%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET653+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n006.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 2.98s 3.19s % Output : Proof 2.98s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET653+3 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n006.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 : Sun Jul 10 23:04:05 EDT 2022 % 0.12/0.34 % CPUTime : % 2.98/3.19 (* PROOF-FOUND *) % 2.98/3.19 % SZS status Theorem % 2.98/3.19 (* BEGIN-PROOF *) % 2.98/3.19 % SZS output start Proof % 2.98/3.19 Theorem prove_relset_1_15 : (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 B D))->((subset B C)->(ilf_type E (relation_type C D))))))))))). % 2.98/3.19 Proof. % 2.98/3.19 assert (zenon_L1_ : forall (zenon_TE_ba : zenon_U) (zenon_TD_bb : zenon_U) (zenon_TB_bc : zenon_U), (forall D : zenon_U, ((ilf_type D (relation_type zenon_TB_bc zenon_TD_bb))->((subset (domain_of D) zenon_TB_bc)/\(subset (range_of D) zenon_TD_bb)))) -> (ilf_type zenon_TE_ba (relation_type zenon_TB_bc zenon_TD_bb)) -> (~(subset (domain_of zenon_TE_ba) zenon_TB_bc)) -> False). % 2.98/3.19 do 3 intro. intros zenon_H17 zenon_H18 zenon_H19. % 2.98/3.19 generalize (zenon_H17 zenon_TE_ba). zenon_intro zenon_H1d. % 2.98/3.19 apply (zenon_imply_s _ _ zenon_H1d); [ zenon_intro zenon_H1f | zenon_intro zenon_H1e ]. % 2.98/3.19 exact (zenon_H1f zenon_H18). % 2.98/3.19 apply (zenon_and_s _ _ zenon_H1e). zenon_intro zenon_H21. zenon_intro zenon_H20. % 2.98/3.19 exact (zenon_H19 zenon_H21). % 2.98/3.19 (* end of lemma zenon_L1_ *) % 2.98/3.19 assert (zenon_L2_ : forall (zenon_TE_ba : zenon_U) (zenon_TD_bn : zenon_U) (zenon_TC_bo : zenon_U) (zenon_TB_bc : zenon_U), (forall D : zenon_U, ((ilf_type D (set_type))->((member D zenon_TB_bc)->(member D zenon_TC_bo)))) -> (ilf_type zenon_TD_bn (set_type)) -> (forall D : zenon_U, ((ilf_type D (set_type))->((member D (domain_of zenon_TE_ba))->(member D zenon_TB_bc)))) -> (member zenon_TD_bn (domain_of zenon_TE_ba)) -> (~(member zenon_TD_bn zenon_TC_bo)) -> False). % 2.98/3.19 do 4 intro. intros zenon_H22 zenon_H23 zenon_H24 zenon_H25 zenon_H26. % 2.98/3.19 generalize (zenon_H22 zenon_TD_bn). zenon_intro zenon_H29. % 2.98/3.19 apply (zenon_imply_s _ _ zenon_H29); [ zenon_intro zenon_H2b | zenon_intro zenon_H2a ]. % 2.98/3.19 exact (zenon_H2b zenon_H23). % 2.98/3.19 apply (zenon_imply_s _ _ zenon_H2a); [ zenon_intro zenon_H2d | zenon_intro zenon_H2c ]. % 2.98/3.19 generalize (zenon_H24 zenon_TD_bn). zenon_intro zenon_H2e. % 2.98/3.19 apply (zenon_imply_s _ _ zenon_H2e); [ zenon_intro zenon_H2b | zenon_intro zenon_H2f ]. % 2.98/3.19 exact (zenon_H2b zenon_H23). % 2.98/3.19 apply (zenon_imply_s _ _ zenon_H2f); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ]. % 2.98/3.19 exact (zenon_H31 zenon_H25). % 2.98/3.19 exact (zenon_H2d zenon_H30). % 2.98/3.19 exact (zenon_H26 zenon_H2c). % 2.98/3.19 (* end of lemma zenon_L2_ *) % 2.98/3.19 apply NNPP. intro zenon_G. % 2.98/3.19 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 B D))->((subset B C)->(ilf_type E (relation_type C D))))))))))) zenon_G); [ zenon_intro zenon_H32; idtac ]. % 2.98/3.19 elim zenon_H32. zenon_intro zenon_TB_bc. zenon_intro zenon_H33. % 2.98/3.19 apply (zenon_notimply_s _ _ zenon_H33). zenon_intro zenon_H35. zenon_intro zenon_H34. % 2.98/3.19 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 zenon_TB_bc D))->((subset zenon_TB_bc C)->(ilf_type E (relation_type C D))))))))) zenon_H34); [ zenon_intro zenon_H36; idtac ]. % 2.98/3.19 elim zenon_H36. zenon_intro zenon_TC_bo. zenon_intro zenon_H37. % 2.98/3.19 apply (zenon_notimply_s _ _ zenon_H37). zenon_intro zenon_H39. zenon_intro zenon_H38. % 2.98/3.19 apply (zenon_notallex_s (fun D : zenon_U => ((ilf_type D (set_type))->(forall E : zenon_U, ((ilf_type E (relation_type zenon_TB_bc D))->((subset zenon_TB_bc zenon_TC_bo)->(ilf_type E (relation_type zenon_TC_bo D))))))) zenon_H38); [ zenon_intro zenon_H3a; idtac ]. % 2.98/3.19 elim zenon_H3a. zenon_intro zenon_TD_bb. zenon_intro zenon_H3b. % 2.98/3.19 apply (zenon_notimply_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 2.98/3.19 apply (zenon_notallex_s (fun E : zenon_U => ((ilf_type E (relation_type zenon_TB_bc zenon_TD_bb))->((subset zenon_TB_bc zenon_TC_bo)->(ilf_type E (relation_type zenon_TC_bo zenon_TD_bb))))) zenon_H3c); [ zenon_intro zenon_H3e; idtac ]. % 2.98/3.19 elim zenon_H3e. zenon_intro zenon_TE_ba. zenon_intro zenon_H3f. % 2.98/3.19 apply (zenon_notimply_s _ _ zenon_H3f). zenon_intro zenon_H18. zenon_intro zenon_H40. % 2.98/3.19 apply (zenon_notimply_s _ _ zenon_H40). zenon_intro zenon_H42. zenon_intro zenon_H41. % 2.98/3.19 generalize (p3 zenon_TB_bc). zenon_intro zenon_H43. % 2.98/3.19 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ]. % 2.98/3.19 exact (zenon_H45 zenon_H35). % 2.98/3.19 generalize (zenon_H44 zenon_TC_bo). zenon_intro zenon_H46. % 2.98/3.19 apply (zenon_imply_s _ _ zenon_H46); [ zenon_intro zenon_H48 | zenon_intro zenon_H47 ]. % 2.98/3.19 exact (zenon_H48 zenon_H39). % 2.98/3.19 generalize (zenon_H47 zenon_TD_bb). zenon_intro zenon_H49. % 2.98/3.19 apply (zenon_imply_s _ _ zenon_H49); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ]. % 2.98/3.19 exact (zenon_H4b zenon_H3d). % 2.98/3.19 generalize (zenon_H4a zenon_TE_ba). zenon_intro zenon_H4c. % 2.98/3.19 apply (zenon_imply_s _ _ zenon_H4c); [ zenon_intro zenon_H1f | zenon_intro zenon_H4d ]. % 2.98/3.19 exact (zenon_H1f zenon_H18). % 2.98/3.19 apply (zenon_imply_s _ _ zenon_H4d); [ zenon_intro zenon_H4f | zenon_intro zenon_H4e ]. % 2.98/3.19 generalize (p6 (domain_of zenon_TE_ba)). zenon_intro zenon_H50. % 2.98/3.19 apply (zenon_imply_s _ _ zenon_H50); [ zenon_intro zenon_H52 | zenon_intro zenon_H51 ]. % 2.98/3.19 