%----Output an unreadable proof
% SZS output start Proof for theBenchmark
thf(type_def_5, type, set_Pr2099245410le_U_o: $tType).
thf(type_def_6, type, produc622718850le_U_o: $tType).
thf(type_def_7, type, produc957084248e_form: $tType).
thf(type_def_8, type, set_Pr1072215906le_U_o: $tType).
thf(type_def_9, type, produc227817602le_U_o: $tType).
thf(type_def_10, type, set_Pr31825690e_form: $tType).
thf(type_def_11, type, produc791938916e_form: $tType).
thf(type_def_12, type, set_Pr1057005944st_nat: $tType).
thf(type_def_13, type, set_Pr1174364408e_form: $tType).
thf(type_def_14, type, set_Pr1189404964e_form: $tType).
thf(type_def_15, type, produc1473535256st_nat: $tType).
thf(type_def_16, type, produc1494932632e_form: $tType).
thf(type_def_17, type, produc825256814e_form: $tType).
thf(type_def_18, type, list_n2139828004le_U_o: $tType).
thf(type_def_19, type, produc890077173st_nat: $tType).
thf(type_def_20, type, set_Pr1560408065st_nat: $tType).
thf(type_def_21, type, set_Pr957084504rm_nat: $tType).
thf(type_def_22, type, set_Pr816919384e_form: $tType).
thf(type_def_23, type, produc1699244961st_nat: $tType).
thf(type_def_24, type, produc117678584rm_nat: $tType).
thf(type_def_25, type, produc1296622072e_form: $tType).
thf(type_def_26, type, list_l461858535e_form: $tType).
thf(type_def_27, type, set_li5074317e_form: $tType).
thf(type_def_28, type, list_s1200803384elle_U: $tType).
thf(type_def_29, type, set_Pr1986765409at_nat: $tType).
thf(type_def_30, type, list_P512754263e_form: $tType).
thf(type_def_31, type, set_Pr554570749e_form: $tType).
thf(type_def_32, type, list_P796095576elle_U: $tType).
thf(type_def_33, type, set_Pr619177522elle_U: $tType).
thf(type_def_34, type, product_prod_nat_nat: $tType).
thf(type_def_35, type, list_list_nat: $tType).
thf(type_def_36, type, set_list_nat: $tType).
thf(type_def_37, type, prover1687215943e_form: $tType).
thf(type_def_38, type, prover_Mirabelle_U: $tType).
thf(type_def_39, type, list_nat: $tType).
thf(type_def_40, type, set_nat: $tType).
thf(type_def_41, type, nat: $tType).
thf(type_def_42, type, sTfun: ($tType * $tType) > $tType).
thf(func_def_0, type, zero_zero_nat: nat).
thf(func_def_1, type, if_list_nat: ($o > list_nat > list_nat > list_nat)).
thf(func_def_2, type, if_lis1812881937e_form: ($o > list_P512754263e_form > list_P512754263e_form > list_P512754263e_form)).
thf(func_def_3, type, append_list_nat: (list_list_nat > list_list_nat > list_list_nat)).
thf(func_def_4, type, append1797078012e_form: (list_l461858535e_form > list_l461858535e_form > list_l461858535e_form)).
thf(func_def_5, type, append_nat: (list_nat > list_nat > list_nat)).
thf(func_def_6, type, append1038020460e_form: (list_P512754263e_form > list_P512754263e_form > list_P512754263e_form)).
thf(func_def_7, type, bind_nat_nat: (list_nat > (nat > list_nat) > list_nat)).
thf(func_def_8, type, bind_n1193922848e_form: (list_nat > (nat > list_P512754263e_form) > list_P512754263e_form)).
thf(func_def_9, type, bind_P1359331232rm_nat: (list_P512754263e_form > (prover1687215943e_form > list_nat) > list_nat)).
thf(func_def_10, type, bind_P1054726576e_form: (list_P512754263e_form > (prover1687215943e_form > list_P512754263e_form) > list_P512754263e_form)).
thf(func_def_11, type, butlast_nat: (list_nat > list_nat)).
thf(func_def_12, type, butlas664258165e_form: (list_P512754263e_form > list_P512754263e_form)).
thf(func_def_13, type, can_select_nat: ((nat > $o) > set_nat > $o)).
thf(func_def_14, type, concat_nat: (list_list_nat > list_nat)).
thf(func_def_15, type, concat1664984646e_form: (list_l461858535e_form > list_P512754263e_form)).
thf(func_def_16, type, insert_nat: (nat > list_nat > list_nat)).
thf(func_def_17, type, insert697320747e_form: (prover1687215943e_form > list_P512754263e_form > list_P512754263e_form)).
thf(func_def_18, type, last_nat: (list_nat > nat)).
thf(func_def_19, type, last_P1811260776e_form: (list_P512754263e_form > prover1687215943e_form)).
thf(func_def_20, type, lenlex_nat: (set_Pr1986765409at_nat > set_Pr1560408065st_nat)).
thf(func_def_21, type, lenlex1927129340e_form: (set_Pr1189404964e_form > set_Pr31825690e_form)).
thf(func_def_22, type, lex_nat: (set_Pr1986765409at_nat > set_Pr1560408065st_nat)).
thf(func_def_23, type, lex_Pr233218909e_form: (set_Pr1189404964e_form > set_Pr31825690e_form)).
thf(func_def_24, type, lexord_nat: (set_Pr1986765409at_nat > set_Pr1560408065st_nat)).
thf(func_def_25, type, lexord1848469012e_form: (set_Pr1189404964e_form > set_Pr31825690e_form)).
thf(func_def_26, type, cons_n50929118le_U_o: ((nat > list_P796095576elle_U > $o) > list_n2139828004le_U_o > list_n2139828004le_U_o)).
thf(func_def_27, type, cons_list_nat: (list_nat > list_list_nat > list_list_nat)).
thf(func_def_28, type, cons_l1379921697e_form: (list_P512754263e_form > list_l461858535e_form > list_l461858535e_form)).
thf(func_def_29, type, cons_nat: (nat > list_nat > list_nat)).
thf(func_def_30, type, cons_P1475164433e_form: (prover1687215943e_form > list_P512754263e_form > list_P512754263e_form)).
thf(func_def_31, type, cons_s32021736elle_U: (set_Pr619177522elle_U > list_s1200803384elle_U > list_s1200803384elle_U)).
thf(func_def_32, type, nil_na1584420238le_U_o: list_n2139828004le_U_o).
thf(func_def_33, type, nil_list_nat: list_list_nat).
thf(func_def_34, type, nil_li1393862353e_form: list_l461858535e_form).
thf(func_def_35, type, nil_nat: list_nat).
thf(func_def_36, type, nil_Pr1384483009e_form: list_P512754263e_form).
thf(func_def_37, type, nil_se944326968elle_U: list_s1200803384elle_U).
thf(func_def_38, type, set_list_nat2: (list_list_nat > set_list_nat)).
thf(func_def_39, type, set_li1219651714e_form: (list_l461858535e_form > set_li5074317e_form)).
thf(func_def_40, type, set_nat2: (list_nat > set_nat)).
thf(func_def_41, type, set_Pr1105237746e_form: (list_P512754263e_form > set_Pr554570749e_form)).
thf(func_def_42, type, list_ex1_nat: ((nat > $o) > list_nat > $o)).
thf(func_def_43, type, list_e2123636798e_form: ((prover1687215943e_form > $o) > list_P512754263e_form > $o)).
