TSTP Solution File: ITP150^1 by cocATP---0.2.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : ITP150^1 : TPTP v7.5.0. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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
% DateTime : Sun Mar 21 13:24:20 EDT 2021
% Result : Timeout 300.02s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ITP150^1 : TPTP v7.5.0. Released v7.5.0.
% 0.07/0.13 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34 % Computer : n018.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 % DateTime : Fri Mar 19 06:51:37 EDT 2021
% 0.13/0.34 % CPUTime :
% 0.13/0.35 ModuleCmd_Load.c(213):ERROR:105: Unable to locate a modulefile for 'python/python27'
% 0.13/0.35 Python 2.7.5
% 0.39/0.62 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x96c128>, <kernel.Type object at 0x96ce60>) of role type named ty_n_t__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_It__Nat__Onat_J
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring polyno1532895200ly_nat:Type
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x96d050>, <kernel.Type object at 0x96cb90>) of role type named ty_n_t__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_Itf__a_J
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring polyno727731844poly_a:Type
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x96c200>, <kernel.Type object at 0x96ce60>) of role type named ty_n_t__List__Olist_It__Nat__Onat_J
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring list_nat:Type
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x96cf38>, <kernel.Type object at 0x96c4d0>) of role type named ty_n_t__List__Olist_Itf__a_J
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring list_a:Type
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x96cb90>, <kernel.Type object at 0x96c200>) of role type named ty_n_t__Nat__Onat
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring nat:Type
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x96c320>, <kernel.Type object at 0x96cc68>) of role type named ty_n_tf__a
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring a:Type
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x96c7a0>, <kernel.Constant object at 0x96ce60>) of role type named sy_c_Groups_Oone__class_Oone_001t__Nat__Onat
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring one_one_nat:nat
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x96c200>, <kernel.Constant object at 0x96ce60>) of role type named sy_c_Groups_Oone__class_Oone_001tf__a
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring one_one_a:a
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x96cb90>, <kernel.DependentProduct object at 0x96c7a0>) of role type named sy_c_Groups_Oplus__class_Oplus_001t__Nat__Onat
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring plus_plus_nat:(nat->(nat->nat))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x96ccb0>, <kernel.DependentProduct object at 0xc06908>) of role type named sy_c_Groups_Oplus__class_Oplus_001tf__a
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring plus_plus_a:(a->(a->a))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xc06cb0>, <kernel.DependentProduct object at 0x96c7a0>) of role type named sy_c_Groups_Otimes__class_Otimes_001t__Nat__Onat
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring times_times_nat:(nat->(nat->nat))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x2adc27cd6638>, <kernel.DependentProduct object at 0x96c290>) of role type named sy_c_Groups_Otimes__class_Otimes_001tf__a
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring times_times_a:(a->(a->a))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xc06908>, <kernel.Constant object at 0x96c200>) of role type named sy_c_Groups_Ozero__class_Ozero_001t__Nat__Onat
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring zero_zero_nat:nat
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xc06bd8>, <kernel.Constant object at 0x96c200>) of role type named sy_c_Groups_Ozero__class_Ozero_001tf__a
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring zero_zero_a:a
% 0.39/0.62 FOF formula (<kernel.Constant object at 0xc06bd8>, <kernel.DependentProduct object at 0x96c7a0>) of role type named sy_c_If_001t__Nat__Onat
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring if_nat:(Prop->(nat->(nat->nat)))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x2adc27cd5ef0>, <kernel.DependentProduct object at 0x96c3b0>) of role type named sy_c_Nat_Ocompow_001_062_It__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_It__Nat__Onat_J_Mt__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_It__Nat__Onat_J_J
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring compow808008746ly_nat:(nat->((polyno1532895200ly_nat->polyno1532895200ly_nat)->(polyno1532895200ly_nat->polyno1532895200ly_nat)))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x2adc27cd5680>, <kernel.DependentProduct object at 0x96c290>) of role type named sy_c_Nat_Ocompow_001_062_It__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_Itf__a_J_Mt__Polynomial____Expression____Mirabelle____dwjuveeage__Opoly_Itf__a_J_J
% 0.39/0.62 Using role type
% 0.39/0.62 Declaring compow1114216044poly_a:(nat->((polyno727731844poly_a->polyno727731844poly_a)->(polyno727731844poly_a->polyno727731844poly_a)))
% 0.39/0.62 FOF formula (<kernel.Constant object at 0x2adc27cd5680>, <kernel.DependentProduct object at 0x96c7a0>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_OIpoly_001tf__a
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno422358502poly_a:(list_a->(polyno727731844poly_a->a))
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x96c3b0>, <kernel.DependentProduct object at 0x969998>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Obehead_001t__Nat__Onat
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno587244178ad_nat:(polyno1532895200ly_nat->polyno1532895200ly_nat)
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x96ce60>, <kernel.DependentProduct object at 0x969488>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Obehead_001tf__a
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno1465139388head_a:(polyno727731844poly_a->polyno727731844poly_a)
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x96c290>, <kernel.DependentProduct object at 0x969cf8>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Odegree_001t__Nat__Onat
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno220183259ee_nat:(polyno1532895200ly_nat->nat)
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x96c3b0>, <kernel.DependentProduct object at 0x969440>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Odegree_001tf__a
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno578545843gree_a:(polyno727731844poly_a->nat)
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x96c290>, <kernel.DependentProduct object at 0x969878>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Odegreen_001t__Nat__Onat
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno1779722485en_nat:(polyno1532895200ly_nat->(nat->nat))
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x96c3b0>, <kernel.DependentProduct object at 0x969cb0>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Odegreen_001tf__a
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno1674775833reen_a:(polyno727731844poly_a->(nat->nat))
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x96ce60>, <kernel.DependentProduct object at 0x969440>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Ohead_001t__Nat__Onat
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno1952548879ad_nat:(polyno1532895200ly_nat->polyno1532895200ly_nat)
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x96ce60>, <kernel.DependentProduct object at 0x969878>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Ohead_001tf__a
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno1884029055head_a:(polyno727731844poly_a->polyno727731844poly_a)
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x969cb0>, <kernel.DependentProduct object at 0x969248>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oheadconst_001t__Nat__Onat
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno524777654st_nat:(polyno1532895200ly_nat->nat)
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x969440>, <kernel.DependentProduct object at 0x969200>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oheadconst_001tf__a
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno2115742616onst_a:(polyno727731844poly_a->a)
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x969878>, <kernel.DependentProduct object at 0x969c20>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oheadn_001t__Nat__Onat
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno544860353dn_nat:(polyno1532895200ly_nat->(nat->polyno1532895200ly_nat))
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x969248>, <kernel.DependentProduct object at 0x969d88>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oheadn_001tf__a
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno567601229eadn_a:(polyno727731844poly_a->(nat->polyno727731844poly_a))
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x969488>, <kernel.DependentProduct object at 0x9697a0>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oisnpoly_001t__Nat__Onat
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno1013235523ly_nat:(polyno1532895200ly_nat->Prop)
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x9697e8>, <kernel.DependentProduct object at 0x969cb0>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oisnpoly_001tf__a
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno190918219poly_a:(polyno727731844poly_a->Prop)
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x969d88>, <kernel.DependentProduct object at 0x969d40>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oisnpolyh_001t__Nat__Onat
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno892049031yh_nat:(polyno1532895200ly_nat->(nat->Prop))
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x9697a0>, <kernel.DependentProduct object at 0x969c68>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oisnpolyh_001tf__a
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno1372495879olyh_a:(polyno727731844poly_a->(nat->Prop))
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x969cb0>, <kernel.DependentProduct object at 0x969488>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OAdd_001t__Nat__Onat
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno1222032024dd_nat:(polyno1532895200ly_nat->(polyno1532895200ly_nat->polyno1532895200ly_nat))
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x969d40>, <kernel.DependentProduct object at 0x969b48>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OAdd_001tf__a
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno1623170614_Add_a:(polyno727731844poly_a->(polyno727731844poly_a->polyno727731844poly_a))
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x969c68>, <kernel.DependentProduct object at 0x969d88>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OBound_001t__Nat__Onat
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno1999838549nd_nat:(nat->polyno1532895200ly_nat)
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x969488>, <kernel.DependentProduct object at 0x9697a0>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OBound_001tf__a
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno2024845497ound_a:(nat->polyno727731844poly_a)
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x969b48>, <kernel.DependentProduct object at 0x969d40>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OCN_001t__Nat__Onat
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno720942678CN_nat:(polyno1532895200ly_nat->(nat->(polyno1532895200ly_nat->polyno1532895200ly_nat)))
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x969d88>, <kernel.DependentProduct object at 0x969050>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OCN_001tf__a
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno1057396216e_CN_a:(polyno727731844poly_a->(nat->(polyno727731844poly_a->polyno727731844poly_a)))
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x9697a0>, <kernel.DependentProduct object at 0x969098>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OC_001t__Nat__Onat
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno2122022170_C_nat:(nat->polyno1532895200ly_nat)
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x969d40>, <kernel.DependentProduct object at 0x9693b0>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OC_001tf__a
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno439679028le_C_a:(a->polyno727731844poly_a)
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x969050>, <kernel.DependentProduct object at 0x969d88>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OMul_001t__Nat__Onat
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno1415441627ul_nat:(polyno1532895200ly_nat->(polyno1532895200ly_nat->polyno1532895200ly_nat))
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x969098>, <kernel.DependentProduct object at 0x969ef0>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OMul_001tf__a
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno1491482291_Mul_a:(polyno727731844poly_a->(polyno727731844poly_a->polyno727731844poly_a))
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x9693b0>, <kernel.DependentProduct object at 0x9697a0>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_ONeg_001t__Nat__Onat
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno1366804583eg_nat:(polyno1532895200ly_nat->polyno1532895200ly_nat)
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x969d88>, <kernel.DependentProduct object at 0x969d40>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_ONeg_001tf__a
% 0.39/0.63 Using role type
% 0.39/0.63 Declaring polyno96675367_Neg_a:(polyno727731844poly_a->polyno727731844poly_a)
% 0.39/0.63 FOF formula (<kernel.Constant object at 0x969ef0>, <kernel.DependentProduct object at 0x969098>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OPw_001t__Nat__Onat
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno359287218Pw_nat:(polyno1532895200ly_nat->(nat->polyno1532895200ly_nat))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x9697a0>, <kernel.DependentProduct object at 0x969e18>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OPw_001tf__a
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno1538138524e_Pw_a:(polyno727731844poly_a->(nat->polyno727731844poly_a))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x969050>, <kernel.DependentProduct object at 0x969dd0>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OSub_001t__Nat__Onat
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno1921014231ub_nat:(polyno1532895200ly_nat->(polyno1532895200ly_nat->polyno1532895200ly_nat))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x969368>, <kernel.DependentProduct object at 0x9693b0>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly_OSub_001tf__a
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno975704247_Sub_a:(polyno727731844poly_a->(polyno727731844poly_a->polyno727731844poly_a))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x969e18>, <kernel.DependentProduct object at 0x969d88>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly__cmul_001t__Nat__Onat
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno1467023772ul_nat:(nat->(polyno1532895200ly_nat->polyno1532895200ly_nat))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x969dd0>, <kernel.DependentProduct object at 0x969ef0>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly__cmul_001tf__a
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno562434098cmul_a:(a->(polyno727731844poly_a->polyno727731844poly_a))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x9693b0>, <kernel.DependentProduct object at 0x969050>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly__deriv_001tf__a
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno212464073eriv_a:(polyno727731844poly_a->polyno727731844poly_a)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x969d88>, <kernel.DependentProduct object at 0x969e18>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opoly__deriv__aux_001tf__a
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno1006823949_aux_a:(a->(polyno727731844poly_a->polyno727731844poly_a))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x969ef0>, <kernel.DependentProduct object at 0x969368>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolymul_001t__Nat__Onat
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno929799083ul_nat:(polyno1532895200ly_nat->(polyno1532895200ly_nat->polyno1532895200ly_nat))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x969050>, <kernel.DependentProduct object at 0x969dd0>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolymul_001tf__a
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno1934269411ymul_a:(polyno727731844poly_a->(polyno727731844poly_a->polyno727731844poly_a))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x969e18>, <kernel.DependentProduct object at 0x964cb0>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolynate_001tf__a
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno955999183nate_a:(polyno727731844poly_a->polyno727731844poly_a)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x9691b8>, <kernel.DependentProduct object at 0x969dd0>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolypow_001t__Nat__Onat
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno1510045887ow_nat:(nat->(polyno1532895200ly_nat->polyno1532895200ly_nat))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x969368>, <kernel.DependentProduct object at 0x969e18>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolypow_001tf__a
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno1371724751ypow_a:(nat->(polyno727731844poly_a->polyno727731844poly_a))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x969dd0>, <kernel.DependentProduct object at 0x964ea8>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolysub_001tf__a
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno1418491367ysub_a:(polyno727731844poly_a->(polyno727731844poly_a->polyno727731844poly_a))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x9691b8>, <kernel.DependentProduct object at 0x964ef0>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolysubst0_001t__Nat__Onat
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno336795754t0_nat:(polyno1532895200ly_nat->(polyno1532895200ly_nat->polyno1532895200ly_nat))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2adc201f9200>, <kernel.DependentProduct object at 0x964cb0>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Opolysubst0_001tf__a
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno1397854436bst0_a:(polyno727731844poly_a->(polyno727731844poly_a->polyno727731844poly_a))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x9691b8>, <kernel.DependentProduct object at 0x964ef0>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oshift1_001t__Nat__Onat
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno1964927358t1_nat:(polyno1532895200ly_nat->polyno1532895200ly_nat)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x964fc8>, <kernel.DependentProduct object at 0x2adc201f8128>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Oshift1_001tf__a
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno784948432ift1_a:(polyno727731844poly_a->polyno727731844poly_a)
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x969dd0>, <kernel.DependentProduct object at 0x2adc201f8128>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Owf__bs_001t__Nat__Onat
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno1438831695bs_nat:(list_nat->(polyno1532895200ly_nat->Prop))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x9691b8>, <kernel.DependentProduct object at 0x2adc201f8758>) of role type named sy_c_Polynomial__Expression__Mirabelle__dwjuveeage_Owf__bs_001tf__a
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring polyno896877631f_bs_a:(list_a->(polyno727731844poly_a->Prop))
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x9691b8>, <kernel.Constant object at 0x964f38>) of role type named sy_v_n0
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring n0:nat
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x964ea8>, <kernel.Constant object at 0x964ef0>) of role type named sy_v_n1
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring n1:nat
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x964fc8>, <kernel.Constant object at 0x2adc201f8758>) of role type named sy_v_p
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring p:polyno727731844poly_a
% 0.48/0.64 FOF formula (<kernel.Constant object at 0x2adc201f8128>, <kernel.Constant object at 0x964fc8>) of role type named sy_v_q
% 0.48/0.64 Using role type
% 0.48/0.64 Declaring q:polyno727731844poly_a
% 0.48/0.64 FOF formula (((eq Prop) (forall (Bs:list_a), (((eq a) ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))) ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p))))) (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) ((polyno1934269411ymul_a q) p))) of role axiom named fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062
% 0.48/0.64 A new axiom: (((eq Prop) (forall (Bs:list_a), (((eq a) ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))) ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p))))) (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) ((polyno1934269411ymul_a q) p)))
% 0.48/0.64 FOF formula ((polyno1372495879olyh_a p) n0) of role axiom named fact_1_np
% 0.48/0.64 A new axiom: ((polyno1372495879olyh_a p) n0)
% 0.48/0.64 FOF formula ((polyno1372495879olyh_a q) n1) of role axiom named fact_2_nq
% 0.48/0.64 A new axiom: ((polyno1372495879olyh_a q) n1)
% 0.48/0.64 FOF formula (forall (P:polyno727731844poly_a) (Q:polyno727731844poly_a), ((polyno190918219poly_a P)->((polyno190918219poly_a Q)->(polyno190918219poly_a ((polyno1934269411ymul_a P) Q))))) of role axiom named fact_3_polymul__norm
% 0.48/0.64 A new axiom: (forall (P:polyno727731844poly_a) (Q:polyno727731844poly_a), ((polyno190918219poly_a P)->((polyno190918219poly_a Q)->(polyno190918219poly_a ((polyno1934269411ymul_a P) Q)))))
% 0.48/0.64 FOF formula (forall (Bs2:list_nat) (P:polyno1532895200ly_nat) (Q:polyno1532895200ly_nat), (((polyno1438831695bs_nat Bs2) P)->(((polyno1438831695bs_nat Bs2) Q)->((polyno1438831695bs_nat Bs2) ((polyno929799083ul_nat P) Q))))) of role axiom named fact_4_wf__bs__polyul
% 0.48/0.65 A new axiom: (forall (Bs2:list_nat) (P:polyno1532895200ly_nat) (Q:polyno1532895200ly_nat), (((polyno1438831695bs_nat Bs2) P)->(((polyno1438831695bs_nat Bs2) Q)->((polyno1438831695bs_nat Bs2) ((polyno929799083ul_nat P) Q)))))
% 0.48/0.65 FOF formula (forall (Bs2:list_a) (P:polyno727731844poly_a) (Q:polyno727731844poly_a), (((polyno896877631f_bs_a Bs2) P)->(((polyno896877631f_bs_a Bs2) Q)->((polyno896877631f_bs_a Bs2) ((polyno1934269411ymul_a P) Q))))) of role axiom named fact_5_wf__bs__polyul
% 0.48/0.65 A new axiom: (forall (Bs2:list_a) (P:polyno727731844poly_a) (Q:polyno727731844poly_a), (((polyno896877631f_bs_a Bs2) P)->(((polyno896877631f_bs_a Bs2) Q)->((polyno896877631f_bs_a Bs2) ((polyno1934269411ymul_a P) Q)))))
% 0.48/0.65 FOF formula (forall (A:polyno1532895200ly_nat) (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat A) ((polyno1415441627ul_nat V) Va))) ((polyno1415441627ul_nat A) ((polyno1415441627ul_nat V) Va)))) of role axiom named fact_6_polymul_Osimps_I20_J
% 0.48/0.65 A new axiom: (forall (A:polyno1532895200ly_nat) (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat A) ((polyno1415441627ul_nat V) Va))) ((polyno1415441627ul_nat A) ((polyno1415441627ul_nat V) Va))))
% 0.48/0.65 FOF formula (forall (A:polyno727731844poly_a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a A) ((polyno1491482291_Mul_a V) Va))) ((polyno1491482291_Mul_a A) ((polyno1491482291_Mul_a V) Va)))) of role axiom named fact_7_polymul_Osimps_I20_J
% 0.48/0.65 A new axiom: (forall (A:polyno727731844poly_a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a A) ((polyno1491482291_Mul_a V) Va))) ((polyno1491482291_Mul_a A) ((polyno1491482291_Mul_a V) Va))))
% 0.48/0.65 FOF formula (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno1415441627ul_nat V) Va)) B)) ((polyno1415441627ul_nat ((polyno1415441627ul_nat V) Va)) B))) of role axiom named fact_8_polymul_Osimps_I8_J
% 0.48/0.65 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno1415441627ul_nat V) Va)) B)) ((polyno1415441627ul_nat ((polyno1415441627ul_nat V) Va)) B)))
% 0.48/0.65 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1491482291_Mul_a V) Va)) B)) ((polyno1491482291_Mul_a ((polyno1491482291_Mul_a V) Va)) B))) of role axiom named fact_9_polymul_Osimps_I8_J
% 0.48/0.65 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1491482291_Mul_a V) Va)) B)) ((polyno1491482291_Mul_a ((polyno1491482291_Mul_a V) Va)) B)))
% 0.48/0.65 FOF formula (forall (Bs2:list_a) (P:polyno727731844poly_a) (Q:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) ((polyno1934269411ymul_a P) Q))) ((times_times_a ((polyno422358502poly_a Bs2) P)) ((polyno422358502poly_a Bs2) Q)))) of role axiom named fact_10_polymul
% 0.48/0.65 A new axiom: (forall (Bs2:list_a) (P:polyno727731844poly_a) (Q:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) ((polyno1934269411ymul_a P) Q))) ((times_times_a ((polyno422358502poly_a Bs2) P)) ((polyno422358502poly_a Bs2) Q))))
% 0.48/0.65 FOF formula (forall (C:nat) (C2:nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (polyno2122022170_C_nat C)) (polyno2122022170_C_nat C2))) (polyno2122022170_C_nat ((times_times_nat C) C2)))) of role axiom named fact_11_polymul_Osimps_I1_J
% 0.48/0.65 A new axiom: (forall (C:nat) (C2:nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (polyno2122022170_C_nat C)) (polyno2122022170_C_nat C2))) (polyno2122022170_C_nat ((times_times_nat C) C2))))
% 0.48/0.65 FOF formula (forall (C:a) (C2:a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno439679028le_C_a C)) (polyno439679028le_C_a C2))) (polyno439679028le_C_a ((times_times_a C) C2)))) of role axiom named fact_12_polymul_Osimps_I1_J
% 0.48/0.66 A new axiom: (forall (C:a) (C2:a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno439679028le_C_a C)) (polyno439679028le_C_a C2))) (polyno439679028le_C_a ((times_times_a C) C2))))
% 0.48/0.66 FOF formula (forall (P:polyno727731844poly_a) (Q:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno955999183nate_a ((polyno1491482291_Mul_a P) Q))) ((polyno1934269411ymul_a (polyno955999183nate_a P)) (polyno955999183nate_a Q)))) of role axiom named fact_13_polynate_Osimps_I4_J
% 0.48/0.66 A new axiom: (forall (P:polyno727731844poly_a) (Q:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno955999183nate_a ((polyno1491482291_Mul_a P) Q))) ((polyno1934269411ymul_a (polyno955999183nate_a P)) (polyno955999183nate_a Q))))
% 0.48/0.66 FOF formula (forall (Vc:polyno1532895200ly_nat) (Vd:polyno1532895200ly_nat) (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno1415441627ul_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb))) ((polyno1415441627ul_nat ((polyno1415441627ul_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb)))) of role axiom named fact_14_polymul_Osimps_I26_J
% 0.48/0.66 A new axiom: (forall (Vc:polyno1532895200ly_nat) (Vd:polyno1532895200ly_nat) (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno1415441627ul_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb))) ((polyno1415441627ul_nat ((polyno1415441627ul_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb))))
% 0.48/0.66 FOF formula (forall (Vc:polyno727731844poly_a) (Vd:polyno727731844poly_a) (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1491482291_Mul_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb))) ((polyno1491482291_Mul_a ((polyno1491482291_Mul_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb)))) of role axiom named fact_15_polymul_Osimps_I26_J
% 0.48/0.66 A new axiom: (forall (Vc:polyno727731844poly_a) (Vd:polyno727731844poly_a) (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1491482291_Mul_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb))) ((polyno1491482291_Mul_a ((polyno1491482291_Mul_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb))))
% 0.48/0.66 FOF formula (forall (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat) (Vc:polyno1532895200ly_nat) (Vd:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno1415441627ul_nat Vc) Vd))) ((polyno1415441627ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno1415441627ul_nat Vc) Vd)))) of role axiom named fact_16_polymul_Osimps_I14_J
% 0.48/0.66 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat) (Vc:polyno1532895200ly_nat) (Vd:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno1415441627ul_nat Vc) Vd))) ((polyno1415441627ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno1415441627ul_nat Vc) Vd))))
% 0.48/0.66 FOF formula (forall (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a) (Vc:polyno727731844poly_a) (Vd:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1491482291_Mul_a Vc) Vd))) ((polyno1491482291_Mul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1491482291_Mul_a Vc) Vd)))) of role axiom named fact_17_polymul_Osimps_I14_J
% 0.48/0.66 A new axiom: (forall (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a) (Vc:polyno727731844poly_a) (Vd:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1491482291_Mul_a Vc) Vd))) ((polyno1491482291_Mul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1491482291_Mul_a Vc) Vd))))
% 0.48/0.66 FOF formula (forall (A:polyno1532895200ly_nat) (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat A) ((polyno1222032024dd_nat V) Va))) ((polyno1415441627ul_nat A) ((polyno1222032024dd_nat V) Va)))) of role axiom named fact_18_polymul_Osimps_I18_J
% 0.48/0.67 A new axiom: (forall (A:polyno1532895200ly_nat) (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat A) ((polyno1222032024dd_nat V) Va))) ((polyno1415441627ul_nat A) ((polyno1222032024dd_nat V) Va))))
% 0.48/0.67 FOF formula (forall (A:polyno727731844poly_a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a A) ((polyno1623170614_Add_a V) Va))) ((polyno1491482291_Mul_a A) ((polyno1623170614_Add_a V) Va)))) of role axiom named fact_19_polymul_Osimps_I18_J
% 0.48/0.67 A new axiom: (forall (A:polyno727731844poly_a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a A) ((polyno1623170614_Add_a V) Va))) ((polyno1491482291_Mul_a A) ((polyno1623170614_Add_a V) Va))))
% 0.48/0.67 FOF formula (forall (X81:polyno727731844poly_a) (X82:nat) (X83:polyno727731844poly_a) (Y81:polyno727731844poly_a) (Y82:nat) (Y83:polyno727731844poly_a), (((eq Prop) (((eq polyno727731844poly_a) (((polyno1057396216e_CN_a X81) X82) X83)) (((polyno1057396216e_CN_a Y81) Y82) Y83))) ((and ((and (((eq polyno727731844poly_a) X81) Y81)) (((eq nat) X82) Y82))) (((eq polyno727731844poly_a) X83) Y83)))) of role axiom named fact_20_poly_Oinject_I8_J
% 0.48/0.67 A new axiom: (forall (X81:polyno727731844poly_a) (X82:nat) (X83:polyno727731844poly_a) (Y81:polyno727731844poly_a) (Y82:nat) (Y83:polyno727731844poly_a), (((eq Prop) (((eq polyno727731844poly_a) (((polyno1057396216e_CN_a X81) X82) X83)) (((polyno1057396216e_CN_a Y81) Y82) Y83))) ((and ((and (((eq polyno727731844poly_a) X81) Y81)) (((eq nat) X82) Y82))) (((eq polyno727731844poly_a) X83) Y83))))
% 0.48/0.67 FOF formula (forall (X81:polyno1532895200ly_nat) (X82:nat) (X83:polyno1532895200ly_nat) (Y81:polyno1532895200ly_nat) (Y82:nat) (Y83:polyno1532895200ly_nat), (((eq Prop) (((eq polyno1532895200ly_nat) (((polyno720942678CN_nat X81) X82) X83)) (((polyno720942678CN_nat Y81) Y82) Y83))) ((and ((and (((eq polyno1532895200ly_nat) X81) Y81)) (((eq nat) X82) Y82))) (((eq polyno1532895200ly_nat) X83) Y83)))) of role axiom named fact_21_poly_Oinject_I8_J
% 0.48/0.67 A new axiom: (forall (X81:polyno1532895200ly_nat) (X82:nat) (X83:polyno1532895200ly_nat) (Y81:polyno1532895200ly_nat) (Y82:nat) (Y83:polyno1532895200ly_nat), (((eq Prop) (((eq polyno1532895200ly_nat) (((polyno720942678CN_nat X81) X82) X83)) (((polyno720942678CN_nat Y81) Y82) Y83))) ((and ((and (((eq polyno1532895200ly_nat) X81) Y81)) (((eq nat) X82) Y82))) (((eq polyno1532895200ly_nat) X83) Y83))))
% 0.48/0.67 FOF formula (forall (X1:a) (Y1:a), (((eq Prop) (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) (polyno439679028le_C_a Y1))) (((eq a) X1) Y1))) of role axiom named fact_22_poly_Oinject_I1_J
% 0.48/0.67 A new axiom: (forall (X1:a) (Y1:a), (((eq Prop) (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) (polyno439679028le_C_a Y1))) (((eq a) X1) Y1)))
% 0.48/0.67 FOF formula (forall (X1:nat) (Y1:nat), (((eq Prop) (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) (polyno2122022170_C_nat Y1))) (((eq nat) X1) Y1))) of role axiom named fact_23_poly_Oinject_I1_J
% 0.48/0.67 A new axiom: (forall (X1:nat) (Y1:nat), (((eq Prop) (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) (polyno2122022170_C_nat Y1))) (((eq nat) X1) Y1)))
% 0.48/0.67 FOF formula (forall (X51:polyno1532895200ly_nat) (X52:polyno1532895200ly_nat) (Y51:polyno1532895200ly_nat) (Y52:polyno1532895200ly_nat), (((eq Prop) (((eq polyno1532895200ly_nat) ((polyno1415441627ul_nat X51) X52)) ((polyno1415441627ul_nat Y51) Y52))) ((and (((eq polyno1532895200ly_nat) X51) Y51)) (((eq polyno1532895200ly_nat) X52) Y52)))) of role axiom named fact_24_poly_Oinject_I5_J
% 0.48/0.67 A new axiom: (forall (X51:polyno1532895200ly_nat) (X52:polyno1532895200ly_nat) (Y51:polyno1532895200ly_nat) (Y52:polyno1532895200ly_nat), (((eq Prop) (((eq polyno1532895200ly_nat) ((polyno1415441627ul_nat X51) X52)) ((polyno1415441627ul_nat Y51) Y52))) ((and (((eq polyno1532895200ly_nat) X51) Y51)) (((eq polyno1532895200ly_nat) X52) Y52))))
% 0.48/0.68 FOF formula (forall (X51:polyno727731844poly_a) (X52:polyno727731844poly_a) (Y51:polyno727731844poly_a) (Y52:polyno727731844poly_a), (((eq Prop) (((eq polyno727731844poly_a) ((polyno1491482291_Mul_a X51) X52)) ((polyno1491482291_Mul_a Y51) Y52))) ((and (((eq polyno727731844poly_a) X51) Y51)) (((eq polyno727731844poly_a) X52) Y52)))) of role axiom named fact_25_poly_Oinject_I5_J
% 0.48/0.68 A new axiom: (forall (X51:polyno727731844poly_a) (X52:polyno727731844poly_a) (Y51:polyno727731844poly_a) (Y52:polyno727731844poly_a), (((eq Prop) (((eq polyno727731844poly_a) ((polyno1491482291_Mul_a X51) X52)) ((polyno1491482291_Mul_a Y51) Y52))) ((and (((eq polyno727731844poly_a) X51) Y51)) (((eq polyno727731844poly_a) X52) Y52))))
% 0.48/0.68 FOF formula (forall (X31:polyno727731844poly_a) (X32:polyno727731844poly_a) (Y31:polyno727731844poly_a) (Y32:polyno727731844poly_a), (((eq Prop) (((eq polyno727731844poly_a) ((polyno1623170614_Add_a X31) X32)) ((polyno1623170614_Add_a Y31) Y32))) ((and (((eq polyno727731844poly_a) X31) Y31)) (((eq polyno727731844poly_a) X32) Y32)))) of role axiom named fact_26_poly_Oinject_I3_J
% 0.48/0.68 A new axiom: (forall (X31:polyno727731844poly_a) (X32:polyno727731844poly_a) (Y31:polyno727731844poly_a) (Y32:polyno727731844poly_a), (((eq Prop) (((eq polyno727731844poly_a) ((polyno1623170614_Add_a X31) X32)) ((polyno1623170614_Add_a Y31) Y32))) ((and (((eq polyno727731844poly_a) X31) Y31)) (((eq polyno727731844poly_a) X32) Y32))))
% 0.48/0.68 FOF formula (forall (X31:polyno1532895200ly_nat) (X32:polyno1532895200ly_nat) (Y31:polyno1532895200ly_nat) (Y32:polyno1532895200ly_nat), (((eq Prop) (((eq polyno1532895200ly_nat) ((polyno1222032024dd_nat X31) X32)) ((polyno1222032024dd_nat Y31) Y32))) ((and (((eq polyno1532895200ly_nat) X31) Y31)) (((eq polyno1532895200ly_nat) X32) Y32)))) of role axiom named fact_27_poly_Oinject_I3_J
% 0.48/0.68 A new axiom: (forall (X31:polyno1532895200ly_nat) (X32:polyno1532895200ly_nat) (Y31:polyno1532895200ly_nat) (Y32:polyno1532895200ly_nat), (((eq Prop) (((eq polyno1532895200ly_nat) ((polyno1222032024dd_nat X31) X32)) ((polyno1222032024dd_nat Y31) Y32))) ((and (((eq polyno1532895200ly_nat) X31) Y31)) (((eq polyno1532895200ly_nat) X32) Y32))))
% 0.48/0.68 FOF formula (forall (Bs2:list_a) (P:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) (polyno955999183nate_a P))) ((polyno422358502poly_a Bs2) P))) of role axiom named fact_28_polynate
% 0.48/0.68 A new axiom: (forall (Bs2:list_a) (P:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) (polyno955999183nate_a P))) ((polyno422358502poly_a Bs2) P)))
% 0.48/0.68 FOF formula (forall (Bs2:list_a) (A:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) ((polyno1491482291_Mul_a A) B))) ((times_times_a ((polyno422358502poly_a Bs2) A)) ((polyno422358502poly_a Bs2) B)))) of role axiom named fact_29_Ipoly_Osimps_I6_J
