%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM924^3 : TPTP v7.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n037.star.cs.uiowa.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory : 32218.625MB
% OS : Linux 3.10.0-693.2.2.el7.x86_64
% CPULimit : 300s
% DateTime : Mon Jan 8 13:12:03 EST 2018
% Result : Unknown 99.94s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM924^3 : TPTP v7.0.0. Released v5.3.0.
% 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.23 % Computer : n037.star.cs.uiowa.edu
% 0.03/0.23 % Model : x86_64 x86_64
% 0.03/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.03/0.23 % Memory : 32218.625MB
% 0.03/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.03/0.23 % CPULimit : 300
% 0.03/0.23 % DateTime : Fri Jan 5 15:51:36 CST 2018
% 0.03/0.23 % CPUTime :
% 0.07/0.26 Python 2.7.13
% 0.29/0.67 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c05e61c68>, <kernel.Type object at 0x2b7c05e61998>) of role type named ty_ty_tc__Int__Oint
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring int:Type
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c06584170>, <kernel.Type object at 0x2b7c05e61638>) of role type named ty_ty_tc__Nat__Onat
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring nat:Type
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c05e61d88>, <kernel.Type object at 0x2b7c05e61ea8>) of role type named ty_ty_tc__RealDef__Oreal
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring real:Type
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c05e61998>, <kernel.Type object at 0x2b7c05e61ab8>) of role type named ty_ty_tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring product_prod_int_int:Type
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c05e61a28>, <kernel.DependentProduct object at 0x2b7c05e61998>) of role type named sy_c_Divides_Odiv__class_Omod_000tc__Int__Oint
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring div_mod_int:(int->(int->int))
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c05e61878>, <kernel.DependentProduct object at 0x2b7c05e61998>) of role type named sy_c_Divides_Odiv__class_Omod_000tc__Nat__Onat
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring div_mod_nat:(nat->(nat->nat))
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c05e61cb0>, <kernel.DependentProduct object at 0x2b7c05b02c68>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring minus_minus_int:(int->(int->int))
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c05b02560>, <kernel.DependentProduct object at 0x2b7c05e61998>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring minus_minus_nat:(nat->(nat->nat))
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c05b02c68>, <kernel.DependentProduct object at 0x2b7c05e616c8>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__RealDef__Oreal
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring minus_minus_real:(real->(real->real))
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c05b025a8>, <kernel.Constant object at 0x2b7c05e616c8>) of role type named sy_c_Groups_Oone__class_Oone_000tc__Int__Oint
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring one_one_int:int
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c05b025a8>, <kernel.Constant object at 0x2b7c05e616c8>) of role type named sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring one_one_nat:nat
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c05e61cb0>, <kernel.Constant object at 0x2b7c05e616c8>) of role type named sy_c_Groups_Oone__class_Oone_000tc__RealDef__Oreal
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring one_one_real:real
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c05e61a28>, <kernel.DependentProduct object at 0x2b7c05eb7b48>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring plus_plus_int:(int->(int->int))
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c06573368>, <kernel.DependentProduct object at 0x2b7c05e616c8>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring plus_plus_nat:(nat->(nat->nat))
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c06573098>, <kernel.DependentProduct object at 0x2b7c05e61ea8>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__RealDef__Oreal
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring plus_plus_real:(real->(real->real))
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c06573098>, <kernel.DependentProduct object at 0x2b7c05e61a28>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring times_times_int:(int->(int->int))
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c05eb7e60>, <kernel.DependentProduct object at 0x2b7c05e61878>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__Nat__Onat
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring times_times_nat:(nat->(nat->nat))
% 0.29/0.67 FOF formula (<kernel.Constant object at 0x2b7c05eb7e60>, <kernel.DependentProduct object at 0x2b7c05e61638>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__RealDef__Oreal
% 0.29/0.67 Using role type
% 0.29/0.67 Declaring times_times_real:(real->(real->real))
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c05e61ea8>, <kernel.Constant object at 0x2b7c05e61638>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring zero_zero_int:int
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c05e61a28>, <kernel.Constant object at 0x2b7c05e61878>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring zero_zero_nat:nat
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c05e61ea8>, <kernel.Constant object at 0x2b7c06581a28>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__RealDef__Oreal
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring zero_zero_real:real
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c05e61878>, <kernel.DependentProduct object at 0x2b7c06581560>) of role type named sy_c_Int2_OMultInv
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring multInv:(int->(int->int))
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c05e61ea8>, <kernel.DependentProduct object at 0x2b7c06581f80>) of role type named sy_c_IntFact_Od22set
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring d22set:(int->(int->Prop))
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c05e61638>, <kernel.DependentProduct object at 0x2b7c065810e0>) of role type named sy_c_IntFact_Ozfact
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring zfact:(int->int)
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c05e61638>, <kernel.DependentProduct object at 0x2b7c065815a8>) of role type named sy_c_IntPrimes_Ozcong
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring zcong:(int->(int->(int->Prop)))
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c06581f80>, <kernel.DependentProduct object at 0x2b7c06581d40>) of role type named sy_c_IntPrimes_Ozprime
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring zprime:(int->Prop)
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c065810e0>, <kernel.DependentProduct object at 0x2b7c06581908>) of role type named sy_c_Int_OBit0
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring bit0:(int->int)
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c065815a8>, <kernel.DependentProduct object at 0x2b7c06581e60>) of role type named sy_c_Int_OBit1
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring bit1:(int->int)
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c06581d40>, <kernel.Constant object at 0x2b7c06581e60>) of role type named sy_c_Int_OMin
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring min:int
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c065810e0>, <kernel.Constant object at 0x2b7c06581e60>) of role type named sy_c_Int_OPls
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring pls:int
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c065815a8>, <kernel.DependentProduct object at 0x2b7c06581a70>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring number_number_of_int:(int->int)
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c06581128>, <kernel.DependentProduct object at 0x2b7c06581638>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__Nat__Onat
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring number_number_of_nat:(int->nat)
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c06581e60>, <kernel.DependentProduct object at 0x2b7c06581710>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__RealDef__Oreal
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring number267125858f_real:(int->real)
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c06581a70>, <kernel.DependentProduct object at 0x2b7c065815a8>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Int__Oint
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring ord_less_int:(int->(int->Prop))
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c06581638>, <kernel.DependentProduct object at 0x2b7c06581d40>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring ord_less_nat:(nat->(nat->Prop))
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c06581710>, <kernel.DependentProduct object at 0x2b7c06581128>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__RealDef__Oreal
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring ord_less_real:(real->(real->Prop))
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c065815a8>, <kernel.DependentProduct object at 0x2b7c06581e60>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Int__Oint
% 0.29/0.68 Using role type
% 0.29/0.68 Declaring ord_less_eq_int:(int->(int->Prop))
% 0.29/0.68 FOF formula (<kernel.Constant object at 0x2b7c06581d40>, <kernel.DependentProduct object at 0x2b7c06581a70>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring ord_less_eq_nat:(nat->(nat->Prop))
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7c06581128>, <kernel.DependentProduct object at 0x2b7c06581638>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__RealDef__Oreal
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring ord_less_eq_real:(real->(real->Prop))
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7c06581e60>, <kernel.DependentProduct object at 0x2b7c06581710>) of role type named sy_c_Power_Opower__class_Opower_000tc__Int__Oint
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring power_power_int:(int->(nat->int))
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7c06581a70>, <kernel.DependentProduct object at 0x2b7c06581ab8>) of role type named sy_c_Power_Opower__class_Opower_000tc__Nat__Onat
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring power_power_nat:(nat->(nat->nat))
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7c06581638>, <kernel.DependentProduct object at 0x2b7c06581680>) of role type named sy_c_Power_Opower__class_Opower_000tc__RealDef__Oreal
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring power_power_real:(real->(nat->real))
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7c06581710>, <kernel.DependentProduct object at 0x2b7c06581d40>) of role type named sy_c_Product__Type_OPair_000tc__Int__Oint_000tc__Int__Oint
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring product_Pair_int_int:(int->(int->product_prod_int_int))
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7c06581ab8>, <kernel.DependentProduct object at 0x2b7c06581128>) of role type named sy_c_Residues_OLegendre
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring legendre:(int->(int->int))
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7c06581680>, <kernel.DependentProduct object at 0x2b7c06581e60>) of role type named sy_c_Residues_OQuadRes
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring quadRes:(int->(int->Prop))
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7c06581d40>, <kernel.DependentProduct object at 0x2b7c065815a8>) of role type named sy_c_Residues_OSR
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring sr:(int->(int->Prop))
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7c06581128>, <kernel.DependentProduct object at 0x2b7c06581710>) of role type named sy_c_Residues_OStandardRes
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring standardRes:(int->(int->int))
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7c06581e60>, <kernel.DependentProduct object at 0x2b7c06581a70>) of role type named sy_c_Rings_Odvd__class_Odvd_000tc__Int__Oint
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring dvd_dvd_int:(int->(int->Prop))
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7c065815a8>, <kernel.DependentProduct object at 0x2b7c06581ab8>) of role type named sy_c_Rings_Odvd__class_Odvd_000tc__Nat__Onat
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring dvd_dvd_nat:(nat->(nat->Prop))
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7c06581710>, <kernel.DependentProduct object at 0x2b7c06581d40>) of role type named sy_c_Rings_Odvd__class_Odvd_000tc__RealDef__Oreal
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring dvd_dvd_real:(real->(real->Prop))
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7c06581560>, <kernel.DependentProduct object at 0x2b7c06581710>) of role type named sy_c_Set_OCollect_000tc__Int__Oint
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring collect_int:((int->Prop)->(int->Prop))
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7bfe1c5ef0>, <kernel.DependentProduct object at 0x2b7c06581e18>) of role type named sy_c_TwoSquares__Mirabelle__dzzvbppuls_Ois__sum2sq
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring twoSqu919416604sum2sq:(int->Prop)
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7c06581d40>, <kernel.DependentProduct object at 0x2b7c06581f38>) of role type named sy_c_TwoSquares__Mirabelle__dzzvbppuls_Osum2sq
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring twoSqu2057625106sum2sq:(product_prod_int_int->int)
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7c06581560>, <kernel.DependentProduct object at 0x2b7c065815a8>) of role type named sy_c_WilsonRuss_Oinv
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring inv:(int->(int->int))
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7c06581e18>, <kernel.DependentProduct object at 0x2b7c065815f0>) of role type named sy_c_WilsonRuss_Owset
% 0.29/0.69 Using role type
% 0.29/0.69 Declaring wset:(int->(int->(int->Prop)))
% 0.29/0.69 FOF formula (<kernel.Constant object at 0x2b7c06581e60>, <kernel.DependentProduct object at 0x2b7c05b084d0>) of role type named sy_c_member_000tc__Int__Oint
% 0.29/0.70 Using role type
% 0.29/0.70 Declaring member_int:(int->((int->Prop)->Prop))
% 0.29/0.70 FOF formula (<kernel.Constant object at 0x2b7c06581ab8>, <kernel.Constant object at 0x2b7c06581e60>) of role type named sy_v_m
% 0.29/0.70 Using role type
% 0.29/0.70 Declaring m:int
% 0.29/0.70 FOF formula (<kernel.Constant object at 0x2b7c065815f0>, <kernel.Constant object at 0x2b7c06581e60>) of role type named sy_v_s1____
% 0.29/0.70 Using role type
% 0.29/0.70 Declaring s1:int
% 0.29/0.70 FOF formula (<kernel.Constant object at 0x2b7c06581560>, <kernel.Constant object at 0x2b7c06581ab8>) of role type named sy_v_s____
% 0.29/0.70 Using role type
% 0.29/0.70 Declaring s:int
% 0.29/0.70 FOF formula (<kernel.Constant object at 0x2b7c065815f0>, <kernel.Constant object at 0x2b7c05b084d0>) of role type named sy_v_t____
% 0.29/0.70 Using role type
% 0.29/0.70 Declaring t:int
% 0.29/0.70 FOF formula ((ord_less_int t) zero_zero_int) of role axiom named fact_0__096t_A_060_A0_096
% 0.29/0.70 A new axiom: ((ord_less_int t) zero_zero_int)
% 0.29/0.70 FOF formula ((ord_less_int t) one_one_int) of role axiom named fact_1_calculation_I1_J
% 0.29/0.70 A new axiom: ((ord_less_int t) one_one_int)
% 0.29/0.70 FOF formula ((ord_less_int ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) zero_zero_int)) of role axiom named fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096
% 0.29/0.70 A new axiom: ((ord_less_int ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) zero_zero_int))
% 0.29/0.70 FOF formula (((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)) of role axiom named fact_3_t
% 0.29/0.70 A new axiom: (((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t))
% 0.29/0.70 FOF formula ((((eq int) t) zero_zero_int)->(((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) zero_zero_int)) of role axiom named fact_4_calculation_I2_J
% 0.29/0.70 A new axiom: ((((eq int) t) zero_zero_int)->(((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) zero_zero_int))
% 0.29/0.70 FOF formula (((ord_less_eq_int one_one_int) t)->False) of role axiom named fact_5__096_126_A1_A_060_061_At_096
% 0.29/0.70 A new axiom: (((ord_less_eq_int one_one_int) t)->False)
% 0.29/0.70 FOF formula ((ord_less_int zero_zero_int) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) of role axiom named fact_6_p0
% 0.29/0.70 A new axiom: ((ord_less_int zero_zero_int) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))
% 0.29/0.70 FOF formula (forall (X:real) (Y:real), (((ord_less_real ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)->False)) of role axiom named fact_7_not__sum__power2__lt__zero
% 0.29/0.70 A new axiom: (forall (X:real) (Y:real), (((ord_less_real ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)->False))
% 0.29/0.70 FOF formula (forall (X:int) (Y:int), (((ord_less_int ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)->False)) of role axiom named fact_8_not__sum__power2__lt__zero
% 0.29/0.70 A new axiom: (forall (X:int) (Y:int), (((ord_less_int ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)->False))
% 0.37/0.72 FOF formula (forall (X_39:real) (Y_31:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((power_power_real X_39) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_31) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq real) X_39) zero_zero_real))) (not (((eq real) Y_31) zero_zero_real))))) of role axiom named fact_9_sum__power2__gt__zero__iff
% 0.37/0.72 A new axiom: (forall (X_39:real) (Y_31:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((power_power_real X_39) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_31) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq real) X_39) zero_zero_real))) (not (((eq real) Y_31) zero_zero_real)))))
% 0.37/0.72 FOF formula (forall (X_39:int) (Y_31:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((power_power_int X_39) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_31) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq int) X_39) zero_zero_int))) (not (((eq int) Y_31) zero_zero_int))))) of role axiom named fact_10_sum__power2__gt__zero__iff
% 0.37/0.72 A new axiom: (forall (X_39:int) (Y_31:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((power_power_int X_39) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_31) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq int) X_39) zero_zero_int))) (not (((eq int) Y_31) zero_zero_int)))))
% 0.37/0.72 FOF formula (forall (X_38:real) (Y_30:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X_38) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_30) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_38) zero_zero_real)) (((eq real) Y_30) zero_zero_real)))) of role axiom named fact_11_sum__power2__eq__zero__iff
% 0.37/0.72 A new axiom: (forall (X_38:real) (Y_30:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X_38) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_30) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_38) zero_zero_real)) (((eq real) Y_30) zero_zero_real))))
% 0.37/0.72 FOF formula (forall (X_38:int) (Y_30:int), ((iff (((eq int) ((plus_plus_int ((power_power_int X_38) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_30) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_38) zero_zero_int)) (((eq int) Y_30) zero_zero_int)))) of role axiom named fact_12_sum__power2__eq__zero__iff
% 0.37/0.72 A new axiom: (forall (X_38:int) (Y_30:int), ((iff (((eq int) ((plus_plus_int ((power_power_int X_38) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_30) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_38) zero_zero_int)) (((eq int) Y_30) zero_zero_int))))
% 0.37/0.72 FOF formula (forall (A_129:real), (((ord_less_real ((power_power_real A_129) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)->False)) of role axiom named fact_13_power2__less__0
% 0.37/0.72 A new axiom: (forall (A_129:real), (((ord_less_real ((power_power_real A_129) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)->False))
% 0.37/0.72 FOF formula (forall (A_129:int), (((ord_less_int ((power_power_int A_129) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)->False)) of role axiom named fact_14_power2__less__0
% 0.37/0.72 A new axiom: (forall (A_129:int), (((ord_less_int ((power_power_int A_129) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)->False))
% 0.37/0.72 FOF formula (forall (A_128:real), ((iff ((ord_less_real zero_zero_real) ((power_power_real A_128) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq real) A_128) zero_zero_real)))) of role axiom named fact_15_zero__less__power2
% 0.37/0.72 A new axiom: (forall (A_128:real), ((iff ((ord_less_real zero_zero_real) ((power_power_real A_128) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq real) A_128) zero_zero_real))))
% 0.37/0.72 FOF formula (forall (A_128:int), ((iff ((ord_less_int zero_zero_int) ((power_power_int A_128) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq int) A_128) zero_zero_int)))) of role axiom named fact_16_zero__less__power2
% 0.37/0.73 A new axiom: (forall (A_128:int), ((iff ((ord_less_int zero_zero_int) ((power_power_int A_128) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq int) A_128) zero_zero_int))))
% 0.37/0.73 FOF formula (((eq real) ((power_power_real one_one_real) (number_number_of_nat (bit0 (bit1 pls))))) one_one_real) of role axiom named fact_17_one__power2
% 0.37/0.73 A new axiom: (((eq real) ((power_power_real one_one_real) (number_number_of_nat (bit0 (bit1 pls))))) one_one_real)
% 0.37/0.73 FOF formula (((eq nat) ((power_power_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls))))) one_one_nat) of role axiom named fact_18_one__power2
% 0.37/0.73 A new axiom: (((eq nat) ((power_power_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls))))) one_one_nat)
% 0.37/0.73 FOF formula (((eq int) ((power_power_int one_one_int) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int) of role axiom named fact_19_one__power2
% 0.37/0.73 A new axiom: (((eq int) ((power_power_int one_one_int) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)
% 0.37/0.73 FOF formula (((eq real) ((power_power_real zero_zero_real) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real) of role axiom named fact_20_zero__power2
% 0.37/0.73 A new axiom: (((eq real) ((power_power_real zero_zero_real) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)
% 0.37/0.73 FOF formula (((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_nat) of role axiom named fact_21_zero__power2
% 0.37/0.73 A new axiom: (((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_nat)
% 0.37/0.73 FOF formula (((eq int) ((power_power_int zero_zero_int) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int) of role axiom named fact_22_zero__power2
% 0.37/0.73 A new axiom: (((eq int) ((power_power_int zero_zero_int) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)
% 0.37/0.73 FOF formula (forall (A_127:real), ((iff (((eq real) ((power_power_real A_127) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)) (((eq real) A_127) zero_zero_real))) of role axiom named fact_23_zero__eq__power2
% 0.37/0.73 A new axiom: (forall (A_127:real), ((iff (((eq real) ((power_power_real A_127) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)) (((eq real) A_127) zero_zero_real)))
% 0.37/0.73 FOF formula (forall (A_127:int), ((iff (((eq int) ((power_power_int A_127) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)) (((eq int) A_127) zero_zero_int))) of role axiom named fact_24_zero__eq__power2
% 0.37/0.73 A new axiom: (forall (A_127:int), ((iff (((eq int) ((power_power_int A_127) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)) (((eq int) A_127) zero_zero_int)))
% 0.37/0.73 FOF formula (forall (W_17:int), (((eq real) ((plus_plus_real one_one_real) (number267125858f_real W_17))) (number267125858f_real ((plus_plus_int (bit1 pls)) W_17)))) of role axiom named fact_25_add__special_I2_J
% 0.37/0.73 A new axiom: (forall (W_17:int), (((eq real) ((plus_plus_real one_one_real) (number267125858f_real W_17))) (number267125858f_real ((plus_plus_int (bit1 pls)) W_17))))
% 0.37/0.73 FOF formula (forall (W_17:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_17))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_17)))) of role axiom named fact_26_add__special_I2_J
% 0.37/0.73 A new axiom: (forall (W_17:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_17))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_17))))
% 0.37/0.73 FOF formula (forall (V_16:int), (((eq real) ((plus_plus_real (number267125858f_real V_16)) one_one_real)) (number267125858f_real ((plus_plus_int V_16) (bit1 pls))))) of role axiom named fact_27_add__special_I3_J
% 0.37/0.73 A new axiom: (forall (V_16:int), (((eq real) ((plus_plus_real (number267125858f_real V_16)) one_one_real)) (number267125858f_real ((plus_plus_int V_16) (bit1 pls)))))
% 0.37/0.73 FOF formula (forall (V_16:int), (((eq int) ((plus_plus_int (number_number_of_int V_16)) one_one_int)) (number_number_of_int ((plus_plus_int V_16) (bit1 pls))))) of role axiom named fact_28_add__special_I3_J
% 0.37/0.73 A new axiom: (forall (V_16:int), (((eq int) ((plus_plus_int (number_number_of_int V_16)) one_one_int)) (number_number_of_int ((plus_plus_int V_16) (bit1 pls)))))
% 0.37/0.73 FOF formula ((ord_less_int t) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) of role axiom named fact_29_t__l__p
% 0.37/0.75 A new axiom: ((ord_less_int t) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))
% 0.37/0.75 FOF formula ((forall (T_1:int), (not (((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) T_1))))->False) of role axiom named fact_30__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_
% 0.37/0.75 A new axiom: ((forall (T_1:int), (not (((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) T_1))))->False)
% 0.37/0.75 FOF formula (zprime ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) of role axiom named fact_31_p
% 0.37/0.75 A new axiom: (zprime ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))
% 0.37/0.75 FOF formula (twoSqu919416604sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)) of role axiom named fact_32_qf1pt
% 0.37/0.75 A new axiom: (twoSqu919416604sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t))
% 0.37/0.75 FOF formula (forall (W:int), ((ord_less_eq_int W) W)) of role axiom named fact_33_zle__refl
% 0.37/0.75 A new axiom: (forall (W:int), ((ord_less_eq_int W) W))
% 0.37/0.75 FOF formula (forall (K:int), (((eq int) (number_number_of_int K)) K)) of role axiom named fact_34_number__of__is__id
% 0.37/0.75 A new axiom: (forall (K:int), (((eq int) (number_number_of_int K)) K))
% 0.37/0.75 FOF formula (forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z))) of role axiom named fact_35_zmult__commute
% 0.37/0.75 A new axiom: (forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z)))
% 0.37/0.75 FOF formula (forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z))) of role axiom named fact_36_zle__linear
% 0.37/0.75 A new axiom: (forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z)))
% 0.37/0.75 FOF formula (forall (V:int) (W:int), (((eq int) ((times_times_int (number_number_of_int V)) (number_number_of_int W))) (number_number_of_int ((times_times_int V) W)))) of role axiom named fact_37_times__numeral__code_I5_J
% 0.37/0.75 A new axiom: (forall (V:int) (W:int), (((eq int) ((times_times_int (number_number_of_int V)) (number_number_of_int W))) (number_number_of_int ((times_times_int V) W))))
% 0.37/0.75 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_eq_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_eq_int K) L))) of role axiom named fact_38_less__eq__number__of__int__code
% 0.37/0.75 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_eq_int K) L)))
% 0.37/0.75 FOF formula (forall (X_37:int) (Y_29:int), ((iff ((ord_less_eq_real (number267125858f_real X_37)) (number267125858f_real Y_29))) ((ord_less_eq_int X_37) Y_29))) of role axiom named fact_39_le__number__of
% 0.37/0.75 A new axiom: (forall (X_37:int) (Y_29:int), ((iff ((ord_less_eq_real (number267125858f_real X_37)) (number267125858f_real Y_29))) ((ord_less_eq_int X_37) Y_29)))
% 0.37/0.75 FOF formula (forall (X_37:int) (Y_29:int), ((iff ((ord_less_eq_int (number_number_of_int X_37)) (number_number_of_int Y_29))) ((ord_less_eq_int X_37) Y_29))) of role axiom named fact_40_le__number__of
% 0.37/0.75 A new axiom: (forall (X_37:int) (Y_29:int), ((iff ((ord_less_eq_int (number_number_of_int X_37)) (number_number_of_int Y_29))) ((ord_less_eq_int X_37) Y_29)))
% 0.37/0.75 FOF formula (forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((times_times_int ((times_times_int Z1) Z2)) Z3)) ((times_times_int Z1) ((times_times_int Z2) Z3)))) of role axiom named fact_41_zmult__assoc
% 0.37/0.75 A new axiom: (forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((times_times_int ((times_times_int Z1) Z2)) Z3)) ((times_times_int Z1) ((times_times_int Z2) Z3))))
% 0.37/0.77 FOF formula (forall (K:int) (I_1:int) (J_1:int), (((ord_less_eq_int I_1) J_1)->(((ord_less_eq_int J_1) K)->((ord_less_eq_int I_1) K)))) of role axiom named fact_42_zle__trans
% 0.37/0.77 A new axiom: (forall (K:int) (I_1:int) (J_1:int), (((ord_less_eq_int I_1) J_1)->(((ord_less_eq_int J_1) K)->((ord_less_eq_int I_1) K))))
% 0.37/0.77 FOF formula (forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W)))) of role axiom named fact_43_zle__antisym
% 0.37/0.77 A new axiom: (forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W))))
% 0.37/0.77 FOF formula (forall (X:int) (Y:nat) (Z:nat), (((eq int) ((power_power_int X) ((plus_plus_nat Y) Z))) ((times_times_int ((power_power_int X) Y)) ((power_power_int X) Z)))) of role axiom named fact_44_zpower__zadd__distrib
% 0.37/0.77 A new axiom: (forall (X:int) (Y:nat) (Z:nat), (((eq int) ((power_power_int X) ((plus_plus_nat Y) Z))) ((times_times_int ((power_power_int X) Y)) ((power_power_int X) Z))))
% 0.37/0.77 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))) of role axiom named fact_45_less__eq__int__code_I16_J
% 0.37/0.77 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2)))
% 0.37/0.77 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit1 L))) ((ord_less_eq_int K) L))) of role axiom named fact_46_rel__simps_I34_J
% 0.37/0.77 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit1 L))) ((ord_less_eq_int K) L)))
% 0.37/0.77 FOF formula ((ord_less_eq_int pls) pls) of role axiom named fact_47_rel__simps_I19_J
% 0.37/0.77 A new axiom: ((ord_less_eq_int pls) pls)
% 0.37/0.77 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit0 K2))) ((ord_less_eq_int K1) K2))) of role axiom named fact_48_less__eq__int__code_I13_J
% 0.37/0.77 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit0 K2))) ((ord_less_eq_int K1) K2)))
% 0.37/0.77 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit0 L))) ((ord_less_eq_int K) L))) of role axiom named fact_49_rel__simps_I31_J
% 0.37/0.77 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit0 L))) ((ord_less_eq_int K) L)))
% 0.37/0.77 FOF formula (forall (Z:int) (W:int), ((iff ((ord_less_int Z) W)) ((and ((ord_less_eq_int Z) W)) (not (((eq int) Z) W))))) of role axiom named fact_50_zless__le
% 0.37/0.77 A new axiom: (forall (Z:int) (W:int), ((iff ((ord_less_int Z) W)) ((and ((ord_less_eq_int Z) W)) (not (((eq int) Z) W)))))
% 0.37/0.77 FOF formula (forall (K:int) (I_1:int) (J_1:int), (((ord_less_eq_int I_1) J_1)->((ord_less_eq_int ((plus_plus_int K) I_1)) ((plus_plus_int K) J_1)))) of role axiom named fact_51_zadd__left__mono
% 0.37/0.77 A new axiom: (forall (K:int) (I_1:int) (J_1:int), (((ord_less_eq_int I_1) J_1)->((ord_less_eq_int ((plus_plus_int K) I_1)) ((plus_plus_int K) J_1))))
% 0.37/0.77 FOF formula (forall (V:int), ((iff (((eq nat) (number_number_of_nat V)) zero_zero_nat)) ((ord_less_eq_int V) pls))) of role axiom named fact_52_eq__number__of__0
% 0.37/0.77 A new axiom: (forall (V:int), ((iff (((eq nat) (number_number_of_nat V)) zero_zero_nat)) ((ord_less_eq_int V) pls)))
% 0.37/0.77 FOF formula (forall (V:int), ((iff (((eq nat) zero_zero_nat) (number_number_of_nat V))) ((ord_less_eq_int V) pls))) of role axiom named fact_53_eq__0__number__of
% 0.37/0.77 A new axiom: (forall (V:int), ((iff (((eq nat) zero_zero_nat) (number_number_of_nat V))) ((ord_less_eq_int V) pls)))
% 0.37/0.77 FOF formula (forall (V_15:int) (V_14:int), (((ord_less_eq_int pls) V_14)->(((ord_less_eq_int pls) V_15)->(((eq real) ((times_times_real (number267125858f_real V_14)) (number267125858f_real V_15))) (number267125858f_real ((times_times_int V_14) V_15)))))) of role axiom named fact_54_semiring__mult__number__of
% 0.37/0.77 A new axiom: (forall (V_15:int) (V_14:int), (((ord_less_eq_int pls) V_14)->(((ord_less_eq_int pls) V_15)->(((eq real) ((times_times_real (number267125858f_real V_14)) (number267125858f_real V_15))) (number267125858f_real ((times_times_int V_14) V_15))))))
% 0.37/0.77 FOF formula (forall (V_15:int) (V_14:int), (((ord_less_eq_int pls) V_14)->(((ord_less_eq_int pls) V_15)->(((eq nat) ((times_times_nat (number_number_of_nat V_14)) (number_number_of_nat V_15))) (number_number_of_nat ((times_times_int V_14) V_15)))))) of role axiom named fact_55_semiring__mult__number__of
% 0.44/0.78 A new axiom: (forall (V_15:int) (V_14:int), (((ord_less_eq_int pls) V_14)->(((ord_less_eq_int pls) V_15)->(((eq nat) ((times_times_nat (number_number_of_nat V_14)) (number_number_of_nat V_15))) (number_number_of_nat ((times_times_int V_14) V_15))))))
% 0.44/0.78 FOF formula (forall (V_15:int) (V_14:int), (((ord_less_eq_int pls) V_14)->(((ord_less_eq_int pls) V_15)->(((eq int) ((times_times_int (number_number_of_int V_14)) (number_number_of_int V_15))) (number_number_of_int ((times_times_int V_14) V_15)))))) of role axiom named fact_56_semiring__mult__number__of
% 0.44/0.78 A new axiom: (forall (V_15:int) (V_14:int), (((ord_less_eq_int pls) V_14)->(((ord_less_eq_int pls) V_15)->(((eq int) ((times_times_int (number_number_of_int V_14)) (number_number_of_int V_15))) (number_number_of_int ((times_times_int V_14) V_15))))))
% 0.44/0.78 FOF formula (forall (V_13:int) (W_16:int) (Z_9:real), (((eq real) ((times_times_real (number267125858f_real V_13)) ((times_times_real (number267125858f_real W_16)) Z_9))) ((times_times_real (number267125858f_real ((times_times_int V_13) W_16))) Z_9))) of role axiom named fact_57_mult__number__of__left
% 0.44/0.78 A new axiom: (forall (V_13:int) (W_16:int) (Z_9:real), (((eq real) ((times_times_real (number267125858f_real V_13)) ((times_times_real (number267125858f_real W_16)) Z_9))) ((times_times_real (number267125858f_real ((times_times_int V_13) W_16))) Z_9)))
% 0.44/0.78 FOF formula (forall (V_13:int) (W_16:int) (Z_9:int), (((eq int) ((times_times_int (number_number_of_int V_13)) ((times_times_int (number_number_of_int W_16)) Z_9))) ((times_times_int (number_number_of_int ((times_times_int V_13) W_16))) Z_9))) of role axiom named fact_58_mult__number__of__left
% 0.44/0.78 A new axiom: (forall (V_13:int) (W_16:int) (Z_9:int), (((eq int) ((times_times_int (number_number_of_int V_13)) ((times_times_int (number_number_of_int W_16)) Z_9))) ((times_times_int (number_number_of_int ((times_times_int V_13) W_16))) Z_9)))
% 0.44/0.78 FOF formula (forall (V_12:int) (W_15:int), (((eq real) ((times_times_real (number267125858f_real V_12)) (number267125858f_real W_15))) (number267125858f_real ((times_times_int V_12) W_15)))) of role axiom named fact_59_arith__simps_I32_J
% 0.44/0.78 A new axiom: (forall (V_12:int) (W_15:int), (((eq real) ((times_times_real (number267125858f_real V_12)) (number267125858f_real W_15))) (number267125858f_real ((times_times_int V_12) W_15))))
% 0.44/0.78 FOF formula (forall (V_12:int) (W_15:int), (((eq int) ((times_times_int (number_number_of_int V_12)) (number_number_of_int W_15))) (number_number_of_int ((times_times_int V_12) W_15)))) of role axiom named fact_60_arith__simps_I32_J
% 0.44/0.78 A new axiom: (forall (V_12:int) (W_15:int), (((eq int) ((times_times_int (number_number_of_int V_12)) (number_number_of_int W_15))) (number_number_of_int ((times_times_int V_12) W_15))))
% 0.44/0.78 FOF formula (forall (V_11:int) (W_14:int), (((eq real) (number267125858f_real ((times_times_int V_11) W_14))) ((times_times_real (number267125858f_real V_11)) (number267125858f_real W_14)))) of role axiom named fact_61_number__of__mult
% 0.44/0.78 A new axiom: (forall (V_11:int) (W_14:int), (((eq real) (number267125858f_real ((times_times_int V_11) W_14))) ((times_times_real (number267125858f_real V_11)) (number267125858f_real W_14))))
% 0.44/0.78 FOF formula (forall (V_11:int) (W_14:int), (((eq int) (number_number_of_int ((times_times_int V_11) W_14))) ((times_times_int (number_number_of_int V_11)) (number_number_of_int W_14)))) of role axiom named fact_62_number__of__mult
% 0.44/0.78 A new axiom: (forall (V_11:int) (W_14:int), (((eq int) (number_number_of_int ((times_times_int V_11) W_14))) ((times_times_int (number_number_of_int V_11)) (number_number_of_int W_14))))
% 0.44/0.78 FOF formula (forall (X_36:real) (Y_28:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real X_36) X_36)) ((times_times_real Y_28) Y_28))) zero_zero_real)) ((and (((eq real) X_36) zero_zero_real)) (((eq real) Y_28) zero_zero_real)))) of role axiom named fact_63_sum__squares__le__zero__iff
% 0.44/0.80 A new axiom: (forall (X_36:real) (Y_28:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real X_36) X_36)) ((times_times_real Y_28) Y_28))) zero_zero_real)) ((and (((eq real) X_36) zero_zero_real)) (((eq real) Y_28) zero_zero_real))))
% 0.44/0.80 FOF formula (forall (X_36:int) (Y_28:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int X_36) X_36)) ((times_times_int Y_28) Y_28))) zero_zero_int)) ((and (((eq int) X_36) zero_zero_int)) (((eq int) Y_28) zero_zero_int)))) of role axiom named fact_64_sum__squares__le__zero__iff
% 0.44/0.80 A new axiom: (forall (X_36:int) (Y_28:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int X_36) X_36)) ((times_times_int Y_28) Y_28))) zero_zero_int)) ((and (((eq int) X_36) zero_zero_int)) (((eq int) Y_28) zero_zero_int))))
% 0.44/0.80 FOF formula (forall (X_35:real) (Y_27:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((times_times_real X_35) X_35)) ((times_times_real Y_27) Y_27)))) of role axiom named fact_65_sum__squares__ge__zero
% 0.44/0.80 A new axiom: (forall (X_35:real) (Y_27:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((times_times_real X_35) X_35)) ((times_times_real Y_27) Y_27))))
% 0.44/0.80 FOF formula (forall (X_35:int) (Y_27:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int X_35) X_35)) ((times_times_int Y_27) Y_27)))) of role axiom named fact_66_sum__squares__ge__zero
% 0.44/0.80 A new axiom: (forall (X_35:int) (Y_27:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int X_35) X_35)) ((times_times_int Y_27) Y_27))))
% 0.44/0.80 FOF formula (forall (X_34:int), ((iff ((ord_less_eq_real (number267125858f_real X_34)) zero_zero_real)) ((ord_less_eq_int X_34) pls))) of role axiom named fact_67_le__special_I3_J
% 0.44/0.80 A new axiom: (forall (X_34:int), ((iff ((ord_less_eq_real (number267125858f_real X_34)) zero_zero_real)) ((ord_less_eq_int X_34) pls)))
% 0.44/0.80 FOF formula (forall (X_34:int), ((iff ((ord_less_eq_int (number_number_of_int X_34)) zero_zero_int)) ((ord_less_eq_int X_34) pls))) of role axiom named fact_68_le__special_I3_J
% 0.44/0.80 A new axiom: (forall (X_34:int), ((iff ((ord_less_eq_int (number_number_of_int X_34)) zero_zero_int)) ((ord_less_eq_int X_34) pls)))
% 0.44/0.80 FOF formula (forall (Y_26:int), ((iff ((ord_less_eq_real zero_zero_real) (number267125858f_real Y_26))) ((ord_less_eq_int pls) Y_26))) of role axiom named fact_69_le__special_I1_J
% 0.44/0.80 A new axiom: (forall (Y_26:int), ((iff ((ord_less_eq_real zero_zero_real) (number267125858f_real Y_26))) ((ord_less_eq_int pls) Y_26)))
% 0.44/0.80 FOF formula (forall (Y_26:int), ((iff ((ord_less_eq_int zero_zero_int) (number_number_of_int Y_26))) ((ord_less_eq_int pls) Y_26))) of role axiom named fact_70_le__special_I1_J
% 0.44/0.80 A new axiom: (forall (Y_26:int), ((iff ((ord_less_eq_int zero_zero_int) (number_number_of_int Y_26))) ((ord_less_eq_int pls) Y_26)))
% 0.44/0.80 FOF formula (forall (V:int), ((iff ((ord_less_nat zero_zero_nat) (number_number_of_nat V))) ((ord_less_int pls) V))) of role axiom named fact_71_less__0__number__of
% 0.44/0.80 A new axiom: (forall (V:int), ((iff ((ord_less_nat zero_zero_nat) (number_number_of_nat V))) ((ord_less_int pls) V)))
% 0.44/0.80 FOF formula (forall (V_10:int) (W_13:int), ((iff ((ord_less_eq_real (number267125858f_real V_10)) (number267125858f_real W_13))) (((ord_less_real (number267125858f_real W_13)) (number267125858f_real V_10))->False))) of role axiom named fact_72_le__number__of__eq__not__less
% 0.44/0.80 A new axiom: (forall (V_10:int) (W_13:int), ((iff ((ord_less_eq_real (number267125858f_real V_10)) (number267125858f_real W_13))) (((ord_less_real (number267125858f_real W_13)) (number267125858f_real V_10))->False)))
% 0.44/0.80 FOF formula (forall (V_10:int) (W_13:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_10)) (number_number_of_nat W_13))) (((ord_less_nat (number_number_of_nat W_13)) (number_number_of_nat V_10))->False))) of role axiom named fact_73_le__number__of__eq__not__less
% 0.44/0.80 A new axiom: (forall (V_10:int) (W_13:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_10)) (number_number_of_nat W_13))) (((ord_less_nat (number_number_of_nat W_13)) (number_number_of_nat V_10))->False)))
% 0.44/0.80 FOF formula (forall (V_10:int) (W_13:int), ((iff ((ord_less_eq_int (number_number_of_int V_10)) (number_number_of_int W_13))) (((ord_less_int (number_number_of_int W_13)) (number_number_of_int V_10))->False))) of role axiom named fact_74_le__number__of__eq__not__less
% 0.44/0.81 A new axiom: (forall (V_10:int) (W_13:int), ((iff ((ord_less_eq_int (number_number_of_int V_10)) (number_number_of_int W_13))) (((ord_less_int (number_number_of_int W_13)) (number_number_of_int V_10))->False)))
% 0.44/0.81 FOF formula (forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_75_rel__simps_I22_J
% 0.44/0.81 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K)))
% 0.44/0.81 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))) of role axiom named fact_76_less__eq__int__code_I14_J
% 0.44/0.81 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2)))
% 0.44/0.81 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))) of role axiom named fact_77_rel__simps_I32_J
% 0.44/0.81 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L)))
% 0.44/0.81 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) pls)) ((ord_less_eq_int K) pls))) of role axiom named fact_78_rel__simps_I27_J
% 0.44/0.81 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) pls)) ((ord_less_eq_int K) pls)))
% 0.44/0.81 FOF formula (forall (K:int), ((iff ((ord_less_eq_int pls) (bit0 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_79_rel__simps_I21_J
% 0.44/0.81 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int pls) (bit0 K))) ((ord_less_eq_int pls) K)))
% 0.44/0.81 FOF formula (forall (Z_8:int) (Z:int) (W_12:int) (W:int), (((ord_less_int W_12) W)->(((ord_less_eq_int Z_8) Z)->((ord_less_int ((plus_plus_int W_12) Z_8)) ((plus_plus_int W) Z))))) of role axiom named fact_80_zadd__zless__mono
% 0.44/0.81 A new axiom: (forall (Z_8:int) (Z:int) (W_12:int) (W:int), (((ord_less_int W_12) W)->(((ord_less_eq_int Z_8) Z)->((ord_less_int ((plus_plus_int W_12) Z_8)) ((plus_plus_int W) Z)))))
% 0.44/0.81 FOF formula (((eq nat) (number_number_of_nat pls)) zero_zero_nat) of role axiom named fact_81_nat__number__of__Pls
% 0.44/0.81 A new axiom: (((eq nat) (number_number_of_nat pls)) zero_zero_nat)
% 0.44/0.81 FOF formula (((eq nat) zero_zero_nat) (number_number_of_nat pls)) of role axiom named fact_82_semiring__norm_I113_J
% 0.44/0.81 A new axiom: (((eq nat) zero_zero_nat) (number_number_of_nat pls))
% 0.44/0.81 FOF formula (forall (X_33:int), ((iff ((ord_less_eq_real (number267125858f_real X_33)) one_one_real)) ((ord_less_eq_int X_33) (bit1 pls)))) of role axiom named fact_83_le__special_I4_J
% 0.44/0.81 A new axiom: (forall (X_33:int), ((iff ((ord_less_eq_real (number267125858f_real X_33)) one_one_real)) ((ord_less_eq_int X_33) (bit1 pls))))
% 0.44/0.81 FOF formula (forall (X_33:int), ((iff ((ord_less_eq_int (number_number_of_int X_33)) one_one_int)) ((ord_less_eq_int X_33) (bit1 pls)))) of role axiom named fact_84_le__special_I4_J
% 0.44/0.81 A new axiom: (forall (X_33:int), ((iff ((ord_less_eq_int (number_number_of_int X_33)) one_one_int)) ((ord_less_eq_int X_33) (bit1 pls))))
% 0.44/0.81 FOF formula (forall (Y_25:int), ((iff ((ord_less_eq_real one_one_real) (number267125858f_real Y_25))) ((ord_less_eq_int (bit1 pls)) Y_25))) of role axiom named fact_85_le__special_I2_J
% 0.44/0.81 A new axiom: (forall (Y_25:int), ((iff ((ord_less_eq_real one_one_real) (number267125858f_real Y_25))) ((ord_less_eq_int (bit1 pls)) Y_25)))
% 0.44/0.81 FOF formula (forall (Y_25:int), ((iff ((ord_less_eq_int one_one_int) (number_number_of_int Y_25))) ((ord_less_eq_int (bit1 pls)) Y_25))) of role axiom named fact_86_le__special_I2_J
% 0.44/0.81 A new axiom: (forall (Y_25:int), ((iff ((ord_less_eq_int one_one_int) (number_number_of_int Y_25))) ((ord_less_eq_int (bit1 pls)) Y_25)))
% 0.44/0.81 FOF formula (((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))) of role axiom named fact_87_nat__1__add__1
% 0.44/0.81 A new axiom: (((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls))))
% 0.44/0.81 FOF formula (forall (W:int), (((eq int) ((times_times_int pls) W)) pls)) of role axiom named fact_88_mult__Pls
% 0.44/0.83 A new axiom: (forall (W:int), (((eq int) ((times_times_int pls) W)) pls))
% 0.44/0.83 FOF formula (forall (K:int) (L:int), (((eq int) ((times_times_int (bit0 K)) L)) (bit0 ((times_times_int K) L)))) of role axiom named fact_89_mult__Bit0
% 0.44/0.83 A new axiom: (forall (K:int) (L:int), (((eq int) ((times_times_int (bit0 K)) L)) (bit0 ((times_times_int K) L))))
% 0.44/0.83 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_int K) L))) of role axiom named fact_90_less__number__of__int__code
% 0.44/0.83 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_int K) L)))
% 0.44/0.83 FOF formula (forall (Z:int), (((eq int) ((times_times_int Z) one_one_int)) Z)) of role axiom named fact_91_zmult__1__right
% 0.44/0.83 A new axiom: (forall (Z:int), (((eq int) ((times_times_int Z) one_one_int)) Z))
% 0.44/0.83 FOF formula (forall (Z:int), (((eq int) ((times_times_int one_one_int) Z)) Z)) of role axiom named fact_92_zmult__1
% 0.44/0.83 A new axiom: (forall (Z:int), (((eq int) ((times_times_int one_one_int) Z)) Z))
% 0.44/0.83 FOF formula (forall (V:int) (W:int), (((eq int) ((plus_plus_int (number_number_of_int V)) (number_number_of_int W))) (number_number_of_int ((plus_plus_int V) W)))) of role axiom named fact_93_plus__numeral__code_I9_J
% 0.44/0.83 A new axiom: (forall (V:int) (W:int), (((eq int) ((plus_plus_int (number_number_of_int V)) (number_number_of_int W))) (number_number_of_int ((plus_plus_int V) W))))
% 0.44/0.83 FOF formula (forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((plus_plus_int Z1) Z2)) W)) ((plus_plus_int ((times_times_int Z1) W)) ((times_times_int Z2) W)))) of role axiom named fact_94_zadd__zmult__distrib
% 0.44/0.83 A new axiom: (forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((plus_plus_int Z1) Z2)) W)) ((plus_plus_int ((times_times_int Z1) W)) ((times_times_int Z2) W))))
% 0.44/0.83 FOF formula (forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((plus_plus_int Z1) Z2))) ((plus_plus_int ((times_times_int W) Z1)) ((times_times_int W) Z2)))) of role axiom named fact_95_zadd__zmult__distrib2
% 0.44/0.83 A new axiom: (forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((plus_plus_int Z1) Z2))) ((plus_plus_int ((times_times_int W) Z1)) ((times_times_int W) Z2))))
% 0.44/0.83 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_96_rel__simps_I29_J
% 0.44/0.83 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls)))
% 0.44/0.83 FOF formula (forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_97_rel__simps_I5_J
% 0.44/0.83 A new axiom: (forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K)))
% 0.44/0.83 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2))) of role axiom named fact_98_less__eq__int__code_I15_J
% 0.44/0.83 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2)))
% 0.44/0.83 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))) of role axiom named fact_99_rel__simps_I33_J
% 0.44/0.83 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit0 L))) ((ord_less_int K) L)))
% 0.44/0.83 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))) of role axiom named fact_100_less__int__code_I14_J
% 0.44/0.83 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2)))
% 0.44/0.83 FOF formula (forall (X_32:int) (A_126:(int->Prop)), ((iff ((member_int X_32) A_126)) (A_126 X_32))) of role axiom named fact_101_mem__def
% 0.44/0.83 A new axiom: (forall (X_32:int) (A_126:(int->Prop)), ((iff ((member_int X_32) A_126)) (A_126 X_32)))
% 0.44/0.83 FOF formula (forall (P_6:(int->Prop)), (((eq (int->Prop)) (collect_int P_6)) P_6)) of role axiom named fact_102_Collect__def
% 0.44/0.83 A new axiom: (forall (P_6:(int->Prop)), (((eq (int->Prop)) (collect_int P_6)) P_6))
% 0.44/0.83 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))) of role axiom named fact_103_rel__simps_I15_J
% 0.44/0.85 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L)))
% 0.44/0.85 FOF formula (forall (V:int) (V_2:int), ((iff ((ord_less_nat (number_number_of_nat V)) (number_number_of_nat V_2))) ((and (((ord_less_int V) V_2)->((ord_less_int pls) V_2))) ((ord_less_int V) V_2)))) of role axiom named fact_104_less__nat__number__of
% 0.44/0.85 A new axiom: (forall (V:int) (V_2:int), ((iff ((ord_less_nat (number_number_of_nat V)) (number_number_of_nat V_2))) ((and (((ord_less_int V) V_2)->((ord_less_int pls) V_2))) ((ord_less_int V) V_2))))
% 0.44/0.85 FOF formula (forall (Z:int), ((iff ((ord_less_eq_int one_one_int) Z)) ((ord_less_int zero_zero_int) Z))) of role axiom named fact_105_int__one__le__iff__zero__less
% 0.44/0.85 A new axiom: (forall (Z:int), ((iff ((ord_less_eq_int one_one_int) Z)) ((ord_less_int zero_zero_int) Z)))
% 0.44/0.85 FOF formula (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat) of role axiom named fact_106_nat__numeral__1__eq__1
% 0.44/0.85 A new axiom: (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat)
% 0.44/0.85 FOF formula (((eq nat) one_one_nat) (number_number_of_nat (bit1 pls))) of role axiom named fact_107_Numeral1__eq1__nat
% 0.44/0.85 A new axiom: (((eq nat) one_one_nat) (number_number_of_nat (bit1 pls)))
% 0.44/0.85 FOF formula (forall (W:int) (Z:int), (((ord_less_int W) Z)->((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z))) of role axiom named fact_108_zless__imp__add1__zle
% 0.44/0.85 A new axiom: (forall (W:int) (Z:int), (((ord_less_int W) Z)->((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z)))
% 0.44/0.85 FOF formula (forall (W:int) (Z:int), ((iff ((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z)) ((ord_less_int W) Z))) of role axiom named fact_109_add1__zle__eq
% 0.44/0.85 A new axiom: (forall (W:int) (Z:int), ((iff ((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z)) ((ord_less_int W) Z)))
% 0.44/0.85 FOF formula (forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((ord_less_eq_int W) Z))) of role axiom named fact_110_zle__add1__eq__le
% 0.44/0.85 A new axiom: (forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((ord_less_eq_int W) Z)))
% 0.44/0.85 FOF formula (forall (V_9:int) (V_8:int), (((ord_less_eq_int pls) V_8)->(((ord_less_eq_int pls) V_9)->(((eq real) ((plus_plus_real (number267125858f_real V_8)) (number267125858f_real V_9))) (number267125858f_real ((plus_plus_int V_8) V_9)))))) of role axiom named fact_111_semiring__add__number__of
% 0.44/0.85 A new axiom: (forall (V_9:int) (V_8:int), (((ord_less_eq_int pls) V_8)->(((ord_less_eq_int pls) V_9)->(((eq real) ((plus_plus_real (number267125858f_real V_8)) (number267125858f_real V_9))) (number267125858f_real ((plus_plus_int V_8) V_9))))))
% 0.44/0.85 FOF formula (forall (V_9:int) (V_8:int), (((ord_less_eq_int pls) V_8)->(((ord_less_eq_int pls) V_9)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_8)) (number_number_of_nat V_9))) (number_number_of_nat ((plus_plus_int V_8) V_9)))))) of role axiom named fact_112_semiring__add__number__of
% 0.44/0.85 A new axiom: (forall (V_9:int) (V_8:int), (((ord_less_eq_int pls) V_8)->(((ord_less_eq_int pls) V_9)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_8)) (number_number_of_nat V_9))) (number_number_of_nat ((plus_plus_int V_8) V_9))))))
% 0.44/0.85 FOF formula (forall (V_9:int) (V_8:int), (((ord_less_eq_int pls) V_8)->(((ord_less_eq_int pls) V_9)->(((eq int) ((plus_plus_int (number_number_of_int V_8)) (number_number_of_int V_9))) (number_number_of_int ((plus_plus_int V_8) V_9)))))) of role axiom named fact_113_semiring__add__number__of
% 0.44/0.85 A new axiom: (forall (V_9:int) (V_8:int), (((ord_less_eq_int pls) V_8)->(((ord_less_eq_int pls) V_9)->(((eq int) ((plus_plus_int (number_number_of_int V_8)) (number_number_of_int V_9))) (number_number_of_int ((plus_plus_int V_8) V_9))))))
% 0.44/0.85 FOF formula (forall (V_2:int) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_2))) (number_number_of_nat V_2)))) ((((ord_less_int V) pls)->False)->((and (((ord_less_int V_2) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_2))) (number_number_of_nat V)))) ((((ord_less_int V_2) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_2))) (number_number_of_nat ((plus_plus_int V) V_2)))))))) of role axiom named fact_114_add__nat__number__of
% 0.52/0.87 A new axiom: (forall (V_2:int) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_2))) (number_number_of_nat V_2)))) ((((ord_less_int V) pls)->False)->((and (((ord_less_int V_2) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_2))) (number_number_of_nat V)))) ((((ord_less_int V_2) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_2))) (number_number_of_nat ((plus_plus_int V) V_2))))))))
% 0.52/0.87 FOF formula (forall (Z:int), (((ord_less_eq_int zero_zero_int) Z)->((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) Z)))) of role axiom named fact_115_le__imp__0__less
% 0.52/0.87 A new axiom: (forall (Z:int), (((ord_less_eq_int zero_zero_int) Z)->((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) Z))))
% 0.52/0.87 FOF formula (forall (X_31:int) (Y_24:int), ((iff (((eq real) (number267125858f_real X_31)) (number267125858f_real Y_24))) (((eq int) X_31) Y_24))) of role axiom named fact_116_eq__number__of
% 0.52/0.87 A new axiom: (forall (X_31:int) (Y_24:int), ((iff (((eq real) (number267125858f_real X_31)) (number267125858f_real Y_24))) (((eq int) X_31) Y_24)))
% 0.52/0.87 FOF formula (forall (X_31:int) (Y_24:int), ((iff (((eq int) (number_number_of_int X_31)) (number_number_of_int Y_24))) (((eq int) X_31) Y_24))) of role axiom named fact_117_eq__number__of
% 0.52/0.87 A new axiom: (forall (X_31:int) (Y_24:int), ((iff (((eq int) (number_number_of_int X_31)) (number_number_of_int Y_24))) (((eq int) X_31) Y_24)))
% 0.52/0.87 FOF formula (forall (W_11:int) (X_30:real), ((iff (((eq real) (number267125858f_real W_11)) X_30)) (((eq real) X_30) (number267125858f_real W_11)))) of role axiom named fact_118_number__of__reorient
% 0.52/0.87 A new axiom: (forall (W_11:int) (X_30:real), ((iff (((eq real) (number267125858f_real W_11)) X_30)) (((eq real) X_30) (number267125858f_real W_11))))
% 0.52/0.87 FOF formula (forall (W_11:int) (X_30:int), ((iff (((eq int) (number_number_of_int W_11)) X_30)) (((eq int) X_30) (number_number_of_int W_11)))) of role axiom named fact_119_number__of__reorient
% 0.52/0.87 A new axiom: (forall (W_11:int) (X_30:int), ((iff (((eq int) (number_number_of_int W_11)) X_30)) (((eq int) X_30) (number_number_of_int W_11))))
% 0.52/0.87 FOF formula (forall (W_11:int) (X_30:nat), ((iff (((eq nat) (number_number_of_nat W_11)) X_30)) (((eq nat) X_30) (number_number_of_nat W_11)))) of role axiom named fact_120_number__of__reorient
% 0.52/0.87 A new axiom: (forall (W_11:int) (X_30:nat), ((iff (((eq nat) (number_number_of_nat W_11)) X_30)) (((eq nat) X_30) (number_number_of_nat W_11))))
% 0.52/0.87 FOF formula (forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L))) of role axiom named fact_121_rel__simps_I51_J
% 0.52/0.87 A new axiom: (forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L)))
% 0.52/0.87 FOF formula (forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L))) of role axiom named fact_122_rel__simps_I48_J
% 0.52/0.87 A new axiom: (forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L)))
% 0.52/0.87 FOF formula (forall (X:int) (Y:int), ((or ((or ((ord_less_int X) Y)) (((eq int) X) Y))) ((ord_less_int Y) X))) of role axiom named fact_123_zless__linear
% 0.52/0.87 A new axiom: (forall (X:int) (Y:int), ((or ((or ((ord_less_int X) Y)) (((eq int) X) Y))) ((ord_less_int Y) X)))
% 0.52/0.87 FOF formula (forall (X_29:real) (Y_23:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X_29) X_29)) ((times_times_real Y_23) Y_23))) zero_zero_real)) ((and (((eq real) X_29) zero_zero_real)) (((eq real) Y_23) zero_zero_real)))) of role axiom named fact_124_sum__squares__eq__zero__iff
% 0.52/0.87 A new axiom: (forall (X_29:real) (Y_23:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X_29) X_29)) ((times_times_real Y_23) Y_23))) zero_zero_real)) ((and (((eq real) X_29) zero_zero_real)) (((eq real) Y_23) zero_zero_real))))
% 0.52/0.87 FOF formula (forall (X_29:int) (Y_23:int), ((iff (((eq int) ((plus_plus_int ((times_times_int X_29) X_29)) ((times_times_int Y_23) Y_23))) zero_zero_int)) ((and (((eq int) X_29) zero_zero_int)) (((eq int) Y_23) zero_zero_int)))) of role axiom named fact_125_sum__squares__eq__zero__iff
% 0.54/0.88 A new axiom: (forall (X_29:int) (Y_23:int), ((iff (((eq int) ((plus_plus_int ((times_times_int X_29) X_29)) ((times_times_int Y_23) Y_23))) zero_zero_int)) ((and (((eq int) X_29) zero_zero_int)) (((eq int) Y_23) zero_zero_int))))
% 0.54/0.88 FOF formula (forall (A_125:real) (B_80:real) (V_7:int), (((eq real) ((times_times_real ((plus_plus_real A_125) B_80)) (number267125858f_real V_7))) ((plus_plus_real ((times_times_real A_125) (number267125858f_real V_7))) ((times_times_real B_80) (number267125858f_real V_7))))) of role axiom named fact_126_left__distrib__number__of
% 0.54/0.88 A new axiom: (forall (A_125:real) (B_80:real) (V_7:int), (((eq real) ((times_times_real ((plus_plus_real A_125) B_80)) (number267125858f_real V_7))) ((plus_plus_real ((times_times_real A_125) (number267125858f_real V_7))) ((times_times_real B_80) (number267125858f_real V_7)))))
% 0.54/0.88 FOF formula (forall (A_125:nat) (B_80:nat) (V_7:int), (((eq nat) ((times_times_nat ((plus_plus_nat A_125) B_80)) (number_number_of_nat V_7))) ((plus_plus_nat ((times_times_nat A_125) (number_number_of_nat V_7))) ((times_times_nat B_80) (number_number_of_nat V_7))))) of role axiom named fact_127_left__distrib__number__of
% 0.54/0.88 A new axiom: (forall (A_125:nat) (B_80:nat) (V_7:int), (((eq nat) ((times_times_nat ((plus_plus_nat A_125) B_80)) (number_number_of_nat V_7))) ((plus_plus_nat ((times_times_nat A_125) (number_number_of_nat V_7))) ((times_times_nat B_80) (number_number_of_nat V_7)))))
% 0.54/0.88 FOF formula (forall (A_125:int) (B_80:int) (V_7:int), (((eq int) ((times_times_int ((plus_plus_int A_125) B_80)) (number_number_of_int V_7))) ((plus_plus_int ((times_times_int A_125) (number_number_of_int V_7))) ((times_times_int B_80) (number_number_of_int V_7))))) of role axiom named fact_128_left__distrib__number__of
% 0.54/0.88 A new axiom: (forall (A_125:int) (B_80:int) (V_7:int), (((eq int) ((times_times_int ((plus_plus_int A_125) B_80)) (number_number_of_int V_7))) ((plus_plus_int ((times_times_int A_125) (number_number_of_int V_7))) ((times_times_int B_80) (number_number_of_int V_7)))))
% 0.54/0.88 FOF formula (forall (V_6:int) (B_79:real) (C_50:real), (((eq real) ((times_times_real (number267125858f_real V_6)) ((plus_plus_real B_79) C_50))) ((plus_plus_real ((times_times_real (number267125858f_real V_6)) B_79)) ((times_times_real (number267125858f_real V_6)) C_50)))) of role axiom named fact_129_right__distrib__number__of
% 0.54/0.88 A new axiom: (forall (V_6:int) (B_79:real) (C_50:real), (((eq real) ((times_times_real (number267125858f_real V_6)) ((plus_plus_real B_79) C_50))) ((plus_plus_real ((times_times_real (number267125858f_real V_6)) B_79)) ((times_times_real (number267125858f_real V_6)) C_50))))
% 0.54/0.88 FOF formula (forall (V_6:int) (B_79:nat) (C_50:nat), (((eq nat) ((times_times_nat (number_number_of_nat V_6)) ((plus_plus_nat B_79) C_50))) ((plus_plus_nat ((times_times_nat (number_number_of_nat V_6)) B_79)) ((times_times_nat (number_number_of_nat V_6)) C_50)))) of role axiom named fact_130_right__distrib__number__of
% 0.54/0.88 A new axiom: (forall (V_6:int) (B_79:nat) (C_50:nat), (((eq nat) ((times_times_nat (number_number_of_nat V_6)) ((plus_plus_nat B_79) C_50))) ((plus_plus_nat ((times_times_nat (number_number_of_nat V_6)) B_79)) ((times_times_nat (number_number_of_nat V_6)) C_50))))
% 0.54/0.88 FOF formula (forall (V_6:int) (B_79:int) (C_50:int), (((eq int) ((times_times_int (number_number_of_int V_6)) ((plus_plus_int B_79) C_50))) ((plus_plus_int ((times_times_int (number_number_of_int V_6)) B_79)) ((times_times_int (number_number_of_int V_6)) C_50)))) of role axiom named fact_131_right__distrib__number__of
% 0.54/0.88 A new axiom: (forall (V_6:int) (B_79:int) (C_50:int), (((eq int) ((times_times_int (number_number_of_int V_6)) ((plus_plus_int B_79) C_50))) ((plus_plus_int ((times_times_int (number_number_of_int V_6)) B_79)) ((times_times_int (number_number_of_int V_6)) C_50))))
% 0.54/0.88 FOF formula (forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((plus_plus_int ((plus_plus_int Z1) Z2)) Z3)) ((plus_plus_int Z1) ((plus_plus_int Z2) Z3)))) of role axiom named fact_132_zadd__assoc
% 0.54/0.90 A new axiom: (forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((plus_plus_int ((plus_plus_int Z1) Z2)) Z3)) ((plus_plus_int Z1) ((plus_plus_int Z2) Z3))))
% 0.54/0.90 FOF formula (forall (X:int) (Y:int) (Z:int), (((eq int) ((plus_plus_int X) ((plus_plus_int Y) Z))) ((plus_plus_int Y) ((plus_plus_int X) Z)))) of role axiom named fact_133_zadd__left__commute
% 0.54/0.90 A new axiom: (forall (X:int) (Y:int) (Z:int), (((eq int) ((plus_plus_int X) ((plus_plus_int Y) Z))) ((plus_plus_int Y) ((plus_plus_int X) Z))))
% 0.54/0.90 FOF formula (forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z))) of role axiom named fact_134_zadd__commute
% 0.54/0.90 A new axiom: (forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z)))
% 0.54/0.90 FOF formula (((eq int) zero_zero_int) (number_number_of_int pls)) of role axiom named fact_135_zero__is__num__zero
% 0.54/0.90 A new axiom: (((eq int) zero_zero_int) (number_number_of_int pls))
% 0.54/0.90 FOF formula (forall (K:int) (I_1:int) (J_1:int), (((ord_less_int I_1) J_1)->(((ord_less_int zero_zero_int) K)->((ord_less_int ((times_times_int K) I_1)) ((times_times_int K) J_1))))) of role axiom named fact_136_zmult__zless__mono2
% 0.54/0.90 A new axiom: (forall (K:int) (I_1:int) (J_1:int), (((ord_less_int I_1) J_1)->(((ord_less_int zero_zero_int) K)->((ord_less_int ((times_times_int K) I_1)) ((times_times_int K) J_1)))))
% 0.54/0.90 FOF formula (forall (X_28:real) (Y_22:real), ((((eq real) ((power_power_real X_28) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_22) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) X_28)->(((ord_less_eq_real zero_zero_real) Y_22)->(((eq real) X_28) Y_22))))) of role axiom named fact_137_power2__eq__imp__eq
% 0.54/0.90 A new axiom: (forall (X_28:real) (Y_22:real), ((((eq real) ((power_power_real X_28) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_22) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) X_28)->(((ord_less_eq_real zero_zero_real) Y_22)->(((eq real) X_28) Y_22)))))
% 0.54/0.90 FOF formula (forall (X_28:nat) (Y_22:nat), ((((eq nat) ((power_power_nat X_28) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_22) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) X_28)->(((ord_less_eq_nat zero_zero_nat) Y_22)->(((eq nat) X_28) Y_22))))) of role axiom named fact_138_power2__eq__imp__eq
% 0.54/0.90 A new axiom: (forall (X_28:nat) (Y_22:nat), ((((eq nat) ((power_power_nat X_28) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_22) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) X_28)->(((ord_less_eq_nat zero_zero_nat) Y_22)->(((eq nat) X_28) Y_22)))))
% 0.54/0.90 FOF formula (forall (X_28:int) (Y_22:int), ((((eq int) ((power_power_int X_28) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_22) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) X_28)->(((ord_less_eq_int zero_zero_int) Y_22)->(((eq int) X_28) Y_22))))) of role axiom named fact_139_power2__eq__imp__eq
% 0.54/0.90 A new axiom: (forall (X_28:int) (Y_22:int), ((((eq int) ((power_power_int X_28) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_22) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) X_28)->(((ord_less_eq_int zero_zero_int) Y_22)->(((eq int) X_28) Y_22)))))
% 0.54/0.90 FOF formula (forall (X_27:real) (Y_21:real), (((ord_less_eq_real ((power_power_real X_27) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_21) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_21)->((ord_less_eq_real X_27) Y_21)))) of role axiom named fact_140_power2__le__imp__le
% 0.54/0.90 A new axiom: (forall (X_27:real) (Y_21:real), (((ord_less_eq_real ((power_power_real X_27) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_21) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_21)->((ord_less_eq_real X_27) Y_21))))
% 0.54/0.90 FOF formula (forall (X_27:nat) (Y_21:nat), (((ord_less_eq_nat ((power_power_nat X_27) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_21) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_21)->((ord_less_eq_nat X_27) Y_21)))) of role axiom named fact_141_power2__le__imp__le
% 0.57/0.92 A new axiom: (forall (X_27:nat) (Y_21:nat), (((ord_less_eq_nat ((power_power_nat X_27) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_21) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_21)->((ord_less_eq_nat X_27) Y_21))))
% 0.57/0.92 FOF formula (forall (X_27:int) (Y_21:int), (((ord_less_eq_int ((power_power_int X_27) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_21) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_21)->((ord_less_eq_int X_27) Y_21)))) of role axiom named fact_142_power2__le__imp__le
% 0.57/0.92 A new axiom: (forall (X_27:int) (Y_21:int), (((ord_less_eq_int ((power_power_int X_27) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_21) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_21)->((ord_less_eq_int X_27) Y_21))))
% 0.57/0.92 FOF formula (forall (A_124:real), ((ord_less_eq_real zero_zero_real) ((power_power_real A_124) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_143_zero__le__power2
% 0.57/0.92 A new axiom: (forall (A_124:real), ((ord_less_eq_real zero_zero_real) ((power_power_real A_124) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.57/0.92 FOF formula (forall (A_124:int), ((ord_less_eq_int zero_zero_int) ((power_power_int A_124) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_144_zero__le__power2
% 0.57/0.92 A new axiom: (forall (A_124:int), ((ord_less_eq_int zero_zero_int) ((power_power_int A_124) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.57/0.92 FOF formula (forall (X_26:real) (Y_20:real), (((ord_less_real ((power_power_real X_26) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_20) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_20)->((ord_less_real X_26) Y_20)))) of role axiom named fact_145_power2__less__imp__less
% 0.57/0.92 A new axiom: (forall (X_26:real) (Y_20:real), (((ord_less_real ((power_power_real X_26) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_20) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_20)->((ord_less_real X_26) Y_20))))
% 0.57/0.92 FOF formula (forall (X_26:nat) (Y_20:nat), (((ord_less_nat ((power_power_nat X_26) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_20) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_20)->((ord_less_nat X_26) Y_20)))) of role axiom named fact_146_power2__less__imp__less
% 0.57/0.92 A new axiom: (forall (X_26:nat) (Y_20:nat), (((ord_less_nat ((power_power_nat X_26) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_20) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_20)->((ord_less_nat X_26) Y_20))))
% 0.57/0.92 FOF formula (forall (X_26:int) (Y_20:int), (((ord_less_int ((power_power_int X_26) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_20) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_20)->((ord_less_int X_26) Y_20)))) of role axiom named fact_147_power2__less__imp__less
% 0.57/0.92 A new axiom: (forall (X_26:int) (Y_20:int), (((ord_less_int ((power_power_int X_26) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_20) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_20)->((ord_less_int X_26) Y_20))))
% 0.57/0.92 FOF formula (forall (X_25:real) (Y_19:real), ((iff ((ord_less_eq_real ((plus_plus_real ((power_power_real X_25) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_19) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_25) zero_zero_real)) (((eq real) Y_19) zero_zero_real)))) of role axiom named fact_148_sum__power2__le__zero__iff
% 0.57/0.92 A new axiom: (forall (X_25:real) (Y_19:real), ((iff ((ord_less_eq_real ((plus_plus_real ((power_power_real X_25) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_19) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_25) zero_zero_real)) (((eq real) Y_19) zero_zero_real))))
% 0.59/0.93 FOF formula (forall (X_25:int) (Y_19:int), ((iff ((ord_less_eq_int ((plus_plus_int ((power_power_int X_25) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_19) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_25) zero_zero_int)) (((eq int) Y_19) zero_zero_int)))) of role axiom named fact_149_sum__power2__le__zero__iff
% 0.59/0.93 A new axiom: (forall (X_25:int) (Y_19:int), ((iff ((ord_less_eq_int ((plus_plus_int ((power_power_int X_25) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_19) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_25) zero_zero_int)) (((eq int) Y_19) zero_zero_int))))
% 0.59/0.93 FOF formula (forall (X_24:real) (Y_18:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((power_power_real X_24) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_18) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_150_sum__power2__ge__zero
% 0.59/0.93 A new axiom: (forall (X_24:real) (Y_18:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((power_power_real X_24) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_18) (number_number_of_nat (bit0 (bit1 pls)))))))
% 0.59/0.93 FOF formula (forall (X_24:int) (Y_18:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((power_power_int X_24) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_18) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_151_sum__power2__ge__zero
% 0.59/0.93 A new axiom: (forall (X_24:int) (Y_18:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((power_power_int X_24) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_18) (number_number_of_nat (bit0 (bit1 pls)))))))
% 0.59/0.93 FOF formula (forall (X_23:real) (Y_17:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((times_times_real X_23) X_23)) ((times_times_real Y_17) Y_17)))) ((or (not (((eq real) X_23) zero_zero_real))) (not (((eq real) Y_17) zero_zero_real))))) of role axiom named fact_152_sum__squares__gt__zero__iff
% 0.59/0.93 A new axiom: (forall (X_23:real) (Y_17:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((times_times_real X_23) X_23)) ((times_times_real Y_17) Y_17)))) ((or (not (((eq real) X_23) zero_zero_real))) (not (((eq real) Y_17) zero_zero_real)))))
% 0.59/0.93 FOF formula (forall (X_23:int) (Y_17:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((times_times_int X_23) X_23)) ((times_times_int Y_17) Y_17)))) ((or (not (((eq int) X_23) zero_zero_int))) (not (((eq int) Y_17) zero_zero_int))))) of role axiom named fact_153_sum__squares__gt__zero__iff
% 0.59/0.93 A new axiom: (forall (X_23:int) (Y_17:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((times_times_int X_23) X_23)) ((times_times_int Y_17) Y_17)))) ((or (not (((eq int) X_23) zero_zero_int))) (not (((eq int) Y_17) zero_zero_int)))))
% 0.59/0.93 FOF formula (forall (X_22:real) (Y_16:real), (((ord_less_real ((plus_plus_real ((times_times_real X_22) X_22)) ((times_times_real Y_16) Y_16))) zero_zero_real)->False)) of role axiom named fact_154_not__sum__squares__lt__zero
% 0.59/0.93 A new axiom: (forall (X_22:real) (Y_16:real), (((ord_less_real ((plus_plus_real ((times_times_real X_22) X_22)) ((times_times_real Y_16) Y_16))) zero_zero_real)->False))
% 0.59/0.93 FOF formula (forall (X_22:int) (Y_16:int), (((ord_less_int ((plus_plus_int ((times_times_int X_22) X_22)) ((times_times_int Y_16) Y_16))) zero_zero_int)->False)) of role axiom named fact_155_not__sum__squares__lt__zero
% 0.59/0.93 A new axiom: (forall (X_22:int) (Y_16:int), (((ord_less_int ((plus_plus_int ((times_times_int X_22) X_22)) ((times_times_int Y_16) Y_16))) zero_zero_int)->False))
% 0.59/0.93 FOF formula (forall (A_123:real), (((eq real) ((times_times_real (number267125858f_real (bit1 pls))) A_123)) A_123)) of role axiom named fact_156_mult__numeral__1
% 0.59/0.93 A new axiom: (forall (A_123:real), (((eq real) ((times_times_real (number267125858f_real (bit1 pls))) A_123)) A_123))
% 0.59/0.93 FOF formula (forall (A_123:int), (((eq int) ((times_times_int (number_number_of_int (bit1 pls))) A_123)) A_123)) of role axiom named fact_157_mult__numeral__1
% 0.59/0.95 A new axiom: (forall (A_123:int), (((eq int) ((times_times_int (number_number_of_int (bit1 pls))) A_123)) A_123))
% 0.59/0.95 FOF formula (forall (A_122:real), (((eq real) ((times_times_real A_122) (number267125858f_real (bit1 pls)))) A_122)) of role axiom named fact_158_mult__numeral__1__right
% 0.59/0.95 A new axiom: (forall (A_122:real), (((eq real) ((times_times_real A_122) (number267125858f_real (bit1 pls)))) A_122))
% 0.59/0.95 FOF formula (forall (A_122:int), (((eq int) ((times_times_int A_122) (number_number_of_int (bit1 pls)))) A_122)) of role axiom named fact_159_mult__numeral__1__right
% 0.59/0.95 A new axiom: (forall (A_122:int), (((eq int) ((times_times_int A_122) (number_number_of_int (bit1 pls)))) A_122))
% 0.59/0.95 FOF formula (((eq int) one_one_int) (number_number_of_int (bit1 pls))) of role axiom named fact_160_one__is__num__one
% 0.59/0.95 A new axiom: (((eq int) one_one_int) (number_number_of_int (bit1 pls)))
% 0.59/0.95 FOF formula (forall (K:int) (L:int), (((eq int) ((times_times_int (bit1 K)) L)) ((plus_plus_int (bit0 ((times_times_int K) L))) L))) of role axiom named fact_161_mult__Bit1
% 0.59/0.95 A new axiom: (forall (K:int) (L:int), (((eq int) ((times_times_int (bit1 K)) L)) ((plus_plus_int (bit0 ((times_times_int K) L))) L)))
% 0.59/0.95 FOF formula (forall (N:int) (M:int), (((ord_less_int zero_zero_int) M)->((iff (((eq int) ((times_times_int M) N)) one_one_int)) ((and (((eq int) M) one_one_int)) (((eq int) N) one_one_int))))) of role axiom named fact_162_pos__zmult__eq__1__iff
% 0.59/0.95 A new axiom: (forall (N:int) (M:int), (((ord_less_int zero_zero_int) M)->((iff (((eq int) ((times_times_int M) N)) one_one_int)) ((and (((eq int) M) one_one_int)) (((eq int) N) one_one_int)))))
% 0.59/0.95 FOF formula (forall (A_121:real), ((iff (((eq real) ((plus_plus_real A_121) A_121)) zero_zero_real)) (((eq real) A_121) zero_zero_real))) of role axiom named fact_163_double__eq__0__iff
% 0.59/0.95 A new axiom: (forall (A_121:real), ((iff (((eq real) ((plus_plus_real A_121) A_121)) zero_zero_real)) (((eq real) A_121) zero_zero_real)))
% 0.59/0.95 FOF formula (forall (A_121:int), ((iff (((eq int) ((plus_plus_int A_121) A_121)) zero_zero_int)) (((eq int) A_121) zero_zero_int))) of role axiom named fact_164_double__eq__0__iff
% 0.59/0.95 A new axiom: (forall (A_121:int), ((iff (((eq int) ((plus_plus_int A_121) A_121)) zero_zero_int)) (((eq int) A_121) zero_zero_int)))
% 0.59/0.95 FOF formula (forall (K:int), (not (((eq int) (bit1 K)) pls))) of role axiom named fact_165_rel__simps_I46_J
% 0.59/0.95 A new axiom: (forall (K:int), (not (((eq int) (bit1 K)) pls)))
% 0.59/0.95 FOF formula (forall (L:int), (not (((eq int) pls) (bit1 L)))) of role axiom named fact_166_rel__simps_I39_J
% 0.59/0.95 A new axiom: (forall (L:int), (not (((eq int) pls) (bit1 L))))
% 0.59/0.95 FOF formula (forall (K:int) (L:int), (not (((eq int) (bit1 K)) (bit0 L)))) of role axiom named fact_167_rel__simps_I50_J
% 0.59/0.95 A new axiom: (forall (K:int) (L:int), (not (((eq int) (bit1 K)) (bit0 L))))
% 0.59/0.95 FOF formula (forall (K:int) (L:int), (not (((eq int) (bit0 K)) (bit1 L)))) of role axiom named fact_168_rel__simps_I49_J
% 0.59/0.95 A new axiom: (forall (K:int) (L:int), (not (((eq int) (bit0 K)) (bit1 L))))
% 0.59/0.95 FOF formula (forall (K:int), ((iff (((eq int) (bit0 K)) pls)) (((eq int) K) pls))) of role axiom named fact_169_rel__simps_I44_J
% 0.59/0.95 A new axiom: (forall (K:int), ((iff (((eq int) (bit0 K)) pls)) (((eq int) K) pls)))
% 0.59/0.95 FOF formula (forall (L:int), ((iff (((eq int) pls) (bit0 L))) (((eq int) pls) L))) of role axiom named fact_170_rel__simps_I38_J
% 0.59/0.95 A new axiom: (forall (L:int), ((iff (((eq int) pls) (bit0 L))) (((eq int) pls) L)))
% 0.59/0.95 FOF formula (((eq int) (bit0 pls)) pls) of role axiom named fact_171_Bit0__Pls
% 0.59/0.95 A new axiom: (((eq int) (bit0 pls)) pls)
% 0.59/0.95 FOF formula (((eq int) pls) zero_zero_int) of role axiom named fact_172_Pls__def
% 0.59/0.95 A new axiom: (((eq int) pls) zero_zero_int)
% 0.59/0.95 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2))) of role axiom named fact_173_less__int__code_I16_J
% 0.59/0.95 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2)))
% 0.59/0.95 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L))) of role axiom named fact_174_rel__simps_I17_J
% 0.59/0.97 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L)))
% 0.59/0.97 FOF formula (((ord_less_int pls) pls)->False) of role axiom named fact_175_rel__simps_I2_J
% 0.59/0.97 A new axiom: (((ord_less_int pls) pls)->False)
% 0.59/0.97 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit0 K2))) ((ord_less_int K1) K2))) of role axiom named fact_176_less__int__code_I13_J
% 0.59/0.97 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit0 K2))) ((ord_less_int K1) K2)))
% 0.59/0.97 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit0 L))) ((ord_less_int K) L))) of role axiom named fact_177_rel__simps_I14_J
% 0.59/0.97 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit0 L))) ((ord_less_int K) L)))
% 0.59/0.97 FOF formula (not (((eq int) zero_zero_int) one_one_int)) of role axiom named fact_178_int__0__neq__1
% 0.59/0.97 A new axiom: (not (((eq int) zero_zero_int) one_one_int))
% 0.59/0.97 FOF formula (forall (K:int), (((eq int) ((plus_plus_int K) pls)) K)) of role axiom named fact_179_add__Pls__right
% 0.59/0.97 A new axiom: (forall (K:int), (((eq int) ((plus_plus_int K) pls)) K))
% 0.59/0.97 FOF formula (forall (K:int), (((eq int) ((plus_plus_int pls) K)) K)) of role axiom named fact_180_add__Pls
% 0.59/0.97 A new axiom: (forall (K:int), (((eq int) ((plus_plus_int pls) K)) K))
% 0.59/0.97 FOF formula (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit0 L))) (bit0 ((plus_plus_int K) L)))) of role axiom named fact_181_add__Bit0__Bit0
% 0.59/0.97 A new axiom: (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit0 L))) (bit0 ((plus_plus_int K) L))))
% 0.59/0.97 FOF formula (forall (K:int), (((eq int) (bit0 K)) ((plus_plus_int K) K))) of role axiom named fact_182_Bit0__def
% 0.59/0.97 A new axiom: (forall (K:int), (((eq int) (bit0 K)) ((plus_plus_int K) K)))
% 0.59/0.97 FOF formula (forall (Z:int), (((eq int) ((plus_plus_int Z) zero_zero_int)) Z)) of role axiom named fact_183_zadd__0__right
% 0.59/0.97 A new axiom: (forall (Z:int), (((eq int) ((plus_plus_int Z) zero_zero_int)) Z))
% 0.59/0.97 FOF formula (forall (Z:int), (((eq int) ((plus_plus_int zero_zero_int) Z)) Z)) of role axiom named fact_184_zadd__0
% 0.59/0.97 A new axiom: (forall (Z:int), (((eq int) ((plus_plus_int zero_zero_int) Z)) Z))
% 0.59/0.97 FOF formula (forall (K:int) (I_1:int) (J_1:int), (((ord_less_int I_1) J_1)->((ord_less_int ((plus_plus_int I_1) K)) ((plus_plus_int J_1) K)))) of role axiom named fact_185_zadd__strict__right__mono
% 0.59/0.97 A new axiom: (forall (K:int) (I_1:int) (J_1:int), (((ord_less_int I_1) J_1)->((ord_less_int ((plus_plus_int I_1) K)) ((plus_plus_int J_1) K))))
% 0.59/0.97 FOF formula (forall (W_10:int), (((eq real) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real W_10))) (number267125858f_real (bit0 W_10)))) of role axiom named fact_186_double__number__of__Bit0
% 0.59/0.97 A new axiom: (forall (W_10:int), (((eq real) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real W_10))) (number267125858f_real (bit0 W_10))))
% 0.59/0.97 FOF formula (forall (W_10:int), (((eq int) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int W_10))) (number_number_of_int (bit0 W_10)))) of role axiom named fact_187_double__number__of__Bit0
% 0.59/0.97 A new axiom: (forall (W_10:int), (((eq int) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int W_10))) (number_number_of_int (bit0 W_10))))
% 0.59/0.97 FOF formula (forall (A_120:real), (((eq real) ((power_power_real A_120) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_real ((times_times_real A_120) A_120)) A_120))) of role axiom named fact_188_power3__eq__cube
% 0.59/0.97 A new axiom: (forall (A_120:real), (((eq real) ((power_power_real A_120) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_real ((times_times_real A_120) A_120)) A_120)))
% 0.59/0.97 FOF formula (forall (A_120:nat), (((eq nat) ((power_power_nat A_120) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_nat ((times_times_nat A_120) A_120)) A_120))) of role axiom named fact_189_power3__eq__cube
% 0.59/0.97 A new axiom: (forall (A_120:nat), (((eq nat) ((power_power_nat A_120) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_nat ((times_times_nat A_120) A_120)) A_120)))
% 0.59/0.98 FOF formula (forall (A_120:int), (((eq int) ((power_power_int A_120) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int A_120) A_120)) A_120))) of role axiom named fact_190_power3__eq__cube
% 0.59/0.98 A new axiom: (forall (A_120:int), (((eq int) ((power_power_int A_120) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int A_120) A_120)) A_120)))
% 0.59/0.98 FOF formula (forall (Z_7:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_7)) ((plus_plus_real Z_7) Z_7))) of role axiom named fact_191_semiring__mult__2
% 0.59/0.98 A new axiom: (forall (Z_7:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_7)) ((plus_plus_real Z_7) Z_7)))
% 0.59/0.98 FOF formula (forall (Z_7:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z_7)) ((plus_plus_nat Z_7) Z_7))) of role axiom named fact_192_semiring__mult__2
% 0.59/0.98 A new axiom: (forall (Z_7:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z_7)) ((plus_plus_nat Z_7) Z_7)))
% 0.59/0.98 FOF formula (forall (Z_7:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_7)) ((plus_plus_int Z_7) Z_7))) of role axiom named fact_193_semiring__mult__2
% 0.59/0.98 A new axiom: (forall (Z_7:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_7)) ((plus_plus_int Z_7) Z_7)))
% 0.59/0.98 FOF formula (forall (Z_6:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_6)) ((plus_plus_real Z_6) Z_6))) of role axiom named fact_194_mult__2
% 0.59/0.98 A new axiom: (forall (Z_6:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_6)) ((plus_plus_real Z_6) Z_6)))
% 0.59/0.98 FOF formula (forall (Z_6:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_6)) ((plus_plus_int Z_6) Z_6))) of role axiom named fact_195_mult__2
% 0.59/0.98 A new axiom: (forall (Z_6:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_6)) ((plus_plus_int Z_6) Z_6)))
% 0.59/0.98 FOF formula (forall (Z_5:real), (((eq real) ((times_times_real Z_5) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_5) Z_5))) of role axiom named fact_196_semiring__mult__2__right
% 0.59/0.98 A new axiom: (forall (Z_5:real), (((eq real) ((times_times_real Z_5) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_5) Z_5)))
% 0.59/0.98 FOF formula (forall (Z_5:nat), (((eq nat) ((times_times_nat Z_5) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z_5) Z_5))) of role axiom named fact_197_semiring__mult__2__right
% 0.59/0.98 A new axiom: (forall (Z_5:nat), (((eq nat) ((times_times_nat Z_5) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z_5) Z_5)))
% 0.59/0.98 FOF formula (forall (Z_5:int), (((eq int) ((times_times_int Z_5) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_5) Z_5))) of role axiom named fact_198_semiring__mult__2__right
% 0.59/0.98 A new axiom: (forall (Z_5:int), (((eq int) ((times_times_int Z_5) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_5) Z_5)))
% 0.59/0.98 FOF formula (forall (Z_4:real), (((eq real) ((times_times_real Z_4) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_4) Z_4))) of role axiom named fact_199_mult__2__right
% 0.59/0.98 A new axiom: (forall (Z_4:real), (((eq real) ((times_times_real Z_4) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_4) Z_4)))
% 0.59/0.98 FOF formula (forall (Z_4:int), (((eq int) ((times_times_int Z_4) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_4) Z_4))) of role axiom named fact_200_mult__2__right
% 0.59/0.98 A new axiom: (forall (Z_4:int), (((eq int) ((times_times_int Z_4) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_4) Z_4)))
% 0.59/0.98 FOF formula (forall (A_119:real), (((eq real) ((power_power_real A_119) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real A_119) A_119))) of role axiom named fact_201_power2__eq__square
% 0.59/0.98 A new axiom: (forall (A_119:real), (((eq real) ((power_power_real A_119) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real A_119) A_119)))
% 0.59/0.98 FOF formula (forall (A_119:nat), (((eq nat) ((power_power_nat A_119) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat A_119) A_119))) of role axiom named fact_202_power2__eq__square
% 0.59/1.00 A new axiom: (forall (A_119:nat), (((eq nat) ((power_power_nat A_119) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat A_119) A_119)))
% 0.59/1.00 FOF formula (forall (A_119:int), (((eq int) ((power_power_int A_119) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int A_119) A_119))) of role axiom named fact_203_power2__eq__square
% 0.59/1.00 A new axiom: (forall (A_119:int), (((eq int) ((power_power_int A_119) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int A_119) A_119)))
% 0.59/1.00 FOF formula (forall (A_118:real), ((iff ((ord_less_real ((plus_plus_real A_118) A_118)) zero_zero_real)) ((ord_less_real A_118) zero_zero_real))) of role axiom named fact_204_even__less__0__iff
% 0.59/1.00 A new axiom: (forall (A_118:real), ((iff ((ord_less_real ((plus_plus_real A_118) A_118)) zero_zero_real)) ((ord_less_real A_118) zero_zero_real)))
% 0.59/1.00 FOF formula (forall (A_118:int), ((iff ((ord_less_int ((plus_plus_int A_118) A_118)) zero_zero_int)) ((ord_less_int A_118) zero_zero_int))) of role axiom named fact_205_even__less__0__iff
% 0.59/1.00 A new axiom: (forall (A_118:int), ((iff ((ord_less_int ((plus_plus_int A_118) A_118)) zero_zero_int)) ((ord_less_int A_118) zero_zero_int)))
% 0.59/1.00 FOF formula (((eq real) (number267125858f_real pls)) zero_zero_real) of role axiom named fact_206_semiring__numeral__0__eq__0
% 0.59/1.00 A new axiom: (((eq real) (number267125858f_real pls)) zero_zero_real)
% 0.59/1.00 FOF formula (((eq nat) (number_number_of_nat pls)) zero_zero_nat) of role axiom named fact_207_semiring__numeral__0__eq__0
% 0.59/1.00 A new axiom: (((eq nat) (number_number_of_nat pls)) zero_zero_nat)
% 0.59/1.00 FOF formula (((eq int) (number_number_of_int pls)) zero_zero_int) of role axiom named fact_208_semiring__numeral__0__eq__0
% 0.59/1.00 A new axiom: (((eq int) (number_number_of_int pls)) zero_zero_int)
% 0.59/1.00 FOF formula (((eq real) (number267125858f_real pls)) zero_zero_real) of role axiom named fact_209_number__of__Pls
% 0.59/1.00 A new axiom: (((eq real) (number267125858f_real pls)) zero_zero_real)
% 0.59/1.00 FOF formula (((eq int) (number_number_of_int pls)) zero_zero_int) of role axiom named fact_210_number__of__Pls
% 0.59/1.00 A new axiom: (((eq int) (number_number_of_int pls)) zero_zero_int)
% 0.59/1.00 FOF formula (((eq real) zero_zero_real) (number267125858f_real pls)) of role axiom named fact_211_semiring__norm_I112_J
% 0.59/1.00 A new axiom: (((eq real) zero_zero_real) (number267125858f_real pls))
% 0.59/1.00 FOF formula (((eq int) zero_zero_int) (number_number_of_int pls)) of role axiom named fact_212_semiring__norm_I112_J
% 0.59/1.00 A new axiom: (((eq int) zero_zero_int) (number_number_of_int pls))
% 0.59/1.00 FOF formula (forall (A_117:real), (((eq real) ((plus_plus_real (number267125858f_real pls)) A_117)) A_117)) of role axiom named fact_213_add__numeral__0
% 0.59/1.00 A new axiom: (forall (A_117:real), (((eq real) ((plus_plus_real (number267125858f_real pls)) A_117)) A_117))
% 0.59/1.00 FOF formula (forall (A_117:int), (((eq int) ((plus_plus_int (number_number_of_int pls)) A_117)) A_117)) of role axiom named fact_214_add__numeral__0
% 0.59/1.00 A new axiom: (forall (A_117:int), (((eq int) ((plus_plus_int (number_number_of_int pls)) A_117)) A_117))
% 0.59/1.00 FOF formula (forall (A_116:real), (((eq real) ((plus_plus_real A_116) (number267125858f_real pls))) A_116)) of role axiom named fact_215_add__numeral__0__right
% 0.59/1.00 A new axiom: (forall (A_116:real), (((eq real) ((plus_plus_real A_116) (number267125858f_real pls))) A_116))
% 0.59/1.00 FOF formula (forall (A_116:int), (((eq int) ((plus_plus_int A_116) (number_number_of_int pls))) A_116)) of role axiom named fact_216_add__numeral__0__right
% 0.59/1.00 A new axiom: (forall (A_116:int), (((eq int) ((plus_plus_int A_116) (number_number_of_int pls))) A_116))
% 0.59/1.00 FOF formula (forall (X_21:int) (Y_15:int), ((iff ((ord_less_real (number267125858f_real X_21)) (number267125858f_real Y_15))) ((ord_less_int X_21) Y_15))) of role axiom named fact_217_less__number__of
% 0.59/1.00 A new axiom: (forall (X_21:int) (Y_15:int), ((iff ((ord_less_real (number267125858f_real X_21)) (number267125858f_real Y_15))) ((ord_less_int X_21) Y_15)))
% 0.59/1.00 FOF formula (forall (X_21:int) (Y_15:int), ((iff ((ord_less_int (number_number_of_int X_21)) (number_number_of_int Y_15))) ((ord_less_int X_21) Y_15))) of role axiom named fact_218_less__number__of
% 0.59/1.01 A new axiom: (forall (X_21:int) (Y_15:int), ((iff ((ord_less_int (number_number_of_int X_21)) (number_number_of_int Y_15))) ((ord_less_int X_21) Y_15)))
% 0.59/1.01 FOF formula (forall (V_5:int) (W_9:int) (Z_3:real), (((eq real) ((plus_plus_real (number267125858f_real V_5)) ((plus_plus_real (number267125858f_real W_9)) Z_3))) ((plus_plus_real (number267125858f_real ((plus_plus_int V_5) W_9))) Z_3))) of role axiom named fact_219_add__number__of__left
% 0.59/1.01 A new axiom: (forall (V_5:int) (W_9:int) (Z_3:real), (((eq real) ((plus_plus_real (number267125858f_real V_5)) ((plus_plus_real (number267125858f_real W_9)) Z_3))) ((plus_plus_real (number267125858f_real ((plus_plus_int V_5) W_9))) Z_3)))
% 0.59/1.01 FOF formula (forall (V_5:int) (W_9:int) (Z_3:int), (((eq int) ((plus_plus_int (number_number_of_int V_5)) ((plus_plus_int (number_number_of_int W_9)) Z_3))) ((plus_plus_int (number_number_of_int ((plus_plus_int V_5) W_9))) Z_3))) of role axiom named fact_220_add__number__of__left
% 0.59/1.01 A new axiom: (forall (V_5:int) (W_9:int) (Z_3:int), (((eq int) ((plus_plus_int (number_number_of_int V_5)) ((plus_plus_int (number_number_of_int W_9)) Z_3))) ((plus_plus_int (number_number_of_int ((plus_plus_int V_5) W_9))) Z_3)))
% 0.59/1.01 FOF formula (forall (V_4:int) (W_8:int), (((eq real) ((plus_plus_real (number267125858f_real V_4)) (number267125858f_real W_8))) (number267125858f_real ((plus_plus_int V_4) W_8)))) of role axiom named fact_221_add__number__of__eq
% 0.59/1.01 A new axiom: (forall (V_4:int) (W_8:int), (((eq real) ((plus_plus_real (number267125858f_real V_4)) (number267125858f_real W_8))) (number267125858f_real ((plus_plus_int V_4) W_8))))
% 0.59/1.01 FOF formula (forall (V_4:int) (W_8:int), (((eq int) ((plus_plus_int (number_number_of_int V_4)) (number_number_of_int W_8))) (number_number_of_int ((plus_plus_int V_4) W_8)))) of role axiom named fact_222_add__number__of__eq
% 0.59/1.01 A new axiom: (forall (V_4:int) (W_8:int), (((eq int) ((plus_plus_int (number_number_of_int V_4)) (number_number_of_int W_8))) (number_number_of_int ((plus_plus_int V_4) W_8))))
% 0.59/1.01 FOF formula (forall (V_3:int) (W_7:int), (((eq real) (number267125858f_real ((plus_plus_int V_3) W_7))) ((plus_plus_real (number267125858f_real V_3)) (number267125858f_real W_7)))) of role axiom named fact_223_number__of__add
% 0.59/1.01 A new axiom: (forall (V_3:int) (W_7:int), (((eq real) (number267125858f_real ((plus_plus_int V_3) W_7))) ((plus_plus_real (number267125858f_real V_3)) (number267125858f_real W_7))))
% 0.59/1.01 FOF formula (forall (V_3:int) (W_7:int), (((eq int) (number_number_of_int ((plus_plus_int V_3) W_7))) ((plus_plus_int (number_number_of_int V_3)) (number_number_of_int W_7)))) of role axiom named fact_224_number__of__add
% 0.59/1.01 A new axiom: (forall (V_3:int) (W_7:int), (((eq int) (number_number_of_int ((plus_plus_int V_3) W_7))) ((plus_plus_int (number_number_of_int V_3)) (number_number_of_int W_7))))
% 0.59/1.01 FOF formula (forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_225_rel__simps_I12_J
% 0.59/1.01 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls)))
% 0.59/1.01 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2))) of role axiom named fact_226_less__int__code_I15_J
% 0.59/1.01 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2)))
% 0.59/1.01 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))) of role axiom named fact_227_rel__simps_I16_J
% 0.59/1.01 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit0 L))) ((ord_less_int K) L)))
% 0.59/1.01 FOF formula (forall (W:int), ((iff ((ord_less_int (bit1 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int))) of role axiom named fact_228_bin__less__0__simps_I4_J
% 0.59/1.01 A new axiom: (forall (W:int), ((iff ((ord_less_int (bit1 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int)))
% 0.59/1.01 FOF formula (forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_229_rel__simps_I10_J
% 0.59/1.01 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls)))
% 0.67/1.03 FOF formula (forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K))) of role axiom named fact_230_rel__simps_I4_J
% 0.67/1.03 A new axiom: (forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K)))
% 0.67/1.03 FOF formula (((ord_less_int pls) zero_zero_int)->False) of role axiom named fact_231_bin__less__0__simps_I1_J
% 0.67/1.03 A new axiom: (((ord_less_int pls) zero_zero_int)->False)
% 0.67/1.03 FOF formula (forall (W:int), ((iff ((ord_less_int (bit0 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int))) of role axiom named fact_232_bin__less__0__simps_I3_J