thf(func_def_44, type, listrel1_nat: (set_Pr1986765409at_nat > set_Pr1560408065st_nat)).
thf(func_def_45, type, listre502458152e_form: (set_Pr1189404964e_form > set_Pr31825690e_form)).
thf(func_def_46, type, listrel_nat_nat: (set_Pr1986765409at_nat > set_Pr1560408065st_nat)).
thf(func_def_47, type, listre318297994e_form: (set_Pr816919384e_form > set_Pr1174364408e_form)).
thf(func_def_48, type, listre483706378rm_nat: (set_Pr957084504rm_nat > set_Pr1057005944st_nat)).
thf(func_def_49, type, listre1908795590e_form: (set_Pr1189404964e_form > set_Pr31825690e_form)).
thf(func_def_50, type, listre290852044le_U_o: (set_Pr1072215906le_U_o > set_Pr2099245410le_U_o)).
thf(func_def_51, type, maps_nat_nat: ((nat > list_nat) > list_nat > list_nat)).
thf(func_def_52, type, maps_n1383976154e_form: ((nat > list_P512754263e_form) > list_nat > list_P512754263e_form)).
thf(func_def_53, type, maps_P1549384538rm_nat: ((prover1687215943e_form > list_nat) > list_P512754263e_form > list_nat)).
thf(func_def_54, type, maps_P2058952566e_form: ((prover1687215943e_form > list_P512754263e_form) > list_P512754263e_form > list_P512754263e_form)).
thf(func_def_55, type, product_lists_nat: (list_list_nat > list_list_nat)).
thf(func_def_56, type, produc168439576e_form: (list_l461858535e_form > list_l461858535e_form)).
thf(func_def_57, type, rotate1_nat: (list_nat > list_nat)).
thf(func_def_58, type, rotate650061876e_form: (list_P512754263e_form > list_P512754263e_form)).
thf(func_def_59, type, subseqs_nat: (list_nat > list_list_nat)).
thf(func_def_60, type, subseq1471997234e_form: (list_P512754263e_form > list_l461858535e_form)).
thf(func_def_61, type, produc939441135st_nat: ((nat > nat > $o) > list_nat > produc890077173st_nat)).
thf(func_def_62, type, produc54611594e_form: ((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > produc957084248e_form)).
thf(func_def_63, type, produc1625736153st_nat: (list_nat > list_nat > produc1699244961st_nat)).
thf(func_def_64, type, produc1617574096e_form: (list_nat > list_P512754263e_form > produc1494932632e_form)).
thf(func_def_65, type, produc1897654224st_nat: (list_P512754263e_form > list_nat > produc1473535256st_nat)).
thf(func_def_66, type, produc891809686e_form: (list_P512754263e_form > list_P512754263e_form > produc791938916e_form)).
thf(func_def_67, type, produc1377086578le_U_o: (list_s1200803384elle_U > list_n2139828004le_U_o > produc622718850le_U_o)).
thf(func_def_68, type, product_Pair_nat_nat: (nat > nat > product_prod_nat_nat)).
thf(func_def_69, type, produc876465968e_form: (nat > prover1687215943e_form > produc1296622072e_form)).
thf(func_def_70, type, produc1041874352rm_nat: (prover1687215943e_form > nat > produc117678584rm_nat)).
thf(func_def_71, type, produc1018812320e_form: (prover1687215943e_form > prover1687215943e_form > produc825256814e_form)).
thf(func_def_72, type, produc1069574002le_U_o: (set_Pr619177522elle_U > (nat > list_P796095576elle_U > $o) > produc227817602le_U_o)).
thf(func_def_73, type, prover1282070756_SEval: (produc227817602le_U_o > (nat > prover_Mirabelle_U) > list_P512754263e_form > $o)).
thf(func_def_74, type, prover1539709396Svalid: (list_P512754263e_form > $o)).
thf(func_def_75, type, prover1577896257_finst: (prover1687215943e_form > nat > prover1687215943e_form)).
thf(func_def_76, type, prover886976490en_nat: (list_list_nat > list_nat)).
thf(func_def_77, type, prover542312166e_form: (list_l461858535e_form > list_P512754263e_form)).
thf(func_def_78, type, prover571163162e_FAll: (prover1687215943e_form > prover1687215943e_form)).
thf(func_def_79, type, prover_Mirabelle_fv: (prover1687215943e_form > list_nat)).
thf(func_def_80, type, prover1847600056is_env: (produc227817602le_U_o > (nat > prover_Mirabelle_U) > $o)).
thf(func_def_81, type, prover1021675886maxvar: (list_nat > nat)).
thf(func_def_82, type, prover2096325705preSuc: (list_nat > list_nat)).
thf(func_def_83, type, prover_Mirabelle_sfv: (list_P512754263e_form > list_nat)).
thf(func_def_84, type, irrefl_nat: (set_Pr1986765409at_nat > $o)).
thf(func_def_85, type, irrefl2121388754e_form: (set_Pr1189404964e_form > $o)).
thf(func_def_86, type, collect_nat: ((nat > $o) > set_nat)).
thf(func_def_87, type, the_elem_nat: (set_nat > nat)).
thf(func_def_88, type, the_el969789074e_form: (set_Pr554570749e_form > prover1687215943e_form)).
thf(func_def_89, type, member_list_nat: (list_nat > set_list_nat > $o)).
thf(func_def_90, type, member1828782574e_form: (list_P512754263e_form > set_li5074317e_form > $o)).
thf(func_def_91, type, member_nat: (nat > set_nat > $o)).
thf(func_def_92, type, member1926390090st_nat: (produc1699244961st_nat > set_Pr1560408065st_nat > $o)).
thf(func_def_93, type, member1471151041e_form: (produc1494932632e_form > set_Pr1174364408e_form > $o)).
thf(func_def_94, type, member1449753665st_nat: (produc1473535256st_nat > set_Pr1057005944st_nat > $o)).
thf(func_def_95, type, member650892795e_form: (produc791938916e_form > set_Pr31825690e_form > $o)).
thf(func_def_96, type, member493452075le_U_o: (produc622718850le_U_o > set_Pr2099245410le_U_o > $o)).
thf(func_def_97, type, member701585322at_nat: (product_prod_nat_nat > set_Pr1986765409at_nat > $o)).
thf(func_def_98, type, member18158113e_form: (produc1296622072e_form > set_Pr816919384e_form > $o)).
thf(func_def_99, type, member986698273rm_nat: (produc117678584rm_nat > set_Pr957084504rm_nat > $o)).
thf(func_def_100, type, member189065477e_form: (produc825256814e_form > set_Pr1189404964e_form > $o)).
thf(func_def_101, type, member1933006123le_U_o: (produc227817602le_U_o > set_Pr1072215906le_U_o > $o)).
thf(func_def_102, type, member1793840734e_form: (prover1687215943e_form > set_Pr554570749e_form > $o)).
thf(func_def_103, type, a: set_Pr619177522elle_U).
thf(func_def_104, type, b: (nat > list_P796095576elle_U > $o)).
thf(func_def_105, type, f: prover1687215943e_form).
thf(func_def_106, type, s: list_P512754263e_form).
thf(func_def_107, type, u: nat).
thf(func_def_109, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
thf(func_def_110, type, vNOT: ($o > $o)).
thf(func_def_113, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_114, type, vAND: ($o > $o > $o)).
thf(func_def_115, type, db1: !>[X0: $tType]:(X0)).
thf(func_def_116, type, db0: !>[X0: $tType]:(X0)).
