TSTP Solution File: NUM926^3 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM926^3 : TPTP v7.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n078.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 13:12:06 EST 2018
% Result : Unknown 178.90s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM926^3 : TPTP v7.0.0. Released v5.3.0.
% 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.23 % Computer : n078.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 16:07:04 CST 2018
% 0.03/0.23 % CPUTime :
% 0.03/0.25 Python 2.7.13
% 0.07/0.50 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce5fb0680>, <kernel.Type object at 0x2b3ce5fb0248>) of role type named ty_ty_tc__Int__Oint
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring int:Type
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce5fb0200>, <kernel.Type object at 0x2b3ce5534f38>) of role type named ty_ty_tc__Nat__Onat
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring nat:Type
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce5fb0440>, <kernel.Type object at 0x2b3ce5534f38>) of role type named ty_ty_tc__RealDef__Oreal
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring real:Type
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce5fb0248>, <kernel.Type object at 0x2b3ce55345a8>) of role type named ty_ty_tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring product_prod_int_int:Type
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce5fb0200>, <kernel.DependentProduct object at 0x2b3ce5534e18>) of role type named sy_c_Divides_Odiv__class_Omod_000tc__Int__Oint
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring div_mod_int:(int->(int->int))
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce5fb0248>, <kernel.DependentProduct object at 0x2b3ce5534200>) of role type named sy_c_Divides_Odiv__class_Omod_000tc__Nat__Onat
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring div_mod_nat:(nat->(nat->nat))
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce5fb0440>, <kernel.DependentProduct object at 0x2b3ce5534ea8>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring minus_minus_int:(int->(int->int))
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce5fb0440>, <kernel.DependentProduct object at 0x2b3ce5534830>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring minus_minus_nat:(nat->(nat->nat))
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce5534200>, <kernel.DependentProduct object at 0x2b3ce5534b00>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__RealDef__Oreal
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring minus_minus_real:(real->(real->real))
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce5534ea8>, <kernel.Constant object at 0x2b3ce5534b00>) of role type named sy_c_Groups_Oone__class_Oone_000tc__Int__Oint
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring one_one_int:int
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce5534e18>, <kernel.Constant object at 0x2b3ce5534b00>) of role type named sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring one_one_nat:nat
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce5534200>, <kernel.Constant object at 0x2b3ce5534b00>) of role type named sy_c_Groups_Oone__class_Oone_000tc__RealDef__Oreal
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring one_one_real:real
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce5534ea8>, <kernel.DependentProduct object at 0x2b3ce55341b8>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring plus_plus_int:(int->(int->int))
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce5534098>, <kernel.DependentProduct object at 0x2b3ce5534a28>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring plus_plus_nat:(nat->(nat->nat))
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce5534b00>, <kernel.DependentProduct object at 0x2b3ce5534680>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__RealDef__Oreal
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring plus_plus_real:(real->(real->real))
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce55341b8>, <kernel.DependentProduct object at 0x2b3ce5534e18>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring times_times_int:(int->(int->int))
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce5534a28>, <kernel.DependentProduct object at 0x2b3ce5534200>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__Nat__Onat
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring times_times_nat:(nat->(nat->nat))
% 0.07/0.50 FOF formula (<kernel.Constant object at 0x2b3ce5534680>, <kernel.DependentProduct object at 0x2b3ce5534ea8>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__RealDef__Oreal
% 0.07/0.50 Using role type
% 0.07/0.50 Declaring times_times_real:(real->(real->real))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce5534e18>, <kernel.Constant object at 0x2b3ce5534ea8>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring zero_zero_int:int
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce5534a28>, <kernel.Constant object at 0x2b3ce5534ea8>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring zero_zero_nat:nat
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce5534680>, <kernel.Constant object at 0x2b3ce5534ea8>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__RealDef__Oreal
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring zero_zero_real:real
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce5534e18>, <kernel.DependentProduct object at 0x2b3ce5534758>) of role type named sy_c_Int2_OMultInv
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring multInv:(int->(int->int))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce5534b00>, <kernel.DependentProduct object at 0x2b3ce55342d8>) of role type named sy_c_IntFact_Od22set
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring d22set:(int->(int->Prop))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce5534ea8>, <kernel.DependentProduct object at 0x2b3ce58f3cf8>) of role type named sy_c_IntFact_Ozfact
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring zfact:(int->int)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce5534758>, <kernel.DependentProduct object at 0x2b3ce58f3fc8>) of role type named sy_c_IntPrimes_Ozcong
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring zcong:(int->(int->(int->Prop)))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce55341b8>, <kernel.DependentProduct object at 0x2b3ce58f3f80>) of role type named sy_c_IntPrimes_Ozprime
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring zprime:(int->Prop)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce55342d8>, <kernel.DependentProduct object at 0x2b3ce588db00>) of role type named sy_c_Int_OBit0
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring bit0:(int->int)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce58f3f80>, <kernel.DependentProduct object at 0x2b3ce588d5f0>) of role type named sy_c_Int_OBit1
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring bit1:(int->int)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce58f3f80>, <kernel.Constant object at 0x2b3ce5534680>) of role type named sy_c_Int_OMin
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring min:int
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce55342d8>, <kernel.Constant object at 0x2b3ce5534680>) of role type named sy_c_Int_OPls
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring pls:int
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce5534ea8>, <kernel.DependentProduct object at 0x2b3ce588dfc8>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring number_number_of_int:(int->int)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce5534b00>, <kernel.DependentProduct object at 0x2b3ce588db48>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__Nat__Onat
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring number_number_of_nat:(int->nat)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce5534ea8>, <kernel.DependentProduct object at 0x2b3ce588d638>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__RealDef__Oreal
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring number267125858f_real:(int->real)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce5534680>, <kernel.DependentProduct object at 0x2b3ce588d2d8>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Int__Oint
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring ord_less_int:(int->(int->Prop))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce5534ea8>, <kernel.DependentProduct object at 0x2b3ce588d5f0>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring ord_less_nat:(nat->(nat->Prop))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce5534ea8>, <kernel.DependentProduct object at 0x2b3ce588d3f8>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__RealDef__Oreal
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring ord_less_real:(real->(real->Prop))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce588d2d8>, <kernel.DependentProduct object at 0x2b3ce588d638>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Int__Oint
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring ord_less_eq_int:(int->(int->Prop))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b3ce588d5f0>, <kernel.DependentProduct object at 0x2b3ce588dfc8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring ord_less_eq_nat:(nat->(nat->Prop))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce588d3f8>, <kernel.DependentProduct object at 0x2b3ce588db00>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__RealDef__Oreal
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring ord_less_eq_real:(real->(real->Prop))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce588d638>, <kernel.DependentProduct object at 0x2b3ce588db48>) of role type named sy_c_Power_Opower__class_Opower_000tc__Int__Oint
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring power_power_int:(int->(nat->int))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce588dfc8>, <kernel.DependentProduct object at 0x2b3ce588df38>) of role type named sy_c_Power_Opower__class_Opower_000tc__Nat__Onat
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring power_power_nat:(nat->(nat->nat))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce588db00>, <kernel.DependentProduct object at 0x2b3ce588dc68>) of role type named sy_c_Power_Opower__class_Opower_000tc__RealDef__Oreal
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring power_power_real:(real->(nat->real))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce588db48>, <kernel.DependentProduct object at 0x2b3ce588d5f0>) of role type named sy_c_Product__Type_OPair_000tc__Int__Oint_000tc__Int__Oint
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring product_Pair_int_int:(int->(int->product_prod_int_int))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce588df38>, <kernel.DependentProduct object at 0x2b3ce588d3f8>) of role type named sy_c_Residues_OLegendre
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring legendre:(int->(int->int))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce588dc68>, <kernel.DependentProduct object at 0x2b3ce588d638>) of role type named sy_c_Residues_OQuadRes
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring quadRes:(int->(int->Prop))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce588d5f0>, <kernel.DependentProduct object at 0x2b3ce588d2d8>) of role type named sy_c_Residues_OSR
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring sr:(int->(int->Prop))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce588d3f8>, <kernel.DependentProduct object at 0x2b3ce588dc68>) of role type named sy_c_Residues_OStandardRes
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring standardRes:(int->(int->int))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce588d638>, <kernel.DependentProduct object at 0x2b3ce5faa560>) of role type named sy_c_Rings_Odvd__class_Odvd_000tc__Int__Oint
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring dvd_dvd_int:(int->(int->Prop))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce588df38>, <kernel.DependentProduct object at 0x2b3ce5faa5a8>) of role type named sy_c_Rings_Odvd__class_Odvd_000tc__Nat__Onat
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring dvd_dvd_nat:(nat->(nat->Prop))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce588d3f8>, <kernel.DependentProduct object at 0x2b3ce5faa3f8>) of role type named sy_c_Rings_Odvd__class_Odvd_000tc__RealDef__Oreal
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring dvd_dvd_real:(real->(real->Prop))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce588d6c8>, <kernel.DependentProduct object at 0x2b3ce5faab00>) of role type named sy_c_Set_OCollect_000tc__Int__Oint
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring collect_int:((int->Prop)->(int->Prop))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce588d638>, <kernel.DependentProduct object at 0x2b3ce5faaf80>) of role type named sy_c_TwoSquares__Mirabelle__dzzvbppuls_Ois__sum2sq
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring twoSqu919416604sum2sq:(int->Prop)
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce588d6c8>, <kernel.DependentProduct object at 0x2b3ce5faae18>) of role type named sy_c_TwoSquares__Mirabelle__dzzvbppuls_Osum2sq
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring twoSqu2057625106sum2sq:(product_prod_int_int->int)
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce588d638>, <kernel.DependentProduct object at 0x2b3ce5faa5a8>) of role type named sy_c_WilsonRuss_Oinv
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring inv:(int->(int->int))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce588d638>, <kernel.DependentProduct object at 0x2b3ce5faa098>) of role type named sy_c_WilsonRuss_Owset
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring wset:(int->(int->(int->Prop)))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b3ce5faa3f8>, <kernel.DependentProduct object at 0x2b3ce5faa248>) of role type named sy_c_member_000tc__Int__Oint
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring member_int:(int->((int->Prop)->Prop))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b3ce5faa488>, <kernel.Constant object at 0x2b3ce5faa3f8>) of role type named sy_v_m
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring m:int
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b3ce5faa248>, <kernel.Constant object at 0x2b3ce5faa3f8>) of role type named sy_v_s1____
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring s1:int
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b3ce5faa560>, <kernel.Constant object at 0x2b3ce5faa3f8>) of role type named sy_v_s____
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring s:int
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b3ce5faa488>, <kernel.Constant object at 0x2b3ce5faa3f8>) of role type named sy_v_t____
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring t:int
% 0.07/0.53 FOF formula ((ord_less_eq_int one_one_int) t) of role axiom named fact_0_tpos
% 0.07/0.53 A new axiom: ((ord_less_eq_int one_one_int) t)
% 0.07/0.53 FOF formula ((((eq int) t) one_one_int)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq 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)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))) of role axiom named fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06
% 0.07/0.53 A new axiom: ((((eq int) t) one_one_int)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq 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)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))))))
% 0.07/0.53 FOF formula (((ord_less_int one_one_int) t)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq 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)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))) of role axiom named fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06
% 0.07/0.53 A new axiom: (((ord_less_int one_one_int) t)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq 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)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))))))
% 0.07/0.53 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_3_t__l__p
% 0.07/0.53 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))
% 0.07/0.53 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_4_p
% 0.07/0.53 A new axiom: (zprime ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))
% 0.07/0.53 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_5_t
% 0.07/0.53 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))
% 0.07/0.53 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_6_qf1pt
% 0.07/0.53 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))
% 0.07/0.53 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_7_zadd__power2
% 0.07/0.55 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)))))))
% 0.07/0.55 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_8_zadd__power3
% 0.07/0.55 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)))))))
% 0.07/0.55 FOF formula (forall (X_44:int) (Y_34:int), (((eq int) ((power_power_int ((plus_plus_int X_44) Y_34)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int X_44) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_34) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) X_44)) Y_34)))) of role axiom named fact_9_power2__sum
% 0.07/0.55 A new axiom: (forall (X_44:int) (Y_34:int), (((eq int) ((power_power_int ((plus_plus_int X_44) Y_34)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int X_44) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_34) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) X_44)) Y_34))))
% 0.07/0.55 FOF formula (forall (X_44:nat) (Y_34:nat), (((eq nat) ((power_power_nat ((plus_plus_nat X_44) Y_34)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat ((plus_plus_nat ((power_power_nat X_44) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_34) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) X_44)) Y_34)))) of role axiom named fact_10_power2__sum
% 0.07/0.55 A new axiom: (forall (X_44:nat) (Y_34:nat), (((eq nat) ((power_power_nat ((plus_plus_nat X_44) Y_34)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat ((plus_plus_nat ((power_power_nat X_44) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_34) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) X_44)) Y_34))))
% 0.07/0.55 FOF formula (forall (X_44:real) (Y_34:real), (((eq real) ((power_power_real ((plus_plus_real X_44) Y_34)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X_44) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_34) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_44)) Y_34)))) of role axiom named fact_11_power2__sum
% 0.07/0.56 A new axiom: (forall (X_44:real) (Y_34:real), (((eq real) ((power_power_real ((plus_plus_real X_44) Y_34)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X_44) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_34) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_44)) Y_34))))
% 0.07/0.56 FOF formula (forall (W_19:int), (((eq int) ((power_power_int (number_number_of_int W_19)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int (number_number_of_int W_19)) (number_number_of_int W_19)))) of role axiom named fact_12_power2__eq__square__number__of
% 0.07/0.56 A new axiom: (forall (W_19:int), (((eq int) ((power_power_int (number_number_of_int W_19)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int (number_number_of_int W_19)) (number_number_of_int W_19))))
% 0.07/0.56 FOF formula (forall (W_19:int), (((eq real) ((power_power_real (number267125858f_real W_19)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real (number267125858f_real W_19)) (number267125858f_real W_19)))) of role axiom named fact_13_power2__eq__square__number__of
% 0.07/0.56 A new axiom: (forall (W_19:int), (((eq real) ((power_power_real (number267125858f_real W_19)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real (number267125858f_real W_19)) (number267125858f_real W_19))))
% 0.07/0.56 FOF formula (forall (W_19:int), (((eq nat) ((power_power_nat (number_number_of_nat W_19)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat (number_number_of_nat W_19)) (number_number_of_nat W_19)))) of role axiom named fact_14_power2__eq__square__number__of
% 0.07/0.56 A new axiom: (forall (W_19:int), (((eq nat) ((power_power_nat (number_number_of_nat W_19)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat (number_number_of_nat W_19)) (number_number_of_nat W_19))))
% 0.07/0.56 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_15_cube__square
% 0.07/0.56 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))))))
% 0.07/0.56 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_16_one__power2
% 0.07/0.56 A new axiom: (((eq int) ((power_power_int one_one_int) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)
% 0.07/0.56 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_17_one__power2
% 0.07/0.56 A new axiom: (((eq nat) ((power_power_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls))))) one_one_nat)
% 0.07/0.56 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_18_one__power2
% 0.07/0.56 A new axiom: (((eq real) ((power_power_real one_one_real) (number_number_of_nat (bit0 (bit1 pls))))) one_one_real)
% 0.07/0.56 FOF formula (forall (X_43:int), (((eq int) ((times_times_int X_43) X_43)) ((power_power_int X_43) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J
% 0.07/0.56 A new axiom: (forall (X_43:int), (((eq int) ((times_times_int X_43) X_43)) ((power_power_int X_43) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.07/0.56 FOF formula (forall (X_43:real), (((eq real) ((times_times_real X_43) X_43)) ((power_power_real X_43) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J
% 0.07/0.56 A new axiom: (forall (X_43:real), (((eq real) ((times_times_real X_43) X_43)) ((power_power_real X_43) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.07/0.56 FOF formula (forall (X_43:nat), (((eq nat) ((times_times_nat X_43) X_43)) ((power_power_nat X_43) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J
% 0.39/0.58 A new axiom: (forall (X_43:nat), (((eq nat) ((times_times_nat X_43) X_43)) ((power_power_nat X_43) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.39/0.58 FOF formula (forall (A_127:int), (((eq int) ((power_power_int A_127) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int A_127) A_127))) of role axiom named fact_22_power2__eq__square
% 0.39/0.58 A new axiom: (forall (A_127:int), (((eq int) ((power_power_int A_127) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int A_127) A_127)))
% 0.39/0.58 FOF formula (forall (A_127:real), (((eq real) ((power_power_real A_127) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real A_127) A_127))) of role axiom named fact_23_power2__eq__square
% 0.39/0.58 A new axiom: (forall (A_127:real), (((eq real) ((power_power_real A_127) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real A_127) A_127)))
% 0.39/0.58 FOF formula (forall (A_127:nat), (((eq nat) ((power_power_nat A_127) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat A_127) A_127))) of role axiom named fact_24_power2__eq__square
% 0.39/0.58 A new axiom: (forall (A_127:nat), (((eq nat) ((power_power_nat A_127) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat A_127) A_127)))
% 0.39/0.58 FOF formula (forall (X_42:int) (N_41:nat), (((eq int) ((power_power_int X_42) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_41))) ((times_times_int ((power_power_int X_42) N_41)) ((power_power_int X_42) N_41)))) of role axiom named fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J
% 0.39/0.58 A new axiom: (forall (X_42:int) (N_41:nat), (((eq int) ((power_power_int X_42) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_41))) ((times_times_int ((power_power_int X_42) N_41)) ((power_power_int X_42) N_41))))
% 0.39/0.58 FOF formula (forall (X_42:real) (N_41:nat), (((eq real) ((power_power_real X_42) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_41))) ((times_times_real ((power_power_real X_42) N_41)) ((power_power_real X_42) N_41)))) of role axiom named fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J
% 0.39/0.58 A new axiom: (forall (X_42:real) (N_41:nat), (((eq real) ((power_power_real X_42) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_41))) ((times_times_real ((power_power_real X_42) N_41)) ((power_power_real X_42) N_41))))
% 0.39/0.58 FOF formula (forall (X_42:nat) (N_41:nat), (((eq nat) ((power_power_nat X_42) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_41))) ((times_times_nat ((power_power_nat X_42) N_41)) ((power_power_nat X_42) N_41)))) of role axiom named fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J
% 0.39/0.58 A new axiom: (forall (X_42:nat) (N_41:nat), (((eq nat) ((power_power_nat X_42) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_41))) ((times_times_nat ((power_power_nat X_42) N_41)) ((power_power_nat X_42) N_41))))
% 0.39/0.58 FOF formula (forall (W_18:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_18))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_18)))) of role axiom named fact_28_add__special_I2_J
% 0.39/0.58 A new axiom: (forall (W_18:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_18))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_18))))
% 0.39/0.58 FOF formula (forall (W_18:int), (((eq real) ((plus_plus_real one_one_real) (number267125858f_real W_18))) (number267125858f_real ((plus_plus_int (bit1 pls)) W_18)))) of role axiom named fact_29_add__special_I2_J
% 0.39/0.58 A new axiom: (forall (W_18:int), (((eq real) ((plus_plus_real one_one_real) (number267125858f_real W_18))) (number267125858f_real ((plus_plus_int (bit1 pls)) W_18))))
% 0.39/0.58 FOF formula (forall (V_20:int), (((eq int) ((plus_plus_int (number_number_of_int V_20)) one_one_int)) (number_number_of_int ((plus_plus_int V_20) (bit1 pls))))) of role axiom named fact_30_add__special_I3_J