% 0.48/0.68 A new axiom: (forall (Bs2:list_a) (A:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) ((polyno1491482291_Mul_a A) B))) ((times_times_a ((polyno422358502poly_a Bs2) A)) ((polyno422358502poly_a Bs2) B))))
% 0.48/0.68 FOF formula (forall (Bs2:list_a) (C:a), (((eq a) ((polyno422358502poly_a Bs2) (polyno439679028le_C_a C))) C)) of role axiom named fact_30_Ipoly_Osimps_I1_J
% 0.48/0.68 A new axiom: (forall (Bs2:list_a) (C:a), (((eq a) ((polyno422358502poly_a Bs2) (polyno439679028le_C_a C))) C))
% 0.48/0.68 FOF formula (forall (X51:polyno1532895200ly_nat) (X52:polyno1532895200ly_nat) (X81:polyno1532895200ly_nat) (X82:nat) (X83:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) ((polyno1415441627ul_nat X51) X52)) (((polyno720942678CN_nat X81) X82) X83)))) of role axiom named fact_31_poly_Odistinct_I49_J
% 0.48/0.68 A new axiom: (forall (X51:polyno1532895200ly_nat) (X52:polyno1532895200ly_nat) (X81:polyno1532895200ly_nat) (X82:nat) (X83:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) ((polyno1415441627ul_nat X51) X52)) (((polyno720942678CN_nat X81) X82) X83))))
% 0.48/0.68 FOF formula (forall (X51:polyno727731844poly_a) (X52:polyno727731844poly_a) (X81:polyno727731844poly_a) (X82:nat) (X83:polyno727731844poly_a), (not (((eq polyno727731844poly_a) ((polyno1491482291_Mul_a X51) X52)) (((polyno1057396216e_CN_a X81) X82) X83)))) of role axiom named fact_32_poly_Odistinct_I49_J
% 0.53/0.69 A new axiom: (forall (X51:polyno727731844poly_a) (X52:polyno727731844poly_a) (X81:polyno727731844poly_a) (X82:nat) (X83:polyno727731844poly_a), (not (((eq polyno727731844poly_a) ((polyno1491482291_Mul_a X51) X52)) (((polyno1057396216e_CN_a X81) X82) X83))))
% 0.53/0.69 FOF formula (forall (X31:polyno727731844poly_a) (X32:polyno727731844poly_a) (X81:polyno727731844poly_a) (X82:nat) (X83:polyno727731844poly_a), (not (((eq polyno727731844poly_a) ((polyno1623170614_Add_a X31) X32)) (((polyno1057396216e_CN_a X81) X82) X83)))) of role axiom named fact_33_poly_Odistinct_I35_J
% 0.53/0.69 A new axiom: (forall (X31:polyno727731844poly_a) (X32:polyno727731844poly_a) (X81:polyno727731844poly_a) (X82:nat) (X83:polyno727731844poly_a), (not (((eq polyno727731844poly_a) ((polyno1623170614_Add_a X31) X32)) (((polyno1057396216e_CN_a X81) X82) X83))))
% 0.53/0.69 FOF formula (forall (X31:polyno1532895200ly_nat) (X32:polyno1532895200ly_nat) (X81:polyno1532895200ly_nat) (X82:nat) (X83:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) ((polyno1222032024dd_nat X31) X32)) (((polyno720942678CN_nat X81) X82) X83)))) of role axiom named fact_34_poly_Odistinct_I35_J
% 0.53/0.69 A new axiom: (forall (X31:polyno1532895200ly_nat) (X32:polyno1532895200ly_nat) (X81:polyno1532895200ly_nat) (X82:nat) (X83:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) ((polyno1222032024dd_nat X31) X32)) (((polyno720942678CN_nat X81) X82) X83))))
% 0.53/0.69 FOF formula (forall (X31:polyno1532895200ly_nat) (X32:polyno1532895200ly_nat) (X51:polyno1532895200ly_nat) (X52:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) ((polyno1222032024dd_nat X31) X32)) ((polyno1415441627ul_nat X51) X52)))) of role axiom named fact_35_poly_Odistinct_I29_J
% 0.53/0.69 A new axiom: (forall (X31:polyno1532895200ly_nat) (X32:polyno1532895200ly_nat) (X51:polyno1532895200ly_nat) (X52:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) ((polyno1222032024dd_nat X31) X32)) ((polyno1415441627ul_nat X51) X52))))
% 0.53/0.69 FOF formula (forall (X31:polyno727731844poly_a) (X32:polyno727731844poly_a) (X51:polyno727731844poly_a) (X52:polyno727731844poly_a), (not (((eq polyno727731844poly_a) ((polyno1623170614_Add_a X31) X32)) ((polyno1491482291_Mul_a X51) X52)))) of role axiom named fact_36_poly_Odistinct_I29_J
% 0.53/0.69 A new axiom: (forall (X31:polyno727731844poly_a) (X32:polyno727731844poly_a) (X51:polyno727731844poly_a) (X52:polyno727731844poly_a), (not (((eq polyno727731844poly_a) ((polyno1623170614_Add_a X31) X32)) ((polyno1491482291_Mul_a X51) X52))))
% 0.53/0.69 FOF formula (forall (X1:a) (X81:polyno727731844poly_a) (X82:nat) (X83:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) (((polyno1057396216e_CN_a X81) X82) X83)))) of role axiom named fact_37_poly_Odistinct_I13_J
% 0.53/0.69 A new axiom: (forall (X1:a) (X81:polyno727731844poly_a) (X82:nat) (X83:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) (((polyno1057396216e_CN_a X81) X82) X83))))
% 0.53/0.69 FOF formula (forall (X1:nat) (X81:polyno1532895200ly_nat) (X82:nat) (X83:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) (((polyno720942678CN_nat X81) X82) X83)))) of role axiom named fact_38_poly_Odistinct_I13_J
% 0.53/0.69 A new axiom: (forall (X1:nat) (X81:polyno1532895200ly_nat) (X82:nat) (X83:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) (((polyno720942678CN_nat X81) X82) X83))))
% 0.53/0.69 FOF formula (forall (X1:nat) (X51:polyno1532895200ly_nat) (X52:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) ((polyno1415441627ul_nat X51) X52)))) of role axiom named fact_39_poly_Odistinct_I7_J
% 0.53/0.69 A new axiom: (forall (X1:nat) (X51:polyno1532895200ly_nat) (X52:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) ((polyno1415441627ul_nat X51) X52))))
% 0.53/0.69 FOF formula (forall (X1:a) (X51:polyno727731844poly_a) (X52:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) ((polyno1491482291_Mul_a X51) X52)))) of role axiom named fact_40_poly_Odistinct_I7_J
% 0.53/0.70 A new axiom: (forall (X1:a) (X51:polyno727731844poly_a) (X52:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) ((polyno1491482291_Mul_a X51) X52))))
% 0.53/0.70 FOF formula (forall (X1:a) (X31:polyno727731844poly_a) (X32:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) ((polyno1623170614_Add_a X31) X32)))) of role axiom named fact_41_poly_Odistinct_I3_J
% 0.53/0.70 A new axiom: (forall (X1:a) (X31:polyno727731844poly_a) (X32:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) ((polyno1623170614_Add_a X31) X32))))
% 0.53/0.70 FOF formula (forall (X1:nat) (X31:polyno1532895200ly_nat) (X32:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) ((polyno1222032024dd_nat X31) X32)))) of role axiom named fact_42_poly_Odistinct_I3_J
% 0.53/0.70 A new axiom: (forall (X1:nat) (X31:polyno1532895200ly_nat) (X32:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) ((polyno1222032024dd_nat X31) X32))))
% 0.53/0.70 FOF formula (forall (Vc:polyno1532895200ly_nat) (Vd:polyno1532895200ly_nat) (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno1222032024dd_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb))) ((polyno1415441627ul_nat ((polyno1222032024dd_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb)))) of role axiom named fact_43_polymul_Osimps_I24_J
% 0.53/0.70 A new axiom: (forall (Vc:polyno1532895200ly_nat) (Vd:polyno1532895200ly_nat) (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno1222032024dd_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb))) ((polyno1415441627ul_nat ((polyno1222032024dd_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb))))
% 0.53/0.70 FOF formula (forall (Vc:polyno727731844poly_a) (Vd:polyno727731844poly_a) (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1623170614_Add_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb))) ((polyno1491482291_Mul_a ((polyno1623170614_Add_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb)))) of role axiom named fact_44_polymul_Osimps_I24_J
% 0.53/0.70 A new axiom: (forall (Vc:polyno727731844poly_a) (Vd:polyno727731844poly_a) (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1623170614_Add_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb))) ((polyno1491482291_Mul_a ((polyno1623170614_Add_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb))))
% 0.53/0.70 FOF formula (forall (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat) (Vc:polyno1532895200ly_nat) (Vd:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno1222032024dd_nat Vc) Vd))) ((polyno1415441627ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno1222032024dd_nat Vc) Vd)))) of role axiom named fact_45_polymul_Osimps_I12_J
% 0.53/0.70 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat) (Vc:polyno1532895200ly_nat) (Vd:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno1222032024dd_nat Vc) Vd))) ((polyno1415441627ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno1222032024dd_nat Vc) Vd))))
% 0.53/0.70 FOF formula (forall (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a) (Vc:polyno727731844poly_a) (Vd:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1623170614_Add_a Vc) Vd))) ((polyno1491482291_Mul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1623170614_Add_a Vc) Vd)))) of role axiom named fact_46_polymul_Osimps_I12_J
% 0.53/0.70 A new axiom: (forall (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a) (Vc:polyno727731844poly_a) (Vd:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1623170614_Add_a Vc) Vd))) ((polyno1491482291_Mul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1623170614_Add_a Vc) Vd))))
% 0.53/0.71 FOF formula (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->Prop)) (polyno892049031yh_nat ((polyno1415441627ul_nat V) Va))) (fun (K:nat)=> False))) of role axiom named fact_47_isnpolyh_Osimps_I6_J
% 0.53/0.71 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->Prop)) (polyno892049031yh_nat ((polyno1415441627ul_nat V) Va))) (fun (K:nat)=> False)))
% 0.53/0.71 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->Prop)) (polyno1372495879olyh_a ((polyno1491482291_Mul_a V) Va))) (fun (K:nat)=> False))) of role axiom named fact_48_isnpolyh_Osimps_I6_J
% 0.53/0.71 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->Prop)) (polyno1372495879olyh_a ((polyno1491482291_Mul_a V) Va))) (fun (K:nat)=> False)))
% 0.53/0.71 FOF formula (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->Prop)) (polyno892049031yh_nat ((polyno1222032024dd_nat V) Va))) (fun (K:nat)=> False))) of role axiom named fact_49_isnpolyh_Osimps_I4_J
% 0.53/0.71 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->Prop)) (polyno892049031yh_nat ((polyno1222032024dd_nat V) Va))) (fun (K:nat)=> False)))
% 0.53/0.71 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->Prop)) (polyno1372495879olyh_a ((polyno1623170614_Add_a V) Va))) (fun (K:nat)=> False))) of role axiom named fact_50_isnpolyh_Osimps_I4_J
% 0.53/0.71 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->Prop)) (polyno1372495879olyh_a ((polyno1623170614_Add_a V) Va))) (fun (K:nat)=> False)))
% 0.53/0.71 FOF formula (forall (C:nat), (((eq (nat->Prop)) (polyno892049031yh_nat (polyno2122022170_C_nat C))) (fun (K:nat)=> True))) of role axiom named fact_51_isnpolyh_Osimps_I1_J
% 0.53/0.71 A new axiom: (forall (C:nat), (((eq (nat->Prop)) (polyno892049031yh_nat (polyno2122022170_C_nat C))) (fun (K:nat)=> True)))
% 0.53/0.71 FOF formula (forall (C:a), (((eq (nat->Prop)) (polyno1372495879olyh_a (polyno439679028le_C_a C))) (fun (K:nat)=> True))) of role axiom named fact_52_isnpolyh_Osimps_I1_J
% 0.53/0.71 A new axiom: (forall (C:a), (((eq (nat->Prop)) (polyno1372495879olyh_a (polyno439679028le_C_a C))) (fun (K:nat)=> True)))
% 0.53/0.71 FOF formula (forall (C:a), (((eq polyno727731844poly_a) (polyno955999183nate_a (polyno439679028le_C_a C))) (polyno439679028le_C_a C))) of role axiom named fact_53_polynate_Osimps_I8_J
% 0.53/0.71 A new axiom: (forall (C:a), (((eq polyno727731844poly_a) (polyno955999183nate_a (polyno439679028le_C_a C))) (polyno439679028le_C_a C)))
% 0.53/0.71 FOF formula (forall (P:polyno727731844poly_a), (polyno190918219poly_a (polyno955999183nate_a P))) of role axiom named fact_54_polynate__norm
% 0.53/0.71 A new axiom: (forall (P:polyno727731844poly_a), (polyno190918219poly_a (polyno955999183nate_a P)))
% 0.53/0.71 FOF formula (forall (P:polyno727731844poly_a) (N0:nat) (Q:polyno727731844poly_a) (N1:nat), (((polyno1372495879olyh_a P) N0)->(((polyno1372495879olyh_a Q) N1)->(((eq Prop) (forall (Bs:list_a), (((eq a) ((polyno422358502poly_a Bs) P)) ((polyno422358502poly_a Bs) Q)))) (((eq polyno727731844poly_a) P) Q))))) of role axiom named fact_55_isnpolyh__unique
% 0.53/0.71 A new axiom: (forall (P:polyno727731844poly_a) (N0:nat) (Q:polyno727731844poly_a) (N1:nat), (((polyno1372495879olyh_a P) N0)->(((polyno1372495879olyh_a Q) N1)->(((eq Prop) (forall (Bs:list_a), (((eq a) ((polyno422358502poly_a Bs) P)) ((polyno422358502poly_a Bs) Q)))) (((eq polyno727731844poly_a) P) Q)))))
% 0.53/0.71 FOF formula (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno1222032024dd_nat V) Va)) B)) ((polyno1415441627ul_nat ((polyno1222032024dd_nat V) Va)) B))) of role axiom named fact_56_polymul_Osimps_I6_J
% 0.53/0.71 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno1222032024dd_nat V) Va)) B)) ((polyno1415441627ul_nat ((polyno1222032024dd_nat V) Va)) B)))
% 0.53/0.71 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1623170614_Add_a V) Va)) B)) ((polyno1491482291_Mul_a ((polyno1623170614_Add_a V) Va)) B))) of role axiom named fact_57_polymul_Osimps_I6_J
% 0.53/0.72 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1623170614_Add_a V) Va)) B)) ((polyno1491482291_Mul_a ((polyno1623170614_Add_a V) Va)) B)))
% 0.53/0.72 FOF formula (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->((forall (Bs3:list_a), (((polyno896877631f_bs_a Bs3) P)->(((eq a) ((polyno422358502poly_a Bs3) P)) zero_zero_a)))->(((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a))))) of role axiom named fact_58_isnpolyh__zero__iff
% 0.53/0.72 A new axiom: (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->((forall (Bs3:list_a), (((polyno896877631f_bs_a Bs3) P)->(((eq a) ((polyno422358502poly_a Bs3) P)) zero_zero_a)))->(((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a)))))
% 0.53/0.72 FOF formula (forall (Bs2:list_a) (C:a) (P:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) ((polyno562434098cmul_a C) P))) ((polyno422358502poly_a Bs2) ((polyno1491482291_Mul_a (polyno439679028le_C_a C)) P)))) of role axiom named fact_59_poly__cmul
% 0.53/0.72 A new axiom: (forall (Bs2:list_a) (C:a) (P:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) ((polyno562434098cmul_a C) P))) ((polyno422358502poly_a Bs2) ((polyno1491482291_Mul_a (polyno439679028le_C_a C)) P))))
% 0.53/0.72 FOF formula (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno439679028le_C_a zero_zero_a)) P)) (polyno439679028le_C_a zero_zero_a)))) of role axiom named fact_60_polymul__0_I2_J
% 0.53/0.72 A new axiom: (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno439679028le_C_a zero_zero_a)) P)) (polyno439679028le_C_a zero_zero_a))))
% 0.53/0.72 FOF formula (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a P) (polyno439679028le_C_a zero_zero_a))) (polyno439679028le_C_a zero_zero_a)))) of role axiom named fact_61_polymul__0_I1_J
% 0.53/0.72 A new axiom: (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a P) (polyno439679028le_C_a zero_zero_a))) (polyno439679028le_C_a zero_zero_a))))
% 0.53/0.72 FOF formula (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno439679028le_C_a one_one_a)) P)) P))) of role axiom named fact_62_polymul__1_I2_J
% 0.53/0.72 A new axiom: (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno439679028le_C_a one_one_a)) P)) P)))
% 0.53/0.72 FOF formula (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a P) (polyno439679028le_C_a one_one_a))) P))) of role axiom named fact_63_polymul__1_I1_J
% 0.53/0.72 A new axiom: (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a P) (polyno439679028le_C_a one_one_a))) P)))
% 0.53/0.72 FOF formula (forall (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno955999183nate_a (((polyno1057396216e_CN_a C) N) P))) (polyno955999183nate_a ((polyno1623170614_Add_a C) ((polyno1491482291_Mul_a (polyno2024845497ound_a N)) P))))) of role axiom named fact_64_polynate_Osimps_I7_J
% 0.53/0.72 A new axiom: (forall (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno955999183nate_a (((polyno1057396216e_CN_a C) N) P))) (polyno955999183nate_a ((polyno1623170614_Add_a C) ((polyno1491482291_Mul_a (polyno2024845497ound_a N)) P)))))
% 0.53/0.72 FOF formula (forall (P:polyno727731844poly_a) (N0:nat) (Q:polyno727731844poly_a) (N1:nat), (((polyno1372495879olyh_a P) N0)->(((polyno1372495879olyh_a Q) N1)->(((eq Prop) (((eq polyno727731844poly_a) ((polyno1934269411ymul_a P) Q)) (polyno439679028le_C_a zero_zero_a))) ((or (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a))) (((eq polyno727731844poly_a) Q) (polyno439679028le_C_a zero_zero_a))))))) of role axiom named fact_65_polymul__eq0__iff
% 0.53/0.73 A new axiom: (forall (P:polyno727731844poly_a) (N0:nat) (Q:polyno727731844poly_a) (N1:nat), (((polyno1372495879olyh_a P) N0)->(((polyno1372495879olyh_a Q) N1)->(((eq Prop) (((eq polyno727731844poly_a) ((polyno1934269411ymul_a P) Q)) (polyno439679028le_C_a zero_zero_a))) ((or (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a))) (((eq polyno727731844poly_a) Q) (polyno439679028le_C_a zero_zero_a)))))))
% 0.53/0.73 FOF formula (forall (Y:a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) ((polyno1623170614_Add_a V) Va))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) ((polyno1623170614_Add_a V) Va)))) of role axiom named fact_66_poly__cmul_Osimps_I4_J
% 0.53/0.73 A new axiom: (forall (Y:a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) ((polyno1623170614_Add_a V) Va))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) ((polyno1623170614_Add_a V) Va))))
% 0.53/0.73 FOF formula (forall (Y:nat) (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) ((polyno1222032024dd_nat V) Va))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) ((polyno1222032024dd_nat V) Va)))) of role axiom named fact_67_poly__cmul_Osimps_I4_J
% 0.53/0.73 A new axiom: (forall (Y:nat) (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) ((polyno1222032024dd_nat V) Va))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) ((polyno1222032024dd_nat V) Va))))
% 0.53/0.73 FOF formula (forall (Y:nat) (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) ((polyno1415441627ul_nat V) Va))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) ((polyno1415441627ul_nat V) Va)))) of role axiom named fact_68_poly__cmul_Osimps_I6_J
% 0.53/0.73 A new axiom: (forall (Y:nat) (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) ((polyno1415441627ul_nat V) Va))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) ((polyno1415441627ul_nat V) Va))))
% 0.53/0.73 FOF formula (forall (Y:a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) ((polyno1491482291_Mul_a V) Va))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) ((polyno1491482291_Mul_a V) Va)))) of role axiom named fact_69_poly__cmul_Osimps_I6_J
% 0.53/0.73 A new axiom: (forall (Y:a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) ((polyno1491482291_Mul_a V) Va))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) ((polyno1491482291_Mul_a V) Va))))
% 0.53/0.73 FOF formula (forall (C2:a) (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a), ((and ((((eq a) C2) zero_zero_a)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a C) N) P)) (polyno439679028le_C_a C2))) (polyno439679028le_C_a zero_zero_a)))) ((not (((eq a) C2) zero_zero_a))->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a C) N) P)) (polyno439679028le_C_a C2))) (((polyno1057396216e_CN_a ((polyno1934269411ymul_a C) (polyno439679028le_C_a C2))) N) ((polyno1934269411ymul_a P) (polyno439679028le_C_a C2))))))) of role axiom named fact_70_polymul_Osimps_I3_J
% 0.53/0.73 A new axiom: (forall (C2:a) (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a), ((and ((((eq a) C2) zero_zero_a)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a C) N) P)) (polyno439679028le_C_a C2))) (polyno439679028le_C_a zero_zero_a)))) ((not (((eq a) C2) zero_zero_a))->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a C) N) P)) (polyno439679028le_C_a C2))) (((polyno1057396216e_CN_a ((polyno1934269411ymul_a C) (polyno439679028le_C_a C2))) N) ((polyno1934269411ymul_a P) (polyno439679028le_C_a C2)))))))
% 0.53/0.74 FOF formula (forall (C2:nat) (C:polyno1532895200ly_nat) (N:nat) (P:polyno1532895200ly_nat), ((and ((((eq nat) C2) zero_zero_nat)->(((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat C) N) P)) (polyno2122022170_C_nat C2))) (polyno2122022170_C_nat zero_zero_nat)))) ((not (((eq nat) C2) zero_zero_nat))->(((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat C) N) P)) (polyno2122022170_C_nat C2))) (((polyno720942678CN_nat ((polyno929799083ul_nat C) (polyno2122022170_C_nat C2))) N) ((polyno929799083ul_nat P) (polyno2122022170_C_nat C2))))))) of role axiom named fact_71_polymul_Osimps_I3_J
% 0.53/0.74 A new axiom: (forall (C2:nat) (C:polyno1532895200ly_nat) (N:nat) (P:polyno1532895200ly_nat), ((and ((((eq nat) C2) zero_zero_nat)->(((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat C) N) P)) (polyno2122022170_C_nat C2))) (polyno2122022170_C_nat zero_zero_nat)))) ((not (((eq nat) C2) zero_zero_nat))->(((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat C) N) P)) (polyno2122022170_C_nat C2))) (((polyno720942678CN_nat ((polyno929799083ul_nat C) (polyno2122022170_C_nat C2))) N) ((polyno929799083ul_nat P) (polyno2122022170_C_nat C2)))))))
% 0.53/0.74 FOF formula (forall (X2:nat) (Y2:nat), (((eq Prop) (((eq polyno727731844poly_a) (polyno2024845497ound_a X2)) (polyno2024845497ound_a Y2))) (((eq nat) X2) Y2))) of role axiom named fact_72_poly_Oinject_I2_J
% 0.53/0.74 A new axiom: (forall (X2:nat) (Y2:nat), (((eq Prop) (((eq polyno727731844poly_a) (polyno2024845497ound_a X2)) (polyno2024845497ound_a Y2))) (((eq nat) X2) Y2)))
% 0.53/0.74 FOF formula (forall (X2:nat) (Y2:nat), (((eq Prop) (((eq polyno1532895200ly_nat) (polyno1999838549nd_nat X2)) (polyno1999838549nd_nat Y2))) (((eq nat) X2) Y2))) of role axiom named fact_73_poly_Oinject_I2_J
% 0.53/0.74 A new axiom: (forall (X2:nat) (Y2:nat), (((eq Prop) (((eq polyno1532895200ly_nat) (polyno1999838549nd_nat X2)) (polyno1999838549nd_nat Y2))) (((eq nat) X2) Y2)))
% 0.53/0.74 FOF formula (forall (N:nat), (((eq polyno727731844poly_a) (polyno955999183nate_a (polyno2024845497ound_a N))) (((polyno1057396216e_CN_a (polyno439679028le_C_a zero_zero_a)) N) (polyno439679028le_C_a one_one_a)))) of role axiom named fact_74_polynate_Osimps_I1_J
% 0.53/0.74 A new axiom: (forall (N:nat), (((eq polyno727731844poly_a) (polyno955999183nate_a (polyno2024845497ound_a N))) (((polyno1057396216e_CN_a (polyno439679028le_C_a zero_zero_a)) N) (polyno439679028le_C_a one_one_a))))
% 0.53/0.74 FOF formula (forall (Y:a) (V:nat), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) (polyno2024845497ound_a V))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) (polyno2024845497ound_a V)))) of role axiom named fact_75_poly__cmul_Osimps_I3_J
% 0.53/0.74 A new axiom: (forall (Y:a) (V:nat), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) (polyno2024845497ound_a V))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) (polyno2024845497ound_a V))))
% 0.53/0.74 FOF formula (forall (Y:nat) (V:nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) (polyno1999838549nd_nat V))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) (polyno1999838549nd_nat V)))) of role axiom named fact_76_poly__cmul_Osimps_I3_J
% 0.53/0.74 A new axiom: (forall (Y:nat) (V:nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) (polyno1999838549nd_nat V))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) (polyno1999838549nd_nat V))))
% 0.53/0.74 FOF formula (forall (X2:nat) (X81:polyno727731844poly_a) (X82:nat) (X83:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno2024845497ound_a X2)) (((polyno1057396216e_CN_a X81) X82) X83)))) of role axiom named fact_77_poly_Odistinct_I25_J
% 0.53/0.74 A new axiom: (forall (X2:nat) (X81:polyno727731844poly_a) (X82:nat) (X83:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno2024845497ound_a X2)) (((polyno1057396216e_CN_a X81) X82) X83))))
% 0.53/0.74 FOF formula (forall (X2:nat) (X81:polyno1532895200ly_nat) (X82:nat) (X83:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno1999838549nd_nat X2)) (((polyno720942678CN_nat X81) X82) X83)))) of role axiom named fact_78_poly_Odistinct_I25_J
% 0.59/0.75 A new axiom: (forall (X2:nat) (X81:polyno1532895200ly_nat) (X82:nat) (X83:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno1999838549nd_nat X2)) (((polyno720942678CN_nat X81) X82) X83))))
% 0.59/0.75 FOF formula (forall (X1:a) (X2:nat), (not (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) (polyno2024845497ound_a X2)))) of role axiom named fact_79_poly_Odistinct_I1_J
% 0.59/0.75 A new axiom: (forall (X1:a) (X2:nat), (not (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) (polyno2024845497ound_a X2))))
% 0.59/0.75 FOF formula (forall (X1:nat) (X2:nat), (not (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) (polyno1999838549nd_nat X2)))) of role axiom named fact_80_poly_Odistinct_I1_J
% 0.59/0.75 A new axiom: (forall (X1:nat) (X2:nat), (not (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) (polyno1999838549nd_nat X2))))
% 0.59/0.75 FOF formula (forall (X2:nat) (X51:polyno1532895200ly_nat) (X52:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno1999838549nd_nat X2)) ((polyno1415441627ul_nat X51) X52)))) of role axiom named fact_81_poly_Odistinct_I19_J
% 0.59/0.75 A new axiom: (forall (X2:nat) (X51:polyno1532895200ly_nat) (X52:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno1999838549nd_nat X2)) ((polyno1415441627ul_nat X51) X52))))
% 0.59/0.75 FOF formula (forall (X2:nat) (X51:polyno727731844poly_a) (X52:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno2024845497ound_a X2)) ((polyno1491482291_Mul_a X51) X52)))) of role axiom named fact_82_poly_Odistinct_I19_J
% 0.59/0.75 A new axiom: (forall (X2:nat) (X51:polyno727731844poly_a) (X52:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno2024845497ound_a X2)) ((polyno1491482291_Mul_a X51) X52))))
% 0.59/0.75 FOF formula (forall (X2:nat) (X31:polyno727731844poly_a) (X32:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno2024845497ound_a X2)) ((polyno1623170614_Add_a X31) X32)))) of role axiom named fact_83_poly_Odistinct_I15_J
% 0.59/0.75 A new axiom: (forall (X2:nat) (X31:polyno727731844poly_a) (X32:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno2024845497ound_a X2)) ((polyno1623170614_Add_a X31) X32))))
% 0.59/0.75 FOF formula (forall (X2:nat) (X31:polyno1532895200ly_nat) (X32:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno1999838549nd_nat X2)) ((polyno1222032024dd_nat X31) X32)))) of role axiom named fact_84_poly_Odistinct_I15_J
% 0.59/0.75 A new axiom: (forall (X2:nat) (X31:polyno1532895200ly_nat) (X32:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno1999838549nd_nat X2)) ((polyno1222032024dd_nat X31) X32))))
% 0.59/0.75 FOF formula (forall (V:nat), (((eq (nat->Prop)) (polyno892049031yh_nat (polyno1999838549nd_nat V))) (fun (K:nat)=> False))) of role axiom named fact_85_isnpolyh_Osimps_I3_J
% 0.59/0.75 A new axiom: (forall (V:nat), (((eq (nat->Prop)) (polyno892049031yh_nat (polyno1999838549nd_nat V))) (fun (K:nat)=> False)))
% 0.59/0.75 FOF formula (forall (V:nat), (((eq (nat->Prop)) (polyno1372495879olyh_a (polyno2024845497ound_a V))) (fun (K:nat)=> False))) of role axiom named fact_86_isnpolyh_Osimps_I3_J
% 0.59/0.75 A new axiom: (forall (V:nat), (((eq (nat->Prop)) (polyno1372495879olyh_a (polyno2024845497ound_a V))) (fun (K:nat)=> False)))
% 0.59/0.75 FOF formula (forall (Y:a) (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) (((polyno1057396216e_CN_a C) N) P))) (((polyno1057396216e_CN_a ((polyno562434098cmul_a Y) C)) N) ((polyno562434098cmul_a Y) P)))) of role axiom named fact_87_poly__cmul_Osimps_I2_J
% 0.59/0.75 A new axiom: (forall (Y:a) (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) (((polyno1057396216e_CN_a C) N) P))) (((polyno1057396216e_CN_a ((polyno562434098cmul_a Y) C)) N) ((polyno562434098cmul_a Y) P))))
% 0.59/0.75 FOF formula (forall (Y:nat) (C:polyno1532895200ly_nat) (N:nat) (P:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) (((polyno720942678CN_nat C) N) P))) (((polyno720942678CN_nat ((polyno1467023772ul_nat Y) C)) N) ((polyno1467023772ul_nat Y) P)))) of role axiom named fact_88_poly__cmul_Osimps_I2_J
% 0.60/0.76 A new axiom: (forall (Y:nat) (C:polyno1532895200ly_nat) (N:nat) (P:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) (((polyno720942678CN_nat C) N) P))) (((polyno720942678CN_nat ((polyno1467023772ul_nat Y) C)) N) ((polyno1467023772ul_nat Y) P))))
% 0.60/0.76 FOF formula (forall (A:polyno1532895200ly_nat) (V:nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat A) (polyno1999838549nd_nat V))) ((polyno1415441627ul_nat A) (polyno1999838549nd_nat V)))) of role axiom named fact_89_polymul_Osimps_I17_J
% 0.60/0.76 A new axiom: (forall (A:polyno1532895200ly_nat) (V:nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat A) (polyno1999838549nd_nat V))) ((polyno1415441627ul_nat A) (polyno1999838549nd_nat V))))
% 0.60/0.76 FOF formula (forall (A:polyno727731844poly_a) (V:nat), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a A) (polyno2024845497ound_a V))) ((polyno1491482291_Mul_a A) (polyno2024845497ound_a V)))) of role axiom named fact_90_polymul_Osimps_I17_J
% 0.60/0.76 A new axiom: (forall (A:polyno727731844poly_a) (V:nat), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a A) (polyno2024845497ound_a V))) ((polyno1491482291_Mul_a A) (polyno2024845497ound_a V))))
% 0.60/0.76 FOF formula (forall (V:nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (polyno1999838549nd_nat V)) B)) ((polyno1415441627ul_nat (polyno1999838549nd_nat V)) B))) of role axiom named fact_91_polymul_Osimps_I5_J
% 0.60/0.76 A new axiom: (forall (V:nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (polyno1999838549nd_nat V)) B)) ((polyno1415441627ul_nat (polyno1999838549nd_nat V)) B)))
% 0.60/0.76 FOF formula (forall (V:nat) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno2024845497ound_a V)) B)) ((polyno1491482291_Mul_a (polyno2024845497ound_a V)) B))) of role axiom named fact_92_polymul_Osimps_I5_J
% 0.60/0.76 A new axiom: (forall (V:nat) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno2024845497ound_a V)) B)) ((polyno1491482291_Mul_a (polyno2024845497ound_a V)) B)))
% 0.60/0.76 FOF formula (forall (Y:a) (X:a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) (polyno439679028le_C_a X))) (polyno439679028le_C_a ((times_times_a Y) X)))) of role axiom named fact_93_poly__cmul_Osimps_I1_J
% 0.60/0.76 A new axiom: (forall (Y:a) (X:a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) (polyno439679028le_C_a X))) (polyno439679028le_C_a ((times_times_a Y) X))))
% 0.60/0.76 FOF formula (forall (Y:nat) (X:nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) (polyno2122022170_C_nat X))) (polyno2122022170_C_nat ((times_times_nat Y) X)))) of role axiom named fact_94_poly__cmul_Osimps_I1_J
% 0.60/0.76 A new axiom: (forall (Y:nat) (X:nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) (polyno2122022170_C_nat X))) (polyno2122022170_C_nat ((times_times_nat Y) X))))
% 0.60/0.76 FOF formula (forall (N:nat), ((polyno892049031yh_nat (polyno2122022170_C_nat one_one_nat)) N)) of role axiom named fact_95_one__normh
% 0.60/0.76 A new axiom: (forall (N:nat), ((polyno892049031yh_nat (polyno2122022170_C_nat one_one_nat)) N))
% 0.60/0.76 FOF formula (forall (N:nat), ((polyno1372495879olyh_a (polyno439679028le_C_a one_one_a)) N)) of role axiom named fact_96_one__normh
% 0.60/0.76 A new axiom: (forall (N:nat), ((polyno1372495879olyh_a (polyno439679028le_C_a one_one_a)) N))
% 0.60/0.76 FOF formula (forall (N:nat), ((polyno892049031yh_nat (polyno2122022170_C_nat zero_zero_nat)) N)) of role axiom named fact_97_zero__normh
% 0.60/0.76 A new axiom: (forall (N:nat), ((polyno892049031yh_nat (polyno2122022170_C_nat zero_zero_nat)) N))
% 0.60/0.76 FOF formula (forall (N:nat), ((polyno1372495879olyh_a (polyno439679028le_C_a zero_zero_a)) N)) of role axiom named fact_98_zero__normh
% 0.60/0.76 A new axiom: (forall (N:nat), ((polyno1372495879olyh_a (polyno439679028le_C_a zero_zero_a)) N))
% 0.60/0.76 FOF formula (((eq (polyno1532895200ly_nat->Prop)) polyno1013235523ly_nat) (fun (P2:polyno1532895200ly_nat)=> ((polyno892049031yh_nat P2) zero_zero_nat))) of role axiom named fact_99_isnpoly__def
% 0.60/0.77 A new axiom: (((eq (polyno1532895200ly_nat->Prop)) polyno1013235523ly_nat) (fun (P2:polyno1532895200ly_nat)=> ((polyno892049031yh_nat P2) zero_zero_nat)))
% 0.60/0.77 FOF formula (((eq (polyno727731844poly_a->Prop)) polyno190918219poly_a) (fun (P2:polyno727731844poly_a)=> ((polyno1372495879olyh_a P2) zero_zero_nat))) of role axiom named fact_100_isnpoly__def
% 0.60/0.77 A new axiom: (((eq (polyno727731844poly_a->Prop)) polyno190918219poly_a) (fun (P2:polyno727731844poly_a)=> ((polyno1372495879olyh_a P2) zero_zero_nat)))
% 0.60/0.77 FOF formula (forall (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat) (Vc:nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat V) Va) Vb)) (polyno1999838549nd_nat Vc))) ((polyno1415441627ul_nat (((polyno720942678CN_nat V) Va) Vb)) (polyno1999838549nd_nat Vc)))) of role axiom named fact_101_polymul_Osimps_I11_J
% 0.60/0.77 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat) (Vc:nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat V) Va) Vb)) (polyno1999838549nd_nat Vc))) ((polyno1415441627ul_nat (((polyno720942678CN_nat V) Va) Vb)) (polyno1999838549nd_nat Vc))))
% 0.60/0.77 FOF formula (forall (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a) (Vc:nat), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a V) Va) Vb)) (polyno2024845497ound_a Vc))) ((polyno1491482291_Mul_a (((polyno1057396216e_CN_a V) Va) Vb)) (polyno2024845497ound_a Vc)))) of role axiom named fact_102_polymul_Osimps_I11_J
% 0.60/0.77 A new axiom: (forall (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a) (Vc:nat), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a V) Va) Vb)) (polyno2024845497ound_a Vc))) ((polyno1491482291_Mul_a (((polyno1057396216e_CN_a V) Va) Vb)) (polyno2024845497ound_a Vc))))
% 0.60/0.77 FOF formula (forall (Vc:nat) (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (polyno1999838549nd_nat Vc)) (((polyno720942678CN_nat V) Va) Vb))) ((polyno1415441627ul_nat (polyno1999838549nd_nat Vc)) (((polyno720942678CN_nat V) Va) Vb)))) of role axiom named fact_103_polymul_Osimps_I23_J
% 0.60/0.77 A new axiom: (forall (Vc:nat) (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (polyno1999838549nd_nat Vc)) (((polyno720942678CN_nat V) Va) Vb))) ((polyno1415441627ul_nat (polyno1999838549nd_nat Vc)) (((polyno720942678CN_nat V) Va) Vb))))
% 0.60/0.77 FOF formula (forall (Vc:nat) (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno2024845497ound_a Vc)) (((polyno1057396216e_CN_a V) Va) Vb))) ((polyno1491482291_Mul_a (polyno2024845497ound_a Vc)) (((polyno1057396216e_CN_a V) Va) Vb)))) of role axiom named fact_104_polymul_Osimps_I23_J
% 0.60/0.77 A new axiom: (forall (Vc:nat) (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno2024845497ound_a Vc)) (((polyno1057396216e_CN_a V) Va) Vb))) ((polyno1491482291_Mul_a (polyno2024845497ound_a Vc)) (((polyno1057396216e_CN_a V) Va) Vb))))
% 0.60/0.77 FOF formula (forall (C:a) (C2:polyno727731844poly_a) (N2:nat) (P3:polyno727731844poly_a), ((and ((((eq a) C) zero_zero_a)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno439679028le_C_a C)) (((polyno1057396216e_CN_a C2) N2) P3))) (polyno439679028le_C_a zero_zero_a)))) ((not (((eq a) C) zero_zero_a))->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno439679028le_C_a C)) (((polyno1057396216e_CN_a C2) N2) P3))) (((polyno1057396216e_CN_a ((polyno1934269411ymul_a (polyno439679028le_C_a C)) C2)) N2) ((polyno1934269411ymul_a (polyno439679028le_C_a C)) P3)))))) of role axiom named fact_105_polymul_Osimps_I2_J
% 0.60/0.77 A new axiom: (forall (C:a) (C2:polyno727731844poly_a) (N2:nat) (P3:polyno727731844poly_a), ((and ((((eq a) C) zero_zero_a)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno439679028le_C_a C)) (((polyno1057396216e_CN_a C2) N2) P3))) (polyno439679028le_C_a zero_zero_a)))) ((not (((eq a) C) zero_zero_a))->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno439679028le_C_a C)) (((polyno1057396216e_CN_a C2) N2) P3))) (((polyno1057396216e_CN_a ((polyno1934269411ymul_a (polyno439679028le_C_a C)) C2)) N2) ((polyno1934269411ymul_a (polyno439679028le_C_a C)) P3))))))
% 0.60/0.78 FOF formula (forall (C:nat) (C2:polyno1532895200ly_nat) (N2:nat) (P3:polyno1532895200ly_nat), ((and ((((eq nat) C) zero_zero_nat)->(((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (polyno2122022170_C_nat C)) (((polyno720942678CN_nat C2) N2) P3))) (polyno2122022170_C_nat zero_zero_nat)))) ((not (((eq nat) C) zero_zero_nat))->(((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (polyno2122022170_C_nat C)) (((polyno720942678CN_nat C2) N2) P3))) (((polyno720942678CN_nat ((polyno929799083ul_nat (polyno2122022170_C_nat C)) C2)) N2) ((polyno929799083ul_nat (polyno2122022170_C_nat C)) P3)))))) of role axiom named fact_106_polymul_Osimps_I2_J