thf(func_def_117, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
thf(func_def_118, type, vOR: ($o > $o > $o)).
thf(func_def_119, type, vPI: !>[X0: $tType]:(((X0 > $o) > $o))).
thf(func_def_120, type, vIMP: ($o > $o > $o)).
thf(func_def_121, type, db2: !>[X0: $tType]:(X0)).
thf(func_def_122, type, db3: !>[X0: $tType]:(X0)).
thf(func_def_123, type, sK0: ((list_P512754263e_form > list_nat > $o) > list_P512754263e_form)).
thf(func_def_124, type, sK1: ((list_P512754263e_form > list_nat > $o) > prover1687215943e_form)).
thf(func_def_125, type, sK2: ((list_P512754263e_form > list_nat > $o) > list_nat)).
thf(func_def_126, type, sK3: ((list_P512754263e_form > list_nat > $o) > nat)).
thf(func_def_127, type, sK4: ((list_P512754263e_form > list_nat > $o) > list_P512754263e_form)).
thf(func_def_128, type, sK5: ((list_P512754263e_form > list_nat > $o) > nat)).
thf(func_def_129, type, sK6: ((list_P512754263e_form > list_nat > $o) > prover1687215943e_form)).
thf(func_def_130, type, sK7: ((list_P512754263e_form > list_nat > $o) > list_nat)).
thf(func_def_131, type, sK8: ((list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_132, type, sK9: ((list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_133, type, sK10: ((list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_134, type, sK11: ((list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_135, type, sK12: ((prover1687215943e_form > $o) > list_P512754263e_form > list_P512754263e_form)).
thf(func_def_136, type, sK13: ((prover1687215943e_form > $o) > list_P512754263e_form > prover1687215943e_form)).
thf(func_def_137, type, sK14: ((prover1687215943e_form > $o) > list_P512754263e_form > list_P512754263e_form)).
thf(func_def_138, type, sK15: ((list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_139, type, sK16: ((list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_140, type, sK17: ((list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_141, type, sK18: ((list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_142, type, sK19: ((list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_143, type, sK20: ((list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_144, type, sK21: ((list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_145, type, sK22: ((list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_146, type, sK23: (nat > list_nat > list_nat)).
thf(func_def_147, type, sK24: (nat > list_nat > list_nat)).
thf(func_def_148, type, sK25: (((nat > nat > $o) > list_nat > $o) > nat > nat > $o)).
thf(func_def_149, type, sK26: (((nat > nat > $o) > list_nat > $o) > nat)).
thf(func_def_150, type, sK27: (((nat > nat > $o) > list_nat > $o) > nat > nat > $o)).
thf(func_def_151, type, sK28: (((nat > nat > $o) > list_nat > $o) > nat > nat > $o)).
thf(func_def_152, type, sK29: (((nat > nat > $o) > list_nat > $o) > list_nat)).
thf(func_def_153, type, sK30: (((nat > nat > $o) > list_nat > $o) > nat)).
thf(func_def_154, type, sK31: (((nat > nat > $o) > list_nat > $o) > nat)).
thf(func_def_155, type, sK32: (list_nat > (nat > $o) > list_nat)).
thf(func_def_156, type, sK33: (list_nat > (nat > $o) > nat)).
thf(func_def_157, type, sK34: (list_nat > (nat > $o) > list_nat)).
thf(func_def_158, type, sK35: (list_nat > nat > list_nat)).
thf(func_def_159, type, sK36: (list_nat > nat > list_nat)).
thf(func_def_160, type, sK37: (list_P512754263e_form > prover1687215943e_form > list_P512754263e_form)).
thf(func_def_161, type, sK38: (list_P512754263e_form > prover1687215943e_form > list_P512754263e_form)).
thf(func_def_162, type, sK39: ((list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_163, type, sK40: ((list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_164, type, sK41: ((list_nat > list_nat > $o) > list_nat)).
thf(func_def_165, type, sK42: ((list_nat > list_nat > $o) > nat)).
thf(func_def_166, type, sK43: ((list_nat > list_nat > $o) > nat)).
thf(func_def_167, type, sK44: ((list_nat > list_nat > $o) > list_nat)).
thf(func_def_168, type, sK45: ((list_nat > list_nat > $o) > list_nat)).
thf(func_def_169, type, sK46: ((list_nat > list_nat > $o) > nat)).
thf(func_def_170, type, sK47: ((list_nat > list_nat > $o) > nat)).
thf(func_def_171, type, sK48: ((list_nat > list_nat > $o) > list_nat)).
thf(func_def_172, type, sK49: (produc227817602le_U_o > nat > list_P796095576elle_U > $o)).
thf(func_def_173, type, sK50: (produc227817602le_U_o > set_Pr619177522elle_U)).
thf(func_def_174, type, sK51: (list_P512754263e_form > prover1687215943e_form > list_P512754263e_form)).
thf(func_def_175, type, sK52: (list_P512754263e_form > prover1687215943e_form > list_P512754263e_form)).
thf(func_def_176, type, sK53: (((nat > nat > $o) > list_nat > $o) > nat)).
thf(func_def_177, type, sK54: (((nat > nat > $o) > list_nat > $o) > list_nat)).
thf(func_def_178, type, sK55: (((nat > nat > $o) > list_nat > $o) > nat > nat > $o)).
thf(func_def_179, type, sK56: (((nat > nat > $o) > list_nat > $o) > nat > nat > $o)).
thf(func_def_180, type, sK57: (list_nat > nat)).
thf(func_def_181, type, sK58: (list_nat > list_nat)).
thf(func_def_182, type, sK59: ((prover1687215943e_form > $o) > list_P512754263e_form > list_P512754263e_form)).
thf(func_def_183, type, sK60: ((prover1687215943e_form > $o) > list_P512754263e_form > list_P512754263e_form)).
thf(func_def_184, type, sK61: ((prover1687215943e_form > $o) > list_P512754263e_form > prover1687215943e_form)).
thf(func_def_185, type, sK62: ((list_nat > list_nat > $o) > list_nat)).
thf(func_def_186, type, sK63: ((list_nat > list_nat > $o) > list_nat)).
thf(func_def_187, type, sK64: ((list_nat > list_nat > $o) > nat)).
thf(func_def_188, type, sK65: ((list_nat > list_nat > $o) > list_nat)).
thf(func_def_189, type, sK66: ((list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_190, type, sK67: ((list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_191, type, sK68: ((list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_192, type, sK69: (produc227817602le_U_o > set_Pr619177522elle_U)).
thf(func_def_193, type, sK70: (produc227817602le_U_o > nat > list_P796095576elle_U > $o)).
thf(func_def_194, type, sK71: (list_P512754263e_form > (prover1687215943e_form > $o) > prover1687215943e_form)).
thf(func_def_195, type, sK72: (list_P512754263e_form > (prover1687215943e_form > $o) > list_P512754263e_form)).
thf(func_def_196, type, sK73: (list_P512754263e_form > (prover1687215943e_form > $o) > list_P512754263e_form)).
thf(func_def_197, type, sK74: (((prover1687215943e_form > nat) > list_P512754263e_form > list_nat > $o) > prover1687215943e_form > nat)).
thf(func_def_198, type, sK75: (((prover1687215943e_form > nat) > list_P512754263e_form > list_nat > $o) > list_nat)).
thf(func_def_199, type, sK76: (((prover1687215943e_form > nat) > list_P512754263e_form > list_nat > $o) > list_P512754263e_form)).