% 0.39/0.58 A new axiom: (forall (V_20:int), (((eq int) ((plus_plus_int (number_number_of_int V_20)) one_one_int)) (number_number_of_int ((plus_plus_int V_20) (bit1 pls)))))
% 0.39/0.58 FOF formula (forall (V_20:int), (((eq real) ((plus_plus_real (number267125858f_real V_20)) one_one_real)) (number267125858f_real ((plus_plus_int V_20) (bit1 pls))))) of role axiom named fact_31_add__special_I3_J
% 0.40/0.60 A new axiom: (forall (V_20:int), (((eq real) ((plus_plus_real (number267125858f_real V_20)) one_one_real)) (number267125858f_real ((plus_plus_int V_20) (bit1 pls)))))
% 0.40/0.60 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_32_one__add__one__is__two
% 0.40/0.60 A new axiom: (((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls))))
% 0.40/0.60 FOF formula (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))) of role axiom named fact_33_one__add__one__is__two
% 0.40/0.60 A new axiom: (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls))))
% 0.40/0.60 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_34__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_
% 0.40/0.60 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)
% 0.40/0.60 FOF formula (forall (W:int), ((ord_less_eq_int W) W)) of role axiom named fact_35_zle__refl
% 0.40/0.60 A new axiom: (forall (W:int), ((ord_less_eq_int W) W))
% 0.40/0.60 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
% 0.40/0.60 A new axiom: (forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z)))
% 0.40/0.60 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_37_zless__le
% 0.40/0.60 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)))))
% 0.40/0.60 FOF formula (forall (X_1:int) (Y_1:int), ((or ((or ((ord_less_int X_1) Y_1)) (((eq int) X_1) Y_1))) ((ord_less_int Y_1) X_1))) of role axiom named fact_38_zless__linear
% 0.40/0.60 A new axiom: (forall (X_1:int) (Y_1:int), ((or ((or ((ord_less_int X_1) Y_1)) (((eq int) X_1) Y_1))) ((ord_less_int Y_1) X_1)))
% 0.40/0.60 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_39_zle__trans
% 0.40/0.60 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))))
% 0.40/0.60 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_40_zle__antisym
% 0.40/0.60 A new axiom: (forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W))))
% 0.40/0.60 FOF formula (forall (X_41:int) (P_6:nat) (Q_6:nat), (((eq int) ((power_power_int ((power_power_int X_41) P_6)) Q_6)) ((power_power_int X_41) ((times_times_nat P_6) Q_6)))) of role axiom named fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J
% 0.40/0.60 A new axiom: (forall (X_41:int) (P_6:nat) (Q_6:nat), (((eq int) ((power_power_int ((power_power_int X_41) P_6)) Q_6)) ((power_power_int X_41) ((times_times_nat P_6) Q_6))))
% 0.40/0.60 FOF formula (forall (X_41:real) (P_6:nat) (Q_6:nat), (((eq real) ((power_power_real ((power_power_real X_41) P_6)) Q_6)) ((power_power_real X_41) ((times_times_nat P_6) Q_6)))) of role axiom named fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J
% 0.40/0.60 A new axiom: (forall (X_41:real) (P_6:nat) (Q_6:nat), (((eq real) ((power_power_real ((power_power_real X_41) P_6)) Q_6)) ((power_power_real X_41) ((times_times_nat P_6) Q_6))))
% 0.40/0.60 FOF formula (forall (X_41:nat) (P_6:nat) (Q_6:nat), (((eq nat) ((power_power_nat ((power_power_nat X_41) P_6)) Q_6)) ((power_power_nat X_41) ((times_times_nat P_6) Q_6)))) of role axiom named fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J
% 0.40/0.61 A new axiom: (forall (X_41:nat) (P_6:nat) (Q_6:nat), (((eq nat) ((power_power_nat ((power_power_nat X_41) P_6)) Q_6)) ((power_power_nat X_41) ((times_times_nat P_6) Q_6))))
% 0.40/0.61 FOF formula (forall (X_40:int), (((eq int) ((power_power_int X_40) one_one_nat)) X_40)) of role axiom named fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J
% 0.40/0.61 A new axiom: (forall (X_40:int), (((eq int) ((power_power_int X_40) one_one_nat)) X_40))
% 0.40/0.61 FOF formula (forall (X_40:real), (((eq real) ((power_power_real X_40) one_one_nat)) X_40)) of role axiom named fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J
% 0.40/0.61 A new axiom: (forall (X_40:real), (((eq real) ((power_power_real X_40) one_one_nat)) X_40))
% 0.40/0.61 FOF formula (forall (X_40:nat), (((eq nat) ((power_power_nat X_40) one_one_nat)) X_40)) of role axiom named fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J
% 0.40/0.61 A new axiom: (forall (X_40:nat), (((eq nat) ((power_power_nat X_40) one_one_nat)) X_40))
% 0.40/0.61 FOF formula (forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int ((power_power_int X_1) Y_1)) Z)) ((power_power_int X_1) ((times_times_nat Y_1) Z)))) of role axiom named fact_47_zpower__zpower
% 0.40/0.61 A new axiom: (forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int ((power_power_int X_1) Y_1)) Z)) ((power_power_int X_1) ((times_times_nat Y_1) Z))))
% 0.40/0.61 FOF formula (forall (V_19:int) (W_17:int), ((iff ((ord_less_eq_int (number_number_of_int V_19)) (number_number_of_int W_17))) (((ord_less_int (number_number_of_int W_17)) (number_number_of_int V_19))->False))) of role axiom named fact_48_le__number__of__eq__not__less
% 0.40/0.61 A new axiom: (forall (V_19:int) (W_17:int), ((iff ((ord_less_eq_int (number_number_of_int V_19)) (number_number_of_int W_17))) (((ord_less_int (number_number_of_int W_17)) (number_number_of_int V_19))->False)))
% 0.40/0.61 FOF formula (forall (V_19:int) (W_17:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_19)) (number_number_of_nat W_17))) (((ord_less_nat (number_number_of_nat W_17)) (number_number_of_nat V_19))->False))) of role axiom named fact_49_le__number__of__eq__not__less
% 0.40/0.61 A new axiom: (forall (V_19:int) (W_17:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_19)) (number_number_of_nat W_17))) (((ord_less_nat (number_number_of_nat W_17)) (number_number_of_nat V_19))->False)))
% 0.40/0.61 FOF formula (forall (V_19:int) (W_17:int), ((iff ((ord_less_eq_real (number267125858f_real V_19)) (number267125858f_real W_17))) (((ord_less_real (number267125858f_real W_17)) (number267125858f_real V_19))->False))) of role axiom named fact_50_le__number__of__eq__not__less
% 0.40/0.61 A new axiom: (forall (V_19:int) (W_17:int), ((iff ((ord_less_eq_real (number267125858f_real V_19)) (number267125858f_real W_17))) (((ord_less_real (number267125858f_real W_17)) (number267125858f_real V_19))->False)))
% 0.40/0.61 FOF formula (forall (X_39:int) (Y_33:int), ((iff ((ord_less_int (number_number_of_int X_39)) (number_number_of_int Y_33))) ((ord_less_int X_39) Y_33))) of role axiom named fact_51_less__number__of
% 0.40/0.61 A new axiom: (forall (X_39:int) (Y_33:int), ((iff ((ord_less_int (number_number_of_int X_39)) (number_number_of_int Y_33))) ((ord_less_int X_39) Y_33)))
% 0.40/0.61 FOF formula (forall (X_39:int) (Y_33:int), ((iff ((ord_less_real (number267125858f_real X_39)) (number267125858f_real Y_33))) ((ord_less_int X_39) Y_33))) of role axiom named fact_52_less__number__of
% 0.40/0.61 A new axiom: (forall (X_39:int) (Y_33:int), ((iff ((ord_less_real (number267125858f_real X_39)) (number267125858f_real Y_33))) ((ord_less_int X_39) Y_33)))
% 0.40/0.61 FOF formula (forall (X_38:int) (Y_32:int), ((iff ((ord_less_eq_int (number_number_of_int X_38)) (number_number_of_int Y_32))) ((ord_less_eq_int X_38) Y_32))) of role axiom named fact_53_le__number__of
% 0.40/0.61 A new axiom: (forall (X_38:int) (Y_32:int), ((iff ((ord_less_eq_int (number_number_of_int X_38)) (number_number_of_int Y_32))) ((ord_less_eq_int X_38) Y_32)))
% 0.40/0.61 FOF formula (forall (X_38:int) (Y_32:int), ((iff ((ord_less_eq_real (number267125858f_real X_38)) (number267125858f_real Y_32))) ((ord_less_eq_int X_38) Y_32))) of role axiom named fact_54_le__number__of
% 0.40/0.61 A new axiom: (forall (X_38:int) (Y_32:int), ((iff ((ord_less_eq_real (number267125858f_real X_38)) (number267125858f_real Y_32))) ((ord_less_eq_int X_38) Y_32)))
% 0.43/0.63 FOF formula (forall (Z_10:int) (Z:int) (W_16:int) (W:int), (((ord_less_int W_16) W)->(((ord_less_eq_int Z_10) Z)->((ord_less_int ((plus_plus_int W_16) Z_10)) ((plus_plus_int W) Z))))) of role axiom named fact_55_zadd__zless__mono
% 0.43/0.63 A new axiom: (forall (Z_10:int) (Z:int) (W_16:int) (W:int), (((ord_less_int W_16) W)->(((ord_less_eq_int Z_10) Z)->((ord_less_int ((plus_plus_int W_16) Z_10)) ((plus_plus_int W) Z)))))
% 0.43/0.63 FOF formula (forall (X_37:int) (P_5:nat) (Q_5:nat), (((eq int) ((times_times_int ((power_power_int X_37) P_5)) ((power_power_int X_37) Q_5))) ((power_power_int X_37) ((plus_plus_nat P_5) Q_5)))) of role axiom named fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J
% 0.43/0.63 A new axiom: (forall (X_37:int) (P_5:nat) (Q_5:nat), (((eq int) ((times_times_int ((power_power_int X_37) P_5)) ((power_power_int X_37) Q_5))) ((power_power_int X_37) ((plus_plus_nat P_5) Q_5))))
% 0.43/0.63 FOF formula (forall (X_37:real) (P_5:nat) (Q_5:nat), (((eq real) ((times_times_real ((power_power_real X_37) P_5)) ((power_power_real X_37) Q_5))) ((power_power_real X_37) ((plus_plus_nat P_5) Q_5)))) of role axiom named fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J
% 0.43/0.63 A new axiom: (forall (X_37:real) (P_5:nat) (Q_5:nat), (((eq real) ((times_times_real ((power_power_real X_37) P_5)) ((power_power_real X_37) Q_5))) ((power_power_real X_37) ((plus_plus_nat P_5) Q_5))))
% 0.43/0.63 FOF formula (forall (X_37:nat) (P_5:nat) (Q_5:nat), (((eq nat) ((times_times_nat ((power_power_nat X_37) P_5)) ((power_power_nat X_37) Q_5))) ((power_power_nat X_37) ((plus_plus_nat P_5) Q_5)))) of role axiom named fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J
% 0.43/0.63 A new axiom: (forall (X_37:nat) (P_5:nat) (Q_5:nat), (((eq nat) ((times_times_nat ((power_power_nat X_37) P_5)) ((power_power_nat X_37) Q_5))) ((power_power_nat X_37) ((plus_plus_nat P_5) Q_5))))
% 0.43/0.63 FOF formula (forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int X_1) ((plus_plus_nat Y_1) Z))) ((times_times_int ((power_power_int X_1) Y_1)) ((power_power_int X_1) Z)))) of role axiom named fact_59_zpower__zadd__distrib
% 0.43/0.63 A new axiom: (forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int X_1) ((plus_plus_nat Y_1) Z))) ((times_times_int ((power_power_int X_1) Y_1)) ((power_power_int X_1) Z))))
% 0.43/0.63 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_60_nat__mult__2
% 0.43/0.63 A new axiom: (forall (Z:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z)) ((plus_plus_nat Z) Z)))
% 0.43/0.63 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_61_nat__mult__2__right
% 0.43/0.63 A new axiom: (forall (Z:nat), (((eq nat) ((times_times_nat Z) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z) Z)))
% 0.43/0.63 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_62_nat__1__add__1
% 0.43/0.63 A new axiom: (((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls))))
% 0.43/0.63 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_63_less__int__code_I16_J
% 0.43/0.63 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2)))
% 0.43/0.63 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_64_rel__simps_I17_J
% 0.43/0.63 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L)))
% 0.43/0.63 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_65_less__eq__int__code_I16_J
% 0.43/0.63 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2)))
% 0.43/0.65 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_66_rel__simps_I34_J
% 0.43/0.65 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit1 L))) ((ord_less_eq_int K) L)))
% 0.43/0.65 FOF formula (((ord_less_int pls) pls)->False) of role axiom named fact_67_rel__simps_I2_J
% 0.43/0.65 A new axiom: (((ord_less_int pls) pls)->False)
% 0.43/0.65 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_68_less__int__code_I13_J
% 0.43/0.65 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit0 K2))) ((ord_less_int K1) K2)))
% 0.43/0.65 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_69_rel__simps_I14_J
% 0.43/0.65 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit0 L))) ((ord_less_int K) L)))
% 0.43/0.65 FOF formula ((ord_less_eq_int pls) pls) of role axiom named fact_70_rel__simps_I19_J
% 0.43/0.65 A new axiom: ((ord_less_eq_int pls) pls)
% 0.43/0.65 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_71_less__eq__int__code_I13_J
% 0.43/0.65 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit0 K2))) ((ord_less_eq_int K1) K2)))
% 0.43/0.65 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_72_rel__simps_I31_J
% 0.43/0.65 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit0 L))) ((ord_less_eq_int K) L)))
% 0.43/0.65 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_73_less__number__of__int__code
% 0.43/0.65 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)))
% 0.43/0.65 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_74_less__eq__number__of__int__code
% 0.43/0.65 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)))
% 0.43/0.65 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_75_zadd__strict__right__mono
% 0.43/0.65 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))))
% 0.43/0.65 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_76_zadd__left__mono
% 0.43/0.65 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))))
% 0.43/0.65 FOF formula (forall (V_6:int) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_6))) (number_number_of_nat V_6)))) ((((ord_less_int V) pls)->False)->((and (((ord_less_int V_6) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_6))) (number_number_of_nat V)))) ((((ord_less_int V_6) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_6))) (number_number_of_nat ((plus_plus_int V) V_6)))))))) of role axiom named fact_77_add__nat__number__of
% 0.43/0.65 A new axiom: (forall (V_6:int) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_6))) (number_number_of_nat V_6)))) ((((ord_less_int V) pls)->False)->((and (((ord_less_int V_6) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_6))) (number_number_of_nat V)))) ((((ord_less_int V_6) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_6))) (number_number_of_nat ((plus_plus_int V) V_6))))))))
% 0.43/0.65 FOF formula (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat) of role axiom named fact_78_nat__numeral__1__eq__1
% 0.43/0.67 A new axiom: (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat)
% 0.43/0.67 FOF formula (((eq nat) one_one_nat) (number_number_of_nat (bit1 pls))) of role axiom named fact_79_Numeral1__eq1__nat
% 0.43/0.67 A new axiom: (((eq nat) one_one_nat) (number_number_of_nat (bit1 pls)))
% 0.43/0.67 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_80_rel__simps_I29_J
% 0.43/0.67 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls)))
% 0.43/0.67 FOF formula (forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_81_rel__simps_I5_J
% 0.43/0.67 A new axiom: (forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K)))
% 0.43/0.67 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_82_less__eq__int__code_I15_J
% 0.43/0.67 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2)))
% 0.43/0.67 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_83_rel__simps_I33_J
% 0.43/0.67 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit0 L))) ((ord_less_int K) L)))
% 0.43/0.67 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_84_less__int__code_I14_J
% 0.43/0.67 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2)))
% 0.43/0.67 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_85_rel__simps_I15_J
% 0.43/0.67 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L)))
% 0.43/0.67 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_86_zless__imp__add1__zle
% 0.43/0.67 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)))
% 0.43/0.67 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_87_add1__zle__eq
% 0.43/0.67 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)))
% 0.43/0.67 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_88_zle__add1__eq__le
% 0.43/0.67 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)))
% 0.43/0.67 FOF formula (zprime (number_number_of_int (bit0 (bit1 pls)))) of role axiom named fact_89_zprime__2
% 0.43/0.67 A new axiom: (zprime (number_number_of_int (bit0 (bit1 pls))))
% 0.43/0.67 FOF formula (forall (Y_1:int) (X_1:int), ((twoSqu919416604sum2sq X_1)->((twoSqu919416604sum2sq Y_1)->(twoSqu919416604sum2sq ((times_times_int X_1) Y_1))))) of role axiom named fact_90_is__mult__sum2sq
% 0.43/0.67 A new axiom: (forall (Y_1:int) (X_1:int), ((twoSqu919416604sum2sq X_1)->((twoSqu919416604sum2sq Y_1)->(twoSqu919416604sum2sq ((times_times_int X_1) Y_1)))))
% 0.43/0.67 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_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J
% 0.43/0.67 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))))
% 0.43/0.67 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_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J
% 0.43/0.68 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))))
% 0.43/0.68 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_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J
% 0.43/0.68 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))))
% 0.43/0.68 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_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J
% 0.43/0.68 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))))
% 0.43/0.68 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_95_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J
% 0.43/0.68 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))))
% 0.43/0.68 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_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J
% 0.43/0.68 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))))
% 0.43/0.68 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_97_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J
% 0.43/0.68 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)))))
% 0.43/0.68 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_98_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J
% 0.43/0.68 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)))))
% 0.43/0.68 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_99_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J
% 0.43/0.68 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)))))
% 0.43/0.70 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_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J
% 0.43/0.70 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)))
% 0.43/0.70 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_101_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J
% 0.43/0.70 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)))
% 0.43/0.70 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_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J
% 0.43/0.70 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)))
% 0.43/0.70 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_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J
% 0.43/0.70 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))))
% 0.43/0.70 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_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J
% 0.43/0.70 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))))
% 0.43/0.70 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_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J
% 0.43/0.70 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))))
% 0.43/0.70 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_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J
% 0.43/0.70 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)))
% 0.43/0.70 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_107_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J
% 0.43/0.70 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)))
% 0.43/0.70 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_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J
% 0.43/0.70 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)))
% 0.51/0.72 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_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J
% 0.51/0.72 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))))
% 0.51/0.72 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_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J
% 0.51/0.72 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))))
% 0.51/0.72 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_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J
% 0.51/0.72 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))))
% 0.51/0.72 FOF formula (forall (A_126:int) (B_73:int), (((eq int) ((times_times_int A_126) B_73)) ((times_times_int B_73) A_126))) of role axiom named fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J
% 0.51/0.72 A new axiom: (forall (A_126:int) (B_73:int), (((eq int) ((times_times_int A_126) B_73)) ((times_times_int B_73) A_126)))
% 0.51/0.72 FOF formula (forall (A_126:nat) (B_73:nat), (((eq nat) ((times_times_nat A_126) B_73)) ((times_times_nat B_73) A_126))) of role axiom named fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J
% 0.51/0.72 A new axiom: (forall (A_126:nat) (B_73:nat), (((eq nat) ((times_times_nat A_126) B_73)) ((times_times_nat B_73) A_126)))
% 0.51/0.72 FOF formula (forall (A_126:real) (B_73:real), (((eq real) ((times_times_real A_126) B_73)) ((times_times_real B_73) A_126))) of role axiom named fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J
% 0.51/0.72 A new axiom: (forall (A_126:real) (B_73:real), (((eq real) ((times_times_real A_126) B_73)) ((times_times_real B_73) A_126)))
% 0.51/0.72 FOF formula (forall (A_125:int) (B_72:int) (C_39:int) (D_11:int), (((eq int) ((plus_plus_int ((plus_plus_int A_125) B_72)) ((plus_plus_int C_39) D_11))) ((plus_plus_int ((plus_plus_int A_125) C_39)) ((plus_plus_int B_72) D_11)))) of role axiom named fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J
% 0.51/0.72 A new axiom: (forall (A_125:int) (B_72:int) (C_39:int) (D_11:int), (((eq int) ((plus_plus_int ((plus_plus_int A_125) B_72)) ((plus_plus_int C_39) D_11))) ((plus_plus_int ((plus_plus_int A_125) C_39)) ((plus_plus_int B_72) D_11))))
% 0.51/0.72 FOF formula (forall (A_125:nat) (B_72:nat) (C_39:nat) (D_11:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_125) B_72)) ((plus_plus_nat C_39) D_11))) ((plus_plus_nat ((plus_plus_nat A_125) C_39)) ((plus_plus_nat B_72) D_11)))) of role axiom named fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J
% 0.51/0.72 A new axiom: (forall (A_125:nat) (B_72:nat) (C_39:nat) (D_11:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_125) B_72)) ((plus_plus_nat C_39) D_11))) ((plus_plus_nat ((plus_plus_nat A_125) C_39)) ((plus_plus_nat B_72) D_11))))
% 0.51/0.72 FOF formula (forall (A_125:real) (B_72:real) (C_39:real) (D_11:real), (((eq real) ((plus_plus_real ((plus_plus_real A_125) B_72)) ((plus_plus_real C_39) D_11))) ((plus_plus_real ((plus_plus_real A_125) C_39)) ((plus_plus_real B_72) D_11)))) of role axiom named fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J
% 0.51/0.72 A new axiom: (forall (A_125:real) (B_72:real) (C_39:real) (D_11:real), (((eq real) ((plus_plus_real ((plus_plus_real A_125) B_72)) ((plus_plus_real C_39) D_11))) ((plus_plus_real ((plus_plus_real A_125) C_39)) ((plus_plus_real B_72) D_11))))
% 0.51/0.72 FOF formula (forall (X_36:int) (A_124:(int->Prop)), ((iff ((member_int X_36) A_124)) (A_124 X_36))) of role axiom named fact_118_mem__def
% 0.51/0.73 A new axiom: (forall (X_36:int) (A_124:(int->Prop)), ((iff ((member_int X_36) A_124)) (A_124 X_36)))
% 0.51/0.73 FOF formula (forall (P_4:(int->Prop)), (((eq (int->Prop)) (collect_int P_4)) P_4)) of role axiom named fact_119_Collect__def
% 0.51/0.73 A new axiom: (forall (P_4:(int->Prop)), (((eq (int->Prop)) (collect_int P_4)) P_4))
% 0.51/0.73 FOF formula (forall (A_123:int) (B_71:int) (C_38:int), (((eq int) ((plus_plus_int ((plus_plus_int A_123) B_71)) C_38)) ((plus_plus_int ((plus_plus_int A_123) C_38)) B_71))) of role axiom named fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J
% 0.51/0.73 A new axiom: (forall (A_123:int) (B_71:int) (C_38:int), (((eq int) ((plus_plus_int ((plus_plus_int A_123) B_71)) C_38)) ((plus_plus_int ((plus_plus_int A_123) C_38)) B_71)))
% 0.51/0.73 FOF formula (forall (A_123:nat) (B_71:nat) (C_38:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_123) B_71)) C_38)) ((plus_plus_nat ((plus_plus_nat A_123) C_38)) B_71))) of role axiom named fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J
% 0.51/0.73 A new axiom: (forall (A_123:nat) (B_71:nat) (C_38:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_123) B_71)) C_38)) ((plus_plus_nat ((plus_plus_nat A_123) C_38)) B_71)))
% 0.51/0.73 FOF formula (forall (A_123:real) (B_71:real) (C_38:real), (((eq real) ((plus_plus_real ((plus_plus_real A_123) B_71)) C_38)) ((plus_plus_real ((plus_plus_real A_123) C_38)) B_71))) of role axiom named fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J
% 0.51/0.73 A new axiom: (forall (A_123:real) (B_71:real) (C_38:real), (((eq real) ((plus_plus_real ((plus_plus_real A_123) B_71)) C_38)) ((plus_plus_real ((plus_plus_real A_123) C_38)) B_71)))
% 0.51/0.73 FOF formula (forall (A_122:int) (B_70:int) (C_37:int), (((eq int) ((plus_plus_int ((plus_plus_int A_122) B_70)) C_37)) ((plus_plus_int A_122) ((plus_plus_int B_70) C_37)))) of role axiom named fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J
% 0.51/0.73 A new axiom: (forall (A_122:int) (B_70:int) (C_37:int), (((eq int) ((plus_plus_int ((plus_plus_int A_122) B_70)) C_37)) ((plus_plus_int A_122) ((plus_plus_int B_70) C_37))))
% 0.51/0.73 FOF formula (forall (A_122:nat) (B_70:nat) (C_37:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_122) B_70)) C_37)) ((plus_plus_nat A_122) ((plus_plus_nat B_70) C_37)))) of role axiom named fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J
% 0.51/0.73 A new axiom: (forall (A_122:nat) (B_70:nat) (C_37:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_122) B_70)) C_37)) ((plus_plus_nat A_122) ((plus_plus_nat B_70) C_37))))