% 0.60/0.78 A new axiom: (forall (C:nat) (C2:polyno1532895200ly_nat) (N2:nat) (P3:polyno1532895200ly_nat), ((and ((((eq nat) C) zero_zero_nat)->(((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (polyno2122022170_C_nat C)) (((polyno720942678CN_nat C2) N2) P3))) (polyno2122022170_C_nat zero_zero_nat)))) ((not (((eq nat) C) zero_zero_nat))->(((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (polyno2122022170_C_nat C)) (((polyno720942678CN_nat C2) N2) P3))) (((polyno720942678CN_nat ((polyno929799083ul_nat (polyno2122022170_C_nat C)) C2)) N2) ((polyno929799083ul_nat (polyno2122022170_C_nat C)) P3))))))
% 0.60/0.78 FOF formula (forall (C:a) (B:a), (((eq Prop) (((eq a) C) ((times_times_a C) B))) ((or (((eq a) C) zero_zero_a)) (((eq a) B) one_one_a)))) of role axiom named fact_107_mult__cancel__left1
% 0.60/0.78 A new axiom: (forall (C:a) (B:a), (((eq Prop) (((eq a) C) ((times_times_a C) B))) ((or (((eq a) C) zero_zero_a)) (((eq a) B) one_one_a))))
% 0.60/0.78 FOF formula (forall (C:a) (A:a), (((eq Prop) (((eq a) ((times_times_a C) A)) C)) ((or (((eq a) C) zero_zero_a)) (((eq a) A) one_one_a)))) of role axiom named fact_108_mult__cancel__left2
% 0.60/0.78 A new axiom: (forall (C:a) (A:a), (((eq Prop) (((eq a) ((times_times_a C) A)) C)) ((or (((eq a) C) zero_zero_a)) (((eq a) A) one_one_a))))
% 0.60/0.78 FOF formula (forall (C:a) (B:a), (((eq Prop) (((eq a) C) ((times_times_a B) C))) ((or (((eq a) C) zero_zero_a)) (((eq a) B) one_one_a)))) of role axiom named fact_109_mult__cancel__right1
% 0.60/0.78 A new axiom: (forall (C:a) (B:a), (((eq Prop) (((eq a) C) ((times_times_a B) C))) ((or (((eq a) C) zero_zero_a)) (((eq a) B) one_one_a))))
% 0.60/0.78 FOF formula (forall (A:a) (C:a), (((eq Prop) (((eq a) ((times_times_a A) C)) C)) ((or (((eq a) C) zero_zero_a)) (((eq a) A) one_one_a)))) of role axiom named fact_110_mult__cancel__right2
% 0.60/0.78 A new axiom: (forall (A:a) (C:a), (((eq Prop) (((eq a) ((times_times_a A) C)) C)) ((or (((eq a) C) zero_zero_a)) (((eq a) A) one_one_a))))
% 0.60/0.78 FOF formula (forall (A:nat), (((eq nat) ((times_times_nat A) one_one_nat)) A)) of role axiom named fact_111_mult_Oright__neutral
% 0.60/0.78 A new axiom: (forall (A:nat), (((eq nat) ((times_times_nat A) one_one_nat)) A))
% 0.60/0.78 FOF formula (forall (A:a), (((eq a) ((times_times_a A) one_one_a)) A)) of role axiom named fact_112_mult_Oright__neutral
% 0.60/0.78 A new axiom: (forall (A:a), (((eq a) ((times_times_a A) one_one_a)) A))
% 0.60/0.78 FOF formula (forall (A:nat), (((eq nat) ((times_times_nat one_one_nat) A)) A)) of role axiom named fact_113_mult_Oleft__neutral
% 0.60/0.78 A new axiom: (forall (A:nat), (((eq nat) ((times_times_nat one_one_nat) A)) A))
% 0.60/0.78 FOF formula (forall (A:a), (((eq a) ((times_times_a one_one_a) A)) A)) of role axiom named fact_114_mult_Oleft__neutral
% 0.60/0.78 A new axiom: (forall (A:a), (((eq a) ((times_times_a one_one_a) A)) A))
% 0.60/0.78 FOF formula (forall (A:nat) (C:nat) (B:nat), (((eq Prop) (((eq nat) ((times_times_nat A) C)) ((times_times_nat B) C))) ((or (((eq nat) C) zero_zero_nat)) (((eq nat) A) B)))) of role axiom named fact_115_mult__cancel__right
% 0.60/0.78 A new axiom: (forall (A:nat) (C:nat) (B:nat), (((eq Prop) (((eq nat) ((times_times_nat A) C)) ((times_times_nat B) C))) ((or (((eq nat) C) zero_zero_nat)) (((eq nat) A) B))))
% 0.60/0.79 FOF formula (forall (A:a) (C:a) (B:a), (((eq Prop) (((eq a) ((times_times_a A) C)) ((times_times_a B) C))) ((or (((eq a) C) zero_zero_a)) (((eq a) A) B)))) of role axiom named fact_116_mult__cancel__right
% 0.60/0.79 A new axiom: (forall (A:a) (C:a) (B:a), (((eq Prop) (((eq a) ((times_times_a A) C)) ((times_times_a B) C))) ((or (((eq a) C) zero_zero_a)) (((eq a) A) B))))
% 0.60/0.79 FOF formula (forall (C:nat) (A:nat) (B:nat), (((eq Prop) (((eq nat) ((times_times_nat C) A)) ((times_times_nat C) B))) ((or (((eq nat) C) zero_zero_nat)) (((eq nat) A) B)))) of role axiom named fact_117_mult__cancel__left
% 0.60/0.79 A new axiom: (forall (C:nat) (A:nat) (B:nat), (((eq Prop) (((eq nat) ((times_times_nat C) A)) ((times_times_nat C) B))) ((or (((eq nat) C) zero_zero_nat)) (((eq nat) A) B))))
% 0.60/0.79 FOF formula (forall (C:a) (A:a) (B:a), (((eq Prop) (((eq a) ((times_times_a C) A)) ((times_times_a C) B))) ((or (((eq a) C) zero_zero_a)) (((eq a) A) B)))) of role axiom named fact_118_mult__cancel__left
% 0.60/0.79 A new axiom: (forall (C:a) (A:a) (B:a), (((eq Prop) (((eq a) ((times_times_a C) A)) ((times_times_a C) B))) ((or (((eq a) C) zero_zero_a)) (((eq a) A) B))))
% 0.60/0.79 FOF formula (forall (A:nat), (((eq nat) ((times_times_nat zero_zero_nat) A)) zero_zero_nat)) of role axiom named fact_119_mult__zero__left
% 0.60/0.79 A new axiom: (forall (A:nat), (((eq nat) ((times_times_nat zero_zero_nat) A)) zero_zero_nat))
% 0.60/0.79 FOF formula (forall (A:a), (((eq a) ((times_times_a zero_zero_a) A)) zero_zero_a)) of role axiom named fact_120_mult__zero__left
% 0.60/0.79 A new axiom: (forall (A:a), (((eq a) ((times_times_a zero_zero_a) A)) zero_zero_a))
% 0.60/0.79 FOF formula (forall (A:nat), (((eq nat) ((times_times_nat A) zero_zero_nat)) zero_zero_nat)) of role axiom named fact_121_mult__zero__right
% 0.60/0.79 A new axiom: (forall (A:nat), (((eq nat) ((times_times_nat A) zero_zero_nat)) zero_zero_nat))
% 0.60/0.79 FOF formula (forall (A:a), (((eq a) ((times_times_a A) zero_zero_a)) zero_zero_a)) of role axiom named fact_122_mult__zero__right
% 0.60/0.79 A new axiom: (forall (A:a), (((eq a) ((times_times_a A) zero_zero_a)) zero_zero_a))
% 0.60/0.79 FOF formula (forall (A:nat) (B:nat), (((eq Prop) (((eq nat) ((times_times_nat A) B)) zero_zero_nat)) ((or (((eq nat) A) zero_zero_nat)) (((eq nat) B) zero_zero_nat)))) of role axiom named fact_123_mult__eq__0__iff
% 0.60/0.79 A new axiom: (forall (A:nat) (B:nat), (((eq Prop) (((eq nat) ((times_times_nat A) B)) zero_zero_nat)) ((or (((eq nat) A) zero_zero_nat)) (((eq nat) B) zero_zero_nat))))
% 0.60/0.79 FOF formula (forall (A:a) (B:a), (((eq Prop) (((eq a) ((times_times_a A) B)) zero_zero_a)) ((or (((eq a) A) zero_zero_a)) (((eq a) B) zero_zero_a)))) of role axiom named fact_124_mult__eq__0__iff
% 0.60/0.79 A new axiom: (forall (A:a) (B:a), (((eq Prop) (((eq a) ((times_times_a A) B)) zero_zero_a)) ((or (((eq a) A) zero_zero_a)) (((eq a) B) zero_zero_a))))
% 0.60/0.79 FOF formula (forall (X:a), (((eq Prop) (((eq a) zero_zero_a) X)) (((eq a) X) zero_zero_a))) of role axiom named fact_125_zero__reorient
% 0.60/0.79 A new axiom: (forall (X:a), (((eq Prop) (((eq a) zero_zero_a) X)) (((eq a) X) zero_zero_a)))
% 0.60/0.79 FOF formula (forall (X:nat), (((eq Prop) (((eq nat) zero_zero_nat) X)) (((eq nat) X) zero_zero_nat))) of role axiom named fact_126_zero__reorient
% 0.60/0.79 A new axiom: (forall (X:nat), (((eq Prop) (((eq nat) zero_zero_nat) X)) (((eq nat) X) zero_zero_nat)))
% 0.60/0.79 FOF formula (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat ((times_times_nat A) B)) C)) ((times_times_nat A) ((times_times_nat B) C)))) of role axiom named fact_127_ab__semigroup__mult__class_Omult__ac_I1_J
% 0.60/0.79 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat ((times_times_nat A) B)) C)) ((times_times_nat A) ((times_times_nat B) C))))
% 0.60/0.79 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a ((times_times_a A) B)) C)) ((times_times_a A) ((times_times_a B) C)))) of role axiom named fact_128_ab__semigroup__mult__class_Omult__ac_I1_J
% 0.60/0.79 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a ((times_times_a A) B)) C)) ((times_times_a A) ((times_times_a B) C))))
% 0.60/0.79 FOF formula (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat ((times_times_nat A) B)) C)) ((times_times_nat A) ((times_times_nat B) C)))) of role axiom named fact_129_mult_Oassoc
% 0.60/0.81 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat ((times_times_nat A) B)) C)) ((times_times_nat A) ((times_times_nat B) C))))
% 0.60/0.81 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a ((times_times_a A) B)) C)) ((times_times_a A) ((times_times_a B) C)))) of role axiom named fact_130_mult_Oassoc
% 0.60/0.81 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a ((times_times_a A) B)) C)) ((times_times_a A) ((times_times_a B) C))))
% 0.60/0.81 FOF formula (((eq (nat->(nat->nat))) times_times_nat) (fun (A2:nat) (B2:nat)=> ((times_times_nat B2) A2))) of role axiom named fact_131_mult_Ocommute
% 0.60/0.81 A new axiom: (((eq (nat->(nat->nat))) times_times_nat) (fun (A2:nat) (B2:nat)=> ((times_times_nat B2) A2)))
% 0.60/0.81 FOF formula (((eq (a->(a->a))) times_times_a) (fun (A2:a) (B2:a)=> ((times_times_a B2) A2))) of role axiom named fact_132_mult_Ocommute
% 0.60/0.81 A new axiom: (((eq (a->(a->a))) times_times_a) (fun (A2:a) (B2:a)=> ((times_times_a B2) A2)))
% 0.60/0.81 FOF formula (forall (B:nat) (A:nat) (C:nat), (((eq nat) ((times_times_nat B) ((times_times_nat A) C))) ((times_times_nat A) ((times_times_nat B) C)))) of role axiom named fact_133_mult_Oleft__commute
% 0.60/0.81 A new axiom: (forall (B:nat) (A:nat) (C:nat), (((eq nat) ((times_times_nat B) ((times_times_nat A) C))) ((times_times_nat A) ((times_times_nat B) C))))
% 0.60/0.81 FOF formula (forall (B:a) (A:a) (C:a), (((eq a) ((times_times_a B) ((times_times_a A) C))) ((times_times_a A) ((times_times_a B) C)))) of role axiom named fact_134_mult_Oleft__commute
% 0.60/0.81 A new axiom: (forall (B:a) (A:a) (C:a), (((eq a) ((times_times_a B) ((times_times_a A) C))) ((times_times_a A) ((times_times_a B) C))))
% 0.60/0.81 FOF formula (forall (X:a), (((eq Prop) (((eq a) one_one_a) X)) (((eq a) X) one_one_a))) of role axiom named fact_135_one__reorient
% 0.60/0.81 A new axiom: (forall (X:a), (((eq Prop) (((eq a) one_one_a) X)) (((eq a) X) one_one_a)))
% 0.60/0.81 FOF formula (forall (X:nat), (((eq Prop) (((eq nat) one_one_nat) X)) (((eq nat) X) one_one_nat))) of role axiom named fact_136_one__reorient
% 0.60/0.81 A new axiom: (forall (X:nat), (((eq Prop) (((eq nat) one_one_nat) X)) (((eq nat) X) one_one_nat)))
% 0.60/0.81 FOF formula (forall (A:nat) (B:nat), ((not (((eq nat) ((times_times_nat A) B)) zero_zero_nat))->((and (not (((eq nat) A) zero_zero_nat))) (not (((eq nat) B) zero_zero_nat))))) of role axiom named fact_137_mult__not__zero
% 0.60/0.81 A new axiom: (forall (A:nat) (B:nat), ((not (((eq nat) ((times_times_nat A) B)) zero_zero_nat))->((and (not (((eq nat) A) zero_zero_nat))) (not (((eq nat) B) zero_zero_nat)))))
% 0.60/0.81 FOF formula (forall (A:a) (B:a), ((not (((eq a) ((times_times_a A) B)) zero_zero_a))->((and (not (((eq a) A) zero_zero_a))) (not (((eq a) B) zero_zero_a))))) of role axiom named fact_138_mult__not__zero
% 0.60/0.81 A new axiom: (forall (A:a) (B:a), ((not (((eq a) ((times_times_a A) B)) zero_zero_a))->((and (not (((eq a) A) zero_zero_a))) (not (((eq a) B) zero_zero_a)))))
% 0.60/0.81 FOF formula (forall (A:nat) (B:nat), ((((eq nat) ((times_times_nat A) B)) zero_zero_nat)->((or (((eq nat) A) zero_zero_nat)) (((eq nat) B) zero_zero_nat)))) of role axiom named fact_139_divisors__zero
% 0.60/0.81 A new axiom: (forall (A:nat) (B:nat), ((((eq nat) ((times_times_nat A) B)) zero_zero_nat)->((or (((eq nat) A) zero_zero_nat)) (((eq nat) B) zero_zero_nat))))
% 0.60/0.81 FOF formula (forall (A:a) (B:a), ((((eq a) ((times_times_a A) B)) zero_zero_a)->((or (((eq a) A) zero_zero_a)) (((eq a) B) zero_zero_a)))) of role axiom named fact_140_divisors__zero
% 0.60/0.81 A new axiom: (forall (A:a) (B:a), ((((eq a) ((times_times_a A) B)) zero_zero_a)->((or (((eq a) A) zero_zero_a)) (((eq a) B) zero_zero_a))))
% 0.60/0.81 FOF formula (forall (A:nat) (B:nat), ((not (((eq nat) A) zero_zero_nat))->((not (((eq nat) B) zero_zero_nat))->(not (((eq nat) ((times_times_nat A) B)) zero_zero_nat))))) of role axiom named fact_141_no__zero__divisors
% 0.60/0.81 A new axiom: (forall (A:nat) (B:nat), ((not (((eq nat) A) zero_zero_nat))->((not (((eq nat) B) zero_zero_nat))->(not (((eq nat) ((times_times_nat A) B)) zero_zero_nat)))))
% 0.60/0.81 FOF formula (forall (A:a) (B:a), ((not (((eq a) A) zero_zero_a))->((not (((eq a) B) zero_zero_a))->(not (((eq a) ((times_times_a A) B)) zero_zero_a))))) of role axiom named fact_142_no__zero__divisors
% 0.65/0.82 A new axiom: (forall (A:a) (B:a), ((not (((eq a) A) zero_zero_a))->((not (((eq a) B) zero_zero_a))->(not (((eq a) ((times_times_a A) B)) zero_zero_a)))))
% 0.65/0.82 FOF formula (forall (C:nat) (A:nat) (B:nat), ((not (((eq nat) C) zero_zero_nat))->(((eq Prop) (((eq nat) ((times_times_nat C) A)) ((times_times_nat C) B))) (((eq nat) A) B)))) of role axiom named fact_143_mult__left__cancel
% 0.65/0.82 A new axiom: (forall (C:nat) (A:nat) (B:nat), ((not (((eq nat) C) zero_zero_nat))->(((eq Prop) (((eq nat) ((times_times_nat C) A)) ((times_times_nat C) B))) (((eq nat) A) B))))
% 0.65/0.82 FOF formula (forall (C:a) (A:a) (B:a), ((not (((eq a) C) zero_zero_a))->(((eq Prop) (((eq a) ((times_times_a C) A)) ((times_times_a C) B))) (((eq a) A) B)))) of role axiom named fact_144_mult__left__cancel
% 0.65/0.82 A new axiom: (forall (C:a) (A:a) (B:a), ((not (((eq a) C) zero_zero_a))->(((eq Prop) (((eq a) ((times_times_a C) A)) ((times_times_a C) B))) (((eq a) A) B))))
% 0.65/0.82 FOF formula (forall (C:nat) (A:nat) (B:nat), ((not (((eq nat) C) zero_zero_nat))->(((eq Prop) (((eq nat) ((times_times_nat A) C)) ((times_times_nat B) C))) (((eq nat) A) B)))) of role axiom named fact_145_mult__right__cancel
% 0.65/0.82 A new axiom: (forall (C:nat) (A:nat) (B:nat), ((not (((eq nat) C) zero_zero_nat))->(((eq Prop) (((eq nat) ((times_times_nat A) C)) ((times_times_nat B) C))) (((eq nat) A) B))))
% 0.65/0.82 FOF formula (forall (C:a) (A:a) (B:a), ((not (((eq a) C) zero_zero_a))->(((eq Prop) (((eq a) ((times_times_a A) C)) ((times_times_a B) C))) (((eq a) A) B)))) of role axiom named fact_146_mult__right__cancel
% 0.65/0.82 A new axiom: (forall (C:a) (A:a) (B:a), ((not (((eq a) C) zero_zero_a))->(((eq Prop) (((eq a) ((times_times_a A) C)) ((times_times_a B) C))) (((eq a) A) B))))
% 0.65/0.82 FOF formula (not (((eq a) zero_zero_a) one_one_a)) of role axiom named fact_147_zero__neq__one
% 0.65/0.82 A new axiom: (not (((eq a) zero_zero_a) one_one_a))
% 0.65/0.82 FOF formula (not (((eq nat) zero_zero_nat) one_one_nat)) of role axiom named fact_148_zero__neq__one
% 0.65/0.82 A new axiom: (not (((eq nat) zero_zero_nat) one_one_nat))
% 0.65/0.82 FOF formula (forall (A:nat), (((eq nat) ((times_times_nat one_one_nat) A)) A)) of role axiom named fact_149_comm__monoid__mult__class_Omult__1
% 0.65/0.82 A new axiom: (forall (A:nat), (((eq nat) ((times_times_nat one_one_nat) A)) A))
% 0.65/0.82 FOF formula (forall (A:a), (((eq a) ((times_times_a one_one_a) A)) A)) of role axiom named fact_150_comm__monoid__mult__class_Omult__1
% 0.65/0.82 A new axiom: (forall (A:a), (((eq a) ((times_times_a one_one_a) A)) A))
% 0.65/0.82 FOF formula (forall (A:nat), (((eq nat) ((times_times_nat A) one_one_nat)) A)) of role axiom named fact_151_mult_Ocomm__neutral
% 0.65/0.82 A new axiom: (forall (A:nat), (((eq nat) ((times_times_nat A) one_one_nat)) A))
% 0.65/0.82 FOF formula (forall (A:a), (((eq a) ((times_times_a A) one_one_a)) A)) of role axiom named fact_152_mult_Ocomm__neutral
% 0.65/0.82 A new axiom: (forall (A:a), (((eq a) ((times_times_a A) one_one_a)) A))
% 0.65/0.82 FOF formula (forall (M:nat) (N:nat), (((eq Prop) (((eq nat) ((times_times_nat M) N)) zero_zero_nat)) ((or (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_153_mult__is__0
% 0.65/0.82 A new axiom: (forall (M:nat) (N:nat), (((eq Prop) (((eq nat) ((times_times_nat M) N)) zero_zero_nat)) ((or (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat))))
% 0.65/0.82 FOF formula (forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat)) of role axiom named fact_154_mult__0__right
% 0.65/0.82 A new axiom: (forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat))
% 0.65/0.82 FOF formula (forall (K2:nat) (M:nat) (N:nat), (((eq Prop) (((eq nat) ((times_times_nat K2) M)) ((times_times_nat K2) N))) ((or (((eq nat) M) N)) (((eq nat) K2) zero_zero_nat)))) of role axiom named fact_155_mult__cancel1
% 0.65/0.82 A new axiom: (forall (K2:nat) (M:nat) (N:nat), (((eq Prop) (((eq nat) ((times_times_nat K2) M)) ((times_times_nat K2) N))) ((or (((eq nat) M) N)) (((eq nat) K2) zero_zero_nat))))
% 0.65/0.82 FOF formula (forall (M:nat) (K2:nat) (N:nat), (((eq Prop) (((eq nat) ((times_times_nat M) K2)) ((times_times_nat N) K2))) ((or (((eq nat) M) N)) (((eq nat) K2) zero_zero_nat)))) of role axiom named fact_156_mult__cancel2
% 0.65/0.83 A new axiom: (forall (M:nat) (K2:nat) (N:nat), (((eq Prop) (((eq nat) ((times_times_nat M) K2)) ((times_times_nat N) K2))) ((or (((eq nat) M) N)) (((eq nat) K2) zero_zero_nat))))
% 0.65/0.83 FOF formula (forall (Bs2:list_a) (P:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) (polyno784948432ift1_a P))) ((polyno422358502poly_a Bs2) ((polyno1491482291_Mul_a (polyno2024845497ound_a zero_zero_nat)) P)))) of role axiom named fact_157_shift1
% 0.65/0.83 A new axiom: (forall (Bs2:list_a) (P:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) (polyno784948432ift1_a P))) ((polyno422358502poly_a Bs2) ((polyno1491482291_Mul_a (polyno2024845497ound_a zero_zero_nat)) P))))
% 0.65/0.83 FOF formula (forall (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat P) N0)->((not (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat)))->((polyno892049031yh_nat (polyno1964927358t1_nat P)) zero_zero_nat)))) of role axiom named fact_158_shift1__isnpolyh
% 0.65/0.83 A new axiom: (forall (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat P) N0)->((not (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat)))->((polyno892049031yh_nat (polyno1964927358t1_nat P)) zero_zero_nat))))
% 0.65/0.83 FOF formula (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->((not (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a)))->((polyno1372495879olyh_a (polyno784948432ift1_a P)) zero_zero_nat)))) of role axiom named fact_159_shift1__isnpolyh
% 0.65/0.83 A new axiom: (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->((not (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a)))->((polyno1372495879olyh_a (polyno784948432ift1_a P)) zero_zero_nat))))
% 0.65/0.83 FOF formula (forall (M:nat) (N:nat), (((eq Prop) (((eq nat) ((times_times_nat M) N)) one_one_nat)) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat)))) of role axiom named fact_160_nat__mult__eq__1__iff
% 0.65/0.83 A new axiom: (forall (M:nat) (N:nat), (((eq Prop) (((eq nat) ((times_times_nat M) N)) one_one_nat)) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat))))
% 0.65/0.83 FOF formula (forall (M:nat) (N:nat), (((eq Prop) (((eq nat) one_one_nat) ((times_times_nat M) N))) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat)))) of role axiom named fact_161_nat__1__eq__mult__iff
% 0.65/0.83 A new axiom: (forall (M:nat) (N:nat), (((eq Prop) (((eq nat) one_one_nat) ((times_times_nat M) N))) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat))))
% 0.65/0.83 FOF formula (forall (N:nat), (((eq nat) ((times_times_nat N) one_one_nat)) N)) of role axiom named fact_162_nat__mult__1__right
% 0.65/0.83 A new axiom: (forall (N:nat), (((eq nat) ((times_times_nat N) one_one_nat)) N))
% 0.65/0.83 FOF formula (forall (N:nat), (((eq nat) ((times_times_nat one_one_nat) N)) N)) of role axiom named fact_163_nat__mult__1
% 0.65/0.83 A new axiom: (forall (N:nat), (((eq nat) ((times_times_nat one_one_nat) N)) N))
% 0.65/0.83 FOF formula (forall (M:nat) (N:nat), ((((eq nat) M) ((times_times_nat M) N))->((or (((eq nat) N) one_one_nat)) (((eq nat) M) zero_zero_nat)))) of role axiom named fact_164_mult__eq__self__implies__10
% 0.65/0.83 A new axiom: (forall (M:nat) (N:nat), ((((eq nat) M) ((times_times_nat M) N))->((or (((eq nat) N) one_one_nat)) (((eq nat) M) zero_zero_nat))))
% 0.65/0.83 FOF formula (forall (N:nat), (((eq nat) ((times_times_nat zero_zero_nat) N)) zero_zero_nat)) of role axiom named fact_165_mult__0
% 0.65/0.83 A new axiom: (forall (N:nat), (((eq nat) ((times_times_nat zero_zero_nat) N)) zero_zero_nat))
% 0.65/0.83 FOF formula (forall (P:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno784948432ift1_a P)) (polyno439679028le_C_a zero_zero_a)))) of role axiom named fact_166_shift1__nz
% 0.65/0.83 A new axiom: (forall (P:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno784948432ift1_a P)) (polyno439679028le_C_a zero_zero_a))))
% 0.65/0.83 FOF formula (forall (P:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno1964927358t1_nat P)) (polyno2122022170_C_nat zero_zero_nat)))) of role axiom named fact_167_shift1__nz
% 0.65/0.83 A new axiom: (forall (P:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno1964927358t1_nat P)) (polyno2122022170_C_nat zero_zero_nat))))
% 0.65/0.84 FOF formula (forall (P:polyno1532895200ly_nat), ((polyno1013235523ly_nat P)->((not (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat)))->(polyno1013235523ly_nat (polyno1964927358t1_nat P))))) of role axiom named fact_168_shift1__isnpoly
% 0.65/0.84 A new axiom: (forall (P:polyno1532895200ly_nat), ((polyno1013235523ly_nat P)->((not (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat)))->(polyno1013235523ly_nat (polyno1964927358t1_nat P)))))
% 0.65/0.84 FOF formula (forall (P:polyno727731844poly_a), ((polyno190918219poly_a P)->((not (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a)))->(polyno190918219poly_a (polyno784948432ift1_a P))))) of role axiom named fact_169_shift1__isnpoly
% 0.65/0.84 A new axiom: (forall (P:polyno727731844poly_a), ((polyno190918219poly_a P)->((not (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a)))->(polyno190918219poly_a (polyno784948432ift1_a P)))))
% 0.65/0.84 FOF formula (((eq (polyno727731844poly_a->polyno727731844poly_a)) polyno784948432ift1_a) ((polyno1057396216e_CN_a (polyno439679028le_C_a zero_zero_a)) zero_zero_nat)) of role axiom named fact_170_shift1__def
% 0.65/0.84 A new axiom: (((eq (polyno727731844poly_a->polyno727731844poly_a)) polyno784948432ift1_a) ((polyno1057396216e_CN_a (polyno439679028le_C_a zero_zero_a)) zero_zero_nat))
% 0.65/0.84 FOF formula (((eq (polyno1532895200ly_nat->polyno1532895200ly_nat)) polyno1964927358t1_nat) ((polyno720942678CN_nat (polyno2122022170_C_nat zero_zero_nat)) zero_zero_nat)) of role axiom named fact_171_shift1__def
% 0.65/0.84 A new axiom: (((eq (polyno1532895200ly_nat->polyno1532895200ly_nat)) polyno1964927358t1_nat) ((polyno720942678CN_nat (polyno2122022170_C_nat zero_zero_nat)) zero_zero_nat))
% 0.65/0.84 FOF formula (forall (K2:nat) (M:nat) (N:nat), (((eq Prop) (((eq nat) ((times_times_nat K2) M)) ((times_times_nat K2) N))) ((or (((eq nat) K2) zero_zero_nat)) (((eq nat) M) N)))) of role axiom named fact_172_nat__mult__eq__cancel__disj
% 0.65/0.84 A new axiom: (forall (K2:nat) (M:nat) (N:nat), (((eq Prop) (((eq nat) ((times_times_nat K2) M)) ((times_times_nat K2) N))) ((or (((eq nat) K2) zero_zero_nat)) (((eq nat) M) N))))
% 0.65/0.84 FOF formula (forall (P:polyno1532895200ly_nat) (N0:nat) (M:nat), (((polyno892049031yh_nat P) N0)->(((eq Prop) (((eq polyno1532895200ly_nat) ((polyno544860353dn_nat P) M)) (polyno2122022170_C_nat zero_zero_nat))) (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat))))) of role axiom named fact_173_headn__nz
% 0.65/0.84 A new axiom: (forall (P:polyno1532895200ly_nat) (N0:nat) (M:nat), (((polyno892049031yh_nat P) N0)->(((eq Prop) (((eq polyno1532895200ly_nat) ((polyno544860353dn_nat P) M)) (polyno2122022170_C_nat zero_zero_nat))) (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat)))))
% 0.65/0.84 FOF formula (forall (P:polyno727731844poly_a) (N0:nat) (M:nat), (((polyno1372495879olyh_a P) N0)->(((eq Prop) (((eq polyno727731844poly_a) ((polyno567601229eadn_a P) M)) (polyno439679028le_C_a zero_zero_a))) (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a))))) of role axiom named fact_174_headn__nz
% 0.65/0.84 A new axiom: (forall (P:polyno727731844poly_a) (N0:nat) (M:nat), (((polyno1372495879olyh_a P) N0)->(((eq Prop) (((eq polyno727731844poly_a) ((polyno567601229eadn_a P) M)) (polyno439679028le_C_a zero_zero_a))) (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a)))))
% 0.65/0.84 FOF formula (forall (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat P) N0)->(((eq Prop) (((eq nat) (polyno524777654st_nat P)) zero_zero_nat)) (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat))))) of role axiom named fact_175_headconst__zero
% 0.65/0.84 A new axiom: (forall (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat P) N0)->(((eq Prop) (((eq nat) (polyno524777654st_nat P)) zero_zero_nat)) (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat)))))
% 0.65/0.84 FOF formula (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq Prop) (((eq a) (polyno2115742616onst_a P)) zero_zero_a)) (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a))))) of role axiom named fact_176_headconst__zero
% 0.69/0.85 A new axiom: (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq Prop) (((eq a) (polyno2115742616onst_a P)) zero_zero_a)) (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a)))))
% 0.69/0.85 FOF formula (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq polyno727731844poly_a) ((polyno1418491367ysub_a P) P)) (polyno439679028le_C_a zero_zero_a)))) of role axiom named fact_177_polysub__same__0
% 0.69/0.85 A new axiom: (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq polyno727731844poly_a) ((polyno1418491367ysub_a P) P)) (polyno439679028le_C_a zero_zero_a))))
% 0.69/0.85 FOF formula (forall (N:nat) (T:polyno1532895200ly_nat) (C:polyno1532895200ly_nat) (P:polyno1532895200ly_nat), ((and ((((eq nat) N) zero_zero_nat)->(((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) (((polyno720942678CN_nat C) N) P))) ((polyno1222032024dd_nat ((polyno336795754t0_nat T) C)) ((polyno1415441627ul_nat T) ((polyno336795754t0_nat T) P)))))) ((not (((eq nat) N) zero_zero_nat))->(((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) (((polyno720942678CN_nat C) N) P))) (((polyno720942678CN_nat ((polyno336795754t0_nat T) C)) N) ((polyno336795754t0_nat T) P)))))) of role axiom named fact_178_polysubst0_Osimps_I8_J
% 0.69/0.85 A new axiom: (forall (N:nat) (T:polyno1532895200ly_nat) (C:polyno1532895200ly_nat) (P:polyno1532895200ly_nat), ((and ((((eq nat) N) zero_zero_nat)->(((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) (((polyno720942678CN_nat C) N) P))) ((polyno1222032024dd_nat ((polyno336795754t0_nat T) C)) ((polyno1415441627ul_nat T) ((polyno336795754t0_nat T) P)))))) ((not (((eq nat) N) zero_zero_nat))->(((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) (((polyno720942678CN_nat C) N) P))) (((polyno720942678CN_nat ((polyno336795754t0_nat T) C)) N) ((polyno336795754t0_nat T) P))))))
% 0.69/0.85 FOF formula (forall (N:nat) (T:polyno727731844poly_a) (C:polyno727731844poly_a) (P:polyno727731844poly_a), ((and ((((eq nat) N) zero_zero_nat)->(((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) (((polyno1057396216e_CN_a C) N) P))) ((polyno1623170614_Add_a ((polyno1397854436bst0_a T) C)) ((polyno1491482291_Mul_a T) ((polyno1397854436bst0_a T) P)))))) ((not (((eq nat) N) zero_zero_nat))->(((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) (((polyno1057396216e_CN_a C) N) P))) (((polyno1057396216e_CN_a ((polyno1397854436bst0_a T) C)) N) ((polyno1397854436bst0_a T) P)))))) of role axiom named fact_179_polysubst0_Osimps_I8_J
% 0.69/0.85 A new axiom: (forall (N:nat) (T:polyno727731844poly_a) (C:polyno727731844poly_a) (P:polyno727731844poly_a), ((and ((((eq nat) N) zero_zero_nat)->(((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) (((polyno1057396216e_CN_a C) N) P))) ((polyno1623170614_Add_a ((polyno1397854436bst0_a T) C)) ((polyno1491482291_Mul_a T) ((polyno1397854436bst0_a T) P)))))) ((not (((eq nat) N) zero_zero_nat))->(((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) (((polyno1057396216e_CN_a C) N) P))) (((polyno1057396216e_CN_a ((polyno1397854436bst0_a T) C)) N) ((polyno1397854436bst0_a T) P))))))
% 0.69/0.85 FOF formula (forall (T:polyno727731844poly_a) (C:a), (((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) (polyno439679028le_C_a C))) (polyno439679028le_C_a C))) of role axiom named fact_180_polysubst0_Osimps_I1_J
% 0.69/0.85 A new axiom: (forall (T:polyno727731844poly_a) (C:a), (((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) (polyno439679028le_C_a C))) (polyno439679028le_C_a C)))
% 0.69/0.85 FOF formula (forall (T:polyno1532895200ly_nat) (C:nat), (((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) (polyno2122022170_C_nat C))) (polyno2122022170_C_nat C))) of role axiom named fact_181_polysubst0_Osimps_I1_J
% 0.69/0.85 A new axiom: (forall (T:polyno1532895200ly_nat) (C:nat), (((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) (polyno2122022170_C_nat C))) (polyno2122022170_C_nat C)))
% 0.69/0.85 FOF formula (forall (T:polyno1532895200ly_nat) (A:polyno1532895200ly_nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) ((polyno1415441627ul_nat A) B))) ((polyno1415441627ul_nat ((polyno336795754t0_nat T) A)) ((polyno336795754t0_nat T) B)))) of role axiom named fact_182_polysubst0_Osimps_I6_J
% 0.69/0.86 A new axiom: (forall (T:polyno1532895200ly_nat) (A:polyno1532895200ly_nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) ((polyno1415441627ul_nat A) B))) ((polyno1415441627ul_nat ((polyno336795754t0_nat T) A)) ((polyno336795754t0_nat T) B))))
% 0.69/0.86 FOF formula (forall (T:polyno727731844poly_a) (A:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) ((polyno1491482291_Mul_a A) B))) ((polyno1491482291_Mul_a ((polyno1397854436bst0_a T) A)) ((polyno1397854436bst0_a T) B)))) of role axiom named fact_183_polysubst0_Osimps_I6_J
% 0.69/0.86 A new axiom: (forall (T:polyno727731844poly_a) (A:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) ((polyno1491482291_Mul_a A) B))) ((polyno1491482291_Mul_a ((polyno1397854436bst0_a T) A)) ((polyno1397854436bst0_a T) B))))
% 0.69/0.86 FOF formula (forall (T:polyno727731844poly_a) (A:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) ((polyno1623170614_Add_a A) B))) ((polyno1623170614_Add_a ((polyno1397854436bst0_a T) A)) ((polyno1397854436bst0_a T) B)))) of role axiom named fact_184_polysubst0_Osimps_I4_J
% 0.69/0.86 A new axiom: (forall (T:polyno727731844poly_a) (A:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) ((polyno1623170614_Add_a A) B))) ((polyno1623170614_Add_a ((polyno1397854436bst0_a T) A)) ((polyno1397854436bst0_a T) B))))
% 0.69/0.86 FOF formula (forall (T:polyno1532895200ly_nat) (A:polyno1532895200ly_nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) ((polyno1222032024dd_nat A) B))) ((polyno1222032024dd_nat ((polyno336795754t0_nat T) A)) ((polyno336795754t0_nat T) B)))) of role axiom named fact_185_polysubst0_Osimps_I4_J
% 0.69/0.86 A new axiom: (forall (T:polyno1532895200ly_nat) (A:polyno1532895200ly_nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) ((polyno1222032024dd_nat A) B))) ((polyno1222032024dd_nat ((polyno336795754t0_nat T) A)) ((polyno336795754t0_nat T) B))))
% 0.69/0.86 FOF formula (forall (V:a), (((eq (nat->polyno727731844poly_a)) (polyno567601229eadn_a (polyno439679028le_C_a V))) (fun (M2:nat)=> (polyno439679028le_C_a V)))) of role axiom named fact_186_headn_Osimps_I2_J
% 0.69/0.86 A new axiom: (forall (V:a), (((eq (nat->polyno727731844poly_a)) (polyno567601229eadn_a (polyno439679028le_C_a V))) (fun (M2:nat)=> (polyno439679028le_C_a V))))
% 0.69/0.86 FOF formula (forall (V:nat), (((eq (nat->polyno1532895200ly_nat)) (polyno544860353dn_nat (polyno2122022170_C_nat V))) (fun (M2:nat)=> (polyno2122022170_C_nat V)))) of role axiom named fact_187_headn_Osimps_I2_J
% 0.69/0.86 A new axiom: (forall (V:nat), (((eq (nat->polyno1532895200ly_nat)) (polyno544860353dn_nat (polyno2122022170_C_nat V))) (fun (M2:nat)=> (polyno2122022170_C_nat V))))
% 0.69/0.86 FOF formula (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->polyno1532895200ly_nat)) (polyno544860353dn_nat ((polyno1415441627ul_nat V) Va))) (fun (M2:nat)=> ((polyno1415441627ul_nat V) Va)))) of role axiom named fact_188_headn_Osimps_I6_J
% 0.69/0.86 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->polyno1532895200ly_nat)) (polyno544860353dn_nat ((polyno1415441627ul_nat V) Va))) (fun (M2:nat)=> ((polyno1415441627ul_nat V) Va))))
% 0.69/0.86 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->polyno727731844poly_a)) (polyno567601229eadn_a ((polyno1491482291_Mul_a V) Va))) (fun (M2:nat)=> ((polyno1491482291_Mul_a V) Va)))) of role axiom named fact_189_headn_Osimps_I6_J
% 0.69/0.86 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->polyno727731844poly_a)) (polyno567601229eadn_a ((polyno1491482291_Mul_a V) Va))) (fun (M2:nat)=> ((polyno1491482291_Mul_a V) Va))))
% 0.69/0.86 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->polyno727731844poly_a)) (polyno567601229eadn_a ((polyno1623170614_Add_a V) Va))) (fun (M2:nat)=> ((polyno1623170614_Add_a V) Va)))) of role axiom named fact_190_headn_Osimps_I4_J
% 0.69/0.86 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->polyno727731844poly_a)) (polyno567601229eadn_a ((polyno1623170614_Add_a V) Va))) (fun (M2:nat)=> ((polyno1623170614_Add_a V) Va))))
% 0.69/0.86 FOF formula (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->polyno1532895200ly_nat)) (polyno544860353dn_nat ((polyno1222032024dd_nat V) Va))) (fun (M2:nat)=> ((polyno1222032024dd_nat V) Va)))) of role axiom named fact_191_headn_Osimps_I4_J
% 0.69/0.86 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->polyno1532895200ly_nat)) (polyno544860353dn_nat ((polyno1222032024dd_nat V) Va))) (fun (M2:nat)=> ((polyno1222032024dd_nat V) Va))))
% 0.69/0.86 FOF formula (forall (V:nat), (((eq (nat->polyno727731844poly_a)) (polyno567601229eadn_a (polyno2024845497ound_a V))) (fun (M2:nat)=> (polyno2024845497ound_a V)))) of role axiom named fact_192_headn_Osimps_I3_J
% 0.69/0.86 A new axiom: (forall (V:nat), (((eq (nat->polyno727731844poly_a)) (polyno567601229eadn_a (polyno2024845497ound_a V))) (fun (M2:nat)=> (polyno2024845497ound_a V))))
% 0.69/0.86 FOF formula (forall (V:nat), (((eq (nat->polyno1532895200ly_nat)) (polyno544860353dn_nat (polyno1999838549nd_nat V))) (fun (M2:nat)=> (polyno1999838549nd_nat V)))) of role axiom named fact_193_headn_Osimps_I3_J
% 0.69/0.86 A new axiom: (forall (V:nat), (((eq (nat->polyno1532895200ly_nat)) (polyno544860353dn_nat (polyno1999838549nd_nat V))) (fun (M2:nat)=> (polyno1999838549nd_nat V))))
% 0.69/0.86 FOF formula (forall (Bs2:list_a) (P:polyno727731844poly_a) (Q:polyno727731844poly_a), (((polyno896877631f_bs_a Bs2) P)->(((polyno896877631f_bs_a Bs2) Q)->((polyno896877631f_bs_a Bs2) ((polyno1418491367ysub_a P) Q))))) of role axiom named fact_194_wf__bs__polysub
% 0.69/0.86 A new axiom: (forall (Bs2:list_a) (P:polyno727731844poly_a) (Q:polyno727731844poly_a), (((polyno896877631f_bs_a Bs2) P)->(((polyno896877631f_bs_a Bs2) Q)->((polyno896877631f_bs_a Bs2) ((polyno1418491367ysub_a P) Q)))))
% 0.69/0.86 FOF formula (forall (P:polyno727731844poly_a) (Q:polyno727731844poly_a), ((polyno190918219poly_a P)->((polyno190918219poly_a Q)->(polyno190918219poly_a ((polyno1418491367ysub_a P) Q))))) of role axiom named fact_195_polysub__norm
% 0.69/0.86 A new axiom: (forall (P:polyno727731844poly_a) (Q:polyno727731844poly_a), ((polyno190918219poly_a P)->((polyno190918219poly_a Q)->(polyno190918219poly_a ((polyno1418491367ysub_a P) Q)))))
% 0.69/0.86 FOF formula (forall (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a), (((eq a) (polyno2115742616onst_a (((polyno1057396216e_CN_a C) N) P))) (polyno2115742616onst_a P))) of role axiom named fact_196_headconst_Osimps_I1_J
% 0.69/0.86 A new axiom: (forall (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a), (((eq a) (polyno2115742616onst_a (((polyno1057396216e_CN_a C) N) P))) (polyno2115742616onst_a P)))
% 0.69/0.86 FOF formula (forall (C:polyno1532895200ly_nat) (N:nat) (P:polyno1532895200ly_nat), (((eq nat) (polyno524777654st_nat (((polyno720942678CN_nat C) N) P))) (polyno524777654st_nat P))) of role axiom named fact_197_headconst_Osimps_I1_J
% 0.69/0.86 A new axiom: (forall (C:polyno1532895200ly_nat) (N:nat) (P:polyno1532895200ly_nat), (((eq nat) (polyno524777654st_nat (((polyno720942678CN_nat C) N) P))) (polyno524777654st_nat P)))
% 0.69/0.86 FOF formula (forall (N:a), (((eq a) (polyno2115742616onst_a (polyno439679028le_C_a N))) N)) of role axiom named fact_198_headconst_Osimps_I2_J
% 0.69/0.86 A new axiom: (forall (N:a), (((eq a) (polyno2115742616onst_a (polyno439679028le_C_a N))) N))