thf(func_def_200, type, sK77: (((prover1687215943e_form > nat) > list_P512754263e_form > list_nat > $o) > list_nat)).
thf(func_def_201, type, sK78: (((prover1687215943e_form > nat) > list_P512754263e_form > list_nat > $o) > prover1687215943e_form > nat)).
thf(func_def_202, type, sK79: (((prover1687215943e_form > nat) > list_P512754263e_form > list_nat > $o) > prover1687215943e_form)).
thf(func_def_203, type, sK80: (((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form > prover1687215943e_form > $o)).
thf(func_def_204, type, sK81: (((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form > prover1687215943e_form > $o)).
thf(func_def_205, type, sK82: (((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_206, type, sK83: (((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_207, type, sK84: ((nat > $o) > list_nat > nat)).
thf(func_def_208, type, sK85: ((nat > $o) > list_nat > list_nat)).
thf(func_def_209, type, sK86: ((nat > $o) > list_nat > list_nat)).
thf(func_def_210, type, sK87: ((list_nat > $o) > nat)).
thf(func_def_211, type, sK88: ((list_nat > $o) > nat)).
thf(func_def_212, type, sK89: ((list_nat > $o) > list_nat)).
thf(func_def_213, type, sK90: ((list_nat > $o) > nat)).
thf(func_def_214, type, sK91: (list_nat > list_nat)).
thf(func_def_215, type, sK92: (list_nat > nat)).
thf(func_def_216, type, sK93: (((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form > prover1687215943e_form > $o)).
thf(func_def_217, type, sK94: (((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_218, type, sK95: (((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form > prover1687215943e_form > $o)).
thf(func_def_219, type, sK96: (((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form > prover1687215943e_form > $o)).
thf(func_def_220, type, sK97: (((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_221, type, sK98: (((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_222, type, sK99: (((prover1687215943e_form > prover1687215943e_form > $o) > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_223, type, sK100: (list_P512754263e_form > prover1687215943e_form)).
thf(func_def_224, type, sK101: (list_P512754263e_form > prover1687215943e_form)).
thf(func_def_225, type, sK102: (list_P512754263e_form > list_P512754263e_form)).
thf(func_def_226, type, sK103: (list_P512754263e_form > prover1687215943e_form)).
thf(func_def_227, type, sK104: (list_nat > list_nat)).
thf(func_def_228, type, sK105: (list_nat > nat)).
thf(func_def_229, type, sK106: ((produc227817602le_U_o > $o) > set_Pr619177522elle_U)).
thf(func_def_230, type, sK107: ((produc227817602le_U_o > $o) > nat > list_P796095576elle_U > $o)).
thf(func_def_231, type, sK108: ((list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_232, type, sK109: ((list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_233, type, sK110: ((list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_234, type, sK111: ((nat > $o) > list_nat > nat)).
thf(func_def_235, type, sK112: ((nat > $o) > list_nat > list_nat)).
thf(func_def_236, type, sK113: ((nat > $o) > list_nat > list_nat)).
thf(func_def_237, type, sK114: (list_P512754263e_form > prover1687215943e_form)).
thf(func_def_238, type, sK115: (list_P512754263e_form > list_P512754263e_form)).
thf(func_def_239, type, sK116: ((list_nat > $o) > nat)).
thf(func_def_240, type, sK117: ((list_nat > $o) > nat)).
thf(func_def_241, type, sK118: ((list_nat > $o) > list_nat)).
thf(func_def_242, type, sK119: ((list_nat > $o) > nat)).
thf(func_def_243, type, sK120: ((list_nat > $o) > nat)).
thf(func_def_244, type, sK121: ((list_nat > $o) > list_nat)).
thf(func_def_245, type, sK122: (nat > prover_Mirabelle_U)).
thf(func_def_246, type, sK123: (list_nat > (nat > $o) > list_nat)).
thf(func_def_247, type, sK124: (list_nat > (nat > $o) > nat)).
thf(func_def_248, type, sK125: (list_nat > (nat > $o) > list_nat)).
thf(func_def_249, type, sK126: ((produc227817602le_U_o > $o) > set_Pr619177522elle_U)).
thf(func_def_250, type, sK127: ((produc227817602le_U_o > $o) > nat > list_P796095576elle_U > $o)).
thf(func_def_251, type, sK128: (list_P512754263e_form > (nat > prover_Mirabelle_U) > (nat > prover_Mirabelle_U) > nat)).
thf(func_def_252, type, sK129: (prover1687215943e_form > list_P512754263e_form > list_P512754263e_form)).
thf(func_def_253, type, sK130: (prover1687215943e_form > list_P512754263e_form > prover1687215943e_form)).
thf(func_def_254, type, sK131: (prover1687215943e_form > list_P512754263e_form > list_P512754263e_form)).
thf(func_def_255, type, sK132: ((list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_256, type, sK133: ((list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_257, type, sK134: ((list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_258, type, sK135: ((list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_259, type, sK136: (list_nat > nat)).
thf(func_def_260, type, sK137: (list_nat > list_nat)).
thf(func_def_261, type, sK138: ((prover1687215943e_form > $o) > list_P512754263e_form > list_P512754263e_form)).
thf(func_def_262, type, sK139: ((prover1687215943e_form > $o) > list_P512754263e_form > prover1687215943e_form)).
thf(func_def_263, type, sK140: ((prover1687215943e_form > $o) > list_P512754263e_form > list_P512754263e_form)).
thf(func_def_264, type, sK141: (((nat > prover1687215943e_form) > list_nat > list_P512754263e_form > $o) > list_nat)).
thf(func_def_265, type, sK142: (((nat > prover1687215943e_form) > list_nat > list_P512754263e_form > $o) > nat)).
thf(func_def_266, type, sK143: (((nat > prover1687215943e_form) > list_nat > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_267, type, sK144: (((nat > prover1687215943e_form) > list_nat > list_P512754263e_form > $o) > nat > prover1687215943e_form)).
thf(func_def_268, type, sK145: (((nat > prover1687215943e_form) > list_nat > list_P512754263e_form > $o) > nat > prover1687215943e_form)).
thf(func_def_269, type, sK146: (((nat > prover1687215943e_form) > list_nat > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_270, type, sK147: (list_P512754263e_form > (prover1687215943e_form > $o) > list_P512754263e_form)).
thf(func_def_271, type, sK148: (list_P512754263e_form > (prover1687215943e_form > $o) > list_P512754263e_form)).
thf(func_def_272, type, sK149: (list_P512754263e_form > (prover1687215943e_form > $o) > prover1687215943e_form)).
thf(func_def_273, type, sK150: ((list_nat > list_nat > $o) > nat)).
thf(func_def_274, type, sK151: ((list_nat > list_nat > $o) > list_nat)).
thf(func_def_275, type, sK152: ((list_nat > list_nat > $o) > nat)).
thf(func_def_276, type, sK153: ((list_nat > list_nat > $o) > list_nat)).
thf(func_def_277, type, sK154: ((list_nat > list_nat > $o) > list_nat)).
thf(func_def_278, type, sK155: ((list_nat > list_nat > $o) > list_nat)).
thf(func_def_279, type, sK156: (list_P512754263e_form > (prover1687215943e_form > $o) > list_P512754263e_form)).
thf(func_def_280, type, sK157: (list_P512754263e_form > (prover1687215943e_form > $o) > prover1687215943e_form)).
thf(func_def_281, type, sK158: (list_P512754263e_form > (prover1687215943e_form > $o) > list_P512754263e_form)).