% 0.51/0.73 FOF formula (forall (A_122:real) (B_70:real) (C_37:real), (((eq real) ((plus_plus_real ((plus_plus_real A_122) B_70)) C_37)) ((plus_plus_real A_122) ((plus_plus_real B_70) C_37)))) of role axiom named fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J
% 0.51/0.73 A new axiom: (forall (A_122:real) (B_70:real) (C_37:real), (((eq real) ((plus_plus_real ((plus_plus_real A_122) B_70)) C_37)) ((plus_plus_real A_122) ((plus_plus_real B_70) C_37))))
% 0.51/0.73 FOF formula (forall (A_121:int) (C_36:int) (D_10:int), (((eq int) ((plus_plus_int A_121) ((plus_plus_int C_36) D_10))) ((plus_plus_int ((plus_plus_int A_121) C_36)) D_10))) of role axiom named fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J
% 0.51/0.73 A new axiom: (forall (A_121:int) (C_36:int) (D_10:int), (((eq int) ((plus_plus_int A_121) ((plus_plus_int C_36) D_10))) ((plus_plus_int ((plus_plus_int A_121) C_36)) D_10)))
% 0.51/0.73 FOF formula (forall (A_121:nat) (C_36:nat) (D_10:nat), (((eq nat) ((plus_plus_nat A_121) ((plus_plus_nat C_36) D_10))) ((plus_plus_nat ((plus_plus_nat A_121) C_36)) D_10))) of role axiom named fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J
% 0.51/0.73 A new axiom: (forall (A_121:nat) (C_36:nat) (D_10:nat), (((eq nat) ((plus_plus_nat A_121) ((plus_plus_nat C_36) D_10))) ((plus_plus_nat ((plus_plus_nat A_121) C_36)) D_10)))
% 0.51/0.73 FOF formula (forall (A_121:real) (C_36:real) (D_10:real), (((eq real) ((plus_plus_real A_121) ((plus_plus_real C_36) D_10))) ((plus_plus_real ((plus_plus_real A_121) C_36)) D_10))) of role axiom named fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J
% 0.51/0.75 A new axiom: (forall (A_121:real) (C_36:real) (D_10:real), (((eq real) ((plus_plus_real A_121) ((plus_plus_real C_36) D_10))) ((plus_plus_real ((plus_plus_real A_121) C_36)) D_10)))
% 0.51/0.75 FOF formula (forall (A_120:int) (C_35:int) (D_9:int), (((eq int) ((plus_plus_int A_120) ((plus_plus_int C_35) D_9))) ((plus_plus_int C_35) ((plus_plus_int A_120) D_9)))) of role axiom named fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J
% 0.51/0.75 A new axiom: (forall (A_120:int) (C_35:int) (D_9:int), (((eq int) ((plus_plus_int A_120) ((plus_plus_int C_35) D_9))) ((plus_plus_int C_35) ((plus_plus_int A_120) D_9))))
% 0.51/0.75 FOF formula (forall (A_120:nat) (C_35:nat) (D_9:nat), (((eq nat) ((plus_plus_nat A_120) ((plus_plus_nat C_35) D_9))) ((plus_plus_nat C_35) ((plus_plus_nat A_120) D_9)))) of role axiom named fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J
% 0.51/0.75 A new axiom: (forall (A_120:nat) (C_35:nat) (D_9:nat), (((eq nat) ((plus_plus_nat A_120) ((plus_plus_nat C_35) D_9))) ((plus_plus_nat C_35) ((plus_plus_nat A_120) D_9))))
% 0.51/0.75 FOF formula (forall (A_120:real) (C_35:real) (D_9:real), (((eq real) ((plus_plus_real A_120) ((plus_plus_real C_35) D_9))) ((plus_plus_real C_35) ((plus_plus_real A_120) D_9)))) of role axiom named fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J
% 0.51/0.75 A new axiom: (forall (A_120:real) (C_35:real) (D_9:real), (((eq real) ((plus_plus_real A_120) ((plus_plus_real C_35) D_9))) ((plus_plus_real C_35) ((plus_plus_real A_120) D_9))))
% 0.51/0.75 FOF formula (forall (A_119:int) (C_34:int), (((eq int) ((plus_plus_int A_119) C_34)) ((plus_plus_int C_34) A_119))) of role axiom named fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J
% 0.51/0.75 A new axiom: (forall (A_119:int) (C_34:int), (((eq int) ((plus_plus_int A_119) C_34)) ((plus_plus_int C_34) A_119)))
% 0.51/0.75 FOF formula (forall (A_119:nat) (C_34:nat), (((eq nat) ((plus_plus_nat A_119) C_34)) ((plus_plus_nat C_34) A_119))) of role axiom named fact_133_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J
% 0.51/0.75 A new axiom: (forall (A_119:nat) (C_34:nat), (((eq nat) ((plus_plus_nat A_119) C_34)) ((plus_plus_nat C_34) A_119)))
% 0.51/0.75 FOF formula (forall (A_119:real) (C_34:real), (((eq real) ((plus_plus_real A_119) C_34)) ((plus_plus_real C_34) A_119))) of role axiom named fact_134_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J
% 0.51/0.75 A new axiom: (forall (A_119:real) (C_34:real), (((eq real) ((plus_plus_real A_119) C_34)) ((plus_plus_real C_34) A_119)))
% 0.51/0.75 FOF formula (forall (X_35:int) (Y_31:int), ((iff (((eq int) (number_number_of_int X_35)) (number_number_of_int Y_31))) (((eq int) X_35) Y_31))) of role axiom named fact_135_eq__number__of
% 0.51/0.75 A new axiom: (forall (X_35:int) (Y_31:int), ((iff (((eq int) (number_number_of_int X_35)) (number_number_of_int Y_31))) (((eq int) X_35) Y_31)))
% 0.51/0.75 FOF formula (forall (X_35:int) (Y_31:int), ((iff (((eq real) (number267125858f_real X_35)) (number267125858f_real Y_31))) (((eq int) X_35) Y_31))) of role axiom named fact_136_eq__number__of
% 0.51/0.75 A new axiom: (forall (X_35:int) (Y_31:int), ((iff (((eq real) (number267125858f_real X_35)) (number267125858f_real Y_31))) (((eq int) X_35) Y_31)))
% 0.51/0.75 FOF formula (forall (W_15:int) (X_34:nat), ((iff (((eq nat) (number_number_of_nat W_15)) X_34)) (((eq nat) X_34) (number_number_of_nat W_15)))) of role axiom named fact_137_number__of__reorient
% 0.51/0.75 A new axiom: (forall (W_15:int) (X_34:nat), ((iff (((eq nat) (number_number_of_nat W_15)) X_34)) (((eq nat) X_34) (number_number_of_nat W_15))))
% 0.51/0.75 FOF formula (forall (W_15:int) (X_34:int), ((iff (((eq int) (number_number_of_int W_15)) X_34)) (((eq int) X_34) (number_number_of_int W_15)))) of role axiom named fact_138_number__of__reorient
% 0.51/0.75 A new axiom: (forall (W_15:int) (X_34:int), ((iff (((eq int) (number_number_of_int W_15)) X_34)) (((eq int) X_34) (number_number_of_int W_15))))
% 0.51/0.75 FOF formula (forall (W_15:int) (X_34:real), ((iff (((eq real) (number267125858f_real W_15)) X_34)) (((eq real) X_34) (number267125858f_real W_15)))) of role axiom named fact_139_number__of__reorient
% 0.51/0.77 A new axiom: (forall (W_15:int) (X_34:real), ((iff (((eq real) (number267125858f_real W_15)) X_34)) (((eq real) X_34) (number267125858f_real W_15))))
% 0.51/0.77 FOF formula (forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L))) of role axiom named fact_140_rel__simps_I51_J
% 0.51/0.77 A new axiom: (forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L)))
% 0.51/0.77 FOF formula (forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L))) of role axiom named fact_141_rel__simps_I48_J
% 0.51/0.77 A new axiom: (forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L)))
% 0.51/0.77 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_142_zmult__assoc
% 0.51/0.77 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))))
% 0.51/0.77 FOF formula (forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z))) of role axiom named fact_143_zmult__commute
% 0.51/0.77 A new axiom: (forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z)))
% 0.51/0.77 FOF formula (forall (K:int), (((eq int) (number_number_of_int K)) K)) of role axiom named fact_144_number__of__is__id
% 0.51/0.77 A new axiom: (forall (K:int), (((eq int) (number_number_of_int K)) K))
% 0.51/0.77 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_145_zadd__assoc
% 0.51/0.77 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))))
% 0.51/0.77 FOF formula (forall (X_1:int) (Y_1:int) (Z:int), (((eq int) ((plus_plus_int X_1) ((plus_plus_int Y_1) Z))) ((plus_plus_int Y_1) ((plus_plus_int X_1) Z)))) of role axiom named fact_146_zadd__left__commute
% 0.51/0.77 A new axiom: (forall (X_1:int) (Y_1:int) (Z:int), (((eq int) ((plus_plus_int X_1) ((plus_plus_int Y_1) Z))) ((plus_plus_int Y_1) ((plus_plus_int X_1) Z))))
% 0.51/0.77 FOF formula (forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z))) of role axiom named fact_147_zadd__commute
% 0.51/0.77 A new axiom: (forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z)))
% 0.51/0.77 FOF formula (forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_148_rel__simps_I12_J
% 0.51/0.77 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls)))
% 0.51/0.77 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_149_less__int__code_I15_J
% 0.51/0.77 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2)))
% 0.51/0.77 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_150_rel__simps_I16_J
% 0.51/0.77 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit0 L))) ((ord_less_int K) L)))
% 0.51/0.77 FOF formula (forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_151_rel__simps_I10_J
% 0.51/0.77 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls)))
% 0.51/0.77 FOF formula (forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K))) of role axiom named fact_152_rel__simps_I4_J
% 0.51/0.77 A new axiom: (forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K)))
% 0.51/0.77 FOF formula (forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_153_rel__simps_I22_J
% 0.51/0.77 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K)))
% 0.51/0.77 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_154_less__eq__int__code_I14_J
% 0.51/0.77 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2)))
% 0.59/0.79 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_155_rel__simps_I32_J
% 0.59/0.79 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L)))
% 0.59/0.79 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) pls)) ((ord_less_eq_int K) pls))) of role axiom named fact_156_rel__simps_I27_J
% 0.59/0.79 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) pls)) ((ord_less_eq_int K) pls)))
% 0.59/0.79 FOF formula (forall (K:int), ((iff ((ord_less_eq_int pls) (bit0 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_157_rel__simps_I21_J
% 0.59/0.79 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int pls) (bit0 K))) ((ord_less_eq_int pls) K)))
% 0.59/0.79 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_158_zless__add1__eq
% 0.59/0.79 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))))
% 0.59/0.79 FOF formula (forall (A_118:int) (N_40:nat), (((eq int) ((power_power_int A_118) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_40))) ((power_power_int ((power_power_int A_118) N_40)) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_159_power__even__eq
% 0.59/0.79 A new axiom: (forall (A_118:int) (N_40:nat), (((eq int) ((power_power_int A_118) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_40))) ((power_power_int ((power_power_int A_118) N_40)) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.59/0.79 FOF formula (forall (A_118:real) (N_40:nat), (((eq real) ((power_power_real A_118) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_40))) ((power_power_real ((power_power_real A_118) N_40)) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_160_power__even__eq
% 0.59/0.79 A new axiom: (forall (A_118:real) (N_40:nat), (((eq real) ((power_power_real A_118) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_40))) ((power_power_real ((power_power_real A_118) N_40)) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.59/0.79 FOF formula (forall (A_118:nat) (N_40:nat), (((eq nat) ((power_power_nat A_118) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_40))) ((power_power_nat ((power_power_nat A_118) N_40)) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_161_power__even__eq
% 0.59/0.79 A new axiom: (forall (A_118:nat) (N_40:nat), (((eq nat) ((power_power_nat A_118) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_40))) ((power_power_nat ((power_power_nat A_118) N_40)) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.59/0.79 FOF formula (forall (X_33:int), ((iff ((ord_less_int (number_number_of_int X_33)) one_one_int)) ((ord_less_int X_33) (bit1 pls)))) of role axiom named fact_162_less__special_I4_J
% 0.59/0.79 A new axiom: (forall (X_33:int), ((iff ((ord_less_int (number_number_of_int X_33)) one_one_int)) ((ord_less_int X_33) (bit1 pls))))
% 0.59/0.79 FOF formula (forall (X_33:int), ((iff ((ord_less_real (number267125858f_real X_33)) one_one_real)) ((ord_less_int X_33) (bit1 pls)))) of role axiom named fact_163_less__special_I4_J
% 0.59/0.79 A new axiom: (forall (X_33:int), ((iff ((ord_less_real (number267125858f_real X_33)) one_one_real)) ((ord_less_int X_33) (bit1 pls))))
% 0.59/0.79 FOF formula (forall (Y_30:int), ((iff ((ord_less_int one_one_int) (number_number_of_int Y_30))) ((ord_less_int (bit1 pls)) Y_30))) of role axiom named fact_164_less__special_I2_J
% 0.59/0.79 A new axiom: (forall (Y_30:int), ((iff ((ord_less_int one_one_int) (number_number_of_int Y_30))) ((ord_less_int (bit1 pls)) Y_30)))
% 0.59/0.79 FOF formula (forall (Y_30:int), ((iff ((ord_less_real one_one_real) (number267125858f_real Y_30))) ((ord_less_int (bit1 pls)) Y_30))) of role axiom named fact_165_less__special_I2_J
% 0.59/0.79 A new axiom: (forall (Y_30:int), ((iff ((ord_less_real one_one_real) (number267125858f_real Y_30))) ((ord_less_int (bit1 pls)) Y_30)))
% 0.59/0.79 FOF formula (forall (X_32:int), ((iff ((ord_less_eq_int (number_number_of_int X_32)) one_one_int)) ((ord_less_eq_int X_32) (bit1 pls)))) of role axiom named fact_166_le__special_I4_J
% 0.59/0.80 A new axiom: (forall (X_32:int), ((iff ((ord_less_eq_int (number_number_of_int X_32)) one_one_int)) ((ord_less_eq_int X_32) (bit1 pls))))
% 0.59/0.80 FOF formula (forall (X_32:int), ((iff ((ord_less_eq_real (number267125858f_real X_32)) one_one_real)) ((ord_less_eq_int X_32) (bit1 pls)))) of role axiom named fact_167_le__special_I4_J
% 0.59/0.80 A new axiom: (forall (X_32:int), ((iff ((ord_less_eq_real (number267125858f_real X_32)) one_one_real)) ((ord_less_eq_int X_32) (bit1 pls))))
% 0.59/0.80 FOF formula (forall (Y_29:int), ((iff ((ord_less_eq_int one_one_int) (number_number_of_int Y_29))) ((ord_less_eq_int (bit1 pls)) Y_29))) of role axiom named fact_168_le__special_I2_J
% 0.59/0.80 A new axiom: (forall (Y_29:int), ((iff ((ord_less_eq_int one_one_int) (number_number_of_int Y_29))) ((ord_less_eq_int (bit1 pls)) Y_29)))
% 0.59/0.80 FOF formula (forall (Y_29:int), ((iff ((ord_less_eq_real one_one_real) (number267125858f_real Y_29))) ((ord_less_eq_int (bit1 pls)) Y_29))) of role axiom named fact_169_le__special_I2_J
% 0.59/0.80 A new axiom: (forall (Y_29:int), ((iff ((ord_less_eq_real one_one_real) (number267125858f_real Y_29))) ((ord_less_eq_int (bit1 pls)) Y_29)))
% 0.59/0.80 FOF formula (forall (W_14:int) (Y_28:int) (X_31:int) (Z_9:int), ((iff (((eq int) ((plus_plus_int ((times_times_int W_14) Y_28)) ((times_times_int X_31) Z_9))) ((plus_plus_int ((times_times_int W_14) Z_9)) ((times_times_int X_31) Y_28)))) ((or (((eq int) W_14) X_31)) (((eq int) Y_28) Z_9)))) of role axiom named fact_170_crossproduct__eq
% 0.59/0.80 A new axiom: (forall (W_14:int) (Y_28:int) (X_31:int) (Z_9:int), ((iff (((eq int) ((plus_plus_int ((times_times_int W_14) Y_28)) ((times_times_int X_31) Z_9))) ((plus_plus_int ((times_times_int W_14) Z_9)) ((times_times_int X_31) Y_28)))) ((or (((eq int) W_14) X_31)) (((eq int) Y_28) Z_9))))
% 0.59/0.80 FOF formula (forall (W_14:nat) (Y_28:nat) (X_31:nat) (Z_9:nat), ((iff (((eq nat) ((plus_plus_nat ((times_times_nat W_14) Y_28)) ((times_times_nat X_31) Z_9))) ((plus_plus_nat ((times_times_nat W_14) Z_9)) ((times_times_nat X_31) Y_28)))) ((or (((eq nat) W_14) X_31)) (((eq nat) Y_28) Z_9)))) of role axiom named fact_171_crossproduct__eq
% 0.59/0.80 A new axiom: (forall (W_14:nat) (Y_28:nat) (X_31:nat) (Z_9:nat), ((iff (((eq nat) ((plus_plus_nat ((times_times_nat W_14) Y_28)) ((times_times_nat X_31) Z_9))) ((plus_plus_nat ((times_times_nat W_14) Z_9)) ((times_times_nat X_31) Y_28)))) ((or (((eq nat) W_14) X_31)) (((eq nat) Y_28) Z_9))))
% 0.59/0.80 FOF formula (forall (W_14:real) (Y_28:real) (X_31:real) (Z_9:real), ((iff (((eq real) ((plus_plus_real ((times_times_real W_14) Y_28)) ((times_times_real X_31) Z_9))) ((plus_plus_real ((times_times_real W_14) Z_9)) ((times_times_real X_31) Y_28)))) ((or (((eq real) W_14) X_31)) (((eq real) Y_28) Z_9)))) of role axiom named fact_172_crossproduct__eq
% 0.59/0.80 A new axiom: (forall (W_14:real) (Y_28:real) (X_31:real) (Z_9:real), ((iff (((eq real) ((plus_plus_real ((times_times_real W_14) Y_28)) ((times_times_real X_31) Z_9))) ((plus_plus_real ((times_times_real W_14) Z_9)) ((times_times_real X_31) Y_28)))) ((or (((eq real) W_14) X_31)) (((eq real) Y_28) Z_9))))
% 0.59/0.80 FOF formula (forall (A_117:int) (M_14:int) (B_69:int), (((eq int) ((plus_plus_int ((times_times_int A_117) M_14)) ((times_times_int B_69) M_14))) ((times_times_int ((plus_plus_int A_117) B_69)) M_14))) of role axiom named fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J
% 0.59/0.80 A new axiom: (forall (A_117:int) (M_14:int) (B_69:int), (((eq int) ((plus_plus_int ((times_times_int A_117) M_14)) ((times_times_int B_69) M_14))) ((times_times_int ((plus_plus_int A_117) B_69)) M_14)))
% 0.59/0.80 FOF formula (forall (A_117:nat) (M_14:nat) (B_69:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_117) M_14)) ((times_times_nat B_69) M_14))) ((times_times_nat ((plus_plus_nat A_117) B_69)) M_14))) of role axiom named fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J
% 0.59/0.80 A new axiom: (forall (A_117:nat) (M_14:nat) (B_69:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_117) M_14)) ((times_times_nat B_69) M_14))) ((times_times_nat ((plus_plus_nat A_117) B_69)) M_14)))
% 0.59/0.82 FOF formula (forall (A_117:real) (M_14:real) (B_69:real), (((eq real) ((plus_plus_real ((times_times_real A_117) M_14)) ((times_times_real B_69) M_14))) ((times_times_real ((plus_plus_real A_117) B_69)) M_14))) of role axiom named fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J
% 0.59/0.82 A new axiom: (forall (A_117:real) (M_14:real) (B_69:real), (((eq real) ((plus_plus_real ((times_times_real A_117) M_14)) ((times_times_real B_69) M_14))) ((times_times_real ((plus_plus_real A_117) B_69)) M_14)))
% 0.59/0.82 FOF formula (forall (A_116:int) (B_68:int) (C_33:int), (((eq int) ((times_times_int ((plus_plus_int A_116) B_68)) C_33)) ((plus_plus_int ((times_times_int A_116) C_33)) ((times_times_int B_68) C_33)))) of role axiom named fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J
% 0.59/0.82 A new axiom: (forall (A_116:int) (B_68:int) (C_33:int), (((eq int) ((times_times_int ((plus_plus_int A_116) B_68)) C_33)) ((plus_plus_int ((times_times_int A_116) C_33)) ((times_times_int B_68) C_33))))
% 0.59/0.82 FOF formula (forall (A_116:nat) (B_68:nat) (C_33:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_116) B_68)) C_33)) ((plus_plus_nat ((times_times_nat A_116) C_33)) ((times_times_nat B_68) C_33)))) of role axiom named fact_177_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J
% 0.59/0.82 A new axiom: (forall (A_116:nat) (B_68:nat) (C_33:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_116) B_68)) C_33)) ((plus_plus_nat ((times_times_nat A_116) C_33)) ((times_times_nat B_68) C_33))))
% 0.59/0.82 FOF formula (forall (A_116:real) (B_68:real) (C_33:real), (((eq real) ((times_times_real ((plus_plus_real A_116) B_68)) C_33)) ((plus_plus_real ((times_times_real A_116) C_33)) ((times_times_real B_68) C_33)))) of role axiom named fact_178_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J
% 0.59/0.82 A new axiom: (forall (A_116:real) (B_68:real) (C_33:real), (((eq real) ((times_times_real ((plus_plus_real A_116) B_68)) C_33)) ((plus_plus_real ((times_times_real A_116) C_33)) ((times_times_real B_68) C_33))))
% 0.59/0.82 FOF formula (forall (C_32:int) (D_8:int) (A_115:int) (B_67:int), ((iff ((and (not (((eq int) A_115) B_67))) (not (((eq int) C_32) D_8)))) (not (((eq int) ((plus_plus_int ((times_times_int A_115) C_32)) ((times_times_int B_67) D_8))) ((plus_plus_int ((times_times_int A_115) D_8)) ((times_times_int B_67) C_32)))))) of role axiom named fact_179_crossproduct__noteq
% 0.59/0.82 A new axiom: (forall (C_32:int) (D_8:int) (A_115:int) (B_67:int), ((iff ((and (not (((eq int) A_115) B_67))) (not (((eq int) C_32) D_8)))) (not (((eq int) ((plus_plus_int ((times_times_int A_115) C_32)) ((times_times_int B_67) D_8))) ((plus_plus_int ((times_times_int A_115) D_8)) ((times_times_int B_67) C_32))))))
% 0.59/0.82 FOF formula (forall (C_32:nat) (D_8:nat) (A_115:nat) (B_67:nat), ((iff ((and (not (((eq nat) A_115) B_67))) (not (((eq nat) C_32) D_8)))) (not (((eq nat) ((plus_plus_nat ((times_times_nat A_115) C_32)) ((times_times_nat B_67) D_8))) ((plus_plus_nat ((times_times_nat A_115) D_8)) ((times_times_nat B_67) C_32)))))) of role axiom named fact_180_crossproduct__noteq
% 0.59/0.82 A new axiom: (forall (C_32:nat) (D_8:nat) (A_115:nat) (B_67:nat), ((iff ((and (not (((eq nat) A_115) B_67))) (not (((eq nat) C_32) D_8)))) (not (((eq nat) ((plus_plus_nat ((times_times_nat A_115) C_32)) ((times_times_nat B_67) D_8))) ((plus_plus_nat ((times_times_nat A_115) D_8)) ((times_times_nat B_67) C_32))))))
% 0.59/0.82 FOF formula (forall (C_32:real) (D_8:real) (A_115:real) (B_67:real), ((iff ((and (not (((eq real) A_115) B_67))) (not (((eq real) C_32) D_8)))) (not (((eq real) ((plus_plus_real ((times_times_real A_115) C_32)) ((times_times_real B_67) D_8))) ((plus_plus_real ((times_times_real A_115) D_8)) ((times_times_real B_67) C_32)))))) of role axiom named fact_181_crossproduct__noteq
% 0.59/0.82 A new axiom: (forall (C_32:real) (D_8:real) (A_115:real) (B_67:real), ((iff ((and (not (((eq real) A_115) B_67))) (not (((eq real) C_32) D_8)))) (not (((eq real) ((plus_plus_real ((times_times_real A_115) C_32)) ((times_times_real B_67) D_8))) ((plus_plus_real ((times_times_real A_115) D_8)) ((times_times_real B_67) C_32))))))
% 0.59/0.82 FOF formula (forall (X_30:int) (Y_27:int) (Z_8:int), (((eq int) ((times_times_int X_30) ((plus_plus_int Y_27) Z_8))) ((plus_plus_int ((times_times_int X_30) Y_27)) ((times_times_int X_30) Z_8)))) of role axiom named fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J
% 0.59/0.83 A new axiom: (forall (X_30:int) (Y_27:int) (Z_8:int), (((eq int) ((times_times_int X_30) ((plus_plus_int Y_27) Z_8))) ((plus_plus_int ((times_times_int X_30) Y_27)) ((times_times_int X_30) Z_8))))
% 0.59/0.83 FOF formula (forall (X_30:nat) (Y_27:nat) (Z_8:nat), (((eq nat) ((times_times_nat X_30) ((plus_plus_nat Y_27) Z_8))) ((plus_plus_nat ((times_times_nat X_30) Y_27)) ((times_times_nat X_30) Z_8)))) of role axiom named fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J
% 0.59/0.83 A new axiom: (forall (X_30:nat) (Y_27:nat) (Z_8:nat), (((eq nat) ((times_times_nat X_30) ((plus_plus_nat Y_27) Z_8))) ((plus_plus_nat ((times_times_nat X_30) Y_27)) ((times_times_nat X_30) Z_8))))
% 0.59/0.83 FOF formula (forall (X_30:real) (Y_27:real) (Z_8:real), (((eq real) ((times_times_real X_30) ((plus_plus_real Y_27) Z_8))) ((plus_plus_real ((times_times_real X_30) Y_27)) ((times_times_real X_30) Z_8)))) of role axiom named fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J
% 0.59/0.83 A new axiom: (forall (X_30:real) (Y_27:real) (Z_8:real), (((eq real) ((times_times_real X_30) ((plus_plus_real Y_27) Z_8))) ((plus_plus_real ((times_times_real X_30) Y_27)) ((times_times_real X_30) Z_8))))
% 0.59/0.83 FOF formula (forall (A_114:int), (((eq int) ((times_times_int A_114) one_one_int)) A_114)) of role axiom named fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J
% 0.59/0.83 A new axiom: (forall (A_114:int), (((eq int) ((times_times_int A_114) one_one_int)) A_114))
% 0.59/0.83 FOF formula (forall (A_114:nat), (((eq nat) ((times_times_nat A_114) one_one_nat)) A_114)) of role axiom named fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J
% 0.59/0.83 A new axiom: (forall (A_114:nat), (((eq nat) ((times_times_nat A_114) one_one_nat)) A_114))
% 0.59/0.83 FOF formula (forall (A_114:real), (((eq real) ((times_times_real A_114) one_one_real)) A_114)) of role axiom named fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J
% 0.59/0.83 A new axiom: (forall (A_114:real), (((eq real) ((times_times_real A_114) one_one_real)) A_114))
% 0.59/0.83 FOF formula (forall (A_113:int), (((eq int) ((times_times_int one_one_int) A_113)) A_113)) of role axiom named fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J
% 0.59/0.83 A new axiom: (forall (A_113:int), (((eq int) ((times_times_int one_one_int) A_113)) A_113))
% 0.59/0.83 FOF formula (forall (A_113:nat), (((eq nat) ((times_times_nat one_one_nat) A_113)) A_113)) of role axiom named fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J
% 0.59/0.83 A new axiom: (forall (A_113:nat), (((eq nat) ((times_times_nat one_one_nat) A_113)) A_113))
% 0.59/0.83 FOF formula (forall (A_113:real), (((eq real) ((times_times_real one_one_real) A_113)) A_113)) of role axiom named fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J
% 0.59/0.83 A new axiom: (forall (A_113:real), (((eq real) ((times_times_real one_one_real) A_113)) A_113))
% 0.59/0.83 FOF formula (forall (X_29:int) (Y_26:int) (Q_4:nat), (((eq int) ((power_power_int ((times_times_int X_29) Y_26)) Q_4)) ((times_times_int ((power_power_int X_29) Q_4)) ((power_power_int Y_26) Q_4)))) of role axiom named fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J
% 0.59/0.83 A new axiom: (forall (X_29:int) (Y_26:int) (Q_4:nat), (((eq int) ((power_power_int ((times_times_int X_29) Y_26)) Q_4)) ((times_times_int ((power_power_int X_29) Q_4)) ((power_power_int Y_26) Q_4))))
% 0.59/0.83 FOF formula (forall (X_29:real) (Y_26:real) (Q_4:nat), (((eq real) ((power_power_real ((times_times_real X_29) Y_26)) Q_4)) ((times_times_real ((power_power_real X_29) Q_4)) ((power_power_real Y_26) Q_4)))) of role axiom named fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J
% 0.59/0.83 A new axiom: (forall (X_29:real) (Y_26:real) (Q_4:nat), (((eq real) ((power_power_real ((times_times_real X_29) Y_26)) Q_4)) ((times_times_real ((power_power_real X_29) Q_4)) ((power_power_real Y_26) Q_4))))
% 0.59/0.85 FOF formula (forall (X_29:nat) (Y_26:nat) (Q_4:nat), (((eq nat) ((power_power_nat ((times_times_nat X_29) Y_26)) Q_4)) ((times_times_nat ((power_power_nat X_29) Q_4)) ((power_power_nat Y_26) Q_4)))) of role axiom named fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J
