%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : SEU101+1 : TPTP v8.1.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n004.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 15:59:23 EDT 2022 % Result : Theorem 0.41s 0.60s % Output : Proof 0.41s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.10/0.12 % Problem : SEU101+1 : TPTP v8.1.0. Released v3.2.0. % 0.10/0.13 % Command : run_zenon %s %d % 0.13/0.34 % Computer : n004.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 Jun 19 22:42:08 EDT 2022 % 0.13/0.34 % CPUTime : % 0.41/0.60 Zenon warning: unused variable (B : zenon_U) in idempotence_k2_xboole_0 % 0.41/0.60 Zenon warning: unused variable (B : zenon_U) in reflexivity_r1_tarski % 0.41/0.60 (* PROOF-FOUND *) % 0.41/0.60 % SZS status Theorem % 0.41/0.60 (* BEGIN-PROOF *) % 0.41/0.60 % SZS output start Proof % 0.41/0.60 Theorem t10_finsub_1 : (forall A : zenon_U, ((preboolean A)<->(forall B : zenon_U, (forall C : zenon_U, (((in B A)/\(in C A))->((in (set_union2 B C) A)/\(in (set_difference B C) A))))))). % 0.41/0.60 Proof. % 0.41/0.60 apply NNPP. intro zenon_G. % 0.41/0.60 apply (zenon_notallex_s (fun A : zenon_U => ((preboolean A)<->(forall B : zenon_U, (forall C : zenon_U, (((in B A)/\(in C A))->((in (set_union2 B C) A)/\(in (set_difference B C) A))))))) zenon_G); [ zenon_intro zenon_H26; idtac ]. % 0.41/0.60 elim zenon_H26. zenon_intro zenon_TA_bn. zenon_intro zenon_H28. % 0.41/0.60 apply (zenon_notequiv_s _ _ zenon_H28); [ zenon_intro zenon_H2c; zenon_intro zenon_H2b | zenon_intro zenon_H2a; zenon_intro zenon_H29 ]. % 0.41/0.60 generalize (d4_finsub_1 zenon_TA_bn). zenon_intro zenon_H2d. % 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H2c; zenon_intro zenon_H2f | zenon_intro zenon_H2a; zenon_intro zenon_H2e ]. % 0.41/0.60 apply (zenon_notand_s _ _ zenon_H2f); [ zenon_intro zenon_H31 | zenon_intro zenon_H30 ]. % 0.41/0.60 generalize (d1_finsub_1 zenon_TA_bn). zenon_intro zenon_H32. % 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H31; zenon_intro zenon_H35 | zenon_intro zenon_H34; zenon_intro zenon_H33 ]. % 0.41/0.60 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((in B zenon_TA_bn)/\(in C zenon_TA_bn))->(in (set_union2 B C) zenon_TA_bn)))) zenon_H35); [ zenon_intro zenon_H36; idtac ]. % 0.41/0.60 elim zenon_H36. zenon_intro zenon_TB_cd. zenon_intro zenon_H38. % 0.41/0.60 apply (zenon_notallex_s (fun C : zenon_U => (((in zenon_TB_cd zenon_TA_bn)/\(in C zenon_TA_bn))->(in (set_union2 zenon_TB_cd C) zenon_TA_bn))) zenon_H38); [ zenon_intro zenon_H39; idtac ]. % 0.41/0.60 elim zenon_H39. zenon_intro zenon_TC_cg. zenon_intro zenon_H3b. % 0.41/0.60 apply (zenon_notimply_s _ _ zenon_H3b). zenon_intro zenon_H3d. zenon_intro