thf(func_def_282, type, sK159: ((list_nat > list_P512754263e_form > $o) > list_nat)).
thf(func_def_283, type, sK160: ((list_nat > list_P512754263e_form > $o) > nat)).
thf(func_def_284, type, sK161: ((list_nat > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_285, type, sK162: ((list_nat > list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_286, type, sK163: ((list_nat > list_P512754263e_form > $o) > list_nat)).
thf(func_def_287, type, sK164: ((list_nat > list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_288, type, sK165: ((list_nat > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_289, type, sK166: ((list_nat > list_P512754263e_form > $o) > nat)).
thf(func_def_290, type, sK167: (prover1687215943e_form > list_P512754263e_form > list_P512754263e_form)).
thf(func_def_291, type, sK168: (prover1687215943e_form > list_P512754263e_form > list_P512754263e_form)).
thf(func_def_292, type, sK169: (list_nat > (nat > $o) > nat)).
thf(func_def_293, type, sK170: (list_nat > (nat > $o) > list_nat)).
thf(func_def_294, type, sK171: (list_nat > (nat > $o) > list_nat)).
thf(func_def_295, type, sK172: ((list_nat > $o) > nat)).
thf(func_def_296, type, sK173: ((list_nat > $o) > list_nat)).
thf(func_def_297, type, sK174: (((nat > nat) > list_nat > list_nat > $o) > nat > nat)).
thf(func_def_298, type, sK175: (((nat > nat) > list_nat > list_nat > $o) > list_nat)).
thf(func_def_299, type, sK176: (((nat > nat) > list_nat > list_nat > $o) > list_nat)).
thf(func_def_300, type, sK177: (((nat > nat) > list_nat > list_nat > $o) > nat)).
thf(func_def_301, type, sK178: (((nat > nat) > list_nat > list_nat > $o) > nat > nat)).
thf(func_def_302, type, sK179: (((nat > nat) > list_nat > list_nat > $o) > list_nat)).
thf(func_def_303, type, sK180: (list_P512754263e_form > list_P512754263e_form)).
thf(func_def_304, type, sK181: (list_P512754263e_form > prover1687215943e_form)).
thf(func_def_305, type, sK182: ((list_nat > $o) > list_nat)).
thf(func_def_306, type, sK183: ((list_nat > $o) > nat)).
thf(func_def_307, type, sK184: ((list_nat > $o) > nat)).
thf(func_def_308, type, sK185: ((list_nat > $o) > nat)).
thf(func_def_309, type, sK186: ((list_nat > $o) > list_nat)).
thf(func_def_310, type, sK187: ((list_nat > $o) > nat)).
thf(func_def_311, type, sK188: ((list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_312, type, sK189: ((list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_313, type, sK190: ((list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_314, type, sK191: ((list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_315, type, sK192: ((list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_316, type, sK193: ((list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_317, type, sK194: (nat > list_nat > list_nat)).
thf(func_def_318, type, sK195: (nat > list_nat > list_nat)).
thf(func_def_319, type, sK196: (list_nat > nat > nat)).
thf(func_def_320, type, sK197: (list_nat > nat > list_nat)).
thf(func_def_321, type, sK198: (list_nat > nat > list_nat)).
thf(func_def_322, type, sK199: (((prover1687215943e_form > prover1687215943e_form) > list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_323, type, sK200: (((prover1687215943e_form > prover1687215943e_form) > list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form > prover1687215943e_form)).
thf(func_def_324, type, sK201: (((prover1687215943e_form > prover1687215943e_form) > list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_325, type, sK202: (((prover1687215943e_form > prover1687215943e_form) > list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_326, type, sK203: (((prover1687215943e_form > prover1687215943e_form) > list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_327, type, sK204: (((prover1687215943e_form > prover1687215943e_form) > list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form > prover1687215943e_form)).
thf(func_def_328, type, sK205: (list_nat > (nat > $o) > list_nat)).
thf(func_def_329, type, sK206: (list_nat > (nat > $o) > nat)).
thf(func_def_330, type, sK207: (list_nat > (nat > $o) > list_nat)).
thf(func_def_331, type, sK208: ((list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_332, type, sK209: ((list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_333, type, sK210: ((list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_334, type, sK211: ((list_P512754263e_form > list_P512754263e_form > $o) > prover1687215943e_form)).
thf(func_def_335, type, sK212: ((list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_336, type, sK213: ((list_P512754263e_form > list_P512754263e_form > $o) > list_P512754263e_form)).
thf(func_def_337, type, sK214: ((list_nat > $o) > nat)).
thf(func_def_338, type, sK215: ((list_nat > $o) > list_nat)).
thf(func_def_339, type, sK216: (list_nat > nat)).
thf(func_def_340, type, sK217: (list_nat > list_nat)).
thf(func_def_341, type, sK218: (list_nat > nat)).
thf(func_def_342, type, sK219: (list_nat > nat)).
thf(func_def_343, type, sK220: ((list_nat > $o) > list_nat)).
thf(func_def_344, type, sK221: ((list_nat > $o) > nat)).
thf(func_def_345, type, sK222: produc227817602le_U_o).
thf(func_def_346, type, sK223: (nat > prover_Mirabelle_U)).
thf(func_def_348, type, sK225: produc227817602le_U_o).
thf(func_def_349, type, sK226: (nat > prover_Mirabelle_U)).
thf(func_def_350, type, sK227: produc227817602le_U_o).
thf(func_def_351, type, sK228: (nat > prover_Mirabelle_U)).
thf(f57,conjecture,(
  ! [X0 : (nat > prover_Mirabelle_U)] : (~(prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ X0) | (prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ X0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2)).
thf(f58,negated_conjecture,(
  ~ ! [X0 : (nat > prover_Mirabelle_U)] : (~(prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ X0) | (prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ X0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))),
  inference(negated_conjecture,[status(cth)],[f57])).
thf(f68,axiom,(
  ! [X2 : list_P512754263e_form,X1 : prover1687215943e_form,X0 : nat] : (~(member_nat @ X0 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X1) @ X2)))) => ((prover1539709396Svalid @ (append1038020460e_form @ X2 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X1 @ X0) @ nil_Pr1384483009e_form))) => (prover1539709396Svalid @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X1) @ X2))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_sound__FAll)).
thf(f127,axiom,(
  ! [X2 : (nat > prover_Mirabelle_U),X0 : set_Pr619177522elle_U,X1 : (nat > list_P796095576elle_U > $o)] : ((prover1847600056is_env @ (produc1069574002le_U_o @ X0 @ X1) @ X2) => (prover1282070756_SEval @ (produc1069574002le_U_o @ X0 @ X1) @ X2 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1)).
thf(f262,axiom,(
  ! [X0 : produc227817602le_U_o] : ~ ! [X2 : (nat > list_P796095576elle_U > $o),X1 : set_Pr619177522elle_U] : (X0 != ((produc1069574002le_U_o @ X1 @ X2)))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_196_old_Oprod_Oexhaust)).
thf(f336,axiom,(
  (prover1539709396Svalid = (^[X0 : list_P512754263e_form] : (! [X2 : (nat > prover_Mirabelle_U),X1 : produc227817602le_U_o] : ((prover1847600056is_env @ X1 @ X2) => (prover1282070756_SEval @ X1 @ X2 @ X0)))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_Svalid__def)).
thf(f339,axiom,(
  ~(member_nat @ u @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))))),
  file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0)).
thf(f409,plain,(
  ~(member_nat @ u @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))))),
  inference(rectify,[],[f339])).
