%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU413+1 : TPTP v8.1.0. Released v3.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n025.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 16:01:57 EDT 2022 % Result : Theorem 0.41s 0.58s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SEU413+1 : TPTP v8.1.0. Released v3.4.0. % 0.11/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n025.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 : Sun Jun 19 21:04:44 EDT 2022 % 0.19/0.33 % CPUTime : % 0.41/0.58 Zenon warning: unused variable (B : zenon_U) in idempotence_k3_xboole_0 % 0.41/0.58 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.41/0.58 (* PROOF-FOUND *) % 0.41/0.58 % SZS status Theorem % 0.41/0.58 (* BEGIN-PROOF *) % 0.41/0.58 % SZS output start Proof % 0.41/0.58 Theorem t23_latsum_1 : (forall A : zenon_U, ((l1_orders_2 A)->(forall B : zenon_U, ((l1_orders_2 B)->(forall C : zenon_U, ((m1_subset_1 C (u1_struct_0 (k1_latsum_1 A B)))->(forall D : zenon_U, ((m1_subset_1 D (u1_struct_0 (k1_latsum_1 A B)))->(((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B)/\((m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B)))/\((r1_orders_2 (k1_latsum_1 A B) C D)/\(r2_hidden D (u1_struct_0 A)))))->(r2_hidden C (u1_struct_0 A))))))))))). % 0.41/0.58 Proof. % 0.41/0.58 apply NNPP. intro zenon_G. % 0.41/0.58 apply (zenon_notallex_s (fun A : zenon_U => ((l1_orders_2 A)->(forall B : zenon_U, ((l1_orders_2 B)->(forall C : zenon_U, ((m1_subset_1 C (u1_struct_0 (k1_latsum_1 A B)))->(forall D : zenon_U, ((m1_subset_1 D (u1_struct_0 (k1_latsum_1 A B)))->(((v12_waybel_0 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) B)/\((m1_subset_1 (k3_xboole_0 (u1_struct_0 A) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B)))/\((r1_orders_2 (k1_latsum_1 A B) C D)/\(r2_hidden D (u1_struct_0 A)))))->(r2_hidden C (u1_struct_0 A))))))))))) zenon_G); [ zenon_intro zenon_H22; idtac ]. % 0.41/0.58 elim zenon_H22. zenon_intro zenon_TA_bj. zenon_intro zenon_H24. % 0.41/0.58 apply (zenon_notimply_s _ _ zenon_H24). zenon_intro zenon_H26. zenon_intro zenon_H25. % 0.41/0.58 apply (zenon_notallex_s (fun B : zenon_U => ((l1_orders_2 B)->(forall C : zenon_U, ((m1_subset_1 C (u1_struct_0 (k1_latsum_1 zenon_TA_bj B)))->(forall D : zenon_U, ((m1_subset_1 D (u1_struct_0 (k1_latsum_1 zenon_TA_bj B)))->(((v12_waybel_0 (k3_xboole_0 (u1_struct_0 zenon_TA_bj) (u1_struct_0 B)) B)/\((m1_subset_1 (k3_xboole_0 (u1_struct_0 zenon_TA_bj) (u1_struct_0 B)) (k1_zfmisc_1 (u1_struct_0 B)))/\((r1_orders_2 (k1_latsum_1 zenon_TA_bj B) C D)/\(r2_hidden D (u1_struct_0 zenon_TA_bj)))))->(r2_hidden C (u1_struct_0 zenon_TA_bj))))))))) zenon_H25); [ zenon_intro zenon_H27; idtac ]. % 0.41/0.58 elim zenon_H27. zenon_intro zenon_TB_bo. zenon_intro zenon_H29. % 0.41/0.58 apply (zenon_notimply_s _ _ zenon_H29). zenon_intro zenon_H2b. zenon_intro zenon_H2a. % 0.41/0.58 apply (zenon_notallex_s (fun C : zenon_U => ((m1_subset_1 C (u1_struct_0 (k1_latsum_1 zenon_TA_bj zenon_TB_bo)))->(forall D : zenon_U, ((m1_subset_1 D (u1_struct_0 (k1_latsum_1 zenon_TA_bj zenon_TB_bo)))->(((v12_waybel_0 (k3_xboole_0 (u1_struct_0 zenon_TA_bj) (u1_struct_0 zenon_TB_bo)) zenon_TB_bo)/\((m1_subset_1 (k3_xboole_0 (u1_struct_0 zenon_TA_bj) (u1_struct_0 zenon_TB_bo)) (k1_zfmisc_1 (u1_struct_0 zenon_TB_bo)))/\((r1_orders_2 (k1_latsum_1 zenon_TA_bj zenon_TB_bo) C D)/\(r2_hidden D (u1_struct_0 zenon_TA_bj)))))->(r2_hidden C (u1_struct_0 zenon_TA_bj))))))) zenon_H2a); [ zenon_intro zenon_H2c; idtac ]. % 0.41/0.58 elim zenon_H2c. zenon_intro zenon_TC_bt. zenon_intro zenon_H2e. % 0.41/0.58 apply (zenon_notimply_s _ _ zenon_H2e). zenon_intro zenon_H30. zenon_intro zenon_H2f. % 0.41/0.58 apply (zenon_notallex_s (fun D : zenon_U => ((m1_subset_1 D (u1_struct_0 (k1_latsum_1 zenon_TA_bj