generalize (p22 (domain_of zenon_TE_ba)). zenon_intro zenon_H53. % 2.98/3.19 exact (zenon_H52 zenon_H53). % 2.98/3.19 generalize (zenon_H51 zenon_TC_bo). zenon_intro zenon_H54. % 2.98/3.19 apply (zenon_imply_s _ _ zenon_H54); [ zenon_intro zenon_H48 | zenon_intro zenon_H55 ]. % 2.98/3.19 exact (zenon_H48 zenon_H39). % 2.98/3.19 apply (zenon_equiv_s _ _ zenon_H55); [ zenon_intro zenon_H4f; zenon_intro zenon_H58 | zenon_intro zenon_H57; zenon_intro zenon_H56 ]. % 2.98/3.19 apply (zenon_notallex_s (fun D : zenon_U => ((ilf_type D (set_type))->((member D (domain_of zenon_TE_ba))->(member D zenon_TC_bo)))) zenon_H58); [ zenon_intro zenon_H59; idtac ]. % 2.98/3.19 elim zenon_H59. zenon_intro zenon_TD_bn. zenon_intro zenon_H5a. % 2.98/3.19 apply (zenon_notimply_s _ _ zenon_H5a). zenon_intro zenon_H23. zenon_intro zenon_H5b. % 2.98/3.19 apply (zenon_notimply_s _ _ zenon_H5b). zenon_intro zenon_H25. zenon_intro zenon_H26. % 2.98/3.19 generalize (p2 zenon_TB_bc). zenon_intro zenon_H5c. % 2.98/3.19 apply (zenon_imply_s _ _ zenon_H5c); [ zenon_intro zenon_H45 | zenon_intro zenon_H5d ]. % 2.98/3.19 exact (zenon_H45 zenon_H35). % 2.98/3.19 generalize (p6 zenon_TB_bc). zenon_intro zenon_H5e. % 2.98/3.19 apply (zenon_imply_s _ _ zenon_H5e); [ zenon_intro zenon_H45 | zenon_intro zenon_H5f ]. % 2.98/3.19 exact (zenon_H45 zenon_H35). % 2.98/3.19 generalize (zenon_H5f zenon_TC_bo). zenon_intro zenon_H60. % 2.98/3.19 apply (zenon_imply_s _ _ zenon_H60); [ zenon_intro zenon_H48 | zenon_intro zenon_H61 ]. % 2.98/3.19 exact (zenon_H48 zenon_H39). % 2.98/3.19 apply (zenon_equiv_s _ _ zenon_H61); [ zenon_intro zenon_H63; zenon_intro zenon_H62 | zenon_intro zenon_H42; zenon_intro zenon_H22 ]. % 2.98/3.19 exact (zenon_H63 zenon_H42). % 2.98/3.19 generalize (zenon_H51 zenon_TB_bc). zenon_intro zenon_H64. % 2.98/3.19 apply (zenon_imply_s _ _ zenon_H64); [ zenon_intro zenon_H45 | zenon_intro zenon_H65 ]. % 2.98/3.19 exact (zenon_H45 zenon_H35). % 2.98/3.19 apply (zenon_equiv_s _ _ zenon_H65); [ zenon_intro zenon_H19; zenon_intro zenon_H66 | zenon_intro zenon_H21; zenon_intro zenon_H24 ]. % 2.98/3.19 generalize (zenon_H5d zenon_TD_bb). zenon_intro zenon_H67. % 2.98/3.19 apply (zenon_imply_s _ _ zenon_H67); [ zenon_intro zenon_H4b | zenon_intro zenon_H17 ]. % 2.98/3.19 exact (zenon_H4b zenon_H3d). % 2.98/3.19 apply (zenon_L1_ zenon_TE_ba zenon_TD_bb zenon_TB_bc); trivial. % 2.98/3.19 apply (zenon_L2_ zenon_TE_ba zenon_TD_bn zenon_TC_bo zenon_TB_bc); trivial. % 2.98/3.19 exact (zenon_H4f zenon_H57). % 2.98/3.19 exact (zenon_H41 zenon_H4e). % 2.98/3.19 Qed. % 2.98/3.19 % SZS output end Proof % 2.98/3.19 (* END-PROOF *) % 2.98/3.19 nodes searched: 194358 % 2.98/3.19 max branch formulas: 13139 % 2.98/3.19 proof nodes created: 10968 % 2.98/3.19 formulas created: 517498 % 2.98/3.19 %------------------------------------------------------------------------------