% 0.59/0.85 A new axiom: (forall (X_29:nat) (Y_26:nat) (Q_4:nat), (((eq nat) ((power_power_nat ((times_times_nat X_29) Y_26)) Q_4)) ((times_times_nat ((power_power_nat X_29) Q_4)) ((power_power_nat Y_26) Q_4))))
% 0.59/0.85 FOF formula (forall (K:int), (not (((eq int) (bit1 K)) pls))) of role axiom named fact_194_rel__simps_I46_J
% 0.59/0.85 A new axiom: (forall (K:int), (not (((eq int) (bit1 K)) pls)))
% 0.59/0.85 FOF formula (forall (L:int), (not (((eq int) pls) (bit1 L)))) of role axiom named fact_195_rel__simps_I39_J
% 0.59/0.85 A new axiom: (forall (L:int), (not (((eq int) pls) (bit1 L))))
% 0.59/0.85 FOF formula (forall (K:int) (L:int), (not (((eq int) (bit1 K)) (bit0 L)))) of role axiom named fact_196_rel__simps_I50_J
% 0.59/0.85 A new axiom: (forall (K:int) (L:int), (not (((eq int) (bit1 K)) (bit0 L))))
% 0.59/0.85 FOF formula (forall (K:int) (L:int), (not (((eq int) (bit0 K)) (bit1 L)))) of role axiom named fact_197_rel__simps_I49_J
% 0.59/0.85 A new axiom: (forall (K:int) (L:int), (not (((eq int) (bit0 K)) (bit1 L))))
% 0.59/0.85 FOF formula (forall (K:int), ((iff (((eq int) (bit0 K)) pls)) (((eq int) K) pls))) of role axiom named fact_198_rel__simps_I44_J
% 0.59/0.85 A new axiom: (forall (K:int), ((iff (((eq int) (bit0 K)) pls)) (((eq int) K) pls)))
% 0.59/0.85 FOF formula (forall (L:int), ((iff (((eq int) pls) (bit0 L))) (((eq int) pls) L))) of role axiom named fact_199_rel__simps_I38_J
% 0.59/0.85 A new axiom: (forall (L:int), ((iff (((eq int) pls) (bit0 L))) (((eq int) pls) L)))
% 0.59/0.85 FOF formula (((eq int) (bit0 pls)) pls) of role axiom named fact_200_Bit0__Pls
% 0.59/0.85 A new axiom: (((eq int) (bit0 pls)) pls)
% 0.59/0.85 FOF formula (forall (W:int), (((eq int) ((times_times_int pls) W)) pls)) of role axiom named fact_201_mult__Pls
% 0.59/0.85 A new axiom: (forall (W:int), (((eq int) ((times_times_int pls) W)) pls))
% 0.59/0.85 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_202_mult__Bit0
% 0.59/0.85 A new axiom: (forall (K:int) (L:int), (((eq int) ((times_times_int (bit0 K)) L)) (bit0 ((times_times_int K) L))))
% 0.59/0.85 FOF formula (forall (K:int), (((eq int) ((plus_plus_int K) pls)) K)) of role axiom named fact_203_add__Pls__right
% 0.59/0.85 A new axiom: (forall (K:int), (((eq int) ((plus_plus_int K) pls)) K))
% 0.59/0.85 FOF formula (forall (K:int), (((eq int) ((plus_plus_int pls) K)) K)) of role axiom named fact_204_add__Pls
% 0.59/0.85 A new axiom: (forall (K:int), (((eq int) ((plus_plus_int pls) K)) K))
% 0.59/0.85 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_205_add__Bit0__Bit0
% 0.59/0.85 A new axiom: (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit0 L))) (bit0 ((plus_plus_int K) L))))
% 0.59/0.85 FOF formula (forall (K:int), (((eq int) (bit0 K)) ((plus_plus_int K) K))) of role axiom named fact_206_Bit0__def
% 0.59/0.85 A new axiom: (forall (K:int), (((eq int) (bit0 K)) ((plus_plus_int K) K)))
% 0.59/0.85 FOF formula (forall (Z:int), (((eq int) ((times_times_int Z) one_one_int)) Z)) of role axiom named fact_207_zmult__1__right
% 0.59/0.85 A new axiom: (forall (Z:int), (((eq int) ((times_times_int Z) one_one_int)) Z))
% 0.59/0.85 FOF formula (forall (Z:int), (((eq int) ((times_times_int one_one_int) Z)) Z)) of role axiom named fact_208_zmult__1
% 0.59/0.85 A new axiom: (forall (Z:int), (((eq int) ((times_times_int one_one_int) Z)) Z))
% 0.59/0.85 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_209_times__numeral__code_I5_J
% 0.59/0.85 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))))
% 0.59/0.85 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_210_zadd__zmult__distrib
% 0.59/0.85 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))))
% 0.68/0.87 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_211_zadd__zmult__distrib2
% 0.68/0.87 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))))
% 0.68/0.87 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_212_plus__numeral__code_I9_J
% 0.68/0.87 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))))
% 0.68/0.87 FOF formula (forall (V_18:int) (V_17:int), (((ord_less_eq_int pls) V_17)->(((ord_less_eq_int pls) V_18)->(((eq int) ((times_times_int (number_number_of_int V_17)) (number_number_of_int V_18))) (number_number_of_int ((times_times_int V_17) V_18)))))) of role axiom named fact_213_semiring__mult__number__of
% 0.68/0.87 A new axiom: (forall (V_18:int) (V_17:int), (((ord_less_eq_int pls) V_17)->(((ord_less_eq_int pls) V_18)->(((eq int) ((times_times_int (number_number_of_int V_17)) (number_number_of_int V_18))) (number_number_of_int ((times_times_int V_17) V_18))))))
% 0.68/0.87 FOF formula (forall (V_18:int) (V_17:int), (((ord_less_eq_int pls) V_17)->(((ord_less_eq_int pls) V_18)->(((eq nat) ((times_times_nat (number_number_of_nat V_17)) (number_number_of_nat V_18))) (number_number_of_nat ((times_times_int V_17) V_18)))))) of role axiom named fact_214_semiring__mult__number__of
% 0.68/0.87 A new axiom: (forall (V_18:int) (V_17:int), (((ord_less_eq_int pls) V_17)->(((ord_less_eq_int pls) V_18)->(((eq nat) ((times_times_nat (number_number_of_nat V_17)) (number_number_of_nat V_18))) (number_number_of_nat ((times_times_int V_17) V_18))))))
% 0.68/0.87 FOF formula (forall (V_18:int) (V_17:int), (((ord_less_eq_int pls) V_17)->(((ord_less_eq_int pls) V_18)->(((eq real) ((times_times_real (number267125858f_real V_17)) (number267125858f_real V_18))) (number267125858f_real ((times_times_int V_17) V_18)))))) of role axiom named fact_215_semiring__mult__number__of
% 0.68/0.87 A new axiom: (forall (V_18:int) (V_17:int), (((ord_less_eq_int pls) V_17)->(((ord_less_eq_int pls) V_18)->(((eq real) ((times_times_real (number267125858f_real V_17)) (number267125858f_real V_18))) (number267125858f_real ((times_times_int V_17) V_18))))))
% 0.68/0.87 FOF formula (forall (V_16:int) (V_15:int), (((ord_less_eq_int pls) V_15)->(((ord_less_eq_int pls) V_16)->(((eq int) ((plus_plus_int (number_number_of_int V_15)) (number_number_of_int V_16))) (number_number_of_int ((plus_plus_int V_15) V_16)))))) of role axiom named fact_216_semiring__add__number__of
% 0.68/0.87 A new axiom: (forall (V_16:int) (V_15:int), (((ord_less_eq_int pls) V_15)->(((ord_less_eq_int pls) V_16)->(((eq int) ((plus_plus_int (number_number_of_int V_15)) (number_number_of_int V_16))) (number_number_of_int ((plus_plus_int V_15) V_16))))))
% 0.68/0.87 FOF formula (forall (V_16:int) (V_15:int), (((ord_less_eq_int pls) V_15)->(((ord_less_eq_int pls) V_16)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_15)) (number_number_of_nat V_16))) (number_number_of_nat ((plus_plus_int V_15) V_16)))))) of role axiom named fact_217_semiring__add__number__of
% 0.68/0.87 A new axiom: (forall (V_16:int) (V_15:int), (((ord_less_eq_int pls) V_15)->(((ord_less_eq_int pls) V_16)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_15)) (number_number_of_nat V_16))) (number_number_of_nat ((plus_plus_int V_15) V_16))))))
% 0.68/0.87 FOF formula (forall (V_16:int) (V_15:int), (((ord_less_eq_int pls) V_15)->(((ord_less_eq_int pls) V_16)->(((eq real) ((plus_plus_real (number267125858f_real V_15)) (number267125858f_real V_16))) (number267125858f_real ((plus_plus_int V_15) V_16)))))) of role axiom named fact_218_semiring__add__number__of
% 0.68/0.87 A new axiom: (forall (V_16:int) (V_15:int), (((ord_less_eq_int pls) V_15)->(((ord_less_eq_int pls) V_16)->(((eq real) ((plus_plus_real (number267125858f_real V_15)) (number267125858f_real V_16))) (number267125858f_real ((plus_plus_int V_15) V_16))))))
% 0.68/0.89 FOF formula (forall (X_1:int), ((ord_less_eq_int X_1) ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_219_power2__ge__self
% 0.68/0.89 A new axiom: (forall (X_1:int), ((ord_less_eq_int X_1) ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.68/0.89 FOF formula (forall (A_112:int) (B_66:int) (V_14:int), (((eq int) ((times_times_int ((plus_plus_int A_112) B_66)) (number_number_of_int V_14))) ((plus_plus_int ((times_times_int A_112) (number_number_of_int V_14))) ((times_times_int B_66) (number_number_of_int V_14))))) of role axiom named fact_220_left__distrib__number__of
% 0.68/0.89 A new axiom: (forall (A_112:int) (B_66:int) (V_14:int), (((eq int) ((times_times_int ((plus_plus_int A_112) B_66)) (number_number_of_int V_14))) ((plus_plus_int ((times_times_int A_112) (number_number_of_int V_14))) ((times_times_int B_66) (number_number_of_int V_14)))))
% 0.68/0.89 FOF formula (forall (A_112:nat) (B_66:nat) (V_14:int), (((eq nat) ((times_times_nat ((plus_plus_nat A_112) B_66)) (number_number_of_nat V_14))) ((plus_plus_nat ((times_times_nat A_112) (number_number_of_nat V_14))) ((times_times_nat B_66) (number_number_of_nat V_14))))) of role axiom named fact_221_left__distrib__number__of
% 0.68/0.89 A new axiom: (forall (A_112:nat) (B_66:nat) (V_14:int), (((eq nat) ((times_times_nat ((plus_plus_nat A_112) B_66)) (number_number_of_nat V_14))) ((plus_plus_nat ((times_times_nat A_112) (number_number_of_nat V_14))) ((times_times_nat B_66) (number_number_of_nat V_14)))))
% 0.68/0.89 FOF formula (forall (A_112:real) (B_66:real) (V_14:int), (((eq real) ((times_times_real ((plus_plus_real A_112) B_66)) (number267125858f_real V_14))) ((plus_plus_real ((times_times_real A_112) (number267125858f_real V_14))) ((times_times_real B_66) (number267125858f_real V_14))))) of role axiom named fact_222_left__distrib__number__of
% 0.68/0.89 A new axiom: (forall (A_112:real) (B_66:real) (V_14:int), (((eq real) ((times_times_real ((plus_plus_real A_112) B_66)) (number267125858f_real V_14))) ((plus_plus_real ((times_times_real A_112) (number267125858f_real V_14))) ((times_times_real B_66) (number267125858f_real V_14)))))
% 0.68/0.89 FOF formula (forall (V_13:int) (B_65:int) (C_31:int), (((eq int) ((times_times_int (number_number_of_int V_13)) ((plus_plus_int B_65) C_31))) ((plus_plus_int ((times_times_int (number_number_of_int V_13)) B_65)) ((times_times_int (number_number_of_int V_13)) C_31)))) of role axiom named fact_223_right__distrib__number__of
% 0.68/0.89 A new axiom: (forall (V_13:int) (B_65:int) (C_31:int), (((eq int) ((times_times_int (number_number_of_int V_13)) ((plus_plus_int B_65) C_31))) ((plus_plus_int ((times_times_int (number_number_of_int V_13)) B_65)) ((times_times_int (number_number_of_int V_13)) C_31))))
% 0.68/0.89 FOF formula (forall (V_13:int) (B_65:nat) (C_31:nat), (((eq nat) ((times_times_nat (number_number_of_nat V_13)) ((plus_plus_nat B_65) C_31))) ((plus_plus_nat ((times_times_nat (number_number_of_nat V_13)) B_65)) ((times_times_nat (number_number_of_nat V_13)) C_31)))) of role axiom named fact_224_right__distrib__number__of
% 0.68/0.89 A new axiom: (forall (V_13:int) (B_65:nat) (C_31:nat), (((eq nat) ((times_times_nat (number_number_of_nat V_13)) ((plus_plus_nat B_65) C_31))) ((plus_plus_nat ((times_times_nat (number_number_of_nat V_13)) B_65)) ((times_times_nat (number_number_of_nat V_13)) C_31))))
% 0.68/0.89 FOF formula (forall (V_13:int) (B_65:real) (C_31:real), (((eq real) ((times_times_real (number267125858f_real V_13)) ((plus_plus_real B_65) C_31))) ((plus_plus_real ((times_times_real (number267125858f_real V_13)) B_65)) ((times_times_real (number267125858f_real V_13)) C_31)))) of role axiom named fact_225_right__distrib__number__of
% 0.68/0.89 A new axiom: (forall (V_13:int) (B_65:real) (C_31:real), (((eq real) ((times_times_real (number267125858f_real V_13)) ((plus_plus_real B_65) C_31))) ((plus_plus_real ((times_times_real (number267125858f_real V_13)) B_65)) ((times_times_real (number267125858f_real V_13)) C_31))))
% 0.68/0.89 FOF formula (forall (A_111:int) (M_13:int), (((eq int) ((plus_plus_int ((times_times_int A_111) M_13)) M_13)) ((times_times_int ((plus_plus_int A_111) one_one_int)) M_13))) of role axiom named fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J
% 0.70/0.90 A new axiom: (forall (A_111:int) (M_13:int), (((eq int) ((plus_plus_int ((times_times_int A_111) M_13)) M_13)) ((times_times_int ((plus_plus_int A_111) one_one_int)) M_13)))
% 0.70/0.90 FOF formula (forall (A_111:nat) (M_13:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_111) M_13)) M_13)) ((times_times_nat ((plus_plus_nat A_111) one_one_nat)) M_13))) of role axiom named fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J
% 0.70/0.90 A new axiom: (forall (A_111:nat) (M_13:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_111) M_13)) M_13)) ((times_times_nat ((plus_plus_nat A_111) one_one_nat)) M_13)))
% 0.70/0.90 FOF formula (forall (A_111:real) (M_13:real), (((eq real) ((plus_plus_real ((times_times_real A_111) M_13)) M_13)) ((times_times_real ((plus_plus_real A_111) one_one_real)) M_13))) of role axiom named fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J
% 0.70/0.90 A new axiom: (forall (A_111:real) (M_13:real), (((eq real) ((plus_plus_real ((times_times_real A_111) M_13)) M_13)) ((times_times_real ((plus_plus_real A_111) one_one_real)) M_13)))
% 0.70/0.90 FOF formula (forall (M_12:int) (A_110:int), (((eq int) ((plus_plus_int M_12) ((times_times_int A_110) M_12))) ((times_times_int ((plus_plus_int A_110) one_one_int)) M_12))) of role axiom named fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J
% 0.70/0.90 A new axiom: (forall (M_12:int) (A_110:int), (((eq int) ((plus_plus_int M_12) ((times_times_int A_110) M_12))) ((times_times_int ((plus_plus_int A_110) one_one_int)) M_12)))
% 0.70/0.90 FOF formula (forall (M_12:nat) (A_110:nat), (((eq nat) ((plus_plus_nat M_12) ((times_times_nat A_110) M_12))) ((times_times_nat ((plus_plus_nat A_110) one_one_nat)) M_12))) of role axiom named fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J
% 0.70/0.90 A new axiom: (forall (M_12:nat) (A_110:nat), (((eq nat) ((plus_plus_nat M_12) ((times_times_nat A_110) M_12))) ((times_times_nat ((plus_plus_nat A_110) one_one_nat)) M_12)))
% 0.70/0.90 FOF formula (forall (M_12:real) (A_110:real), (((eq real) ((plus_plus_real M_12) ((times_times_real A_110) M_12))) ((times_times_real ((plus_plus_real A_110) one_one_real)) M_12))) of role axiom named fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J
% 0.70/0.90 A new axiom: (forall (M_12:real) (A_110:real), (((eq real) ((plus_plus_real M_12) ((times_times_real A_110) M_12))) ((times_times_real ((plus_plus_real A_110) one_one_real)) M_12)))
% 0.70/0.90 FOF formula (forall (M_11:int), (((eq int) ((plus_plus_int M_11) M_11)) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) M_11))) of role axiom named fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J
% 0.70/0.90 A new axiom: (forall (M_11:int), (((eq int) ((plus_plus_int M_11) M_11)) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) M_11)))
% 0.70/0.90 FOF formula (forall (M_11:nat), (((eq nat) ((plus_plus_nat M_11) M_11)) ((times_times_nat ((plus_plus_nat one_one_nat) one_one_nat)) M_11))) of role axiom named fact_233_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J
% 0.70/0.90 A new axiom: (forall (M_11:nat), (((eq nat) ((plus_plus_nat M_11) M_11)) ((times_times_nat ((plus_plus_nat one_one_nat) one_one_nat)) M_11)))
% 0.70/0.90 FOF formula (forall (M_11:real), (((eq real) ((plus_plus_real M_11) M_11)) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) M_11))) of role axiom named fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J
% 0.70/0.90 A new axiom: (forall (M_11:real), (((eq real) ((plus_plus_real M_11) M_11)) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) M_11)))
% 0.70/0.90 FOF formula (forall (A_109:int), (((eq int) ((plus_plus_int (number_number_of_int pls)) A_109)) A_109)) of role axiom named fact_235_add__numeral__0
% 0.70/0.90 A new axiom: (forall (A_109:int), (((eq int) ((plus_plus_int (number_number_of_int pls)) A_109)) A_109))
% 0.70/0.90 FOF formula (forall (A_109:real), (((eq real) ((plus_plus_real (number267125858f_real pls)) A_109)) A_109)) of role axiom named fact_236_add__numeral__0
% 0.70/0.92 A new axiom: (forall (A_109:real), (((eq real) ((plus_plus_real (number267125858f_real pls)) A_109)) A_109))
% 0.70/0.92 FOF formula (forall (A_108:int), (((eq int) ((plus_plus_int A_108) (number_number_of_int pls))) A_108)) of role axiom named fact_237_add__numeral__0__right
% 0.70/0.92 A new axiom: (forall (A_108:int), (((eq int) ((plus_plus_int A_108) (number_number_of_int pls))) A_108))
% 0.70/0.92 FOF formula (forall (A_108:real), (((eq real) ((plus_plus_real A_108) (number267125858f_real pls))) A_108)) of role axiom named fact_238_add__numeral__0__right
% 0.70/0.92 A new axiom: (forall (A_108:real), (((eq real) ((plus_plus_real A_108) (number267125858f_real pls))) A_108))
% 0.70/0.92 FOF formula (forall (V_12:int) (W_13:int) (Z_7:int), (((eq int) ((times_times_int (number_number_of_int V_12)) ((times_times_int (number_number_of_int W_13)) Z_7))) ((times_times_int (number_number_of_int ((times_times_int V_12) W_13))) Z_7))) of role axiom named fact_239_mult__number__of__left
% 0.70/0.92 A new axiom: (forall (V_12:int) (W_13:int) (Z_7:int), (((eq int) ((times_times_int (number_number_of_int V_12)) ((times_times_int (number_number_of_int W_13)) Z_7))) ((times_times_int (number_number_of_int ((times_times_int V_12) W_13))) Z_7)))
% 0.70/0.92 FOF formula (forall (V_12:int) (W_13:int) (Z_7:real), (((eq real) ((times_times_real (number267125858f_real V_12)) ((times_times_real (number267125858f_real W_13)) Z_7))) ((times_times_real (number267125858f_real ((times_times_int V_12) W_13))) Z_7))) of role axiom named fact_240_mult__number__of__left
% 0.70/0.92 A new axiom: (forall (V_12:int) (W_13:int) (Z_7:real), (((eq real) ((times_times_real (number267125858f_real V_12)) ((times_times_real (number267125858f_real W_13)) Z_7))) ((times_times_real (number267125858f_real ((times_times_int V_12) W_13))) Z_7)))
% 0.70/0.92 FOF formula (forall (V_11:int) (W_12:int), (((eq int) ((times_times_int (number_number_of_int V_11)) (number_number_of_int W_12))) (number_number_of_int ((times_times_int V_11) W_12)))) of role axiom named fact_241_arith__simps_I32_J
% 0.70/0.92 A new axiom: (forall (V_11:int) (W_12:int), (((eq int) ((times_times_int (number_number_of_int V_11)) (number_number_of_int W_12))) (number_number_of_int ((times_times_int V_11) W_12))))
% 0.70/0.92 FOF formula (forall (V_11:int) (W_12:int), (((eq real) ((times_times_real (number267125858f_real V_11)) (number267125858f_real W_12))) (number267125858f_real ((times_times_int V_11) W_12)))) of role axiom named fact_242_arith__simps_I32_J
% 0.70/0.92 A new axiom: (forall (V_11:int) (W_12:int), (((eq real) ((times_times_real (number267125858f_real V_11)) (number267125858f_real W_12))) (number267125858f_real ((times_times_int V_11) W_12))))
% 0.70/0.92 FOF formula (forall (V_10:int) (W_11:int), (((eq int) (number_number_of_int ((times_times_int V_10) W_11))) ((times_times_int (number_number_of_int V_10)) (number_number_of_int W_11)))) of role axiom named fact_243_number__of__mult
% 0.70/0.92 A new axiom: (forall (V_10:int) (W_11:int), (((eq int) (number_number_of_int ((times_times_int V_10) W_11))) ((times_times_int (number_number_of_int V_10)) (number_number_of_int W_11))))
% 0.70/0.92 FOF formula (forall (V_10:int) (W_11:int), (((eq real) (number267125858f_real ((times_times_int V_10) W_11))) ((times_times_real (number267125858f_real V_10)) (number267125858f_real W_11)))) of role axiom named fact_244_number__of__mult
% 0.70/0.92 A new axiom: (forall (V_10:int) (W_11:int), (((eq real) (number267125858f_real ((times_times_int V_10) W_11))) ((times_times_real (number267125858f_real V_10)) (number267125858f_real W_11))))
% 0.70/0.92 FOF formula (forall (V_9:int) (W_10:int) (Z_6:int), (((eq int) ((plus_plus_int (number_number_of_int V_9)) ((plus_plus_int (number_number_of_int W_10)) Z_6))) ((plus_plus_int (number_number_of_int ((plus_plus_int V_9) W_10))) Z_6))) of role axiom named fact_245_add__number__of__left
% 0.70/0.92 A new axiom: (forall (V_9:int) (W_10:int) (Z_6:int), (((eq int) ((plus_plus_int (number_number_of_int V_9)) ((plus_plus_int (number_number_of_int W_10)) Z_6))) ((plus_plus_int (number_number_of_int ((plus_plus_int V_9) W_10))) Z_6)))
% 0.70/0.92 FOF formula (forall (V_9:int) (W_10:int) (Z_6:real), (((eq real) ((plus_plus_real (number267125858f_real V_9)) ((plus_plus_real (number267125858f_real W_10)) Z_6))) ((plus_plus_real (number267125858f_real ((plus_plus_int V_9) W_10))) Z_6))) of role axiom named fact_246_add__number__of__left
% 0.73/0.93 A new axiom: (forall (V_9:int) (W_10:int) (Z_6:real), (((eq real) ((plus_plus_real (number267125858f_real V_9)) ((plus_plus_real (number267125858f_real W_10)) Z_6))) ((plus_plus_real (number267125858f_real ((plus_plus_int V_9) W_10))) Z_6)))
% 0.73/0.93 FOF formula (forall (V_8:int) (W_9:int), (((eq int) ((plus_plus_int (number_number_of_int V_8)) (number_number_of_int W_9))) (number_number_of_int ((plus_plus_int V_8) W_9)))) of role axiom named fact_247_add__number__of__eq
% 0.73/0.93 A new axiom: (forall (V_8:int) (W_9:int), (((eq int) ((plus_plus_int (number_number_of_int V_8)) (number_number_of_int W_9))) (number_number_of_int ((plus_plus_int V_8) W_9))))
% 0.73/0.93 FOF formula (forall (V_8:int) (W_9:int), (((eq real) ((plus_plus_real (number267125858f_real V_8)) (number267125858f_real W_9))) (number267125858f_real ((plus_plus_int V_8) W_9)))) of role axiom named fact_248_add__number__of__eq
% 0.73/0.93 A new axiom: (forall (V_8:int) (W_9:int), (((eq real) ((plus_plus_real (number267125858f_real V_8)) (number267125858f_real W_9))) (number267125858f_real ((plus_plus_int V_8) W_9))))
% 0.73/0.93 FOF formula (forall (V_7:int) (W_8:int), (((eq int) (number_number_of_int ((plus_plus_int V_7) W_8))) ((plus_plus_int (number_number_of_int V_7)) (number_number_of_int W_8)))) of role axiom named fact_249_number__of__add
% 0.73/0.93 A new axiom: (forall (V_7:int) (W_8:int), (((eq int) (number_number_of_int ((plus_plus_int V_7) W_8))) ((plus_plus_int (number_number_of_int V_7)) (number_number_of_int W_8))))
% 0.73/0.93 FOF formula (forall (V_7:int) (W_8:int), (((eq real) (number267125858f_real ((plus_plus_int V_7) W_8))) ((plus_plus_real (number267125858f_real V_7)) (number267125858f_real W_8)))) of role axiom named fact_250_number__of__add
% 0.73/0.93 A new axiom: (forall (V_7:int) (W_8:int), (((eq real) (number267125858f_real ((plus_plus_int V_7) W_8))) ((plus_plus_real (number267125858f_real V_7)) (number267125858f_real W_8))))
% 0.73/0.93 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_251_add__Bit1__Bit0
% 0.73/0.93 A new axiom: (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit0 L))) (bit1 ((plus_plus_int K) L))))
% 0.73/0.93 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_252_add__Bit0__Bit1
% 0.73/0.93 A new axiom: (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit1 L))) (bit1 ((plus_plus_int K) L))))
% 0.73/0.93 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_253_Bit1__def
% 0.73/0.93 A new axiom: (forall (K:int), (((eq int) (bit1 K)) ((plus_plus_int ((plus_plus_int one_one_int) K)) K)))
% 0.73/0.93 FOF formula (forall (W_7:int), (((eq int) (number_number_of_int (bit1 W_7))) ((plus_plus_int ((plus_plus_int one_one_int) (number_number_of_int W_7))) (number_number_of_int W_7)))) of role axiom named fact_254_number__of__Bit1
% 0.73/0.93 A new axiom: (forall (W_7:int), (((eq int) (number_number_of_int (bit1 W_7))) ((plus_plus_int ((plus_plus_int one_one_int) (number_number_of_int W_7))) (number_number_of_int W_7))))
% 0.73/0.93 FOF formula (forall (W_7:int), (((eq real) (number267125858f_real (bit1 W_7))) ((plus_plus_real ((plus_plus_real one_one_real) (number267125858f_real W_7))) (number267125858f_real W_7)))) of role axiom named fact_255_number__of__Bit1
% 0.73/0.93 A new axiom: (forall (W_7:int), (((eq real) (number267125858f_real (bit1 W_7))) ((plus_plus_real ((plus_plus_real one_one_real) (number267125858f_real W_7))) (number267125858f_real W_7))))
% 0.73/0.93 FOF formula (forall (A_107:int), (((eq int) ((times_times_int (number_number_of_int (bit1 pls))) A_107)) A_107)) of role axiom named fact_256_mult__numeral__1
% 0.73/0.93 A new axiom: (forall (A_107:int), (((eq int) ((times_times_int (number_number_of_int (bit1 pls))) A_107)) A_107))
% 0.73/0.93 FOF formula (forall (A_107:real), (((eq real) ((times_times_real (number267125858f_real (bit1 pls))) A_107)) A_107)) of role axiom named fact_257_mult__numeral__1
% 0.73/0.94 A new axiom: (forall (A_107:real), (((eq real) ((times_times_real (number267125858f_real (bit1 pls))) A_107)) A_107))
% 0.73/0.94 FOF formula (forall (A_106:int), (((eq int) ((times_times_int A_106) (number_number_of_int (bit1 pls)))) A_106)) of role axiom named fact_258_mult__numeral__1__right
% 0.73/0.94 A new axiom: (forall (A_106:int), (((eq int) ((times_times_int A_106) (number_number_of_int (bit1 pls)))) A_106))
% 0.73/0.94 FOF formula (forall (A_106:real), (((eq real) ((times_times_real A_106) (number267125858f_real (bit1 pls)))) A_106)) of role axiom named fact_259_mult__numeral__1__right
% 0.73/0.94 A new axiom: (forall (A_106:real), (((eq real) ((times_times_real A_106) (number267125858f_real (bit1 pls)))) A_106))
% 0.73/0.94 FOF formula (((eq int) (number_number_of_int (bit1 pls))) one_one_int) of role axiom named fact_260_semiring__numeral__1__eq__1
% 0.73/0.94 A new axiom: (((eq int) (number_number_of_int (bit1 pls))) one_one_int)
% 0.73/0.94 FOF formula (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat) of role axiom named fact_261_semiring__numeral__1__eq__1
% 0.73/0.94 A new axiom: (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat)
% 0.73/0.94 FOF formula (((eq real) (number267125858f_real (bit1 pls))) one_one_real) of role axiom named fact_262_semiring__numeral__1__eq__1
% 0.73/0.94 A new axiom: (((eq real) (number267125858f_real (bit1 pls))) one_one_real)
% 0.73/0.94 FOF formula (((eq int) (number_number_of_int (bit1 pls))) one_one_int) of role axiom named fact_263_numeral__1__eq__1
% 0.73/0.94 A new axiom: (((eq int) (number_number_of_int (bit1 pls))) one_one_int)
% 0.73/0.94 FOF formula (((eq real) (number267125858f_real (bit1 pls))) one_one_real) of role axiom named fact_264_numeral__1__eq__1
% 0.73/0.94 A new axiom: (((eq real) (number267125858f_real (bit1 pls))) one_one_real)