thf(f410,plain,(
  ~ (((member_nat @ u @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))))) = $true)),
  inference(fool_elimination,[],[f409])).
thf(f454,plain,(
  ! [X0 : (nat > prover_Mirabelle_U),X1 : set_Pr619177522elle_U,X2 : (nat > list_P796095576elle_U > $o)] : ((prover1847600056is_env @ (produc1069574002le_U_o @ X1 @ X2) @ X0) => (prover1282070756_SEval @ (produc1069574002le_U_o @ X1 @ X2) @ X0 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))),
  inference(rectify,[],[f127])).
thf(f455,plain,(
  ! [X1 : set_Pr619177522elle_U,X0 : (nat > prover_Mirabelle_U),X2 : (nat > list_P796095576elle_U > $o)] : ((((prover1847600056is_env @ (produc1069574002le_U_o @ X1 @ X2) @ X0)) = $true) => ($true = ((prover1282070756_SEval @ (produc1069574002le_U_o @ X1 @ X2) @ X0 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))))),
  inference(fool_elimination,[],[f454])).
thf(f609,plain,(
  (prover1539709396Svalid = (^[X0 : list_P512754263e_form] : (! [X1 : (nat > prover_Mirabelle_U),X2 : produc227817602le_U_o] : ((prover1847600056is_env @ X2 @ X1) => (prover1282070756_SEval @ X2 @ X1 @ X0)))))),
  inference(rectify,[],[f336])).
thf(f610,plain,(
  (prover1539709396Svalid = (^[Y0 : list_P512754263e_form]: (!! @ produc227817602le_U_o @ (^[Y1 : produc227817602le_U_o]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y2 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ Y1 @ Y2) => (prover1282070756_SEval @ Y1 @ Y2 @ Y0))))))))),
  inference(fool_elimination,[],[f609])).
thf(f636,plain,(
  ! [X0 : list_P512754263e_form,X1 : prover1687215943e_form,X2 : nat] : (~(member_nat @ X2 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X1) @ X0)))) => ((prover1539709396Svalid @ (append1038020460e_form @ X0 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X1 @ X2) @ nil_Pr1384483009e_form))) => (prover1539709396Svalid @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X1) @ X0))))),
  inference(rectify,[],[f68])).
thf(f637,plain,(
  ! [X0 : list_P512754263e_form,X1 : prover1687215943e_form,X2 : nat] : (~ (((member_nat @ X2 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X1) @ X0))))) = $true) => ((((prover1539709396Svalid @ (append1038020460e_form @ X0 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X1 @ X2) @ nil_Pr1384483009e_form)))) = $true) => (((prover1539709396Svalid @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X1) @ X0))) = $true)))),
  inference(fool_elimination,[],[f636])).
thf(f731,plain,(
  ~ ! [X0 : (nat > prover_Mirabelle_U)] : (~(prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ X0) | (prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ X0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))),
  inference(rectify,[],[f58])).
thf(f732,plain,(
  ~ ! [X0 : (nat > prover_Mirabelle_U)] : (~ (((prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ X0)) = $true) | (((prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ X0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))) = $true))),
  inference(fool_elimination,[],[f731])).
thf(f822,plain,(
  (((member_nat @ u @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))))) != $true)),
  inference(flattening,[],[f410])).
thf(f823,plain,(
  ~ ! [X0 : (nat > prover_Mirabelle_U)] : ((((prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ X0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))) = $true) | (((prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ X0)) != $true))),
  inference(flattening,[],[f732])).
thf(f838,plain,(
  ! [X0 : produc227817602le_U_o] : ~ ! [X2 : set_Pr619177522elle_U,X1 : (nat > list_P796095576elle_U > $o)] : (((produc1069574002le_U_o @ X2 @ X1)) != X0)),
  inference(rectify,[],[f262])).
thf(f843,plain,(
  ! [X2 : nat,X0 : list_P512754263e_form,X1 : prover1687215943e_form] : ((((member_nat @ X2 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X1) @ X0))))) != $true) => ((((prover1539709396Svalid @ (append1038020460e_form @ X0 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X1 @ X2) @ nil_Pr1384483009e_form)))) = $true) => (((prover1539709396Svalid @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X1) @ X0))) = $true)))),
  inference(flattening,[],[f637])).
thf(f872,plain,(
  ! [X1 : set_Pr619177522elle_U,X2 : (nat > list_P796095576elle_U > $o),X0 : (nat > prover_Mirabelle_U)] : (($true = ((prover1282070756_SEval @ (produc1069574002le_U_o @ X1 @ X2) @ X0 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))) | (((prover1847600056is_env @ (produc1069574002le_U_o @ X1 @ X2) @ X0)) != $true))),
  inference(ennf_transformation,[],[f455])).
thf(f902,plain,(
  ! [X2 : nat,X0 : list_P512754263e_form,X1 : prover1687215943e_form] : (((((prover1539709396Svalid @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X1) @ X0))) = $true) | (((prover1539709396Svalid @ (append1038020460e_form @ X0 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X1 @ X2) @ nil_Pr1384483009e_form)))) != $true)) | (((member_nat @ X2 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X1) @ X0))))) = $true))),
  inference(ennf_transformation,[],[f843])).
thf(f903,plain,(
  ! [X1 : prover1687215943e_form,X2 : nat,X0 : list_P512754263e_form] : ((((prover1539709396Svalid @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X1) @ X0))) = $true) | (((prover1539709396Svalid @ (append1038020460e_form @ X0 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X1 @ X2) @ nil_Pr1384483009e_form)))) != $true) | (((member_nat @ X2 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X1) @ X0))))) = $true))),
  inference(flattening,[],[f902])).
thf(f904,plain,(
  ! [X0 : produc227817602le_U_o] : ? [X1 : (nat > list_P796095576elle_U > $o),X2 : set_Pr619177522elle_U] : (((produc1069574002le_U_o @ X2 @ X1)) = X0)),
  inference(ennf_transformation,[],[f838])).
thf(f908,plain,(
  ? [X0 : (nat > prover_Mirabelle_U)] : ((((prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ X0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))) != $true) & (((prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ X0)) = $true))),
  inference(ennf_transformation,[],[f823])).
thf(f1020,plain,(
  ! [X0 : produc227817602le_U_o] : (((produc1069574002le_U_o @ (sK50 @ X0) @ (sK49 @ X0))) = X0)),
  inference(skolemize,[status(esa),new_symbols(skolem,[vAPP]),skolemize(X10,$thf(sK7 @ X1)),skolemize(X10,$thf(sK7 @ X1))],[f904])).
thf(f1032,plain,(
  ! [X0 : set_Pr619177522elle_U,X1 : (nat > list_P796095576elle_U > $o),X2 : (nat > prover_Mirabelle_U)] : ((((prover1282070756_SEval @ (produc1069574002le_U_o @ X0 @ X1) @ X2 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form)))) = $true) | (((prover1847600056is_env @ (produc1069574002le_U_o @ X0 @ X1) @ X2)) != $true))),
  inference(rectify,[],[f872])).
thf(f1038,plain,(
  ! [X0 : prover1687215943e_form,X1 : nat,X2 : list_P512754263e_form] : ((((prover1539709396Svalid @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2))) = $true) | (((prover1539709396Svalid @ (append1038020460e_form @ X2 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X0 @ X1) @ nil_Pr1384483009e_form)))) != $true) | ($true = ((member_nat @ X1 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)))))))),
  inference(rectify,[],[f903])).