% 0.67/1.03 A new axiom: (forall (W:int), ((iff ((ord_less_int (bit0 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int)))
% 0.67/1.03 FOF formula (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit0 L))) (bit1 ((plus_plus_int K) L)))) of role axiom named fact_233_add__Bit1__Bit0
% 0.67/1.03 A new axiom: (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit0 L))) (bit1 ((plus_plus_int K) L))))
% 0.67/1.03 FOF formula (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit1 L))) (bit1 ((plus_plus_int K) L)))) of role axiom named fact_234_add__Bit0__Bit1
% 0.67/1.03 A new axiom: (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit1 L))) (bit1 ((plus_plus_int K) L))))
% 0.67/1.03 FOF formula ((ord_less_int zero_zero_int) one_one_int) of role axiom named fact_235_int__0__less__1
% 0.67/1.03 A new axiom: ((ord_less_int zero_zero_int) one_one_int)
% 0.67/1.03 FOF formula (forall (K:int), (((eq int) (bit1 K)) ((plus_plus_int ((plus_plus_int one_one_int) K)) K))) of role axiom named fact_236_Bit1__def
% 0.67/1.03 A new axiom: (forall (K:int), (((eq int) (bit1 K)) ((plus_plus_int ((plus_plus_int one_one_int) K)) K)))
% 0.67/1.03 FOF formula (forall (Z:int), (not (((eq int) ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int))) of role axiom named fact_237_odd__nonzero
% 0.67/1.03 A new axiom: (forall (Z:int), (not (((eq int) ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int)))
% 0.67/1.03 FOF formula (forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((or ((ord_less_int W) Z)) (((eq int) W) Z)))) of role axiom named fact_238_zless__add1__eq
% 0.67/1.03 A new axiom: (forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((or ((ord_less_int W) Z)) (((eq int) W) Z))))
% 0.67/1.03 FOF formula (forall (W_6:int), (((eq real) ((power_power_real (number267125858f_real W_6)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real (number267125858f_real W_6)) (number267125858f_real W_6)))) of role axiom named fact_239_power2__eq__square__number__of
% 0.67/1.03 A new axiom: (forall (W_6:int), (((eq real) ((power_power_real (number267125858f_real W_6)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real (number267125858f_real W_6)) (number267125858f_real W_6))))
% 0.67/1.03 FOF formula (forall (W_6:int), (((eq nat) ((power_power_nat (number_number_of_nat W_6)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat (number_number_of_nat W_6)) (number_number_of_nat W_6)))) of role axiom named fact_240_power2__eq__square__number__of
% 0.67/1.03 A new axiom: (forall (W_6:int), (((eq nat) ((power_power_nat (number_number_of_nat W_6)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat (number_number_of_nat W_6)) (number_number_of_nat W_6))))
% 0.67/1.03 FOF formula (forall (W_6:int), (((eq int) ((power_power_int (number_number_of_int W_6)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int (number_number_of_int W_6)) (number_number_of_int W_6)))) of role axiom named fact_241_power2__eq__square__number__of
% 0.67/1.03 A new axiom: (forall (W_6:int), (((eq int) ((power_power_int (number_number_of_int W_6)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int (number_number_of_int W_6)) (number_number_of_int W_6))))
% 0.67/1.03 FOF formula (forall (X_20:real) (Y_14:real), (((eq real) ((power_power_real ((plus_plus_real X_20) Y_14)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X_20) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_14) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_20)) Y_14)))) of role axiom named fact_242_power2__sum
% 0.67/1.04 A new axiom: (forall (X_20:real) (Y_14:real), (((eq real) ((power_power_real ((plus_plus_real X_20) Y_14)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X_20) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_14) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_20)) Y_14))))
% 0.67/1.04 FOF formula (forall (X_20:nat) (Y_14:nat), (((eq nat) ((power_power_nat ((plus_plus_nat X_20) Y_14)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat ((plus_plus_nat ((power_power_nat X_20) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_14) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) X_20)) Y_14)))) of role axiom named fact_243_power2__sum
% 0.67/1.04 A new axiom: (forall (X_20:nat) (Y_14:nat), (((eq nat) ((power_power_nat ((plus_plus_nat X_20) Y_14)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat ((plus_plus_nat ((power_power_nat X_20) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_14) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) X_20)) Y_14))))
% 0.67/1.04 FOF formula (forall (X_20:int) (Y_14:int), (((eq int) ((power_power_int ((plus_plus_int X_20) Y_14)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int X_20) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_14) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) X_20)) Y_14)))) of role axiom named fact_244_power2__sum
% 0.67/1.04 A new axiom: (forall (X_20:int) (Y_14:int), (((eq int) ((power_power_int ((plus_plus_int X_20) Y_14)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int X_20) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_14) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) X_20)) Y_14))))
% 0.67/1.04 FOF formula (forall (W_5:int), (((eq real) (number267125858f_real (bit0 W_5))) ((plus_plus_real ((plus_plus_real zero_zero_real) (number267125858f_real W_5))) (number267125858f_real W_5)))) of role axiom named fact_245_number__of__Bit0
% 0.67/1.04 A new axiom: (forall (W_5:int), (((eq real) (number267125858f_real (bit0 W_5))) ((plus_plus_real ((plus_plus_real zero_zero_real) (number267125858f_real W_5))) (number267125858f_real W_5))))
% 0.67/1.04 FOF formula (forall (W_5:int), (((eq int) (number_number_of_int (bit0 W_5))) ((plus_plus_int ((plus_plus_int zero_zero_int) (number_number_of_int W_5))) (number_number_of_int W_5)))) of role axiom named fact_246_number__of__Bit0
% 0.67/1.04 A new axiom: (forall (W_5:int), (((eq int) (number_number_of_int (bit0 W_5))) ((plus_plus_int ((plus_plus_int zero_zero_int) (number_number_of_int W_5))) (number_number_of_int W_5))))
% 0.67/1.04 FOF formula (forall (W_4:int), (((eq real) (number267125858f_real (bit1 W_4))) ((plus_plus_real ((plus_plus_real one_one_real) (number267125858f_real W_4))) (number267125858f_real W_4)))) of role axiom named fact_247_number__of__Bit1
% 0.67/1.04 A new axiom: (forall (W_4:int), (((eq real) (number267125858f_real (bit1 W_4))) ((plus_plus_real ((plus_plus_real one_one_real) (number267125858f_real W_4))) (number267125858f_real W_4))))
% 0.67/1.04 FOF formula (forall (W_4:int), (((eq int) (number_number_of_int (bit1 W_4))) ((plus_plus_int ((plus_plus_int one_one_int) (number_number_of_int W_4))) (number_number_of_int W_4)))) of role axiom named fact_248_number__of__Bit1
% 0.67/1.04 A new axiom: (forall (W_4:int), (((eq int) (number_number_of_int (bit1 W_4))) ((plus_plus_int ((plus_plus_int one_one_int) (number_number_of_int W_4))) (number_number_of_int W_4))))
% 0.67/1.04 FOF formula (((eq real) (number267125858f_real (bit1 pls))) one_one_real) of role axiom named fact_249_semiring__numeral__1__eq__1
% 0.67/1.04 A new axiom: (((eq real) (number267125858f_real (bit1 pls))) one_one_real)
% 0.67/1.04 FOF formula (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat) of role axiom named fact_250_semiring__numeral__1__eq__1
% 0.67/1.06 A new axiom: (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat)
% 0.67/1.06 FOF formula (((eq int) (number_number_of_int (bit1 pls))) one_one_int) of role axiom named fact_251_semiring__numeral__1__eq__1
% 0.67/1.06 A new axiom: (((eq int) (number_number_of_int (bit1 pls))) one_one_int)
% 0.67/1.06 FOF formula (((eq real) (number267125858f_real (bit1 pls))) one_one_real) of role axiom named fact_252_numeral__1__eq__1
% 0.67/1.06 A new axiom: (((eq real) (number267125858f_real (bit1 pls))) one_one_real)
% 0.67/1.06 FOF formula (((eq int) (number_number_of_int (bit1 pls))) one_one_int) of role axiom named fact_253_numeral__1__eq__1
% 0.67/1.06 A new axiom: (((eq int) (number_number_of_int (bit1 pls))) one_one_int)
% 0.67/1.06 FOF formula (((eq real) one_one_real) (number267125858f_real (bit1 pls))) of role axiom named fact_254_semiring__norm_I110_J
% 0.67/1.06 A new axiom: (((eq real) one_one_real) (number267125858f_real (bit1 pls)))
% 0.67/1.06 FOF formula (((eq int) one_one_int) (number_number_of_int (bit1 pls))) of role axiom named fact_255_semiring__norm_I110_J
% 0.67/1.06 A new axiom: (((eq int) one_one_int) (number_number_of_int (bit1 pls)))
% 0.67/1.06 FOF formula (forall (Z:int), ((iff ((ord_less_int ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int)) ((ord_less_int Z) zero_zero_int))) of role axiom named fact_256_odd__less__0
% 0.67/1.06 A new axiom: (forall (Z:int), ((iff ((ord_less_int ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int)) ((ord_less_int Z) zero_zero_int)))
% 0.67/1.06 FOF formula (forall (X_19:int), ((iff ((ord_less_real (number267125858f_real X_19)) zero_zero_real)) ((ord_less_int X_19) pls))) of role axiom named fact_257_less__special_I3_J
% 0.67/1.06 A new axiom: (forall (X_19:int), ((iff ((ord_less_real (number267125858f_real X_19)) zero_zero_real)) ((ord_less_int X_19) pls)))
% 0.67/1.06 FOF formula (forall (X_19:int), ((iff ((ord_less_int (number_number_of_int X_19)) zero_zero_int)) ((ord_less_int X_19) pls))) of role axiom named fact_258_less__special_I3_J
% 0.67/1.06 A new axiom: (forall (X_19:int), ((iff ((ord_less_int (number_number_of_int X_19)) zero_zero_int)) ((ord_less_int X_19) pls)))
% 0.67/1.06 FOF formula (forall (Y_13:int), ((iff ((ord_less_real zero_zero_real) (number267125858f_real Y_13))) ((ord_less_int pls) Y_13))) of role axiom named fact_259_less__special_I1_J
% 0.67/1.06 A new axiom: (forall (Y_13:int), ((iff ((ord_less_real zero_zero_real) (number267125858f_real Y_13))) ((ord_less_int pls) Y_13)))
% 0.67/1.06 FOF formula (forall (Y_13:int), ((iff ((ord_less_int zero_zero_int) (number_number_of_int Y_13))) ((ord_less_int pls) Y_13))) of role axiom named fact_260_less__special_I1_J
% 0.67/1.06 A new axiom: (forall (Y_13:int), ((iff ((ord_less_int zero_zero_int) (number_number_of_int Y_13))) ((ord_less_int pls) Y_13)))
% 0.67/1.06 FOF formula (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))) of role axiom named fact_261_semiring__one__add__one__is__two
% 0.67/1.06 A new axiom: (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls))))
% 0.67/1.06 FOF formula (((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))) of role axiom named fact_262_semiring__one__add__one__is__two
% 0.67/1.06 A new axiom: (((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls))))
% 0.67/1.06 FOF formula (((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))) of role axiom named fact_263_semiring__one__add__one__is__two
% 0.67/1.06 A new axiom: (((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls))))
% 0.67/1.06 FOF formula (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))) of role axiom named fact_264_one__add__one__is__two
% 0.67/1.06 A new axiom: (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls))))
% 0.67/1.06 FOF formula (((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))) of role axiom named fact_265_one__add__one__is__two
% 0.67/1.06 A new axiom: (((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls))))
% 0.67/1.07 FOF formula (forall (X_18:int), ((iff ((ord_less_real (number267125858f_real X_18)) one_one_real)) ((ord_less_int X_18) (bit1 pls)))) of role axiom named fact_266_less__special_I4_J
% 0.67/1.07 A new axiom: (forall (X_18:int), ((iff ((ord_less_real (number267125858f_real X_18)) one_one_real)) ((ord_less_int X_18) (bit1 pls))))
% 0.67/1.07 FOF formula (forall (X_18:int), ((iff ((ord_less_int (number_number_of_int X_18)) one_one_int)) ((ord_less_int X_18) (bit1 pls)))) of role axiom named fact_267_less__special_I4_J
% 0.67/1.07 A new axiom: (forall (X_18:int), ((iff ((ord_less_int (number_number_of_int X_18)) one_one_int)) ((ord_less_int X_18) (bit1 pls))))
% 0.67/1.07 FOF formula (forall (Y_12:int), ((iff ((ord_less_real one_one_real) (number267125858f_real Y_12))) ((ord_less_int (bit1 pls)) Y_12))) of role axiom named fact_268_less__special_I2_J
% 0.67/1.07 A new axiom: (forall (Y_12:int), ((iff ((ord_less_real one_one_real) (number267125858f_real Y_12))) ((ord_less_int (bit1 pls)) Y_12)))
% 0.67/1.07 FOF formula (forall (Y_12:int), ((iff ((ord_less_int one_one_int) (number_number_of_int Y_12))) ((ord_less_int (bit1 pls)) Y_12))) of role axiom named fact_269_less__special_I2_J
% 0.67/1.07 A new axiom: (forall (Y_12:int), ((iff ((ord_less_int one_one_int) (number_number_of_int Y_12))) ((ord_less_int (bit1 pls)) Y_12)))
% 0.67/1.07 FOF formula ((dvd_dvd_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) of role axiom named fact_270__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096
% 0.67/1.07 A new axiom: ((dvd_dvd_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int))
% 0.67/1.07 FOF formula (forall (A:int) (B:int), (((eq int) ((power_power_int ((plus_plus_int A) B)) (number_number_of_nat (bit1 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((plus_plus_int ((power_power_int A) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls)))))) B))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) A)) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))) ((power_power_int B) (number_number_of_nat (bit1 (bit1 pls))))))) of role axiom named fact_271_zadd__power3
% 0.67/1.07 A new axiom: (forall (A:int) (B:int), (((eq int) ((power_power_int ((plus_plus_int A) B)) (number_number_of_nat (bit1 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((plus_plus_int ((power_power_int A) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls)))))) B))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) A)) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))) ((power_power_int B) (number_number_of_nat (bit1 (bit1 pls)))))))
% 0.67/1.07 FOF formula (forall (A:int) (B:int), (((eq int) ((power_power_int ((plus_plus_int A) B)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A)) B))) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_272_zadd__power2
% 0.67/1.07 A new axiom: (forall (A:int) (B:int), (((eq int) ((power_power_int ((plus_plus_int A) B)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A)) B))) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls)))))))
% 0.67/1.07 FOF formula (forall (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_int X) (number_number_of_int (bit0 (bit1 pls))))->((or (((eq int) X) zero_zero_int)) (((eq int) X) one_one_int))))) of role axiom named fact_273_int__pos__lt__two__imp__zero__or__one
% 0.75/1.09 A new axiom: (forall (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_int X) (number_number_of_int (bit0 (bit1 pls))))->((or (((eq int) X) zero_zero_int)) (((eq int) X) one_one_int)))))
% 0.75/1.09 FOF formula ((and ((and ((ord_less_eq_int zero_zero_int) s)) ((ord_less_int s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) of role axiom named fact_274_s0p
% 0.75/1.09 A new axiom: ((and ((and ((ord_less_eq_int zero_zero_int) s)) ((ord_less_int s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))
% 0.75/1.09 FOF formula (forall (A:int), (((eq int) ((times_times_int A) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_int A) (number_number_of_nat (bit1 (bit1 pls)))))) of role axiom named fact_275_cube__square
% 0.75/1.09 A new axiom: (forall (A:int), (((eq int) ((times_times_int A) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_int A) (number_number_of_nat (bit1 (bit1 pls))))))
% 0.75/1.09 FOF formula (forall (X:int), ((ord_less_eq_int X) ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_276_power2__ge__self
% 0.75/1.09 A new axiom: (forall (X:int), ((ord_less_eq_int X) ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.75/1.09 FOF formula (forall (R:int) (Q:int) (A:int), (((ord_less_int zero_zero_int) A)->((((eq int) A) ((plus_plus_int R) ((times_times_int A) Q)))->(((ord_less_int R) A)->((ord_less_eq_int one_one_int) Q))))) of role axiom named fact_277_self__quotient__aux1
% 0.75/1.09 A new axiom: (forall (R:int) (Q:int) (A:int), (((ord_less_int zero_zero_int) A)->((((eq int) A) ((plus_plus_int R) ((times_times_int A) Q)))->(((ord_less_int R) A)->((ord_less_eq_int one_one_int) Q)))))
% 0.75/1.09 FOF formula (forall (R:int) (Q:int) (A:int), (((ord_less_int zero_zero_int) A)->((((eq int) A) ((plus_plus_int R) ((times_times_int A) Q)))->(((ord_less_eq_int zero_zero_int) R)->((ord_less_eq_int Q) one_one_int))))) of role axiom named fact_278_self__quotient__aux2
% 0.75/1.09 A new axiom: (forall (R:int) (Q:int) (A:int), (((ord_less_int zero_zero_int) A)->((((eq int) A) ((plus_plus_int R) ((times_times_int A) Q)))->(((ord_less_eq_int zero_zero_int) R)->((ord_less_eq_int Q) one_one_int)))))
% 0.75/1.09 FOF formula ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 (bit1 pls)))) of role axiom named fact_279_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J
% 0.75/1.09 A new axiom: ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 (bit1 pls))))
% 0.75/1.09 FOF formula (forall (X_17:real) (N_25:nat), (((eq real) ((power_power_real X_17) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_25))) ((times_times_real ((power_power_real X_17) N_25)) ((power_power_real X_17) N_25)))) of role axiom named fact_280_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J
% 0.75/1.09 A new axiom: (forall (X_17:real) (N_25:nat), (((eq real) ((power_power_real X_17) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_25))) ((times_times_real ((power_power_real X_17) N_25)) ((power_power_real X_17) N_25))))
% 0.75/1.09 FOF formula (forall (X_17:nat) (N_25:nat), (((eq nat) ((power_power_nat X_17) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_25))) ((times_times_nat ((power_power_nat X_17) N_25)) ((power_power_nat X_17) N_25)))) of role axiom named fact_281_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J
% 0.75/1.09 A new axiom: (forall (X_17:nat) (N_25:nat), (((eq nat) ((power_power_nat X_17) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_25))) ((times_times_nat ((power_power_nat X_17) N_25)) ((power_power_nat X_17) N_25))))
% 0.75/1.09 FOF formula (forall (X_17:int) (N_25:nat), (((eq int) ((power_power_int X_17) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_25))) ((times_times_int ((power_power_int X_17) N_25)) ((power_power_int X_17) N_25)))) of role axiom named fact_282_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J
% 0.75/1.11 A new axiom: (forall (X_17:int) (N_25:nat), (((eq int) ((power_power_int X_17) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_25))) ((times_times_int ((power_power_int X_17) N_25)) ((power_power_int X_17) N_25))))
% 0.75/1.11 FOF formula (forall (X_16:real), (((eq real) ((times_times_real X_16) X_16)) ((power_power_real X_16) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_283_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J
% 0.75/1.11 A new axiom: (forall (X_16:real), (((eq real) ((times_times_real X_16) X_16)) ((power_power_real X_16) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.75/1.11 FOF formula (forall (X_16:nat), (((eq nat) ((times_times_nat X_16) X_16)) ((power_power_nat X_16) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_284_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J
% 0.75/1.11 A new axiom: (forall (X_16:nat), (((eq nat) ((times_times_nat X_16) X_16)) ((power_power_nat X_16) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.75/1.11 FOF formula (forall (X_16:int), (((eq int) ((times_times_int X_16) X_16)) ((power_power_int X_16) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J
% 0.75/1.11 A new axiom: (forall (X_16:int), (((eq int) ((times_times_int X_16) X_16)) ((power_power_int X_16) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.75/1.11 FOF formula (((zcong ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int s1) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) of role axiom named fact_286__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096
% 0.75/1.11 A new axiom: (((zcong ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int s1) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))
% 0.75/1.11 FOF formula ((ex int) (fun (X_1:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X_1)) ((ord_less_int X_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) X_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (forall (Y_1:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y_1)) ((ord_less_int Y_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) Y_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))->(((eq int) Y_1) X_1)))))) of role axiom named fact_287__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1
% 0.75/1.11 A new axiom: ((ex int) (fun (X_1:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X_1)) ((ord_less_int X_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) X_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (forall (Y_1:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y_1)) ((ord_less_int Y_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) Y_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))->(((eq int) Y_1) X_1))))))
% 0.75/1.11 FOF formula ((forall (S_1:int), (((and ((and ((ord_less_eq_int zero_zero_int) S_1)) ((ord_less_int S_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) S_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))->False))->False) of role axiom named fact_288__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_
% 0.75/1.11 A new axiom: ((forall (S_1:int), (((and ((and ((ord_less_eq_int zero_zero_int) S_1)) ((ord_less_int S_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) S_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))->False))->False)
% 0.75/1.13 FOF formula (((zcong ((power_power_int s1) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) of role axiom named fact_289_s1
% 0.75/1.13 A new axiom: (((zcong ((power_power_int s1) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))
% 0.75/1.13 FOF formula (forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or (((eq nat) N) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X)))) of role axiom named fact_290_zero__less__power__nat__eq
% 0.75/1.13 A new axiom: (forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or (((eq nat) N) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X))))
% 0.75/1.13 FOF formula (forall (A:int) (N:nat) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((power_power_int A) N))->((dvd_dvd_int P_1) A)))) of role axiom named fact_291_zprime__zdvd__power
% 0.75/1.13 A new axiom: (forall (A:int) (N:nat) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((power_power_int A) N))->((dvd_dvd_int P_1) A))))
% 0.75/1.13 FOF formula (forall (X_15:real) (P_5:nat) (Q_6:nat), (((eq real) ((power_power_real ((power_power_real X_15) P_5)) Q_6)) ((power_power_real X_15) ((times_times_nat P_5) Q_6)))) of role axiom named fact_292_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J
% 0.75/1.13 A new axiom: (forall (X_15:real) (P_5:nat) (Q_6:nat), (((eq real) ((power_power_real ((power_power_real X_15) P_5)) Q_6)) ((power_power_real X_15) ((times_times_nat P_5) Q_6))))
% 0.75/1.13 FOF formula (forall (X_15:nat) (P_5:nat) (Q_6:nat), (((eq nat) ((power_power_nat ((power_power_nat X_15) P_5)) Q_6)) ((power_power_nat X_15) ((times_times_nat P_5) Q_6)))) of role axiom named fact_293_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J
% 0.75/1.13 A new axiom: (forall (X_15:nat) (P_5:nat) (Q_6:nat), (((eq nat) ((power_power_nat ((power_power_nat X_15) P_5)) Q_6)) ((power_power_nat X_15) ((times_times_nat P_5) Q_6))))
% 0.75/1.13 FOF formula (forall (X_15:int) (P_5:nat) (Q_6:nat), (((eq int) ((power_power_int ((power_power_int X_15) P_5)) Q_6)) ((power_power_int X_15) ((times_times_nat P_5) Q_6)))) of role axiom named fact_294_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J
% 0.75/1.13 A new axiom: (forall (X_15:int) (P_5:nat) (Q_6:nat), (((eq int) ((power_power_int ((power_power_int X_15) P_5)) Q_6)) ((power_power_int X_15) ((times_times_nat P_5) Q_6))))
% 0.75/1.13 FOF formula (forall (N:nat) (A:int) (B:int) (P_1:int), ((zprime P_1)->((((dvd_dvd_int P_1) B)->False)->(((dvd_dvd_int ((power_power_int P_1) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P_1) N)) A))))) of role axiom named fact_295_zprime__power__zdvd__cancel__right
% 0.75/1.13 A new axiom: (forall (N:nat) (A:int) (B:int) (P_1:int), ((zprime P_1)->((((dvd_dvd_int P_1) B)->False)->(((dvd_dvd_int ((power_power_int P_1) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P_1) N)) A)))))
% 0.75/1.13 FOF formula (forall (N:nat) (B:int) (A:int) (P_1:int), ((zprime P_1)->((((dvd_dvd_int P_1) A)->False)->(((dvd_dvd_int ((power_power_int P_1) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P_1) N)) B))))) of role axiom named fact_296_zprime__power__zdvd__cancel__left
% 0.75/1.13 A new axiom: (forall (N:nat) (B:int) (A:int) (P_1:int), ((zprime P_1)->((((dvd_dvd_int P_1) A)->False)->(((dvd_dvd_int ((power_power_int P_1) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P_1) N)) B)))))
% 0.75/1.13 FOF formula (forall (X:int) (Y:nat) (Z:nat), (((eq int) ((power_power_int ((power_power_int X) Y)) Z)) ((power_power_int X) ((times_times_nat Y) Z)))) of role axiom named fact_297_zpower__zpower
% 0.75/1.13 A new axiom: (forall (X:int) (Y:nat) (Z:nat), (((eq int) ((power_power_int ((power_power_int X) Y)) Z)) ((power_power_int X) ((times_times_nat Y) Z))))
% 0.75/1.13 FOF formula (forall (N:int) (M:int), (((ord_less_int zero_zero_int) M)->(((ord_less_int M) N)->(((dvd_dvd_int N) M)->False)))) of role axiom named fact_298_zdvd__not__zless
% 0.75/1.14 A new axiom: (forall (N:int) (M:int), (((ord_less_int zero_zero_int) M)->(((ord_less_int M) N)->(((dvd_dvd_int N) M)->False))))
% 0.75/1.14 FOF formula (forall (N:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->(((ord_less_eq_int zero_zero_int) N)->(((dvd_dvd_int M) N)->(((dvd_dvd_int N) M)->(((eq int) M) N)))))) of role axiom named fact_299_zdvd__antisym__nonneg
% 0.75/1.14 A new axiom: (forall (N:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->(((ord_less_eq_int zero_zero_int) N)->(((dvd_dvd_int M) N)->(((dvd_dvd_int N) M)->(((eq int) M) N))))))
% 0.75/1.14 FOF formula (forall (K:int) (M:int) (N:int), (((dvd_dvd_int ((times_times_int K) M)) ((times_times_int K) N))->((not (((eq int) K) zero_zero_int))->((dvd_dvd_int M) N)))) of role axiom named fact_300_zdvd__mult__cancel
% 0.75/1.14 A new axiom: (forall (K:int) (M:int) (N:int), (((dvd_dvd_int ((times_times_int K) M)) ((times_times_int K) N))->((not (((eq int) K) zero_zero_int))->((dvd_dvd_int M) N))))
% 0.75/1.14 FOF formula (forall (K:int) (N:int) (M:int), ((iff ((dvd_dvd_int K) ((plus_plus_int N) ((times_times_int K) M)))) ((dvd_dvd_int K) N))) of role axiom named fact_301_zdvd__reduce
% 0.75/1.14 A new axiom: (forall (K:int) (N:int) (M:int), ((iff ((dvd_dvd_int K) ((plus_plus_int N) ((times_times_int K) M)))) ((dvd_dvd_int K) N)))
% 0.75/1.14 FOF formula (forall (C:int) (X:int) (T:int) (A:int) (D:int), (((dvd_dvd_int A) D)->((iff ((dvd_dvd_int A) ((plus_plus_int X) T))) ((dvd_dvd_int A) ((plus_plus_int ((plus_plus_int X) ((times_times_int C) D))) T))))) of role axiom named fact_302_zdvd__period
% 0.75/1.14 A new axiom: (forall (C:int) (X:int) (T:int) (A:int) (D:int), (((dvd_dvd_int A) D)->((iff ((dvd_dvd_int A) ((plus_plus_int X) T))) ((dvd_dvd_int A) ((plus_plus_int ((plus_plus_int X) ((times_times_int C) D))) T)))))
% 0.75/1.14 FOF formula (zprime (number_number_of_int (bit0 (bit1 pls)))) of role axiom named fact_303_zprime__2
% 0.75/1.14 A new axiom: (zprime (number_number_of_int (bit0 (bit1 pls))))
% 0.75/1.14 FOF formula (forall (Z:int) (N:int), (((dvd_dvd_int Z) N)->(((ord_less_int zero_zero_int) N)->((ord_less_eq_int Z) N)))) of role axiom named fact_304_zdvd__imp__le
% 0.75/1.14 A new axiom: (forall (Z:int) (N:int), (((dvd_dvd_int Z) N)->(((ord_less_int zero_zero_int) N)->((ord_less_eq_int Z) N))))
% 0.75/1.14 FOF formula (forall (Y:int) (X:int), ((twoSqu919416604sum2sq X)->((twoSqu919416604sum2sq Y)->(twoSqu919416604sum2sq ((times_times_int X) Y))))) of role axiom named fact_305_is__mult__sum2sq
% 0.75/1.14 A new axiom: (forall (Y:int) (X:int), ((twoSqu919416604sum2sq X)->((twoSqu919416604sum2sq Y)->(twoSqu919416604sum2sq ((times_times_int X) Y)))))
% 0.75/1.14 FOF formula (forall (V:int) (V_2:int), ((iff ((ord_less_eq_nat (number_number_of_nat V)) (number_number_of_nat V_2))) ((((ord_less_eq_int V) V_2)->False)->((ord_less_eq_int V) pls)))) of role axiom named fact_306_le__nat__number__of
% 0.75/1.14 A new axiom: (forall (V:int) (V_2:int), ((iff ((ord_less_eq_nat (number_number_of_nat V)) (number_number_of_nat V_2))) ((((ord_less_eq_int V) V_2)->False)->((ord_less_eq_int V) pls))))
% 0.75/1.14 FOF formula (forall (Lx_6:real) (Ly_4:real) (Rx_6:real) (Ry_4:real), (((eq real) ((times_times_real ((times_times_real Lx_6) Ly_4)) ((times_times_real Rx_6) Ry_4))) ((times_times_real ((times_times_real Lx_6) Rx_6)) ((times_times_real Ly_4) Ry_4)))) of role axiom named fact_307_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J
% 0.75/1.14 A new axiom: (forall (Lx_6:real) (Ly_4:real) (Rx_6:real) (Ry_4:real), (((eq real) ((times_times_real ((times_times_real Lx_6) Ly_4)) ((times_times_real Rx_6) Ry_4))) ((times_times_real ((times_times_real Lx_6) Rx_6)) ((times_times_real Ly_4) Ry_4))))
% 0.75/1.14 FOF formula (forall (Lx_6:nat) (Ly_4:nat) (Rx_6:nat) (Ry_4:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_6) Ly_4)) ((times_times_nat Rx_6) Ry_4))) ((times_times_nat ((times_times_nat Lx_6) Rx_6)) ((times_times_nat Ly_4) Ry_4)))) of role axiom named fact_308_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J
% 0.75/1.14 A new axiom: (forall (Lx_6:nat) (Ly_4:nat) (Rx_6:nat) (Ry_4:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_6) Ly_4)) ((times_times_nat Rx_6) Ry_4))) ((times_times_nat ((times_times_nat Lx_6) Rx_6)) ((times_times_nat Ly_4) Ry_4))))
% 0.75/1.16 FOF formula (forall (Lx_6:int) (Ly_4:int) (Rx_6:int) (Ry_4:int), (((eq int) ((times_times_int ((times_times_int Lx_6) Ly_4)) ((times_times_int Rx_6) Ry_4))) ((times_times_int ((times_times_int Lx_6) Rx_6)) ((times_times_int Ly_4) Ry_4)))) of role axiom named fact_309_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J
% 0.75/1.16 A new axiom: (forall (Lx_6:int) (Ly_4:int) (Rx_6:int) (Ry_4:int), (((eq int) ((times_times_int ((times_times_int Lx_6) Ly_4)) ((times_times_int Rx_6) Ry_4))) ((times_times_int ((times_times_int Lx_6) Rx_6)) ((times_times_int Ly_4) Ry_4))))
% 0.75/1.16 FOF formula (forall (Lx_5:real) (Ly_3:real) (Rx_5:real) (Ry_3:real), (((eq real) ((times_times_real ((times_times_real Lx_5) Ly_3)) ((times_times_real Rx_5) Ry_3))) ((times_times_real Rx_5) ((times_times_real ((times_times_real Lx_5) Ly_3)) Ry_3)))) of role axiom named fact_310_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J
% 0.75/1.16 A new axiom: (forall (Lx_5:real) (Ly_3:real) (Rx_5:real) (Ry_3:real), (((eq real) ((times_times_real ((times_times_real Lx_5) Ly_3)) ((times_times_real Rx_5) Ry_3))) ((times_times_real Rx_5) ((times_times_real ((times_times_real Lx_5) Ly_3)) Ry_3))))
% 0.75/1.16 FOF formula (forall (Lx_5:nat) (Ly_3:nat) (Rx_5:nat) (Ry_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) ((times_times_nat Rx_5) Ry_3))) ((times_times_nat Rx_5) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) Ry_3)))) of role axiom named fact_311_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J
% 0.75/1.16 A new axiom: (forall (Lx_5:nat) (Ly_3:nat) (Rx_5:nat) (Ry_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) ((times_times_nat Rx_5) Ry_3))) ((times_times_nat Rx_5) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) Ry_3))))
% 0.75/1.16 FOF formula (forall (Lx_5:int) (Ly_3:int) (Rx_5:int) (Ry_3:int), (((eq int) ((times_times_int ((times_times_int Lx_5) Ly_3)) ((times_times_int Rx_5) Ry_3))) ((times_times_int Rx_5) ((times_times_int ((times_times_int Lx_5) Ly_3)) Ry_3)))) of role axiom named fact_312_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J
% 0.75/1.16 A new axiom: (forall (Lx_5:int) (Ly_3:int) (Rx_5:int) (Ry_3:int), (((eq int) ((times_times_int ((times_times_int Lx_5) Ly_3)) ((times_times_int Rx_5) Ry_3))) ((times_times_int Rx_5) ((times_times_int ((times_times_int Lx_5) Ly_3)) Ry_3))))
% 0.75/1.16 FOF formula (forall (Lx_4:real) (Ly_2:real) (Rx_4:real) (Ry_2:real), (((eq real) ((times_times_real ((times_times_real Lx_4) Ly_2)) ((times_times_real Rx_4) Ry_2))) ((times_times_real Lx_4) ((times_times_real Ly_2) ((times_times_real Rx_4) Ry_2))))) of role axiom named fact_313_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J
% 0.75/1.16 A new axiom: (forall (Lx_4:real) (Ly_2:real) (Rx_4:real) (Ry_2:real), (((eq real) ((times_times_real ((times_times_real Lx_4) Ly_2)) ((times_times_real Rx_4) Ry_2))) ((times_times_real Lx_4) ((times_times_real Ly_2) ((times_times_real Rx_4) Ry_2)))))
% 0.75/1.16 FOF formula (forall (Lx_4:nat) (Ly_2:nat) (Rx_4:nat) (Ry_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_4) Ly_2)) ((times_times_nat Rx_4) Ry_2))) ((times_times_nat Lx_4) ((times_times_nat Ly_2) ((times_times_nat Rx_4) Ry_2))))) of role axiom named fact_314_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J
% 0.75/1.16 A new axiom: (forall (Lx_4:nat) (Ly_2:nat) (Rx_4:nat) (Ry_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_4) Ly_2)) ((times_times_nat Rx_4) Ry_2))) ((times_times_nat Lx_4) ((times_times_nat Ly_2) ((times_times_nat Rx_4) Ry_2)))))
% 0.75/1.16 FOF formula (forall (Lx_4:int) (Ly_2:int) (Rx_4:int) (Ry_2:int), (((eq int) ((times_times_int ((times_times_int Lx_4) Ly_2)) ((times_times_int Rx_4) Ry_2))) ((times_times_int Lx_4) ((times_times_int Ly_2) ((times_times_int Rx_4) Ry_2))))) of role axiom named fact_315_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J
% 0.75/1.16 A new axiom: (forall (Lx_4:int) (Ly_2:int) (Rx_4:int) (Ry_2:int), (((eq int) ((times_times_int ((times_times_int Lx_4) Ly_2)) ((times_times_int Rx_4) Ry_2))) ((times_times_int Lx_4) ((times_times_int Ly_2) ((times_times_int Rx_4) Ry_2)))))
% 0.83/1.18 FOF formula (forall (Lx_3:real) (Ly_1:real) (Rx_3:real), (((eq real) ((times_times_real ((times_times_real Lx_3) Ly_1)) Rx_3)) ((times_times_real ((times_times_real Lx_3) Rx_3)) Ly_1))) of role axiom named fact_316_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J
% 0.83/1.18 A new axiom: (forall (Lx_3:real) (Ly_1:real) (Rx_3:real), (((eq real) ((times_times_real ((times_times_real Lx_3) Ly_1)) Rx_3)) ((times_times_real ((times_times_real Lx_3) Rx_3)) Ly_1)))
% 0.83/1.18 FOF formula (forall (Lx_3:nat) (Ly_1:nat) (Rx_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_3) Ly_1)) Rx_3)) ((times_times_nat ((times_times_nat Lx_3) Rx_3)) Ly_1))) of role axiom named fact_317_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J
% 0.83/1.18 A new axiom: (forall (Lx_3:nat) (Ly_1:nat) (Rx_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_3) Ly_1)) Rx_3)) ((times_times_nat ((times_times_nat Lx_3) Rx_3)) Ly_1)))
% 0.83/1.18 FOF formula (forall (Lx_3:int) (Ly_1:int) (Rx_3:int), (((eq int) ((times_times_int ((times_times_int Lx_3) Ly_1)) Rx_3)) ((times_times_int ((times_times_int Lx_3) Rx_3)) Ly_1))) of role axiom named fact_318_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J
% 0.83/1.18 A new axiom: (forall (Lx_3:int) (Ly_1:int) (Rx_3:int), (((eq int) ((times_times_int ((times_times_int Lx_3) Ly_1)) Rx_3)) ((times_times_int ((times_times_int Lx_3) Rx_3)) Ly_1)))
% 0.83/1.18 FOF formula (forall (Lx_2:real) (Ly:real) (Rx_2:real), (((eq real) ((times_times_real ((times_times_real Lx_2) Ly)) Rx_2)) ((times_times_real Lx_2) ((times_times_real Ly) Rx_2)))) of role axiom named fact_319_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J
% 0.83/1.18 A new axiom: (forall (Lx_2:real) (Ly:real) (Rx_2:real), (((eq real) ((times_times_real ((times_times_real Lx_2) Ly)) Rx_2)) ((times_times_real Lx_2) ((times_times_real Ly) Rx_2))))
% 0.83/1.18 FOF formula (forall (Lx_2:nat) (Ly:nat) (Rx_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_2) Ly)) Rx_2)) ((times_times_nat Lx_2) ((times_times_nat Ly) Rx_2)))) of role axiom named fact_320_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J
% 0.83/1.18 A new axiom: (forall (Lx_2:nat) (Ly:nat) (Rx_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_2) Ly)) Rx_2)) ((times_times_nat Lx_2) ((times_times_nat Ly) Rx_2))))
% 0.83/1.18 FOF formula (forall (Lx_2:int) (Ly:int) (Rx_2:int), (((eq int) ((times_times_int ((times_times_int Lx_2) Ly)) Rx_2)) ((times_times_int Lx_2) ((times_times_int Ly) Rx_2)))) of role axiom named fact_321_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J
% 0.83/1.18 A new axiom: (forall (Lx_2:int) (Ly:int) (Rx_2:int), (((eq int) ((times_times_int ((times_times_int Lx_2) Ly)) Rx_2)) ((times_times_int Lx_2) ((times_times_int Ly) Rx_2))))
% 0.83/1.18 FOF formula (forall (Lx_1:real) (Rx_1:real) (Ry_1:real), (((eq real) ((times_times_real Lx_1) ((times_times_real Rx_1) Ry_1))) ((times_times_real ((times_times_real Lx_1) Rx_1)) Ry_1))) of role axiom named fact_322_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J
% 0.83/1.18 A new axiom: (forall (Lx_1:real) (Rx_1:real) (Ry_1:real), (((eq real) ((times_times_real Lx_1) ((times_times_real Rx_1) Ry_1))) ((times_times_real ((times_times_real Lx_1) Rx_1)) Ry_1)))
% 0.83/1.18 FOF formula (forall (Lx_1:nat) (Rx_1:nat) (Ry_1:nat), (((eq nat) ((times_times_nat Lx_1) ((times_times_nat Rx_1) Ry_1))) ((times_times_nat ((times_times_nat Lx_1) Rx_1)) Ry_1))) of role axiom named fact_323_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J
% 0.83/1.18 A new axiom: (forall (Lx_1:nat) (Rx_1:nat) (Ry_1:nat), (((eq nat) ((times_times_nat Lx_1) ((times_times_nat Rx_1) Ry_1))) ((times_times_nat ((times_times_nat Lx_1) Rx_1)) Ry_1)))
% 0.83/1.18 FOF formula (forall (Lx_1:int) (Rx_1:int) (Ry_1:int), (((eq int) ((times_times_int Lx_1) ((times_times_int Rx_1) Ry_1))) ((times_times_int ((times_times_int Lx_1) Rx_1)) Ry_1))) of role axiom named fact_324_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J
% 0.83/1.18 A new axiom: (forall (Lx_1:int) (Rx_1:int) (Ry_1:int), (((eq int) ((times_times_int Lx_1) ((times_times_int Rx_1) Ry_1))) ((times_times_int ((times_times_int Lx_1) Rx_1)) Ry_1)))
% 0.83/1.18 FOF formula (forall (Lx:real) (Rx:real) (Ry:real), (((eq real) ((times_times_real Lx) ((times_times_real Rx) Ry))) ((times_times_real Rx) ((times_times_real Lx) Ry)))) of role axiom named fact_325_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J
% 0.84/1.19 A new axiom: (forall (Lx:real) (Rx:real) (Ry:real), (((eq real) ((times_times_real Lx) ((times_times_real Rx) Ry))) ((times_times_real Rx) ((times_times_real Lx) Ry))))
% 0.84/1.19 FOF formula (forall (Lx:nat) (Rx:nat) (Ry:nat), (((eq nat) ((times_times_nat Lx) ((times_times_nat Rx) Ry))) ((times_times_nat Rx) ((times_times_nat Lx) Ry)))) of role axiom named fact_326_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J
% 0.84/1.19 A new axiom: (forall (Lx:nat) (Rx:nat) (Ry:nat), (((eq nat) ((times_times_nat Lx) ((times_times_nat Rx) Ry))) ((times_times_nat Rx) ((times_times_nat Lx) Ry))))
% 0.84/1.19 FOF formula (forall (Lx:int) (Rx:int) (Ry:int), (((eq int) ((times_times_int Lx) ((times_times_int Rx) Ry))) ((times_times_int Rx) ((times_times_int Lx) Ry)))) of role axiom named fact_327_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J
% 0.84/1.19 A new axiom: (forall (Lx:int) (Rx:int) (Ry:int), (((eq int) ((times_times_int Lx) ((times_times_int Rx) Ry))) ((times_times_int Rx) ((times_times_int Lx) Ry))))
% 0.84/1.19 FOF formula (forall (A_115:real) (B_78:real), (((eq real) ((times_times_real A_115) B_78)) ((times_times_real B_78) A_115))) of role axiom named fact_328_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J
% 0.84/1.19 A new axiom: (forall (A_115:real) (B_78:real), (((eq real) ((times_times_real A_115) B_78)) ((times_times_real B_78) A_115)))
% 0.84/1.19 FOF formula (forall (A_115:nat) (B_78:nat), (((eq nat) ((times_times_nat A_115) B_78)) ((times_times_nat B_78) A_115))) of role axiom named fact_329_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J
% 0.84/1.19 A new axiom: (forall (A_115:nat) (B_78:nat), (((eq nat) ((times_times_nat A_115) B_78)) ((times_times_nat B_78) A_115)))
% 0.84/1.19 FOF formula (forall (A_115:int) (B_78:int), (((eq int) ((times_times_int A_115) B_78)) ((times_times_int B_78) A_115))) of role axiom named fact_330_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J
% 0.84/1.19 A new axiom: (forall (A_115:int) (B_78:int), (((eq int) ((times_times_int A_115) B_78)) ((times_times_int B_78) A_115)))
% 0.84/1.19 FOF formula (forall (A_114:real) (C_49:real), (((eq real) ((plus_plus_real A_114) C_49)) ((plus_plus_real C_49) A_114))) of role axiom named fact_331_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J
% 0.84/1.19 A new axiom: (forall (A_114:real) (C_49:real), (((eq real) ((plus_plus_real A_114) C_49)) ((plus_plus_real C_49) A_114)))
% 0.84/1.19 FOF formula (forall (A_114:nat) (C_49:nat), (((eq nat) ((plus_plus_nat A_114) C_49)) ((plus_plus_nat C_49) A_114))) of role axiom named fact_332_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J
% 0.84/1.19 A new axiom: (forall (A_114:nat) (C_49:nat), (((eq nat) ((plus_plus_nat A_114) C_49)) ((plus_plus_nat C_49) A_114)))
% 0.84/1.19 FOF formula (forall (A_114:int) (C_49:int), (((eq int) ((plus_plus_int A_114) C_49)) ((plus_plus_int C_49) A_114))) of role axiom named fact_333_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J
% 0.84/1.19 A new axiom: (forall (A_114:int) (C_49:int), (((eq int) ((plus_plus_int A_114) C_49)) ((plus_plus_int C_49) A_114)))
% 0.84/1.19 FOF formula (forall (A_113:real) (C_48:real) (D_14:real), (((eq real) ((plus_plus_real A_113) ((plus_plus_real C_48) D_14))) ((plus_plus_real C_48) ((plus_plus_real A_113) D_14)))) of role axiom named fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J
% 0.84/1.19 A new axiom: (forall (A_113:real) (C_48:real) (D_14:real), (((eq real) ((plus_plus_real A_113) ((plus_plus_real C_48) D_14))) ((plus_plus_real C_48) ((plus_plus_real A_113) D_14))))
% 0.84/1.19 FOF formula (forall (A_113:nat) (C_48:nat) (D_14:nat), (((eq nat) ((plus_plus_nat A_113) ((plus_plus_nat C_48) D_14))) ((plus_plus_nat C_48) ((plus_plus_nat A_113) D_14)))) of role axiom named fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J
% 0.84/1.19 A new axiom: (forall (A_113:nat) (C_48:nat) (D_14:nat), (((eq nat) ((plus_plus_nat A_113) ((plus_plus_nat C_48) D_14))) ((plus_plus_nat C_48) ((plus_plus_nat A_113) D_14))))
% 0.84/1.21 FOF formula (forall (A_113:int) (C_48:int) (D_14:int), (((eq int) ((plus_plus_int A_113) ((plus_plus_int C_48) D_14))) ((plus_plus_int C_48) ((plus_plus_int A_113) D_14)))) of role axiom named fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J
% 0.84/1.21 A new axiom: (forall (A_113:int) (C_48:int) (D_14:int), (((eq int) ((plus_plus_int A_113) ((plus_plus_int C_48) D_14))) ((plus_plus_int C_48) ((plus_plus_int A_113) D_14))))
% 0.84/1.21 FOF formula (forall (A_112:real) (C_47:real) (D_13:real), (((eq real) ((plus_plus_real A_112) ((plus_plus_real C_47) D_13))) ((plus_plus_real ((plus_plus_real A_112) C_47)) D_13))) of role axiom named fact_337_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J
% 0.84/1.21 A new axiom: (forall (A_112:real) (C_47:real) (D_13:real), (((eq real) ((plus_plus_real A_112) ((plus_plus_real C_47) D_13))) ((plus_plus_real ((plus_plus_real A_112) C_47)) D_13)))
% 0.84/1.21 FOF formula (forall (A_112:nat) (C_47:nat) (D_13:nat), (((eq nat) ((plus_plus_nat A_112) ((plus_plus_nat C_47) D_13))) ((plus_plus_nat ((plus_plus_nat A_112) C_47)) D_13))) of role axiom named fact_338_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J
% 0.84/1.21 A new axiom: (forall (A_112:nat) (C_47:nat) (D_13:nat), (((eq nat) ((plus_plus_nat A_112) ((plus_plus_nat C_47) D_13))) ((plus_plus_nat ((plus_plus_nat A_112) C_47)) D_13)))
% 0.84/1.21 FOF formula (forall (A_112:int) (C_47:int) (D_13:int), (((eq int) ((plus_plus_int A_112) ((plus_plus_int C_47) D_13))) ((plus_plus_int ((plus_plus_int A_112) C_47)) D_13))) of role axiom named fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J
% 0.84/1.21 A new axiom: (forall (A_112:int) (C_47:int) (D_13:int), (((eq int) ((plus_plus_int A_112) ((plus_plus_int C_47) D_13))) ((plus_plus_int ((plus_plus_int A_112) C_47)) D_13)))
% 0.84/1.21 FOF formula (forall (A_111:real) (B_77:real) (C_46:real), (((eq real) ((plus_plus_real ((plus_plus_real A_111) B_77)) C_46)) ((plus_plus_real A_111) ((plus_plus_real B_77) C_46)))) of role axiom named fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J
% 0.84/1.21 A new axiom: (forall (A_111:real) (B_77:real) (C_46:real), (((eq real) ((plus_plus_real ((plus_plus_real A_111) B_77)) C_46)) ((plus_plus_real A_111) ((plus_plus_real B_77) C_46))))
% 0.84/1.21 FOF formula (forall (A_111:nat) (B_77:nat) (C_46:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_111) B_77)) C_46)) ((plus_plus_nat A_111) ((plus_plus_nat B_77) C_46)))) of role axiom named fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J
% 0.84/1.21 A new axiom: (forall (A_111:nat) (B_77:nat) (C_46:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_111) B_77)) C_46)) ((plus_plus_nat A_111) ((plus_plus_nat B_77) C_46))))
% 0.84/1.21 FOF formula (forall (A_111:int) (B_77:int) (C_46:int), (((eq int) ((plus_plus_int ((plus_plus_int A_111) B_77)) C_46)) ((plus_plus_int A_111) ((plus_plus_int B_77) C_46)))) of role axiom named fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J
% 0.84/1.21 A new axiom: (forall (A_111:int) (B_77:int) (C_46:int), (((eq int) ((plus_plus_int ((plus_plus_int A_111) B_77)) C_46)) ((plus_plus_int A_111) ((plus_plus_int B_77) C_46))))
% 0.84/1.21 FOF formula (forall (A_110:real) (B_76:real) (C_45:real), (((eq real) ((plus_plus_real ((plus_plus_real A_110) B_76)) C_45)) ((plus_plus_real ((plus_plus_real A_110) C_45)) B_76))) of role axiom named fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J
% 0.84/1.21 A new axiom: (forall (A_110:real) (B_76:real) (C_45:real), (((eq real) ((plus_plus_real ((plus_plus_real A_110) B_76)) C_45)) ((plus_plus_real ((plus_plus_real A_110) C_45)) B_76)))
% 0.84/1.21 FOF formula (forall (A_110:nat) (B_76:nat) (C_45:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_110) B_76)) C_45)) ((plus_plus_nat ((plus_plus_nat A_110) C_45)) B_76))) of role axiom named fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J
% 0.84/1.21 A new axiom: (forall (A_110:nat) (B_76:nat) (C_45:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_110) B_76)) C_45)) ((plus_plus_nat ((plus_plus_nat A_110) C_45)) B_76)))
% 0.84/1.21 FOF formula (forall (A_110:int) (B_76:int) (C_45:int), (((eq int) ((plus_plus_int ((plus_plus_int A_110) B_76)) C_45)) ((plus_plus_int ((plus_plus_int A_110) C_45)) B_76))) of role axiom named fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J
% 0.88/1.23 A new axiom: (forall (A_110:int) (B_76:int) (C_45:int), (((eq int) ((plus_plus_int ((plus_plus_int A_110) B_76)) C_45)) ((plus_plus_int ((plus_plus_int A_110) C_45)) B_76)))
% 0.88/1.23 FOF formula (forall (A_109:real) (B_75:real) (C_44:real) (D_12:real), (((eq real) ((plus_plus_real ((plus_plus_real A_109) B_75)) ((plus_plus_real C_44) D_12))) ((plus_plus_real ((plus_plus_real A_109) C_44)) ((plus_plus_real B_75) D_12)))) of role axiom named fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J
% 0.88/1.23 A new axiom: (forall (A_109:real) (B_75:real) (C_44:real) (D_12:real), (((eq real) ((plus_plus_real ((plus_plus_real A_109) B_75)) ((plus_plus_real C_44) D_12))) ((plus_plus_real ((plus_plus_real A_109) C_44)) ((plus_plus_real B_75) D_12))))
% 0.88/1.23 FOF formula (forall (A_109:nat) (B_75:nat) (C_44:nat) (D_12:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_109) B_75)) ((plus_plus_nat C_44) D_12))) ((plus_plus_nat ((plus_plus_nat A_109) C_44)) ((plus_plus_nat B_75) D_12)))) of role axiom named fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J
% 0.88/1.23 A new axiom: (forall (A_109:nat) (B_75:nat) (C_44:nat) (D_12:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_109) B_75)) ((plus_plus_nat C_44) D_12))) ((plus_plus_nat ((plus_plus_nat A_109) C_44)) ((plus_plus_nat B_75) D_12))))
% 0.88/1.23 FOF formula (forall (A_109:int) (B_75:int) (C_44:int) (D_12:int), (((eq int) ((plus_plus_int ((plus_plus_int A_109) B_75)) ((plus_plus_int C_44) D_12))) ((plus_plus_int ((plus_plus_int A_109) C_44)) ((plus_plus_int B_75) D_12)))) of role axiom named fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J
% 0.88/1.23 A new axiom: (forall (A_109:int) (B_75:int) (C_44:int) (D_12:int), (((eq int) ((plus_plus_int ((plus_plus_int A_109) B_75)) ((plus_plus_int C_44) D_12))) ((plus_plus_int ((plus_plus_int A_109) C_44)) ((plus_plus_int B_75) D_12))))
% 0.88/1.23 FOF formula (forall (X_14:real), (((eq real) ((power_power_real X_14) one_one_nat)) X_14)) of role axiom named fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J
% 0.88/1.23 A new axiom: (forall (X_14:real), (((eq real) ((power_power_real X_14) one_one_nat)) X_14))
% 0.88/1.23 FOF formula (forall (X_14:nat), (((eq nat) ((power_power_nat X_14) one_one_nat)) X_14)) of role axiom named fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J
% 0.88/1.23 A new axiom: (forall (X_14:nat), (((eq nat) ((power_power_nat X_14) one_one_nat)) X_14))
% 0.88/1.23 FOF formula (forall (X_14:int), (((eq int) ((power_power_int X_14) one_one_nat)) X_14)) of role axiom named fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J
% 0.88/1.23 A new axiom: (forall (X_14:int), (((eq int) ((power_power_int X_14) one_one_nat)) X_14))
% 0.88/1.23 FOF formula (forall (X:nat) (W:int), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) (number_number_of_nat W)))) ((or (((eq nat) (number_number_of_nat W)) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X)))) of role axiom named fact_352_zero__less__power__nat__eq__number__of
% 0.88/1.23 A new axiom: (forall (X:nat) (W:int), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) (number_number_of_nat W)))) ((or (((eq nat) (number_number_of_nat W)) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X))))
% 0.88/1.23 FOF formula (forall (Z:nat), (((eq nat) ((times_times_nat Z) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z) Z))) of role axiom named fact_353_nat__mult__2__right
% 0.88/1.23 A new axiom: (forall (Z:nat), (((eq nat) ((times_times_nat Z) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z) Z)))
% 0.88/1.23 FOF formula (forall (Z:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z)) ((plus_plus_nat Z) Z))) of role axiom named fact_354_nat__mult__2
% 0.88/1.23 A new axiom: (forall (Z:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z)) ((plus_plus_nat Z) Z)))
% 0.88/1.23 FOF formula (forall (V_2:int) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((times_times_nat (number_number_of_nat V)) (number_number_of_nat V_2))) zero_zero_nat))) ((((ord_less_int V) pls)->False)->(((eq nat) ((times_times_nat (number_number_of_nat V)) (number_number_of_nat V_2))) (number_number_of_nat ((times_times_int V) V_2)))))) of role axiom named fact_355_mult__nat__number__of
% 0.88/1.24 A new axiom: (forall (V_2:int) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((times_times_nat (number_number_of_nat V)) (number_number_of_nat V_2))) zero_zero_nat))) ((((ord_less_int V) pls)->False)->(((eq nat) ((times_times_nat (number_number_of_nat V)) (number_number_of_nat V_2))) (number_number_of_nat ((times_times_int V) V_2))))))
% 0.88/1.24 FOF formula (forall (V_2:int) (K:nat) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((times_times_nat (number_number_of_nat V)) ((times_times_nat (number_number_of_nat V_2)) K))) zero_zero_nat))) ((((ord_less_int V) pls)->False)->(((eq nat) ((times_times_nat (number_number_of_nat V)) ((times_times_nat (number_number_of_nat V_2)) K))) ((times_times_nat (number_number_of_nat ((times_times_int V) V_2))) K))))) of role axiom named fact_356_nat__number__of__mult__left
% 0.88/1.24 A new axiom: (forall (V_2:int) (K:nat) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((times_times_nat (number_number_of_nat V)) ((times_times_nat (number_number_of_nat V_2)) K))) zero_zero_nat))) ((((ord_less_int V) pls)->False)->(((eq nat) ((times_times_nat (number_number_of_nat V)) ((times_times_nat (number_number_of_nat V_2)) K))) ((times_times_nat (number_number_of_nat ((times_times_int V) V_2))) K)))))
% 0.88/1.24 FOF formula (forall (A_108:real) (N_24:nat), (((eq real) ((power_power_real A_108) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_24))) ((power_power_real ((power_power_real A_108) N_24)) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_357_power__even__eq
% 0.88/1.24 A new axiom: (forall (A_108:real) (N_24:nat), (((eq real) ((power_power_real A_108) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_24))) ((power_power_real ((power_power_real A_108) N_24)) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.88/1.24 FOF formula (forall (A_108:nat) (N_24:nat), (((eq nat) ((power_power_nat A_108) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_24))) ((power_power_nat ((power_power_nat A_108) N_24)) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_358_power__even__eq
% 0.88/1.24 A new axiom: (forall (A_108:nat) (N_24:nat), (((eq nat) ((power_power_nat A_108) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_24))) ((power_power_nat ((power_power_nat A_108) N_24)) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.88/1.24 FOF formula (forall (A_108:int) (N_24:nat), (((eq int) ((power_power_int A_108) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_24))) ((power_power_int ((power_power_int A_108) N_24)) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_359_power__even__eq
% 0.88/1.24 A new axiom: (forall (A_108:int) (N_24:nat), (((eq int) ((power_power_int A_108) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_24))) ((power_power_int ((power_power_int A_108) N_24)) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.88/1.24 FOF formula (forall (A_107:real) (K_3:nat), (((ord_less_eq_real ((power_power_real A_107) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_3))) zero_zero_real)->(((eq real) A_107) zero_zero_real))) of role axiom named fact_360_even__power__le__0__imp__0
% 0.88/1.24 A new axiom: (forall (A_107:real) (K_3:nat), (((ord_less_eq_real ((power_power_real A_107) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_3))) zero_zero_real)->(((eq real) A_107) zero_zero_real)))
% 0.88/1.24 FOF formula (forall (A_107:int) (K_3:nat), (((ord_less_eq_int ((power_power_int A_107) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_3))) zero_zero_int)->(((eq int) A_107) zero_zero_int))) of role axiom named fact_361_even__power__le__0__imp__0
% 0.88/1.24 A new axiom: (forall (A_107:int) (K_3:nat), (((ord_less_eq_int ((power_power_int A_107) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_3))) zero_zero_int)->(((eq int) A_107) zero_zero_int)))
% 0.88/1.24 FOF formula (forall (A_106:real), (((eq real) ((times_times_real zero_zero_real) A_106)) zero_zero_real)) of role axiom named fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J
% 0.88/1.25 A new axiom: (forall (A_106:real), (((eq real) ((times_times_real zero_zero_real) A_106)) zero_zero_real))
% 0.88/1.25 FOF formula (forall (A_106:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_106)) zero_zero_nat)) of role axiom named fact_363_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J
% 0.88/1.25 A new axiom: (forall (A_106:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_106)) zero_zero_nat))
% 0.88/1.25 FOF formula (forall (A_106:int), (((eq int) ((times_times_int zero_zero_int) A_106)) zero_zero_int)) of role axiom named fact_364_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J
% 0.88/1.25 A new axiom: (forall (A_106:int), (((eq int) ((times_times_int zero_zero_int) A_106)) zero_zero_int))
% 0.88/1.25 FOF formula (forall (A_105:real), (((eq real) ((times_times_real A_105) zero_zero_real)) zero_zero_real)) of role axiom named fact_365_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J
% 0.88/1.25 A new axiom: (forall (A_105:real), (((eq real) ((times_times_real A_105) zero_zero_real)) zero_zero_real))
% 0.88/1.25 FOF formula (forall (A_105:nat), (((eq nat) ((times_times_nat A_105) zero_zero_nat)) zero_zero_nat)) of role axiom named fact_366_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J
% 0.88/1.25 A new axiom: (forall (A_105:nat), (((eq nat) ((times_times_nat A_105) zero_zero_nat)) zero_zero_nat))
% 0.88/1.25 FOF formula (forall (A_105:int), (((eq int) ((times_times_int A_105) zero_zero_int)) zero_zero_int)) of role axiom named fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J
% 0.88/1.25 A new axiom: (forall (A_105:int), (((eq int) ((times_times_int A_105) zero_zero_int)) zero_zero_int))
% 0.88/1.25 FOF formula (forall (A_104:real), (((eq real) ((plus_plus_real zero_zero_real) A_104)) A_104)) of role axiom named fact_368_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J
% 0.88/1.25 A new axiom: (forall (A_104:real), (((eq real) ((plus_plus_real zero_zero_real) A_104)) A_104))
% 0.88/1.25 FOF formula (forall (A_104:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_104)) A_104)) of role axiom named fact_369_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J
% 0.88/1.25 A new axiom: (forall (A_104:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_104)) A_104))
% 0.88/1.25 FOF formula (forall (A_104:int), (((eq int) ((plus_plus_int zero_zero_int) A_104)) A_104)) of role axiom named fact_370_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J
% 0.88/1.25 A new axiom: (forall (A_104:int), (((eq int) ((plus_plus_int zero_zero_int) A_104)) A_104))
% 0.88/1.25 FOF formula (forall (A_103:real), (((eq real) ((plus_plus_real A_103) zero_zero_real)) A_103)) of role axiom named fact_371_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J
% 0.88/1.25 A new axiom: (forall (A_103:real), (((eq real) ((plus_plus_real A_103) zero_zero_real)) A_103))
% 0.88/1.25 FOF formula (forall (A_103:nat), (((eq nat) ((plus_plus_nat A_103) zero_zero_nat)) A_103)) of role axiom named fact_372_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J
% 0.88/1.25 A new axiom: (forall (A_103:nat), (((eq nat) ((plus_plus_nat A_103) zero_zero_nat)) A_103))
% 0.88/1.25 FOF formula (forall (A_103:int), (((eq int) ((plus_plus_int A_103) zero_zero_int)) A_103)) of role axiom named fact_373_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J
% 0.88/1.25 A new axiom: (forall (A_103:int), (((eq int) ((plus_plus_int A_103) zero_zero_int)) A_103))
% 0.88/1.25 FOF formula (forall (B_74:real) (A_102:real), ((iff (((eq real) B_74) ((plus_plus_real B_74) A_102))) (((eq real) A_102) zero_zero_real))) of role axiom named fact_374_add__0__iff
% 0.88/1.25 A new axiom: (forall (B_74:real) (A_102:real), ((iff (((eq real) B_74) ((plus_plus_real B_74) A_102))) (((eq real) A_102) zero_zero_real)))
% 0.88/1.25 FOF formula (forall (B_74:nat) (A_102:nat), ((iff (((eq nat) B_74) ((plus_plus_nat B_74) A_102))) (((eq nat) A_102) zero_zero_nat))) of role axiom named fact_375_add__0__iff
% 0.88/1.25 A new axiom: (forall (B_74:nat) (A_102:nat), ((iff (((eq nat) B_74) ((plus_plus_nat B_74) A_102))) (((eq nat) A_102) zero_zero_nat)))
% 0.88/1.25 FOF formula (forall (B_74:int) (A_102:int), ((iff (((eq int) B_74) ((plus_plus_int B_74) A_102))) (((eq int) A_102) zero_zero_int))) of role axiom named fact_376_add__0__iff
% 0.88/1.27 A new axiom: (forall (B_74:int) (A_102:int), ((iff (((eq int) B_74) ((plus_plus_int B_74) A_102))) (((eq int) A_102) zero_zero_int)))
% 0.88/1.27 FOF formula (forall (X_13:real) (Y_11:real) (Z_2:real), (((eq real) ((times_times_real X_13) ((plus_plus_real Y_11) Z_2))) ((plus_plus_real ((times_times_real X_13) Y_11)) ((times_times_real X_13) Z_2)))) of role axiom named fact_377_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J
% 0.88/1.27 A new axiom: (forall (X_13:real) (Y_11:real) (Z_2:real), (((eq real) ((times_times_real X_13) ((plus_plus_real Y_11) Z_2))) ((plus_plus_real ((times_times_real X_13) Y_11)) ((times_times_real X_13) Z_2))))
% 0.88/1.27 FOF formula (forall (X_13:nat) (Y_11:nat) (Z_2:nat), (((eq nat) ((times_times_nat X_13) ((plus_plus_nat Y_11) Z_2))) ((plus_plus_nat ((times_times_nat X_13) Y_11)) ((times_times_nat X_13) Z_2)))) of role axiom named fact_378_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J
% 0.88/1.27 A new axiom: (forall (X_13:nat) (Y_11:nat) (Z_2:nat), (((eq nat) ((times_times_nat X_13) ((plus_plus_nat Y_11) Z_2))) ((plus_plus_nat ((times_times_nat X_13) Y_11)) ((times_times_nat X_13) Z_2))))
% 0.88/1.27 FOF formula (forall (X_13:int) (Y_11:int) (Z_2:int), (((eq int) ((times_times_int X_13) ((plus_plus_int Y_11) Z_2))) ((plus_plus_int ((times_times_int X_13) Y_11)) ((times_times_int X_13) Z_2)))) of role axiom named fact_379_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J
% 0.88/1.27 A new axiom: (forall (X_13:int) (Y_11:int) (Z_2:int), (((eq int) ((times_times_int X_13) ((plus_plus_int Y_11) Z_2))) ((plus_plus_int ((times_times_int X_13) Y_11)) ((times_times_int X_13) Z_2))))
% 0.88/1.27 FOF formula (forall (C_43:real) (D_11:real) (A_101:real) (B_73:real), ((iff ((and (not (((eq real) A_101) B_73))) (not (((eq real) C_43) D_11)))) (not (((eq real) ((plus_plus_real ((times_times_real A_101) C_43)) ((times_times_real B_73) D_11))) ((plus_plus_real ((times_times_real A_101) D_11)) ((times_times_real B_73) C_43)))))) of role axiom named fact_380_crossproduct__noteq
% 0.88/1.27 A new axiom: (forall (C_43:real) (D_11:real) (A_101:real) (B_73:real), ((iff ((and (not (((eq real) A_101) B_73))) (not (((eq real) C_43) D_11)))) (not (((eq real) ((plus_plus_real ((times_times_real A_101) C_43)) ((times_times_real B_73) D_11))) ((plus_plus_real ((times_times_real A_101) D_11)) ((times_times_real B_73) C_43))))))
% 0.88/1.27 FOF formula (forall (C_43:nat) (D_11:nat) (A_101:nat) (B_73:nat), ((iff ((and (not (((eq nat) A_101) B_73))) (not (((eq nat) C_43) D_11)))) (not (((eq nat) ((plus_plus_nat ((times_times_nat A_101) C_43)) ((times_times_nat B_73) D_11))) ((plus_plus_nat ((times_times_nat A_101) D_11)) ((times_times_nat B_73) C_43)))))) of role axiom named fact_381_crossproduct__noteq
% 0.88/1.27 A new axiom: (forall (C_43:nat) (D_11:nat) (A_101:nat) (B_73:nat), ((iff ((and (not (((eq nat) A_101) B_73))) (not (((eq nat) C_43) D_11)))) (not (((eq nat) ((plus_plus_nat ((times_times_nat A_101) C_43)) ((times_times_nat B_73) D_11))) ((plus_plus_nat ((times_times_nat A_101) D_11)) ((times_times_nat B_73) C_43))))))
% 0.88/1.27 FOF formula (forall (C_43:int) (D_11:int) (A_101:int) (B_73:int), ((iff ((and (not (((eq int) A_101) B_73))) (not (((eq int) C_43) D_11)))) (not (((eq int) ((plus_plus_int ((times_times_int A_101) C_43)) ((times_times_int B_73) D_11))) ((plus_plus_int ((times_times_int A_101) D_11)) ((times_times_int B_73) C_43)))))) of role axiom named fact_382_crossproduct__noteq
% 0.88/1.27 A new axiom: (forall (C_43:int) (D_11:int) (A_101:int) (B_73:int), ((iff ((and (not (((eq int) A_101) B_73))) (not (((eq int) C_43) D_11)))) (not (((eq int) ((plus_plus_int ((times_times_int A_101) C_43)) ((times_times_int B_73) D_11))) ((plus_plus_int ((times_times_int A_101) D_11)) ((times_times_int B_73) C_43))))))
% 0.88/1.27 FOF formula (forall (A_100:real) (B_72:real) (C_42:real), (((eq real) ((times_times_real ((plus_plus_real A_100) B_72)) C_42)) ((plus_plus_real ((times_times_real A_100) C_42)) ((times_times_real B_72) C_42)))) of role axiom named fact_383_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J
% 0.88/1.27 A new axiom: (forall (A_100:real) (B_72:real) (C_42:real), (((eq real) ((times_times_real ((plus_plus_real A_100) B_72)) C_42)) ((plus_plus_real ((times_times_real A_100) C_42)) ((times_times_real B_72) C_42))))
% 0.88/1.29 FOF formula (forall (A_100:nat) (B_72:nat) (C_42:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_100) B_72)) C_42)) ((plus_plus_nat ((times_times_nat A_100) C_42)) ((times_times_nat B_72) C_42)))) of role axiom named fact_384_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J
% 0.88/1.29 A new axiom: (forall (A_100:nat) (B_72:nat) (C_42:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_100) B_72)) C_42)) ((plus_plus_nat ((times_times_nat A_100) C_42)) ((times_times_nat B_72) C_42))))
% 0.88/1.29 FOF formula (forall (A_100:int) (B_72:int) (C_42:int), (((eq int) ((times_times_int ((plus_plus_int A_100) B_72)) C_42)) ((plus_plus_int ((times_times_int A_100) C_42)) ((times_times_int B_72) C_42)))) of role axiom named fact_385_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J
% 0.88/1.29 A new axiom: (forall (A_100:int) (B_72:int) (C_42:int), (((eq int) ((times_times_int ((plus_plus_int A_100) B_72)) C_42)) ((plus_plus_int ((times_times_int A_100) C_42)) ((times_times_int B_72) C_42))))
% 0.88/1.29 FOF formula (forall (A_99:real) (M_13:real) (B_71:real), (((eq real) ((plus_plus_real ((times_times_real A_99) M_13)) ((times_times_real B_71) M_13))) ((times_times_real ((plus_plus_real A_99) B_71)) M_13))) of role axiom named fact_386_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J
% 0.88/1.29 A new axiom: (forall (A_99:real) (M_13:real) (B_71:real), (((eq real) ((plus_plus_real ((times_times_real A_99) M_13)) ((times_times_real B_71) M_13))) ((times_times_real ((plus_plus_real A_99) B_71)) M_13)))
% 0.88/1.29 FOF formula (forall (A_99:nat) (M_13:nat) (B_71:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_99) M_13)) ((times_times_nat B_71) M_13))) ((times_times_nat ((plus_plus_nat A_99) B_71)) M_13))) of role axiom named fact_387_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J
% 0.88/1.29 A new axiom: (forall (A_99:nat) (M_13:nat) (B_71:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_99) M_13)) ((times_times_nat B_71) M_13))) ((times_times_nat ((plus_plus_nat A_99) B_71)) M_13)))
% 0.88/1.29 FOF formula (forall (A_99:int) (M_13:int) (B_71:int), (((eq int) ((plus_plus_int ((times_times_int A_99) M_13)) ((times_times_int B_71) M_13))) ((times_times_int ((plus_plus_int A_99) B_71)) M_13))) of role axiom named fact_388_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J
% 0.88/1.29 A new axiom: (forall (A_99:int) (M_13:int) (B_71:int), (((eq int) ((plus_plus_int ((times_times_int A_99) M_13)) ((times_times_int B_71) M_13))) ((times_times_int ((plus_plus_int A_99) B_71)) M_13)))
% 0.88/1.29 FOF formula (forall (W_3:real) (Y_10:real) (X_12:real) (Z_1:real), ((iff (((eq real) ((plus_plus_real ((times_times_real W_3) Y_10)) ((times_times_real X_12) Z_1))) ((plus_plus_real ((times_times_real W_3) Z_1)) ((times_times_real X_12) Y_10)))) ((or (((eq real) W_3) X_12)) (((eq real) Y_10) Z_1)))) of role axiom named fact_389_crossproduct__eq
% 0.88/1.29 A new axiom: (forall (W_3:real) (Y_10:real) (X_12:real) (Z_1:real), ((iff (((eq real) ((plus_plus_real ((times_times_real W_3) Y_10)) ((times_times_real X_12) Z_1))) ((plus_plus_real ((times_times_real W_3) Z_1)) ((times_times_real X_12) Y_10)))) ((or (((eq real) W_3) X_12)) (((eq real) Y_10) Z_1))))
% 0.88/1.29 FOF formula (forall (W_3:nat) (Y_10:nat) (X_12:nat) (Z_1:nat), ((iff (((eq nat) ((plus_plus_nat ((times_times_nat W_3) Y_10)) ((times_times_nat X_12) Z_1))) ((plus_plus_nat ((times_times_nat W_3) Z_1)) ((times_times_nat X_12) Y_10)))) ((or (((eq nat) W_3) X_12)) (((eq nat) Y_10) Z_1)))) of role axiom named fact_390_crossproduct__eq
% 0.88/1.29 A new axiom: (forall (W_3:nat) (Y_10:nat) (X_12:nat) (Z_1:nat), ((iff (((eq nat) ((plus_plus_nat ((times_times_nat W_3) Y_10)) ((times_times_nat X_12) Z_1))) ((plus_plus_nat ((times_times_nat W_3) Z_1)) ((times_times_nat X_12) Y_10)))) ((or (((eq nat) W_3) X_12)) (((eq nat) Y_10) Z_1))))
% 0.88/1.29 FOF formula (forall (W_3:int) (Y_10:int) (X_12:int) (Z_1:int), ((iff (((eq int) ((plus_plus_int ((times_times_int W_3) Y_10)) ((times_times_int X_12) Z_1))) ((plus_plus_int ((times_times_int W_3) Z_1)) ((times_times_int X_12) Y_10)))) ((or (((eq int) W_3) X_12)) (((eq int) Y_10) Z_1)))) of role axiom named fact_391_crossproduct__eq
% 0.88/1.30 A new axiom: (forall (W_3:int) (Y_10:int) (X_12:int) (Z_1:int), ((iff (((eq int) ((plus_plus_int ((times_times_int W_3) Y_10)) ((times_times_int X_12) Z_1))) ((plus_plus_int ((times_times_int W_3) Z_1)) ((times_times_int X_12) Y_10)))) ((or (((eq int) W_3) X_12)) (((eq int) Y_10) Z_1))))
% 0.88/1.30 FOF formula (forall (A_98:real), (((eq real) ((times_times_real one_one_real) A_98)) A_98)) of role axiom named fact_392_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J
% 0.88/1.30 A new axiom: (forall (A_98:real), (((eq real) ((times_times_real one_one_real) A_98)) A_98))
% 0.88/1.30 FOF formula (forall (A_98:nat), (((eq nat) ((times_times_nat one_one_nat) A_98)) A_98)) of role axiom named fact_393_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J
% 0.88/1.30 A new axiom: (forall (A_98:nat), (((eq nat) ((times_times_nat one_one_nat) A_98)) A_98))
% 0.88/1.30 FOF formula (forall (A_98:int), (((eq int) ((times_times_int one_one_int) A_98)) A_98)) of role axiom named fact_394_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J
% 0.88/1.30 A new axiom: (forall (A_98:int), (((eq int) ((times_times_int one_one_int) A_98)) A_98))
% 0.88/1.30 FOF formula (forall (A_97:real), (((eq real) ((times_times_real A_97) one_one_real)) A_97)) of role axiom named fact_395_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J
% 0.88/1.30 A new axiom: (forall (A_97:real), (((eq real) ((times_times_real A_97) one_one_real)) A_97))
% 0.88/1.30 FOF formula (forall (A_97:nat), (((eq nat) ((times_times_nat A_97) one_one_nat)) A_97)) of role axiom named fact_396_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J
% 0.88/1.30 A new axiom: (forall (A_97:nat), (((eq nat) ((times_times_nat A_97) one_one_nat)) A_97))
% 0.88/1.30 FOF formula (forall (A_97:int), (((eq int) ((times_times_int A_97) one_one_int)) A_97)) of role axiom named fact_397_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J
% 0.88/1.30 A new axiom: (forall (A_97:int), (((eq int) ((times_times_int A_97) one_one_int)) A_97))
% 0.88/1.30 FOF formula (forall (X_11:real) (Y_9:real) (Q_5:nat), (((eq real) ((power_power_real ((times_times_real X_11) Y_9)) Q_5)) ((times_times_real ((power_power_real X_11) Q_5)) ((power_power_real Y_9) Q_5)))) of role axiom named fact_398_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J
% 0.88/1.30 A new axiom: (forall (X_11:real) (Y_9:real) (Q_5:nat), (((eq real) ((power_power_real ((times_times_real X_11) Y_9)) Q_5)) ((times_times_real ((power_power_real X_11) Q_5)) ((power_power_real Y_9) Q_5))))
% 0.88/1.30 FOF formula (forall (X_11:nat) (Y_9:nat) (Q_5:nat), (((eq nat) ((power_power_nat ((times_times_nat X_11) Y_9)) Q_5)) ((times_times_nat ((power_power_nat X_11) Q_5)) ((power_power_nat Y_9) Q_5)))) of role axiom named fact_399_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J
% 0.88/1.30 A new axiom: (forall (X_11:nat) (Y_9:nat) (Q_5:nat), (((eq nat) ((power_power_nat ((times_times_nat X_11) Y_9)) Q_5)) ((times_times_nat ((power_power_nat X_11) Q_5)) ((power_power_nat Y_9) Q_5))))
% 0.88/1.30 FOF formula (forall (X_11:int) (Y_9:int) (Q_5:nat), (((eq int) ((power_power_int ((times_times_int X_11) Y_9)) Q_5)) ((times_times_int ((power_power_int X_11) Q_5)) ((power_power_int Y_9) Q_5)))) of role axiom named fact_400_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J
% 0.88/1.30 A new axiom: (forall (X_11:int) (Y_9:int) (Q_5:nat), (((eq int) ((power_power_int ((times_times_int X_11) Y_9)) Q_5)) ((times_times_int ((power_power_int X_11) Q_5)) ((power_power_int Y_9) Q_5))))
% 0.88/1.30 FOF formula (forall (X_10:real) (P_4:nat) (Q_4:nat), (((eq real) ((times_times_real ((power_power_real X_10) P_4)) ((power_power_real X_10) Q_4))) ((power_power_real X_10) ((plus_plus_nat P_4) Q_4)))) of role axiom named fact_401_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J
% 0.88/1.30 A new axiom: (forall (X_10:real) (P_4:nat) (Q_4:nat), (((eq real) ((times_times_real ((power_power_real X_10) P_4)) ((power_power_real X_10) Q_4))) ((power_power_real X_10) ((plus_plus_nat P_4) Q_4))))
% 0.88/1.30 FOF formula (forall (X_10:nat) (P_4:nat) (Q_4:nat), (((eq nat) ((times_times_nat ((power_power_nat X_10) P_4)) ((power_power_nat X_10) Q_4))) ((power_power_nat X_10) ((plus_plus_nat P_4) Q_4)))) of role axiom named fact_402_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J
% 0.97/1.32 A new axiom: (forall (X_10:nat) (P_4:nat) (Q_4:nat), (((eq nat) ((times_times_nat ((power_power_nat X_10) P_4)) ((power_power_nat X_10) Q_4))) ((power_power_nat X_10) ((plus_plus_nat P_4) Q_4))))
% 0.97/1.32 FOF formula (forall (X_10:int) (P_4:nat) (Q_4:nat), (((eq int) ((times_times_int ((power_power_int X_10) P_4)) ((power_power_int X_10) Q_4))) ((power_power_int X_10) ((plus_plus_nat P_4) Q_4)))) of role axiom named fact_403_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J
% 0.97/1.32 A new axiom: (forall (X_10:int) (P_4:nat) (Q_4:nat), (((eq int) ((times_times_int ((power_power_int X_10) P_4)) ((power_power_int X_10) Q_4))) ((power_power_int X_10) ((plus_plus_nat P_4) Q_4))))
% 0.97/1.32 FOF formula (forall (X_9:real), (((eq real) ((power_power_real X_9) zero_zero_nat)) one_one_real)) of role axiom named fact_404_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J
% 0.97/1.32 A new axiom: (forall (X_9:real), (((eq real) ((power_power_real X_9) zero_zero_nat)) one_one_real))
% 0.97/1.32 FOF formula (forall (X_9:nat), (((eq nat) ((power_power_nat X_9) zero_zero_nat)) one_one_nat)) of role axiom named fact_405_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J
% 0.97/1.32 A new axiom: (forall (X_9:nat), (((eq nat) ((power_power_nat X_9) zero_zero_nat)) one_one_nat))
% 0.97/1.32 FOF formula (forall (X_9:int), (((eq int) ((power_power_int X_9) zero_zero_nat)) one_one_int)) of role axiom named fact_406_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J
% 0.97/1.32 A new axiom: (forall (X_9:int), (((eq int) ((power_power_int X_9) zero_zero_nat)) one_one_int))
% 0.97/1.32 FOF formula ((ord_less_eq_int zero_zero_int) zero_zero_int) of role axiom named fact_407_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J
% 0.97/1.32 A new axiom: ((ord_less_eq_int zero_zero_int) zero_zero_int)
% 0.97/1.32 FOF formula (forall (A_96:real) (N_23:nat), ((ord_less_eq_real zero_zero_real) ((power_power_real A_96) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_23)))) of role axiom named fact_408_zero__le__even__power_H
% 0.97/1.32 A new axiom: (forall (A_96:real) (N_23:nat), ((ord_less_eq_real zero_zero_real) ((power_power_real A_96) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_23))))
% 0.97/1.32 FOF formula (forall (A_96:int) (N_23:nat), ((ord_less_eq_int zero_zero_int) ((power_power_int A_96) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_23)))) of role axiom named fact_409_zero__le__even__power_H
% 0.97/1.32 A new axiom: (forall (A_96:int) (N_23:nat), ((ord_less_eq_int zero_zero_int) ((power_power_int A_96) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_23))))
% 0.97/1.32 FOF formula (forall (C_41:real) (D_10:real) (A_95:real) (B_70:real) (R_3:real), ((not (((eq real) R_3) zero_zero_real))->(((and (((eq real) A_95) B_70)) (not (((eq real) C_41) D_10)))->(not (((eq real) ((plus_plus_real A_95) ((times_times_real R_3) C_41))) ((plus_plus_real B_70) ((times_times_real R_3) D_10))))))) of role axiom named fact_410_add__scale__eq__noteq
% 0.97/1.32 A new axiom: (forall (C_41:real) (D_10:real) (A_95:real) (B_70:real) (R_3:real), ((not (((eq real) R_3) zero_zero_real))->(((and (((eq real) A_95) B_70)) (not (((eq real) C_41) D_10)))->(not (((eq real) ((plus_plus_real A_95) ((times_times_real R_3) C_41))) ((plus_plus_real B_70) ((times_times_real R_3) D_10)))))))
% 0.97/1.32 FOF formula (forall (C_41:nat) (D_10:nat) (A_95:nat) (B_70:nat) (R_3:nat), ((not (((eq nat) R_3) zero_zero_nat))->(((and (((eq nat) A_95) B_70)) (not (((eq nat) C_41) D_10)))->(not (((eq nat) ((plus_plus_nat A_95) ((times_times_nat R_3) C_41))) ((plus_plus_nat B_70) ((times_times_nat R_3) D_10))))))) of role axiom named fact_411_add__scale__eq__noteq
% 0.97/1.32 A new axiom: (forall (C_41:nat) (D_10:nat) (A_95:nat) (B_70:nat) (R_3:nat), ((not (((eq nat) R_3) zero_zero_nat))->(((and (((eq nat) A_95) B_70)) (not (((eq nat) C_41) D_10)))->(not (((eq nat) ((plus_plus_nat A_95) ((times_times_nat R_3) C_41))) ((plus_plus_nat B_70) ((times_times_nat R_3) D_10)))))))
% 0.97/1.32 FOF formula (forall (C_41:int) (D_10:int) (A_95:int) (B_70:int) (R_3:int), ((not (((eq int) R_3) zero_zero_int))->(((and (((eq int) A_95) B_70)) (not (((eq int) C_41) D_10)))->(not (((eq int) ((plus_plus_int A_95) ((times_times_int R_3) C_41))) ((plus_plus_int B_70) ((times_times_int R_3) D_10))))))) of role axiom named fact_412_add__scale__eq__noteq
% 0.97/1.33 A new axiom: (forall (C_41:int) (D_10:int) (A_95:int) (B_70:int) (R_3:int), ((not (((eq int) R_3) zero_zero_int))->(((and (((eq int) A_95) B_70)) (not (((eq int) C_41) D_10)))->(not (((eq int) ((plus_plus_int A_95) ((times_times_int R_3) C_41))) ((plus_plus_int B_70) ((times_times_int R_3) D_10)))))))
% 0.97/1.33 FOF formula (forall (M_12:real), (((eq real) ((plus_plus_real M_12) M_12)) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) M_12))) of role axiom named fact_413_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J
% 0.97/1.33 A new axiom: (forall (M_12:real), (((eq real) ((plus_plus_real M_12) M_12)) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) M_12)))
% 0.97/1.33 FOF formula (forall (M_12:nat), (((eq nat) ((plus_plus_nat M_12) M_12)) ((times_times_nat ((plus_plus_nat one_one_nat) one_one_nat)) M_12))) of role axiom named fact_414_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J
% 0.97/1.33 A new axiom: (forall (M_12:nat), (((eq nat) ((plus_plus_nat M_12) M_12)) ((times_times_nat ((plus_plus_nat one_one_nat) one_one_nat)) M_12)))
% 0.97/1.33 FOF formula (forall (M_12:int), (((eq int) ((plus_plus_int M_12) M_12)) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) M_12))) of role axiom named fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J
% 0.97/1.33 A new axiom: (forall (M_12:int), (((eq int) ((plus_plus_int M_12) M_12)) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) M_12)))
% 0.97/1.33 FOF formula (forall (M_11:real) (A_94:real), (((eq real) ((plus_plus_real M_11) ((times_times_real A_94) M_11))) ((times_times_real ((plus_plus_real A_94) one_one_real)) M_11))) of role axiom named fact_416_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J
% 0.97/1.33 A new axiom: (forall (M_11:real) (A_94:real), (((eq real) ((plus_plus_real M_11) ((times_times_real A_94) M_11))) ((times_times_real ((plus_plus_real A_94) one_one_real)) M_11)))
% 0.97/1.33 FOF formula (forall (M_11:nat) (A_94:nat), (((eq nat) ((plus_plus_nat M_11) ((times_times_nat A_94) M_11))) ((times_times_nat ((plus_plus_nat A_94) one_one_nat)) M_11))) of role axiom named fact_417_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J
% 0.97/1.33 A new axiom: (forall (M_11:nat) (A_94:nat), (((eq nat) ((plus_plus_nat M_11) ((times_times_nat A_94) M_11))) ((times_times_nat ((plus_plus_nat A_94) one_one_nat)) M_11)))
% 0.97/1.33 FOF formula (forall (M_11:int) (A_94:int), (((eq int) ((plus_plus_int M_11) ((times_times_int A_94) M_11))) ((times_times_int ((plus_plus_int A_94) one_one_int)) M_11))) of role axiom named fact_418_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J
% 0.97/1.33 A new axiom: (forall (M_11:int) (A_94:int), (((eq int) ((plus_plus_int M_11) ((times_times_int A_94) M_11))) ((times_times_int ((plus_plus_int A_94) one_one_int)) M_11)))
% 0.97/1.33 FOF formula (forall (A_93:real) (M_10:real), (((eq real) ((plus_plus_real ((times_times_real A_93) M_10)) M_10)) ((times_times_real ((plus_plus_real A_93) one_one_real)) M_10))) of role axiom named fact_419_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J
% 0.97/1.33 A new axiom: (forall (A_93:real) (M_10:real), (((eq real) ((plus_plus_real ((times_times_real A_93) M_10)) M_10)) ((times_times_real ((plus_plus_real A_93) one_one_real)) M_10)))
% 0.97/1.33 FOF formula (forall (A_93:nat) (M_10:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_93) M_10)) M_10)) ((times_times_nat ((plus_plus_nat A_93) one_one_nat)) M_10))) of role axiom named fact_420_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J
% 0.97/1.33 A new axiom: (forall (A_93:nat) (M_10:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_93) M_10)) M_10)) ((times_times_nat ((plus_plus_nat A_93) one_one_nat)) M_10)))
% 0.97/1.33 FOF formula (forall (A_93:int) (M_10:int), (((eq int) ((plus_plus_int ((times_times_int A_93) M_10)) M_10)) ((times_times_int ((plus_plus_int A_93) one_one_int)) M_10))) of role axiom named fact_421_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J
% 0.97/1.35 A new axiom: (forall (A_93:int) (M_10:int), (((eq int) ((plus_plus_int ((times_times_int A_93) M_10)) M_10)) ((times_times_int ((plus_plus_int A_93) one_one_int)) M_10)))
% 0.97/1.35 FOF formula (forall (A_92:real) (W_2:int), ((iff (((eq real) ((power_power_real A_92) (number_number_of_nat W_2))) zero_zero_real)) ((and (((eq real) A_92) zero_zero_real)) (not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat))))) of role axiom named fact_422_power__eq__0__iff__number__of
% 0.97/1.35 A new axiom: (forall (A_92:real) (W_2:int), ((iff (((eq real) ((power_power_real A_92) (number_number_of_nat W_2))) zero_zero_real)) ((and (((eq real) A_92) zero_zero_real)) (not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat)))))
% 0.97/1.35 FOF formula (forall (A_92:nat) (W_2:int), ((iff (((eq nat) ((power_power_nat A_92) (number_number_of_nat W_2))) zero_zero_nat)) ((and (((eq nat) A_92) zero_zero_nat)) (not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat))))) of role axiom named fact_423_power__eq__0__iff__number__of
% 0.97/1.35 A new axiom: (forall (A_92:nat) (W_2:int), ((iff (((eq nat) ((power_power_nat A_92) (number_number_of_nat W_2))) zero_zero_nat)) ((and (((eq nat) A_92) zero_zero_nat)) (not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat)))))
% 0.97/1.35 FOF formula (forall (A_92:int) (W_2:int), ((iff (((eq int) ((power_power_int A_92) (number_number_of_nat W_2))) zero_zero_int)) ((and (((eq int) A_92) zero_zero_int)) (not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat))))) of role axiom named fact_424_power__eq__0__iff__number__of
% 0.97/1.35 A new axiom: (forall (A_92:int) (W_2:int), ((iff (((eq int) ((power_power_int A_92) (number_number_of_nat W_2))) zero_zero_int)) ((and (((eq int) A_92) zero_zero_int)) (not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat)))))
% 0.97/1.35 FOF formula (forall (B:int) (A:int), (((ord_less_int zero_zero_int) A)->(((ord_less_int zero_zero_int) ((times_times_int A) B))->((ord_less_int zero_zero_int) B)))) of role axiom named fact_425_pos__zmult__pos
% 0.97/1.35 A new axiom: (forall (B:int) (A:int), (((ord_less_int zero_zero_int) A)->(((ord_less_int zero_zero_int) ((times_times_int A) B))->((ord_less_int zero_zero_int) B))))
% 0.97/1.35 FOF formula ((ord_less_eq_int zero_zero_int) one_one_int) of role axiom named fact_426_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J
% 0.97/1.35 A new axiom: ((ord_less_eq_int zero_zero_int) one_one_int)
% 0.97/1.35 FOF formula (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((times_times_int X) Y))))) of role axiom named fact_427_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J
% 0.97/1.35 A new axiom: (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((times_times_int X) Y)))))
% 0.97/1.35 FOF formula (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X) Y))))) of role axiom named fact_428_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J
% 0.97/1.35 A new axiom: (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X) Y)))))
% 0.97/1.35 FOF formula (forall (N:nat) (X:int), (((ord_less_eq_int zero_zero_int) X)->((ord_less_eq_int zero_zero_int) ((power_power_int X) N)))) of role axiom named fact_429_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J
% 0.97/1.35 A new axiom: (forall (N:nat) (X:int), (((ord_less_eq_int zero_zero_int) X)->((ord_less_eq_int zero_zero_int) ((power_power_int X) N))))
% 0.97/1.35 FOF formula (forall (W_1:int), ((and ((((eq nat) (number_number_of_nat W_1)) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_1))) one_one_real))) ((not (((eq nat) (number_number_of_nat W_1)) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_1))) zero_zero_real)))) of role axiom named fact_430_power__0__left__number__of
% 0.97/1.35 A new axiom: (forall (W_1:int), ((and ((((eq nat) (number_number_of_nat W_1)) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_1))) one_one_real))) ((not (((eq nat) (number_number_of_nat W_1)) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_1))) zero_zero_real))))
% 0.97/1.36 FOF formula (forall (W_1:int), ((and ((((eq nat) (number_number_of_nat W_1)) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_1))) one_one_nat))) ((not (((eq nat) (number_number_of_nat W_1)) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_1))) zero_zero_nat)))) of role axiom named fact_431_power__0__left__number__of
% 0.97/1.36 A new axiom: (forall (W_1:int), ((and ((((eq nat) (number_number_of_nat W_1)) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_1))) one_one_nat))) ((not (((eq nat) (number_number_of_nat W_1)) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_1))) zero_zero_nat))))
% 0.97/1.36 FOF formula (forall (W_1:int), ((and ((((eq nat) (number_number_of_nat W_1)) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_1))) one_one_int))) ((not (((eq nat) (number_number_of_nat W_1)) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_1))) zero_zero_int)))) of role axiom named fact_432_power__0__left__number__of
% 0.97/1.37 A new axiom: (forall (W_1:int), ((and ((((eq nat) (number_number_of_nat W_1)) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_1))) one_one_int))) ((not (((eq nat) (number_number_of_nat W_1)) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_1))) zero_zero_int))))
% 0.97/1.37 FOF formula ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 (bit1 pls)))) of role axiom named fact_433_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J
% 0.97/1.37 A new axiom: ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 (bit1 pls))))
% 0.97/1.37 FOF formula (forall (B_69:int) (Q_3:int) (R_2:int), (((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_69) Q_3)) R_2))->(((ord_less_int R_2) B_69)->(((ord_less_int zero_zero_int) B_69)->((ord_less_eq_int zero_zero_int) Q_3))))) of role axiom named fact_434_q__pos__lemma
% 0.97/1.37 A new axiom: (forall (B_69:int) (Q_3:int) (R_2:int), (((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_69) Q_3)) R_2))->(((ord_less_int R_2) B_69)->(((ord_less_int zero_zero_int) B_69)->((ord_less_eq_int zero_zero_int) Q_3)))))
% 0.97/1.37 FOF formula (forall (B_69:int) (Q_3:int) (R_2:int), (((ord_less_int ((plus_plus_int ((times_times_int B_69) Q_3)) R_2)) zero_zero_int)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B_69)->((ord_less_eq_int Q_3) zero_zero_int))))) of role axiom named fact_435_q__neg__lemma
% 0.97/1.37 A new axiom: (forall (B_69:int) (Q_3:int) (R_2:int), (((ord_less_int ((plus_plus_int ((times_times_int B_69) Q_3)) R_2)) zero_zero_int)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B_69)->((ord_less_eq_int Q_3) zero_zero_int)))))
% 0.97/1.37 FOF formula (forall (B:int) (Q_3:int) (R_2:int) (Q:int) (R:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B) Q_3)) R_2)) ((plus_plus_int ((times_times_int B) Q)) R))->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int R_2) B)->(((ord_less_int R) B)->((ord_less_eq_int Q_3) Q)))))) of role axiom named fact_436_unique__quotient__lemma
% 0.97/1.37 A new axiom: (forall (B:int) (Q_3:int) (R_2:int) (Q:int) (R:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B) Q_3)) R_2)) ((plus_plus_int ((times_times_int B) Q)) R))->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int R_2) B)->(((ord_less_int R) B)->((ord_less_eq_int Q_3) Q))))))
% 0.97/1.37 FOF formula (forall (B:int) (Q:int) (R:int) (B_69:int) (Q_3:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B) Q)) R)) ((plus_plus_int ((times_times_int B_69) Q_3)) R_2))->(((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_69) Q_3)) R_2))->(((ord_less_int R_2) B_69)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int zero_zero_int) B_69)->(((ord_less_eq_int B_69) B)->((ord_less_eq_int Q) Q_3)))))))) of role axiom named fact_437_zdiv__mono2__lemma
% 1.04/1.38 A new axiom: (forall (B:int) (Q:int) (R:int) (B_69:int) (Q_3:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B) Q)) R)) ((plus_plus_int ((times_times_int B_69) Q_3)) R_2))->(((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_69) Q_3)) R_2))->(((ord_less_int R_2) B_69)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int zero_zero_int) B_69)->(((ord_less_eq_int B_69) B)->((ord_less_eq_int Q) Q_3))))))))
% 1.04/1.38 FOF formula (forall (B:int) (Q_3:int) (R_2:int) (Q:int) (R:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B) Q_3)) R_2)) ((plus_plus_int ((times_times_int B) Q)) R))->(((ord_less_eq_int R) zero_zero_int)->(((ord_less_int B) R)->(((ord_less_int B) R_2)->((ord_less_eq_int Q) Q_3)))))) of role axiom named fact_438_unique__quotient__lemma__neg
% 1.04/1.38 A new axiom: (forall (B:int) (Q_3:int) (R_2:int) (Q:int) (R:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B) Q_3)) R_2)) ((plus_plus_int ((times_times_int B) Q)) R))->(((ord_less_eq_int R) zero_zero_int)->(((ord_less_int B) R)->(((ord_less_int B) R_2)->((ord_less_eq_int Q) Q_3))))))
% 1.04/1.38 FOF formula (forall (B:int) (Q:int) (R:int) (B_69:int) (Q_3:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B) Q)) R)) ((plus_plus_int ((times_times_int B_69) Q_3)) R_2))->(((ord_less_int ((plus_plus_int ((times_times_int B_69) Q_3)) R_2)) zero_zero_int)->(((ord_less_int R) B)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B_69)->(((ord_less_eq_int B_69) B)->((ord_less_eq_int Q_3) Q)))))))) of role axiom named fact_439_zdiv__mono2__neg__lemma
% 1.04/1.38 A new axiom: (forall (B:int) (Q:int) (R:int) (B_69:int) (Q_3:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B) Q)) R)) ((plus_plus_int ((times_times_int B_69) Q_3)) R_2))->(((ord_less_int ((plus_plus_int ((times_times_int B_69) Q_3)) R_2)) zero_zero_int)->(((ord_less_int R) B)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B_69)->(((ord_less_eq_int B_69) B)->((ord_less_eq_int Q_3) Q))))))))
% 1.04/1.38 FOF formula (forall (X:int), (((eq int) ((power_power_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int X) (number_number_of_nat (bit0 (bit0 (bit1 pls))))))) of role axiom named fact_440_quartic__square__square
% 1.04/1.38 A new axiom: (forall (X:int), (((eq int) ((power_power_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int X) (number_number_of_nat (bit0 (bit0 (bit1 pls)))))))
% 1.04/1.38 FOF formula (((zcong ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) of role axiom named fact_441_s
% 1.04/1.38 A new axiom: (((zcong ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))
% 1.04/1.38 FOF formula (forall (Y:int) (X:int) (P_1:int), (((((zcong X) zero_zero_int) P_1)->False)->((((zcong ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls))))) X) P_1)->(((dvd_dvd_int P_1) Y)->False)))) of role axiom named fact_442_Euler_Oaux____1
% 1.04/1.38 A new axiom: (forall (Y:int) (X:int) (P_1:int), (((((zcong X) zero_zero_int) P_1)->False)->((((zcong ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls))))) X) P_1)->(((dvd_dvd_int P_1) Y)->False))))
% 1.04/1.38 FOF formula (forall (P_1:int), ((iff (zprime P_1)) ((and ((ord_less_int one_one_int) P_1)) (forall (M_2:int), (((and ((ord_less_eq_int zero_zero_int) M_2)) ((dvd_dvd_int M_2) P_1))->((or (((eq int) M_2) one_one_int)) (((eq int) M_2) P_1))))))) of role axiom named fact_443_zprime__def
% 1.04/1.38 A new axiom: (forall (P_1:int), ((iff (zprime P_1)) ((and ((ord_less_int one_one_int) P_1)) (forall (M_2:int), (((and ((ord_less_eq_int zero_zero_int) M_2)) ((dvd_dvd_int M_2) P_1))->((or (((eq int) M_2) one_one_int)) (((eq int) M_2) P_1)))))))
% 1.04/1.40 FOF formula (forall (P_1:int), ((zprime P_1)->((not (((eq int) P_1) (number_number_of_int (bit0 (bit1 pls)))))->((not (((eq int) P_1) (number_number_of_int (bit1 (bit1 pls)))))->((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P_1))))) of role axiom named fact_444_prime__g__5
% 1.04/1.40 A new axiom: (forall (P_1:int), ((zprime P_1)->((not (((eq int) P_1) (number_number_of_int (bit0 (bit1 pls)))))->((not (((eq int) P_1) (number_number_of_int (bit1 (bit1 pls)))))->((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P_1)))))
% 1.04/1.40 FOF formula ((ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls)))) of role axiom named fact_445_pos2
% 1.04/1.40 A new axiom: ((ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls))))
% 1.04/1.40 FOF formula (forall (N_22:nat) (A_91:real) (B_68:real), (((ord_less_real A_91) B_68)->(((ord_less_eq_real zero_zero_real) A_91)->(((ord_less_nat zero_zero_nat) N_22)->((ord_less_real ((power_power_real A_91) N_22)) ((power_power_real B_68) N_22)))))) of role axiom named fact_446_power__strict__mono
% 1.04/1.40 A new axiom: (forall (N_22:nat) (A_91:real) (B_68:real), (((ord_less_real A_91) B_68)->(((ord_less_eq_real zero_zero_real) A_91)->(((ord_less_nat zero_zero_nat) N_22)->((ord_less_real ((power_power_real A_91) N_22)) ((power_power_real B_68) N_22))))))
% 1.04/1.40 FOF formula (forall (N_22:nat) (A_91:nat) (B_68:nat), (((ord_less_nat A_91) B_68)->(((ord_less_eq_nat zero_zero_nat) A_91)->(((ord_less_nat zero_zero_nat) N_22)->((ord_less_nat ((power_power_nat A_91) N_22)) ((power_power_nat B_68) N_22)))))) of role axiom named fact_447_power__strict__mono
% 1.04/1.40 A new axiom: (forall (N_22:nat) (A_91:nat) (B_68:nat), (((ord_less_nat A_91) B_68)->(((ord_less_eq_nat zero_zero_nat) A_91)->(((ord_less_nat zero_zero_nat) N_22)->((ord_less_nat ((power_power_nat A_91) N_22)) ((power_power_nat B_68) N_22))))))
% 1.04/1.40 FOF formula (forall (N_22:nat) (A_91:int) (B_68:int), (((ord_less_int A_91) B_68)->(((ord_less_eq_int zero_zero_int) A_91)->(((ord_less_nat zero_zero_nat) N_22)->((ord_less_int ((power_power_int A_91) N_22)) ((power_power_int B_68) N_22)))))) of role axiom named fact_448_power__strict__mono
% 1.04/1.40 A new axiom: (forall (N_22:nat) (A_91:int) (B_68:int), (((ord_less_int A_91) B_68)->(((ord_less_eq_int zero_zero_int) A_91)->(((ord_less_nat zero_zero_nat) N_22)->((ord_less_int ((power_power_int A_91) N_22)) ((power_power_int B_68) N_22))))))
% 1.04/1.40 FOF formula (forall (V_1:real) (U_1:real) (Y_8:real) (X_8:real) (A_90:real), (((ord_less_real X_8) A_90)->(((ord_less_real Y_8) A_90)->(((ord_less_eq_real zero_zero_real) U_1)->(((ord_less_eq_real zero_zero_real) V_1)->((((eq real) ((plus_plus_real U_1) V_1)) one_one_real)->((ord_less_real ((plus_plus_real ((times_times_real U_1) X_8)) ((times_times_real V_1) Y_8))) A_90))))))) of role axiom named fact_449_convex__bound__lt
% 1.04/1.40 A new axiom: (forall (V_1:real) (U_1:real) (Y_8:real) (X_8:real) (A_90:real), (((ord_less_real X_8) A_90)->(((ord_less_real Y_8) A_90)->(((ord_less_eq_real zero_zero_real) U_1)->(((ord_less_eq_real zero_zero_real) V_1)->((((eq real) ((plus_plus_real U_1) V_1)) one_one_real)->((ord_less_real ((plus_plus_real ((times_times_real U_1) X_8)) ((times_times_real V_1) Y_8))) A_90)))))))
% 1.04/1.40 FOF formula (forall (V_1:int) (U_1:int) (Y_8:int) (X_8:int) (A_90:int), (((ord_less_int X_8) A_90)->(((ord_less_int Y_8) A_90)->(((ord_less_eq_int zero_zero_int) U_1)->(((ord_less_eq_int zero_zero_int) V_1)->((((eq int) ((plus_plus_int U_1) V_1)) one_one_int)->((ord_less_int ((plus_plus_int ((times_times_int U_1) X_8)) ((times_times_int V_1) Y_8))) A_90))))))) of role axiom named fact_450_convex__bound__lt