% 0.69/0.86 FOF formula (forall (N:nat), (((eq nat) (polyno524777654st_nat (polyno2122022170_C_nat N))) N)) of role axiom named fact_199_headconst_Osimps_I2_J
% 0.69/0.86 A new axiom: (forall (N:nat), (((eq nat) (polyno524777654st_nat (polyno2122022170_C_nat N))) N))
% 0.69/0.86 FOF formula (forall (N:nat) (T:polyno727731844poly_a), ((and ((((eq nat) N) zero_zero_nat)->(((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) (polyno2024845497ound_a N))) T))) ((not (((eq nat) N) zero_zero_nat))->(((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) (polyno2024845497ound_a N))) (polyno2024845497ound_a N))))) of role axiom named fact_200_polysubst0_Osimps_I2_J
% 0.69/0.87 A new axiom: (forall (N:nat) (T:polyno727731844poly_a), ((and ((((eq nat) N) zero_zero_nat)->(((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) (polyno2024845497ound_a N))) T))) ((not (((eq nat) N) zero_zero_nat))->(((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) (polyno2024845497ound_a N))) (polyno2024845497ound_a N)))))
% 0.69/0.87 FOF formula (forall (N:nat) (T:polyno1532895200ly_nat), ((and ((((eq nat) N) zero_zero_nat)->(((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) (polyno1999838549nd_nat N))) T))) ((not (((eq nat) N) zero_zero_nat))->(((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) (polyno1999838549nd_nat N))) (polyno1999838549nd_nat N))))) of role axiom named fact_201_polysubst0_Osimps_I2_J
% 0.69/0.87 A new axiom: (forall (N:nat) (T:polyno1532895200ly_nat), ((and ((((eq nat) N) zero_zero_nat)->(((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) (polyno1999838549nd_nat N))) T))) ((not (((eq nat) N) zero_zero_nat))->(((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) (polyno1999838549nd_nat N))) (polyno1999838549nd_nat N)))))
% 0.69/0.87 FOF formula (forall (P:polyno727731844poly_a) (N0:nat) (Q:polyno727731844poly_a) (N1:nat), (((polyno1372495879olyh_a P) N0)->(((polyno1372495879olyh_a Q) N1)->(((eq Prop) (((eq polyno727731844poly_a) ((polyno1418491367ysub_a P) Q)) (polyno439679028le_C_a zero_zero_a))) (((eq polyno727731844poly_a) P) Q))))) of role axiom named fact_202_polysub__0
% 0.69/0.87 A new axiom: (forall (P:polyno727731844poly_a) (N0:nat) (Q:polyno727731844poly_a) (N1:nat), (((polyno1372495879olyh_a P) N0)->(((polyno1372495879olyh_a Q) N1)->(((eq Prop) (((eq polyno727731844poly_a) ((polyno1418491367ysub_a P) Q)) (polyno439679028le_C_a zero_zero_a))) (((eq polyno727731844poly_a) P) Q)))))
% 0.69/0.87 FOF formula (forall (P:polyno1532895200ly_nat) (N:nat) (M:nat), (((polyno892049031yh_nat P) N)->((not (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat)))->(not (((eq polyno1532895200ly_nat) ((polyno544860353dn_nat P) M)) (polyno2122022170_C_nat zero_zero_nat)))))) of role axiom named fact_203_headnz
% 0.69/0.87 A new axiom: (forall (P:polyno1532895200ly_nat) (N:nat) (M:nat), (((polyno892049031yh_nat P) N)->((not (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat)))->(not (((eq polyno1532895200ly_nat) ((polyno544860353dn_nat P) M)) (polyno2122022170_C_nat zero_zero_nat))))))
% 0.69/0.87 FOF formula (forall (P:polyno727731844poly_a) (N:nat) (M:nat), (((polyno1372495879olyh_a P) N)->((not (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a)))->(not (((eq polyno727731844poly_a) ((polyno567601229eadn_a P) M)) (polyno439679028le_C_a zero_zero_a)))))) of role axiom named fact_204_headnz
% 0.69/0.87 A new axiom: (forall (P:polyno727731844poly_a) (N:nat) (M:nat), (((polyno1372495879olyh_a P) N)->((not (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a)))->(not (((eq polyno727731844poly_a) ((polyno567601229eadn_a P) M)) (polyno439679028le_C_a zero_zero_a))))))
% 0.69/0.87 FOF formula (forall (C:polyno1532895200ly_nat) (N:nat) (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat (((polyno720942678CN_nat C) N) P)) N0)->(((eq nat) (polyno220183259ee_nat C)) zero_zero_nat))) of role axiom named fact_205_degree__npolyhCN
% 0.69/0.87 A new axiom: (forall (C:polyno1532895200ly_nat) (N:nat) (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat (((polyno720942678CN_nat C) N) P)) N0)->(((eq nat) (polyno220183259ee_nat C)) zero_zero_nat)))
% 0.69/0.87 FOF formula (forall (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a (((polyno1057396216e_CN_a C) N) P)) N0)->(((eq nat) (polyno578545843gree_a C)) zero_zero_nat))) of role axiom named fact_206_degree__npolyhCN
% 0.69/0.87 A new axiom: (forall (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a (((polyno1057396216e_CN_a C) N) P)) N0)->(((eq nat) (polyno578545843gree_a C)) zero_zero_nat)))
% 0.69/0.87 FOF formula (forall (V:nat), (((eq polyno727731844poly_a) (polyno212464073eriv_a (polyno2024845497ound_a V))) (polyno439679028le_C_a zero_zero_a))) of role axiom named fact_207_poly__deriv_Osimps_I3_J
% 0.69/0.88 A new axiom: (forall (V:nat), (((eq polyno727731844poly_a) (polyno212464073eriv_a (polyno2024845497ound_a V))) (polyno439679028le_C_a zero_zero_a)))
% 0.69/0.88 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno212464073eriv_a ((polyno1623170614_Add_a V) Va))) (polyno439679028le_C_a zero_zero_a))) of role axiom named fact_208_poly__deriv_Osimps_I4_J
% 0.69/0.88 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno212464073eriv_a ((polyno1623170614_Add_a V) Va))) (polyno439679028le_C_a zero_zero_a)))
% 0.69/0.88 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno212464073eriv_a ((polyno1491482291_Mul_a V) Va))) (polyno439679028le_C_a zero_zero_a))) of role axiom named fact_209_poly__deriv_Osimps_I6_J
% 0.69/0.88 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno212464073eriv_a ((polyno1491482291_Mul_a V) Va))) (polyno439679028le_C_a zero_zero_a)))
% 0.69/0.88 FOF formula (forall (V:a), (((eq nat) (polyno578545843gree_a (polyno439679028le_C_a V))) zero_zero_nat)) of role axiom named fact_210_degree_Osimps_I2_J
% 0.69/0.88 A new axiom: (forall (V:a), (((eq nat) (polyno578545843gree_a (polyno439679028le_C_a V))) zero_zero_nat))
% 0.69/0.88 FOF formula (forall (V:nat), (((eq nat) (polyno220183259ee_nat (polyno2122022170_C_nat V))) zero_zero_nat)) of role axiom named fact_211_degree_Osimps_I2_J
% 0.69/0.88 A new axiom: (forall (V:nat), (((eq nat) (polyno220183259ee_nat (polyno2122022170_C_nat V))) zero_zero_nat))
% 0.69/0.88 FOF formula (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq nat) (polyno220183259ee_nat ((polyno1415441627ul_nat V) Va))) zero_zero_nat)) of role axiom named fact_212_degree_Osimps_I6_J
% 0.69/0.88 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq nat) (polyno220183259ee_nat ((polyno1415441627ul_nat V) Va))) zero_zero_nat))
% 0.69/0.88 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq nat) (polyno578545843gree_a ((polyno1491482291_Mul_a V) Va))) zero_zero_nat)) of role axiom named fact_213_degree_Osimps_I6_J
% 0.69/0.88 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq nat) (polyno578545843gree_a ((polyno1491482291_Mul_a V) Va))) zero_zero_nat))
% 0.69/0.88 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq nat) (polyno578545843gree_a ((polyno1623170614_Add_a V) Va))) zero_zero_nat)) of role axiom named fact_214_degree_Osimps_I4_J
% 0.69/0.88 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq nat) (polyno578545843gree_a ((polyno1623170614_Add_a V) Va))) zero_zero_nat))
% 0.69/0.88 FOF formula (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq nat) (polyno220183259ee_nat ((polyno1222032024dd_nat V) Va))) zero_zero_nat)) of role axiom named fact_215_degree_Osimps_I4_J
% 0.69/0.88 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq nat) (polyno220183259ee_nat ((polyno1222032024dd_nat V) Va))) zero_zero_nat))
% 0.69/0.88 FOF formula (forall (V:nat), (((eq nat) (polyno578545843gree_a (polyno2024845497ound_a V))) zero_zero_nat)) of role axiom named fact_216_degree_Osimps_I3_J
% 0.69/0.88 A new axiom: (forall (V:nat), (((eq nat) (polyno578545843gree_a (polyno2024845497ound_a V))) zero_zero_nat))
% 0.69/0.88 FOF formula (forall (V:nat), (((eq nat) (polyno220183259ee_nat (polyno1999838549nd_nat V))) zero_zero_nat)) of role axiom named fact_217_degree_Osimps_I3_J
% 0.69/0.88 A new axiom: (forall (V:nat), (((eq nat) (polyno220183259ee_nat (polyno1999838549nd_nat V))) zero_zero_nat))
% 0.69/0.88 FOF formula (forall (V:a), (((eq polyno727731844poly_a) (polyno212464073eriv_a (polyno439679028le_C_a V))) (polyno439679028le_C_a zero_zero_a))) of role axiom named fact_218_poly__deriv_Osimps_I2_J
% 0.69/0.88 A new axiom: (forall (V:a), (((eq polyno727731844poly_a) (polyno212464073eriv_a (polyno439679028le_C_a V))) (polyno439679028le_C_a zero_zero_a)))
% 0.69/0.88 FOF formula (forall (C:polyno727731844poly_a) (P:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno212464073eriv_a (((polyno1057396216e_CN_a C) zero_zero_nat) P))) ((polyno1006823949_aux_a one_one_a) P))) of role axiom named fact_219_poly__deriv_Osimps_I1_J
% 0.69/0.89 A new axiom: (forall (C:polyno727731844poly_a) (P:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno212464073eriv_a (((polyno1057396216e_CN_a C) zero_zero_nat) P))) ((polyno1006823949_aux_a one_one_a) P)))
% 0.69/0.89 FOF formula (forall (Bs2:list_a) (N:nat) (P:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) (((compow1114216044poly_a N) polyno784948432ift1_a) P))) ((polyno422358502poly_a Bs2) ((polyno1934269411ymul_a (((compow1114216044poly_a N) polyno784948432ift1_a) (polyno439679028le_C_a one_one_a))) P)))) of role axiom named fact_220_funpow__shift1__1
% 0.69/0.89 A new axiom: (forall (Bs2:list_a) (N:nat) (P:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) (((compow1114216044poly_a N) polyno784948432ift1_a) P))) ((polyno422358502poly_a Bs2) ((polyno1934269411ymul_a (((compow1114216044poly_a N) polyno784948432ift1_a) (polyno439679028le_C_a one_one_a))) P))))
% 0.69/0.89 FOF formula (forall (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat P) N0)->(((eq Prop) (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat P)) (polyno2122022170_C_nat zero_zero_nat))) (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat))))) of role axiom named fact_221_head__nz
% 0.69/0.89 A new axiom: (forall (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat P) N0)->(((eq Prop) (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat P)) (polyno2122022170_C_nat zero_zero_nat))) (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat)))))
% 0.69/0.89 FOF formula (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq Prop) (((eq polyno727731844poly_a) (polyno1884029055head_a P)) (polyno439679028le_C_a zero_zero_a))) (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a))))) of role axiom named fact_222_head__nz
% 0.69/0.89 A new axiom: (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq Prop) (((eq polyno727731844poly_a) (polyno1884029055head_a P)) (polyno439679028le_C_a zero_zero_a))) (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a)))))
% 0.69/0.89 FOF formula (forall (C:polyno1532895200ly_nat) (N:nat) (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat (((polyno720942678CN_nat C) N) P)) N0)->(((eq nat) ((polyno1779722485en_nat C) N)) zero_zero_nat))) of role axiom named fact_223_degreen__npolyhCN
% 0.69/0.89 A new axiom: (forall (C:polyno1532895200ly_nat) (N:nat) (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat (((polyno720942678CN_nat C) N) P)) N0)->(((eq nat) ((polyno1779722485en_nat C) N)) zero_zero_nat)))
% 0.69/0.89 FOF formula (forall (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a (((polyno1057396216e_CN_a C) N) P)) N0)->(((eq nat) ((polyno1674775833reen_a C) N)) zero_zero_nat))) of role axiom named fact_224_degreen__npolyhCN
% 0.69/0.89 A new axiom: (forall (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a (((polyno1057396216e_CN_a C) N) P)) N0)->(((eq nat) ((polyno1674775833reen_a C) N)) zero_zero_nat)))
% 0.69/0.89 FOF formula (forall (F:(polyno727731844poly_a->polyno727731844poly_a)) (X:polyno727731844poly_a), (((eq polyno727731844poly_a) (((compow1114216044poly_a zero_zero_nat) F) X)) X)) of role axiom named fact_225_funpow__0
% 0.69/0.89 A new axiom: (forall (F:(polyno727731844poly_a->polyno727731844poly_a)) (X:polyno727731844poly_a), (((eq polyno727731844poly_a) (((compow1114216044poly_a zero_zero_nat) F) X)) X))
% 0.69/0.89 FOF formula (forall (F:(polyno1532895200ly_nat->polyno1532895200ly_nat)) (X:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (((compow808008746ly_nat zero_zero_nat) F) X)) X)) of role axiom named fact_226_funpow__0
% 0.69/0.89 A new axiom: (forall (F:(polyno1532895200ly_nat->polyno1532895200ly_nat)) (X:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (((compow808008746ly_nat zero_zero_nat) F) X)) X))
% 0.69/0.89 FOF formula (forall (F:(polyno727731844poly_a->polyno727731844poly_a)) (N:nat) (X:polyno727731844poly_a), (((eq polyno727731844poly_a) (F (((compow1114216044poly_a N) F) X))) (((compow1114216044poly_a N) F) (F X)))) of role axiom named fact_227_funpow__swap1
% 0.69/0.89 A new axiom: (forall (F:(polyno727731844poly_a->polyno727731844poly_a)) (N:nat) (X:polyno727731844poly_a), (((eq polyno727731844poly_a) (F (((compow1114216044poly_a N) F) X))) (((compow1114216044poly_a N) F) (F X))))
% 0.69/0.89 FOF formula (forall (F:(polyno1532895200ly_nat->polyno1532895200ly_nat)) (N:nat) (X:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (F (((compow808008746ly_nat N) F) X))) (((compow808008746ly_nat N) F) (F X)))) of role axiom named fact_228_funpow__swap1
% 0.69/0.89 A new axiom: (forall (F:(polyno1532895200ly_nat->polyno1532895200ly_nat)) (N:nat) (X:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (F (((compow808008746ly_nat N) F) X))) (((compow808008746ly_nat N) F) (F X))))
% 0.69/0.89 FOF formula (forall (N:nat) (F:(polyno1532895200ly_nat->polyno1532895200ly_nat)) (P:polyno1532895200ly_nat) (K2:nat), ((forall (P4:polyno1532895200ly_nat), (((polyno892049031yh_nat P4) N)->((polyno892049031yh_nat (F P4)) N)))->(((polyno892049031yh_nat P) N)->((polyno892049031yh_nat (((compow808008746ly_nat K2) F) P)) N)))) of role axiom named fact_229_funpow__isnpolyh
% 0.69/0.89 A new axiom: (forall (N:nat) (F:(polyno1532895200ly_nat->polyno1532895200ly_nat)) (P:polyno1532895200ly_nat) (K2:nat), ((forall (P4:polyno1532895200ly_nat), (((polyno892049031yh_nat P4) N)->((polyno892049031yh_nat (F P4)) N)))->(((polyno892049031yh_nat P) N)->((polyno892049031yh_nat (((compow808008746ly_nat K2) F) P)) N))))
% 0.69/0.89 FOF formula (forall (N:nat) (F:(polyno727731844poly_a->polyno727731844poly_a)) (P:polyno727731844poly_a) (K2:nat), ((forall (P4:polyno727731844poly_a), (((polyno1372495879olyh_a P4) N)->((polyno1372495879olyh_a (F P4)) N)))->(((polyno1372495879olyh_a P) N)->((polyno1372495879olyh_a (((compow1114216044poly_a K2) F) P)) N)))) of role axiom named fact_230_funpow__isnpolyh
% 0.69/0.89 A new axiom: (forall (N:nat) (F:(polyno727731844poly_a->polyno727731844poly_a)) (P:polyno727731844poly_a) (K2:nat), ((forall (P4:polyno727731844poly_a), (((polyno1372495879olyh_a P4) N)->((polyno1372495879olyh_a (F P4)) N)))->(((polyno1372495879olyh_a P) N)->((polyno1372495879olyh_a (((compow1114216044poly_a K2) F) P)) N))))
% 0.69/0.89 FOF formula (forall (N:nat) (M:nat) (F:(polyno727731844poly_a->polyno727731844poly_a)), (((eq (polyno727731844poly_a->polyno727731844poly_a)) ((compow1114216044poly_a N) ((compow1114216044poly_a M) F))) ((compow1114216044poly_a ((times_times_nat M) N)) F))) of role axiom named fact_231_funpow__mult
% 0.69/0.89 A new axiom: (forall (N:nat) (M:nat) (F:(polyno727731844poly_a->polyno727731844poly_a)), (((eq (polyno727731844poly_a->polyno727731844poly_a)) ((compow1114216044poly_a N) ((compow1114216044poly_a M) F))) ((compow1114216044poly_a ((times_times_nat M) N)) F)))
% 0.69/0.89 FOF formula (forall (N:nat) (M:nat) (F:(polyno1532895200ly_nat->polyno1532895200ly_nat)), (((eq (polyno1532895200ly_nat->polyno1532895200ly_nat)) ((compow808008746ly_nat N) ((compow808008746ly_nat M) F))) ((compow808008746ly_nat ((times_times_nat M) N)) F))) of role axiom named fact_232_funpow__mult
% 0.69/0.89 A new axiom: (forall (N:nat) (M:nat) (F:(polyno1532895200ly_nat->polyno1532895200ly_nat)), (((eq (polyno1532895200ly_nat->polyno1532895200ly_nat)) ((compow808008746ly_nat N) ((compow808008746ly_nat M) F))) ((compow808008746ly_nat ((times_times_nat M) N)) F)))
% 0.69/0.89 FOF formula (forall (V:a), (((eq polyno727731844poly_a) (polyno1884029055head_a (polyno439679028le_C_a V))) (polyno439679028le_C_a V))) of role axiom named fact_233_head_Osimps_I2_J
% 0.69/0.89 A new axiom: (forall (V:a), (((eq polyno727731844poly_a) (polyno1884029055head_a (polyno439679028le_C_a V))) (polyno439679028le_C_a V)))
% 0.69/0.89 FOF formula (forall (V:nat), (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat (polyno2122022170_C_nat V))) (polyno2122022170_C_nat V))) of role axiom named fact_234_head_Osimps_I2_J
% 0.69/0.89 A new axiom: (forall (V:nat), (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat (polyno2122022170_C_nat V))) (polyno2122022170_C_nat V)))
% 0.69/0.89 FOF formula (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat ((polyno1415441627ul_nat V) Va))) ((polyno1415441627ul_nat V) Va))) of role axiom named fact_235_head_Osimps_I6_J
% 0.69/0.90 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat ((polyno1415441627ul_nat V) Va))) ((polyno1415441627ul_nat V) Va)))
% 0.69/0.90 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1884029055head_a ((polyno1491482291_Mul_a V) Va))) ((polyno1491482291_Mul_a V) Va))) of role axiom named fact_236_head_Osimps_I6_J
% 0.69/0.90 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1884029055head_a ((polyno1491482291_Mul_a V) Va))) ((polyno1491482291_Mul_a V) Va)))
% 0.69/0.90 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1884029055head_a ((polyno1623170614_Add_a V) Va))) ((polyno1623170614_Add_a V) Va))) of role axiom named fact_237_head_Osimps_I4_J
% 0.69/0.90 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1884029055head_a ((polyno1623170614_Add_a V) Va))) ((polyno1623170614_Add_a V) Va)))
% 0.69/0.90 FOF formula (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat ((polyno1222032024dd_nat V) Va))) ((polyno1222032024dd_nat V) Va))) of role axiom named fact_238_head_Osimps_I4_J
% 0.69/0.90 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat ((polyno1222032024dd_nat V) Va))) ((polyno1222032024dd_nat V) Va)))
% 0.69/0.90 FOF formula (forall (V:nat), (((eq polyno727731844poly_a) (polyno1884029055head_a (polyno2024845497ound_a V))) (polyno2024845497ound_a V))) of role axiom named fact_239_head_Osimps_I3_J
% 0.69/0.90 A new axiom: (forall (V:nat), (((eq polyno727731844poly_a) (polyno1884029055head_a (polyno2024845497ound_a V))) (polyno2024845497ound_a V)))
% 0.69/0.90 FOF formula (forall (V:nat), (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat (polyno1999838549nd_nat V))) (polyno1999838549nd_nat V))) of role axiom named fact_240_head_Osimps_I3_J
% 0.69/0.90 A new axiom: (forall (V:nat), (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat (polyno1999838549nd_nat V))) (polyno1999838549nd_nat V)))
% 0.69/0.90 FOF formula (forall (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat P) N0)->((polyno892049031yh_nat (polyno1952548879ad_nat P)) N0))) of role axiom named fact_241_head__isnpolyh
% 0.69/0.90 A new axiom: (forall (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat P) N0)->((polyno892049031yh_nat (polyno1952548879ad_nat P)) N0)))
% 0.69/0.90 FOF formula (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->((polyno1372495879olyh_a (polyno1884029055head_a P)) N0))) of role axiom named fact_242_head__isnpolyh
% 0.69/0.90 A new axiom: (forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->((polyno1372495879olyh_a (polyno1884029055head_a P)) N0)))
% 0.69/0.90 FOF formula (forall (V:a), (((eq (nat->nat)) (polyno1674775833reen_a (polyno439679028le_C_a V))) (fun (M2:nat)=> zero_zero_nat))) of role axiom named fact_243_degreen_Osimps_I2_J
% 0.69/0.90 A new axiom: (forall (V:a), (((eq (nat->nat)) (polyno1674775833reen_a (polyno439679028le_C_a V))) (fun (M2:nat)=> zero_zero_nat)))
% 0.69/0.90 FOF formula (forall (V:nat), (((eq (nat->nat)) (polyno1779722485en_nat (polyno2122022170_C_nat V))) (fun (M2:nat)=> zero_zero_nat))) of role axiom named fact_244_degreen_Osimps_I2_J
% 0.69/0.90 A new axiom: (forall (V:nat), (((eq (nat->nat)) (polyno1779722485en_nat (polyno2122022170_C_nat V))) (fun (M2:nat)=> zero_zero_nat)))
% 0.69/0.90 FOF formula (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->nat)) (polyno1779722485en_nat ((polyno1415441627ul_nat V) Va))) (fun (M2:nat)=> zero_zero_nat))) of role axiom named fact_245_degreen_Osimps_I6_J
% 0.69/0.90 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->nat)) (polyno1779722485en_nat ((polyno1415441627ul_nat V) Va))) (fun (M2:nat)=> zero_zero_nat)))
% 0.69/0.91 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->nat)) (polyno1674775833reen_a ((polyno1491482291_Mul_a V) Va))) (fun (M2:nat)=> zero_zero_nat))) of role axiom named fact_246_degreen_Osimps_I6_J
% 0.69/0.91 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->nat)) (polyno1674775833reen_a ((polyno1491482291_Mul_a V) Va))) (fun (M2:nat)=> zero_zero_nat)))
% 0.69/0.91 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->nat)) (polyno1674775833reen_a ((polyno1623170614_Add_a V) Va))) (fun (M2:nat)=> zero_zero_nat))) of role axiom named fact_247_degreen_Osimps_I4_J
% 0.69/0.91 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->nat)) (polyno1674775833reen_a ((polyno1623170614_Add_a V) Va))) (fun (M2:nat)=> zero_zero_nat)))
% 0.69/0.91 FOF formula (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->nat)) (polyno1779722485en_nat ((polyno1222032024dd_nat V) Va))) (fun (M2:nat)=> zero_zero_nat))) of role axiom named fact_248_degreen_Osimps_I4_J
% 0.69/0.91 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->nat)) (polyno1779722485en_nat ((polyno1222032024dd_nat V) Va))) (fun (M2:nat)=> zero_zero_nat)))
% 0.69/0.91 FOF formula (forall (V:nat), (((eq (nat->nat)) (polyno1674775833reen_a (polyno2024845497ound_a V))) (fun (M2:nat)=> zero_zero_nat))) of role axiom named fact_249_degreen_Osimps_I3_J
% 0.69/0.91 A new axiom: (forall (V:nat), (((eq (nat->nat)) (polyno1674775833reen_a (polyno2024845497ound_a V))) (fun (M2:nat)=> zero_zero_nat)))
% 0.69/0.91 FOF formula (forall (V:nat), (((eq (nat->nat)) (polyno1779722485en_nat (polyno1999838549nd_nat V))) (fun (M2:nat)=> zero_zero_nat))) of role axiom named fact_250_degreen_Osimps_I3_J
% 0.69/0.91 A new axiom: (forall (V:nat), (((eq (nat->nat)) (polyno1779722485en_nat (polyno1999838549nd_nat V))) (fun (M2:nat)=> zero_zero_nat)))
% 0.69/0.91 FOF formula (forall (C:polyno727731844poly_a) (P:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1884029055head_a (((polyno1057396216e_CN_a C) zero_zero_nat) P))) (polyno1884029055head_a P))) of role axiom named fact_251_head_Osimps_I1_J
% 0.69/0.91 A new axiom: (forall (C:polyno727731844poly_a) (P:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1884029055head_a (((polyno1057396216e_CN_a C) zero_zero_nat) P))) (polyno1884029055head_a P)))
% 0.69/0.91 FOF formula (forall (C:polyno1532895200ly_nat) (P:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat (((polyno720942678CN_nat C) zero_zero_nat) P))) (polyno1952548879ad_nat P))) of role axiom named fact_252_head_Osimps_I1_J
% 0.69/0.91 A new axiom: (forall (C:polyno1532895200ly_nat) (P:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat (((polyno720942678CN_nat C) zero_zero_nat) P))) (polyno1952548879ad_nat P)))
% 0.69/0.91 FOF formula (((eq (polyno727731844poly_a->polyno727731844poly_a)) polyno1884029055head_a) (fun (P2:polyno727731844poly_a)=> ((polyno567601229eadn_a P2) zero_zero_nat))) of role axiom named fact_253_head__eq__headn0
% 0.69/0.91 A new axiom: (((eq (polyno727731844poly_a->polyno727731844poly_a)) polyno1884029055head_a) (fun (P2:polyno727731844poly_a)=> ((polyno567601229eadn_a P2) zero_zero_nat)))
% 0.69/0.91 FOF formula (((eq (polyno1532895200ly_nat->polyno1532895200ly_nat)) polyno1952548879ad_nat) (fun (P2:polyno1532895200ly_nat)=> ((polyno544860353dn_nat P2) zero_zero_nat))) of role axiom named fact_254_head__eq__headn0
% 0.69/0.91 A new axiom: (((eq (polyno1532895200ly_nat->polyno1532895200ly_nat)) polyno1952548879ad_nat) (fun (P2:polyno1532895200ly_nat)=> ((polyno544860353dn_nat P2) zero_zero_nat)))
% 0.69/0.91 FOF formula (forall (N:a) (V:a), (((eq polyno727731844poly_a) ((polyno1006823949_aux_a N) (polyno439679028le_C_a V))) ((polyno562434098cmul_a N) (polyno439679028le_C_a V)))) of role axiom named fact_255_poly__deriv__aux_Osimps_I2_J
% 0.69/0.91 A new axiom: (forall (N:a) (V:a), (((eq polyno727731844poly_a) ((polyno1006823949_aux_a N) (polyno439679028le_C_a V))) ((polyno562434098cmul_a N) (polyno439679028le_C_a V))))
% 0.69/0.91 FOF formula (forall (N:a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1006823949_aux_a N) ((polyno1491482291_Mul_a V) Va))) ((polyno562434098cmul_a N) ((polyno1491482291_Mul_a V) Va)))) of role axiom named fact_256_poly__deriv__aux_Osimps_I6_J
% 0.69/0.92 A new axiom: (forall (N:a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1006823949_aux_a N) ((polyno1491482291_Mul_a V) Va))) ((polyno562434098cmul_a N) ((polyno1491482291_Mul_a V) Va))))
% 0.69/0.92 FOF formula (forall (P:polyno1532895200ly_nat) (N:nat), ((polyno1013235523ly_nat P)->((not (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat)))->(polyno1013235523ly_nat (((compow808008746ly_nat N) polyno1964927358t1_nat) P))))) of role axiom named fact_257_funpow__shift1__isnpoly
% 0.69/0.92 A new axiom: (forall (P:polyno1532895200ly_nat) (N:nat), ((polyno1013235523ly_nat P)->((not (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat)))->(polyno1013235523ly_nat (((compow808008746ly_nat N) polyno1964927358t1_nat) P)))))
% 0.69/0.92 FOF formula (forall (P:polyno727731844poly_a) (N:nat), ((polyno190918219poly_a P)->((not (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a)))->(polyno190918219poly_a (((compow1114216044poly_a N) polyno784948432ift1_a) P))))) of role axiom named fact_258_funpow__shift1__isnpoly
% 0.69/0.92 A new axiom: (forall (P:polyno727731844poly_a) (N:nat), ((polyno190918219poly_a P)->((not (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a)))->(polyno190918219poly_a (((compow1114216044poly_a N) polyno784948432ift1_a) P)))))
% 0.69/0.92 FOF formula (forall (Bs2:list_a) (N:nat) (P:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) (((compow1114216044poly_a N) polyno784948432ift1_a) P))) ((polyno422358502poly_a Bs2) ((polyno1491482291_Mul_a ((polyno1538138524e_Pw_a (polyno2024845497ound_a zero_zero_nat)) N)) P)))) of role axiom named fact_259_funpow__shift1
% 0.69/0.92 A new axiom: (forall (Bs2:list_a) (N:nat) (P:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) (((compow1114216044poly_a N) polyno784948432ift1_a) P))) ((polyno422358502poly_a Bs2) ((polyno1491482291_Mul_a ((polyno1538138524e_Pw_a (polyno2024845497ound_a zero_zero_nat)) N)) P))))
% 0.69/0.92 FOF formula (forall (A:nat) (B:nat) (C:nat), (((eq Prop) (((eq nat) ((plus_plus_nat A) B)) ((plus_plus_nat A) C))) (((eq nat) B) C))) of role axiom named fact_260_add__left__cancel
% 0.69/0.92 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((eq Prop) (((eq nat) ((plus_plus_nat A) B)) ((plus_plus_nat A) C))) (((eq nat) B) C)))
% 0.69/0.92 FOF formula (forall (B:nat) (A:nat) (C:nat), (((eq Prop) (((eq nat) ((plus_plus_nat B) A)) ((plus_plus_nat C) A))) (((eq nat) B) C))) of role axiom named fact_261_add__right__cancel
% 0.69/0.92 A new axiom: (forall (B:nat) (A:nat) (C:nat), (((eq Prop) (((eq nat) ((plus_plus_nat B) A)) ((plus_plus_nat C) A))) (((eq nat) B) C)))
% 0.69/0.92 FOF formula (forall (M:nat) (N:nat), (((eq Prop) (((eq nat) ((plus_plus_nat M) N)) zero_zero_nat)) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_262_add__is__0
% 0.69/0.92 A new axiom: (forall (M:nat) (N:nat), (((eq Prop) (((eq nat) ((plus_plus_nat M) N)) zero_zero_nat)) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat))))
% 0.69/0.92 FOF formula (forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M)) of role axiom named fact_263_Nat_Oadd__0__right
% 0.69/0.92 A new axiom: (forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M))
% 0.69/0.92 FOF formula (forall (X:nat) (Y:nat), (((eq Prop) (((eq nat) zero_zero_nat) ((plus_plus_nat X) Y))) ((and (((eq nat) X) zero_zero_nat)) (((eq nat) Y) zero_zero_nat)))) of role axiom named fact_264_zero__eq__add__iff__both__eq__0
% 0.69/0.92 A new axiom: (forall (X:nat) (Y:nat), (((eq Prop) (((eq nat) zero_zero_nat) ((plus_plus_nat X) Y))) ((and (((eq nat) X) zero_zero_nat)) (((eq nat) Y) zero_zero_nat))))
% 0.69/0.92 FOF formula (forall (X:nat) (Y:nat), (((eq Prop) (((eq nat) ((plus_plus_nat X) Y)) zero_zero_nat)) ((and (((eq nat) X) zero_zero_nat)) (((eq nat) Y) zero_zero_nat)))) of role axiom named fact_265_add__eq__0__iff__both__eq__0
% 0.69/0.92 A new axiom: (forall (X:nat) (Y:nat), (((eq Prop) (((eq nat) ((plus_plus_nat X) Y)) zero_zero_nat)) ((and (((eq nat) X) zero_zero_nat)) (((eq nat) Y) zero_zero_nat))))
% 0.69/0.93 FOF formula (forall (A:nat) (B:nat), (((eq Prop) (((eq nat) A) ((plus_plus_nat A) B))) (((eq nat) B) zero_zero_nat))) of role axiom named fact_266_add__cancel__right__right
% 0.69/0.93 A new axiom: (forall (A:nat) (B:nat), (((eq Prop) (((eq nat) A) ((plus_plus_nat A) B))) (((eq nat) B) zero_zero_nat)))
% 0.69/0.93 FOF formula (forall (A:nat) (B:nat), (((eq Prop) (((eq nat) A) ((plus_plus_nat B) A))) (((eq nat) B) zero_zero_nat))) of role axiom named fact_267_add__cancel__right__left
% 0.69/0.93 A new axiom: (forall (A:nat) (B:nat), (((eq Prop) (((eq nat) A) ((plus_plus_nat B) A))) (((eq nat) B) zero_zero_nat)))
% 0.69/0.93 FOF formula (forall (A:nat) (B:nat), (((eq Prop) (((eq nat) ((plus_plus_nat A) B)) A)) (((eq nat) B) zero_zero_nat))) of role axiom named fact_268_add__cancel__left__right
% 0.69/0.93 A new axiom: (forall (A:nat) (B:nat), (((eq Prop) (((eq nat) ((plus_plus_nat A) B)) A)) (((eq nat) B) zero_zero_nat)))
% 0.69/0.93 FOF formula (forall (B:nat) (A:nat), (((eq Prop) (((eq nat) ((plus_plus_nat B) A)) A)) (((eq nat) B) zero_zero_nat))) of role axiom named fact_269_add__cancel__left__left
% 0.69/0.93 A new axiom: (forall (B:nat) (A:nat), (((eq Prop) (((eq nat) ((plus_plus_nat B) A)) A)) (((eq nat) B) zero_zero_nat)))
% 0.69/0.93 FOF formula (forall (A:nat), (((eq nat) ((plus_plus_nat A) zero_zero_nat)) A)) of role axiom named fact_270_add_Oright__neutral
% 0.69/0.93 A new axiom: (forall (A:nat), (((eq nat) ((plus_plus_nat A) zero_zero_nat)) A))
% 0.69/0.93 FOF formula (forall (A:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A)) A)) of role axiom named fact_271_add_Oleft__neutral
% 0.69/0.93 A new axiom: (forall (A:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A)) A))
% 0.69/0.93 FOF formula (forall (_TPTP_I:nat) (U:nat) (J:nat) (K2:nat), (((eq nat) ((plus_plus_nat ((times_times_nat _TPTP_I) U)) ((plus_plus_nat ((times_times_nat J) U)) K2))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat _TPTP_I) J)) U)) K2))) of role axiom named fact_272_left__add__mult__distrib
% 0.69/0.93 A new axiom: (forall (_TPTP_I:nat) (U:nat) (J:nat) (K2:nat), (((eq nat) ((plus_plus_nat ((times_times_nat _TPTP_I) U)) ((plus_plus_nat ((times_times_nat J) U)) K2))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat _TPTP_I) J)) U)) K2)))
% 0.69/0.93 FOF formula (forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N)) of role axiom named fact_273_plus__nat_Oadd__0
% 0.69/0.93 A new axiom: (forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N))
% 0.69/0.93 FOF formula (forall (M:nat) (N:nat), ((((eq nat) ((plus_plus_nat M) N)) M)->(((eq nat) N) zero_zero_nat))) of role axiom named fact_274_add__eq__self__zero
% 0.69/0.93 A new axiom: (forall (M:nat) (N:nat), ((((eq nat) ((plus_plus_nat M) N)) M)->(((eq nat) N) zero_zero_nat)))
% 0.69/0.93 FOF formula (forall (V:polyno727731844poly_a) (Va:nat), (((eq (nat->Prop)) (polyno1372495879olyh_a ((polyno1538138524e_Pw_a V) Va))) (fun (K:nat)=> False))) of role axiom named fact_275_isnpolyh_Osimps_I8_J
% 0.69/0.93 A new axiom: (forall (V:polyno727731844poly_a) (Va:nat), (((eq (nat->Prop)) (polyno1372495879olyh_a ((polyno1538138524e_Pw_a V) Va))) (fun (K:nat)=> False)))
% 0.69/0.93 FOF formula (forall (K2:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K2) ((plus_plus_nat M) N))) ((plus_plus_nat ((times_times_nat K2) M)) ((times_times_nat K2) N)))) of role axiom named fact_276_add__mult__distrib2
% 0.69/0.93 A new axiom: (forall (K2:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K2) ((plus_plus_nat M) N))) ((plus_plus_nat ((times_times_nat K2) M)) ((times_times_nat K2) N))))
% 0.69/0.93 FOF formula (forall (M:nat) (N:nat) (K2:nat), (((eq nat) ((times_times_nat ((plus_plus_nat M) N)) K2)) ((plus_plus_nat ((times_times_nat M) K2)) ((times_times_nat N) K2)))) of role axiom named fact_277_add__mult__distrib
% 0.69/0.93 A new axiom: (forall (M:nat) (N:nat) (K2:nat), (((eq nat) ((times_times_nat ((plus_plus_nat M) N)) K2)) ((plus_plus_nat ((times_times_nat M) K2)) ((times_times_nat N) K2))))
% 0.69/0.93 FOF formula (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A) B)) C)) ((plus_plus_nat A) ((plus_plus_nat B) C)))) of role axiom named fact_278_ab__semigroup__add__class_Oadd__ac_I1_J
% 0.69/0.93 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A) B)) C)) ((plus_plus_nat A) ((plus_plus_nat B) C))))
% 0.78/0.94 FOF formula (forall (_TPTP_I:nat) (J:nat) (K2:nat) (L:nat), (((and (((eq nat) _TPTP_I) J)) (((eq nat) K2) L))->(((eq nat) ((plus_plus_nat _TPTP_I) K2)) ((plus_plus_nat J) L)))) of role axiom named fact_279_add__mono__thms__linordered__semiring_I4_J
% 0.78/0.94 A new axiom: (forall (_TPTP_I:nat) (J:nat) (K2:nat) (L:nat), (((and (((eq nat) _TPTP_I) J)) (((eq nat) K2) L))->(((eq nat) ((plus_plus_nat _TPTP_I) K2)) ((plus_plus_nat J) L))))
% 0.78/0.94 FOF formula (forall (A3:nat) (K2:nat) (A:nat) (B:nat), ((((eq nat) A3) ((plus_plus_nat K2) A))->(((eq nat) ((plus_plus_nat A3) B)) ((plus_plus_nat K2) ((plus_plus_nat A) B))))) of role axiom named fact_280_group__cancel_Oadd1
% 0.78/0.94 A new axiom: (forall (A3:nat) (K2:nat) (A:nat) (B:nat), ((((eq nat) A3) ((plus_plus_nat K2) A))->(((eq nat) ((plus_plus_nat A3) B)) ((plus_plus_nat K2) ((plus_plus_nat A) B)))))
% 0.78/0.94 FOF formula (forall (B3:nat) (K2:nat) (B:nat) (A:nat), ((((eq nat) B3) ((plus_plus_nat K2) B))->(((eq nat) ((plus_plus_nat A) B3)) ((plus_plus_nat K2) ((plus_plus_nat A) B))))) of role axiom named fact_281_group__cancel_Oadd2
% 0.78/0.94 A new axiom: (forall (B3:nat) (K2:nat) (B:nat) (A:nat), ((((eq nat) B3) ((plus_plus_nat K2) B))->(((eq nat) ((plus_plus_nat A) B3)) ((plus_plus_nat K2) ((plus_plus_nat A) B)))))
% 0.78/0.94 FOF formula (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A) B)) C)) ((plus_plus_nat A) ((plus_plus_nat B) C)))) of role axiom named fact_282_add_Oassoc
% 0.78/0.94 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A) B)) C)) ((plus_plus_nat A) ((plus_plus_nat B) C))))
% 0.78/0.94 FOF formula (((eq (nat->(nat->nat))) plus_plus_nat) (fun (A2:nat) (B2:nat)=> ((plus_plus_nat B2) A2))) of role axiom named fact_283_add_Ocommute
% 0.78/0.94 A new axiom: (((eq (nat->(nat->nat))) plus_plus_nat) (fun (A2:nat) (B2:nat)=> ((plus_plus_nat B2) A2)))
% 0.78/0.94 FOF formula (forall (B:nat) (A:nat) (C:nat), (((eq nat) ((plus_plus_nat B) ((plus_plus_nat A) C))) ((plus_plus_nat A) ((plus_plus_nat B) C)))) of role axiom named fact_284_add_Oleft__commute
% 0.78/0.94 A new axiom: (forall (B:nat) (A:nat) (C:nat), (((eq nat) ((plus_plus_nat B) ((plus_plus_nat A) C))) ((plus_plus_nat A) ((plus_plus_nat B) C))))
% 0.78/0.94 FOF formula (forall (A:nat) (B:nat) (C:nat), ((((eq nat) ((plus_plus_nat A) B)) ((plus_plus_nat A) C))->(((eq nat) B) C))) of role axiom named fact_285_add__left__imp__eq
% 0.78/0.94 A new axiom: (forall (A:nat) (B:nat) (C:nat), ((((eq nat) ((plus_plus_nat A) B)) ((plus_plus_nat A) C))->(((eq nat) B) C)))
% 0.78/0.94 FOF formula (forall (B:nat) (A:nat) (C:nat), ((((eq nat) ((plus_plus_nat B) A)) ((plus_plus_nat C) A))->(((eq nat) B) C))) of role axiom named fact_286_add__right__imp__eq
% 0.78/0.94 A new axiom: (forall (B:nat) (A:nat) (C:nat), ((((eq nat) ((plus_plus_nat B) A)) ((plus_plus_nat C) A))->(((eq nat) B) C)))
% 0.78/0.94 FOF formula (forall (A:nat) (E:nat) (B:nat) (C:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A) E)) ((plus_plus_nat ((times_times_nat B) E)) C))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat A) B)) E)) C))) of role axiom named fact_287_combine__common__factor
% 0.78/0.94 A new axiom: (forall (A:nat) (E:nat) (B:nat) (C:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A) E)) ((plus_plus_nat ((times_times_nat B) E)) C))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat A) B)) E)) C)))