% 0.73/0.94 FOF formula (((eq int) one_one_int) (number_number_of_int (bit1 pls))) of role axiom named fact_265_semiring__norm_I110_J
% 0.73/0.94 A new axiom: (((eq int) one_one_int) (number_number_of_int (bit1 pls)))
% 0.73/0.94 FOF formula (((eq real) one_one_real) (number267125858f_real (bit1 pls))) of role axiom named fact_266_semiring__norm_I110_J
% 0.73/0.94 A new axiom: (((eq real) one_one_real) (number267125858f_real (bit1 pls)))
% 0.73/0.94 FOF formula (((eq int) one_one_int) (number_number_of_int (bit1 pls))) of role axiom named fact_267_one__is__num__one
% 0.73/0.94 A new axiom: (((eq int) one_one_int) (number_number_of_int (bit1 pls)))
% 0.73/0.94 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_268_mult__Bit1
% 0.73/0.94 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)))
% 0.73/0.94 FOF formula (forall (W_6:int), (((eq int) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int W_6))) (number_number_of_int (bit0 W_6)))) of role axiom named fact_269_double__number__of__Bit0
% 0.73/0.94 A new axiom: (forall (W_6:int), (((eq int) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int W_6))) (number_number_of_int (bit0 W_6))))
% 0.73/0.94 FOF formula (forall (W_6:int), (((eq real) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real W_6))) (number267125858f_real (bit0 W_6)))) of role axiom named fact_270_double__number__of__Bit0
% 0.73/0.94 A new axiom: (forall (W_6:int), (((eq real) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real W_6))) (number267125858f_real (bit0 W_6))))
% 0.73/0.94 FOF formula (forall (A_105:int), (((eq int) ((power_power_int A_105) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int A_105) A_105)) A_105))) of role axiom named fact_271_power3__eq__cube
% 0.73/0.94 A new axiom: (forall (A_105:int), (((eq int) ((power_power_int A_105) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int A_105) A_105)) A_105)))
% 0.73/0.94 FOF formula (forall (A_105:real), (((eq real) ((power_power_real A_105) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_real ((times_times_real A_105) A_105)) A_105))) of role axiom named fact_272_power3__eq__cube
% 0.73/0.94 A new axiom: (forall (A_105:real), (((eq real) ((power_power_real A_105) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_real ((times_times_real A_105) A_105)) A_105)))
% 0.73/0.96 FOF formula (forall (A_105:nat), (((eq nat) ((power_power_nat A_105) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_nat ((times_times_nat A_105) A_105)) A_105))) of role axiom named fact_273_power3__eq__cube
% 0.73/0.96 A new axiom: (forall (A_105:nat), (((eq nat) ((power_power_nat A_105) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_nat ((times_times_nat A_105) A_105)) A_105)))
% 0.73/0.96 FOF formula (forall (X_1:int), (((eq int) ((power_power_int ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int X_1) (number_number_of_nat (bit0 (bit0 (bit1 pls))))))) of role axiom named fact_274_quartic__square__square
% 0.73/0.96 A new axiom: (forall (X_1:int), (((eq int) ((power_power_int ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int X_1) (number_number_of_nat (bit0 (bit0 (bit1 pls)))))))
% 0.73/0.96 FOF formula (forall (Z_5:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_5)) ((plus_plus_int Z_5) Z_5))) of role axiom named fact_275_semiring__mult__2
% 0.73/0.96 A new axiom: (forall (Z_5:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_5)) ((plus_plus_int Z_5) Z_5)))
% 0.73/0.96 FOF formula (forall (Z_5:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z_5)) ((plus_plus_nat Z_5) Z_5))) of role axiom named fact_276_semiring__mult__2
% 0.73/0.96 A new axiom: (forall (Z_5:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z_5)) ((plus_plus_nat Z_5) Z_5)))
% 0.73/0.96 FOF formula (forall (Z_5:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_5)) ((plus_plus_real Z_5) Z_5))) of role axiom named fact_277_semiring__mult__2
% 0.73/0.96 A new axiom: (forall (Z_5:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_5)) ((plus_plus_real Z_5) Z_5)))
% 0.73/0.96 FOF formula (forall (Z_4:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_4)) ((plus_plus_int Z_4) Z_4))) of role axiom named fact_278_mult__2
% 0.73/0.96 A new axiom: (forall (Z_4:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_4)) ((plus_plus_int Z_4) Z_4)))
% 0.73/0.96 FOF formula (forall (Z_4:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_4)) ((plus_plus_real Z_4) Z_4))) of role axiom named fact_279_mult__2
% 0.73/0.96 A new axiom: (forall (Z_4:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_4)) ((plus_plus_real Z_4) Z_4)))
% 0.73/0.96 FOF formula (forall (Z_3:int), (((eq int) ((times_times_int Z_3) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_3) Z_3))) of role axiom named fact_280_semiring__mult__2__right
% 0.73/0.96 A new axiom: (forall (Z_3:int), (((eq int) ((times_times_int Z_3) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_3) Z_3)))
% 0.73/0.96 FOF formula (forall (Z_3:nat), (((eq nat) ((times_times_nat Z_3) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z_3) Z_3))) of role axiom named fact_281_semiring__mult__2__right
% 0.73/0.96 A new axiom: (forall (Z_3:nat), (((eq nat) ((times_times_nat Z_3) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z_3) Z_3)))
% 0.73/0.96 FOF formula (forall (Z_3:real), (((eq real) ((times_times_real Z_3) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_3) Z_3))) of role axiom named fact_282_semiring__mult__2__right
% 0.73/0.96 A new axiom: (forall (Z_3:real), (((eq real) ((times_times_real Z_3) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_3) Z_3)))
% 0.73/0.96 FOF formula (forall (Z_2:int), (((eq int) ((times_times_int Z_2) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_2) Z_2))) of role axiom named fact_283_mult__2__right
% 0.73/0.96 A new axiom: (forall (Z_2:int), (((eq int) ((times_times_int Z_2) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_2) Z_2)))
% 0.73/0.96 FOF formula (forall (Z_2:real), (((eq real) ((times_times_real Z_2) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_2) Z_2))) of role axiom named fact_284_mult__2__right
% 0.73/0.98 A new axiom: (forall (Z_2:real), (((eq real) ((times_times_real Z_2) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_2) Z_2)))
% 0.73/0.98 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_285_semiring__one__add__one__is__two
% 0.73/0.98 A new axiom: (((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls))))
% 0.73/0.98 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_286_semiring__one__add__one__is__two
% 0.73/0.98 A new axiom: (((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls))))
% 0.73/0.98 FOF formula (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))) of role axiom named fact_287_semiring__one__add__one__is__two
% 0.73/0.98 A new axiom: (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls))))
% 0.73/0.98 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_288_p0
% 0.73/0.98 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))
% 0.73/0.98 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_289__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096
% 0.73/0.98 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))
% 0.73/0.98 FOF formula (forall (P:int), ((zprime P)->((not (((eq int) P) (number_number_of_int (bit0 (bit1 pls)))))->((not (((eq int) P) (number_number_of_int (bit1 (bit1 pls)))))->((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P))))) of role axiom named fact_290_prime__g__5
% 0.73/0.98 A new axiom: (forall (P:int), ((zprime P)->((not (((eq int) P) (number_number_of_int (bit0 (bit1 pls)))))->((not (((eq int) P) (number_number_of_int (bit1 (bit1 pls)))))->((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P)))))
% 0.73/0.98 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_291__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096
% 0.73/0.98 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))
% 0.73/0.98 FOF formula (forall (X_1:real) (Y_1:real), (((eq real) ((power_power_real ((plus_plus_real X_1) Y_1)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_1)) Y_1)))) of role axiom named fact_292_real__sum__squared__expand
% 0.73/0.98 A new axiom: (forall (X_1:real) (Y_1:real), (((eq real) ((power_power_real ((plus_plus_real X_1) Y_1)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_1)) Y_1))))
% 0.73/0.98 FOF formula (forall (X_1:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit0 (bit1 pls))))) ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_1)) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_293_four__x__squared
% 0.73/0.99 A new axiom: (forall (X_1:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit0 (bit1 pls))))) ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_1)) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.73/0.99 FOF formula (forall (N_39:nat) (A_104:int), (((ord_less_int one_one_int) A_104)->((ord_less_int ((power_power_int A_104) N_39)) ((times_times_int A_104) ((power_power_int A_104) N_39))))) of role axiom named fact_294_power__less__power__Suc
% 0.73/0.99 A new axiom: (forall (N_39:nat) (A_104:int), (((ord_less_int one_one_int) A_104)->((ord_less_int ((power_power_int A_104) N_39)) ((times_times_int A_104) ((power_power_int A_104) N_39)))))
% 0.73/0.99 FOF formula (forall (N_39:nat) (A_104:nat), (((ord_less_nat one_one_nat) A_104)->((ord_less_nat ((power_power_nat A_104) N_39)) ((times_times_nat A_104) ((power_power_nat A_104) N_39))))) of role axiom named fact_295_power__less__power__Suc
% 0.73/0.99 A new axiom: (forall (N_39:nat) (A_104:nat), (((ord_less_nat one_one_nat) A_104)->((ord_less_nat ((power_power_nat A_104) N_39)) ((times_times_nat A_104) ((power_power_nat A_104) N_39)))))
% 0.73/0.99 FOF formula (forall (N_39:nat) (A_104:real), (((ord_less_real one_one_real) A_104)->((ord_less_real ((power_power_real A_104) N_39)) ((times_times_real A_104) ((power_power_real A_104) N_39))))) of role axiom named fact_296_power__less__power__Suc
% 0.73/0.99 A new axiom: (forall (N_39:nat) (A_104:real), (((ord_less_real one_one_real) A_104)->((ord_less_real ((power_power_real A_104) N_39)) ((times_times_real A_104) ((power_power_real A_104) N_39)))))
% 0.73/0.99 FOF formula (forall (N_38:nat) (A_103:int), (((ord_less_int one_one_int) A_103)->((ord_less_int one_one_int) ((times_times_int A_103) ((power_power_int A_103) N_38))))) of role axiom named fact_297_power__gt1__lemma
% 0.73/0.99 A new axiom: (forall (N_38:nat) (A_103:int), (((ord_less_int one_one_int) A_103)->((ord_less_int one_one_int) ((times_times_int A_103) ((power_power_int A_103) N_38)))))
% 0.73/0.99 FOF formula (forall (N_38:nat) (A_103:nat), (((ord_less_nat one_one_nat) A_103)->((ord_less_nat one_one_nat) ((times_times_nat A_103) ((power_power_nat A_103) N_38))))) of role axiom named fact_298_power__gt1__lemma
% 0.73/0.99 A new axiom: (forall (N_38:nat) (A_103:nat), (((ord_less_nat one_one_nat) A_103)->((ord_less_nat one_one_nat) ((times_times_nat A_103) ((power_power_nat A_103) N_38)))))
% 0.73/0.99 FOF formula (forall (N_38:nat) (A_103:real), (((ord_less_real one_one_real) A_103)->((ord_less_real one_one_real) ((times_times_real A_103) ((power_power_real A_103) N_38))))) of role axiom named fact_299_power__gt1__lemma
% 0.73/0.99 A new axiom: (forall (N_38:nat) (A_103:real), (((ord_less_real one_one_real) A_103)->((ord_less_real one_one_real) ((times_times_real A_103) ((power_power_real A_103) N_38)))))
% 0.73/0.99 FOF formula (forall (M_10:nat) (N_37:nat) (A_102:int), (((ord_less_int one_one_int) A_102)->(((ord_less_eq_int ((power_power_int A_102) M_10)) ((power_power_int A_102) N_37))->((ord_less_eq_nat M_10) N_37)))) of role axiom named fact_300_power__le__imp__le__exp
% 0.73/0.99 A new axiom: (forall (M_10:nat) (N_37:nat) (A_102:int), (((ord_less_int one_one_int) A_102)->(((ord_less_eq_int ((power_power_int A_102) M_10)) ((power_power_int A_102) N_37))->((ord_less_eq_nat M_10) N_37))))
% 0.73/0.99 FOF formula (forall (M_10:nat) (N_37:nat) (A_102:nat), (((ord_less_nat one_one_nat) A_102)->(((ord_less_eq_nat ((power_power_nat A_102) M_10)) ((power_power_nat A_102) N_37))->((ord_less_eq_nat M_10) N_37)))) of role axiom named fact_301_power__le__imp__le__exp
% 0.73/0.99 A new axiom: (forall (M_10:nat) (N_37:nat) (A_102:nat), (((ord_less_nat one_one_nat) A_102)->(((ord_less_eq_nat ((power_power_nat A_102) M_10)) ((power_power_nat A_102) N_37))->((ord_less_eq_nat M_10) N_37))))
% 0.73/0.99 FOF formula (forall (M_10:nat) (N_37:nat) (A_102:real), (((ord_less_real one_one_real) A_102)->(((ord_less_eq_real ((power_power_real A_102) M_10)) ((power_power_real A_102) N_37))->((ord_less_eq_nat M_10) N_37)))) of role axiom named fact_302_power__le__imp__le__exp
% 0.73/0.99 A new axiom: (forall (M_10:nat) (N_37:nat) (A_102:real), (((ord_less_real one_one_real) A_102)->(((ord_less_eq_real ((power_power_real A_102) M_10)) ((power_power_real A_102) N_37))->((ord_less_eq_nat M_10) N_37))))
% 0.81/1.01 FOF formula (forall (X_28:nat) (Y_25:nat) (B_64:int), (((ord_less_int one_one_int) B_64)->((iff ((ord_less_eq_int ((power_power_int B_64) X_28)) ((power_power_int B_64) Y_25))) ((ord_less_eq_nat X_28) Y_25)))) of role axiom named fact_303_power__increasing__iff
% 0.81/1.01 A new axiom: (forall (X_28:nat) (Y_25:nat) (B_64:int), (((ord_less_int one_one_int) B_64)->((iff ((ord_less_eq_int ((power_power_int B_64) X_28)) ((power_power_int B_64) Y_25))) ((ord_less_eq_nat X_28) Y_25))))
% 0.81/1.01 FOF formula (forall (X_28:nat) (Y_25:nat) (B_64:nat), (((ord_less_nat one_one_nat) B_64)->((iff ((ord_less_eq_nat ((power_power_nat B_64) X_28)) ((power_power_nat B_64) Y_25))) ((ord_less_eq_nat X_28) Y_25)))) of role axiom named fact_304_power__increasing__iff
% 0.81/1.01 A new axiom: (forall (X_28:nat) (Y_25:nat) (B_64:nat), (((ord_less_nat one_one_nat) B_64)->((iff ((ord_less_eq_nat ((power_power_nat B_64) X_28)) ((power_power_nat B_64) Y_25))) ((ord_less_eq_nat X_28) Y_25))))
% 0.81/1.01 FOF formula (forall (X_28:nat) (Y_25:nat) (B_64:real), (((ord_less_real one_one_real) B_64)->((iff ((ord_less_eq_real ((power_power_real B_64) X_28)) ((power_power_real B_64) Y_25))) ((ord_less_eq_nat X_28) Y_25)))) of role axiom named fact_305_power__increasing__iff
% 0.81/1.01 A new axiom: (forall (X_28:nat) (Y_25:nat) (B_64:real), (((ord_less_real one_one_real) B_64)->((iff ((ord_less_eq_real ((power_power_real B_64) X_28)) ((power_power_real B_64) Y_25))) ((ord_less_eq_nat X_28) Y_25))))
% 0.81/1.01 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_306__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096
% 0.81/1.01 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))
% 0.81/1.01 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_307_s0p
% 0.81/1.01 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)))
% 0.81/1.01 FOF formula ((ex int) (fun (X:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X)) ((ord_less_int X) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) X) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (forall (Y:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y)) ((ord_less_int Y) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) Y) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))->(((eq int) Y) X)))))) of role axiom named fact_308__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
% 0.81/1.01 A new axiom: ((ex int) (fun (X:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X)) ((ord_less_int X) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) X) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (forall (Y:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y)) ((ord_less_int Y) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) Y) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))->(((eq int) Y) X))))))
% 0.81/1.03 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_309__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_
% 0.81/1.03 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)
% 0.81/1.03 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_310_s1
% 0.81/1.03 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))
% 0.81/1.03 FOF formula (forall (A_101:int) (N_36:nat), ((iff (((eq int) ((power_power_int A_101) N_36)) zero_zero_int)) ((and (((eq int) A_101) zero_zero_int)) (not (((eq nat) N_36) zero_zero_nat))))) of role axiom named fact_311_power__eq__0__iff
% 0.81/1.03 A new axiom: (forall (A_101:int) (N_36:nat), ((iff (((eq int) ((power_power_int A_101) N_36)) zero_zero_int)) ((and (((eq int) A_101) zero_zero_int)) (not (((eq nat) N_36) zero_zero_nat)))))
% 0.81/1.03 FOF formula (forall (A_101:nat) (N_36:nat), ((iff (((eq nat) ((power_power_nat A_101) N_36)) zero_zero_nat)) ((and (((eq nat) A_101) zero_zero_nat)) (not (((eq nat) N_36) zero_zero_nat))))) of role axiom named fact_312_power__eq__0__iff
% 0.81/1.03 A new axiom: (forall (A_101:nat) (N_36:nat), ((iff (((eq nat) ((power_power_nat A_101) N_36)) zero_zero_nat)) ((and (((eq nat) A_101) zero_zero_nat)) (not (((eq nat) N_36) zero_zero_nat)))))
% 0.81/1.03 FOF formula (forall (A_101:real) (N_36:nat), ((iff (((eq real) ((power_power_real A_101) N_36)) zero_zero_real)) ((and (((eq real) A_101) zero_zero_real)) (not (((eq nat) N_36) zero_zero_nat))))) of role axiom named fact_313_power__eq__0__iff
% 0.81/1.03 A new axiom: (forall (A_101:real) (N_36:nat), ((iff (((eq real) ((power_power_real A_101) N_36)) zero_zero_real)) ((and (((eq real) A_101) zero_zero_real)) (not (((eq nat) N_36) zero_zero_nat)))))
% 0.81/1.03 FOF formula (forall (A_100:real) (M_9:nat) (N_35:nat), (((ord_less_eq_nat M_9) N_35)->((dvd_dvd_real ((power_power_real A_100) M_9)) ((power_power_real A_100) N_35)))) of role axiom named fact_314_le__imp__power__dvd
% 0.81/1.03 A new axiom: (forall (A_100:real) (M_9:nat) (N_35:nat), (((ord_less_eq_nat M_9) N_35)->((dvd_dvd_real ((power_power_real A_100) M_9)) ((power_power_real A_100) N_35))))
% 0.81/1.03 FOF formula (forall (A_100:int) (M_9:nat) (N_35:nat), (((ord_less_eq_nat M_9) N_35)->((dvd_dvd_int ((power_power_int A_100) M_9)) ((power_power_int A_100) N_35)))) of role axiom named fact_315_le__imp__power__dvd
% 0.81/1.03 A new axiom: (forall (A_100:int) (M_9:nat) (N_35:nat), (((ord_less_eq_nat M_9) N_35)->((dvd_dvd_int ((power_power_int A_100) M_9)) ((power_power_int A_100) N_35))))
% 0.81/1.03 FOF formula (forall (A_100:nat) (M_9:nat) (N_35:nat), (((ord_less_eq_nat M_9) N_35)->((dvd_dvd_nat ((power_power_nat A_100) M_9)) ((power_power_nat A_100) N_35)))) of role axiom named fact_316_le__imp__power__dvd
% 0.81/1.03 A new axiom: (forall (A_100:nat) (M_9:nat) (N_35:nat), (((ord_less_eq_nat M_9) N_35)->((dvd_dvd_nat ((power_power_nat A_100) M_9)) ((power_power_nat A_100) N_35))))
% 0.81/1.03 FOF formula (forall (N_34:nat) (M_8:nat) (X_27:real) (Y_24:real), (((dvd_dvd_real X_27) Y_24)->(((ord_less_eq_nat N_34) M_8)->((dvd_dvd_real ((power_power_real X_27) N_34)) ((power_power_real Y_24) M_8))))) of role axiom named fact_317_dvd__power__le
% 0.81/1.05 A new axiom: (forall (N_34:nat) (M_8:nat) (X_27:real) (Y_24:real), (((dvd_dvd_real X_27) Y_24)->(((ord_less_eq_nat N_34) M_8)->((dvd_dvd_real ((power_power_real X_27) N_34)) ((power_power_real Y_24) M_8)))))
% 0.81/1.05 FOF formula (forall (N_34:nat) (M_8:nat) (X_27:int) (Y_24:int), (((dvd_dvd_int X_27) Y_24)->(((ord_less_eq_nat N_34) M_8)->((dvd_dvd_int ((power_power_int X_27) N_34)) ((power_power_int Y_24) M_8))))) of role axiom named fact_318_dvd__power__le
% 0.81/1.05 A new axiom: (forall (N_34:nat) (M_8:nat) (X_27:int) (Y_24:int), (((dvd_dvd_int X_27) Y_24)->(((ord_less_eq_nat N_34) M_8)->((dvd_dvd_int ((power_power_int X_27) N_34)) ((power_power_int Y_24) M_8)))))
% 0.81/1.05 FOF formula (forall (N_34:nat) (M_8:nat) (X_27:nat) (Y_24:nat), (((dvd_dvd_nat X_27) Y_24)->(((ord_less_eq_nat N_34) M_8)->((dvd_dvd_nat ((power_power_nat X_27) N_34)) ((power_power_nat Y_24) M_8))))) of role axiom named fact_319_dvd__power__le
% 0.81/1.05 A new axiom: (forall (N_34:nat) (M_8:nat) (X_27:nat) (Y_24:nat), (((dvd_dvd_nat X_27) Y_24)->(((ord_less_eq_nat N_34) M_8)->((dvd_dvd_nat ((power_power_nat X_27) N_34)) ((power_power_nat Y_24) M_8)))))
% 0.81/1.05 FOF formula (forall (M_7:nat) (A_99:real) (N_33:nat) (B_63:real), (((dvd_dvd_real ((power_power_real A_99) N_33)) B_63)->(((ord_less_eq_nat M_7) N_33)->((dvd_dvd_real ((power_power_real A_99) M_7)) B_63)))) of role axiom named fact_320_power__le__dvd
% 0.81/1.05 A new axiom: (forall (M_7:nat) (A_99:real) (N_33:nat) (B_63:real), (((dvd_dvd_real ((power_power_real A_99) N_33)) B_63)->(((ord_less_eq_nat M_7) N_33)->((dvd_dvd_real ((power_power_real A_99) M_7)) B_63))))
% 0.81/1.05 FOF formula (forall (M_7:nat) (A_99:int) (N_33:nat) (B_63:int), (((dvd_dvd_int ((power_power_int A_99) N_33)) B_63)->(((ord_less_eq_nat M_7) N_33)->((dvd_dvd_int ((power_power_int A_99) M_7)) B_63)))) of role axiom named fact_321_power__le__dvd
% 0.81/1.05 A new axiom: (forall (M_7:nat) (A_99:int) (N_33:nat) (B_63:int), (((dvd_dvd_int ((power_power_int A_99) N_33)) B_63)->(((ord_less_eq_nat M_7) N_33)->((dvd_dvd_int ((power_power_int A_99) M_7)) B_63))))
% 0.81/1.05 FOF formula (forall (M_7:nat) (A_99:nat) (N_33:nat) (B_63:nat), (((dvd_dvd_nat ((power_power_nat A_99) N_33)) B_63)->(((ord_less_eq_nat M_7) N_33)->((dvd_dvd_nat ((power_power_nat A_99) M_7)) B_63)))) of role axiom named fact_322_power__le__dvd
% 0.81/1.05 A new axiom: (forall (M_7:nat) (A_99:nat) (N_33:nat) (B_63:nat), (((dvd_dvd_nat ((power_power_nat A_99) N_33)) B_63)->(((ord_less_eq_nat M_7) N_33)->((dvd_dvd_nat ((power_power_nat A_99) M_7)) B_63))))
% 0.81/1.05 FOF formula (forall (A_98:int) (N_32:nat) (B_62:int), ((((eq int) ((power_power_int A_98) N_32)) ((power_power_int B_62) N_32))->(((ord_less_eq_int zero_zero_int) A_98)->(((ord_less_eq_int zero_zero_int) B_62)->(((ord_less_nat zero_zero_nat) N_32)->(((eq int) A_98) B_62)))))) of role axiom named fact_323_power__eq__imp__eq__base
% 0.81/1.05 A new axiom: (forall (A_98:int) (N_32:nat) (B_62:int), ((((eq int) ((power_power_int A_98) N_32)) ((power_power_int B_62) N_32))->(((ord_less_eq_int zero_zero_int) A_98)->(((ord_less_eq_int zero_zero_int) B_62)->(((ord_less_nat zero_zero_nat) N_32)->(((eq int) A_98) B_62))))))
% 0.81/1.05 FOF formula (forall (A_98:nat) (N_32:nat) (B_62:nat), ((((eq nat) ((power_power_nat A_98) N_32)) ((power_power_nat B_62) N_32))->(((ord_less_eq_nat zero_zero_nat) A_98)->(((ord_less_eq_nat zero_zero_nat) B_62)->(((ord_less_nat zero_zero_nat) N_32)->(((eq nat) A_98) B_62)))))) of role axiom named fact_324_power__eq__imp__eq__base
% 0.81/1.05 A new axiom: (forall (A_98:nat) (N_32:nat) (B_62:nat), ((((eq nat) ((power_power_nat A_98) N_32)) ((power_power_nat B_62) N_32))->(((ord_less_eq_nat zero_zero_nat) A_98)->(((ord_less_eq_nat zero_zero_nat) B_62)->(((ord_less_nat zero_zero_nat) N_32)->(((eq nat) A_98) B_62))))))
% 0.81/1.05 FOF formula (forall (A_98:real) (N_32:nat) (B_62:real), ((((eq real) ((power_power_real A_98) N_32)) ((power_power_real B_62) N_32))->(((ord_less_eq_real zero_zero_real) A_98)->(((ord_less_eq_real zero_zero_real) B_62)->(((ord_less_nat zero_zero_nat) N_32)->(((eq real) A_98) B_62)))))) of role axiom named fact_325_power__eq__imp__eq__base
% 0.81/1.05 A new axiom: (forall (A_98:real) (N_32:nat) (B_62:real), ((((eq real) ((power_power_real A_98) N_32)) ((power_power_real B_62) N_32))->(((ord_less_eq_real zero_zero_real) A_98)->(((ord_less_eq_real zero_zero_real) B_62)->(((ord_less_nat zero_zero_nat) N_32)->(((eq real) A_98) B_62))))))
% 0.81/1.06 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_326_zdvd__not__zless
% 0.81/1.06 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))))
% 0.81/1.06 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_327_zdvd__antisym__nonneg
% 0.81/1.06 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))))))
% 0.81/1.06 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_328_zdvd__mult__cancel
% 0.81/1.06 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))))
% 0.81/1.06 FOF formula (forall (N_31:nat) (X_26:real) (Y_23:real), (((dvd_dvd_real X_26) Y_23)->((dvd_dvd_real ((power_power_real X_26) N_31)) ((power_power_real Y_23) N_31)))) of role axiom named fact_329_dvd__power__same
% 0.81/1.06 A new axiom: (forall (N_31:nat) (X_26:real) (Y_23:real), (((dvd_dvd_real X_26) Y_23)->((dvd_dvd_real ((power_power_real X_26) N_31)) ((power_power_real Y_23) N_31))))
% 0.81/1.06 FOF formula (forall (N_31:nat) (X_26:int) (Y_23:int), (((dvd_dvd_int X_26) Y_23)->((dvd_dvd_int ((power_power_int X_26) N_31)) ((power_power_int Y_23) N_31)))) of role axiom named fact_330_dvd__power__same
% 0.81/1.06 A new axiom: (forall (N_31:nat) (X_26:int) (Y_23:int), (((dvd_dvd_int X_26) Y_23)->((dvd_dvd_int ((power_power_int X_26) N_31)) ((power_power_int Y_23) N_31))))
% 0.81/1.06 FOF formula (forall (N_31:nat) (X_26:nat) (Y_23:nat), (((dvd_dvd_nat X_26) Y_23)->((dvd_dvd_nat ((power_power_nat X_26) N_31)) ((power_power_nat Y_23) N_31)))) of role axiom named fact_331_dvd__power__same
% 0.81/1.06 A new axiom: (forall (N_31:nat) (X_26:nat) (Y_23:nat), (((dvd_dvd_nat X_26) Y_23)->((dvd_dvd_nat ((power_power_nat X_26) N_31)) ((power_power_nat Y_23) N_31))))
% 0.81/1.06 FOF formula (forall (N_30:nat) (A_97:int), ((not (((eq int) A_97) zero_zero_int))->(not (((eq int) ((power_power_int A_97) N_30)) zero_zero_int)))) of role axiom named fact_332_field__power__not__zero
% 0.81/1.06 A new axiom: (forall (N_30:nat) (A_97:int), ((not (((eq int) A_97) zero_zero_int))->(not (((eq int) ((power_power_int A_97) N_30)) zero_zero_int))))
% 0.81/1.06 FOF formula (forall (N_30:nat) (A_97:real), ((not (((eq real) A_97) zero_zero_real))->(not (((eq real) ((power_power_real A_97) N_30)) zero_zero_real)))) of role axiom named fact_333_field__power__not__zero
% 0.81/1.06 A new axiom: (forall (N_30:nat) (A_97:real), ((not (((eq real) A_97) zero_zero_real))->(not (((eq real) ((power_power_real A_97) N_30)) zero_zero_real))))
% 0.81/1.06 FOF formula (forall (N_29:nat), ((and ((((eq nat) N_29) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) N_29)) one_one_int))) ((not (((eq nat) N_29) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) N_29)) zero_zero_int)))) of role axiom named fact_334_power__0__left
