%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : GRP643+1 : TPTP v8.1.0. Released v3.4.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n027.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 12:36:34 EDT 2022 % Result : Theorem 0.41s 0.57s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : GRP643+1 : TPTP v8.1.0. Released v3.4.0. % 0.12/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n027.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 : Mon Jun 13 17:52:47 EDT 2022 % 0.13/0.35 % CPUTime : % 0.41/0.57 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.41/0.57 (* PROOF-FOUND *) % 0.41/0.57 % SZS status Theorem % 0.41/0.57 (* BEGIN-PROOF *) % 0.41/0.57 % SZS output start Proof % 0.41/0.57 Theorem t21_latsubgr : (forall A : zenon_U, (((~(v3_struct_0 A))/\((v3_group_1 A)/\((v4_group_1 A)/\(l1_group_1 A))))->(forall B : zenon_U, (((v1_group_1 B)/\(m1_group_2 B A))->(forall C : zenon_U, ((m1_subset_1 C (u1_struct_0 A))->(forall D : zenon_U, ((m1_subset_1 D (u1_struct_0 A))->(((r2_hidden C (k1_funct_1 (k1_latsubgr A) B))/\(r2_hidden D (k1_funct_1 (k1_latsubgr A) B)))->(r2_hidden (k1_group_1 A C D) (k1_funct_1 (k1_latsubgr A) B))))))))))). % 0.41/0.57 Proof. % 0.41/0.57 apply NNPP. intro zenon_G. % 0.41/0.57 apply (zenon_notallex_s (fun A : zenon_U => (((~(v3_struct_0 A))/\((v3_group_1 A)/\((v4_group_1 A)/\(l1_group_1 A))))->(forall B : zenon_U, (((v1_group_1 B)/\(m1_group_2 B A))->(forall C : zenon_U, ((m1_subset_1 C (u1_struct_0 A))->(forall D : zenon_U, ((m1_subset_1 D (u1_struct_0 A))->(((r2_hidden C (k1_funct_1 (k1_latsubgr A) B))/\(r2_hidden D (k1_funct_1 (k1_latsubgr A) B)))->(r2_hidden (k1_group_1 A C D) (k1_funct_1 (k1_latsubgr A) B))))))))))) zenon_G); [ zenon_intro zenon_H2f; idtac ]. % 0.41/0.57 elim zenon_H2f. zenon_intro zenon_TA_bw. zenon_intro zenon_H31. % 0.41/0.57 apply (zenon_notimply_s _ _ zenon_H31). zenon_intro zenon_H33. zenon_intro zenon_H32. % 0.41/0.57 apply (zenon_and_s _ _ zenon_H33). zenon_intro zenon_H35. zenon_intro zenon_H34. % 0.41/0.57 apply (zenon_and_s _ _ zenon_H34). zenon_intro zenon_H37. zenon_intro zenon_H36. % 0.41/0.57 apply (zenon_and_s _ _ zenon_H36). zenon_intro zenon_H39. zenon_intro zenon_H38. % 0.41/0.57 apply (zenon_notallex_s (fun B : zenon_U => (((v1_group_1 B)/\(m1_group_2 B zenon_TA_bw))->(forall C : zenon_U, ((m1_subset_1 C (u1_struct_0 zenon_TA_bw))->(forall D : zenon_U, ((m1_subset_1 D (u1_struct_0 zenon_TA_bw))->(((r2_hidden C (k1_funct_1 (k1_latsubgr zenon_TA_bw) B))/\(r2_hidden D (k1_funct_1 (k1_latsubgr zenon_TA_bw) B)))->(r2_hidden (k1_group_1 zenon_TA_bw C D) (k1_funct_1 (k1_latsubgr zenon_TA_bw) B))))))))) zenon_H32); [ zenon_intro zenon_H3a; idtac ]. % 0.41/0.57 elim zenon_H3a. zenon_intro zenon_TB_ch. zenon_intro zenon_H3c. % 0.41/0.57 apply (zenon_notimply_s _ _ zenon_H3c). zenon_intro zenon_H3e. zenon_intro zenon_H3d. % 0.41/0.57 apply (zenon_and_s _ _ zenon_H3e). zenon_intro zenon_H40. zenon_intro zenon_H3f. % 0.41/0.57 apply (zenon_notallex_s (fun C : zenon_U => ((m1_subset_1 C (u1_struct_0 zenon_TA_bw))->(forall D : zenon_U, ((m1_subset_1 