% 0.78/0.94 FOF formula (forall (A:a) (E:a) (B:a) (C:a), (((eq a) ((plus_plus_a ((times_times_a A) E)) ((plus_plus_a ((times_times_a B) E)) C))) ((plus_plus_a ((times_times_a ((plus_plus_a A) B)) E)) C))) of role axiom named fact_288_combine__common__factor
% 0.78/0.94 A new axiom: (forall (A:a) (E:a) (B:a) (C:a), (((eq a) ((plus_plus_a ((times_times_a A) E)) ((plus_plus_a ((times_times_a B) E)) C))) ((plus_plus_a ((times_times_a ((plus_plus_a A) B)) E)) C)))
% 0.78/0.94 FOF formula (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A) B)) C)) ((plus_plus_nat ((times_times_nat A) C)) ((times_times_nat B) C)))) of role axiom named fact_289_distrib__right
% 0.78/0.94 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A) B)) C)) ((plus_plus_nat ((times_times_nat A) C)) ((times_times_nat B) C))))
% 0.78/0.95 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a ((plus_plus_a A) B)) C)) ((plus_plus_a ((times_times_a A) C)) ((times_times_a B) C)))) of role axiom named fact_290_distrib__right
% 0.78/0.95 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a ((plus_plus_a A) B)) C)) ((plus_plus_a ((times_times_a A) C)) ((times_times_a B) C))))
% 0.78/0.95 FOF formula (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat A) ((plus_plus_nat B) C))) ((plus_plus_nat ((times_times_nat A) B)) ((times_times_nat A) C)))) of role axiom named fact_291_distrib__left
% 0.78/0.95 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat A) ((plus_plus_nat B) C))) ((plus_plus_nat ((times_times_nat A) B)) ((times_times_nat A) C))))
% 0.78/0.95 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a A) ((plus_plus_a B) C))) ((plus_plus_a ((times_times_a A) B)) ((times_times_a A) C)))) of role axiom named fact_292_distrib__left
% 0.78/0.95 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a A) ((plus_plus_a B) C))) ((plus_plus_a ((times_times_a A) B)) ((times_times_a A) C))))
% 0.78/0.95 FOF formula (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A) B)) C)) ((plus_plus_nat ((times_times_nat A) C)) ((times_times_nat B) C)))) of role axiom named fact_293_comm__semiring__class_Odistrib
% 0.78/0.95 A new axiom: (forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A) B)) C)) ((plus_plus_nat ((times_times_nat A) C)) ((times_times_nat B) C))))
% 0.78/0.95 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a ((plus_plus_a A) B)) C)) ((plus_plus_a ((times_times_a A) C)) ((times_times_a B) C)))) of role axiom named fact_294_comm__semiring__class_Odistrib
% 0.78/0.95 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a ((plus_plus_a A) B)) C)) ((plus_plus_a ((times_times_a A) C)) ((times_times_a B) C))))
% 0.78/0.95 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a A) ((plus_plus_a B) C))) ((plus_plus_a ((times_times_a A) B)) ((times_times_a A) C)))) of role axiom named fact_295_ring__class_Oring__distribs_I1_J
% 0.78/0.95 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a A) ((plus_plus_a B) C))) ((plus_plus_a ((times_times_a A) B)) ((times_times_a A) C))))
% 0.78/0.95 FOF formula (forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a ((plus_plus_a A) B)) C)) ((plus_plus_a ((times_times_a A) C)) ((times_times_a B) C)))) of role axiom named fact_296_ring__class_Oring__distribs_I2_J
% 0.78/0.95 A new axiom: (forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a ((plus_plus_a A) B)) C)) ((plus_plus_a ((times_times_a A) C)) ((times_times_a B) C))))
% 0.78/0.95 FOF formula (forall (X51:polyno727731844poly_a) (X52:polyno727731844poly_a) (X71:polyno727731844poly_a) (X72:nat), (not (((eq polyno727731844poly_a) ((polyno1491482291_Mul_a X51) X52)) ((polyno1538138524e_Pw_a X71) X72)))) of role axiom named fact_297_poly_Odistinct_I47_J
% 0.78/0.95 A new axiom: (forall (X51:polyno727731844poly_a) (X52:polyno727731844poly_a) (X71:polyno727731844poly_a) (X72:nat), (not (((eq polyno727731844poly_a) ((polyno1491482291_Mul_a X51) X52)) ((polyno1538138524e_Pw_a X71) X72))))
% 0.78/0.95 FOF formula (forall (A:nat), (((eq nat) ((plus_plus_nat A) zero_zero_nat)) A)) of role axiom named fact_298_add_Ocomm__neutral
% 0.78/0.95 A new axiom: (forall (A:nat), (((eq nat) ((plus_plus_nat A) zero_zero_nat)) A))
% 0.78/0.95 FOF formula (forall (A:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A)) A)) of role axiom named fact_299_comm__monoid__add__class_Oadd__0
% 0.78/0.95 A new axiom: (forall (A:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A)) A))
% 0.78/0.95 FOF formula (forall (X1:a) (X71:polyno727731844poly_a) (X72:nat), (not (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) ((polyno1538138524e_Pw_a X71) X72)))) of role axiom named fact_300_poly_Odistinct_I11_J
% 0.78/0.95 A new axiom: (forall (X1:a) (X71:polyno727731844poly_a) (X72:nat), (not (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) ((polyno1538138524e_Pw_a X71) X72))))
% 0.78/0.95 FOF formula (forall (X1:nat) (X71:polyno1532895200ly_nat) (X72:nat), (not (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) ((polyno359287218Pw_nat X71) X72)))) of role axiom named fact_301_poly_Odistinct_I11_J
% 0.78/0.96 A new axiom: (forall (X1:nat) (X71:polyno1532895200ly_nat) (X72:nat), (not (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) ((polyno359287218Pw_nat X71) X72))))
% 0.78/0.96 FOF formula (forall (A:polyno1532895200ly_nat) (V:polyno1532895200ly_nat) (Va:nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat A) ((polyno359287218Pw_nat V) Va))) ((polyno1415441627ul_nat A) ((polyno359287218Pw_nat V) Va)))) of role axiom named fact_302_polymul_Osimps_I22_J
% 0.78/0.96 A new axiom: (forall (A:polyno1532895200ly_nat) (V:polyno1532895200ly_nat) (Va:nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat A) ((polyno359287218Pw_nat V) Va))) ((polyno1415441627ul_nat A) ((polyno359287218Pw_nat V) Va))))
% 0.78/0.96 FOF formula (forall (A:polyno727731844poly_a) (V:polyno727731844poly_a) (Va:nat), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a A) ((polyno1538138524e_Pw_a V) Va))) ((polyno1491482291_Mul_a A) ((polyno1538138524e_Pw_a V) Va)))) of role axiom named fact_303_polymul_Osimps_I22_J
% 0.78/0.96 A new axiom: (forall (A:polyno727731844poly_a) (V:polyno727731844poly_a) (Va:nat), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a A) ((polyno1538138524e_Pw_a V) Va))) ((polyno1491482291_Mul_a A) ((polyno1538138524e_Pw_a V) Va))))
% 0.78/0.96 FOF formula (forall (V:polyno1532895200ly_nat) (Va:nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno359287218Pw_nat V) Va)) B)) ((polyno1415441627ul_nat ((polyno359287218Pw_nat V) Va)) B))) of role axiom named fact_304_polymul_Osimps_I10_J
% 0.78/0.96 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno359287218Pw_nat V) Va)) B)) ((polyno1415441627ul_nat ((polyno359287218Pw_nat V) Va)) B)))
% 0.78/0.96 FOF formula (forall (V:polyno727731844poly_a) (Va:nat) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1538138524e_Pw_a V) Va)) B)) ((polyno1491482291_Mul_a ((polyno1538138524e_Pw_a V) Va)) B))) of role axiom named fact_305_polymul_Osimps_I10_J
% 0.78/0.96 A new axiom: (forall (V:polyno727731844poly_a) (Va:nat) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1538138524e_Pw_a V) Va)) B)) ((polyno1491482291_Mul_a ((polyno1538138524e_Pw_a V) Va)) B)))
% 0.78/0.96 FOF formula (forall (Bs2:list_a) (A:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) ((polyno1623170614_Add_a A) B))) ((plus_plus_a ((polyno422358502poly_a Bs2) A)) ((polyno422358502poly_a Bs2) B)))) of role axiom named fact_306_Ipoly_Osimps_I4_J
% 0.78/0.96 A new axiom: (forall (Bs2:list_a) (A:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) ((polyno1623170614_Add_a A) B))) ((plus_plus_a ((polyno422358502poly_a Bs2) A)) ((polyno422358502poly_a Bs2) B))))
% 0.78/0.96 FOF formula (forall (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat) (Vc:polyno1532895200ly_nat) (Vd:nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno359287218Pw_nat Vc) Vd))) ((polyno1415441627ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno359287218Pw_nat Vc) Vd)))) of role axiom named fact_307_polymul_Osimps_I16_J
% 0.78/0.96 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat) (Vc:polyno1532895200ly_nat) (Vd:nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno359287218Pw_nat Vc) Vd))) ((polyno1415441627ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno359287218Pw_nat Vc) Vd))))
% 0.78/0.96 FOF formula (forall (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a) (Vc:polyno727731844poly_a) (Vd:nat), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1538138524e_Pw_a Vc) Vd))) ((polyno1491482291_Mul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1538138524e_Pw_a Vc) Vd)))) of role axiom named fact_308_polymul_Osimps_I16_J
% 0.78/0.96 A new axiom: (forall (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a) (Vc:polyno727731844poly_a) (Vd:nat), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1538138524e_Pw_a Vc) Vd))) ((polyno1491482291_Mul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1538138524e_Pw_a Vc) Vd))))
% 0.78/0.96 FOF formula (forall (Vc:polyno1532895200ly_nat) (Vd:nat) (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno359287218Pw_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb))) ((polyno1415441627ul_nat ((polyno359287218Pw_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb)))) of role axiom named fact_309_polymul_Osimps_I28_J
% 0.78/0.96 A new axiom: (forall (Vc:polyno1532895200ly_nat) (Vd:nat) (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno359287218Pw_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb))) ((polyno1415441627ul_nat ((polyno359287218Pw_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb))))
% 0.78/0.96 FOF formula (forall (Vc:polyno727731844poly_a) (Vd:nat) (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1538138524e_Pw_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb))) ((polyno1491482291_Mul_a ((polyno1538138524e_Pw_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb)))) of role axiom named fact_310_polymul_Osimps_I28_J
% 0.78/0.96 A new axiom: (forall (Vc:polyno727731844poly_a) (Vd:nat) (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1538138524e_Pw_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb))) ((polyno1491482291_Mul_a ((polyno1538138524e_Pw_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb))))
% 0.78/0.96 FOF formula (forall (Y:a) (V:polyno727731844poly_a) (Va:nat), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) ((polyno1538138524e_Pw_a V) Va))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) ((polyno1538138524e_Pw_a V) Va)))) of role axiom named fact_311_poly__cmul_Osimps_I8_J
% 0.78/0.96 A new axiom: (forall (Y:a) (V:polyno727731844poly_a) (Va:nat), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) ((polyno1538138524e_Pw_a V) Va))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) ((polyno1538138524e_Pw_a V) Va))))
% 0.78/0.96 FOF formula (forall (Y:nat) (V:polyno1532895200ly_nat) (Va:nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) ((polyno359287218Pw_nat V) Va))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) ((polyno359287218Pw_nat V) Va)))) of role axiom named fact_312_poly__cmul_Osimps_I8_J
% 0.78/0.96 A new axiom: (forall (Y:nat) (V:polyno1532895200ly_nat) (Va:nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) ((polyno359287218Pw_nat V) Va))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) ((polyno359287218Pw_nat V) Va))))
% 0.78/0.96 FOF formula (forall (V:polyno727731844poly_a) (Va:nat), (((eq polyno727731844poly_a) (polyno212464073eriv_a ((polyno1538138524e_Pw_a V) Va))) (polyno439679028le_C_a zero_zero_a))) of role axiom named fact_313_poly__deriv_Osimps_I8_J
% 0.78/0.96 A new axiom: (forall (V:polyno727731844poly_a) (Va:nat), (((eq polyno727731844poly_a) (polyno212464073eriv_a ((polyno1538138524e_Pw_a V) Va))) (polyno439679028le_C_a zero_zero_a)))
% 0.78/0.96 FOF formula (forall (P:polyno727731844poly_a) (N:nat) (Bs2:list_a), (((polyno1372495879olyh_a P) N)->(((eq a) ((polyno422358502poly_a Bs2) ((polyno1623170614_Add_a ((polyno1491482291_Mul_a (polyno1884029055head_a P)) ((polyno1538138524e_Pw_a (polyno2024845497ound_a zero_zero_nat)) (polyno578545843gree_a P)))) (polyno1465139388head_a P)))) ((polyno422358502poly_a Bs2) P)))) of role axiom named fact_314_behead
% 0.78/0.96 A new axiom: (forall (P:polyno727731844poly_a) (N:nat) (Bs2:list_a), (((polyno1372495879olyh_a P) N)->(((eq a) ((polyno422358502poly_a Bs2) ((polyno1623170614_Add_a ((polyno1491482291_Mul_a (polyno1884029055head_a P)) ((polyno1538138524e_Pw_a (polyno2024845497ound_a zero_zero_nat)) (polyno578545843gree_a P)))) (polyno1465139388head_a P)))) ((polyno422358502poly_a Bs2) P))))
% 0.78/0.96 FOF formula (forall (P:polyno727731844poly_a) (N:nat), (((polyno1372495879olyh_a P) N)->((polyno1372495879olyh_a (polyno1465139388head_a P)) N))) of role axiom named fact_315_behead__isnpolyh
% 0.78/0.97 A new axiom: (forall (P:polyno727731844poly_a) (N:nat), (((polyno1372495879olyh_a P) N)->((polyno1372495879olyh_a (polyno1465139388head_a P)) N)))
% 0.78/0.97 FOF formula (forall (V:a), (((eq polyno727731844poly_a) (polyno1465139388head_a (polyno439679028le_C_a V))) (polyno439679028le_C_a zero_zero_a))) of role axiom named fact_316_behead_Osimps_I2_J
% 0.78/0.97 A new axiom: (forall (V:a), (((eq polyno727731844poly_a) (polyno1465139388head_a (polyno439679028le_C_a V))) (polyno439679028le_C_a zero_zero_a)))
% 0.78/0.97 FOF formula (forall (V:nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat (polyno2122022170_C_nat V))) (polyno2122022170_C_nat zero_zero_nat))) of role axiom named fact_317_behead_Osimps_I2_J
% 0.78/0.97 A new axiom: (forall (V:nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat (polyno2122022170_C_nat V))) (polyno2122022170_C_nat zero_zero_nat)))
% 0.78/0.97 FOF formula (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat ((polyno1415441627ul_nat V) Va))) (polyno2122022170_C_nat zero_zero_nat))) of role axiom named fact_318_behead_Osimps_I6_J
% 0.78/0.97 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat ((polyno1415441627ul_nat V) Va))) (polyno2122022170_C_nat zero_zero_nat)))
% 0.78/0.97 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1465139388head_a ((polyno1491482291_Mul_a V) Va))) (polyno439679028le_C_a zero_zero_a))) of role axiom named fact_319_behead_Osimps_I6_J
% 0.78/0.97 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1465139388head_a ((polyno1491482291_Mul_a V) Va))) (polyno439679028le_C_a zero_zero_a)))
% 0.78/0.97 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1465139388head_a ((polyno1623170614_Add_a V) Va))) (polyno439679028le_C_a zero_zero_a))) of role axiom named fact_320_behead_Osimps_I4_J
% 0.78/0.97 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1465139388head_a ((polyno1623170614_Add_a V) Va))) (polyno439679028le_C_a zero_zero_a)))
% 0.78/0.97 FOF formula (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat ((polyno1222032024dd_nat V) Va))) (polyno2122022170_C_nat zero_zero_nat))) of role axiom named fact_321_behead_Osimps_I4_J
% 0.78/0.97 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat ((polyno1222032024dd_nat V) Va))) (polyno2122022170_C_nat zero_zero_nat)))
% 0.78/0.97 FOF formula (forall (V:nat), (((eq polyno727731844poly_a) (polyno1465139388head_a (polyno2024845497ound_a V))) (polyno439679028le_C_a zero_zero_a))) of role axiom named fact_322_behead_Osimps_I3_J
% 0.78/0.97 A new axiom: (forall (V:nat), (((eq polyno727731844poly_a) (polyno1465139388head_a (polyno2024845497ound_a V))) (polyno439679028le_C_a zero_zero_a)))
% 0.78/0.97 FOF formula (forall (V:nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat (polyno1999838549nd_nat V))) (polyno2122022170_C_nat zero_zero_nat))) of role axiom named fact_323_behead_Osimps_I3_J
% 0.78/0.97 A new axiom: (forall (V:nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat (polyno1999838549nd_nat V))) (polyno2122022170_C_nat zero_zero_nat)))
% 0.78/0.97 FOF formula (forall (V:polyno727731844poly_a) (Va:nat), (((eq polyno727731844poly_a) (polyno1465139388head_a ((polyno1538138524e_Pw_a V) Va))) (polyno439679028le_C_a zero_zero_a))) of role axiom named fact_324_behead_Osimps_I8_J
% 0.78/0.97 A new axiom: (forall (V:polyno727731844poly_a) (Va:nat), (((eq polyno727731844poly_a) (polyno1465139388head_a ((polyno1538138524e_Pw_a V) Va))) (polyno439679028le_C_a zero_zero_a)))
% 0.78/0.97 FOF formula (forall (V:polyno1532895200ly_nat) (Va:nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat ((polyno359287218Pw_nat V) Va))) (polyno2122022170_C_nat zero_zero_nat))) of role axiom named fact_325_behead_Osimps_I8_J
% 0.78/0.97 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat ((polyno359287218Pw_nat V) Va))) (polyno2122022170_C_nat zero_zero_nat)))
% 0.78/0.98 FOF formula (forall (R:nat) (A:nat) (B:nat) (C:nat) (D:nat), ((not (((eq nat) R) zero_zero_nat))->(((and (((eq nat) A) B)) (not (((eq nat) C) D)))->(not (((eq nat) ((plus_plus_nat A) ((times_times_nat R) C))) ((plus_plus_nat B) ((times_times_nat R) D))))))) of role axiom named fact_326_add__scale__eq__noteq
% 0.78/0.98 A new axiom: (forall (R:nat) (A:nat) (B:nat) (C:nat) (D:nat), ((not (((eq nat) R) zero_zero_nat))->(((and (((eq nat) A) B)) (not (((eq nat) C) D)))->(not (((eq nat) ((plus_plus_nat A) ((times_times_nat R) C))) ((plus_plus_nat B) ((times_times_nat R) D)))))))
% 0.78/0.98 FOF formula (forall (R:a) (A:a) (B:a) (C:a) (D:a), ((not (((eq a) R) zero_zero_a))->(((and (((eq a) A) B)) (not (((eq a) C) D)))->(not (((eq a) ((plus_plus_a A) ((times_times_a R) C))) ((plus_plus_a B) ((times_times_a R) D))))))) of role axiom named fact_327_add__scale__eq__noteq
% 0.78/0.98 A new axiom: (forall (R:a) (A:a) (B:a) (C:a) (D:a), ((not (((eq a) R) zero_zero_a))->(((and (((eq a) A) B)) (not (((eq a) C) D)))->(not (((eq a) ((plus_plus_a A) ((times_times_a R) C))) ((plus_plus_a B) ((times_times_a R) D)))))))
% 0.78/0.98 FOF formula (forall (B:nat) (A:nat), (((eq Prop) (((eq nat) B) ((plus_plus_nat B) A))) (((eq nat) A) zero_zero_nat))) of role axiom named fact_328_add__0__iff
% 0.78/0.98 A new axiom: (forall (B:nat) (A:nat), (((eq Prop) (((eq nat) B) ((plus_plus_nat B) A))) (((eq nat) A) zero_zero_nat)))
% 0.78/0.98 FOF formula (forall (A:nat) (B:nat) (C:nat) (D:nat), (((eq Prop) ((and (not (((eq nat) A) B))) (not (((eq nat) C) D)))) (not (((eq nat) ((plus_plus_nat ((times_times_nat A) C)) ((times_times_nat B) D))) ((plus_plus_nat ((times_times_nat A) D)) ((times_times_nat B) C)))))) of role axiom named fact_329_crossproduct__noteq
% 0.78/0.98 A new axiom: (forall (A:nat) (B:nat) (C:nat) (D:nat), (((eq Prop) ((and (not (((eq nat) A) B))) (not (((eq nat) C) D)))) (not (((eq nat) ((plus_plus_nat ((times_times_nat A) C)) ((times_times_nat B) D))) ((plus_plus_nat ((times_times_nat A) D)) ((times_times_nat B) C))))))
% 0.78/0.98 FOF formula (forall (A:a) (B:a) (C:a) (D:a), (((eq Prop) ((and (not (((eq a) A) B))) (not (((eq a) C) D)))) (not (((eq a) ((plus_plus_a ((times_times_a A) C)) ((times_times_a B) D))) ((plus_plus_a ((times_times_a A) D)) ((times_times_a B) C)))))) of role axiom named fact_330_crossproduct__noteq
% 0.78/0.98 A new axiom: (forall (A:a) (B:a) (C:a) (D:a), (((eq Prop) ((and (not (((eq a) A) B))) (not (((eq a) C) D)))) (not (((eq a) ((plus_plus_a ((times_times_a A) C)) ((times_times_a B) D))) ((plus_plus_a ((times_times_a A) D)) ((times_times_a B) C))))))
% 0.78/0.98 FOF formula (forall (W:nat) (Y:nat) (X:nat) (Z:nat), (((eq Prop) (((eq nat) ((plus_plus_nat ((times_times_nat W) Y)) ((times_times_nat X) Z))) ((plus_plus_nat ((times_times_nat W) Z)) ((times_times_nat X) Y)))) ((or (((eq nat) W) X)) (((eq nat) Y) Z)))) of role axiom named fact_331_crossproduct__eq
% 0.78/0.98 A new axiom: (forall (W:nat) (Y:nat) (X:nat) (Z:nat), (((eq Prop) (((eq nat) ((plus_plus_nat ((times_times_nat W) Y)) ((times_times_nat X) Z))) ((plus_plus_nat ((times_times_nat W) Z)) ((times_times_nat X) Y)))) ((or (((eq nat) W) X)) (((eq nat) Y) Z))))
% 0.78/0.98 FOF formula (forall (W:a) (Y:a) (X:a) (Z:a), (((eq Prop) (((eq a) ((plus_plus_a ((times_times_a W) Y)) ((times_times_a X) Z))) ((plus_plus_a ((times_times_a W) Z)) ((times_times_a X) Y)))) ((or (((eq a) W) X)) (((eq a) Y) Z)))) of role axiom named fact_332_crossproduct__eq
% 0.78/0.98 A new axiom: (forall (W:a) (Y:a) (X:a) (Z:a), (((eq Prop) (((eq a) ((plus_plus_a ((times_times_a W) Y)) ((times_times_a X) Z))) ((plus_plus_a ((times_times_a W) Z)) ((times_times_a X) Y)))) ((or (((eq a) W) X)) (((eq a) Y) Z))))
% 0.78/0.98 FOF formula (forall (P5:(nat->(nat->Prop))) (A:nat) (B:nat), ((forall (A4:nat) (B4:nat), (((eq Prop) ((P5 A4) B4)) ((P5 B4) A4)))->((forall (A4:nat), ((P5 A4) zero_zero_nat))->((forall (A4:nat) (B4:nat), (((P5 A4) B4)->((P5 A4) ((plus_plus_nat A4) B4))))->((P5 A) B))))) of role axiom named fact_333_Euclid__induct
% 0.78/0.98 A new axiom: (forall (P5:(nat->(nat->Prop))) (A:nat) (B:nat), ((forall (A4:nat) (B4:nat), (((eq Prop) ((P5 A4) B4)) ((P5 B4) A4)))->((forall (A4:nat), ((P5 A4) zero_zero_nat))->((forall (A4:nat) (B4:nat), (((P5 A4) B4)->((P5 A4) ((plus_plus_nat A4) B4))))->((P5 A) B)))))
% 0.83/0.99 FOF formula (forall (A:nat), (((eq nat) ((plus_plus_nat A) zero_zero_nat)) A)) of role axiom named fact_334_verit__sum__simplify
% 0.83/0.99 A new axiom: (forall (A:nat), (((eq nat) ((plus_plus_nat A) zero_zero_nat)) A))
% 0.83/0.99 FOF formula (((eq (polyno727731844poly_a->polyno727731844poly_a)) (polyno1371724751ypow_a zero_zero_nat)) (fun (P2:polyno727731844poly_a)=> (polyno439679028le_C_a one_one_a))) of role axiom named fact_335_polypow_Osimps_I1_J
% 0.83/0.99 A new axiom: (((eq (polyno727731844poly_a->polyno727731844poly_a)) (polyno1371724751ypow_a zero_zero_nat)) (fun (P2:polyno727731844poly_a)=> (polyno439679028le_C_a one_one_a)))
% 0.83/0.99 FOF formula (((eq (polyno1532895200ly_nat->polyno1532895200ly_nat)) (polyno1510045887ow_nat zero_zero_nat)) (fun (P2:polyno1532895200ly_nat)=> (polyno2122022170_C_nat one_one_nat))) of role axiom named fact_336_polypow_Osimps_I1_J
% 0.83/0.99 A new axiom: (((eq (polyno1532895200ly_nat->polyno1532895200ly_nat)) (polyno1510045887ow_nat zero_zero_nat)) (fun (P2:polyno1532895200ly_nat)=> (polyno2122022170_C_nat one_one_nat)))
% 0.83/0.99 FOF formula (forall (X:polyno1532895200ly_nat) (Y:(nat->nat)), ((((eq (nat->nat)) (polyno1779722485en_nat X)) Y)->((forall (C3:polyno1532895200ly_nat) (N3:nat) (P4:polyno1532895200ly_nat), ((((eq polyno1532895200ly_nat) X) (((polyno720942678CN_nat C3) N3) P4))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> (((if_nat (((eq nat) N3) M2)) ((plus_plus_nat one_one_nat) ((polyno1779722485en_nat P4) N3))) zero_zero_nat))))))->((((ex nat) (fun (V2:nat)=> (((eq polyno1532895200ly_nat) X) (polyno2122022170_C_nat V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex nat) (fun (V2:nat)=> (((eq polyno1532895200ly_nat) X) (polyno1999838549nd_nat V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno1532895200ly_nat) (fun (V2:polyno1532895200ly_nat)=> ((ex polyno1532895200ly_nat) (fun (Va2:polyno1532895200ly_nat)=> (((eq polyno1532895200ly_nat) X) ((polyno1222032024dd_nat V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno1532895200ly_nat) (fun (V2:polyno1532895200ly_nat)=> ((ex polyno1532895200ly_nat) (fun (Va2:polyno1532895200ly_nat)=> (((eq polyno1532895200ly_nat) X) ((polyno1921014231ub_nat V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno1532895200ly_nat) (fun (V2:polyno1532895200ly_nat)=> ((ex polyno1532895200ly_nat) (fun (Va2:polyno1532895200ly_nat)=> (((eq polyno1532895200ly_nat) X) ((polyno1415441627ul_nat V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno1532895200ly_nat) (fun (V2:polyno1532895200ly_nat)=> (((eq polyno1532895200ly_nat) X) (polyno1366804583eg_nat V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno1532895200ly_nat) (fun (V2:polyno1532895200ly_nat)=> ((ex nat) (fun (Va2:nat)=> (((eq polyno1532895200ly_nat) X) ((polyno359287218Pw_nat V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->False)))))))))) of role axiom named fact_337_degreen_Oelims
% 0.83/0.99 A new axiom: (forall (X:polyno1532895200ly_nat) (Y:(nat->nat)), ((((eq (nat->nat)) (polyno1779722485en_nat X)) Y)->((forall (C3:polyno1532895200ly_nat) (N3:nat) (P4:polyno1532895200ly_nat), ((((eq polyno1532895200ly_nat) X) (((polyno720942678CN_nat C3) N3) P4))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> (((if_nat (((eq nat) N3) M2)) ((plus_plus_nat one_one_nat) ((polyno1779722485en_nat P4) N3))) zero_zero_nat))))))->((((ex nat) (fun (V2:nat)=> (((eq polyno1532895200ly_nat) X) (polyno2122022170_C_nat V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex nat) (fun (V2:nat)=> (((eq polyno1532895200ly_nat) X) (polyno1999838549nd_nat V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno1532895200ly_nat) (fun (V2:polyno1532895200ly_nat)=> ((ex polyno1532895200ly_nat) (fun (Va2:polyno1532895200ly_nat)=> (((eq polyno1532895200ly_nat) X) ((polyno1222032024dd_nat V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno1532895200ly_nat) (fun (V2:polyno1532895200ly_nat)=> ((ex polyno1532895200ly_nat) (fun (Va2:polyno1532895200ly_nat)=> (((eq polyno1532895200ly_nat) X) ((polyno1921014231ub_nat V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno1532895200ly_nat) (fun (V2:polyno1532895200ly_nat)=> ((ex polyno1532895200ly_nat) (fun (Va2:polyno1532895200ly_nat)=> (((eq polyno1532895200ly_nat) X) ((polyno1415441627ul_nat V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno1532895200ly_nat) (fun (V2:polyno1532895200ly_nat)=> (((eq polyno1532895200ly_nat) X) (polyno1366804583eg_nat V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno1532895200ly_nat) (fun (V2:polyno1532895200ly_nat)=> ((ex nat) (fun (Va2:nat)=> (((eq polyno1532895200ly_nat) X) ((polyno359287218Pw_nat V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->False))))))))))
% 0.83/1.00 FOF formula (forall (X:polyno727731844poly_a) (Y:(nat->nat)), ((((eq (nat->nat)) (polyno1674775833reen_a X)) Y)->((forall (C3:polyno727731844poly_a) (N3:nat) (P4:polyno727731844poly_a), ((((eq polyno727731844poly_a) X) (((polyno1057396216e_CN_a C3) N3) P4))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> (((if_nat (((eq nat) N3) M2)) ((plus_plus_nat one_one_nat) ((polyno1674775833reen_a P4) N3))) zero_zero_nat))))))->((((ex a) (fun (V2:a)=> (((eq polyno727731844poly_a) X) (polyno439679028le_C_a V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex nat) (fun (V2:nat)=> (((eq polyno727731844poly_a) X) (polyno2024845497ound_a V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno727731844poly_a) (fun (V2:polyno727731844poly_a)=> ((ex polyno727731844poly_a) (fun (Va2:polyno727731844poly_a)=> (((eq polyno727731844poly_a) X) ((polyno1623170614_Add_a V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno727731844poly_a) (fun (V2:polyno727731844poly_a)=> ((ex polyno727731844poly_a) (fun (Va2:polyno727731844poly_a)=> (((eq polyno727731844poly_a) X) ((polyno975704247_Sub_a V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno727731844poly_a) (fun (V2:polyno727731844poly_a)=> ((ex polyno727731844poly_a) (fun (Va2:polyno727731844poly_a)=> (((eq polyno727731844poly_a) X) ((polyno1491482291_Mul_a V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno727731844poly_a) (fun (V2:polyno727731844poly_a)=> (((eq polyno727731844poly_a) X) (polyno96675367_Neg_a V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno727731844poly_a) (fun (V2:polyno727731844poly_a)=> ((ex nat) (fun (Va2:nat)=> (((eq polyno727731844poly_a) X) ((polyno1538138524e_Pw_a V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->False)))))))))) of role axiom named fact_338_degreen_Oelims
% 0.83/1.00 A new axiom: (forall (X:polyno727731844poly_a) (Y:(nat->nat)), ((((eq (nat->nat)) (polyno1674775833reen_a X)) Y)->((forall (C3:polyno727731844poly_a) (N3:nat) (P4:polyno727731844poly_a), ((((eq polyno727731844poly_a) X) (((polyno1057396216e_CN_a C3) N3) P4))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> (((if_nat (((eq nat) N3) M2)) ((plus_plus_nat one_one_nat) ((polyno1674775833reen_a P4) N3))) zero_zero_nat))))))->((((ex a) (fun (V2:a)=> (((eq polyno727731844poly_a) X) (polyno439679028le_C_a V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex nat) (fun (V2:nat)=> (((eq polyno727731844poly_a) X) (polyno2024845497ound_a V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno727731844poly_a) (fun (V2:polyno727731844poly_a)=> ((ex polyno727731844poly_a) (fun (Va2:polyno727731844poly_a)=> (((eq polyno727731844poly_a) X) ((polyno1623170614_Add_a V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno727731844poly_a) (fun (V2:polyno727731844poly_a)=> ((ex polyno727731844poly_a) (fun (Va2:polyno727731844poly_a)=> (((eq polyno727731844poly_a) X) ((polyno975704247_Sub_a V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno727731844poly_a) (fun (V2:polyno727731844poly_a)=> ((ex polyno727731844poly_a) (fun (Va2:polyno727731844poly_a)=> (((eq polyno727731844poly_a) X) ((polyno1491482291_Mul_a V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno727731844poly_a) (fun (V2:polyno727731844poly_a)=> (((eq polyno727731844poly_a) X) (polyno96675367_Neg_a V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno727731844poly_a) (fun (V2:polyno727731844poly_a)=> ((ex nat) (fun (Va2:nat)=> (((eq polyno727731844poly_a) X) ((polyno1538138524e_Pw_a V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->False))))))))))
% 0.83/1.00 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1465139388head_a ((polyno975704247_Sub_a V) Va))) (polyno439679028le_C_a zero_zero_a))) of role axiom named fact_339_behead_Osimps_I5_J
% 0.83/1.00 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1465139388head_a ((polyno975704247_Sub_a V) Va))) (polyno439679028le_C_a zero_zero_a)))
% 0.83/1.00 FOF formula (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat ((polyno1921014231ub_nat V) Va))) (polyno2122022170_C_nat zero_zero_nat))) of role axiom named fact_340_behead_Osimps_I5_J
% 0.83/1.00 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat ((polyno1921014231ub_nat V) Va))) (polyno2122022170_C_nat zero_zero_nat)))
% 0.83/1.00 FOF formula (forall (Y:a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) ((polyno975704247_Sub_a V) Va))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) ((polyno975704247_Sub_a V) Va)))) of role axiom named fact_341_poly__cmul_Osimps_I5_J
% 0.83/1.00 A new axiom: (forall (Y:a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) ((polyno975704247_Sub_a V) Va))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) ((polyno975704247_Sub_a V) Va))))
% 0.83/1.00 FOF formula (forall (Y:nat) (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) ((polyno1921014231ub_nat V) Va))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) ((polyno1921014231ub_nat V) Va)))) of role axiom named fact_342_poly__cmul_Osimps_I5_J
% 0.83/1.00 A new axiom: (forall (Y:nat) (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) ((polyno1921014231ub_nat V) Va))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) ((polyno1921014231ub_nat V) Va))))
% 0.83/1.00 FOF formula (forall (V:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1465139388head_a (polyno96675367_Neg_a V))) (polyno439679028le_C_a zero_zero_a))) of role axiom named fact_343_behead_Osimps_I7_J
% 0.83/1.00 A new axiom: (forall (V:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1465139388head_a (polyno96675367_Neg_a V))) (polyno439679028le_C_a zero_zero_a)))
% 0.83/1.00 FOF formula (forall (V:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat (polyno1366804583eg_nat V))) (polyno2122022170_C_nat zero_zero_nat))) of role axiom named fact_344_behead_Osimps_I7_J
% 0.83/1.00 A new axiom: (forall (V:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat (polyno1366804583eg_nat V))) (polyno2122022170_C_nat zero_zero_nat)))
% 0.83/1.00 FOF formula (forall (Y:a) (V:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) (polyno96675367_Neg_a V))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) (polyno96675367_Neg_a V)))) of role axiom named fact_345_poly__cmul_Osimps_I7_J
% 0.83/1.00 A new axiom: (forall (Y:a) (V:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) (polyno96675367_Neg_a V))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) (polyno96675367_Neg_a V))))
% 0.83/1.01 FOF formula (forall (Y:nat) (V:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) (polyno1366804583eg_nat V))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) (polyno1366804583eg_nat V)))) of role axiom named fact_346_poly__cmul_Osimps_I7_J
% 0.83/1.01 A new axiom: (forall (Y:nat) (V:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) (polyno1366804583eg_nat V))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) (polyno1366804583eg_nat V))))
% 0.83/1.01 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno212464073eriv_a ((polyno975704247_Sub_a V) Va))) (polyno439679028le_C_a zero_zero_a))) of role axiom named fact_347_poly__deriv_Osimps_I5_J
% 0.83/1.01 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno212464073eriv_a ((polyno975704247_Sub_a V) Va))) (polyno439679028le_C_a zero_zero_a)))
% 0.83/1.01 FOF formula (forall (V:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno212464073eriv_a (polyno96675367_Neg_a V))) (polyno439679028le_C_a zero_zero_a))) of role axiom named fact_348_poly__deriv_Osimps_I7_J
% 0.83/1.01 A new axiom: (forall (V:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno212464073eriv_a (polyno96675367_Neg_a V))) (polyno439679028le_C_a zero_zero_a)))
% 0.83/1.01 FOF formula (forall (P:polyno727731844poly_a) (N:nat) (K2:nat), (((polyno1372495879olyh_a P) N)->((polyno1372495879olyh_a ((polyno1371724751ypow_a K2) P)) N))) of role axiom named fact_349_polypow__normh
% 0.83/1.01 A new axiom: (forall (P:polyno727731844poly_a) (N:nat) (K2:nat), (((polyno1372495879olyh_a P) N)->((polyno1372495879olyh_a ((polyno1371724751ypow_a K2) P)) N)))
% 0.83/1.01 FOF formula (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno1921014231ub_nat V) Va)) B)) ((polyno1415441627ul_nat ((polyno1921014231ub_nat V) Va)) B))) of role axiom named fact_350_polymul_Osimps_I7_J
% 0.83/1.01 A new axiom: (forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno1921014231ub_nat V) Va)) B)) ((polyno1415441627ul_nat ((polyno1921014231ub_nat V) Va)) B)))
% 0.83/1.01 FOF formula (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno975704247_Sub_a V) Va)) B)) ((polyno1491482291_Mul_a ((polyno975704247_Sub_a V) Va)) B))) of role axiom named fact_351_polymul_Osimps_I7_J
% 0.83/1.01 A new axiom: (forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno975704247_Sub_a V) Va)) B)) ((polyno1491482291_Mul_a ((polyno975704247_Sub_a V) Va)) B)))
% 0.83/1.01 FOF formula (forall (P5:Prop), ((or (((eq Prop) P5) True)) (((eq Prop) P5) False))) of role axiom named help_If_3_1_If_001t__Nat__Onat_T
% 0.83/1.01 A new axiom: (forall (P5:Prop), ((or (((eq Prop) P5) True)) (((eq Prop) P5) False)))
% 0.83/1.01 FOF formula (forall (X:nat) (Y:nat), (((eq nat) (((if_nat False) X) Y)) Y)) of role axiom named help_If_2_1_If_001t__Nat__Onat_T
% 0.83/1.01 A new axiom: (forall (X:nat) (Y:nat), (((eq nat) (((if_nat False) X) Y)) Y))
% 0.83/1.01 FOF formula (forall (X:nat) (Y:nat), (((eq nat) (((if_nat True) X) Y)) X)) of role axiom named help_If_1_1_If_001t__Nat__Onat_T
% 0.83/1.01 A new axiom: (forall (X:nat) (Y:nat), (((eq nat) (((if_nat True) X) Y)) X))
% 0.83/1.01 FOF formula (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) ((polyno1934269411ymul_a q) p)) of role conjecture named conj_0
% 0.83/1.01 Conjecture to prove = (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) ((polyno1934269411ymul_a q) p)):Prop
% 0.83/1.01 Parameter polyno1532895200ly_nat_DUMMY:polyno1532895200ly_nat.
% 0.83/1.01 Parameter list_nat_DUMMY:list_nat.
% 0.83/1.01 Parameter list_a_DUMMY:list_a.
% 0.83/1.01 We need to prove ['(((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) ((polyno1934269411ymul_a q) p))']
% 0.83/1.01 Parameter polyno1532895200ly_nat:Type.
% 0.83/1.01 Parameter polyno727731844poly_a:Type.
% 0.83/1.01 Parameter list_nat:Type.
% 0.83/1.01 Parameter list_a:Type.
% 0.83/1.01 Parameter nat:Type.
% 0.83/1.01 Parameter a:Type.
% 0.83/1.01 Parameter one_one_nat:nat.
% 0.83/1.01 Parameter one_one_a:a.
% 0.83/1.01 Parameter plus_plus_nat:(nat->(nat->nat)).
% 0.83/1.01 Parameter plus_plus_a:(a->(a->a)).
% 0.83/1.01 Parameter times_times_nat:(nat->(nat->nat)).
% 0.83/1.01 Parameter times_times_a:(a->(a->a)).
% 0.83/1.01 Parameter zero_zero_nat:nat.
% 0.83/1.01 Parameter zero_zero_a:a.
% 0.83/1.01 Parameter if_nat:(Prop->(nat->(nat->nat))).
% 0.83/1.01 Parameter compow808008746ly_nat:(nat->((polyno1532895200ly_nat->polyno1532895200ly_nat)->(polyno1532895200ly_nat->polyno1532895200ly_nat))).