% 0.81/1.06 A new axiom: (forall (N_29:nat), ((and ((((eq nat) N_29) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) N_29)) one_one_int))) ((not (((eq nat) N_29) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) N_29)) zero_zero_int))))
% 0.81/1.06 FOF formula (forall (N_29:nat), ((and ((((eq nat) N_29) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) N_29)) one_one_nat))) ((not (((eq nat) N_29) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) N_29)) zero_zero_nat)))) of role axiom named fact_335_power__0__left
% 0.81/1.06 A new axiom: (forall (N_29:nat), ((and ((((eq nat) N_29) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) N_29)) one_one_nat))) ((not (((eq nat) N_29) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) N_29)) zero_zero_nat))))
% 0.81/1.08 FOF formula (forall (N_29:nat), ((and ((((eq nat) N_29) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) N_29)) one_one_real))) ((not (((eq nat) N_29) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) N_29)) zero_zero_real)))) of role axiom named fact_336_power__0__left
% 0.81/1.08 A new axiom: (forall (N_29:nat), ((and ((((eq nat) N_29) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) N_29)) one_one_real))) ((not (((eq nat) N_29) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) N_29)) zero_zero_real))))
% 0.81/1.08 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_337_zdvd__imp__le
% 0.81/1.08 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))))
% 0.81/1.08 FOF formula (forall (N_28:nat) (A_96:int) (B_61:int), (((ord_less_int A_96) B_61)->(((ord_less_eq_int zero_zero_int) A_96)->(((ord_less_nat zero_zero_nat) N_28)->((ord_less_int ((power_power_int A_96) N_28)) ((power_power_int B_61) N_28)))))) of role axiom named fact_338_power__strict__mono
% 0.81/1.08 A new axiom: (forall (N_28:nat) (A_96:int) (B_61:int), (((ord_less_int A_96) B_61)->(((ord_less_eq_int zero_zero_int) A_96)->(((ord_less_nat zero_zero_nat) N_28)->((ord_less_int ((power_power_int A_96) N_28)) ((power_power_int B_61) N_28))))))
% 0.81/1.08 FOF formula (forall (N_28:nat) (A_96:nat) (B_61:nat), (((ord_less_nat A_96) B_61)->(((ord_less_eq_nat zero_zero_nat) A_96)->(((ord_less_nat zero_zero_nat) N_28)->((ord_less_nat ((power_power_nat A_96) N_28)) ((power_power_nat B_61) N_28)))))) of role axiom named fact_339_power__strict__mono
% 0.81/1.08 A new axiom: (forall (N_28:nat) (A_96:nat) (B_61:nat), (((ord_less_nat A_96) B_61)->(((ord_less_eq_nat zero_zero_nat) A_96)->(((ord_less_nat zero_zero_nat) N_28)->((ord_less_nat ((power_power_nat A_96) N_28)) ((power_power_nat B_61) N_28))))))
% 0.81/1.08 FOF formula (forall (N_28:nat) (A_96:real) (B_61:real), (((ord_less_real A_96) B_61)->(((ord_less_eq_real zero_zero_real) A_96)->(((ord_less_nat zero_zero_nat) N_28)->((ord_less_real ((power_power_real A_96) N_28)) ((power_power_real B_61) N_28)))))) of role axiom named fact_340_power__strict__mono
% 0.81/1.08 A new axiom: (forall (N_28:nat) (A_96:real) (B_61:real), (((ord_less_real A_96) B_61)->(((ord_less_eq_real zero_zero_real) A_96)->(((ord_less_nat zero_zero_nat) N_28)->((ord_less_real ((power_power_real A_96) N_28)) ((power_power_real B_61) N_28))))))
% 0.81/1.08 FOF formula (forall (A_95:int), (((eq int) ((times_times_int zero_zero_int) A_95)) zero_zero_int)) of role axiom named fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J
% 0.81/1.08 A new axiom: (forall (A_95:int), (((eq int) ((times_times_int zero_zero_int) A_95)) zero_zero_int))
% 0.81/1.08 FOF formula (forall (A_95:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_95)) zero_zero_nat)) of role axiom named fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J
% 0.81/1.08 A new axiom: (forall (A_95:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_95)) zero_zero_nat))
% 0.81/1.08 FOF formula (forall (A_95:real), (((eq real) ((times_times_real zero_zero_real) A_95)) zero_zero_real)) of role axiom named fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J
% 0.81/1.08 A new axiom: (forall (A_95:real), (((eq real) ((times_times_real zero_zero_real) A_95)) zero_zero_real))
% 0.81/1.08 FOF formula (forall (A_94:int), (((eq int) ((times_times_int A_94) zero_zero_int)) zero_zero_int)) of role axiom named fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J
% 0.81/1.08 A new axiom: (forall (A_94:int), (((eq int) ((times_times_int A_94) zero_zero_int)) zero_zero_int))
% 0.81/1.08 FOF formula (forall (A_94:nat), (((eq nat) ((times_times_nat A_94) zero_zero_nat)) zero_zero_nat)) of role axiom named fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J
% 0.81/1.08 A new axiom: (forall (A_94:nat), (((eq nat) ((times_times_nat A_94) zero_zero_nat)) zero_zero_nat))
% 0.81/1.08 FOF formula (forall (A_94:real), (((eq real) ((times_times_real A_94) zero_zero_real)) zero_zero_real)) of role axiom named fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J
% 0.89/1.09 A new axiom: (forall (A_94:real), (((eq real) ((times_times_real A_94) zero_zero_real)) zero_zero_real))
% 0.89/1.09 FOF formula (forall (A_93:int), (((eq int) ((plus_plus_int zero_zero_int) A_93)) A_93)) of role axiom named fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J
% 0.89/1.09 A new axiom: (forall (A_93:int), (((eq int) ((plus_plus_int zero_zero_int) A_93)) A_93))
% 0.89/1.09 FOF formula (forall (A_93:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_93)) A_93)) of role axiom named fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J
% 0.89/1.09 A new axiom: (forall (A_93:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_93)) A_93))
% 0.89/1.09 FOF formula (forall (A_93:real), (((eq real) ((plus_plus_real zero_zero_real) A_93)) A_93)) of role axiom named fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J
% 0.89/1.09 A new axiom: (forall (A_93:real), (((eq real) ((plus_plus_real zero_zero_real) A_93)) A_93))
% 0.89/1.09 FOF formula (forall (A_92:int), (((eq int) ((plus_plus_int A_92) zero_zero_int)) A_92)) of role axiom named fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J
% 0.89/1.09 A new axiom: (forall (A_92:int), (((eq int) ((plus_plus_int A_92) zero_zero_int)) A_92))
% 0.89/1.09 FOF formula (forall (A_92:nat), (((eq nat) ((plus_plus_nat A_92) zero_zero_nat)) A_92)) of role axiom named fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J
% 0.89/1.09 A new axiom: (forall (A_92:nat), (((eq nat) ((plus_plus_nat A_92) zero_zero_nat)) A_92))
% 0.89/1.09 FOF formula (forall (A_92:real), (((eq real) ((plus_plus_real A_92) zero_zero_real)) A_92)) of role axiom named fact_352_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J
% 0.89/1.09 A new axiom: (forall (A_92:real), (((eq real) ((plus_plus_real A_92) zero_zero_real)) A_92))
% 0.89/1.09 FOF formula (forall (B_60:int) (A_91:int), ((iff (((eq int) B_60) ((plus_plus_int B_60) A_91))) (((eq int) A_91) zero_zero_int))) of role axiom named fact_353_add__0__iff
% 0.89/1.09 A new axiom: (forall (B_60:int) (A_91:int), ((iff (((eq int) B_60) ((plus_plus_int B_60) A_91))) (((eq int) A_91) zero_zero_int)))
% 0.89/1.09 FOF formula (forall (B_60:nat) (A_91:nat), ((iff (((eq nat) B_60) ((plus_plus_nat B_60) A_91))) (((eq nat) A_91) zero_zero_nat))) of role axiom named fact_354_add__0__iff
% 0.89/1.09 A new axiom: (forall (B_60:nat) (A_91:nat), ((iff (((eq nat) B_60) ((plus_plus_nat B_60) A_91))) (((eq nat) A_91) zero_zero_nat)))
% 0.89/1.09 FOF formula (forall (B_60:real) (A_91:real), ((iff (((eq real) B_60) ((plus_plus_real B_60) A_91))) (((eq real) A_91) zero_zero_real))) of role axiom named fact_355_add__0__iff
% 0.89/1.09 A new axiom: (forall (B_60:real) (A_91:real), ((iff (((eq real) B_60) ((plus_plus_real B_60) A_91))) (((eq real) A_91) zero_zero_real)))
% 0.89/1.09 FOF formula (forall (A_90:int), ((iff (((eq int) ((plus_plus_int A_90) A_90)) zero_zero_int)) (((eq int) A_90) zero_zero_int))) of role axiom named fact_356_double__eq__0__iff
% 0.89/1.09 A new axiom: (forall (A_90:int), ((iff (((eq int) ((plus_plus_int A_90) A_90)) zero_zero_int)) (((eq int) A_90) zero_zero_int)))
% 0.89/1.09 FOF formula (forall (A_90:real), ((iff (((eq real) ((plus_plus_real A_90) A_90)) zero_zero_real)) (((eq real) A_90) zero_zero_real))) of role axiom named fact_357_double__eq__0__iff
% 0.89/1.09 A new axiom: (forall (A_90:real), ((iff (((eq real) ((plus_plus_real A_90) A_90)) zero_zero_real)) (((eq real) A_90) zero_zero_real)))
% 0.89/1.09 FOF formula (((eq int) pls) zero_zero_int) of role axiom named fact_358_Pls__def
% 0.89/1.09 A new axiom: (((eq int) pls) zero_zero_int)
% 0.89/1.09 FOF formula (not (((eq int) zero_zero_int) one_one_int)) of role axiom named fact_359_int__0__neq__1
% 0.89/1.09 A new axiom: (not (((eq int) zero_zero_int) one_one_int))
% 0.89/1.09 FOF formula (forall (Z:int), (((eq int) ((plus_plus_int zero_zero_int) Z)) Z)) of role axiom named fact_360_zadd__0
% 0.89/1.09 A new axiom: (forall (Z:int), (((eq int) ((plus_plus_int zero_zero_int) Z)) Z))
% 0.89/1.09 FOF formula (forall (Z:int), (((eq int) ((plus_plus_int Z) zero_zero_int)) Z)) of role axiom named fact_361_zadd__0__right
% 0.89/1.09 A new axiom: (forall (Z:int), (((eq int) ((plus_plus_int Z) zero_zero_int)) Z))
% 0.89/1.09 FOF formula (forall (N_27:nat) (A_89:int), (((ord_less_eq_int zero_zero_int) A_89)->((ord_less_eq_int zero_zero_int) ((power_power_int A_89) N_27)))) of role axiom named fact_362_zero__le__power
% 0.89/1.11 A new axiom: (forall (N_27:nat) (A_89:int), (((ord_less_eq_int zero_zero_int) A_89)->((ord_less_eq_int zero_zero_int) ((power_power_int A_89) N_27))))
% 0.89/1.11 FOF formula (forall (N_27:nat) (A_89:nat), (((ord_less_eq_nat zero_zero_nat) A_89)->((ord_less_eq_nat zero_zero_nat) ((power_power_nat A_89) N_27)))) of role axiom named fact_363_zero__le__power
% 0.89/1.11 A new axiom: (forall (N_27:nat) (A_89:nat), (((ord_less_eq_nat zero_zero_nat) A_89)->((ord_less_eq_nat zero_zero_nat) ((power_power_nat A_89) N_27))))
% 0.89/1.11 FOF formula (forall (N_27:nat) (A_89:real), (((ord_less_eq_real zero_zero_real) A_89)->((ord_less_eq_real zero_zero_real) ((power_power_real A_89) N_27)))) of role axiom named fact_364_zero__le__power
% 0.89/1.11 A new axiom: (forall (N_27:nat) (A_89:real), (((ord_less_eq_real zero_zero_real) A_89)->((ord_less_eq_real zero_zero_real) ((power_power_real A_89) N_27))))
% 0.89/1.11 FOF formula (forall (N_26:nat) (A_88:int) (B_59:int), (((ord_less_eq_int A_88) B_59)->(((ord_less_eq_int zero_zero_int) A_88)->((ord_less_eq_int ((power_power_int A_88) N_26)) ((power_power_int B_59) N_26))))) of role axiom named fact_365_power__mono
% 0.89/1.11 A new axiom: (forall (N_26:nat) (A_88:int) (B_59:int), (((ord_less_eq_int A_88) B_59)->(((ord_less_eq_int zero_zero_int) A_88)->((ord_less_eq_int ((power_power_int A_88) N_26)) ((power_power_int B_59) N_26)))))
% 0.89/1.11 FOF formula (forall (N_26:nat) (A_88:nat) (B_59:nat), (((ord_less_eq_nat A_88) B_59)->(((ord_less_eq_nat zero_zero_nat) A_88)->((ord_less_eq_nat ((power_power_nat A_88) N_26)) ((power_power_nat B_59) N_26))))) of role axiom named fact_366_power__mono
% 0.89/1.11 A new axiom: (forall (N_26:nat) (A_88:nat) (B_59:nat), (((ord_less_eq_nat A_88) B_59)->(((ord_less_eq_nat zero_zero_nat) A_88)->((ord_less_eq_nat ((power_power_nat A_88) N_26)) ((power_power_nat B_59) N_26)))))
% 0.89/1.11 FOF formula (forall (N_26:nat) (A_88:real) (B_59:real), (((ord_less_eq_real A_88) B_59)->(((ord_less_eq_real zero_zero_real) A_88)->((ord_less_eq_real ((power_power_real A_88) N_26)) ((power_power_real B_59) N_26))))) of role axiom named fact_367_power__mono
% 0.89/1.11 A new axiom: (forall (N_26:nat) (A_88:real) (B_59:real), (((ord_less_eq_real A_88) B_59)->(((ord_less_eq_real zero_zero_real) A_88)->((ord_less_eq_real ((power_power_real A_88) N_26)) ((power_power_real B_59) N_26)))))
% 0.89/1.11 FOF formula (forall (N_25:nat) (A_87:int), (((ord_less_int zero_zero_int) A_87)->((ord_less_int zero_zero_int) ((power_power_int A_87) N_25)))) of role axiom named fact_368_zero__less__power
% 0.89/1.11 A new axiom: (forall (N_25:nat) (A_87:int), (((ord_less_int zero_zero_int) A_87)->((ord_less_int zero_zero_int) ((power_power_int A_87) N_25))))
% 0.89/1.11 FOF formula (forall (N_25:nat) (A_87:nat), (((ord_less_nat zero_zero_nat) A_87)->((ord_less_nat zero_zero_nat) ((power_power_nat A_87) N_25)))) of role axiom named fact_369_zero__less__power
% 0.89/1.11 A new axiom: (forall (N_25:nat) (A_87:nat), (((ord_less_nat zero_zero_nat) A_87)->((ord_less_nat zero_zero_nat) ((power_power_nat A_87) N_25))))
% 0.89/1.11 FOF formula (forall (N_25:nat) (A_87:real), (((ord_less_real zero_zero_real) A_87)->((ord_less_real zero_zero_real) ((power_power_real A_87) N_25)))) of role axiom named fact_370_zero__less__power
% 0.89/1.11 A new axiom: (forall (N_25:nat) (A_87:real), (((ord_less_real zero_zero_real) A_87)->((ord_less_real zero_zero_real) ((power_power_real A_87) N_25))))
% 0.89/1.11 FOF formula (forall (Z:nat) (X_1:int) (Y_1:nat) (P:int), ((((zcong ((power_power_int X_1) Y_1)) one_one_int) P)->(((zcong ((power_power_int X_1) ((times_times_nat Y_1) Z))) one_one_int) P))) of role axiom named fact_371_zcong__zpower__zmult
% 0.89/1.11 A new axiom: (forall (Z:nat) (X_1:int) (Y_1:nat) (P:int), ((((zcong ((power_power_int X_1) Y_1)) one_one_int) P)->(((zcong ((power_power_int X_1) ((times_times_nat Y_1) Z))) one_one_int) P)))
% 0.89/1.11 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_372_zdvd__reduce
% 0.89/1.11 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)))
% 0.89/1.13 FOF formula (forall (C:int) (X_1:int) (T:int) (A:int) (D:int), (((dvd_dvd_int A) D)->((iff ((dvd_dvd_int A) ((plus_plus_int X_1) T))) ((dvd_dvd_int A) ((plus_plus_int ((plus_plus_int X_1) ((times_times_int C) D))) T))))) of role axiom named fact_373_zdvd__period
% 0.89/1.13 A new axiom: (forall (C:int) (X_1:int) (T:int) (A:int) (D:int), (((dvd_dvd_int A) D)->((iff ((dvd_dvd_int A) ((plus_plus_int X_1) T))) ((dvd_dvd_int A) ((plus_plus_int ((plus_plus_int X_1) ((times_times_int C) D))) T)))))
% 0.89/1.13 FOF formula (forall (A_86:int) (N_24:nat) (B_58:int), (((ord_less_int ((power_power_int A_86) N_24)) ((power_power_int B_58) N_24))->(((ord_less_eq_int zero_zero_int) B_58)->((ord_less_int A_86) B_58)))) of role axiom named fact_374_power__less__imp__less__base
% 0.89/1.13 A new axiom: (forall (A_86:int) (N_24:nat) (B_58:int), (((ord_less_int ((power_power_int A_86) N_24)) ((power_power_int B_58) N_24))->(((ord_less_eq_int zero_zero_int) B_58)->((ord_less_int A_86) B_58))))
% 0.89/1.13 FOF formula (forall (A_86:nat) (N_24:nat) (B_58:nat), (((ord_less_nat ((power_power_nat A_86) N_24)) ((power_power_nat B_58) N_24))->(((ord_less_eq_nat zero_zero_nat) B_58)->((ord_less_nat A_86) B_58)))) of role axiom named fact_375_power__less__imp__less__base
% 0.89/1.13 A new axiom: (forall (A_86:nat) (N_24:nat) (B_58:nat), (((ord_less_nat ((power_power_nat A_86) N_24)) ((power_power_nat B_58) N_24))->(((ord_less_eq_nat zero_zero_nat) B_58)->((ord_less_nat A_86) B_58))))
% 0.89/1.13 FOF formula (forall (A_86:real) (N_24:nat) (B_58:real), (((ord_less_real ((power_power_real A_86) N_24)) ((power_power_real B_58) N_24))->(((ord_less_eq_real zero_zero_real) B_58)->((ord_less_real A_86) B_58)))) of role axiom named fact_376_power__less__imp__less__base
% 0.89/1.13 A new axiom: (forall (A_86:real) (N_24:nat) (B_58:real), (((ord_less_real ((power_power_real A_86) N_24)) ((power_power_real B_58) N_24))->(((ord_less_eq_real zero_zero_real) B_58)->((ord_less_real A_86) B_58))))
% 0.89/1.13 FOF formula (forall (A_85:int) (N_23:nat) (N_22:nat), (((ord_less_eq_nat N_23) N_22)->(((ord_less_eq_int zero_zero_int) A_85)->(((ord_less_eq_int A_85) one_one_int)->((ord_less_eq_int ((power_power_int A_85) N_22)) ((power_power_int A_85) N_23)))))) of role axiom named fact_377_power__decreasing
% 0.89/1.13 A new axiom: (forall (A_85:int) (N_23:nat) (N_22:nat), (((ord_less_eq_nat N_23) N_22)->(((ord_less_eq_int zero_zero_int) A_85)->(((ord_less_eq_int A_85) one_one_int)->((ord_less_eq_int ((power_power_int A_85) N_22)) ((power_power_int A_85) N_23))))))
% 0.89/1.13 FOF formula (forall (A_85:nat) (N_23:nat) (N_22:nat), (((ord_less_eq_nat N_23) N_22)->(((ord_less_eq_nat zero_zero_nat) A_85)->(((ord_less_eq_nat A_85) one_one_nat)->((ord_less_eq_nat ((power_power_nat A_85) N_22)) ((power_power_nat A_85) N_23)))))) of role axiom named fact_378_power__decreasing
% 0.89/1.13 A new axiom: (forall (A_85:nat) (N_23:nat) (N_22:nat), (((ord_less_eq_nat N_23) N_22)->(((ord_less_eq_nat zero_zero_nat) A_85)->(((ord_less_eq_nat A_85) one_one_nat)->((ord_less_eq_nat ((power_power_nat A_85) N_22)) ((power_power_nat A_85) N_23))))))
% 0.89/1.13 FOF formula (forall (A_85:real) (N_23:nat) (N_22:nat), (((ord_less_eq_nat N_23) N_22)->(((ord_less_eq_real zero_zero_real) A_85)->(((ord_less_eq_real A_85) one_one_real)->((ord_less_eq_real ((power_power_real A_85) N_22)) ((power_power_real A_85) N_23)))))) of role axiom named fact_379_power__decreasing
% 0.89/1.13 A new axiom: (forall (A_85:real) (N_23:nat) (N_22:nat), (((ord_less_eq_nat N_23) N_22)->(((ord_less_eq_real zero_zero_real) A_85)->(((ord_less_eq_real A_85) one_one_real)->((ord_less_eq_real ((power_power_real A_85) N_22)) ((power_power_real A_85) N_23))))))
% 0.89/1.13 FOF formula (forall (A_84:int) (N_21:nat) (N_20:nat), (((ord_less_nat N_21) N_20)->(((ord_less_int zero_zero_int) A_84)->(((ord_less_int A_84) one_one_int)->((ord_less_int ((power_power_int A_84) N_20)) ((power_power_int A_84) N_21)))))) of role axiom named fact_380_power__strict__decreasing
% 0.89/1.13 A new axiom: (forall (A_84:int) (N_21:nat) (N_20:nat), (((ord_less_nat N_21) N_20)->(((ord_less_int zero_zero_int) A_84)->(((ord_less_int A_84) one_one_int)->((ord_less_int ((power_power_int A_84) N_20)) ((power_power_int A_84) N_21))))))
% 0.89/1.15 FOF formula (forall (A_84:nat) (N_21:nat) (N_20:nat), (((ord_less_nat N_21) N_20)->(((ord_less_nat zero_zero_nat) A_84)->(((ord_less_nat A_84) one_one_nat)->((ord_less_nat ((power_power_nat A_84) N_20)) ((power_power_nat A_84) N_21)))))) of role axiom named fact_381_power__strict__decreasing
% 0.89/1.15 A new axiom: (forall (A_84:nat) (N_21:nat) (N_20:nat), (((ord_less_nat N_21) N_20)->(((ord_less_nat zero_zero_nat) A_84)->(((ord_less_nat A_84) one_one_nat)->((ord_less_nat ((power_power_nat A_84) N_20)) ((power_power_nat A_84) N_21))))))
% 0.89/1.15 FOF formula (forall (A_84:real) (N_21:nat) (N_20:nat), (((ord_less_nat N_21) N_20)->(((ord_less_real zero_zero_real) A_84)->(((ord_less_real A_84) one_one_real)->((ord_less_real ((power_power_real A_84) N_20)) ((power_power_real A_84) N_21)))))) of role axiom named fact_382_power__strict__decreasing
% 0.89/1.15 A new axiom: (forall (A_84:real) (N_21:nat) (N_20:nat), (((ord_less_nat N_21) N_20)->(((ord_less_real zero_zero_real) A_84)->(((ord_less_real A_84) one_one_real)->((ord_less_real ((power_power_real A_84) N_20)) ((power_power_real A_84) N_21))))))
% 0.89/1.15 FOF formula (forall (A_83:int), ((iff ((ord_less_int ((plus_plus_int A_83) A_83)) zero_zero_int)) ((ord_less_int A_83) zero_zero_int))) of role axiom named fact_383_even__less__0__iff
% 0.89/1.15 A new axiom: (forall (A_83:int), ((iff ((ord_less_int ((plus_plus_int A_83) A_83)) zero_zero_int)) ((ord_less_int A_83) zero_zero_int)))
% 0.89/1.15 FOF formula (forall (A_83:real), ((iff ((ord_less_real ((plus_plus_real A_83) A_83)) zero_zero_real)) ((ord_less_real A_83) zero_zero_real))) of role axiom named fact_384_even__less__0__iff
% 0.89/1.15 A new axiom: (forall (A_83:real), ((iff ((ord_less_real ((plus_plus_real A_83) A_83)) zero_zero_real)) ((ord_less_real A_83) zero_zero_real)))
% 0.89/1.15 FOF formula (forall (X_25:int) (Y_22:int), ((iff (((eq int) ((plus_plus_int ((times_times_int X_25) X_25)) ((times_times_int Y_22) Y_22))) zero_zero_int)) ((and (((eq int) X_25) zero_zero_int)) (((eq int) Y_22) zero_zero_int)))) of role axiom named fact_385_sum__squares__eq__zero__iff
% 0.89/1.15 A new axiom: (forall (X_25:int) (Y_22:int), ((iff (((eq int) ((plus_plus_int ((times_times_int X_25) X_25)) ((times_times_int Y_22) Y_22))) zero_zero_int)) ((and (((eq int) X_25) zero_zero_int)) (((eq int) Y_22) zero_zero_int))))
% 0.89/1.15 FOF formula (forall (X_25:real) (Y_22:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X_25) X_25)) ((times_times_real Y_22) Y_22))) zero_zero_real)) ((and (((eq real) X_25) zero_zero_real)) (((eq real) Y_22) zero_zero_real)))) of role axiom named fact_386_sum__squares__eq__zero__iff
% 0.89/1.15 A new axiom: (forall (X_25:real) (Y_22:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X_25) X_25)) ((times_times_real Y_22) Y_22))) zero_zero_real)) ((and (((eq real) X_25) zero_zero_real)) (((eq real) Y_22) zero_zero_real))))
% 0.89/1.15 FOF formula (forall (C_30:int) (D_7:int) (A_82:int) (B_57:int) (R_3:int), ((not (((eq int) R_3) zero_zero_int))->(((and (((eq int) A_82) B_57)) (not (((eq int) C_30) D_7)))->(not (((eq int) ((plus_plus_int A_82) ((times_times_int R_3) C_30))) ((plus_plus_int B_57) ((times_times_int R_3) D_7))))))) of role axiom named fact_387_add__scale__eq__noteq
% 0.89/1.15 A new axiom: (forall (C_30:int) (D_7:int) (A_82:int) (B_57:int) (R_3:int), ((not (((eq int) R_3) zero_zero_int))->(((and (((eq int) A_82) B_57)) (not (((eq int) C_30) D_7)))->(not (((eq int) ((plus_plus_int A_82) ((times_times_int R_3) C_30))) ((plus_plus_int B_57) ((times_times_int R_3) D_7)))))))
% 0.89/1.15 FOF formula (forall (C_30:nat) (D_7:nat) (A_82:nat) (B_57:nat) (R_3:nat), ((not (((eq nat) R_3) zero_zero_nat))->(((and (((eq nat) A_82) B_57)) (not (((eq nat) C_30) D_7)))->(not (((eq nat) ((plus_plus_nat A_82) ((times_times_nat R_3) C_30))) ((plus_plus_nat B_57) ((times_times_nat R_3) D_7))))))) of role axiom named fact_388_add__scale__eq__noteq
% 0.89/1.15 A new axiom: (forall (C_30:nat) (D_7:nat) (A_82:nat) (B_57:nat) (R_3:nat), ((not (((eq nat) R_3) zero_zero_nat))->(((and (((eq nat) A_82) B_57)) (not (((eq nat) C_30) D_7)))->(not (((eq nat) ((plus_plus_nat A_82) ((times_times_nat R_3) C_30))) ((plus_plus_nat B_57) ((times_times_nat R_3) D_7)))))))
% 0.89/1.16 FOF formula (forall (C_30:real) (D_7:real) (A_82:real) (B_57:real) (R_3:real), ((not (((eq real) R_3) zero_zero_real))->(((and (((eq real) A_82) B_57)) (not (((eq real) C_30) D_7)))->(not (((eq real) ((plus_plus_real A_82) ((times_times_real R_3) C_30))) ((plus_plus_real B_57) ((times_times_real R_3) D_7))))))) of role axiom named fact_389_add__scale__eq__noteq
% 0.89/1.16 A new axiom: (forall (C_30:real) (D_7:real) (A_82:real) (B_57:real) (R_3:real), ((not (((eq real) R_3) zero_zero_real))->(((and (((eq real) A_82) B_57)) (not (((eq real) C_30) D_7)))->(not (((eq real) ((plus_plus_real A_82) ((times_times_real R_3) C_30))) ((plus_plus_real B_57) ((times_times_real R_3) D_7)))))))
% 0.89/1.16 FOF formula (forall (A:int) (N:nat) (P:int), ((zprime P)->(((dvd_dvd_int P) ((power_power_int A) N))->((dvd_dvd_int P) A)))) of role axiom named fact_390_zprime__zdvd__power
% 0.89/1.16 A new axiom: (forall (A:int) (N:nat) (P:int), ((zprime P)->(((dvd_dvd_int P) ((power_power_int A) N))->((dvd_dvd_int P) A))))
% 0.89/1.16 FOF formula (((eq int) zero_zero_int) (number_number_of_int pls)) of role axiom named fact_391_semiring__norm_I112_J
% 0.89/1.16 A new axiom: (((eq int) zero_zero_int) (number_number_of_int pls))
% 0.89/1.16 FOF formula (((eq real) zero_zero_real) (number267125858f_real pls)) of role axiom named fact_392_semiring__norm_I112_J
% 0.89/1.16 A new axiom: (((eq real) zero_zero_real) (number267125858f_real pls))
% 0.89/1.16 FOF formula (((eq int) (number_number_of_int pls)) zero_zero_int) of role axiom named fact_393_number__of__Pls
% 0.89/1.16 A new axiom: (((eq int) (number_number_of_int pls)) zero_zero_int)
% 0.89/1.16 FOF formula (((eq real) (number267125858f_real pls)) zero_zero_real) of role axiom named fact_394_number__of__Pls
% 0.89/1.16 A new axiom: (((eq real) (number267125858f_real pls)) zero_zero_real)
% 0.89/1.16 FOF formula (((eq int) (number_number_of_int pls)) zero_zero_int) of role axiom named fact_395_semiring__numeral__0__eq__0
% 0.89/1.16 A new axiom: (((eq int) (number_number_of_int pls)) zero_zero_int)
% 0.89/1.16 FOF formula (((eq nat) (number_number_of_nat pls)) zero_zero_nat) of role axiom named fact_396_semiring__numeral__0__eq__0
% 0.89/1.16 A new axiom: (((eq nat) (number_number_of_nat pls)) zero_zero_nat)
% 0.89/1.16 FOF formula (((eq real) (number267125858f_real pls)) zero_zero_real) of role axiom named fact_397_semiring__numeral__0__eq__0
% 0.89/1.16 A new axiom: (((eq real) (number267125858f_real pls)) zero_zero_real)
% 0.89/1.16 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_398_bin__less__0__simps_I4_J
% 0.89/1.16 A new axiom: (forall (W:int), ((iff ((ord_less_int (bit1 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int)))
% 0.89/1.16 FOF formula (((ord_less_int pls) zero_zero_int)->False) of role axiom named fact_399_bin__less__0__simps_I1_J
% 0.89/1.16 A new axiom: (((ord_less_int pls) zero_zero_int)->False)
% 0.89/1.16 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_400_bin__less__0__simps_I3_J
% 0.89/1.16 A new axiom: (forall (W:int), ((iff ((ord_less_int (bit0 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int)))
% 0.89/1.16 FOF formula (((eq int) zero_zero_int) (number_number_of_int pls)) of role axiom named fact_401_zero__is__num__zero
% 0.89/1.16 A new axiom: (((eq int) zero_zero_int) (number_number_of_int pls))
% 0.89/1.16 FOF formula ((ord_less_int zero_zero_int) one_one_int) of role axiom named fact_402_int__0__less__1
% 0.89/1.16 A new axiom: ((ord_less_int zero_zero_int) one_one_int)
% 0.89/1.16 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_403_pos__zmult__pos
% 0.89/1.16 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))))
% 0.89/1.16 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_404_zmult__zless__mono2
% 0.89/1.16 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)))))
% 0.99/1.18 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_405_odd__nonzero