zenon_TB_bo)))->(((v12_waybel_0 (k3_xboole_0 (u1_struct_0 zenon_TA_bj) (u1_struct_0 zenon_TB_bo)) zenon_TB_bo)/\((m1_subset_1 (k3_xboole_0 (u1_struct_0 zenon_TA_bj) (u1_struct_0 zenon_TB_bo)) (k1_zfmisc_1 (u1_struct_0 zenon_TB_bo)))/\((r1_orders_2 (k1_latsum_1 zenon_TA_bj zenon_TB_bo) zenon_TC_bt D)/\(r2_hidden D (u1_struct_0 zenon_TA_bj)))))->(r2_hidden zenon_TC_bt (u1_struct_0 zenon_TA_bj))))) zenon_H2f); [ zenon_intro zenon_H31; idtac ]. % 0.41/0.58 elim zenon_H31. zenon_intro zenon_TD_by. zenon_intro zenon_H33. % 0.41/0.58 apply (zenon_notimply_s _ _ zenon_H33). zenon_intro zenon_H35. zenon_intro zenon_H34. % 0.41/0.58 apply (zenon_notimply_s _ _ zenon_H34). zenon_intro zenon_H37. zenon_intro zenon_H36. % 0.41/0.58 apply (zenon_and_s _ _ zenon_H37). zenon_intro zenon_H39. zenon_intro zenon_H38. % 0.41/0.58 apply (zenon_and_s _ _ zenon_H38). zenon_intro zenon_H3b. zenon_intro zenon_H3a. % 0.41/0.58 apply (zenon_and_s _ _ zenon_H3a). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 0.41/0.58 generalize (t21_latsum_1 zenon_TA_bj). zenon_intro zenon_H3e. % 0.41/0.58 apply (zenon_imply_s _ _ zenon_H3e); [ zenon_intro zenon_H40 | zenon_intro zenon_H3f ]. % 0.41/0.58 exact (zenon_H40 zenon_H26). % 0.41/0.58 generalize (zenon_H3f zenon_TB_bo). zenon_intro zenon_H41. % 0.41/0.58 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 0.41/0.58 exact (zenon_H43 zenon_H2b). % 0.41/0.58 generalize (zenon_H42 zenon_TC_bt). zenon_intro zenon_H44. % 0.41/0.58 generalize (zenon_H44 zenon_TD_by). zenon_intro zenon_H45. % 0.41/0.58 apply (zenon_imply_s _ _ zenon_H45); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 0.41/0.58 apply (zenon_notand_s _ _ zenon_H47); [ zenon_intro zenon_H49 | zenon_intro zenon_H48 ]. % 0.41/0.58 exact (zenon_H49 zenon_H39). % 0.41/0.58 apply (zenon_notand_s _ _ zenon_H48); [ zenon_intro zenon_H4b | zenon_intro zenon_H4a ]. % 0.41/0.58 exact (zenon_H4b zenon_H3b). % 0.41/0.58 apply (zenon_notand_s _ _ zenon_H4a); [ zenon_intro zenon_H4d | zenon_intro zenon_H4c ]. % 0.41/0.58 generalize (d9_orders_2 (k1_latsum_1 zenon_TA_bj zenon_TB_bo)). zenon_intro zenon_H4e. % 0.41/0.58 apply (zenon_imply_s _ _ zenon_H4e); [ zenon_intro zenon_H50 | zenon_intro zenon_H4f ]. % 0.41/0.58 generalize (dt_k1_latsum_1 zenon_TA_bj). zenon_intro zenon_H51. % 0.41/0.58 generalize (zenon_H51 zenon_TB_bo). zenon_intro zenon_H52. % 0.41/0.58 apply (zenon_imply_s _ _ zenon_H52); [ zenon_intro zenon_H54 | zenon_intro zenon_H53 ]. % 0.41/0.58 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H40 | zenon_intro zenon_H43 ]. % 0.41/0.58 exact (zenon_H40 zenon_H26). % 0.41/0.58 exact (zenon_H43 zenon_H2b). % 0.41/0.58 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 0.41/0.58 exact (zenon_H50 zenon_H55). % 0.41/0.58 generalize (zenon_H4f zenon_TC_bt). zenon_intro zenon_H57. % 0.41/0.58 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H59 | zenon_intro zenon_H58 ]. % 0.41/0.58 exact (zenon_H59 zenon_H30). % 0.41/0.58 generalize (zenon_H58 zenon_TD_by). zenon_intro zenon_H5a. % 0.41/0.58 apply (zenon_imply_s _ _ zenon_H5a); [ zenon_intro zenon_H5c | zenon_intro zenon_H5b ]. % 0.41/0.58 exact (zenon_H5c zenon_H35). % 0.41/0.58 apply (zenon_equiv_s _ _ zenon_H5b); [ zenon_intro zenon_H5e; zenon_intro zenon_H4d | zenon_intro zenon_H3d; zenon_intro zenon_H5d ]. % 0.41/0.58 exact (zenon_H5e zenon_H3d). % 0.41/0.58 exact (zenon_H4d zenon_H5d). % 0.41/0.58 exact (zenon_H4c zenon_H3c). % 0.41/0.58 exact (zenon_H36 zenon_H46). % 0.41/0.58 Qed. % 0.41/0.58 % SZS output end Proof % 0.41/0.58 (* END-PROOF *) % 0.41/0.58 nodes searched: 2301 % 0.41/0.58 max branch formulas: 936 % 0.41/0.58 proof nodes created: 186 % 0.41/0.58 formulas created: 9034 % 0.41/0.58 %------------------------------------------------------------------------------