thf(f1081,plain,(
  (((prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ sK122 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))) != $true) & (((prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ sK122)) = $true)),
  inference(skolemize,[status(esa),new_symbols(skolem,[sK122]),skolemize(X0,$thf(sK122))],[f908])).
thf(f1198,plain,(
  ( ! [X0 : produc227817602le_U_o] : ((((produc1069574002le_U_o @ (sK50 @ X0) @ (sK49 @ X0))) = X0)) )),
  inference(cnf_transformation,[],[f1020])).
thf(f1216,plain,(
  ( ! [X2 : (nat > prover_Mirabelle_U),X0 : set_Pr619177522elle_U,X1 : (nat > list_P796095576elle_U > $o)] : ((((prover1847600056is_env @ (produc1069574002le_U_o @ X0 @ X1) @ X2)) != $true) | (((prover1282070756_SEval @ (produc1069574002le_U_o @ X0 @ X1) @ X2 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form)))) = $true)) )),
  inference(cnf_transformation,[],[f1032])).
thf(f1225,plain,(
  ( ! [X2 : list_P512754263e_form,X0 : prover1687215943e_form,X1 : nat] : ((((prover1539709396Svalid @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2))) = $true) | (((prover1539709396Svalid @ (append1038020460e_form @ X2 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X0 @ X1) @ nil_Pr1384483009e_form)))) != $true) | ($true = ((member_nat @ X1 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2))))))) )),
  inference(cnf_transformation,[],[f1038])).
thf(f1280,plain,(
  (((prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ sK122)) = $true)),
  inference(cnf_transformation,[],[f1081])).
thf(f1281,plain,(
  (((prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ sK122 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))) != $true)),
  inference(cnf_transformation,[],[f1081])).
thf(f1319,plain,(
  (prover1539709396Svalid = (^[Y0 : list_P512754263e_form]: (!! @ produc227817602le_U_o @ (^[Y1 : produc227817602le_U_o]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y2 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ Y1 @ Y2) => (prover1282070756_SEval @ Y1 @ Y2 @ Y0))))))))),
  inference(cnf_transformation,[],[f610])).
thf(f1334,plain,(
  (((member_nat @ u @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))))) != $true)),
  inference(cnf_transformation,[],[f822])).
thf(f1376,definition,(
  ( ! [X0 : $o] : (($false = X0) | ($true = X0)) )),
  introduced(theory,[fool_exhaustiveness_axiom])).
thf(f1377,plain,(
  ( ! [X2 : list_P512754263e_form,X0 : prover1687215943e_form,X1 : nat] : (((((^[Y0 : list_P512754263e_form]: (!! @ produc227817602le_U_o @ (^[Y1 : produc227817602le_U_o]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y2 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ Y1 @ Y2) => (prover1282070756_SEval @ Y1 @ Y2 @ Y0))))))) @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2))) = $true) | ($true = ((member_nat @ X1 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)))))) | ((((^[Y0 : list_P512754263e_form]: (!! @ produc227817602le_U_o @ (^[Y1 : produc227817602le_U_o]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y2 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ Y1 @ Y2) => (prover1282070756_SEval @ Y1 @ Y2 @ Y0))))))) @ (append1038020460e_form @ X2 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X0 @ X1) @ nil_Pr1384483009e_form)))) != $true)) )),
  inference(definition_unfolding,[],[f1225,f1319,f1319])).
thf(f1390,plain,(
  ( ! [X2 : list_P512754263e_form,X0 : prover1687215943e_form,X1 : nat] : ((((!! @ produc227817602le_U_o @ (^[Y0 : produc227817602le_U_o]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ Y0 @ Y1) => (prover1282070756_SEval @ Y0 @ Y1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)))))))) = $true) | ($true = ((member_nat @ X1 @ (set_nat2 @ (prover_Mirabelle_sfv @ (cons_P1475164433e_form @ (prover571163162e_FAll @ X0) @ X2)))))) | (((!! @ produc227817602le_U_o @ (^[Y0 : produc227817602le_U_o]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ Y0 @ Y1) => (prover1282070756_SEval @ Y0 @ Y1 @ (append1038020460e_form @ X2 @ (cons_P1475164433e_form @ (prover1577896257_finst @ X0 @ X1) @ nil_Pr1384483009e_form))))))))) != $true)) )),
  inference(beta-eta_normalization,[],[f1377])).
thf(f1393,plain,(
  ($true != $true) | (((!! @ produc227817602le_U_o @ (^[Y0 : produc227817602le_U_o]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ Y0 @ Y1) => (prover1282070756_SEval @ Y0 @ Y1 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))))))) != $true) | (((!! @ produc227817602le_U_o @ (^[Y0 : produc227817602le_U_o]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ Y0 @ Y1) => (prover1282070756_SEval @ Y0 @ Y1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))))))) = $true)),
  inference(superposition,[],[f1334,f1390])).
thf(f1401,plain,(
  (((!! @ produc227817602le_U_o @ (^[Y0 : produc227817602le_U_o]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ Y0 @ Y1) => (prover1282070756_SEval @ Y0 @ Y1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))))))) = $true) | ($false = (((^[Y0 : produc227817602le_U_o]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ Y0 @ Y1) => (prover1282070756_SEval @ Y0 @ Y1 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))))) @ sK222))) | ($true != $true)),
  inference(sigma_proxy_clausification,[],[f1393])).
thf(f1402,plain,(
  ( ! [X1 : produc227817602le_U_o] : (((((^[Y0 : produc227817602le_U_o]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ Y0 @ Y1) => (prover1282070756_SEval @ Y0 @ Y1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))))) @ X1)) = $true) | ($true != $true) | ($false = (((^[Y0 : produc227817602le_U_o]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ Y0 @ Y1) => (prover1282070756_SEval @ Y0 @ Y1 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))))) @ sK222)))) )),
  inference(pi_proxy_clausification,[],[f1401])).
thf(f1403,plain,(
  ( ! [X1 : produc227817602le_U_o] : (($false = (((^[Y0 : produc227817602le_U_o]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ Y0 @ Y1) => (prover1282070756_SEval @ Y0 @ Y1 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))))) @ sK222))) | ((((^[Y0 : produc227817602le_U_o]: (!! @ (nat > prover_Mirabelle_U) @ (^[Y1 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ Y0 @ Y1) => (prover1282070756_SEval @ Y0 @ Y1 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))))) @ X1)) = $true)) )),
  inference(trivial_inequality_removal,[],[f1402])).
thf(f1404,plain,(
  ( ! [X1 : produc227817602le_U_o] : (($false = ((!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ sK222 @ Y0) => (prover1282070756_SEval @ sK222 @ Y0 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form)))))))) | (((!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ X1 @ Y0) => (prover1282070756_SEval @ X1 @ Y0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))))) = $true)) )),
  inference(beta-eta_normalization,[],[f1403])).
thf(f1405,plain,(
  ( ! [X1 : produc227817602le_U_o] : (((((^[Y0 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ sK222 @ Y0) => (prover1282070756_SEval @ sK222 @ Y0 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))) @ sK223)) = $false) | (((!! @ (nat > prover_Mirabelle_U) @ (^[Y0 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ X1 @ Y0) => (prover1282070756_SEval @ X1 @ Y0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))))) = $true)) )),
  inference(sigma_proxy_clausification,[],[f1404])).