% 0.99/1.18 A new axiom: (forall (Z:int), (not (((eq int) ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int)))
% 0.99/1.18 FOF formula (forall (N_19:nat) (A_81:int), (((ord_less_int zero_zero_int) A_81)->(((ord_less_int A_81) one_one_int)->((ord_less_int ((times_times_int A_81) ((power_power_int A_81) N_19))) ((power_power_int A_81) N_19))))) of role axiom named fact_406_power__Suc__less
% 0.99/1.18 A new axiom: (forall (N_19:nat) (A_81:int), (((ord_less_int zero_zero_int) A_81)->(((ord_less_int A_81) one_one_int)->((ord_less_int ((times_times_int A_81) ((power_power_int A_81) N_19))) ((power_power_int A_81) N_19)))))
% 0.99/1.18 FOF formula (forall (N_19:nat) (A_81:nat), (((ord_less_nat zero_zero_nat) A_81)->(((ord_less_nat A_81) one_one_nat)->((ord_less_nat ((times_times_nat A_81) ((power_power_nat A_81) N_19))) ((power_power_nat A_81) N_19))))) of role axiom named fact_407_power__Suc__less
% 0.99/1.18 A new axiom: (forall (N_19:nat) (A_81:nat), (((ord_less_nat zero_zero_nat) A_81)->(((ord_less_nat A_81) one_one_nat)->((ord_less_nat ((times_times_nat A_81) ((power_power_nat A_81) N_19))) ((power_power_nat A_81) N_19)))))
% 0.99/1.18 FOF formula (forall (N_19:nat) (A_81:real), (((ord_less_real zero_zero_real) A_81)->(((ord_less_real A_81) one_one_real)->((ord_less_real ((times_times_real A_81) ((power_power_real A_81) N_19))) ((power_power_real A_81) N_19))))) of role axiom named fact_408_power__Suc__less
% 0.99/1.18 A new axiom: (forall (N_19:nat) (A_81:real), (((ord_less_real zero_zero_real) A_81)->(((ord_less_real A_81) one_one_real)->((ord_less_real ((times_times_real A_81) ((power_power_real A_81) N_19))) ((power_power_real A_81) N_19)))))
% 0.99/1.18 FOF formula (forall (N:nat) (B:int) (A:int) (P:int), ((zprime P)->((((dvd_dvd_int P) A)->False)->(((dvd_dvd_int ((power_power_int P) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P) N)) B))))) of role axiom named fact_409_zprime__power__zdvd__cancel__left
% 0.99/1.18 A new axiom: (forall (N:nat) (B:int) (A:int) (P:int), ((zprime P)->((((dvd_dvd_int P) A)->False)->(((dvd_dvd_int ((power_power_int P) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P) N)) B)))))
% 0.99/1.18 FOF formula (forall (N:nat) (A:int) (B:int) (P:int), ((zprime P)->((((dvd_dvd_int P) B)->False)->(((dvd_dvd_int ((power_power_int P) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P) N)) A))))) of role axiom named fact_410_zprime__power__zdvd__cancel__right
% 0.99/1.18 A new axiom: (forall (N:nat) (A:int) (B:int) (P:int), ((zprime P)->((((dvd_dvd_int P) B)->False)->(((dvd_dvd_int ((power_power_int P) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P) N)) A)))))
% 0.99/1.18 FOF formula (forall (X_24:int) (Y_21:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int X_24) X_24)) ((times_times_int Y_21) Y_21)))) of role axiom named fact_411_sum__squares__ge__zero
% 0.99/1.18 A new axiom: (forall (X_24:int) (Y_21:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int X_24) X_24)) ((times_times_int Y_21) Y_21))))
% 0.99/1.18 FOF formula (forall (X_24:real) (Y_21:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((times_times_real X_24) X_24)) ((times_times_real Y_21) Y_21)))) of role axiom named fact_412_sum__squares__ge__zero
% 0.99/1.18 A new axiom: (forall (X_24:real) (Y_21:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((times_times_real X_24) X_24)) ((times_times_real Y_21) Y_21))))
% 0.99/1.18 FOF formula (forall (X_23:int) (Y_20:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int X_23) X_23)) ((times_times_int Y_20) Y_20))) zero_zero_int)) ((and (((eq int) X_23) zero_zero_int)) (((eq int) Y_20) zero_zero_int)))) of role axiom named fact_413_sum__squares__le__zero__iff
% 0.99/1.18 A new axiom: (forall (X_23:int) (Y_20:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int X_23) X_23)) ((times_times_int Y_20) Y_20))) zero_zero_int)) ((and (((eq int) X_23) zero_zero_int)) (((eq int) Y_20) zero_zero_int))))
% 0.99/1.20 FOF formula (forall (X_23:real) (Y_20:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real X_23) X_23)) ((times_times_real Y_20) Y_20))) zero_zero_real)) ((and (((eq real) X_23) zero_zero_real)) (((eq real) Y_20) zero_zero_real)))) of role axiom named fact_414_sum__squares__le__zero__iff
% 0.99/1.20 A new axiom: (forall (X_23:real) (Y_20:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real X_23) X_23)) ((times_times_real Y_20) Y_20))) zero_zero_real)) ((and (((eq real) X_23) zero_zero_real)) (((eq real) Y_20) zero_zero_real))))
% 0.99/1.20 FOF formula (forall (V:int) (V_6:int), ((iff ((ord_less_nat (number_number_of_nat V)) (number_number_of_nat V_6))) ((and (((ord_less_int V) V_6)->((ord_less_int pls) V_6))) ((ord_less_int V) V_6)))) of role axiom named fact_415_less__nat__number__of
% 0.99/1.20 A new axiom: (forall (V:int) (V_6:int), ((iff ((ord_less_nat (number_number_of_nat V)) (number_number_of_nat V_6))) ((and (((ord_less_int V) V_6)->((ord_less_int pls) V_6))) ((ord_less_int V) V_6))))
% 0.99/1.20 FOF formula (forall (X_22:int) (Y_19:int), (((ord_less_int ((plus_plus_int ((times_times_int X_22) X_22)) ((times_times_int Y_19) Y_19))) zero_zero_int)->False)) of role axiom named fact_416_not__sum__squares__lt__zero
% 0.99/1.20 A new axiom: (forall (X_22:int) (Y_19:int), (((ord_less_int ((plus_plus_int ((times_times_int X_22) X_22)) ((times_times_int Y_19) Y_19))) zero_zero_int)->False))
% 0.99/1.20 FOF formula (forall (X_22:real) (Y_19:real), (((ord_less_real ((plus_plus_real ((times_times_real X_22) X_22)) ((times_times_real Y_19) Y_19))) zero_zero_real)->False)) of role axiom named fact_417_not__sum__squares__lt__zero
% 0.99/1.20 A new axiom: (forall (X_22:real) (Y_19:real), (((ord_less_real ((plus_plus_real ((times_times_real X_22) X_22)) ((times_times_real Y_19) Y_19))) zero_zero_real)->False))
% 0.99/1.20 FOF formula (forall (X_21:int) (Y_18:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((times_times_int X_21) X_21)) ((times_times_int Y_18) Y_18)))) ((or (not (((eq int) X_21) zero_zero_int))) (not (((eq int) Y_18) zero_zero_int))))) of role axiom named fact_418_sum__squares__gt__zero__iff
% 0.99/1.20 A new axiom: (forall (X_21:int) (Y_18:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((times_times_int X_21) X_21)) ((times_times_int Y_18) Y_18)))) ((or (not (((eq int) X_21) zero_zero_int))) (not (((eq int) Y_18) zero_zero_int)))))
% 0.99/1.20 FOF formula (forall (X_21:real) (Y_18:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((times_times_real X_21) X_21)) ((times_times_real Y_18) Y_18)))) ((or (not (((eq real) X_21) zero_zero_real))) (not (((eq real) Y_18) zero_zero_real))))) of role axiom named fact_419_sum__squares__gt__zero__iff
% 0.99/1.20 A new axiom: (forall (X_21:real) (Y_18:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((times_times_real X_21) X_21)) ((times_times_real Y_18) Y_18)))) ((or (not (((eq real) X_21) zero_zero_real))) (not (((eq real) Y_18) zero_zero_real)))))
% 0.99/1.20 FOF formula (forall (V:int) (V_6:int), ((iff ((ord_less_eq_nat (number_number_of_nat V)) (number_number_of_nat V_6))) ((((ord_less_eq_int V) V_6)->False)->((ord_less_eq_int V) pls)))) of role axiom named fact_420_le__nat__number__of
% 0.99/1.20 A new axiom: (forall (V:int) (V_6:int), ((iff ((ord_less_eq_nat (number_number_of_nat V)) (number_number_of_nat V_6))) ((((ord_less_eq_int V) V_6)->False)->((ord_less_eq_int V) pls))))
% 0.99/1.20 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_421_number__of__Bit0
% 0.99/1.20 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))))
% 0.99/1.20 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_422_number__of__Bit0
% 0.99/1.20 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))))
% 1.02/1.21 FOF formula (forall (A_80:int), (((eq int) ((power_power_int A_80) one_one_nat)) A_80)) of role axiom named fact_423_power__one__right
% 1.02/1.21 A new axiom: (forall (A_80:int), (((eq int) ((power_power_int A_80) one_one_nat)) A_80))
% 1.02/1.21 FOF formula (forall (A_80:real), (((eq real) ((power_power_real A_80) one_one_nat)) A_80)) of role axiom named fact_424_power__one__right
% 1.02/1.21 A new axiom: (forall (A_80:real), (((eq real) ((power_power_real A_80) one_one_nat)) A_80))
% 1.02/1.21 FOF formula (forall (A_80:nat), (((eq nat) ((power_power_nat A_80) one_one_nat)) A_80)) of role axiom named fact_425_power__one__right
% 1.02/1.21 A new axiom: (forall (A_80:nat), (((eq nat) ((power_power_nat A_80) one_one_nat)) A_80))
% 1.02/1.21 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_426_int__one__le__iff__zero__less
% 1.02/1.21 A new axiom: (forall (Z:int), ((iff ((ord_less_eq_int one_one_int) Z)) ((ord_less_int zero_zero_int) Z)))
% 1.02/1.21 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_427_pos__zmult__eq__1__iff
% 1.02/1.21 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)))))
% 1.02/1.21 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_428_odd__less__0
% 1.02/1.21 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)))
% 1.02/1.21 FOF formula (forall (Y_17:int), ((iff ((ord_less_int zero_zero_int) (number_number_of_int Y_17))) ((ord_less_int pls) Y_17))) of role axiom named fact_429_less__special_I1_J
% 1.02/1.21 A new axiom: (forall (Y_17:int), ((iff ((ord_less_int zero_zero_int) (number_number_of_int Y_17))) ((ord_less_int pls) Y_17)))
% 1.02/1.21 FOF formula (forall (Y_17:int), ((iff ((ord_less_real zero_zero_real) (number267125858f_real Y_17))) ((ord_less_int pls) Y_17))) of role axiom named fact_430_less__special_I1_J
% 1.02/1.21 A new axiom: (forall (Y_17:int), ((iff ((ord_less_real zero_zero_real) (number267125858f_real Y_17))) ((ord_less_int pls) Y_17)))
% 1.02/1.21 FOF formula (forall (X_20:int), ((iff ((ord_less_int (number_number_of_int X_20)) zero_zero_int)) ((ord_less_int X_20) pls))) of role axiom named fact_431_less__special_I3_J
% 1.02/1.21 A new axiom: (forall (X_20:int), ((iff ((ord_less_int (number_number_of_int X_20)) zero_zero_int)) ((ord_less_int X_20) pls)))
% 1.02/1.21 FOF formula (forall (X_20:int), ((iff ((ord_less_real (number267125858f_real X_20)) zero_zero_real)) ((ord_less_int X_20) pls))) of role axiom named fact_432_less__special_I3_J
% 1.02/1.21 A new axiom: (forall (X_20:int), ((iff ((ord_less_real (number267125858f_real X_20)) zero_zero_real)) ((ord_less_int X_20) pls)))
% 1.02/1.21 FOF formula (forall (Y_16:int), ((iff ((ord_less_eq_real zero_zero_real) (number267125858f_real Y_16))) ((ord_less_eq_int pls) Y_16))) of role axiom named fact_433_le__special_I1_J
% 1.02/1.21 A new axiom: (forall (Y_16:int), ((iff ((ord_less_eq_real zero_zero_real) (number267125858f_real Y_16))) ((ord_less_eq_int pls) Y_16)))
% 1.02/1.21 FOF formula (forall (Y_16:int), ((iff ((ord_less_eq_int zero_zero_int) (number_number_of_int Y_16))) ((ord_less_eq_int pls) Y_16))) of role axiom named fact_434_le__special_I1_J
% 1.02/1.21 A new axiom: (forall (Y_16:int), ((iff ((ord_less_eq_int zero_zero_int) (number_number_of_int Y_16))) ((ord_less_eq_int pls) Y_16)))
% 1.02/1.21 FOF formula (forall (X_19:int), ((iff ((ord_less_eq_real (number267125858f_real X_19)) zero_zero_real)) ((ord_less_eq_int X_19) pls))) of role axiom named fact_435_le__special_I3_J
% 1.02/1.21 A new axiom: (forall (X_19:int), ((iff ((ord_less_eq_real (number267125858f_real X_19)) zero_zero_real)) ((ord_less_eq_int X_19) pls)))
% 1.02/1.21 FOF formula (forall (X_19:int), ((iff ((ord_less_eq_int (number_number_of_int X_19)) zero_zero_int)) ((ord_less_eq_int X_19) pls))) of role axiom named fact_436_le__special_I3_J
% 1.04/1.23 A new axiom: (forall (X_19:int), ((iff ((ord_less_eq_int (number_number_of_int X_19)) zero_zero_int)) ((ord_less_eq_int X_19) pls)))
% 1.04/1.23 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_437_le__imp__0__less
% 1.04/1.23 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))))
% 1.04/1.23 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_438_zero__power2
% 1.04/1.23 A new axiom: (((eq real) ((power_power_real zero_zero_real) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)
% 1.04/1.23 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_439_zero__power2
% 1.04/1.23 A new axiom: (((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_nat)
% 1.04/1.23 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_440_zero__power2
% 1.04/1.23 A new axiom: (((eq int) ((power_power_int zero_zero_int) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)
% 1.04/1.23 FOF formula (forall (A_79:real), ((iff (((eq real) ((power_power_real A_79) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)) (((eq real) A_79) zero_zero_real))) of role axiom named fact_441_zero__eq__power2
% 1.04/1.23 A new axiom: (forall (A_79:real), ((iff (((eq real) ((power_power_real A_79) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)) (((eq real) A_79) zero_zero_real)))
% 1.04/1.23 FOF formula (forall (A_79:int), ((iff (((eq int) ((power_power_int A_79) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)) (((eq int) A_79) zero_zero_int))) of role axiom named fact_442_zero__eq__power2
% 1.04/1.23 A new axiom: (forall (A_79:int), ((iff (((eq int) ((power_power_int A_79) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)) (((eq int) A_79) zero_zero_int)))
% 1.04/1.23 FOF formula (forall (A_78:real), ((ord_less_eq_real zero_zero_real) ((power_power_real A_78) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_443_zero__le__power2
% 1.04/1.23 A new axiom: (forall (A_78:real), ((ord_less_eq_real zero_zero_real) ((power_power_real A_78) (number_number_of_nat (bit0 (bit1 pls))))))
% 1.04/1.23 FOF formula (forall (A_78:int), ((ord_less_eq_int zero_zero_int) ((power_power_int A_78) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_444_zero__le__power2
% 1.04/1.23 A new axiom: (forall (A_78:int), ((ord_less_eq_int zero_zero_int) ((power_power_int A_78) (number_number_of_nat (bit0 (bit1 pls))))))
% 1.04/1.23 FOF formula (forall (X_18:real) (Y_15:real), (((ord_less_eq_real ((power_power_real X_18) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_15) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_15)->((ord_less_eq_real X_18) Y_15)))) of role axiom named fact_445_power2__le__imp__le
% 1.04/1.23 A new axiom: (forall (X_18:real) (Y_15:real), (((ord_less_eq_real ((power_power_real X_18) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_15) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_15)->((ord_less_eq_real X_18) Y_15))))
% 1.04/1.23 FOF formula (forall (X_18:nat) (Y_15:nat), (((ord_less_eq_nat ((power_power_nat X_18) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_15) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_15)->((ord_less_eq_nat X_18) Y_15)))) of role axiom named fact_446_power2__le__imp__le
% 1.04/1.23 A new axiom: (forall (X_18:nat) (Y_15:nat), (((ord_less_eq_nat ((power_power_nat X_18) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_15) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_15)->((ord_less_eq_nat X_18) Y_15))))
% 1.04/1.23 FOF formula (forall (X_18:int) (Y_15:int), (((ord_less_eq_int ((power_power_int X_18) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_15) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_15)->((ord_less_eq_int X_18) Y_15)))) of role axiom named fact_447_power2__le__imp__le
% 1.04/1.24 A new axiom: (forall (X_18:int) (Y_15:int), (((ord_less_eq_int ((power_power_int X_18) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_15) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_15)->((ord_less_eq_int X_18) Y_15))))
% 1.04/1.24 FOF formula (forall (X_17:real) (Y_14:real), ((((eq real) ((power_power_real X_17) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_14) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) X_17)->(((ord_less_eq_real zero_zero_real) Y_14)->(((eq real) X_17) Y_14))))) of role axiom named fact_448_power2__eq__imp__eq
% 1.04/1.24 A new axiom: (forall (X_17:real) (Y_14:real), ((((eq real) ((power_power_real X_17) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_14) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) X_17)->(((ord_less_eq_real zero_zero_real) Y_14)->(((eq real) X_17) Y_14)))))
% 1.04/1.24 FOF formula (forall (X_17:nat) (Y_14:nat), ((((eq nat) ((power_power_nat X_17) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_14) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) X_17)->(((ord_less_eq_nat zero_zero_nat) Y_14)->(((eq nat) X_17) Y_14))))) of role axiom named fact_449_power2__eq__imp__eq
% 1.04/1.24 A new axiom: (forall (X_17:nat) (Y_14:nat), ((((eq nat) ((power_power_nat X_17) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_14) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) X_17)->(((ord_less_eq_nat zero_zero_nat) Y_14)->(((eq nat) X_17) Y_14)))))
% 1.04/1.24 FOF formula (forall (X_17:int) (Y_14:int), ((((eq int) ((power_power_int X_17) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_14) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) X_17)->(((ord_less_eq_int zero_zero_int) Y_14)->(((eq int) X_17) Y_14))))) of role axiom named fact_450_power2__eq__imp__eq
% 1.04/1.24 A new axiom: (forall (X_17:int) (Y_14:int), ((((eq int) ((power_power_int X_17) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_14) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) X_17)->(((ord_less_eq_int zero_zero_int) Y_14)->(((eq int) X_17) Y_14)))))
% 1.04/1.24 FOF formula (forall (A_77:real), (((ord_less_real ((power_power_real A_77) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)->False)) of role axiom named fact_451_power2__less__0
% 1.04/1.24 A new axiom: (forall (A_77:real), (((ord_less_real ((power_power_real A_77) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)->False))
% 1.04/1.24 FOF formula (forall (A_77:int), (((ord_less_int ((power_power_int A_77) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)->False)) of role axiom named fact_452_power2__less__0
% 1.04/1.24 A new axiom: (forall (A_77:int), (((ord_less_int ((power_power_int A_77) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)->False))
% 1.04/1.24 FOF formula (forall (A_76:real), ((iff ((ord_less_real zero_zero_real) ((power_power_real A_76) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq real) A_76) zero_zero_real)))) of role axiom named fact_453_zero__less__power2
% 1.04/1.24 A new axiom: (forall (A_76:real), ((iff ((ord_less_real zero_zero_real) ((power_power_real A_76) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq real) A_76) zero_zero_real))))
% 1.04/1.24 FOF formula (forall (A_76:int), ((iff ((ord_less_int zero_zero_int) ((power_power_int A_76) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq int) A_76) zero_zero_int)))) of role axiom named fact_454_zero__less__power2
% 1.04/1.24 A new axiom: (forall (A_76:int), ((iff ((ord_less_int zero_zero_int) ((power_power_int A_76) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq int) A_76) zero_zero_int))))
% 1.04/1.24 FOF formula (forall (X_16:real) (Y_13:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X_16) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_13) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_16) zero_zero_real)) (((eq real) Y_13) zero_zero_real)))) of role axiom named fact_455_sum__power2__eq__zero__iff
% 1.04/1.26 A new axiom: (forall (X_16:real) (Y_13:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X_16) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_13) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_16) zero_zero_real)) (((eq real) Y_13) zero_zero_real))))
% 1.04/1.26 FOF formula (forall (X_16:int) (Y_13:int), ((iff (((eq int) ((plus_plus_int ((power_power_int X_16) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_13) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_16) zero_zero_int)) (((eq int) Y_13) zero_zero_int)))) of role axiom named fact_456_sum__power2__eq__zero__iff
% 1.04/1.26 A new axiom: (forall (X_16:int) (Y_13:int), ((iff (((eq int) ((plus_plus_int ((power_power_int X_16) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_13) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_16) zero_zero_int)) (((eq int) Y_13) zero_zero_int))))
% 1.04/1.26 FOF formula (forall (A_75:nat) (N_18:nat), (((eq nat) ((times_times_nat ((power_power_nat A_75) N_18)) A_75)) ((times_times_nat A_75) ((power_power_nat A_75) N_18)))) of role axiom named fact_457_power__commutes
% 1.04/1.26 A new axiom: (forall (A_75:nat) (N_18:nat), (((eq nat) ((times_times_nat ((power_power_nat A_75) N_18)) A_75)) ((times_times_nat A_75) ((power_power_nat A_75) N_18))))
% 1.04/1.26 FOF formula (forall (A_75:real) (N_18:nat), (((eq real) ((times_times_real ((power_power_real A_75) N_18)) A_75)) ((times_times_real A_75) ((power_power_real A_75) N_18)))) of role axiom named fact_458_power__commutes
% 1.04/1.26 A new axiom: (forall (A_75:real) (N_18:nat), (((eq real) ((times_times_real ((power_power_real A_75) N_18)) A_75)) ((times_times_real A_75) ((power_power_real A_75) N_18))))
% 1.04/1.26 FOF formula (forall (A_75:int) (N_18:nat), (((eq int) ((times_times_int ((power_power_int A_75) N_18)) A_75)) ((times_times_int A_75) ((power_power_int A_75) N_18)))) of role axiom named fact_459_power__commutes
% 1.04/1.26 A new axiom: (forall (A_75:int) (N_18:nat), (((eq int) ((times_times_int ((power_power_int A_75) N_18)) A_75)) ((times_times_int A_75) ((power_power_int A_75) N_18))))
% 1.04/1.26 FOF formula (forall (A_74:nat) (B_56:nat) (N_17:nat), (((eq nat) ((power_power_nat ((times_times_nat A_74) B_56)) N_17)) ((times_times_nat ((power_power_nat A_74) N_17)) ((power_power_nat B_56) N_17)))) of role axiom named fact_460_power__mult__distrib
% 1.04/1.26 A new axiom: (forall (A_74:nat) (B_56:nat) (N_17:nat), (((eq nat) ((power_power_nat ((times_times_nat A_74) B_56)) N_17)) ((times_times_nat ((power_power_nat A_74) N_17)) ((power_power_nat B_56) N_17))))
% 1.04/1.26 FOF formula (forall (A_74:real) (B_56:real) (N_17:nat), (((eq real) ((power_power_real ((times_times_real A_74) B_56)) N_17)) ((times_times_real ((power_power_real A_74) N_17)) ((power_power_real B_56) N_17)))) of role axiom named fact_461_power__mult__distrib
% 1.04/1.26 A new axiom: (forall (A_74:real) (B_56:real) (N_17:nat), (((eq real) ((power_power_real ((times_times_real A_74) B_56)) N_17)) ((times_times_real ((power_power_real A_74) N_17)) ((power_power_real B_56) N_17))))
% 1.04/1.26 FOF formula (forall (A_74:int) (B_56:int) (N_17:nat), (((eq int) ((power_power_int ((times_times_int A_74) B_56)) N_17)) ((times_times_int ((power_power_int A_74) N_17)) ((power_power_int B_56) N_17)))) of role axiom named fact_462_power__mult__distrib
% 1.04/1.26 A new axiom: (forall (A_74:int) (B_56:int) (N_17:nat), (((eq int) ((power_power_int ((times_times_int A_74) B_56)) N_17)) ((times_times_int ((power_power_int A_74) N_17)) ((power_power_int B_56) N_17))))
% 1.04/1.26 FOF formula (forall (A_73:nat) (M_6:nat) (N_16:nat), (((eq nat) ((power_power_nat A_73) ((plus_plus_nat M_6) N_16))) ((times_times_nat ((power_power_nat A_73) M_6)) ((power_power_nat A_73) N_16)))) of role axiom named fact_463_power__add
% 1.04/1.26 A new axiom: (forall (A_73:nat) (M_6:nat) (N_16:nat), (((eq nat) ((power_power_nat A_73) ((plus_plus_nat M_6) N_16))) ((times_times_nat ((power_power_nat A_73) M_6)) ((power_power_nat A_73) N_16))))
% 1.04/1.28 FOF formula (forall (A_73:real) (M_6:nat) (N_16:nat), (((eq real) ((power_power_real A_73) ((plus_plus_nat M_6) N_16))) ((times_times_real ((power_power_real A_73) M_6)) ((power_power_real A_73) N_16)))) of role axiom named fact_464_power__add
% 1.04/1.28 A new axiom: (forall (A_73:real) (M_6:nat) (N_16:nat), (((eq real) ((power_power_real A_73) ((plus_plus_nat M_6) N_16))) ((times_times_real ((power_power_real A_73) M_6)) ((power_power_real A_73) N_16))))
% 1.04/1.28 FOF formula (forall (A_73:int) (M_6:nat) (N_16:nat), (((eq int) ((power_power_int A_73) ((plus_plus_nat M_6) N_16))) ((times_times_int ((power_power_int A_73) M_6)) ((power_power_int A_73) N_16)))) of role axiom named fact_465_power__add
% 1.04/1.28 A new axiom: (forall (A_73:int) (M_6:nat) (N_16:nat), (((eq int) ((power_power_int A_73) ((plus_plus_nat M_6) N_16))) ((times_times_int ((power_power_int A_73) M_6)) ((power_power_int A_73) N_16))))
% 1.04/1.28 FOF formula (forall (N_15:nat), (((eq real) ((power_power_real one_one_real) N_15)) one_one_real)) of role axiom named fact_466_power__one
% 1.04/1.28 A new axiom: (forall (N_15:nat), (((eq real) ((power_power_real one_one_real) N_15)) one_one_real))
% 1.04/1.28 FOF formula (forall (N_15:nat), (((eq nat) ((power_power_nat one_one_nat) N_15)) one_one_nat)) of role axiom named fact_467_power__one
% 1.04/1.28 A new axiom: (forall (N_15:nat), (((eq nat) ((power_power_nat one_one_nat) N_15)) one_one_nat))
% 1.04/1.28 FOF formula (forall (N_15:nat), (((eq int) ((power_power_int one_one_int) N_15)) one_one_int)) of role axiom named fact_468_power__one
% 1.04/1.28 A new axiom: (forall (N_15:nat), (((eq int) ((power_power_int one_one_int) N_15)) one_one_int))
% 1.04/1.28 FOF formula (forall (A_72:nat) (M_5:nat) (N_14:nat), (((eq nat) ((power_power_nat A_72) ((times_times_nat M_5) N_14))) ((power_power_nat ((power_power_nat A_72) M_5)) N_14))) of role axiom named fact_469_power__mult
% 1.04/1.28 A new axiom: (forall (A_72:nat) (M_5:nat) (N_14:nat), (((eq nat) ((power_power_nat A_72) ((times_times_nat M_5) N_14))) ((power_power_nat ((power_power_nat A_72) M_5)) N_14)))
% 1.04/1.28 FOF formula (forall (A_72:real) (M_5:nat) (N_14:nat), (((eq real) ((power_power_real A_72) ((times_times_nat M_5) N_14))) ((power_power_real ((power_power_real A_72) M_5)) N_14))) of role axiom named fact_470_power__mult
% 1.04/1.28 A new axiom: (forall (A_72:real) (M_5:nat) (N_14:nat), (((eq real) ((power_power_real A_72) ((times_times_nat M_5) N_14))) ((power_power_real ((power_power_real A_72) M_5)) N_14)))
% 1.04/1.28 FOF formula (forall (A_72:int) (M_5:nat) (N_14:nat), (((eq int) ((power_power_int A_72) ((times_times_nat M_5) N_14))) ((power_power_int ((power_power_int A_72) M_5)) N_14))) of role axiom named fact_471_power__mult