zenon_H3c. % 0.41/0.60 apply (zenon_and_s _ _ zenon_H3d). zenon_intro zenon_H3f. zenon_intro zenon_H3e. % 0.41/0.60 generalize (zenon_H2b zenon_TB_cd). zenon_intro zenon_H40. % 0.41/0.60 generalize (zenon_H40 zenon_TC_cg). zenon_intro zenon_H41. % 0.41/0.60 apply (zenon_imply_s _ _ zenon_H41); [ zenon_intro zenon_H43 | zenon_intro zenon_H42 ]. % 0.41/0.60 apply (zenon_notand_s _ _ zenon_H43); [ zenon_intro zenon_H45 | zenon_intro zenon_H44 ]. % 0.41/0.60 exact (zenon_H45 zenon_H3f). % 0.41/0.60 exact (zenon_H44 zenon_H3e). % 0.41/0.60 apply (zenon_and_s _ _ zenon_H42). zenon_intro zenon_H47. zenon_intro zenon_H46. % 0.41/0.60 exact (zenon_H3c zenon_H47). % 0.41/0.60 exact (zenon_H31 zenon_H34). % 0.41/0.60 generalize (d3_finsub_1 zenon_TA_bn). zenon_intro zenon_H48. % 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H48); [ zenon_intro zenon_H30; zenon_intro zenon_H4b | zenon_intro zenon_H4a; zenon_intro zenon_H49 ]. % 0.41/0.60 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((in B zenon_TA_bn)/\(in C zenon_TA_bn))->(in (set_difference B C) zenon_TA_bn)))) zenon_H4b); [ zenon_intro zenon_H4c; idtac ]. % 0.41/0.60 elim zenon_H4c. zenon_intro zenon_TB_cz. zenon_intro zenon_H4e. % 0.41/0.60 apply (zenon_notallex_s (fun C : zenon_U => (((in zenon_TB_cz zenon_TA_bn)/\(in C zenon_TA_bn))->(in (set_difference zenon_TB_cz C) zenon_TA_bn))) zenon_H4e); [ zenon_intro zenon_H4f; idtac ]. % 0.41/0.60 elim zenon_H4f. zenon_intro zenon_TC_dc. zenon_intro zenon_H51. % 0.41/0.60 apply (zenon_notimply_s _ _ zenon_H51). zenon_intro zenon_H53. zenon_intro zenon_H52. % 0.41/0.60 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H55. zenon_intro zenon_H54. % 0.41/0.60 generalize (zenon_H2b zenon_TB_cz). zenon_intro zenon_H56. % 0.41/0.60 generalize (zenon_H56 zenon_TC_dc). zenon_intro zenon_H57. % 0.41/0.60 apply (zenon_imply_s _ _ zenon_H57); [ zenon_intro zenon_H59 | zenon_intro zenon_H58 ]. % 0.41/0.60 apply (zenon_notand_s _ _ zenon_H59); [ zenon_intro zenon_H5b | zenon_intro zenon_H5a ]. % 0.41/0.60 exact (zenon_H5b zenon_H55). % 0.41/0.60 exact (zenon_H5a zenon_H54). % 0.41/0.60 apply (zenon_and_s _ _ zenon_H58). zenon_intro zenon_H5d. zenon_intro zenon_H5c. % 0.41/0.60 exact (zenon_H52 zenon_H5c). % 0.41/0.60 exact (zenon_H30 zenon_H4a). % 0.41/0.60 exact (zenon_H2c zenon_H2a). % 0.41/0.60 generalize (d4_finsub_1 zenon_TA_bn). zenon_intro zenon_H2d. % 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H2d); [ zenon_intro zenon_H2c; zenon_intro zenon_H2f | zenon_intro zenon_H2a; zenon_intro zenon_H2e ]. % 0.41/0.60 exact (zenon_H2c zenon_H2a). % 0.41/0.60 apply (zenon_and_s _ _ zenon_H2e). zenon_intro zenon_H34. zenon_intro zenon_H4a. % 0.41/0.60 