% 1.04/1.40 A new axiom: (forall (V_1:int) (U_1:int) (Y_8:int) (X_8:int) (A_90:int), (((ord_less_int X_8) A_90)->(((ord_less_int Y_8) A_90)->(((ord_less_eq_int zero_zero_int) U_1)->(((ord_less_eq_int zero_zero_int) V_1)->((((eq int) ((plus_plus_int U_1) V_1)) one_one_int)->((ord_less_int ((plus_plus_int ((times_times_int U_1) X_8)) ((times_times_int V_1) Y_8))) A_90)))))))
% 1.04/1.40 FOF formula (forall (Y:int) (N:nat) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((power_power_int Y) N))->(((ord_less_nat zero_zero_nat) N)->((dvd_dvd_int P_1) Y))))) of role axiom named fact_451_zpower__zdvd__prop2
% 1.04/1.42 A new axiom: (forall (Y:int) (N:nat) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((power_power_int Y) N))->(((ord_less_nat zero_zero_nat) N)->((dvd_dvd_int P_1) Y)))))
% 1.04/1.42 FOF formula (forall (A_89:nat), ((dvd_dvd_nat A_89) zero_zero_nat)) of role axiom named fact_452_dvd__0__right
% 1.04/1.42 A new axiom: (forall (A_89:nat), ((dvd_dvd_nat A_89) zero_zero_nat))
% 1.04/1.42 FOF formula (forall (A_89:int), ((dvd_dvd_int A_89) zero_zero_int)) of role axiom named fact_453_dvd__0__right
% 1.04/1.42 A new axiom: (forall (A_89:int), ((dvd_dvd_int A_89) zero_zero_int))
% 1.04/1.42 FOF formula (forall (A_89:real), ((dvd_dvd_real A_89) zero_zero_real)) of role axiom named fact_454_dvd__0__right
% 1.04/1.42 A new axiom: (forall (A_89:real), ((dvd_dvd_real A_89) zero_zero_real))
% 1.04/1.42 FOF formula ((forall (S1:int), ((((zcong ((power_power_int S1) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))->False))->False) of role axiom named fact_455__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_
% 1.04/1.42 A new axiom: ((forall (S1:int), ((((zcong ((power_power_int S1) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))->False))->False)
% 1.04/1.42 FOF formula (((eq int) ((legendre (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) one_one_int) of role axiom named fact_456__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096
% 1.04/1.42 A new axiom: (((eq int) ((legendre (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) one_one_int)
% 1.04/1.42 FOF formula (forall (K:int), ((iff (((eq int) (bit1 K)) min)) (((eq int) K) min))) of role axiom named fact_457_rel__simps_I47_J
% 1.04/1.42 A new axiom: (forall (K:int), ((iff (((eq int) (bit1 K)) min)) (((eq int) K) min)))
% 1.04/1.42 FOF formula (forall (L:int), ((iff (((eq int) min) (bit1 L))) (((eq int) min) L))) of role axiom named fact_458_rel__simps_I43_J
% 1.04/1.42 A new axiom: (forall (L:int), ((iff (((eq int) min) (bit1 L))) (((eq int) min) L)))
% 1.04/1.42 FOF formula (((eq int) (bit1 min)) min) of role axiom named fact_459_Bit1__Min
% 1.04/1.42 A new axiom: (((eq int) (bit1 min)) min)
% 1.04/1.42 FOF formula (not (((eq int) pls) min)) of role axiom named fact_460_rel__simps_I37_J
% 1.04/1.42 A new axiom: (not (((eq int) pls) min))
% 1.04/1.42 FOF formula (not (((eq int) min) pls)) of role axiom named fact_461_rel__simps_I40_J
% 1.04/1.42 A new axiom: (not (((eq int) min) pls))
% 1.04/1.42 FOF formula (forall (K:int), (not (((eq int) (bit0 K)) min))) of role axiom named fact_462_rel__simps_I45_J
% 1.04/1.42 A new axiom: (forall (K:int), (not (((eq int) (bit0 K)) min)))
% 1.04/1.42 FOF formula (forall (L:int), (not (((eq int) min) (bit0 L)))) of role axiom named fact_463_rel__simps_I42_J
% 1.04/1.42 A new axiom: (forall (L:int), (not (((eq int) min) (bit0 L))))
% 1.04/1.42 FOF formula (((ord_less_int min) min)->False) of role axiom named fact_464_rel__simps_I7_J
% 1.04/1.42 A new axiom: (((ord_less_int min) min)->False)
% 1.04/1.42 FOF formula ((ord_less_eq_int min) min) of role axiom named fact_465_rel__simps_I24_J
% 1.04/1.42 A new axiom: ((ord_less_eq_int min) min)
% 1.04/1.42 FOF formula (forall (K:int), ((iff ((ord_less_int (bit1 K)) min)) ((ord_less_int K) min))) of role axiom named fact_466_rel__simps_I13_J
% 1.04/1.42 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit1 K)) min)) ((ord_less_int K) min)))
% 1.04/1.42 FOF formula (forall (K:int), ((iff ((ord_less_int min) (bit1 K))) ((ord_less_int min) K))) of role axiom named fact_467_rel__simps_I9_J
% 1.04/1.42 A new axiom: (forall (K:int), ((iff ((ord_less_int min) (bit1 K))) ((ord_less_int min) K)))
% 1.04/1.42 FOF formula (((ord_less_int pls) min)->False) of role axiom named fact_468_rel__simps_I3_J
% 1.04/1.42 A new axiom: (((ord_less_int pls) min)->False)
% 1.04/1.42 FOF formula ((ord_less_int min) pls) of role axiom named fact_469_rel__simps_I6_J
% 1.04/1.42 A new axiom: ((ord_less_int min) pls)
% 1.04/1.42 FOF formula (forall (K:int), ((iff ((ord_less_int min) (bit0 K))) ((ord_less_int min) K))) of role axiom named fact_470_rel__simps_I8_J
% 1.04/1.43 A new axiom: (forall (K:int), ((iff ((ord_less_int min) (bit0 K))) ((ord_less_int min) K)))
% 1.04/1.43 FOF formula ((ord_less_int min) zero_zero_int) of role axiom named fact_471_bin__less__0__simps_I2_J
% 1.04/1.43 A new axiom: ((ord_less_int min) zero_zero_int)
% 1.04/1.43 FOF formula (forall (K:int), ((iff ((ord_less_eq_int min) (bit1 K))) ((ord_less_eq_int min) K))) of role axiom named fact_472_rel__simps_I26_J
% 1.04/1.43 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int min) (bit1 K))) ((ord_less_eq_int min) K)))
% 1.04/1.43 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) min)) ((ord_less_eq_int K) min))) of role axiom named fact_473_rel__simps_I30_J
% 1.04/1.43 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) min)) ((ord_less_eq_int K) min)))
% 1.04/1.43 FOF formula ((ord_less_eq_int min) pls) of role axiom named fact_474_rel__simps_I23_J
% 1.04/1.43 A new axiom: ((ord_less_eq_int min) pls)
% 1.04/1.43 FOF formula (((ord_less_eq_int pls) min)->False) of role axiom named fact_475_rel__simps_I20_J
% 1.04/1.43 A new axiom: (((ord_less_eq_int pls) min)->False)
% 1.04/1.43 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) min)) ((ord_less_eq_int K) min))) of role axiom named fact_476_rel__simps_I28_J
% 1.04/1.43 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) min)) ((ord_less_eq_int K) min)))
% 1.04/1.43 FOF formula (not (((eq int) (number_number_of_int pls)) (number_number_of_int min))) of role axiom named fact_477_eq__number__of__Pls__Min
% 1.04/1.43 A new axiom: (not (((eq int) (number_number_of_int pls)) (number_number_of_int min)))
% 1.04/1.43 FOF formula (forall (K:int), ((iff ((ord_less_int (bit0 K)) min)) ((ord_less_eq_int K) min))) of role axiom named fact_478_rel__simps_I11_J
% 1.04/1.43 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit0 K)) min)) ((ord_less_eq_int K) min)))
% 1.04/1.43 FOF formula (forall (K:int), ((iff ((ord_less_eq_int min) (bit0 K))) ((ord_less_int min) K))) of role axiom named fact_479_rel__simps_I25_J
% 1.04/1.43 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int min) (bit0 K))) ((ord_less_int min) K)))
% 1.04/1.43 FOF formula (forall (M:int) (N:int), ((iff (((eq int) ((times_times_int M) N)) one_one_int)) ((or ((and (((eq int) M) one_one_int)) (((eq int) N) one_one_int))) ((and (((eq int) M) (number_number_of_int min))) (((eq int) N) (number_number_of_int min)))))) of role axiom named fact_480_zmult__eq__1__iff
% 1.04/1.43 A new axiom: (forall (M:int) (N:int), ((iff (((eq int) ((times_times_int M) N)) one_one_int)) ((or ((and (((eq int) M) one_one_int)) (((eq int) N) one_one_int))) ((and (((eq int) M) (number_number_of_int min))) (((eq int) N) (number_number_of_int min))))))
% 1.04/1.43 FOF formula (forall (M:int) (N:int), ((((eq int) ((times_times_int M) N)) one_one_int)->((or (((eq int) M) one_one_int)) (((eq int) M) (number_number_of_int min))))) of role axiom named fact_481_pos__zmult__eq__1__iff__lemma
% 1.04/1.43 A new axiom: (forall (M:int) (N:int), ((((eq int) ((times_times_int M) N)) one_one_int)->((or (((eq int) M) one_one_int)) (((eq int) M) (number_number_of_int min)))))
% 1.04/1.43 FOF formula (forall (X_7:real) (Y_7:real), ((not (((eq real) X_7) Y_7))->((((ord_less_real X_7) Y_7)->False)->((ord_less_real Y_7) X_7)))) of role axiom named fact_482_linorder__neqE__linordered__idom
% 1.04/1.43 A new axiom: (forall (X_7:real) (Y_7:real), ((not (((eq real) X_7) Y_7))->((((ord_less_real X_7) Y_7)->False)->((ord_less_real Y_7) X_7))))
% 1.04/1.43 FOF formula (forall (X_7:int) (Y_7:int), ((not (((eq int) X_7) Y_7))->((((ord_less_int X_7) Y_7)->False)->((ord_less_int Y_7) X_7)))) of role axiom named fact_483_linorder__neqE__linordered__idom
% 1.04/1.43 A new axiom: (forall (X_7:int) (Y_7:int), ((not (((eq int) X_7) Y_7))->((((ord_less_int X_7) Y_7)->False)->((ord_less_int Y_7) X_7))))
% 1.04/1.43 FOF formula (forall (A_88:nat), ((dvd_dvd_nat A_88) A_88)) of role axiom named fact_484_dvd__refl
% 1.04/1.43 A new axiom: (forall (A_88:nat), ((dvd_dvd_nat A_88) A_88))
% 1.04/1.43 FOF formula (forall (A_88:int), ((dvd_dvd_int A_88) A_88)) of role axiom named fact_485_dvd__refl
% 1.04/1.43 A new axiom: (forall (A_88:int), ((dvd_dvd_int A_88) A_88))
% 1.04/1.43 FOF formula (forall (C_40:nat) (A_87:nat) (B_67:nat), (((dvd_dvd_nat A_87) B_67)->(((dvd_dvd_nat B_67) C_40)->((dvd_dvd_nat A_87) C_40)))) of role axiom named fact_486_dvd__trans
% 1.04/1.43 A new axiom: (forall (C_40:nat) (A_87:nat) (B_67:nat), (((dvd_dvd_nat A_87) B_67)->(((dvd_dvd_nat B_67) C_40)->((dvd_dvd_nat A_87) C_40))))
% 1.04/1.46 FOF formula (forall (C_40:int) (A_87:int) (B_67:int), (((dvd_dvd_int A_87) B_67)->(((dvd_dvd_int B_67) C_40)->((dvd_dvd_int A_87) C_40)))) of role axiom named fact_487_dvd__trans
% 1.04/1.46 A new axiom: (forall (C_40:int) (A_87:int) (B_67:int), (((dvd_dvd_int A_87) B_67)->(((dvd_dvd_int B_67) C_40)->((dvd_dvd_int A_87) C_40))))
% 1.04/1.46 FOF formula (forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) (((zcong B) A) M))) of role axiom named fact_488_zcong__sym
% 1.04/1.46 A new axiom: (forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) (((zcong B) A) M)))
% 1.04/1.46 FOF formula (forall (K:int) (M:int), (((zcong K) K) M)) of role axiom named fact_489_zcong__refl
% 1.04/1.46 A new axiom: (forall (K:int) (M:int), (((zcong K) K) M))
% 1.04/1.46 FOF formula (forall (D:int) (C:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((eq int) B) C)->((((zcong C) D) M)->(((zcong A) D) M))))) of role axiom named fact_490_zcong__eq__trans
% 1.04/1.46 A new axiom: (forall (D:int) (C:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((eq int) B) C)->((((zcong C) D) M)->(((zcong A) D) M)))))
% 1.04/1.46 FOF formula (forall (C:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((zcong B) C) M)->(((zcong A) C) M)))) of role axiom named fact_491_zcong__trans
% 1.04/1.46 A new axiom: (forall (C:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((zcong B) C) M)->(((zcong A) C) M))))
% 1.04/1.46 FOF formula (forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((((zcong X) (number_number_of_int min)) P_1)->((((zcong X) one_one_int) P_1)->False)))) of role axiom named fact_492_zcong__neg__1__impl__ne__1
% 1.04/1.46 A new axiom: (forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((((zcong X) (number_number_of_int min)) P_1)->((((zcong X) one_one_int) P_1)->False))))
% 1.04/1.46 FOF formula (forall (X_6:real) (Y_6:real), (((ord_less_eq_real X_6) Y_6)->((not (((eq real) X_6) Y_6))->((ord_less_real X_6) Y_6)))) of role axiom named fact_493_order__le__neq__implies__less
% 1.04/1.46 A new axiom: (forall (X_6:real) (Y_6:real), (((ord_less_eq_real X_6) Y_6)->((not (((eq real) X_6) Y_6))->((ord_less_real X_6) Y_6))))
% 1.04/1.46 FOF formula (forall (X_6:nat) (Y_6:nat), (((ord_less_eq_nat X_6) Y_6)->((not (((eq nat) X_6) Y_6))->((ord_less_nat X_6) Y_6)))) of role axiom named fact_494_order__le__neq__implies__less
% 1.04/1.46 A new axiom: (forall (X_6:nat) (Y_6:nat), (((ord_less_eq_nat X_6) Y_6)->((not (((eq nat) X_6) Y_6))->((ord_less_nat X_6) Y_6))))
% 1.04/1.46 FOF formula (forall (X_6:int) (Y_6:int), (((ord_less_eq_int X_6) Y_6)->((not (((eq int) X_6) Y_6))->((ord_less_int X_6) Y_6)))) of role axiom named fact_495_order__le__neq__implies__less
% 1.04/1.46 A new axiom: (forall (X_6:int) (Y_6:int), (((ord_less_eq_int X_6) Y_6)->((not (((eq int) X_6) Y_6))->((ord_less_int X_6) Y_6))))
% 1.04/1.46 FOF formula (forall (A_86:real) (B_66:real), ((((eq real) ((times_times_real A_86) B_66)) zero_zero_real)->((or (((eq real) A_86) zero_zero_real)) (((eq real) B_66) zero_zero_real)))) of role axiom named fact_496_divisors__zero
% 1.04/1.46 A new axiom: (forall (A_86:real) (B_66:real), ((((eq real) ((times_times_real A_86) B_66)) zero_zero_real)->((or (((eq real) A_86) zero_zero_real)) (((eq real) B_66) zero_zero_real))))
% 1.04/1.46 FOF formula (forall (A_86:nat) (B_66:nat), ((((eq nat) ((times_times_nat A_86) B_66)) zero_zero_nat)->((or (((eq nat) A_86) zero_zero_nat)) (((eq nat) B_66) zero_zero_nat)))) of role axiom named fact_497_divisors__zero
% 1.04/1.46 A new axiom: (forall (A_86:nat) (B_66:nat), ((((eq nat) ((times_times_nat A_86) B_66)) zero_zero_nat)->((or (((eq nat) A_86) zero_zero_nat)) (((eq nat) B_66) zero_zero_nat))))
% 1.04/1.46 FOF formula (forall (A_86:int) (B_66:int), ((((eq int) ((times_times_int A_86) B_66)) zero_zero_int)->((or (((eq int) A_86) zero_zero_int)) (((eq int) B_66) zero_zero_int)))) of role axiom named fact_498_divisors__zero
% 1.04/1.46 A new axiom: (forall (A_86:int) (B_66:int), ((((eq int) ((times_times_int A_86) B_66)) zero_zero_int)->((or (((eq int) A_86) zero_zero_int)) (((eq int) B_66) zero_zero_int))))
% 1.04/1.46 FOF formula (forall (B_65:real) (A_85:real), ((not (((eq real) A_85) zero_zero_real))->((not (((eq real) B_65) zero_zero_real))->(not (((eq real) ((times_times_real A_85) B_65)) zero_zero_real))))) of role axiom named fact_499_no__zero__divisors
% 1.04/1.47 A new axiom: (forall (B_65:real) (A_85:real), ((not (((eq real) A_85) zero_zero_real))->((not (((eq real) B_65) zero_zero_real))->(not (((eq real) ((times_times_real A_85) B_65)) zero_zero_real)))))
% 1.04/1.47 FOF formula (forall (B_65:nat) (A_85:nat), ((not (((eq nat) A_85) zero_zero_nat))->((not (((eq nat) B_65) zero_zero_nat))->(not (((eq nat) ((times_times_nat A_85) B_65)) zero_zero_nat))))) of role axiom named fact_500_no__zero__divisors
% 1.04/1.47 A new axiom: (forall (B_65:nat) (A_85:nat), ((not (((eq nat) A_85) zero_zero_nat))->((not (((eq nat) B_65) zero_zero_nat))->(not (((eq nat) ((times_times_nat A_85) B_65)) zero_zero_nat)))))
% 1.04/1.47 FOF formula (forall (B_65:int) (A_85:int), ((not (((eq int) A_85) zero_zero_int))->((not (((eq int) B_65) zero_zero_int))->(not (((eq int) ((times_times_int A_85) B_65)) zero_zero_int))))) of role axiom named fact_501_no__zero__divisors
% 1.04/1.47 A new axiom: (forall (B_65:int) (A_85:int), ((not (((eq int) A_85) zero_zero_int))->((not (((eq int) B_65) zero_zero_int))->(not (((eq int) ((times_times_int A_85) B_65)) zero_zero_int)))))
% 1.04/1.47 FOF formula (forall (A_84:real) (B_64:real), ((iff (((eq real) ((times_times_real A_84) B_64)) zero_zero_real)) ((or (((eq real) A_84) zero_zero_real)) (((eq real) B_64) zero_zero_real)))) of role axiom named fact_502_mult__eq__0__iff
% 1.04/1.47 A new axiom: (forall (A_84:real) (B_64:real), ((iff (((eq real) ((times_times_real A_84) B_64)) zero_zero_real)) ((or (((eq real) A_84) zero_zero_real)) (((eq real) B_64) zero_zero_real))))
% 1.04/1.47 FOF formula (forall (A_84:int) (B_64:int), ((iff (((eq int) ((times_times_int A_84) B_64)) zero_zero_int)) ((or (((eq int) A_84) zero_zero_int)) (((eq int) B_64) zero_zero_int)))) of role axiom named fact_503_mult__eq__0__iff
% 1.04/1.47 A new axiom: (forall (A_84:int) (B_64:int), ((iff (((eq int) ((times_times_int A_84) B_64)) zero_zero_int)) ((or (((eq int) A_84) zero_zero_int)) (((eq int) B_64) zero_zero_int))))
% 1.04/1.47 FOF formula (forall (A_83:real), (((eq real) ((times_times_real A_83) zero_zero_real)) zero_zero_real)) of role axiom named fact_504_mult__zero__right
% 1.04/1.47 A new axiom: (forall (A_83:real), (((eq real) ((times_times_real A_83) zero_zero_real)) zero_zero_real))
% 1.04/1.47 FOF formula (forall (A_83:nat), (((eq nat) ((times_times_nat A_83) zero_zero_nat)) zero_zero_nat)) of role axiom named fact_505_mult__zero__right
% 1.04/1.47 A new axiom: (forall (A_83:nat), (((eq nat) ((times_times_nat A_83) zero_zero_nat)) zero_zero_nat))
% 1.04/1.47 FOF formula (forall (A_83:int), (((eq int) ((times_times_int A_83) zero_zero_int)) zero_zero_int)) of role axiom named fact_506_mult__zero__right
% 1.04/1.47 A new axiom: (forall (A_83:int), (((eq int) ((times_times_int A_83) zero_zero_int)) zero_zero_int))
% 1.04/1.47 FOF formula (forall (A_82:real), (((eq real) ((times_times_real zero_zero_real) A_82)) zero_zero_real)) of role axiom named fact_507_mult__zero__left
% 1.04/1.47 A new axiom: (forall (A_82:real), (((eq real) ((times_times_real zero_zero_real) A_82)) zero_zero_real))
% 1.04/1.47 FOF formula (forall (A_82:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_82)) zero_zero_nat)) of role axiom named fact_508_mult__zero__left
% 1.04/1.47 A new axiom: (forall (A_82:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_82)) zero_zero_nat))
% 1.04/1.47 FOF formula (forall (A_82:int), (((eq int) ((times_times_int zero_zero_int) A_82)) zero_zero_int)) of role axiom named fact_509_mult__zero__left
% 1.04/1.47 A new axiom: (forall (A_82:int), (((eq int) ((times_times_int zero_zero_int) A_82)) zero_zero_int))
% 1.04/1.47 FOF formula (not (((eq real) zero_zero_real) one_one_real)) of role axiom named fact_510_zero__neq__one
% 1.04/1.47 A new axiom: (not (((eq real) zero_zero_real) one_one_real))
% 1.04/1.47 FOF formula (not (((eq nat) zero_zero_nat) one_one_nat)) of role axiom named fact_511_zero__neq__one
% 1.04/1.47 A new axiom: (not (((eq nat) zero_zero_nat) one_one_nat))
% 1.04/1.47 FOF formula (not (((eq int) zero_zero_int) one_one_int)) of role axiom named fact_512_zero__neq__one
% 1.04/1.47 A new axiom: (not (((eq int) zero_zero_int) one_one_int))
% 1.04/1.47 FOF formula (not (((eq real) one_one_real) zero_zero_real)) of role axiom named fact_513_one__neq__zero
% 1.13/1.48 A new axiom: (not (((eq real) one_one_real) zero_zero_real))
% 1.13/1.48 FOF formula (not (((eq nat) one_one_nat) zero_zero_nat)) of role axiom named fact_514_one__neq__zero
% 1.13/1.48 A new axiom: (not (((eq nat) one_one_nat) zero_zero_nat))
% 1.13/1.48 FOF formula (not (((eq int) one_one_int) zero_zero_int)) of role axiom named fact_515_one__neq__zero
% 1.13/1.48 A new axiom: (not (((eq int) one_one_int) zero_zero_int))
% 1.13/1.48 FOF formula (forall (A_81:real) (E:real) (B_63:real) (C_39:real), (((eq real) ((plus_plus_real ((times_times_real A_81) E)) ((plus_plus_real ((times_times_real B_63) E)) C_39))) ((plus_plus_real ((times_times_real ((plus_plus_real A_81) B_63)) E)) C_39))) of role axiom named fact_516_combine__common__factor
% 1.13/1.48 A new axiom: (forall (A_81:real) (E:real) (B_63:real) (C_39:real), (((eq real) ((plus_plus_real ((times_times_real A_81) E)) ((plus_plus_real ((times_times_real B_63) E)) C_39))) ((plus_plus_real ((times_times_real ((plus_plus_real A_81) B_63)) E)) C_39)))
% 1.13/1.48 FOF formula (forall (A_81:nat) (E:nat) (B_63:nat) (C_39:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_81) E)) ((plus_plus_nat ((times_times_nat B_63) E)) C_39))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat A_81) B_63)) E)) C_39))) of role axiom named fact_517_combine__common__factor
% 1.13/1.48 A new axiom: (forall (A_81:nat) (E:nat) (B_63:nat) (C_39:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_81) E)) ((plus_plus_nat ((times_times_nat B_63) E)) C_39))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat A_81) B_63)) E)) C_39)))
% 1.13/1.48 FOF formula (forall (A_81:int) (E:int) (B_63:int) (C_39:int), (((eq int) ((plus_plus_int ((times_times_int A_81) E)) ((plus_plus_int ((times_times_int B_63) E)) C_39))) ((plus_plus_int ((times_times_int ((plus_plus_int A_81) B_63)) E)) C_39))) of role axiom named fact_518_combine__common__factor
% 1.13/1.48 A new axiom: (forall (A_81:int) (E:int) (B_63:int) (C_39:int), (((eq int) ((plus_plus_int ((times_times_int A_81) E)) ((plus_plus_int ((times_times_int B_63) E)) C_39))) ((plus_plus_int ((times_times_int ((plus_plus_int A_81) B_63)) E)) C_39)))
% 1.13/1.48 FOF formula (forall (A_80:real) (B_62:real) (C_38:real), (((eq real) ((times_times_real ((plus_plus_real A_80) B_62)) C_38)) ((plus_plus_real ((times_times_real A_80) C_38)) ((times_times_real B_62) C_38)))) of role axiom named fact_519_comm__semiring__class_Odistrib
% 1.13/1.48 A new axiom: (forall (A_80:real) (B_62:real) (C_38:real), (((eq real) ((times_times_real ((plus_plus_real A_80) B_62)) C_38)) ((plus_plus_real ((times_times_real A_80) C_38)) ((times_times_real B_62) C_38))))
% 1.13/1.48 FOF formula (forall (A_80:nat) (B_62:nat) (C_38:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_80) B_62)) C_38)) ((plus_plus_nat ((times_times_nat A_80) C_38)) ((times_times_nat B_62) C_38)))) of role axiom named fact_520_comm__semiring__class_Odistrib
% 1.13/1.48 A new axiom: (forall (A_80:nat) (B_62:nat) (C_38:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_80) B_62)) C_38)) ((plus_plus_nat ((times_times_nat A_80) C_38)) ((times_times_nat B_62) C_38))))
% 1.13/1.48 FOF formula (forall (A_80:int) (B_62:int) (C_38:int), (((eq int) ((times_times_int ((plus_plus_int A_80) B_62)) C_38)) ((plus_plus_int ((times_times_int A_80) C_38)) ((times_times_int B_62) C_38)))) of role axiom named fact_521_comm__semiring__class_Odistrib
% 1.13/1.48 A new axiom: (forall (A_80:int) (B_62:int) (C_38:int), (((eq int) ((times_times_int ((plus_plus_int A_80) B_62)) C_38)) ((plus_plus_int ((times_times_int A_80) C_38)) ((times_times_int B_62) C_38))))
% 1.13/1.48 FOF formula (forall (N_21:nat) (A_79:real), ((not (((eq real) A_79) zero_zero_real))->(not (((eq real) ((power_power_real A_79) N_21)) zero_zero_real)))) of role axiom named fact_522_field__power__not__zero
% 1.13/1.48 A new axiom: (forall (N_21:nat) (A_79:real), ((not (((eq real) A_79) zero_zero_real))->(not (((eq real) ((power_power_real A_79) N_21)) zero_zero_real))))
% 1.13/1.48 FOF formula (forall (N_21:nat) (A_79:int), ((not (((eq int) A_79) zero_zero_int))->(not (((eq int) ((power_power_int A_79) N_21)) zero_zero_int)))) of role axiom named fact_523_field__power__not__zero
% 1.13/1.48 A new axiom: (forall (N_21:nat) (A_79:int), ((not (((eq int) A_79) zero_zero_int))->(not (((eq int) ((power_power_int A_79) N_21)) zero_zero_int))))
% 1.14/1.50 FOF formula (forall (A_78:nat), (((dvd_dvd_nat zero_zero_nat) A_78)->(((eq nat) A_78) zero_zero_nat))) of role axiom named fact_524_dvd__0__left
% 1.14/1.50 A new axiom: (forall (A_78:nat), (((dvd_dvd_nat zero_zero_nat) A_78)->(((eq nat) A_78) zero_zero_nat)))
% 1.14/1.50 FOF formula (forall (A_78:int), (((dvd_dvd_int zero_zero_int) A_78)->(((eq int) A_78) zero_zero_int))) of role axiom named fact_525_dvd__0__left
% 1.14/1.50 A new axiom: (forall (A_78:int), (((dvd_dvd_int zero_zero_int) A_78)->(((eq int) A_78) zero_zero_int)))
% 1.14/1.50 FOF formula (forall (A_78:real), (((dvd_dvd_real zero_zero_real) A_78)->(((eq real) A_78) zero_zero_real))) of role axiom named fact_526_dvd__0__left
% 1.14/1.50 A new axiom: (forall (A_78:real), (((dvd_dvd_real zero_zero_real) A_78)->(((eq real) A_78) zero_zero_real)))
% 1.14/1.50 FOF formula (forall (A_77:real) (B_61:real) (N_20:nat), (((eq real) ((power_power_real ((times_times_real A_77) B_61)) N_20)) ((times_times_real ((power_power_real A_77) N_20)) ((power_power_real B_61) N_20)))) of role axiom named fact_527_power__mult__distrib
% 1.14/1.50 A new axiom: (forall (A_77:real) (B_61:real) (N_20:nat), (((eq real) ((power_power_real ((times_times_real A_77) B_61)) N_20)) ((times_times_real ((power_power_real A_77) N_20)) ((power_power_real B_61) N_20))))
% 1.14/1.50 FOF formula (forall (A_77:nat) (B_61:nat) (N_20:nat), (((eq nat) ((power_power_nat ((times_times_nat A_77) B_61)) N_20)) ((times_times_nat ((power_power_nat A_77) N_20)) ((power_power_nat B_61) N_20)))) of role axiom named fact_528_power__mult__distrib
% 1.14/1.50 A new axiom: (forall (A_77:nat) (B_61:nat) (N_20:nat), (((eq nat) ((power_power_nat ((times_times_nat A_77) B_61)) N_20)) ((times_times_nat ((power_power_nat A_77) N_20)) ((power_power_nat B_61) N_20))))
% 1.14/1.50 FOF formula (forall (A_77:int) (B_61:int) (N_20:nat), (((eq int) ((power_power_int ((times_times_int A_77) B_61)) N_20)) ((times_times_int ((power_power_int A_77) N_20)) ((power_power_int B_61) N_20)))) of role axiom named fact_529_power__mult__distrib
% 1.14/1.50 A new axiom: (forall (A_77:int) (B_61:int) (N_20:nat), (((eq int) ((power_power_int ((times_times_int A_77) B_61)) N_20)) ((times_times_int ((power_power_int A_77) N_20)) ((power_power_int B_61) N_20))))
% 1.14/1.50 FOF formula (forall (A_76:real) (N_19:nat), (((eq real) ((times_times_real ((power_power_real A_76) N_19)) A_76)) ((times_times_real A_76) ((power_power_real A_76) N_19)))) of role axiom named fact_530_power__commutes
% 1.14/1.50 A new axiom: (forall (A_76:real) (N_19:nat), (((eq real) ((times_times_real ((power_power_real A_76) N_19)) A_76)) ((times_times_real A_76) ((power_power_real A_76) N_19))))
% 1.14/1.50 FOF formula (forall (A_76:nat) (N_19:nat), (((eq nat) ((times_times_nat ((power_power_nat A_76) N_19)) A_76)) ((times_times_nat A_76) ((power_power_nat A_76) N_19)))) of role axiom named fact_531_power__commutes
% 1.14/1.50 A new axiom: (forall (A_76:nat) (N_19:nat), (((eq nat) ((times_times_nat ((power_power_nat A_76) N_19)) A_76)) ((times_times_nat A_76) ((power_power_nat A_76) N_19))))
% 1.14/1.50 FOF formula (forall (A_76:int) (N_19:nat), (((eq int) ((times_times_int ((power_power_int A_76) N_19)) A_76)) ((times_times_int A_76) ((power_power_int A_76) N_19)))) of role axiom named fact_532_power__commutes
% 1.14/1.50 A new axiom: (forall (A_76:int) (N_19:nat), (((eq int) ((times_times_int ((power_power_int A_76) N_19)) A_76)) ((times_times_int A_76) ((power_power_int A_76) N_19))))
% 1.14/1.50 FOF formula (forall (A_75:nat) (B_60:nat), ((dvd_dvd_nat A_75) ((times_times_nat A_75) B_60))) of role axiom named fact_533_dvd__triv__left
% 1.14/1.50 A new axiom: (forall (A_75:nat) (B_60:nat), ((dvd_dvd_nat A_75) ((times_times_nat A_75) B_60)))
% 1.14/1.50 FOF formula (forall (A_75:int) (B_60:int), ((dvd_dvd_int A_75) ((times_times_int A_75) B_60))) of role axiom named fact_534_dvd__triv__left
% 1.14/1.50 A new axiom: (forall (A_75:int) (B_60:int), ((dvd_dvd_int A_75) ((times_times_int A_75) B_60)))
% 1.14/1.50 FOF formula (forall (A_75:real) (B_60:real), ((dvd_dvd_real A_75) ((times_times_real A_75) B_60))) of role axiom named fact_535_dvd__triv__left
% 1.14/1.50 A new axiom: (forall (A_75:real) (B_60:real), ((dvd_dvd_real A_75) ((times_times_real A_75) B_60)))
% 1.14/1.50 FOF formula (forall (A_74:nat) (B_59:nat), ((dvd_dvd_nat A_74) ((times_times_nat B_59) A_74))) of role axiom named fact_536_dvd__triv__right
% 1.18/1.52 A new axiom: (forall (A_74:nat) (B_59:nat), ((dvd_dvd_nat A_74) ((times_times_nat B_59) A_74)))
% 1.18/1.52 FOF formula (forall (A_74:int) (B_59:int), ((dvd_dvd_int A_74) ((times_times_int B_59) A_74))) of role axiom named fact_537_dvd__triv__right
% 1.18/1.52 A new axiom: (forall (A_74:int) (B_59:int), ((dvd_dvd_int A_74) ((times_times_int B_59) A_74)))
% 1.18/1.52 FOF formula (forall (A_74:real) (B_59:real), ((dvd_dvd_real A_74) ((times_times_real B_59) A_74))) of role axiom named fact_538_dvd__triv__right
% 1.18/1.52 A new axiom: (forall (A_74:real) (B_59:real), ((dvd_dvd_real A_74) ((times_times_real B_59) A_74)))
% 1.18/1.52 FOF formula (forall (C_37:nat) (A_73:nat) (B_58:nat), (((dvd_dvd_nat A_73) B_58)->((dvd_dvd_nat A_73) ((times_times_nat B_58) C_37)))) of role axiom named fact_539_dvd__mult2
% 1.18/1.52 A new axiom: (forall (C_37:nat) (A_73:nat) (B_58:nat), (((dvd_dvd_nat A_73) B_58)->((dvd_dvd_nat A_73) ((times_times_nat B_58) C_37))))
% 1.18/1.52 FOF formula (forall (C_37:int) (A_73:int) (B_58:int), (((dvd_dvd_int A_73) B_58)->((dvd_dvd_int A_73) ((times_times_int B_58) C_37)))) of role axiom named fact_540_dvd__mult2
% 1.18/1.52 A new axiom: (forall (C_37:int) (A_73:int) (B_58:int), (((dvd_dvd_int A_73) B_58)->((dvd_dvd_int A_73) ((times_times_int B_58) C_37))))
% 1.18/1.52 FOF formula (forall (C_37:real) (A_73:real) (B_58:real), (((dvd_dvd_real A_73) B_58)->((dvd_dvd_real A_73) ((times_times_real B_58) C_37)))) of role axiom named fact_541_dvd__mult2
% 1.18/1.52 A new axiom: (forall (C_37:real) (A_73:real) (B_58:real), (((dvd_dvd_real A_73) B_58)->((dvd_dvd_real A_73) ((times_times_real B_58) C_37))))
% 1.18/1.52 FOF formula (forall (B_57:nat) (A_72:nat) (C_36:nat), (((dvd_dvd_nat A_72) C_36)->((dvd_dvd_nat A_72) ((times_times_nat B_57) C_36)))) of role axiom named fact_542_dvd__mult
% 1.18/1.52 A new axiom: (forall (B_57:nat) (A_72:nat) (C_36:nat), (((dvd_dvd_nat A_72) C_36)->((dvd_dvd_nat A_72) ((times_times_nat B_57) C_36))))
% 1.18/1.52 FOF formula (forall (B_57:int) (A_72:int) (C_36:int), (((dvd_dvd_int A_72) C_36)->((dvd_dvd_int A_72) ((times_times_int B_57) C_36)))) of role axiom named fact_543_dvd__mult
% 1.18/1.52 A new axiom: (forall (B_57:int) (A_72:int) (C_36:int), (((dvd_dvd_int A_72) C_36)->((dvd_dvd_int A_72) ((times_times_int B_57) C_36))))
% 1.18/1.52 FOF formula (forall (B_57:real) (A_72:real) (C_36:real), (((dvd_dvd_real A_72) C_36)->((dvd_dvd_real A_72) ((times_times_real B_57) C_36)))) of role axiom named fact_544_dvd__mult
% 1.18/1.52 A new axiom: (forall (B_57:real) (A_72:real) (C_36:real), (((dvd_dvd_real A_72) C_36)->((dvd_dvd_real A_72) ((times_times_real B_57) C_36))))
% 1.18/1.52 FOF formula (forall (C_35:nat) (D_9:nat) (A_71:nat) (B_56:nat), (((dvd_dvd_nat A_71) B_56)->(((dvd_dvd_nat C_35) D_9)->((dvd_dvd_nat ((times_times_nat A_71) C_35)) ((times_times_nat B_56) D_9))))) of role axiom named fact_545_mult__dvd__mono
% 1.18/1.52 A new axiom: (forall (C_35:nat) (D_9:nat) (A_71:nat) (B_56:nat), (((dvd_dvd_nat A_71) B_56)->(((dvd_dvd_nat C_35) D_9)->((dvd_dvd_nat ((times_times_nat A_71) C_35)) ((times_times_nat B_56) D_9)))))
% 1.18/1.52 FOF formula (forall (C_35:int) (D_9:int) (A_71:int) (B_56:int), (((dvd_dvd_int A_71) B_56)->(((dvd_dvd_int C_35) D_9)->((dvd_dvd_int ((times_times_int A_71) C_35)) ((times_times_int B_56) D_9))))) of role axiom named fact_546_mult__dvd__mono
% 1.18/1.52 A new axiom: (forall (C_35:int) (D_9:int) (A_71:int) (B_56:int), (((dvd_dvd_int A_71) B_56)->(((dvd_dvd_int C_35) D_9)->((dvd_dvd_int ((times_times_int A_71) C_35)) ((times_times_int B_56) D_9)))))
% 1.18/1.52 FOF formula (forall (C_35:real) (D_9:real) (A_71:real) (B_56:real), (((dvd_dvd_real A_71) B_56)->(((dvd_dvd_real C_35) D_9)->((dvd_dvd_real ((times_times_real A_71) C_35)) ((times_times_real B_56) D_9))))) of role axiom named fact_547_mult__dvd__mono
% 1.18/1.52 A new axiom: (forall (C_35:real) (D_9:real) (A_71:real) (B_56:real), (((dvd_dvd_real A_71) B_56)->(((dvd_dvd_real C_35) D_9)->((dvd_dvd_real ((times_times_real A_71) C_35)) ((times_times_real B_56) D_9)))))
% 1.18/1.52 FOF formula (forall (A_70:nat) (B_55:nat) (K_2:nat), ((((eq nat) A_70) ((times_times_nat B_55) K_2))->((dvd_dvd_nat B_55) A_70))) of role axiom named fact_548_dvdI
% 1.18/1.52 A new axiom: (forall (A_70:nat) (B_55:nat) (K_2:nat), ((((eq nat) A_70) ((times_times_nat B_55) K_2))->((dvd_dvd_nat B_55) A_70)))
% 1.18/1.54 FOF formula (forall (A_70:int) (B_55:int) (K_2:int), ((((eq int) A_70) ((times_times_int B_55) K_2))->((dvd_dvd_int B_55) A_70))) of role axiom named fact_549_dvdI
% 1.18/1.54 A new axiom: (forall (A_70:int) (B_55:int) (K_2:int), ((((eq int) A_70) ((times_times_int B_55) K_2))->((dvd_dvd_int B_55) A_70)))
% 1.18/1.54 FOF formula (forall (A_70:real) (B_55:real) (K_2:real), ((((eq real) A_70) ((times_times_real B_55) K_2))->((dvd_dvd_real B_55) A_70))) of role axiom named fact_550_dvdI
% 1.18/1.54 A new axiom: (forall (A_70:real) (B_55:real) (K_2:real), ((((eq real) A_70) ((times_times_real B_55) K_2))->((dvd_dvd_real B_55) A_70)))
% 1.18/1.54 FOF formula (forall (A_69:nat) (B_54:nat) (C_34:nat), (((dvd_dvd_nat ((times_times_nat A_69) B_54)) C_34)->((dvd_dvd_nat A_69) C_34))) of role axiom named fact_551_dvd__mult__left
% 1.18/1.54 A new axiom: (forall (A_69:nat) (B_54:nat) (C_34:nat), (((dvd_dvd_nat ((times_times_nat A_69) B_54)) C_34)->((dvd_dvd_nat A_69) C_34)))
% 1.18/1.54 FOF formula (forall (A_69:int) (B_54:int) (C_34:int), (((dvd_dvd_int ((times_times_int A_69) B_54)) C_34)->((dvd_dvd_int A_69) C_34))) of role axiom named fact_552_dvd__mult__left
% 1.18/1.54 A new axiom: (forall (A_69:int) (B_54:int) (C_34:int), (((dvd_dvd_int ((times_times_int A_69) B_54)) C_34)->((dvd_dvd_int A_69) C_34)))
% 1.18/1.54 FOF formula (forall (A_69:real) (B_54:real) (C_34:real), (((dvd_dvd_real ((times_times_real A_69) B_54)) C_34)->((dvd_dvd_real A_69) C_34))) of role axiom named fact_553_dvd__mult__left
% 1.18/1.54 A new axiom: (forall (A_69:real) (B_54:real) (C_34:real), (((dvd_dvd_real ((times_times_real A_69) B_54)) C_34)->((dvd_dvd_real A_69) C_34)))
% 1.18/1.54 FOF formula (forall (A_68:nat) (B_53:nat) (C_33:nat), (((dvd_dvd_nat ((times_times_nat A_68) B_53)) C_33)->((dvd_dvd_nat B_53) C_33))) of role axiom named fact_554_dvd__mult__right
% 1.18/1.54 A new axiom: (forall (A_68:nat) (B_53:nat) (C_33:nat), (((dvd_dvd_nat ((times_times_nat A_68) B_53)) C_33)->((dvd_dvd_nat B_53) C_33)))
% 1.18/1.54 FOF formula (forall (A_68:int) (B_53:int) (C_33:int), (((dvd_dvd_int ((times_times_int A_68) B_53)) C_33)->((dvd_dvd_int B_53) C_33))) of role axiom named fact_555_dvd__mult__right
% 1.18/1.54 A new axiom: (forall (A_68:int) (B_53:int) (C_33:int), (((dvd_dvd_int ((times_times_int A_68) B_53)) C_33)->((dvd_dvd_int B_53) C_33)))
% 1.18/1.54 FOF formula (forall (A_68:real) (B_53:real) (C_33:real), (((dvd_dvd_real ((times_times_real A_68) B_53)) C_33)->((dvd_dvd_real B_53) C_33))) of role axiom named fact_556_dvd__mult__right
% 1.18/1.54 A new axiom: (forall (A_68:real) (B_53:real) (C_33:real), (((dvd_dvd_real ((times_times_real A_68) B_53)) C_33)->((dvd_dvd_real B_53) C_33)))
% 1.18/1.54 FOF formula (forall (C_32:nat) (A_67:nat) (B_52:nat), (((dvd_dvd_nat A_67) B_52)->(((dvd_dvd_nat A_67) C_32)->((dvd_dvd_nat A_67) ((plus_plus_nat B_52) C_32))))) of role axiom named fact_557_dvd__add
% 1.18/1.54 A new axiom: (forall (C_32:nat) (A_67:nat) (B_52:nat), (((dvd_dvd_nat A_67) B_52)->(((dvd_dvd_nat A_67) C_32)->((dvd_dvd_nat A_67) ((plus_plus_nat B_52) C_32)))))
% 1.18/1.54 FOF formula (forall (C_32:int) (A_67:int) (B_52:int), (((dvd_dvd_int A_67) B_52)->(((dvd_dvd_int A_67) C_32)->((dvd_dvd_int A_67) ((plus_plus_int B_52) C_32))))) of role axiom named fact_558_dvd__add
% 1.18/1.54 A new axiom: (forall (C_32:int) (A_67:int) (B_52:int), (((dvd_dvd_int A_67) B_52)->(((dvd_dvd_int A_67) C_32)->((dvd_dvd_int A_67) ((plus_plus_int B_52) C_32)))))
% 1.18/1.54 FOF formula (forall (C_32:real) (A_67:real) (B_52:real), (((dvd_dvd_real A_67) B_52)->(((dvd_dvd_real A_67) C_32)->((dvd_dvd_real A_67) ((plus_plus_real B_52) C_32))))) of role axiom named fact_559_dvd__add
% 1.18/1.54 A new axiom: (forall (C_32:real) (A_67:real) (B_52:real), (((dvd_dvd_real A_67) B_52)->(((dvd_dvd_real A_67) C_32)->((dvd_dvd_real A_67) ((plus_plus_real B_52) C_32)))))
% 1.18/1.54 FOF formula (forall (N_18:nat), (((eq real) ((power_power_real one_one_real) N_18)) one_one_real)) of role axiom named fact_560_power__one
% 1.18/1.54 A new axiom: (forall (N_18:nat), (((eq real) ((power_power_real one_one_real) N_18)) one_one_real))
% 1.18/1.54 FOF formula (forall (N_18:nat), (((eq nat) ((power_power_nat one_one_nat) N_18)) one_one_nat)) of role axiom named fact_561_power__one
% 1.18/1.56 A new axiom: (forall (N_18:nat), (((eq nat) ((power_power_nat one_one_nat) N_18)) one_one_nat))
% 1.18/1.56 FOF formula (forall (N_18:nat), (((eq int) ((power_power_int one_one_int) N_18)) one_one_int)) of role axiom named fact_562_power__one
% 1.18/1.56 A new axiom: (forall (N_18:nat), (((eq int) ((power_power_int one_one_int) N_18)) one_one_int))
% 1.18/1.56 FOF formula (forall (A_66:nat), ((dvd_dvd_nat one_one_nat) A_66)) of role axiom named fact_563_one__dvd
% 1.18/1.56 A new axiom: (forall (A_66:nat), ((dvd_dvd_nat one_one_nat) A_66))
% 1.18/1.56 FOF formula (forall (A_66:int), ((dvd_dvd_int one_one_int) A_66)) of role axiom named fact_564_one__dvd
% 1.18/1.56 A new axiom: (forall (A_66:int), ((dvd_dvd_int one_one_int) A_66))
% 1.18/1.56 FOF formula (forall (A_66:real), ((dvd_dvd_real one_one_real) A_66)) of role axiom named fact_565_one__dvd
% 1.18/1.56 A new axiom: (forall (A_66:real), ((dvd_dvd_real one_one_real) A_66))
% 1.18/1.56 FOF formula (forall (N_17:nat) (X_5:nat) (Y_5:nat), (((dvd_dvd_nat X_5) Y_5)->((dvd_dvd_nat ((power_power_nat X_5) N_17)) ((power_power_nat Y_5) N_17)))) of role axiom named fact_566_dvd__power__same
% 1.18/1.56 A new axiom: (forall (N_17:nat) (X_5:nat) (Y_5:nat), (((dvd_dvd_nat X_5) Y_5)->((dvd_dvd_nat ((power_power_nat X_5) N_17)) ((power_power_nat Y_5) N_17))))
% 1.18/1.56 FOF formula (forall (N_17:nat) (X_5:int) (Y_5:int), (((dvd_dvd_int X_5) Y_5)->((dvd_dvd_int ((power_power_int X_5) N_17)) ((power_power_int Y_5) N_17)))) of role axiom named fact_567_dvd__power__same
% 1.18/1.56 A new axiom: (forall (N_17:nat) (X_5:int) (Y_5:int), (((dvd_dvd_int X_5) Y_5)->((dvd_dvd_int ((power_power_int X_5) N_17)) ((power_power_int Y_5) N_17))))
% 1.18/1.56 FOF formula (forall (N_17:nat) (X_5:real) (Y_5:real), (((dvd_dvd_real X_5) Y_5)->((dvd_dvd_real ((power_power_real X_5) N_17)) ((power_power_real Y_5) N_17)))) of role axiom named fact_568_dvd__power__same
% 1.18/1.56 A new axiom: (forall (N_17:nat) (X_5:real) (Y_5:real), (((dvd_dvd_real X_5) Y_5)->((dvd_dvd_real ((power_power_real X_5) N_17)) ((power_power_real Y_5) N_17))))
% 1.18/1.56 FOF formula (forall (M_9:nat) (A_65:nat) (N_16:nat) (B_51:nat), (((dvd_dvd_nat ((power_power_nat A_65) N_16)) B_51)->(((ord_less_eq_nat M_9) N_16)->((dvd_dvd_nat ((power_power_nat A_65) M_9)) B_51)))) of role axiom named fact_569_power__le__dvd
% 1.18/1.56 A new axiom: (forall (M_9:nat) (A_65:nat) (N_16:nat) (B_51:nat), (((dvd_dvd_nat ((power_power_nat A_65) N_16)) B_51)->(((ord_less_eq_nat M_9) N_16)->((dvd_dvd_nat ((power_power_nat A_65) M_9)) B_51))))
% 1.18/1.56 FOF formula (forall (M_9:nat) (A_65:int) (N_16:nat) (B_51:int), (((dvd_dvd_int ((power_power_int A_65) N_16)) B_51)->(((ord_less_eq_nat M_9) N_16)->((dvd_dvd_int ((power_power_int A_65) M_9)) B_51)))) of role axiom named fact_570_power__le__dvd
% 1.18/1.56 A new axiom: (forall (M_9:nat) (A_65:int) (N_16:nat) (B_51:int), (((dvd_dvd_int ((power_power_int A_65) N_16)) B_51)->(((ord_less_eq_nat M_9) N_16)->((dvd_dvd_int ((power_power_int A_65) M_9)) B_51))))
% 1.18/1.56 FOF formula (forall (M_9:nat) (A_65:real) (N_16:nat) (B_51:real), (((dvd_dvd_real ((power_power_real A_65) N_16)) B_51)->(((ord_less_eq_nat M_9) N_16)->((dvd_dvd_real ((power_power_real A_65) M_9)) B_51)))) of role axiom named fact_571_power__le__dvd
% 1.18/1.56 A new axiom: (forall (M_9:nat) (A_65:real) (N_16:nat) (B_51:real), (((dvd_dvd_real ((power_power_real A_65) N_16)) B_51)->(((ord_less_eq_nat M_9) N_16)->((dvd_dvd_real ((power_power_real A_65) M_9)) B_51))))
% 1.18/1.56 FOF formula (forall (N_15:nat) (M_8:nat) (X_4:nat) (Y_4:nat), (((dvd_dvd_nat X_4) Y_4)->(((ord_less_eq_nat N_15) M_8)->((dvd_dvd_nat ((power_power_nat X_4) N_15)) ((power_power_nat Y_4) M_8))))) of role axiom named fact_572_dvd__power__le
% 1.18/1.56 A new axiom: (forall (N_15:nat) (M_8:nat) (X_4:nat) (Y_4:nat), (((dvd_dvd_nat X_4) Y_4)->(((ord_less_eq_nat N_15) M_8)->((dvd_dvd_nat ((power_power_nat X_4) N_15)) ((power_power_nat Y_4) M_8)))))
% 1.18/1.56 FOF formula (forall (N_15:nat) (M_8:nat) (X_4:int) (Y_4:int), (((dvd_dvd_int X_4) Y_4)->(((ord_less_eq_nat N_15) M_8)->((dvd_dvd_int ((power_power_int X_4) N_15)) ((power_power_int Y_4) M_8))))) of role axiom named fact_573_dvd__power__le
% 1.18/1.56 A new axiom: (forall (N_15:nat) (M_8:nat) (X_4:int) (Y_4:int), (((dvd_dvd_int X_4) Y_4)->(((ord_less_eq_nat N_15) M_8)->((dvd_dvd_int ((power_power_int X_4) N_15)) ((power_power_int Y_4) M_8)))))
% 1.18/1.58 FOF formula (forall (N_15:nat) (M_8:nat) (X_4:real) (Y_4:real), (((dvd_dvd_real X_4) Y_4)->(((ord_less_eq_nat N_15) M_8)->((dvd_dvd_real ((power_power_real X_4) N_15)) ((power_power_real Y_4) M_8))))) of role axiom named fact_574_dvd__power__le
% 1.18/1.58 A new axiom: (forall (N_15:nat) (M_8:nat) (X_4:real) (Y_4:real), (((dvd_dvd_real X_4) Y_4)->(((ord_less_eq_nat N_15) M_8)->((dvd_dvd_real ((power_power_real X_4) N_15)) ((power_power_real Y_4) M_8)))))
% 1.18/1.58 FOF formula (forall (A_64:nat) (M_7:nat) (N_14:nat), (((ord_less_eq_nat M_7) N_14)->((dvd_dvd_nat ((power_power_nat A_64) M_7)) ((power_power_nat A_64) N_14)))) of role axiom named fact_575_le__imp__power__dvd
% 1.18/1.58 A new axiom: (forall (A_64:nat) (M_7:nat) (N_14:nat), (((ord_less_eq_nat M_7) N_14)->((dvd_dvd_nat ((power_power_nat A_64) M_7)) ((power_power_nat A_64) N_14))))
% 1.18/1.58 FOF formula (forall (A_64:int) (M_7:nat) (N_14:nat), (((ord_less_eq_nat M_7) N_14)->((dvd_dvd_int ((power_power_int A_64) M_7)) ((power_power_int A_64) N_14)))) of role axiom named fact_576_le__imp__power__dvd
% 1.18/1.58 A new axiom: (forall (A_64:int) (M_7:nat) (N_14:nat), (((ord_less_eq_nat M_7) N_14)->((dvd_dvd_int ((power_power_int A_64) M_7)) ((power_power_int A_64) N_14))))
% 1.18/1.58 FOF formula (forall (A_64:real) (M_7:nat) (N_14:nat), (((ord_less_eq_nat M_7) N_14)->((dvd_dvd_real ((power_power_real A_64) M_7)) ((power_power_real A_64) N_14)))) of role axiom named fact_577_le__imp__power__dvd
% 1.18/1.58 A new axiom: (forall (A_64:real) (M_7:nat) (N_14:nat), (((ord_less_eq_nat M_7) N_14)->((dvd_dvd_real ((power_power_real A_64) M_7)) ((power_power_real A_64) N_14))))
% 1.18/1.58 FOF formula (forall (M:nat) (N:nat) (I_1:nat), (((ord_less_nat zero_zero_nat) I_1)->(((ord_less_nat ((power_power_nat I_1) M)) ((power_power_nat I_1) N))->((ord_less_nat M) N)))) of role axiom named fact_578_nat__power__less__imp__less
% 1.18/1.58 A new axiom: (forall (M:nat) (N:nat) (I_1:nat), (((ord_less_nat zero_zero_nat) I_1)->(((ord_less_nat ((power_power_nat I_1) M)) ((power_power_nat I_1) N))->((ord_less_nat M) N))))
% 1.18/1.58 FOF formula (forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or ((ord_less_nat zero_zero_nat) X)) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_579_nat__zero__less__power__iff
% 1.18/1.58 A new axiom: (forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or ((ord_less_nat zero_zero_nat) X)) (((eq nat) N) zero_zero_nat))))
% 1.18/1.58 FOF formula (forall (A_63:real) (M_6:nat) (N_13:nat), (((eq real) ((power_power_real A_63) ((times_times_nat M_6) N_13))) ((power_power_real ((power_power_real A_63) M_6)) N_13))) of role axiom named fact_580_power__mult
% 1.18/1.58 A new axiom: (forall (A_63:real) (M_6:nat) (N_13:nat), (((eq real) ((power_power_real A_63) ((times_times_nat M_6) N_13))) ((power_power_real ((power_power_real A_63) M_6)) N_13)))
% 1.18/1.58 FOF formula (forall (A_63:nat) (M_6:nat) (N_13:nat), (((eq nat) ((power_power_nat A_63) ((times_times_nat M_6) N_13))) ((power_power_nat ((power_power_nat A_63) M_6)) N_13))) of role axiom named fact_581_power__mult
% 1.18/1.58 A new axiom: (forall (A_63:nat) (M_6:nat) (N_13:nat), (((eq nat) ((power_power_nat A_63) ((times_times_nat M_6) N_13))) ((power_power_nat ((power_power_nat A_63) M_6)) N_13)))
% 1.18/1.58 FOF formula (forall (A_63:int) (M_6:nat) (N_13:nat), (((eq int) ((power_power_int A_63) ((times_times_nat M_6) N_13))) ((power_power_int ((power_power_int A_63) M_6)) N_13))) of role axiom named fact_582_power__mult
% 1.18/1.58 A new axiom: (forall (A_63:int) (M_6:nat) (N_13:nat), (((eq int) ((power_power_int A_63) ((times_times_nat M_6) N_13))) ((power_power_int ((power_power_int A_63) M_6)) N_13)))
% 1.18/1.58 FOF formula (forall (B:int) (A:int) (C:int), (((ord_less_int A) C)->(((ord_less_int B) C)->((or ((ord_less_eq_int A) B)) ((ord_less_eq_int B) A))))) of role axiom named fact_583_Euler_Oaux2
% 1.18/1.58 A new axiom: (forall (B:int) (A:int) (C:int), (((ord_less_int A) C)->(((ord_less_int B) C)->((or ((ord_less_eq_int A) B)) ((ord_less_eq_int B) A)))))
% 1.18/1.58 FOF formula (forall (A_62:real), (((eq real) ((power_power_real A_62) one_one_nat)) A_62)) of role axiom named fact_584_power__one__right
% 1.18/1.60 A new axiom: (forall (A_62:real), (((eq real) ((power_power_real A_62) one_one_nat)) A_62))
% 1.18/1.60 FOF formula (forall (A_62:nat), (((eq nat) ((power_power_nat A_62) one_one_nat)) A_62)) of role axiom named fact_585_power__one__right
% 1.18/1.60 A new axiom: (forall (A_62:nat), (((eq nat) ((power_power_nat A_62) one_one_nat)) A_62))
% 1.18/1.60 FOF formula (forall (A_62:int), (((eq int) ((power_power_int A_62) one_one_nat)) A_62)) of role axiom named fact_586_power__one__right
% 1.18/1.60 A new axiom: (forall (A_62:int), (((eq int) ((power_power_int A_62) one_one_nat)) A_62))
% 1.18/1.60 FOF formula (forall (M:int), (((zcong M) zero_zero_int) M)) of role axiom named fact_587_zcong__id
% 1.18/1.60 A new axiom: (forall (M:int), (((zcong M) zero_zero_int) M))
% 1.18/1.60 FOF formula (forall (A:int) (B:int), ((iff (((zcong A) B) zero_zero_int)) (((eq int) A) B))) of role axiom named fact_588_IntPrimes_Ozcong__zero
% 1.18/1.60 A new axiom: (forall (A:int) (B:int), ((iff (((zcong A) B) zero_zero_int)) (((eq int) A) B)))
% 1.18/1.60 FOF formula (forall (A:int) (B:int), (((zcong A) B) one_one_int)) of role axiom named fact_589_zcong__1
% 1.18/1.60 A new axiom: (forall (A:int) (B:int), (((zcong A) B) one_one_int))
% 1.18/1.60 FOF formula (forall (A:int) (M:int) (B:int), (((zcong ((times_times_int A) M)) ((times_times_int B) M)) M)) of role axiom named fact_590_zcong__zmult__self
% 1.18/1.60 A new axiom: (forall (A:int) (M:int) (B:int), (((zcong ((times_times_int A) M)) ((times_times_int B) M)) M))
% 1.18/1.60 FOF formula (forall (C:int) (D:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((iff (((zcong C) ((times_times_int A) D)) M)) (((zcong C) ((times_times_int B) D)) M)))) of role axiom named fact_591_zcong__zmult__prop1
% 1.18/1.60 A new axiom: (forall (C:int) (D:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((iff (((zcong C) ((times_times_int A) D)) M)) (((zcong C) ((times_times_int B) D)) M))))
% 1.18/1.60 FOF formula (forall (C:int) (D:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((iff (((zcong C) ((times_times_int D) A)) M)) (((zcong C) ((times_times_int D) B)) M)))) of role axiom named fact_592_zcong__zmult__prop2
% 1.18/1.60 A new axiom: (forall (C:int) (D:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((iff (((zcong C) ((times_times_int D) A)) M)) (((zcong C) ((times_times_int D) B)) M))))
% 1.18/1.60 FOF formula (forall (K:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->(((zcong ((times_times_int A) K)) ((times_times_int B) K)) M))) of role axiom named fact_593_zcong__scalar
% 1.18/1.60 A new axiom: (forall (K:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->(((zcong ((times_times_int A) K)) ((times_times_int B) K)) M)))
% 1.18/1.60 FOF formula (forall (K:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->(((zcong ((times_times_int K) A)) ((times_times_int K) B)) M))) of role axiom named fact_594_zcong__scalar2
% 1.18/1.60 A new axiom: (forall (K:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->(((zcong ((times_times_int K) A)) ((times_times_int K) B)) M)))
% 1.18/1.60 FOF formula (forall (C:int) (D:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((zcong C) D) M)->(((zcong ((times_times_int A) C)) ((times_times_int B) D)) M)))) of role axiom named fact_595_zcong__zmult
% 1.18/1.60 A new axiom: (forall (C:int) (D:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((zcong C) D) M)->(((zcong ((times_times_int A) C)) ((times_times_int B) D)) M))))
% 1.18/1.60 FOF formula (forall (C:int) (D:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((zcong C) D) M)->(((zcong ((plus_plus_int A) C)) ((plus_plus_int B) D)) M)))) of role axiom named fact_596_zcong__zadd
% 1.18/1.60 A new axiom: (forall (C:int) (D:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((zcong C) D) M)->(((zcong ((plus_plus_int A) C)) ((plus_plus_int B) D)) M))))
% 1.18/1.60 FOF formula (forall (C:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->(((zcong ((plus_plus_int A) C)) ((plus_plus_int B) C)) M))) of role axiom named fact_597_zcong__shift
% 1.18/1.60 A new axiom: (forall (C:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->(((zcong ((plus_plus_int A) C)) ((plus_plus_int B) C)) M)))
% 1.18/1.60 FOF formula (forall (Z:nat) (X:int) (Y:int) (M:int), ((((zcong X) Y) M)->(((zcong ((power_power_int X) Z)) ((power_power_int Y) Z)) M))) of role axiom named fact_598_zcong__zpower
% 1.18/1.60 A new axiom: (forall (Z:nat) (X:int) (Y:int) (M:int), ((((zcong X) Y) M)->(((zcong ((power_power_int X) Z)) ((power_power_int Y) Z)) M)))
% 1.27/1.62 FOF formula (forall (N_12:nat), (((eq real) ((power_power_real (number267125858f_real min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_12))) one_one_real)) of role axiom named fact_599_power__m1__even
% 1.27/1.62 A new axiom: (forall (N_12:nat), (((eq real) ((power_power_real (number267125858f_real min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_12))) one_one_real))
% 1.27/1.62 FOF formula (forall (N_12:nat), (((eq int) ((power_power_int (number_number_of_int min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_12))) one_one_int)) of role axiom named fact_600_power__m1__even
% 1.27/1.62 A new axiom: (forall (N_12:nat), (((eq int) ((power_power_int (number_number_of_int min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_12))) one_one_int))
% 1.27/1.62 FOF formula (forall (B_50:real) (A_61:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_61)) ((ord_less_eq_real B_50) zero_zero_real))) ((and ((ord_less_eq_real A_61) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_50)))->((ord_less_eq_real ((times_times_real A_61) B_50)) zero_zero_real))) of role axiom named fact_601_split__mult__neg__le
% 1.27/1.62 A new axiom: (forall (B_50:real) (A_61:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_61)) ((ord_less_eq_real B_50) zero_zero_real))) ((and ((ord_less_eq_real A_61) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_50)))->((ord_less_eq_real ((times_times_real A_61) B_50)) zero_zero_real)))
% 1.27/1.62 FOF formula (forall (B_50:nat) (A_61:nat), (((or ((and ((ord_less_eq_nat zero_zero_nat) A_61)) ((ord_less_eq_nat B_50) zero_zero_nat))) ((and ((ord_less_eq_nat A_61) zero_zero_nat)) ((ord_less_eq_nat zero_zero_nat) B_50)))->((ord_less_eq_nat ((times_times_nat A_61) B_50)) zero_zero_nat))) of role axiom named fact_602_split__mult__neg__le
% 1.27/1.62 A new axiom: (forall (B_50:nat) (A_61:nat), (((or ((and ((ord_less_eq_nat zero_zero_nat) A_61)) ((ord_less_eq_nat B_50) zero_zero_nat))) ((and ((ord_less_eq_nat A_61) zero_zero_nat)) ((ord_less_eq_nat zero_zero_nat) B_50)))->((ord_less_eq_nat ((times_times_nat A_61) B_50)) zero_zero_nat)))
% 1.27/1.62 FOF formula (forall (B_50:int) (A_61:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_61)) ((ord_less_eq_int B_50) zero_zero_int))) ((and ((ord_less_eq_int A_61) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_50)))->((ord_less_eq_int ((times_times_int A_61) B_50)) zero_zero_int))) of role axiom named fact_603_split__mult__neg__le
% 1.27/1.62 A new axiom: (forall (B_50:int) (A_61:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_61)) ((ord_less_eq_int B_50) zero_zero_int))) ((and ((ord_less_eq_int A_61) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_50)))->((ord_less_eq_int ((times_times_int A_61) B_50)) zero_zero_int)))
% 1.27/1.62 FOF formula (forall (B_49:real) (A_60:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_60)) ((ord_less_eq_real zero_zero_real) B_49))) ((and ((ord_less_eq_real A_60) zero_zero_real)) ((ord_less_eq_real B_49) zero_zero_real)))->((ord_less_eq_real zero_zero_real) ((times_times_real A_60) B_49)))) of role axiom named fact_604_split__mult__pos__le
% 1.27/1.62 A new axiom: (forall (B_49:real) (A_60:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_60)) ((ord_less_eq_real zero_zero_real) B_49))) ((and ((ord_less_eq_real A_60) zero_zero_real)) ((ord_less_eq_real B_49) zero_zero_real)))->((ord_less_eq_real zero_zero_real) ((times_times_real A_60) B_49))))
% 1.27/1.62 FOF formula (forall (B_49:int) (A_60:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_60)) ((ord_less_eq_int zero_zero_int) B_49))) ((and ((ord_less_eq_int A_60) zero_zero_int)) ((ord_less_eq_int B_49) zero_zero_int)))->((ord_less_eq_int zero_zero_int) ((times_times_int A_60) B_49)))) of role axiom named fact_605_split__mult__pos__le
% 1.27/1.62 A new axiom: (forall (B_49:int) (A_60:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_60)) ((ord_less_eq_int zero_zero_int) B_49))) ((and ((ord_less_eq_int A_60) zero_zero_int)) ((ord_less_eq_int B_49) zero_zero_int)))->((ord_less_eq_int zero_zero_int) ((times_times_int A_60) B_49))))
% 1.27/1.64 FOF formula (forall (C_31:real) (D_8:real) (A_59:real) (B_48:real), (((ord_less_eq_real A_59) B_48)->(((ord_less_eq_real C_31) D_8)->(((ord_less_eq_real zero_zero_real) B_48)->(((ord_less_eq_real zero_zero_real) C_31)->((ord_less_eq_real ((times_times_real A_59) C_31)) ((times_times_real B_48) D_8))))))) of role axiom named fact_606_mult__mono
% 1.27/1.64 A new axiom: (forall (C_31:real) (D_8:real) (A_59:real) (B_48:real), (((ord_less_eq_real A_59) B_48)->(((ord_less_eq_real C_31) D_8)->(((ord_less_eq_real zero_zero_real) B_48)->(((ord_less_eq_real zero_zero_real) C_31)->((ord_less_eq_real ((times_times_real A_59) C_31)) ((times_times_real B_48) D_8)))))))
% 1.27/1.64 FOF formula (forall (C_31:nat) (D_8:nat) (A_59:nat) (B_48:nat), (((ord_less_eq_nat A_59) B_48)->(((ord_less_eq_nat C_31) D_8)->(((ord_less_eq_nat zero_zero_nat) B_48)->(((ord_less_eq_nat zero_zero_nat) C_31)->((ord_less_eq_nat ((times_times_nat A_59) C_31)) ((times_times_nat B_48) D_8))))))) of role axiom named fact_607_mult__mono
% 1.27/1.64 A new axiom: (forall (C_31:nat) (D_8:nat) (A_59:nat) (B_48:nat), (((ord_less_eq_nat A_59) B_48)->(((ord_less_eq_nat C_31) D_8)->(((ord_less_eq_nat zero_zero_nat) B_48)->(((ord_less_eq_nat zero_zero_nat) C_31)->((ord_less_eq_nat ((times_times_nat A_59) C_31)) ((times_times_nat B_48) D_8)))))))
% 1.27/1.64 FOF formula (forall (C_31:int) (D_8:int) (A_59:int) (B_48:int), (((ord_less_eq_int A_59) B_48)->(((ord_less_eq_int C_31) D_8)->(((ord_less_eq_int zero_zero_int) B_48)->(((ord_less_eq_int zero_zero_int) C_31)->((ord_less_eq_int ((times_times_int A_59) C_31)) ((times_times_int B_48) D_8))))))) of role axiom named fact_608_mult__mono
% 1.27/1.64 A new axiom: (forall (C_31:int) (D_8:int) (A_59:int) (B_48:int), (((ord_less_eq_int A_59) B_48)->(((ord_less_eq_int C_31) D_8)->(((ord_less_eq_int zero_zero_int) B_48)->(((ord_less_eq_int zero_zero_int) C_31)->((ord_less_eq_int ((times_times_int A_59) C_31)) ((times_times_int B_48) D_8)))))))
% 1.27/1.64 FOF formula (forall (C_30:real) (D_7:real) (A_58:real) (B_47:real), (((ord_less_eq_real A_58) B_47)->(((ord_less_eq_real C_30) D_7)->(((ord_less_eq_real zero_zero_real) A_58)->(((ord_less_eq_real zero_zero_real) C_30)->((ord_less_eq_real ((times_times_real A_58) C_30)) ((times_times_real B_47) D_7))))))) of role axiom named fact_609_mult__mono_H
% 1.27/1.64 A new axiom: (forall (C_30:real) (D_7:real) (A_58:real) (B_47:real), (((ord_less_eq_real A_58) B_47)->(((ord_less_eq_real C_30) D_7)->(((ord_less_eq_real zero_zero_real) A_58)->(((ord_less_eq_real zero_zero_real) C_30)->((ord_less_eq_real ((times_times_real A_58) C_30)) ((times_times_real B_47) D_7)))))))
% 1.27/1.64 FOF formula (forall (C_30:nat) (D_7:nat) (A_58:nat) (B_47:nat), (((ord_less_eq_nat A_58) B_47)->(((ord_less_eq_nat C_30) D_7)->(((ord_less_eq_nat zero_zero_nat) A_58)->(((ord_less_eq_nat zero_zero_nat) C_30)->((ord_less_eq_nat ((times_times_nat A_58) C_30)) ((times_times_nat B_47) D_7))))))) of role axiom named fact_610_mult__mono_H
% 1.27/1.64 A new axiom: (forall (C_30:nat) (D_7:nat) (A_58:nat) (B_47:nat), (((ord_less_eq_nat A_58) B_47)->(((ord_less_eq_nat C_30) D_7)->(((ord_less_eq_nat zero_zero_nat) A_58)->(((ord_less_eq_nat zero_zero_nat) C_30)->((ord_less_eq_nat ((times_times_nat A_58) C_30)) ((times_times_nat B_47) D_7)))))))
% 1.27/1.64 FOF formula (forall (C_30:int) (D_7:int) (A_58:int) (B_47:int), (((ord_less_eq_int A_58) B_47)->(((ord_less_eq_int C_30) D_7)->(((ord_less_eq_int zero_zero_int) A_58)->(((ord_less_eq_int zero_zero_int) C_30)->((ord_less_eq_int ((times_times_int A_58) C_30)) ((times_times_int B_47) D_7))))))) of role axiom named fact_611_mult__mono_H
% 1.27/1.64 A new axiom: (forall (C_30:int) (D_7:int) (A_58:int) (B_47:int), (((ord_less_eq_int A_58) B_47)->(((ord_less_eq_int C_30) D_7)->(((ord_less_eq_int zero_zero_int) A_58)->(((ord_less_eq_int zero_zero_int) C_30)->((ord_less_eq_int ((times_times_int A_58) C_30)) ((times_times_int B_47) D_7)))))))
% 1.27/1.64 FOF formula (forall (C_29:real) (B_46:real) (A_57:real), (((ord_less_eq_real B_46) A_57)->(((ord_less_eq_real C_29) zero_zero_real)->((ord_less_eq_real ((times_times_real C_29) A_57)) ((times_times_real C_29) B_46))))) of role axiom named fact_612_mult__left__mono__neg
% 1.27/1.64 A new axiom: (forall (C_29:real) (B_46:real) (A_57:real), (((ord_less_eq_real B_46) A_57)->(((ord_less_eq_real C_29) zero_zero_real)->((ord_less_eq_real ((times_times_real C_29) A_57)) ((times_times_real C_29) B_46)))))
% 1.27/1.66 FOF formula (forall (C_29:int) (B_46:int) (A_57:int), (((ord_less_eq_int B_46) A_57)->(((ord_less_eq_int C_29) zero_zero_int)->((ord_less_eq_int ((times_times_int C_29) A_57)) ((times_times_int C_29) B_46))))) of role axiom named fact_613_mult__left__mono__neg
% 1.27/1.66 A new axiom: (forall (C_29:int) (B_46:int) (A_57:int), (((ord_less_eq_int B_46) A_57)->(((ord_less_eq_int C_29) zero_zero_int)->((ord_less_eq_int ((times_times_int C_29) A_57)) ((times_times_int C_29) B_46)))))
% 1.27/1.66 FOF formula (forall (C_28:real) (B_45:real) (A_56:real), (((ord_less_eq_real B_45) A_56)->(((ord_less_eq_real C_28) zero_zero_real)->((ord_less_eq_real ((times_times_real A_56) C_28)) ((times_times_real B_45) C_28))))) of role axiom named fact_614_mult__right__mono__neg
% 1.27/1.66 A new axiom: (forall (C_28:real) (B_45:real) (A_56:real), (((ord_less_eq_real B_45) A_56)->(((ord_less_eq_real C_28) zero_zero_real)->((ord_less_eq_real ((times_times_real A_56) C_28)) ((times_times_real B_45) C_28)))))
% 1.27/1.66 FOF formula (forall (C_28:int) (B_45:int) (A_56:int), (((ord_less_eq_int B_45) A_56)->(((ord_less_eq_int C_28) zero_zero_int)->((ord_less_eq_int ((times_times_int A_56) C_28)) ((times_times_int B_45) C_28))))) of role axiom named fact_615_mult__right__mono__neg
% 1.27/1.66 A new axiom: (forall (C_28:int) (B_45:int) (A_56:int), (((ord_less_eq_int B_45) A_56)->(((ord_less_eq_int C_28) zero_zero_int)->((ord_less_eq_int ((times_times_int A_56) C_28)) ((times_times_int B_45) C_28)))))
% 1.27/1.66 FOF formula (forall (C_27:real) (A_55:real) (B_44:real), (((ord_less_eq_real A_55) B_44)->(((ord_less_eq_real zero_zero_real) C_27)->((ord_less_eq_real ((times_times_real C_27) A_55)) ((times_times_real C_27) B_44))))) of role axiom named fact_616_comm__mult__left__mono
% 1.27/1.66 A new axiom: (forall (C_27:real) (A_55:real) (B_44:real), (((ord_less_eq_real A_55) B_44)->(((ord_less_eq_real zero_zero_real) C_27)->((ord_less_eq_real ((times_times_real C_27) A_55)) ((times_times_real C_27) B_44)))))
% 1.27/1.66 FOF formula (forall (C_27:nat) (A_55:nat) (B_44:nat), (((ord_less_eq_nat A_55) B_44)->(((ord_less_eq_nat zero_zero_nat) C_27)->((ord_less_eq_nat ((times_times_nat C_27) A_55)) ((times_times_nat C_27) B_44))))) of role axiom named fact_617_comm__mult__left__mono
% 1.27/1.66 A new axiom: (forall (C_27:nat) (A_55:nat) (B_44:nat), (((ord_less_eq_nat A_55) B_44)->(((ord_less_eq_nat zero_zero_nat) C_27)->((ord_less_eq_nat ((times_times_nat C_27) A_55)) ((times_times_nat C_27) B_44)))))
% 1.27/1.66 FOF formula (forall (C_27:int) (A_55:int) (B_44:int), (((ord_less_eq_int A_55) B_44)->(((ord_less_eq_int zero_zero_int) C_27)->((ord_less_eq_int ((times_times_int C_27) A_55)) ((times_times_int C_27) B_44))))) of role axiom named fact_618_comm__mult__left__mono
% 1.27/1.66 A new axiom: (forall (C_27:int) (A_55:int) (B_44:int), (((ord_less_eq_int A_55) B_44)->(((ord_less_eq_int zero_zero_int) C_27)->((ord_less_eq_int ((times_times_int C_27) A_55)) ((times_times_int C_27) B_44)))))
% 1.27/1.66 FOF formula (forall (C_26:real) (A_54:real) (B_43:real), (((ord_less_eq_real A_54) B_43)->(((ord_less_eq_real zero_zero_real) C_26)->((ord_less_eq_real ((times_times_real C_26) A_54)) ((times_times_real C_26) B_43))))) of role axiom named fact_619_mult__left__mono
% 1.27/1.66 A new axiom: (forall (C_26:real) (A_54:real) (B_43:real), (((ord_less_eq_real A_54) B_43)->(((ord_less_eq_real zero_zero_real) C_26)->((ord_less_eq_real ((times_times_real C_26) A_54)) ((times_times_real C_26) B_43)))))
% 1.27/1.66 FOF formula (forall (C_26:nat) (A_54:nat) (B_43:nat), (((ord_less_eq_nat A_54) B_43)->(((ord_less_eq_nat zero_zero_nat) C_26)->((ord_less_eq_nat ((times_times_nat C_26) A_54)) ((times_times_nat C_26) B_43))))) of role axiom named fact_620_mult__left__mono
% 1.27/1.66 A new axiom: (forall (C_26:nat) (A_54:nat) (B_43:nat), (((ord_less_eq_nat A_54) B_43)->(((ord_less_eq_nat zero_zero_nat) C_26)->((ord_less_eq_nat ((times_times_nat C_26) A_54)) ((times_times_nat C_26) B_43)))))
% 1.27/1.66 FOF formula (forall (C_26:int) (A_54:int) (B_43:int), (((ord_less_eq_int A_54) B_43)->(((ord_less_eq_int zero_zero_int) C_26)->((ord_less_eq_int ((times_times_int C_26) A_54)) ((times_times_int C_26) B_43))))) of role axiom named fact_621_mult__left__mono
% 1.27/1.67 A new axiom: (forall (C_26:int) (A_54:int) (B_43:int), (((ord_less_eq_int A_54) B_43)->(((ord_less_eq_int zero_zero_int) C_26)->((ord_less_eq_int ((times_times_int C_26) A_54)) ((times_times_int C_26) B_43)))))
% 1.27/1.67 FOF formula (forall (C_25:real) (A_53:real) (B_42:real), (((ord_less_eq_real A_53) B_42)->(((ord_less_eq_real zero_zero_real) C_25)->((ord_less_eq_real ((times_times_real A_53) C_25)) ((times_times_real B_42) C_25))))) of role axiom named fact_622_mult__right__mono
% 1.27/1.67 A new axiom: (forall (C_25:real) (A_53:real) (B_42:real), (((ord_less_eq_real A_53) B_42)->(((ord_less_eq_real zero_zero_real) C_25)->((ord_less_eq_real ((times_times_real A_53) C_25)) ((times_times_real B_42) C_25)))))
% 1.27/1.67 FOF formula (forall (C_25:nat) (A_53:nat) (B_42:nat), (((ord_less_eq_nat A_53) B_42)->(((ord_less_eq_nat zero_zero_nat) C_25)->((ord_less_eq_nat ((times_times_nat A_53) C_25)) ((times_times_nat B_42) C_25))))) of role axiom named fact_623_mult__right__mono
% 1.27/1.67 A new axiom: (forall (C_25:nat) (A_53:nat) (B_42:nat), (((ord_less_eq_nat A_53) B_42)->(((ord_less_eq_nat zero_zero_nat) C_25)->((ord_less_eq_nat ((times_times_nat A_53) C_25)) ((times_times_nat B_42) C_25)))))
% 1.27/1.67 FOF formula (forall (C_25:int) (A_53:int) (B_42:int), (((ord_less_eq_int A_53) B_42)->(((ord_less_eq_int zero_zero_int) C_25)->((ord_less_eq_int ((times_times_int A_53) C_25)) ((times_times_int B_42) C_25))))) of role axiom named fact_624_mult__right__mono
% 1.27/1.67 A new axiom: (forall (C_25:int) (A_53:int) (B_42:int), (((ord_less_eq_int A_53) B_42)->(((ord_less_eq_int zero_zero_int) C_25)->((ord_less_eq_int ((times_times_int A_53) C_25)) ((times_times_int B_42) C_25)))))
% 1.27/1.67 FOF formula (forall (B_41:real) (A_52:real), (((ord_less_eq_real A_52) zero_zero_real)->(((ord_less_eq_real B_41) zero_zero_real)->((ord_less_eq_real zero_zero_real) ((times_times_real A_52) B_41))))) of role axiom named fact_625_mult__nonpos__nonpos
% 1.27/1.67 A new axiom: (forall (B_41:real) (A_52:real), (((ord_less_eq_real A_52) zero_zero_real)->(((ord_less_eq_real B_41) zero_zero_real)->((ord_less_eq_real zero_zero_real) ((times_times_real A_52) B_41)))))
% 1.27/1.67 FOF formula (forall (B_41:int) (A_52:int), (((ord_less_eq_int A_52) zero_zero_int)->(((ord_less_eq_int B_41) zero_zero_int)->((ord_less_eq_int zero_zero_int) ((times_times_int A_52) B_41))))) of role axiom named fact_626_mult__nonpos__nonpos
% 1.27/1.67 A new axiom: (forall (B_41:int) (A_52:int), (((ord_less_eq_int A_52) zero_zero_int)->(((ord_less_eq_int B_41) zero_zero_int)->((ord_less_eq_int zero_zero_int) ((times_times_int A_52) B_41)))))
% 1.27/1.67 FOF formula (forall (B_40:real) (A_51:real), (((ord_less_eq_real A_51) zero_zero_real)->(((ord_less_eq_real zero_zero_real) B_40)->((ord_less_eq_real ((times_times_real A_51) B_40)) zero_zero_real)))) of role axiom named fact_627_mult__nonpos__nonneg
% 1.27/1.67 A new axiom: (forall (B_40:real) (A_51:real), (((ord_less_eq_real A_51) zero_zero_real)->(((ord_less_eq_real zero_zero_real) B_40)->((ord_less_eq_real ((times_times_real A_51) B_40)) zero_zero_real))))
% 1.27/1.67 FOF formula (forall (B_40:nat) (A_51:nat), (((ord_less_eq_nat A_51) zero_zero_nat)->(((ord_less_eq_nat zero_zero_nat) B_40)->((ord_less_eq_nat ((times_times_nat A_51) B_40)) zero_zero_nat)))) of role axiom named fact_628_mult__nonpos__nonneg
% 1.27/1.67 A new axiom: (forall (B_40:nat) (A_51:nat), (((ord_less_eq_nat A_51) zero_zero_nat)->(((ord_less_eq_nat zero_zero_nat) B_40)->((ord_less_eq_nat ((times_times_nat A_51) B_40)) zero_zero_nat))))
% 1.27/1.67 FOF formula (forall (B_40:int) (A_51:int), (((ord_less_eq_int A_51) zero_zero_int)->(((ord_less_eq_int zero_zero_int) B_40)->((ord_less_eq_int ((times_times_int A_51) B_40)) zero_zero_int)))) of role axiom named fact_629_mult__nonpos__nonneg
% 1.27/1.67 A new axiom: (forall (B_40:int) (A_51:int), (((ord_less_eq_int A_51) zero_zero_int)->(((ord_less_eq_int zero_zero_int) B_40)->((ord_less_eq_int ((times_times_int A_51) B_40)) zero_zero_int))))
% 1.27/1.67 FOF formula (forall (B_39:real) (A_50:real), (((ord_less_eq_real zero_zero_real) A_50)->(((ord_less_eq_real B_39) zero_zero_real)->((ord_less_eq_real ((times_times_real B_39) A_50)) zero_zero_real)))) of role axiom named fact_630_mult__nonneg__nonpos2
% 1.35/1.69 A new axiom: (forall (B_39:real) (A_50:real), (((ord_less_eq_real zero_zero_real) A_50)->(((ord_less_eq_real B_39) zero_zero_real)->((ord_less_eq_real ((times_times_real B_39) A_50)) zero_zero_real))))
% 1.35/1.69 FOF formula (forall (B_39:nat) (A_50:nat), (((ord_less_eq_nat zero_zero_nat) A_50)->(((ord_less_eq_nat B_39) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat B_39) A_50)) zero_zero_nat)))) of role axiom named fact_631_mult__nonneg__nonpos2
% 1.35/1.69 A new axiom: (forall (B_39:nat) (A_50:nat), (((ord_less_eq_nat zero_zero_nat) A_50)->(((ord_less_eq_nat B_39) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat B_39) A_50)) zero_zero_nat))))
% 1.35/1.69 FOF formula (forall (B_39:int) (A_50:int), (((ord_less_eq_int zero_zero_int) A_50)->(((ord_less_eq_int B_39) zero_zero_int)->((ord_less_eq_int ((times_times_int B_39) A_50)) zero_zero_int)))) of role axiom named fact_632_mult__nonneg__nonpos2
% 1.35/1.69 A new axiom: (forall (B_39:int) (A_50:int), (((ord_less_eq_int zero_zero_int) A_50)->(((ord_less_eq_int B_39) zero_zero_int)->((ord_less_eq_int ((times_times_int B_39) A_50)) zero_zero_int))))
% 1.35/1.69 FOF formula (forall (B_38:real) (A_49:real), (((ord_less_eq_real zero_zero_real) A_49)->(((ord_less_eq_real B_38) zero_zero_real)->((ord_less_eq_real ((times_times_real A_49) B_38)) zero_zero_real)))) of role axiom named fact_633_mult__nonneg__nonpos
% 1.35/1.69 A new axiom: (forall (B_38:real) (A_49:real), (((ord_less_eq_real zero_zero_real) A_49)->(((ord_less_eq_real B_38) zero_zero_real)->((ord_less_eq_real ((times_times_real A_49) B_38)) zero_zero_real))))
% 1.35/1.69 FOF formula (forall (B_38:nat) (A_49:nat), (((ord_less_eq_nat zero_zero_nat) A_49)->(((ord_less_eq_nat B_38) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat A_49) B_38)) zero_zero_nat)))) of role axiom named fact_634_mult__nonneg__nonpos
% 1.35/1.69 A new axiom: (forall (B_38:nat) (A_49:nat), (((ord_less_eq_nat zero_zero_nat) A_49)->(((ord_less_eq_nat B_38) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat A_49) B_38)) zero_zero_nat))))
% 1.35/1.69 FOF formula (forall (B_38:int) (A_49:int), (((ord_less_eq_int zero_zero_int) A_49)->(((ord_less_eq_int B_38) zero_zero_int)->((ord_less_eq_int ((times_times_int A_49) B_38)) zero_zero_int)))) of role axiom named fact_635_mult__nonneg__nonpos
% 1.35/1.69 A new axiom: (forall (B_38:int) (A_49:int), (((ord_less_eq_int zero_zero_int) A_49)->(((ord_less_eq_int B_38) zero_zero_int)->((ord_less_eq_int ((times_times_int A_49) B_38)) zero_zero_int))))
% 1.35/1.69 FOF formula (forall (B_37:real) (A_48:real), (((ord_less_eq_real zero_zero_real) A_48)->(((ord_less_eq_real zero_zero_real) B_37)->((ord_less_eq_real zero_zero_real) ((times_times_real A_48) B_37))))) of role axiom named fact_636_mult__nonneg__nonneg
% 1.35/1.69 A new axiom: (forall (B_37:real) (A_48:real), (((ord_less_eq_real zero_zero_real) A_48)->(((ord_less_eq_real zero_zero_real) B_37)->((ord_less_eq_real zero_zero_real) ((times_times_real A_48) B_37)))))
% 1.35/1.69 FOF formula (forall (B_37:nat) (A_48:nat), (((ord_less_eq_nat zero_zero_nat) A_48)->(((ord_less_eq_nat zero_zero_nat) B_37)->((ord_less_eq_nat zero_zero_nat) ((times_times_nat A_48) B_37))))) of role axiom named fact_637_mult__nonneg__nonneg
% 1.35/1.69 A new axiom: (forall (B_37:nat) (A_48:nat), (((ord_less_eq_nat zero_zero_nat) A_48)->(((ord_less_eq_nat zero_zero_nat) B_37)->((ord_less_eq_nat zero_zero_nat) ((times_times_nat A_48) B_37)))))
% 1.35/1.69 FOF formula (forall (B_37:int) (A_48:int), (((ord_less_eq_int zero_zero_int) A_48)->(((ord_less_eq_int zero_zero_int) B_37)->((ord_less_eq_int zero_zero_int) ((times_times_int A_48) B_37))))) of role axiom named fact_638_mult__nonneg__nonneg
% 1.35/1.69 A new axiom: (forall (B_37:int) (A_48:int), (((ord_less_eq_int zero_zero_int) A_48)->(((ord_less_eq_int zero_zero_int) B_37)->((ord_less_eq_int zero_zero_int) ((times_times_int A_48) B_37)))))
% 1.35/1.69 FOF formula (forall (A_47:real) (B_36:real), ((iff ((ord_less_eq_real ((times_times_real A_47) B_36)) zero_zero_real)) ((or ((and ((ord_less_eq_real zero_zero_real) A_47)) ((ord_less_eq_real B_36) zero_zero_real))) ((and ((ord_less_eq_real A_47) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_36))))) of role axiom named fact_639_mult__le__0__iff
% 1.35/1.70 A new axiom: (forall (A_47:real) (B_36:real), ((iff ((ord_less_eq_real ((times_times_real A_47) B_36)) zero_zero_real)) ((or ((and ((ord_less_eq_real zero_zero_real) A_47)) ((ord_less_eq_real B_36) zero_zero_real))) ((and ((ord_less_eq_real A_47) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_36)))))
% 1.35/1.70 FOF formula (forall (A_47:int) (B_36:int), ((iff ((ord_less_eq_int ((times_times_int A_47) B_36)) zero_zero_int)) ((or ((and ((ord_less_eq_int zero_zero_int) A_47)) ((ord_less_eq_int B_36) zero_zero_int))) ((and ((ord_less_eq_int A_47) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_36))))) of role axiom named fact_640_mult__le__0__iff
% 1.35/1.70 A new axiom: (forall (A_47:int) (B_36:int), ((iff ((ord_less_eq_int ((times_times_int A_47) B_36)) zero_zero_int)) ((or ((and ((ord_less_eq_int zero_zero_int) A_47)) ((ord_less_eq_int B_36) zero_zero_int))) ((and ((ord_less_eq_int A_47) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_36)))))
% 1.35/1.70 FOF formula (forall (A_46:real) (B_35:real), ((iff ((ord_less_eq_real zero_zero_real) ((times_times_real A_46) B_35))) ((or ((and ((ord_less_eq_real zero_zero_real) A_46)) ((ord_less_eq_real zero_zero_real) B_35))) ((and ((ord_less_eq_real A_46) zero_zero_real)) ((ord_less_eq_real B_35) zero_zero_real))))) of role axiom named fact_641_zero__le__mult__iff
% 1.35/1.70 A new axiom: (forall (A_46:real) (B_35:real), ((iff ((ord_less_eq_real zero_zero_real) ((times_times_real A_46) B_35))) ((or ((and ((ord_less_eq_real zero_zero_real) A_46)) ((ord_less_eq_real zero_zero_real) B_35))) ((and ((ord_less_eq_real A_46) zero_zero_real)) ((ord_less_eq_real B_35) zero_zero_real)))))
% 1.35/1.70 FOF formula (forall (A_46:int) (B_35:int), ((iff ((ord_less_eq_int zero_zero_int) ((times_times_int A_46) B_35))) ((or ((and ((ord_less_eq_int zero_zero_int) A_46)) ((ord_less_eq_int zero_zero_int) B_35))) ((and ((ord_less_eq_int A_46) zero_zero_int)) ((ord_less_eq_int B_35) zero_zero_int))))) of role axiom named fact_642_zero__le__mult__iff
% 1.35/1.70 A new axiom: (forall (A_46:int) (B_35:int), ((iff ((ord_less_eq_int zero_zero_int) ((times_times_int A_46) B_35))) ((or ((and ((ord_less_eq_int zero_zero_int) A_46)) ((ord_less_eq_int zero_zero_int) B_35))) ((and ((ord_less_eq_int A_46) zero_zero_int)) ((ord_less_eq_int B_35) zero_zero_int)))))
% 1.35/1.70 FOF formula (forall (A_45:real), ((ord_less_eq_real zero_zero_real) ((times_times_real A_45) A_45))) of role axiom named fact_643_zero__le__square
% 1.35/1.70 A new axiom: (forall (A_45:real), ((ord_less_eq_real zero_zero_real) ((times_times_real A_45) A_45)))
% 1.35/1.70 FOF formula (forall (A_45:int), ((ord_less_eq_int zero_zero_int) ((times_times_int A_45) A_45))) of role axiom named fact_644_zero__le__square
% 1.35/1.70 A new axiom: (forall (A_45:int), ((ord_less_eq_int zero_zero_int) ((times_times_int A_45) A_45)))
% 1.35/1.70 FOF formula (forall (C_24:real) (B_34:real) (A_44:real), (((ord_less_real B_34) A_44)->(((ord_less_real C_24) zero_zero_real)->((ord_less_real ((times_times_real C_24) A_44)) ((times_times_real C_24) B_34))))) of role axiom named fact_645_mult__strict__left__mono__neg
% 1.35/1.70 A new axiom: (forall (C_24:real) (B_34:real) (A_44:real), (((ord_less_real B_34) A_44)->(((ord_less_real C_24) zero_zero_real)->((ord_less_real ((times_times_real C_24) A_44)) ((times_times_real C_24) B_34)))))
% 1.35/1.70 FOF formula (forall (C_24:int) (B_34:int) (A_44:int), (((ord_less_int B_34) A_44)->(((ord_less_int C_24) zero_zero_int)->((ord_less_int ((times_times_int C_24) A_44)) ((times_times_int C_24) B_34))))) of role axiom named fact_646_mult__strict__left__mono__neg
% 1.35/1.70 A new axiom: (forall (C_24:int) (B_34:int) (A_44:int), (((ord_less_int B_34) A_44)->(((ord_less_int C_24) zero_zero_int)->((ord_less_int ((times_times_int C_24) A_44)) ((times_times_int C_24) B_34)))))
% 1.35/1.70 FOF formula (forall (C_23:real) (B_33:real) (A_43:real), (((ord_less_real B_33) A_43)->(((ord_less_real C_23) zero_zero_real)->((ord_less_real ((times_times_real A_43) C_23)) ((times_times_real B_33) C_23))))) of role axiom named fact_647_mult__strict__right__mono__neg
% 1.35/1.72 A new axiom: (forall (C_23:real) (B_33:real) (A_43:real), (((ord_less_real B_33) A_43)->(((ord_less_real C_23) zero_zero_real)->((ord_less_real ((times_times_real A_43) C_23)) ((times_times_real B_33) C_23)))))
% 1.35/1.72 FOF formula (forall (C_23:int) (B_33:int) (A_43:int), (((ord_less_int B_33) A_43)->(((ord_less_int C_23) zero_zero_int)->((ord_less_int ((times_times_int A_43) C_23)) ((times_times_int B_33) C_23))))) of role axiom named fact_648_mult__strict__right__mono__neg
% 1.35/1.72 A new axiom: (forall (C_23:int) (B_33:int) (A_43:int), (((ord_less_int B_33) A_43)->(((ord_less_int C_23) zero_zero_int)->((ord_less_int ((times_times_int A_43) C_23)) ((times_times_int B_33) C_23)))))
% 1.35/1.72 FOF formula (forall (C_22:real) (A_42:real) (B_32:real), (((ord_less_real A_42) B_32)->(((ord_less_real zero_zero_real) C_22)->((ord_less_real ((times_times_real C_22) A_42)) ((times_times_real C_22) B_32))))) of role axiom named fact_649_comm__mult__strict__left__mono
% 1.35/1.72 A new axiom: (forall (C_22:real) (A_42:real) (B_32:real), (((ord_less_real A_42) B_32)->(((ord_less_real zero_zero_real) C_22)->((ord_less_real ((times_times_real C_22) A_42)) ((times_times_real C_22) B_32)))))
% 1.35/1.72 FOF formula (forall (C_22:nat) (A_42:nat) (B_32:nat), (((ord_less_nat A_42) B_32)->(((ord_less_nat zero_zero_nat) C_22)->((ord_less_nat ((times_times_nat C_22) A_42)) ((times_times_nat C_22) B_32))))) of role axiom named fact_650_comm__mult__strict__left__mono
% 1.35/1.72 A new axiom: (forall (C_22:nat) (A_42:nat) (B_32:nat), (((ord_less_nat A_42) B_32)->(((ord_less_nat zero_zero_nat) C_22)->((ord_less_nat ((times_times_nat C_22) A_42)) ((times_times_nat C_22) B_32)))))
% 1.35/1.72 FOF formula (forall (C_22:int) (A_42:int) (B_32:int), (((ord_less_int A_42) B_32)->(((ord_less_int zero_zero_int) C_22)->((ord_less_int ((times_times_int C_22) A_42)) ((times_times_int C_22) B_32))))) of role axiom named fact_651_comm__mult__strict__left__mono
% 1.35/1.72 A new axiom: (forall (C_22:int) (A_42:int) (B_32:int), (((ord_less_int A_42) B_32)->(((ord_less_int zero_zero_int) C_22)->((ord_less_int ((times_times_int C_22) A_42)) ((times_times_int C_22) B_32)))))
% 1.35/1.72 FOF formula (forall (C_21:real) (A_41:real) (B_31:real), (((ord_less_real A_41) B_31)->(((ord_less_real zero_zero_real) C_21)->((ord_less_real ((times_times_real C_21) A_41)) ((times_times_real C_21) B_31))))) of role axiom named fact_652_mult__strict__left__mono
% 1.35/1.72 A new axiom: (forall (C_21:real) (A_41:real) (B_31:real), (((ord_less_real A_41) B_31)->(((ord_less_real zero_zero_real) C_21)->((ord_less_real ((times_times_real C_21) A_41)) ((times_times_real C_21) B_31)))))
% 1.35/1.72 FOF formula (forall (C_21:nat) (A_41:nat) (B_31:nat), (((ord_less_nat A_41) B_31)->(((ord_less_nat zero_zero_nat) C_21)->((ord_less_nat ((times_times_nat C_21) A_41)) ((times_times_nat C_21) B_31))))) of role axiom named fact_653_mult__strict__left__mono
% 1.35/1.72 A new axiom: (forall (C_21:nat) (A_41:nat) (B_31:nat), (((ord_less_nat A_41) B_31)->(((ord_less_nat zero_zero_nat) C_21)->((ord_less_nat ((times_times_nat C_21) A_41)) ((times_times_nat C_21) B_31)))))
% 1.35/1.72 FOF formula (forall (C_21:int) (A_41:int) (B_31:int), (((ord_less_int A_41) B_31)->(((ord_less_int zero_zero_int) C_21)->((ord_less_int ((times_times_int C_21) A_41)) ((times_times_int C_21) B_31))))) of role axiom named fact_654_mult__strict__left__mono
% 1.35/1.72 A new axiom: (forall (C_21:int) (A_41:int) (B_31:int), (((ord_less_int A_41) B_31)->(((ord_less_int zero_zero_int) C_21)->((ord_less_int ((times_times_int C_21) A_41)) ((times_times_int C_21) B_31)))))
% 1.35/1.72 FOF formula (forall (C_20:real) (A_40:real) (B_30:real), (((ord_less_real A_40) B_30)->(((ord_less_real zero_zero_real) C_20)->((ord_less_real ((times_times_real A_40) C_20)) ((times_times_real B_30) C_20))))) of role axiom named fact_655_mult__strict__right__mono
% 1.35/1.72 A new axiom: (forall (C_20:real) (A_40:real) (B_30:real), (((ord_less_real A_40) B_30)->(((ord_less_real zero_zero_real) C_20)->((ord_less_real ((times_times_real A_40) C_20)) ((times_times_real B_30) C_20)))))
% 1.35/1.72 FOF formula (forall (C_20:nat) (A_40:nat) (B_30:nat), (((ord_less_nat A_40) B_30)->(((ord_less_nat zero_zero_nat) C_20)->((ord_less_nat ((times_times_nat A_40) C_20)) ((times_times_nat B_30) C_20))))) of role axiom named fact_656_mult__strict__right__mono
% 1.35/1.74 A new axiom: (forall (C_20:nat) (A_40:nat) (B_30:nat), (((ord_less_nat A_40) B_30)->(((ord_less_nat zero_zero_nat) C_20)->((ord_less_nat ((times_times_nat A_40) C_20)) ((times_times_nat B_30) C_20)))))
% 1.35/1.74 FOF formula (forall (C_20:int) (A_40:int) (B_30:int), (((ord_less_int A_40) B_30)->(((ord_less_int zero_zero_int) C_20)->((ord_less_int ((times_times_int A_40) C_20)) ((times_times_int B_30) C_20))))) of role axiom named fact_657_mult__strict__right__mono
% 1.35/1.74 A new axiom: (forall (C_20:int) (A_40:int) (B_30:int), (((ord_less_int A_40) B_30)->(((ord_less_int zero_zero_int) C_20)->((ord_less_int ((times_times_int A_40) C_20)) ((times_times_int B_30) C_20)))))
% 1.35/1.74 FOF formula (forall (B_29:real) (A_39:real), (((ord_less_real A_39) zero_zero_real)->(((ord_less_real B_29) zero_zero_real)->((ord_less_real zero_zero_real) ((times_times_real A_39) B_29))))) of role axiom named fact_658_mult__neg__neg
% 1.35/1.74 A new axiom: (forall (B_29:real) (A_39:real), (((ord_less_real A_39) zero_zero_real)->(((ord_less_real B_29) zero_zero_real)->((ord_less_real zero_zero_real) ((times_times_real A_39) B_29)))))
% 1.35/1.74 FOF formula (forall (B_29:int) (A_39:int), (((ord_less_int A_39) zero_zero_int)->(((ord_less_int B_29) zero_zero_int)->((ord_less_int zero_zero_int) ((times_times_int A_39) B_29))))) of role axiom named fact_659_mult__neg__neg
% 1.35/1.74 A new axiom: (forall (B_29:int) (A_39:int), (((ord_less_int A_39) zero_zero_int)->(((ord_less_int B_29) zero_zero_int)->((ord_less_int zero_zero_int) ((times_times_int A_39) B_29)))))
% 1.35/1.74 FOF formula (forall (B_28:real) (A_38:real), (((ord_less_real A_38) zero_zero_real)->(((ord_less_real zero_zero_real) B_28)->((ord_less_real ((times_times_real A_38) B_28)) zero_zero_real)))) of role axiom named fact_660_mult__neg__pos
% 1.35/1.74 A new axiom: (forall (B_28:real) (A_38:real), (((ord_less_real A_38) zero_zero_real)->(((ord_less_real zero_zero_real) B_28)->((ord_less_real ((times_times_real A_38) B_28)) zero_zero_real))))
% 1.35/1.74 FOF formula (forall (B_28:nat) (A_38:nat), (((ord_less_nat A_38) zero_zero_nat)->(((ord_less_nat zero_zero_nat) B_28)->((ord_less_nat ((times_times_nat A_38) B_28)) zero_zero_nat)))) of role axiom named fact_661_mult__neg__pos
% 1.35/1.74 A new axiom: (forall (B_28:nat) (A_38:nat), (((ord_less_nat A_38) zero_zero_nat)->(((ord_less_nat zero_zero_nat) B_28)->((ord_less_nat ((times_times_nat A_38) B_28)) zero_zero_nat))))
% 1.35/1.74 FOF formula (forall (B_28:int) (A_38:int), (((ord_less_int A_38) zero_zero_int)->(((ord_less_int zero_zero_int) B_28)->((ord_less_int ((times_times_int A_38) B_28)) zero_zero_int)))) of role axiom named fact_662_mult__neg__pos
% 1.35/1.74 A new axiom: (forall (B_28:int) (A_38:int), (((ord_less_int A_38) zero_zero_int)->(((ord_less_int zero_zero_int) B_28)->((ord_less_int ((times_times_int A_38) B_28)) zero_zero_int))))
% 1.35/1.74 FOF formula (forall (A_37:real) (B_27:real) (C_19:real), (((ord_less_real C_19) zero_zero_real)->((iff ((ord_less_real ((times_times_real C_19) A_37)) ((times_times_real C_19) B_27))) ((ord_less_real B_27) A_37)))) of role axiom named fact_663_mult__less__cancel__left__neg
% 1.35/1.74 A new axiom: (forall (A_37:real) (B_27:real) (C_19:real), (((ord_less_real C_19) zero_zero_real)->((iff ((ord_less_real ((times_times_real C_19) A_37)) ((times_times_real C_19) B_27))) ((ord_less_real B_27) A_37))))
% 1.35/1.74 FOF formula (forall (A_37:int) (B_27:int) (C_19:int), (((ord_less_int C_19) zero_zero_int)->((iff ((ord_less_int ((times_times_int C_19) A_37)) ((times_times_int C_19) B_27))) ((ord_less_int B_27) A_37)))) of role axiom named fact_664_mult__less__cancel__left__neg
% 1.35/1.74 A new axiom: (forall (A_37:int) (B_27:int) (C_19:int), (((ord_less_int C_19) zero_zero_int)->((iff ((ord_less_int ((times_times_int C_19) A_37)) ((times_times_int C_19) B_27))) ((ord_less_int B_27) A_37))))
% 1.35/1.74 FOF formula (forall (B_26:real) (A_36:real), (((ord_less_real zero_zero_real) ((times_times_real B_26) A_36))->(((ord_less_real zero_zero_real) A_36)->((ord_less_real zero_zero_real) B_26)))) of role axiom named fact_665_zero__less__mult__pos2
% 1.35/1.76 A new axiom: (forall (B_26:real) (A_36:real), (((ord_less_real zero_zero_real) ((times_times_real B_26) A_36))->(((ord_less_real zero_zero_real) A_36)->((ord_less_real zero_zero_real) B_26))))
% 1.35/1.76 FOF formula (forall (B_26:nat) (A_36:nat), (((ord_less_nat zero_zero_nat) ((times_times_nat B_26) A_36))->(((ord_less_nat zero_zero_nat) A_36)->((ord_less_nat zero_zero_nat) B_26)))) of role axiom named fact_666_zero__less__mult__pos2
% 1.35/1.76 A new axiom: (forall (B_26:nat) (A_36:nat), (((ord_less_nat zero_zero_nat) ((times_times_nat B_26) A_36))->(((ord_less_nat zero_zero_nat) A_36)->((ord_less_nat zero_zero_nat) B_26))))
% 1.35/1.76 FOF formula (forall (B_26:int) (A_36:int), (((ord_less_int zero_zero_int) ((times_times_int B_26) A_36))->(((ord_less_int zero_zero_int) A_36)->((ord_less_int zero_zero_int) B_26)))) of role axiom named fact_667_zero__less__mult__pos2
% 1.35/1.76 A new axiom: (forall (B_26:int) (A_36:int), (((ord_less_int zero_zero_int) ((times_times_int B_26) A_36))->(((ord_less_int zero_zero_int) A_36)->((ord_less_int zero_zero_int) B_26))))
% 1.35/1.76 FOF formula (forall (A_35:real) (B_25:real), (((ord_less_real zero_zero_real) ((times_times_real A_35) B_25))->(((ord_less_real zero_zero_real) A_35)->((ord_less_real zero_zero_real) B_25)))) of role axiom named fact_668_zero__less__mult__pos
% 1.35/1.76 A new axiom: (forall (A_35:real) (B_25:real), (((ord_less_real zero_zero_real) ((times_times_real A_35) B_25))->(((ord_less_real zero_zero_real) A_35)->((ord_less_real zero_zero_real) B_25))))
% 1.35/1.76 FOF formula (forall (A_35:nat) (B_25:nat), (((ord_less_nat zero_zero_nat) ((times_times_nat A_35) B_25))->(((ord_less_nat zero_zero_nat) A_35)->((ord_less_nat zero_zero_nat) B_25)))) of role axiom named fact_669_zero__less__mult__pos
% 1.35/1.76 A new axiom: (forall (A_35:nat) (B_25:nat), (((ord_less_nat zero_zero_nat) ((times_times_nat A_35) B_25))->(((ord_less_nat zero_zero_nat) A_35)->((ord_less_nat zero_zero_nat) B_25))))
% 1.35/1.76 FOF formula (forall (A_35:int) (B_25:int), (((ord_less_int zero_zero_int) ((times_times_int A_35) B_25))->(((ord_less_int zero_zero_int) A_35)->((ord_less_int zero_zero_int) B_25)))) of role axiom named fact_670_zero__less__mult__pos
% 1.35/1.76 A new axiom: (forall (A_35:int) (B_25:int), (((ord_less_int zero_zero_int) ((times_times_int A_35) B_25))->(((ord_less_int zero_zero_int) A_35)->((ord_less_int zero_zero_int) B_25))))
% 1.35/1.76 FOF formula (forall (B_24:real) (A_34:real), (((ord_less_real zero_zero_real) A_34)->(((ord_less_real B_24) zero_zero_real)->((ord_less_real ((times_times_real B_24) A_34)) zero_zero_real)))) of role axiom named fact_671_mult__pos__neg2
% 1.35/1.76 A new axiom: (forall (B_24:real) (A_34:real), (((ord_less_real zero_zero_real) A_34)->(((ord_less_real B_24) zero_zero_real)->((ord_less_real ((times_times_real B_24) A_34)) zero_zero_real))))
% 1.35/1.76 FOF formula (forall (B_24:nat) (A_34:nat), (((ord_less_nat zero_zero_nat) A_34)->(((ord_less_nat B_24) zero_zero_nat)->((ord_less_nat ((times_times_nat B_24) A_34)) zero_zero_nat)))) of role axiom named fact_672_mult__pos__neg2
% 1.35/1.76 A new axiom: (forall (B_24:nat) (A_34:nat), (((ord_less_nat zero_zero_nat) A_34)->(((ord_less_nat B_24) zero_zero_nat)->((ord_less_nat ((times_times_nat B_24) A_34)) zero_zero_nat))))
% 1.35/1.76 FOF formula (forall (B_24:int) (A_34:int), (((ord_less_int zero_zero_int) A_34)->(((ord_less_int B_24) zero_zero_int)->((ord_less_int ((times_times_int B_24) A_34)) zero_zero_int)))) of role axiom named fact_673_mult__pos__neg2
% 1.35/1.76 A new axiom: (forall (B_24:int) (A_34:int), (((ord_less_int zero_zero_int) A_34)->(((ord_less_int B_24) zero_zero_int)->((ord_less_int ((times_times_int B_24) A_34)) zero_zero_int))))
% 1.35/1.76 FOF formula (forall (B_23:real) (A_33:real), (((ord_less_real zero_zero_real) A_33)->(((ord_less_real B_23) zero_zero_real)->((ord_less_real ((times_times_real A_33) B_23)) zero_zero_real)))) of role axiom named fact_674_mult__pos__neg
% 1.35/1.76 A new axiom: (forall (B_23:real) (A_33:real), (((ord_less_real zero_zero_real) A_33)->(((ord_less_real B_23) zero_zero_real)->((ord_less_real ((times_times_real A_33) B_23)) zero_zero_real))))
% 1.35/1.76 FOF formula (forall (B_23:nat) (A_33:nat), (((ord_less_nat zero_zero_nat) A_33)->(((ord_less_nat B_23) zero_zero_nat)->((ord_less_nat ((times_times_nat A_33) B_23)) zero_zero_nat)))) of role axiom named fact_675_mult__pos__neg
% 1.35/1.77 A new axiom: (forall (B_23:nat) (A_33:nat), (((ord_less_nat zero_zero_nat) A_33)->(((ord_less_nat B_23) zero_zero_nat)->((ord_less_nat ((times_times_nat A_33) B_23)) zero_zero_nat))))
% 1.35/1.77 FOF formula (forall (B_23:int) (A_33:int), (((ord_less_int zero_zero_int) A_33)->(((ord_less_int B_23) zero_zero_int)->((ord_less_int ((times_times_int A_33) B_23)) zero_zero_int)))) of role axiom named fact_676_mult__pos__neg
% 1.35/1.77 A new axiom: (forall (B_23:int) (A_33:int), (((ord_less_int zero_zero_int) A_33)->(((ord_less_int B_23) zero_zero_int)->((ord_less_int ((times_times_int A_33) B_23)) zero_zero_int))))
% 1.35/1.77 FOF formula (forall (B_22:real) (A_32:real), (((ord_less_real zero_zero_real) A_32)->(((ord_less_real zero_zero_real) B_22)->((ord_less_real zero_zero_real) ((times_times_real A_32) B_22))))) of role axiom named fact_677_mult__pos__pos
% 1.35/1.77 A new axiom: (forall (B_22:real) (A_32:real), (((ord_less_real zero_zero_real) A_32)->(((ord_less_real zero_zero_real) B_22)->((ord_less_real zero_zero_real) ((times_times_real A_32) B_22)))))
% 1.35/1.77 FOF formula (forall (B_22:nat) (A_32:nat), (((ord_less_nat zero_zero_nat) A_32)->(((ord_less_nat zero_zero_nat) B_22)->((ord_less_nat zero_zero_nat) ((times_times_nat A_32) B_22))))) of role axiom named fact_678_mult__pos__pos
% 1.35/1.77 A new axiom: (forall (B_22:nat) (A_32:nat), (((ord_less_nat zero_zero_nat) A_32)->(((ord_less_nat zero_zero_nat) B_22)->((ord_less_nat zero_zero_nat) ((times_times_nat A_32) B_22)))))
% 1.35/1.77 FOF formula (forall (B_22:int) (A_32:int), (((ord_less_int zero_zero_int) A_32)->(((ord_less_int zero_zero_int) B_22)->((ord_less_int zero_zero_int) ((times_times_int A_32) B_22))))) of role axiom named fact_679_mult__pos__pos
% 1.35/1.77 A new axiom: (forall (B_22:int) (A_32:int), (((ord_less_int zero_zero_int) A_32)->(((ord_less_int zero_zero_int) B_22)->((ord_less_int zero_zero_int) ((times_times_int A_32) B_22)))))
% 1.35/1.77 FOF formula (forall (A_31:real) (B_21:real) (C_18:real), (((ord_less_real zero_zero_real) C_18)->((iff ((ord_less_real ((times_times_real C_18) A_31)) ((times_times_real C_18) B_21))) ((ord_less_real A_31) B_21)))) of role axiom named fact_680_mult__less__cancel__left__pos
% 1.35/1.77 A new axiom: (forall (A_31:real) (B_21:real) (C_18:real), (((ord_less_real zero_zero_real) C_18)->((iff ((ord_less_real ((times_times_real C_18) A_31)) ((times_times_real C_18) B_21))) ((ord_less_real A_31) B_21))))
% 1.35/1.77 FOF formula (forall (A_31:int) (B_21:int) (C_18:int), (((ord_less_int zero_zero_int) C_18)->((iff ((ord_less_int ((times_times_int C_18) A_31)) ((times_times_int C_18) B_21))) ((ord_less_int A_31) B_21)))) of role axiom named fact_681_mult__less__cancel__left__pos
% 1.35/1.77 A new axiom: (forall (A_31:int) (B_21:int) (C_18:int), (((ord_less_int zero_zero_int) C_18)->((iff ((ord_less_int ((times_times_int C_18) A_31)) ((times_times_int C_18) B_21))) ((ord_less_int A_31) B_21))))
% 1.35/1.77 FOF formula (forall (C_17:real) (A_30:real) (B_20:real), ((iff ((ord_less_real ((times_times_real C_17) A_30)) ((times_times_real C_17) B_20))) ((or ((and ((ord_less_real zero_zero_real) C_17)) ((ord_less_real A_30) B_20))) ((and ((ord_less_real C_17) zero_zero_real)) ((ord_less_real B_20) A_30))))) of role axiom named fact_682_mult__less__cancel__left__disj
% 1.35/1.77 A new axiom: (forall (C_17:real) (A_30:real) (B_20:real), ((iff ((ord_less_real ((times_times_real C_17) A_30)) ((times_times_real C_17) B_20))) ((or ((and ((ord_less_real zero_zero_real) C_17)) ((ord_less_real A_30) B_20))) ((and ((ord_less_real C_17) zero_zero_real)) ((ord_less_real B_20) A_30)))))
% 1.35/1.77 FOF formula (forall (C_17:int) (A_30:int) (B_20:int), ((iff ((ord_less_int ((times_times_int C_17) A_30)) ((times_times_int C_17) B_20))) ((or ((and ((ord_less_int zero_zero_int) C_17)) ((ord_less_int A_30) B_20))) ((and ((ord_less_int C_17) zero_zero_int)) ((ord_less_int B_20) A_30))))) of role axiom named fact_683_mult__less__cancel__left__disj
% 1.35/1.77 A new axiom: (forall (C_17:int) (A_30:int) (B_20:int), ((iff ((ord_less_int ((times_times_int C_17) A_30)) ((times_times_int C_17) B_20))) ((or ((and ((ord_less_int zero_zero_int) C_17)) ((ord_less_int A_30) B_20))) ((and ((ord_less_int C_17) zero_zero_int)) ((ord_less_int B_20) A_30)))))
% 1.44/1.79 FOF formula (forall (A_29:real) (C_16:real) (B_19:real), ((iff ((ord_less_real ((times_times_real A_29) C_16)) ((times_times_real B_19) C_16))) ((or ((and ((ord_less_real zero_zero_real) C_16)) ((ord_less_real A_29) B_19))) ((and ((ord_less_real C_16) zero_zero_real)) ((ord_less_real B_19) A_29))))) of role axiom named fact_684_mult__less__cancel__right__disj
% 1.44/1.79 A new axiom: (forall (A_29:real) (C_16:real) (B_19:real), ((iff ((ord_less_real ((times_times_real A_29) C_16)) ((times_times_real B_19) C_16))) ((or ((and ((ord_less_real zero_zero_real) C_16)) ((ord_less_real A_29) B_19))) ((and ((ord_less_real C_16) zero_zero_real)) ((ord_less_real B_19) A_29)))))
% 1.44/1.79 FOF formula (forall (A_29:int) (C_16:int) (B_19:int), ((iff ((ord_less_int ((times_times_int A_29) C_16)) ((times_times_int B_19) C_16))) ((or ((and ((ord_less_int zero_zero_int) C_16)) ((ord_less_int A_29) B_19))) ((and ((ord_less_int C_16) zero_zero_int)) ((ord_less_int B_19) A_29))))) of role axiom named fact_685_mult__less__cancel__right__disj
% 1.44/1.79 A new axiom: (forall (A_29:int) (C_16:int) (B_19:int), ((iff ((ord_less_int ((times_times_int A_29) C_16)) ((times_times_int B_19) C_16))) ((or ((and ((ord_less_int zero_zero_int) C_16)) ((ord_less_int A_29) B_19))) ((and ((ord_less_int C_16) zero_zero_int)) ((ord_less_int B_19) A_29)))))
% 1.44/1.79 FOF formula (forall (A_28:real), (((ord_less_real ((times_times_real A_28) A_28)) zero_zero_real)->False)) of role axiom named fact_686_not__square__less__zero
% 1.44/1.79 A new axiom: (forall (A_28:real), (((ord_less_real ((times_times_real A_28) A_28)) zero_zero_real)->False))
% 1.44/1.79 FOF formula (forall (A_28:int), (((ord_less_int ((times_times_int A_28) A_28)) zero_zero_int)->False)) of role axiom named fact_687_not__square__less__zero
% 1.44/1.79 A new axiom: (forall (A_28:int), (((ord_less_int ((times_times_int A_28) A_28)) zero_zero_int)->False))
% 1.44/1.79 FOF formula (forall (B_18:real) (C_15:real) (A_27:real), (((ord_less_real zero_zero_real) A_27)->(((ord_less_real B_18) C_15)->((ord_less_real B_18) ((plus_plus_real A_27) C_15))))) of role axiom named fact_688_pos__add__strict
% 1.44/1.79 A new axiom: (forall (B_18:real) (C_15:real) (A_27:real), (((ord_less_real zero_zero_real) A_27)->(((ord_less_real B_18) C_15)->((ord_less_real B_18) ((plus_plus_real A_27) C_15)))))
% 1.44/1.79 FOF formula (forall (B_18:nat) (C_15:nat) (A_27:nat), (((ord_less_nat zero_zero_nat) A_27)->(((ord_less_nat B_18) C_15)->((ord_less_nat B_18) ((plus_plus_nat A_27) C_15))))) of role axiom named fact_689_pos__add__strict
% 1.44/1.79 A new axiom: (forall (B_18:nat) (C_15:nat) (A_27:nat), (((ord_less_nat zero_zero_nat) A_27)->(((ord_less_nat B_18) C_15)->((ord_less_nat B_18) ((plus_plus_nat A_27) C_15)))))
% 1.44/1.79 FOF formula (forall (B_18:int) (C_15:int) (A_27:int), (((ord_less_int zero_zero_int) A_27)->(((ord_less_int B_18) C_15)->((ord_less_int B_18) ((plus_plus_int A_27) C_15))))) of role axiom named fact_690_pos__add__strict
% 1.44/1.79 A new axiom: (forall (B_18:int) (C_15:int) (A_27:int), (((ord_less_int zero_zero_int) A_27)->(((ord_less_int B_18) C_15)->((ord_less_int B_18) ((plus_plus_int A_27) C_15)))))
% 1.44/1.79 FOF formula ((ord_less_eq_real zero_zero_real) one_one_real) of role axiom named fact_691_zero__le__one
% 1.44/1.79 A new axiom: ((ord_less_eq_real zero_zero_real) one_one_real)
% 1.44/1.79 FOF formula ((ord_less_eq_nat zero_zero_nat) one_one_nat) of role axiom named fact_692_zero__le__one
% 1.44/1.79 A new axiom: ((ord_less_eq_nat zero_zero_nat) one_one_nat)
% 1.44/1.79 FOF formula ((ord_less_eq_int zero_zero_int) one_one_int) of role axiom named fact_693_zero__le__one
% 1.44/1.79 A new axiom: ((ord_less_eq_int zero_zero_int) one_one_int)
% 1.44/1.79 FOF formula (((ord_less_eq_real one_one_real) zero_zero_real)->False) of role axiom named fact_694_not__one__le__zero
% 1.44/1.79 A new axiom: (((ord_less_eq_real one_one_real) zero_zero_real)->False)
% 1.44/1.79 FOF formula (((ord_less_eq_nat one_one_nat) zero_zero_nat)->False) of role axiom named fact_695_not__one__le__zero
% 1.44/1.79 A new axiom: (((ord_less_eq_nat one_one_nat) zero_zero_nat)->False)
