon_intro zenon_H68; zenon_intro zenon_H67 | zenon_intro zenon_H66; zenon_intro zenon_H26 ]. % 0.47/0.66 generalize (p6 zenon_TB_bb). zenon_intro zenon_H69. % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H69); [ zenon_intro zenon_H50 | zenon_intro zenon_H6a ]. % 0.47/0.66 exact (zenon_H50 zenon_H41). % 0.47/0.66 generalize (zenon_H6a zenon_TC_bn). zenon_intro zenon_H6b. % 0.47/0.66 apply (zenon_imply_s _ _ zenon_H6b); [ zenon_intro zenon_H2a | zenon_intro zenon_H6c ]. % 0.47/0.66 exact (zenon_H2a zenon_H23). % 0.47/0.66 apply (zenon_equiv_s _ _ zenon_H6c); [ zenon_intro zenon_H6d; zenon_intro zenon_H67 | zenon_intro zenon_H4d; zenon_intro zenon_H26 ]. % 0.47/0.66 exact (zenon_H6d zenon_H4d). % 0.47/0.66 exact (zenon_H67 zenon_H26). % 0.47/0.66 apply (zenon_L2_ zenon_TB_bb zenon_TC_bn zenon_TE_ba); trivial. % 0.47/0.66 exact (zenon_H4c zenon_H58). % 0.47/0.66 Qed. % 0.47/0.66 % SZS output end Proof % 0.47/0.66 (* END-PROOF *) % 0.47/0.66 nodes searched: 9442 % 0.47/0.66 max branch formulas: 3176 % 0.47/0.66 proof nodes created: 676 % 0.47/0.66 formulas created: 44384 % 0.47/0.66 %------------------------------------------------------------------------------