%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SET666+3 : TPTP v8.1.0. Released v2.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n009.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 06:37:50 EDT 2022 % Result : Theorem 0.41s 0.63s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : SET666+3 : TPTP v8.1.0. Released v2.2.0. % 0.03/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n009.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % 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 : Sun Jul 10 17:09:07 EDT 2022 % 0.13/0.34 % CPUTime : % 0.41/0.63 (* PROOF-FOUND *) % 0.41/0.63 % SZS status Theorem % 0.41/0.63 (* BEGIN-PROOF *) % 0.41/0.63 % SZS output start Proof % 0.41/0.63 Theorem prove_relset_1_29 : (forall B : zenon_U, ((ilf_type B (set_type))->(ilf_type (identity_relation_of B) (identity_relation_of_type B)))). % 0.41/0.63 Proof. % 0.41/0.63 assert (zenon_L1_ : forall (zenon_TB_ba : zenon_U), (~(ilf_type (identity_relation_of zenon_TB_ba) (set_type))) -> False). % 0.41/0.63 do 1 intro. intros zenon_H19. % 0.41/0.63 generalize (p24 (identity_relation_of zenon_TB_ba)). zenon_intro zenon_H1b. % 0.41/0.63 exact (zenon_H19 zenon_H1b). % 0.41/0.63 (* end of lemma zenon_L1_ *) % 0.41/0.63 assert (zenon_L2_ : forall (zenon_TB_ba : zenon_U), (ilf_type zenon_TB_ba (set_type)) -> (~(ilf_type (cross_product zenon_TB_ba zenon_TB_ba) (set_type))) -> False). % 0.41/0.63 do 1 intro. intros zenon_H1c zenon_H1d. % 0.41/0.63 generalize (p8 zenon_TB_ba). zenon_intro zenon_H1e. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H1e); [ zenon_intro zenon_H20 | zenon_intro zenon_H1f ]. % 0.41/0.63 exact (zenon_H20 zenon_H1c). % 0.41/0.63 generalize (zenon_H1f zenon_TB_ba). zenon_intro zenon_H21. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H21); [ zenon_intro zenon_H20 | zenon_intro zenon_H22 ]. % 0.41/0.63 exact (zenon_H20 zenon_H1c). % 0.41/0.63 exact (zenon_H1d zenon_H22). % 0.41/0.63 (* end of lemma zenon_L2_ *) % 0.41/0.63 assert (zenon_L3_ : forall (zenon_TB_ba : zenon_U), (ilf_type zenon_TB_ba (set_type)) -> (~(ilf_type (power_set (cross_product zenon_TB_ba zenon_TB_ba)) (set_type))) -> False). % 0.41/0.63 do 1 intro. intros zenon_H1c zenon_H23. % 0.41/0.63 generalize (p17 (cross_product zenon_TB_ba zenon_TB_ba)). zenon_intro zenon_H24. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H24); [ zenon_intro zenon_H1d | zenon_intro zenon_H25 ]. % 0.41/0.63 apply (zenon_L2_ zenon_TB_ba); trivial. % 0.41/0.63 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H27. zenon_intro zenon_H26. % 0.41/0.63 exact (zenon_H23 zenon_H26). % 0.41/0.63 (* end of lemma zenon_L3_ *) % 0.41/0.63 apply NNPP. intro zenon_G. % 0.41/0.63 apply (zenon_notallex_s (fun B : zenon_U => ((ilf_type B (set_type))->(ilf_type (identity_relation_of B) (identity_relation_of_type B)))) zenon_G); [ zenon_intro zenon_H28; idtac ]. % 0.41/0.63 elim zenon_H28. zenon_intro zenon_TB_ba. zenon_intro zenon_H29. % 0.41/0.63 apply (zenon_notimply_s _ _ zenon_H29). zenon_intro zenon_H1c. zenon_intro zenon_H2a. % 0.41/0.63 generalize (p6 zenon_TB_ba). zenon_intro zenon_H2b. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H2b); [ zenon_intro zenon_H20 | zenon_intro zenon_H2c ]. % 0.41/0.63 exact (zenon_H20 zenon_H1c). % 0.41/0.63 generalize (zenon_H2c (identity_relation_of zenon_TB_ba)). zenon_intro zenon_H2d. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H2d); [ zenon_intro zenon_H19 | zenon_intro zenon_H2e ]. % 0.41/0.63 apply (zenon_L1_ zenon_TB_ba); trivial. % 0.41/0.63 apply (zenon_equiv_s _ _ zenon_H2e); [ zenon_intro zenon_H2a; zenon_intro zenon_H31 | zenon_intro zenon_H30; zenon_intro zenon_H2f ]. % 0.41/0.63 generalize (p1 zenon_TB_ba). zenon_intro zenon_H32. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H32); [ zenon_intro zenon_H20 | zenon_intro zenon_H33 ]. % 0.41/0.63 exact (zenon_H20 zenon_H1c). % 0.41/0.63 generalize (zenon_H33 zenon_TB_ba). zenon_intro zenon_H34. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H34); [ zenon_intro zenon_H20 | zenon_intro zenon_H35 ]. % 0.41/0.63 exact (zenon_H20 zenon_H1c). % 0.41/0.63 apply (zenon_and_s _ _ zenon_H35). zenon_intro zenon_H37. zenon_intro zenon_H36. % 0.41/0.63 generalize (zenon_H37 (identity_relation_of zenon_TB_ba)). zenon_intro zenon_H38. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H38); [ zenon_intro zenon_H39 | zenon_intro zenon_H2f ]. % 0.41/0.63 generalize (p12 (cross_product zenon_TB_ba zenon_TB_ba)). zenon_intro zenon_H3a. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H3a); [ zenon_intro zenon_H1d | zenon_intro zenon_H3b ]. % 0.41/0.63 apply (zenon_L2_ zenon_TB_ba); trivial. % 0.41/0.63 generalize (zenon_H3b (identity_relation_of zenon_TB_ba)). zenon_intro zenon_H3c. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H3c); [ zenon_intro zenon_H19 | zenon_intro zenon_H3d ]. % 0.41/0.63 apply (zenon_L1_ zenon_TB_ba); trivial. % 0.41/0.63 apply (zenon_equiv_s _ _ zenon_H3d); [ zenon_intro zenon_H39; zenon_intro zenon_H40 | zenon_intro zenon_H3f; zenon_intro zenon_H3e ]. % 0.41/0.63 generalize (p18 (identity_relation_of zenon_TB_ba)). zenon_intro zenon_H41. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H19 | zenon_intro zenon_H42 ]. % 0.41/0.63 apply (zenon_L1_ zenon_TB_ba); trivial. % 0.41/0.63 generalize (p22 (power_set (cross_product zenon_TB_ba zenon_TB_ba))). zenon_intro zenon_H43. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H43); [ zenon_intro zenon_H23 | zenon_intro zenon_H44 ]. % 0.41/0.63 apply (zenon_L3_ zenon_TB_ba); trivial. % 0.41/0.63 apply (zenon_equiv_s _ _ zenon_H44); [ zenon_intro zenon_H27; zenon_intro zenon_H47 | zenon_intro zenon_H46; zenon_intro zenon_H45 ]. % 0.41/0.63 generalize (zenon_H42 (power_set (cross_product zenon_TB_ba zenon_TB_ba))). zenon_intro zenon_H48. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H48); [ zenon_intro zenon_H4a | zenon_intro zenon_H49 ]. % 0.41/0.63 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H4b | zenon_intro zenon_H23 ]. % 0.41/0.63 exact (zenon_H4b zenon_H27). % 0.41/0.63 apply (zenon_L3_ zenon_TB_ba); trivial. % 0.41/0.63 apply (zenon_equiv_s _ _ zenon_H49); [ zenon_intro zenon_H40; zenon_intro zenon_H4d | zenon_intro zenon_H3e; zenon_intro zenon_H4c ]. % 0.41/0.63 generalize (p16 (identity_relation_of zenon_TB_ba)). zenon_intro zenon_H4e. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H19 | zenon_intro zenon_H4f ]. % 0.41/0.63 apply (zenon_L1_ zenon_TB_ba); trivial. % 0.41/0.63 generalize (zenon_H4f (cross_product zenon_TB_ba zenon_TB_ba)). zenon_intro zenon_H50. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H50); [ zenon_intro zenon_H1d | zenon_intro zenon_H51 ]. % 0.41/0.63 apply (zenon_L2_ zenon_TB_ba); trivial. % 0.41/0.63 apply (zenon_equiv_s _ _ zenon_H51); [ zenon_intro zenon_H4d; zenon_intro zenon_H53 | zenon_intro zenon_H4c; zenon_intro zenon_H52 ]. % 0.41/0.63 generalize (p14 (identity_relation_of zenon_TB_ba)). zenon_intro zenon_H54. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H54); [ zenon_intro zenon_H19 | zenon_intro zenon_H55 ]. % 0.41/0.63 apply (zenon_L1_ zenon_TB_ba); trivial. % 0.41/0.63 generalize (zenon_H55 (cross_product zenon_TB_ba zenon_TB_ba)). zenon_intro zenon_H56. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H56); [ zenon_intro zenon_H1d | zenon_intro zenon_H57 ]. % 0.41/0.63 apply (zenon_L2_ zenon_TB_ba); trivial. % 0.41/0.63 apply (zenon_equiv_s _ _ zenon_H57); [ zenon_intro zenon_H59; zenon_intro zenon_H53 | zenon_intro zenon_H58; zenon_intro zenon_H52 ]. % 0.41/0.63 generalize (p3 zenon_TB_ba). zenon_intro zenon_H5a. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H5a); [ zenon_intro zenon_H20 | zenon_intro zenon_H58 ]. % 0.41/0.63 exact (zenon_H20 zenon_H1c). % 0.41/0.63 exact (zenon_H59 zenon_H58). % 0.41/0.63 exact (zenon_H53 zenon_H52). % 0.41/0.63 exact (zenon_H4d zenon_H4c). % 0.41/0.63 exact (zenon_H40 zenon_H3e). % 0.41/0.63 generalize (p17 (cross_product zenon_TB_ba zenon_TB_ba)). zenon_intro zenon_H24. % 0.41/0.63 apply (zenon_imply_s _ _ zenon_H24); [ zenon_intro zenon_H1d | zenon_intro zenon_H25 ]. % 0.41/0.63 apply (zenon_L2_ zenon_TB_ba); trivial. % 0.41/0.63 apply (zenon_and_s _ _ zenon_H25). zenon_intro zenon_H27. zenon_intro zenon_H26. % 0.41/0.63 exact (zenon_H27 zenon_H46). % 0.41/0.63 exact (zenon_H39 zenon_H3f). % 0.41/0.63 exact (zenon_H31 zenon_H2f). % 0.41/0.63 exact (zenon_H2a zenon_H30). % 0.41/0.63 Qed. % 0.41/0.63 % SZS output end Proof % 0.41/0.63 (* END-PROOF *) % 0.41/0.63 nodes searched: 5782 % 0.41/0.63 max branch formulas: 1221 % 0.41/0.63 proof nodes created: 495 % 0.41/0.63 formulas created: 27534 % 0.41/0.63 %------------------------------------------------------------------------------