% 1.44/1.79 FOF formula (((ord_less_eq_int one_one_int) zero_zero_int)->False) of role axiom named fact_696_not__one__le__zero
% 1.44/1.80 A new axiom: (((ord_less_eq_int one_one_int) zero_zero_int)->False)
% 1.44/1.80 FOF formula ((ord_less_real zero_zero_real) one_one_real) of role axiom named fact_697_zero__less__one
% 1.44/1.80 A new axiom: ((ord_less_real zero_zero_real) one_one_real)
% 1.44/1.80 FOF formula ((ord_less_nat zero_zero_nat) one_one_nat) of role axiom named fact_698_zero__less__one
% 1.44/1.80 A new axiom: ((ord_less_nat zero_zero_nat) one_one_nat)
% 1.44/1.80 FOF formula ((ord_less_int zero_zero_int) one_one_int) of role axiom named fact_699_zero__less__one
% 1.44/1.80 A new axiom: ((ord_less_int zero_zero_int) one_one_int)
% 1.44/1.80 FOF formula (((ord_less_real one_one_real) zero_zero_real)->False) of role axiom named fact_700_not__one__less__zero
% 1.44/1.80 A new axiom: (((ord_less_real one_one_real) zero_zero_real)->False)
% 1.44/1.80 FOF formula (((ord_less_nat one_one_nat) zero_zero_nat)->False) of role axiom named fact_701_not__one__less__zero
% 1.44/1.80 A new axiom: (((ord_less_nat one_one_nat) zero_zero_nat)->False)
% 1.44/1.80 FOF formula (((ord_less_int one_one_int) zero_zero_int)->False) of role axiom named fact_702_not__one__less__zero
% 1.44/1.80 A new axiom: (((ord_less_int one_one_int) zero_zero_int)->False)
% 1.44/1.80 FOF formula (forall (N_11:nat) (A_26:real) (B_17:real), (((ord_less_eq_real A_26) B_17)->(((ord_less_eq_real zero_zero_real) A_26)->((ord_less_eq_real ((power_power_real A_26) N_11)) ((power_power_real B_17) N_11))))) of role axiom named fact_703_power__mono
% 1.44/1.80 A new axiom: (forall (N_11:nat) (A_26:real) (B_17:real), (((ord_less_eq_real A_26) B_17)->(((ord_less_eq_real zero_zero_real) A_26)->((ord_less_eq_real ((power_power_real A_26) N_11)) ((power_power_real B_17) N_11)))))
% 1.44/1.80 FOF formula (forall (N_11:nat) (A_26:nat) (B_17:nat), (((ord_less_eq_nat A_26) B_17)->(((ord_less_eq_nat zero_zero_nat) A_26)->((ord_less_eq_nat ((power_power_nat A_26) N_11)) ((power_power_nat B_17) N_11))))) of role axiom named fact_704_power__mono
% 1.44/1.80 A new axiom: (forall (N_11:nat) (A_26:nat) (B_17:nat), (((ord_less_eq_nat A_26) B_17)->(((ord_less_eq_nat zero_zero_nat) A_26)->((ord_less_eq_nat ((power_power_nat A_26) N_11)) ((power_power_nat B_17) N_11)))))
% 1.44/1.80 FOF formula (forall (N_11:nat) (A_26:int) (B_17:int), (((ord_less_eq_int A_26) B_17)->(((ord_less_eq_int zero_zero_int) A_26)->((ord_less_eq_int ((power_power_int A_26) N_11)) ((power_power_int B_17) N_11))))) of role axiom named fact_705_power__mono
% 1.44/1.80 A new axiom: (forall (N_11:nat) (A_26:int) (B_17:int), (((ord_less_eq_int A_26) B_17)->(((ord_less_eq_int zero_zero_int) A_26)->((ord_less_eq_int ((power_power_int A_26) N_11)) ((power_power_int B_17) N_11)))))
% 1.44/1.80 FOF formula (forall (N_10:nat) (A_25:real), (((ord_less_eq_real zero_zero_real) A_25)->((ord_less_eq_real zero_zero_real) ((power_power_real A_25) N_10)))) of role axiom named fact_706_zero__le__power
% 1.44/1.80 A new axiom: (forall (N_10:nat) (A_25:real), (((ord_less_eq_real zero_zero_real) A_25)->((ord_less_eq_real zero_zero_real) ((power_power_real A_25) N_10))))
% 1.44/1.80 FOF formula (forall (N_10:nat) (A_25:nat), (((ord_less_eq_nat zero_zero_nat) A_25)->((ord_less_eq_nat zero_zero_nat) ((power_power_nat A_25) N_10)))) of role axiom named fact_707_zero__le__power
% 1.44/1.80 A new axiom: (forall (N_10:nat) (A_25:nat), (((ord_less_eq_nat zero_zero_nat) A_25)->((ord_less_eq_nat zero_zero_nat) ((power_power_nat A_25) N_10))))
% 1.44/1.80 FOF formula (forall (N_10:nat) (A_25:int), (((ord_less_eq_int zero_zero_int) A_25)->((ord_less_eq_int zero_zero_int) ((power_power_int A_25) N_10)))) of role axiom named fact_708_zero__le__power
% 1.44/1.80 A new axiom: (forall (N_10:nat) (A_25:int), (((ord_less_eq_int zero_zero_int) A_25)->((ord_less_eq_int zero_zero_int) ((power_power_int A_25) N_10))))
% 1.44/1.80 FOF formula (forall (N_9:real) (M_5:real), (((ord_less_real one_one_real) M_5)->(((ord_less_real one_one_real) N_9)->((ord_less_real one_one_real) ((times_times_real M_5) N_9))))) of role axiom named fact_709_less__1__mult
% 1.44/1.80 A new axiom: (forall (N_9:real) (M_5:real), (((ord_less_real one_one_real) M_5)->(((ord_less_real one_one_real) N_9)->((ord_less_real one_one_real) ((times_times_real M_5) N_9)))))
% 1.44/1.80 FOF formula (forall (N_9:nat) (M_5:nat), (((ord_less_nat one_one_nat) M_5)->(((ord_less_nat one_one_nat) N_9)->((ord_less_nat one_one_nat) ((times_times_nat M_5) N_9))))) of role axiom named fact_710_less__1__mult
% 1.48/1.82 A new axiom: (forall (N_9:nat) (M_5:nat), (((ord_less_nat one_one_nat) M_5)->(((ord_less_nat one_one_nat) N_9)->((ord_less_nat one_one_nat) ((times_times_nat M_5) N_9)))))
% 1.48/1.82 FOF formula (forall (N_9:int) (M_5:int), (((ord_less_int one_one_int) M_5)->(((ord_less_int one_one_int) N_9)->((ord_less_int one_one_int) ((times_times_int M_5) N_9))))) of role axiom named fact_711_less__1__mult
% 1.48/1.82 A new axiom: (forall (N_9:int) (M_5:int), (((ord_less_int one_one_int) M_5)->(((ord_less_int one_one_int) N_9)->((ord_less_int one_one_int) ((times_times_int M_5) N_9)))))
% 1.48/1.82 FOF formula (forall (N_8:nat) (A_24:real), (((ord_less_real zero_zero_real) A_24)->((ord_less_real zero_zero_real) ((power_power_real A_24) N_8)))) of role axiom named fact_712_zero__less__power
% 1.48/1.82 A new axiom: (forall (N_8:nat) (A_24:real), (((ord_less_real zero_zero_real) A_24)->((ord_less_real zero_zero_real) ((power_power_real A_24) N_8))))
% 1.48/1.82 FOF formula (forall (N_8:nat) (A_24:nat), (((ord_less_nat zero_zero_nat) A_24)->((ord_less_nat zero_zero_nat) ((power_power_nat A_24) N_8)))) of role axiom named fact_713_zero__less__power
% 1.48/1.82 A new axiom: (forall (N_8:nat) (A_24:nat), (((ord_less_nat zero_zero_nat) A_24)->((ord_less_nat zero_zero_nat) ((power_power_nat A_24) N_8))))
% 1.48/1.82 FOF formula (forall (N_8:nat) (A_24:int), (((ord_less_int zero_zero_int) A_24)->((ord_less_int zero_zero_int) ((power_power_int A_24) N_8)))) of role axiom named fact_714_zero__less__power
% 1.48/1.82 A new axiom: (forall (N_8:nat) (A_24:int), (((ord_less_int zero_zero_int) A_24)->((ord_less_int zero_zero_int) ((power_power_int A_24) N_8))))
% 1.48/1.82 FOF formula (forall (A_23:real), ((ord_less_real A_23) ((plus_plus_real A_23) one_one_real))) of role axiom named fact_715_less__add__one
% 1.48/1.82 A new axiom: (forall (A_23:real), ((ord_less_real A_23) ((plus_plus_real A_23) one_one_real)))
% 1.48/1.82 FOF formula (forall (A_23:nat), ((ord_less_nat A_23) ((plus_plus_nat A_23) one_one_nat))) of role axiom named fact_716_less__add__one
% 1.48/1.82 A new axiom: (forall (A_23:nat), ((ord_less_nat A_23) ((plus_plus_nat A_23) one_one_nat)))
% 1.48/1.82 FOF formula (forall (A_23:int), ((ord_less_int A_23) ((plus_plus_int A_23) one_one_int))) of role axiom named fact_717_less__add__one
% 1.48/1.82 A new axiom: (forall (A_23:int), ((ord_less_int A_23) ((plus_plus_int A_23) one_one_int)))
% 1.48/1.82 FOF formula (forall (C_14:int) (A_22:int) (B_16:int), ((iff ((dvd_dvd_int ((times_times_int C_14) A_22)) ((times_times_int C_14) B_16))) ((or (((eq int) C_14) zero_zero_int)) ((dvd_dvd_int A_22) B_16)))) of role axiom named fact_718_dvd__mult__cancel__left
% 1.48/1.82 A new axiom: (forall (C_14:int) (A_22:int) (B_16:int), ((iff ((dvd_dvd_int ((times_times_int C_14) A_22)) ((times_times_int C_14) B_16))) ((or (((eq int) C_14) zero_zero_int)) ((dvd_dvd_int A_22) B_16))))
% 1.48/1.82 FOF formula (forall (C_14:real) (A_22:real) (B_16:real), ((iff ((dvd_dvd_real ((times_times_real C_14) A_22)) ((times_times_real C_14) B_16))) ((or (((eq real) C_14) zero_zero_real)) ((dvd_dvd_real A_22) B_16)))) of role axiom named fact_719_dvd__mult__cancel__left
% 1.48/1.82 A new axiom: (forall (C_14:real) (A_22:real) (B_16:real), ((iff ((dvd_dvd_real ((times_times_real C_14) A_22)) ((times_times_real C_14) B_16))) ((or (((eq real) C_14) zero_zero_real)) ((dvd_dvd_real A_22) B_16))))
% 1.48/1.82 FOF formula (forall (A_21:int) (C_13:int) (B_15:int), ((iff ((dvd_dvd_int ((times_times_int A_21) C_13)) ((times_times_int B_15) C_13))) ((or (((eq int) C_13) zero_zero_int)) ((dvd_dvd_int A_21) B_15)))) of role axiom named fact_720_dvd__mult__cancel__right
% 1.48/1.82 A new axiom: (forall (A_21:int) (C_13:int) (B_15:int), ((iff ((dvd_dvd_int ((times_times_int A_21) C_13)) ((times_times_int B_15) C_13))) ((or (((eq int) C_13) zero_zero_int)) ((dvd_dvd_int A_21) B_15))))
% 1.48/1.82 FOF formula (forall (A_21:real) (C_13:real) (B_15:real), ((iff ((dvd_dvd_real ((times_times_real A_21) C_13)) ((times_times_real B_15) C_13))) ((or (((eq real) C_13) zero_zero_real)) ((dvd_dvd_real A_21) B_15)))) of role axiom named fact_721_dvd__mult__cancel__right
% 1.48/1.82 A new axiom: (forall (A_21:real) (C_13:real) (B_15:real), ((iff ((dvd_dvd_real ((times_times_real A_21) C_13)) ((times_times_real B_15) C_13))) ((or (((eq real) C_13) zero_zero_real)) ((dvd_dvd_real A_21) B_15))))
% 1.48/1.84 FOF formula (forall (A_20:real) (N_7:nat) (N_6:nat), (((ord_less_eq_nat N_7) N_6)->(((ord_less_eq_real one_one_real) A_20)->((ord_less_eq_real ((power_power_real A_20) N_7)) ((power_power_real A_20) N_6))))) of role axiom named fact_722_power__increasing
% 1.48/1.84 A new axiom: (forall (A_20:real) (N_7:nat) (N_6:nat), (((ord_less_eq_nat N_7) N_6)->(((ord_less_eq_real one_one_real) A_20)->((ord_less_eq_real ((power_power_real A_20) N_7)) ((power_power_real A_20) N_6)))))
% 1.48/1.84 FOF formula (forall (A_20:nat) (N_7:nat) (N_6:nat), (((ord_less_eq_nat N_7) N_6)->(((ord_less_eq_nat one_one_nat) A_20)->((ord_less_eq_nat ((power_power_nat A_20) N_7)) ((power_power_nat A_20) N_6))))) of role axiom named fact_723_power__increasing
% 1.48/1.84 A new axiom: (forall (A_20:nat) (N_7:nat) (N_6:nat), (((ord_less_eq_nat N_7) N_6)->(((ord_less_eq_nat one_one_nat) A_20)->((ord_less_eq_nat ((power_power_nat A_20) N_7)) ((power_power_nat A_20) N_6)))))
% 1.48/1.84 FOF formula (forall (A_20:int) (N_7:nat) (N_6:nat), (((ord_less_eq_nat N_7) N_6)->(((ord_less_eq_int one_one_int) A_20)->((ord_less_eq_int ((power_power_int A_20) N_7)) ((power_power_int A_20) N_6))))) of role axiom named fact_724_power__increasing
% 1.48/1.84 A new axiom: (forall (A_20:int) (N_7:nat) (N_6:nat), (((ord_less_eq_nat N_7) N_6)->(((ord_less_eq_int one_one_int) A_20)->((ord_less_eq_int ((power_power_int A_20) N_7)) ((power_power_int A_20) N_6)))))
% 1.48/1.84 FOF formula (forall (N_5:nat) (A_19:real), (((ord_less_eq_real one_one_real) A_19)->((ord_less_eq_real one_one_real) ((power_power_real A_19) N_5)))) of role axiom named fact_725_one__le__power
% 1.48/1.84 A new axiom: (forall (N_5:nat) (A_19:real), (((ord_less_eq_real one_one_real) A_19)->((ord_less_eq_real one_one_real) ((power_power_real A_19) N_5))))
% 1.48/1.84 FOF formula (forall (N_5:nat) (A_19:nat), (((ord_less_eq_nat one_one_nat) A_19)->((ord_less_eq_nat one_one_nat) ((power_power_nat A_19) N_5)))) of role axiom named fact_726_one__le__power
% 1.48/1.84 A new axiom: (forall (N_5:nat) (A_19:nat), (((ord_less_eq_nat one_one_nat) A_19)->((ord_less_eq_nat one_one_nat) ((power_power_nat A_19) N_5))))
% 1.48/1.84 FOF formula (forall (N_5:nat) (A_19:int), (((ord_less_eq_int one_one_int) A_19)->((ord_less_eq_int one_one_int) ((power_power_int A_19) N_5)))) of role axiom named fact_727_one__le__power
% 1.48/1.84 A new axiom: (forall (N_5:nat) (A_19:int), (((ord_less_eq_int one_one_int) A_19)->((ord_less_eq_int one_one_int) ((power_power_int A_19) N_5))))
% 1.48/1.84 FOF formula (forall (M_4:nat) (N_4:nat) (A_18:real), (((ord_less_real one_one_real) A_18)->((iff (((eq real) ((power_power_real A_18) M_4)) ((power_power_real A_18) N_4))) (((eq nat) M_4) N_4)))) of role axiom named fact_728_power__inject__exp
% 1.48/1.84 A new axiom: (forall (M_4:nat) (N_4:nat) (A_18:real), (((ord_less_real one_one_real) A_18)->((iff (((eq real) ((power_power_real A_18) M_4)) ((power_power_real A_18) N_4))) (((eq nat) M_4) N_4))))
% 1.48/1.84 FOF formula (forall (M_4:nat) (N_4:nat) (A_18:nat), (((ord_less_nat one_one_nat) A_18)->((iff (((eq nat) ((power_power_nat A_18) M_4)) ((power_power_nat A_18) N_4))) (((eq nat) M_4) N_4)))) of role axiom named fact_729_power__inject__exp
% 1.48/1.84 A new axiom: (forall (M_4:nat) (N_4:nat) (A_18:nat), (((ord_less_nat one_one_nat) A_18)->((iff (((eq nat) ((power_power_nat A_18) M_4)) ((power_power_nat A_18) N_4))) (((eq nat) M_4) N_4))))
% 1.48/1.84 FOF formula (forall (M_4:nat) (N_4:nat) (A_18:int), (((ord_less_int one_one_int) A_18)->((iff (((eq int) ((power_power_int A_18) M_4)) ((power_power_int A_18) N_4))) (((eq nat) M_4) N_4)))) of role axiom named fact_730_power__inject__exp
% 1.48/1.84 A new axiom: (forall (M_4:nat) (N_4:nat) (A_18:int), (((ord_less_int one_one_int) A_18)->((iff (((eq int) ((power_power_int A_18) M_4)) ((power_power_int A_18) N_4))) (((eq nat) M_4) N_4))))
% 1.48/1.84 FOF formula (forall (A_17:real) (N_3:nat), ((iff (((eq real) ((power_power_real A_17) N_3)) zero_zero_real)) ((and (((eq real) A_17) zero_zero_real)) (not (((eq nat) N_3) zero_zero_nat))))) of role axiom named fact_731_power__eq__0__iff
% 1.48/1.84 A new axiom: (forall (A_17:real) (N_3:nat), ((iff (((eq real) ((power_power_real A_17) N_3)) zero_zero_real)) ((and (((eq real) A_17) zero_zero_real)) (not (((eq nat) N_3) zero_zero_nat)))))
% 1.48/1.86 FOF formula (forall (A_17:nat) (N_3:nat), ((iff (((eq nat) ((power_power_nat A_17) N_3)) zero_zero_nat)) ((and (((eq nat) A_17) zero_zero_nat)) (not (((eq nat) N_3) zero_zero_nat))))) of role axiom named fact_732_power__eq__0__iff
% 1.48/1.86 A new axiom: (forall (A_17:nat) (N_3:nat), ((iff (((eq nat) ((power_power_nat A_17) N_3)) zero_zero_nat)) ((and (((eq nat) A_17) zero_zero_nat)) (not (((eq nat) N_3) zero_zero_nat)))))
% 1.48/1.86 FOF formula (forall (A_17:int) (N_3:nat), ((iff (((eq int) ((power_power_int A_17) N_3)) zero_zero_int)) ((and (((eq int) A_17) zero_zero_int)) (not (((eq nat) N_3) zero_zero_nat))))) of role axiom named fact_733_power__eq__0__iff
% 1.48/1.86 A new axiom: (forall (A_17:int) (N_3:nat), ((iff (((eq int) ((power_power_int A_17) N_3)) zero_zero_int)) ((and (((eq int) A_17) zero_zero_int)) (not (((eq nat) N_3) zero_zero_nat)))))
% 1.48/1.86 FOF formula (forall (A_16:real), (((eq real) ((power_power_real A_16) zero_zero_nat)) one_one_real)) of role axiom named fact_734_power__0
% 1.48/1.86 A new axiom: (forall (A_16:real), (((eq real) ((power_power_real A_16) zero_zero_nat)) one_one_real))
% 1.48/1.86 FOF formula (forall (A_16:nat), (((eq nat) ((power_power_nat A_16) zero_zero_nat)) one_one_nat)) of role axiom named fact_735_power__0
% 1.48/1.86 A new axiom: (forall (A_16:nat), (((eq nat) ((power_power_nat A_16) zero_zero_nat)) one_one_nat))
% 1.48/1.86 FOF formula (forall (A_16:int), (((eq int) ((power_power_int A_16) zero_zero_nat)) one_one_int)) of role axiom named fact_736_power__0
% 1.48/1.86 A new axiom: (forall (A_16:int), (((eq int) ((power_power_int A_16) zero_zero_nat)) one_one_int))
% 1.48/1.86 FOF formula (forall (A_15:real) (M_3:nat) (N_2:nat), (((eq real) ((power_power_real A_15) ((plus_plus_nat M_3) N_2))) ((times_times_real ((power_power_real A_15) M_3)) ((power_power_real A_15) N_2)))) of role axiom named fact_737_power__add
% 1.48/1.86 A new axiom: (forall (A_15:real) (M_3:nat) (N_2:nat), (((eq real) ((power_power_real A_15) ((plus_plus_nat M_3) N_2))) ((times_times_real ((power_power_real A_15) M_3)) ((power_power_real A_15) N_2))))
% 1.48/1.86 FOF formula (forall (A_15:nat) (M_3:nat) (N_2:nat), (((eq nat) ((power_power_nat A_15) ((plus_plus_nat M_3) N_2))) ((times_times_nat ((power_power_nat A_15) M_3)) ((power_power_nat A_15) N_2)))) of role axiom named fact_738_power__add
% 1.48/1.86 A new axiom: (forall (A_15:nat) (M_3:nat) (N_2:nat), (((eq nat) ((power_power_nat A_15) ((plus_plus_nat M_3) N_2))) ((times_times_nat ((power_power_nat A_15) M_3)) ((power_power_nat A_15) N_2))))
% 1.48/1.86 FOF formula (forall (A_15:int) (M_3:nat) (N_2:nat), (((eq int) ((power_power_int A_15) ((plus_plus_nat M_3) N_2))) ((times_times_int ((power_power_int A_15) M_3)) ((power_power_int A_15) N_2)))) of role axiom named fact_739_power__add
% 1.48/1.86 A new axiom: (forall (A_15:int) (M_3:nat) (N_2:nat), (((eq int) ((power_power_int A_15) ((plus_plus_nat M_3) N_2))) ((times_times_int ((power_power_int A_15) M_3)) ((power_power_int A_15) N_2))))
% 1.48/1.86 FOF formula (forall (B:int) (M:int) (A:int), (((ord_less_int zero_zero_int) A)->(((ord_less_int A) M)->(((ord_less_int zero_zero_int) B)->(((ord_less_int B) A)->((((zcong A) B) M)->False)))))) of role axiom named fact_740_zcong__not
% 1.48/1.86 A new axiom: (forall (B:int) (M:int) (A:int), (((ord_less_int zero_zero_int) A)->(((ord_less_int A) M)->(((ord_less_int zero_zero_int) B)->(((ord_less_int B) A)->((((zcong A) B) M)->False))))))
% 1.48/1.86 FOF formula (forall (M:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int X) M)->((((zcong X) zero_zero_int) M)->False)))) of role axiom named fact_741_zcong__not__zero
% 1.48/1.86 A new axiom: (forall (M:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int X) M)->((((zcong X) zero_zero_int) M)->False))))
% 1.48/1.86 FOF formula (forall (M:int) (Y:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int zero_zero_int) Y)->(((ord_less_int zero_zero_int) M)->((((zcong X) Y) M)->(((ord_less_int X) M)->(((ord_less_int Y) M)->(((eq int) X) Y)))))))) of role axiom named fact_742_zcong__less__eq
% 1.48/1.86 A new axiom: (forall (M:int) (Y:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int zero_zero_int) Y)->(((ord_less_int zero_zero_int) M)->((((zcong X) Y) M)->(((ord_less_int X) M)->(((ord_less_int Y) M)->(((eq int) X) Y))))))))
% 1.48/1.87 FOF formula (forall (N:int) (M:int), (((dvd_dvd_int N) M)->((or ((ord_less_eq_int M) zero_zero_int)) ((ord_less_eq_int N) M)))) of role axiom named fact_743_zdvd__bounds
% 1.48/1.87 A new axiom: (forall (N:int) (M:int), (((dvd_dvd_int N) M)->((or ((ord_less_eq_int M) zero_zero_int)) ((ord_less_eq_int N) M))))
% 1.48/1.87 FOF formula (forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) ((ex int) (fun (K_1:int)=> (((eq int) B) ((plus_plus_int A) ((times_times_int M) K_1))))))) of role axiom named fact_744_zcong__iff__lin
% 1.48/1.87 A new axiom: (forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) ((ex int) (fun (K_1:int)=> (((eq int) B) ((plus_plus_int A) ((times_times_int M) K_1)))))))
% 1.48/1.87 FOF formula (forall (X:int) (P_1:int), ((iff (((zcong X) zero_zero_int) P_1)) ((dvd_dvd_int P_1) X))) of role axiom named fact_745_zcong__eq__zdvd__prop
% 1.48/1.87 A new axiom: (forall (X:int) (P_1:int), ((iff (((zcong X) zero_zero_int) P_1)) ((dvd_dvd_int P_1) X)))
% 1.48/1.87 FOF formula (forall (A:int) (M:int), ((iff (((zcong A) zero_zero_int) M)) ((dvd_dvd_int M) A))) of role axiom named fact_746_zcong__zero__equiv__div
% 1.48/1.87 A new axiom: (forall (A:int) (M:int), ((iff (((zcong A) zero_zero_int) M)) ((dvd_dvd_int M) A)))
% 1.48/1.87 FOF formula (forall (M:int) (N:int) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((times_times_int M) N))->((or ((dvd_dvd_int P_1) M)) ((dvd_dvd_int P_1) N))))) of role axiom named fact_747_zprime__zdvd__zmult__better
% 1.48/1.87 A new axiom: (forall (M:int) (N:int) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((times_times_int M) N))->((or ((dvd_dvd_int P_1) M)) ((dvd_dvd_int P_1) N)))))
% 1.48/1.87 FOF formula (forall (C_12:real) (A_14:real) (B_14:real), (((ord_less_eq_real ((times_times_real C_12) A_14)) ((times_times_real C_12) B_14))->(((ord_less_real zero_zero_real) C_12)->((ord_less_eq_real A_14) B_14)))) of role axiom named fact_748_mult__left__le__imp__le
% 1.48/1.87 A new axiom: (forall (C_12:real) (A_14:real) (B_14:real), (((ord_less_eq_real ((times_times_real C_12) A_14)) ((times_times_real C_12) B_14))->(((ord_less_real zero_zero_real) C_12)->((ord_less_eq_real A_14) B_14))))
% 1.48/1.87 FOF formula (forall (C_12:nat) (A_14:nat) (B_14:nat), (((ord_less_eq_nat ((times_times_nat C_12) A_14)) ((times_times_nat C_12) B_14))->(((ord_less_nat zero_zero_nat) C_12)->((ord_less_eq_nat A_14) B_14)))) of role axiom named fact_749_mult__left__le__imp__le
% 1.48/1.87 A new axiom: (forall (C_12:nat) (A_14:nat) (B_14:nat), (((ord_less_eq_nat ((times_times_nat C_12) A_14)) ((times_times_nat C_12) B_14))->(((ord_less_nat zero_zero_nat) C_12)->((ord_less_eq_nat A_14) B_14))))
% 1.48/1.87 FOF formula (forall (C_12:int) (A_14:int) (B_14:int), (((ord_less_eq_int ((times_times_int C_12) A_14)) ((times_times_int C_12) B_14))->(((ord_less_int zero_zero_int) C_12)->((ord_less_eq_int A_14) B_14)))) of role axiom named fact_750_mult__left__le__imp__le
% 1.48/1.87 A new axiom: (forall (C_12:int) (A_14:int) (B_14:int), (((ord_less_eq_int ((times_times_int C_12) A_14)) ((times_times_int C_12) B_14))->(((ord_less_int zero_zero_int) C_12)->((ord_less_eq_int A_14) B_14))))
% 1.48/1.87 FOF formula (forall (A_13:real) (C_11:real) (B_13:real), (((ord_less_eq_real ((times_times_real A_13) C_11)) ((times_times_real B_13) C_11))->(((ord_less_real zero_zero_real) C_11)->((ord_less_eq_real A_13) B_13)))) of role axiom named fact_751_mult__right__le__imp__le
% 1.48/1.87 A new axiom: (forall (A_13:real) (C_11:real) (B_13:real), (((ord_less_eq_real ((times_times_real A_13) C_11)) ((times_times_real B_13) C_11))->(((ord_less_real zero_zero_real) C_11)->((ord_less_eq_real A_13) B_13))))
% 1.48/1.87 FOF formula (forall (A_13:nat) (C_11:nat) (B_13:nat), (((ord_less_eq_nat ((times_times_nat A_13) C_11)) ((times_times_nat B_13) C_11))->(((ord_less_nat zero_zero_nat) C_11)->((ord_less_eq_nat A_13) B_13)))) of role axiom named fact_752_mult__right__le__imp__le
% 1.48/1.87 A new axiom: (forall (A_13:nat) (C_11:nat) (B_13:nat), (((ord_less_eq_nat ((times_times_nat A_13) C_11)) ((times_times_nat B_13) C_11))->(((ord_less_nat zero_zero_nat) C_11)->((ord_less_eq_nat A_13) B_13))))
% 1.48/1.89 FOF formula (forall (A_13:int) (C_11:int) (B_13:int), (((ord_less_eq_int ((times_times_int A_13) C_11)) ((times_times_int B_13) C_11))->(((ord_less_int zero_zero_int) C_11)->((ord_less_eq_int A_13) B_13)))) of role axiom named fact_753_mult__right__le__imp__le
% 1.48/1.89 A new axiom: (forall (A_13:int) (C_11:int) (B_13:int), (((ord_less_eq_int ((times_times_int A_13) C_11)) ((times_times_int B_13) C_11))->(((ord_less_int zero_zero_int) C_11)->((ord_less_eq_int A_13) B_13))))
% 1.48/1.89 FOF formula (forall (C_10:real) (A_12:real) (B_12:real), (((ord_less_real ((times_times_real C_10) A_12)) ((times_times_real C_10) B_12))->(((ord_less_eq_real zero_zero_real) C_10)->((ord_less_real A_12) B_12)))) of role axiom named fact_754_mult__less__imp__less__left
% 1.48/1.89 A new axiom: (forall (C_10:real) (A_12:real) (B_12:real), (((ord_less_real ((times_times_real C_10) A_12)) ((times_times_real C_10) B_12))->(((ord_less_eq_real zero_zero_real) C_10)->((ord_less_real A_12) B_12))))
% 1.48/1.89 FOF formula (forall (C_10:nat) (A_12:nat) (B_12:nat), (((ord_less_nat ((times_times_nat C_10) A_12)) ((times_times_nat C_10) B_12))->(((ord_less_eq_nat zero_zero_nat) C_10)->((ord_less_nat A_12) B_12)))) of role axiom named fact_755_mult__less__imp__less__left
% 1.48/1.89 A new axiom: (forall (C_10:nat) (A_12:nat) (B_12:nat), (((ord_less_nat ((times_times_nat C_10) A_12)) ((times_times_nat C_10) B_12))->(((ord_less_eq_nat zero_zero_nat) C_10)->((ord_less_nat A_12) B_12))))
% 1.48/1.89 FOF formula (forall (C_10:int) (A_12:int) (B_12:int), (((ord_less_int ((times_times_int C_10) A_12)) ((times_times_int C_10) B_12))->(((ord_less_eq_int zero_zero_int) C_10)->((ord_less_int A_12) B_12)))) of role axiom named fact_756_mult__less__imp__less__left
% 1.48/1.89 A new axiom: (forall (C_10:int) (A_12:int) (B_12:int), (((ord_less_int ((times_times_int C_10) A_12)) ((times_times_int C_10) B_12))->(((ord_less_eq_int zero_zero_int) C_10)->((ord_less_int A_12) B_12))))
% 1.48/1.89 FOF formula (forall (C_9:real) (A_11:real) (B_11:real), (((ord_less_real ((times_times_real C_9) A_11)) ((times_times_real C_9) B_11))->(((ord_less_eq_real zero_zero_real) C_9)->((ord_less_real A_11) B_11)))) of role axiom named fact_757_mult__left__less__imp__less
% 1.48/1.89 A new axiom: (forall (C_9:real) (A_11:real) (B_11:real), (((ord_less_real ((times_times_real C_9) A_11)) ((times_times_real C_9) B_11))->(((ord_less_eq_real zero_zero_real) C_9)->((ord_less_real A_11) B_11))))
% 1.48/1.89 FOF formula (forall (C_9:nat) (A_11:nat) (B_11:nat), (((ord_less_nat ((times_times_nat C_9) A_11)) ((times_times_nat C_9) B_11))->(((ord_less_eq_nat zero_zero_nat) C_9)->((ord_less_nat A_11) B_11)))) of role axiom named fact_758_mult__left__less__imp__less
% 1.48/1.89 A new axiom: (forall (C_9:nat) (A_11:nat) (B_11:nat), (((ord_less_nat ((times_times_nat C_9) A_11)) ((times_times_nat C_9) B_11))->(((ord_less_eq_nat zero_zero_nat) C_9)->((ord_less_nat A_11) B_11))))
% 1.48/1.89 FOF formula (forall (C_9:int) (A_11:int) (B_11:int), (((ord_less_int ((times_times_int C_9) A_11)) ((times_times_int C_9) B_11))->(((ord_less_eq_int zero_zero_int) C_9)->((ord_less_int A_11) B_11)))) of role axiom named fact_759_mult__left__less__imp__less
% 1.48/1.89 A new axiom: (forall (C_9:int) (A_11:int) (B_11:int), (((ord_less_int ((times_times_int C_9) A_11)) ((times_times_int C_9) B_11))->(((ord_less_eq_int zero_zero_int) C_9)->((ord_less_int A_11) B_11))))
% 1.48/1.89 FOF formula (forall (A_10:real) (C_8:real) (B_10:real), (((ord_less_real ((times_times_real A_10) C_8)) ((times_times_real B_10) C_8))->(((ord_less_eq_real zero_zero_real) C_8)->((ord_less_real A_10) B_10)))) of role axiom named fact_760_mult__less__imp__less__right
% 1.48/1.89 A new axiom: (forall (A_10:real) (C_8:real) (B_10:real), (((ord_less_real ((times_times_real A_10) C_8)) ((times_times_real B_10) C_8))->(((ord_less_eq_real zero_zero_real) C_8)->((ord_less_real A_10) B_10))))
% 1.48/1.89 FOF formula (forall (A_10:nat) (C_8:nat) (B_10:nat), (((ord_less_nat ((times_times_nat A_10) C_8)) ((times_times_nat B_10) C_8))->(((ord_less_eq_nat zero_zero_nat) C_8)->((ord_less_nat A_10) B_10)))) of role axiom named fact_761_mult__less__imp__less__right
% 1.48/1.89 A new axiom: (forall (A_10:nat) (C_8:nat) (B_10:nat), (((ord_less_nat ((times_times_nat A_10) C_8)) ((times_times_nat B_10) C_8))->(((ord_less_eq_nat zero_zero_nat) C_8)->((ord_less_nat A_10) B_10))))
% 1.57/1.91 FOF formula (forall (A_10:int) (C_8:int) (B_10:int), (((ord_less_int ((times_times_int A_10) C_8)) ((times_times_int B_10) C_8))->(((ord_less_eq_int zero_zero_int) C_8)->((ord_less_int A_10) B_10)))) of role axiom named fact_762_mult__less__imp__less__right
% 1.57/1.91 A new axiom: (forall (A_10:int) (C_8:int) (B_10:int), (((ord_less_int ((times_times_int A_10) C_8)) ((times_times_int B_10) C_8))->(((ord_less_eq_int zero_zero_int) C_8)->((ord_less_int A_10) B_10))))
% 1.57/1.91 FOF formula (forall (A_9:real) (C_7:real) (B_9:real), (((ord_less_real ((times_times_real A_9) C_7)) ((times_times_real B_9) C_7))->(((ord_less_eq_real zero_zero_real) C_7)->((ord_less_real A_9) B_9)))) of role axiom named fact_763_mult__right__less__imp__less
% 1.57/1.91 A new axiom: (forall (A_9:real) (C_7:real) (B_9:real), (((ord_less_real ((times_times_real A_9) C_7)) ((times_times_real B_9) C_7))->(((ord_less_eq_real zero_zero_real) C_7)->((ord_less_real A_9) B_9))))
% 1.57/1.91 FOF formula (forall (A_9:nat) (C_7:nat) (B_9:nat), (((ord_less_nat ((times_times_nat A_9) C_7)) ((times_times_nat B_9) C_7))->(((ord_less_eq_nat zero_zero_nat) C_7)->((ord_less_nat A_9) B_9)))) of role axiom named fact_764_mult__right__less__imp__less
% 1.57/1.91 A new axiom: (forall (A_9:nat) (C_7:nat) (B_9:nat), (((ord_less_nat ((times_times_nat A_9) C_7)) ((times_times_nat B_9) C_7))->(((ord_less_eq_nat zero_zero_nat) C_7)->((ord_less_nat A_9) B_9))))
% 1.57/1.91 FOF formula (forall (A_9:int) (C_7:int) (B_9:int), (((ord_less_int ((times_times_int A_9) C_7)) ((times_times_int B_9) C_7))->(((ord_less_eq_int zero_zero_int) C_7)->((ord_less_int A_9) B_9)))) of role axiom named fact_765_mult__right__less__imp__less
% 1.57/1.91 A new axiom: (forall (A_9:int) (C_7:int) (B_9:int), (((ord_less_int ((times_times_int A_9) C_7)) ((times_times_int B_9) C_7))->(((ord_less_eq_int zero_zero_int) C_7)->((ord_less_int A_9) B_9))))
% 1.57/1.91 FOF formula (forall (C_6:real) (D_6:real) (A_8:real) (B_8:real), (((ord_less_eq_real A_8) B_8)->(((ord_less_real C_6) D_6)->(((ord_less_real zero_zero_real) A_8)->(((ord_less_eq_real zero_zero_real) C_6)->((ord_less_real ((times_times_real A_8) C_6)) ((times_times_real B_8) D_6))))))) of role axiom named fact_766_mult__le__less__imp__less
% 1.57/1.91 A new axiom: (forall (C_6:real) (D_6:real) (A_8:real) (B_8:real), (((ord_less_eq_real A_8) B_8)->(((ord_less_real C_6) D_6)->(((ord_less_real zero_zero_real) A_8)->(((ord_less_eq_real zero_zero_real) C_6)->((ord_less_real ((times_times_real A_8) C_6)) ((times_times_real B_8) D_6)))))))
% 1.57/1.91 FOF formula (forall (C_6:nat) (D_6:nat) (A_8:nat) (B_8:nat), (((ord_less_eq_nat A_8) B_8)->(((ord_less_nat C_6) D_6)->(((ord_less_nat zero_zero_nat) A_8)->(((ord_less_eq_nat zero_zero_nat) C_6)->((ord_less_nat ((times_times_nat A_8) C_6)) ((times_times_nat B_8) D_6))))))) of role axiom named fact_767_mult__le__less__imp__less
% 1.57/1.91 A new axiom: (forall (C_6:nat) (D_6:nat) (A_8:nat) (B_8:nat), (((ord_less_eq_nat A_8) B_8)->(((ord_less_nat C_6) D_6)->(((ord_less_nat zero_zero_nat) A_8)->(((ord_less_eq_nat zero_zero_nat) C_6)->((ord_less_nat ((times_times_nat A_8) C_6)) ((times_times_nat B_8) D_6)))))))
% 1.57/1.91 FOF formula (forall (C_6:int) (D_6:int) (A_8:int) (B_8:int), (((ord_less_eq_int A_8) B_8)->(((ord_less_int C_6) D_6)->(((ord_less_int zero_zero_int) A_8)->(((ord_less_eq_int zero_zero_int) C_6)->((ord_less_int ((times_times_int A_8) C_6)) ((times_times_int B_8) D_6))))))) of role axiom named fact_768_mult__le__less__imp__less
% 1.57/1.91 A new axiom: (forall (C_6:int) (D_6:int) (A_8:int) (B_8:int), (((ord_less_eq_int A_8) B_8)->(((ord_less_int C_6) D_6)->(((ord_less_int zero_zero_int) A_8)->(((ord_less_eq_int zero_zero_int) C_6)->((ord_less_int ((times_times_int A_8) C_6)) ((times_times_int B_8) D_6)))))))
% 1.57/1.91 FOF formula (forall (C_5:real) (D_5:real) (A_7:real) (B_7:real), (((ord_less_real A_7) B_7)->(((ord_less_eq_real C_5) D_5)->(((ord_less_eq_real zero_zero_real) A_7)->(((ord_less_real zero_zero_real) C_5)->((ord_less_real ((times_times_real A_7) C_5)) ((times_times_real B_7) D_5))))))) of role axiom named fact_769_mult__less__le__imp__less
% 1.57/1.93 A new axiom: (forall (C_5:real) (D_5:real) (A_7:real) (B_7:real), (((ord_less_real A_7) B_7)->(((ord_less_eq_real C_5) D_5)->(((ord_less_eq_real zero_zero_real) A_7)->(((ord_less_real zero_zero_real) C_5)->((ord_less_real ((times_times_real A_7) C_5)) ((times_times_real B_7) D_5)))))))
% 1.57/1.93 FOF formula (forall (C_5:nat) (D_5:nat) (A_7:nat) (B_7:nat), (((ord_less_nat A_7) B_7)->(((ord_less_eq_nat C_5) D_5)->(((ord_less_eq_nat zero_zero_nat) A_7)->(((ord_less_nat zero_zero_nat) C_5)->((ord_less_nat ((times_times_nat A_7) C_5)) ((times_times_nat B_7) D_5))))))) of role axiom named fact_770_mult__less__le__imp__less
% 1.57/1.93 A new axiom: (forall (C_5:nat) (D_5:nat) (A_7:nat) (B_7:nat), (((ord_less_nat A_7) B_7)->(((ord_less_eq_nat C_5) D_5)->(((ord_less_eq_nat zero_zero_nat) A_7)->(((ord_less_nat zero_zero_nat) C_5)->((ord_less_nat ((times_times_nat A_7) C_5)) ((times_times_nat B_7) D_5)))))))
% 1.57/1.93 FOF formula (forall (C_5:int) (D_5:int) (A_7:int) (B_7:int), (((ord_less_int A_7) B_7)->(((ord_less_eq_int C_5) D_5)->(((ord_less_eq_int zero_zero_int) A_7)->(((ord_less_int zero_zero_int) C_5)->((ord_less_int ((times_times_int A_7) C_5)) ((times_times_int B_7) D_5))))))) of role axiom named fact_771_mult__less__le__imp__less
% 1.57/1.93 A new axiom: (forall (C_5:int) (D_5:int) (A_7:int) (B_7:int), (((ord_less_int A_7) B_7)->(((ord_less_eq_int C_5) D_5)->(((ord_less_eq_int zero_zero_int) A_7)->(((ord_less_int zero_zero_int) C_5)->((ord_less_int ((times_times_int A_7) C_5)) ((times_times_int B_7) D_5)))))))
% 1.57/1.93 FOF formula (forall (C_4:real) (D_4:real) (A_6:real) (B_6:real), (((ord_less_real A_6) B_6)->(((ord_less_real C_4) D_4)->(((ord_less_eq_real zero_zero_real) A_6)->(((ord_less_eq_real zero_zero_real) C_4)->((ord_less_real ((times_times_real A_6) C_4)) ((times_times_real B_6) D_4))))))) of role axiom named fact_772_mult__strict__mono_H
% 1.57/1.93 A new axiom: (forall (C_4:real) (D_4:real) (A_6:real) (B_6:real), (((ord_less_real A_6) B_6)->(((ord_less_real C_4) D_4)->(((ord_less_eq_real zero_zero_real) A_6)->(((ord_less_eq_real zero_zero_real) C_4)->((ord_less_real ((times_times_real A_6) C_4)) ((times_times_real B_6) D_4)))))))
% 1.57/1.93 FOF formula (forall (C_4:nat) (D_4:nat) (A_6:nat) (B_6:nat), (((ord_less_nat A_6) B_6)->(((ord_less_nat C_4) D_4)->(((ord_less_eq_nat zero_zero_nat) A_6)->(((ord_less_eq_nat zero_zero_nat) C_4)->((ord_less_nat ((times_times_nat A_6) C_4)) ((times_times_nat B_6) D_4))))))) of role axiom named fact_773_mult__strict__mono_H
% 1.57/1.93 A new axiom: (forall (C_4:nat) (D_4:nat) (A_6:nat) (B_6:nat), (((ord_less_nat A_6) B_6)->(((ord_less_nat C_4) D_4)->(((ord_less_eq_nat zero_zero_nat) A_6)->(((ord_less_eq_nat zero_zero_nat) C_4)->((ord_less_nat ((times_times_nat A_6) C_4)) ((times_times_nat B_6) D_4)))))))
% 1.57/1.93 FOF formula (forall (C_4:int) (D_4:int) (A_6:int) (B_6:int), (((ord_less_int A_6) B_6)->(((ord_less_int C_4) D_4)->(((ord_less_eq_int zero_zero_int) A_6)->(((ord_less_eq_int zero_zero_int) C_4)->((ord_less_int ((times_times_int A_6) C_4)) ((times_times_int B_6) D_4))))))) of role axiom named fact_774_mult__strict__mono_H
% 1.57/1.93 A new axiom: (forall (C_4:int) (D_4:int) (A_6:int) (B_6:int), (((ord_less_int A_6) B_6)->(((ord_less_int C_4) D_4)->(((ord_less_eq_int zero_zero_int) A_6)->(((ord_less_eq_int zero_zero_int) C_4)->((ord_less_int ((times_times_int A_6) C_4)) ((times_times_int B_6) D_4)))))))
% 1.57/1.93 FOF formula (forall (C_3:real) (D_3:real) (A_5:real) (B_5:real), (((ord_less_real A_5) B_5)->(((ord_less_real C_3) D_3)->(((ord_less_real zero_zero_real) B_5)->(((ord_less_eq_real zero_zero_real) C_3)->((ord_less_real ((times_times_real A_5) C_3)) ((times_times_real B_5) D_3))))))) of role axiom named fact_775_mult__strict__mono
% 1.57/1.93 A new axiom: (forall (C_3:real) (D_3:real) (A_5:real) (B_5:real), (((ord_less_real A_5) B_5)->(((ord_less_real C_3) D_3)->(((ord_less_real zero_zero_real) B_5)->(((ord_less_eq_real zero_zero_real) C_3)->((ord_less_real ((times_times_real A_5) C_3)) ((times_times_real B_5) D_3)))))))
% 1.57/1.93 FOF formula (forall (C_3:nat) (D_3:nat) (A_5:nat) (B_5:nat), (((ord_less_nat A_5) B_5)->(((ord_less_nat C_3) D_3)->(((ord_less_nat zero_zero_nat) B_5)->(((ord_less_eq_nat zero_zero_nat) C_3)->((ord_less_nat ((times_times_nat A_5) C_3)) ((times_times_nat B_5) D_3))))))) of role axiom named fact_776_mult__strict__mono
% 1.57/1.95 A new axiom: (forall (C_3:nat) (D_3:nat) (A_5:nat) (B_5:nat), (((ord_less_nat A_5) B_5)->(((ord_less_nat C_3) D_3)->(((ord_less_nat zero_zero_nat) B_5)->(((ord_less_eq_nat zero_zero_nat) C_3)->((ord_less_nat ((times_times_nat A_5) C_3)) ((times_times_nat B_5) D_3)))))))
% 1.57/1.95 FOF formula (forall (C_3:int) (D_3:int) (A_5:int) (B_5:int), (((ord_less_int A_5) B_5)->(((ord_less_int C_3) D_3)->(((ord_less_int zero_zero_int) B_5)->(((ord_less_eq_int zero_zero_int) C_3)->((ord_less_int ((times_times_int A_5) C_3)) ((times_times_int B_5) D_3))))))) of role axiom named fact_777_mult__strict__mono
% 1.57/1.95 A new axiom: (forall (C_3:int) (D_3:int) (A_5:int) (B_5:int), (((ord_less_int A_5) B_5)->(((ord_less_int C_3) D_3)->(((ord_less_int zero_zero_int) B_5)->(((ord_less_eq_int zero_zero_int) C_3)->((ord_less_int ((times_times_int A_5) C_3)) ((times_times_int B_5) D_3)))))))
% 1.57/1.95 FOF formula (forall (A_4:real) (B_4:real) (C_2:real), (((ord_less_real C_2) zero_zero_real)->((iff ((ord_less_eq_real ((times_times_real C_2) A_4)) ((times_times_real C_2) B_4))) ((ord_less_eq_real B_4) A_4)))) of role axiom named fact_778_mult__le__cancel__left__neg
% 1.57/1.95 A new axiom: (forall (A_4:real) (B_4:real) (C_2:real), (((ord_less_real C_2) zero_zero_real)->((iff ((ord_less_eq_real ((times_times_real C_2) A_4)) ((times_times_real C_2) B_4))) ((ord_less_eq_real B_4) A_4))))
% 1.57/1.95 FOF formula (forall (A_4:int) (B_4:int) (C_2:int), (((ord_less_int C_2) zero_zero_int)->((iff ((ord_less_eq_int ((times_times_int C_2) A_4)) ((times_times_int C_2) B_4))) ((ord_less_eq_int B_4) A_4)))) of role axiom named fact_779_mult__le__cancel__left__neg
% 1.57/1.95 A new axiom: (forall (A_4:int) (B_4:int) (C_2:int), (((ord_less_int C_2) zero_zero_int)->((iff ((ord_less_eq_int ((times_times_int C_2) A_4)) ((times_times_int C_2) B_4))) ((ord_less_eq_int B_4) A_4))))
% 1.57/1.95 FOF formula (forall (A_3:real) (B_3:real) (C_1:real), (((ord_less_real zero_zero_real) C_1)->((iff ((ord_less_eq_real ((times_times_real C_1) A_3)) ((times_times_real C_1) B_3))) ((ord_less_eq_real A_3) B_3)))) of role axiom named fact_780_mult__le__cancel__left__pos
% 1.57/1.95 A new axiom: (forall (A_3:real) (B_3:real) (C_1:real), (((ord_less_real zero_zero_real) C_1)->((iff ((ord_less_eq_real ((times_times_real C_1) A_3)) ((times_times_real C_1) B_3))) ((ord_less_eq_real A_3) B_3))))
% 1.57/1.95 FOF formula (forall (A_3:int) (B_3:int) (C_1:int), (((ord_less_int zero_zero_int) C_1)->((iff ((ord_less_eq_int ((times_times_int C_1) A_3)) ((times_times_int C_1) B_3))) ((ord_less_eq_int A_3) B_3)))) of role axiom named fact_781_mult__le__cancel__left__pos
% 1.57/1.95 A new axiom: (forall (A_3:int) (B_3:int) (C_1:int), (((ord_less_int zero_zero_int) C_1)->((iff ((ord_less_eq_int ((times_times_int C_1) A_3)) ((times_times_int C_1) B_3))) ((ord_less_eq_int A_3) B_3))))
% 1.57/1.95 FOF formula (forall (Y_3:real) (X_3:real), (((ord_less_eq_real zero_zero_real) X_3)->(((ord_less_eq_real zero_zero_real) Y_3)->(((ord_less_eq_real Y_3) one_one_real)->((ord_less_eq_real ((times_times_real Y_3) X_3)) X_3))))) of role axiom named fact_782_mult__left__le__one__le
% 1.57/1.95 A new axiom: (forall (Y_3:real) (X_3:real), (((ord_less_eq_real zero_zero_real) X_3)->(((ord_less_eq_real zero_zero_real) Y_3)->(((ord_less_eq_real Y_3) one_one_real)->((ord_less_eq_real ((times_times_real Y_3) X_3)) X_3)))))
% 1.57/1.95 FOF formula (forall (Y_3:int) (X_3:int), (((ord_less_eq_int zero_zero_int) X_3)->(((ord_less_eq_int zero_zero_int) Y_3)->(((ord_less_eq_int Y_3) one_one_int)->((ord_less_eq_int ((times_times_int Y_3) X_3)) X_3))))) of role axiom named fact_783_mult__left__le__one__le
% 1.57/1.95 A new axiom: (forall (Y_3:int) (X_3:int), (((ord_less_eq_int zero_zero_int) X_3)->(((ord_less_eq_int zero_zero_int) Y_3)->(((ord_less_eq_int Y_3) one_one_int)->((ord_less_eq_int ((times_times_int Y_3) X_3)) X_3)))))
% 1.57/1.95 FOF formula (forall (Y_2:real) (X_2:real), (((ord_less_eq_real zero_zero_real) X_2)->(((ord_less_eq_real zero_zero_real) Y_2)->(((ord_less_eq_real Y_2) one_one_real)->((ord_less_eq_real ((times_times_real X_2) Y_2)) X_2))))) of role axiom named fact_784_mult__right__le__one__le
% 1.57/1.97 A new axiom: (forall (Y_2:real) (X_2:real), (((ord_less_eq_real zero_zero_real) X_2)->(((ord_less_eq_real zero_zero_real) Y_2)->(((ord_less_eq_real Y_2) one_one_real)->((ord_less_eq_real ((times_times_real X_2) Y_2)) X_2)))))
% 1.57/1.97 FOF formula (forall (Y_2:int) (X_2:int), (((ord_less_eq_int zero_zero_int) X_2)->(((ord_less_eq_int zero_zero_int) Y_2)->(((ord_less_eq_int Y_2) one_one_int)->((ord_less_eq_int ((times_times_int X_2) Y_2)) X_2))))) of role axiom named fact_785_mult__right__le__one__le
% 1.57/1.97 A new axiom: (forall (Y_2:int) (X_2:int), (((ord_less_eq_int zero_zero_int) X_2)->(((ord_less_eq_int zero_zero_int) Y_2)->(((ord_less_eq_int Y_2) one_one_int)->((ord_less_eq_int ((times_times_int X_2) Y_2)) X_2)))))
% 1.57/1.97 FOF formula ((ord_less_real zero_zero_real) ((plus_plus_real one_one_real) one_one_real)) of role axiom named fact_786_zero__less__two
% 1.57/1.97 A new axiom: ((ord_less_real zero_zero_real) ((plus_plus_real one_one_real) one_one_real))
% 1.57/1.97 FOF formula ((ord_less_nat zero_zero_nat) ((plus_plus_nat one_one_nat) one_one_nat)) of role axiom named fact_787_zero__less__two
% 1.57/1.97 A new axiom: ((ord_less_nat zero_zero_nat) ((plus_plus_nat one_one_nat) one_one_nat))
% 1.57/1.97 FOF formula ((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) one_one_int)) of role axiom named fact_788_zero__less__two
% 1.57/1.97 A new axiom: ((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) one_one_int))
% 1.57/1.97 FOF formula (forall (X:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit0 (bit1 pls))))) ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X)) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_789_four__x__squared
% 1.57/1.97 A new axiom: (forall (X:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit0 (bit1 pls))))) ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X)) (number_number_of_nat (bit0 (bit1 pls))))))
% 1.57/1.97 FOF formula (forall (M:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_int X) M)->((((zcong X) zero_zero_int) M)->(((eq int) X) zero_zero_int))))) of role axiom named fact_790_Int2_Ozcong__zero
% 1.57/1.97 A new axiom: (forall (M:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_int X) M)->((((zcong X) zero_zero_int) M)->(((eq int) X) zero_zero_int)))))
% 1.57/1.97 FOF formula (forall (M:int) (A:int), (((ord_less_eq_int zero_zero_int) A)->(((ord_less_int A) M)->((((zcong A) zero_zero_int) M)->(((eq int) A) zero_zero_int))))) of role axiom named fact_791_zcong__zless__0
% 1.57/1.97 A new axiom: (forall (M:int) (A:int), (((ord_less_eq_int zero_zero_int) A)->(((ord_less_int A) M)->((((zcong A) zero_zero_int) M)->(((eq int) A) zero_zero_int)))))
% 1.57/1.97 FOF formula (forall (B:int) (M:int) (A:int), (((ord_less_eq_int zero_zero_int) A)->(((ord_less_int A) M)->(((ord_less_eq_int zero_zero_int) B)->(((ord_less_int B) M)->((((zcong A) B) M)->(((eq int) A) B))))))) of role axiom named fact_792_zcong__zless__imp__eq
% 1.57/1.97 A new axiom: (forall (B:int) (M:int) (A:int), (((ord_less_eq_int zero_zero_int) A)->(((ord_less_int A) M)->(((ord_less_eq_int zero_zero_int) B)->(((ord_less_int B) M)->((((zcong A) B) M)->(((eq int) A) B)))))))
% 1.57/1.97 FOF formula (forall (P_1:int) (Y:int) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((dvd_dvd_int P_1) Y)->((dvd_dvd_int P_1) ((power_power_int Y) N))))) of role axiom named fact_793_zpower__zdvd__prop1
% 1.57/1.97 A new axiom: (forall (P_1:int) (Y:int) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((dvd_dvd_int P_1) Y)->((dvd_dvd_int P_1) ((power_power_int Y) N)))))
% 1.57/1.97 FOF formula (forall (Z:nat) (X:int) (Y:nat) (P_1:int), ((((zcong ((power_power_int X) Y)) one_one_int) P_1)->(((zcong ((power_power_int X) ((times_times_nat Y) Z))) one_one_int) P_1))) of role axiom named fact_794_zcong__zpower__zmult
% 1.57/1.97 A new axiom: (forall (Z:nat) (X:int) (Y:nat) (P_1:int), ((((zcong ((power_power_int X) Y)) one_one_int) P_1)->(((zcong ((power_power_int X) ((times_times_nat Y) Z))) one_one_int) P_1)))
% 1.65/1.99 FOF formula (forall (Y:int) (X:int) (P_1:int), ((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((((zcong Y) zero_zero_int) P_1)->False)->((((zcong ((times_times_int X) Y)) zero_zero_int) P_1)->False))))) of role axiom named fact_795_zcong__zmult__prop3
% 1.65/1.99 A new axiom: (forall (Y:int) (X:int) (P_1:int), ((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((((zcong Y) zero_zero_int) P_1)->False)->((((zcong ((times_times_int X) Y)) zero_zero_int) P_1)->False)))))
% 1.65/1.99 FOF formula (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) B)) zero_zero_int) P_1)->((or (((zcong A) zero_zero_int) P_1)) (((zcong B) zero_zero_int) P_1)))))) of role axiom named fact_796_zcong__zprime__prod__zero
% 1.65/1.99 A new axiom: (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) B)) zero_zero_int) P_1)->((or (((zcong A) zero_zero_int) P_1)) (((zcong B) zero_zero_int) P_1))))))
% 1.65/1.99 FOF formula (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->(((and ((((zcong A) zero_zero_int) P_1)->False)) ((((zcong B) zero_zero_int) P_1)->False))->((((zcong ((times_times_int A) B)) zero_zero_int) P_1)->False))))) of role axiom named fact_797_zcong__zprime__prod__zero__contra
% 1.65/1.99 A new axiom: (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->(((and ((((zcong A) zero_zero_int) P_1)->False)) ((((zcong B) zero_zero_int) P_1)->False))->((((zcong ((times_times_int A) B)) zero_zero_int) P_1)->False)))))
% 1.65/1.99 FOF formula (forall (N:int) (P_1:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->((zprime P_1)->(((dvd_dvd_int P_1) ((times_times_int M) N))->((or ((dvd_dvd_int P_1) M)) ((dvd_dvd_int P_1) N)))))) of role axiom named fact_798_zprime__zdvd__zmult
% 1.65/1.99 A new axiom: (forall (N:int) (P_1:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->((zprime P_1)->(((dvd_dvd_int P_1) ((times_times_int M) N))->((or ((dvd_dvd_int P_1) M)) ((dvd_dvd_int P_1) N))))))
% 1.65/1.99 FOF formula ((quadRes ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) (number_number_of_int min)) of role axiom named fact_799__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096
% 1.65/1.99 A new axiom: ((quadRes ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) (number_number_of_int min))
% 1.65/1.99 FOF formula ((dvd_dvd_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((minus_minus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_int min))) of role axiom named fact_800__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096
% 1.65/1.99 A new axiom: ((dvd_dvd_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((minus_minus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_int min)))
% 1.65/1.99 FOF formula (forall (J_1:nat) (K:nat) (M:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) M)->((((zcong ((power_power_int (number_number_of_int min)) J_1)) ((power_power_int (number_number_of_int min)) K)) M)->(((eq int) ((power_power_int (number_number_of_int min)) J_1)) ((power_power_int (number_number_of_int min)) K))))) of role axiom named fact_801_neg__one__power__eq__mod__m
% 1.65/1.99 A new axiom: (forall (J_1:nat) (K:nat) (M:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) M)->((((zcong ((power_power_int (number_number_of_int min)) J_1)) ((power_power_int (number_number_of_int min)) K)) M)->(((eq int) ((power_power_int (number_number_of_int min)) J_1)) ((power_power_int (number_number_of_int min)) K)))))
% 1.65/1.99 FOF formula (forall (M:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) M)->((((zcong one_one_int) (number_number_of_int min)) M)->False))) of role axiom named fact_802_one__not__neg__one__mod__m
% 1.65/1.99 A new axiom: (forall (M:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) M)->((((zcong one_one_int) (number_number_of_int min)) M)->False)))
% 1.65/1.99 FOF formula (((eq int) ((minus_minus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_int min))) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) of role axiom named fact_803__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096
% 1.65/2.00 A new axiom: (((eq int) ((minus_minus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_int min))) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int))
% 1.65/2.00 FOF formula ((((quadRes ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) (number_number_of_int min))->False)->(not (((eq int) ((legendre (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) one_one_int))) of role axiom named fact_804__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N
% 1.65/2.00 A new axiom: ((((quadRes ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) (number_number_of_int min))->False)->(not (((eq int) ((legendre (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) one_one_int)))
% 1.65/2.00 FOF formula (forall (X:real), ((iff (((ord_less_real zero_zero_real) ((times_times_real X) X))->False)) (((eq real) X) zero_zero_real))) of role axiom named fact_805_not__real__square__gt__zero
% 1.65/2.00 A new axiom: (forall (X:real), ((iff (((ord_less_real zero_zero_real) ((times_times_real X) X))->False)) (((eq real) X) zero_zero_real)))
% 1.65/2.00 FOF formula (forall (K:int), (((eq int) ((minus_minus_int K) pls)) K)) of role axiom named fact_806_diff__bin__simps_I1_J
% 1.65/2.00 A new axiom: (forall (K:int), (((eq int) ((minus_minus_int K) pls)) K))
% 1.65/2.00 FOF formula (forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit0 K)) (bit0 L))) (bit0 ((minus_minus_int K) L)))) of role axiom named fact_807_diff__bin__simps_I7_J
% 1.65/2.00 A new axiom: (forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit0 K)) (bit0 L))) (bit0 ((minus_minus_int K) L))))
% 1.65/2.00 FOF formula (forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((minus_minus_int Z1) Z2)) W)) ((minus_minus_int ((times_times_int Z1) W)) ((times_times_int Z2) W)))) of role axiom named fact_808_zdiff__zmult__distrib
% 1.65/2.00 A new axiom: (forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((minus_minus_int Z1) Z2)) W)) ((minus_minus_int ((times_times_int Z1) W)) ((times_times_int Z2) W))))
% 1.65/2.00 FOF formula (forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((minus_minus_int Z1) Z2))) ((minus_minus_int ((times_times_int W) Z1)) ((times_times_int W) Z2)))) of role axiom named fact_809_zdiff__zmult__distrib2
% 1.65/2.00 A new axiom: (forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((minus_minus_int Z1) Z2))) ((minus_minus_int ((times_times_int W) Z1)) ((times_times_int W) Z2))))
% 1.65/2.00 FOF formula (forall (A:int) (B:int) (C:int), ((((eq int) ((minus_minus_int A) B)) C)->(((eq int) A) ((plus_plus_int C) B)))) of role axiom named fact_810_Int2_Oaux1
% 1.65/2.00 A new axiom: (forall (A:int) (B:int) (C:int), ((((eq int) ((minus_minus_int A) B)) C)->(((eq int) A) ((plus_plus_int C) B))))
% 1.65/2.00 FOF formula (forall (C:int) (D:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((zcong C) D) M)->(((zcong ((minus_minus_int A) C)) ((minus_minus_int B) D)) M)))) of role axiom named fact_811_zcong__zdiff
% 1.65/2.00 A new axiom: (forall (C:int) (D:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((zcong C) D) M)->(((zcong ((minus_minus_int A) C)) ((minus_minus_int B) D)) M))))
% 1.65/2.00 FOF formula (forall (K:int) (M:int) (N:int), (((dvd_dvd_int K) ((minus_minus_int M) N))->(((dvd_dvd_int K) N)->((dvd_dvd_int K) M)))) of role axiom named fact_812_zdvd__zdiffD
% 1.65/2.00 A new axiom: (forall (K:int) (M:int) (N:int), (((dvd_dvd_int K) ((minus_minus_int M) N))->(((dvd_dvd_int K) N)->((dvd_dvd_int K) M))))
% 1.65/2.00 FOF formula (forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit1 K)) (bit0 L))) (bit1 ((minus_minus_int K) L)))) of role axiom named fact_813_diff__bin__simps_I9_J
% 1.65/2.00 A new axiom: (forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit1 K)) (bit0 L))) (bit1 ((minus_minus_int K) L))))
% 1.65/2.03 FOF formula (forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit1 K)) (bit1 L))) (bit0 ((minus_minus_int K) L)))) of role axiom named fact_814_diff__bin__simps_I10_J
% 1.65/2.03 A new axiom: (forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit1 K)) (bit1 L))) (bit0 ((minus_minus_int K) L))))
% 1.65/2.03 FOF formula (forall (L:int), (((eq int) ((minus_minus_int pls) (bit0 L))) (bit0 ((minus_minus_int pls) L)))) of role axiom named fact_815_diff__bin__simps_I3_J
% 1.65/2.03 A new axiom: (forall (L:int), (((eq int) ((minus_minus_int pls) (bit0 L))) (bit0 ((minus_minus_int pls) L))))
% 1.65/2.03 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_int K) L)) ((ord_less_int ((minus_minus_int K) L)) zero_zero_int))) of role axiom named fact_816_less__bin__lemma
% 1.65/2.03 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int K) L)) ((ord_less_int ((minus_minus_int K) L)) zero_zero_int)))
% 1.65/2.03 FOF formula (forall (A:int) (R:int) (B:int) (M:int) (C:int) (D:int) (N:int), (((eq int) ((plus_plus_int ((times_times_int ((minus_minus_int A) ((times_times_int R) B))) M)) ((times_times_int ((minus_minus_int C) ((times_times_int R) D))) N))) ((minus_minus_int ((plus_plus_int ((times_times_int A) M)) ((times_times_int C) N))) ((times_times_int R) ((plus_plus_int ((times_times_int B) M)) ((times_times_int D) N)))))) of role axiom named fact_817_xzgcda__linear__aux1
% 1.65/2.03 A new axiom: (forall (A:int) (R:int) (B:int) (M:int) (C:int) (D:int) (N:int), (((eq int) ((plus_plus_int ((times_times_int ((minus_minus_int A) ((times_times_int R) B))) M)) ((times_times_int ((minus_minus_int C) ((times_times_int R) D))) N))) ((minus_minus_int ((plus_plus_int ((times_times_int A) M)) ((times_times_int C) N))) ((times_times_int R) ((plus_plus_int ((times_times_int B) M)) ((times_times_int D) N))))))
% 1.65/2.03 FOF formula (forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) ((dvd_dvd_int M) ((minus_minus_int A) B)))) of role axiom named fact_818_zcong__def
% 1.65/2.03 A new axiom: (forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) ((dvd_dvd_int M) ((minus_minus_int A) B))))
% 1.65/2.03 FOF formula (forall (A:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int X) A)->((not (((eq int) X) ((minus_minus_int A) one_one_int)))->((ord_less_int X) ((minus_minus_int A) one_one_int)))))) of role axiom named fact_819_Euler_Oaux1
% 1.65/2.03 A new axiom: (forall (A:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int X) A)->((not (((eq int) X) ((minus_minus_int A) one_one_int)))->((ord_less_int X) ((minus_minus_int A) one_one_int))))))
% 1.65/2.03 FOF formula (forall (W:int) (Z:int), ((iff ((ord_less_eq_int W) ((minus_minus_int Z) one_one_int))) ((ord_less_int W) Z))) of role axiom named fact_820_zle__diff1__eq
% 1.65/2.03 A new axiom: (forall (W:int) (Z:int), ((iff ((ord_less_eq_int W) ((minus_minus_int Z) one_one_int))) ((ord_less_int W) Z)))
% 1.65/2.03 FOF formula (forall (L:int), (((eq int) ((minus_minus_int pls) (bit1 L))) (bit1 ((minus_minus_int min) L)))) of role axiom named fact_821_diff__bin__simps_I4_J
% 1.65/2.03 A new axiom: (forall (L:int), (((eq int) ((minus_minus_int pls) (bit1 L))) (bit1 ((minus_minus_int min) L))))
% 1.65/2.03 FOF formula (forall (L:int), (((eq int) ((minus_minus_int min) (bit0 L))) (bit1 ((minus_minus_int min) L)))) of role axiom named fact_822_diff__bin__simps_I5_J
% 1.65/2.03 A new axiom: (forall (L:int), (((eq int) ((minus_minus_int min) (bit0 L))) (bit1 ((minus_minus_int min) L))))
% 1.65/2.03 FOF formula (forall (L:int), (((eq int) ((minus_minus_int min) (bit1 L))) (bit0 ((minus_minus_int min) L)))) of role axiom named fact_823_diff__bin__simps_I6_J
% 1.65/2.03 A new axiom: (forall (L:int), (((eq int) ((minus_minus_int min) (bit1 L))) (bit0 ((minus_minus_int min) L))))
% 1.65/2.03 FOF formula (forall (A:int) (P_1:int), ((iff (((zcong ((times_times_int A) ((minus_minus_int P_1) one_one_int))) one_one_int) P_1)) (((zcong A) ((minus_minus_int P_1) one_one_int)) P_1))) of role axiom named fact_824_inv__not__p__minus__1__aux
% 1.65/2.03 A new axiom: (forall (A:int) (P_1:int), ((iff (((zcong ((times_times_int A) ((minus_minus_int P_1) one_one_int))) one_one_int) P_1)) (((zcong A) ((minus_minus_int P_1) one_one_int)) P_1)))
% 1.65/2.03 FOF formula (forall (I_1:nat) (M:nat) (N:nat), (((dvd_dvd_nat ((power_power_nat I_1) M)) ((power_power_nat I_1) N))->(((ord_less_nat one_one_nat) I_1)->((ord_less_eq_nat M) N)))) of role axiom named fact_825_power__dvd__imp__le
% 1.65/2.04 A new axiom: (forall (I_1:nat) (M:nat) (N:nat), (((dvd_dvd_nat ((power_power_nat I_1) M)) ((power_power_nat I_1) N))->(((ord_less_nat one_one_nat) I_1)->((ord_less_eq_nat M) N))))
% 1.65/2.04 FOF formula (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P_1)->((((zcong ((times_times_int A) A)) one_one_int) P_1)->((or (((eq int) A) one_one_int)) (((eq int) A) ((minus_minus_int P_1) one_one_int)))))))) of role axiom named fact_826_zcong__square__zless
% 1.65/2.04 A new axiom: (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P_1)->((((zcong ((times_times_int A) A)) one_one_int) P_1)->((or (((eq int) A) one_one_int)) (((eq int) A) ((minus_minus_int P_1) one_one_int))))))))
% 1.65/2.04 FOF formula (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) A)) one_one_int) P_1)->((or (((zcong A) one_one_int) P_1)) (((zcong A) ((minus_minus_int P_1) one_one_int)) P_1)))))) of role axiom named fact_827_zcong__square
% 1.65/2.04 A new axiom: (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) A)) one_one_int) P_1)->((or (((zcong A) one_one_int) P_1)) (((zcong A) ((minus_minus_int P_1) one_one_int)) P_1))))))
% 1.65/2.04 FOF formula (forall (A:int) (B:int), (((eq int) ((times_times_int ((plus_plus_int A) B)) ((minus_minus_int A) B))) ((minus_minus_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_828_zspecial__product
% 1.65/2.04 A new axiom: (forall (A:int) (B:int), (((eq int) ((times_times_int ((plus_plus_int A) B)) ((minus_minus_int A) B))) ((minus_minus_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls)))))))
% 1.65/2.04 FOF formula (forall (A:int) (B:int), (((eq int) ((power_power_int ((minus_minus_int A) B)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((minus_minus_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A)) B))) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_829_zdiff__power2
% 1.65/2.04 A new axiom: (forall (A:int) (B:int), (((eq int) ((power_power_int ((minus_minus_int A) B)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((minus_minus_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A)) B))) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls)))))))
% 1.65/2.04 FOF formula (forall (A:int) (B:int), (((eq int) ((power_power_int ((minus_minus_int A) B)) (number_number_of_nat (bit1 (bit1 pls))))) ((minus_minus_int ((plus_plus_int ((minus_minus_int ((power_power_int A) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls)))))) B))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) A)) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))) ((power_power_int B) (number_number_of_nat (bit1 (bit1 pls))))))) of role axiom named fact_830_zdiff__power3
% 1.65/2.04 A new axiom: (forall (A:int) (B:int), (((eq int) ((power_power_int ((minus_minus_int A) B)) (number_number_of_nat (bit1 (bit1 pls))))) ((minus_minus_int ((plus_plus_int ((minus_minus_int ((power_power_int A) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls)))))) B))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) A)) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))) ((power_power_int B) (number_number_of_nat (bit1 (bit1 pls)))))))
% 1.65/2.06 FOF formula (forall (N:nat), ((or (((eq int) ((power_power_int (number_number_of_int min)) N)) one_one_int)) (((eq int) ((power_power_int (number_number_of_int min)) N)) (number_number_of_int min)))) of role axiom named fact_831_neg__one__power
% 1.65/2.06 A new axiom: (forall (N:nat), ((or (((eq int) ((power_power_int (number_number_of_int min)) N)) one_one_int)) (((eq int) ((power_power_int (number_number_of_int min)) N)) (number_number_of_int min))))
% 1.65/2.06 FOF formula (forall (M:int), ((zprime ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) M)) one_one_int))->(((eq int) ((legendre (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) M)) one_one_int))) one_one_int))) of role axiom named fact_832_Legendre__1mod4
% 1.65/2.06 A new axiom: (forall (M:int), ((zprime ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) M)) one_one_int))->(((eq int) ((legendre (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) M)) one_one_int))) one_one_int)))
% 1.65/2.06 FOF formula (forall (A:int) (P_1:int), ((and ((((zcong A) zero_zero_int) P_1)->(((eq int) ((legendre A) P_1)) zero_zero_int))) (((((zcong A) zero_zero_int) P_1)->False)->((and (((quadRes P_1) A)->(((eq int) ((legendre A) P_1)) one_one_int))) ((((quadRes P_1) A)->False)->(((eq int) ((legendre A) P_1)) (number_number_of_int min))))))) of role axiom named fact_833_Legendre__def
% 1.65/2.06 A new axiom: (forall (A:int) (P_1:int), ((and ((((zcong A) zero_zero_int) P_1)->(((eq int) ((legendre A) P_1)) zero_zero_int))) (((((zcong A) zero_zero_int) P_1)->False)->((and (((quadRes P_1) A)->(((eq int) ((legendre A) P_1)) one_one_int))) ((((quadRes P_1) A)->False)->(((eq int) ((legendre A) P_1)) (number_number_of_int min)))))))
% 1.65/2.06 FOF formula (forall (M:int) (X:int), ((iff ((quadRes M) X)) ((ex int) (fun (Y_1:int)=> (((zcong ((power_power_int Y_1) (number_number_of_nat (bit0 (bit1 pls))))) X) M))))) of role axiom named fact_834_QuadRes__def
% 1.65/2.06 A new axiom: (forall (M:int) (X:int), ((iff ((quadRes M) X)) ((ex int) (fun (Y_1:int)=> (((zcong ((power_power_int Y_1) (number_number_of_nat (bit0 (bit1 pls))))) X) M)))))
% 1.65/2.06 FOF formula (forall (X:real) (Y:real), (((eq real) ((power_power_real ((plus_plus_real X) Y)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X)) Y)))) of role axiom named fact_835_real__sum__squared__expand
% 1.65/2.06 A new axiom: (forall (X:real) (Y:real), (((eq real) ((power_power_real ((plus_plus_real X) Y)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X)) Y))))
% 1.65/2.06 FOF formula (forall (N:nat) (M:nat), (((dvd_dvd_nat N) M)->((or ((or (((eq nat) M) zero_zero_nat)) (((eq nat) M) N))) ((ord_less_eq_nat ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N)) M)))) of role axiom named fact_836_divides__cases
% 1.65/2.06 A new axiom: (forall (N:nat) (M:nat), (((dvd_dvd_nat N) M)->((or ((or (((eq nat) M) zero_zero_nat)) (((eq nat) M) N))) ((ord_less_eq_nat ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N)) M))))
% 1.65/2.06 FOF formula (forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) ((dvd_dvd_nat Y) X))) (((eq nat) X) Y))) of role axiom named fact_837_divides__antisym
% 1.65/2.06 A new axiom: (forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) ((dvd_dvd_nat Y) X))) (((eq nat) X) Y)))
% 1.65/2.06 FOF formula (forall (B:nat) (D:nat) (A:nat), (((dvd_dvd_nat D) A)->(((dvd_dvd_nat D) ((plus_plus_nat A) B))->((dvd_dvd_nat D) B)))) of role axiom named fact_838_divides__add__revr
% 1.65/2.06 A new axiom: (forall (B:nat) (D:nat) (A:nat), (((dvd_dvd_nat D) A)->(((dvd_dvd_nat D) ((plus_plus_nat A) B))->((dvd_dvd_nat D) B))))
% 1.74/2.08 FOF formula (forall (C:nat) (A:nat) (B:nat), (((dvd_dvd_nat A) B)->((dvd_dvd_nat ((times_times_nat A) C)) ((times_times_nat B) C)))) of role axiom named fact_839_divides__mul__r
% 1.74/2.08 A new axiom: (forall (C:nat) (A:nat) (B:nat), (((dvd_dvd_nat A) B)->((dvd_dvd_nat ((times_times_nat A) C)) ((times_times_nat B) C))))
% 1.74/2.08 FOF formula (forall (C:nat) (A:nat) (B:nat), (((dvd_dvd_nat A) B)->((dvd_dvd_nat ((times_times_nat C) A)) ((times_times_nat C) B)))) of role axiom named fact_840_divides__mul__l
% 1.74/2.08 A new axiom: (forall (C:nat) (A:nat) (B:nat), (((dvd_dvd_nat A) B)->((dvd_dvd_nat ((times_times_nat C) A)) ((times_times_nat C) B))))
% 1.74/2.08 FOF formula (forall (N:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->((dvd_dvd_nat ((power_power_nat X) N)) ((power_power_nat Y) N)))) of role axiom named fact_841_divides__exp
% 1.74/2.08 A new axiom: (forall (N:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->((dvd_dvd_nat ((power_power_nat X) N)) ((power_power_nat Y) N))))
% 1.74/2.08 FOF formula (forall (N:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((times_times_nat M) N)) zero_zero_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((times_times_nat M) N)) ((plus_plus_nat N) ((times_times_nat ((minus_minus_nat M) one_one_nat)) N)))))) of role axiom named fact_842_mult__eq__if
% 1.74/2.08 A new axiom: (forall (N:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((times_times_nat M) N)) zero_zero_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((times_times_nat M) N)) ((plus_plus_nat N) ((times_times_nat ((minus_minus_nat M) one_one_nat)) N))))))
% 1.74/2.08 FOF formula (forall (P_1:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((power_power_nat P_1) M)) one_one_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((power_power_nat P_1) M)) ((times_times_nat P_1) ((power_power_nat P_1) ((minus_minus_nat M) one_one_nat))))))) of role axiom named fact_843_power__eq__if
% 1.74/2.08 A new axiom: (forall (P_1:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((power_power_nat P_1) M)) one_one_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((power_power_nat P_1) M)) ((times_times_nat P_1) ((power_power_nat P_1) ((minus_minus_nat M) one_one_nat)))))))
% 1.74/2.08 FOF formula (forall (X:nat) (Y:nat), (((eq nat) ((minus_minus_nat ((power_power_nat X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((plus_plus_nat X) Y)) ((minus_minus_nat X) Y)))) of role axiom named fact_844_diff__square
% 1.74/2.08 A new axiom: (forall (X:nat) (Y:nat), (((eq nat) ((minus_minus_nat ((power_power_nat X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((plus_plus_nat X) Y)) ((minus_minus_nat X) Y))))
% 1.74/2.08 FOF formula (forall (A:nat) (B:nat), (((dvd_dvd_nat A) B)->((or (((eq nat) B) zero_zero_nat)) ((ord_less_eq_nat A) B)))) of role axiom named fact_845_divides__ge
% 1.74/2.08 A new axiom: (forall (A:nat) (B:nat), (((dvd_dvd_nat A) B)->((or (((eq nat) B) zero_zero_nat)) ((ord_less_eq_nat A) B))))
% 1.74/2.08 FOF formula (forall (M:nat) (K:nat) (N:nat), ((iff ((dvd_dvd_nat ((times_times_nat M) K)) ((times_times_nat N) K))) ((or (((eq nat) K) zero_zero_nat)) ((dvd_dvd_nat M) N)))) of role axiom named fact_846_nat__mult__dvd__cancel__disj_H
% 1.74/2.08 A new axiom: (forall (M:nat) (K:nat) (N:nat), ((iff ((dvd_dvd_nat ((times_times_nat M) K)) ((times_times_nat N) K))) ((or (((eq nat) K) zero_zero_nat)) ((dvd_dvd_nat M) N))))
% 1.74/2.08 FOF formula (forall (N:nat) (M:nat), ((iff (((eq nat) ((times_times_nat N) M)) one_one_nat)) ((and (((eq nat) N) one_one_nat)) (((eq nat) M) one_one_nat)))) of role axiom named fact_847_nat__mult__eq__one
% 1.74/2.08 A new axiom: (forall (N:nat) (M:nat), ((iff (((eq nat) ((times_times_nat N) M)) one_one_nat)) ((and (((eq nat) N) one_one_nat)) (((eq nat) M) one_one_nat))))
% 1.74/2.08 FOF formula (forall (M:nat) (N:nat), ((iff (((eq nat) ((power_power_nat M) N)) zero_zero_nat)) ((and (not (((eq nat) N) zero_zero_nat))) (((eq nat) M) zero_zero_nat)))) of role axiom named fact_848_nat__power__eq__0__iff
% 1.74/2.08 A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) ((power_power_nat M) N)) zero_zero_nat)) ((and (not (((eq nat) N) zero_zero_nat))) (((eq nat) M) zero_zero_nat))))
% 1.74/2.10 FOF formula (forall (X:nat) (Y:nat) (N:nat), ((not (((eq nat) N) zero_zero_nat))->(((dvd_dvd_nat ((power_power_nat X) N)) Y)->((dvd_dvd_nat X) Y)))) of role axiom named fact_849_divides__exp2
% 1.74/2.10 A new axiom: (forall (X:nat) (Y:nat) (N:nat), ((not (((eq nat) N) zero_zero_nat))->(((dvd_dvd_nat ((power_power_nat X) N)) Y)->((dvd_dvd_nat X) Y))))
% 1.74/2.10 FOF formula (forall (A:nat) (N:nat) (B:nat), (((dvd_dvd_nat ((power_power_nat A) N)) ((power_power_nat B) N))->((not (((eq nat) N) zero_zero_nat))->((dvd_dvd_nat A) B)))) of role axiom named fact_850_divides__rev
% 1.74/2.10 A new axiom: (forall (A:nat) (N:nat) (B:nat), (((dvd_dvd_nat ((power_power_nat A) N)) ((power_power_nat B) N))->((not (((eq nat) N) zero_zero_nat))->((dvd_dvd_nat A) B))))
% 1.74/2.10 FOF formula (forall (X:nat) (N:nat), ((iff (((eq nat) ((power_power_nat X) N)) one_one_nat)) ((or (((eq nat) X) one_one_nat)) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_851_exp__eq__1
% 1.74/2.10 A new axiom: (forall (X:nat) (N:nat), ((iff (((eq nat) ((power_power_nat X) N)) one_one_nat)) ((or (((eq nat) X) one_one_nat)) (((eq nat) N) zero_zero_nat))))
% 1.74/2.10 FOF formula (forall (X:nat) (Q:nat) (N:nat) (R:nat), ((((eq nat) X) ((plus_plus_nat ((times_times_nat Q) N)) R))->(((ord_less_nat zero_zero_nat) R)->(((ord_less_nat R) N)->(((dvd_dvd_nat N) X)->False))))) of role axiom named fact_852_divides__div__not
% 1.74/2.10 A new axiom: (forall (X:nat) (Q:nat) (N:nat) (R:nat), ((((eq nat) X) ((plus_plus_nat ((times_times_nat Q) N)) R))->(((ord_less_nat zero_zero_nat) R)->(((ord_less_nat R) N)->(((dvd_dvd_nat N) X)->False)))))
% 1.74/2.10 FOF formula (forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real)))) of role axiom named fact_853_realpow__two__sum__zero__iff
% 1.74/2.10 A new axiom: (forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real))))
% 1.74/2.10 FOF formula (forall (A:real) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_real zero_zero_real) A)->((ex real) (fun (X_1:real)=> ((and ((and ((ord_less_real zero_zero_real) X_1)) (((eq real) ((power_power_real X_1) N)) A))) (forall (Y_1:real), (((and ((ord_less_real zero_zero_real) Y_1)) (((eq real) ((power_power_real Y_1) N)) A))->(((eq real) Y_1) X_1))))))))) of role axiom named fact_854_realpow__pos__nth__unique
% 1.74/2.10 A new axiom: (forall (A:real) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_real zero_zero_real) A)->((ex real) (fun (X_1:real)=> ((and ((and ((ord_less_real zero_zero_real) X_1)) (((eq real) ((power_power_real X_1) N)) A))) (forall (Y_1:real), (((and ((ord_less_real zero_zero_real) Y_1)) (((eq real) ((power_power_real Y_1) N)) A))->(((eq real) Y_1) X_1)))))))))
% 1.74/2.10 FOF formula (forall (A:real) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_real zero_zero_real) A)->((ex real) (fun (R_1:real)=> ((and ((ord_less_real zero_zero_real) R_1)) (((eq real) ((power_power_real R_1) N)) A))))))) of role axiom named fact_855_realpow__pos__nth
% 1.74/2.10 A new axiom: (forall (A:real) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_real zero_zero_real) A)->((ex real) (fun (R_1:real)=> ((and ((ord_less_real zero_zero_real) R_1)) (((eq real) ((power_power_real R_1) N)) A)))))))
% 1.74/2.10 FOF formula (forall (N:nat) (M:nat), (((ord_less_nat zero_zero_nat) M)->((iff ((dvd_dvd_nat ((times_times_nat N) M)) M)) (((eq nat) N) one_one_nat)))) of role axiom named fact_856_dvd__mult__cancel2
% 1.74/2.10 A new axiom: (forall (N:nat) (M:nat), (((ord_less_nat zero_zero_nat) M)->((iff ((dvd_dvd_nat ((times_times_nat N) M)) M)) (((eq nat) N) one_one_nat))))
% 1.74/2.10 FOF formula (forall (X:nat), ((dvd_dvd_nat X) X)) of role axiom named fact_857_dvd_Oorder__refl
% 1.74/2.10 A new axiom: (forall (X:nat), ((dvd_dvd_nat X) X))
% 1.76/2.12 FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_858_less__zeroE
% 1.76/2.12 A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False))
% 1.76/2.12 FOF formula (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) of role axiom named fact_859_le0
% 1.76/2.12 A new axiom: (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N))
% 1.76/2.12 FOF formula (forall (I_1:nat) (J_1:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J_1)) K)) ((minus_minus_nat ((minus_minus_nat I_1) K)) J_1))) of role axiom named fact_860_diff__commute
% 1.76/2.12 A new axiom: (forall (I_1:nat) (J_1:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J_1)) K)) ((minus_minus_nat ((minus_minus_nat I_1) K)) J_1)))
% 1.76/2.12 FOF formula (forall (N:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N)) zero_zero_nat)) of role axiom named fact_861_diff__0__eq__0
% 1.76/2.12 A new axiom: (forall (N:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N)) zero_zero_nat))
% 1.76/2.12 FOF formula (forall (M:nat), (((eq nat) ((minus_minus_nat M) zero_zero_nat)) M)) of role axiom named fact_862_minus__nat_Odiff__0
% 1.76/2.12 A new axiom: (forall (M:nat), (((eq nat) ((minus_minus_nat M) zero_zero_nat)) M))
% 1.76/2.12 FOF formula (forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat)) of role axiom named fact_863_diff__self__eq__0
% 1.76/2.12 A new axiom: (forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat))
% 1.76/2.12 FOF formula (forall (M:nat) (N:nat), ((((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)->((((eq nat) ((minus_minus_nat N) M)) zero_zero_nat)->(((eq nat) M) N)))) of role axiom named fact_864_diffs0__imp__equal
% 1.76/2.12 A new axiom: (forall (M:nat) (N:nat), ((((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)->((((eq nat) ((minus_minus_nat N) M)) zero_zero_nat)->(((eq nat) M) N))))
% 1.76/2.12 FOF formula (not (((eq real) zero_zero_real) one_one_real)) of role axiom named fact_865_real__zero__not__eq__one
% 1.76/2.12 A new axiom: (not (((eq real) zero_zero_real) one_one_real))
% 1.76/2.12 FOF formula (forall (X:real) (Y:real), ((iff ((ord_less_eq_real X) Y)) ((ord_less_eq_real ((minus_minus_real X) Y)) zero_zero_real))) of role axiom named fact_866_real__le__eq__diff
% 1.76/2.12 A new axiom: (forall (X:real) (Y:real), ((iff ((ord_less_eq_real X) Y)) ((ord_less_eq_real ((minus_minus_real X) Y)) zero_zero_real)))
% 1.76/2.12 FOF formula (forall (X:real) (Y:real), ((iff ((ord_less_real X) Y)) ((and ((ord_less_eq_real X) Y)) (not (((eq real) X) Y))))) of role axiom named fact_867_real__less__def
% 1.76/2.12 A new axiom: (forall (X:real) (Y:real), ((iff ((ord_less_real X) Y)) ((and ((ord_less_eq_real X) Y)) (not (((eq real) X) Y)))))
% 1.76/2.12 FOF formula (forall (X:real) (Y:real), ((iff ((ord_less_eq_real X) Y)) ((or ((ord_less_real X) Y)) (((eq real) X) Y)))) of role axiom named fact_868_less__eq__real__def
% 1.76/2.12 A new axiom: (forall (X:real) (Y:real), ((iff ((ord_less_eq_real X) Y)) ((or ((ord_less_real X) Y)) (((eq real) X) Y))))
% 1.76/2.12 FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_869_less__not__refl
% 1.76/2.12 A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False))
% 1.76/2.12 FOF formula (forall (M:nat) (N:nat), ((iff (not (((eq nat) M) N))) ((or ((ord_less_nat M) N)) ((ord_less_nat N) M)))) of role axiom named fact_870_nat__neq__iff
% 1.76/2.12 A new axiom: (forall (M:nat) (N:nat), ((iff (not (((eq nat) M) N))) ((or ((ord_less_nat M) N)) ((ord_less_nat N) M))))
% 1.76/2.12 FOF formula (forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X)))) of role axiom named fact_871_linorder__neqE__nat
% 1.76/2.12 A new axiom: (forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X))))
% 1.76/2.12 FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_872_less__irrefl__nat
% 1.76/2.12 A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False))
% 1.76/2.12 FOF formula (forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N)))) of role axiom named fact_873_less__not__refl2
% 1.76/2.12 A new axiom: (forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N))))
% 1.76/2.12 FOF formula (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))) of role axiom named fact_874_less__not__refl3
% 1.78/2.14 A new axiom: (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T))))
% 1.78/2.14 FOF formula (forall (P:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P N) M))->(((((eq nat) M) N)->((P N) M))->((((ord_less_nat N) M)->((P N) M))->((P N) M))))) of role axiom named fact_875_nat__less__cases
% 1.78/2.14 A new axiom: (forall (P:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P N) M))->(((((eq nat) M) N)->((P N) M))->((((ord_less_nat N) M)->((P N) M))->((P N) M)))))
% 1.78/2.14 FOF formula (forall (N:nat) (J_1:nat) (K:nat), (((ord_less_nat J_1) K)->((ord_less_nat ((minus_minus_nat J_1) N)) K))) of role axiom named fact_876_less__imp__diff__less
% 1.78/2.14 A new axiom: (forall (N:nat) (J_1:nat) (K:nat), (((ord_less_nat J_1) K)->((ord_less_nat ((minus_minus_nat J_1) N)) K)))
% 1.78/2.14 FOF formula (forall (L:nat) (M:nat) (N:nat), (((ord_less_nat M) N)->(((ord_less_nat M) L)->((ord_less_nat ((minus_minus_nat L) N)) ((minus_minus_nat L) M))))) of role axiom named fact_877_diff__less__mono2
% 1.78/2.14 A new axiom: (forall (L:nat) (M:nat) (N:nat), (((ord_less_nat M) N)->(((ord_less_nat M) L)->((ord_less_nat ((minus_minus_nat L) N)) ((minus_minus_nat L) M)))))
% 1.78/2.14 FOF formula (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False))) of role axiom named fact_878_dvd_Oless__asym
% 1.78/2.14 A new axiom: (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False)))
% 1.78/2.14 FOF formula (forall (Z:nat) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) Z)) (((dvd_dvd_nat Z) Y)->False))->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False))))) of role axiom named fact_879_dvd_Oless__trans
% 1.78/2.14 A new axiom: (forall (Z:nat) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) Z)) (((dvd_dvd_nat Z) Y)->False))->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False)))))
% 1.78/2.14 FOF formula (forall (A:nat) (B:nat), (((and ((dvd_dvd_nat A) B)) (((dvd_dvd_nat B) A)->False))->(((and ((dvd_dvd_nat B) A)) (((dvd_dvd_nat A) B)->False))->False))) of role axiom named fact_880_dvd_Oless__asym_H
% 1.78/2.14 A new axiom: (forall (A:nat) (B:nat), (((and ((dvd_dvd_nat A) B)) (((dvd_dvd_nat B) A)->False))->(((and ((dvd_dvd_nat B) A)) (((dvd_dvd_nat A) B)->False))->False)))
% 1.78/2.14 FOF formula (forall (Z:nat) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((dvd_dvd_nat Y) Z)->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False))))) of role axiom named fact_881_dvd_Oless__le__trans
% 1.78/2.14 A new axiom: (forall (Z:nat) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((dvd_dvd_nat Y) Z)->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False)))))
% 1.78/2.14 FOF formula (forall (C:nat) (A:nat) (B:nat), (((and ((dvd_dvd_nat A) B)) (((dvd_dvd_nat B) A)->False))->((((eq nat) B) C)->((and ((dvd_dvd_nat A) C)) (((dvd_dvd_nat C) A)->False))))) of role axiom named fact_882_dvd_Oord__less__eq__trans
% 1.78/2.14 A new axiom: (forall (C:nat) (A:nat) (B:nat), (((and ((dvd_dvd_nat A) B)) (((dvd_dvd_nat B) A)->False))->((((eq nat) B) C)->((and ((dvd_dvd_nat A) C)) (((dvd_dvd_nat C) A)->False)))))
% 1.78/2.14 FOF formula (forall (P:Prop) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->P))) of role axiom named fact_883_dvd_Oless__imp__triv
% 1.78/2.14 A new axiom: (forall (P:Prop) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->P)))
% 1.78/2.14 FOF formula (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) Y) X)))) of role axiom named fact_884_dvd_Oless__imp__not__eq2
% 1.78/2.14 A new axiom: (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) Y) X))))
% 1.78/2.14 FOF formula (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) X) Y)))) of role axiom named fact_885_dvd_Oless__imp__not__eq
% 1.78/2.16 A new axiom: (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) X) Y))))
% 1.78/2.16 FOF formula (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False))) of role axiom named fact_886_dvd_Oless__imp__not__less
% 1.78/2.16 A new axiom: (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False)))
% 1.78/2.16 FOF formula (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->((dvd_dvd_nat X) Y))) of role axiom named fact_887_dvd_Oless__imp__le
% 1.78/2.16 A new axiom: (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->((dvd_dvd_nat X) Y)))
% 1.78/2.16 FOF formula (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False))) of role axiom named fact_888_dvd_Oless__not__sym
% 1.78/2.16 A new axiom: (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False)))
% 1.78/2.16 FOF formula (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) X) Y)))) of role axiom named fact_889_dvd_Oless__imp__neq
% 1.78/2.16 A new axiom: (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) X) Y))))
% 1.78/2.16 FOF formula (forall (Z:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((and ((dvd_dvd_nat Y) Z)) (((dvd_dvd_nat Z) Y)->False))->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False))))) of role axiom named fact_890_dvd_Ole__less__trans
% 1.78/2.16 A new axiom: (forall (Z:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((and ((dvd_dvd_nat Y) Z)) (((dvd_dvd_nat Z) Y)->False))->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False)))))
% 1.78/2.16 FOF formula (forall (C:nat) (A:nat) (B:nat), ((((eq nat) A) B)->(((and ((dvd_dvd_nat B) C)) (((dvd_dvd_nat C) B)->False))->((and ((dvd_dvd_nat A) C)) (((dvd_dvd_nat C) A)->False))))) of role axiom named fact_891_dvd_Oord__eq__less__trans
% 1.78/2.17 A new axiom: (forall (C:nat) (A:nat) (B:nat), ((((eq nat) A) B)->(((and ((dvd_dvd_nat B) C)) (((dvd_dvd_nat C) B)->False))->((and ((dvd_dvd_nat A) C)) (((dvd_dvd_nat C) A)->False)))))
% 1.78/2.17 FOF formula (forall (N:nat) (K:nat) (M:nat), (((dvd_dvd_nat K) M)->(((dvd_dvd_nat K) N)->((dvd_dvd_nat K) ((minus_minus_nat M) N))))) of role axiom named fact_892_dvd__diff__nat
% 1.78/2.17 A new axiom: (forall (N:nat) (K:nat) (M:nat), (((dvd_dvd_nat K) M)->(((dvd_dvd_nat K) N)->((dvd_dvd_nat K) ((minus_minus_nat M) N)))))
% 1.78/2.17 FOF formula (forall (Z:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((dvd_dvd_nat Y) Z)->((dvd_dvd_nat X) Z)))) of role axiom named fact_893_dvd_Oorder__trans
% 1.78/2.17 A new axiom: (forall (Z:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((dvd_dvd_nat Y) Z)->((dvd_dvd_nat X) Z))))
% 1.78/2.17 FOF formula (forall (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((dvd_dvd_nat Y) X)->(((eq nat) X) Y)))) of role axiom named fact_894_dvd_Oantisym
% 1.78/2.17 A new axiom: (forall (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((dvd_dvd_nat Y) X)->(((eq nat) X) Y))))
% 1.78/2.17 FOF formula (forall (M:nat) (N:nat), (((dvd_dvd_nat M) N)->(((dvd_dvd_nat N) M)->(((eq nat) M) N)))) of role axiom named fact_895_dvd__antisym
% 1.78/2.17 A new axiom: (forall (M:nat) (N:nat), (((dvd_dvd_nat M) N)->(((dvd_dvd_nat N) M)->(((eq nat) M) N))))
% 1.78/2.17 FOF formula (forall (C:nat) (A:nat) (B:nat), (((dvd_dvd_nat A) B)->((((eq nat) B) C)->((dvd_dvd_nat A) C)))) of role axiom named fact_896_dvd_Oord__le__eq__trans
% 1.78/2.17 A new axiom: (forall (C:nat) (A:nat) (B:nat), (((dvd_dvd_nat A) B)->((((eq nat) B) C)->((dvd_dvd_nat A) C))))
% 1.78/2.17 FOF formula (forall (C:nat) (A:nat) (B:nat), ((((eq nat) A) B)->(((dvd_dvd_nat B) C)->((dvd_dvd_nat A) C)))) of role axiom named fact_897_dvd_Oord__eq__le__trans
% 1.78/2.17 A new axiom: (forall (C:nat) (A:nat) (B:nat), ((((eq nat) A) B)->(((dvd_dvd_nat B) C)->((dvd_dvd_nat A) C))))
% 1.78/2.17 FOF formula (forall (A:nat) (B:nat), (((dvd_dvd_nat A) B)->((not (((eq nat) A) B))->((and ((dvd_dvd_nat A) B)) (((dvd_dvd_nat B) A)->False))))) of role axiom named fact_898_dvd_Ole__neq__trans
% 1.78/2.19 A new axiom: (forall (A:nat) (B:nat), (((dvd_dvd_nat A) B)->((not (((eq nat) A) B))->((and ((dvd_dvd_nat A) B)) (((dvd_dvd_nat B) A)->False)))))
% 1.78/2.19 FOF formula (forall (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->((or ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) (((eq nat) X) Y)))) of role axiom named fact_899_dvd_Ole__imp__less__or__eq
% 1.78/2.19 A new axiom: (forall (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->((or ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) (((eq nat) X) Y))))
% 1.78/2.19 FOF formula (forall (Y:nat) (X:nat), (((dvd_dvd_nat Y) X)->((iff ((dvd_dvd_nat X) Y)) (((eq nat) X) Y)))) of role axiom named fact_900_dvd_Oantisym__conv
% 1.78/2.19 A new axiom: (forall (Y:nat) (X:nat), (((dvd_dvd_nat Y) X)->((iff ((dvd_dvd_nat X) Y)) (((eq nat) X) Y))))
% 1.78/2.19 FOF formula (forall (X:nat) (Y:nat), ((((eq nat) X) Y)->((dvd_dvd_nat X) Y))) of role axiom named fact_901_dvd_Oeq__refl
% 1.78/2.19 A new axiom: (forall (X:nat) (Y:nat), ((((eq nat) X) Y)->((dvd_dvd_nat X) Y)))
% 1.78/2.19 FOF formula (forall (A:nat) (B:nat), ((not (((eq nat) A) B))->(((dvd_dvd_nat A) B)->((and ((dvd_dvd_nat A) B)) (((dvd_dvd_nat B) A)->False))))) of role axiom named fact_902_dvd_Oneq__le__trans
% 1.78/2.19 A new axiom: (forall (A:nat) (B:nat), ((not (((eq nat) A) B))->(((dvd_dvd_nat A) B)->((and ((dvd_dvd_nat A) B)) (((dvd_dvd_nat B) A)->False)))))
% 1.78/2.19 FOF formula (forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False)))) of role axiom named fact_903_dvd_Oless__le__not__le
% 1.78/2.19 A new axiom: (forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))))
% 1.78/2.19 FOF formula (forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) ((and ((dvd_dvd_nat X) Y)) (not (((eq nat) X) Y))))) of role axiom named fact_904_dvd_Oless__le
% 1.78/2.19 A new axiom: (forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) ((and ((dvd_dvd_nat X) Y)) (not (((eq nat) X) Y)))))
% 1.78/2.19 FOF formula (forall (X:nat) (Y:nat), ((iff ((dvd_dvd_nat X) Y)) ((or ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) (((eq nat) X) Y)))) of role axiom named fact_905_dvd_Ole__less
% 1.78/2.19 A new axiom: (forall (X:nat) (Y:nat), ((iff ((dvd_dvd_nat X) Y)) ((or ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) (((eq nat) X) Y))))
% 1.78/2.19 FOF formula (forall (X:nat) (Y:nat), ((iff (((eq nat) X) Y)) ((and ((dvd_dvd_nat X) Y)) ((dvd_dvd_nat Y) X)))) of role axiom named fact_906_dvd_Oeq__iff
% 1.78/2.19 A new axiom: (forall (X:nat) (Y:nat), ((iff (((eq nat) X) Y)) ((and ((dvd_dvd_nat X) Y)) ((dvd_dvd_nat Y) X))))
% 1.78/2.19 FOF formula (forall (X:nat), (((and ((dvd_dvd_nat X) X)) (((dvd_dvd_nat X) X)->False))->False)) of role axiom named fact_907_dvd_Oless__irrefl
% 1.78/2.19 A new axiom: (forall (X:nat), (((and ((dvd_dvd_nat X) X)) (((dvd_dvd_nat X) X)->False))->False))
% 1.78/2.19 FOF formula (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) N)) ((plus_plus_nat N) M))) of role axiom named fact_908_nat__add__commute
% 1.78/2.19 A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) N)) ((plus_plus_nat N) M)))
% 1.78/2.19 FOF formula (forall (X:nat) (Y:nat) (Z:nat), (((eq nat) ((plus_plus_nat X) ((plus_plus_nat Y) Z))) ((plus_plus_nat Y) ((plus_plus_nat X) Z)))) of role axiom named fact_909_nat__add__left__commute
% 1.78/2.19 A new axiom: (forall (X:nat) (Y:nat) (Z:nat), (((eq nat) ((plus_plus_nat X) ((plus_plus_nat Y) Z))) ((plus_plus_nat Y) ((plus_plus_nat X) Z))))
% 1.78/2.19 FOF formula (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M) N)) K)) ((plus_plus_nat M) ((plus_plus_nat N) K)))) of role axiom named fact_910_nat__add__assoc
% 1.78/2.19 A new axiom: (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M) N)) K)) ((plus_plus_nat M) ((plus_plus_nat N) K))))
% 1.78/2.19 FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) (((eq nat) M) N))) of role axiom named fact_911_nat__add__left__cancel
% 1.78/2.19 A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) (((eq nat) M) N)))
% 1.78/2.21 FOF formula (forall (M:nat) (K:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) K)) ((plus_plus_nat N) K))) (((eq nat) M) N))) of role axiom named fact_912_nat__add__right__cancel
% 1.78/2.21 A new axiom: (forall (M:nat) (K:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) K)) ((plus_plus_nat N) K))) (((eq nat) M) N)))
% 1.78/2.21 FOF formula (forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) N)) N)) M)) of role axiom named fact_913_diff__add__inverse2
% 1.78/2.21 A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) N)) N)) M))
% 1.78/2.21 FOF formula (forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat N) M)) N)) M)) of role axiom named fact_914_diff__add__inverse
% 1.78/2.21 A new axiom: (forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat N) M)) N)) M))
% 1.78/2.21 FOF formula (forall (I_1:nat) (J_1:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J_1)) K)) ((minus_minus_nat I_1) ((plus_plus_nat J_1) K)))) of role axiom named fact_915_diff__diff__left
% 1.78/2.21 A new axiom: (forall (I_1:nat) (J_1:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J_1)) K)) ((minus_minus_nat I_1) ((plus_plus_nat J_1) K))))
% 1.78/2.21 FOF formula (forall (K:nat) (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((minus_minus_nat M) N))) of role axiom named fact_916_Nat_Odiff__cancel
% 1.78/2.21 A new axiom: (forall (K:nat) (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((minus_minus_nat M) N)))
% 1.78/2.21 FOF formula (forall (M:nat) (K:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) K)) ((plus_plus_nat N) K))) ((minus_minus_nat M) N))) of role axiom named fact_917_diff__cancel2
% 1.78/2.21 A new axiom: (forall (M:nat) (K:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) K)) ((plus_plus_nat N) K))) ((minus_minus_nat M) N)))
% 1.78/2.21 FOF formula (forall (Z1:real) (Z2:real) (Z3:real), (((eq real) ((times_times_real ((times_times_real Z1) Z2)) Z3)) ((times_times_real Z1) ((times_times_real Z2) Z3)))) of role axiom named fact_918_real__mult__assoc
% 1.78/2.21 A new axiom: (forall (Z1:real) (Z2:real) (Z3:real), (((eq real) ((times_times_real ((times_times_real Z1) Z2)) Z3)) ((times_times_real Z1) ((times_times_real Z2) Z3))))
% 1.78/2.21 FOF formula (forall (Z:real) (W:real), (((eq real) ((times_times_real Z) W)) ((times_times_real W) Z))) of role axiom named fact_919_real__mult__commute
% 1.78/2.21 A new axiom: (forall (Z:real) (W:real), (((eq real) ((times_times_real Z) W)) ((times_times_real W) Z)))
% 1.78/2.21 FOF formula (forall (Z:real), (((eq real) ((times_times_real one_one_real) Z)) Z)) of role axiom named fact_920_real__mult__1
% 1.78/2.21 A new axiom: (forall (Z:real), (((eq real) ((times_times_real one_one_real) Z)) Z))
% 1.78/2.21 FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N)))) of role axiom named fact_921_le__antisym
% 1.78/2.21 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N))))
% 1.78/2.21 FOF formula (forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat J_1) K)->((ord_less_eq_nat I_1) K)))) of role axiom named fact_922_le__trans
% 1.78/2.21 A new axiom: (forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat J_1) K)->((ord_less_eq_nat I_1) K))))
% 1.78/2.21 FOF formula (forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N))) of role axiom named fact_923_eq__imp__le
% 1.78/2.21 A new axiom: (forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N)))
% 1.78/2.21 FOF formula (forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M))) of role axiom named fact_924_nat__le__linear
% 1.78/2.21 A new axiom: (forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M)))
% 1.78/2.21 FOF formula (forall (N:nat), ((ord_less_eq_nat N) N)) of role axiom named fact_925_le__refl
% 1.78/2.21 A new axiom: (forall (N:nat), ((ord_less_eq_nat N) N))
% 1.78/2.21 FOF formula (forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff ((ord_less_eq_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((ord_less_eq_nat M) N))))) of role axiom named fact_926_le__diff__iff
% 1.87/2.23 A new axiom: (forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff ((ord_less_eq_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((ord_less_eq_nat M) N)))))
% 1.87/2.23 FOF formula (forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->(((eq nat) ((minus_minus_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((minus_minus_nat M) N))))) of role axiom named fact_927_Nat_Odiff__diff__eq
% 1.87/2.23 A new axiom: (forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->(((eq nat) ((minus_minus_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((minus_minus_nat M) N)))))
% 1.87/2.23 FOF formula (forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff (((eq nat) ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) (((eq nat) M) N))))) of role axiom named fact_928_eq__diff__iff
% 1.87/2.23 A new axiom: (forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff (((eq nat) ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) (((eq nat) M) N)))))
% 1.87/2.23 FOF formula (forall (I_1:nat) (N:nat), (((ord_less_eq_nat I_1) N)->(((eq nat) ((minus_minus_nat N) ((minus_minus_nat N) I_1))) I_1))) of role axiom named fact_929_diff__diff__cancel
% 1.87/2.23 A new axiom: (forall (I_1:nat) (N:nat), (((ord_less_eq_nat I_1) N)->(((eq nat) ((minus_minus_nat N) ((minus_minus_nat N) I_1))) I_1)))
% 1.87/2.23 FOF formula (forall (L:nat) (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat ((minus_minus_nat M) L)) ((minus_minus_nat N) L)))) of role axiom named fact_930_diff__le__mono
% 1.87/2.23 A new axiom: (forall (L:nat) (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat ((minus_minus_nat M) L)) ((minus_minus_nat N) L))))
% 1.87/2.23 FOF formula (forall (L:nat) (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat ((minus_minus_nat L) N)) ((minus_minus_nat L) M)))) of role axiom named fact_931_diff__le__mono2
% 1.87/2.23 A new axiom: (forall (L:nat) (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat ((minus_minus_nat L) N)) ((minus_minus_nat L) M))))
% 1.87/2.23 FOF formula (forall (M:nat) (N:nat), ((ord_less_eq_nat ((minus_minus_nat M) N)) M)) of role axiom named fact_932_Nat_Odiff__le__self
% 1.87/2.23 A new axiom: (forall (M:nat) (N:nat), ((ord_less_eq_nat ((minus_minus_nat M) N)) M))
% 1.87/2.23 FOF formula (forall (M:nat) (N:nat), (((eq nat) ((times_times_nat M) N)) ((times_times_nat N) M))) of role axiom named fact_933_nat__mult__commute
% 1.87/2.23 A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((times_times_nat M) N)) ((times_times_nat N) M)))
% 1.87/2.23 FOF formula (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((times_times_nat M) N)) K)) ((times_times_nat M) ((times_times_nat N) K)))) of role axiom named fact_934_nat__mult__assoc
% 1.87/2.23 A new axiom: (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((times_times_nat M) N)) K)) ((times_times_nat M) ((times_times_nat N) K))))
% 1.87/2.23 FOF formula (forall (K:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K) ((minus_minus_nat M) N))) ((minus_minus_nat ((times_times_nat K) M)) ((times_times_nat K) N)))) of role axiom named fact_935_diff__mult__distrib2
% 1.87/2.23 A new axiom: (forall (K:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K) ((minus_minus_nat M) N))) ((minus_minus_nat ((times_times_nat K) M)) ((times_times_nat K) N))))
% 1.87/2.23 FOF formula (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((minus_minus_nat M) N)) K)) ((minus_minus_nat ((times_times_nat M) K)) ((times_times_nat N) K)))) of role axiom named fact_936_diff__mult__distrib
% 1.87/2.23 A new axiom: (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((minus_minus_nat M) N)) K)) ((minus_minus_nat ((times_times_nat M) K)) ((times_times_nat N) K))))
% 1.87/2.23 FOF formula (forall (Z:real) (X:real) (Y:real), (((ord_less_eq_real X) Y)->((ord_less_eq_real ((plus_plus_real Z) X)) ((plus_plus_real Z) Y)))) of role axiom named fact_937_real__add__left__mono
% 1.87/2.23 A new axiom: (forall (Z:real) (X:real) (Y:real), (((ord_less_eq_real X) Y)->((ord_less_eq_real ((plus_plus_real Z) X)) ((plus_plus_real Z) Y))))
% 1.87/2.23 FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_938_not__less0
% 1.87/2.24 A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False))
% 1.87/2.24 FOF formula (forall (N:nat), ((iff (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N))) of role axiom named fact_939_neq0__conv
% 1.87/2.24 A new axiom: (forall (N:nat), ((iff (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N)))
% 1.87/2.24 FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_940_less__nat__zero__code
% 1.87/2.24 A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False))
% 1.87/2.24 FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->(not (((eq nat) N) zero_zero_nat)))) of role axiom named fact_941_gr__implies__not0
% 1.87/2.24 A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->(not (((eq nat) N) zero_zero_nat))))
% 1.87/2.24 FOF formula (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N))) of role axiom named fact_942_gr0I
% 1.87/2.24 A new axiom: (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N)))
% 1.87/2.24 FOF formula (forall (M:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_nat zero_zero_nat) M)->((ord_less_nat ((minus_minus_nat M) N)) M)))) of role axiom named fact_943_diff__less
% 1.87/2.24 A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_nat zero_zero_nat) M)->((ord_less_nat ((minus_minus_nat M) N)) M))))
% 1.87/2.24 FOF formula (forall (N:nat) (M:nat), ((iff ((ord_less_nat zero_zero_nat) ((minus_minus_nat N) M))) ((ord_less_nat M) N))) of role axiom named fact_944_zero__less__diff