% 0.83/1.01 Parameter compow1114216044poly_a:(nat->((polyno727731844poly_a->polyno727731844poly_a)->(polyno727731844poly_a->polyno727731844poly_a))).
% 0.83/1.01 Parameter polyno422358502poly_a:(list_a->(polyno727731844poly_a->a)).
% 0.83/1.01 Parameter polyno587244178ad_nat:(polyno1532895200ly_nat->polyno1532895200ly_nat).
% 0.83/1.01 Parameter polyno1465139388head_a:(polyno727731844poly_a->polyno727731844poly_a).
% 0.83/1.01 Parameter polyno220183259ee_nat:(polyno1532895200ly_nat->nat).
% 0.83/1.01 Parameter polyno578545843gree_a:(polyno727731844poly_a->nat).
% 0.83/1.01 Parameter polyno1779722485en_nat:(polyno1532895200ly_nat->(nat->nat)).
% 0.83/1.01 Parameter polyno1674775833reen_a:(polyno727731844poly_a->(nat->nat)).
% 0.83/1.01 Parameter polyno1952548879ad_nat:(polyno1532895200ly_nat->polyno1532895200ly_nat).
% 0.83/1.01 Parameter polyno1884029055head_a:(polyno727731844poly_a->polyno727731844poly_a).
% 0.83/1.01 Parameter polyno524777654st_nat:(polyno1532895200ly_nat->nat).
% 0.83/1.01 Parameter polyno2115742616onst_a:(polyno727731844poly_a->a).
% 0.83/1.01 Parameter polyno544860353dn_nat:(polyno1532895200ly_nat->(nat->polyno1532895200ly_nat)).
% 0.83/1.01 Parameter polyno567601229eadn_a:(polyno727731844poly_a->(nat->polyno727731844poly_a)).
% 0.83/1.01 Parameter polyno1013235523ly_nat:(polyno1532895200ly_nat->Prop).
% 0.83/1.01 Parameter polyno190918219poly_a:(polyno727731844poly_a->Prop).
% 0.83/1.01 Parameter polyno892049031yh_nat:(polyno1532895200ly_nat->(nat->Prop)).
% 0.83/1.01 Parameter polyno1372495879olyh_a:(polyno727731844poly_a->(nat->Prop)).
% 0.83/1.01 Parameter polyno1222032024dd_nat:(polyno1532895200ly_nat->(polyno1532895200ly_nat->polyno1532895200ly_nat)).
% 0.83/1.01 Parameter polyno1623170614_Add_a:(polyno727731844poly_a->(polyno727731844poly_a->polyno727731844poly_a)).
% 0.83/1.01 Parameter polyno1999838549nd_nat:(nat->polyno1532895200ly_nat).
% 0.83/1.01 Parameter polyno2024845497ound_a:(nat->polyno727731844poly_a).
% 0.83/1.01 Parameter polyno720942678CN_nat:(polyno1532895200ly_nat->(nat->(polyno1532895200ly_nat->polyno1532895200ly_nat))).
% 0.83/1.01 Parameter polyno1057396216e_CN_a:(polyno727731844poly_a->(nat->(polyno727731844poly_a->polyno727731844poly_a))).
% 0.83/1.01 Parameter polyno2122022170_C_nat:(nat->polyno1532895200ly_nat).
% 0.83/1.01 Parameter polyno439679028le_C_a:(a->polyno727731844poly_a).
% 0.83/1.01 Parameter polyno1415441627ul_nat:(polyno1532895200ly_nat->(polyno1532895200ly_nat->polyno1532895200ly_nat)).
% 0.83/1.01 Parameter polyno1491482291_Mul_a:(polyno727731844poly_a->(polyno727731844poly_a->polyno727731844poly_a)).
% 0.83/1.01 Parameter polyno1366804583eg_nat:(polyno1532895200ly_nat->polyno1532895200ly_nat).
% 0.83/1.01 Parameter polyno96675367_Neg_a:(polyno727731844poly_a->polyno727731844poly_a).
% 0.83/1.01 Parameter polyno359287218Pw_nat:(polyno1532895200ly_nat->(nat->polyno1532895200ly_nat)).
% 0.83/1.01 Parameter polyno1538138524e_Pw_a:(polyno727731844poly_a->(nat->polyno727731844poly_a)).
% 0.83/1.01 Parameter polyno1921014231ub_nat:(polyno1532895200ly_nat->(polyno1532895200ly_nat->polyno1532895200ly_nat)).
% 0.83/1.01 Parameter polyno975704247_Sub_a:(polyno727731844poly_a->(polyno727731844poly_a->polyno727731844poly_a)).
% 0.83/1.01 Parameter polyno1467023772ul_nat:(nat->(polyno1532895200ly_nat->polyno1532895200ly_nat)).
% 0.83/1.01 Parameter polyno562434098cmul_a:(a->(polyno727731844poly_a->polyno727731844poly_a)).
% 0.83/1.01 Parameter polyno212464073eriv_a:(polyno727731844poly_a->polyno727731844poly_a).
% 0.83/1.01 Parameter polyno1006823949_aux_a:(a->(polyno727731844poly_a->polyno727731844poly_a)).
% 0.83/1.01 Parameter polyno929799083ul_nat:(polyno1532895200ly_nat->(polyno1532895200ly_nat->polyno1532895200ly_nat)).
% 0.83/1.01 Parameter polyno1934269411ymul_a:(polyno727731844poly_a->(polyno727731844poly_a->polyno727731844poly_a)).
% 0.83/1.01 Parameter polyno955999183nate_a:(polyno727731844poly_a->polyno727731844poly_a).
% 0.83/1.01 Parameter polyno1510045887ow_nat:(nat->(polyno1532895200ly_nat->polyno1532895200ly_nat)).
% 0.83/1.01 Parameter polyno1371724751ypow_a:(nat->(polyno727731844poly_a->polyno727731844poly_a)).
% 0.83/1.02 Parameter polyno1418491367ysub_a:(polyno727731844poly_a->(polyno727731844poly_a->polyno727731844poly_a)).
% 0.83/1.02 Parameter polyno336795754t0_nat:(polyno1532895200ly_nat->(polyno1532895200ly_nat->polyno1532895200ly_nat)).
% 0.83/1.02 Parameter polyno1397854436bst0_a:(polyno727731844poly_a->(polyno727731844poly_a->polyno727731844poly_a)).
% 0.83/1.02 Parameter polyno1964927358t1_nat:(polyno1532895200ly_nat->polyno1532895200ly_nat).
% 0.83/1.02 Parameter polyno784948432ift1_a:(polyno727731844poly_a->polyno727731844poly_a).
% 0.83/1.02 Parameter polyno1438831695bs_nat:(list_nat->(polyno1532895200ly_nat->Prop)).
% 0.83/1.02 Parameter polyno896877631f_bs_a:(list_a->(polyno727731844poly_a->Prop)).
% 0.83/1.02 Parameter n0:nat.
% 0.83/1.02 Parameter n1:nat.
% 0.83/1.02 Parameter p:polyno727731844poly_a.
% 0.83/1.02 Parameter q:polyno727731844poly_a.
% 0.83/1.02 Axiom fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062:(((eq Prop) (forall (Bs:list_a), (((eq a) ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))) ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p))))) (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) ((polyno1934269411ymul_a q) p))).
% 0.83/1.02 Axiom fact_1_np:((polyno1372495879olyh_a p) n0).
% 0.83/1.02 Axiom fact_2_nq:((polyno1372495879olyh_a q) n1).
% 0.83/1.02 Axiom fact_3_polymul__norm:(forall (P:polyno727731844poly_a) (Q:polyno727731844poly_a), ((polyno190918219poly_a P)->((polyno190918219poly_a Q)->(polyno190918219poly_a ((polyno1934269411ymul_a P) Q))))).
% 0.83/1.02 Axiom fact_4_wf__bs__polyul:(forall (Bs2:list_nat) (P:polyno1532895200ly_nat) (Q:polyno1532895200ly_nat), (((polyno1438831695bs_nat Bs2) P)->(((polyno1438831695bs_nat Bs2) Q)->((polyno1438831695bs_nat Bs2) ((polyno929799083ul_nat P) Q))))).
% 0.83/1.02 Axiom fact_5_wf__bs__polyul:(forall (Bs2:list_a) (P:polyno727731844poly_a) (Q:polyno727731844poly_a), (((polyno896877631f_bs_a Bs2) P)->(((polyno896877631f_bs_a Bs2) Q)->((polyno896877631f_bs_a Bs2) ((polyno1934269411ymul_a P) Q))))).
% 0.83/1.02 Axiom fact_6_polymul_Osimps_I20_J:(forall (A:polyno1532895200ly_nat) (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat A) ((polyno1415441627ul_nat V) Va))) ((polyno1415441627ul_nat A) ((polyno1415441627ul_nat V) Va)))).
% 0.83/1.02 Axiom fact_7_polymul_Osimps_I20_J:(forall (A:polyno727731844poly_a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a A) ((polyno1491482291_Mul_a V) Va))) ((polyno1491482291_Mul_a A) ((polyno1491482291_Mul_a V) Va)))).
% 0.83/1.02 Axiom fact_8_polymul_Osimps_I8_J:(forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno1415441627ul_nat V) Va)) B)) ((polyno1415441627ul_nat ((polyno1415441627ul_nat V) Va)) B))).
% 0.83/1.02 Axiom fact_9_polymul_Osimps_I8_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1491482291_Mul_a V) Va)) B)) ((polyno1491482291_Mul_a ((polyno1491482291_Mul_a V) Va)) B))).
% 0.83/1.02 Axiom fact_10_polymul:(forall (Bs2:list_a) (P:polyno727731844poly_a) (Q:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) ((polyno1934269411ymul_a P) Q))) ((times_times_a ((polyno422358502poly_a Bs2) P)) ((polyno422358502poly_a Bs2) Q)))).
% 0.83/1.02 Axiom fact_11_polymul_Osimps_I1_J:(forall (C:nat) (C2:nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (polyno2122022170_C_nat C)) (polyno2122022170_C_nat C2))) (polyno2122022170_C_nat ((times_times_nat C) C2)))).
% 0.83/1.02 Axiom fact_12_polymul_Osimps_I1_J:(forall (C:a) (C2:a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno439679028le_C_a C)) (polyno439679028le_C_a C2))) (polyno439679028le_C_a ((times_times_a C) C2)))).
% 0.83/1.02 Axiom fact_13_polynate_Osimps_I4_J:(forall (P:polyno727731844poly_a) (Q:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno955999183nate_a ((polyno1491482291_Mul_a P) Q))) ((polyno1934269411ymul_a (polyno955999183nate_a P)) (polyno955999183nate_a Q)))).
% 0.83/1.02 Axiom fact_14_polymul_Osimps_I26_J:(forall (Vc:polyno1532895200ly_nat) (Vd:polyno1532895200ly_nat) (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno1415441627ul_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb))) ((polyno1415441627ul_nat ((polyno1415441627ul_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb)))).
% 0.83/1.02 Axiom fact_15_polymul_Osimps_I26_J:(forall (Vc:polyno727731844poly_a) (Vd:polyno727731844poly_a) (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1491482291_Mul_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb))) ((polyno1491482291_Mul_a ((polyno1491482291_Mul_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb)))).
% 0.83/1.02 Axiom fact_16_polymul_Osimps_I14_J:(forall (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat) (Vc:polyno1532895200ly_nat) (Vd:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno1415441627ul_nat Vc) Vd))) ((polyno1415441627ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno1415441627ul_nat Vc) Vd)))).
% 0.83/1.02 Axiom fact_17_polymul_Osimps_I14_J:(forall (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a) (Vc:polyno727731844poly_a) (Vd:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1491482291_Mul_a Vc) Vd))) ((polyno1491482291_Mul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1491482291_Mul_a Vc) Vd)))).
% 0.83/1.02 Axiom fact_18_polymul_Osimps_I18_J:(forall (A:polyno1532895200ly_nat) (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat A) ((polyno1222032024dd_nat V) Va))) ((polyno1415441627ul_nat A) ((polyno1222032024dd_nat V) Va)))).
% 0.83/1.02 Axiom fact_19_polymul_Osimps_I18_J:(forall (A:polyno727731844poly_a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a A) ((polyno1623170614_Add_a V) Va))) ((polyno1491482291_Mul_a A) ((polyno1623170614_Add_a V) Va)))).
% 0.83/1.02 Axiom fact_20_poly_Oinject_I8_J:(forall (X81:polyno727731844poly_a) (X82:nat) (X83:polyno727731844poly_a) (Y81:polyno727731844poly_a) (Y82:nat) (Y83:polyno727731844poly_a), (((eq Prop) (((eq polyno727731844poly_a) (((polyno1057396216e_CN_a X81) X82) X83)) (((polyno1057396216e_CN_a Y81) Y82) Y83))) ((and ((and (((eq polyno727731844poly_a) X81) Y81)) (((eq nat) X82) Y82))) (((eq polyno727731844poly_a) X83) Y83)))).
% 0.83/1.02 Axiom fact_21_poly_Oinject_I8_J:(forall (X81:polyno1532895200ly_nat) (X82:nat) (X83:polyno1532895200ly_nat) (Y81:polyno1532895200ly_nat) (Y82:nat) (Y83:polyno1532895200ly_nat), (((eq Prop) (((eq polyno1532895200ly_nat) (((polyno720942678CN_nat X81) X82) X83)) (((polyno720942678CN_nat Y81) Y82) Y83))) ((and ((and (((eq polyno1532895200ly_nat) X81) Y81)) (((eq nat) X82) Y82))) (((eq polyno1532895200ly_nat) X83) Y83)))).
% 0.83/1.02 Axiom fact_22_poly_Oinject_I1_J:(forall (X1:a) (Y1:a), (((eq Prop) (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) (polyno439679028le_C_a Y1))) (((eq a) X1) Y1))).
% 0.83/1.02 Axiom fact_23_poly_Oinject_I1_J:(forall (X1:nat) (Y1:nat), (((eq Prop) (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) (polyno2122022170_C_nat Y1))) (((eq nat) X1) Y1))).
% 0.83/1.02 Axiom fact_24_poly_Oinject_I5_J:(forall (X51:polyno1532895200ly_nat) (X52:polyno1532895200ly_nat) (Y51:polyno1532895200ly_nat) (Y52:polyno1532895200ly_nat), (((eq Prop) (((eq polyno1532895200ly_nat) ((polyno1415441627ul_nat X51) X52)) ((polyno1415441627ul_nat Y51) Y52))) ((and (((eq polyno1532895200ly_nat) X51) Y51)) (((eq polyno1532895200ly_nat) X52) Y52)))).
% 0.83/1.02 Axiom fact_25_poly_Oinject_I5_J:(forall (X51:polyno727731844poly_a) (X52:polyno727731844poly_a) (Y51:polyno727731844poly_a) (Y52:polyno727731844poly_a), (((eq Prop) (((eq polyno727731844poly_a) ((polyno1491482291_Mul_a X51) X52)) ((polyno1491482291_Mul_a Y51) Y52))) ((and (((eq polyno727731844poly_a) X51) Y51)) (((eq polyno727731844poly_a) X52) Y52)))).
% 0.83/1.02 Axiom fact_26_poly_Oinject_I3_J:(forall (X31:polyno727731844poly_a) (X32:polyno727731844poly_a) (Y31:polyno727731844poly_a) (Y32:polyno727731844poly_a), (((eq Prop) (((eq polyno727731844poly_a) ((polyno1623170614_Add_a X31) X32)) ((polyno1623170614_Add_a Y31) Y32))) ((and (((eq polyno727731844poly_a) X31) Y31)) (((eq polyno727731844poly_a) X32) Y32)))).
% 0.83/1.02 Axiom fact_27_poly_Oinject_I3_J:(forall (X31:polyno1532895200ly_nat) (X32:polyno1532895200ly_nat) (Y31:polyno1532895200ly_nat) (Y32:polyno1532895200ly_nat), (((eq Prop) (((eq polyno1532895200ly_nat) ((polyno1222032024dd_nat X31) X32)) ((polyno1222032024dd_nat Y31) Y32))) ((and (((eq polyno1532895200ly_nat) X31) Y31)) (((eq polyno1532895200ly_nat) X32) Y32)))).
% 0.83/1.02 Axiom fact_28_polynate:(forall (Bs2:list_a) (P:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) (polyno955999183nate_a P))) ((polyno422358502poly_a Bs2) P))).
% 0.83/1.02 Axiom fact_29_Ipoly_Osimps_I6_J:(forall (Bs2:list_a) (A:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) ((polyno1491482291_Mul_a A) B))) ((times_times_a ((polyno422358502poly_a Bs2) A)) ((polyno422358502poly_a Bs2) B)))).
% 0.83/1.02 Axiom fact_30_Ipoly_Osimps_I1_J:(forall (Bs2:list_a) (C:a), (((eq a) ((polyno422358502poly_a Bs2) (polyno439679028le_C_a C))) C)).
% 0.83/1.02 Axiom fact_31_poly_Odistinct_I49_J:(forall (X51:polyno1532895200ly_nat) (X52:polyno1532895200ly_nat) (X81:polyno1532895200ly_nat) (X82:nat) (X83:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) ((polyno1415441627ul_nat X51) X52)) (((polyno720942678CN_nat X81) X82) X83)))).
% 0.83/1.02 Axiom fact_32_poly_Odistinct_I49_J:(forall (X51:polyno727731844poly_a) (X52:polyno727731844poly_a) (X81:polyno727731844poly_a) (X82:nat) (X83:polyno727731844poly_a), (not (((eq polyno727731844poly_a) ((polyno1491482291_Mul_a X51) X52)) (((polyno1057396216e_CN_a X81) X82) X83)))).
% 0.83/1.02 Axiom fact_33_poly_Odistinct_I35_J:(forall (X31:polyno727731844poly_a) (X32:polyno727731844poly_a) (X81:polyno727731844poly_a) (X82:nat) (X83:polyno727731844poly_a), (not (((eq polyno727731844poly_a) ((polyno1623170614_Add_a X31) X32)) (((polyno1057396216e_CN_a X81) X82) X83)))).
% 0.83/1.02 Axiom fact_34_poly_Odistinct_I35_J:(forall (X31:polyno1532895200ly_nat) (X32:polyno1532895200ly_nat) (X81:polyno1532895200ly_nat) (X82:nat) (X83:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) ((polyno1222032024dd_nat X31) X32)) (((polyno720942678CN_nat X81) X82) X83)))).
% 0.83/1.02 Axiom fact_35_poly_Odistinct_I29_J:(forall (X31:polyno1532895200ly_nat) (X32:polyno1532895200ly_nat) (X51:polyno1532895200ly_nat) (X52:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) ((polyno1222032024dd_nat X31) X32)) ((polyno1415441627ul_nat X51) X52)))).
% 0.83/1.02 Axiom fact_36_poly_Odistinct_I29_J:(forall (X31:polyno727731844poly_a) (X32:polyno727731844poly_a) (X51:polyno727731844poly_a) (X52:polyno727731844poly_a), (not (((eq polyno727731844poly_a) ((polyno1623170614_Add_a X31) X32)) ((polyno1491482291_Mul_a X51) X52)))).
% 0.83/1.02 Axiom fact_37_poly_Odistinct_I13_J:(forall (X1:a) (X81:polyno727731844poly_a) (X82:nat) (X83:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) (((polyno1057396216e_CN_a X81) X82) X83)))).
% 0.83/1.02 Axiom fact_38_poly_Odistinct_I13_J:(forall (X1:nat) (X81:polyno1532895200ly_nat) (X82:nat) (X83:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) (((polyno720942678CN_nat X81) X82) X83)))).
% 0.83/1.02 Axiom fact_39_poly_Odistinct_I7_J:(forall (X1:nat) (X51:polyno1532895200ly_nat) (X52:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) ((polyno1415441627ul_nat X51) X52)))).
% 0.83/1.02 Axiom fact_40_poly_Odistinct_I7_J:(forall (X1:a) (X51:polyno727731844poly_a) (X52:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) ((polyno1491482291_Mul_a X51) X52)))).
% 0.83/1.02 Axiom fact_41_poly_Odistinct_I3_J:(forall (X1:a) (X31:polyno727731844poly_a) (X32:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) ((polyno1623170614_Add_a X31) X32)))).
% 0.83/1.02 Axiom fact_42_poly_Odistinct_I3_J:(forall (X1:nat) (X31:polyno1532895200ly_nat) (X32:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) ((polyno1222032024dd_nat X31) X32)))).
% 0.83/1.02 Axiom fact_43_polymul_Osimps_I24_J:(forall (Vc:polyno1532895200ly_nat) (Vd:polyno1532895200ly_nat) (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno1222032024dd_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb))) ((polyno1415441627ul_nat ((polyno1222032024dd_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb)))).
% 0.83/1.02 Axiom fact_44_polymul_Osimps_I24_J:(forall (Vc:polyno727731844poly_a) (Vd:polyno727731844poly_a) (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1623170614_Add_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb))) ((polyno1491482291_Mul_a ((polyno1623170614_Add_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb)))).
% 0.83/1.02 Axiom fact_45_polymul_Osimps_I12_J:(forall (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat) (Vc:polyno1532895200ly_nat) (Vd:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno1222032024dd_nat Vc) Vd))) ((polyno1415441627ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno1222032024dd_nat Vc) Vd)))).
% 0.83/1.02 Axiom fact_46_polymul_Osimps_I12_J:(forall (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a) (Vc:polyno727731844poly_a) (Vd:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1623170614_Add_a Vc) Vd))) ((polyno1491482291_Mul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1623170614_Add_a Vc) Vd)))).
% 0.83/1.02 Axiom fact_47_isnpolyh_Osimps_I6_J:(forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->Prop)) (polyno892049031yh_nat ((polyno1415441627ul_nat V) Va))) (fun (K:nat)=> False))).
% 0.83/1.02 Axiom fact_48_isnpolyh_Osimps_I6_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->Prop)) (polyno1372495879olyh_a ((polyno1491482291_Mul_a V) Va))) (fun (K:nat)=> False))).
% 0.83/1.02 Axiom fact_49_isnpolyh_Osimps_I4_J:(forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->Prop)) (polyno892049031yh_nat ((polyno1222032024dd_nat V) Va))) (fun (K:nat)=> False))).
% 0.83/1.02 Axiom fact_50_isnpolyh_Osimps_I4_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->Prop)) (polyno1372495879olyh_a ((polyno1623170614_Add_a V) Va))) (fun (K:nat)=> False))).
% 0.83/1.02 Axiom fact_51_isnpolyh_Osimps_I1_J:(forall (C:nat), (((eq (nat->Prop)) (polyno892049031yh_nat (polyno2122022170_C_nat C))) (fun (K:nat)=> True))).
% 0.83/1.02 Axiom fact_52_isnpolyh_Osimps_I1_J:(forall (C:a), (((eq (nat->Prop)) (polyno1372495879olyh_a (polyno439679028le_C_a C))) (fun (K:nat)=> True))).
% 0.83/1.02 Axiom fact_53_polynate_Osimps_I8_J:(forall (C:a), (((eq polyno727731844poly_a) (polyno955999183nate_a (polyno439679028le_C_a C))) (polyno439679028le_C_a C))).
% 0.83/1.02 Axiom fact_54_polynate__norm:(forall (P:polyno727731844poly_a), (polyno190918219poly_a (polyno955999183nate_a P))).
% 0.83/1.02 Axiom fact_55_isnpolyh__unique:(forall (P:polyno727731844poly_a) (N0:nat) (Q:polyno727731844poly_a) (N1:nat), (((polyno1372495879olyh_a P) N0)->(((polyno1372495879olyh_a Q) N1)->(((eq Prop) (forall (Bs:list_a), (((eq a) ((polyno422358502poly_a Bs) P)) ((polyno422358502poly_a Bs) Q)))) (((eq polyno727731844poly_a) P) Q))))).
% 0.83/1.02 Axiom fact_56_polymul_Osimps_I6_J:(forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno1222032024dd_nat V) Va)) B)) ((polyno1415441627ul_nat ((polyno1222032024dd_nat V) Va)) B))).
% 0.83/1.02 Axiom fact_57_polymul_Osimps_I6_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1623170614_Add_a V) Va)) B)) ((polyno1491482291_Mul_a ((polyno1623170614_Add_a V) Va)) B))).
% 0.83/1.02 Axiom fact_58_isnpolyh__zero__iff:(forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->((forall (Bs3:list_a), (((polyno896877631f_bs_a Bs3) P)->(((eq a) ((polyno422358502poly_a Bs3) P)) zero_zero_a)))->(((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a))))).
% 0.83/1.02 Axiom fact_59_poly__cmul:(forall (Bs2:list_a) (C:a) (P:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) ((polyno562434098cmul_a C) P))) ((polyno422358502poly_a Bs2) ((polyno1491482291_Mul_a (polyno439679028le_C_a C)) P)))).
% 0.83/1.02 Axiom fact_60_polymul__0_I2_J:(forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno439679028le_C_a zero_zero_a)) P)) (polyno439679028le_C_a zero_zero_a)))).
% 0.83/1.02 Axiom fact_61_polymul__0_I1_J:(forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a P) (polyno439679028le_C_a zero_zero_a))) (polyno439679028le_C_a zero_zero_a)))).
% 0.83/1.02 Axiom fact_62_polymul__1_I2_J:(forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno439679028le_C_a one_one_a)) P)) P))).
% 0.83/1.02 Axiom fact_63_polymul__1_I1_J:(forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a P) (polyno439679028le_C_a one_one_a))) P))).
% 0.83/1.02 Axiom fact_64_polynate_Osimps_I7_J:(forall (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno955999183nate_a (((polyno1057396216e_CN_a C) N) P))) (polyno955999183nate_a ((polyno1623170614_Add_a C) ((polyno1491482291_Mul_a (polyno2024845497ound_a N)) P))))).
% 0.83/1.02 Axiom fact_65_polymul__eq0__iff:(forall (P:polyno727731844poly_a) (N0:nat) (Q:polyno727731844poly_a) (N1:nat), (((polyno1372495879olyh_a P) N0)->(((polyno1372495879olyh_a Q) N1)->(((eq Prop) (((eq polyno727731844poly_a) ((polyno1934269411ymul_a P) Q)) (polyno439679028le_C_a zero_zero_a))) ((or (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a))) (((eq polyno727731844poly_a) Q) (polyno439679028le_C_a zero_zero_a))))))).
% 0.83/1.02 Axiom fact_66_poly__cmul_Osimps_I4_J:(forall (Y:a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) ((polyno1623170614_Add_a V) Va))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) ((polyno1623170614_Add_a V) Va)))).
% 0.83/1.02 Axiom fact_67_poly__cmul_Osimps_I4_J:(forall (Y:nat) (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) ((polyno1222032024dd_nat V) Va))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) ((polyno1222032024dd_nat V) Va)))).
% 0.83/1.02 Axiom fact_68_poly__cmul_Osimps_I6_J:(forall (Y:nat) (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) ((polyno1415441627ul_nat V) Va))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) ((polyno1415441627ul_nat V) Va)))).
% 0.83/1.02 Axiom fact_69_poly__cmul_Osimps_I6_J:(forall (Y:a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) ((polyno1491482291_Mul_a V) Va))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) ((polyno1491482291_Mul_a V) Va)))).
% 0.83/1.02 Axiom fact_70_polymul_Osimps_I3_J:(forall (C2:a) (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a), ((and ((((eq a) C2) zero_zero_a)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a C) N) P)) (polyno439679028le_C_a C2))) (polyno439679028le_C_a zero_zero_a)))) ((not (((eq a) C2) zero_zero_a))->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a C) N) P)) (polyno439679028le_C_a C2))) (((polyno1057396216e_CN_a ((polyno1934269411ymul_a C) (polyno439679028le_C_a C2))) N) ((polyno1934269411ymul_a P) (polyno439679028le_C_a C2))))))).
% 0.83/1.02 Axiom fact_71_polymul_Osimps_I3_J:(forall (C2:nat) (C:polyno1532895200ly_nat) (N:nat) (P:polyno1532895200ly_nat), ((and ((((eq nat) C2) zero_zero_nat)->(((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat C) N) P)) (polyno2122022170_C_nat C2))) (polyno2122022170_C_nat zero_zero_nat)))) ((not (((eq nat) C2) zero_zero_nat))->(((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat C) N) P)) (polyno2122022170_C_nat C2))) (((polyno720942678CN_nat ((polyno929799083ul_nat C) (polyno2122022170_C_nat C2))) N) ((polyno929799083ul_nat P) (polyno2122022170_C_nat C2))))))).
% 0.83/1.02 Axiom fact_72_poly_Oinject_I2_J:(forall (X2:nat) (Y2:nat), (((eq Prop) (((eq polyno727731844poly_a) (polyno2024845497ound_a X2)) (polyno2024845497ound_a Y2))) (((eq nat) X2) Y2))).
% 0.83/1.02 Axiom fact_73_poly_Oinject_I2_J:(forall (X2:nat) (Y2:nat), (((eq Prop) (((eq polyno1532895200ly_nat) (polyno1999838549nd_nat X2)) (polyno1999838549nd_nat Y2))) (((eq nat) X2) Y2))).
% 0.83/1.02 Axiom fact_74_polynate_Osimps_I1_J:(forall (N:nat), (((eq polyno727731844poly_a) (polyno955999183nate_a (polyno2024845497ound_a N))) (((polyno1057396216e_CN_a (polyno439679028le_C_a zero_zero_a)) N) (polyno439679028le_C_a one_one_a)))).
% 0.83/1.02 Axiom fact_75_poly__cmul_Osimps_I3_J:(forall (Y:a) (V:nat), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) (polyno2024845497ound_a V))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) (polyno2024845497ound_a V)))).
% 0.83/1.02 Axiom fact_76_poly__cmul_Osimps_I3_J:(forall (Y:nat) (V:nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) (polyno1999838549nd_nat V))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) (polyno1999838549nd_nat V)))).
% 0.83/1.02 Axiom fact_77_poly_Odistinct_I25_J:(forall (X2:nat) (X81:polyno727731844poly_a) (X82:nat) (X83:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno2024845497ound_a X2)) (((polyno1057396216e_CN_a X81) X82) X83)))).
% 0.83/1.02 Axiom fact_78_poly_Odistinct_I25_J:(forall (X2:nat) (X81:polyno1532895200ly_nat) (X82:nat) (X83:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno1999838549nd_nat X2)) (((polyno720942678CN_nat X81) X82) X83)))).
% 0.83/1.02 Axiom fact_79_poly_Odistinct_I1_J:(forall (X1:a) (X2:nat), (not (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) (polyno2024845497ound_a X2)))).
% 0.83/1.02 Axiom fact_80_poly_Odistinct_I1_J:(forall (X1:nat) (X2:nat), (not (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) (polyno1999838549nd_nat X2)))).
% 0.83/1.02 Axiom fact_81_poly_Odistinct_I19_J:(forall (X2:nat) (X51:polyno1532895200ly_nat) (X52:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno1999838549nd_nat X2)) ((polyno1415441627ul_nat X51) X52)))).
% 0.83/1.02 Axiom fact_82_poly_Odistinct_I19_J:(forall (X2:nat) (X51:polyno727731844poly_a) (X52:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno2024845497ound_a X2)) ((polyno1491482291_Mul_a X51) X52)))).
% 0.83/1.02 Axiom fact_83_poly_Odistinct_I15_J:(forall (X2:nat) (X31:polyno727731844poly_a) (X32:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno2024845497ound_a X2)) ((polyno1623170614_Add_a X31) X32)))).
% 0.83/1.02 Axiom fact_84_poly_Odistinct_I15_J:(forall (X2:nat) (X31:polyno1532895200ly_nat) (X32:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno1999838549nd_nat X2)) ((polyno1222032024dd_nat X31) X32)))).
% 0.83/1.02 Axiom fact_85_isnpolyh_Osimps_I3_J:(forall (V:nat), (((eq (nat->Prop)) (polyno892049031yh_nat (polyno1999838549nd_nat V))) (fun (K:nat)=> False))).
% 0.83/1.02 Axiom fact_86_isnpolyh_Osimps_I3_J:(forall (V:nat), (((eq (nat->Prop)) (polyno1372495879olyh_a (polyno2024845497ound_a V))) (fun (K:nat)=> False))).
% 0.83/1.02 Axiom fact_87_poly__cmul_Osimps_I2_J:(forall (Y:a) (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) (((polyno1057396216e_CN_a C) N) P))) (((polyno1057396216e_CN_a ((polyno562434098cmul_a Y) C)) N) ((polyno562434098cmul_a Y) P)))).
% 0.83/1.02 Axiom fact_88_poly__cmul_Osimps_I2_J:(forall (Y:nat) (C:polyno1532895200ly_nat) (N:nat) (P:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) (((polyno720942678CN_nat C) N) P))) (((polyno720942678CN_nat ((polyno1467023772ul_nat Y) C)) N) ((polyno1467023772ul_nat Y) P)))).
% 0.83/1.02 Axiom fact_89_polymul_Osimps_I17_J:(forall (A:polyno1532895200ly_nat) (V:nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat A) (polyno1999838549nd_nat V))) ((polyno1415441627ul_nat A) (polyno1999838549nd_nat V)))).
% 0.83/1.02 Axiom fact_90_polymul_Osimps_I17_J:(forall (A:polyno727731844poly_a) (V:nat), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a A) (polyno2024845497ound_a V))) ((polyno1491482291_Mul_a A) (polyno2024845497ound_a V)))).
% 0.83/1.02 Axiom fact_91_polymul_Osimps_I5_J:(forall (V:nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (polyno1999838549nd_nat V)) B)) ((polyno1415441627ul_nat (polyno1999838549nd_nat V)) B))).
% 0.83/1.02 Axiom fact_92_polymul_Osimps_I5_J:(forall (V:nat) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno2024845497ound_a V)) B)) ((polyno1491482291_Mul_a (polyno2024845497ound_a V)) B))).
% 0.83/1.02 Axiom fact_93_poly__cmul_Osimps_I1_J:(forall (Y:a) (X:a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) (polyno439679028le_C_a X))) (polyno439679028le_C_a ((times_times_a Y) X)))).
% 0.83/1.02 Axiom fact_94_poly__cmul_Osimps_I1_J:(forall (Y:nat) (X:nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) (polyno2122022170_C_nat X))) (polyno2122022170_C_nat ((times_times_nat Y) X)))).
% 0.83/1.02 Axiom fact_95_one__normh:(forall (N:nat), ((polyno892049031yh_nat (polyno2122022170_C_nat one_one_nat)) N)).
% 0.83/1.02 Axiom fact_96_one__normh:(forall (N:nat), ((polyno1372495879olyh_a (polyno439679028le_C_a one_one_a)) N)).
% 0.83/1.02 Axiom fact_97_zero__normh:(forall (N:nat), ((polyno892049031yh_nat (polyno2122022170_C_nat zero_zero_nat)) N)).
% 0.83/1.02 Axiom fact_98_zero__normh:(forall (N:nat), ((polyno1372495879olyh_a (polyno439679028le_C_a zero_zero_a)) N)).
% 0.83/1.02 Axiom fact_99_isnpoly__def:(((eq (polyno1532895200ly_nat->Prop)) polyno1013235523ly_nat) (fun (P2:polyno1532895200ly_nat)=> ((polyno892049031yh_nat P2) zero_zero_nat))).
% 0.83/1.02 Axiom fact_100_isnpoly__def:(((eq (polyno727731844poly_a->Prop)) polyno190918219poly_a) (fun (P2:polyno727731844poly_a)=> ((polyno1372495879olyh_a P2) zero_zero_nat))).
% 0.83/1.02 Axiom fact_101_polymul_Osimps_I11_J:(forall (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat) (Vc:nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat V) Va) Vb)) (polyno1999838549nd_nat Vc))) ((polyno1415441627ul_nat (((polyno720942678CN_nat V) Va) Vb)) (polyno1999838549nd_nat Vc)))).
% 0.83/1.02 Axiom fact_102_polymul_Osimps_I11_J:(forall (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a) (Vc:nat), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a V) Va) Vb)) (polyno2024845497ound_a Vc))) ((polyno1491482291_Mul_a (((polyno1057396216e_CN_a V) Va) Vb)) (polyno2024845497ound_a Vc)))).
% 0.83/1.02 Axiom fact_103_polymul_Osimps_I23_J:(forall (Vc:nat) (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (polyno1999838549nd_nat Vc)) (((polyno720942678CN_nat V) Va) Vb))) ((polyno1415441627ul_nat (polyno1999838549nd_nat Vc)) (((polyno720942678CN_nat V) Va) Vb)))).
% 0.83/1.02 Axiom fact_104_polymul_Osimps_I23_J:(forall (Vc:nat) (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno2024845497ound_a Vc)) (((polyno1057396216e_CN_a V) Va) Vb))) ((polyno1491482291_Mul_a (polyno2024845497ound_a Vc)) (((polyno1057396216e_CN_a V) Va) Vb)))).
% 0.83/1.02 Axiom fact_105_polymul_Osimps_I2_J:(forall (C:a) (C2:polyno727731844poly_a) (N2:nat) (P3:polyno727731844poly_a), ((and ((((eq a) C) zero_zero_a)->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno439679028le_C_a C)) (((polyno1057396216e_CN_a C2) N2) P3))) (polyno439679028le_C_a zero_zero_a)))) ((not (((eq a) C) zero_zero_a))->(((eq polyno727731844poly_a) ((polyno1934269411ymul_a (polyno439679028le_C_a C)) (((polyno1057396216e_CN_a C2) N2) P3))) (((polyno1057396216e_CN_a ((polyno1934269411ymul_a (polyno439679028le_C_a C)) C2)) N2) ((polyno1934269411ymul_a (polyno439679028le_C_a C)) P3)))))).
% 0.83/1.02 Axiom fact_106_polymul_Osimps_I2_J:(forall (C:nat) (C2:polyno1532895200ly_nat) (N2:nat) (P3:polyno1532895200ly_nat), ((and ((((eq nat) C) zero_zero_nat)->(((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (polyno2122022170_C_nat C)) (((polyno720942678CN_nat C2) N2) P3))) (polyno2122022170_C_nat zero_zero_nat)))) ((not (((eq nat) C) zero_zero_nat))->(((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (polyno2122022170_C_nat C)) (((polyno720942678CN_nat C2) N2) P3))) (((polyno720942678CN_nat ((polyno929799083ul_nat (polyno2122022170_C_nat C)) C2)) N2) ((polyno929799083ul_nat (polyno2122022170_C_nat C)) P3)))))).
% 0.83/1.02 Axiom fact_107_mult__cancel__left1:(forall (C:a) (B:a), (((eq Prop) (((eq a) C) ((times_times_a C) B))) ((or (((eq a) C) zero_zero_a)) (((eq a) B) one_one_a)))).
% 0.83/1.02 Axiom fact_108_mult__cancel__left2:(forall (C:a) (A:a), (((eq Prop) (((eq a) ((times_times_a C) A)) C)) ((or (((eq a) C) zero_zero_a)) (((eq a) A) one_one_a)))).
% 0.83/1.02 Axiom fact_109_mult__cancel__right1:(forall (C:a) (B:a), (((eq Prop) (((eq a) C) ((times_times_a B) C))) ((or (((eq a) C) zero_zero_a)) (((eq a) B) one_one_a)))).
% 0.83/1.02 Axiom fact_110_mult__cancel__right2:(forall (A:a) (C:a), (((eq Prop) (((eq a) ((times_times_a A) C)) C)) ((or (((eq a) C) zero_zero_a)) (((eq a) A) one_one_a)))).
% 0.83/1.02 Axiom fact_111_mult_Oright__neutral:(forall (A:nat), (((eq nat) ((times_times_nat A) one_one_nat)) A)).
% 0.83/1.02 Axiom fact_112_mult_Oright__neutral:(forall (A:a), (((eq a) ((times_times_a A) one_one_a)) A)).
% 0.83/1.02 Axiom fact_113_mult_Oleft__neutral:(forall (A:nat), (((eq nat) ((times_times_nat one_one_nat) A)) A)).
% 0.83/1.02 Axiom fact_114_mult_Oleft__neutral:(forall (A:a), (((eq a) ((times_times_a one_one_a) A)) A)).
% 0.83/1.02 Axiom fact_115_mult__cancel__right:(forall (A:nat) (C:nat) (B:nat), (((eq Prop) (((eq nat) ((times_times_nat A) C)) ((times_times_nat B) C))) ((or (((eq nat) C) zero_zero_nat)) (((eq nat) A) B)))).
% 0.83/1.02 Axiom fact_116_mult__cancel__right:(forall (A:a) (C:a) (B:a), (((eq Prop) (((eq a) ((times_times_a A) C)) ((times_times_a B) C))) ((or (((eq a) C) zero_zero_a)) (((eq a) A) B)))).