D (u1_struct_0 zenon_TA_bw))->(((r2_hidden C (k1_funct_1 (k1_latsubgr zenon_TA_bw) zenon_TB_ch))/\(r2_hidden D (k1_funct_1 (k1_latsubgr zenon_TA_bw) zenon_TB_ch)))->(r2_hidden (k1_group_1 zenon_TA_bw C D) (k1_funct_1 (k1_latsubgr zenon_TA_bw) zenon_TB_ch))))))) zenon_H3d); [ zenon_intro zenon_H41; idtac ]. % 0.41/0.57 elim zenon_H41. zenon_intro zenon_TC_co. zenon_intro zenon_H43. % 0.41/0.57 apply (zenon_notimply_s _ _ zenon_H43). zenon_intro zenon_H45. zenon_intro zenon_H44. % 0.41/0.57 apply (zenon_notallex_s (fun D : zenon_U => ((m1_subset_1 D (u1_struct_0 zenon_TA_bw))->(((r2_hidden zenon_TC_co (k1_funct_1 (k1_latsubgr zenon_TA_bw) zenon_TB_ch))/\(r2_hidden D (k1_funct_1 (k1_latsubgr zenon_TA_bw) zenon_TB_ch)))->(r2_hidden (k1_group_1 zenon_TA_bw zenon_TC_co D) (k1_funct_1 (k1_latsubgr zenon_TA_bw) zenon_TB_ch))))) zenon_H44); [ zenon_intro zenon_H46; idtac ]. % 0.41/0.57 elim zenon_H46. zenon_intro zenon_TD_ct. zenon_intro zenon_H48. % 0.41/0.57 apply (zenon_notimply_s _ _ zenon_H48). zenon_intro zenon_H4a. zenon_intro zenon_H49. % 0.41/0.57 apply (zenon_notimply_s _ _ zenon_H49). zenon_intro zenon_H4c. zenon_intro zenon_H4b. % 0.41/0.57 apply (zenon_and_s _ _ zenon_H4c). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 0.41/0.57 generalize (t18_latsubgr zenon_TA_bw). zenon_intro zenon_H4f. % 0.41/0.57 apply (zenon_imply_s _ _ zenon_H4f); [ zenon_intro zenon_H51 | zenon_intro zenon_H50 ]. % 0.41/0.57 apply (zenon_notand_s _ _ zenon_H51); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ]. % 0.41/0.57 exact (zenon_H53 zenon_H35). % 0.41/0.57 apply (zenon_notand_s _ _ zenon_H52); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 0.41/0.57 exact (zenon_H55 zenon_H37). % 0.41/0.57 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ]. % 0.41/0.57 exact (zenon_H57 zenon_H39). % 0.41/0.57 exact (zenon_H56 zenon_H38). % 0.41/0.57 generalize (zenon_H50 zenon_TB_ch). zenon_intro zenon_H58. % 0.41/0.57 apply (zenon_imply_s _ _ zenon_H58); [ zenon_intro zenon_H5a | zenon_intro zenon_H59 ]. % 0.41/0.57 apply (zenon_notand_s _ _ zenon_H5a); [ zenon_intro zenon_H5c | zenon_intro zenon_H5b ]. % 0.41/0.57 exact (zenon_H5c zenon_H40). % 0.41/0.57 exact (zenon_H5b zenon_H3f). % 0.41/0.57 generalize (zenon_H59 (k1_group_1 zenon_TA_bw zenon_TC_co zenon_TD_ct)). zenon_intro zenon_H5d. % 0.41/0.57 apply (zenon_imply_s _ _ zenon_H5d); [ zenon_intro zenon_H5f | zenon_intro zenon_H5e ]. % 0.41/0.57 generalize (dt_k1_group_1 zenon_TA_bw). zenon_intro zenon_H60. % 0.41/0.57 generalize (zenon_H60 zenon_TC_co). zenon_intro zenon_H61. % 0.41/0.57 generalize (zenon_H61 zenon_TD_ct). zenon_intro zenon_H62. % 0.41/0.57 apply (zenon_imply_s _ _ zenon_H62); [ zenon_intro zenon_H64 | zenon_intro zenon_H63 ]. % 0.41/0.57 apply (zenon_notand_s _ _ zenon_H64); [ zenon_intro zenon_H53 | zenon_intro zenon_H65 ]. % 0.41/0.57 exact (zenon_H53 zenon_H35). % 0.41/0.57 apply (zenon_notand_s _ _ zenon_H65); [ zenon_intro zenon_H56 | zenon_intro zenon_H66 ]. % 0.41/0.57 exact (zenon_H56 zenon_H38). % 0.41/0.57 apply (zenon_notand_s _ _ zenon_H66); [ zenon_intro zenon_H68 | zenon_intro zenon_H67 ]. % 0.41/0.57 exact (zenon_H68 zenon_H45). % 0.41/0.57 exact (zenon_H67 zenon_H4a). % 0.41/0.57 exact (zenon_H5f zenon_H63). % 0.41/0.57 apply (zenon_equiv_s _ _ zenon_H5e); [ zenon_intro zenon_H4b; zenon_intro zenon_H6b | zenon_intro zenon_H6a; zenon_intro zenon_H69 ]. % 0.41/0.57 generalize (t59_group_2 zenon_TA_bw). zenon_intro zenon_H6c. % 0.41/0.57 apply (zenon_imply_s _ _ zenon_H6c); [ zenon_intro zenon_H51 | zenon_intro zenon_H6d ]. % 0.41/0.57 apply (zenon_notand_s _ _ zenon_H51); [ zenon_intro zenon_H53 | zenon_intro zenon_H52 ]. % 0.41/0.57 exact (zenon_H53 zenon_H35). % 0.41/0.57 apply (zenon_notand_s _ _ zenon_H52); [ zenon_intro zenon_H55 | zenon_intro zenon_H54 ]. % 0.41/0.57 exact (zenon_H55 zenon_H37). % 0.41/0.57 apply (zenon_notand_s _ _ zenon_H54); [ zenon_intro zenon_H57 | zenon_intro zenon_H56 ]. % 0.41/0.57 exact (zenon_H57 zenon_H39). % 0.41/0.57 exact (zenon_H56 zenon_H38). % 0.41/0.57 generalize (zenon_H6d zenon_TC_co). zenon_intro zenon_H6e. % 0.41/0.57 apply (zenon_imply_s _ _ zenon_H6e); [ zenon_intro zenon_H68 | zenon_intro zenon_H6f ]. % 0.41/0.57 exact (zenon_H68 zenon_H45). % 0.41/0.57 generalize (zenon_H6f zenon_TD_ct). zenon_intro zenon_H70. % 0.41/0.57 apply (zenon_imply_s _ _ zenon_H70); [ zenon_intro zenon_H67 | zenon_intro zenon_H71 ]. % 0.41/0.57 exact (zenon_H67 zenon_H4a). % 0.41/0.57 generalize (zenon_H71 zenon_TB_ch). zenon_intro zenon_H72. % 0.41/0.57 apply (zenon_imply_s _ _ zenon_H72); [ zenon_intro zenon_H5b | zenon_intro zenon_H73 ]. % 0.41/0.57 exact (zenon_H5b zenon_H3f). % 0.41/0.57 apply (zenon_imply_s _ _ zenon_H73); [ zenon_intro zenon_H74 | zenon_intro zenon_H69 ]. % 0.41/0.57 apply (zenon_notand_s _ _ zenon_H74); [ zenon_intro zenon_H76 | zenon_intro zenon_H75 ]. % 0.41/0.57 generalize (zenon_H59 zenon_TC_co). zenon_intro zenon_H77. % 0.41/0.57 apply (zenon_imply_s _ _ zenon_H77); [ zenon_intro zenon_H68 | zenon_intro zenon_H78 ]. % 0.41/0.57 exact (zenon_H68 zenon_H45). % 0.41/0.57 apply (zenon_equiv_s _ _ zenon_H78); [ zenon_intro zenon_H7a; zenon_intro zenon_H76 | zenon_intro zenon_H4e; zenon_intro zenon_H79 ]. % 0.41/0.57 exact (zenon_H7a zenon_H4e). % 0.41/0.57 exact (zenon_H76 zenon_H79). % 0.41/0.57 generalize (zenon_H59 zenon_TD_ct). zenon_intro zenon_H7b. % 0.41/0.57 apply (zenon_imply_s _ _ zenon_H7b); [ zenon_intro zenon_H67 | zenon_intro zenon_H7c ]. % 0.41/0.57 exact (zenon_H67 zenon_H4a). % 0.41/0.57 apply (zenon_equiv_s _ _ zenon_H7c); [ zenon_intro zenon_H7e; zenon_intro zenon_H75 | zenon_intro zenon_H4d; zenon_intro zenon_H7d ]. % 0.41/0.57 exact (zenon_H7e zenon_H4d). % 0.41/0.57 exact (zenon_H75 zenon_H7d). % 0.41/0.57 exact (zenon_H6b zenon_H69). % 0.41/0.57 exact (zenon_H4b zenon_H6a). % 0.41/0.57 Qed. % 0.41/0.57 % SZS output end Proof % 0.41/0.57 (* END-PROOF *) % 0.41/0.57 nodes searched: 1553 % 0.41/0.57 max branch formulas: 813 % 0.41/0.57 proof nodes created: 167 % 0.41/0.57 formulas created: 7692 % 0.41/0.57 %------------------------------------------------------------------------------