% 1.87/2.24 A new axiom: (forall (N:nat) (M:nat), ((iff ((ord_less_nat zero_zero_nat) ((minus_minus_nat N) M))) ((ord_less_nat M) N)))
% 1.87/2.24 FOF formula (forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N)) of role axiom named fact_945_plus__nat_Oadd__0
% 1.87/2.24 A new axiom: (forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N))
% 1.87/2.24 FOF formula (forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M)) of role axiom named fact_946_Nat_Oadd__0__right
% 1.87/2.24 A new axiom: (forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M))
% 1.87/2.24 FOF formula (forall (M:nat) (N:nat), ((iff (((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_947_add__is__0
% 1.87/2.24 A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) N)) zero_zero_nat)) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat))))
% 1.87/2.24 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_948_add__eq__self__zero
% 1.87/2.24 A new axiom: (forall (M:nat) (N:nat), ((((eq nat) ((plus_plus_nat M) N)) M)->(((eq nat) N) zero_zero_nat)))
% 1.87/2.24 FOF formula (forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat N) ((plus_plus_nat N) M))) zero_zero_nat)) of role axiom named fact_949_diff__add__0
% 1.87/2.24 A new axiom: (forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat N) ((plus_plus_nat N) M))) zero_zero_nat))
% 1.87/2.24 FOF formula (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) of role axiom named fact_950_less__eq__nat_Osimps_I1_J
% 1.87/2.24 A new axiom: (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N))
% 1.87/2.24 FOF formula (forall (N:nat), ((iff ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat))) of role axiom named fact_951_le__0__eq
% 1.87/2.24 A new axiom: (forall (N:nat), ((iff ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))
% 1.87/2.24 FOF formula (forall (M:nat) (N:nat), ((iff (((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)) ((ord_less_eq_nat M) N))) of role axiom named fact_952_diff__is__0__eq
% 1.87/2.24 A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)) ((ord_less_eq_nat M) N)))
% 1.87/2.24 FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((eq nat) ((minus_minus_nat M) N)) zero_zero_nat))) of role axiom named fact_953_diff__is__0__eq_H
% 1.87/2.24 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)))
% 1.87/2.24 FOF formula (forall (N:nat), (((eq nat) ((times_times_nat zero_zero_nat) N)) zero_zero_nat)) of role axiom named fact_954_mult__0
% 1.87/2.27 A new axiom: (forall (N:nat), (((eq nat) ((times_times_nat zero_zero_nat) N)) zero_zero_nat))
% 1.87/2.27 FOF formula (forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat)) of role axiom named fact_955_mult__0__right
% 1.87/2.27 A new axiom: (forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat))
% 1.87/2.27 FOF formula (forall (M:nat) (N:nat), ((iff (((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_956_mult__is__0
% 1.87/2.27 A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) N)) zero_zero_nat)) ((or (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat))))
% 1.87/2.27 FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) ((or (((eq nat) M) N)) (((eq nat) K) zero_zero_nat)))) of role axiom named fact_957_mult__cancel1
% 1.87/2.27 A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) ((or (((eq nat) M) N)) (((eq nat) K) zero_zero_nat))))
% 1.87/2.27 FOF formula (forall (M:nat) (K:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) K)) ((times_times_nat N) K))) ((or (((eq nat) M) N)) (((eq nat) K) zero_zero_nat)))) of role axiom named fact_958_mult__cancel2
% 1.87/2.27 A new axiom: (forall (M:nat) (K:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) K)) ((times_times_nat N) K))) ((or (((eq nat) M) N)) (((eq nat) K) zero_zero_nat))))
% 1.87/2.27 FOF formula (forall (A:real) (B:real) (C:real), ((not (((eq real) C) zero_zero_real))->((iff (((eq real) ((times_times_real C) A)) ((times_times_real C) B))) (((eq real) A) B)))) of role axiom named fact_959_real__mult__left__cancel
% 1.87/2.27 A new axiom: (forall (A:real) (B:real) (C:real), ((not (((eq real) C) zero_zero_real))->((iff (((eq real) ((times_times_real C) A)) ((times_times_real C) B))) (((eq real) A) B))))
% 1.87/2.27 FOF formula (forall (A:real) (B:real) (C:real), ((not (((eq real) C) zero_zero_real))->((iff (((eq real) ((times_times_real A) C)) ((times_times_real B) C))) (((eq real) A) B)))) of role axiom named fact_960_real__mult__right__cancel
% 1.87/2.27 A new axiom: (forall (A:real) (B:real) (C:real), ((not (((eq real) C) zero_zero_real))->((iff (((eq real) ((times_times_real A) C)) ((times_times_real B) C))) (((eq real) A) B))))
% 1.87/2.27 FOF formula (forall (I_1:nat) (J_1:nat), (((ord_less_nat ((plus_plus_nat I_1) J_1)) I_1)->False)) of role axiom named fact_961_not__add__less1
% 1.87/2.27 A new axiom: (forall (I_1:nat) (J_1:nat), (((ord_less_nat ((plus_plus_nat I_1) J_1)) I_1)->False))
% 1.87/2.27 FOF formula (forall (J_1:nat) (I_1:nat), (((ord_less_nat ((plus_plus_nat J_1) I_1)) I_1)->False)) of role axiom named fact_962_not__add__less2
% 1.87/2.27 A new axiom: (forall (J_1:nat) (I_1:nat), (((ord_less_nat ((plus_plus_nat J_1) I_1)) I_1)->False))
% 1.87/2.27 FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_nat M) N))) of role axiom named fact_963_nat__add__left__cancel__less
% 1.87/2.27 A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_nat M) N)))
% 1.87/2.27 FOF formula (forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat I_1) ((plus_plus_nat J_1) M)))) of role axiom named fact_964_trans__less__add1
% 1.87/2.27 A new axiom: (forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat I_1) ((plus_plus_nat J_1) M))))
% 1.87/2.27 FOF formula (forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat I_1) ((plus_plus_nat M) J_1)))) of role axiom named fact_965_trans__less__add2
% 1.87/2.27 A new axiom: (forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat I_1) ((plus_plus_nat M) J_1))))
% 1.87/2.27 FOF formula (forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J_1) K)))) of role axiom named fact_966_add__less__mono1
% 1.87/2.27 A new axiom: (forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J_1) K))))
% 1.87/2.27 FOF formula (forall (K:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J_1) L))))) of role axiom named fact_967_add__less__mono
% 1.87/2.29 A new axiom: (forall (K:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J_1) L)))))
% 1.87/2.29 FOF formula (forall (M:nat) (N:nat) (K:nat) (L:nat), (((ord_less_nat K) L)->((((eq nat) ((plus_plus_nat M) L)) ((plus_plus_nat K) N))->((ord_less_nat M) N)))) of role axiom named fact_968_less__add__eq__less
% 1.87/2.29 A new axiom: (forall (M:nat) (N:nat) (K:nat) (L:nat), (((ord_less_nat K) L)->((((eq nat) ((plus_plus_nat M) L)) ((plus_plus_nat K) N))->((ord_less_nat M) N))))
% 1.87/2.29 FOF formula (forall (I_1:nat) (J_1:nat) (K:nat), (((ord_less_nat ((plus_plus_nat I_1) J_1)) K)->((ord_less_nat I_1) K))) of role axiom named fact_969_add__lessD1
% 1.87/2.29 A new axiom: (forall (I_1:nat) (J_1:nat) (K:nat), (((ord_less_nat ((plus_plus_nat I_1) J_1)) K)->((ord_less_nat I_1) K)))
% 1.87/2.29 FOF formula (forall (M:nat) (N:nat), ((((ord_less_nat M) N)->False)->(((eq nat) ((plus_plus_nat N) ((minus_minus_nat M) N))) M))) of role axiom named fact_970_add__diff__inverse
% 1.87/2.29 A new axiom: (forall (M:nat) (N:nat), ((((ord_less_nat M) N)->False)->(((eq nat) ((plus_plus_nat N) ((minus_minus_nat M) N))) M)))
% 1.87/2.29 FOF formula (forall (I_1:nat) (J_1:nat) (K:nat), ((iff ((ord_less_nat I_1) ((minus_minus_nat J_1) K))) ((ord_less_nat ((plus_plus_nat I_1) K)) J_1))) of role axiom named fact_971_less__diff__conv
% 1.87/2.29 A new axiom: (forall (I_1:nat) (J_1:nat) (K:nat), ((iff ((ord_less_nat I_1) ((minus_minus_nat J_1) K))) ((ord_less_nat ((plus_plus_nat I_1) K)) J_1)))
% 1.87/2.29 FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) N)) ((and ((ord_less_eq_nat M) N)) (not (((eq nat) M) N))))) of role axiom named fact_972_nat__less__le
% 1.87/2.29 A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) N)) ((and ((ord_less_eq_nat M) N)) (not (((eq nat) M) N)))))
% 1.87/2.29 FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((or ((ord_less_nat M) N)) (((eq nat) M) N)))) of role axiom named fact_973_le__eq__less__or__eq
% 1.87/2.29 A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((or ((ord_less_nat M) N)) (((eq nat) M) N))))
% 1.87/2.29 FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N))) of role axiom named fact_974_less__imp__le__nat
% 1.87/2.29 A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N)))
% 1.87/2.29 FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((not (((eq nat) M) N))->((ord_less_nat M) N)))) of role axiom named fact_975_le__neq__implies__less
% 1.87/2.29 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((not (((eq nat) M) N))->((ord_less_nat M) N))))
% 1.87/2.29 FOF formula (forall (M:nat) (N:nat), (((or ((ord_less_nat M) N)) (((eq nat) M) N))->((ord_less_eq_nat M) N))) of role axiom named fact_976_less__or__eq__imp__le
% 1.87/2.29 A new axiom: (forall (M:nat) (N:nat), (((or ((ord_less_nat M) N)) (((eq nat) M) N))->((ord_less_eq_nat M) N)))
% 1.87/2.29 FOF formula (forall (C:nat) (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat C) A)->((ord_less_nat ((minus_minus_nat A) C)) ((minus_minus_nat B) C))))) of role axiom named fact_977_diff__less__mono
% 1.87/2.29 A new axiom: (forall (C:nat) (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat C) A)->((ord_less_nat ((minus_minus_nat A) C)) ((minus_minus_nat B) C)))))
% 1.87/2.29 FOF formula (forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff ((ord_less_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((ord_less_nat M) N))))) of role axiom named fact_978_less__diff__iff
% 1.87/2.29 A new axiom: (forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff ((ord_less_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((ord_less_nat M) N)))))
% 1.87/2.29 FOF formula (forall (K:nat) (N:nat), ((iff ((dvd_dvd_nat K) ((plus_plus_nat N) K))) ((dvd_dvd_nat K) N))) of role axiom named fact_979_dvd__reduce
% 1.87/2.29 A new axiom: (forall (K:nat) (N:nat), ((iff ((dvd_dvd_nat K) ((plus_plus_nat N) K))) ((dvd_dvd_nat K) N)))
% 1.87/2.29 FOF formula (forall (K:nat) (M:nat) (N:nat), (((dvd_dvd_nat K) ((minus_minus_nat M) N))->(((dvd_dvd_nat K) N)->(((ord_less_eq_nat N) M)->((dvd_dvd_nat K) M))))) of role axiom named fact_980_dvd__diffD
% 1.95/2.31 A new axiom: (forall (K:nat) (M:nat) (N:nat), (((dvd_dvd_nat K) ((minus_minus_nat M) N))->(((dvd_dvd_nat K) N)->(((ord_less_eq_nat N) M)->((dvd_dvd_nat K) M)))))
% 1.95/2.31 FOF formula (forall (K:nat) (M:nat) (N:nat), (((dvd_dvd_nat K) ((minus_minus_nat M) N))->(((dvd_dvd_nat K) M)->(((ord_less_eq_nat N) M)->((dvd_dvd_nat K) N))))) of role axiom named fact_981_dvd__diffD1
% 1.95/2.31 A new axiom: (forall (K:nat) (M:nat) (N:nat), (((dvd_dvd_nat K) ((minus_minus_nat M) N))->(((dvd_dvd_nat K) M)->(((ord_less_eq_nat N) M)->((dvd_dvd_nat K) N)))))
% 1.95/2.31 FOF formula (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat M) N))) of role axiom named fact_982_le__add2
% 1.95/2.31 A new axiom: (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat M) N)))
% 1.95/2.31 FOF formula (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M))) of role axiom named fact_983_le__add1
% 1.95/2.31 A new axiom: (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M)))
% 1.95/2.31 FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) ((plus_plus_nat M) K_1)))))) of role axiom named fact_984_le__iff__add
% 1.95/2.31 A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) ((plus_plus_nat M) K_1))))))
% 1.95/2.31 FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_eq_nat M) N))) of role axiom named fact_985_nat__add__left__cancel__le
% 1.95/2.31 A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_eq_nat M) N)))
% 1.95/2.31 FOF formula (forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat I_1) ((plus_plus_nat J_1) M)))) of role axiom named fact_986_trans__le__add1
% 1.95/2.31 A new axiom: (forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat I_1) ((plus_plus_nat J_1) M))))
% 1.95/2.31 FOF formula (forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat I_1) ((plus_plus_nat M) J_1)))) of role axiom named fact_987_trans__le__add2
% 1.95/2.31 A new axiom: (forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat I_1) ((plus_plus_nat M) J_1))))
% 1.95/2.31 FOF formula (forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J_1) K)))) of role axiom named fact_988_add__le__mono1
% 1.95/2.31 A new axiom: (forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J_1) K))))
% 1.95/2.31 FOF formula (forall (K:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J_1) L))))) of role axiom named fact_989_add__le__mono
% 1.95/2.31 A new axiom: (forall (K:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J_1) L)))))
% 1.95/2.31 FOF formula (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat K) N))) of role axiom named fact_990_add__leD2
% 1.95/2.31 A new axiom: (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat K) N)))
% 1.95/2.31 FOF formula (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat M) N))) of role axiom named fact_991_add__leD1
% 1.95/2.31 A new axiom: (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat M) N)))
% 1.95/2.31 FOF formula (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((((ord_less_eq_nat M) N)->(((ord_less_eq_nat K) N)->False))->False))) of role axiom named fact_992_add__leE
% 1.95/2.31 A new axiom: (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((((ord_less_eq_nat M) N)->(((ord_less_eq_nat K) N)->False))->False)))
% 1.95/2.31 FOF formula (forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->(((eq nat) ((minus_minus_nat I_1) ((minus_minus_nat J_1) K))) ((minus_minus_nat ((plus_plus_nat I_1) K)) J_1)))) of role axiom named fact_993_diff__diff__right
% 1.95/2.33 A new axiom: (forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->(((eq nat) ((minus_minus_nat I_1) ((minus_minus_nat J_1) K))) ((minus_minus_nat ((plus_plus_nat I_1) K)) J_1))))
% 1.95/2.33 FOF formula (forall (J_1:nat) (K:nat) (I_1:nat), ((iff ((ord_less_eq_nat ((minus_minus_nat J_1) K)) I_1)) ((ord_less_eq_nat J_1) ((plus_plus_nat I_1) K)))) of role axiom named fact_994_le__diff__conv
% 1.95/2.33 A new axiom: (forall (J_1:nat) (K:nat) (I_1:nat), ((iff ((ord_less_eq_nat ((minus_minus_nat J_1) K)) I_1)) ((ord_less_eq_nat J_1) ((plus_plus_nat I_1) K))))
% 1.95/2.33 FOF formula (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat K) N)->((ord_less_eq_nat M) ((minus_minus_nat ((plus_plus_nat N) M)) K)))) of role axiom named fact_995_le__add__diff
% 1.95/2.33 A new axiom: (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat K) N)->((ord_less_eq_nat M) ((minus_minus_nat ((plus_plus_nat N) M)) K))))
% 1.95/2.33 FOF formula (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((plus_plus_nat N) ((minus_minus_nat M) N))) M))) of role axiom named fact_996_le__add__diff__inverse
% 1.95/2.33 A new axiom: (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((plus_plus_nat N) ((minus_minus_nat M) N))) M)))
% 1.95/2.33 FOF formula (forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->(((eq nat) ((plus_plus_nat I_1) ((minus_minus_nat J_1) K))) ((minus_minus_nat ((plus_plus_nat I_1) J_1)) K)))) of role axiom named fact_997_add__diff__assoc
% 1.95/2.33 A new axiom: (forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->(((eq nat) ((plus_plus_nat I_1) ((minus_minus_nat J_1) K))) ((minus_minus_nat ((plus_plus_nat I_1) J_1)) K))))
% 1.95/2.33 FOF formula (forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->((iff ((ord_less_eq_nat I_1) ((minus_minus_nat J_1) K))) ((ord_less_eq_nat ((plus_plus_nat I_1) K)) J_1)))) of role axiom named fact_998_le__diff__conv2
% 1.95/2.33 A new axiom: (forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->((iff ((ord_less_eq_nat I_1) ((minus_minus_nat J_1) K))) ((ord_less_eq_nat ((plus_plus_nat I_1) K)) J_1))))
% 1.95/2.33 FOF formula (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((plus_plus_nat ((minus_minus_nat M) N)) N)) M))) of role axiom named fact_999_le__add__diff__inverse2
% 1.95/2.33 A new axiom: (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((plus_plus_nat ((minus_minus_nat M) N)) N)) M)))
% 1.95/2.33 FOF formula (forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff (((eq nat) ((minus_minus_nat J_1) I_1)) K)) (((eq nat) J_1) ((plus_plus_nat K) I_1))))) of role axiom named fact_1000_le__imp__diff__is__add
% 1.95/2.33 A new axiom: (forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff (((eq nat) ((minus_minus_nat J_1) I_1)) K)) (((eq nat) J_1) ((plus_plus_nat K) I_1)))))
% 1.95/2.33 FOF formula (forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat I_1) J_1)) K)) ((plus_plus_nat I_1) ((minus_minus_nat J_1) K))))) of role axiom named fact_1001_diff__add__assoc
% 1.95/2.33 A new axiom: (forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat I_1) J_1)) K)) ((plus_plus_nat I_1) ((minus_minus_nat J_1) K)))))
% 1.95/2.33 FOF formula (forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->(((eq nat) ((plus_plus_nat ((minus_minus_nat J_1) K)) I_1)) ((minus_minus_nat ((plus_plus_nat J_1) I_1)) K)))) of role axiom named fact_1002_add__diff__assoc2
% 1.95/2.33 A new axiom: (forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->(((eq nat) ((plus_plus_nat ((minus_minus_nat J_1) K)) I_1)) ((minus_minus_nat ((plus_plus_nat J_1) I_1)) K))))
% 1.95/2.33 FOF formula (forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat J_1) I_1)) K)) ((plus_plus_nat ((minus_minus_nat J_1) K)) I_1)))) of role axiom named fact_1003_diff__add__assoc2
% 1.95/2.33 A new axiom: (forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat J_1) I_1)) K)) ((plus_plus_nat ((minus_minus_nat J_1) K)) I_1))))
% 1.95/2.35 FOF formula (forall (K:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K) ((plus_plus_nat M) N))) ((plus_plus_nat ((times_times_nat K) M)) ((times_times_nat K) N)))) of role axiom named fact_1004_add__mult__distrib2
% 1.95/2.35 A new axiom: (forall (K:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K) ((plus_plus_nat M) N))) ((plus_plus_nat ((times_times_nat K) M)) ((times_times_nat K) N))))
% 1.95/2.35 FOF formula (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((plus_plus_nat M) N)) K)) ((plus_plus_nat ((times_times_nat M) K)) ((times_times_nat N) K)))) of role axiom named fact_1005_add__mult__distrib
% 1.95/2.35 A new axiom: (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((plus_plus_nat M) N)) K)) ((plus_plus_nat ((times_times_nat M) K)) ((times_times_nat N) K))))
% 1.95/2.35 FOF formula (forall (M:nat), ((iff ((dvd_dvd_nat M) one_one_nat)) (((eq nat) M) one_one_nat))) of role axiom named fact_1006_nat__dvd__1__iff__1
% 1.95/2.35 A new axiom: (forall (M:nat), ((iff ((dvd_dvd_nat M) one_one_nat)) (((eq nat) M) one_one_nat)))
% 1.95/2.35 FOF formula (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) M))) of role axiom named fact_1007_le__square
% 1.95/2.35 A new axiom: (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) M)))
% 1.95/2.35 FOF formula (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) ((times_times_nat M) M)))) of role axiom named fact_1008_le__cube
% 1.95/2.35 A new axiom: (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) ((times_times_nat M) M))))
% 1.95/2.35 FOF formula (forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J_1) K)))) of role axiom named fact_1009_mult__le__mono1
% 1.95/2.35 A new axiom: (forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J_1) K))))
% 1.95/2.35 FOF formula (forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((times_times_nat K) I_1)) ((times_times_nat K) J_1)))) of role axiom named fact_1010_mult__le__mono2
% 1.95/2.35 A new axiom: (forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((times_times_nat K) I_1)) ((times_times_nat K) J_1))))
% 1.95/2.35 FOF formula (forall (K:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J_1) L))))) of role axiom named fact_1011_mult__le__mono
% 1.95/2.35 A new axiom: (forall (K:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J_1) L)))))
% 1.95/2.35 FOF formula (forall (N:nat), (((eq nat) ((times_times_nat one_one_nat) N)) N)) of role axiom named fact_1012_nat__mult__1
% 1.95/2.35 A new axiom: (forall (N:nat), (((eq nat) ((times_times_nat one_one_nat) N)) N))
% 1.95/2.35 FOF formula (forall (M:nat) (N:nat), ((iff (((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_1013_nat__1__eq__mult__iff
% 1.95/2.35 A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) one_one_nat) ((times_times_nat M) N))) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat))))
% 1.95/2.35 FOF formula (forall (N:nat), (((eq nat) ((times_times_nat N) one_one_nat)) N)) of role axiom named fact_1014_nat__mult__1__right
% 1.95/2.35 A new axiom: (forall (N:nat), (((eq nat) ((times_times_nat N) one_one_nat)) N))
% 1.95/2.35 FOF formula (forall (M:nat) (N:nat), ((iff (((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_1015_nat__mult__eq__1__iff
% 1.95/2.35 A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) N)) one_one_nat)) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat))))
% 1.95/2.35 FOF formula (forall (Z1:real) (Z2:real) (W:real), (((eq real) ((times_times_real ((plus_plus_real Z1) Z2)) W)) ((plus_plus_real ((times_times_real Z1) W)) ((times_times_real Z2) W)))) of role axiom named fact_1016_real__add__mult__distrib
% 1.95/2.35 A new axiom: (forall (Z1:real) (Z2:real) (W:real), (((eq real) ((times_times_real ((plus_plus_real Z1) Z2)) W)) ((plus_plus_real ((times_times_real Z1) W)) ((times_times_real Z2) W))))
% 1.95/2.37 FOF formula (forall (N:nat) (M:nat), (((ord_less_nat zero_zero_nat) M)->(((ord_less_nat M) N)->(((dvd_dvd_nat N) M)->False)))) of role axiom named fact_1017_nat__dvd__not__less
% 1.95/2.37 A new axiom: (forall (N:nat) (M:nat), (((ord_less_nat zero_zero_nat) M)->(((ord_less_nat M) N)->(((dvd_dvd_nat N) M)->False))))
% 1.95/2.37 FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M) N))) ((or ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N)))) of role axiom named fact_1018_add__gr__0
% 1.95/2.37 A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M) N))) ((or ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N))))
% 1.95/2.37 FOF formula (forall (P:(nat->Prop)) (A:nat) (B:nat), ((iff (P ((minus_minus_nat A) B))) (((or ((and ((ord_less_nat A) B)) ((P zero_zero_nat)->False))) ((ex nat) (fun (D_2:nat)=> ((and (((eq nat) A) ((plus_plus_nat B) D_2))) ((P D_2)->False)))))->False))) of role axiom named fact_1019_nat__diff__split__asm
% 1.95/2.37 A new axiom: (forall (P:(nat->Prop)) (A:nat) (B:nat), ((iff (P ((minus_minus_nat A) B))) (((or ((and ((ord_less_nat A) B)) ((P zero_zero_nat)->False))) ((ex nat) (fun (D_2:nat)=> ((and (((eq nat) A) ((plus_plus_nat B) D_2))) ((P D_2)->False)))))->False)))
% 1.95/2.37 FOF formula (forall (P:(nat->Prop)) (A:nat) (B:nat), ((iff (P ((minus_minus_nat A) B))) ((and (((ord_less_nat A) B)->(P zero_zero_nat))) (forall (D_2:nat), ((((eq nat) A) ((plus_plus_nat B) D_2))->(P D_2)))))) of role axiom named fact_1020_nat__diff__split
% 1.95/2.37 A new axiom: (forall (P:(nat->Prop)) (A:nat) (B:nat), ((iff (P ((minus_minus_nat A) B))) ((and (((ord_less_nat A) B)->(P zero_zero_nat))) (forall (D_2:nat), ((((eq nat) A) ((plus_plus_nat B) D_2))->(P D_2))))))
% 1.95/2.37 FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((times_times_nat M) N))) ((and ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N)))) of role axiom named fact_1021_nat__0__less__mult__iff
% 1.95/2.37 A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((times_times_nat M) N))) ((and ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N))))
% 1.95/2.37 FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M) N)))) of role axiom named fact_1022_mult__less__cancel1
% 1.95/2.37 A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M) N))))
% 1.95/2.37 FOF formula (forall (M:nat) (K:nat) (N:nat), ((iff ((ord_less_nat ((times_times_nat M) K)) ((times_times_nat N) K))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M) N)))) of role axiom named fact_1023_mult__less__cancel2
% 1.95/2.37 A new axiom: (forall (M:nat) (K:nat) (N:nat), ((iff ((ord_less_nat ((times_times_nat M) K)) ((times_times_nat N) K))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M) N))))
% 1.95/2.37 FOF formula (forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat I_1) K)) ((times_times_nat J_1) K))))) of role axiom named fact_1024_mult__less__mono1
% 1.95/2.37 A new axiom: (forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat I_1) K)) ((times_times_nat J_1) K)))))
% 1.95/2.37 FOF formula (forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat K) I_1)) ((times_times_nat K) J_1))))) of role axiom named fact_1025_mult__less__mono2
% 1.95/2.37 A new axiom: (forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat K) I_1)) ((times_times_nat K) J_1)))))
% 1.95/2.37 FOF formula (forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real X) Z)) ((times_times_real Y) Z))) ((ord_less_eq_real X) Y)))) of role axiom named fact_1026_real__mult__le__cancel__iff1
% 2.04/2.39 A new axiom: (forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real X) Z)) ((times_times_real Y) Z))) ((ord_less_eq_real X) Y))))
% 2.04/2.39 FOF formula (forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real Z) X)) ((times_times_real Z) Y))) ((ord_less_eq_real X) Y)))) of role axiom named fact_1027_real__mult__le__cancel__iff2
% 2.04/2.39 A new axiom: (forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real Z) X)) ((times_times_real Z) Y))) ((ord_less_eq_real X) Y))))
% 2.04/2.39 FOF formula (forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->(((ord_less_real X) Y)->((ord_less_real ((times_times_real Z) X)) ((times_times_real Z) Y))))) of role axiom named fact_1028_real__mult__less__mono2
% 2.04/2.39 A new axiom: (forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->(((ord_less_real X) Y)->((ord_less_real ((times_times_real Z) X)) ((times_times_real Z) Y)))))
% 2.04/2.39 FOF formula (forall (Y:real) (X:real), (((ord_less_real zero_zero_real) X)->(((ord_less_real zero_zero_real) Y)->((ord_less_real zero_zero_real) ((times_times_real X) Y))))) of role axiom named fact_1029_real__mult__order
% 2.04/2.39 A new axiom: (forall (Y:real) (X:real), (((ord_less_real zero_zero_real) X)->(((ord_less_real zero_zero_real) Y)->((ord_less_real zero_zero_real) ((times_times_real X) Y)))))
% 2.04/2.39 FOF formula (forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_real ((times_times_real X) Z)) ((times_times_real Y) Z))) ((ord_less_real X) Y)))) of role axiom named fact_1030_real__mult__less__iff1
% 2.04/2.39 A new axiom: (forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_real ((times_times_real X) Z)) ((times_times_real Y) Z))) ((ord_less_real X) Y))))
% 2.04/2.39 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_1031_mult__eq__self__implies__10
% 2.04/2.39 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))))
% 2.04/2.39 FOF formula (forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X) X)) ((times_times_real Y) Y))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real)))) of role axiom named fact_1032_real__two__squares__add__zero__iff
% 2.04/2.39 A new axiom: (forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X) X)) ((times_times_real Y) Y))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real))))
% 2.04/2.39 FOF formula (forall (K:nat) (N:nat), (((dvd_dvd_nat K) N)->(((ord_less_nat zero_zero_nat) N)->((ord_less_eq_nat K) N)))) of role axiom named fact_1033_dvd__imp__le
% 2.04/2.39 A new axiom: (forall (K:nat) (N:nat), (((dvd_dvd_nat K) N)->(((ord_less_nat zero_zero_nat) N)->((ord_less_eq_nat K) N))))
% 2.04/2.39 FOF formula (forall (K:nat) (M:nat) (N:nat), (((dvd_dvd_nat ((times_times_nat K) M)) ((times_times_nat K) N))->(((ord_less_nat zero_zero_nat) K)->((dvd_dvd_nat M) N)))) of role axiom named fact_1034_dvd__mult__cancel
% 2.04/2.39 A new axiom: (forall (K:nat) (M:nat) (N:nat), (((dvd_dvd_nat ((times_times_nat K) M)) ((times_times_nat K) N))->(((ord_less_nat zero_zero_nat) K)->((dvd_dvd_nat M) N))))
% 2.04/2.39 FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((times_times_nat K) M)) ((times_times_nat K) N))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M) N)))) of role axiom named fact_1035_mult__le__cancel1
% 2.04/2.39 A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((times_times_nat K) M)) ((times_times_nat K) N))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M) N))))
% 2.04/2.39 FOF formula (forall (M:nat) (K:nat) (N:nat), ((iff ((ord_less_eq_nat ((times_times_nat M) K)) ((times_times_nat N) K))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M) N)))) of role axiom named fact_1036_mult__le__cancel2
% 2.04/2.39 A new axiom: (forall (M:nat) (K:nat) (N:nat), ((iff ((ord_less_eq_nat ((times_times_nat M) K)) ((times_times_nat N) K))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M) N))))
% 2.06/2.41 FOF formula (forall (N:nat), ((ord_less_eq_real one_one_real) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N))) of role axiom named fact_1037_two__realpow__ge__one
% 2.06/2.41 A new axiom: (forall (N:nat), ((ord_less_eq_real one_one_real) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N)))
% 2.06/2.41 FOF formula (forall (N:nat) (M:nat), (((ord_less_nat zero_zero_nat) M)->((iff ((dvd_dvd_nat ((times_times_nat M) N)) M)) (((eq nat) N) one_one_nat)))) of role axiom named fact_1038_dvd__mult__cancel1
% 2.06/2.41 A new axiom: (forall (N:nat) (M:nat), (((ord_less_nat zero_zero_nat) M)->((iff ((dvd_dvd_nat ((times_times_nat M) N)) M)) (((eq nat) N) one_one_nat))))
% 2.06/2.41 FOF formula (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N)) (forall (_TPTP_I:nat), (((ord_less_eq_nat _TPTP_I) K_1)->((P _TPTP_I)->False))))) (P ((plus_plus_nat K_1) one_one_nat)))))))) of role axiom named fact_1039_ex__least__nat__less
% 2.06/2.41 A new axiom: (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N)) (forall (_TPTP_I:nat), (((ord_less_eq_nat _TPTP_I) K_1)->((P _TPTP_I)->False))))) (P ((plus_plus_nat K_1) one_one_nat))))))))
% 2.06/2.41 FOF formula (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((ord_less_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N))))) of role axiom named fact_1040_nat__less__add__iff2
% 2.06/2.41 A new axiom: (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((ord_less_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N)))))
% 2.06/2.41 FOF formula (forall (U:nat) (M:nat) (N:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((ord_less_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N)))) of role axiom named fact_1041_nat__less__add__iff1
% 2.06/2.41 A new axiom: (forall (U:nat) (M:nat) (N:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((ord_less_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N))))
% 2.06/2.41 FOF formula (forall (W:real), ((ord_less_eq_real W) W)) of role axiom named fact_1042_real__le__refl
% 2.06/2.41 A new axiom: (forall (W:real), ((ord_less_eq_real W) W))
% 2.06/2.41 FOF formula (forall (Z:real) (W:real), ((or ((ord_less_eq_real Z) W)) ((ord_less_eq_real W) Z))) of role axiom named fact_1043_real__le__linear
% 2.06/2.41 A new axiom: (forall (Z:real) (W:real), ((or ((ord_less_eq_real Z) W)) ((ord_less_eq_real W) Z)))
% 2.06/2.41 FOF formula (forall (K:real) (I_1:real) (J_1:real), (((ord_less_eq_real I_1) J_1)->(((ord_less_eq_real J_1) K)->((ord_less_eq_real I_1) K)))) of role axiom named fact_1044_real__le__trans
% 2.06/2.41 A new axiom: (forall (K:real) (I_1:real) (J_1:real), (((ord_less_eq_real I_1) J_1)->(((ord_less_eq_real J_1) K)->((ord_less_eq_real I_1) K))))
% 2.06/2.41 FOF formula (forall (Z:real) (W:real), (((ord_less_eq_real Z) W)->(((ord_less_eq_real W) Z)->(((eq real) Z) W)))) of role axiom named fact_1045_real__le__antisym
% 2.06/2.41 A new axiom: (forall (Z:real) (W:real), (((ord_less_eq_real Z) W)->(((ord_less_eq_real W) Z)->(((eq real) Z) W))))
% 2.06/2.41 FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) ((or (((eq nat) K) zero_zero_nat)) (((eq nat) M) N)))) of role axiom named fact_1046_nat__mult__eq__cancel__disj
% 2.06/2.41 A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) ((or (((eq nat) K) zero_zero_nat)) (((eq nat) M) N))))
% 2.07/2.43 FOF formula (forall (I_1:nat) (U:nat) (J_1:nat) (K:nat), (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) ((plus_plus_nat ((times_times_nat J_1) U)) K))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat I_1) J_1)) U)) K))) of role axiom named fact_1047_left__add__mult__distrib
% 2.07/2.43 A new axiom: (forall (I_1:nat) (U:nat) (J_1:nat) (K:nat), (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) ((plus_plus_nat ((times_times_nat J_1) U)) K))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat I_1) J_1)) U)) K)))
% 2.07/2.43 FOF formula (forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((ord_less_nat M) N)))) of role axiom named fact_1048_nat__mult__less__cancel1
% 2.07/2.43 A new axiom: (forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((ord_less_nat M) N))))
% 2.07/2.43 FOF formula (forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) (((eq nat) M) N)))) of role axiom named fact_1049_nat__mult__eq__cancel1
% 2.07/2.43 A new axiom: (forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) (((eq nat) M) N))))
% 2.07/2.43 FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff ((dvd_dvd_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((or (((eq nat) K) zero_zero_nat)) ((dvd_dvd_nat M) N)))) of role axiom named fact_1050_nat__mult__dvd__cancel__disj
% 2.07/2.43 A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff ((dvd_dvd_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((or (((eq nat) K) zero_zero_nat)) ((dvd_dvd_nat M) N))))
% 2.07/2.43 FOF formula (forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((dvd_dvd_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((dvd_dvd_nat M) N)))) of role axiom named fact_1051_nat__mult__dvd__cancel1
% 2.07/2.43 A new axiom: (forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((dvd_dvd_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((dvd_dvd_nat M) N))))
% 2.07/2.43 FOF formula (forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_eq_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((ord_less_eq_nat M) N)))) of role axiom named fact_1052_nat__mult__le__cancel1
% 2.07/2.43 A new axiom: (forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_eq_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((ord_less_eq_nat M) N))))
% 2.07/2.43 FOF formula (forall (U:nat) (M:nat) (N:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N)))) of role axiom named fact_1053_nat__le__add__iff1
% 2.07/2.43 A new axiom: (forall (U:nat) (M:nat) (N:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N))))
% 2.07/2.43 FOF formula (forall (U:nat) (M:nat) (N:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((minus_minus_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N)))) of role axiom named fact_1054_nat__diff__add__eq1
% 2.07/2.43 A new axiom: (forall (U:nat) (M:nat) (N:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((minus_minus_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N))))
% 2.07/2.43 FOF formula (forall (U:nat) (M:nat) (N:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) (((eq nat) ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N)))) of role axiom named fact_1055_nat__eq__add__iff1
% 2.07/2.45 A new axiom: (forall (U:nat) (M:nat) (N:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) (((eq nat) ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N))))
% 2.07/2.45 FOF formula (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((ord_less_eq_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N))))) of role axiom named fact_1056_nat__le__add__iff2
% 2.07/2.45 A new axiom: (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((ord_less_eq_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N)))))
% 2.07/2.45 FOF formula (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((minus_minus_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N))))) of role axiom named fact_1057_nat__diff__add__eq2
% 2.07/2.45 A new axiom: (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((minus_minus_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N)))))
% 2.07/2.45 FOF formula (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) (((eq nat) M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N))))) of role axiom named fact_1058_nat__eq__add__iff2
% 2.07/2.45 A new axiom: (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) (((eq nat) M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N)))))
% 2.07/2.45 FOF formula (forall (N:int), (((ord_less_eq_int zero_zero_int) (number_number_of_int N))->((and ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 N)))) ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 N)))))) of role axiom named fact_1059_number__of1
% 2.07/2.45 A new axiom: (forall (N:int), (((ord_less_eq_int zero_zero_int) (number_number_of_int N))->((and ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 N)))) ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 N))))))
% 2.07/2.45 FOF formula (forall (A:int), (((ord_less_int one_one_int) A)->((ex int) (fun (P_3:int)=> ((and (zprime P_3)) ((dvd_dvd_int P_3) A)))))) of role axiom named fact_1060_zprime__factor__exists
% 2.07/2.45 A new axiom: (forall (A:int), (((ord_less_int one_one_int) A)->((ex int) (fun (P_3:int)=> ((and (zprime P_3)) ((dvd_dvd_int P_3) A))))))
% 2.07/2.45 FOF formula (forall (P_2:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_2))->((iff ((and ((ord_less_eq_int zero_zero_int) X)) P)) ((and ((ord_less_eq_int zero_zero_int) X)) P_2)))) of role axiom named fact_1061_conj__le__cong
% 2.07/2.45 A new axiom: (forall (P_2:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_2))->((iff ((and ((ord_less_eq_int zero_zero_int) X)) P)) ((and ((ord_less_eq_int zero_zero_int) X)) P_2))))
% 2.07/2.45 FOF formula (forall (P_2:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_2))->((iff (((ord_less_eq_int zero_zero_int) X)->P)) (((ord_less_eq_int zero_zero_int) X)->P_2)))) of role axiom named fact_1062_imp__le__cong
% 2.07/2.45 A new axiom: (forall (P_2:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_2))->((iff (((ord_less_eq_int zero_zero_int) X)->P)) (((ord_less_eq_int zero_zero_int) X)->P_2))))
% 2.07/2.47 FOF formula (forall (M:int) (T:int) (K:int), ((not (((eq int) K) zero_zero_int))->((iff ((dvd_dvd_int M) T)) ((dvd_dvd_int ((times_times_int K) M)) ((times_times_int K) T))))) of role axiom named fact_1063_zdvd__mono
% 2.07/2.47 A new axiom: (forall (M:int) (T:int) (K:int), ((not (((eq int) K) zero_zero_int))->((iff ((dvd_dvd_int M) T)) ((dvd_dvd_int ((times_times_int K) M)) ((times_times_int K) T)))))
% 2.07/2.47 FOF formula ((ord_less_eq_int zero_zero_int) (number_number_of_int pls)) of role axiom named fact_1064_number__of2
% 2.07/2.47 A new axiom: ((ord_less_eq_int zero_zero_int) (number_number_of_int pls))
% 2.07/2.47 FOF formula (forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) ((times_times_int K) D))))))))) of role axiom named fact_1065_decr__mult__lemma
% 2.07/2.47 A new axiom: (forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) ((times_times_int K) D)))))))))
% 2.07/2.47 FOF formula (forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) ((times_times_int K) D))))))))) of role axiom named fact_1066_incr__mult__lemma
% 2.07/2.47 A new axiom: (forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) ((times_times_int K) D)))))))))
% 2.07/2.47 FOF formula (forall (A:int) (M:int), (((ord_less_int zero_zero_int) M)->((ex int) (fun (X_1:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X_1)) ((ord_less_int X_1) M))) (((zcong A) X_1) M))) (forall (Y_1:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y_1)) ((ord_less_int Y_1) M))) (((zcong A) Y_1) M))->(((eq int) Y_1) X_1)))))))) of role axiom named fact_1067_zcong__zless__unique
% 2.07/2.47 A new axiom: (forall (A:int) (M:int), (((ord_less_int zero_zero_int) M)->((ex int) (fun (X_1:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X_1)) ((ord_less_int X_1) M))) (((zcong A) X_1) M))) (forall (Y_1:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y_1)) ((ord_less_int Y_1) M))) (((zcong A) Y_1) M))->(((eq int) Y_1) X_1))))))))
% 2.07/2.47 FOF formula (((eq int) (twoSqu2057625106sum2sq ((product_Pair_int_int s) one_one_int))) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)) of role axiom named fact_1068__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096
% 2.07/2.47 A new axiom: (((eq int) (twoSqu2057625106sum2sq ((product_Pair_int_int s) one_one_int))) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t))
% 2.07/2.47 FOF formula (forall (A:int) (B:int) (P_1:int) (Q:int), (((eq int) ((times_times_int (twoSqu2057625106sum2sq ((product_Pair_int_int A) B))) (twoSqu2057625106sum2sq ((product_Pair_int_int P_1) Q)))) (twoSqu2057625106sum2sq ((product_Pair_int_int ((plus_plus_int ((times_times_int A) P_1)) ((times_times_int B) Q))) ((minus_minus_int ((times_times_int A) Q)) ((times_times_int B) P_1)))))) of role axiom named fact_1069_mult__sum2sq
% 2.07/2.47 A new axiom: (forall (A:int) (B:int) (P_1:int) (Q:int), (((eq int) ((times_times_int (twoSqu2057625106sum2sq ((product_Pair_int_int A) B))) (twoSqu2057625106sum2sq ((product_Pair_int_int P_1) Q)))) (twoSqu2057625106sum2sq ((product_Pair_int_int ((plus_plus_int ((times_times_int A) P_1)) ((times_times_int B) Q))) ((minus_minus_int ((times_times_int A) Q)) ((times_times_int B) P_1))))))
% 2.07/2.47 FOF formula (forall (X:int), ((iff (twoSqu919416604sum2sq X)) ((ex int) (fun (A_2:int)=> ((ex int) (fun (B_2:int)=> (((eq int) (twoSqu2057625106sum2sq ((product_Pair_int_int A_2) B_2))) X))))))) of role axiom named fact_1070_is__sum2sq__def
% 2.07/2.49 A new axiom: (forall (X:int), ((iff (twoSqu919416604sum2sq X)) ((ex int) (fun (A_2:int)=> ((ex int) (fun (B_2:int)=> (((eq int) (twoSqu2057625106sum2sq ((product_Pair_int_int A_2) B_2))) X)))))))
% 2.07/2.49 FOF formula (forall (A:int) (B:int), (((ord_less_eq_int A) ((minus_minus_int B) one_one_int))->((ord_less_int A) B))) of role axiom named fact_1071_norR__mem__unique__aux
% 2.07/2.49 A new axiom: (forall (A:int) (B:int), (((ord_less_eq_int A) ((minus_minus_int B) one_one_int))->((ord_less_int A) B)))
% 2.07/2.49 FOF formula (forall (P_1:int), ((zprime P_1)->(((zcong (zfact ((minus_minus_int P_1) one_one_int))) (number_number_of_int min)) P_1))) of role axiom named fact_1072_Wilson__Russ
% 2.07/2.49 A new axiom: (forall (P_1:int), ((zprime P_1)->(((zcong (zfact ((minus_minus_int P_1) one_one_int))) (number_number_of_int min)) P_1)))
% 2.07/2.49 FOF formula (forall (N:int), ((and (((ord_less_eq_int N) zero_zero_int)->(((eq int) (zfact N)) one_one_int))) ((((ord_less_eq_int N) zero_zero_int)->False)->(((eq int) (zfact N)) ((times_times_int N) (zfact ((minus_minus_int N) one_one_int))))))) of role axiom named fact_1073_zfact_Osimps
% 2.07/2.49 A new axiom: (forall (N:int), ((and (((ord_less_eq_int N) zero_zero_int)->(((eq int) (zfact N)) one_one_int))) ((((ord_less_eq_int N) zero_zero_int)->False)->(((eq int) (zfact N)) ((times_times_int N) (zfact ((minus_minus_int N) one_one_int)))))))
% 2.07/2.49 FOF formula (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P_1)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P_1)->(((eq int) ((inv P_1) ((inv P_1) A))) A)))))) of role axiom named fact_1074_inv__inv
% 2.07/2.49 A new axiom: (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P_1)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P_1)->(((eq int) ((inv P_1) ((inv P_1) A))) A))))))
% 2.07/2.49 FOF formula (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->((ord_less_int ((inv P_1) A)) ((minus_minus_int P_1) one_one_int)))))) of role axiom named fact_1075_inv__less__p__minus__1
% 2.07/2.49 A new axiom: (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->((ord_less_int ((inv P_1) A)) ((minus_minus_int P_1) one_one_int))))))
% 2.07/2.49 FOF formula (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->((ord_less_int one_one_int) ((inv P_1) A)))))) of role axiom named fact_1076_inv__g__1
% 2.07/2.49 A new axiom: (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->((ord_less_int one_one_int) ((inv P_1) A))))))
% 2.07/2.49 FOF formula (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(not (((eq int) ((inv P_1) A)) ((minus_minus_int P_1) one_one_int))))))) of role axiom named fact_1077_inv__not__p__minus__1
% 2.07/2.49 A new axiom: (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(not (((eq int) ((inv P_1) A)) ((minus_minus_int P_1) one_one_int)))))))
% 2.07/2.49 FOF formula (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(not (((eq int) ((inv P_1) A)) one_one_int)))))) of role axiom named fact_1078_inv__not__1
% 2.07/2.49 A new axiom: (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(not (((eq int) ((inv P_1) A)) one_one_int))))))
% 2.07/2.49 FOF formula (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(not (((eq int) A) ((inv P_1) A))))))) of role axiom named fact_1079_inv__distinct
% 2.07/2.49 A new axiom: (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(not (((eq int) A) ((inv P_1) A)))))))
% 2.07/2.51 FOF formula (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(not (((eq int) ((inv P_1) A)) zero_zero_int)))))) of role axiom named fact_1080_inv__not__0
% 2.07/2.51 A new axiom: (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(not (((eq int) ((inv P_1) A)) zero_zero_int))))))
% 2.07/2.51 FOF formula (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P_1)->(((zcong ((times_times_int A) ((inv P_1) A))) one_one_int) P_1))))) of role axiom named fact_1081_inv__is__inv
% 2.07/2.51 A new axiom: (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P_1)->(((zcong ((times_times_int A) ((inv P_1) A))) one_one_int) P_1)))))
% 2.07/2.51 FOF formula (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P_1)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(((member_int B) ((wset A) P_1))->((member_int ((inv P_1) B)) ((wset A) P_1))))))) of role axiom named fact_1082_wset__mem__inv__mem
% 2.07/2.51 A new axiom: (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P_1)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(((member_int B) ((wset A) P_1))->((member_int ((inv P_1) B)) ((wset A) P_1)))))))
% 2.07/2.51 FOF formula (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P_1)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(((ord_less_int one_one_int) B)->(((ord_less_int B) ((minus_minus_int P_1) one_one_int))->(((member_int ((inv P_1) B)) ((wset A) P_1))->((member_int B) ((wset A) P_1))))))))) of role axiom named fact_1083_wset__inv__mem__mem
% 2.07/2.51 A new axiom: (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P_1)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(((ord_less_int one_one_int) B)->(((ord_less_int B) ((minus_minus_int P_1) one_one_int))->(((member_int ((inv P_1) B)) ((wset A) P_1))->((member_int B) ((wset A) P_1)))))))))
% 2.07/2.51 FOF formula (forall (P_1:int) (A:int), (((ord_less_int one_one_int) A)->((member_int A) ((wset A) P_1)))) of role axiom named fact_1084_wset__mem__mem
% 2.07/2.51 A new axiom: (forall (P_1:int) (A:int), (((ord_less_int one_one_int) A)->((member_int A) ((wset A) P_1))))
% 2.07/2.51 FOF formula (forall (B:int) (P_1:int) (A:int), (((ord_less_int one_one_int) A)->(((member_int B) ((wset ((minus_minus_int A) one_one_int)) P_1))->((member_int B) ((wset A) P_1))))) of role axiom named fact_1085_wset__subset
% 2.07/2.51 A new axiom: (forall (B:int) (P_1:int) (A:int), (((ord_less_int one_one_int) A)->(((member_int B) ((wset ((minus_minus_int A) one_one_int)) P_1))->((member_int B) ((wset A) P_1)))))
% 2.07/2.51 FOF formula (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(((member_int B) ((wset A) P_1))->((ord_less_int one_one_int) B))))) of role axiom named fact_1086_wset__g__1
% 2.07/2.51 A new axiom: (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(((member_int B) ((wset A) P_1))->((ord_less_int one_one_int) B)))))
% 2.07/2.51 FOF formula (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(((member_int B) ((wset A) P_1))->((ord_less_int B) ((minus_minus_int P_1) one_one_int)))))) of role axiom named fact_1087_wset__less
% 2.07/2.51 A new axiom: (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(((member_int B) ((wset A) P_1))->((ord_less_int B) ((minus_minus_int P_1) one_one_int))))))
% 2.07/2.51 FOF formula (forall (B:int) (P_1:int) (A:int), (((ord_less_int one_one_int) A)->((((member_int B) ((wset ((minus_minus_int A) one_one_int)) P_1))->False)->(((member_int B) ((wset A) P_1))->((or (((eq int) B) A)) (((eq int) B) ((inv P_1) A))))))) of role axiom named fact_1088_wset__mem__imp__or
% 2.17/2.54 A new axiom: (forall (B:int) (P_1:int) (A:int), (((ord_less_int one_one_int) A)->((((member_int B) ((wset ((minus_minus_int A) one_one_int)) P_1))->False)->(((member_int B) ((wset A) P_1))->((or (((eq int) B) A)) (((eq int) B) ((inv P_1) A)))))))
% 2.17/2.54 FOF formula (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(((ord_less_int one_one_int) B)->(((ord_less_eq_int B) A)->((member_int B) ((wset A) P_1))))))) of role axiom named fact_1089_wset__mem
% 2.17/2.54 A new axiom: (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(((ord_less_int one_one_int) B)->(((ord_less_eq_int B) A)->((member_int B) ((wset A) P_1)))))))
% 2.17/2.54 FOF formula (forall (J_1:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->(((((zcong A) zero_zero_int) P_1)->False)->(((((zcong J_1) zero_zero_int) P_1)->False)->((((quadRes P_1) A)->False)->((((zcong J_1) ((times_times_int A) ((multInv P_1) J_1))) P_1)->False))))))) of role axiom named fact_1090_MultInvPair__distinct
% 2.17/2.54 A new axiom: (forall (J_1:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->(((((zcong A) zero_zero_int) P_1)->False)->(((((zcong J_1) zero_zero_int) P_1)->False)->((((quadRes P_1) A)->False)->((((zcong J_1) ((times_times_int A) ((multInv P_1) J_1))) P_1)->False)))))))
% 2.17/2.54 FOF formula (forall (P:(int->Prop)) (I_1:int) (K:int), (((ord_less_eq_int I_1) K)->((P K)->((forall (_TPTP_I:int), (((ord_less_eq_int _TPTP_I) K)->((P _TPTP_I)->(P ((minus_minus_int _TPTP_I) one_one_int)))))->(P I_1))))) of role axiom named fact_1091_int__le__induct
% 2.17/2.54 A new axiom: (forall (P:(int->Prop)) (I_1:int) (K:int), (((ord_less_eq_int I_1) K)->((P K)->((forall (_TPTP_I:int), (((ord_less_eq_int _TPTP_I) K)->((P _TPTP_I)->(P ((minus_minus_int _TPTP_I) one_one_int)))))->(P I_1)))))
% 2.17/2.54 FOF formula (forall (J_1:int) (A:int) (P_1:int) (K:int), ((((zcong J_1) ((times_times_int A) ((multInv P_1) K))) P_1)->(((zcong ((times_times_int J_1) K)) ((times_times_int ((times_times_int A) ((multInv P_1) K))) K)) P_1))) of role axiom named fact_1092_aux______1
% 2.17/2.54 A new axiom: (forall (J_1:int) (A:int) (P_1:int) (K:int), ((((zcong J_1) ((times_times_int A) ((multInv P_1) K))) P_1)->(((zcong ((times_times_int J_1) K)) ((times_times_int ((times_times_int A) ((multInv P_1) K))) K)) P_1)))
% 2.17/2.54 FOF formula (forall (J_1:int) (K:int) (A:int) (P_1:int), ((((zcong ((times_times_int J_1) K)) A) P_1)->(((zcong ((times_times_int ((times_times_int ((multInv P_1) J_1)) J_1)) K)) ((times_times_int ((multInv P_1) J_1)) A)) P_1))) of role axiom named fact_1093_aux______3
% 2.17/2.54 A new axiom: (forall (J_1:int) (K:int) (A:int) (P_1:int), ((((zcong ((times_times_int J_1) K)) A) P_1)->(((zcong ((times_times_int ((times_times_int ((multInv P_1) J_1)) J_1)) K)) ((times_times_int ((multInv P_1) J_1)) A)) P_1)))
% 2.17/2.54 FOF formula (forall (X:int) (Y:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((((zcong X) Y) P_1)->(((zcong ((multInv P_1) X)) ((multInv P_1) Y)) P_1)))) of role axiom named fact_1094_MultInv__prop1
% 2.17/2.54 A new axiom: (forall (X:int) (Y:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((((zcong X) Y) P_1)->(((zcong ((multInv P_1) X)) ((multInv P_1) Y)) P_1))))
% 2.17/2.54 FOF formula (forall (A:int) (J_1:int) (K:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((((zcong J_1) K) P_1)->(((zcong ((times_times_int A) ((multInv P_1) J_1))) ((times_times_int A) ((multInv P_1) K))) P_1)))) of role axiom named fact_1095_MultInv__zcong__prop1
% 2.17/2.54 A new axiom: (forall (A:int) (J_1:int) (K:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((((zcong J_1) K) P_1)->(((zcong ((times_times_int A) ((multInv P_1) J_1))) ((times_times_int A) ((multInv P_1) K))) P_1))))
% 2.17/2.54 FOF formula (forall (Y:int) (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((((zcong Y) zero_zero_int) P_1)->False)->((((zcong ((multInv P_1) X)) ((multInv P_1) Y)) P_1)->(((zcong X) Y) P_1))))))) of role axiom named fact_1096_MultInv__prop5
% 2.17/2.56 A new axiom: (forall (Y:int) (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((((zcong Y) zero_zero_int) P_1)->False)->((((zcong ((multInv P_1) X)) ((multInv P_1) Y)) P_1)->(((zcong X) Y) P_1)))))))
% 2.17/2.56 FOF formula (forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((zcong ((multInv P_1) ((multInv P_1) X))) X) P_1))))) of role axiom named fact_1097_MultInv__prop4
% 2.17/2.56 A new axiom: (forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((zcong ((multInv P_1) ((multInv P_1) X))) X) P_1)))))
% 2.17/2.56 FOF formula (forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->((((zcong ((multInv P_1) X)) zero_zero_int) P_1)->False))))) of role axiom named fact_1098_MultInv__prop3
% 2.17/2.56 A new axiom: (forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->((((zcong ((multInv P_1) X)) zero_zero_int) P_1)->False)))))
% 2.17/2.56 FOF formula (forall (K:int) (A:int) (J_1:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong J_1) zero_zero_int) P_1)->False)->((((zcong ((times_times_int ((times_times_int ((multInv P_1) J_1)) J_1)) K)) ((times_times_int ((multInv P_1) J_1)) A)) P_1)->(((zcong K) ((times_times_int A) ((multInv P_1) J_1))) P_1)))))) of role axiom named fact_1099_aux______4
% 2.17/2.56 A new axiom: (forall (K:int) (A:int) (J_1:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong J_1) zero_zero_int) P_1)->False)->((((zcong ((times_times_int ((times_times_int ((multInv P_1) J_1)) J_1)) K)) ((times_times_int ((multInv P_1) J_1)) A)) P_1)->(((zcong K) ((times_times_int A) ((multInv P_1) J_1))) P_1))))))
% 2.17/2.56 FOF formula (forall (J_1:int) (A:int) (K:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong K) zero_zero_int) P_1)->False)->((((zcong ((times_times_int J_1) K)) ((times_times_int ((times_times_int A) ((multInv P_1) K))) K)) P_1)->(((zcong ((times_times_int J_1) K)) A) P_1)))))) of role axiom named fact_1100_aux______2
% 2.17/2.56 A new axiom: (forall (J_1:int) (A:int) (K:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong K) zero_zero_int) P_1)->False)->((((zcong ((times_times_int J_1) K)) ((times_times_int ((times_times_int A) ((multInv P_1) K))) K)) P_1)->(((zcong ((times_times_int J_1) K)) A) P_1))))))
% 2.17/2.56 FOF formula (forall (A:int) (J_1:int) (K:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong K) zero_zero_int) P_1)->False)->(((((zcong J_1) zero_zero_int) P_1)->False)->((((zcong J_1) ((times_times_int A) ((multInv P_1) K))) P_1)->(((zcong K) ((times_times_int A) ((multInv P_1) J_1))) P_1))))))) of role axiom named fact_1101_MultInv__zcong__prop2
% 2.17/2.56 A new axiom: (forall (A:int) (J_1:int) (K:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong K) zero_zero_int) P_1)->False)->(((((zcong J_1) zero_zero_int) P_1)->False)->((((zcong J_1) ((times_times_int A) ((multInv P_1) K))) P_1)->(((zcong K) ((times_times_int A) ((multInv P_1) J_1))) P_1)))))))
% 2.17/2.56 FOF formula (forall (J_1:int) (K:int) (A:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong A) zero_zero_int) P_1)->False)->(((((zcong K) zero_zero_int) P_1)->False)->(((((zcong J_1) zero_zero_int) P_1)->False)->((((zcong ((times_times_int A) ((multInv P_1) J_1))) ((times_times_int A) ((multInv P_1) K))) P_1)->(((zcong J_1) K) P_1)))))))) of role axiom named fact_1102_MultInv__zcong__prop3
% 2.17/2.58 A new axiom: (forall (J_1:int) (K:int) (A:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong A) zero_zero_int) P_1)->False)->(((((zcong K) zero_zero_int) P_1)->False)->(((((zcong J_1) zero_zero_int) P_1)->False)->((((zcong ((times_times_int A) ((multInv P_1) J_1))) ((times_times_int A) ((multInv P_1) K))) P_1)->(((zcong J_1) K) P_1))))))))
% 2.17/2.58 FOF formula (forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((zcong ((times_times_int ((times_times_int X) ((multInv P_1) X))) ((multInv P_1) ((multInv P_1) X)))) X) P_1))))) of role axiom named fact_1103_Int2_Oaux____2
% 2.17/2.58 A new axiom: (forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((zcong ((times_times_int ((times_times_int X) ((multInv P_1) X))) ((multInv P_1) ((multInv P_1) X)))) X) P_1)))))
% 2.17/2.58 FOF formula (forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((zcong ((multInv P_1) ((multInv P_1) X))) ((times_times_int ((times_times_int X) ((multInv P_1) X))) ((multInv P_1) ((multInv P_1) X)))) P_1))))) of role axiom named fact_1104_Int2_Oaux____1
% 2.17/2.58 A new axiom: (forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((zcong ((multInv P_1) ((multInv P_1) X))) ((times_times_int ((times_times_int X) ((multInv P_1) X))) ((multInv P_1) ((multInv P_1) X)))) P_1)))))
% 2.17/2.58 FOF formula (forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((zcong ((times_times_int ((multInv P_1) X)) X)) one_one_int) P_1))))) of role axiom named fact_1105_MultInv__prop2a
% 2.17/2.58 A new axiom: (forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((zcong ((times_times_int ((multInv P_1) X)) X)) one_one_int) P_1)))))
% 2.17/2.58 FOF formula (forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((zcong ((times_times_int X) ((multInv P_1) X))) one_one_int) P_1))))) of role axiom named fact_1106_MultInv__prop2
% 2.17/2.58 A new axiom: (forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((zcong ((times_times_int X) ((multInv P_1) X))) one_one_int) P_1)))))
% 2.17/2.58 FOF formula (forall (X:int) (P:(int->Prop)), ((forall (A_2:int), ((((ord_less_int one_one_int) A_2)->(P ((minus_minus_int A_2) one_one_int)))->(P A_2)))->(P X))) of role axiom named fact_1107_d22set__induct__old
% 2.17/2.58 A new axiom: (forall (X:int) (P:(int->Prop)), ((forall (A_2:int), ((((ord_less_int one_one_int) A_2)->(P ((minus_minus_int A_2) one_one_int)))->(P A_2)))->(P X)))
% 2.17/2.58 FOF formula (forall (P:(int->Prop)) (I_1:int) (K:int), (((ord_less_int I_1) K)->((P ((minus_minus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int _TPTP_I) K)->((P _TPTP_I)->(P ((minus_minus_int _TPTP_I) one_one_int)))))->(P I_1))))) of role axiom named fact_1108_int__less__induct
% 2.17/2.58 A new axiom: (forall (P:(int->Prop)) (I_1:int) (K:int), (((ord_less_int I_1) K)->((P ((minus_minus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int _TPTP_I) K)->((P _TPTP_I)->(P ((minus_minus_int _TPTP_I) one_one_int)))))->(P I_1)))))
% 2.17/2.58 FOF formula (forall (P:(int->Prop)) (K:int) (I_1:int), (((ord_less_eq_int K) I_1)->((P K)->((forall (_TPTP_I:int), (((ord_less_eq_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->(P I_1))))) of role axiom named fact_1109_int__ge__induct
% 2.17/2.58 A new axiom: (forall (P:(int->Prop)) (K:int) (I_1:int), (((ord_less_eq_int K) I_1)->((P K)->((forall (_TPTP_I:int), (((ord_less_eq_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->(P I_1)))))
% 2.17/2.58 FOF formula (forall (P:(int->Prop)) (K:int) (I_1:int), (((ord_less_int K) I_1)->((P ((plus_plus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->(P I_1))))) of role axiom named fact_1110_int__gr__induct
% 2.25/2.60 A new axiom: (forall (P:(int->Prop)) (K:int) (I_1:int), (((ord_less_int K) I_1)->((P ((plus_plus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->(P I_1)))))
% 2.25/2.60 FOF formula (forall (M:nat) (K:nat) (F:(nat->nat)), ((forall (M_2:nat) (N_1:nat), (((ord_less_nat M_2) N_1)->((ord_less_nat (F M_2)) (F N_1))))->((ord_less_eq_nat ((plus_plus_nat (F M)) K)) (F ((plus_plus_nat M) K))))) of role axiom named fact_1111_mono__nat__linear__lb
% 2.25/2.60 A new axiom: (forall (M:nat) (K:nat) (F:(nat->nat)), ((forall (M_2:nat) (N_1:nat), (((ord_less_nat M_2) N_1)->((ord_less_nat (F M_2)) (F N_1))))->((ord_less_eq_nat ((plus_plus_nat (F M)) K)) (F ((plus_plus_nat M) K)))))
% 2.25/2.60 FOF formula (forall (P_1:int), ((zprime P_1)->(((eq (int->Prop)) (d22set ((minus_minus_int P_1) (number_number_of_int (bit0 (bit1 pls)))))) ((wset ((minus_minus_int P_1) (number_number_of_int (bit0 (bit1 pls))))) P_1)))) of role axiom named fact_1112_d22set__eq__wset
% 2.25/2.60 A new axiom: (forall (P_1:int), ((zprime P_1)->(((eq (int->Prop)) (d22set ((minus_minus_int P_1) (number_number_of_int (bit0 (bit1 pls)))))) ((wset ((minus_minus_int P_1) (number_number_of_int (bit0 (bit1 pls))))) P_1))))
% 2.25/2.60 FOF formula (forall (A:int) (B:int), (((ord_less_int A) B)->(((member_int B) (d22set A))->False))) of role axiom named fact_1113_d22set__le__swap
% 2.25/2.60 A new axiom: (forall (A:int) (B:int), (((ord_less_int A) B)->(((member_int B) (d22set A))->False)))
% 2.25/2.60 FOF formula (forall (B:int) (A:int), (((member_int B) (d22set A))->((ord_less_eq_int B) A))) of role axiom named fact_1114_d22set__le
% 2.25/2.60 A new axiom: (forall (B:int) (A:int), (((member_int B) (d22set A))->((ord_less_eq_int B) A)))
% 2.25/2.60 FOF formula (forall (B:int) (A:int), (((member_int B) (d22set A))->((ord_less_int one_one_int) B))) of role axiom named fact_1115_d22set__g__1
% 2.25/2.60 A new axiom: (forall (B:int) (A:int), (((member_int B) (d22set A))->((ord_less_int one_one_int) B)))
% 2.25/2.60 FOF formula (forall (A:int) (B:int), (((ord_less_int one_one_int) B)->(((ord_less_eq_int B) A)->((member_int B) (d22set A))))) of role axiom named fact_1116_d22set__mem
% 2.25/2.60 A new axiom: (forall (A:int) (B:int), (((ord_less_int one_one_int) B)->(((ord_less_eq_int B) A)->((member_int B) (d22set A)))))
% 2.25/2.60 FOF formula (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_eq_nat K_1) N)) (forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) K_1)->((P _TPTP_I)->False))))) (P K_1))))))) of role axiom named fact_1117_ex__least__nat__le
% 2.25/2.60 A new axiom: (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_eq_nat K_1) N)) (forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) K_1)->((P _TPTP_I)->False))))) (P K_1)))))))
% 2.25/2.60 FOF formula (forall (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ex nat) (fun (K_1:nat)=> ((and ((ord_less_nat zero_zero_nat) K_1)) (((eq nat) ((plus_plus_nat I_1) K_1)) J_1)))))) of role axiom named fact_1118_less__imp__add__positive
% 2.25/2.60 A new axiom: (forall (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ex nat) (fun (K_1:nat)=> ((and ((ord_less_nat zero_zero_nat) K_1)) (((eq nat) ((plus_plus_nat I_1) K_1)) J_1))))))
% 2.25/2.60 FOF formula (forall (A:int) (B:int) (N:nat), ((not (((eq nat) N) zero_zero_nat))->((iff ((dvd_dvd_int ((power_power_int A) N)) ((power_power_int B) N))) ((dvd_dvd_int A) B)))) of role axiom named fact_1119_pow__divides__eq__int
% 2.25/2.60 A new axiom: (forall (A:int) (B:int) (N:nat), ((not (((eq nat) N) zero_zero_nat))->((iff ((dvd_dvd_int ((power_power_int A) N)) ((power_power_int B) N))) ((dvd_dvd_int A) B))))
% 2.25/2.60 FOF formula (forall (A:int) (N:nat) (B:int), (((dvd_dvd_int ((power_power_int A) N)) ((power_power_int B) N))->((not (((eq nat) N) zero_zero_nat))->((dvd_dvd_int A) B)))) of role axiom named fact_1120_pow__divides__pow__int
% 2.25/2.62 A new axiom: (forall (A:int) (N:nat) (B:int), (((dvd_dvd_int ((power_power_int A) N)) ((power_power_int B) N))->((not (((eq nat) N) zero_zero_nat))->((dvd_dvd_int A) B))))
% 2.25/2.62 FOF formula (forall (A:nat), (((dvd_dvd_nat zero_zero_nat) A)->(((eq nat) A) zero_zero_nat))) of role axiom named fact_1121_gcd__lcm__complete__lattice__nat_Otop__le
% 2.25/2.62 A new axiom: (forall (A:nat), (((dvd_dvd_nat zero_zero_nat) A)->(((eq nat) A) zero_zero_nat)))
% 2.25/2.62 FOF formula (forall (A:nat), ((iff ((dvd_dvd_nat zero_zero_nat) A)) (((eq nat) A) zero_zero_nat))) of role axiom named fact_1122_gcd__lcm__complete__lattice__nat_Otop__unique
% 2.25/2.62 A new axiom: (forall (A:nat), ((iff ((dvd_dvd_nat zero_zero_nat) A)) (((eq nat) A) zero_zero_nat)))
% 2.25/2.62 FOF formula (forall (A:nat), ((iff (not (((eq nat) A) zero_zero_nat))) ((and ((dvd_dvd_nat A) zero_zero_nat)) (((dvd_dvd_nat zero_zero_nat) A)->False)))) of role axiom named fact_1123_gcd__lcm__complete__lattice__nat_Oless__top
% 2.25/2.62 A new axiom: (forall (A:nat), ((iff (not (((eq nat) A) zero_zero_nat))) ((and ((dvd_dvd_nat A) zero_zero_nat)) (((dvd_dvd_nat zero_zero_nat) A)->False))))
% 2.25/2.62 FOF formula (forall (A:nat), ((dvd_dvd_nat A) zero_zero_nat)) of role axiom named fact_1124_gcd__lcm__complete__lattice__nat_Otop__greatest
% 2.25/2.62 A new axiom: (forall (A:nat), ((dvd_dvd_nat A) zero_zero_nat))
% 2.25/2.62 FOF formula (forall (A:nat), (((and ((dvd_dvd_nat zero_zero_nat) A)) (((dvd_dvd_nat A) zero_zero_nat)->False))->False)) of role axiom named fact_1125_gcd__lcm__complete__lattice__nat_Onot__top__less
% 2.25/2.62 A new axiom: (forall (A:nat), (((and ((dvd_dvd_nat zero_zero_nat) A)) (((dvd_dvd_nat A) zero_zero_nat)->False))->False))
% 2.25/2.62 FOF formula (forall (A:nat), (((dvd_dvd_nat A) one_one_nat)->(((eq nat) A) one_one_nat))) of role axiom named fact_1126_gcd__lcm__complete__lattice__nat_Ole__bot
% 2.25/2.62 A new axiom: (forall (A:nat), (((dvd_dvd_nat A) one_one_nat)->(((eq nat) A) one_one_nat)))
% 2.25/2.62 FOF formula (forall (A:nat), ((iff ((dvd_dvd_nat A) one_one_nat)) (((eq nat) A) one_one_nat))) of role axiom named fact_1127_gcd__lcm__complete__lattice__nat_Obot__unique
% 2.25/2.62 A new axiom: (forall (A:nat), ((iff ((dvd_dvd_nat A) one_one_nat)) (((eq nat) A) one_one_nat)))
% 2.25/2.62 FOF formula (forall (A:nat), ((iff (not (((eq nat) A) one_one_nat))) ((and ((dvd_dvd_nat one_one_nat) A)) (((dvd_dvd_nat A) one_one_nat)->False)))) of role axiom named fact_1128_gcd__lcm__complete__lattice__nat_Obot__less
% 2.25/2.62 A new axiom: (forall (A:nat), ((iff (not (((eq nat) A) one_one_nat))) ((and ((dvd_dvd_nat one_one_nat) A)) (((dvd_dvd_nat A) one_one_nat)->False))))
% 2.25/2.62 FOF formula (forall (A:nat), ((dvd_dvd_nat one_one_nat) A)) of role axiom named fact_1129_gcd__lcm__complete__lattice__nat_Obot__least
% 2.25/2.62 A new axiom: (forall (A:nat), ((dvd_dvd_nat one_one_nat) A))
% 2.25/2.62 FOF formula (forall (A:nat), (((and ((dvd_dvd_nat A) one_one_nat)) (((dvd_dvd_nat one_one_nat) A)->False))->False)) of role axiom named fact_1130_gcd__lcm__complete__lattice__nat_Onot__less__bot
% 2.25/2.62 A new axiom: (forall (A:nat), (((and ((dvd_dvd_nat A) one_one_nat)) (((dvd_dvd_nat one_one_nat) A)->False))->False))
% 2.25/2.62 FOF formula (forall (M:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((dvd_dvd_nat M) N)->((ord_less_nat zero_zero_nat) M)))) of role axiom named fact_1131_dvd__pos__nat
% 2.25/2.62 A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((dvd_dvd_nat M) N)->((ord_less_nat zero_zero_nat) M))))
% 2.25/2.62 FOF formula (forall (A:nat) (B:nat) (N:nat), ((not (((eq nat) N) zero_zero_nat))->((iff ((dvd_dvd_nat ((power_power_nat A) N)) ((power_power_nat B) N))) ((dvd_dvd_nat A) B)))) of role axiom named fact_1132_pow__divides__eq__nat
% 2.25/2.62 A new axiom: (forall (A:nat) (B:nat) (N:nat), ((not (((eq nat) N) zero_zero_nat))->((iff ((dvd_dvd_nat ((power_power_nat A) N)) ((power_power_nat B) N))) ((dvd_dvd_nat A) B))))
% 2.25/2.62 FOF formula (forall (M:nat) (N:nat), (((dvd_dvd_nat M) N)->((or ((ord_less_eq_nat M) N)) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_1133_divides__le
% 2.25/2.62 A new axiom: (forall (M:nat) (N:nat), (((dvd_dvd_nat M) N)->((or ((ord_less_eq_nat M) N)) (((eq nat) N) zero_zero_nat))))
% 2.25/2.62 FOF formula (forall (N:nat) (M:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((((eq nat) ((times_times_nat K) N)) ((times_times_nat K) M))->(((eq nat) N) M)))) of role axiom named fact_1134_mult__left__cancel
% 2.25/2.64 A new axiom: (forall (N:nat) (M:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((((eq nat) ((times_times_nat K) N)) ((times_times_nat K) M))->(((eq nat) N) M))))
% 2.25/2.64 FOF formula (forall (P_1:int), (((eq (int->Prop)) (sr P_1)) (collect_int (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) ((ord_less_int X_1) P_1)))))) of role axiom named fact_1135_SR__def
% 2.25/2.64 A new axiom: (forall (P_1:int), (((eq (int->Prop)) (sr P_1)) (collect_int (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) ((ord_less_int X_1) P_1))))))
% 2.25/2.64 FOF formula (forall (V:int) (W:int), ((and (((ord_less_eq_int zero_zero_int) (number_number_of_int W))->(((eq int) ((div_mod_int (number_number_of_int (bit1 V))) (number_number_of_int (bit0 W)))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) ((div_mod_int (number_number_of_int V)) (number_number_of_int W)))) one_one_int)))) ((((ord_less_eq_int zero_zero_int) (number_number_of_int W))->False)->(((eq int) ((div_mod_int (number_number_of_int (bit1 V))) (number_number_of_int (bit0 W)))) ((minus_minus_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) ((div_mod_int ((plus_plus_int (number_number_of_int V)) one_one_int)) (number_number_of_int W)))) one_one_int))))) of role axiom named fact_1136_zmod__number__of__Bit1
% 2.25/2.64 A new axiom: (forall (V:int) (W:int), ((and (((ord_less_eq_int zero_zero_int) (number_number_of_int W))->(((eq int) ((div_mod_int (number_number_of_int (bit1 V))) (number_number_of_int (bit0 W)))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) ((div_mod_int (number_number_of_int V)) (number_number_of_int W)))) one_one_int)))) ((((ord_less_eq_int zero_zero_int) (number_number_of_int W))->False)->(((eq int) ((div_mod_int (number_number_of_int (bit1 V))) (number_number_of_int (bit0 W)))) ((minus_minus_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) ((div_mod_int ((plus_plus_int (number_number_of_int V)) one_one_int)) (number_number_of_int W)))) one_one_int)))))
% 2.25/2.64 FOF formula (forall (B:int) (A:int), (((ord_less_eq_int A) zero_zero_int)->(((eq int) ((div_mod_int ((plus_plus_int one_one_int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) B))) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A))) ((minus_minus_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) ((div_mod_int ((plus_plus_int B) one_one_int)) A))) one_one_int)))) of role axiom named fact_1137_neg__zmod__mult__2
% 2.25/2.64 A new axiom: (forall (B:int) (A:int), (((ord_less_eq_int A) zero_zero_int)->(((eq int) ((div_mod_int ((plus_plus_int one_one_int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) B))) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A))) ((minus_minus_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) ((div_mod_int ((plus_plus_int B) one_one_int)) A))) one_one_int))))
% 2.25/2.64 FOF formula (forall (A:int) (B:int) (C:int), (((eq int) ((div_mod_int ((times_times_int A) ((div_mod_int B) C))) C)) ((div_mod_int ((times_times_int A) B)) C))) of role axiom named fact_1138_zmod__simps_I3_J
% 2.25/2.64 A new axiom: (forall (A:int) (B:int) (C:int), (((eq int) ((div_mod_int ((times_times_int A) ((div_mod_int B) C))) C)) ((div_mod_int ((times_times_int A) B)) C)))
% 2.25/2.64 FOF formula (forall (A:int) (B:int) (C:int), (((eq int) ((div_mod_int ((times_times_int A) B)) C)) ((div_mod_int ((times_times_int A) ((div_mod_int B) C))) C))) of role axiom named fact_1139_zmod__zmult1__eq
% 2.25/2.64 A new axiom: (forall (A:int) (B:int) (C:int), (((eq int) ((div_mod_int ((times_times_int A) B)) C)) ((div_mod_int ((times_times_int A) ((div_mod_int B) C))) C)))
% 2.25/2.64 FOF formula (forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) (((zcong ((div_mod_int A) M)) ((div_mod_int B) M)) M))) of role axiom named fact_1140_zcong__zmod
% 2.25/2.64 A new axiom: (forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) (((zcong ((div_mod_int A) M)) ((div_mod_int B) M)) M)))
% 2.25/2.64 FOF formula (forall (X:int) (M:int) (Y:nat), (((eq int) ((div_mod_int ((power_power_int ((div_mod_int X) M)) Y)) M)) ((div_mod_int ((power_power_int X) Y)) M))) of role axiom named fact_1141_zpower__zmod
% 2.25/2.66 A new axiom: (forall (X:int) (M:int) (Y:nat), (((eq int) ((div_mod_int ((power_power_int ((div_mod_int X) M)) Y)) M)) ((div_mod_int ((power_power_int X) Y)) M)))
% 2.25/2.66 FOF formula (forall (X:int) (M:int), (((zcong X) ((div_mod_int X) M)) M)) of role axiom named fact_1142_mod__mod__is__mod
% 2.25/2.66 A new axiom: (forall (X:int) (M:int), (((zcong X) ((div_mod_int X) M)) M))
% 2.25/2.66 FOF formula (forall (X:int) (M:int) (Y:int), ((((eq int) ((div_mod_int X) M)) ((div_mod_int Y) M))->(((zcong X) Y) M))) of role axiom named fact_1143_Residues_Oaux
% 2.25/2.66 A new axiom: (forall (X:int) (M:int) (Y:int), ((((eq int) ((div_mod_int X) M)) ((div_mod_int Y) M))->(((zcong X) Y) M)))
% 2.25/2.66 FOF formula (forall (N:int) (F:int) (M:int), (((dvd_dvd_int F) M)->(((dvd_dvd_int F) N)->((dvd_dvd_int F) ((div_mod_int M) N))))) of role axiom named fact_1144_zdvd__zmod
% 2.25/2.66 A new axiom: (forall (N:int) (F:int) (M:int), (((dvd_dvd_int F) M)->(((dvd_dvd_int F) N)->((dvd_dvd_int F) ((div_mod_int M) N)))))
% 2.25/2.66 FOF formula (forall (K:int) (M:int) (N:int), (((dvd_dvd_int K) ((div_mod_int M) N))->(((dvd_dvd_int K) N)->((dvd_dvd_int K) M)))) of role axiom named fact_1145_zdvd__zmod__imp__zdvd
% 2.25/2.66 A new axiom: (forall (K:int) (M:int) (N:int), (((dvd_dvd_int K) ((div_mod_int M) N))->(((dvd_dvd_int K) N)->((dvd_dvd_int K) M))))
% 2.25/2.66 FOF formula (forall (A:int), (((eq int) ((div_mod_int A) A)) zero_zero_int)) of role axiom named fact_1146_zmod__self
% 2.25/2.66 A new axiom: (forall (A:int), (((eq int) ((div_mod_int A) A)) zero_zero_int))
% 2.25/2.66 FOF formula (forall (B:int), (((eq int) ((div_mod_int zero_zero_int) B)) zero_zero_int)) of role axiom named fact_1147_zmod__zero
% 2.25/2.66 A new axiom: (forall (B:int), (((eq int) ((div_mod_int zero_zero_int) B)) zero_zero_int))
% 2.25/2.66 FOF formula (forall (X:int) (N:int) (Y:int), ((iff (((eq int) ((div_mod_int X) N)) ((div_mod_int Y) N))) ((dvd_dvd_int N) ((minus_minus_int X) Y)))) of role axiom named fact_1148_zmod__eq__dvd__iff
% 2.25/2.66 A new axiom: (forall (X:int) (N:int) (Y:int), ((iff (((eq int) ((div_mod_int X) N)) ((div_mod_int Y) N))) ((dvd_dvd_int N) ((minus_minus_int X) Y))))
% 2.25/2.66 FOF formula (forall (M:int) (D:int), ((iff (((eq int) ((div_mod_int M) D)) zero_zero_int)) ((ex int) (fun (Q_1:int)=> (((eq int) M) ((times_times_int D) Q_1)))))) of role axiom named fact_1149_zmod__eq__0__iff
% 2.25/2.66 A new axiom: (forall (M:int) (D:int), ((iff (((eq int) ((div_mod_int M) D)) zero_zero_int)) ((ex int) (fun (Q_1:int)=> (((eq int) M) ((times_times_int D) Q_1))))))
% 2.25/2.66 FOF formula (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((div_mod_int X) Y))))) of role axiom named fact_1150_Divides_Otransfer__nat__int__function__closures_I2_J
% 2.25/2.66 A new axiom: (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((div_mod_int X) Y)))))
% 2.25/2.66 FOF formula (forall (K:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->((ord_less_eq_int ((div_mod_int M) K)) M))) of role axiom named fact_1151_zmod__le__nonneg__dividend
% 2.25/2.66 A new axiom: (forall (K:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->((ord_less_eq_int ((div_mod_int M) K)) M)))
% 2.25/2.66 FOF formula (forall (A:int) (B:int), (((ord_less_int zero_zero_int) B)->((ord_less_int ((div_mod_int A) B)) B))) of role axiom named fact_1152_pos__mod__bound
% 2.25/2.66 A new axiom: (forall (A:int) (B:int), (((ord_less_int zero_zero_int) B)->((ord_less_int ((div_mod_int A) B)) B)))
% 2.25/2.66 FOF formula (forall (A:int) (B:int), (((ord_less_int B) zero_zero_int)->((ord_less_int B) ((div_mod_int A) B)))) of role axiom named fact_1153_neg__mod__bound
% 2.25/2.66 A new axiom: (forall (A:int) (B:int), (((ord_less_int B) zero_zero_int)->((ord_less_int B) ((div_mod_int A) B))))
% 2.25/2.66 FOF formula (forall (X:int) (M:int) (Y:int), (((eq int) ((div_mod_int ((minus_minus_int ((div_mod_int X) M)) Y)) M)) ((div_mod_int ((minus_minus_int X) Y)) M))) of role axiom named fact_1154_zdiff__zmod__left
% 2.25/2.66 A new axiom: (forall (X:int) (M:int) (Y:int), (((eq int) ((div_mod_int ((minus_minus_int ((div_mod_int X) M)) Y)) M)) ((div_mod_int ((minus_minus_int X) Y)) M)))
% 2.33/2.68 FOF formula (forall (X:int) (Y:int) (M:int), (((eq int) ((div_mod_int ((minus_minus_int X) ((div_mod_int Y) M))) M)) ((div_mod_int ((minus_minus_int X) Y)) M))) of role axiom named fact_1155_zdiff__zmod__right
% 2.33/2.68 A new axiom: (forall (X:int) (Y:int) (M:int), (((eq int) ((div_mod_int ((minus_minus_int X) ((div_mod_int Y) M))) M)) ((div_mod_int ((minus_minus_int X) Y)) M)))
% 2.33/2.68 FOF formula (forall (X:int) (Y:int), ((iff ((dvd_dvd_int (number_number_of_int X)) (number_number_of_int Y))) (((eq int) ((div_mod_int (number_number_of_int Y)) (number_number_of_int X))) zero_zero_int))) of role axiom named fact_1156_zdvd__iff__zmod__eq__0__number__of
% 2.33/2.68 A new axiom: (forall (X:int) (Y:int), ((iff ((dvd_dvd_int (number_number_of_int X)) (number_number_of_int Y))) (((eq int) ((div_mod_int (number_number_of_int Y)) (number_number_of_int X))) zero_zero_int)))
% 2.33/2.68 FOF formula (forall (A:int), (((eq int) ((div_mod_int A) (number_number_of_int min))) zero_zero_int)) of role axiom named fact_1157_zmod__minus1__right
% 2.33/2.68 A new axiom: (forall (A:int), (((eq int) ((div_mod_int A) (number_number_of_int min))) zero_zero_int))
% 2.33/2.68 FOF formula (forall (A:int) (B:int) (M:int), (((ord_less_int zero_zero_int) M)->(((dvd_dvd_int M) B)->(((eq int) ((div_mod_int ((div_mod_int A) B)) M)) ((div_mod_int A) M))))) of role axiom named fact_1158_zmod__zdvd__zmod
% 2.33/2.68 A new axiom: (forall (A:int) (B:int) (M:int), (((ord_less_int zero_zero_int) M)->(((dvd_dvd_int M) B)->(((eq int) ((div_mod_int ((div_mod_int A) B)) M)) ((div_mod_int A) M)))))
% 2.33/2.68 FOF formula (forall (A:int) (B:int) (M:int), (((ord_less_int zero_zero_int) M)->((iff (((zcong A) B) M)) (((eq int) ((div_mod_int A) M)) ((div_mod_int B) M))))) of role axiom named fact_1159_zcong__zmod__eq
% 2.33/2.68 A new axiom: (forall (A:int) (B:int) (M:int), (((ord_less_int zero_zero_int) M)->((iff (((zcong A) B) M)) (((eq int) ((div_mod_int A) M)) ((div_mod_int B) M)))))
% 2.33/2.68 FOF formula (forall (A:int) (B:int), (((ord_less_int zero_zero_int) B)->((ord_less_eq_int zero_zero_int) ((div_mod_int A) B)))) of role axiom named fact_1160_pos__mod__sign
% 2.33/2.68 A new axiom: (forall (A:int) (B:int), (((ord_less_int zero_zero_int) B)->((ord_less_eq_int zero_zero_int) ((div_mod_int A) B))))
% 2.33/2.68 FOF formula (forall (A:int) (B:int), (((ord_less_int zero_zero_int) B)->((and ((ord_less_eq_int zero_zero_int) ((div_mod_int A) B))) ((ord_less_int ((div_mod_int A) B)) B)))) of role axiom named fact_1161_pos__mod__conj
% 2.33/2.68 A new axiom: (forall (A:int) (B:int), (((ord_less_int zero_zero_int) B)->((and ((ord_less_eq_int zero_zero_int) ((div_mod_int A) B))) ((ord_less_int ((div_mod_int A) B)) B))))
% 2.33/2.68 FOF formula (forall (B:int) (A:int), (((ord_less_eq_int zero_zero_int) A)->(((ord_less_int A) B)->(((eq int) ((div_mod_int A) B)) A)))) of role axiom named fact_1162_mod__pos__pos__trivial
% 2.33/2.68 A new axiom: (forall (B:int) (A:int), (((ord_less_eq_int zero_zero_int) A)->(((ord_less_int A) B)->(((eq int) ((div_mod_int A) B)) A))))
% 2.33/2.68 FOF formula (forall (A:int) (B:int), (((ord_less_int B) zero_zero_int)->((ord_less_eq_int ((div_mod_int A) B)) zero_zero_int))) of role axiom named fact_1163_neg__mod__sign
% 2.33/2.68 A new axiom: (forall (A:int) (B:int), (((ord_less_int B) zero_zero_int)->((ord_less_eq_int ((div_mod_int A) B)) zero_zero_int)))
% 2.33/2.68 FOF formula (forall (A:int) (B:int), (((ord_less_int B) zero_zero_int)->((and ((ord_less_eq_int ((div_mod_int A) B)) zero_zero_int)) ((ord_less_int B) ((div_mod_int A) B))))) of role axiom named fact_1164_neg__mod__conj
% 2.33/2.68 A new axiom: (forall (A:int) (B:int), (((ord_less_int B) zero_zero_int)->((and ((ord_less_eq_int ((div_mod_int A) B)) zero_zero_int)) ((ord_less_int B) ((div_mod_int A) B)))))
% 2.33/2.68 FOF formula (forall (B:int) (A:int), (((ord_less_eq_int A) zero_zero_int)->(((ord_less_int B) A)->(((eq int) ((div_mod_int A) B)) A)))) of role axiom named fact_1165_mod__neg__neg__trivial
% 2.33/2.68 A new axiom: (forall (B:int) (A:int), (((ord_less_eq_int A) zero_zero_int)->(((ord_less_int B) A)->(((eq int) ((div_mod_int A) B)) A))))
% 2.33/2.68 FOF formula (forall (B:int) (A:int), (((ord_less_int zero_zero_int) A)->(((ord_less_eq_int ((plus_plus_int A) B)) zero_zero_int)->(((eq int) ((div_mod_int A) B)) ((plus_plus_int A) B))))) of role axiom named fact_1166_mod__pos__neg__trivial
% 2.34/2.70 A new axiom: (forall (B:int) (A:int), (((ord_less_int zero_zero_int) A)->(((ord_less_eq_int ((plus_plus_int A) B)) zero_zero_int)->(((eq int) ((div_mod_int A) B)) ((plus_plus_int A) B)))))
% 2.34/2.70 FOF formula (forall (V:int) (W:int), (((eq int) ((div_mod_int (number_number_of_int (bit0 V))) (number_number_of_int (bit0 W)))) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) ((div_mod_int (number_number_of_int V)) (number_number_of_int W))))) of role axiom named fact_1167_zmod__number__of__Bit0
% 2.34/2.70 A new axiom: (forall (V:int) (W:int), (((eq int) ((div_mod_int (number_number_of_int (bit0 V))) (number_number_of_int (bit0 W)))) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) ((div_mod_int (number_number_of_int V)) (number_number_of_int W)))))
% 2.34/2.70 FOF formula (forall (A_1:int) (B_1:int) (Q_2:int) (Y:int), ((((eq int) A_1) ((plus_plus_int ((times_times_int B_1) Q_2)) Y))->(((and (((ord_less_int zero_zero_int) B_1)->((and ((ord_less_eq_int zero_zero_int) Y)) ((ord_less_int Y) B_1)))) ((((ord_less_int zero_zero_int) B_1)->False)->((and ((ord_less_int B_1) Y)) ((ord_less_eq_int Y) zero_zero_int))))->((not (((eq int) B_1) zero_zero_int))->(((eq int) ((div_mod_int A_1) B_1)) Y))))) of role axiom named fact_1168_divmod__int__rel__mod__eq
% 2.34/2.70 A new axiom: (forall (A_1:int) (B_1:int) (Q_2:int) (Y:int), ((((eq int) A_1) ((plus_plus_int ((times_times_int B_1) Q_2)) Y))->(((and (((ord_less_int zero_zero_int) B_1)->((and ((ord_less_eq_int zero_zero_int) Y)) ((ord_less_int Y) B_1)))) ((((ord_less_int zero_zero_int) B_1)->False)->((and ((ord_less_int B_1) Y)) ((ord_less_eq_int Y) zero_zero_int))))->((not (((eq int) B_1) zero_zero_int))->(((eq int) ((div_mod_int A_1) B_1)) Y)))))
% 2.34/2.70 FOF formula (forall (Q:int) (B:int) (R:int) (C:int), (((ord_less_int zero_zero_int) C)->(((ord_less_int B) R)->(((ord_less_eq_int R) zero_zero_int)->((ord_less_eq_int ((plus_plus_int ((times_times_int B) ((div_mod_int Q) C))) R)) zero_zero_int))))) of role axiom named fact_1169_zmult2__lemma__aux2
% 2.34/2.70 A new axiom: (forall (Q:int) (B:int) (R:int) (C:int), (((ord_less_int zero_zero_int) C)->(((ord_less_int B) R)->(((ord_less_eq_int R) zero_zero_int)->((ord_less_eq_int ((plus_plus_int ((times_times_int B) ((div_mod_int Q) C))) R)) zero_zero_int)))))
% 2.34/2.70 FOF formula (forall (Q:int) (B:int) (R:int) (C:int), (((ord_less_int zero_zero_int) C)->(((ord_less_int B) R)->(((ord_less_eq_int R) zero_zero_int)->((ord_less_int ((times_times_int B) C)) ((plus_plus_int ((times_times_int B) ((div_mod_int Q) C))) R)))))) of role axiom named fact_1170_zmult2__lemma__aux1
% 2.34/2.70 A new axiom: (forall (Q:int) (B:int) (R:int) (C:int), (((ord_less_int zero_zero_int) C)->(((ord_less_int B) R)->(((ord_less_eq_int R) zero_zero_int)->((ord_less_int ((times_times_int B) C)) ((plus_plus_int ((times_times_int B) ((div_mod_int Q) C))) R))))))
% 2.34/2.70 FOF formula (forall (Q:int) (B:int) (R:int) (C:int), (((ord_less_int zero_zero_int) C)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int R) B)->((ord_less_int ((plus_plus_int ((times_times_int B) ((div_mod_int Q) C))) R)) ((times_times_int B) C)))))) of role axiom named fact_1171_zmult2__lemma__aux4
% 2.34/2.70 A new axiom: (forall (Q:int) (B:int) (R:int) (C:int), (((ord_less_int zero_zero_int) C)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int R) B)->((ord_less_int ((plus_plus_int ((times_times_int B) ((div_mod_int Q) C))) R)) ((times_times_int B) C))))))
% 2.34/2.70 FOF formula (forall (Q:int) (B:int) (R:int) (C:int), (((ord_less_int zero_zero_int) C)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int R) B)->((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B) ((div_mod_int Q) C))) R)))))) of role axiom named fact_1172_zmult2__lemma__aux3
% 2.34/2.70 A new axiom: (forall (Q:int) (B:int) (R:int) (C:int), (((ord_less_int zero_zero_int) C)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int R) B)->((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B) ((div_mod_int Q) C))) R))))))
% 2.34/2.70 FOF formula (forall (P:(int->Prop)) (N:int) (K:int), ((iff (P ((div_mod_int N) K))) ((and ((and ((((eq int) K) zero_zero_int)->(P N))) (((ord_less_int zero_zero_int) K)->(forall (_TPTP_I:int) (J:int), (((and ((and ((ord_less_eq_int zero_zero_int) J)) ((ord_less_int J) K))) (((eq int) N) ((plus_plus_int ((times_times_int K) _TPTP_I)) J)))->(P J)))))) (((ord_less_int K) zero_zero_int)->(forall (_TPTP_I:int) (J:int), (((and ((and ((ord_less_int K) J)) ((ord_less_eq_int J) zero_zero_int))) (((eq int) N) ((plus_plus_int ((times_times_int K) _TPTP_I)) J)))->(P J))))))) of role axiom named fact_1173_split__zmod
% 2.36/2.72 A new axiom: (forall (P:(int->Prop)) (N:int) (K:int), ((iff (P ((div_mod_int N) K))) ((and ((and ((((eq int) K) zero_zero_int)->(P N))) (((ord_less_int zero_zero_int) K)->(forall (_TPTP_I:int) (J:int), (((and ((and ((ord_less_eq_int zero_zero_int) J)) ((ord_less_int J) K))) (((eq int) N) ((plus_plus_int ((times_times_int K) _TPTP_I)) J)))->(P J)))))) (((ord_less_int K) zero_zero_int)->(forall (_TPTP_I:int) (J:int), (((and ((and ((ord_less_int K) J)) ((ord_less_eq_int J) zero_zero_int))) (((eq int) N) ((plus_plus_int ((times_times_int K) _TPTP_I)) J)))->(P J)))))))
% 2.36/2.72 FOF formula (forall (X:int), ((iff (not (((eq int) ((div_mod_int X) (number_number_of_int (bit0 (bit1 pls))))) zero_zero_int))) (((eq int) ((div_mod_int X) (number_number_of_int (bit0 (bit1 pls))))) one_one_int))) of role axiom named fact_1174_neq__one__mod__two
% 2.36/2.72 A new axiom: (forall (X:int), ((iff (not (((eq int) ((div_mod_int X) (number_number_of_int (bit0 (bit1 pls))))) zero_zero_int))) (((eq int) ((div_mod_int X) (number_number_of_int (bit0 (bit1 pls))))) one_one_int)))
% 2.36/2.72 FOF formula (forall (B:int), (((ord_less_int zero_zero_int) B)->(((eq int) ((div_mod_int (number_number_of_int min)) B)) ((minus_minus_int B) one_one_int)))) of role axiom named fact_1175_zmod__minus1
% 2.36/2.72 A new axiom: (forall (B:int), (((ord_less_int zero_zero_int) B)->(((eq int) ((div_mod_int (number_number_of_int min)) B)) ((minus_minus_int B) one_one_int))))
% 2.36/2.72 FOF formula (forall (B:int) (A:int), (((ord_less_eq_int zero_zero_int) A)->(((eq int) ((div_mod_int ((plus_plus_int one_one_int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) B))) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A))) ((plus_plus_int one_one_int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) ((div_mod_int B) A)))))) of role axiom named fact_1176_pos__zmod__mult__2
% 2.36/2.72 A new axiom: (forall (B:int) (A:int), (((ord_less_eq_int zero_zero_int) A)->(((eq int) ((div_mod_int ((plus_plus_int one_one_int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) B))) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A))) ((plus_plus_int one_one_int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) ((div_mod_int B) A))))))
% 2.36/2.72 FOF formula (forall (M_1:int) (D_1:int), ((((eq int) ((div_mod_int M_1) D_1)) zero_zero_int)->((ex int) (fun (Q_1:int)=> (((eq int) M_1) ((times_times_int D_1) Q_1)))))) of role axiom named fact_1177_zmod__eq__0D
% 2.36/2.72 A new axiom: (forall (M_1:int) (D_1:int), ((((eq int) ((div_mod_int M_1) D_1)) zero_zero_int)->((ex int) (fun (Q_1:int)=> (((eq int) M_1) ((times_times_int D_1) Q_1))))))
% 2.36/2.72 FOF formula (forall (X:int) (Y:int) (M:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) M)->(((zcong ((times_times_int ((standardRes M) X)) ((standardRes M) Y))) ((times_times_int X) Y)) M))) of role axiom named fact_1178_StandardRes__prop4
% 2.36/2.72 A new axiom: (forall (X:int) (Y:int) (M:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) M)->(((zcong ((times_times_int ((standardRes M) X)) ((standardRes M) Y))) ((times_times_int X) Y)) M)))
% 2.36/2.72 FOF formula (forall (M:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->((ord_less_eq_nat ((div_mod_nat M) N)) N))) of role axiom named fact_1179_mod__le__divisor
% 2.36/2.72 A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->((ord_less_eq_nat ((div_mod_nat M) N)) N)))
% 2.36/2.72 FOF formula (forall (K:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K) ((div_mod_nat M) N))) ((div_mod_nat ((times_times_nat K) M)) ((times_times_nat K) N)))) of role axiom named fact_1180_mod__mult__distrib2
% 2.38/2.74 A new axiom: (forall (K:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K) ((div_mod_nat M) N))) ((div_mod_nat ((times_times_nat K) M)) ((times_times_nat K) N))))
% 2.38/2.74 FOF formula (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((div_mod_nat M) N)) K)) ((div_mod_nat ((times_times_nat M) K)) ((times_times_nat N) K)))) of role axiom named fact_1181_mod__mult__distrib
% 2.38/2.74 A new axiom: (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((div_mod_nat M) N)) K)) ((div_mod_nat ((times_times_nat M) K)) ((times_times_nat N) K))))
% 2.38/2.74 FOF formula (forall (M:int) (X:int), (((eq int) ((standardRes M) X)) ((div_mod_int X) M))) of role axiom named fact_1182_StandardRes__def
% 2.38/2.74 A new axiom: (forall (M:int) (X:int), (((eq int) ((standardRes M) X)) ((div_mod_int X) M)))
% 2.38/2.74 FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->(((eq nat) ((div_mod_nat M) N)) M))) of role axiom named fact_1183_mod__less
% 2.38/2.74 A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->(((eq nat) ((div_mod_nat M) N)) M)))
% 2.38/2.74 FOF formula (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((div_mod_nat M) N)) ((div_mod_nat ((minus_minus_nat M) N)) N)))) of role axiom named fact_1184_le__mod__geq
% 2.38/2.74 A new axiom: (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((div_mod_nat M) N)) ((div_mod_nat ((minus_minus_nat M) N)) N))))
% 2.38/2.74 FOF formula (forall (K:nat) (N:nat) (M:nat), (((eq nat) ((div_mod_nat ((plus_plus_nat ((times_times_nat K) N)) M)) N)) ((div_mod_nat M) N))) of role axiom named fact_1185_mod__mult__self3
% 2.38/2.74 A new axiom: (forall (K:nat) (N:nat) (M:nat), (((eq nat) ((div_mod_nat ((plus_plus_nat ((times_times_nat K) N)) M)) N)) ((div_mod_nat M) N)))
% 2.38/2.74 FOF formula (forall (M:nat) (N:nat), ((((ord_less_nat M) N)->False)->(((eq nat) ((div_mod_nat M) N)) ((div_mod_nat ((minus_minus_nat M) N)) N)))) of role axiom named fact_1186_mod__geq
% 2.38/2.74 A new axiom: (forall (M:nat) (N:nat), ((((ord_less_nat M) N)->False)->(((eq nat) ((div_mod_nat M) N)) ((div_mod_nat ((minus_minus_nat M) N)) N))))
% 2.38/2.74 FOF formula (forall (M:nat) (N:nat), ((and (((ord_less_nat M) N)->(((eq nat) ((div_mod_nat M) N)) M))) ((((ord_less_nat M) N)->False)->(((eq nat) ((div_mod_nat M) N)) ((div_mod_nat ((minus_minus_nat M) N)) N))))) of role axiom named fact_1187_mod__if
% 2.38/2.74 A new axiom: (forall (M:nat) (N:nat), ((and (((ord_less_nat M) N)->(((eq nat) ((div_mod_nat M) N)) M))) ((((ord_less_nat M) N)->False)->(((eq nat) ((div_mod_nat M) N)) ((div_mod_nat ((minus_minus_nat M) N)) N)))))
% 2.38/2.74 FOF formula (forall (M:nat) (D:nat), ((iff (((eq nat) ((div_mod_nat M) D)) zero_zero_nat)) ((ex nat) (fun (Q_1:nat)=> (((eq nat) M) ((times_times_nat D) Q_1)))))) of role axiom named fact_1188_mod__eq__0__iff
% 2.38/2.74 A new axiom: (forall (M:nat) (D:nat), ((iff (((eq nat) ((div_mod_nat M) D)) zero_zero_nat)) ((ex nat) (fun (Q_1:nat)=> (((eq nat) M) ((times_times_nat D) Q_1))))))
% 2.38/2.74 FOF formula (forall (M:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->((ord_less_nat ((div_mod_nat M) N)) N))) of role axiom named fact_1189_mod__less__divisor
% 2.38/2.74 A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->((ord_less_nat ((div_mod_nat M) N)) N)))
% 2.38/2.74 FOF formula (forall (M:nat) (N:nat), ((ord_less_eq_nat ((div_mod_nat M) N)) M)) of role axiom named fact_1190_mod__less__eq__dividend
% 2.38/2.74 A new axiom: (forall (M:nat) (N:nat), ((ord_less_eq_nat ((div_mod_nat M) N)) M))
% 2.38/2.74 FOF formula (forall (M:int) (X:int), ((iff (((eq int) ((standardRes M) X)) zero_zero_int)) (((zcong X) zero_zero_int) M))) of role axiom named fact_1191_StandardRes__eq__zcong
% 2.38/2.74 A new axiom: (forall (M:int) (X:int), ((iff (((eq int) ((standardRes M) X)) zero_zero_int)) (((zcong X) zero_zero_int) M)))
% 2.38/2.74 FOF formula (forall (X:int) (P_1:int), ((iff ((((zcong X) zero_zero_int) P_1)->False)) (not (((eq int) ((standardRes P_1) X)) zero_zero_int)))) of role axiom named fact_1192_StandardRes__prop3
% 2.38/2.74 A new axiom: (forall (X:int) (P_1:int), ((iff ((((zcong X) zero_zero_int) P_1)->False)) (not (((eq int) ((standardRes P_1) X)) zero_zero_int))))
% 2.38/2.74 FOF formula (forall (X:int) (M:int), (((zcong X) ((standardRes M) X)) M)) of role axiom named fact_1193_StandardRes__prop1
% 2.38/2.76 A new axiom: (forall (X:int) (M:int), (((zcong X) ((standardRes M) X)) M))
% 2.38/2.76 FOF formula (forall (X:int) (P_1:int), (((ord_less_int zero_zero_int) P_1)->((ord_less_int ((standardRes P_1) X)) P_1))) of role axiom named fact_1194_StandardRes__ubound
% 2.38/2.76 A new axiom: (forall (X:int) (P_1:int), (((ord_less_int zero_zero_int) P_1)->((ord_less_int ((standardRes P_1) X)) P_1)))
% 2.38/2.76 FOF formula (forall (X:int) (P_1:int), (((member_int X) (sr P_1))->(((eq int) ((standardRes P_1) X)) X))) of role axiom named fact_1195_StandardRes__SR__prop
% 2.38/2.76 A new axiom: (forall (X:int) (P_1:int), (((member_int X) (sr P_1))->(((eq int) ((standardRes P_1) X)) X)))
% 2.38/2.76 FOF formula (forall (P:(nat->Prop)) (N:nat) (K:nat), ((iff (P ((div_mod_nat N) K))) ((and ((((eq nat) K) zero_zero_nat)->(P N))) ((not (((eq nat) K) zero_zero_nat))->(forall (_TPTP_I:nat) (J:nat), (((ord_less_nat J) K)->((((eq nat) N) ((plus_plus_nat ((times_times_nat K) _TPTP_I)) J))->(P J)))))))) of role axiom named fact_1196_split__mod
% 2.38/2.76 A new axiom: (forall (P:(nat->Prop)) (N:nat) (K:nat), ((iff (P ((div_mod_nat N) K))) ((and ((((eq nat) K) zero_zero_nat)->(P N))) ((not (((eq nat) K) zero_zero_nat))->(forall (_TPTP_I:nat) (J:nat), (((ord_less_nat J) K)->((((eq nat) N) ((plus_plus_nat ((times_times_nat K) _TPTP_I)) J))->(P J))))))))
% 2.38/2.76 FOF formula (forall (Q:nat) (R:nat) (B:nat) (C:nat), (((ord_less_nat zero_zero_nat) C)->(((ord_less_nat R) B)->((ord_less_nat ((plus_plus_nat ((times_times_nat B) ((div_mod_nat Q) C))) R)) ((times_times_nat B) C))))) of role axiom named fact_1197_mod__lemma
% 2.38/2.76 A new axiom: (forall (Q:nat) (R:nat) (B:nat) (C:nat), (((ord_less_nat zero_zero_nat) C)->(((ord_less_nat R) B)->((ord_less_nat ((plus_plus_nat ((times_times_nat B) ((div_mod_nat Q) C))) R)) ((times_times_nat B) C)))))
% 2.38/2.76 FOF formula ((ord_less_int ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) zero_zero_int) of role conjecture named conj_0
% 2.38/2.76 Conjecture to prove = ((ord_less_int ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) zero_zero_int):Prop
% 2.38/2.76 Parameter product_prod_int_int_DUMMY:product_prod_int_int.