% 0.83/1.02 Axiom fact_117_mult__cancel__left:(forall (C:nat) (A:nat) (B:nat), (((eq Prop) (((eq nat) ((times_times_nat C) A)) ((times_times_nat C) B))) ((or (((eq nat) C) zero_zero_nat)) (((eq nat) A) B)))).
% 0.83/1.02 Axiom fact_118_mult__cancel__left:(forall (C:a) (A:a) (B:a), (((eq Prop) (((eq a) ((times_times_a C) A)) ((times_times_a C) B))) ((or (((eq a) C) zero_zero_a)) (((eq a) A) B)))).
% 0.83/1.02 Axiom fact_119_mult__zero__left:(forall (A:nat), (((eq nat) ((times_times_nat zero_zero_nat) A)) zero_zero_nat)).
% 0.83/1.02 Axiom fact_120_mult__zero__left:(forall (A:a), (((eq a) ((times_times_a zero_zero_a) A)) zero_zero_a)).
% 0.83/1.02 Axiom fact_121_mult__zero__right:(forall (A:nat), (((eq nat) ((times_times_nat A) zero_zero_nat)) zero_zero_nat)).
% 0.83/1.02 Axiom fact_122_mult__zero__right:(forall (A:a), (((eq a) ((times_times_a A) zero_zero_a)) zero_zero_a)).
% 0.83/1.02 Axiom fact_123_mult__eq__0__iff:(forall (A:nat) (B:nat), (((eq Prop) (((eq nat) ((times_times_nat A) B)) zero_zero_nat)) ((or (((eq nat) A) zero_zero_nat)) (((eq nat) B) zero_zero_nat)))).
% 0.83/1.02 Axiom fact_124_mult__eq__0__iff:(forall (A:a) (B:a), (((eq Prop) (((eq a) ((times_times_a A) B)) zero_zero_a)) ((or (((eq a) A) zero_zero_a)) (((eq a) B) zero_zero_a)))).
% 0.83/1.02 Axiom fact_125_zero__reorient:(forall (X:a), (((eq Prop) (((eq a) zero_zero_a) X)) (((eq a) X) zero_zero_a))).
% 0.83/1.02 Axiom fact_126_zero__reorient:(forall (X:nat), (((eq Prop) (((eq nat) zero_zero_nat) X)) (((eq nat) X) zero_zero_nat))).
% 0.83/1.02 Axiom fact_127_ab__semigroup__mult__class_Omult__ac_I1_J:(forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat ((times_times_nat A) B)) C)) ((times_times_nat A) ((times_times_nat B) C)))).
% 0.83/1.02 Axiom fact_128_ab__semigroup__mult__class_Omult__ac_I1_J:(forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a ((times_times_a A) B)) C)) ((times_times_a A) ((times_times_a B) C)))).
% 0.83/1.02 Axiom fact_129_mult_Oassoc:(forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat ((times_times_nat A) B)) C)) ((times_times_nat A) ((times_times_nat B) C)))).
% 0.83/1.02 Axiom fact_130_mult_Oassoc:(forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a ((times_times_a A) B)) C)) ((times_times_a A) ((times_times_a B) C)))).
% 0.83/1.02 Axiom fact_131_mult_Ocommute:(((eq (nat->(nat->nat))) times_times_nat) (fun (A2:nat) (B2:nat)=> ((times_times_nat B2) A2))).
% 0.83/1.02 Axiom fact_132_mult_Ocommute:(((eq (a->(a->a))) times_times_a) (fun (A2:a) (B2:a)=> ((times_times_a B2) A2))).
% 0.83/1.02 Axiom fact_133_mult_Oleft__commute:(forall (B:nat) (A:nat) (C:nat), (((eq nat) ((times_times_nat B) ((times_times_nat A) C))) ((times_times_nat A) ((times_times_nat B) C)))).
% 0.83/1.03 Axiom fact_134_mult_Oleft__commute:(forall (B:a) (A:a) (C:a), (((eq a) ((times_times_a B) ((times_times_a A) C))) ((times_times_a A) ((times_times_a B) C)))).
% 0.83/1.03 Axiom fact_135_one__reorient:(forall (X:a), (((eq Prop) (((eq a) one_one_a) X)) (((eq a) X) one_one_a))).
% 0.83/1.03 Axiom fact_136_one__reorient:(forall (X:nat), (((eq Prop) (((eq nat) one_one_nat) X)) (((eq nat) X) one_one_nat))).
% 0.83/1.03 Axiom fact_137_mult__not__zero:(forall (A:nat) (B:nat), ((not (((eq nat) ((times_times_nat A) B)) zero_zero_nat))->((and (not (((eq nat) A) zero_zero_nat))) (not (((eq nat) B) zero_zero_nat))))).
% 0.83/1.03 Axiom fact_138_mult__not__zero:(forall (A:a) (B:a), ((not (((eq a) ((times_times_a A) B)) zero_zero_a))->((and (not (((eq a) A) zero_zero_a))) (not (((eq a) B) zero_zero_a))))).
% 0.83/1.03 Axiom fact_139_divisors__zero:(forall (A:nat) (B:nat), ((((eq nat) ((times_times_nat A) B)) zero_zero_nat)->((or (((eq nat) A) zero_zero_nat)) (((eq nat) B) zero_zero_nat)))).
% 0.83/1.03 Axiom fact_140_divisors__zero:(forall (A:a) (B:a), ((((eq a) ((times_times_a A) B)) zero_zero_a)->((or (((eq a) A) zero_zero_a)) (((eq a) B) zero_zero_a)))).
% 0.83/1.03 Axiom fact_141_no__zero__divisors:(forall (A:nat) (B:nat), ((not (((eq nat) A) zero_zero_nat))->((not (((eq nat) B) zero_zero_nat))->(not (((eq nat) ((times_times_nat A) B)) zero_zero_nat))))).
% 0.83/1.03 Axiom fact_142_no__zero__divisors:(forall (A:a) (B:a), ((not (((eq a) A) zero_zero_a))->((not (((eq a) B) zero_zero_a))->(not (((eq a) ((times_times_a A) B)) zero_zero_a))))).
% 0.83/1.03 Axiom fact_143_mult__left__cancel:(forall (C:nat) (A:nat) (B:nat), ((not (((eq nat) C) zero_zero_nat))->(((eq Prop) (((eq nat) ((times_times_nat C) A)) ((times_times_nat C) B))) (((eq nat) A) B)))).
% 0.83/1.03 Axiom fact_144_mult__left__cancel:(forall (C:a) (A:a) (B:a), ((not (((eq a) C) zero_zero_a))->(((eq Prop) (((eq a) ((times_times_a C) A)) ((times_times_a C) B))) (((eq a) A) B)))).
% 0.83/1.03 Axiom fact_145_mult__right__cancel:(forall (C:nat) (A:nat) (B:nat), ((not (((eq nat) C) zero_zero_nat))->(((eq Prop) (((eq nat) ((times_times_nat A) C)) ((times_times_nat B) C))) (((eq nat) A) B)))).
% 0.83/1.03 Axiom fact_146_mult__right__cancel:(forall (C:a) (A:a) (B:a), ((not (((eq a) C) zero_zero_a))->(((eq Prop) (((eq a) ((times_times_a A) C)) ((times_times_a B) C))) (((eq a) A) B)))).
% 0.83/1.03 Axiom fact_147_zero__neq__one:(not (((eq a) zero_zero_a) one_one_a)).
% 0.83/1.03 Axiom fact_148_zero__neq__one:(not (((eq nat) zero_zero_nat) one_one_nat)).
% 0.83/1.03 Axiom fact_149_comm__monoid__mult__class_Omult__1:(forall (A:nat), (((eq nat) ((times_times_nat one_one_nat) A)) A)).
% 0.83/1.03 Axiom fact_150_comm__monoid__mult__class_Omult__1:(forall (A:a), (((eq a) ((times_times_a one_one_a) A)) A)).
% 0.83/1.03 Axiom fact_151_mult_Ocomm__neutral:(forall (A:nat), (((eq nat) ((times_times_nat A) one_one_nat)) A)).
% 0.83/1.03 Axiom fact_152_mult_Ocomm__neutral:(forall (A:a), (((eq a) ((times_times_a A) one_one_a)) A)).
% 0.83/1.03 Axiom fact_153_mult__is__0:(forall (M:nat) (N:nat), (((eq Prop) (((eq nat) ((times_times_nat M) N)) zero_zero_nat)) ((or (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))).
% 0.83/1.03 Axiom fact_154_mult__0__right:(forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat)).
% 0.83/1.03 Axiom fact_155_mult__cancel1:(forall (K2:nat) (M:nat) (N:nat), (((eq Prop) (((eq nat) ((times_times_nat K2) M)) ((times_times_nat K2) N))) ((or (((eq nat) M) N)) (((eq nat) K2) zero_zero_nat)))).
% 0.83/1.03 Axiom fact_156_mult__cancel2:(forall (M:nat) (K2:nat) (N:nat), (((eq Prop) (((eq nat) ((times_times_nat M) K2)) ((times_times_nat N) K2))) ((or (((eq nat) M) N)) (((eq nat) K2) zero_zero_nat)))).
% 0.83/1.03 Axiom fact_157_shift1:(forall (Bs2:list_a) (P:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) (polyno784948432ift1_a P))) ((polyno422358502poly_a Bs2) ((polyno1491482291_Mul_a (polyno2024845497ound_a zero_zero_nat)) P)))).
% 0.83/1.03 Axiom fact_158_shift1__isnpolyh:(forall (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat P) N0)->((not (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat)))->((polyno892049031yh_nat (polyno1964927358t1_nat P)) zero_zero_nat)))).
% 0.83/1.03 Axiom fact_159_shift1__isnpolyh:(forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->((not (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a)))->((polyno1372495879olyh_a (polyno784948432ift1_a P)) zero_zero_nat)))).
% 0.83/1.03 Axiom fact_160_nat__mult__eq__1__iff:(forall (M:nat) (N:nat), (((eq Prop) (((eq nat) ((times_times_nat M) N)) one_one_nat)) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat)))).
% 0.83/1.03 Axiom fact_161_nat__1__eq__mult__iff:(forall (M:nat) (N:nat), (((eq Prop) (((eq nat) one_one_nat) ((times_times_nat M) N))) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat)))).
% 0.83/1.03 Axiom fact_162_nat__mult__1__right:(forall (N:nat), (((eq nat) ((times_times_nat N) one_one_nat)) N)).
% 0.83/1.03 Axiom fact_163_nat__mult__1:(forall (N:nat), (((eq nat) ((times_times_nat one_one_nat) N)) N)).
% 0.83/1.03 Axiom fact_164_mult__eq__self__implies__10:(forall (M:nat) (N:nat), ((((eq nat) M) ((times_times_nat M) N))->((or (((eq nat) N) one_one_nat)) (((eq nat) M) zero_zero_nat)))).
% 0.83/1.03 Axiom fact_165_mult__0:(forall (N:nat), (((eq nat) ((times_times_nat zero_zero_nat) N)) zero_zero_nat)).
% 0.83/1.03 Axiom fact_166_shift1__nz:(forall (P:polyno727731844poly_a), (not (((eq polyno727731844poly_a) (polyno784948432ift1_a P)) (polyno439679028le_C_a zero_zero_a)))).
% 0.83/1.03 Axiom fact_167_shift1__nz:(forall (P:polyno1532895200ly_nat), (not (((eq polyno1532895200ly_nat) (polyno1964927358t1_nat P)) (polyno2122022170_C_nat zero_zero_nat)))).
% 0.83/1.03 Axiom fact_168_shift1__isnpoly:(forall (P:polyno1532895200ly_nat), ((polyno1013235523ly_nat P)->((not (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat)))->(polyno1013235523ly_nat (polyno1964927358t1_nat P))))).
% 0.83/1.03 Axiom fact_169_shift1__isnpoly:(forall (P:polyno727731844poly_a), ((polyno190918219poly_a P)->((not (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a)))->(polyno190918219poly_a (polyno784948432ift1_a P))))).
% 0.83/1.03 Axiom fact_170_shift1__def:(((eq (polyno727731844poly_a->polyno727731844poly_a)) polyno784948432ift1_a) ((polyno1057396216e_CN_a (polyno439679028le_C_a zero_zero_a)) zero_zero_nat)).
% 0.83/1.03 Axiom fact_171_shift1__def:(((eq (polyno1532895200ly_nat->polyno1532895200ly_nat)) polyno1964927358t1_nat) ((polyno720942678CN_nat (polyno2122022170_C_nat zero_zero_nat)) zero_zero_nat)).
% 0.83/1.03 Axiom fact_172_nat__mult__eq__cancel__disj:(forall (K2:nat) (M:nat) (N:nat), (((eq Prop) (((eq nat) ((times_times_nat K2) M)) ((times_times_nat K2) N))) ((or (((eq nat) K2) zero_zero_nat)) (((eq nat) M) N)))).
% 0.83/1.03 Axiom fact_173_headn__nz:(forall (P:polyno1532895200ly_nat) (N0:nat) (M:nat), (((polyno892049031yh_nat P) N0)->(((eq Prop) (((eq polyno1532895200ly_nat) ((polyno544860353dn_nat P) M)) (polyno2122022170_C_nat zero_zero_nat))) (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat))))).
% 0.83/1.03 Axiom fact_174_headn__nz:(forall (P:polyno727731844poly_a) (N0:nat) (M:nat), (((polyno1372495879olyh_a P) N0)->(((eq Prop) (((eq polyno727731844poly_a) ((polyno567601229eadn_a P) M)) (polyno439679028le_C_a zero_zero_a))) (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a))))).
% 0.83/1.03 Axiom fact_175_headconst__zero:(forall (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat P) N0)->(((eq Prop) (((eq nat) (polyno524777654st_nat P)) zero_zero_nat)) (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat))))).
% 0.83/1.03 Axiom fact_176_headconst__zero:(forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq Prop) (((eq a) (polyno2115742616onst_a P)) zero_zero_a)) (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a))))).
% 0.83/1.03 Axiom fact_177_polysub__same__0:(forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq polyno727731844poly_a) ((polyno1418491367ysub_a P) P)) (polyno439679028le_C_a zero_zero_a)))).
% 0.83/1.03 Axiom fact_178_polysubst0_Osimps_I8_J:(forall (N:nat) (T:polyno1532895200ly_nat) (C:polyno1532895200ly_nat) (P:polyno1532895200ly_nat), ((and ((((eq nat) N) zero_zero_nat)->(((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) (((polyno720942678CN_nat C) N) P))) ((polyno1222032024dd_nat ((polyno336795754t0_nat T) C)) ((polyno1415441627ul_nat T) ((polyno336795754t0_nat T) P)))))) ((not (((eq nat) N) zero_zero_nat))->(((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) (((polyno720942678CN_nat C) N) P))) (((polyno720942678CN_nat ((polyno336795754t0_nat T) C)) N) ((polyno336795754t0_nat T) P)))))).
% 0.83/1.03 Axiom fact_179_polysubst0_Osimps_I8_J:(forall (N:nat) (T:polyno727731844poly_a) (C:polyno727731844poly_a) (P:polyno727731844poly_a), ((and ((((eq nat) N) zero_zero_nat)->(((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) (((polyno1057396216e_CN_a C) N) P))) ((polyno1623170614_Add_a ((polyno1397854436bst0_a T) C)) ((polyno1491482291_Mul_a T) ((polyno1397854436bst0_a T) P)))))) ((not (((eq nat) N) zero_zero_nat))->(((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) (((polyno1057396216e_CN_a C) N) P))) (((polyno1057396216e_CN_a ((polyno1397854436bst0_a T) C)) N) ((polyno1397854436bst0_a T) P)))))).
% 0.83/1.03 Axiom fact_180_polysubst0_Osimps_I1_J:(forall (T:polyno727731844poly_a) (C:a), (((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) (polyno439679028le_C_a C))) (polyno439679028le_C_a C))).
% 0.83/1.03 Axiom fact_181_polysubst0_Osimps_I1_J:(forall (T:polyno1532895200ly_nat) (C:nat), (((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) (polyno2122022170_C_nat C))) (polyno2122022170_C_nat C))).
% 0.83/1.03 Axiom fact_182_polysubst0_Osimps_I6_J:(forall (T:polyno1532895200ly_nat) (A:polyno1532895200ly_nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) ((polyno1415441627ul_nat A) B))) ((polyno1415441627ul_nat ((polyno336795754t0_nat T) A)) ((polyno336795754t0_nat T) B)))).
% 0.83/1.03 Axiom fact_183_polysubst0_Osimps_I6_J:(forall (T:polyno727731844poly_a) (A:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) ((polyno1491482291_Mul_a A) B))) ((polyno1491482291_Mul_a ((polyno1397854436bst0_a T) A)) ((polyno1397854436bst0_a T) B)))).
% 0.83/1.03 Axiom fact_184_polysubst0_Osimps_I4_J:(forall (T:polyno727731844poly_a) (A:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) ((polyno1623170614_Add_a A) B))) ((polyno1623170614_Add_a ((polyno1397854436bst0_a T) A)) ((polyno1397854436bst0_a T) B)))).
% 0.83/1.03 Axiom fact_185_polysubst0_Osimps_I4_J:(forall (T:polyno1532895200ly_nat) (A:polyno1532895200ly_nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) ((polyno1222032024dd_nat A) B))) ((polyno1222032024dd_nat ((polyno336795754t0_nat T) A)) ((polyno336795754t0_nat T) B)))).
% 0.83/1.03 Axiom fact_186_headn_Osimps_I2_J:(forall (V:a), (((eq (nat->polyno727731844poly_a)) (polyno567601229eadn_a (polyno439679028le_C_a V))) (fun (M2:nat)=> (polyno439679028le_C_a V)))).
% 0.83/1.03 Axiom fact_187_headn_Osimps_I2_J:(forall (V:nat), (((eq (nat->polyno1532895200ly_nat)) (polyno544860353dn_nat (polyno2122022170_C_nat V))) (fun (M2:nat)=> (polyno2122022170_C_nat V)))).
% 0.83/1.03 Axiom fact_188_headn_Osimps_I6_J:(forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->polyno1532895200ly_nat)) (polyno544860353dn_nat ((polyno1415441627ul_nat V) Va))) (fun (M2:nat)=> ((polyno1415441627ul_nat V) Va)))).
% 0.83/1.03 Axiom fact_189_headn_Osimps_I6_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->polyno727731844poly_a)) (polyno567601229eadn_a ((polyno1491482291_Mul_a V) Va))) (fun (M2:nat)=> ((polyno1491482291_Mul_a V) Va)))).
% 0.83/1.03 Axiom fact_190_headn_Osimps_I4_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->polyno727731844poly_a)) (polyno567601229eadn_a ((polyno1623170614_Add_a V) Va))) (fun (M2:nat)=> ((polyno1623170614_Add_a V) Va)))).
% 0.83/1.03 Axiom fact_191_headn_Osimps_I4_J:(forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->polyno1532895200ly_nat)) (polyno544860353dn_nat ((polyno1222032024dd_nat V) Va))) (fun (M2:nat)=> ((polyno1222032024dd_nat V) Va)))).
% 0.83/1.03 Axiom fact_192_headn_Osimps_I3_J:(forall (V:nat), (((eq (nat->polyno727731844poly_a)) (polyno567601229eadn_a (polyno2024845497ound_a V))) (fun (M2:nat)=> (polyno2024845497ound_a V)))).
% 0.83/1.03 Axiom fact_193_headn_Osimps_I3_J:(forall (V:nat), (((eq (nat->polyno1532895200ly_nat)) (polyno544860353dn_nat (polyno1999838549nd_nat V))) (fun (M2:nat)=> (polyno1999838549nd_nat V)))).
% 0.83/1.03 Axiom fact_194_wf__bs__polysub:(forall (Bs2:list_a) (P:polyno727731844poly_a) (Q:polyno727731844poly_a), (((polyno896877631f_bs_a Bs2) P)->(((polyno896877631f_bs_a Bs2) Q)->((polyno896877631f_bs_a Bs2) ((polyno1418491367ysub_a P) Q))))).
% 0.83/1.03 Axiom fact_195_polysub__norm:(forall (P:polyno727731844poly_a) (Q:polyno727731844poly_a), ((polyno190918219poly_a P)->((polyno190918219poly_a Q)->(polyno190918219poly_a ((polyno1418491367ysub_a P) Q))))).
% 0.83/1.03 Axiom fact_196_headconst_Osimps_I1_J:(forall (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a), (((eq a) (polyno2115742616onst_a (((polyno1057396216e_CN_a C) N) P))) (polyno2115742616onst_a P))).
% 0.83/1.03 Axiom fact_197_headconst_Osimps_I1_J:(forall (C:polyno1532895200ly_nat) (N:nat) (P:polyno1532895200ly_nat), (((eq nat) (polyno524777654st_nat (((polyno720942678CN_nat C) N) P))) (polyno524777654st_nat P))).
% 0.83/1.03 Axiom fact_198_headconst_Osimps_I2_J:(forall (N:a), (((eq a) (polyno2115742616onst_a (polyno439679028le_C_a N))) N)).
% 0.83/1.03 Axiom fact_199_headconst_Osimps_I2_J:(forall (N:nat), (((eq nat) (polyno524777654st_nat (polyno2122022170_C_nat N))) N)).
% 0.83/1.03 Axiom fact_200_polysubst0_Osimps_I2_J:(forall (N:nat) (T:polyno727731844poly_a), ((and ((((eq nat) N) zero_zero_nat)->(((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) (polyno2024845497ound_a N))) T))) ((not (((eq nat) N) zero_zero_nat))->(((eq polyno727731844poly_a) ((polyno1397854436bst0_a T) (polyno2024845497ound_a N))) (polyno2024845497ound_a N))))).
% 0.83/1.03 Axiom fact_201_polysubst0_Osimps_I2_J:(forall (N:nat) (T:polyno1532895200ly_nat), ((and ((((eq nat) N) zero_zero_nat)->(((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) (polyno1999838549nd_nat N))) T))) ((not (((eq nat) N) zero_zero_nat))->(((eq polyno1532895200ly_nat) ((polyno336795754t0_nat T) (polyno1999838549nd_nat N))) (polyno1999838549nd_nat N))))).
% 0.83/1.03 Axiom fact_202_polysub__0:(forall (P:polyno727731844poly_a) (N0:nat) (Q:polyno727731844poly_a) (N1:nat), (((polyno1372495879olyh_a P) N0)->(((polyno1372495879olyh_a Q) N1)->(((eq Prop) (((eq polyno727731844poly_a) ((polyno1418491367ysub_a P) Q)) (polyno439679028le_C_a zero_zero_a))) (((eq polyno727731844poly_a) P) Q))))).
% 0.83/1.03 Axiom fact_203_headnz:(forall (P:polyno1532895200ly_nat) (N:nat) (M:nat), (((polyno892049031yh_nat P) N)->((not (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat)))->(not (((eq polyno1532895200ly_nat) ((polyno544860353dn_nat P) M)) (polyno2122022170_C_nat zero_zero_nat)))))).
% 0.83/1.03 Axiom fact_204_headnz:(forall (P:polyno727731844poly_a) (N:nat) (M:nat), (((polyno1372495879olyh_a P) N)->((not (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a)))->(not (((eq polyno727731844poly_a) ((polyno567601229eadn_a P) M)) (polyno439679028le_C_a zero_zero_a)))))).
% 0.83/1.03 Axiom fact_205_degree__npolyhCN:(forall (C:polyno1532895200ly_nat) (N:nat) (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat (((polyno720942678CN_nat C) N) P)) N0)->(((eq nat) (polyno220183259ee_nat C)) zero_zero_nat))).
% 0.83/1.03 Axiom fact_206_degree__npolyhCN:(forall (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a (((polyno1057396216e_CN_a C) N) P)) N0)->(((eq nat) (polyno578545843gree_a C)) zero_zero_nat))).
% 0.83/1.03 Axiom fact_207_poly__deriv_Osimps_I3_J:(forall (V:nat), (((eq polyno727731844poly_a) (polyno212464073eriv_a (polyno2024845497ound_a V))) (polyno439679028le_C_a zero_zero_a))).
% 0.83/1.03 Axiom fact_208_poly__deriv_Osimps_I4_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno212464073eriv_a ((polyno1623170614_Add_a V) Va))) (polyno439679028le_C_a zero_zero_a))).
% 0.83/1.03 Axiom fact_209_poly__deriv_Osimps_I6_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno212464073eriv_a ((polyno1491482291_Mul_a V) Va))) (polyno439679028le_C_a zero_zero_a))).
% 0.83/1.03 Axiom fact_210_degree_Osimps_I2_J:(forall (V:a), (((eq nat) (polyno578545843gree_a (polyno439679028le_C_a V))) zero_zero_nat)).
% 0.83/1.03 Axiom fact_211_degree_Osimps_I2_J:(forall (V:nat), (((eq nat) (polyno220183259ee_nat (polyno2122022170_C_nat V))) zero_zero_nat)).
% 0.83/1.03 Axiom fact_212_degree_Osimps_I6_J:(forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq nat) (polyno220183259ee_nat ((polyno1415441627ul_nat V) Va))) zero_zero_nat)).
% 0.83/1.03 Axiom fact_213_degree_Osimps_I6_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq nat) (polyno578545843gree_a ((polyno1491482291_Mul_a V) Va))) zero_zero_nat)).
% 0.83/1.03 Axiom fact_214_degree_Osimps_I4_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq nat) (polyno578545843gree_a ((polyno1623170614_Add_a V) Va))) zero_zero_nat)).
% 0.83/1.03 Axiom fact_215_degree_Osimps_I4_J:(forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq nat) (polyno220183259ee_nat ((polyno1222032024dd_nat V) Va))) zero_zero_nat)).
% 0.83/1.03 Axiom fact_216_degree_Osimps_I3_J:(forall (V:nat), (((eq nat) (polyno578545843gree_a (polyno2024845497ound_a V))) zero_zero_nat)).
% 0.83/1.03 Axiom fact_217_degree_Osimps_I3_J:(forall (V:nat), (((eq nat) (polyno220183259ee_nat (polyno1999838549nd_nat V))) zero_zero_nat)).
% 0.83/1.03 Axiom fact_218_poly__deriv_Osimps_I2_J:(forall (V:a), (((eq polyno727731844poly_a) (polyno212464073eriv_a (polyno439679028le_C_a V))) (polyno439679028le_C_a zero_zero_a))).
% 0.83/1.03 Axiom fact_219_poly__deriv_Osimps_I1_J:(forall (C:polyno727731844poly_a) (P:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno212464073eriv_a (((polyno1057396216e_CN_a C) zero_zero_nat) P))) ((polyno1006823949_aux_a one_one_a) P))).
% 0.83/1.03 Axiom fact_220_funpow__shift1__1:(forall (Bs2:list_a) (N:nat) (P:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) (((compow1114216044poly_a N) polyno784948432ift1_a) P))) ((polyno422358502poly_a Bs2) ((polyno1934269411ymul_a (((compow1114216044poly_a N) polyno784948432ift1_a) (polyno439679028le_C_a one_one_a))) P)))).
% 0.83/1.03 Axiom fact_221_head__nz:(forall (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat P) N0)->(((eq Prop) (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat P)) (polyno2122022170_C_nat zero_zero_nat))) (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat))))).
% 0.83/1.03 Axiom fact_222_head__nz:(forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->(((eq Prop) (((eq polyno727731844poly_a) (polyno1884029055head_a P)) (polyno439679028le_C_a zero_zero_a))) (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a))))).
% 0.83/1.03 Axiom fact_223_degreen__npolyhCN:(forall (C:polyno1532895200ly_nat) (N:nat) (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat (((polyno720942678CN_nat C) N) P)) N0)->(((eq nat) ((polyno1779722485en_nat C) N)) zero_zero_nat))).
% 0.83/1.03 Axiom fact_224_degreen__npolyhCN:(forall (C:polyno727731844poly_a) (N:nat) (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a (((polyno1057396216e_CN_a C) N) P)) N0)->(((eq nat) ((polyno1674775833reen_a C) N)) zero_zero_nat))).
% 0.83/1.03 Axiom fact_225_funpow__0:(forall (F:(polyno727731844poly_a->polyno727731844poly_a)) (X:polyno727731844poly_a), (((eq polyno727731844poly_a) (((compow1114216044poly_a zero_zero_nat) F) X)) X)).
% 0.83/1.03 Axiom fact_226_funpow__0:(forall (F:(polyno1532895200ly_nat->polyno1532895200ly_nat)) (X:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (((compow808008746ly_nat zero_zero_nat) F) X)) X)).
% 0.83/1.03 Axiom fact_227_funpow__swap1:(forall (F:(polyno727731844poly_a->polyno727731844poly_a)) (N:nat) (X:polyno727731844poly_a), (((eq polyno727731844poly_a) (F (((compow1114216044poly_a N) F) X))) (((compow1114216044poly_a N) F) (F X)))).
% 0.83/1.03 Axiom fact_228_funpow__swap1:(forall (F:(polyno1532895200ly_nat->polyno1532895200ly_nat)) (N:nat) (X:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (F (((compow808008746ly_nat N) F) X))) (((compow808008746ly_nat N) F) (F X)))).
% 0.83/1.03 Axiom fact_229_funpow__isnpolyh:(forall (N:nat) (F:(polyno1532895200ly_nat->polyno1532895200ly_nat)) (P:polyno1532895200ly_nat) (K2:nat), ((forall (P4:polyno1532895200ly_nat), (((polyno892049031yh_nat P4) N)->((polyno892049031yh_nat (F P4)) N)))->(((polyno892049031yh_nat P) N)->((polyno892049031yh_nat (((compow808008746ly_nat K2) F) P)) N)))).
% 0.83/1.03 Axiom fact_230_funpow__isnpolyh:(forall (N:nat) (F:(polyno727731844poly_a->polyno727731844poly_a)) (P:polyno727731844poly_a) (K2:nat), ((forall (P4:polyno727731844poly_a), (((polyno1372495879olyh_a P4) N)->((polyno1372495879olyh_a (F P4)) N)))->(((polyno1372495879olyh_a P) N)->((polyno1372495879olyh_a (((compow1114216044poly_a K2) F) P)) N)))).
% 0.83/1.03 Axiom fact_231_funpow__mult:(forall (N:nat) (M:nat) (F:(polyno727731844poly_a->polyno727731844poly_a)), (((eq (polyno727731844poly_a->polyno727731844poly_a)) ((compow1114216044poly_a N) ((compow1114216044poly_a M) F))) ((compow1114216044poly_a ((times_times_nat M) N)) F))).
% 0.83/1.03 Axiom fact_232_funpow__mult:(forall (N:nat) (M:nat) (F:(polyno1532895200ly_nat->polyno1532895200ly_nat)), (((eq (polyno1532895200ly_nat->polyno1532895200ly_nat)) ((compow808008746ly_nat N) ((compow808008746ly_nat M) F))) ((compow808008746ly_nat ((times_times_nat M) N)) F))).
% 0.83/1.03 Axiom fact_233_head_Osimps_I2_J:(forall (V:a), (((eq polyno727731844poly_a) (polyno1884029055head_a (polyno439679028le_C_a V))) (polyno439679028le_C_a V))).
% 0.83/1.03 Axiom fact_234_head_Osimps_I2_J:(forall (V:nat), (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat (polyno2122022170_C_nat V))) (polyno2122022170_C_nat V))).
% 0.83/1.03 Axiom fact_235_head_Osimps_I6_J:(forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat ((polyno1415441627ul_nat V) Va))) ((polyno1415441627ul_nat V) Va))).
% 0.83/1.03 Axiom fact_236_head_Osimps_I6_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1884029055head_a ((polyno1491482291_Mul_a V) Va))) ((polyno1491482291_Mul_a V) Va))).
% 0.83/1.03 Axiom fact_237_head_Osimps_I4_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1884029055head_a ((polyno1623170614_Add_a V) Va))) ((polyno1623170614_Add_a V) Va))).
% 0.83/1.03 Axiom fact_238_head_Osimps_I4_J:(forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat ((polyno1222032024dd_nat V) Va))) ((polyno1222032024dd_nat V) Va))).
% 0.83/1.03 Axiom fact_239_head_Osimps_I3_J:(forall (V:nat), (((eq polyno727731844poly_a) (polyno1884029055head_a (polyno2024845497ound_a V))) (polyno2024845497ound_a V))).
% 0.83/1.03 Axiom fact_240_head_Osimps_I3_J:(forall (V:nat), (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat (polyno1999838549nd_nat V))) (polyno1999838549nd_nat V))).
% 0.83/1.03 Axiom fact_241_head__isnpolyh:(forall (P:polyno1532895200ly_nat) (N0:nat), (((polyno892049031yh_nat P) N0)->((polyno892049031yh_nat (polyno1952548879ad_nat P)) N0))).
% 0.83/1.03 Axiom fact_242_head__isnpolyh:(forall (P:polyno727731844poly_a) (N0:nat), (((polyno1372495879olyh_a P) N0)->((polyno1372495879olyh_a (polyno1884029055head_a P)) N0))).
% 0.83/1.03 Axiom fact_243_degreen_Osimps_I2_J:(forall (V:a), (((eq (nat->nat)) (polyno1674775833reen_a (polyno439679028le_C_a V))) (fun (M2:nat)=> zero_zero_nat))).
% 0.83/1.03 Axiom fact_244_degreen_Osimps_I2_J:(forall (V:nat), (((eq (nat->nat)) (polyno1779722485en_nat (polyno2122022170_C_nat V))) (fun (M2:nat)=> zero_zero_nat))).
% 0.83/1.03 Axiom fact_245_degreen_Osimps_I6_J:(forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->nat)) (polyno1779722485en_nat ((polyno1415441627ul_nat V) Va))) (fun (M2:nat)=> zero_zero_nat))).
% 0.83/1.03 Axiom fact_246_degreen_Osimps_I6_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->nat)) (polyno1674775833reen_a ((polyno1491482291_Mul_a V) Va))) (fun (M2:nat)=> zero_zero_nat))).
% 0.83/1.03 Axiom fact_247_degreen_Osimps_I4_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq (nat->nat)) (polyno1674775833reen_a ((polyno1623170614_Add_a V) Va))) (fun (M2:nat)=> zero_zero_nat))).
% 0.83/1.03 Axiom fact_248_degreen_Osimps_I4_J:(forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq (nat->nat)) (polyno1779722485en_nat ((polyno1222032024dd_nat V) Va))) (fun (M2:nat)=> zero_zero_nat))).
% 0.83/1.03 Axiom fact_249_degreen_Osimps_I3_J:(forall (V:nat), (((eq (nat->nat)) (polyno1674775833reen_a (polyno2024845497ound_a V))) (fun (M2:nat)=> zero_zero_nat))).
% 0.83/1.03 Axiom fact_250_degreen_Osimps_I3_J:(forall (V:nat), (((eq (nat->nat)) (polyno1779722485en_nat (polyno1999838549nd_nat V))) (fun (M2:nat)=> zero_zero_nat))).
% 0.83/1.03 Axiom fact_251_head_Osimps_I1_J:(forall (C:polyno727731844poly_a) (P:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1884029055head_a (((polyno1057396216e_CN_a C) zero_zero_nat) P))) (polyno1884029055head_a P))).
% 0.83/1.03 Axiom fact_252_head_Osimps_I1_J:(forall (C:polyno1532895200ly_nat) (P:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno1952548879ad_nat (((polyno720942678CN_nat C) zero_zero_nat) P))) (polyno1952548879ad_nat P))).
% 0.83/1.03 Axiom fact_253_head__eq__headn0:(((eq (polyno727731844poly_a->polyno727731844poly_a)) polyno1884029055head_a) (fun (P2:polyno727731844poly_a)=> ((polyno567601229eadn_a P2) zero_zero_nat))).
% 0.83/1.03 Axiom fact_254_head__eq__headn0:(((eq (polyno1532895200ly_nat->polyno1532895200ly_nat)) polyno1952548879ad_nat) (fun (P2:polyno1532895200ly_nat)=> ((polyno544860353dn_nat P2) zero_zero_nat))).
% 0.83/1.03 Axiom fact_255_poly__deriv__aux_Osimps_I2_J:(forall (N:a) (V:a), (((eq polyno727731844poly_a) ((polyno1006823949_aux_a N) (polyno439679028le_C_a V))) ((polyno562434098cmul_a N) (polyno439679028le_C_a V)))).
% 0.83/1.03 Axiom fact_256_poly__deriv__aux_Osimps_I6_J:(forall (N:a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1006823949_aux_a N) ((polyno1491482291_Mul_a V) Va))) ((polyno562434098cmul_a N) ((polyno1491482291_Mul_a V) Va)))).
% 0.83/1.03 Axiom fact_257_funpow__shift1__isnpoly:(forall (P:polyno1532895200ly_nat) (N:nat), ((polyno1013235523ly_nat P)->((not (((eq polyno1532895200ly_nat) P) (polyno2122022170_C_nat zero_zero_nat)))->(polyno1013235523ly_nat (((compow808008746ly_nat N) polyno1964927358t1_nat) P))))).
% 0.83/1.03 Axiom fact_258_funpow__shift1__isnpoly:(forall (P:polyno727731844poly_a) (N:nat), ((polyno190918219poly_a P)->((not (((eq polyno727731844poly_a) P) (polyno439679028le_C_a zero_zero_a)))->(polyno190918219poly_a (((compow1114216044poly_a N) polyno784948432ift1_a) P))))).
% 0.83/1.03 Axiom fact_259_funpow__shift1:(forall (Bs2:list_a) (N:nat) (P:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) (((compow1114216044poly_a N) polyno784948432ift1_a) P))) ((polyno422358502poly_a Bs2) ((polyno1491482291_Mul_a ((polyno1538138524e_Pw_a (polyno2024845497ound_a zero_zero_nat)) N)) P)))).
% 0.83/1.03 Axiom fact_260_add__left__cancel:(forall (A:nat) (B:nat) (C:nat), (((eq Prop) (((eq nat) ((plus_plus_nat A) B)) ((plus_plus_nat A) C))) (((eq nat) B) C))).
% 0.83/1.03 Axiom fact_261_add__right__cancel:(forall (B:nat) (A:nat) (C:nat), (((eq Prop) (((eq nat) ((plus_plus_nat B) A)) ((plus_plus_nat C) A))) (((eq nat) B) C))).
% 0.83/1.03 Axiom fact_262_add__is__0:(forall (M:nat) (N:nat), (((eq Prop) (((eq nat) ((plus_plus_nat M) N)) zero_zero_nat)) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))).
% 0.83/1.03 Axiom fact_263_Nat_Oadd__0__right:(forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M)).
% 0.83/1.03 Axiom fact_264_zero__eq__add__iff__both__eq__0:(forall (X:nat) (Y:nat), (((eq Prop) (((eq nat) zero_zero_nat) ((plus_plus_nat X) Y))) ((and (((eq nat) X) zero_zero_nat)) (((eq nat) Y) zero_zero_nat)))).
% 0.83/1.03 Axiom fact_265_add__eq__0__iff__both__eq__0:(forall (X:nat) (Y:nat), (((eq Prop) (((eq nat) ((plus_plus_nat X) Y)) zero_zero_nat)) ((and (((eq nat) X) zero_zero_nat)) (((eq nat) Y) zero_zero_nat)))).
% 0.83/1.03 Axiom fact_266_add__cancel__right__right:(forall (A:nat) (B:nat), (((eq Prop) (((eq nat) A) ((plus_plus_nat A) B))) (((eq nat) B) zero_zero_nat))).
% 0.83/1.03 Axiom fact_267_add__cancel__right__left:(forall (A:nat) (B:nat), (((eq Prop) (((eq nat) A) ((plus_plus_nat B) A))) (((eq nat) B) zero_zero_nat))).
% 0.83/1.03 Axiom fact_268_add__cancel__left__right:(forall (A:nat) (B:nat), (((eq Prop) (((eq nat) ((plus_plus_nat A) B)) A)) (((eq nat) B) zero_zero_nat))).
% 0.83/1.03 Axiom fact_269_add__cancel__left__left:(forall (B:nat) (A:nat), (((eq Prop) (((eq nat) ((plus_plus_nat B) A)) A)) (((eq nat) B) zero_zero_nat))).
% 0.83/1.03 Axiom fact_270_add_Oright__neutral:(forall (A:nat), (((eq nat) ((plus_plus_nat A) zero_zero_nat)) A)).
% 0.83/1.03 Axiom fact_271_add_Oleft__neutral:(forall (A:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A)) A)).
% 0.83/1.03 Axiom fact_272_left__add__mult__distrib:(forall (_TPTP_I:nat) (U:nat) (J:nat) (K2:nat), (((eq nat) ((plus_plus_nat ((times_times_nat _TPTP_I) U)) ((plus_plus_nat ((times_times_nat J) U)) K2))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat _TPTP_I) J)) U)) K2))).
% 0.83/1.03 Axiom fact_273_plus__nat_Oadd__0:(forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N)).