thf(f1406,plain,(
  ( ! [X2 : (nat > prover_Mirabelle_U),X1 : produc227817602le_U_o] : (((((^[Y0 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ sK222 @ Y0) => (prover1282070756_SEval @ sK222 @ Y0 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))) @ sK223)) = $false) | ((((^[Y0 : nat > prover_Mirabelle_U]: ((prover1847600056is_env @ X1 @ Y0) => (prover1282070756_SEval @ X1 @ Y0 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))) @ X2)) = $true)) )),
  inference(pi_proxy_clausification,[],[f1405])).
thf(f1407,plain,(
  ( ! [X2 : (nat > prover_Mirabelle_U),X1 : produc227817602le_U_o] : (((((prover1847600056is_env @ X1 @ X2) => (prover1282070756_SEval @ X1 @ X2 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))) = $true) | ((((prover1847600056is_env @ sK222 @ sK223) => (prover1282070756_SEval @ sK222 @ sK223 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))) = $false)) )),
  inference(beta-eta_normalization,[],[f1406])).
thf(f1408,plain,(
  ( ! [X2 : (nat > prover_Mirabelle_U),X1 : produc227817602le_U_o] : ((((prover1282070756_SEval @ X1 @ X2 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))) = $true) | ((((prover1847600056is_env @ sK222 @ sK223) => (prover1282070756_SEval @ sK222 @ sK223 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))) = $false) | (((prover1847600056is_env @ X1 @ X2)) = $false)) )),
  inference(imp_proxy_clausification,[],[f1407])).
thf(f1409,plain,(
  ( ! [X2 : (nat > prover_Mirabelle_U),X1 : produc227817602le_U_o] : ((((prover1847600056is_env @ X1 @ X2)) = $false) | ($false = ((prover1282070756_SEval @ sK222 @ sK223 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))) | (((prover1282070756_SEval @ X1 @ X2 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))) = $true)) )),
  inference(imp_proxy_clausification,[],[f1408])).
thf(f1410,plain,(
  ( ! [X2 : (nat > prover_Mirabelle_U),X1 : produc227817602le_U_o] : ((((prover1847600056is_env @ sK222 @ sK223)) = $true) | (((prover1847600056is_env @ X1 @ X2)) = $false) | (((prover1282070756_SEval @ X1 @ X2 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))) = $true)) )),
  inference(imp_proxy_clausification,[],[f1408])).
thf(f1441,definition,(
  spl224_1 <=> (((prover1847600056is_env @ sK222 @ sK223)) = $true)),
  introduced(definition,[new_symbols(definition,[spl224_1])],[avatar_definition])).
thf(f1443,plain,(
  (((prover1847600056is_env @ sK222 @ sK223)) = $true) | ~spl224_1),
  inference(avatar_component_clause,[],[f1441])).
thf(f1445,definition,(
  spl224_2 <=> ! [X2 : (nat > prover_Mirabelle_U),X1 : produc227817602le_U_o] : ((((prover1847600056is_env @ X1 @ X2)) = $false) | (((prover1282070756_SEval @ X1 @ X2 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))) = $true))),
  introduced(definition,[new_symbols(definition,[spl224_2])],[avatar_definition])).
thf(f1446,plain,(
  ( ! [X2 : (nat > prover_Mirabelle_U),X1 : produc227817602le_U_o] : ((((prover1282070756_SEval @ X1 @ X2 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))) = $true) | (((prover1847600056is_env @ X1 @ X2)) = $false)) ) | ~spl224_2),
  inference(avatar_component_clause,[],[f1445])).
thf(f1447,plain,(
  spl224_1 | spl224_2),
  inference(avatar_split_clause,[],[f1410,f1445,f1441])).
thf(f1449,definition,(
  spl224_3 <=> ($false = ((prover1282070756_SEval @ sK222 @ sK223 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form)))))),
  introduced(definition,[new_symbols(definition,[spl224_3])],[avatar_definition])).
thf(f1451,plain,(
  ($false = ((prover1282070756_SEval @ sK222 @ sK223 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form))))) | ~spl224_3),
  inference(avatar_component_clause,[],[f1449])).
thf(f1452,plain,(
  spl224_2 | spl224_3),
  inference(avatar_split_clause,[],[f1409,f1449,f1445])).
thf(f1589,plain,(
  ($false = ((prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ sK122 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s)))) | ($true != $true)),
  inference(superposition,[],[f1281,f1376])).
thf(f1592,plain,(
  ($false = ((prover1282070756_SEval @ (produc1069574002le_U_o @ a @ b) @ sK122 @ (cons_P1475164433e_form @ (prover571163162e_FAll @ f) @ s))))),
  inference(trivial_inequality_removal,[],[f1589])).
thf(f1694,plain,(
  ( ! [X0 : produc227817602le_U_o,X1 : (nat > prover_Mirabelle_U)] : ((((prover1847600056is_env @ X0 @ X1)) != $true) | (((prover1282070756_SEval @ X0 @ X1 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form)))) = $true)) )),
  inference(superposition,[],[f1216,f1198])).
thf(f1897,plain,(
  ($false = $true) | ($false = ((prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ sK122))) | ~spl224_2),
  inference(superposition,[],[f1446,f1592])).
thf(f1918,plain,(
  ($false = ((prover1847600056is_env @ (produc1069574002le_U_o @ a @ b) @ sK122))) | ~spl224_2),
  inference(trivial_inequality_removal,[],[f1897])).
thf(f1934,plain,(
  ($false = $true) | ~spl224_2),
  inference(superposition,[],[f1918,f1280])).
thf(f1942,plain,(
  $false | ~spl224_2),
  inference(trivial_inequality_removal,[],[f1934])).
thf(f1943,plain,(
  ~spl224_2),
  inference(avatar_contradiction_clause,[],[f1942])).
thf(f2004,plain,(
  ($true != $true) | (((prover1282070756_SEval @ sK222 @ sK223 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form)))) = $true) | ~spl224_1),
  inference(superposition,[],[f1694,f1443])).
thf(f2005,plain,(
  (((prover1282070756_SEval @ sK222 @ sK223 @ (append1038020460e_form @ s @ (cons_P1475164433e_form @ (prover1577896257_finst @ f @ u) @ nil_Pr1384483009e_form)))) = $true) | ~spl224_1),
  inference(trivial_inequality_removal,[],[f2004])).
thf(f2007,plain,(
  ($false = $true) | (~spl224_1 | ~spl224_3)),
  inference(forward_demodulation,[],[f2005,f1451])).
thf(f2008,plain,(
  $false | (~spl224_1 | ~spl224_3)),
  inference(trivial_inequality_removal,[],[f2007])).
thf(f2009,plain,(
  ~spl224_1 | ~spl224_3),
  inference(avatar_contradiction_clause,[],[f2008])).
cnf(s1, plain, spl224_1 | spl224_2, inference(sat_conversion,[],[f1447])).
cnf(s2, plain, spl224_2 | spl224_3, inference(sat_conversion,[],[f1452])).
cnf(s10, plain, ~spl224_2, inference(sat_conversion,[],[f1943])).
cnf(s15, plain, ~spl224_1 | ~spl224_3, inference(sat_conversion,[],[f2009])).
cnf(s20, plain, spl224_3, inference(rat,[],[s2,s10])).
cnf(s21, plain, ~spl224_1, inference(rat,[],[s15,s20])).
cnf(s22, plain, $false, inference(rat,[],[s1,s10,s21])).
thf(f2010,plain,(
  $false),
  inference(avatar_sat_refutation,[],[s22])).
% SZS output end Proof for theBenchmark