% 2.38/2.76 We need to prove ['((ord_less_int ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) zero_zero_int)']
% 2.38/2.76 Parameter int:Type.
% 2.38/2.76 Parameter nat:Type.
% 2.38/2.76 Parameter real:Type.
% 2.38/2.76 Parameter product_prod_int_int:Type.
% 2.38/2.76 Parameter div_mod_int:(int->(int->int)).
% 2.38/2.76 Parameter div_mod_nat:(nat->(nat->nat)).
% 2.38/2.76 Parameter minus_minus_int:(int->(int->int)).
% 2.38/2.76 Parameter minus_minus_nat:(nat->(nat->nat)).
% 2.38/2.76 Parameter minus_minus_real:(real->(real->real)).
% 2.38/2.76 Parameter one_one_int:int.
% 2.38/2.76 Parameter one_one_nat:nat.
% 2.38/2.76 Parameter one_one_real:real.
% 2.38/2.76 Parameter plus_plus_int:(int->(int->int)).
% 2.38/2.76 Parameter plus_plus_nat:(nat->(nat->nat)).
% 2.38/2.76 Parameter plus_plus_real:(real->(real->real)).
% 2.38/2.76 Parameter times_times_int:(int->(int->int)).
% 2.38/2.76 Parameter times_times_nat:(nat->(nat->nat)).
% 2.38/2.76 Parameter times_times_real:(real->(real->real)).
% 2.38/2.76 Parameter zero_zero_int:int.
% 2.38/2.76 Parameter zero_zero_nat:nat.
% 2.38/2.76 Parameter zero_zero_real:real.
% 2.38/2.76 Parameter multInv:(int->(int->int)).
% 2.38/2.76 Parameter d22set:(int->(int->Prop)).
% 2.38/2.76 Parameter zfact:(int->int).
% 2.38/2.76 Parameter zcong:(int->(int->(int->Prop))).
% 2.38/2.76 Parameter zprime:(int->Prop).
% 2.38/2.76 Parameter bit0:(int->int).
% 2.38/2.76 Parameter bit1:(int->int).
% 2.38/2.76 Parameter min:int.
% 2.38/2.76 Parameter pls:int.
% 2.38/2.76 Parameter number_number_of_int:(int->int).
% 2.38/2.76 Parameter number_number_of_nat:(int->nat).
% 2.38/2.76 Parameter number267125858f_real:(int->real).
% 2.38/2.76 Parameter ord_less_int:(int->(int->Prop)).
% 2.38/2.76 Parameter ord_less_nat:(nat->(nat->Prop)).
% 2.38/2.76 Parameter ord_less_real:(real->(real->Prop)).
% 2.38/2.76 Parameter ord_less_eq_int:(int->(int->Prop)).
% 2.38/2.76 Parameter ord_less_eq_nat:(nat->(nat->Prop)).
% 2.38/2.76 Parameter ord_less_eq_real:(real->(real->Prop)).
% 2.38/2.76 Parameter power_power_int:(int->(nat->int)).
% 2.38/2.76 Parameter power_power_nat:(nat->(nat->nat)).
% 2.38/2.76 Parameter power_power_real:(real->(nat->real)).
% 2.38/2.76 Parameter product_Pair_int_int:(int->(int->product_prod_int_int)).
% 2.38/2.76 Parameter legendre:(int->(int->int)).
% 2.38/2.76 Parameter quadRes:(int->(int->Prop)).
% 2.38/2.76 Parameter sr:(int->(int->Prop)).
% 2.38/2.76 Parameter standardRes:(int->(int->int)).
% 2.38/2.76 Parameter dvd_dvd_int:(int->(int->Prop)).
% 2.38/2.76 Parameter dvd_dvd_nat:(nat->(nat->Prop)).
% 2.38/2.76 Parameter dvd_dvd_real:(real->(real->Prop)).
% 2.38/2.76 Parameter collect_int:((int->Prop)->(int->Prop)).
% 2.38/2.76 Parameter twoSqu919416604sum2sq:(int->Prop).
% 2.38/2.76 Parameter twoSqu2057625106sum2sq:(product_prod_int_int->int).
% 2.38/2.76 Parameter inv:(int->(int->int)).
% 2.38/2.76 Parameter wset:(int->(int->(int->Prop))).
% 2.38/2.76 Parameter member_int:(int->((int->Prop)->Prop)).
% 2.38/2.76 Parameter m:int.
% 2.38/2.76 Parameter s1:int.
% 2.38/2.76 Parameter s:int.
% 2.38/2.76 Parameter t:int.
% 2.38/2.76 Axiom fact_0__096t_A_060_A0_096:((ord_less_int t) zero_zero_int).
% 2.38/2.76 Axiom fact_1_calculation_I1_J:((ord_less_int t) one_one_int).
% 2.38/2.76 Axiom fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096:((ord_less_int ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) zero_zero_int)).
% 2.38/2.76 Axiom fact_3_t:(((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)).
% 2.38/2.76 Axiom fact_4_calculation_I2_J:((((eq int) t) zero_zero_int)->(((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) zero_zero_int)).
% 2.38/2.76 Axiom fact_5__096_126_A1_A_060_061_At_096:(((ord_less_eq_int one_one_int) t)->False).
% 2.38/2.76 Axiom fact_6_p0:((ord_less_int zero_zero_int) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)).
% 2.38/2.76 Axiom fact_7_not__sum__power2__lt__zero:(forall (X:real) (Y:real), (((ord_less_real ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)->False)).
% 2.38/2.76 Axiom fact_8_not__sum__power2__lt__zero:(forall (X:int) (Y:int), (((ord_less_int ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)->False)).
% 2.38/2.76 Axiom fact_9_sum__power2__gt__zero__iff:(forall (X_39:real) (Y_31:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((power_power_real X_39) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_31) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq real) X_39) zero_zero_real))) (not (((eq real) Y_31) zero_zero_real))))).
% 2.38/2.76 Axiom fact_10_sum__power2__gt__zero__iff:(forall (X_39:int) (Y_31:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((power_power_int X_39) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_31) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq int) X_39) zero_zero_int))) (not (((eq int) Y_31) zero_zero_int))))).
% 2.38/2.76 Axiom fact_11_sum__power2__eq__zero__iff:(forall (X_38:real) (Y_30:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X_38) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_30) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_38) zero_zero_real)) (((eq real) Y_30) zero_zero_real)))).
% 2.38/2.76 Axiom fact_12_sum__power2__eq__zero__iff:(forall (X_38:int) (Y_30:int), ((iff (((eq int) ((plus_plus_int ((power_power_int X_38) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_30) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_38) zero_zero_int)) (((eq int) Y_30) zero_zero_int)))).
% 2.38/2.76 Axiom fact_13_power2__less__0:(forall (A_129:real), (((ord_less_real ((power_power_real A_129) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)->False)).
% 2.38/2.76 Axiom fact_14_power2__less__0:(forall (A_129:int), (((ord_less_int ((power_power_int A_129) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)->False)).
% 2.38/2.76 Axiom fact_15_zero__less__power2:(forall (A_128:real), ((iff ((ord_less_real zero_zero_real) ((power_power_real A_128) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq real) A_128) zero_zero_real)))).
% 2.38/2.76 Axiom fact_16_zero__less__power2:(forall (A_128:int), ((iff ((ord_less_int zero_zero_int) ((power_power_int A_128) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq int) A_128) zero_zero_int)))).
% 2.38/2.76 Axiom fact_17_one__power2:(((eq real) ((power_power_real one_one_real) (number_number_of_nat (bit0 (bit1 pls))))) one_one_real).
% 2.38/2.76 Axiom fact_18_one__power2:(((eq nat) ((power_power_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls))))) one_one_nat).
% 2.38/2.76 Axiom fact_19_one__power2:(((eq int) ((power_power_int one_one_int) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int).
% 2.38/2.76 Axiom fact_20_zero__power2:(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real).
% 2.38/2.76 Axiom fact_21_zero__power2:(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_nat).
% 2.38/2.76 Axiom fact_22_zero__power2:(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int).
% 2.38/2.76 Axiom fact_23_zero__eq__power2:(forall (A_127:real), ((iff (((eq real) ((power_power_real A_127) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)) (((eq real) A_127) zero_zero_real))).
% 2.38/2.76 Axiom fact_24_zero__eq__power2:(forall (A_127:int), ((iff (((eq int) ((power_power_int A_127) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)) (((eq int) A_127) zero_zero_int))).
% 2.38/2.76 Axiom fact_25_add__special_I2_J:(forall (W_17:int), (((eq real) ((plus_plus_real one_one_real) (number267125858f_real W_17))) (number267125858f_real ((plus_plus_int (bit1 pls)) W_17)))).
% 2.38/2.76 Axiom fact_26_add__special_I2_J:(forall (W_17:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_17))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_17)))).
% 2.38/2.76 Axiom fact_27_add__special_I3_J:(forall (V_16:int), (((eq real) ((plus_plus_real (number267125858f_real V_16)) one_one_real)) (number267125858f_real ((plus_plus_int V_16) (bit1 pls))))).
% 2.38/2.76 Axiom fact_28_add__special_I3_J:(forall (V_16:int), (((eq int) ((plus_plus_int (number_number_of_int V_16)) one_one_int)) (number_number_of_int ((plus_plus_int V_16) (bit1 pls))))).
% 2.38/2.76 Axiom fact_29_t__l__p:((ord_less_int t) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)).
% 2.38/2.76 Axiom fact_30__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_:((forall (T_1:int), (not (((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) T_1))))->False).
% 2.38/2.76 Axiom fact_31_p:(zprime ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)).
% 2.38/2.76 Axiom fact_32_qf1pt:(twoSqu919416604sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)).
% 2.38/2.76 Axiom fact_33_zle__refl:(forall (W:int), ((ord_less_eq_int W) W)).
% 2.38/2.76 Axiom fact_34_number__of__is__id:(forall (K:int), (((eq int) (number_number_of_int K)) K)).
% 2.38/2.76 Axiom fact_35_zmult__commute:(forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z))).
% 2.38/2.76 Axiom fact_36_zle__linear:(forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z))).
% 2.38/2.76 Axiom fact_37_times__numeral__code_I5_J:(forall (V:int) (W:int), (((eq int) ((times_times_int (number_number_of_int V)) (number_number_of_int W))) (number_number_of_int ((times_times_int V) W)))).
% 2.38/2.76 Axiom fact_38_less__eq__number__of__int__code:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_eq_int K) L))).
% 2.38/2.76 Axiom fact_39_le__number__of:(forall (X_37:int) (Y_29:int), ((iff ((ord_less_eq_real (number267125858f_real X_37)) (number267125858f_real Y_29))) ((ord_less_eq_int X_37) Y_29))).
% 2.38/2.76 Axiom fact_40_le__number__of:(forall (X_37:int) (Y_29:int), ((iff ((ord_less_eq_int (number_number_of_int X_37)) (number_number_of_int Y_29))) ((ord_less_eq_int X_37) Y_29))).
% 2.38/2.76 Axiom fact_41_zmult__assoc:(forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((times_times_int ((times_times_int Z1) Z2)) Z3)) ((times_times_int Z1) ((times_times_int Z2) Z3)))).
% 2.38/2.77 Axiom fact_42_zle__trans:(forall (K:int) (I_1:int) (J_1:int), (((ord_less_eq_int I_1) J_1)->(((ord_less_eq_int J_1) K)->((ord_less_eq_int I_1) K)))).
% 2.38/2.77 Axiom fact_43_zle__antisym:(forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W)))).
% 2.38/2.77 Axiom fact_44_zpower__zadd__distrib:(forall (X:int) (Y:nat) (Z:nat), (((eq int) ((power_power_int X) ((plus_plus_nat Y) Z))) ((times_times_int ((power_power_int X) Y)) ((power_power_int X) Z)))).
% 2.38/2.77 Axiom fact_45_less__eq__int__code_I16_J:(forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))).
% 2.38/2.77 Axiom fact_46_rel__simps_I34_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit1 L))) ((ord_less_eq_int K) L))).
% 2.38/2.77 Axiom fact_47_rel__simps_I19_J:((ord_less_eq_int pls) pls).
% 2.38/2.77 Axiom fact_48_less__eq__int__code_I13_J:(forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit0 K2))) ((ord_less_eq_int K1) K2))).
% 2.38/2.77 Axiom fact_49_rel__simps_I31_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit0 L))) ((ord_less_eq_int K) L))).
% 2.38/2.77 Axiom fact_50_zless__le:(forall (Z:int) (W:int), ((iff ((ord_less_int Z) W)) ((and ((ord_less_eq_int Z) W)) (not (((eq int) Z) W))))).
% 2.38/2.77 Axiom fact_51_zadd__left__mono:(forall (K:int) (I_1:int) (J_1:int), (((ord_less_eq_int I_1) J_1)->((ord_less_eq_int ((plus_plus_int K) I_1)) ((plus_plus_int K) J_1)))).
% 2.38/2.77 Axiom fact_52_eq__number__of__0:(forall (V:int), ((iff (((eq nat) (number_number_of_nat V)) zero_zero_nat)) ((ord_less_eq_int V) pls))).
% 2.38/2.77 Axiom fact_53_eq__0__number__of:(forall (V:int), ((iff (((eq nat) zero_zero_nat) (number_number_of_nat V))) ((ord_less_eq_int V) pls))).
% 2.38/2.77 Axiom fact_54_semiring__mult__number__of:(forall (V_15:int) (V_14:int), (((ord_less_eq_int pls) V_14)->(((ord_less_eq_int pls) V_15)->(((eq real) ((times_times_real (number267125858f_real V_14)) (number267125858f_real V_15))) (number267125858f_real ((times_times_int V_14) V_15)))))).
% 2.38/2.77 Axiom fact_55_semiring__mult__number__of:(forall (V_15:int) (V_14:int), (((ord_less_eq_int pls) V_14)->(((ord_less_eq_int pls) V_15)->(((eq nat) ((times_times_nat (number_number_of_nat V_14)) (number_number_of_nat V_15))) (number_number_of_nat ((times_times_int V_14) V_15)))))).
% 2.38/2.77 Axiom fact_56_semiring__mult__number__of:(forall (V_15:int) (V_14:int), (((ord_less_eq_int pls) V_14)->(((ord_less_eq_int pls) V_15)->(((eq int) ((times_times_int (number_number_of_int V_14)) (number_number_of_int V_15))) (number_number_of_int ((times_times_int V_14) V_15)))))).
% 2.38/2.77 Axiom fact_57_mult__number__of__left:(forall (V_13:int) (W_16:int) (Z_9:real), (((eq real) ((times_times_real (number267125858f_real V_13)) ((times_times_real (number267125858f_real W_16)) Z_9))) ((times_times_real (number267125858f_real ((times_times_int V_13) W_16))) Z_9))).
% 2.38/2.77 Axiom fact_58_mult__number__of__left:(forall (V_13:int) (W_16:int) (Z_9:int), (((eq int) ((times_times_int (number_number_of_int V_13)) ((times_times_int (number_number_of_int W_16)) Z_9))) ((times_times_int (number_number_of_int ((times_times_int V_13) W_16))) Z_9))).
% 2.38/2.77 Axiom fact_59_arith__simps_I32_J:(forall (V_12:int) (W_15:int), (((eq real) ((times_times_real (number267125858f_real V_12)) (number267125858f_real W_15))) (number267125858f_real ((times_times_int V_12) W_15)))).
% 2.38/2.77 Axiom fact_60_arith__simps_I32_J:(forall (V_12:int) (W_15:int), (((eq int) ((times_times_int (number_number_of_int V_12)) (number_number_of_int W_15))) (number_number_of_int ((times_times_int V_12) W_15)))).
% 2.38/2.77 Axiom fact_61_number__of__mult:(forall (V_11:int) (W_14:int), (((eq real) (number267125858f_real ((times_times_int V_11) W_14))) ((times_times_real (number267125858f_real V_11)) (number267125858f_real W_14)))).
% 2.38/2.77 Axiom fact_62_number__of__mult:(forall (V_11:int) (W_14:int), (((eq int) (number_number_of_int ((times_times_int V_11) W_14))) ((times_times_int (number_number_of_int V_11)) (number_number_of_int W_14)))).
% 2.38/2.77 Axiom fact_63_sum__squares__le__zero__iff:(forall (X_36:real) (Y_28:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real X_36) X_36)) ((times_times_real Y_28) Y_28))) zero_zero_real)) ((and (((eq real) X_36) zero_zero_real)) (((eq real) Y_28) zero_zero_real)))).
% 2.38/2.77 Axiom fact_64_sum__squares__le__zero__iff:(forall (X_36:int) (Y_28:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int X_36) X_36)) ((times_times_int Y_28) Y_28))) zero_zero_int)) ((and (((eq int) X_36) zero_zero_int)) (((eq int) Y_28) zero_zero_int)))).
% 2.38/2.77 Axiom fact_65_sum__squares__ge__zero:(forall (X_35:real) (Y_27:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((times_times_real X_35) X_35)) ((times_times_real Y_27) Y_27)))).
% 2.38/2.77 Axiom fact_66_sum__squares__ge__zero:(forall (X_35:int) (Y_27:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int X_35) X_35)) ((times_times_int Y_27) Y_27)))).
% 2.38/2.77 Axiom fact_67_le__special_I3_J:(forall (X_34:int), ((iff ((ord_less_eq_real (number267125858f_real X_34)) zero_zero_real)) ((ord_less_eq_int X_34) pls))).
% 2.38/2.77 Axiom fact_68_le__special_I3_J:(forall (X_34:int), ((iff ((ord_less_eq_int (number_number_of_int X_34)) zero_zero_int)) ((ord_less_eq_int X_34) pls))).
% 2.38/2.77 Axiom fact_69_le__special_I1_J:(forall (Y_26:int), ((iff ((ord_less_eq_real zero_zero_real) (number267125858f_real Y_26))) ((ord_less_eq_int pls) Y_26))).
% 2.38/2.77 Axiom fact_70_le__special_I1_J:(forall (Y_26:int), ((iff ((ord_less_eq_int zero_zero_int) (number_number_of_int Y_26))) ((ord_less_eq_int pls) Y_26))).
% 2.38/2.77 Axiom fact_71_less__0__number__of:(forall (V:int), ((iff ((ord_less_nat zero_zero_nat) (number_number_of_nat V))) ((ord_less_int pls) V))).
% 2.38/2.77 Axiom fact_72_le__number__of__eq__not__less:(forall (V_10:int) (W_13:int), ((iff ((ord_less_eq_real (number267125858f_real V_10)) (number267125858f_real W_13))) (((ord_less_real (number267125858f_real W_13)) (number267125858f_real V_10))->False))).
% 2.38/2.77 Axiom fact_73_le__number__of__eq__not__less:(forall (V_10:int) (W_13:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_10)) (number_number_of_nat W_13))) (((ord_less_nat (number_number_of_nat W_13)) (number_number_of_nat V_10))->False))).
% 2.38/2.77 Axiom fact_74_le__number__of__eq__not__less:(forall (V_10:int) (W_13:int), ((iff ((ord_less_eq_int (number_number_of_int V_10)) (number_number_of_int W_13))) (((ord_less_int (number_number_of_int W_13)) (number_number_of_int V_10))->False))).
% 2.38/2.77 Axiom fact_75_rel__simps_I22_J:(forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K))).
% 2.38/2.77 Axiom fact_76_less__eq__int__code_I14_J:(forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))).
% 2.38/2.77 Axiom fact_77_rel__simps_I32_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))).
% 2.38/2.77 Axiom fact_78_rel__simps_I27_J:(forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) pls)) ((ord_less_eq_int K) pls))).
% 2.38/2.77 Axiom fact_79_rel__simps_I21_J:(forall (K:int), ((iff ((ord_less_eq_int pls) (bit0 K))) ((ord_less_eq_int pls) K))).
% 2.38/2.77 Axiom fact_80_zadd__zless__mono:(forall (Z_8:int) (Z:int) (W_12:int) (W:int), (((ord_less_int W_12) W)->(((ord_less_eq_int Z_8) Z)->((ord_less_int ((plus_plus_int W_12) Z_8)) ((plus_plus_int W) Z))))).
% 2.38/2.77 Axiom fact_81_nat__number__of__Pls:(((eq nat) (number_number_of_nat pls)) zero_zero_nat).
% 2.38/2.77 Axiom fact_82_semiring__norm_I113_J:(((eq nat) zero_zero_nat) (number_number_of_nat pls)).
% 2.38/2.77 Axiom fact_83_le__special_I4_J:(forall (X_33:int), ((iff ((ord_less_eq_real (number267125858f_real X_33)) one_one_real)) ((ord_less_eq_int X_33) (bit1 pls)))).
% 2.38/2.77 Axiom fact_84_le__special_I4_J:(forall (X_33:int), ((iff ((ord_less_eq_int (number_number_of_int X_33)) one_one_int)) ((ord_less_eq_int X_33) (bit1 pls)))).
% 2.38/2.77 Axiom fact_85_le__special_I2_J:(forall (Y_25:int), ((iff ((ord_less_eq_real one_one_real) (number267125858f_real Y_25))) ((ord_less_eq_int (bit1 pls)) Y_25))).
% 2.38/2.77 Axiom fact_86_le__special_I2_J:(forall (Y_25:int), ((iff ((ord_less_eq_int one_one_int) (number_number_of_int Y_25))) ((ord_less_eq_int (bit1 pls)) Y_25))).
% 2.38/2.77 Axiom fact_87_nat__1__add__1:(((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))).
% 2.38/2.77 Axiom fact_88_mult__Pls:(forall (W:int), (((eq int) ((times_times_int pls) W)) pls)).
% 2.38/2.77 Axiom fact_89_mult__Bit0:(forall (K:int) (L:int), (((eq int) ((times_times_int (bit0 K)) L)) (bit0 ((times_times_int K) L)))).
% 2.38/2.77 Axiom fact_90_less__number__of__int__code:(forall (K:int) (L:int), ((iff ((ord_less_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_int K) L))).
% 2.38/2.77 Axiom fact_91_zmult__1__right:(forall (Z:int), (((eq int) ((times_times_int Z) one_one_int)) Z)).
% 2.38/2.77 Axiom fact_92_zmult__1:(forall (Z:int), (((eq int) ((times_times_int one_one_int) Z)) Z)).
% 2.38/2.77 Axiom fact_93_plus__numeral__code_I9_J:(forall (V:int) (W:int), (((eq int) ((plus_plus_int (number_number_of_int V)) (number_number_of_int W))) (number_number_of_int ((plus_plus_int V) W)))).
% 2.38/2.77 Axiom fact_94_zadd__zmult__distrib:(forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((plus_plus_int Z1) Z2)) W)) ((plus_plus_int ((times_times_int Z1) W)) ((times_times_int Z2) W)))).
% 2.38/2.77 Axiom fact_95_zadd__zmult__distrib2:(forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((plus_plus_int Z1) Z2))) ((plus_plus_int ((times_times_int W) Z1)) ((times_times_int W) Z2)))).
% 2.38/2.77 Axiom fact_96_rel__simps_I29_J:(forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls))).
% 2.38/2.77 Axiom fact_97_rel__simps_I5_J:(forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K))).
% 2.38/2.77 Axiom fact_98_less__eq__int__code_I15_J:(forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2))).
% 2.38/2.77 Axiom fact_99_rel__simps_I33_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))).
% 2.38/2.77 Axiom fact_100_less__int__code_I14_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))).
% 2.38/2.77 Axiom fact_101_mem__def:(forall (X_32:int) (A_126:(int->Prop)), ((iff ((member_int X_32) A_126)) (A_126 X_32))).
% 2.38/2.77 Axiom fact_102_Collect__def:(forall (P_6:(int->Prop)), (((eq (int->Prop)) (collect_int P_6)) P_6)).
% 2.38/2.77 Axiom fact_103_rel__simps_I15_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))).
% 2.38/2.77 Axiom fact_104_less__nat__number__of:(forall (V:int) (V_2:int), ((iff ((ord_less_nat (number_number_of_nat V)) (number_number_of_nat V_2))) ((and (((ord_less_int V) V_2)->((ord_less_int pls) V_2))) ((ord_less_int V) V_2)))).
% 2.38/2.77 Axiom fact_105_int__one__le__iff__zero__less:(forall (Z:int), ((iff ((ord_less_eq_int one_one_int) Z)) ((ord_less_int zero_zero_int) Z))).
% 2.38/2.77 Axiom fact_106_nat__numeral__1__eq__1:(((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat).
% 2.38/2.77 Axiom fact_107_Numeral1__eq1__nat:(((eq nat) one_one_nat) (number_number_of_nat (bit1 pls))).
% 2.38/2.77 Axiom fact_108_zless__imp__add1__zle:(forall (W:int) (Z:int), (((ord_less_int W) Z)->((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z))).
% 2.38/2.77 Axiom fact_109_add1__zle__eq:(forall (W:int) (Z:int), ((iff ((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z)) ((ord_less_int W) Z))).
% 2.38/2.77 Axiom fact_110_zle__add1__eq__le:(forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((ord_less_eq_int W) Z))).
% 2.38/2.77 Axiom fact_111_semiring__add__number__of:(forall (V_9:int) (V_8:int), (((ord_less_eq_int pls) V_8)->(((ord_less_eq_int pls) V_9)->(((eq real) ((plus_plus_real (number267125858f_real V_8)) (number267125858f_real V_9))) (number267125858f_real ((plus_plus_int V_8) V_9)))))).
% 2.38/2.77 Axiom fact_112_semiring__add__number__of:(forall (V_9:int) (V_8:int), (((ord_less_eq_int pls) V_8)->(((ord_less_eq_int pls) V_9)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_8)) (number_number_of_nat V_9))) (number_number_of_nat ((plus_plus_int V_8) V_9)))))).
% 2.38/2.77 Axiom fact_113_semiring__add__number__of:(forall (V_9:int) (V_8:int), (((ord_less_eq_int pls) V_8)->(((ord_less_eq_int pls) V_9)->(((eq int) ((plus_plus_int (number_number_of_int V_8)) (number_number_of_int V_9))) (number_number_of_int ((plus_plus_int V_8) V_9)))))).
% 2.38/2.77 Axiom fact_114_add__nat__number__of:(forall (V_2:int) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_2))) (number_number_of_nat V_2)))) ((((ord_less_int V) pls)->False)->((and (((ord_less_int V_2) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_2))) (number_number_of_nat V)))) ((((ord_less_int V_2) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_2))) (number_number_of_nat ((plus_plus_int V) V_2)))))))).
% 2.38/2.77 Axiom fact_115_le__imp__0__less:(forall (Z:int), (((ord_less_eq_int zero_zero_int) Z)->((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) Z)))).
% 2.38/2.77 Axiom fact_116_eq__number__of:(forall (X_31:int) (Y_24:int), ((iff (((eq real) (number267125858f_real X_31)) (number267125858f_real Y_24))) (((eq int) X_31) Y_24))).
% 2.38/2.77 Axiom fact_117_eq__number__of:(forall (X_31:int) (Y_24:int), ((iff (((eq int) (number_number_of_int X_31)) (number_number_of_int Y_24))) (((eq int) X_31) Y_24))).
% 2.38/2.77 Axiom fact_118_number__of__reorient:(forall (W_11:int) (X_30:real), ((iff (((eq real) (number267125858f_real W_11)) X_30)) (((eq real) X_30) (number267125858f_real W_11)))).
% 2.38/2.77 Axiom fact_119_number__of__reorient:(forall (W_11:int) (X_30:int), ((iff (((eq int) (number_number_of_int W_11)) X_30)) (((eq int) X_30) (number_number_of_int W_11)))).
% 2.38/2.77 Axiom fact_120_number__of__reorient:(forall (W_11:int) (X_30:nat), ((iff (((eq nat) (number_number_of_nat W_11)) X_30)) (((eq nat) X_30) (number_number_of_nat W_11)))).
% 2.38/2.77 Axiom fact_121_rel__simps_I51_J:(forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L))).
% 2.38/2.77 Axiom fact_122_rel__simps_I48_J:(forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L))).
% 2.38/2.77 Axiom fact_123_zless__linear:(forall (X:int) (Y:int), ((or ((or ((ord_less_int X) Y)) (((eq int) X) Y))) ((ord_less_int Y) X))).
% 2.38/2.77 Axiom fact_124_sum__squares__eq__zero__iff:(forall (X_29:real) (Y_23:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X_29) X_29)) ((times_times_real Y_23) Y_23))) zero_zero_real)) ((and (((eq real) X_29) zero_zero_real)) (((eq real) Y_23) zero_zero_real)))).
% 2.38/2.77 Axiom fact_125_sum__squares__eq__zero__iff:(forall (X_29:int) (Y_23:int), ((iff (((eq int) ((plus_plus_int ((times_times_int X_29) X_29)) ((times_times_int Y_23) Y_23))) zero_zero_int)) ((and (((eq int) X_29) zero_zero_int)) (((eq int) Y_23) zero_zero_int)))).
% 2.38/2.77 Axiom fact_126_left__distrib__number__of:(forall (A_125:real) (B_80:real) (V_7:int), (((eq real) ((times_times_real ((plus_plus_real A_125) B_80)) (number267125858f_real V_7))) ((plus_plus_real ((times_times_real A_125) (number267125858f_real V_7))) ((times_times_real B_80) (number267125858f_real V_7))))).
% 2.38/2.77 Axiom fact_127_left__distrib__number__of:(forall (A_125:nat) (B_80:nat) (V_7:int), (((eq nat) ((times_times_nat ((plus_plus_nat A_125) B_80)) (number_number_of_nat V_7))) ((plus_plus_nat ((times_times_nat A_125) (number_number_of_nat V_7))) ((times_times_nat B_80) (number_number_of_nat V_7))))).
% 2.38/2.77 Axiom fact_128_left__distrib__number__of:(forall (A_125:int) (B_80:int) (V_7:int), (((eq int) ((times_times_int ((plus_plus_int A_125) B_80)) (number_number_of_int V_7))) ((plus_plus_int ((times_times_int A_125) (number_number_of_int V_7))) ((times_times_int B_80) (number_number_of_int V_7))))).
% 2.38/2.77 Axiom fact_129_right__distrib__number__of:(forall (V_6:int) (B_79:real) (C_50:real), (((eq real) ((times_times_real (number267125858f_real V_6)) ((plus_plus_real B_79) C_50))) ((plus_plus_real ((times_times_real (number267125858f_real V_6)) B_79)) ((times_times_real (number267125858f_real V_6)) C_50)))).
% 2.38/2.77 Axiom fact_130_right__distrib__number__of:(forall (V_6:int) (B_79:nat) (C_50:nat), (((eq nat) ((times_times_nat (number_number_of_nat V_6)) ((plus_plus_nat B_79) C_50))) ((plus_plus_nat ((times_times_nat (number_number_of_nat V_6)) B_79)) ((times_times_nat (number_number_of_nat V_6)) C_50)))).
% 2.38/2.77 Axiom fact_131_right__distrib__number__of:(forall (V_6:int) (B_79:int) (C_50:int), (((eq int) ((times_times_int (number_number_of_int V_6)) ((plus_plus_int B_79) C_50))) ((plus_plus_int ((times_times_int (number_number_of_int V_6)) B_79)) ((times_times_int (number_number_of_int V_6)) C_50)))).
% 2.38/2.77 Axiom fact_132_zadd__assoc:(forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((plus_plus_int ((plus_plus_int Z1) Z2)) Z3)) ((plus_plus_int Z1) ((plus_plus_int Z2) Z3)))).
% 2.38/2.77 Axiom fact_133_zadd__left__commute:(forall (X:int) (Y:int) (Z:int), (((eq int) ((plus_plus_int X) ((plus_plus_int Y) Z))) ((plus_plus_int Y) ((plus_plus_int X) Z)))).
% 2.38/2.77 Axiom fact_134_zadd__commute:(forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z))).
% 2.38/2.77 Axiom fact_135_zero__is__num__zero:(((eq int) zero_zero_int) (number_number_of_int pls)).
% 2.38/2.77 Axiom fact_136_zmult__zless__mono2:(forall (K:int) (I_1:int) (J_1:int), (((ord_less_int I_1) J_1)->(((ord_less_int zero_zero_int) K)->((ord_less_int ((times_times_int K) I_1)) ((times_times_int K) J_1))))).
% 2.38/2.77 Axiom fact_137_power2__eq__imp__eq:(forall (X_28:real) (Y_22:real), ((((eq real) ((power_power_real X_28) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_22) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) X_28)->(((ord_less_eq_real zero_zero_real) Y_22)->(((eq real) X_28) Y_22))))).
% 2.38/2.77 Axiom fact_138_power2__eq__imp__eq:(forall (X_28:nat) (Y_22:nat), ((((eq nat) ((power_power_nat X_28) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_22) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) X_28)->(((ord_less_eq_nat zero_zero_nat) Y_22)->(((eq nat) X_28) Y_22))))).
% 2.38/2.77 Axiom fact_139_power2__eq__imp__eq:(forall (X_28:int) (Y_22:int), ((((eq int) ((power_power_int X_28) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_22) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) X_28)->(((ord_less_eq_int zero_zero_int) Y_22)->(((eq int) X_28) Y_22))))).
% 2.38/2.77 Axiom fact_140_power2__le__imp__le:(forall (X_27:real) (Y_21:real), (((ord_less_eq_real ((power_power_real X_27) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_21) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_21)->((ord_less_eq_real X_27) Y_21)))).
% 2.38/2.77 Axiom fact_141_power2__le__imp__le:(forall (X_27:nat) (Y_21:nat), (((ord_less_eq_nat ((power_power_nat X_27) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_21) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_21)->((ord_less_eq_nat X_27) Y_21)))).
% 2.38/2.77 Axiom fact_142_power2__le__imp__le:(forall (X_27:int) (Y_21:int), (((ord_less_eq_int ((power_power_int X_27) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_21) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_21)->((ord_less_eq_int X_27) Y_21)))).
% 2.38/2.77 Axiom fact_143_zero__le__power2:(forall (A_124:real), ((ord_less_eq_real zero_zero_real) ((power_power_real A_124) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.38/2.77 Axiom fact_144_zero__le__power2:(forall (A_124:int), ((ord_less_eq_int zero_zero_int) ((power_power_int A_124) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.38/2.77 Axiom fact_145_power2__less__imp__less:(forall (X_26:real) (Y_20:real), (((ord_less_real ((power_power_real X_26) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_20) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_20)->((ord_less_real X_26) Y_20)))).
% 2.38/2.77 Axiom fact_146_power2__less__imp__less:(forall (X_26:nat) (Y_20:nat), (((ord_less_nat ((power_power_nat X_26) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_20) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_20)->((ord_less_nat X_26) Y_20)))).
% 2.38/2.77 Axiom fact_147_power2__less__imp__less:(forall (X_26:int) (Y_20:int), (((ord_less_int ((power_power_int X_26) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_20) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_20)->((ord_less_int X_26) Y_20)))).
% 2.38/2.77 Axiom fact_148_sum__power2__le__zero__iff:(forall (X_25:real) (Y_19:real), ((iff ((ord_less_eq_real ((plus_plus_real ((power_power_real X_25) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_19) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_25) zero_zero_real)) (((eq real) Y_19) zero_zero_real)))).
% 2.38/2.77 Axiom fact_149_sum__power2__le__zero__iff:(forall (X_25:int) (Y_19:int), ((iff ((ord_less_eq_int ((plus_plus_int ((power_power_int X_25) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_19) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_25) zero_zero_int)) (((eq int) Y_19) zero_zero_int)))).
% 2.38/2.77 Axiom fact_150_sum__power2__ge__zero:(forall (X_24:real) (Y_18:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((power_power_real X_24) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_18) (number_number_of_nat (bit0 (bit1 pls))))))).
% 2.38/2.77 Axiom fact_151_sum__power2__ge__zero:(forall (X_24:int) (Y_18:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((power_power_int X_24) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_18) (number_number_of_nat (bit0 (bit1 pls))))))).
% 2.38/2.77 Axiom fact_152_sum__squares__gt__zero__iff:(forall (X_23:real) (Y_17:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((times_times_real X_23) X_23)) ((times_times_real Y_17) Y_17)))) ((or (not (((eq real) X_23) zero_zero_real))) (not (((eq real) Y_17) zero_zero_real))))).
% 2.38/2.77 Axiom fact_153_sum__squares__gt__zero__iff:(forall (X_23:int) (Y_17:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((times_times_int X_23) X_23)) ((times_times_int Y_17) Y_17)))) ((or (not (((eq int) X_23) zero_zero_int))) (not (((eq int) Y_17) zero_zero_int))))).
% 2.38/2.77 Axiom fact_154_not__sum__squares__lt__zero:(forall (X_22:real) (Y_16:real), (((ord_less_real ((plus_plus_real ((times_times_real X_22) X_22)) ((times_times_real Y_16) Y_16))) zero_zero_real)->False)).
% 2.38/2.77 Axiom fact_155_not__sum__squares__lt__zero:(forall (X_22:int) (Y_16:int), (((ord_less_int ((plus_plus_int ((times_times_int X_22) X_22)) ((times_times_int Y_16) Y_16))) zero_zero_int)->False)).
% 2.38/2.77 Axiom fact_156_mult__numeral__1:(forall (A_123:real), (((eq real) ((times_times_real (number267125858f_real (bit1 pls))) A_123)) A_123)).
% 2.38/2.77 Axiom fact_157_mult__numeral__1:(forall (A_123:int), (((eq int) ((times_times_int (number_number_of_int (bit1 pls))) A_123)) A_123)).
% 2.38/2.77 Axiom fact_158_mult__numeral__1__right:(forall (A_122:real), (((eq real) ((times_times_real A_122) (number267125858f_real (bit1 pls)))) A_122)).
% 2.38/2.77 Axiom fact_159_mult__numeral__1__right:(forall (A_122:int), (((eq int) ((times_times_int A_122) (number_number_of_int (bit1 pls)))) A_122)).
% 2.38/2.77 Axiom fact_160_one__is__num__one:(((eq int) one_one_int) (number_number_of_int (bit1 pls))).
% 2.38/2.77 Axiom fact_161_mult__Bit1:(forall (K:int) (L:int), (((eq int) ((times_times_int (bit1 K)) L)) ((plus_plus_int (bit0 ((times_times_int K) L))) L))).
% 2.38/2.77 Axiom fact_162_pos__zmult__eq__1__iff:(forall (N:int) (M:int), (((ord_less_int zero_zero_int) M)->((iff (((eq int) ((times_times_int M) N)) one_one_int)) ((and (((eq int) M) one_one_int)) (((eq int) N) one_one_int))))).
% 2.38/2.77 Axiom fact_163_double__eq__0__iff:(forall (A_121:real), ((iff (((eq real) ((plus_plus_real A_121) A_121)) zero_zero_real)) (((eq real) A_121) zero_zero_real))).
% 2.38/2.77 Axiom fact_164_double__eq__0__iff:(forall (A_121:int), ((iff (((eq int) ((plus_plus_int A_121) A_121)) zero_zero_int)) (((eq int) A_121) zero_zero_int))).
% 2.38/2.77 Axiom fact_165_rel__simps_I46_J:(forall (K:int), (not (((eq int) (bit1 K)) pls))).
% 2.38/2.77 Axiom fact_166_rel__simps_I39_J:(forall (L:int), (not (((eq int) pls) (bit1 L)))).
% 2.38/2.77 Axiom fact_167_rel__simps_I50_J:(forall (K:int) (L:int), (not (((eq int) (bit1 K)) (bit0 L)))).
% 2.38/2.77 Axiom fact_168_rel__simps_I49_J:(forall (K:int) (L:int), (not (((eq int) (bit0 K)) (bit1 L)))).
% 2.38/2.77 Axiom fact_169_rel__simps_I44_J:(forall (K:int), ((iff (((eq int) (bit0 K)) pls)) (((eq int) K) pls))).
% 2.38/2.77 Axiom fact_170_rel__simps_I38_J:(forall (L:int), ((iff (((eq int) pls) (bit0 L))) (((eq int) pls) L))).
% 2.38/2.77 Axiom fact_171_Bit0__Pls:(((eq int) (bit0 pls)) pls).
% 2.38/2.77 Axiom fact_172_Pls__def:(((eq int) pls) zero_zero_int).
% 2.38/2.77 Axiom fact_173_less__int__code_I16_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2))).
% 2.38/2.77 Axiom fact_174_rel__simps_I17_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L))).
% 2.38/2.77 Axiom fact_175_rel__simps_I2_J:(((ord_less_int pls) pls)->False).
% 2.38/2.77 Axiom fact_176_less__int__code_I13_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit0 K2))) ((ord_less_int K1) K2))).
% 2.38/2.78 Axiom fact_177_rel__simps_I14_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit0 L))) ((ord_less_int K) L))).
% 2.38/2.78 Axiom fact_178_int__0__neq__1:(not (((eq int) zero_zero_int) one_one_int)).
% 2.38/2.78 Axiom fact_179_add__Pls__right:(forall (K:int), (((eq int) ((plus_plus_int K) pls)) K)).
% 2.38/2.78 Axiom fact_180_add__Pls:(forall (K:int), (((eq int) ((plus_plus_int pls) K)) K)).
% 2.38/2.78 Axiom fact_181_add__Bit0__Bit0:(forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit0 L))) (bit0 ((plus_plus_int K) L)))).
% 2.38/2.78 Axiom fact_182_Bit0__def:(forall (K:int), (((eq int) (bit0 K)) ((plus_plus_int K) K))).
% 2.38/2.78 Axiom fact_183_zadd__0__right:(forall (Z:int), (((eq int) ((plus_plus_int Z) zero_zero_int)) Z)).
% 2.38/2.78 Axiom fact_184_zadd__0:(forall (Z:int), (((eq int) ((plus_plus_int zero_zero_int) Z)) Z)).
% 2.38/2.78 Axiom fact_185_zadd__strict__right__mono:(forall (K:int) (I_1:int) (J_1:int), (((ord_less_int I_1) J_1)->((ord_less_int ((plus_plus_int I_1) K)) ((plus_plus_int J_1) K)))).
% 2.38/2.78 Axiom fact_186_double__number__of__Bit0:(forall (W_10:int), (((eq real) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real W_10))) (number267125858f_real (bit0 W_10)))).
% 2.38/2.78 Axiom fact_187_double__number__of__Bit0:(forall (W_10:int), (((eq int) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int W_10))) (number_number_of_int (bit0 W_10)))).
% 2.38/2.78 Axiom fact_188_power3__eq__cube:(forall (A_120:real), (((eq real) ((power_power_real A_120) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_real ((times_times_real A_120) A_120)) A_120))).
% 2.38/2.78 Axiom fact_189_power3__eq__cube:(forall (A_120:nat), (((eq nat) ((power_power_nat A_120) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_nat ((times_times_nat A_120) A_120)) A_120))).
% 2.38/2.78 Axiom fact_190_power3__eq__cube:(forall (A_120:int), (((eq int) ((power_power_int A_120) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int A_120) A_120)) A_120))).
% 2.38/2.78 Axiom fact_191_semiring__mult__2:(forall (Z_7:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_7)) ((plus_plus_real Z_7) Z_7))).
% 2.38/2.78 Axiom fact_192_semiring__mult__2:(forall (Z_7:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z_7)) ((plus_plus_nat Z_7) Z_7))).
% 2.38/2.78 Axiom fact_193_semiring__mult__2:(forall (Z_7:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_7)) ((plus_plus_int Z_7) Z_7))).
% 2.38/2.78 Axiom fact_194_mult__2:(forall (Z_6:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_6)) ((plus_plus_real Z_6) Z_6))).
% 2.38/2.78 Axiom fact_195_mult__2:(forall (Z_6:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_6)) ((plus_plus_int Z_6) Z_6))).
% 2.38/2.78 Axiom fact_196_semiring__mult__2__right:(forall (Z_5:real), (((eq real) ((times_times_real Z_5) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_5) Z_5))).
% 2.38/2.78 Axiom fact_197_semiring__mult__2__right:(forall (Z_5:nat), (((eq nat) ((times_times_nat Z_5) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z_5) Z_5))).
% 2.38/2.78 Axiom fact_198_semiring__mult__2__right:(forall (Z_5:int), (((eq int) ((times_times_int Z_5) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_5) Z_5))).
% 2.38/2.78 Axiom fact_199_mult__2__right:(forall (Z_4:real), (((eq real) ((times_times_real Z_4) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_4) Z_4))).
% 2.38/2.78 Axiom fact_200_mult__2__right:(forall (Z_4:int), (((eq int) ((times_times_int Z_4) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_4) Z_4))).
% 2.38/2.78 Axiom fact_201_power2__eq__square:(forall (A_119:real), (((eq real) ((power_power_real A_119) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real A_119) A_119))).
% 2.38/2.78 Axiom fact_202_power2__eq__square:(forall (A_119:nat), (((eq nat) ((power_power_nat A_119) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat A_119) A_119))).
% 2.38/2.78 Axiom fact_203_power2__eq__square:(forall (A_119:int), (((eq int) ((power_power_int A_119) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int A_119) A_119))).
% 2.38/2.78 Axiom fact_204_even__less__0__iff:(forall (A_118:real), ((iff ((ord_less_real ((plus_plus_real A_118) A_118)) zero_zero_real)) ((ord_less_real A_118) zero_zero_real))).
% 2.38/2.78 Axiom fact_205_even__less__0__iff:(forall (A_118:int), ((iff ((ord_less_int ((plus_plus_int A_118) A_118)) zero_zero_int)) ((ord_less_int A_118) zero_zero_int))).
% 2.38/2.78 Axiom fact_206_semiring__numeral__0__eq__0:(((eq real) (number267125858f_real pls)) zero_zero_real).
% 2.38/2.78 Axiom fact_207_semiring__numeral__0__eq__0:(((eq nat) (number_number_of_nat pls)) zero_zero_nat).
% 2.38/2.78 Axiom fact_208_semiring__numeral__0__eq__0:(((eq int) (number_number_of_int pls)) zero_zero_int).
% 2.38/2.78 Axiom fact_209_number__of__Pls:(((eq real) (number267125858f_real pls)) zero_zero_real).
% 2.38/2.78 Axiom fact_210_number__of__Pls:(((eq int) (number_number_of_int pls)) zero_zero_int).
% 2.38/2.78 Axiom fact_211_semiring__norm_I112_J:(((eq real) zero_zero_real) (number267125858f_real pls)).
% 2.38/2.78 Axiom fact_212_semiring__norm_I112_J:(((eq int) zero_zero_int) (number_number_of_int pls)).
% 2.38/2.78 Axiom fact_213_add__numeral__0:(forall (A_117:real), (((eq real) ((plus_plus_real (number267125858f_real pls)) A_117)) A_117)).
% 2.38/2.78 Axiom fact_214_add__numeral__0:(forall (A_117:int), (((eq int) ((plus_plus_int (number_number_of_int pls)) A_117)) A_117)).
% 2.38/2.78 Axiom fact_215_add__numeral__0__right:(forall (A_116:real), (((eq real) ((plus_plus_real A_116) (number267125858f_real pls))) A_116)).
% 2.38/2.78 Axiom fact_216_add__numeral__0__right:(forall (A_116:int), (((eq int) ((plus_plus_int A_116) (number_number_of_int pls))) A_116)).
% 2.38/2.78 Axiom fact_217_less__number__of:(forall (X_21:int) (Y_15:int), ((iff ((ord_less_real (number267125858f_real X_21)) (number267125858f_real Y_15))) ((ord_less_int X_21) Y_15))).
% 2.38/2.78 Axiom fact_218_less__number__of:(forall (X_21:int) (Y_15:int), ((iff ((ord_less_int (number_number_of_int X_21)) (number_number_of_int Y_15))) ((ord_less_int X_21) Y_15))).
% 2.38/2.78 Axiom fact_219_add__number__of__left:(forall (V_5:int) (W_9:int) (Z_3:real), (((eq real) ((plus_plus_real (number267125858f_real V_5)) ((plus_plus_real (number267125858f_real W_9)) Z_3))) ((plus_plus_real (number267125858f_real ((plus_plus_int V_5) W_9))) Z_3))).
% 2.38/2.78 Axiom fact_220_add__number__of__left:(forall (V_5:int) (W_9:int) (Z_3:int), (((eq int) ((plus_plus_int (number_number_of_int V_5)) ((plus_plus_int (number_number_of_int W_9)) Z_3))) ((plus_plus_int (number_number_of_int ((plus_plus_int V_5) W_9))) Z_3))).
% 2.38/2.78 Axiom fact_221_add__number__of__eq:(forall (V_4:int) (W_8:int), (((eq real) ((plus_plus_real (number267125858f_real V_4)) (number267125858f_real W_8))) (number267125858f_real ((plus_plus_int V_4) W_8)))).
% 2.38/2.78 Axiom fact_222_add__number__of__eq:(forall (V_4:int) (W_8:int), (((eq int) ((plus_plus_int (number_number_of_int V_4)) (number_number_of_int W_8))) (number_number_of_int ((plus_plus_int V_4) W_8)))).
% 2.38/2.78 Axiom fact_223_number__of__add:(forall (V_3:int) (W_7:int), (((eq real) (number267125858f_real ((plus_plus_int V_3) W_7))) ((plus_plus_real (number267125858f_real V_3)) (number267125858f_real W_7)))).
% 2.38/2.78 Axiom fact_224_number__of__add:(forall (V_3:int) (W_7:int), (((eq int) (number_number_of_int ((plus_plus_int V_3) W_7))) ((plus_plus_int (number_number_of_int V_3)) (number_number_of_int W_7)))).
% 2.38/2.78 Axiom fact_225_rel__simps_I12_J:(forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls))).
% 2.38/2.78 Axiom fact_226_less__int__code_I15_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2))).
% 2.38/2.78 Axiom fact_227_rel__simps_I16_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))).
% 2.38/2.78 Axiom fact_228_bin__less__0__simps_I4_J:(forall (W:int), ((iff ((ord_less_int (bit1 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int))).
% 2.38/2.78 Axiom fact_229_rel__simps_I10_J:(forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls))).
% 2.38/2.78 Axiom fact_230_rel__simps_I4_J:(forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K))).
% 2.38/2.78 Axiom fact_231_bin__less__0__simps_I1_J:(((ord_less_int pls) zero_zero_int)->False).
% 2.38/2.78 Axiom fact_232_bin__less__0__simps_I3_J:(forall (W:int), ((iff ((ord_less_int (bit0 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int))).
% 2.38/2.78 Axiom fact_233_add__Bit1__Bit0:(forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit0 L))) (bit1 ((plus_plus_int K) L)))).
% 2.38/2.78 Axiom fact_234_add__Bit0__Bit1:(forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit1 L))) (bit1 ((plus_plus_int K) L)))).
% 2.38/2.78 Axiom fact_235_int__0__less__1:((ord_less_int zero_zero_int) one_one_int).
% 2.38/2.78 Axiom fact_236_Bit1__def:(forall (K:int), (((eq int) (bit1 K)) ((plus_plus_int ((plus_plus_int one_one_int) K)) K))).
% 2.38/2.78 Axiom fact_237_odd__nonzero:(forall (Z:int), (not (((eq int) ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int))).
% 2.38/2.78 Axiom fact_238_zless__add1__eq:(forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((or ((ord_less_int W) Z)) (((eq int) W) Z)))).
% 2.38/2.78 Axiom fact_239_power2__eq__square__number__of:(forall (W_6:int), (((eq real) ((power_power_real (number267125858f_real W_6)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real (number267125858f_real W_6)) (number267125858f_real W_6)))).
% 2.38/2.78 Axiom fact_240_power2__eq__square__number__of:(forall (W_6:int), (((eq nat) ((power_power_nat (number_number_of_nat W_6)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat (number_number_of_nat W_6)) (number_number_of_nat W_6)))).
% 2.38/2.78 Axiom fact_241_power2__eq__square__number__of:(forall (W_6:int), (((eq int) ((power_power_int (number_number_of_int W_6)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int (number_number_of_int W_6)) (number_number_of_int W_6)))).
% 2.38/2.78 Axiom fact_242_power2__sum:(forall (X_20:real) (Y_14:real), (((eq real) ((power_power_real ((plus_plus_real X_20) Y_14)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X_20) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_14) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_20)) Y_14)))).
% 2.38/2.78 Axiom fact_243_power2__sum:(forall (X_20:nat) (Y_14:nat), (((eq nat) ((power_power_nat ((plus_plus_nat X_20) Y_14)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat ((plus_plus_nat ((power_power_nat X_20) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_14) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) X_20)) Y_14)))).
% 2.38/2.78 Axiom fact_244_power2__sum:(forall (X_20:int) (Y_14:int), (((eq int) ((power_power_int ((plus_plus_int X_20) Y_14)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int X_20) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_14) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) X_20)) Y_14)))).
% 2.38/2.78 Axiom fact_245_number__of__Bit0:(forall (W_5:int), (((eq real) (number267125858f_real (bit0 W_5))) ((plus_plus_real ((plus_plus_real zero_zero_real) (number267125858f_real W_5))) (number267125858f_real W_5)))).
% 2.38/2.78 Axiom fact_246_number__of__Bit0:(forall (W_5:int), (((eq int) (number_number_of_int (bit0 W_5))) ((plus_plus_int ((plus_plus_int zero_zero_int) (number_number_of_int W_5))) (number_number_of_int W_5)))).
% 2.38/2.78 Axiom fact_247_number__of__Bit1:(forall (W_4:int), (((eq real) (number267125858f_real (bit1 W_4))) ((plus_plus_real ((plus_plus_real one_one_real) (number267125858f_real W_4))) (number267125858f_real W_4)))).
% 2.38/2.78 Axiom fact_248_number__of__Bit1:(forall (W_4:int), (((eq int) (number_number_of_int (bit1 W_4))) ((plus_plus_int ((plus_plus_int one_one_int) (number_number_of_int W_4))) (number_number_of_int W_4)))).
% 2.38/2.78 Axiom fact_249_semiring__numeral__1__eq__1:(((eq real) (number267125858f_real (bit1 pls))) one_one_real).
% 2.38/2.78 Axiom fact_250_semiring__numeral__1__eq__1:(((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat).
% 2.38/2.78 Axiom fact_251_semiring__numeral__1__eq__1:(((eq int) (number_number_of_int (bit1 pls))) one_one_int).
% 2.38/2.78 Axiom fact_252_numeral__1__eq__1:(((eq real) (number267125858f_real (bit1 pls))) one_one_real).
% 2.38/2.78 Axiom fact_253_numeral__1__eq__1:(((eq int) (number_number_of_int (bit1 pls))) one_one_int).
% 2.38/2.78 Axiom fact_254_semiring__norm_I110_J:(((eq real) one_one_real) (number267125858f_real (bit1 pls))).
% 2.38/2.78 Axiom fact_255_semiring__norm_I110_J:(((eq int) one_one_int) (number_number_of_int (bit1 pls))).
% 2.38/2.78 Axiom fact_256_odd__less__0:(forall (Z:int), ((iff ((ord_less_int ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int)) ((ord_less_int Z) zero_zero_int))).
% 2.38/2.78 Axiom fact_257_less__special_I3_J:(forall (X_19:int), ((iff ((ord_less_real (number267125858f_real X_19)) zero_zero_real)) ((ord_less_int X_19) pls))).
% 2.38/2.78 Axiom fact_258_less__special_I3_J:(forall (X_19:int), ((iff ((ord_less_int (number_number_of_int X_19)) zero_zero_int)) ((ord_less_int X_19) pls))).
% 2.38/2.78 Axiom fact_259_less__special_I1_J:(forall (Y_13:int), ((iff ((ord_less_real zero_zero_real) (number267125858f_real Y_13))) ((ord_less_int pls) Y_13))).
% 2.38/2.78 Axiom fact_260_less__special_I1_J:(forall (Y_13:int), ((iff ((ord_less_int zero_zero_int) (number_number_of_int Y_13))) ((ord_less_int pls) Y_13))).
% 2.38/2.78 Axiom fact_261_semiring__one__add__one__is__two:(((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))).
% 2.38/2.78 Axiom fact_262_semiring__one__add__one__is__two:(((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))).
% 2.38/2.78 Axiom fact_263_semiring__one__add__one__is__two:(((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))).
% 2.38/2.78 Axiom fact_264_one__add__one__is__two:(((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))).
% 2.38/2.78 Axiom fact_265_one__add__one__is__two:(((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))).
% 2.38/2.78 Axiom fact_266_less__special_I4_J:(forall (X_18:int), ((iff ((ord_less_real (number267125858f_real X_18)) one_one_real)) ((ord_less_int X_18) (bit1 pls)))).
% 2.38/2.78 Axiom fact_267_less__special_I4_J:(forall (X_18:int), ((iff ((ord_less_int (number_number_of_int X_18)) one_one_int)) ((ord_less_int X_18) (bit1 pls)))).
% 2.38/2.78 Axiom fact_268_less__special_I2_J:(forall (Y_12:int), ((iff ((ord_less_real one_one_real) (number267125858f_real Y_12))) ((ord_less_int (bit1 pls)) Y_12))).
% 2.38/2.78 Axiom fact_269_less__special_I2_J:(forall (Y_12:int), ((iff ((ord_less_int one_one_int) (number_number_of_int Y_12))) ((ord_less_int (bit1 pls)) Y_12))).
% 2.38/2.78 Axiom fact_270__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096:((dvd_dvd_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)).
% 2.38/2.78 Axiom fact_271_zadd__power3:(forall (A:int) (B:int), (((eq int) ((power_power_int ((plus_plus_int A) B)) (number_number_of_nat (bit1 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((plus_plus_int ((power_power_int A) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls)))))) B))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) A)) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))) ((power_power_int B) (number_number_of_nat (bit1 (bit1 pls))))))).
% 2.38/2.78 Axiom fact_272_zadd__power2:(forall (A:int) (B:int), (((eq int) ((power_power_int ((plus_plus_int A) B)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A)) B))) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))).
% 2.38/2.78 Axiom fact_273_int__pos__lt__two__imp__zero__or__one:(forall (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_int X) (number_number_of_int (bit0 (bit1 pls))))->((or (((eq int) X) zero_zero_int)) (((eq int) X) one_one_int))))).
% 2.38/2.78 Axiom fact_274_s0p:((and ((and ((ord_less_eq_int zero_zero_int) s)) ((ord_less_int s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))).
% 2.38/2.78 Axiom fact_275_cube__square:(forall (A:int), (((eq int) ((times_times_int A) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_int A) (number_number_of_nat (bit1 (bit1 pls)))))).
% 2.38/2.78 Axiom fact_276_power2__ge__self:(forall (X:int), ((ord_less_eq_int X) ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.38/2.78 Axiom fact_277_self__quotient__aux1:(forall (R:int) (Q:int) (A:int), (((ord_less_int zero_zero_int) A)->((((eq int) A) ((plus_plus_int R) ((times_times_int A) Q)))->(((ord_less_int R) A)->((ord_less_eq_int one_one_int) Q))))).
% 2.38/2.78 Axiom fact_278_self__quotient__aux2:(forall (R:int) (Q:int) (A:int), (((ord_less_int zero_zero_int) A)->((((eq int) A) ((plus_plus_int R) ((times_times_int A) Q)))->(((ord_less_eq_int zero_zero_int) R)->((ord_less_eq_int Q) one_one_int))))).
% 2.38/2.78 Axiom fact_279_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J:((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 (bit1 pls)))).
% 2.38/2.78 Axiom fact_280_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J:(forall (X_17:real) (N_25:nat), (((eq real) ((power_power_real X_17) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_25))) ((times_times_real ((power_power_real X_17) N_25)) ((power_power_real X_17) N_25)))).
% 2.38/2.78 Axiom fact_281_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J:(forall (X_17:nat) (N_25:nat), (((eq nat) ((power_power_nat X_17) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_25))) ((times_times_nat ((power_power_nat X_17) N_25)) ((power_power_nat X_17) N_25)))).
% 2.38/2.78 Axiom fact_282_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J:(forall (X_17:int) (N_25:nat), (((eq int) ((power_power_int X_17) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_25))) ((times_times_int ((power_power_int X_17) N_25)) ((power_power_int X_17) N_25)))).
% 2.38/2.78 Axiom fact_283_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J:(forall (X_16:real), (((eq real) ((times_times_real X_16) X_16)) ((power_power_real X_16) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.38/2.78 Axiom fact_284_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J:(forall (X_16:nat), (((eq nat) ((times_times_nat X_16) X_16)) ((power_power_nat X_16) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.38/2.78 Axiom fact_285_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J:(forall (X_16:int), (((eq int) ((times_times_int X_16) X_16)) ((power_power_int X_16) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.38/2.78 Axiom fact_286__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096:(((zcong ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int s1) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)).
% 2.38/2.78 Axiom fact_287__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1:((ex int) (fun (X_1:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X_1)) ((ord_less_int X_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) X_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (forall (Y_1:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y_1)) ((ord_less_int Y_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) Y_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))->(((eq int) Y_1) X_1)))))).
% 2.38/2.78 Axiom fact_288__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_:((forall (S_1:int), (((and ((and ((ord_less_eq_int zero_zero_int) S_1)) ((ord_less_int S_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) S_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))->False))->False).
% 2.38/2.78 Axiom fact_289_s1:(((zcong ((power_power_int s1) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)).
% 2.38/2.78 Axiom fact_290_zero__less__power__nat__eq:(forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or (((eq nat) N) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X)))).
% 2.38/2.78 Axiom fact_291_zprime__zdvd__power:(forall (A:int) (N:nat) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((power_power_int A) N))->((dvd_dvd_int P_1) A)))).
% 2.38/2.78 Axiom fact_292_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J:(forall (X_15:real) (P_5:nat) (Q_6:nat), (((eq real) ((power_power_real ((power_power_real X_15) P_5)) Q_6)) ((power_power_real X_15) ((times_times_nat P_5) Q_6)))).
% 2.38/2.78 Axiom fact_293_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J:(forall (X_15:nat) (P_5:nat) (Q_6:nat), (((eq nat) ((power_power_nat ((power_power_nat X_15) P_5)) Q_6)) ((power_power_nat X_15) ((times_times_nat P_5) Q_6)))).
% 2.38/2.78 Axiom fact_294_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J:(forall (X_15:int) (P_5:nat) (Q_6:nat), (((eq int) ((power_power_int ((power_power_int X_15) P_5)) Q_6)) ((power_power_int X_15) ((times_times_nat P_5) Q_6)))).
% 2.38/2.78 Axiom fact_295_zprime__power__zdvd__cancel__right:(forall (N:nat) (A:int) (B:int) (P_1:int), ((zprime P_1)->((((dvd_dvd_int P_1) B)->False)->(((dvd_dvd_int ((power_power_int P_1) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P_1) N)) A))))).
% 2.38/2.78 Axiom fact_296_zprime__power__zdvd__cancel__left:(forall (N:nat) (B:int) (A:int) (P_1:int), ((zprime P_1)->((((dvd_dvd_int P_1) A)->False)->(((dvd_dvd_int ((power_power_int P_1) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P_1) N)) B))))).
% 2.38/2.78 Axiom fact_297_zpower__zpower:(forall (X:int) (Y:nat) (Z:nat), (((eq int) ((power_power_int ((power_power_int X) Y)) Z)) ((power_power_int X) ((times_times_nat Y) Z)))).
% 2.38/2.78 Axiom fact_298_zdvd__not__zless:(forall (N:int) (M:int), (((ord_less_int zero_zero_int) M)->(((ord_less_int M) N)->(((dvd_dvd_int N) M)->False)))).
% 2.38/2.78 Axiom fact_299_zdvd__antisym__nonneg:(forall (N:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->(((ord_less_eq_int zero_zero_int) N)->(((dvd_dvd_int M) N)->(((dvd_dvd_int N) M)->(((eq int) M) N)))))).
% 2.38/2.78 Axiom fact_300_zdvd__mult__cancel:(forall (K:int) (M:int) (N:int), (((dvd_dvd_int ((times_times_int K) M)) ((times_times_int K) N))->((not (((eq int) K) zero_zero_int))->((dvd_dvd_int M) N)))).
% 2.38/2.78 Axiom fact_301_zdvd__reduce:(forall (K:int) (N:int) (M:int), ((iff ((dvd_dvd_int K) ((plus_plus_int N) ((times_times_int K) M)))) ((dvd_dvd_int K) N))).
% 2.38/2.78 Axiom fact_302_zdvd__period:(forall (C:int) (X:int) (T:int) (A:int) (D:int), (((dvd_dvd_int A) D)->((iff ((dvd_dvd_int A) ((plus_plus_int X) T))) ((dvd_dvd_int A) ((plus_plus_int ((plus_plus_int X) ((times_times_int C) D))) T))))).
% 2.38/2.78 Axiom fact_303_zprime__2:(zprime (number_number_of_int (bit0 (bit1 pls)))).
% 2.38/2.78 Axiom fact_304_zdvd__imp__le:(forall (Z:int) (N:int), (((dvd_dvd_int Z) N)->(((ord_less_int zero_zero_int) N)->((ord_less_eq_int Z) N)))).
% 2.38/2.78 Axiom fact_305_is__mult__sum2sq:(forall (Y:int) (X:int), ((twoSqu919416604sum2sq X)->((twoSqu919416604sum2sq Y)->(twoSqu919416604sum2sq ((times_times_int X) Y))))).
% 2.38/2.78 Axiom fact_306_le__nat__number__of:(forall (V:int) (V_2:int), ((iff ((ord_less_eq_nat (number_number_of_nat V)) (number_number_of_nat V_2))) ((((ord_less_eq_int V) V_2)->False)->((ord_less_eq_int V) pls)))).
% 2.38/2.78 Axiom fact_307_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J:(forall (Lx_6:real) (Ly_4:real) (Rx_6:real) (Ry_4:real), (((eq real) ((times_times_real ((times_times_real Lx_6) Ly_4)) ((times_times_real Rx_6) Ry_4))) ((times_times_real ((times_times_real Lx_6) Rx_6)) ((times_times_real Ly_4) Ry_4)))).
% 2.38/2.78 Axiom fact_308_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J:(forall (Lx_6:nat) (Ly_4:nat) (Rx_6:nat) (Ry_4:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_6) Ly_4)) ((times_times_nat Rx_6) Ry_4))) ((times_times_nat ((times_times_nat Lx_6) Rx_6)) ((times_times_nat Ly_4) Ry_4)))).
% 2.38/2.79 Axiom fact_309_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J:(forall (Lx_6:int) (Ly_4:int) (Rx_6:int) (Ry_4:int), (((eq int) ((times_times_int ((times_times_int Lx_6) Ly_4)) ((times_times_int Rx_6) Ry_4))) ((times_times_int ((times_times_int Lx_6) Rx_6)) ((times_times_int Ly_4) Ry_4)))).
% 2.38/2.79 Axiom fact_310_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J:(forall (Lx_5:real) (Ly_3:real) (Rx_5:real) (Ry_3:real), (((eq real) ((times_times_real ((times_times_real Lx_5) Ly_3)) ((times_times_real Rx_5) Ry_3))) ((times_times_real Rx_5) ((times_times_real ((times_times_real Lx_5) Ly_3)) Ry_3)))).
% 2.38/2.79 Axiom fact_311_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J:(forall (Lx_5:nat) (Ly_3:nat) (Rx_5:nat) (Ry_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) ((times_times_nat Rx_5) Ry_3))) ((times_times_nat Rx_5) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) Ry_3)))).
% 2.38/2.79 Axiom fact_312_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J:(forall (Lx_5:int) (Ly_3:int) (Rx_5:int) (Ry_3:int), (((eq int) ((times_times_int ((times_times_int Lx_5) Ly_3)) ((times_times_int Rx_5) Ry_3))) ((times_times_int Rx_5) ((times_times_int ((times_times_int Lx_5) Ly_3)) Ry_3)))).
% 2.38/2.79 Axiom fact_313_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J:(forall (Lx_4:real) (Ly_2:real) (Rx_4:real) (Ry_2:real), (((eq real) ((times_times_real ((times_times_real Lx_4) Ly_2)) ((times_times_real Rx_4) Ry_2))) ((times_times_real Lx_4) ((times_times_real Ly_2) ((times_times_real Rx_4) Ry_2))))).
% 2.38/2.79 Axiom fact_314_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J:(forall (Lx_4:nat) (Ly_2:nat) (Rx_4:nat) (Ry_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_4) Ly_2)) ((times_times_nat Rx_4) Ry_2))) ((times_times_nat Lx_4) ((times_times_nat Ly_2) ((times_times_nat Rx_4) Ry_2))))).
% 2.38/2.79 Axiom fact_315_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J:(forall (Lx_4:int) (Ly_2:int) (Rx_4:int) (Ry_2:int), (((eq int) ((times_times_int ((times_times_int Lx_4) Ly_2)) ((times_times_int Rx_4) Ry_2))) ((times_times_int Lx_4) ((times_times_int Ly_2) ((times_times_int Rx_4) Ry_2))))).
% 2.38/2.79 Axiom fact_316_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J:(forall (Lx_3:real) (Ly_1:real) (Rx_3:real), (((eq real) ((times_times_real ((times_times_real Lx_3) Ly_1)) Rx_3)) ((times_times_real ((times_times_real Lx_3) Rx_3)) Ly_1))).
% 2.38/2.79 Axiom fact_317_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J:(forall (Lx_3:nat) (Ly_1:nat) (Rx_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_3) Ly_1)) Rx_3)) ((times_times_nat ((times_times_nat Lx_3) Rx_3)) Ly_1))).
% 2.38/2.79 Axiom fact_318_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J:(forall (Lx_3:int) (Ly_1:int) (Rx_3:int), (((eq int) ((times_times_int ((times_times_int Lx_3) Ly_1)) Rx_3)) ((times_times_int ((times_times_int Lx_3) Rx_3)) Ly_1))).
% 2.38/2.79 Axiom fact_319_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J:(forall (Lx_2:real) (Ly:real) (Rx_2:real), (((eq real) ((times_times_real ((times_times_real Lx_2) Ly)) Rx_2)) ((times_times_real Lx_2) ((times_times_real Ly) Rx_2)))).
% 2.38/2.79 Axiom fact_320_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J:(forall (Lx_2:nat) (Ly:nat) (Rx_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_2) Ly)) Rx_2)) ((times_times_nat Lx_2) ((times_times_nat Ly) Rx_2)))).
% 2.38/2.79 Axiom fact_321_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J:(forall (Lx_2:int) (Ly:int) (Rx_2:int), (((eq int) ((times_times_int ((times_times_int Lx_2) Ly)) Rx_2)) ((times_times_int Lx_2) ((times_times_int Ly) Rx_2)))).
% 2.38/2.79 Axiom fact_322_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J:(forall (Lx_1:real) (Rx_1:real) (Ry_1:real), (((eq real) ((times_times_real Lx_1) ((times_times_real Rx_1) Ry_1))) ((times_times_real ((times_times_real Lx_1) Rx_1)) Ry_1))).
% 2.38/2.79 Axiom fact_323_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J:(forall (Lx_1:nat) (Rx_1:nat) (Ry_1:nat), (((eq nat) ((times_times_nat Lx_1) ((times_times_nat Rx_1) Ry_1))) ((times_times_nat ((times_times_nat Lx_1) Rx_1)) Ry_1))).
% 2.38/2.79 Axiom fact_324_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J:(forall (Lx_1:int) (Rx_1:int) (Ry_1:int), (((eq int) ((times_times_int Lx_1) ((times_times_int Rx_1) Ry_1))) ((times_times_int ((times_times_int Lx_1) Rx_1)) Ry_1))).
% 2.38/2.79 Axiom fact_325_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J:(forall (Lx:real) (Rx:real) (Ry:real), (((eq real) ((times_times_real Lx) ((times_times_real Rx) Ry))) ((times_times_real Rx) ((times_times_real Lx) Ry)))).
% 2.38/2.79 Axiom fact_326_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J:(forall (Lx:nat) (Rx:nat) (Ry:nat), (((eq nat) ((times_times_nat Lx) ((times_times_nat Rx) Ry))) ((times_times_nat Rx) ((times_times_nat Lx) Ry)))).
% 2.38/2.79 Axiom fact_327_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J:(forall (Lx:int) (Rx:int) (Ry:int), (((eq int) ((times_times_int Lx) ((times_times_int Rx) Ry))) ((times_times_int Rx) ((times_times_int Lx) Ry)))).
% 2.38/2.79 Axiom fact_328_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J:(forall (A_115:real) (B_78:real), (((eq real) ((times_times_real A_115) B_78)) ((times_times_real B_78) A_115))).
% 2.38/2.79 Axiom fact_329_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J:(forall (A_115:nat) (B_78:nat), (((eq nat) ((times_times_nat A_115) B_78)) ((times_times_nat B_78) A_115))).
% 2.38/2.79 Axiom fact_330_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J:(forall (A_115:int) (B_78:int), (((eq int) ((times_times_int A_115) B_78)) ((times_times_int B_78) A_115))).
% 2.38/2.79 Axiom fact_331_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A_114:real) (C_49:real), (((eq real) ((plus_plus_real A_114) C_49)) ((plus_plus_real C_49) A_114))).
% 2.38/2.79 Axiom fact_332_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A_114:nat) (C_49:nat), (((eq nat) ((plus_plus_nat A_114) C_49)) ((plus_plus_nat C_49) A_114))).
% 2.38/2.79 Axiom fact_333_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A_114:int) (C_49:int), (((eq int) ((plus_plus_int A_114) C_49)) ((plus_plus_int C_49) A_114))).
% 2.38/2.79 Axiom fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_113:real) (C_48:real) (D_14:real), (((eq real) ((plus_plus_real A_113) ((plus_plus_real C_48) D_14))) ((plus_plus_real C_48) ((plus_plus_real A_113) D_14)))).
% 2.38/2.79 Axiom fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_113:nat) (C_48:nat) (D_14:nat), (((eq nat) ((plus_plus_nat A_113) ((plus_plus_nat C_48) D_14))) ((plus_plus_nat C_48) ((plus_plus_nat A_113) D_14)))).
% 2.38/2.79 Axiom fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_113:int) (C_48:int) (D_14:int), (((eq int) ((plus_plus_int A_113) ((plus_plus_int C_48) D_14))) ((plus_plus_int C_48) ((plus_plus_int A_113) D_14)))).
% 2.38/2.79 Axiom fact_337_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_112:real) (C_47:real) (D_13:real), (((eq real) ((plus_plus_real A_112) ((plus_plus_real C_47) D_13))) ((plus_plus_real ((plus_plus_real A_112) C_47)) D_13))).
% 2.38/2.79 Axiom fact_338_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_112:nat) (C_47:nat) (D_13:nat), (((eq nat) ((plus_plus_nat A_112) ((plus_plus_nat C_47) D_13))) ((plus_plus_nat ((plus_plus_nat A_112) C_47)) D_13))).
% 2.38/2.79 Axiom fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_112:int) (C_47:int) (D_13:int), (((eq int) ((plus_plus_int A_112) ((plus_plus_int C_47) D_13))) ((plus_plus_int ((plus_plus_int A_112) C_47)) D_13))).
% 2.38/2.79 Axiom fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_111:real) (B_77:real) (C_46:real), (((eq real) ((plus_plus_real ((plus_plus_real A_111) B_77)) C_46)) ((plus_plus_real A_111) ((plus_plus_real B_77) C_46)))).
% 2.38/2.79 Axiom fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_111:nat) (B_77:nat) (C_46:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_111) B_77)) C_46)) ((plus_plus_nat A_111) ((plus_plus_nat B_77) C_46)))).
% 2.38/2.79 Axiom fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_111:int) (B_77:int) (C_46:int), (((eq int) ((plus_plus_int ((plus_plus_int A_111) B_77)) C_46)) ((plus_plus_int A_111) ((plus_plus_int B_77) C_46)))).
% 2.38/2.79 Axiom fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_110:real) (B_76:real) (C_45:real), (((eq real) ((plus_plus_real ((plus_plus_real A_110) B_76)) C_45)) ((plus_plus_real ((plus_plus_real A_110) C_45)) B_76))).
% 2.38/2.79 Axiom fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_110:nat) (B_76:nat) (C_45:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_110) B_76)) C_45)) ((plus_plus_nat ((plus_plus_nat A_110) C_45)) B_76))).
% 2.38/2.79 Axiom fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_110:int) (B_76:int) (C_45:int), (((eq int) ((plus_plus_int ((plus_plus_int A_110) B_76)) C_45)) ((plus_plus_int ((plus_plus_int A_110) C_45)) B_76))).
% 2.38/2.79 Axiom fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_109:real) (B_75:real) (C_44:real) (D_12:real), (((eq real) ((plus_plus_real ((plus_plus_real A_109) B_75)) ((plus_plus_real C_44) D_12))) ((plus_plus_real ((plus_plus_real A_109) C_44)) ((plus_plus_real B_75) D_12)))).
% 2.38/2.79 Axiom fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_109:nat) (B_75:nat) (C_44:nat) (D_12:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_109) B_75)) ((plus_plus_nat C_44) D_12))) ((plus_plus_nat ((plus_plus_nat A_109) C_44)) ((plus_plus_nat B_75) D_12)))).
% 2.38/2.79 Axiom fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_109:int) (B_75:int) (C_44:int) (D_12:int), (((eq int) ((plus_plus_int ((plus_plus_int A_109) B_75)) ((plus_plus_int C_44) D_12))) ((plus_plus_int ((plus_plus_int A_109) C_44)) ((plus_plus_int B_75) D_12)))).
% 2.38/2.79 Axiom fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J:(forall (X_14:real), (((eq real) ((power_power_real X_14) one_one_nat)) X_14)).
% 2.38/2.79 Axiom fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J:(forall (X_14:nat), (((eq nat) ((power_power_nat X_14) one_one_nat)) X_14)).
% 2.38/2.79 Axiom fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J:(forall (X_14:int), (((eq int) ((power_power_int X_14) one_one_nat)) X_14)).
% 2.38/2.79 Axiom fact_352_zero__less__power__nat__eq__number__of:(forall (X:nat) (W:int), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) (number_number_of_nat W)))) ((or (((eq nat) (number_number_of_nat W)) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X)))).
% 2.38/2.79 Axiom fact_353_nat__mult__2__right:(forall (Z:nat), (((eq nat) ((times_times_nat Z) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z) Z))).
% 2.38/2.79 Axiom fact_354_nat__mult__2:(forall (Z:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z)) ((plus_plus_nat Z) Z))).
% 2.38/2.79 Axiom fact_355_mult__nat__number__of:(forall (V_2:int) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((times_times_nat (number_number_of_nat V)) (number_number_of_nat V_2))) zero_zero_nat))) ((((ord_less_int V) pls)->False)->(((eq nat) ((times_times_nat (number_number_of_nat V)) (number_number_of_nat V_2))) (number_number_of_nat ((times_times_int V) V_2)))))).
% 2.38/2.79 Axiom fact_356_nat__number__of__mult__left:(forall (V_2:int) (K:nat) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((times_times_nat (number_number_of_nat V)) ((times_times_nat (number_number_of_nat V_2)) K))) zero_zero_nat))) ((((ord_less_int V) pls)->False)->(((eq nat) ((times_times_nat (number_number_of_nat V)) ((times_times_nat (number_number_of_nat V_2)) K))) ((times_times_nat (number_number_of_nat ((times_times_int V) V_2))) K))))).