% 0.83/1.03 Axiom fact_274_add__eq__self__zero:(forall (M:nat) (N:nat), ((((eq nat) ((plus_plus_nat M) N)) M)->(((eq nat) N) zero_zero_nat))).
% 0.83/1.03 Axiom fact_275_isnpolyh_Osimps_I8_J:(forall (V:polyno727731844poly_a) (Va:nat), (((eq (nat->Prop)) (polyno1372495879olyh_a ((polyno1538138524e_Pw_a V) Va))) (fun (K:nat)=> False))).
% 0.83/1.03 Axiom fact_276_add__mult__distrib2:(forall (K2:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K2) ((plus_plus_nat M) N))) ((plus_plus_nat ((times_times_nat K2) M)) ((times_times_nat K2) N)))).
% 0.83/1.03 Axiom fact_277_add__mult__distrib:(forall (M:nat) (N:nat) (K2:nat), (((eq nat) ((times_times_nat ((plus_plus_nat M) N)) K2)) ((plus_plus_nat ((times_times_nat M) K2)) ((times_times_nat N) K2)))).
% 0.83/1.03 Axiom fact_278_ab__semigroup__add__class_Oadd__ac_I1_J:(forall (A:nat) (B:nat) (C:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A) B)) C)) ((plus_plus_nat A) ((plus_plus_nat B) C)))).
% 0.83/1.03 Axiom fact_279_add__mono__thms__linordered__semiring_I4_J:(forall (_TPTP_I:nat) (J:nat) (K2:nat) (L:nat), (((and (((eq nat) _TPTP_I) J)) (((eq nat) K2) L))->(((eq nat) ((plus_plus_nat _TPTP_I) K2)) ((plus_plus_nat J) L)))).
% 0.83/1.03 Axiom fact_280_group__cancel_Oadd1:(forall (A3:nat) (K2:nat) (A:nat) (B:nat), ((((eq nat) A3) ((plus_plus_nat K2) A))->(((eq nat) ((plus_plus_nat A3) B)) ((plus_plus_nat K2) ((plus_plus_nat A) B))))).
% 0.83/1.03 Axiom fact_281_group__cancel_Oadd2:(forall (B3:nat) (K2:nat) (B:nat) (A:nat), ((((eq nat) B3) ((plus_plus_nat K2) B))->(((eq nat) ((plus_plus_nat A) B3)) ((plus_plus_nat K2) ((plus_plus_nat A) B))))).
% 0.83/1.03 Axiom fact_282_add_Oassoc:(forall (A:nat) (B:nat) (C:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A) B)) C)) ((plus_plus_nat A) ((plus_plus_nat B) C)))).
% 0.83/1.03 Axiom fact_283_add_Ocommute:(((eq (nat->(nat->nat))) plus_plus_nat) (fun (A2:nat) (B2:nat)=> ((plus_plus_nat B2) A2))).
% 0.83/1.03 Axiom fact_284_add_Oleft__commute:(forall (B:nat) (A:nat) (C:nat), (((eq nat) ((plus_plus_nat B) ((plus_plus_nat A) C))) ((plus_plus_nat A) ((plus_plus_nat B) C)))).
% 0.83/1.03 Axiom fact_285_add__left__imp__eq:(forall (A:nat) (B:nat) (C:nat), ((((eq nat) ((plus_plus_nat A) B)) ((plus_plus_nat A) C))->(((eq nat) B) C))).
% 0.83/1.03 Axiom fact_286_add__right__imp__eq:(forall (B:nat) (A:nat) (C:nat), ((((eq nat) ((plus_plus_nat B) A)) ((plus_plus_nat C) A))->(((eq nat) B) C))).
% 0.83/1.03 Axiom fact_287_combine__common__factor:(forall (A:nat) (E:nat) (B:nat) (C:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A) E)) ((plus_plus_nat ((times_times_nat B) E)) C))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat A) B)) E)) C))).
% 0.83/1.03 Axiom fact_288_combine__common__factor:(forall (A:a) (E:a) (B:a) (C:a), (((eq a) ((plus_plus_a ((times_times_a A) E)) ((plus_plus_a ((times_times_a B) E)) C))) ((plus_plus_a ((times_times_a ((plus_plus_a A) B)) E)) C))).
% 0.83/1.03 Axiom fact_289_distrib__right:(forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A) B)) C)) ((plus_plus_nat ((times_times_nat A) C)) ((times_times_nat B) C)))).
% 0.83/1.03 Axiom fact_290_distrib__right:(forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a ((plus_plus_a A) B)) C)) ((plus_plus_a ((times_times_a A) C)) ((times_times_a B) C)))).
% 0.83/1.03 Axiom fact_291_distrib__left:(forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat A) ((plus_plus_nat B) C))) ((plus_plus_nat ((times_times_nat A) B)) ((times_times_nat A) C)))).
% 0.83/1.03 Axiom fact_292_distrib__left:(forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a A) ((plus_plus_a B) C))) ((plus_plus_a ((times_times_a A) B)) ((times_times_a A) C)))).
% 0.83/1.03 Axiom fact_293_comm__semiring__class_Odistrib:(forall (A:nat) (B:nat) (C:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A) B)) C)) ((plus_plus_nat ((times_times_nat A) C)) ((times_times_nat B) C)))).
% 0.83/1.03 Axiom fact_294_comm__semiring__class_Odistrib:(forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a ((plus_plus_a A) B)) C)) ((plus_plus_a ((times_times_a A) C)) ((times_times_a B) C)))).
% 0.83/1.03 Axiom fact_295_ring__class_Oring__distribs_I1_J:(forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a A) ((plus_plus_a B) C))) ((plus_plus_a ((times_times_a A) B)) ((times_times_a A) C)))).
% 0.83/1.03 Axiom fact_296_ring__class_Oring__distribs_I2_J:(forall (A:a) (B:a) (C:a), (((eq a) ((times_times_a ((plus_plus_a A) B)) C)) ((plus_plus_a ((times_times_a A) C)) ((times_times_a B) C)))).
% 0.83/1.03 Axiom fact_297_poly_Odistinct_I47_J:(forall (X51:polyno727731844poly_a) (X52:polyno727731844poly_a) (X71:polyno727731844poly_a) (X72:nat), (not (((eq polyno727731844poly_a) ((polyno1491482291_Mul_a X51) X52)) ((polyno1538138524e_Pw_a X71) X72)))).
% 0.83/1.03 Axiom fact_298_add_Ocomm__neutral:(forall (A:nat), (((eq nat) ((plus_plus_nat A) zero_zero_nat)) A)).
% 0.83/1.03 Axiom fact_299_comm__monoid__add__class_Oadd__0:(forall (A:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A)) A)).
% 0.83/1.03 Axiom fact_300_poly_Odistinct_I11_J:(forall (X1:a) (X71:polyno727731844poly_a) (X72:nat), (not (((eq polyno727731844poly_a) (polyno439679028le_C_a X1)) ((polyno1538138524e_Pw_a X71) X72)))).
% 0.83/1.03 Axiom fact_301_poly_Odistinct_I11_J:(forall (X1:nat) (X71:polyno1532895200ly_nat) (X72:nat), (not (((eq polyno1532895200ly_nat) (polyno2122022170_C_nat X1)) ((polyno359287218Pw_nat X71) X72)))).
% 0.83/1.03 Axiom fact_302_polymul_Osimps_I22_J:(forall (A:polyno1532895200ly_nat) (V:polyno1532895200ly_nat) (Va:nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat A) ((polyno359287218Pw_nat V) Va))) ((polyno1415441627ul_nat A) ((polyno359287218Pw_nat V) Va)))).
% 0.83/1.03 Axiom fact_303_polymul_Osimps_I22_J:(forall (A:polyno727731844poly_a) (V:polyno727731844poly_a) (Va:nat), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a A) ((polyno1538138524e_Pw_a V) Va))) ((polyno1491482291_Mul_a A) ((polyno1538138524e_Pw_a V) Va)))).
% 0.83/1.03 Axiom fact_304_polymul_Osimps_I10_J:(forall (V:polyno1532895200ly_nat) (Va:nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno359287218Pw_nat V) Va)) B)) ((polyno1415441627ul_nat ((polyno359287218Pw_nat V) Va)) B))).
% 0.83/1.03 Axiom fact_305_polymul_Osimps_I10_J:(forall (V:polyno727731844poly_a) (Va:nat) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1538138524e_Pw_a V) Va)) B)) ((polyno1491482291_Mul_a ((polyno1538138524e_Pw_a V) Va)) B))).
% 0.83/1.03 Axiom fact_306_Ipoly_Osimps_I4_J:(forall (Bs2:list_a) (A:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq a) ((polyno422358502poly_a Bs2) ((polyno1623170614_Add_a A) B))) ((plus_plus_a ((polyno422358502poly_a Bs2) A)) ((polyno422358502poly_a Bs2) B)))).
% 0.83/1.03 Axiom fact_307_polymul_Osimps_I16_J:(forall (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat) (Vc:polyno1532895200ly_nat) (Vd:nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno359287218Pw_nat Vc) Vd))) ((polyno1415441627ul_nat (((polyno720942678CN_nat V) Va) Vb)) ((polyno359287218Pw_nat Vc) Vd)))).
% 0.83/1.03 Axiom fact_308_polymul_Osimps_I16_J:(forall (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a) (Vc:polyno727731844poly_a) (Vd:nat), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1538138524e_Pw_a Vc) Vd))) ((polyno1491482291_Mul_a (((polyno1057396216e_CN_a V) Va) Vb)) ((polyno1538138524e_Pw_a Vc) Vd)))).
% 0.83/1.03 Axiom fact_309_polymul_Osimps_I28_J:(forall (Vc:polyno1532895200ly_nat) (Vd:nat) (V:polyno1532895200ly_nat) (Va:nat) (Vb:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno359287218Pw_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb))) ((polyno1415441627ul_nat ((polyno359287218Pw_nat Vc) Vd)) (((polyno720942678CN_nat V) Va) Vb)))).
% 0.83/1.03 Axiom fact_310_polymul_Osimps_I28_J:(forall (Vc:polyno727731844poly_a) (Vd:nat) (V:polyno727731844poly_a) (Va:nat) (Vb:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno1538138524e_Pw_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb))) ((polyno1491482291_Mul_a ((polyno1538138524e_Pw_a Vc) Vd)) (((polyno1057396216e_CN_a V) Va) Vb)))).
% 0.83/1.04 Axiom fact_311_poly__cmul_Osimps_I8_J:(forall (Y:a) (V:polyno727731844poly_a) (Va:nat), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) ((polyno1538138524e_Pw_a V) Va))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) ((polyno1538138524e_Pw_a V) Va)))).
% 0.83/1.04 Axiom fact_312_poly__cmul_Osimps_I8_J:(forall (Y:nat) (V:polyno1532895200ly_nat) (Va:nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) ((polyno359287218Pw_nat V) Va))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) ((polyno359287218Pw_nat V) Va)))).
% 0.83/1.04 Axiom fact_313_poly__deriv_Osimps_I8_J:(forall (V:polyno727731844poly_a) (Va:nat), (((eq polyno727731844poly_a) (polyno212464073eriv_a ((polyno1538138524e_Pw_a V) Va))) (polyno439679028le_C_a zero_zero_a))).
% 0.83/1.04 Axiom fact_314_behead:(forall (P:polyno727731844poly_a) (N:nat) (Bs2:list_a), (((polyno1372495879olyh_a P) N)->(((eq a) ((polyno422358502poly_a Bs2) ((polyno1623170614_Add_a ((polyno1491482291_Mul_a (polyno1884029055head_a P)) ((polyno1538138524e_Pw_a (polyno2024845497ound_a zero_zero_nat)) (polyno578545843gree_a P)))) (polyno1465139388head_a P)))) ((polyno422358502poly_a Bs2) P)))).
% 0.83/1.04 Axiom fact_315_behead__isnpolyh:(forall (P:polyno727731844poly_a) (N:nat), (((polyno1372495879olyh_a P) N)->((polyno1372495879olyh_a (polyno1465139388head_a P)) N))).
% 0.83/1.04 Axiom fact_316_behead_Osimps_I2_J:(forall (V:a), (((eq polyno727731844poly_a) (polyno1465139388head_a (polyno439679028le_C_a V))) (polyno439679028le_C_a zero_zero_a))).
% 0.83/1.04 Axiom fact_317_behead_Osimps_I2_J:(forall (V:nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat (polyno2122022170_C_nat V))) (polyno2122022170_C_nat zero_zero_nat))).
% 0.83/1.04 Axiom fact_318_behead_Osimps_I6_J:(forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat ((polyno1415441627ul_nat V) Va))) (polyno2122022170_C_nat zero_zero_nat))).
% 0.83/1.04 Axiom fact_319_behead_Osimps_I6_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1465139388head_a ((polyno1491482291_Mul_a V) Va))) (polyno439679028le_C_a zero_zero_a))).
% 0.83/1.04 Axiom fact_320_behead_Osimps_I4_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1465139388head_a ((polyno1623170614_Add_a V) Va))) (polyno439679028le_C_a zero_zero_a))).
% 0.83/1.04 Axiom fact_321_behead_Osimps_I4_J:(forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat ((polyno1222032024dd_nat V) Va))) (polyno2122022170_C_nat zero_zero_nat))).
% 0.83/1.04 Axiom fact_322_behead_Osimps_I3_J:(forall (V:nat), (((eq polyno727731844poly_a) (polyno1465139388head_a (polyno2024845497ound_a V))) (polyno439679028le_C_a zero_zero_a))).
% 0.83/1.04 Axiom fact_323_behead_Osimps_I3_J:(forall (V:nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat (polyno1999838549nd_nat V))) (polyno2122022170_C_nat zero_zero_nat))).
% 0.83/1.04 Axiom fact_324_behead_Osimps_I8_J:(forall (V:polyno727731844poly_a) (Va:nat), (((eq polyno727731844poly_a) (polyno1465139388head_a ((polyno1538138524e_Pw_a V) Va))) (polyno439679028le_C_a zero_zero_a))).
% 0.83/1.04 Axiom fact_325_behead_Osimps_I8_J:(forall (V:polyno1532895200ly_nat) (Va:nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat ((polyno359287218Pw_nat V) Va))) (polyno2122022170_C_nat zero_zero_nat))).
% 0.83/1.04 Axiom fact_326_add__scale__eq__noteq:(forall (R:nat) (A:nat) (B:nat) (C:nat) (D:nat), ((not (((eq nat) R) zero_zero_nat))->(((and (((eq nat) A) B)) (not (((eq nat) C) D)))->(not (((eq nat) ((plus_plus_nat A) ((times_times_nat R) C))) ((plus_plus_nat B) ((times_times_nat R) D))))))).
% 0.83/1.04 Axiom fact_327_add__scale__eq__noteq:(forall (R:a) (A:a) (B:a) (C:a) (D:a), ((not (((eq a) R) zero_zero_a))->(((and (((eq a) A) B)) (not (((eq a) C) D)))->(not (((eq a) ((plus_plus_a A) ((times_times_a R) C))) ((plus_plus_a B) ((times_times_a R) D))))))).
% 0.83/1.04 Axiom fact_328_add__0__iff:(forall (B:nat) (A:nat), (((eq Prop) (((eq nat) B) ((plus_plus_nat B) A))) (((eq nat) A) zero_zero_nat))).
% 0.83/1.04 Axiom fact_329_crossproduct__noteq:(forall (A:nat) (B:nat) (C:nat) (D:nat), (((eq Prop) ((and (not (((eq nat) A) B))) (not (((eq nat) C) D)))) (not (((eq nat) ((plus_plus_nat ((times_times_nat A) C)) ((times_times_nat B) D))) ((plus_plus_nat ((times_times_nat A) D)) ((times_times_nat B) C)))))).
% 0.83/1.04 Axiom fact_330_crossproduct__noteq:(forall (A:a) (B:a) (C:a) (D:a), (((eq Prop) ((and (not (((eq a) A) B))) (not (((eq a) C) D)))) (not (((eq a) ((plus_plus_a ((times_times_a A) C)) ((times_times_a B) D))) ((plus_plus_a ((times_times_a A) D)) ((times_times_a B) C)))))).
% 0.83/1.04 Axiom fact_331_crossproduct__eq:(forall (W:nat) (Y:nat) (X:nat) (Z:nat), (((eq Prop) (((eq nat) ((plus_plus_nat ((times_times_nat W) Y)) ((times_times_nat X) Z))) ((plus_plus_nat ((times_times_nat W) Z)) ((times_times_nat X) Y)))) ((or (((eq nat) W) X)) (((eq nat) Y) Z)))).
% 0.83/1.04 Axiom fact_332_crossproduct__eq:(forall (W:a) (Y:a) (X:a) (Z:a), (((eq Prop) (((eq a) ((plus_plus_a ((times_times_a W) Y)) ((times_times_a X) Z))) ((plus_plus_a ((times_times_a W) Z)) ((times_times_a X) Y)))) ((or (((eq a) W) X)) (((eq a) Y) Z)))).
% 0.83/1.04 Axiom fact_333_Euclid__induct:(forall (P5:(nat->(nat->Prop))) (A:nat) (B:nat), ((forall (A4:nat) (B4:nat), (((eq Prop) ((P5 A4) B4)) ((P5 B4) A4)))->((forall (A4:nat), ((P5 A4) zero_zero_nat))->((forall (A4:nat) (B4:nat), (((P5 A4) B4)->((P5 A4) ((plus_plus_nat A4) B4))))->((P5 A) B))))).
% 0.83/1.04 Axiom fact_334_verit__sum__simplify:(forall (A:nat), (((eq nat) ((plus_plus_nat A) zero_zero_nat)) A)).
% 0.83/1.04 Axiom fact_335_polypow_Osimps_I1_J:(((eq (polyno727731844poly_a->polyno727731844poly_a)) (polyno1371724751ypow_a zero_zero_nat)) (fun (P2:polyno727731844poly_a)=> (polyno439679028le_C_a one_one_a))).
% 0.83/1.04 Axiom fact_336_polypow_Osimps_I1_J:(((eq (polyno1532895200ly_nat->polyno1532895200ly_nat)) (polyno1510045887ow_nat zero_zero_nat)) (fun (P2:polyno1532895200ly_nat)=> (polyno2122022170_C_nat one_one_nat))).
% 0.83/1.04 Axiom fact_337_degreen_Oelims:(forall (X:polyno1532895200ly_nat) (Y:(nat->nat)), ((((eq (nat->nat)) (polyno1779722485en_nat X)) Y)->((forall (C3:polyno1532895200ly_nat) (N3:nat) (P4:polyno1532895200ly_nat), ((((eq polyno1532895200ly_nat) X) (((polyno720942678CN_nat C3) N3) P4))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> (((if_nat (((eq nat) N3) M2)) ((plus_plus_nat one_one_nat) ((polyno1779722485en_nat P4) N3))) zero_zero_nat))))))->((((ex nat) (fun (V2:nat)=> (((eq polyno1532895200ly_nat) X) (polyno2122022170_C_nat V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex nat) (fun (V2:nat)=> (((eq polyno1532895200ly_nat) X) (polyno1999838549nd_nat V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno1532895200ly_nat) (fun (V2:polyno1532895200ly_nat)=> ((ex polyno1532895200ly_nat) (fun (Va2:polyno1532895200ly_nat)=> (((eq polyno1532895200ly_nat) X) ((polyno1222032024dd_nat V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno1532895200ly_nat) (fun (V2:polyno1532895200ly_nat)=> ((ex polyno1532895200ly_nat) (fun (Va2:polyno1532895200ly_nat)=> (((eq polyno1532895200ly_nat) X) ((polyno1921014231ub_nat V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno1532895200ly_nat) (fun (V2:polyno1532895200ly_nat)=> ((ex polyno1532895200ly_nat) (fun (Va2:polyno1532895200ly_nat)=> (((eq polyno1532895200ly_nat) X) ((polyno1415441627ul_nat V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno1532895200ly_nat) (fun (V2:polyno1532895200ly_nat)=> (((eq polyno1532895200ly_nat) X) (polyno1366804583eg_nat V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno1532895200ly_nat) (fun (V2:polyno1532895200ly_nat)=> ((ex nat) (fun (Va2:nat)=> (((eq polyno1532895200ly_nat) X) ((polyno359287218Pw_nat V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->False)))))))))).
% 0.83/1.04 Axiom fact_338_degreen_Oelims:(forall (X:polyno727731844poly_a) (Y:(nat->nat)), ((((eq (nat->nat)) (polyno1674775833reen_a X)) Y)->((forall (C3:polyno727731844poly_a) (N3:nat) (P4:polyno727731844poly_a), ((((eq polyno727731844poly_a) X) (((polyno1057396216e_CN_a C3) N3) P4))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> (((if_nat (((eq nat) N3) M2)) ((plus_plus_nat one_one_nat) ((polyno1674775833reen_a P4) N3))) zero_zero_nat))))))->((((ex a) (fun (V2:a)=> (((eq polyno727731844poly_a) X) (polyno439679028le_C_a V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex nat) (fun (V2:nat)=> (((eq polyno727731844poly_a) X) (polyno2024845497ound_a V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno727731844poly_a) (fun (V2:polyno727731844poly_a)=> ((ex polyno727731844poly_a) (fun (Va2:polyno727731844poly_a)=> (((eq polyno727731844poly_a) X) ((polyno1623170614_Add_a V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno727731844poly_a) (fun (V2:polyno727731844poly_a)=> ((ex polyno727731844poly_a) (fun (Va2:polyno727731844poly_a)=> (((eq polyno727731844poly_a) X) ((polyno975704247_Sub_a V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno727731844poly_a) (fun (V2:polyno727731844poly_a)=> ((ex polyno727731844poly_a) (fun (Va2:polyno727731844poly_a)=> (((eq polyno727731844poly_a) X) ((polyno1491482291_Mul_a V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno727731844poly_a) (fun (V2:polyno727731844poly_a)=> (((eq polyno727731844poly_a) X) (polyno96675367_Neg_a V2))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->((((ex polyno727731844poly_a) (fun (V2:polyno727731844poly_a)=> ((ex nat) (fun (Va2:nat)=> (((eq polyno727731844poly_a) X) ((polyno1538138524e_Pw_a V2) Va2))))))->(not (((eq (nat->nat)) Y) (fun (M2:nat)=> zero_zero_nat))))->False)))))))))).
% 0.83/1.04 Axiom fact_339_behead_Osimps_I5_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1465139388head_a ((polyno975704247_Sub_a V) Va))) (polyno439679028le_C_a zero_zero_a))).
% 0.83/1.04 Axiom fact_340_behead_Osimps_I5_J:(forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat ((polyno1921014231ub_nat V) Va))) (polyno2122022170_C_nat zero_zero_nat))).
% 0.83/1.04 Axiom fact_341_poly__cmul_Osimps_I5_J:(forall (Y:a) (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) ((polyno975704247_Sub_a V) Va))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) ((polyno975704247_Sub_a V) Va)))).
% 0.83/1.04 Axiom fact_342_poly__cmul_Osimps_I5_J:(forall (Y:nat) (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) ((polyno1921014231ub_nat V) Va))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) ((polyno1921014231ub_nat V) Va)))).
% 0.83/1.04 Axiom fact_343_behead_Osimps_I7_J:(forall (V:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno1465139388head_a (polyno96675367_Neg_a V))) (polyno439679028le_C_a zero_zero_a))).
% 0.83/1.04 Axiom fact_344_behead_Osimps_I7_J:(forall (V:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) (polyno587244178ad_nat (polyno1366804583eg_nat V))) (polyno2122022170_C_nat zero_zero_nat))).
% 0.83/1.04 Axiom fact_345_poly__cmul_Osimps_I7_J:(forall (Y:a) (V:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno562434098cmul_a Y) (polyno96675367_Neg_a V))) ((polyno1934269411ymul_a (polyno439679028le_C_a Y)) (polyno96675367_Neg_a V)))).
% 0.83/1.04 Axiom fact_346_poly__cmul_Osimps_I7_J:(forall (Y:nat) (V:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno1467023772ul_nat Y) (polyno1366804583eg_nat V))) ((polyno929799083ul_nat (polyno2122022170_C_nat Y)) (polyno1366804583eg_nat V)))).
% 0.83/1.04 Axiom fact_347_poly__deriv_Osimps_I5_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno212464073eriv_a ((polyno975704247_Sub_a V) Va))) (polyno439679028le_C_a zero_zero_a))).
% 0.83/1.04 Axiom fact_348_poly__deriv_Osimps_I7_J:(forall (V:polyno727731844poly_a), (((eq polyno727731844poly_a) (polyno212464073eriv_a (polyno96675367_Neg_a V))) (polyno439679028le_C_a zero_zero_a))).
% 0.83/1.04 Axiom fact_349_polypow__normh:(forall (P:polyno727731844poly_a) (N:nat) (K2:nat), (((polyno1372495879olyh_a P) N)->((polyno1372495879olyh_a ((polyno1371724751ypow_a K2) P)) N))).
% 39.46/39.67 Axiom fact_350_polymul_Osimps_I7_J:(forall (V:polyno1532895200ly_nat) (Va:polyno1532895200ly_nat) (B:polyno1532895200ly_nat), (((eq polyno1532895200ly_nat) ((polyno929799083ul_nat ((polyno1921014231ub_nat V) Va)) B)) ((polyno1415441627ul_nat ((polyno1921014231ub_nat V) Va)) B))).
% 39.46/39.67 Axiom fact_351_polymul_Osimps_I7_J:(forall (V:polyno727731844poly_a) (Va:polyno727731844poly_a) (B:polyno727731844poly_a), (((eq polyno727731844poly_a) ((polyno1934269411ymul_a ((polyno975704247_Sub_a V) Va)) B)) ((polyno1491482291_Mul_a ((polyno975704247_Sub_a V) Va)) B))).
% 39.46/39.67 Axiom help_If_3_1_If_001t__Nat__Onat_T:(forall (P5:Prop), ((or (((eq Prop) P5) True)) (((eq Prop) P5) False))).
% 39.46/39.67 Axiom help_If_2_1_If_001t__Nat__Onat_T:(forall (X:nat) (Y:nat), (((eq nat) (((if_nat False) X) Y)) Y)).
% 39.46/39.67 Axiom help_If_1_1_If_001t__Nat__Onat_T:(forall (X:nat) (Y:nat), (((eq nat) (((if_nat True) X) Y)) X)).
% 39.46/39.67 Trying to prove (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) ((polyno1934269411ymul_a q) p))
% 39.46/39.67 Found fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_0620:=(fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno1934269411ymul_a p) q)))):((P ((polyno1934269411ymul_a p) q))->(P ((polyno1934269411ymul_a p) q)))
% 39.46/39.67 Found (fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno1934269411ymul_a p) q)))) as proof of (P0 ((polyno1934269411ymul_a p) q))
% 39.46/39.67 Found (fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno1934269411ymul_a p) q)))) as proof of (P0 ((polyno1934269411ymul_a p) q))
% 39.46/39.67 Found eq_ref00:=(eq_ref0 b):(((eq polyno727731844poly_a) b) b)
% 39.46/39.67 Found (eq_ref0 b) as proof of (((eq polyno727731844poly_a) b) ((polyno1934269411ymul_a q) p))
% 39.46/39.67 Found ((eq_ref polyno727731844poly_a) b) as proof of (((eq polyno727731844poly_a) b) ((polyno1934269411ymul_a q) p))
% 39.46/39.67 Found ((eq_ref polyno727731844poly_a) b) as proof of (((eq polyno727731844poly_a) b) ((polyno1934269411ymul_a q) p))
% 39.46/39.67 Found ((eq_ref polyno727731844poly_a) b) as proof of (((eq polyno727731844poly_a) b) ((polyno1934269411ymul_a q) p))
% 39.46/39.67 Found eq_ref00:=(eq_ref0 ((polyno1934269411ymul_a p) q)):(((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) ((polyno1934269411ymul_a p) q))
% 39.46/39.67 Found (eq_ref0 ((polyno1934269411ymul_a p) q)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) b)
% 39.46/39.67 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) b)
% 39.46/39.67 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) b)
% 39.46/39.67 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) b)
% 39.46/39.67 Found fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_0621:=(fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))))):((P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q)))->(P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))))
% 86.38/86.64 Found (fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))))) as proof of (P0 ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q)))
% 86.38/86.64 Found (fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))))) as proof of (P0 ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q)))
% 86.38/86.64 Found eq_ref00:=(eq_ref0 b):(((eq polyno727731844poly_a) b) b)
% 86.38/86.64 Found (eq_ref0 b) as proof of (((eq polyno727731844poly_a) b) ((polyno1934269411ymul_a p) q))
% 86.38/86.64 Found ((eq_ref polyno727731844poly_a) b) as proof of (((eq polyno727731844poly_a) b) ((polyno1934269411ymul_a p) q))
% 86.38/86.64 Found ((eq_ref polyno727731844poly_a) b) as proof of (((eq polyno727731844poly_a) b) ((polyno1934269411ymul_a p) q))
% 86.38/86.64 Found ((eq_ref polyno727731844poly_a) b) as proof of (((eq polyno727731844poly_a) b) ((polyno1934269411ymul_a p) q))
% 86.38/86.64 Found eq_ref00:=(eq_ref0 ((polyno1934269411ymul_a q) p)):(((eq polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) ((polyno1934269411ymul_a q) p))
% 86.38/86.64 Found (eq_ref0 ((polyno1934269411ymul_a q) p)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) b)
% 86.38/86.64 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) b)
% 86.38/86.64 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) b)
% 86.38/86.64 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) b)
% 86.38/86.64 Found fact_335_polypow_Osimps_I1_J0:=(fact_335_polypow_Osimps_I1_J (fun (x:(polyno727731844poly_a->polyno727731844poly_a))=> (P ((polyno1934269411ymul_a p) q)))):((P ((polyno1934269411ymul_a p) q))->(P ((polyno1934269411ymul_a p) q)))
% 86.38/86.64 Found (fact_335_polypow_Osimps_I1_J (fun (x:(polyno727731844poly_a->polyno727731844poly_a))=> (P ((polyno1934269411ymul_a p) q)))) as proof of (P0 ((polyno1934269411ymul_a p) q))
% 86.38/86.64 Found (fact_335_polypow_Osimps_I1_J (fun (x:(polyno727731844poly_a->polyno727731844poly_a))=> (P ((polyno1934269411ymul_a p) q)))) as proof of (P0 ((polyno1934269411ymul_a p) q))
% 86.38/86.64 Found x:(P ((polyno1934269411ymul_a p) q))
% 86.38/86.64 Instantiate: b:=((polyno1934269411ymul_a p) q):polyno727731844poly_a
% 86.38/86.64 Found x as proof of (P0 b)
% 86.38/86.64 Found fact_10_polymul000:=(fact_10_polymul00 q):(((eq a) ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))) ((times_times_a ((polyno422358502poly_a Bs) p)) ((polyno422358502poly_a Bs) q)))
% 86.38/86.64 Found (fact_10_polymul00 q) as proof of (((eq a) ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))) b)
% 86.38/86.64 Found ((fact_10_polymul0 p) q) as proof of (((eq a) ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))) b)
% 86.38/86.64 Found (((fact_10_polymul Bs) p) q) as proof of (((eq a) ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))) b)
% 86.38/86.64 Found (((fact_10_polymul Bs) p) q) as proof of (((eq a) ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))) b)
% 86.38/86.64 Found (((fact_10_polymul Bs) p) q) as proof of (((eq a) ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))) b)
% 86.38/86.64 Found eq_ref00:=(eq_ref0 b):(((eq a) b) b)
% 86.38/86.64 Found (eq_ref0 b) as proof of (((eq a) b) ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p)))
% 86.38/86.64 Found ((eq_ref a) b) as proof of (((eq a) b) ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p)))
% 86.38/86.64 Found ((eq_ref a) b) as proof of (((eq a) b) ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p)))
% 86.38/86.64 Found ((eq_ref a) b) as proof of (((eq a) b) ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p)))
% 156.29/156.53 Found eq_ref00:=(eq_ref0 ((polyno1934269411ymul_a p) q)):(((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) ((polyno1934269411ymul_a p) q))
% 156.29/156.53 Found (eq_ref0 ((polyno1934269411ymul_a p) q)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) b)
% 156.29/156.53 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) b)
% 156.29/156.53 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) b)
% 156.29/156.53 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) b)
% 156.29/156.53 Found eq_ref00:=(eq_ref0 b):(((eq polyno727731844poly_a) b) b)
% 156.29/156.53 Found (eq_ref0 b) as proof of (((eq polyno727731844poly_a) b) ((polyno1934269411ymul_a q) p))
% 156.29/156.53 Found ((eq_ref polyno727731844poly_a) b) as proof of (((eq polyno727731844poly_a) b) ((polyno1934269411ymul_a q) p))
% 156.29/156.53 Found ((eq_ref polyno727731844poly_a) b) as proof of (((eq polyno727731844poly_a) b) ((polyno1934269411ymul_a q) p))
% 156.29/156.53 Found ((eq_ref polyno727731844poly_a) b) as proof of (((eq polyno727731844poly_a) b) ((polyno1934269411ymul_a q) p))
% 156.29/156.53 Found eq_ref00:=(eq_ref0 b):(((eq polyno727731844poly_a) b) b)
% 156.29/156.53 Found (eq_ref0 b) as proof of (((eq polyno727731844poly_a) b) ((polyno1934269411ymul_a q) p))
% 156.29/156.53 Found ((eq_ref polyno727731844poly_a) b) as proof of (((eq polyno727731844poly_a) b) ((polyno1934269411ymul_a q) p))
% 156.29/156.53 Found ((eq_ref polyno727731844poly_a) b) as proof of (((eq polyno727731844poly_a) b) ((polyno1934269411ymul_a q) p))
% 156.29/156.53 Found ((eq_ref polyno727731844poly_a) b) as proof of (((eq polyno727731844poly_a) b) ((polyno1934269411ymul_a q) p))
% 156.29/156.53 Found eq_ref00:=(eq_ref0 ((polyno1934269411ymul_a p) q)):(((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) ((polyno1934269411ymul_a p) q))
% 156.29/156.53 Found (eq_ref0 ((polyno1934269411ymul_a p) q)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) b)
% 156.29/156.53 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) b)
% 156.29/156.53 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) b)
% 156.29/156.53 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a p) q)) b)
% 156.29/156.53 Found x:(P0 b)
% 156.29/156.53 Instantiate: b:=((polyno1934269411ymul_a p) q):polyno727731844poly_a
% 156.29/156.53 Found (fun (x:(P0 b))=> x) as proof of (P0 ((polyno1934269411ymul_a p) q))
% 156.29/156.53 Found (fun (P0:(polyno727731844poly_a->Prop)) (x:(P0 b))=> x) as proof of ((P0 b)->(P0 ((polyno1934269411ymul_a p) q)))
% 156.29/156.53 Found (fun (P0:(polyno727731844poly_a->Prop)) (x:(P0 b))=> x) as proof of (P b)
% 156.29/156.53 Found eq_ref00:=(eq_ref0 ((polyno1934269411ymul_a q) p)):(((eq polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) ((polyno1934269411ymul_a q) p))
% 156.29/156.53 Found (eq_ref0 ((polyno1934269411ymul_a q) p)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) b)
% 156.29/156.53 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) b)
% 156.29/156.53 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) b)
% 156.29/156.53 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) b)
% 156.29/156.53 Found fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_0621:=(fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p))))):((P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p)))->(P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p))))
% 197.20/197.54 Found (fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p))))) as proof of (P0 ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p)))
% 197.20/197.54 Found (fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p))))) as proof of (P0 ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p)))
% 197.20/197.54 Found fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_0621:=(fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p))))):((P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p)))->(P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p))))
% 197.20/197.54 Found (fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p))))) as proof of (P0 ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p)))
% 197.20/197.54 Found (fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p))))) as proof of (P0 ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a q) p)))
% 197.20/197.54 Found fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_0620:=(fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno1934269411ymul_a p) q)))):((P ((polyno1934269411ymul_a p) q))->(P ((polyno1934269411ymul_a p) q)))
% 197.20/197.54 Found (fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno1934269411ymul_a p) q)))) as proof of (P0 ((polyno1934269411ymul_a p) q))
% 197.20/197.54 Found (fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno1934269411ymul_a p) q)))) as proof of (P0 ((polyno1934269411ymul_a p) q))
% 197.20/197.54 Found fact_132_mult_Ocommute0:=(fact_132_mult_Ocommute (fun (x:(a->(a->a)))=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))))):((P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q)))->(P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))))
% 197.20/197.54 Found (fact_132_mult_Ocommute (fun (x:(a->(a->a)))=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))))) as proof of (P0 ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q)))
% 246.31/246.69 Found (fact_132_mult_Ocommute (fun (x:(a->(a->a)))=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))))) as proof of (P0 ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q)))
% 246.31/246.69 Found fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_0621:=(fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q)))))):((P ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q))))->(P ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q)))))
% 246.31/246.69 Found (fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q)))))) as proof of (P0 ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q))))
% 246.31/246.69 Found (fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q)))))) as proof of (P0 ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q))))
% 246.31/246.69 Found eq_ref00:=(eq_ref0 ((polyno1934269411ymul_a q) p)):(((eq polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) ((polyno1934269411ymul_a q) p))
% 246.31/246.69 Found (eq_ref0 ((polyno1934269411ymul_a q) p)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) b)
% 246.31/246.69 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) b)
% 246.31/246.69 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) b)
% 246.31/246.69 Found ((eq_ref polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) as proof of (((eq polyno727731844poly_a) ((polyno1934269411ymul_a q) p)) b)
% 246.31/246.69 Found fact_170_shift1__def0:=(fact_170_shift1__def (fun (x:(polyno727731844poly_a->polyno727731844poly_a))=> (P ((polyno1934269411ymul_a p) q)))):((P ((polyno1934269411ymul_a p) q))->(P ((polyno1934269411ymul_a p) q)))
% 246.31/246.69 Found (fact_170_shift1__def (fun (x:(polyno727731844poly_a->polyno727731844poly_a))=> (P ((polyno1934269411ymul_a p) q)))) as proof of (P0 ((polyno1934269411ymul_a p) q))
% 246.31/246.69 Found (fact_170_shift1__def (fun (x:(polyno727731844poly_a->polyno727731844poly_a))=> (P ((polyno1934269411ymul_a p) q)))) as proof of (P0 ((polyno1934269411ymul_a p) q))
% 246.31/246.69 Found fact_28_polynate001:=(fact_28_polynate00 (fun (x:a)=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))))):((P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q)))->(P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))))
% 246.31/246.69 Found (fact_28_polynate00 (fun (x:a)=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))))) as proof of (P0 ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q)))
% 246.31/246.69 Found (fact_28_polynate00 (fun (x:a)=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))))) as proof of (P0 ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q)))
% 246.31/246.69 Found fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_0621:=(fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q)))))):((P ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q))))->(P ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q)))))
% 281.25/281.67 Found (fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q)))))) as proof of (P0 ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q))))
% 281.25/281.67 Found (fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q)))))) as proof of (P0 ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q))))
% 281.25/281.67 Found fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_0621:=(fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))))):((P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q)))->(P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))))
% 281.25/281.67 Found (fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))))) as proof of (P0 ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q)))
% 281.25/281.67 Found (fact_0__092_060open_062_I_092_060forall_062bs_O_AIpoly_Abs_A_Ip_A_K_092_060_094sub_062p_Aq_J_A_061_AIpoly_Abs_A_Iq_A_K_092_060_094sub_062p_Ap_J_J_A_061_A_Ip_A_K_092_060_094sub_062p_Aq_A_061_Aq_A_K_092_060_094sub_062p_Ap_J_092_060close_062 (fun (x:Prop)=> (P ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q))))) as proof of (P0 ((polyno422358502poly_a Bs) ((polyno1934269411ymul_a p) q)))
% 281.25/281.67 Found fact_132_mult_Ocommute0:=(fact_132_mult_Ocommute (fun (x:(a->(a->a)))=> (P ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q)))))):((P ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q))))->(P ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q)))))
% 281.25/281.67 Found (fact_132_mult_Ocommute (fun (x:(a->(a->a)))=> (P ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q)))))) as proof of (P0 ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q))))
% 281.25/281.67 Found (fact_132_mult_Ocommute (fun (x:(a->(a->a)))=> (P ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q)))))) as proof of (P0 ((polyno422358502poly_a Bs) (polyno955999183nate_a ((polyno1934269411ymul_a p) q))))
% 281.25/281.67 Found x:(P ((polyno1934269411ymul_a q) p))
% 281.25/281.67 Instantiate: b:=((polyno1934269411ymul_a q) p):polyno727731844poly_a
% 281.25/281.67 Found x as proof of (P0 b)
% 281.25/281.67 Found fact_170_shift1__def0:=(fact_170_shift1__def (fun (x:(polyno727731844poly_
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