generalize (d1_finsub_1 zenon_TA_bn). zenon_intro zenon_H32. % 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H32); [ zenon_intro zenon_H31; zenon_intro zenon_H35 | zenon_intro zenon_H34; zenon_intro zenon_H33 ]. % 0.41/0.60 exact (zenon_H31 zenon_H34). % 0.41/0.60 generalize (d3_finsub_1 zenon_TA_bn). zenon_intro zenon_H48. % 0.41/0.60 apply (zenon_equiv_s _ _ zenon_H48); [ zenon_intro zenon_H30; zenon_intro zenon_H4b | zenon_intro zenon_H4a; zenon_intro zenon_H49 ]. % 0.41/0.60 exact (zenon_H30 zenon_H4a). % 0.41/0.60 apply (zenon_notallex_s (fun B : zenon_U => (forall C : zenon_U, (((in B zenon_TA_bn)/\(in C zenon_TA_bn))->((in (set_union2 B C) zenon_TA_bn)/\(in (set_difference B C) zenon_TA_bn))))) zenon_H29); [ zenon_intro zenon_H5e; idtac ]. % 0.41/0.60 elim zenon_H5e. zenon_intro zenon_TB_dr. zenon_intro zenon_H60. % 0.41/0.60 apply (zenon_notallex_s (fun C : zenon_U => (((in zenon_TB_dr zenon_TA_bn)/\(in C zenon_TA_bn))->((in (set_union2 zenon_TB_dr C) zenon_TA_bn)/\(in (set_difference zenon_TB_dr C) zenon_TA_bn)))) zenon_H60); [ zenon_intro zenon_H61; idtac ]. % 0.41/0.60 elim zenon_H61. zenon_intro zenon_TC_du. zenon_intro zenon_H63. % 0.41/0.60 apply (zenon_notimply_s _ _ zenon_H63). zenon_intro zenon_H65. zenon_intro zenon_H64. % 0.41/0.60 apply (zenon_and_s _ _ zenon_H65). zenon_intro zenon_H67. zenon_intro zenon_H66. % 0.41/0.60 apply (zenon_notand_s _ _ zenon_H64); [ zenon_intro zenon_H69 | zenon_intro zenon_H68 ]. % 0.41/0.60 generalize (zenon_H33 zenon_TB_dr). zenon_intro zenon_H6a. % 0.41/0.60 generalize (zenon_H6a zenon_TC_du). zenon_intro zenon_H6b. % 0.41/0.60 apply (zenon_imply_s _ _ zenon_H6b); [ zenon_intro zenon_H6d | zenon_intro zenon_H6c ]. % 0.41/0.60 apply (zenon_notand_s _ _ zenon_H6d); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ]. % 0.41/0.60 exact (zenon_H6f zenon_H67). % 0.41/0.60 exact (zenon_H6e zenon_H66). % 0.41/0.60 exact (zenon_H69 zenon_H6c). % 0.41/0.60 generalize (zenon_H49 zenon_TB_dr). zenon_intro zenon_H70. % 0.41/0.60 generalize (zenon_H70 zenon_TC_du). zenon_intro zenon_H71. % 0.41/0.60 apply (zenon_imply_s _ _ zenon_H71); [ zenon_intro zenon_H6d | zenon_intro zenon_H72 ]. % 0.41/0.60 apply (zenon_notand_s _ _ zenon_H6d); [ zenon_intro zenon_H6f | zenon_intro zenon_H6e ]. % 0.41/0.60 exact (zenon_H6f zenon_H67). % 0.41/0.60 exact (zenon_H6e zenon_H66). % 0.41/0.60 exact (zenon_H68 zenon_H72). % 0.41/0.60 Qed. % 0.41/0.60 % SZS output end Proof % 0.41/0.60 (* END-PROOF *) % 0.41/0.60 nodes searched: 2860 % 0.41/0.60 max branch formulas: 473 % 0.41/0.60 proof nodes created: 294 % 0.41/0.60 formulas created: 9982 % 0.41/0.60 %------------------------------------------------------------------------------