% 2.38/2.79 Axiom fact_357_power__even__eq:(forall (A_108:real) (N_24:nat), (((eq real) ((power_power_real A_108) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_24))) ((power_power_real ((power_power_real A_108) N_24)) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.38/2.79 Axiom fact_358_power__even__eq:(forall (A_108:nat) (N_24:nat), (((eq nat) ((power_power_nat A_108) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_24))) ((power_power_nat ((power_power_nat A_108) N_24)) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.38/2.79 Axiom fact_359_power__even__eq:(forall (A_108:int) (N_24:nat), (((eq int) ((power_power_int A_108) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_24))) ((power_power_int ((power_power_int A_108) N_24)) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.38/2.79 Axiom fact_360_even__power__le__0__imp__0:(forall (A_107:real) (K_3:nat), (((ord_less_eq_real ((power_power_real A_107) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_3))) zero_zero_real)->(((eq real) A_107) zero_zero_real))).
% 2.38/2.79 Axiom fact_361_even__power__le__0__imp__0:(forall (A_107:int) (K_3:nat), (((ord_less_eq_int ((power_power_int A_107) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_3))) zero_zero_int)->(((eq int) A_107) zero_zero_int))).
% 2.38/2.79 Axiom fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J:(forall (A_106:real), (((eq real) ((times_times_real zero_zero_real) A_106)) zero_zero_real)).
% 2.38/2.79 Axiom fact_363_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J:(forall (A_106:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_106)) zero_zero_nat)).
% 2.38/2.79 Axiom fact_364_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J:(forall (A_106:int), (((eq int) ((times_times_int zero_zero_int) A_106)) zero_zero_int)).
% 2.38/2.79 Axiom fact_365_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J:(forall (A_105:real), (((eq real) ((times_times_real A_105) zero_zero_real)) zero_zero_real)).
% 2.38/2.79 Axiom fact_366_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J:(forall (A_105:nat), (((eq nat) ((times_times_nat A_105) zero_zero_nat)) zero_zero_nat)).
% 2.38/2.79 Axiom fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J:(forall (A_105:int), (((eq int) ((times_times_int A_105) zero_zero_int)) zero_zero_int)).
% 2.38/2.79 Axiom fact_368_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J:(forall (A_104:real), (((eq real) ((plus_plus_real zero_zero_real) A_104)) A_104)).
% 2.38/2.79 Axiom fact_369_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J:(forall (A_104:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_104)) A_104)).
% 2.38/2.79 Axiom fact_370_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J:(forall (A_104:int), (((eq int) ((plus_plus_int zero_zero_int) A_104)) A_104)).
% 2.38/2.79 Axiom fact_371_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J:(forall (A_103:real), (((eq real) ((plus_plus_real A_103) zero_zero_real)) A_103)).
% 2.38/2.79 Axiom fact_372_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J:(forall (A_103:nat), (((eq nat) ((plus_plus_nat A_103) zero_zero_nat)) A_103)).
% 2.38/2.79 Axiom fact_373_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J:(forall (A_103:int), (((eq int) ((plus_plus_int A_103) zero_zero_int)) A_103)).
% 2.38/2.79 Axiom fact_374_add__0__iff:(forall (B_74:real) (A_102:real), ((iff (((eq real) B_74) ((plus_plus_real B_74) A_102))) (((eq real) A_102) zero_zero_real))).
% 2.38/2.79 Axiom fact_375_add__0__iff:(forall (B_74:nat) (A_102:nat), ((iff (((eq nat) B_74) ((plus_plus_nat B_74) A_102))) (((eq nat) A_102) zero_zero_nat))).
% 2.38/2.79 Axiom fact_376_add__0__iff:(forall (B_74:int) (A_102:int), ((iff (((eq int) B_74) ((plus_plus_int B_74) A_102))) (((eq int) A_102) zero_zero_int))).
% 2.38/2.79 Axiom fact_377_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J:(forall (X_13:real) (Y_11:real) (Z_2:real), (((eq real) ((times_times_real X_13) ((plus_plus_real Y_11) Z_2))) ((plus_plus_real ((times_times_real X_13) Y_11)) ((times_times_real X_13) Z_2)))).
% 2.38/2.79 Axiom fact_378_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J:(forall (X_13:nat) (Y_11:nat) (Z_2:nat), (((eq nat) ((times_times_nat X_13) ((plus_plus_nat Y_11) Z_2))) ((plus_plus_nat ((times_times_nat X_13) Y_11)) ((times_times_nat X_13) Z_2)))).
% 2.38/2.79 Axiom fact_379_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J:(forall (X_13:int) (Y_11:int) (Z_2:int), (((eq int) ((times_times_int X_13) ((plus_plus_int Y_11) Z_2))) ((plus_plus_int ((times_times_int X_13) Y_11)) ((times_times_int X_13) Z_2)))).
% 2.38/2.79 Axiom fact_380_crossproduct__noteq:(forall (C_43:real) (D_11:real) (A_101:real) (B_73:real), ((iff ((and (not (((eq real) A_101) B_73))) (not (((eq real) C_43) D_11)))) (not (((eq real) ((plus_plus_real ((times_times_real A_101) C_43)) ((times_times_real B_73) D_11))) ((plus_plus_real ((times_times_real A_101) D_11)) ((times_times_real B_73) C_43)))))).
% 2.38/2.79 Axiom fact_381_crossproduct__noteq:(forall (C_43:nat) (D_11:nat) (A_101:nat) (B_73:nat), ((iff ((and (not (((eq nat) A_101) B_73))) (not (((eq nat) C_43) D_11)))) (not (((eq nat) ((plus_plus_nat ((times_times_nat A_101) C_43)) ((times_times_nat B_73) D_11))) ((plus_plus_nat ((times_times_nat A_101) D_11)) ((times_times_nat B_73) C_43)))))).
% 2.38/2.79 Axiom fact_382_crossproduct__noteq:(forall (C_43:int) (D_11:int) (A_101:int) (B_73:int), ((iff ((and (not (((eq int) A_101) B_73))) (not (((eq int) C_43) D_11)))) (not (((eq int) ((plus_plus_int ((times_times_int A_101) C_43)) ((times_times_int B_73) D_11))) ((plus_plus_int ((times_times_int A_101) D_11)) ((times_times_int B_73) C_43)))))).
% 2.38/2.79 Axiom fact_383_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J:(forall (A_100:real) (B_72:real) (C_42:real), (((eq real) ((times_times_real ((plus_plus_real A_100) B_72)) C_42)) ((plus_plus_real ((times_times_real A_100) C_42)) ((times_times_real B_72) C_42)))).
% 2.38/2.79 Axiom fact_384_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J:(forall (A_100:nat) (B_72:nat) (C_42:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_100) B_72)) C_42)) ((plus_plus_nat ((times_times_nat A_100) C_42)) ((times_times_nat B_72) C_42)))).
% 2.38/2.79 Axiom fact_385_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J:(forall (A_100:int) (B_72:int) (C_42:int), (((eq int) ((times_times_int ((plus_plus_int A_100) B_72)) C_42)) ((plus_plus_int ((times_times_int A_100) C_42)) ((times_times_int B_72) C_42)))).
% 2.38/2.79 Axiom fact_386_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J:(forall (A_99:real) (M_13:real) (B_71:real), (((eq real) ((plus_plus_real ((times_times_real A_99) M_13)) ((times_times_real B_71) M_13))) ((times_times_real ((plus_plus_real A_99) B_71)) M_13))).
% 2.38/2.79 Axiom fact_387_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J:(forall (A_99:nat) (M_13:nat) (B_71:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_99) M_13)) ((times_times_nat B_71) M_13))) ((times_times_nat ((plus_plus_nat A_99) B_71)) M_13))).
% 2.38/2.79 Axiom fact_388_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J:(forall (A_99:int) (M_13:int) (B_71:int), (((eq int) ((plus_plus_int ((times_times_int A_99) M_13)) ((times_times_int B_71) M_13))) ((times_times_int ((plus_plus_int A_99) B_71)) M_13))).
% 2.38/2.79 Axiom fact_389_crossproduct__eq:(forall (W_3:real) (Y_10:real) (X_12:real) (Z_1:real), ((iff (((eq real) ((plus_plus_real ((times_times_real W_3) Y_10)) ((times_times_real X_12) Z_1))) ((plus_plus_real ((times_times_real W_3) Z_1)) ((times_times_real X_12) Y_10)))) ((or (((eq real) W_3) X_12)) (((eq real) Y_10) Z_1)))).
% 2.38/2.79 Axiom fact_390_crossproduct__eq:(forall (W_3:nat) (Y_10:nat) (X_12:nat) (Z_1:nat), ((iff (((eq nat) ((plus_plus_nat ((times_times_nat W_3) Y_10)) ((times_times_nat X_12) Z_1))) ((plus_plus_nat ((times_times_nat W_3) Z_1)) ((times_times_nat X_12) Y_10)))) ((or (((eq nat) W_3) X_12)) (((eq nat) Y_10) Z_1)))).
% 2.38/2.79 Axiom fact_391_crossproduct__eq:(forall (W_3:int) (Y_10:int) (X_12:int) (Z_1:int), ((iff (((eq int) ((plus_plus_int ((times_times_int W_3) Y_10)) ((times_times_int X_12) Z_1))) ((plus_plus_int ((times_times_int W_3) Z_1)) ((times_times_int X_12) Y_10)))) ((or (((eq int) W_3) X_12)) (((eq int) Y_10) Z_1)))).
% 2.38/2.79 Axiom fact_392_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J:(forall (A_98:real), (((eq real) ((times_times_real one_one_real) A_98)) A_98)).
% 2.38/2.79 Axiom fact_393_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J:(forall (A_98:nat), (((eq nat) ((times_times_nat one_one_nat) A_98)) A_98)).
% 2.38/2.79 Axiom fact_394_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J:(forall (A_98:int), (((eq int) ((times_times_int one_one_int) A_98)) A_98)).
% 2.38/2.79 Axiom fact_395_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J:(forall (A_97:real), (((eq real) ((times_times_real A_97) one_one_real)) A_97)).
% 2.38/2.79 Axiom fact_396_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J:(forall (A_97:nat), (((eq nat) ((times_times_nat A_97) one_one_nat)) A_97)).
% 2.38/2.79 Axiom fact_397_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J:(forall (A_97:int), (((eq int) ((times_times_int A_97) one_one_int)) A_97)).
% 2.38/2.79 Axiom fact_398_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J:(forall (X_11:real) (Y_9:real) (Q_5:nat), (((eq real) ((power_power_real ((times_times_real X_11) Y_9)) Q_5)) ((times_times_real ((power_power_real X_11) Q_5)) ((power_power_real Y_9) Q_5)))).
% 2.38/2.79 Axiom fact_399_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J:(forall (X_11:nat) (Y_9:nat) (Q_5:nat), (((eq nat) ((power_power_nat ((times_times_nat X_11) Y_9)) Q_5)) ((times_times_nat ((power_power_nat X_11) Q_5)) ((power_power_nat Y_9) Q_5)))).
% 2.38/2.79 Axiom fact_400_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J:(forall (X_11:int) (Y_9:int) (Q_5:nat), (((eq int) ((power_power_int ((times_times_int X_11) Y_9)) Q_5)) ((times_times_int ((power_power_int X_11) Q_5)) ((power_power_int Y_9) Q_5)))).
% 2.38/2.79 Axiom fact_401_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J:(forall (X_10:real) (P_4:nat) (Q_4:nat), (((eq real) ((times_times_real ((power_power_real X_10) P_4)) ((power_power_real X_10) Q_4))) ((power_power_real X_10) ((plus_plus_nat P_4) Q_4)))).
% 2.38/2.79 Axiom fact_402_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J:(forall (X_10:nat) (P_4:nat) (Q_4:nat), (((eq nat) ((times_times_nat ((power_power_nat X_10) P_4)) ((power_power_nat X_10) Q_4))) ((power_power_nat X_10) ((plus_plus_nat P_4) Q_4)))).
% 2.38/2.79 Axiom fact_403_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J:(forall (X_10:int) (P_4:nat) (Q_4:nat), (((eq int) ((times_times_int ((power_power_int X_10) P_4)) ((power_power_int X_10) Q_4))) ((power_power_int X_10) ((plus_plus_nat P_4) Q_4)))).
% 2.38/2.79 Axiom fact_404_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J:(forall (X_9:real), (((eq real) ((power_power_real X_9) zero_zero_nat)) one_one_real)).
% 2.38/2.79 Axiom fact_405_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J:(forall (X_9:nat), (((eq nat) ((power_power_nat X_9) zero_zero_nat)) one_one_nat)).
% 2.38/2.79 Axiom fact_406_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J:(forall (X_9:int), (((eq int) ((power_power_int X_9) zero_zero_nat)) one_one_int)).
% 2.38/2.79 Axiom fact_407_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J:((ord_less_eq_int zero_zero_int) zero_zero_int).
% 2.38/2.79 Axiom fact_408_zero__le__even__power_H:(forall (A_96:real) (N_23:nat), ((ord_less_eq_real zero_zero_real) ((power_power_real A_96) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_23)))).
% 2.38/2.79 Axiom fact_409_zero__le__even__power_H:(forall (A_96:int) (N_23:nat), ((ord_less_eq_int zero_zero_int) ((power_power_int A_96) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_23)))).
% 2.38/2.79 Axiom fact_410_add__scale__eq__noteq:(forall (C_41:real) (D_10:real) (A_95:real) (B_70:real) (R_3:real), ((not (((eq real) R_3) zero_zero_real))->(((and (((eq real) A_95) B_70)) (not (((eq real) C_41) D_10)))->(not (((eq real) ((plus_plus_real A_95) ((times_times_real R_3) C_41))) ((plus_plus_real B_70) ((times_times_real R_3) D_10))))))).
% 2.38/2.79 Axiom fact_411_add__scale__eq__noteq:(forall (C_41:nat) (D_10:nat) (A_95:nat) (B_70:nat) (R_3:nat), ((not (((eq nat) R_3) zero_zero_nat))->(((and (((eq nat) A_95) B_70)) (not (((eq nat) C_41) D_10)))->(not (((eq nat) ((plus_plus_nat A_95) ((times_times_nat R_3) C_41))) ((plus_plus_nat B_70) ((times_times_nat R_3) D_10))))))).
% 2.38/2.79 Axiom fact_412_add__scale__eq__noteq:(forall (C_41:int) (D_10:int) (A_95:int) (B_70:int) (R_3:int), ((not (((eq int) R_3) zero_zero_int))->(((and (((eq int) A_95) B_70)) (not (((eq int) C_41) D_10)))->(not (((eq int) ((plus_plus_int A_95) ((times_times_int R_3) C_41))) ((plus_plus_int B_70) ((times_times_int R_3) D_10))))))).
% 2.38/2.79 Axiom fact_413_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J:(forall (M_12:real), (((eq real) ((plus_plus_real M_12) M_12)) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) M_12))).
% 2.38/2.79 Axiom fact_414_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J:(forall (M_12:nat), (((eq nat) ((plus_plus_nat M_12) M_12)) ((times_times_nat ((plus_plus_nat one_one_nat) one_one_nat)) M_12))).
% 2.38/2.79 Axiom fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J:(forall (M_12:int), (((eq int) ((plus_plus_int M_12) M_12)) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) M_12))).
% 2.38/2.79 Axiom fact_416_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J:(forall (M_11:real) (A_94:real), (((eq real) ((plus_plus_real M_11) ((times_times_real A_94) M_11))) ((times_times_real ((plus_plus_real A_94) one_one_real)) M_11))).
% 2.38/2.79 Axiom fact_417_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J:(forall (M_11:nat) (A_94:nat), (((eq nat) ((plus_plus_nat M_11) ((times_times_nat A_94) M_11))) ((times_times_nat ((plus_plus_nat A_94) one_one_nat)) M_11))).
% 2.38/2.79 Axiom fact_418_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J:(forall (M_11:int) (A_94:int), (((eq int) ((plus_plus_int M_11) ((times_times_int A_94) M_11))) ((times_times_int ((plus_plus_int A_94) one_one_int)) M_11))).
% 2.38/2.79 Axiom fact_419_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J:(forall (A_93:real) (M_10:real), (((eq real) ((plus_plus_real ((times_times_real A_93) M_10)) M_10)) ((times_times_real ((plus_plus_real A_93) one_one_real)) M_10))).
% 2.38/2.79 Axiom fact_420_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J:(forall (A_93:nat) (M_10:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_93) M_10)) M_10)) ((times_times_nat ((plus_plus_nat A_93) one_one_nat)) M_10))).
% 2.38/2.79 Axiom fact_421_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J:(forall (A_93:int) (M_10:int), (((eq int) ((plus_plus_int ((times_times_int A_93) M_10)) M_10)) ((times_times_int ((plus_plus_int A_93) one_one_int)) M_10))).
% 2.38/2.79 Axiom fact_422_power__eq__0__iff__number__of:(forall (A_92:real) (W_2:int), ((iff (((eq real) ((power_power_real A_92) (number_number_of_nat W_2))) zero_zero_real)) ((and (((eq real) A_92) zero_zero_real)) (not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat))))).
% 2.38/2.79 Axiom fact_423_power__eq__0__iff__number__of:(forall (A_92:nat) (W_2:int), ((iff (((eq nat) ((power_power_nat A_92) (number_number_of_nat W_2))) zero_zero_nat)) ((and (((eq nat) A_92) zero_zero_nat)) (not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat))))).
% 2.38/2.79 Axiom fact_424_power__eq__0__iff__number__of:(forall (A_92:int) (W_2:int), ((iff (((eq int) ((power_power_int A_92) (number_number_of_nat W_2))) zero_zero_int)) ((and (((eq int) A_92) zero_zero_int)) (not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat))))).
% 2.38/2.79 Axiom fact_425_pos__zmult__pos:(forall (B:int) (A:int), (((ord_less_int zero_zero_int) A)->(((ord_less_int zero_zero_int) ((times_times_int A) B))->((ord_less_int zero_zero_int) B)))).
% 2.38/2.79 Axiom fact_426_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J:((ord_less_eq_int zero_zero_int) one_one_int).
% 2.38/2.79 Axiom fact_427_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J:(forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((times_times_int X) Y))))).
% 2.38/2.79 Axiom fact_428_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J:(forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X) Y))))).
% 2.38/2.79 Axiom fact_429_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J:(forall (N:nat) (X:int), (((ord_less_eq_int zero_zero_int) X)->((ord_less_eq_int zero_zero_int) ((power_power_int X) N)))).
% 2.38/2.79 Axiom fact_430_power__0__left__number__of:(forall (W_1:int), ((and ((((eq nat) (number_number_of_nat W_1)) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_1))) one_one_real))) ((not (((eq nat) (number_number_of_nat W_1)) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_1))) zero_zero_real)))).
% 2.38/2.79 Axiom fact_431_power__0__left__number__of:(forall (W_1:int), ((and ((((eq nat) (number_number_of_nat W_1)) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_1))) one_one_nat))) ((not (((eq nat) (number_number_of_nat W_1)) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_1))) zero_zero_nat)))).
% 2.38/2.80 Axiom fact_432_power__0__left__number__of:(forall (W_1:int), ((and ((((eq nat) (number_number_of_nat W_1)) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_1))) one_one_int))) ((not (((eq nat) (number_number_of_nat W_1)) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_1))) zero_zero_int)))).
% 2.38/2.80 Axiom fact_433_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J:((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 (bit1 pls)))).
% 2.38/2.80 Axiom fact_434_q__pos__lemma:(forall (B_69:int) (Q_3:int) (R_2:int), (((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_69) Q_3)) R_2))->(((ord_less_int R_2) B_69)->(((ord_less_int zero_zero_int) B_69)->((ord_less_eq_int zero_zero_int) Q_3))))).
% 2.38/2.80 Axiom fact_435_q__neg__lemma:(forall (B_69:int) (Q_3:int) (R_2:int), (((ord_less_int ((plus_plus_int ((times_times_int B_69) Q_3)) R_2)) zero_zero_int)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B_69)->((ord_less_eq_int Q_3) zero_zero_int))))).
% 2.38/2.80 Axiom fact_436_unique__quotient__lemma:(forall (B:int) (Q_3:int) (R_2:int) (Q:int) (R:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B) Q_3)) R_2)) ((plus_plus_int ((times_times_int B) Q)) R))->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int R_2) B)->(((ord_less_int R) B)->((ord_less_eq_int Q_3) Q)))))).
% 2.38/2.80 Axiom fact_437_zdiv__mono2__lemma:(forall (B:int) (Q:int) (R:int) (B_69:int) (Q_3:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B) Q)) R)) ((plus_plus_int ((times_times_int B_69) Q_3)) R_2))->(((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_69) Q_3)) R_2))->(((ord_less_int R_2) B_69)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int zero_zero_int) B_69)->(((ord_less_eq_int B_69) B)->((ord_less_eq_int Q) Q_3)))))))).
% 2.38/2.80 Axiom fact_438_unique__quotient__lemma__neg:(forall (B:int) (Q_3:int) (R_2:int) (Q:int) (R:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B) Q_3)) R_2)) ((plus_plus_int ((times_times_int B) Q)) R))->(((ord_less_eq_int R) zero_zero_int)->(((ord_less_int B) R)->(((ord_less_int B) R_2)->((ord_less_eq_int Q) Q_3)))))).
% 2.38/2.80 Axiom fact_439_zdiv__mono2__neg__lemma:(forall (B:int) (Q:int) (R:int) (B_69:int) (Q_3:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B) Q)) R)) ((plus_plus_int ((times_times_int B_69) Q_3)) R_2))->(((ord_less_int ((plus_plus_int ((times_times_int B_69) Q_3)) R_2)) zero_zero_int)->(((ord_less_int R) B)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B_69)->(((ord_less_eq_int B_69) B)->((ord_less_eq_int Q_3) Q)))))))).
% 2.38/2.80 Axiom fact_440_quartic__square__square:(forall (X:int), (((eq int) ((power_power_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int X) (number_number_of_nat (bit0 (bit0 (bit1 pls))))))).
% 2.38/2.80 Axiom fact_441_s:(((zcong ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)).
% 2.38/2.80 Axiom fact_442_Euler_Oaux____1:(forall (Y:int) (X:int) (P_1:int), (((((zcong X) zero_zero_int) P_1)->False)->((((zcong ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls))))) X) P_1)->(((dvd_dvd_int P_1) Y)->False)))).
% 2.38/2.80 Axiom fact_443_zprime__def:(forall (P_1:int), ((iff (zprime P_1)) ((and ((ord_less_int one_one_int) P_1)) (forall (M_2:int), (((and ((ord_less_eq_int zero_zero_int) M_2)) ((dvd_dvd_int M_2) P_1))->((or (((eq int) M_2) one_one_int)) (((eq int) M_2) P_1))))))).
% 2.38/2.80 Axiom fact_444_prime__g__5:(forall (P_1:int), ((zprime P_1)->((not (((eq int) P_1) (number_number_of_int (bit0 (bit1 pls)))))->((not (((eq int) P_1) (number_number_of_int (bit1 (bit1 pls)))))->((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P_1))))).
% 2.38/2.80 Axiom fact_445_pos2:((ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls)))).
% 2.38/2.80 Axiom fact_446_power__strict__mono:(forall (N_22:nat) (A_91:real) (B_68:real), (((ord_less_real A_91) B_68)->(((ord_less_eq_real zero_zero_real) A_91)->(((ord_less_nat zero_zero_nat) N_22)->((ord_less_real ((power_power_real A_91) N_22)) ((power_power_real B_68) N_22)))))).
% 2.38/2.80 Axiom fact_447_power__strict__mono:(forall (N_22:nat) (A_91:nat) (B_68:nat), (((ord_less_nat A_91) B_68)->(((ord_less_eq_nat zero_zero_nat) A_91)->(((ord_less_nat zero_zero_nat) N_22)->((ord_less_nat ((power_power_nat A_91) N_22)) ((power_power_nat B_68) N_22)))))).
% 2.38/2.80 Axiom fact_448_power__strict__mono:(forall (N_22:nat) (A_91:int) (B_68:int), (((ord_less_int A_91) B_68)->(((ord_less_eq_int zero_zero_int) A_91)->(((ord_less_nat zero_zero_nat) N_22)->((ord_less_int ((power_power_int A_91) N_22)) ((power_power_int B_68) N_22)))))).
% 2.38/2.80 Axiom fact_449_convex__bound__lt:(forall (V_1:real) (U_1:real) (Y_8:real) (X_8:real) (A_90:real), (((ord_less_real X_8) A_90)->(((ord_less_real Y_8) A_90)->(((ord_less_eq_real zero_zero_real) U_1)->(((ord_less_eq_real zero_zero_real) V_1)->((((eq real) ((plus_plus_real U_1) V_1)) one_one_real)->((ord_less_real ((plus_plus_real ((times_times_real U_1) X_8)) ((times_times_real V_1) Y_8))) A_90))))))).
% 2.38/2.80 Axiom fact_450_convex__bound__lt:(forall (V_1:int) (U_1:int) (Y_8:int) (X_8:int) (A_90:int), (((ord_less_int X_8) A_90)->(((ord_less_int Y_8) A_90)->(((ord_less_eq_int zero_zero_int) U_1)->(((ord_less_eq_int zero_zero_int) V_1)->((((eq int) ((plus_plus_int U_1) V_1)) one_one_int)->((ord_less_int ((plus_plus_int ((times_times_int U_1) X_8)) ((times_times_int V_1) Y_8))) A_90))))))).
% 2.38/2.80 Axiom fact_451_zpower__zdvd__prop2:(forall (Y:int) (N:nat) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((power_power_int Y) N))->(((ord_less_nat zero_zero_nat) N)->((dvd_dvd_int P_1) Y))))).
% 2.38/2.80 Axiom fact_452_dvd__0__right:(forall (A_89:nat), ((dvd_dvd_nat A_89) zero_zero_nat)).
% 2.38/2.80 Axiom fact_453_dvd__0__right:(forall (A_89:int), ((dvd_dvd_int A_89) zero_zero_int)).
% 2.38/2.80 Axiom fact_454_dvd__0__right:(forall (A_89:real), ((dvd_dvd_real A_89) zero_zero_real)).
% 2.38/2.80 Axiom fact_455__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_:((forall (S1:int), ((((zcong ((power_power_int S1) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))->False))->False).
% 2.38/2.80 Axiom fact_456__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096:(((eq int) ((legendre (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) one_one_int).
% 2.38/2.80 Axiom fact_457_rel__simps_I47_J:(forall (K:int), ((iff (((eq int) (bit1 K)) min)) (((eq int) K) min))).
% 2.38/2.80 Axiom fact_458_rel__simps_I43_J:(forall (L:int), ((iff (((eq int) min) (bit1 L))) (((eq int) min) L))).
% 2.38/2.80 Axiom fact_459_Bit1__Min:(((eq int) (bit1 min)) min).
% 2.38/2.80 Axiom fact_460_rel__simps_I37_J:(not (((eq int) pls) min)).
% 2.38/2.80 Axiom fact_461_rel__simps_I40_J:(not (((eq int) min) pls)).
% 2.38/2.80 Axiom fact_462_rel__simps_I45_J:(forall (K:int), (not (((eq int) (bit0 K)) min))).
% 2.38/2.80 Axiom fact_463_rel__simps_I42_J:(forall (L:int), (not (((eq int) min) (bit0 L)))).
% 2.38/2.80 Axiom fact_464_rel__simps_I7_J:(((ord_less_int min) min)->False).
% 2.38/2.80 Axiom fact_465_rel__simps_I24_J:((ord_less_eq_int min) min).
% 2.38/2.80 Axiom fact_466_rel__simps_I13_J:(forall (K:int), ((iff ((ord_less_int (bit1 K)) min)) ((ord_less_int K) min))).
% 2.38/2.80 Axiom fact_467_rel__simps_I9_J:(forall (K:int), ((iff ((ord_less_int min) (bit1 K))) ((ord_less_int min) K))).
% 2.38/2.80 Axiom fact_468_rel__simps_I3_J:(((ord_less_int pls) min)->False).
% 2.38/2.80 Axiom fact_469_rel__simps_I6_J:((ord_less_int min) pls).
% 2.38/2.80 Axiom fact_470_rel__simps_I8_J:(forall (K:int), ((iff ((ord_less_int min) (bit0 K))) ((ord_less_int min) K))).
% 2.38/2.80 Axiom fact_471_bin__less__0__simps_I2_J:((ord_less_int min) zero_zero_int).
% 2.38/2.80 Axiom fact_472_rel__simps_I26_J:(forall (K:int), ((iff ((ord_less_eq_int min) (bit1 K))) ((ord_less_eq_int min) K))).
% 2.38/2.80 Axiom fact_473_rel__simps_I30_J:(forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) min)) ((ord_less_eq_int K) min))).
% 2.38/2.80 Axiom fact_474_rel__simps_I23_J:((ord_less_eq_int min) pls).
% 2.38/2.80 Axiom fact_475_rel__simps_I20_J:(((ord_less_eq_int pls) min)->False).
% 2.38/2.80 Axiom fact_476_rel__simps_I28_J:(forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) min)) ((ord_less_eq_int K) min))).
% 2.38/2.80 Axiom fact_477_eq__number__of__Pls__Min:(not (((eq int) (number_number_of_int pls)) (number_number_of_int min))).
% 2.38/2.80 Axiom fact_478_rel__simps_I11_J:(forall (K:int), ((iff ((ord_less_int (bit0 K)) min)) ((ord_less_eq_int K) min))).
% 2.38/2.80 Axiom fact_479_rel__simps_I25_J:(forall (K:int), ((iff ((ord_less_eq_int min) (bit0 K))) ((ord_less_int min) K))).
% 2.38/2.80 Axiom fact_480_zmult__eq__1__iff:(forall (M:int) (N:int), ((iff (((eq int) ((times_times_int M) N)) one_one_int)) ((or ((and (((eq int) M) one_one_int)) (((eq int) N) one_one_int))) ((and (((eq int) M) (number_number_of_int min))) (((eq int) N) (number_number_of_int min)))))).
% 2.38/2.80 Axiom fact_481_pos__zmult__eq__1__iff__lemma:(forall (M:int) (N:int), ((((eq int) ((times_times_int M) N)) one_one_int)->((or (((eq int) M) one_one_int)) (((eq int) M) (number_number_of_int min))))).
% 2.38/2.80 Axiom fact_482_linorder__neqE__linordered__idom:(forall (X_7:real) (Y_7:real), ((not (((eq real) X_7) Y_7))->((((ord_less_real X_7) Y_7)->False)->((ord_less_real Y_7) X_7)))).
% 2.38/2.80 Axiom fact_483_linorder__neqE__linordered__idom:(forall (X_7:int) (Y_7:int), ((not (((eq int) X_7) Y_7))->((((ord_less_int X_7) Y_7)->False)->((ord_less_int Y_7) X_7)))).
% 2.38/2.80 Axiom fact_484_dvd__refl:(forall (A_88:nat), ((dvd_dvd_nat A_88) A_88)).
% 2.38/2.80 Axiom fact_485_dvd__refl:(forall (A_88:int), ((dvd_dvd_int A_88) A_88)).
% 2.38/2.80 Axiom fact_486_dvd__trans:(forall (C_40:nat) (A_87:nat) (B_67:nat), (((dvd_dvd_nat A_87) B_67)->(((dvd_dvd_nat B_67) C_40)->((dvd_dvd_nat A_87) C_40)))).
% 2.38/2.80 Axiom fact_487_dvd__trans:(forall (C_40:int) (A_87:int) (B_67:int), (((dvd_dvd_int A_87) B_67)->(((dvd_dvd_int B_67) C_40)->((dvd_dvd_int A_87) C_40)))).
% 2.38/2.80 Axiom fact_488_zcong__sym:(forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) (((zcong B) A) M))).
% 2.38/2.80 Axiom fact_489_zcong__refl:(forall (K:int) (M:int), (((zcong K) K) M)).
% 2.38/2.80 Axiom fact_490_zcong__eq__trans:(forall (D:int) (C:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((eq int) B) C)->((((zcong C) D) M)->(((zcong A) D) M))))).
% 2.38/2.80 Axiom fact_491_zcong__trans:(forall (C:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((zcong B) C) M)->(((zcong A) C) M)))).
% 2.38/2.80 Axiom fact_492_zcong__neg__1__impl__ne__1:(forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((((zcong X) (number_number_of_int min)) P_1)->((((zcong X) one_one_int) P_1)->False)))).
% 2.38/2.80 Axiom fact_493_order__le__neq__implies__less:(forall (X_6:real) (Y_6:real), (((ord_less_eq_real X_6) Y_6)->((not (((eq real) X_6) Y_6))->((ord_less_real X_6) Y_6)))).
% 2.38/2.80 Axiom fact_494_order__le__neq__implies__less:(forall (X_6:nat) (Y_6:nat), (((ord_less_eq_nat X_6) Y_6)->((not (((eq nat) X_6) Y_6))->((ord_less_nat X_6) Y_6)))).
% 2.38/2.80 Axiom fact_495_order__le__neq__implies__less:(forall (X_6:int) (Y_6:int), (((ord_less_eq_int X_6) Y_6)->((not (((eq int) X_6) Y_6))->((ord_less_int X_6) Y_6)))).
% 2.38/2.80 Axiom fact_496_divisors__zero:(forall (A_86:real) (B_66:real), ((((eq real) ((times_times_real A_86) B_66)) zero_zero_real)->((or (((eq real) A_86) zero_zero_real)) (((eq real) B_66) zero_zero_real)))).
% 2.38/2.80 Axiom fact_497_divisors__zero:(forall (A_86:nat) (B_66:nat), ((((eq nat) ((times_times_nat A_86) B_66)) zero_zero_nat)->((or (((eq nat) A_86) zero_zero_nat)) (((eq nat) B_66) zero_zero_nat)))).
% 2.38/2.80 Axiom fact_498_divisors__zero:(forall (A_86:int) (B_66:int), ((((eq int) ((times_times_int A_86) B_66)) zero_zero_int)->((or (((eq int) A_86) zero_zero_int)) (((eq int) B_66) zero_zero_int)))).
% 2.38/2.80 Axiom fact_499_no__zero__divisors:(forall (B_65:real) (A_85:real), ((not (((eq real) A_85) zero_zero_real))->((not (((eq real) B_65) zero_zero_real))->(not (((eq real) ((times_times_real A_85) B_65)) zero_zero_real))))).
% 2.38/2.80 Axiom fact_500_no__zero__divisors:(forall (B_65:nat) (A_85:nat), ((not (((eq nat) A_85) zero_zero_nat))->((not (((eq nat) B_65) zero_zero_nat))->(not (((eq nat) ((times_times_nat A_85) B_65)) zero_zero_nat))))).
% 2.38/2.80 Axiom fact_501_no__zero__divisors:(forall (B_65:int) (A_85:int), ((not (((eq int) A_85) zero_zero_int))->((not (((eq int) B_65) zero_zero_int))->(not (((eq int) ((times_times_int A_85) B_65)) zero_zero_int))))).
% 2.38/2.80 Axiom fact_502_mult__eq__0__iff:(forall (A_84:real) (B_64:real), ((iff (((eq real) ((times_times_real A_84) B_64)) zero_zero_real)) ((or (((eq real) A_84) zero_zero_real)) (((eq real) B_64) zero_zero_real)))).
% 2.38/2.80 Axiom fact_503_mult__eq__0__iff:(forall (A_84:int) (B_64:int), ((iff (((eq int) ((times_times_int A_84) B_64)) zero_zero_int)) ((or (((eq int) A_84) zero_zero_int)) (((eq int) B_64) zero_zero_int)))).
% 2.38/2.80 Axiom fact_504_mult__zero__right:(forall (A_83:real), (((eq real) ((times_times_real A_83) zero_zero_real)) zero_zero_real)).
% 2.38/2.80 Axiom fact_505_mult__zero__right:(forall (A_83:nat), (((eq nat) ((times_times_nat A_83) zero_zero_nat)) zero_zero_nat)).
% 2.38/2.80 Axiom fact_506_mult__zero__right:(forall (A_83:int), (((eq int) ((times_times_int A_83) zero_zero_int)) zero_zero_int)).
% 2.38/2.80 Axiom fact_507_mult__zero__left:(forall (A_82:real), (((eq real) ((times_times_real zero_zero_real) A_82)) zero_zero_real)).
% 2.38/2.80 Axiom fact_508_mult__zero__left:(forall (A_82:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_82)) zero_zero_nat)).
% 2.38/2.80 Axiom fact_509_mult__zero__left:(forall (A_82:int), (((eq int) ((times_times_int zero_zero_int) A_82)) zero_zero_int)).
% 2.38/2.80 Axiom fact_510_zero__neq__one:(not (((eq real) zero_zero_real) one_one_real)).
% 2.38/2.80 Axiom fact_511_zero__neq__one:(not (((eq nat) zero_zero_nat) one_one_nat)).
% 2.38/2.80 Axiom fact_512_zero__neq__one:(not (((eq int) zero_zero_int) one_one_int)).
% 2.38/2.80 Axiom fact_513_one__neq__zero:(not (((eq real) one_one_real) zero_zero_real)).
% 2.38/2.80 Axiom fact_514_one__neq__zero:(not (((eq nat) one_one_nat) zero_zero_nat)).
% 2.38/2.80 Axiom fact_515_one__neq__zero:(not (((eq int) one_one_int) zero_zero_int)).
% 2.38/2.80 Axiom fact_516_combine__common__factor:(forall (A_81:real) (E:real) (B_63:real) (C_39:real), (((eq real) ((plus_plus_real ((times_times_real A_81) E)) ((plus_plus_real ((times_times_real B_63) E)) C_39))) ((plus_plus_real ((times_times_real ((plus_plus_real A_81) B_63)) E)) C_39))).
% 2.38/2.80 Axiom fact_517_combine__common__factor:(forall (A_81:nat) (E:nat) (B_63:nat) (C_39:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_81) E)) ((plus_plus_nat ((times_times_nat B_63) E)) C_39))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat A_81) B_63)) E)) C_39))).
% 2.38/2.80 Axiom fact_518_combine__common__factor:(forall (A_81:int) (E:int) (B_63:int) (C_39:int), (((eq int) ((plus_plus_int ((times_times_int A_81) E)) ((plus_plus_int ((times_times_int B_63) E)) C_39))) ((plus_plus_int ((times_times_int ((plus_plus_int A_81) B_63)) E)) C_39))).
% 2.38/2.80 Axiom fact_519_comm__semiring__class_Odistrib:(forall (A_80:real) (B_62:real) (C_38:real), (((eq real) ((times_times_real ((plus_plus_real A_80) B_62)) C_38)) ((plus_plus_real ((times_times_real A_80) C_38)) ((times_times_real B_62) C_38)))).
% 2.38/2.80 Axiom fact_520_comm__semiring__class_Odistrib:(forall (A_80:nat) (B_62:nat) (C_38:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_80) B_62)) C_38)) ((plus_plus_nat ((times_times_nat A_80) C_38)) ((times_times_nat B_62) C_38)))).
% 2.38/2.80 Axiom fact_521_comm__semiring__class_Odistrib:(forall (A_80:int) (B_62:int) (C_38:int), (((eq int) ((times_times_int ((plus_plus_int A_80) B_62)) C_38)) ((plus_plus_int ((times_times_int A_80) C_38)) ((times_times_int B_62) C_38)))).
% 2.38/2.80 Axiom fact_522_field__power__not__zero:(forall (N_21:nat) (A_79:real), ((not (((eq real) A_79) zero_zero_real))->(not (((eq real) ((power_power_real A_79) N_21)) zero_zero_real)))).
% 2.38/2.80 Axiom fact_523_field__power__not__zero:(forall (N_21:nat) (A_79:int), ((not (((eq int) A_79) zero_zero_int))->(not (((eq int) ((power_power_int A_79) N_21)) zero_zero_int)))).
% 2.38/2.80 Axiom fact_524_dvd__0__left:(forall (A_78:nat), (((dvd_dvd_nat zero_zero_nat) A_78)->(((eq nat) A_78) zero_zero_nat))).
% 2.38/2.80 Axiom fact_525_dvd__0__left:(forall (A_78:int), (((dvd_dvd_int zero_zero_int) A_78)->(((eq int) A_78) zero_zero_int))).
% 2.38/2.80 Axiom fact_526_dvd__0__left:(forall (A_78:real), (((dvd_dvd_real zero_zero_real) A_78)->(((eq real) A_78) zero_zero_real))).
% 2.38/2.80 Axiom fact_527_power__mult__distrib:(forall (A_77:real) (B_61:real) (N_20:nat), (((eq real) ((power_power_real ((times_times_real A_77) B_61)) N_20)) ((times_times_real ((power_power_real A_77) N_20)) ((power_power_real B_61) N_20)))).
% 2.38/2.80 Axiom fact_528_power__mult__distrib:(forall (A_77:nat) (B_61:nat) (N_20:nat), (((eq nat) ((power_power_nat ((times_times_nat A_77) B_61)) N_20)) ((times_times_nat ((power_power_nat A_77) N_20)) ((power_power_nat B_61) N_20)))).
% 2.38/2.80 Axiom fact_529_power__mult__distrib:(forall (A_77:int) (B_61:int) (N_20:nat), (((eq int) ((power_power_int ((times_times_int A_77) B_61)) N_20)) ((times_times_int ((power_power_int A_77) N_20)) ((power_power_int B_61) N_20)))).
% 2.38/2.80 Axiom fact_530_power__commutes:(forall (A_76:real) (N_19:nat), (((eq real) ((times_times_real ((power_power_real A_76) N_19)) A_76)) ((times_times_real A_76) ((power_power_real A_76) N_19)))).
% 2.38/2.80 Axiom fact_531_power__commutes:(forall (A_76:nat) (N_19:nat), (((eq nat) ((times_times_nat ((power_power_nat A_76) N_19)) A_76)) ((times_times_nat A_76) ((power_power_nat A_76) N_19)))).
% 2.38/2.80 Axiom fact_532_power__commutes:(forall (A_76:int) (N_19:nat), (((eq int) ((times_times_int ((power_power_int A_76) N_19)) A_76)) ((times_times_int A_76) ((power_power_int A_76) N_19)))).
% 2.38/2.80 Axiom fact_533_dvd__triv__left:(forall (A_75:nat) (B_60:nat), ((dvd_dvd_nat A_75) ((times_times_nat A_75) B_60))).
% 2.38/2.80 Axiom fact_534_dvd__triv__left:(forall (A_75:int) (B_60:int), ((dvd_dvd_int A_75) ((times_times_int A_75) B_60))).
% 2.38/2.80 Axiom fact_535_dvd__triv__left:(forall (A_75:real) (B_60:real), ((dvd_dvd_real A_75) ((times_times_real A_75) B_60))).
% 2.38/2.80 Axiom fact_536_dvd__triv__right:(forall (A_74:nat) (B_59:nat), ((dvd_dvd_nat A_74) ((times_times_nat B_59) A_74))).
% 2.38/2.80 Axiom fact_537_dvd__triv__right:(forall (A_74:int) (B_59:int), ((dvd_dvd_int A_74) ((times_times_int B_59) A_74))).
% 2.38/2.80 Axiom fact_538_dvd__triv__right:(forall (A_74:real) (B_59:real), ((dvd_dvd_real A_74) ((times_times_real B_59) A_74))).
% 2.38/2.80 Axiom fact_539_dvd__mult2:(forall (C_37:nat) (A_73:nat) (B_58:nat), (((dvd_dvd_nat A_73) B_58)->((dvd_dvd_nat A_73) ((times_times_nat B_58) C_37)))).
% 2.38/2.80 Axiom fact_540_dvd__mult2:(forall (C_37:int) (A_73:int) (B_58:int), (((dvd_dvd_int A_73) B_58)->((dvd_dvd_int A_73) ((times_times_int B_58) C_37)))).
% 2.38/2.80 Axiom fact_541_dvd__mult2:(forall (C_37:real) (A_73:real) (B_58:real), (((dvd_dvd_real A_73) B_58)->((dvd_dvd_real A_73) ((times_times_real B_58) C_37)))).
% 2.38/2.80 Axiom fact_542_dvd__mult:(forall (B_57:nat) (A_72:nat) (C_36:nat), (((dvd_dvd_nat A_72) C_36)->((dvd_dvd_nat A_72) ((times_times_nat B_57) C_36)))).
% 2.38/2.80 Axiom fact_543_dvd__mult:(forall (B_57:int) (A_72:int) (C_36:int), (((dvd_dvd_int A_72) C_36)->((dvd_dvd_int A_72) ((times_times_int B_57) C_36)))).
% 2.38/2.80 Axiom fact_544_dvd__mult:(forall (B_57:real) (A_72:real) (C_36:real), (((dvd_dvd_real A_72) C_36)->((dvd_dvd_real A_72) ((times_times_real B_57) C_36)))).
% 2.38/2.80 Axiom fact_545_mult__dvd__mono:(forall (C_35:nat) (D_9:nat) (A_71:nat) (B_56:nat), (((dvd_dvd_nat A_71) B_56)->(((dvd_dvd_nat C_35) D_9)->((dvd_dvd_nat ((times_times_nat A_71) C_35)) ((times_times_nat B_56) D_9))))).
% 2.38/2.80 Axiom fact_546_mult__dvd__mono:(forall (C_35:int) (D_9:int) (A_71:int) (B_56:int), (((dvd_dvd_int A_71) B_56)->(((dvd_dvd_int C_35) D_9)->((dvd_dvd_int ((times_times_int A_71) C_35)) ((times_times_int B_56) D_9))))).
% 2.38/2.80 Axiom fact_547_mult__dvd__mono:(forall (C_35:real) (D_9:real) (A_71:real) (B_56:real), (((dvd_dvd_real A_71) B_56)->(((dvd_dvd_real C_35) D_9)->((dvd_dvd_real ((times_times_real A_71) C_35)) ((times_times_real B_56) D_9))))).
% 2.38/2.80 Axiom fact_548_dvdI:(forall (A_70:nat) (B_55:nat) (K_2:nat), ((((eq nat) A_70) ((times_times_nat B_55) K_2))->((dvd_dvd_nat B_55) A_70))).
% 2.38/2.80 Axiom fact_549_dvdI:(forall (A_70:int) (B_55:int) (K_2:int), ((((eq int) A_70) ((times_times_int B_55) K_2))->((dvd_dvd_int B_55) A_70))).
% 2.38/2.80 Axiom fact_550_dvdI:(forall (A_70:real) (B_55:real) (K_2:real), ((((eq real) A_70) ((times_times_real B_55) K_2))->((dvd_dvd_real B_55) A_70))).
% 2.38/2.80 Axiom fact_551_dvd__mult__left:(forall (A_69:nat) (B_54:nat) (C_34:nat), (((dvd_dvd_nat ((times_times_nat A_69) B_54)) C_34)->((dvd_dvd_nat A_69) C_34))).
% 2.38/2.81 Axiom fact_552_dvd__mult__left:(forall (A_69:int) (B_54:int) (C_34:int), (((dvd_dvd_int ((times_times_int A_69) B_54)) C_34)->((dvd_dvd_int A_69) C_34))).
% 2.38/2.81 Axiom fact_553_dvd__mult__left:(forall (A_69:real) (B_54:real) (C_34:real), (((dvd_dvd_real ((times_times_real A_69) B_54)) C_34)->((dvd_dvd_real A_69) C_34))).
% 2.38/2.81 Axiom fact_554_dvd__mult__right:(forall (A_68:nat) (B_53:nat) (C_33:nat), (((dvd_dvd_nat ((times_times_nat A_68) B_53)) C_33)->((dvd_dvd_nat B_53) C_33))).
% 2.38/2.81 Axiom fact_555_dvd__mult__right:(forall (A_68:int) (B_53:int) (C_33:int), (((dvd_dvd_int ((times_times_int A_68) B_53)) C_33)->((dvd_dvd_int B_53) C_33))).
% 2.38/2.81 Axiom fact_556_dvd__mult__right:(forall (A_68:real) (B_53:real) (C_33:real), (((dvd_dvd_real ((times_times_real A_68) B_53)) C_33)->((dvd_dvd_real B_53) C_33))).
% 2.38/2.81 Axiom fact_557_dvd__add:(forall (C_32:nat) (A_67:nat) (B_52:nat), (((dvd_dvd_nat A_67) B_52)->(((dvd_dvd_nat A_67) C_32)->((dvd_dvd_nat A_67) ((plus_plus_nat B_52) C_32))))).
% 2.38/2.81 Axiom fact_558_dvd__add:(forall (C_32:int) (A_67:int) (B_52:int), (((dvd_dvd_int A_67) B_52)->(((dvd_dvd_int A_67) C_32)->((dvd_dvd_int A_67) ((plus_plus_int B_52) C_32))))).
% 2.38/2.81 Axiom fact_559_dvd__add:(forall (C_32:real) (A_67:real) (B_52:real), (((dvd_dvd_real A_67) B_52)->(((dvd_dvd_real A_67) C_32)->((dvd_dvd_real A_67) ((plus_plus_real B_52) C_32))))).
% 2.38/2.81 Axiom fact_560_power__one:(forall (N_18:nat), (((eq real) ((power_power_real one_one_real) N_18)) one_one_real)).
% 2.38/2.81 Axiom fact_561_power__one:(forall (N_18:nat), (((eq nat) ((power_power_nat one_one_nat) N_18)) one_one_nat)).
% 2.38/2.81 Axiom fact_562_power__one:(forall (N_18:nat), (((eq int) ((power_power_int one_one_int) N_18)) one_one_int)).
% 2.38/2.81 Axiom fact_563_one__dvd:(forall (A_66:nat), ((dvd_dvd_nat one_one_nat) A_66)).
% 2.38/2.81 Axiom fact_564_one__dvd:(forall (A_66:int), ((dvd_dvd_int one_one_int) A_66)).
% 2.38/2.81 Axiom fact_565_one__dvd:(forall (A_66:real), ((dvd_dvd_real one_one_real) A_66)).
% 2.38/2.81 Axiom fact_566_dvd__power__same:(forall (N_17:nat) (X_5:nat) (Y_5:nat), (((dvd_dvd_nat X_5) Y_5)->((dvd_dvd_nat ((power_power_nat X_5) N_17)) ((power_power_nat Y_5) N_17)))).
% 2.38/2.81 Axiom fact_567_dvd__power__same:(forall (N_17:nat) (X_5:int) (Y_5:int), (((dvd_dvd_int X_5) Y_5)->((dvd_dvd_int ((power_power_int X_5) N_17)) ((power_power_int Y_5) N_17)))).
% 2.38/2.81 Axiom fact_568_dvd__power__same:(forall (N_17:nat) (X_5:real) (Y_5:real), (((dvd_dvd_real X_5) Y_5)->((dvd_dvd_real ((power_power_real X_5) N_17)) ((power_power_real Y_5) N_17)))).
% 2.38/2.81 Axiom fact_569_power__le__dvd:(forall (M_9:nat) (A_65:nat) (N_16:nat) (B_51:nat), (((dvd_dvd_nat ((power_power_nat A_65) N_16)) B_51)->(((ord_less_eq_nat M_9) N_16)->((dvd_dvd_nat ((power_power_nat A_65) M_9)) B_51)))).
% 2.38/2.81 Axiom fact_570_power__le__dvd:(forall (M_9:nat) (A_65:int) (N_16:nat) (B_51:int), (((dvd_dvd_int ((power_power_int A_65) N_16)) B_51)->(((ord_less_eq_nat M_9) N_16)->((dvd_dvd_int ((power_power_int A_65) M_9)) B_51)))).
% 2.38/2.81 Axiom fact_571_power__le__dvd:(forall (M_9:nat) (A_65:real) (N_16:nat) (B_51:real), (((dvd_dvd_real ((power_power_real A_65) N_16)) B_51)->(((ord_less_eq_nat M_9) N_16)->((dvd_dvd_real ((power_power_real A_65) M_9)) B_51)))).
% 2.38/2.81 Axiom fact_572_dvd__power__le:(forall (N_15:nat) (M_8:nat) (X_4:nat) (Y_4:nat), (((dvd_dvd_nat X_4) Y_4)->(((ord_less_eq_nat N_15) M_8)->((dvd_dvd_nat ((power_power_nat X_4) N_15)) ((power_power_nat Y_4) M_8))))).
% 2.38/2.81 Axiom fact_573_dvd__power__le:(forall (N_15:nat) (M_8:nat) (X_4:int) (Y_4:int), (((dvd_dvd_int X_4) Y_4)->(((ord_less_eq_nat N_15) M_8)->((dvd_dvd_int ((power_power_int X_4) N_15)) ((power_power_int Y_4) M_8))))).
% 2.38/2.81 Axiom fact_574_dvd__power__le:(forall (N_15:nat) (M_8:nat) (X_4:real) (Y_4:real), (((dvd_dvd_real X_4) Y_4)->(((ord_less_eq_nat N_15) M_8)->((dvd_dvd_real ((power_power_real X_4) N_15)) ((power_power_real Y_4) M_8))))).
% 2.38/2.81 Axiom fact_575_le__imp__power__dvd:(forall (A_64:nat) (M_7:nat) (N_14:nat), (((ord_less_eq_nat M_7) N_14)->((dvd_dvd_nat ((power_power_nat A_64) M_7)) ((power_power_nat A_64) N_14)))).
% 2.38/2.81 Axiom fact_576_le__imp__power__dvd:(forall (A_64:int) (M_7:nat) (N_14:nat), (((ord_less_eq_nat M_7) N_14)->((dvd_dvd_int ((power_power_int A_64) M_7)) ((power_power_int A_64) N_14)))).
% 2.38/2.81 Axiom fact_577_le__imp__power__dvd:(forall (A_64:real) (M_7:nat) (N_14:nat), (((ord_less_eq_nat M_7) N_14)->((dvd_dvd_real ((power_power_real A_64) M_7)) ((power_power_real A_64) N_14)))).
% 2.38/2.81 Axiom fact_578_nat__power__less__imp__less:(forall (M:nat) (N:nat) (I_1:nat), (((ord_less_nat zero_zero_nat) I_1)->(((ord_less_nat ((power_power_nat I_1) M)) ((power_power_nat I_1) N))->((ord_less_nat M) N)))).
% 2.38/2.81 Axiom fact_579_nat__zero__less__power__iff:(forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or ((ord_less_nat zero_zero_nat) X)) (((eq nat) N) zero_zero_nat)))).
% 2.38/2.81 Axiom fact_580_power__mult:(forall (A_63:real) (M_6:nat) (N_13:nat), (((eq real) ((power_power_real A_63) ((times_times_nat M_6) N_13))) ((power_power_real ((power_power_real A_63) M_6)) N_13))).
% 2.38/2.81 Axiom fact_581_power__mult:(forall (A_63:nat) (M_6:nat) (N_13:nat), (((eq nat) ((power_power_nat A_63) ((times_times_nat M_6) N_13))) ((power_power_nat ((power_power_nat A_63) M_6)) N_13))).
% 2.38/2.81 Axiom fact_582_power__mult:(forall (A_63:int) (M_6:nat) (N_13:nat), (((eq int) ((power_power_int A_63) ((times_times_nat M_6) N_13))) ((power_power_int ((power_power_int A_63) M_6)) N_13))).
% 2.38/2.81 Axiom fact_583_Euler_Oaux2:(forall (B:int) (A:int) (C:int), (((ord_less_int A) C)->(((ord_less_int B) C)->((or ((ord_less_eq_int A) B)) ((ord_less_eq_int B) A))))).
% 2.38/2.81 Axiom fact_584_power__one__right:(forall (A_62:real), (((eq real) ((power_power_real A_62) one_one_nat)) A_62)).
% 2.38/2.81 Axiom fact_585_power__one__right:(forall (A_62:nat), (((eq nat) ((power_power_nat A_62) one_one_nat)) A_62)).
% 2.38/2.81 Axiom fact_586_power__one__right:(forall (A_62:int), (((eq int) ((power_power_int A_62) one_one_nat)) A_62)).
% 2.38/2.81 Axiom fact_587_zcong__id:(forall (M:int), (((zcong M) zero_zero_int) M)).
% 2.38/2.81 Axiom fact_588_IntPrimes_Ozcong__zero:(forall (A:int) (B:int), ((iff (((zcong A) B) zero_zero_int)) (((eq int) A) B))).
% 2.38/2.81 Axiom fact_589_zcong__1:(forall (A:int) (B:int), (((zcong A) B) one_one_int)).
% 2.38/2.81 Axiom fact_590_zcong__zmult__self:(forall (A:int) (M:int) (B:int), (((zcong ((times_times_int A) M)) ((times_times_int B) M)) M)).
% 2.38/2.81 Axiom fact_591_zcong__zmult__prop1:(forall (C:int) (D:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((iff (((zcong C) ((times_times_int A) D)) M)) (((zcong C) ((times_times_int B) D)) M)))).
% 2.38/2.81 Axiom fact_592_zcong__zmult__prop2:(forall (C:int) (D:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((iff (((zcong C) ((times_times_int D) A)) M)) (((zcong C) ((times_times_int D) B)) M)))).
% 2.38/2.81 Axiom fact_593_zcong__scalar:(forall (K:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->(((zcong ((times_times_int A) K)) ((times_times_int B) K)) M))).
% 2.38/2.81 Axiom fact_594_zcong__scalar2:(forall (K:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->(((zcong ((times_times_int K) A)) ((times_times_int K) B)) M))).
% 2.38/2.81 Axiom fact_595_zcong__zmult:(forall (C:int) (D:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((zcong C) D) M)->(((zcong ((times_times_int A) C)) ((times_times_int B) D)) M)))).
% 2.38/2.81 Axiom fact_596_zcong__zadd:(forall (C:int) (D:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((zcong C) D) M)->(((zcong ((plus_plus_int A) C)) ((plus_plus_int B) D)) M)))).
% 2.38/2.81 Axiom fact_597_zcong__shift:(forall (C:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->(((zcong ((plus_plus_int A) C)) ((plus_plus_int B) C)) M))).
% 2.38/2.81 Axiom fact_598_zcong__zpower:(forall (Z:nat) (X:int) (Y:int) (M:int), ((((zcong X) Y) M)->(((zcong ((power_power_int X) Z)) ((power_power_int Y) Z)) M))).
% 2.38/2.81 Axiom fact_599_power__m1__even:(forall (N_12:nat), (((eq real) ((power_power_real (number267125858f_real min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_12))) one_one_real)).
% 2.38/2.81 Axiom fact_600_power__m1__even:(forall (N_12:nat), (((eq int) ((power_power_int (number_number_of_int min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_12))) one_one_int)).
% 2.38/2.81 Axiom fact_601_split__mult__neg__le:(forall (B_50:real) (A_61:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_61)) ((ord_less_eq_real B_50) zero_zero_real))) ((and ((ord_less_eq_real A_61) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_50)))->((ord_less_eq_real ((times_times_real A_61) B_50)) zero_zero_real))).
% 2.38/2.81 Axiom fact_602_split__mult__neg__le:(forall (B_50:nat) (A_61:nat), (((or ((and ((ord_less_eq_nat zero_zero_nat) A_61)) ((ord_less_eq_nat B_50) zero_zero_nat))) ((and ((ord_less_eq_nat A_61) zero_zero_nat)) ((ord_less_eq_nat zero_zero_nat) B_50)))->((ord_less_eq_nat ((times_times_nat A_61) B_50)) zero_zero_nat))).
% 2.38/2.81 Axiom fact_603_split__mult__neg__le:(forall (B_50:int) (A_61:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_61)) ((ord_less_eq_int B_50) zero_zero_int))) ((and ((ord_less_eq_int A_61) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_50)))->((ord_less_eq_int ((times_times_int A_61) B_50)) zero_zero_int))).
% 2.38/2.81 Axiom fact_604_split__mult__pos__le:(forall (B_49:real) (A_60:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_60)) ((ord_less_eq_real zero_zero_real) B_49))) ((and ((ord_less_eq_real A_60) zero_zero_real)) ((ord_less_eq_real B_49) zero_zero_real)))->((ord_less_eq_real zero_zero_real) ((times_times_real A_60) B_49)))).
% 2.38/2.81 Axiom fact_605_split__mult__pos__le:(forall (B_49:int) (A_60:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_60)) ((ord_less_eq_int zero_zero_int) B_49))) ((and ((ord_less_eq_int A_60) zero_zero_int)) ((ord_less_eq_int B_49) zero_zero_int)))->((ord_less_eq_int zero_zero_int) ((times_times_int A_60) B_49)))).
% 2.38/2.81 Axiom fact_606_mult__mono:(forall (C_31:real) (D_8:real) (A_59:real) (B_48:real), (((ord_less_eq_real A_59) B_48)->(((ord_less_eq_real C_31) D_8)->(((ord_less_eq_real zero_zero_real) B_48)->(((ord_less_eq_real zero_zero_real) C_31)->((ord_less_eq_real ((times_times_real A_59) C_31)) ((times_times_real B_48) D_8))))))).
% 2.38/2.81 Axiom fact_607_mult__mono:(forall (C_31:nat) (D_8:nat) (A_59:nat) (B_48:nat), (((ord_less_eq_nat A_59) B_48)->(((ord_less_eq_nat C_31) D_8)->(((ord_less_eq_nat zero_zero_nat) B_48)->(((ord_less_eq_nat zero_zero_nat) C_31)->((ord_less_eq_nat ((times_times_nat A_59) C_31)) ((times_times_nat B_48) D_8))))))).
% 2.38/2.81 Axiom fact_608_mult__mono:(forall (C_31:int) (D_8:int) (A_59:int) (B_48:int), (((ord_less_eq_int A_59) B_48)->(((ord_less_eq_int C_31) D_8)->(((ord_less_eq_int zero_zero_int) B_48)->(((ord_less_eq_int zero_zero_int) C_31)->((ord_less_eq_int ((times_times_int A_59) C_31)) ((times_times_int B_48) D_8))))))).
% 2.38/2.81 Axiom fact_609_mult__mono_H:(forall (C_30:real) (D_7:real) (A_58:real) (B_47:real), (((ord_less_eq_real A_58) B_47)->(((ord_less_eq_real C_30) D_7)->(((ord_less_eq_real zero_zero_real) A_58)->(((ord_less_eq_real zero_zero_real) C_30)->((ord_less_eq_real ((times_times_real A_58) C_30)) ((times_times_real B_47) D_7))))))).
% 2.38/2.81 Axiom fact_610_mult__mono_H:(forall (C_30:nat) (D_7:nat) (A_58:nat) (B_47:nat), (((ord_less_eq_nat A_58) B_47)->(((ord_less_eq_nat C_30) D_7)->(((ord_less_eq_nat zero_zero_nat) A_58)->(((ord_less_eq_nat zero_zero_nat) C_30)->((ord_less_eq_nat ((times_times_nat A_58) C_30)) ((times_times_nat B_47) D_7))))))).
% 2.38/2.81 Axiom fact_611_mult__mono_H:(forall (C_30:int) (D_7:int) (A_58:int) (B_47:int), (((ord_less_eq_int A_58) B_47)->(((ord_less_eq_int C_30) D_7)->(((ord_less_eq_int zero_zero_int) A_58)->(((ord_less_eq_int zero_zero_int) C_30)->((ord_less_eq_int ((times_times_int A_58) C_30)) ((times_times_int B_47) D_7))))))).
% 2.38/2.81 Axiom fact_612_mult__left__mono__neg:(forall (C_29:real) (B_46:real) (A_57:real), (((ord_less_eq_real B_46) A_57)->(((ord_less_eq_real C_29) zero_zero_real)->((ord_less_eq_real ((times_times_real C_29) A_57)) ((times_times_real C_29) B_46))))).
% 2.38/2.81 Axiom fact_613_mult__left__mono__neg:(forall (C_29:int) (B_46:int) (A_57:int), (((ord_less_eq_int B_46) A_57)->(((ord_less_eq_int C_29) zero_zero_int)->((ord_less_eq_int ((times_times_int C_29) A_57)) ((times_times_int C_29) B_46))))).
% 2.38/2.81 Axiom fact_614_mult__right__mono__neg:(forall (C_28:real) (B_45:real) (A_56:real), (((ord_less_eq_real B_45) A_56)->(((ord_less_eq_real C_28) zero_zero_real)->((ord_less_eq_real ((times_times_real A_56) C_28)) ((times_times_real B_45) C_28))))).
% 2.38/2.81 Axiom fact_615_mult__right__mono__neg:(forall (C_28:int) (B_45:int) (A_56:int), (((ord_less_eq_int B_45) A_56)->(((ord_less_eq_int C_28) zero_zero_int)->((ord_less_eq_int ((times_times_int A_56) C_28)) ((times_times_int B_45) C_28))))).
% 2.38/2.81 Axiom fact_616_comm__mult__left__mono:(forall (C_27:real) (A_55:real) (B_44:real), (((ord_less_eq_real A_55) B_44)->(((ord_less_eq_real zero_zero_real) C_27)->((ord_less_eq_real ((times_times_real C_27) A_55)) ((times_times_real C_27) B_44))))).
% 2.38/2.81 Axiom fact_617_comm__mult__left__mono:(forall (C_27:nat) (A_55:nat) (B_44:nat), (((ord_less_eq_nat A_55) B_44)->(((ord_less_eq_nat zero_zero_nat) C_27)->((ord_less_eq_nat ((times_times_nat C_27) A_55)) ((times_times_nat C_27) B_44))))).
% 2.38/2.81 Axiom fact_618_comm__mult__left__mono:(forall (C_27:int) (A_55:int) (B_44:int), (((ord_less_eq_int A_55) B_44)->(((ord_less_eq_int zero_zero_int) C_27)->((ord_less_eq_int ((times_times_int C_27) A_55)) ((times_times_int C_27) B_44))))).
% 2.38/2.81 Axiom fact_619_mult__left__mono:(forall (C_26:real) (A_54:real) (B_43:real), (((ord_less_eq_real A_54) B_43)->(((ord_less_eq_real zero_zero_real) C_26)->((ord_less_eq_real ((times_times_real C_26) A_54)) ((times_times_real C_26) B_43))))).
% 2.38/2.81 Axiom fact_620_mult__left__mono:(forall (C_26:nat) (A_54:nat) (B_43:nat), (((ord_less_eq_nat A_54) B_43)->(((ord_less_eq_nat zero_zero_nat) C_26)->((ord_less_eq_nat ((times_times_nat C_26) A_54)) ((times_times_nat C_26) B_43))))).
% 2.38/2.81 Axiom fact_621_mult__left__mono:(forall (C_26:int) (A_54:int) (B_43:int), (((ord_less_eq_int A_54) B_43)->(((ord_less_eq_int zero_zero_int) C_26)->((ord_less_eq_int ((times_times_int C_26) A_54)) ((times_times_int C_26) B_43))))).
% 2.38/2.81 Axiom fact_622_mult__right__mono:(forall (C_25:real) (A_53:real) (B_42:real), (((ord_less_eq_real A_53) B_42)->(((ord_less_eq_real zero_zero_real) C_25)->((ord_less_eq_real ((times_times_real A_53) C_25)) ((times_times_real B_42) C_25))))).
% 2.38/2.81 Axiom fact_623_mult__right__mono:(forall (C_25:nat) (A_53:nat) (B_42:nat), (((ord_less_eq_nat A_53) B_42)->(((ord_less_eq_nat zero_zero_nat) C_25)->((ord_less_eq_nat ((times_times_nat A_53) C_25)) ((times_times_nat B_42) C_25))))).
% 2.38/2.81 Axiom fact_624_mult__right__mono:(forall (C_25:int) (A_53:int) (B_42:int), (((ord_less_eq_int A_53) B_42)->(((ord_less_eq_int zero_zero_int) C_25)->((ord_less_eq_int ((times_times_int A_53) C_25)) ((times_times_int B_42) C_25))))).
% 2.38/2.81 Axiom fact_625_mult__nonpos__nonpos:(forall (B_41:real) (A_52:real), (((ord_less_eq_real A_52) zero_zero_real)->(((ord_less_eq_real B_41) zero_zero_real)->((ord_less_eq_real zero_zero_real) ((times_times_real A_52) B_41))))).
% 2.38/2.81 Axiom fact_626_mult__nonpos__nonpos:(forall (B_41:int) (A_52:int), (((ord_less_eq_int A_52) zero_zero_int)->(((ord_less_eq_int B_41) zero_zero_int)->((ord_less_eq_int zero_zero_int) ((times_times_int A_52) B_41))))).
% 2.38/2.81 Axiom fact_627_mult__nonpos__nonneg:(forall (B_40:real) (A_51:real), (((ord_less_eq_real A_51) zero_zero_real)->(((ord_less_eq_real zero_zero_real) B_40)->((ord_less_eq_real ((times_times_real A_51) B_40)) zero_zero_real)))).
% 2.38/2.81 Axiom fact_628_mult__nonpos__nonneg:(forall (B_40:nat) (A_51:nat), (((ord_less_eq_nat A_51) zero_zero_nat)->(((ord_less_eq_nat zero_zero_nat) B_40)->((ord_less_eq_nat ((times_times_nat A_51) B_40)) zero_zero_nat)))).
% 2.38/2.81 Axiom fact_629_mult__nonpos__nonneg:(forall (B_40:int) (A_51:int), (((ord_less_eq_int A_51) zero_zero_int)->(((ord_less_eq_int zero_zero_int) B_40)->((ord_less_eq_int ((times_times_int A_51) B_40)) zero_zero_int)))).
% 2.38/2.81 Axiom fact_630_mult__nonneg__nonpos2:(forall (B_39:real) (A_50:real), (((ord_less_eq_real zero_zero_real) A_50)->(((ord_less_eq_real B_39) zero_zero_real)->((ord_less_eq_real ((times_times_real B_39) A_50)) zero_zero_real)))).
% 2.38/2.81 Axiom fact_631_mult__nonneg__nonpos2:(forall (B_39:nat) (A_50:nat), (((ord_less_eq_nat zero_zero_nat) A_50)->(((ord_less_eq_nat B_39) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat B_39) A_50)) zero_zero_nat)))).
% 2.38/2.81 Axiom fact_632_mult__nonneg__nonpos2:(forall (B_39:int) (A_50:int), (((ord_less_eq_int zero_zero_int) A_50)->(((ord_less_eq_int B_39) zero_zero_int)->((ord_less_eq_int ((times_times_int B_39) A_50)) zero_zero_int)))).
% 2.38/2.81 Axiom fact_633_mult__nonneg__nonpos:(forall (B_38:real) (A_49:real), (((ord_less_eq_real zero_zero_real) A_49)->(((ord_less_eq_real B_38) zero_zero_real)->((ord_less_eq_real ((times_times_real A_49) B_38)) zero_zero_real)))).
% 2.38/2.81 Axiom fact_634_mult__nonneg__nonpos:(forall (B_38:nat) (A_49:nat), (((ord_less_eq_nat zero_zero_nat) A_49)->(((ord_less_eq_nat B_38) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat A_49) B_38)) zero_zero_nat)))).
% 2.38/2.81 Axiom fact_635_mult__nonneg__nonpos:(forall (B_38:int) (A_49:int), (((ord_less_eq_int zero_zero_int) A_49)->(((ord_less_eq_int B_38) zero_zero_int)->((ord_less_eq_int ((times_times_int A_49) B_38)) zero_zero_int)))).
% 2.38/2.81 Axiom fact_636_mult__nonneg__nonneg:(forall (B_37:real) (A_48:real), (((ord_less_eq_real zero_zero_real) A_48)->(((ord_less_eq_real zero_zero_real) B_37)->((ord_less_eq_real zero_zero_real) ((times_times_real A_48) B_37))))).
% 2.38/2.81 Axiom fact_637_mult__nonneg__nonneg:(forall (B_37:nat) (A_48:nat), (((ord_less_eq_nat zero_zero_nat) A_48)->(((ord_less_eq_nat zero_zero_nat) B_37)->((ord_less_eq_nat zero_zero_nat) ((times_times_nat A_48) B_37))))).
% 2.38/2.81 Axiom fact_638_mult__nonneg__nonneg:(forall (B_37:int) (A_48:int), (((ord_less_eq_int zero_zero_int) A_48)->(((ord_less_eq_int zero_zero_int) B_37)->((ord_less_eq_int zero_zero_int) ((times_times_int A_48) B_37))))).
% 2.38/2.81 Axiom fact_639_mult__le__0__iff:(forall (A_47:real) (B_36:real), ((iff ((ord_less_eq_real ((times_times_real A_47) B_36)) zero_zero_real)) ((or ((and ((ord_less_eq_real zero_zero_real) A_47)) ((ord_less_eq_real B_36) zero_zero_real))) ((and ((ord_less_eq_real A_47) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_36))))).
% 2.38/2.81 Axiom fact_640_mult__le__0__iff:(forall (A_47:int) (B_36:int), ((iff ((ord_less_eq_int ((times_times_int A_47) B_36)) zero_zero_int)) ((or ((and ((ord_less_eq_int zero_zero_int) A_47)) ((ord_less_eq_int B_36) zero_zero_int))) ((and ((ord_less_eq_int A_47) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_36))))).
% 2.38/2.81 Axiom fact_641_zero__le__mult__iff:(forall (A_46:real) (B_35:real), ((iff ((ord_less_eq_real zero_zero_real) ((times_times_real A_46) B_35))) ((or ((and ((ord_less_eq_real zero_zero_real) A_46)) ((ord_less_eq_real zero_zero_real) B_35))) ((and ((ord_less_eq_real A_46) zero_zero_real)) ((ord_less_eq_real B_35) zero_zero_real))))).
% 2.38/2.81 Axiom fact_642_zero__le__mult__iff:(forall (A_46:int) (B_35:int), ((iff ((ord_less_eq_int zero_zero_int) ((times_times_int A_46) B_35))) ((or ((and ((ord_less_eq_int zero_zero_int) A_46)) ((ord_less_eq_int zero_zero_int) B_35))) ((and ((ord_less_eq_int A_46) zero_zero_int)) ((ord_less_eq_int B_35) zero_zero_int))))).
% 2.38/2.81 Axiom fact_643_zero__le__square:(forall (A_45:real), ((ord_less_eq_real zero_zero_real) ((times_times_real A_45) A_45))).
% 2.38/2.81 Axiom fact_644_zero__le__square:(forall (A_45:int), ((ord_less_eq_int zero_zero_int) ((times_times_int A_45) A_45))).
% 2.38/2.81 Axiom fact_645_mult__strict__left__mono__neg:(forall (C_24:real) (B_34:real) (A_44:real), (((ord_less_real B_34) A_44)->(((ord_less_real C_24) zero_zero_real)->((ord_less_real ((times_times_real C_24) A_44)) ((times_times_real C_24) B_34))))).
% 2.38/2.81 Axiom fact_646_mult__strict__left__mono__neg:(forall (C_24:int) (B_34:int) (A_44:int), (((ord_less_int B_34) A_44)->(((ord_less_int C_24) zero_zero_int)->((ord_less_int ((times_times_int C_24) A_44)) ((times_times_int C_24) B_34))))).
% 2.38/2.81 Axiom fact_647_mult__strict__right__mono__neg:(forall (C_23:real) (B_33:real) (A_43:real), (((ord_less_real B_33) A_43)->(((ord_less_real C_23) zero_zero_real)->((ord_less_real ((times_times_real A_43) C_23)) ((times_times_real B_33) C_23))))).
% 2.38/2.81 Axiom fact_648_mult__strict__right__mono__neg:(forall (C_23:int) (B_33:int) (A_43:int), (((ord_less_int B_33) A_43)->(((ord_less_int C_23) zero_zero_int)->((ord_less_int ((times_times_int A_43) C_23)) ((times_times_int B_33) C_23))))).
% 2.38/2.81 Axiom fact_649_comm__mult__strict__left__mono:(forall (C_22:real) (A_42:real) (B_32:real), (((ord_less_real A_42) B_32)->(((ord_less_real zero_zero_real) C_22)->((ord_less_real ((times_times_real C_22) A_42)) ((times_times_real C_22) B_32))))).
% 2.38/2.81 Axiom fact_650_comm__mult__strict__left__mono:(forall (C_22:nat) (A_42:nat) (B_32:nat), (((ord_less_nat A_42) B_32)->(((ord_less_nat zero_zero_nat) C_22)->((ord_less_nat ((times_times_nat C_22) A_42)) ((times_times_nat C_22) B_32))))).
% 2.38/2.82 Axiom fact_651_comm__mult__strict__left__mono:(forall (C_22:int) (A_42:int) (B_32:int), (((ord_less_int A_42) B_32)->(((ord_less_int zero_zero_int) C_22)->((ord_less_int ((times_times_int C_22) A_42)) ((times_times_int C_22) B_32))))).
% 2.38/2.82 Axiom fact_652_mult__strict__left__mono:(forall (C_21:real) (A_41:real) (B_31:real), (((ord_less_real A_41) B_31)->(((ord_less_real zero_zero_real) C_21)->((ord_less_real ((times_times_real C_21) A_41)) ((times_times_real C_21) B_31))))).
% 2.38/2.82 Axiom fact_653_mult__strict__left__mono:(forall (C_21:nat) (A_41:nat) (B_31:nat), (((ord_less_nat A_41) B_31)->(((ord_less_nat zero_zero_nat) C_21)->((ord_less_nat ((times_times_nat C_21) A_41)) ((times_times_nat C_21) B_31))))).
% 2.38/2.82 Axiom fact_654_mult__strict__left__mono:(forall (C_21:int) (A_41:int) (B_31:int), (((ord_less_int A_41) B_31)->(((ord_less_int zero_zero_int) C_21)->((ord_less_int ((times_times_int C_21) A_41)) ((times_times_int C_21) B_31))))).
% 2.38/2.82 Axiom fact_655_mult__strict__right__mono:(forall (C_20:real) (A_40:real) (B_30:real), (((ord_less_real A_40) B_30)->(((ord_less_real zero_zero_real) C_20)->((ord_less_real ((times_times_real A_40) C_20)) ((times_times_real B_30) C_20))))).
% 2.38/2.82 Axiom fact_656_mult__strict__right__mono:(forall (C_20:nat) (A_40:nat) (B_30:nat), (((ord_less_nat A_40) B_30)->(((ord_less_nat zero_zero_nat) C_20)->((ord_less_nat ((times_times_nat A_40) C_20)) ((times_times_nat B_30) C_20))))).
% 2.38/2.82 Axiom fact_657_mult__strict__right__mono:(forall (C_20:int) (A_40:int) (B_30:int), (((ord_less_int A_40) B_30)->(((ord_less_int zero_zero_int) C_20)->((ord_less_int ((times_times_int A_40) C_20)) ((times_times_int B_30) C_20))))).
% 2.38/2.82 Axiom fact_658_mult__neg__neg:(forall (B_29:real) (A_39:real), (((ord_less_real A_39) zero_zero_real)->(((ord_less_real B_29) zero_zero_real)->((ord_less_real zero_zero_real) ((times_times_real A_39) B_29))))).
% 2.38/2.82 Axiom fact_659_mult__neg__neg:(forall (B_29:int) (A_39:int), (((ord_less_int A_39) zero_zero_int)->(((ord_less_int B_29) zero_zero_int)->((ord_less_int zero_zero_int) ((times_times_int A_39) B_29))))).
% 2.38/2.82 Axiom fact_660_mult__neg__pos:(forall (B_28:real) (A_38:real), (((ord_less_real A_38) zero_zero_real)->(((ord_less_real zero_zero_real) B_28)->((ord_less_real ((times_times_real A_38) B_28)) zero_zero_real)))).
% 2.38/2.82 Axiom fact_661_mult__neg__pos:(forall (B_28:nat) (A_38:nat), (((ord_less_nat A_38) zero_zero_nat)->(((ord_less_nat zero_zero_nat) B_28)->((ord_less_nat ((times_times_nat A_38) B_28)) zero_zero_nat)))).
% 2.38/2.82 Axiom fact_662_mult__neg__pos:(forall (B_28:int) (A_38:int), (((ord_less_int A_38) zero_zero_int)->(((ord_less_int zero_zero_int) B_28)->((ord_less_int ((times_times_int A_38) B_28)) zero_zero_int)))).
% 2.38/2.82 Axiom fact_663_mult__less__cancel__left__neg:(forall (A_37:real) (B_27:real) (C_19:real), (((ord_less_real C_19) zero_zero_real)->((iff ((ord_less_real ((times_times_real C_19) A_37)) ((times_times_real C_19) B_27))) ((ord_less_real B_27) A_37)))).
% 2.38/2.82 Axiom fact_664_mult__less__cancel__left__neg:(forall (A_37:int) (B_27:int) (C_19:int), (((ord_less_int C_19) zero_zero_int)->((iff ((ord_less_int ((times_times_int C_19) A_37)) ((times_times_int C_19) B_27))) ((ord_less_int B_27) A_37)))).
% 2.38/2.82 Axiom fact_665_zero__less__mult__pos2:(forall (B_26:real) (A_36:real), (((ord_less_real zero_zero_real) ((times_times_real B_26) A_36))->(((ord_less_real zero_zero_real) A_36)->((ord_less_real zero_zero_real) B_26)))).
% 2.38/2.82 Axiom fact_666_zero__less__mult__pos2:(forall (B_26:nat) (A_36:nat), (((ord_less_nat zero_zero_nat) ((times_times_nat B_26) A_36))->(((ord_less_nat zero_zero_nat) A_36)->((ord_less_nat zero_zero_nat) B_26)))).
% 2.38/2.82 Axiom fact_667_zero__less__mult__pos2:(forall (B_26:int) (A_36:int), (((ord_less_int zero_zero_int) ((times_times_int B_26) A_36))->(((ord_less_int zero_zero_int) A_36)->((ord_less_int zero_zero_int) B_26)))).
% 2.38/2.82 Axiom fact_668_zero__less__mult__pos:(forall (A_35:real) (B_25:real), (((ord_less_real zero_zero_real) ((times_times_real A_35) B_25))->(((ord_less_real zero_zero_real) A_35)->((ord_less_real zero_zero_real) B_25)))).
% 2.48/2.82 Axiom fact_669_zero__less__mult__pos:(forall (A_35:nat) (B_25:nat), (((ord_less_nat zero_zero_nat) ((times_times_nat A_35) B_25))->(((ord_less_nat zero_zero_nat) A_35)->((ord_less_nat zero_zero_nat) B_25)))).
% 2.48/2.82 Axiom fact_670_zero__less__mult__pos:(forall (A_35:int) (B_25:int), (((ord_less_int zero_zero_int) ((times_times_int A_35) B_25))->(((ord_less_int zero_zero_int) A_35)->((ord_less_int zero_zero_int) B_25)))).
% 2.48/2.82 Axiom fact_671_mult__pos__neg2:(forall (B_24:real) (A_34:real), (((ord_less_real zero_zero_real) A_34)->(((ord_less_real B_24) zero_zero_real)->((ord_less_real ((times_times_real B_24) A_34)) zero_zero_real)))).
% 2.48/2.82 Axiom fact_672_mult__pos__neg2:(forall (B_24:nat) (A_34:nat), (((ord_less_nat zero_zero_nat) A_34)->(((ord_less_nat B_24) zero_zero_nat)->((ord_less_nat ((times_times_nat B_24) A_34)) zero_zero_nat)))).
% 2.48/2.82 Axiom fact_673_mult__pos__neg2:(forall (B_24:int) (A_34:int), (((ord_less_int zero_zero_int) A_34)->(((ord_less_int B_24) zero_zero_int)->((ord_less_int ((times_times_int B_24) A_34)) zero_zero_int)))).
% 2.48/2.82 Axiom fact_674_mult__pos__neg:(forall (B_23:real) (A_33:real), (((ord_less_real zero_zero_real) A_33)->(((ord_less_real B_23) zero_zero_real)->((ord_less_real ((times_times_real A_33) B_23)) zero_zero_real)))).
% 2.48/2.82 Axiom fact_675_mult__pos__neg:(forall (B_23:nat) (A_33:nat), (((ord_less_nat zero_zero_nat) A_33)->(((ord_less_nat B_23) zero_zero_nat)->((ord_less_nat ((times_times_nat A_33) B_23)) zero_zero_nat)))).
% 2.48/2.82 Axiom fact_676_mult__pos__neg:(forall (B_23:int) (A_33:int), (((ord_less_int zero_zero_int) A_33)->(((ord_less_int B_23) zero_zero_int)->((ord_less_int ((times_times_int A_33) B_23)) zero_zero_int)))).
% 2.48/2.82 Axiom fact_677_mult__pos__pos:(forall (B_22:real) (A_32:real), (((ord_less_real zero_zero_real) A_32)->(((ord_less_real zero_zero_real) B_22)->((ord_less_real zero_zero_real) ((times_times_real A_32) B_22))))).
% 2.48/2.82 Axiom fact_678_mult__pos__pos:(forall (B_22:nat) (A_32:nat), (((ord_less_nat zero_zero_nat) A_32)->(((ord_less_nat zero_zero_nat) B_22)->((ord_less_nat zero_zero_nat) ((times_times_nat A_32) B_22))))).
% 2.48/2.82 Axiom fact_679_mult__pos__pos:(forall (B_22:int) (A_32:int), (((ord_less_int zero_zero_int) A_32)->(((ord_less_int zero_zero_int) B_22)->((ord_less_int zero_zero_int) ((times_times_int A_32) B_22))))).
% 2.48/2.82 Axiom fact_680_mult__less__cancel__left__pos:(forall (A_31:real) (B_21:real) (C_18:real), (((ord_less_real zero_zero_real) C_18)->((iff ((ord_less_real ((times_times_real C_18) A_31)) ((times_times_real C_18) B_21))) ((ord_less_real A_31) B_21)))).
% 2.48/2.82 Axiom fact_681_mult__less__cancel__left__pos:(forall (A_31:int) (B_21:int) (C_18:int), (((ord_less_int zero_zero_int) C_18)->((iff ((ord_less_int ((times_times_int C_18) A_31)) ((times_times_int C_18) B_21))) ((ord_less_int A_31) B_21)))).
% 2.48/2.82 Axiom fact_682_mult__less__cancel__left__disj:(forall (C_17:real) (A_30:real) (B_20:real), ((iff ((ord_less_real ((times_times_real C_17) A_30)) ((times_times_real C_17) B_20))) ((or ((and ((ord_less_real zero_zero_real) C_17)) ((ord_less_real A_30) B_20))) ((and ((ord_less_real C_17) zero_zero_real)) ((ord_less_real B_20) A_30))))).
% 2.48/2.82 Axiom fact_683_mult__less__cancel__left__disj:(forall (C_17:int) (A_30:int) (B_20:int), ((iff ((ord_less_int ((times_times_int C_17) A_30)) ((times_times_int C_17) B_20))) ((or ((and ((ord_less_int zero_zero_int) C_17)) ((ord_less_int A_30) B_20))) ((and ((ord_less_int C_17) zero_zero_int)) ((ord_less_int B_20) A_30))))).
% 2.48/2.82 Axiom fact_684_mult__less__cancel__right__disj:(forall (A_29:real) (C_16:real) (B_19:real), ((iff ((ord_less_real ((times_times_real A_29) C_16)) ((times_times_real B_19) C_16))) ((or ((and ((ord_less_real zero_zero_real) C_16)) ((ord_less_real A_29) B_19))) ((and ((ord_less_real C_16) zero_zero_real)) ((ord_less_real B_19) A_29))))).
% 2.48/2.82 Axiom fact_685_mult__less__cancel__right__disj:(forall (A_29:int) (C_16:int) (B_19:int), ((iff ((ord_less_int ((times_times_int A_29) C_16)) ((times_times_int B_19) C_16))) ((or ((and ((ord_less_int zero_zero_int) C_16)) ((ord_less_int A_29) B_19))) ((and ((ord_less_int C_16) zero_zero_int)) ((ord_less_int B_19) A_29))))).
% 2.48/2.82 Axiom fact_686_not__square__less__zero:(forall (A_28:real), (((ord_less_real ((times_times_real A_28) A_28)) zero_zero_real)->False)).
% 2.48/2.82 Axiom fact_687_not__square__less__zero:(forall (A_28:int), (((ord_less_int ((times_times_int A_28) A_28)) zero_zero_int)->False)).
% 2.48/2.82 Axiom fact_688_pos__add__strict:(forall (B_18:real) (C_15:real) (A_27:real), (((ord_less_real zero_zero_real) A_27)->(((ord_less_real B_18) C_15)->((ord_less_real B_18) ((plus_plus_real A_27) C_15))))).
% 2.48/2.82 Axiom fact_689_pos__add__strict:(forall (B_18:nat) (C_15:nat) (A_27:nat), (((ord_less_nat zero_zero_nat) A_27)->(((ord_less_nat B_18) C_15)->((ord_less_nat B_18) ((plus_plus_nat A_27) C_15))))).
% 2.48/2.82 Axiom fact_690_pos__add__strict:(forall (B_18:int) (C_15:int) (A_27:int), (((ord_less_int zero_zero_int) A_27)->(((ord_less_int B_18) C_15)->((ord_less_int B_18) ((plus_plus_int A_27) C_15))))).
% 2.48/2.82 Axiom fact_691_zero__le__one:((ord_less_eq_real zero_zero_real) one_one_real).
% 2.48/2.82 Axiom fact_692_zero__le__one:((ord_less_eq_nat zero_zero_nat) one_one_nat).
% 2.48/2.82 Axiom fact_693_zero__le__one:((ord_less_eq_int zero_zero_int) one_one_int).
% 2.48/2.82 Axiom fact_694_not__one__le__zero:(((ord_less_eq_real one_one_real) zero_zero_real)->False).
% 2.48/2.82 Axiom fact_695_not__one__le__zero:(((ord_less_eq_nat one_one_nat) zero_zero_nat)->False).
% 2.48/2.82 Axiom fact_696_not__one__le__zero:(((ord_less_eq_int one_one_int) zero_zero_int)->False).
% 2.48/2.82 Axiom fact_697_zero__less__one:((ord_less_real zero_zero_real) one_one_real).
% 2.48/2.82 Axiom fact_698_zero__less__one:((ord_less_nat zero_zero_nat) one_one_nat).
% 2.48/2.82 Axiom fact_699_zero__less__one:((ord_less_int zero_zero_int) one_one_int).
% 2.48/2.82 Axiom fact_700_not__one__less__zero:(((ord_less_real one_one_real) zero_zero_real)->False).
% 2.48/2.82 Axiom fact_701_not__one__less__zero:(((ord_less_nat one_one_nat) zero_zero_nat)->False).
% 2.48/2.82 Axiom fact_702_not__one__less__zero:(((ord_less_int one_one_int) zero_zero_int)->False).
% 2.48/2.82 Axiom fact_703_power__mono:(forall (N_11:nat) (A_26:real) (B_17:real), (((ord_less_eq_real A_26) B_17)->(((ord_less_eq_real zero_zero_real) A_26)->((ord_less_eq_real ((power_power_real A_26) N_11)) ((power_power_real B_17) N_11))))).
% 2.48/2.82 Axiom fact_704_power__mono:(forall (N_11:nat) (A_26:nat) (B_17:nat), (((ord_less_eq_nat A_26) B_17)->(((ord_less_eq_nat zero_zero_nat) A_26)->((ord_less_eq_nat ((power_power_nat A_26) N_11)) ((power_power_nat B_17) N_11))))).
% 2.48/2.82 Axiom fact_705_power__mono:(forall (N_11:nat) (A_26:int) (B_17:int), (((ord_less_eq_int A_26) B_17)->(((ord_less_eq_int zero_zero_int) A_26)->((ord_less_eq_int ((power_power_int A_26) N_11)) ((power_power_int B_17) N_11))))).
% 2.48/2.82 Axiom fact_706_zero__le__power:(forall (N_10:nat) (A_25:real), (((ord_less_eq_real zero_zero_real) A_25)->((ord_less_eq_real zero_zero_real) ((power_power_real A_25) N_10)))).
% 2.48/2.82 Axiom fact_707_zero__le__power:(forall (N_10:nat) (A_25:nat), (((ord_less_eq_nat zero_zero_nat) A_25)->((ord_less_eq_nat zero_zero_nat) ((power_power_nat A_25) N_10)))).
% 2.48/2.82 Axiom fact_708_zero__le__power:(forall (N_10:nat) (A_25:int), (((ord_less_eq_int zero_zero_int) A_25)->((ord_less_eq_int zero_zero_int) ((power_power_int A_25) N_10)))).
% 2.48/2.82 Axiom fact_709_less__1__mult:(forall (N_9:real) (M_5:real), (((ord_less_real one_one_real) M_5)->(((ord_less_real one_one_real) N_9)->((ord_less_real one_one_real) ((times_times_real M_5) N_9))))).
% 2.48/2.82 Axiom fact_710_less__1__mult:(forall (N_9:nat) (M_5:nat), (((ord_less_nat one_one_nat) M_5)->(((ord_less_nat one_one_nat) N_9)->((ord_less_nat one_one_nat) ((times_times_nat M_5) N_9))))).
% 2.48/2.82 Axiom fact_711_less__1__mult:(forall (N_9:int) (M_5:int), (((ord_less_int one_one_int) M_5)->(((ord_less_int one_one_int) N_9)->((ord_less_int one_one_int) ((times_times_int M_5) N_9))))).
% 2.48/2.82 Axiom fact_712_zero__less__power:(forall (N_8:nat) (A_24:real), (((ord_less_real zero_zero_real) A_24)->((ord_less_real zero_zero_real) ((power_power_real A_24) N_8)))).
% 2.48/2.82 Axiom fact_713_zero__less__power:(forall (N_8:nat) (A_24:nat), (((ord_less_nat zero_zero_nat) A_24)->((ord_less_nat zero_zero_nat) ((power_power_nat A_24) N_8)))).
% 2.48/2.82 Axiom fact_714_zero__less__power:(forall (N_8:nat) (A_24:int), (((ord_less_int zero_zero_int) A_24)->((ord_less_int zero_zero_int) ((power_power_int A_24) N_8)))).
% 2.48/2.82 Axiom fact_715_less__add__one:(forall (A_23:real), ((ord_less_real A_23) ((plus_plus_real A_23) one_one_real))).
% 2.48/2.82 Axiom fact_716_less__add__one:(forall (A_23:nat), ((ord_less_nat A_23) ((plus_plus_nat A_23) one_one_nat))).
% 2.48/2.82 Axiom fact_717_less__add__one:(forall (A_23:int), ((ord_less_int A_23) ((plus_plus_int A_23) one_one_int))).
% 2.48/2.82 Axiom fact_718_dvd__mult__cancel__left:(forall (C_14:int) (A_22:int) (B_16:int), ((iff ((dvd_dvd_int ((times_times_int C_14) A_22)) ((times_times_int C_14) B_16))) ((or (((eq int) C_14) zero_zero_int)) ((dvd_dvd_int A_22) B_16)))).
% 2.48/2.82 Axiom fact_719_dvd__mult__cancel__left:(forall (C_14:real) (A_22:real) (B_16:real), ((iff ((dvd_dvd_real ((times_times_real C_14) A_22)) ((times_times_real C_14) B_16))) ((or (((eq real) C_14) zero_zero_real)) ((dvd_dvd_real A_22) B_16)))).
% 2.48/2.82 Axiom fact_720_dvd__mult__cancel__right:(forall (A_21:int) (C_13:int) (B_15:int), ((iff ((dvd_dvd_int ((times_times_int A_21) C_13)) ((times_times_int B_15) C_13))) ((or (((eq int) C_13) zero_zero_int)) ((dvd_dvd_int A_21) B_15)))).
% 2.48/2.82 Axiom fact_721_dvd__mult__cancel__right:(forall (A_21:real) (C_13:real) (B_15:real), ((iff ((dvd_dvd_real ((times_times_real A_21) C_13)) ((times_times_real B_15) C_13))) ((or (((eq real) C_13) zero_zero_real)) ((dvd_dvd_real A_21) B_15)))).
% 2.48/2.82 Axiom fact_722_power__increasing:(forall (A_20:real) (N_7:nat) (N_6:nat), (((ord_less_eq_nat N_7) N_6)->(((ord_less_eq_real one_one_real) A_20)->((ord_less_eq_real ((power_power_real A_20) N_7)) ((power_power_real A_20) N_6))))).
% 2.48/2.82 Axiom fact_723_power__increasing:(forall (A_20:nat) (N_7:nat) (N_6:nat), (((ord_less_eq_nat N_7) N_6)->(((ord_less_eq_nat one_one_nat) A_20)->((ord_less_eq_nat ((power_power_nat A_20) N_7)) ((power_power_nat A_20) N_6))))).
% 2.48/2.82 Axiom fact_724_power__increasing:(forall (A_20:int) (N_7:nat) (N_6:nat), (((ord_less_eq_nat N_7) N_6)->(((ord_less_eq_int one_one_int) A_20)->((ord_less_eq_int ((power_power_int A_20) N_7)) ((power_power_int A_20) N_6))))).
% 2.48/2.82 Axiom fact_725_one__le__power:(forall (N_5:nat) (A_19:real), (((ord_less_eq_real one_one_real) A_19)->((ord_less_eq_real one_one_real) ((power_power_real A_19) N_5)))).
% 2.48/2.82 Axiom fact_726_one__le__power:(forall (N_5:nat) (A_19:nat), (((ord_less_eq_nat one_one_nat) A_19)->((ord_less_eq_nat one_one_nat) ((power_power_nat A_19) N_5)))).
% 2.48/2.82 Axiom fact_727_one__le__power:(forall (N_5:nat) (A_19:int), (((ord_less_eq_int one_one_int) A_19)->((ord_less_eq_int one_one_int) ((power_power_int A_19) N_5)))).
% 2.48/2.82 Axiom fact_728_power__inject__exp:(forall (M_4:nat) (N_4:nat) (A_18:real), (((ord_less_real one_one_real) A_18)->((iff (((eq real) ((power_power_real A_18) M_4)) ((power_power_real A_18) N_4))) (((eq nat) M_4) N_4)))).
% 2.48/2.82 Axiom fact_729_power__inject__exp:(forall (M_4:nat) (N_4:nat) (A_18:nat), (((ord_less_nat one_one_nat) A_18)->((iff (((eq nat) ((power_power_nat A_18) M_4)) ((power_power_nat A_18) N_4))) (((eq nat) M_4) N_4)))).
% 2.48/2.82 Axiom fact_730_power__inject__exp:(forall (M_4:nat) (N_4:nat) (A_18:int), (((ord_less_int one_one_int) A_18)->((iff (((eq int) ((power_power_int A_18) M_4)) ((power_power_int A_18) N_4))) (((eq nat) M_4) N_4)))).
% 2.48/2.82 Axiom fact_731_power__eq__0__iff:(forall (A_17:real) (N_3:nat), ((iff (((eq real) ((power_power_real A_17) N_3)) zero_zero_real)) ((and (((eq real) A_17) zero_zero_real)) (not (((eq nat) N_3) zero_zero_nat))))).
% 2.48/2.82 Axiom fact_732_power__eq__0__iff:(forall (A_17:nat) (N_3:nat), ((iff (((eq nat) ((power_power_nat A_17) N_3)) zero_zero_nat)) ((and (((eq nat) A_17) zero_zero_nat)) (not (((eq nat) N_3) zero_zero_nat))))).
% 2.48/2.82 Axiom fact_733_power__eq__0__iff:(forall (A_17:int) (N_3:nat), ((iff (((eq int) ((power_power_int A_17) N_3)) zero_zero_int)) ((and (((eq int) A_17) zero_zero_int)) (not (((eq nat) N_3) zero_zero_nat))))).
% 2.48/2.82 Axiom fact_734_power__0:(forall (A_16:real), (((eq real) ((power_power_real A_16) zero_zero_nat)) one_one_real)).
% 2.48/2.82 Axiom fact_735_power__0:(forall (A_16:nat), (((eq nat) ((power_power_nat A_16) zero_zero_nat)) one_one_nat)).
% 2.48/2.82 Axiom fact_736_power__0:(forall (A_16:int), (((eq int) ((power_power_int A_16) zero_zero_nat)) one_one_int)).
% 2.48/2.82 Axiom fact_737_power__add:(forall (A_15:real) (M_3:nat) (N_2:nat), (((eq real) ((power_power_real A_15) ((plus_plus_nat M_3) N_2))) ((times_times_real ((power_power_real A_15) M_3)) ((power_power_real A_15) N_2)))).
% 2.48/2.82 Axiom fact_738_power__add:(forall (A_15:nat) (M_3:nat) (N_2:nat), (((eq nat) ((power_power_nat A_15) ((plus_plus_nat M_3) N_2))) ((times_times_nat ((power_power_nat A_15) M_3)) ((power_power_nat A_15) N_2)))).
% 2.48/2.82 Axiom fact_739_power__add:(forall (A_15:int) (M_3:nat) (N_2:nat), (((eq int) ((power_power_int A_15) ((plus_plus_nat M_3) N_2))) ((times_times_int ((power_power_int A_15) M_3)) ((power_power_int A_15) N_2)))).
% 2.48/2.82 Axiom fact_740_zcong__not:(forall (B:int) (M:int) (A:int), (((ord_less_int zero_zero_int) A)->(((ord_less_int A) M)->(((ord_less_int zero_zero_int) B)->(((ord_less_int B) A)->((((zcong A) B) M)->False)))))).
% 2.48/2.82 Axiom fact_741_zcong__not__zero:(forall (M:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int X) M)->((((zcong X) zero_zero_int) M)->False)))).
% 2.48/2.82 Axiom fact_742_zcong__less__eq:(forall (M:int) (Y:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int zero_zero_int) Y)->(((ord_less_int zero_zero_int) M)->((((zcong X) Y) M)->(((ord_less_int X) M)->(((ord_less_int Y) M)->(((eq int) X) Y)))))))).
% 2.48/2.82 Axiom fact_743_zdvd__bounds:(forall (N:int) (M:int), (((dvd_dvd_int N) M)->((or ((ord_less_eq_int M) zero_zero_int)) ((ord_less_eq_int N) M)))).
% 2.48/2.82 Axiom fact_744_zcong__iff__lin:(forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) ((ex int) (fun (K_1:int)=> (((eq int) B) ((plus_plus_int A) ((times_times_int M) K_1))))))).
% 2.48/2.82 Axiom fact_745_zcong__eq__zdvd__prop:(forall (X:int) (P_1:int), ((iff (((zcong X) zero_zero_int) P_1)) ((dvd_dvd_int P_1) X))).
% 2.48/2.82 Axiom fact_746_zcong__zero__equiv__div:(forall (A:int) (M:int), ((iff (((zcong A) zero_zero_int) M)) ((dvd_dvd_int M) A))).
% 2.48/2.82 Axiom fact_747_zprime__zdvd__zmult__better:(forall (M:int) (N:int) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((times_times_int M) N))->((or ((dvd_dvd_int P_1) M)) ((dvd_dvd_int P_1) N))))).
% 2.48/2.82 Axiom fact_748_mult__left__le__imp__le:(forall (C_12:real) (A_14:real) (B_14:real), (((ord_less_eq_real ((times_times_real C_12) A_14)) ((times_times_real C_12) B_14))->(((ord_less_real zero_zero_real) C_12)->((ord_less_eq_real A_14) B_14)))).
% 2.48/2.82 Axiom fact_749_mult__left__le__imp__le:(forall (C_12:nat) (A_14:nat) (B_14:nat), (((ord_less_eq_nat ((times_times_nat C_12) A_14)) ((times_times_nat C_12) B_14))->(((ord_less_nat zero_zero_nat) C_12)->((ord_less_eq_nat A_14) B_14)))).
% 2.48/2.82 Axiom fact_750_mult__left__le__imp__le:(forall (C_12:int) (A_14:int) (B_14:int), (((ord_less_eq_int ((times_times_int C_12) A_14)) ((times_times_int C_12) B_14))->(((ord_less_int zero_zero_int) C_12)->((ord_less_eq_int A_14) B_14)))).
% 2.48/2.82 Axiom fact_751_mult__right__le__imp__le:(forall (A_13:real) (C_11:real) (B_13:real), (((ord_less_eq_real ((times_times_real A_13) C_11)) ((times_times_real B_13) C_11))->(((ord_less_real zero_zero_real) C_11)->((ord_less_eq_real A_13) B_13)))).
% 2.48/2.82 Axiom fact_752_mult__right__le__imp__le:(forall (A_13:nat) (C_11:nat) (B_13:nat), (((ord_less_eq_nat ((times_times_nat A_13) C_11)) ((times_times_nat B_13) C_11))->(((ord_less_nat zero_zero_nat) C_11)->((ord_less_eq_nat A_13) B_13)))).
% 2.48/2.82 Axiom fact_753_mult__right__le__imp__le:(forall (A_13:int) (C_11:int) (B_13:int), (((ord_less_eq_int ((times_times_int A_13) C_11)) ((times_times_int B_13) C_11))->(((ord_less_int zero_zero_int) C_11)->((ord_less_eq_int A_13) B_13)))).
% 2.48/2.82 Axiom fact_754_mult__less__imp__less__left:(forall (C_10:real) (A_12:real) (B_12:real), (((ord_less_real ((times_times_real C_10) A_12)) ((times_times_real C_10) B_12))->(((ord_less_eq_real zero_zero_real) C_10)->((ord_less_real A_12) B_12)))).
% 2.48/2.82 Axiom fact_755_mult__less__imp__less__left:(forall (C_10:nat) (A_12:nat) (B_12:nat), (((ord_less_nat ((times_times_nat C_10) A_12)) ((times_times_nat C_10) B_12))->(((ord_less_eq_nat zero_zero_nat) C_10)->((ord_less_nat A_12) B_12)))).
% 2.48/2.82 Axiom fact_756_mult__less__imp__less__left:(forall (C_10:int) (A_12:int) (B_12:int), (((ord_less_int ((times_times_int C_10) A_12)) ((times_times_int C_10) B_12))->(((ord_less_eq_int zero_zero_int) C_10)->((ord_less_int A_12) B_12)))).
% 2.48/2.83 Axiom fact_757_mult__left__less__imp__less:(forall (C_9:real) (A_11:real) (B_11:real), (((ord_less_real ((times_times_real C_9) A_11)) ((times_times_real C_9) B_11))->(((ord_less_eq_real zero_zero_real) C_9)->((ord_less_real A_11) B_11)))).
% 2.48/2.83 Axiom fact_758_mult__left__less__imp__less:(forall (C_9:nat) (A_11:nat) (B_11:nat), (((ord_less_nat ((times_times_nat C_9) A_11)) ((times_times_nat C_9) B_11))->(((ord_less_eq_nat zero_zero_nat) C_9)->((ord_less_nat A_11) B_11)))).
% 2.48/2.83 Axiom fact_759_mult__left__less__imp__less:(forall (C_9:int) (A_11:int) (B_11:int), (((ord_less_int ((times_times_int C_9) A_11)) ((times_times_int C_9) B_11))->(((ord_less_eq_int zero_zero_int) C_9)->((ord_less_int A_11) B_11)))).
% 2.48/2.83 Axiom fact_760_mult__less__imp__less__right:(forall (A_10:real) (C_8:real) (B_10:real), (((ord_less_real ((times_times_real A_10) C_8)) ((times_times_real B_10) C_8))->(((ord_less_eq_real zero_zero_real) C_8)->((ord_less_real A_10) B_10)))).
% 2.48/2.83 Axiom fact_761_mult__less__imp__less__right:(forall (A_10:nat) (C_8:nat) (B_10:nat), (((ord_less_nat ((times_times_nat A_10) C_8)) ((times_times_nat B_10) C_8))->(((ord_less_eq_nat zero_zero_nat) C_8)->((ord_less_nat A_10) B_10)))).
% 2.48/2.83 Axiom fact_762_mult__less__imp__less__right:(forall (A_10:int) (C_8:int) (B_10:int), (((ord_less_int ((times_times_int A_10) C_8)) ((times_times_int B_10) C_8))->(((ord_less_eq_int zero_zero_int) C_8)->((ord_less_int A_10) B_10)))).
% 2.48/2.83 Axiom fact_763_mult__right__less__imp__less:(forall (A_9:real) (C_7:real) (B_9:real), (((ord_less_real ((times_times_real A_9) C_7)) ((times_times_real B_9) C_7))->(((ord_less_eq_real zero_zero_real) C_7)->((ord_less_real A_9) B_9)))).
% 2.48/2.83 Axiom fact_764_mult__right__less__imp__less:(forall (A_9:nat) (C_7:nat) (B_9:nat), (((ord_less_nat ((times_times_nat A_9) C_7)) ((times_times_nat B_9) C_7))->(((ord_less_eq_nat zero_zero_nat) C_7)->((ord_less_nat A_9) B_9)))).
% 2.48/2.83 Axiom fact_765_mult__right__less__imp__less:(forall (A_9:int) (C_7:int) (B_9:int), (((ord_less_int ((times_times_int A_9) C_7)) ((times_times_int B_9) C_7))->(((ord_less_eq_int zero_zero_int) C_7)->((ord_less_int A_9) B_9)))).
% 2.48/2.83 Axiom fact_766_mult__le__less__imp__less:(forall (C_6:real) (D_6:real) (A_8:real) (B_8:real), (((ord_less_eq_real A_8) B_8)->(((ord_less_real C_6) D_6)->(((ord_less_real zero_zero_real) A_8)->(((ord_less_eq_real zero_zero_real) C_6)->((ord_less_real ((times_times_real A_8) C_6)) ((times_times_real B_8) D_6))))))).
% 2.48/2.83 Axiom fact_767_mult__le__less__imp__less:(forall (C_6:nat) (D_6:nat) (A_8:nat) (B_8:nat), (((ord_less_eq_nat A_8) B_8)->(((ord_less_nat C_6) D_6)->(((ord_less_nat zero_zero_nat) A_8)->(((ord_less_eq_nat zero_zero_nat) C_6)->((ord_less_nat ((times_times_nat A_8) C_6)) ((times_times_nat B_8) D_6))))))).
% 2.48/2.83 Axiom fact_768_mult__le__less__imp__less:(forall (C_6:int) (D_6:int) (A_8:int) (B_8:int), (((ord_less_eq_int A_8) B_8)->(((ord_less_int C_6) D_6)->(((ord_less_int zero_zero_int) A_8)->(((ord_less_eq_int zero_zero_int) C_6)->((ord_less_int ((times_times_int A_8) C_6)) ((times_times_int B_8) D_6))))))).
% 2.48/2.83 Axiom fact_769_mult__less__le__imp__less:(forall (C_5:real) (D_5:real) (A_7:real) (B_7:real), (((ord_less_real A_7) B_7)->(((ord_less_eq_real C_5) D_5)->(((ord_less_eq_real zero_zero_real) A_7)->(((ord_less_real zero_zero_real) C_5)->((ord_less_real ((times_times_real A_7) C_5)) ((times_times_real B_7) D_5))))))).
% 2.48/2.83 Axiom fact_770_mult__less__le__imp__less:(forall (C_5:nat) (D_5:nat) (A_7:nat) (B_7:nat), (((ord_less_nat A_7) B_7)->(((ord_less_eq_nat C_5) D_5)->(((ord_less_eq_nat zero_zero_nat) A_7)->(((ord_less_nat zero_zero_nat) C_5)->((ord_less_nat ((times_times_nat A_7) C_5)) ((times_times_nat B_7) D_5))))))).
% 2.48/2.83 Axiom fact_771_mult__less__le__imp__less:(forall (C_5:int) (D_5:int) (A_7:int) (B_7:int), (((ord_less_int A_7) B_7)->(((ord_less_eq_int C_5) D_5)->(((ord_less_eq_int zero_zero_int) A_7)->(((ord_less_int zero_zero_int) C_5)->((ord_less_int ((times_times_int A_7) C_5)) ((times_times_int B_7) D_5))))))).
% 2.48/2.83 Axiom fact_772_mult__strict__mono_H:(forall (C_4:real) (D_4:real) (A_6:real) (B_6:real), (((ord_less_real A_6) B_6)->(((ord_less_real C_4) D_4)->(((ord_less_eq_real zero_zero_real) A_6)->(((ord_less_eq_real zero_zero_real) C_4)->((ord_less_real ((times_times_real A_6) C_4)) ((times_times_real B_6) D_4))))))).
% 2.48/2.83 Axiom fact_773_mult__strict__mono_H:(forall (C_4:nat) (D_4:nat) (A_6:nat) (B_6:nat), (((ord_less_nat A_6) B_6)->(((ord_less_nat C_4) D_4)->(((ord_less_eq_nat zero_zero_nat) A_6)->(((ord_less_eq_nat zero_zero_nat) C_4)->((ord_less_nat ((times_times_nat A_6) C_4)) ((times_times_nat B_6) D_4))))))).
% 2.48/2.83 Axiom fact_774_mult__strict__mono_H:(forall (C_4:int) (D_4:int) (A_6:int) (B_6:int), (((ord_less_int A_6) B_6)->(((ord_less_int C_4) D_4)->(((ord_less_eq_int zero_zero_int) A_6)->(((ord_less_eq_int zero_zero_int) C_4)->((ord_less_int ((times_times_int A_6) C_4)) ((times_times_int B_6) D_4))))))).
% 2.48/2.83 Axiom fact_775_mult__strict__mono:(forall (C_3:real) (D_3:real) (A_5:real) (B_5:real), (((ord_less_real A_5) B_5)->(((ord_less_real C_3) D_3)->(((ord_less_real zero_zero_real) B_5)->(((ord_less_eq_real zero_zero_real) C_3)->((ord_less_real ((times_times_real A_5) C_3)) ((times_times_real B_5) D_3))))))).
% 2.48/2.83 Axiom fact_776_mult__strict__mono:(forall (C_3:nat) (D_3:nat) (A_5:nat) (B_5:nat), (((ord_less_nat A_5) B_5)->(((ord_less_nat C_3) D_3)->(((ord_less_nat zero_zero_nat) B_5)->(((ord_less_eq_nat zero_zero_nat) C_3)->((ord_less_nat ((times_times_nat A_5) C_3)) ((times_times_nat B_5) D_3))))))).
% 2.48/2.83 Axiom fact_777_mult__strict__mono:(forall (C_3:int) (D_3:int) (A_5:int) (B_5:int), (((ord_less_int A_5) B_5)->(((ord_less_int C_3) D_3)->(((ord_less_int zero_zero_int) B_5)->(((ord_less_eq_int zero_zero_int) C_3)->((ord_less_int ((times_times_int A_5) C_3)) ((times_times_int B_5) D_3))))))).
% 2.48/2.83 Axiom fact_778_mult__le__cancel__left__neg:(forall (A_4:real) (B_4:real) (C_2:real), (((ord_less_real C_2) zero_zero_real)->((iff ((ord_less_eq_real ((times_times_real C_2) A_4)) ((times_times_real C_2) B_4))) ((ord_less_eq_real B_4) A_4)))).
% 2.48/2.83 Axiom fact_779_mult__le__cancel__left__neg:(forall (A_4:int) (B_4:int) (C_2:int), (((ord_less_int C_2) zero_zero_int)->((iff ((ord_less_eq_int ((times_times_int C_2) A_4)) ((times_times_int C_2) B_4))) ((ord_less_eq_int B_4) A_4)))).
% 2.48/2.83 Axiom fact_780_mult__le__cancel__left__pos:(forall (A_3:real) (B_3:real) (C_1:real), (((ord_less_real zero_zero_real) C_1)->((iff ((ord_less_eq_real ((times_times_real C_1) A_3)) ((times_times_real C_1) B_3))) ((ord_less_eq_real A_3) B_3)))).
% 2.48/2.83 Axiom fact_781_mult__le__cancel__left__pos:(forall (A_3:int) (B_3:int) (C_1:int), (((ord_less_int zero_zero_int) C_1)->((iff ((ord_less_eq_int ((times_times_int C_1) A_3)) ((times_times_int C_1) B_3))) ((ord_less_eq_int A_3) B_3)))).
% 2.48/2.83 Axiom fact_782_mult__left__le__one__le:(forall (Y_3:real) (X_3:real), (((ord_less_eq_real zero_zero_real) X_3)->(((ord_less_eq_real zero_zero_real) Y_3)->(((ord_less_eq_real Y_3) one_one_real)->((ord_less_eq_real ((times_times_real Y_3) X_3)) X_3))))).
% 2.48/2.83 Axiom fact_783_mult__left__le__one__le:(forall (Y_3:int) (X_3:int), (((ord_less_eq_int zero_zero_int) X_3)->(((ord_less_eq_int zero_zero_int) Y_3)->(((ord_less_eq_int Y_3) one_one_int)->((ord_less_eq_int ((times_times_int Y_3) X_3)) X_3))))).
% 2.48/2.83 Axiom fact_784_mult__right__le__one__le:(forall (Y_2:real) (X_2:real), (((ord_less_eq_real zero_zero_real) X_2)->(((ord_less_eq_real zero_zero_real) Y_2)->(((ord_less_eq_real Y_2) one_one_real)->((ord_less_eq_real ((times_times_real X_2) Y_2)) X_2))))).
% 2.48/2.83 Axiom fact_785_mult__right__le__one__le:(forall (Y_2:int) (X_2:int), (((ord_less_eq_int zero_zero_int) X_2)->(((ord_less_eq_int zero_zero_int) Y_2)->(((ord_less_eq_int Y_2) one_one_int)->((ord_less_eq_int ((times_times_int X_2) Y_2)) X_2))))).
% 2.48/2.83 Axiom fact_786_zero__less__two:((ord_less_real zero_zero_real) ((plus_plus_real one_one_real) one_one_real)).
% 2.48/2.83 Axiom fact_787_zero__less__two:((ord_less_nat zero_zero_nat) ((plus_plus_nat one_one_nat) one_one_nat)).
% 2.48/2.83 Axiom fact_788_zero__less__two:((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) one_one_int)).
% 2.48/2.83 Axiom fact_789_four__x__squared:(forall (X:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit0 (bit1 pls))))) ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X)) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.48/2.83 Axiom fact_790_Int2_Ozcong__zero:(forall (M:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_int X) M)->((((zcong X) zero_zero_int) M)->(((eq int) X) zero_zero_int))))).
% 2.48/2.83 Axiom fact_791_zcong__zless__0:(forall (M:int) (A:int), (((ord_less_eq_int zero_zero_int) A)->(((ord_less_int A) M)->((((zcong A) zero_zero_int) M)->(((eq int) A) zero_zero_int))))).
% 2.48/2.83 Axiom fact_792_zcong__zless__imp__eq:(forall (B:int) (M:int) (A:int), (((ord_less_eq_int zero_zero_int) A)->(((ord_less_int A) M)->(((ord_less_eq_int zero_zero_int) B)->(((ord_less_int B) M)->((((zcong A) B) M)->(((eq int) A) B))))))).
% 2.48/2.83 Axiom fact_793_zpower__zdvd__prop1:(forall (P_1:int) (Y:int) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((dvd_dvd_int P_1) Y)->((dvd_dvd_int P_1) ((power_power_int Y) N))))).
% 2.48/2.83 Axiom fact_794_zcong__zpower__zmult:(forall (Z:nat) (X:int) (Y:nat) (P_1:int), ((((zcong ((power_power_int X) Y)) one_one_int) P_1)->(((zcong ((power_power_int X) ((times_times_nat Y) Z))) one_one_int) P_1))).
% 2.48/2.83 Axiom fact_795_zcong__zmult__prop3:(forall (Y:int) (X:int) (P_1:int), ((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((((zcong Y) zero_zero_int) P_1)->False)->((((zcong ((times_times_int X) Y)) zero_zero_int) P_1)->False))))).
% 2.48/2.83 Axiom fact_796_zcong__zprime__prod__zero:(forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) B)) zero_zero_int) P_1)->((or (((zcong A) zero_zero_int) P_1)) (((zcong B) zero_zero_int) P_1)))))).
% 2.48/2.83 Axiom fact_797_zcong__zprime__prod__zero__contra:(forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->(((and ((((zcong A) zero_zero_int) P_1)->False)) ((((zcong B) zero_zero_int) P_1)->False))->((((zcong ((times_times_int A) B)) zero_zero_int) P_1)->False))))).
% 2.48/2.83 Axiom fact_798_zprime__zdvd__zmult:(forall (N:int) (P_1:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->((zprime P_1)->(((dvd_dvd_int P_1) ((times_times_int M) N))->((or ((dvd_dvd_int P_1) M)) ((dvd_dvd_int P_1) N)))))).
% 2.48/2.83 Axiom fact_799__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096:((quadRes ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) (number_number_of_int min)).
% 2.48/2.83 Axiom fact_800__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096:((dvd_dvd_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((minus_minus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_int min))).
% 2.48/2.83 Axiom fact_801_neg__one__power__eq__mod__m:(forall (J_1:nat) (K:nat) (M:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) M)->((((zcong ((power_power_int (number_number_of_int min)) J_1)) ((power_power_int (number_number_of_int min)) K)) M)->(((eq int) ((power_power_int (number_number_of_int min)) J_1)) ((power_power_int (number_number_of_int min)) K))))).
% 2.48/2.83 Axiom fact_802_one__not__neg__one__mod__m:(forall (M:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) M)->((((zcong one_one_int) (number_number_of_int min)) M)->False))).
% 2.48/2.83 Axiom fact_803__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096:(((eq int) ((minus_minus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_int min))) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)).
% 2.48/2.83 Axiom fact_804__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N:((((quadRes ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) (number_number_of_int min))->False)->(not (((eq int) ((legendre (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) one_one_int))).
% 2.48/2.83 Axiom fact_805_not__real__square__gt__zero:(forall (X:real), ((iff (((ord_less_real zero_zero_real) ((times_times_real X) X))->False)) (((eq real) X) zero_zero_real))).
% 2.48/2.83 Axiom fact_806_diff__bin__simps_I1_J:(forall (K:int), (((eq int) ((minus_minus_int K) pls)) K)).
% 2.48/2.83 Axiom fact_807_diff__bin__simps_I7_J:(forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit0 K)) (bit0 L))) (bit0 ((minus_minus_int K) L)))).
% 2.48/2.83 Axiom fact_808_zdiff__zmult__distrib:(forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((minus_minus_int Z1) Z2)) W)) ((minus_minus_int ((times_times_int Z1) W)) ((times_times_int Z2) W)))).
% 2.48/2.83 Axiom fact_809_zdiff__zmult__distrib2:(forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((minus_minus_int Z1) Z2))) ((minus_minus_int ((times_times_int W) Z1)) ((times_times_int W) Z2)))).
% 2.48/2.83 Axiom fact_810_Int2_Oaux1:(forall (A:int) (B:int) (C:int), ((((eq int) ((minus_minus_int A) B)) C)->(((eq int) A) ((plus_plus_int C) B)))).
% 2.48/2.83 Axiom fact_811_zcong__zdiff:(forall (C:int) (D:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((zcong C) D) M)->(((zcong ((minus_minus_int A) C)) ((minus_minus_int B) D)) M)))).
% 2.48/2.83 Axiom fact_812_zdvd__zdiffD:(forall (K:int) (M:int) (N:int), (((dvd_dvd_int K) ((minus_minus_int M) N))->(((dvd_dvd_int K) N)->((dvd_dvd_int K) M)))).
% 2.48/2.83 Axiom fact_813_diff__bin__simps_I9_J:(forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit1 K)) (bit0 L))) (bit1 ((minus_minus_int K) L)))).
% 2.48/2.83 Axiom fact_814_diff__bin__simps_I10_J:(forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit1 K)) (bit1 L))) (bit0 ((minus_minus_int K) L)))).
% 2.48/2.83 Axiom fact_815_diff__bin__simps_I3_J:(forall (L:int), (((eq int) ((minus_minus_int pls) (bit0 L))) (bit0 ((minus_minus_int pls) L)))).
% 2.48/2.83 Axiom fact_816_less__bin__lemma:(forall (K:int) (L:int), ((iff ((ord_less_int K) L)) ((ord_less_int ((minus_minus_int K) L)) zero_zero_int))).
% 2.48/2.83 Axiom fact_817_xzgcda__linear__aux1:(forall (A:int) (R:int) (B:int) (M:int) (C:int) (D:int) (N:int), (((eq int) ((plus_plus_int ((times_times_int ((minus_minus_int A) ((times_times_int R) B))) M)) ((times_times_int ((minus_minus_int C) ((times_times_int R) D))) N))) ((minus_minus_int ((plus_plus_int ((times_times_int A) M)) ((times_times_int C) N))) ((times_times_int R) ((plus_plus_int ((times_times_int B) M)) ((times_times_int D) N)))))).
% 2.48/2.83 Axiom fact_818_zcong__def:(forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) ((dvd_dvd_int M) ((minus_minus_int A) B)))).
% 2.48/2.83 Axiom fact_819_Euler_Oaux1:(forall (A:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int X) A)->((not (((eq int) X) ((minus_minus_int A) one_one_int)))->((ord_less_int X) ((minus_minus_int A) one_one_int)))))).
% 2.48/2.83 Axiom fact_820_zle__diff1__eq:(forall (W:int) (Z:int), ((iff ((ord_less_eq_int W) ((minus_minus_int Z) one_one_int))) ((ord_less_int W) Z))).
% 2.48/2.83 Axiom fact_821_diff__bin__simps_I4_J:(forall (L:int), (((eq int) ((minus_minus_int pls) (bit1 L))) (bit1 ((minus_minus_int min) L)))).
% 2.48/2.83 Axiom fact_822_diff__bin__simps_I5_J:(forall (L:int), (((eq int) ((minus_minus_int min) (bit0 L))) (bit1 ((minus_minus_int min) L)))).
% 2.48/2.83 Axiom fact_823_diff__bin__simps_I6_J:(forall (L:int), (((eq int) ((minus_minus_int min) (bit1 L))) (bit0 ((minus_minus_int min) L)))).
% 2.48/2.83 Axiom fact_824_inv__not__p__minus__1__aux:(forall (A:int) (P_1:int), ((iff (((zcong ((times_times_int A) ((minus_minus_int P_1) one_one_int))) one_one_int) P_1)) (((zcong A) ((minus_minus_int P_1) one_one_int)) P_1))).
% 2.48/2.83 Axiom fact_825_power__dvd__imp__le:(forall (I_1:nat) (M:nat) (N:nat), (((dvd_dvd_nat ((power_power_nat I_1) M)) ((power_power_nat I_1) N))->(((ord_less_nat one_one_nat) I_1)->((ord_less_eq_nat M) N)))).
% 2.48/2.83 Axiom fact_826_zcong__square__zless:(forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P_1)->((((zcong ((times_times_int A) A)) one_one_int) P_1)->((or (((eq int) A) one_one_int)) (((eq int) A) ((minus_minus_int P_1) one_one_int)))))))).
% 2.48/2.83 Axiom fact_827_zcong__square:(forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) A)) one_one_int) P_1)->((or (((zcong A) one_one_int) P_1)) (((zcong A) ((minus_minus_int P_1) one_one_int)) P_1)))))).
% 2.48/2.83 Axiom fact_828_zspecial__product:(forall (A:int) (B:int), (((eq int) ((times_times_int ((plus_plus_int A) B)) ((minus_minus_int A) B))) ((minus_minus_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))).
% 2.48/2.83 Axiom fact_829_zdiff__power2:(forall (A:int) (B:int), (((eq int) ((power_power_int ((minus_minus_int A) B)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((minus_minus_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A)) B))) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))).
% 2.48/2.83 Axiom fact_830_zdiff__power3:(forall (A:int) (B:int), (((eq int) ((power_power_int ((minus_minus_int A) B)) (number_number_of_nat (bit1 (bit1 pls))))) ((minus_minus_int ((plus_plus_int ((minus_minus_int ((power_power_int A) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls)))))) B))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) A)) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))) ((power_power_int B) (number_number_of_nat (bit1 (bit1 pls))))))).
% 2.48/2.83 Axiom fact_831_neg__one__power:(forall (N:nat), ((or (((eq int) ((power_power_int (number_number_of_int min)) N)) one_one_int)) (((eq int) ((power_power_int (number_number_of_int min)) N)) (number_number_of_int min)))).
% 2.48/2.83 Axiom fact_832_Legendre__1mod4:(forall (M:int), ((zprime ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) M)) one_one_int))->(((eq int) ((legendre (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) M)) one_one_int))) one_one_int))).
% 2.48/2.83 Axiom fact_833_Legendre__def:(forall (A:int) (P_1:int), ((and ((((zcong A) zero_zero_int) P_1)->(((eq int) ((legendre A) P_1)) zero_zero_int))) (((((zcong A) zero_zero_int) P_1)->False)->((and (((quadRes P_1) A)->(((eq int) ((legendre A) P_1)) one_one_int))) ((((quadRes P_1) A)->False)->(((eq int) ((legendre A) P_1)) (number_number_of_int min))))))).
% 2.48/2.83 Axiom fact_834_QuadRes__def:(forall (M:int) (X:int), ((iff ((quadRes M) X)) ((ex int) (fun (Y_1:int)=> (((zcong ((power_power_int Y_1) (number_number_of_nat (bit0 (bit1 pls))))) X) M))))).
% 2.48/2.83 Axiom fact_835_real__sum__squared__expand:(forall (X:real) (Y:real), (((eq real) ((power_power_real ((plus_plus_real X) Y)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X)) Y)))).
% 2.48/2.83 Axiom fact_836_divides__cases:(forall (N:nat) (M:nat), (((dvd_dvd_nat N) M)->((or ((or (((eq nat) M) zero_zero_nat)) (((eq nat) M) N))) ((ord_less_eq_nat ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N)) M)))).
% 2.48/2.83 Axiom fact_837_divides__antisym:(forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) ((dvd_dvd_nat Y) X))) (((eq nat) X) Y))).
% 2.48/2.83 Axiom fact_838_divides__add__revr:(forall (B:nat) (D:nat) (A:nat), (((dvd_dvd_nat D) A)->(((dvd_dvd_nat D) ((plus_plus_nat A) B))->((dvd_dvd_nat D) B)))).
% 2.48/2.83 Axiom fact_839_divides__mul__r:(forall (C:nat) (A:nat) (B:nat), (((dvd_dvd_nat A) B)->((dvd_dvd_nat ((times_times_nat A) C)) ((times_times_nat B) C)))).
% 2.48/2.83 Axiom fact_840_divides__mul__l:(forall (C:nat) (A:nat) (B:nat), (((dvd_dvd_nat A) B)->((dvd_dvd_nat ((times_times_nat C) A)) ((times_times_nat C) B)))).
% 2.48/2.83 Axiom fact_841_divides__exp:(forall (N:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->((dvd_dvd_nat ((power_power_nat X) N)) ((power_power_nat Y) N)))).
% 2.48/2.83 Axiom fact_842_mult__eq__if:(forall (N:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((times_times_nat M) N)) zero_zero_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((times_times_nat M) N)) ((plus_plus_nat N) ((times_times_nat ((minus_minus_nat M) one_one_nat)) N)))))).
% 2.48/2.83 Axiom fact_843_power__eq__if:(forall (P_1:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((power_power_nat P_1) M)) one_one_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((power_power_nat P_1) M)) ((times_times_nat P_1) ((power_power_nat P_1) ((minus_minus_nat M) one_one_nat))))))).
% 2.48/2.84 Axiom fact_844_diff__square:(forall (X:nat) (Y:nat), (((eq nat) ((minus_minus_nat ((power_power_nat X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((plus_plus_nat X) Y)) ((minus_minus_nat X) Y)))).
% 2.48/2.84 Axiom fact_845_divides__ge:(forall (A:nat) (B:nat), (((dvd_dvd_nat A) B)->((or (((eq nat) B) zero_zero_nat)) ((ord_less_eq_nat A) B)))).
% 2.48/2.84 Axiom fact_846_nat__mult__dvd__cancel__disj_H:(forall (M:nat) (K:nat) (N:nat), ((iff ((dvd_dvd_nat ((times_times_nat M) K)) ((times_times_nat N) K))) ((or (((eq nat) K) zero_zero_nat)) ((dvd_dvd_nat M) N)))).
% 2.48/2.84 Axiom fact_847_nat__mult__eq__one:(forall (N:nat) (M:nat), ((iff (((eq nat) ((times_times_nat N) M)) one_one_nat)) ((and (((eq nat) N) one_one_nat)) (((eq nat) M) one_one_nat)))).
% 2.48/2.84 Axiom fact_848_nat__power__eq__0__iff:(forall (M:nat) (N:nat), ((iff (((eq nat) ((power_power_nat M) N)) zero_zero_nat)) ((and (not (((eq nat) N) zero_zero_nat))) (((eq nat) M) zero_zero_nat)))).
% 2.48/2.84 Axiom fact_849_divides__exp2:(forall (X:nat) (Y:nat) (N:nat), ((not (((eq nat) N) zero_zero_nat))->(((dvd_dvd_nat ((power_power_nat X) N)) Y)->((dvd_dvd_nat X) Y)))).
% 2.48/2.84 Axiom fact_850_divides__rev:(forall (A:nat) (N:nat) (B:nat), (((dvd_dvd_nat ((power_power_nat A) N)) ((power_power_nat B) N))->((not (((eq nat) N) zero_zero_nat))->((dvd_dvd_nat A) B)))).
% 2.48/2.84 Axiom fact_851_exp__eq__1:(forall (X:nat) (N:nat), ((iff (((eq nat) ((power_power_nat X) N)) one_one_nat)) ((or (((eq nat) X) one_one_nat)) (((eq nat) N) zero_zero_nat)))).
% 2.48/2.84 Axiom fact_852_divides__div__not:(forall (X:nat) (Q:nat) (N:nat) (R:nat), ((((eq nat) X) ((plus_plus_nat ((times_times_nat Q) N)) R))->(((ord_less_nat zero_zero_nat) R)->(((ord_less_nat R) N)->(((dvd_dvd_nat N) X)->False))))).
% 2.48/2.84 Axiom fact_853_realpow__two__sum__zero__iff:(forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real)))).
% 2.48/2.84 Axiom fact_854_realpow__pos__nth__unique:(forall (A:real) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_real zero_zero_real) A)->((ex real) (fun (X_1:real)=> ((and ((and ((ord_less_real zero_zero_real) X_1)) (((eq real) ((power_power_real X_1) N)) A))) (forall (Y_1:real), (((and ((ord_less_real zero_zero_real) Y_1)) (((eq real) ((power_power_real Y_1) N)) A))->(((eq real) Y_1) X_1))))))))).
% 2.48/2.84 Axiom fact_855_realpow__pos__nth:(forall (A:real) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_real zero_zero_real) A)->((ex real) (fun (R_1:real)=> ((and ((ord_less_real zero_zero_real) R_1)) (((eq real) ((power_power_real R_1) N)) A))))))).
% 2.48/2.84 Axiom fact_856_dvd__mult__cancel2:(forall (N:nat) (M:nat), (((ord_less_nat zero_zero_nat) M)->((iff ((dvd_dvd_nat ((times_times_nat N) M)) M)) (((eq nat) N) one_one_nat)))).
% 2.48/2.84 Axiom fact_857_dvd_Oorder__refl:(forall (X:nat), ((dvd_dvd_nat X) X)).
% 2.48/2.84 Axiom fact_858_less__zeroE:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)).
% 2.48/2.84 Axiom fact_859_le0:(forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)).
% 2.48/2.84 Axiom fact_860_diff__commute:(forall (I_1:nat) (J_1:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J_1)) K)) ((minus_minus_nat ((minus_minus_nat I_1) K)) J_1))).
% 2.48/2.84 Axiom fact_861_diff__0__eq__0:(forall (N:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N)) zero_zero_nat)).
% 2.48/2.84 Axiom fact_862_minus__nat_Odiff__0:(forall (M:nat), (((eq nat) ((minus_minus_nat M) zero_zero_nat)) M)).
% 2.48/2.84 Axiom fact_863_diff__self__eq__0:(forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat)).
% 2.48/2.84 Axiom fact_864_diffs0__imp__equal:(forall (M:nat) (N:nat), ((((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)->((((eq nat) ((minus_minus_nat N) M)) zero_zero_nat)->(((eq nat) M) N)))).
% 2.48/2.84 Axiom fact_865_real__zero__not__eq__one:(not (((eq real) zero_zero_real) one_one_real)).
% 2.48/2.84 Axiom fact_866_real__le__eq__diff:(forall (X:real) (Y:real), ((iff ((ord_less_eq_real X) Y)) ((ord_less_eq_real ((minus_minus_real X) Y)) zero_zero_real))).
% 2.48/2.84 Axiom fact_867_real__less__def:(forall (X:real) (Y:real), ((iff ((ord_less_real X) Y)) ((and ((ord_less_eq_real X) Y)) (not (((eq real) X) Y))))).
% 2.48/2.84 Axiom fact_868_less__eq__real__def:(forall (X:real) (Y:real), ((iff ((ord_less_eq_real X) Y)) ((or ((ord_less_real X) Y)) (((eq real) X) Y)))).
% 2.48/2.84 Axiom fact_869_less__not__refl:(forall (N:nat), (((ord_less_nat N) N)->False)).
% 2.48/2.84 Axiom fact_870_nat__neq__iff:(forall (M:nat) (N:nat), ((iff (not (((eq nat) M) N))) ((or ((ord_less_nat M) N)) ((ord_less_nat N) M)))).
% 2.48/2.84 Axiom fact_871_linorder__neqE__nat:(forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X)))).
% 2.48/2.84 Axiom fact_872_less__irrefl__nat:(forall (N:nat), (((ord_less_nat N) N)->False)).
% 2.48/2.84 Axiom fact_873_less__not__refl2:(forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N)))).
% 2.48/2.84 Axiom fact_874_less__not__refl3:(forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))).
% 2.48/2.84 Axiom fact_875_nat__less__cases:(forall (P:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P N) M))->(((((eq nat) M) N)->((P N) M))->((((ord_less_nat N) M)->((P N) M))->((P N) M))))).
% 2.48/2.84 Axiom fact_876_less__imp__diff__less:(forall (N:nat) (J_1:nat) (K:nat), (((ord_less_nat J_1) K)->((ord_less_nat ((minus_minus_nat J_1) N)) K))).
% 2.48/2.84 Axiom fact_877_diff__less__mono2:(forall (L:nat) (M:nat) (N:nat), (((ord_less_nat M) N)->(((ord_less_nat M) L)->((ord_less_nat ((minus_minus_nat L) N)) ((minus_minus_nat L) M))))).
% 2.48/2.84 Axiom fact_878_dvd_Oless__asym:(forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False))).
% 2.48/2.84 Axiom fact_879_dvd_Oless__trans:(forall (Z:nat) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) Z)) (((dvd_dvd_nat Z) Y)->False))->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False))))).
% 2.48/2.84 Axiom fact_880_dvd_Oless__asym_H:(forall (A:nat) (B:nat), (((and ((dvd_dvd_nat A) B)) (((dvd_dvd_nat B) A)->False))->(((and ((dvd_dvd_nat B) A)) (((dvd_dvd_nat A) B)->False))->False))).
% 2.48/2.84 Axiom fact_881_dvd_Oless__le__trans:(forall (Z:nat) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((dvd_dvd_nat Y) Z)->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False))))).
% 2.48/2.84 Axiom fact_882_dvd_Oord__less__eq__trans:(forall (C:nat) (A:nat) (B:nat), (((and ((dvd_dvd_nat A) B)) (((dvd_dvd_nat B) A)->False))->((((eq nat) B) C)->((and ((dvd_dvd_nat A) C)) (((dvd_dvd_nat C) A)->False))))).
% 2.48/2.84 Axiom fact_883_dvd_Oless__imp__triv:(forall (P:Prop) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->P))).
% 2.48/2.84 Axiom fact_884_dvd_Oless__imp__not__eq2:(forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) Y) X)))).
% 2.48/2.84 Axiom fact_885_dvd_Oless__imp__not__eq:(forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) X) Y)))).
% 2.48/2.84 Axiom fact_886_dvd_Oless__imp__not__less:(forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False))).
% 2.48/2.84 Axiom fact_887_dvd_Oless__imp__le:(forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->((dvd_dvd_nat X) Y))).
% 2.48/2.84 Axiom fact_888_dvd_Oless__not__sym:(forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False))).
% 2.48/2.84 Axiom fact_889_dvd_Oless__imp__neq:(forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) X) Y)))).
% 2.48/2.84 Axiom fact_890_dvd_Ole__less__trans:(forall (Z:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((and ((dvd_dvd_nat Y) Z)) (((dvd_dvd_nat Z) Y)->False))->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False))))).
% 2.48/2.84 Axiom fact_891_dvd_Oord__eq__less__trans:(forall (C:nat) (A:nat) (B:nat), ((((eq nat) A) B)->(((and ((dvd_dvd_nat B) C)) (((dvd_dvd_nat C) B)->False))->((and ((dvd_dvd_nat A) C)) (((dvd_dvd_nat C) A)->False))))).
% 2.48/2.84 Axiom fact_892_dvd__diff__nat:(forall (N:nat) (K:nat) (M:nat), (((dvd_dvd_nat K) M)->(((dvd_dvd_nat K) N)->((dvd_dvd_nat K) ((minus_minus_nat M) N))))).
% 2.48/2.84 Axiom fact_893_dvd_Oorder__trans:(forall (Z:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((dvd_dvd_nat Y) Z)->((dvd_dvd_nat X) Z)))).
% 2.48/2.84 Axiom fact_894_dvd_Oantisym:(forall (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((dvd_dvd_nat Y) X)->(((eq nat) X) Y)))).
% 2.48/2.84 Axiom fact_895_dvd__antisym:(forall (M:nat) (N:nat), (((dvd_dvd_nat M) N)->(((dvd_dvd_nat N) M)->(((eq nat) M) N)))).
% 2.48/2.84 Axiom fact_896_dvd_Oord__le__eq__trans:(forall (C:nat) (A:nat) (B:nat), (((dvd_dvd_nat A) B)->((((eq nat) B) C)->((dvd_dvd_nat A) C)))).
% 2.48/2.84 Axiom fact_897_dvd_Oord__eq__le__trans:(forall (C:nat) (A:nat) (B:nat), ((((eq nat) A) B)->(((dvd_dvd_nat B) C)->((dvd_dvd_nat A) C)))).
% 2.48/2.84 Axiom fact_898_dvd_Ole__neq__trans:(forall (A:nat) (B:nat), (((dvd_dvd_nat A) B)->((not (((eq nat) A) B))->((and ((dvd_dvd_nat A) B)) (((dvd_dvd_nat B) A)->False))))).
% 2.48/2.84 Axiom fact_899_dvd_Ole__imp__less__or__eq:(forall (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->((or ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) (((eq nat) X) Y)))).
% 2.48/2.84 Axiom fact_900_dvd_Oantisym__conv:(forall (Y:nat) (X:nat), (((dvd_dvd_nat Y) X)->((iff ((dvd_dvd_nat X) Y)) (((eq nat) X) Y)))).
% 2.48/2.84 Axiom fact_901_dvd_Oeq__refl:(forall (X:nat) (Y:nat), ((((eq nat) X) Y)->((dvd_dvd_nat X) Y))).
% 2.48/2.84 Axiom fact_902_dvd_Oneq__le__trans:(forall (A:nat) (B:nat), ((not (((eq nat) A) B))->(((dvd_dvd_nat A) B)->((and ((dvd_dvd_nat A) B)) (((dvd_dvd_nat B) A)->False))))).
% 2.48/2.84 Axiom fact_903_dvd_Oless__le__not__le:(forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False)))).
% 2.48/2.84 Axiom fact_904_dvd_Oless__le:(forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) ((and ((dvd_dvd_nat X) Y)) (not (((eq nat) X) Y))))).
% 2.48/2.84 Axiom fact_905_dvd_Ole__less:(forall (X:nat) (Y:nat), ((iff ((dvd_dvd_nat X) Y)) ((or ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) (((eq nat) X) Y)))).
% 2.48/2.84 Axiom fact_906_dvd_Oeq__iff:(forall (X:nat) (Y:nat), ((iff (((eq nat) X) Y)) ((and ((dvd_dvd_nat X) Y)) ((dvd_dvd_nat Y) X)))).
% 2.48/2.84 Axiom fact_907_dvd_Oless__irrefl:(forall (X:nat), (((and ((dvd_dvd_nat X) X)) (((dvd_dvd_nat X) X)->False))->False)).
% 2.48/2.84 Axiom fact_908_nat__add__commute:(forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) N)) ((plus_plus_nat N) M))).
% 2.48/2.84 Axiom fact_909_nat__add__left__commute:(forall (X:nat) (Y:nat) (Z:nat), (((eq nat) ((plus_plus_nat X) ((plus_plus_nat Y) Z))) ((plus_plus_nat Y) ((plus_plus_nat X) Z)))).
% 2.48/2.84 Axiom fact_910_nat__add__assoc:(forall (M:nat) (N:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M) N)) K)) ((plus_plus_nat M) ((plus_plus_nat N) K)))).
% 2.48/2.84 Axiom fact_911_nat__add__left__cancel:(forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) (((eq nat) M) N))).
% 2.48/2.84 Axiom fact_912_nat__add__right__cancel:(forall (M:nat) (K:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) K)) ((plus_plus_nat N) K))) (((eq nat) M) N))).
% 2.48/2.84 Axiom fact_913_diff__add__inverse2:(forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) N)) N)) M)).
% 2.48/2.84 Axiom fact_914_diff__add__inverse:(forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat N) M)) N)) M)).
% 2.48/2.84 Axiom fact_915_diff__diff__left:(forall (I_1:nat) (J_1:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J_1)) K)) ((minus_minus_nat I_1) ((plus_plus_nat J_1) K)))).
% 2.48/2.84 Axiom fact_916_Nat_Odiff__cancel:(forall (K:nat) (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((minus_minus_nat M) N))).
% 2.48/2.84 Axiom fact_917_diff__cancel2:(forall (M:nat) (K:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) K)) ((plus_plus_nat N) K))) ((minus_minus_nat M) N))).
% 2.48/2.84 Axiom fact_918_real__mult__assoc:(forall (Z1:real) (Z2:real) (Z3:real), (((eq real) ((times_times_real ((times_times_real Z1) Z2)) Z3)) ((times_times_real Z1) ((times_times_real Z2) Z3)))).
% 2.48/2.84 Axiom fact_919_real__mult__commute:(forall (Z:real) (W:real), (((eq real) ((times_times_real Z) W)) ((times_times_real W) Z))).
% 2.48/2.84 Axiom fact_920_real__mult__1:(forall (Z:real), (((eq real) ((times_times_real one_one_real) Z)) Z)).
% 2.48/2.84 Axiom fact_921_le__antisym:(forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N)))).
% 2.48/2.84 Axiom fact_922_le__trans:(forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat J_1) K)->((ord_less_eq_nat I_1) K)))).
% 2.48/2.84 Axiom fact_923_eq__imp__le:(forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N))).
% 2.48/2.84 Axiom fact_924_nat__le__linear:(forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M))).
% 2.48/2.84 Axiom fact_925_le__refl:(forall (N:nat), ((ord_less_eq_nat N) N)).
% 2.48/2.84 Axiom fact_926_le__diff__iff:(forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff ((ord_less_eq_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((ord_less_eq_nat M) N))))).
% 2.48/2.84 Axiom fact_927_Nat_Odiff__diff__eq:(forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->(((eq nat) ((minus_minus_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((minus_minus_nat M) N))))).
% 2.48/2.84 Axiom fact_928_eq__diff__iff:(forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff (((eq nat) ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) (((eq nat) M) N))))).
% 2.48/2.84 Axiom fact_929_diff__diff__cancel:(forall (I_1:nat) (N:nat), (((ord_less_eq_nat I_1) N)->(((eq nat) ((minus_minus_nat N) ((minus_minus_nat N) I_1))) I_1))).
% 2.48/2.84 Axiom fact_930_diff__le__mono:(forall (L:nat) (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat ((minus_minus_nat M) L)) ((minus_minus_nat N) L)))).
% 2.48/2.84 Axiom fact_931_diff__le__mono2:(forall (L:nat) (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((ord_less_eq_nat ((minus_minus_nat L) N)) ((minus_minus_nat L) M)))).
% 2.48/2.84 Axiom fact_932_Nat_Odiff__le__self:(forall (M:nat) (N:nat), ((ord_less_eq_nat ((minus_minus_nat M) N)) M)).
% 2.48/2.84 Axiom fact_933_nat__mult__commute:(forall (M:nat) (N:nat), (((eq nat) ((times_times_nat M) N)) ((times_times_nat N) M))).
% 2.48/2.84 Axiom fact_934_nat__mult__assoc:(forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((times_times_nat M) N)) K)) ((times_times_nat M) ((times_times_nat N) K)))).
% 2.48/2.84 Axiom fact_935_diff__mult__distrib2:(forall (K:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K) ((minus_minus_nat M) N))) ((minus_minus_nat ((times_times_nat K) M)) ((times_times_nat K) N)))).
% 2.48/2.84 Axiom fact_936_diff__mult__distrib:(forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((minus_minus_nat M) N)) K)) ((minus_minus_nat ((times_times_nat M) K)) ((times_times_nat N) K)))).
% 2.48/2.84 Axiom fact_937_real__add__left__mono:(forall (Z:real) (X:real) (Y:real), (((ord_less_eq_real X) Y)->((ord_less_eq_real ((plus_plus_real Z) X)) ((plus_plus_real Z) Y)))).
% 2.48/2.84 Axiom fact_938_not__less0:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)).
% 2.48/2.84 Axiom fact_939_neq0__conv:(forall (N:nat), ((iff (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N))).
% 2.48/2.84 Axiom fact_940_less__nat__zero__code:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)).
% 2.48/2.84 Axiom fact_941_gr__implies__not0:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->(not (((eq nat) N) zero_zero_nat)))).
% 2.48/2.84 Axiom fact_942_gr0I:(forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N))).
% 2.48/2.84 Axiom fact_943_diff__less:(forall (M:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_nat zero_zero_nat) M)->((ord_less_nat ((minus_minus_nat M) N)) M)))).
% 2.48/2.84 Axiom fact_944_zero__less__diff:(forall (N:nat) (M:nat), ((iff ((ord_less_nat zero_zero_nat) ((minus_minus_nat N) M))) ((ord_less_nat M) N))).
% 2.48/2.84 Axiom fact_945_plus__nat_Oadd__0:(forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N)).
% 2.48/2.84 Axiom fact_946_Nat_Oadd__0__right:(forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M)).
% 2.48/2.85 Axiom fact_947_add__is__0:(forall (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) N)) zero_zero_nat)) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))).
% 2.48/2.85 Axiom fact_948_add__eq__self__zero:(forall (M:nat) (N:nat), ((((eq nat) ((plus_plus_nat M) N)) M)->(((eq nat) N) zero_zero_nat))).
% 2.48/2.85 Axiom fact_949_diff__add__0:(forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat N) ((plus_plus_nat N) M))) zero_zero_nat)).
% 2.48/2.85 Axiom fact_950_less__eq__nat_Osimps_I1_J:(forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)).
% 2.48/2.85 Axiom fact_951_le__0__eq:(forall (N:nat), ((iff ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat))).
% 2.48/2.85 Axiom fact_952_diff__is__0__eq:(forall (M:nat) (N:nat), ((iff (((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)) ((ord_less_eq_nat M) N))).
% 2.48/2.85 Axiom fact_953_diff__is__0__eq_H:(forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((eq nat) ((minus_minus_nat M) N)) zero_zero_nat))).
% 2.48/2.85 Axiom fact_954_mult__0:(forall (N:nat), (((eq nat) ((times_times_nat zero_zero_nat) N)) zero_zero_nat)).
% 2.48/2.85 Axiom fact_955_mult__0__right:(forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat)).
% 2.48/2.85 Axiom fact_956_mult__is__0:(forall (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) N)) zero_zero_nat)) ((or (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))).
% 2.48/2.85 Axiom fact_957_mult__cancel1:(forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) ((or (((eq nat) M) N)) (((eq nat) K) zero_zero_nat)))).
% 2.48/2.85 Axiom fact_958_mult__cancel2:(forall (M:nat) (K:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) K)) ((times_times_nat N) K))) ((or (((eq nat) M) N)) (((eq nat) K) zero_zero_nat)))).
% 2.48/2.85 Axiom fact_959_real__mult__left__cancel:(forall (A:real) (B:real) (C:real), ((not (((eq real) C) zero_zero_real))->((iff (((eq real) ((times_times_real C) A)) ((times_times_real C) B))) (((eq real) A) B)))).
% 2.48/2.85 Axiom fact_960_real__mult__right__cancel:(forall (A:real) (B:real) (C:real), ((not (((eq real) C) zero_zero_real))->((iff (((eq real) ((times_times_real A) C)) ((times_times_real B) C))) (((eq real) A) B)))).
% 2.48/2.85 Axiom fact_961_not__add__less1:(forall (I_1:nat) (J_1:nat), (((ord_less_nat ((plus_plus_nat I_1) J_1)) I_1)->False)).
% 2.48/2.85 Axiom fact_962_not__add__less2:(forall (J_1:nat) (I_1:nat), (((ord_less_nat ((plus_plus_nat J_1) I_1)) I_1)->False)).
% 2.48/2.85 Axiom fact_963_nat__add__left__cancel__less:(forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_nat M) N))).
% 2.48/2.85 Axiom fact_964_trans__less__add1:(forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat I_1) ((plus_plus_nat J_1) M)))).
% 2.48/2.85 Axiom fact_965_trans__less__add2:(forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat I_1) ((plus_plus_nat M) J_1)))).
% 2.48/2.85 Axiom fact_966_add__less__mono1:(forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J_1) K)))).
% 2.48/2.85 Axiom fact_967_add__less__mono:(forall (K:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J_1) L))))).
% 2.48/2.85 Axiom fact_968_less__add__eq__less:(forall (M:nat) (N:nat) (K:nat) (L:nat), (((ord_less_nat K) L)->((((eq nat) ((plus_plus_nat M) L)) ((plus_plus_nat K) N))->((ord_less_nat M) N)))).
% 2.48/2.85 Axiom fact_969_add__lessD1:(forall (I_1:nat) (J_1:nat) (K:nat), (((ord_less_nat ((plus_plus_nat I_1) J_1)) K)->((ord_less_nat I_1) K))).
% 2.48/2.85 Axiom fact_970_add__diff__inverse:(forall (M:nat) (N:nat), ((((ord_less_nat M) N)->False)->(((eq nat) ((plus_plus_nat N) ((minus_minus_nat M) N))) M))).
% 2.48/2.85 Axiom fact_971_less__diff__conv:(forall (I_1:nat) (J_1:nat) (K:nat), ((iff ((ord_less_nat I_1) ((minus_minus_nat J_1) K))) ((ord_less_nat ((plus_plus_nat I_1) K)) J_1))).
% 2.48/2.85 Axiom fact_972_nat__less__le:(forall (M:nat) (N:nat), ((iff ((ord_less_nat M) N)) ((and ((ord_less_eq_nat M) N)) (not (((eq nat) M) N))))).
% 2.48/2.85 Axiom fact_973_le__eq__less__or__eq:(forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((or ((ord_less_nat M) N)) (((eq nat) M) N)))).
% 2.48/2.85 Axiom fact_974_less__imp__le__nat:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N))).
% 2.48/2.85 Axiom fact_975_le__neq__implies__less:(forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((not (((eq nat) M) N))->((ord_less_nat M) N)))).
% 2.48/2.85 Axiom fact_976_less__or__eq__imp__le:(forall (M:nat) (N:nat), (((or ((ord_less_nat M) N)) (((eq nat) M) N))->((ord_less_eq_nat M) N))).
% 2.48/2.85 Axiom fact_977_diff__less__mono:(forall (C:nat) (A:nat) (B:nat), (((ord_less_nat A) B)->(((ord_less_eq_nat C) A)->((ord_less_nat ((minus_minus_nat A) C)) ((minus_minus_nat B) C))))).
% 2.48/2.85 Axiom fact_978_less__diff__iff:(forall (N:nat) (K:nat) (M:nat), (((ord_less_eq_nat K) M)->(((ord_less_eq_nat K) N)->((iff ((ord_less_nat ((minus_minus_nat M) K)) ((minus_minus_nat N) K))) ((ord_less_nat M) N))))).
% 2.48/2.85 Axiom fact_979_dvd__reduce:(forall (K:nat) (N:nat), ((iff ((dvd_dvd_nat K) ((plus_plus_nat N) K))) ((dvd_dvd_nat K) N))).
% 2.48/2.85 Axiom fact_980_dvd__diffD:(forall (K:nat) (M:nat) (N:nat), (((dvd_dvd_nat K) ((minus_minus_nat M) N))->(((dvd_dvd_nat K) N)->(((ord_less_eq_nat N) M)->((dvd_dvd_nat K) M))))).
% 2.48/2.85 Axiom fact_981_dvd__diffD1:(forall (K:nat) (M:nat) (N:nat), (((dvd_dvd_nat K) ((minus_minus_nat M) N))->(((dvd_dvd_nat K) M)->(((ord_less_eq_nat N) M)->((dvd_dvd_nat K) N))))).
% 2.48/2.85 Axiom fact_982_le__add2:(forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat M) N))).
% 2.48/2.85 Axiom fact_983_le__add1:(forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M))).
% 2.48/2.85 Axiom fact_984_le__iff__add:(forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) ((plus_plus_nat M) K_1)))))).
% 2.48/2.85 Axiom fact_985_nat__add__left__cancel__le:(forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_eq_nat M) N))).
% 2.48/2.85 Axiom fact_986_trans__le__add1:(forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat I_1) ((plus_plus_nat J_1) M)))).
% 2.48/2.85 Axiom fact_987_trans__le__add2:(forall (M:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat I_1) ((plus_plus_nat M) J_1)))).
% 2.48/2.85 Axiom fact_988_add__le__mono1:(forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J_1) K)))).
% 2.48/2.85 Axiom fact_989_add__le__mono:(forall (K:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J_1) L))))).
% 2.48/2.85 Axiom fact_990_add__leD2:(forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat K) N))).
% 2.48/2.85 Axiom fact_991_add__leD1:(forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat M) N))).
% 2.48/2.85 Axiom fact_992_add__leE:(forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((((ord_less_eq_nat M) N)->(((ord_less_eq_nat K) N)->False))->False))).
% 2.48/2.85 Axiom fact_993_diff__diff__right:(forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->(((eq nat) ((minus_minus_nat I_1) ((minus_minus_nat J_1) K))) ((minus_minus_nat ((plus_plus_nat I_1) K)) J_1)))).
% 2.48/2.85 Axiom fact_994_le__diff__conv:(forall (J_1:nat) (K:nat) (I_1:nat), ((iff ((ord_less_eq_nat ((minus_minus_nat J_1) K)) I_1)) ((ord_less_eq_nat J_1) ((plus_plus_nat I_1) K)))).
% 2.48/2.85 Axiom fact_995_le__add__diff:(forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat K) N)->((ord_less_eq_nat M) ((minus_minus_nat ((plus_plus_nat N) M)) K)))).
% 2.48/2.85 Axiom fact_996_le__add__diff__inverse:(forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((plus_plus_nat N) ((minus_minus_nat M) N))) M))).
% 2.48/2.85 Axiom fact_997_add__diff__assoc:(forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->(((eq nat) ((plus_plus_nat I_1) ((minus_minus_nat J_1) K))) ((minus_minus_nat ((plus_plus_nat I_1) J_1)) K)))).
% 2.48/2.85 Axiom fact_998_le__diff__conv2:(forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->((iff ((ord_less_eq_nat I_1) ((minus_minus_nat J_1) K))) ((ord_less_eq_nat ((plus_plus_nat I_1) K)) J_1)))).
% 2.48/2.85 Axiom fact_999_le__add__diff__inverse2:(forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((plus_plus_nat ((minus_minus_nat M) N)) N)) M))).
% 2.48/2.85 Axiom fact_1000_le__imp__diff__is__add:(forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff (((eq nat) ((minus_minus_nat J_1) I_1)) K)) (((eq nat) J_1) ((plus_plus_nat K) I_1))))).
% 2.48/2.85 Axiom fact_1001_diff__add__assoc:(forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat I_1) J_1)) K)) ((plus_plus_nat I_1) ((minus_minus_nat J_1) K))))).
% 2.48/2.85 Axiom fact_1002_add__diff__assoc2:(forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->(((eq nat) ((plus_plus_nat ((minus_minus_nat J_1) K)) I_1)) ((minus_minus_nat ((plus_plus_nat J_1) I_1)) K)))).
% 2.48/2.85 Axiom fact_1003_diff__add__assoc2:(forall (I_1:nat) (K:nat) (J_1:nat), (((ord_less_eq_nat K) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat J_1) I_1)) K)) ((plus_plus_nat ((minus_minus_nat J_1) K)) I_1)))).
% 2.48/2.85 Axiom fact_1004_add__mult__distrib2:(forall (K:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K) ((plus_plus_nat M) N))) ((plus_plus_nat ((times_times_nat K) M)) ((times_times_nat K) N)))).
% 2.48/2.85 Axiom fact_1005_add__mult__distrib:(forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((plus_plus_nat M) N)) K)) ((plus_plus_nat ((times_times_nat M) K)) ((times_times_nat N) K)))).
% 2.48/2.85 Axiom fact_1006_nat__dvd__1__iff__1:(forall (M:nat), ((iff ((dvd_dvd_nat M) one_one_nat)) (((eq nat) M) one_one_nat))).
% 2.48/2.85 Axiom fact_1007_le__square:(forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) M))).
% 2.48/2.85 Axiom fact_1008_le__cube:(forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) ((times_times_nat M) M)))).
% 2.48/2.85 Axiom fact_1009_mult__le__mono1:(forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J_1) K)))).
% 2.48/2.85 Axiom fact_1010_mult__le__mono2:(forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((ord_less_eq_nat ((times_times_nat K) I_1)) ((times_times_nat K) J_1)))).
% 2.48/2.85 Axiom fact_1011_mult__le__mono:(forall (K:nat) (L:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J_1) L))))).
% 2.48/2.85 Axiom fact_1012_nat__mult__1:(forall (N:nat), (((eq nat) ((times_times_nat one_one_nat) N)) N)).
% 2.48/2.85 Axiom fact_1013_nat__1__eq__mult__iff:(forall (M:nat) (N:nat), ((iff (((eq nat) one_one_nat) ((times_times_nat M) N))) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat)))).
% 2.48/2.85 Axiom fact_1014_nat__mult__1__right:(forall (N:nat), (((eq nat) ((times_times_nat N) one_one_nat)) N)).
% 2.48/2.85 Axiom fact_1015_nat__mult__eq__1__iff:(forall (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) N)) one_one_nat)) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat)))).
% 2.48/2.85 Axiom fact_1016_real__add__mult__distrib:(forall (Z1:real) (Z2:real) (W:real), (((eq real) ((times_times_real ((plus_plus_real Z1) Z2)) W)) ((plus_plus_real ((times_times_real Z1) W)) ((times_times_real Z2) W)))).
% 2.48/2.85 Axiom fact_1017_nat__dvd__not__less:(forall (N:nat) (M:nat), (((ord_less_nat zero_zero_nat) M)->(((ord_less_nat M) N)->(((dvd_dvd_nat N) M)->False)))).
% 2.48/2.85 Axiom fact_1018_add__gr__0:(forall (M:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M) N))) ((or ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N)))).
% 2.48/2.85 Axiom fact_1019_nat__diff__split__asm:(forall (P:(nat->Prop)) (A:nat) (B:nat), ((iff (P ((minus_minus_nat A) B))) (((or ((and ((ord_less_nat A) B)) ((P zero_zero_nat)->False))) ((ex nat) (fun (D_2:nat)=> ((and (((eq nat) A) ((plus_plus_nat B) D_2))) ((P D_2)->False)))))->False))).
% 2.48/2.85 Axiom fact_1020_nat__diff__split:(forall (P:(nat->Prop)) (A:nat) (B:nat), ((iff (P ((minus_minus_nat A) B))) ((and (((ord_less_nat A) B)->(P zero_zero_nat))) (forall (D_2:nat), ((((eq nat) A) ((plus_plus_nat B) D_2))->(P D_2)))))).
% 2.48/2.85 Axiom fact_1021_nat__0__less__mult__iff:(forall (M:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((times_times_nat M) N))) ((and ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N)))).
% 2.48/2.85 Axiom fact_1022_mult__less__cancel1:(forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M) N)))).
% 2.48/2.85 Axiom fact_1023_mult__less__cancel2:(forall (M:nat) (K:nat) (N:nat), ((iff ((ord_less_nat ((times_times_nat M) K)) ((times_times_nat N) K))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M) N)))).
% 2.48/2.85 Axiom fact_1024_mult__less__mono1:(forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat I_1) K)) ((times_times_nat J_1) K))))).
% 2.48/2.85 Axiom fact_1025_mult__less__mono2:(forall (K:nat) (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat K) I_1)) ((times_times_nat K) J_1))))).
% 2.48/2.85 Axiom fact_1026_real__mult__le__cancel__iff1:(forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real X) Z)) ((times_times_real Y) Z))) ((ord_less_eq_real X) Y)))).
% 2.48/2.85 Axiom fact_1027_real__mult__le__cancel__iff2:(forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real Z) X)) ((times_times_real Z) Y))) ((ord_less_eq_real X) Y)))).
% 2.48/2.85 Axiom fact_1028_real__mult__less__mono2:(forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->(((ord_less_real X) Y)->((ord_less_real ((times_times_real Z) X)) ((times_times_real Z) Y))))).
% 2.48/2.85 Axiom fact_1029_real__mult__order:(forall (Y:real) (X:real), (((ord_less_real zero_zero_real) X)->(((ord_less_real zero_zero_real) Y)->((ord_less_real zero_zero_real) ((times_times_real X) Y))))).
% 2.48/2.85 Axiom fact_1030_real__mult__less__iff1:(forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_real ((times_times_real X) Z)) ((times_times_real Y) Z))) ((ord_less_real X) Y)))).
% 2.48/2.85 Axiom fact_1031_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)))).
% 2.48/2.85 Axiom fact_1032_real__two__squares__add__zero__iff:(forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X) X)) ((times_times_real Y) Y))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real)))).
% 2.48/2.85 Axiom fact_1033_dvd__imp__le:(forall (K:nat) (N:nat), (((dvd_dvd_nat K) N)->(((ord_less_nat zero_zero_nat) N)->((ord_less_eq_nat K) N)))).
% 2.48/2.85 Axiom fact_1034_dvd__mult__cancel:(forall (K:nat) (M:nat) (N:nat), (((dvd_dvd_nat ((times_times_nat K) M)) ((times_times_nat K) N))->(((ord_less_nat zero_zero_nat) K)->((dvd_dvd_nat M) N)))).
% 2.48/2.85 Axiom fact_1035_mult__le__cancel1:(forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((times_times_nat K) M)) ((times_times_nat K) N))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M) N)))).
% 2.48/2.85 Axiom fact_1036_mult__le__cancel2:(forall (M:nat) (K:nat) (N:nat), ((iff ((ord_less_eq_nat ((times_times_nat M) K)) ((times_times_nat N) K))) (((ord_less_nat zero_zero_nat) K)->((ord_less_eq_nat M) N)))).
% 2.48/2.85 Axiom fact_1037_two__realpow__ge__one:(forall (N:nat), ((ord_less_eq_real one_one_real) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N))).
% 2.48/2.85 Axiom fact_1038_dvd__mult__cancel1:(forall (N:nat) (M:nat), (((ord_less_nat zero_zero_nat) M)->((iff ((dvd_dvd_nat ((times_times_nat M) N)) M)) (((eq nat) N) one_one_nat)))).
% 2.48/2.85 Axiom fact_1039_ex__least__nat__less:(forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N)) (forall (_TPTP_I:nat), (((ord_less_eq_nat _TPTP_I) K_1)->((P _TPTP_I)->False))))) (P ((plus_plus_nat K_1) one_one_nat)))))))).
% 2.48/2.85 Axiom fact_1040_nat__less__add__iff2:(forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((ord_less_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N))))).
% 2.48/2.85 Axiom fact_1041_nat__less__add__iff1:(forall (U:nat) (M:nat) (N:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((ord_less_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N)))).
% 2.48/2.85 Axiom fact_1042_real__le__refl:(forall (W:real), ((ord_less_eq_real W) W)).
% 2.48/2.85 Axiom fact_1043_real__le__linear:(forall (Z:real) (W:real), ((or ((ord_less_eq_real Z) W)) ((ord_less_eq_real W) Z))).
% 2.48/2.85 Axiom fact_1044_real__le__trans:(forall (K:real) (I_1:real) (J_1:real), (((ord_less_eq_real I_1) J_1)->(((ord_less_eq_real J_1) K)->((ord_less_eq_real I_1) K)))).
% 2.48/2.85 Axiom fact_1045_real__le__antisym:(forall (Z:real) (W:real), (((ord_less_eq_real Z) W)->(((ord_less_eq_real W) Z)->(((eq real) Z) W)))).
% 2.48/2.85 Axiom fact_1046_nat__mult__eq__cancel__disj:(forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) ((or (((eq nat) K) zero_zero_nat)) (((eq nat) M) N)))).
% 2.48/2.85 Axiom fact_1047_left__add__mult__distrib:(forall (I_1:nat) (U:nat) (J_1:nat) (K:nat), (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) ((plus_plus_nat ((times_times_nat J_1) U)) K))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat I_1) J_1)) U)) K))).
% 2.48/2.85 Axiom fact_1048_nat__mult__less__cancel1:(forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((ord_less_nat M) N)))).
% 2.48/2.85 Axiom fact_1049_nat__mult__eq__cancel1:(forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff (((eq nat) ((times_times_nat K) M)) ((times_times_nat K) N))) (((eq nat) M) N)))).
% 2.48/2.85 Axiom fact_1050_nat__mult__dvd__cancel__disj:(forall (K:nat) (M:nat) (N:nat), ((iff ((dvd_dvd_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((or (((eq nat) K) zero_zero_nat)) ((dvd_dvd_nat M) N)))).
% 2.48/2.85 Axiom fact_1051_nat__mult__dvd__cancel1:(forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((dvd_dvd_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((dvd_dvd_nat M) N)))).
% 2.48/2.85 Axiom fact_1052_nat__mult__le__cancel1:(forall (M:nat) (N:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((iff ((ord_less_eq_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((ord_less_eq_nat M) N)))).
% 2.48/2.85 Axiom fact_1053_nat__le__add__iff1:(forall (U:nat) (M:nat) (N:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N)))).
% 2.48/2.85 Axiom fact_1054_nat__diff__add__eq1:(forall (U:nat) (M:nat) (N:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((minus_minus_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N)))).
% 2.48/2.85 Axiom fact_1055_nat__eq__add__iff1:(forall (U:nat) (M:nat) (N:nat) (J_1:nat) (I_1:nat), (((ord_less_eq_nat J_1) I_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) (((eq nat) ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J_1)) U)) M)) N)))).
% 2.48/2.85 Axiom fact_1056_nat__le__add__iff2:(forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((ord_less_eq_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N))))).
% 2.48/2.85 Axiom fact_1057_nat__diff__add__eq2:(forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) ((minus_minus_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N))))).
% 2.48/2.85 Axiom fact_1058_nat__eq__add__iff2:(forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J_1:nat), (((ord_less_eq_nat I_1) J_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J_1) U)) N))) (((eq nat) M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J_1) I_1)) U)) N))))).
% 2.48/2.86 Axiom fact_1059_number__of1:(forall (N:int), (((ord_less_eq_int zero_zero_int) (number_number_of_int N))->((and ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 N)))) ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 N)))))).
% 2.48/2.86 Axiom fact_1060_zprime__factor__exists:(forall (A:int), (((ord_less_int one_one_int) A)->((ex int) (fun (P_3:int)=> ((and (zprime P_3)) ((dvd_dvd_int P_3) A)))))).
% 2.48/2.86 Axiom fact_1061_conj__le__cong:(forall (P_2:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_2))->((iff ((and ((ord_less_eq_int zero_zero_int) X)) P)) ((and ((ord_less_eq_int zero_zero_int) X)) P_2)))).
% 2.48/2.86 Axiom fact_1062_imp__le__cong:(forall (P_2:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_2))->((iff (((ord_less_eq_int zero_zero_int) X)->P)) (((ord_less_eq_int zero_zero_int) X)->P_2)))).
% 2.48/2.86 Axiom fact_1063_zdvd__mono:(forall (M:int) (T:int) (K:int), ((not (((eq int) K) zero_zero_int))->((iff ((dvd_dvd_int M) T)) ((dvd_dvd_int ((times_times_int K) M)) ((times_times_int K) T))))).
% 2.48/2.86 Axiom fact_1064_number__of2:((ord_less_eq_int zero_zero_int) (number_number_of_int pls)).
% 2.48/2.86 Axiom fact_1065_decr__mult__lemma:(forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) ((times_times_int K) D))))))))).
% 2.48/2.86 Axiom fact_1066_incr__mult__lemma:(forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) ((times_times_int K) D))))))))).
% 2.48/2.86 Axiom fact_1067_zcong__zless__unique:(forall (A:int) (M:int), (((ord_less_int zero_zero_int) M)->((ex int) (fun (X_1:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X_1)) ((ord_less_int X_1) M))) (((zcong A) X_1) M))) (forall (Y_1:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y_1)) ((ord_less_int Y_1) M))) (((zcong A) Y_1) M))->(((eq int) Y_1) X_1)))))))).
% 2.48/2.86 Axiom fact_1068__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096:(((eq int) (twoSqu2057625106sum2sq ((product_Pair_int_int s) one_one_int))) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)).
% 2.48/2.86 Axiom fact_1069_mult__sum2sq:(forall (A:int) (B:int) (P_1:int) (Q:int), (((eq int) ((times_times_int (twoSqu2057625106sum2sq ((product_Pair_int_int A) B))) (twoSqu2057625106sum2sq ((product_Pair_int_int P_1) Q)))) (twoSqu2057625106sum2sq ((product_Pair_int_int ((plus_plus_int ((times_times_int A) P_1)) ((times_times_int B) Q))) ((minus_minus_int ((times_times_int A) Q)) ((times_times_int B) P_1)))))).
% 2.48/2.86 Axiom fact_1070_is__sum2sq__def:(forall (X:int), ((iff (twoSqu919416604sum2sq X)) ((ex int) (fun (A_2:int)=> ((ex int) (fun (B_2:int)=> (((eq int) (twoSqu2057625106sum2sq ((product_Pair_int_int A_2) B_2))) X))))))).
% 2.48/2.86 Axiom fact_1071_norR__mem__unique__aux:(forall (A:int) (B:int), (((ord_less_eq_int A) ((minus_minus_int B) one_one_int))->((ord_less_int A) B))).
% 2.48/2.86 Axiom fact_1072_Wilson__Russ:(forall (P_1:int), ((zprime P_1)->(((zcong (zfact ((minus_minus_int P_1) one_one_int))) (number_number_of_int min)) P_1))).
% 2.48/2.86 Axiom fact_1073_zfact_Osimps:(forall (N:int), ((and (((ord_less_eq_int N) zero_zero_int)->(((eq int) (zfact N)) one_one_int))) ((((ord_less_eq_int N) zero_zero_int)->False)->(((eq int) (zfact N)) ((times_times_int N) (zfact ((minus_minus_int N) one_one_int))))))).
% 2.48/2.86 Axiom fact_1074_inv__inv:(forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P_1)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P_1)->(((eq int) ((inv P_1) ((inv P_1) A))) A)))))).
% 2.48/2.86 Axiom fact_1075_inv__less__p__minus__1:(forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->((ord_less_int ((inv P_1) A)) ((minus_minus_int P_1) one_one_int)))))).
% 2.48/2.86 Axiom fact_1076_inv__g__1:(forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->((ord_less_int one_one_int) ((inv P_1) A)))))).
% 2.48/2.86 Axiom fact_1077_inv__not__p__minus__1:(forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(not (((eq int) ((inv P_1) A)) ((minus_minus_int P_1) one_one_int))))))).
% 2.48/2.86 Axiom fact_1078_inv__not__1:(forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(not (((eq int) ((inv P_1) A)) one_one_int)))))).
% 2.48/2.86 Axiom fact_1079_inv__distinct:(forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(not (((eq int) A) ((inv P_1) A))))))).
% 2.48/2.86 Axiom fact_1080_inv__not__0:(forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(not (((eq int) ((inv P_1) A)) zero_zero_int)))))).
% 2.48/2.86 Axiom fact_1081_inv__is__inv:(forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P_1)->(((zcong ((times_times_int A) ((inv P_1) A))) one_one_int) P_1))))).
% 2.48/2.86 Axiom fact_1082_wset__mem__inv__mem:(forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P_1)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(((member_int B) ((wset A) P_1))->((member_int ((inv P_1) B)) ((wset A) P_1))))))).
% 2.48/2.86 Axiom fact_1083_wset__inv__mem__mem:(forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P_1)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(((ord_less_int one_one_int) B)->(((ord_less_int B) ((minus_minus_int P_1) one_one_int))->(((member_int ((inv P_1) B)) ((wset A) P_1))->((member_int B) ((wset A) P_1))))))))).
% 2.48/2.86 Axiom fact_1084_wset__mem__mem:(forall (P_1:int) (A:int), (((ord_less_int one_one_int) A)->((member_int A) ((wset A) P_1)))).
% 2.48/2.86 Axiom fact_1085_wset__subset:(forall (B:int) (P_1:int) (A:int), (((ord_less_int one_one_int) A)->(((member_int B) ((wset ((minus_minus_int A) one_one_int)) P_1))->((member_int B) ((wset A) P_1))))).
% 2.48/2.86 Axiom fact_1086_wset__g__1:(forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(((member_int B) ((wset A) P_1))->((ord_less_int one_one_int) B))))).
% 2.48/2.86 Axiom fact_1087_wset__less:(forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(((member_int B) ((wset A) P_1))->((ord_less_int B) ((minus_minus_int P_1) one_one_int)))))).
% 2.48/2.86 Axiom fact_1088_wset__mem__imp__or:(forall (B:int) (P_1:int) (A:int), (((ord_less_int one_one_int) A)->((((member_int B) ((wset ((minus_minus_int A) one_one_int)) P_1))->False)->(((member_int B) ((wset A) P_1))->((or (((eq int) B) A)) (((eq int) B) ((inv P_1) A))))))).
% 2.48/2.86 Axiom fact_1089_wset__mem:(forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int A) ((minus_minus_int P_1) one_one_int))->(((ord_less_int one_one_int) B)->(((ord_less_eq_int B) A)->((member_int B) ((wset A) P_1))))))).
% 2.48/2.86 Axiom fact_1090_MultInvPair__distinct:(forall (J_1:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->(((((zcong A) zero_zero_int) P_1)->False)->(((((zcong J_1) zero_zero_int) P_1)->False)->((((quadRes P_1) A)->False)->((((zcong J_1) ((times_times_int A) ((multInv P_1) J_1))) P_1)->False))))))).
% 2.48/2.86 Axiom fact_1091_int__le__induct:(forall (P:(int->Prop)) (I_1:int) (K:int), (((ord_less_eq_int I_1) K)->((P K)->((forall (_TPTP_I:int), (((ord_less_eq_int _TPTP_I) K)->((P _TPTP_I)->(P ((minus_minus_int _TPTP_I) one_one_int)))))->(P I_1))))).
% 2.48/2.86 Axiom fact_1092_aux______1:(forall (J_1:int) (A:int) (P_1:int) (K:int), ((((zcong J_1) ((times_times_int A) ((multInv P_1) K))) P_1)->(((zcong ((times_times_int J_1) K)) ((times_times_int ((times_times_int A) ((multInv P_1) K))) K)) P_1))).
% 2.48/2.86 Axiom fact_1093_aux______3:(forall (J_1:int) (K:int) (A:int) (P_1:int), ((((zcong ((times_times_int J_1) K)) A) P_1)->(((zcong ((times_times_int ((times_times_int ((multInv P_1) J_1)) J_1)) K)) ((times_times_int ((multInv P_1) J_1)) A)) P_1))).
% 2.48/2.86 Axiom fact_1094_MultInv__prop1:(forall (X:int) (Y:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((((zcong X) Y) P_1)->(((zcong ((multInv P_1) X)) ((multInv P_1) Y)) P_1)))).
% 2.48/2.86 Axiom fact_1095_MultInv__zcong__prop1:(forall (A:int) (J_1:int) (K:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((((zcong J_1) K) P_1)->(((zcong ((times_times_int A) ((multInv P_1) J_1))) ((times_times_int A) ((multInv P_1) K))) P_1)))).
% 2.48/2.86 Axiom fact_1096_MultInv__prop5:(forall (Y:int) (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((((zcong Y) zero_zero_int) P_1)->False)->((((zcong ((multInv P_1) X)) ((multInv P_1) Y)) P_1)->(((zcong X) Y) P_1))))))).
% 2.48/2.86 Axiom fact_1097_MultInv__prop4:(forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((zcong ((multInv P_1) ((multInv P_1) X))) X) P_1))))).
% 2.48/2.86 Axiom fact_1098_MultInv__prop3:(forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->((((zcong ((multInv P_1) X)) zero_zero_int) P_1)->False))))).
% 2.48/2.86 Axiom fact_1099_aux______4:(forall (K:int) (A:int) (J_1:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong J_1) zero_zero_int) P_1)->False)->((((zcong ((times_times_int ((times_times_int ((multInv P_1) J_1)) J_1)) K)) ((times_times_int ((multInv P_1) J_1)) A)) P_1)->(((zcong K) ((times_times_int A) ((multInv P_1) J_1))) P_1)))))).
% 2.48/2.86 Axiom fact_1100_aux______2:(forall (J_1:int) (A:int) (K:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong K) zero_zero_int) P_1)->False)->((((zcong ((times_times_int J_1) K)) ((times_times_int ((times_times_int A) ((multInv P_1) K))) K)) P_1)->(((zcong ((times_times_int J_1) K)) A) P_1)))))).
% 2.48/2.86 Axiom fact_1101_MultInv__zcong__prop2:(forall (A:int) (J_1:int) (K:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong K) zero_zero_int) P_1)->False)->(((((zcong J_1) zero_zero_int) P_1)->False)->((((zcong J_1) ((times_times_int A) ((multInv P_1) K))) P_1)->(((zcong K) ((times_times_int A) ((multInv P_1) J_1))) P_1))))))).
% 2.48/2.86 Axiom fact_1102_MultInv__zcong__prop3:(forall (J_1:int) (K:int) (A:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong A) zero_zero_int) P_1)->False)->(((((zcong K) zero_zero_int) P_1)->False)->(((((zcong J_1) zero_zero_int) P_1)->False)->((((zcong ((times_times_int A) ((multInv P_1) J_1))) ((times_times_int A) ((multInv P_1) K))) P_1)->(((zcong J_1) K) P_1)))))))).
% 2.48/2.86 Axiom fact_1103_Int2_Oaux____2:(forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((zcong ((times_times_int ((times_times_int X) ((multInv P_1) X))) ((multInv P_1) ((multInv P_1) X)))) X) P_1))))).
% 2.48/2.86 Axiom fact_1104_Int2_Oaux____1:(forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((zcong ((multInv P_1) ((multInv P_1) X))) ((times_times_int ((times_times_int X) ((multInv P_1) X))) ((multInv P_1) ((multInv P_1) X)))) P_1))))).
% 2.48/2.86 Axiom fact_1105_MultInv__prop2a:(forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((zcong ((times_times_int ((multInv P_1) X)) X)) one_one_int) P_1))))).
% 2.48/2.86 Axiom fact_1106_MultInv__prop2:(forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((zcong ((times_times_int X) ((multInv P_1) X))) one_one_int) P_1))))).
% 2.48/2.86 Axiom fact_1107_d22set__induct__old:(forall (X:int) (P:(int->Prop)), ((forall (A_2:int), ((((ord_less_int one_one_int) A_2)->(P ((minus_minus_int A_2) one_one_int)))->(P A_2)))->(P X))).
% 2.48/2.86 Axiom fact_1108_int__less__induct:(forall (P:(int->Prop)) (I_1:int) (K:int), (((ord_less_int I_1) K)->((P ((minus_minus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int _TPTP_I) K)->((P _TPTP_I)->(P ((minus_minus_int _TPTP_I) one_one_int)))))->(P I_1))))).
% 2.48/2.86 Axiom fact_1109_int__ge__induct:(forall (P:(int->Prop)) (K:int) (I_1:int), (((ord_less_eq_int K) I_1)->((P K)->((forall (_TPTP_I:int), (((ord_less_eq_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->(P I_1))))).
% 2.48/2.86 Axiom fact_1110_int__gr__induct:(forall (P:(int->Prop)) (K:int) (I_1:int), (((ord_less_int K) I_1)->((P ((plus_plus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->(P I_1))))).
% 2.48/2.86 Axiom fact_1111_mono__nat__linear__lb:(forall (M:nat) (K:nat) (F:(nat->nat)), ((forall (M_2:nat) (N_1:nat), (((ord_less_nat M_2) N_1)->((ord_less_nat (F M_2)) (F N_1))))->((ord_less_eq_nat ((plus_plus_nat (F M)) K)) (F ((plus_plus_nat M) K))))).
% 2.48/2.86 Axiom fact_1112_d22set__eq__wset:(forall (P_1:int), ((zprime P_1)->(((eq (int->Prop)) (d22set ((minus_minus_int P_1) (number_number_of_int (bit0 (bit1 pls)))))) ((wset ((minus_minus_int P_1) (number_number_of_int (bit0 (bit1 pls))))) P_1)))).
% 2.48/2.86 Axiom fact_1113_d22set__le__swap:(forall (A:int) (B:int), (((ord_less_int A) B)->(((member_int B) (d22set A))->False))).
% 2.48/2.86 Axiom fact_1114_d22set__le:(forall (B:int) (A:int), (((member_int B) (d22set A))->((ord_less_eq_int B) A))).
% 2.48/2.86 Axiom fact_1115_d22set__g__1:(forall (B:int) (A:int), (((member_int B) (d22set A))->((ord_less_int one_one_int) B))).
% 2.48/2.86 Axiom fact_1116_d22set__mem:(forall (A:int) (B:int), (((ord_less_int one_one_int) B)->(((ord_less_eq_int B) A)->((member_int B) (d22set A))))).
% 2.48/2.86 Axiom fact_1117_ex__least__nat__le:(forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_eq_nat K_1) N)) (forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) K_1)->((P _TPTP_I)->False))))) (P K_1))))))).
% 2.48/2.86 Axiom fact_1118_less__imp__add__positive:(forall (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ex nat) (fun (K_1:nat)=> ((and ((ord_less_nat zero_zero_nat) K_1)) (((eq nat) ((plus_plus_nat I_1) K_1)) J_1)))))).
% 2.48/2.86 Axiom fact_1119_pow__divides__eq__int:(forall (A:int) (B:int) (N:nat), ((not (((eq nat) N) zero_zero_nat))->((iff ((dvd_dvd_int ((power_power_int A) N)) ((power_power_int B) N))) ((dvd_dvd_int A) B)))).
% 2.48/2.86 Axiom fact_1120_pow__divides__pow__int:(forall (A:int) (N:nat) (B:int), (((dvd_dvd_int ((power_power_int A) N)) ((power_power_int B) N))->((not (((eq nat) N) zero_zero_nat))->((dvd_dvd_int A) B)))).
% 2.48/2.86 Axiom fact_1121_gcd__lcm__complete__lattice__nat_Otop__le:(forall (A:nat), (((dvd_dvd_nat zero_zero_nat) A)->(((eq nat) A) zero_zero_nat))).
% 2.48/2.86 Axiom fact_1122_gcd__lcm__complete__lattice__nat_Otop__unique:(forall (A:nat), ((iff ((dvd_dvd_nat zero_zero_nat) A)) (((eq nat) A) zero_zero_nat))).
% 2.48/2.86 Axiom fact_1123_gcd__lcm__complete__lattice__nat_Oless__top:(forall (A:nat), ((iff (not (((eq nat) A) zero_zero_nat))) ((and ((dvd_dvd_nat A) zero_zero_nat)) (((dvd_dvd_nat zero_zero_nat) A)->False)))).
% 2.48/2.86 Axiom fact_1124_gcd__lcm__complete__lattice__nat_Otop__greatest:(forall (A:nat), ((dvd_dvd_nat A) zero_zero_nat)).
% 2.48/2.86 Axiom fact_1125_gcd__lcm__complete__lattice__nat_Onot__top__less:(forall (A:nat), (((and ((dvd_dvd_nat zero_zero_nat) A)) (((dvd_dvd_nat A) zero_zero_nat)->False))->False)).
% 2.48/2.86 Axiom fact_1126_gcd__lcm__complete__lattice__nat_Ole__bot:(forall (A:nat), (((dvd_dvd_nat A) one_one_nat)->(((eq nat) A) one_one_nat))).
% 2.48/2.86 Axiom fact_1127_gcd__lcm__complete__lattice__nat_Obot__unique:(forall (A:nat), ((iff ((dvd_dvd_nat A) one_one_nat)) (((eq nat) A) one_one_nat))).
% 2.48/2.86 Axiom fact_1128_gcd__lcm__complete__lattice__nat_Obot__less:(forall (A:nat), ((iff (not (((eq nat) A) one_one_nat))) ((and ((dvd_dvd_nat one_one_nat) A)) (((dvd_dvd_nat A) one_one_nat)->False)))).
% 2.48/2.87 Axiom fact_1129_gcd__lcm__complete__lattice__nat_Obot__least:(forall (A:nat), ((dvd_dvd_nat one_one_nat) A)).
% 2.48/2.87 Axiom fact_1130_gcd__lcm__complete__lattice__nat_Onot__less__bot:(forall (A:nat), (((and ((dvd_dvd_nat A) one_one_nat)) (((dvd_dvd_nat one_one_nat) A)->False))->False)).
% 2.48/2.87 Axiom fact_1131_dvd__pos__nat:(forall (M:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((dvd_dvd_nat M) N)->((ord_less_nat zero_zero_nat) M)))).
% 2.48/2.87 Axiom fact_1132_pow__divides__eq__nat:(forall (A:nat) (B:nat) (N:nat), ((not (((eq nat) N) zero_zero_nat))->((iff ((dvd_dvd_nat ((power_power_nat A) N)) ((power_power_nat B) N))) ((dvd_dvd_nat A) B)))).
% 2.48/2.87 Axiom fact_1133_divides__le:(forall (M:nat) (N:nat), (((dvd_dvd_nat M) N)->((or ((ord_less_eq_nat M) N)) (((eq nat) N) zero_zero_nat)))).
% 2.48/2.87 Axiom fact_1134_mult__left__cancel:(forall (N:nat) (M:nat) (K:nat), (((ord_less_nat zero_zero_nat) K)->((((eq nat) ((times_times_nat K) N)) ((times_times_nat K) M))->(((eq nat) N) M)))).
% 2.48/2.87 Axiom fact_1135_SR__def:(forall (P_1:int), (((eq (int->Prop)) (sr P_1)) (collect_int (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) ((ord_less_int X_1) P_1)))))).
% 2.48/2.87 Axiom fact_1136_zmod__number__of__Bit1:(forall (V:int) (W:int), ((and (((ord_less_eq_int zero_zero_int) (number_number_of_int W))->(((eq int) ((div_mod_int (number_number_of_int (bit1 V))) (number_number_of_int (bit0 W)))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) ((div_mod_int (number_number_of_int V)) (number_number_of_int W)))) one_one_int)))) ((((ord_less_eq_int zero_zero_int) (number_number_of_int W))->False)->(((eq int) ((div_mod_int (number_number_of_int (bit1 V))) (number_number_of_int (bit0 W)))) ((minus_minus_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) ((div_mod_int ((plus_plus_int (number_number_of_int V)) one_one_int)) (number_number_of_int W)))) one_one_int))))).
% 2.48/2.87 Axiom fact_1137_neg__zmod__mult__2:(forall (B:int) (A:int), (((ord_less_eq_int A) zero_zero_int)->(((eq int) ((div_mod_int ((plus_plus_int one_one_int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) B))) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A))) ((minus_minus_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) ((div_mod_int ((plus_plus_int B) one_one_int)) A))) one_one_int)))).
% 2.48/2.87 Axiom fact_1138_zmod__simps_I3_J:(forall (A:int) (B:int) (C:int), (((eq int) ((div_mod_int ((times_times_int A) ((div_mod_int B) C))) C)) ((div_mod_int ((times_times_int A) B)) C))).
% 2.48/2.87 Axiom fact_1139_zmod__zmult1__eq:(forall (A:int) (B:int) (C:int), (((eq int) ((div_mod_int ((times_times_int A) B)) C)) ((div_mod_int ((times_times_int A) ((div_mod_int B) C))) C))).
% 2.48/2.87 Axiom fact_1140_zcong__zmod:(forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) (((zcong ((div_mod_int A) M)) ((div_mod_int B) M)) M))).
% 2.48/2.87 Axiom fact_1141_zpower__zmod:(forall (X:int) (M:int) (Y:nat), (((eq int) ((div_mod_int ((power_power_int ((div_mod_int X) M)) Y)) M)) ((div_mod_int ((power_power_int X) Y)) M))).
% 2.48/2.87 Axiom fact_1142_mod__mod__is__mod:(forall (X:int) (M:int), (((zcong X) ((div_mod_int X) M)) M)).
% 2.48/2.87 Axiom fact_1143_Residues_Oaux:(forall (X:int) (M:int) (Y:int), ((((eq int) ((div_mod_int X) M)) ((div_mod_int Y) M))->(((zcong X) Y) M))).
% 2.48/2.87 Axiom fact_1144_zdvd__zmod:(forall (N:int) (F:int) (M:int), (((dvd_dvd_int F) M)->(((dvd_dvd_int F) N)->((dvd_dvd_int F) ((div_mod_int M) N))))).
% 2.48/2.87 Axiom fact_1145_zdvd__zmod__imp__zdvd:(forall (K:int) (M:int) (N:int), (((dvd_dvd_int K) ((div_mod_int M) N))->(((dvd_dvd_int K) N)->((dvd_dvd_int K) M)))).
% 2.48/2.87 Axiom fact_1146_zmod__self:(forall (A:int), (((eq int) ((div_mod_int A) A)) zero_zero_int)).
% 2.48/2.87 Axiom fact_1147_zmod__zero:(forall (B:int), (((eq int) ((div_mod_int zero_zero_int) B)) zero_zero_int)).
% 2.48/2.87 Axiom fact_1148_zmod__eq__dvd__iff:(forall (X:int) (N:int) (Y:int), ((iff (((eq int) ((div_mod_int X) N)) ((div_mod_int Y) N))) ((dvd_dvd_int N) ((minus_minus_int X) Y)))).
% 2.48/2.87 Axiom fact_1149_zmod__eq__0__iff:(forall (M:int) (D:int), ((iff (((eq int) ((div_mod_int M) D)) zero_zero_int)) ((ex int) (fun (Q_1:int)=> (((eq int) M) ((times_times_int D) Q_1)))))).
% 2.48/2.87 Axiom fact_1150_Divides_Otransfer__nat__int__function__closures_I2_J:(forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((div_mod_int X) Y))))).
% 2.48/2.87 Axiom fact_1151_zmod__le__nonneg__dividend:(forall (K:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->((ord_less_eq_int ((div_mod_int M) K)) M))).
% 2.48/2.87 Axiom fact_1152_pos__mod__bound:(forall (A:int) (B:int), (((ord_less_int zero_zero_int) B)->((ord_less_int ((div_mod_int A) B)) B))).
% 2.48/2.87 Axiom fact_1153_neg__mod__bound:(forall (A:int) (B:int), (((ord_less_int B) zero_zero_int)->((ord_less_int B) ((div_mod_int A) B)))).
% 2.48/2.87 Axiom fact_1154_zdiff__zmod__left:(forall (X:int) (M:int) (Y:int), (((eq int) ((div_mod_int ((minus_minus_int ((div_mod_int X) M)) Y)) M)) ((div_mod_int ((minus_minus_int X) Y)) M))).
% 2.48/2.87 Axiom fact_1155_zdiff__zmod__right:(forall (X:int) (Y:int) (M:int), (((eq int) ((div_mod_int ((minus_minus_int X) ((div_mod_int Y) M))) M)) ((div_mod_int ((minus_minus_int X) Y)) M))).
% 2.48/2.87 Axiom fact_1156_zdvd__iff__zmod__eq__0__number__of:(forall (X:int) (Y:int), ((iff ((dvd_dvd_int (number_number_of_int X)) (number_number_of_int Y))) (((eq int) ((div_mod_int (number_number_of_int Y)) (number_number_of_int X))) zero_zero_int))).
% 2.48/2.87 Axiom fact_1157_zmod__minus1__right:(forall (A:int), (((eq int) ((div_mod_int A) (number_number_of_int min))) zero_zero_int)).
% 2.48/2.87 Axiom fact_1158_zmod__zdvd__zmod:(forall (A:int) (B:int) (M:int), (((ord_less_int zero_zero_int) M)->(((dvd_dvd_int M) B)->(((eq int) ((div_mod_int ((div_mod_int A) B)) M)) ((div_mod_int A) M))))).
% 2.48/2.87 Axiom fact_1159_zcong__zmod__eq:(forall (A:int) (B:int) (M:int), (((ord_less_int zero_zero_int) M)->((iff (((zcong A) B) M)) (((eq int) ((div_mod_int A) M)) ((div_mod_int B) M))))).
% 2.48/2.87 Axiom fact_1160_pos__mod__sign:(forall (A:int) (B:int), (((ord_less_int zero_zero_int) B)->((ord_less_eq_int zero_zero_int) ((div_mod_int A) B)))).
% 2.48/2.87 Axiom fact_1161_pos__mod__conj:(forall (A:int) (B:int), (((ord_less_int zero_zero_int) B)->((and ((ord_less_eq_int zero_zero_int) ((div_mod_int A) B))) ((ord_less_int ((div_mod_int A) B)) B)))).
% 2.48/2.87 Axiom fact_1162_mod__pos__pos__trivial:(forall (B:int) (A:int), (((ord_less_eq_int zero_zero_int) A)->(((ord_less_int A) B)->(((eq int) ((div_mod_int A) B)) A)))).
% 2.48/2.87 Axiom fact_1163_neg__mod__sign:(forall (A:int) (B:int), (((ord_less_int B) zero_zero_int)->((ord_less_eq_int ((div_mod_int A) B)) zero_zero_int))).
% 2.48/2.87 Axiom fact_1164_neg__mod__conj:(forall (A:int) (B:int), (((ord_less_int B) zero_zero_int)->((and ((ord_less_eq_int ((div_mod_int A) B)) zero_zero_int)) ((ord_less_int B) ((div_mod_int A) B))))).
% 2.48/2.87 Axiom fact_1165_mod__neg__neg__trivial:(forall (B:int) (A:int), (((ord_less_eq_int A) zero_zero_int)->(((ord_less_int B) A)->(((eq int) ((div_mod_int A) B)) A)))).
% 2.48/2.87 Axiom fact_1166_mod__pos__neg__trivial:(forall (B:int) (A:int), (((ord_less_int zero_zero_int) A)->(((ord_less_eq_int ((plus_plus_int A) B)) zero_zero_int)->(((eq int) ((div_mod_int A) B)) ((plus_plus_int A) B))))).
% 2.48/2.87 Axiom fact_1167_zmod__number__of__Bit0:(forall (V:int) (W:int), (((eq int) ((div_mod_int (number_number_of_int (bit0 V))) (number_number_of_int (bit0 W)))) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) ((div_mod_int (number_number_of_int V)) (number_number_of_int W))))).
% 2.48/2.87 Axiom fact_1168_divmod__int__rel__mod__eq:(forall (A_1:int) (B_1:int) (Q_2:int) (Y:int), ((((eq int) A_1) ((plus_plus_int ((times_times_int B_1) Q_2)) Y))->(((and (((ord_less_int zero_zero_int) B_1)->((and ((ord_less_eq_int zero_zero_int) Y)) ((ord_less_int Y) B_1)))) ((((ord_less_int zero_zero_int) B_1)->False)->((and ((ord_less_int B_1) Y)) ((ord_less_eq_int Y) zero_zero_int))))->((not (((eq int) B_1) zero_zero_int))->(((eq int) ((div_mod_int A_1) B_1)) Y))))).
% 2.48/2.87 Axiom fact_1169_zmult2__lemma__aux2:(forall (Q:int) (B:int) (R:int) (C:int), (((ord_less_int zero_zero_int) C)->(((ord_less_int B) R)->(((ord_less_eq_int R) zero_zero_int)->((ord_less_eq_int ((plus_plus_int ((times_times_int B) ((div_mod_int Q) C))) R)) zero_zero_int))))).
% 2.48/2.87 Axiom fact_1170_zmult2__lemma__aux1:(forall (Q:int) (B:int) (R:int) (C:int), (((ord_less_int zero_zero_int) C)->(((ord_less_int B) R)->(((ord_less_eq_int R) zero_zero_int)->((ord_less_int ((times_times_int B) C)) ((plus_plus_int ((times_times_int B) ((div_mod_int Q) C))) R)))))).
% 2.48/2.87 Axiom fact_1171_zmult2__lemma__aux4:(forall (Q:int) (B:int) (R:int) (C:int), (((ord_less_int zero_zero_int) C)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int R) B)->((ord_less_int ((plus_plus_int ((times_times_int B) ((div_mod_int Q) C))) R)) ((times_times_int B) C)))))).
% 2.48/2.87 Axiom fact_1172_zmult2__lemma__aux3:(forall (Q:int) (B:int) (R:int) (C:int), (((ord_less_int zero_zero_int) C)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int R) B)->((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B) ((div_mod_int Q) C))) R)))))).
% 2.48/2.87 Axiom fact_1173_split__zmod:(forall (P:(int->Prop)) (N:int) (K:int), ((iff (P ((div_mod_int N) K))) ((and ((and ((((eq int) K) zero_zero_int)->(P N))) (((ord_less_int zero_zero_int) K)->(forall (_TPTP_I:int) (J:int), (((and ((and ((ord_less_eq_int zero_zero_int) J)) ((ord_less_int J) K))) (((eq int) N) ((plus_plus_int ((times_times_int K) _TPTP_I)) J)))->(P J)))))) (((ord_less_int K) zero_zero_int)->(forall (_TPTP_I:int) (J:int), (((and ((and ((ord_less_int K) J)) ((ord_less_eq_int J) zero_zero_int))) (((eq int) N) ((plus_plus_int ((times_times_int K) _TPTP_I)) J)))->(P J))))))).
% 2.48/2.87 Axiom fact_1174_neq__one__mod__two:(forall (X:int), ((iff (not (((eq int) ((div_mod_int X) (number_number_of_int (bit0 (bit1 pls))))) zero_zero_int))) (((eq int) ((div_mod_int X) (number_number_of_int (bit0 (bit1 pls))))) one_one_int))).
% 2.48/2.87 Axiom fact_1175_zmod__minus1:(forall (B:int), (((ord_less_int zero_zero_int) B)->(((eq int) ((div_mod_int (number_number_of_int min)) B)) ((minus_minus_int B) one_one_int)))).
% 2.48/2.87 Axiom fact_1176_pos__zmod__mult__2:(forall (B:int) (A:int), (((ord_less_eq_int zero_zero_int) A)->(((eq int) ((div_mod_int ((plus_plus_int one_one_int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) B))) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A))) ((plus_plus_int one_one_int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) ((div_mod_int B) A)))))).
% 2.48/2.87 Axiom fact_1177_zmod__eq__0D:(forall (M_1:int) (D_1:int), ((((eq int) ((div_mod_int M_1) D_1)) zero_zero_int)->((ex int) (fun (Q_1:int)=> (((eq int) M_1) ((times_times_int D_1) Q_1)))))).
% 2.48/2.87 Axiom fact_1178_StandardRes__prop4:(forall (X:int) (Y:int) (M:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) M)->(((zcong ((times_times_int ((standardRes M) X)) ((standardRes M) Y))) ((times_times_int X) Y)) M))).
% 2.48/2.87 Axiom fact_1179_mod__le__divisor:(forall (M:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->((ord_less_eq_nat ((div_mod_nat M) N)) N))).
% 2.48/2.87 Axiom fact_1180_mod__mult__distrib2:(forall (K:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K) ((div_mod_nat M) N))) ((div_mod_nat ((times_times_nat K) M)) ((times_times_nat K) N)))).
% 2.48/2.87 Axiom fact_1181_mod__mult__distrib:(forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((div_mod_nat M) N)) K)) ((div_mod_nat ((times_times_nat M) K)) ((times_times_nat N) K)))).
% 2.48/2.87 Axiom fact_1182_StandardRes__def:(forall (M:int) (X:int), (((eq int) ((standardRes M) X)) ((div_mod_int X) M))).
% 2.48/2.87 Axiom fact_1183_mod__less:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->(((eq nat) ((div_mod_nat M) N)) M))).
% 2.48/2.87 Axiom fact_1184_le__mod__geq:(forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((div_mod_nat M) N)) ((div_mod_nat ((minus_minus_nat M) N)) N)))).
% 2.48/2.87 Axiom fact_1185_mod__mult__self3:(forall (K:nat) (N:nat) (M:nat), (((eq nat) ((div_mod_nat ((plus_plus_nat ((times_times_nat K) N)) M)) N)) ((div_mod_nat M) N))).
% 2.48/2.87 Axiom fact_1186_mod__geq:(forall (M:nat) (N:nat), ((((ord_less_nat M) N)->False)->(((eq nat) ((div_mod_nat M) N)) ((div_mod_nat ((minus_minus_nat M) N)) N)))).
% 2.48/2.87 Axiom fact_1187_mod__if:(forall (M:nat) (N:nat), ((and (((ord_less_nat M) N)->(((eq nat) ((div_mod_nat M) N)) M))) ((((ord_less_nat M) N)->False)->(((eq nat) ((div_mod_nat M) N)) ((div_mod_nat ((minus_minus_nat M) N)) N))))).
% 2.48/2.87 Axiom fact_1188_mod__eq__0__iff:(forall (M:nat) (D:nat), ((iff (((eq nat) ((div_mod_nat M) D)) zero_zero_nat)) ((ex nat) (fun (Q_1:nat)=> (((eq nat) M) ((times_times_nat D) Q_1)))))).
% 99.75/100.11 Axiom fact_1189_mod__less__divisor:(forall (M:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->((ord_less_nat ((div_mod_nat M) N)) N))).
% 99.75/100.11 Axiom fact_1190_mod__less__eq__dividend:(forall (M:nat) (N:nat), ((ord_less_eq_nat ((div_mod_nat M) N)) M)).
% 99.75/100.11 Axiom fact_1191_StandardRes__eq__zcong:(forall (M:int) (X:int), ((iff (((eq int) ((standardRes M) X)) zero_zero_int)) (((zcong X) zero_zero_int) M))).
% 99.75/100.11 Axiom fact_1192_StandardRes__prop3:(forall (X:int) (P_1:int), ((iff ((((zcong X) zero_zero_int) P_1)->False)) (not (((eq int) ((standardRes P_1) X)) zero_zero_int)))).
% 99.75/100.11 Axiom fact_1193_StandardRes__prop1:(forall (X:int) (M:int), (((zcong X) ((standardRes M) X)) M)).
% 99.75/100.11 Axiom fact_1194_StandardRes__ubound:(forall (X:int) (P_1:int), (((ord_less_int zero_zero_int) P_1)->((ord_less_int ((standardRes P_1) X)) P_1))).
% 99.75/100.11 Axiom fact_1195_StandardRes__SR__prop:(forall (X:int) (P_1:int), (((member_int X) (sr P_1))->(((eq int) ((standardRes P_1) X)) X))).
% 99.75/100.11 Axiom fact_1196_split__mod:(forall (P:(nat->Prop)) (N:nat) (K:nat), ((iff (P ((div_mod_nat N) K))) ((and ((((eq nat) K) zero_zero_nat)->(P N))) ((not (((eq nat) K) zero_zero_nat))->(forall (_TPTP_I:nat) (J:nat), (((ord_less_nat J) K)->((((eq nat) N) ((plus_plus_nat ((times_times_nat K) _TPTP_I)) J))->(P J)))))))).
% 99.75/100.11 Axiom fact_1197_mod__lemma:(forall (Q:nat) (R:nat) (B:nat) (C:nat), (((ord_less_nat zero_zero_nat) C)->(((ord_less_nat R) B)->((ord_less_nat ((plus_plus_nat ((times_times_nat B) ((div_mod_nat Q) C))) R)) ((times_times_nat B) C))))).
% 99.75/100.11 Trying to prove ((ord_less_int ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) zero_zero_int)
% 99.75/100.11 Found fact_407_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J:((ord_less_eq_int zero_zero_int) zero_zero_int)
% 99.75/100.11 Found fact_407_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J as proof of ((ord_less_eq_int zero_zero_int) zero_zero_int)
% 99.75/100.11 Unexpected exception Unexpected matching of length 0 when specializating fact_883_dvd_Oless__imp__triv:(forall (P:Prop) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->P))) with fact_274_s0p:((and ((and ((ord_less_eq_int zero_zero_int) s)) ((ord_less_int s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) at 3 (i=3 v=fact_274_s0p:((and ((and ((ord_less_eq_int zero_zero_int) s)) ((ord_less_int s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) terms[i].vartype=((and ((dvd_dvd_nat X0) Y0)) (((dvd_dvd_nat Y0) X0)->False)))
% 99.75/100.11 Traceback (most recent call last):
% 99.75/100.11 File "CASC.py", line 80, in <module>
% 99.75/100.11 proof=problem.solve()
% 99.75/100.11 File "/export/starexec/sandbox/solver/bin/TPTP.py", line 95, in solve
% 99.75/100.11 for x in self.solveyielding():
% 99.75/100.11 File "/export/starexec/sandbox/solver/bin/TPTP.py", line 83, in solveyielding
% 99.75/100.11 for proof in proofgen: yield proof
% 99.75/100.11 File "/export/starexec/sandbox/solver/bin/prover.py", line 422, in proveyielding
% 99.75/100.11 results=node.look() #Can add nodes
% 99.75/100.11 File "/export/starexec/sandbox/solver/bin/prover.py", line 1705, in look
% 99.75/100.11 dt=destructor_ass.x.boundingspecialization(self.context,assump.x,destructor.destroyingpos)
% 99.75/100.11 File "/export/starexec/sandbox/solver/bin/kernel.py", line 1057, in boundingspecialization
% 99.75/100.11 raise SpecializationError("Unexpected matching of length %d when specializating %s:%s with %s:%s at %s (i=%d v=%s:%s terms[i].vartype=%s)" % (len(matching),self,self.gettype(basecontext),value,value.gettype(basecontext),index,i,v,v_type,terms[i].vartype))
% 99.75/100.11 kernel.SpecializationError: Unexpected matching of length 0 when specializating fact_883_dvd_Oless__imp__triv:(forall (P:Prop) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->P))) with fact_274_s0p:((and ((and ((ord_less_eq_int zero_zero_int) s)) ((ord_less_int s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) at 3 (i=3 v=fact_274_s0p:((and ((and ((ord_less_eq_int zero_zero_int) s)) ((ord_less_int s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) terms[i].vartype=((and ((dvd_dvd_nat X0) Y0)) (((dvd_dvd_nat Y0) X0)->False)))
%------------------------------------------------------------------------------