% 1.04/1.28 A new axiom: (forall (A_72:int) (M_5:nat) (N_14:nat), (((eq int) ((power_power_int A_72) ((times_times_nat M_5) N_14))) ((power_power_int ((power_power_int A_72) M_5)) N_14)))
% 1.04/1.28 FOF formula (forall (X_15:real) (Y_12:real), (((ord_less_real ((power_power_real X_15) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_12)->((ord_less_real X_15) Y_12)))) of role axiom named fact_472_power2__less__imp__less
% 1.04/1.28 A new axiom: (forall (X_15:real) (Y_12:real), (((ord_less_real ((power_power_real X_15) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_12)->((ord_less_real X_15) Y_12))))
% 1.04/1.28 FOF formula (forall (X_15:nat) (Y_12:nat), (((ord_less_nat ((power_power_nat X_15) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_12)->((ord_less_nat X_15) Y_12)))) of role axiom named fact_473_power2__less__imp__less
% 1.04/1.28 A new axiom: (forall (X_15:nat) (Y_12:nat), (((ord_less_nat ((power_power_nat X_15) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_12)->((ord_less_nat X_15) Y_12))))
% 1.04/1.28 FOF formula (forall (X_15:int) (Y_12:int), (((ord_less_int ((power_power_int X_15) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_12)->((ord_less_int X_15) Y_12)))) of role axiom named fact_474_power2__less__imp__less
% 1.04/1.29 A new axiom: (forall (X_15:int) (Y_12:int), (((ord_less_int ((power_power_int X_15) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_12)->((ord_less_int X_15) Y_12))))
% 1.04/1.29 FOF formula (forall (X_14:real) (Y_11:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((power_power_real X_14) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_11) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_475_sum__power2__ge__zero
% 1.04/1.29 A new axiom: (forall (X_14:real) (Y_11:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((power_power_real X_14) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_11) (number_number_of_nat (bit0 (bit1 pls)))))))
% 1.04/1.29 FOF formula (forall (X_14:int) (Y_11:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((power_power_int X_14) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_11) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_476_sum__power2__ge__zero
% 1.04/1.29 A new axiom: (forall (X_14:int) (Y_11:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((power_power_int X_14) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_11) (number_number_of_nat (bit0 (bit1 pls)))))))
% 1.04/1.29 FOF formula (forall (X_13:real) (Y_10:real), ((iff ((ord_less_eq_real ((plus_plus_real ((power_power_real X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_10) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_13) zero_zero_real)) (((eq real) Y_10) zero_zero_real)))) of role axiom named fact_477_sum__power2__le__zero__iff
% 1.04/1.29 A new axiom: (forall (X_13:real) (Y_10:real), ((iff ((ord_less_eq_real ((plus_plus_real ((power_power_real X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_10) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_13) zero_zero_real)) (((eq real) Y_10) zero_zero_real))))
% 1.04/1.29 FOF formula (forall (X_13:int) (Y_10:int), ((iff ((ord_less_eq_int ((plus_plus_int ((power_power_int X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_10) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_13) zero_zero_int)) (((eq int) Y_10) zero_zero_int)))) of role axiom named fact_478_sum__power2__le__zero__iff
% 1.04/1.29 A new axiom: (forall (X_13:int) (Y_10:int), ((iff ((ord_less_eq_int ((plus_plus_int ((power_power_int X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_10) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_13) zero_zero_int)) (((eq int) Y_10) zero_zero_int))))
% 1.04/1.29 FOF formula (forall (X_12:real) (Y_9:real), (((ord_less_real ((plus_plus_real ((power_power_real X_12) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_9) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)->False)) of role axiom named fact_479_not__sum__power2__lt__zero
% 1.04/1.29 A new axiom: (forall (X_12:real) (Y_9:real), (((ord_less_real ((plus_plus_real ((power_power_real X_12) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_9) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)->False))
% 1.04/1.29 FOF formula (forall (X_12:int) (Y_9:int), (((ord_less_int ((plus_plus_int ((power_power_int X_12) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_9) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)->False)) of role axiom named fact_480_not__sum__power2__lt__zero
% 1.04/1.29 A new axiom: (forall (X_12:int) (Y_9:int), (((ord_less_int ((plus_plus_int ((power_power_int X_12) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_9) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)->False))
% 1.04/1.29 FOF formula (forall (X_11:real) (Y_8:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((power_power_real X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_8) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq real) X_11) zero_zero_real))) (not (((eq real) Y_8) zero_zero_real))))) of role axiom named fact_481_sum__power2__gt__zero__iff
% 1.04/1.31 A new axiom: (forall (X_11:real) (Y_8:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((power_power_real X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_8) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq real) X_11) zero_zero_real))) (not (((eq real) Y_8) zero_zero_real)))))
% 1.04/1.31 FOF formula (forall (X_11:int) (Y_8:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((power_power_int X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_8) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq int) X_11) zero_zero_int))) (not (((eq int) Y_8) zero_zero_int))))) of role axiom named fact_482_sum__power2__gt__zero__iff
% 1.04/1.31 A new axiom: (forall (X_11:int) (Y_8:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((power_power_int X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_8) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq int) X_11) zero_zero_int))) (not (((eq int) Y_8) zero_zero_int)))))
% 1.04/1.31 FOF formula (forall (A_71:real) (N_13:nat), ((ord_less_eq_real zero_zero_real) ((power_power_real A_71) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_13)))) of role axiom named fact_483_zero__le__even__power_H
% 1.04/1.31 A new axiom: (forall (A_71:real) (N_13:nat), ((ord_less_eq_real zero_zero_real) ((power_power_real A_71) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_13))))
% 1.04/1.31 FOF formula (forall (A_71:int) (N_13:nat), ((ord_less_eq_int zero_zero_int) ((power_power_int A_71) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_13)))) of role axiom named fact_484_zero__le__even__power_H
% 1.04/1.31 A new axiom: (forall (A_71:int) (N_13:nat), ((ord_less_eq_int zero_zero_int) ((power_power_int A_71) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_13))))
% 1.04/1.31 FOF formula (forall (N_12:nat) (A_70:real), (((ord_less_eq_real one_one_real) A_70)->((ord_less_eq_real one_one_real) ((power_power_real A_70) N_12)))) of role axiom named fact_485_one__le__power
% 1.04/1.31 A new axiom: (forall (N_12:nat) (A_70:real), (((ord_less_eq_real one_one_real) A_70)->((ord_less_eq_real one_one_real) ((power_power_real A_70) N_12))))
% 1.04/1.31 FOF formula (forall (N_12:nat) (A_70:nat), (((ord_less_eq_nat one_one_nat) A_70)->((ord_less_eq_nat one_one_nat) ((power_power_nat A_70) N_12)))) of role axiom named fact_486_one__le__power
% 1.04/1.31 A new axiom: (forall (N_12:nat) (A_70:nat), (((ord_less_eq_nat one_one_nat) A_70)->((ord_less_eq_nat one_one_nat) ((power_power_nat A_70) N_12))))
% 1.04/1.31 FOF formula (forall (N_12:nat) (A_70:int), (((ord_less_eq_int one_one_int) A_70)->((ord_less_eq_int one_one_int) ((power_power_int A_70) N_12)))) of role axiom named fact_487_one__le__power
% 1.04/1.31 A new axiom: (forall (N_12:nat) (A_70:int), (((ord_less_eq_int one_one_int) A_70)->((ord_less_eq_int one_one_int) ((power_power_int A_70) N_12))))
% 1.04/1.31 FOF formula (forall (A_69:real) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_real one_one_real) A_69)->((ord_less_eq_real ((power_power_real A_69) N_11)) ((power_power_real A_69) N_10))))) of role axiom named fact_488_power__increasing
% 1.04/1.31 A new axiom: (forall (A_69:real) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_real one_one_real) A_69)->((ord_less_eq_real ((power_power_real A_69) N_11)) ((power_power_real A_69) N_10)))))
% 1.04/1.31 FOF formula (forall (A_69:nat) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_nat one_one_nat) A_69)->((ord_less_eq_nat ((power_power_nat A_69) N_11)) ((power_power_nat A_69) N_10))))) of role axiom named fact_489_power__increasing
% 1.04/1.31 A new axiom: (forall (A_69:nat) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_nat one_one_nat) A_69)->((ord_less_eq_nat ((power_power_nat A_69) N_11)) ((power_power_nat A_69) N_10)))))
% 1.04/1.31 FOF formula (forall (A_69:int) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_int one_one_int) A_69)->((ord_less_eq_int ((power_power_int A_69) N_11)) ((power_power_int A_69) N_10))))) of role axiom named fact_490_power__increasing
% 1.14/1.33 A new axiom: (forall (A_69:int) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_int one_one_int) A_69)->((ord_less_eq_int ((power_power_int A_69) N_11)) ((power_power_int A_69) N_10)))))
% 1.14/1.33 FOF formula (forall (M_4:nat) (N_9:nat) (A_68:real), (((ord_less_real one_one_real) A_68)->((iff (((eq real) ((power_power_real A_68) M_4)) ((power_power_real A_68) N_9))) (((eq nat) M_4) N_9)))) of role axiom named fact_491_power__inject__exp
% 1.14/1.33 A new axiom: (forall (M_4:nat) (N_9:nat) (A_68:real), (((ord_less_real one_one_real) A_68)->((iff (((eq real) ((power_power_real A_68) M_4)) ((power_power_real A_68) N_9))) (((eq nat) M_4) N_9))))
% 1.14/1.33 FOF formula (forall (M_4:nat) (N_9:nat) (A_68:nat), (((ord_less_nat one_one_nat) A_68)->((iff (((eq nat) ((power_power_nat A_68) M_4)) ((power_power_nat A_68) N_9))) (((eq nat) M_4) N_9)))) of role axiom named fact_492_power__inject__exp
% 1.14/1.33 A new axiom: (forall (M_4:nat) (N_9:nat) (A_68:nat), (((ord_less_nat one_one_nat) A_68)->((iff (((eq nat) ((power_power_nat A_68) M_4)) ((power_power_nat A_68) N_9))) (((eq nat) M_4) N_9))))
% 1.14/1.33 FOF formula (forall (M_4:nat) (N_9:nat) (A_68:int), (((ord_less_int one_one_int) A_68)->((iff (((eq int) ((power_power_int A_68) M_4)) ((power_power_int A_68) N_9))) (((eq nat) M_4) N_9)))) of role axiom named fact_493_power__inject__exp
% 1.14/1.33 A new axiom: (forall (M_4:nat) (N_9:nat) (A_68:int), (((ord_less_int one_one_int) A_68)->((iff (((eq int) ((power_power_int A_68) M_4)) ((power_power_int A_68) N_9))) (((eq nat) M_4) N_9))))
% 1.14/1.33 FOF formula (forall (X_10:nat) (Y_7:nat) (B_55:real), (((ord_less_real one_one_real) B_55)->((iff ((ord_less_real ((power_power_real B_55) X_10)) ((power_power_real B_55) Y_7))) ((ord_less_nat X_10) Y_7)))) of role axiom named fact_494_power__strict__increasing__iff
% 1.14/1.33 A new axiom: (forall (X_10:nat) (Y_7:nat) (B_55:real), (((ord_less_real one_one_real) B_55)->((iff ((ord_less_real ((power_power_real B_55) X_10)) ((power_power_real B_55) Y_7))) ((ord_less_nat X_10) Y_7))))
% 1.14/1.33 FOF formula (forall (X_10:nat) (Y_7:nat) (B_55:nat), (((ord_less_nat one_one_nat) B_55)->((iff ((ord_less_nat ((power_power_nat B_55) X_10)) ((power_power_nat B_55) Y_7))) ((ord_less_nat X_10) Y_7)))) of role axiom named fact_495_power__strict__increasing__iff
% 1.14/1.33 A new axiom: (forall (X_10:nat) (Y_7:nat) (B_55:nat), (((ord_less_nat one_one_nat) B_55)->((iff ((ord_less_nat ((power_power_nat B_55) X_10)) ((power_power_nat B_55) Y_7))) ((ord_less_nat X_10) Y_7))))
% 1.14/1.33 FOF formula (forall (X_10:nat) (Y_7:nat) (B_55:int), (((ord_less_int one_one_int) B_55)->((iff ((ord_less_int ((power_power_int B_55) X_10)) ((power_power_int B_55) Y_7))) ((ord_less_nat X_10) Y_7)))) of role axiom named fact_496_power__strict__increasing__iff
% 1.14/1.33 A new axiom: (forall (X_10:nat) (Y_7:nat) (B_55:int), (((ord_less_int one_one_int) B_55)->((iff ((ord_less_int ((power_power_int B_55) X_10)) ((power_power_int B_55) Y_7))) ((ord_less_nat X_10) Y_7))))
% 1.14/1.33 FOF formula (forall (M_3:nat) (N_8:nat) (A_67:real), (((ord_less_real one_one_real) A_67)->(((ord_less_real ((power_power_real A_67) M_3)) ((power_power_real A_67) N_8))->((ord_less_nat M_3) N_8)))) of role axiom named fact_497_power__less__imp__less__exp
% 1.14/1.33 A new axiom: (forall (M_3:nat) (N_8:nat) (A_67:real), (((ord_less_real one_one_real) A_67)->(((ord_less_real ((power_power_real A_67) M_3)) ((power_power_real A_67) N_8))->((ord_less_nat M_3) N_8))))
% 1.14/1.33 FOF formula (forall (M_3:nat) (N_8:nat) (A_67:nat), (((ord_less_nat one_one_nat) A_67)->(((ord_less_nat ((power_power_nat A_67) M_3)) ((power_power_nat A_67) N_8))->((ord_less_nat M_3) N_8)))) of role axiom named fact_498_power__less__imp__less__exp
% 1.14/1.33 A new axiom: (forall (M_3:nat) (N_8:nat) (A_67:nat), (((ord_less_nat one_one_nat) A_67)->(((ord_less_nat ((power_power_nat A_67) M_3)) ((power_power_nat A_67) N_8))->((ord_less_nat M_3) N_8))))
% 1.14/1.33 FOF formula (forall (M_3:nat) (N_8:nat) (A_67:int), (((ord_less_int one_one_int) A_67)->(((ord_less_int ((power_power_int A_67) M_3)) ((power_power_int A_67) N_8))->((ord_less_nat M_3) N_8)))) of role axiom named fact_499_power__less__imp__less__exp
% 1.14/1.35 A new axiom: (forall (M_3:nat) (N_8:nat) (A_67:int), (((ord_less_int one_one_int) A_67)->(((ord_less_int ((power_power_int A_67) M_3)) ((power_power_int A_67) N_8))->((ord_less_nat M_3) N_8))))
% 1.14/1.35 FOF formula (forall (A_66:real) (N_7:nat) (N_6:nat), (((ord_less_nat N_7) N_6)->(((ord_less_real one_one_real) A_66)->((ord_less_real ((power_power_real A_66) N_7)) ((power_power_real A_66) N_6))))) of role axiom named fact_500_power__strict__increasing
% 1.14/1.35 A new axiom: (forall (A_66:real) (N_7:nat) (N_6:nat), (((ord_less_nat N_7) N_6)->(((ord_less_real one_one_real) A_66)->((ord_less_real ((power_power_real A_66) N_7)) ((power_power_real A_66) N_6)))))
% 1.14/1.35 FOF formula (forall (A_66:nat) (N_7:nat) (N_6:nat), (((ord_less_nat N_7) N_6)->(((ord_less_nat one_one_nat) A_66)->((ord_less_nat ((power_power_nat A_66) N_7)) ((power_power_nat A_66) N_6))))) of role axiom named fact_501_power__strict__increasing
% 1.14/1.35 A new axiom: (forall (A_66:nat) (N_7:nat) (N_6:nat), (((ord_less_nat N_7) N_6)->(((ord_less_nat one_one_nat) A_66)->((ord_less_nat ((power_power_nat A_66) N_7)) ((power_power_nat A_66) N_6)))))
% 1.14/1.35 FOF formula (forall (A_66:int) (N_7:nat) (N_6:nat), (((ord_less_nat N_7) N_6)->(((ord_less_int one_one_int) A_66)->((ord_less_int ((power_power_int A_66) N_7)) ((power_power_int A_66) N_6))))) of role axiom named fact_502_power__strict__increasing
% 1.14/1.35 A new axiom: (forall (A_66:int) (N_7:nat) (N_6:nat), (((ord_less_nat N_7) N_6)->(((ord_less_int one_one_int) A_66)->((ord_less_int ((power_power_int A_66) N_7)) ((power_power_int A_66) N_6)))))
% 1.14/1.35 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_503_s
% 1.14/1.35 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))
% 1.14/1.35 FOF formula (forall (Y_1:int) (X_1:int) (P:int), (((((zcong X_1) zero_zero_int) P)->False)->((((zcong ((power_power_int Y_1) (number_number_of_nat (bit0 (bit1 pls))))) X_1) P)->(((dvd_dvd_int P) Y_1)->False)))) of role axiom named fact_504_Euler_Oaux____1
% 1.14/1.35 A new axiom: (forall (Y_1:int) (X_1:int) (P:int), (((((zcong X_1) zero_zero_int) P)->False)->((((zcong ((power_power_int Y_1) (number_number_of_nat (bit0 (bit1 pls))))) X_1) P)->(((dvd_dvd_int P) Y_1)->False))))
% 1.14/1.35 FOF formula (forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_int X_1) (number_number_of_int (bit0 (bit1 pls))))->((or (((eq int) X_1) zero_zero_int)) (((eq int) X_1) one_one_int))))) of role axiom named fact_505_int__pos__lt__two__imp__zero__or__one
% 1.14/1.35 A new axiom: (forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_int X_1) (number_number_of_int (bit0 (bit1 pls))))->((or (((eq int) X_1) zero_zero_int)) (((eq int) X_1) one_one_int)))))
% 1.14/1.35 FOF formula (forall (A_65:real) (K_3:nat), (((ord_less_eq_real ((power_power_real A_65) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_3))) zero_zero_real)->(((eq real) A_65) zero_zero_real))) of role axiom named fact_506_even__power__le__0__imp__0
% 1.14/1.35 A new axiom: (forall (A_65:real) (K_3:nat), (((ord_less_eq_real ((power_power_real A_65) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_3))) zero_zero_real)->(((eq real) A_65) zero_zero_real)))
% 1.14/1.35 FOF formula (forall (A_65:int) (K_3:nat), (((ord_less_eq_int ((power_power_int A_65) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_3))) zero_zero_int)->(((eq int) A_65) zero_zero_int))) of role axiom named fact_507_even__power__le__0__imp__0
% 1.14/1.35 A new axiom: (forall (A_65:int) (K_3:nat), (((ord_less_eq_int ((power_power_int A_65) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_3))) zero_zero_int)->(((eq int) A_65) zero_zero_int)))
% 1.14/1.35 FOF formula (forall (P:int), ((iff (zprime P)) ((and ((ord_less_int one_one_int) P)) (forall (M_2:int), (((and ((ord_less_eq_int zero_zero_int) M_2)) ((dvd_dvd_int M_2) P))->((or (((eq int) M_2) one_one_int)) (((eq int) M_2) P))))))) of role axiom named fact_508_zprime__def
% 1.14/1.36 A new axiom: (forall (P:int), ((iff (zprime P)) ((and ((ord_less_int one_one_int) P)) (forall (M_2:int), (((and ((ord_less_eq_int zero_zero_int) M_2)) ((dvd_dvd_int M_2) P))->((or (((eq int) M_2) one_one_int)) (((eq int) M_2) P)))))))
% 1.14/1.36 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_509_self__quotient__aux2
% 1.14/1.36 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)))))
% 1.14/1.36 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_510_self__quotient__aux1
% 1.14/1.36 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)))))
% 1.14/1.36 FOF formula ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 (bit1 pls)))) of role axiom named fact_511_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J
% 1.14/1.36 A new axiom: ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 (bit1 pls))))
% 1.14/1.36 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_512__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_
% 1.14/1.36 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)
% 1.14/1.36 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_513__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096
% 1.14/1.36 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)
% 1.14/1.36 FOF formula (forall (X_1:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) N))) ((or ((ord_less_nat zero_zero_nat) X_1)) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_514_nat__zero__less__power__iff
% 1.14/1.36 A new axiom: (forall (X_1:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) N))) ((or ((ord_less_nat zero_zero_nat) X_1)) (((eq nat) N) zero_zero_nat))))
% 1.14/1.36 FOF formula (forall (X_1:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) N))) ((or (((eq nat) N) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X_1)))) of role axiom named fact_515_zero__less__power__nat__eq
% 1.14/1.36 A new axiom: (forall (X_1:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) N))) ((or (((eq nat) N) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X_1))))
% 1.14/1.36 FOF formula (forall (X_1:nat) (W:int), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) (number_number_of_nat W)))) ((or (((eq nat) (number_number_of_nat W)) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X_1)))) of role axiom named fact_516_zero__less__power__nat__eq__number__of
% 1.14/1.36 A new axiom: (forall (X_1:nat) (W:int), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) (number_number_of_nat W)))) ((or (((eq nat) (number_number_of_nat W)) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X_1))))
% 1.14/1.36 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_517_nat__power__less__imp__less
% 1.14/1.38 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))))
% 1.14/1.38 FOF formula (forall (K:int), ((iff (((eq int) (bit1 K)) min)) (((eq int) K) min))) of role axiom named fact_518_rel__simps_I47_J
% 1.14/1.38 A new axiom: (forall (K:int), ((iff (((eq int) (bit1 K)) min)) (((eq int) K) min)))
% 1.14/1.38 FOF formula (forall (L:int), ((iff (((eq int) min) (bit1 L))) (((eq int) min) L))) of role axiom named fact_519_rel__simps_I43_J
% 1.14/1.38 A new axiom: (forall (L:int), ((iff (((eq int) min) (bit1 L))) (((eq int) min) L)))
% 1.14/1.38 FOF formula (((eq int) (bit1 min)) min) of role axiom named fact_520_Bit1__Min
% 1.14/1.38 A new axiom: (((eq int) (bit1 min)) min)
% 1.14/1.38 FOF formula (not (((eq int) pls) min)) of role axiom named fact_521_rel__simps_I37_J
% 1.14/1.38 A new axiom: (not (((eq int) pls) min))
% 1.14/1.38 FOF formula (not (((eq int) min) pls)) of role axiom named fact_522_rel__simps_I40_J
% 1.14/1.38 A new axiom: (not (((eq int) min) pls))
% 1.14/1.38 FOF formula (forall (K:int), (not (((eq int) (bit0 K)) min))) of role axiom named fact_523_rel__simps_I45_J
% 1.14/1.38 A new axiom: (forall (K:int), (not (((eq int) (bit0 K)) min)))
% 1.14/1.38 FOF formula (forall (L:int), (not (((eq int) min) (bit0 L)))) of role axiom named fact_524_rel__simps_I42_J
% 1.14/1.38 A new axiom: (forall (L:int), (not (((eq int) min) (bit0 L))))
% 1.14/1.38 FOF formula (((ord_less_int min) min)->False) of role axiom named fact_525_rel__simps_I7_J
% 1.14/1.38 A new axiom: (((ord_less_int min) min)->False)
% 1.14/1.38 FOF formula ((ord_less_eq_int min) min) of role axiom named fact_526_rel__simps_I24_J
% 1.14/1.38 A new axiom: ((ord_less_eq_int min) min)
% 1.14/1.38 FOF formula (forall (X_1:real), ((iff (((ord_less_real zero_zero_real) ((times_times_real X_1) X_1))->False)) (((eq real) X_1) zero_zero_real))) of role axiom named fact_527_not__real__square__gt__zero
% 1.14/1.38 A new axiom: (forall (X_1:real), ((iff (((ord_less_real zero_zero_real) ((times_times_real X_1) X_1))->False)) (((eq real) X_1) zero_zero_real)))
% 1.14/1.38 FOF formula (forall (K:int), ((iff ((ord_less_int (bit1 K)) min)) ((ord_less_int K) min))) of role axiom named fact_528_rel__simps_I13_J
% 1.14/1.38 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit1 K)) min)) ((ord_less_int K) min)))
% 1.14/1.38 FOF formula (forall (K:int), ((iff ((ord_less_int min) (bit1 K))) ((ord_less_int min) K))) of role axiom named fact_529_rel__simps_I9_J
% 1.14/1.38 A new axiom: (forall (K:int), ((iff ((ord_less_int min) (bit1 K))) ((ord_less_int min) K)))
% 1.14/1.38 FOF formula (((ord_less_int pls) min)->False) of role axiom named fact_530_rel__simps_I3_J
% 1.14/1.38 A new axiom: (((ord_less_int pls) min)->False)
% 1.14/1.38 FOF formula ((ord_less_int min) pls) of role axiom named fact_531_rel__simps_I6_J
% 1.14/1.38 A new axiom: ((ord_less_int min) pls)
% 1.14/1.38 FOF formula (forall (K:int), ((iff ((ord_less_int min) (bit0 K))) ((ord_less_int min) K))) of role axiom named fact_532_rel__simps_I8_J
% 1.14/1.38 A new axiom: (forall (K:int), ((iff ((ord_less_int min) (bit0 K))) ((ord_less_int min) K)))
% 1.14/1.38 FOF formula ((ord_less_int min) zero_zero_int) of role axiom named fact_533_bin__less__0__simps_I2_J
% 1.14/1.38 A new axiom: ((ord_less_int min) zero_zero_int)
% 1.14/1.38 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) min)) ((ord_less_eq_int K) min))) of role axiom named fact_534_rel__simps_I30_J
% 1.14/1.38 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) min)) ((ord_less_eq_int K) min)))
% 1.14/1.38 FOF formula (forall (K:int), ((iff ((ord_less_eq_int min) (bit1 K))) ((ord_less_eq_int min) K))) of role axiom named fact_535_rel__simps_I26_J
% 1.14/1.38 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int min) (bit1 K))) ((ord_less_eq_int min) K)))
% 1.14/1.38 FOF formula (((ord_less_eq_int pls) min)->False) of role axiom named fact_536_rel__simps_I20_J
% 1.14/1.38 A new axiom: (((ord_less_eq_int pls) min)->False)
% 1.14/1.38 FOF formula ((ord_less_eq_int min) pls) of role axiom named fact_537_rel__simps_I23_J
% 1.14/1.38 A new axiom: ((ord_less_eq_int min) pls)
% 1.14/1.38 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) min)) ((ord_less_eq_int K) min))) of role axiom named fact_538_rel__simps_I28_J
% 1.14/1.38 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) min)) ((ord_less_eq_int K) min)))
% 1.14/1.39 FOF formula (not (((eq int) (number_number_of_int pls)) (number_number_of_int min))) of role axiom named fact_539_eq__number__of__Pls__Min
% 1.14/1.39 A new axiom: (not (((eq int) (number_number_of_int pls)) (number_number_of_int min)))
% 1.14/1.39 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_540_power__dvd__imp__le
% 1.14/1.39 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))))
% 1.14/1.39 FOF formula (forall (X_9:real), (((eq real) ((power_power_real X_9) zero_zero_nat)) one_one_real)) of role axiom named fact_541_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J
% 1.14/1.39 A new axiom: (forall (X_9:real), (((eq real) ((power_power_real X_9) zero_zero_nat)) one_one_real))
% 1.14/1.39 FOF formula (forall (X_9:nat), (((eq nat) ((power_power_nat X_9) zero_zero_nat)) one_one_nat)) of role axiom named fact_542_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J
% 1.14/1.39 A new axiom: (forall (X_9:nat), (((eq nat) ((power_power_nat X_9) zero_zero_nat)) one_one_nat))
% 1.14/1.39 FOF formula (forall (X_9:int), (((eq int) ((power_power_int X_9) zero_zero_nat)) one_one_int)) of role axiom named fact_543_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J
% 1.14/1.39 A new axiom: (forall (X_9:int), (((eq int) ((power_power_int X_9) zero_zero_nat)) one_one_int))
% 1.14/1.39 FOF formula (forall (A_64:real), (((eq real) ((power_power_real A_64) zero_zero_nat)) one_one_real)) of role axiom named fact_544_power__0
% 1.14/1.39 A new axiom: (forall (A_64:real), (((eq real) ((power_power_real A_64) zero_zero_nat)) one_one_real))
% 1.14/1.39 FOF formula (forall (A_64:nat), (((eq nat) ((power_power_nat A_64) zero_zero_nat)) one_one_nat)) of role axiom named fact_545_power__0
% 1.14/1.39 A new axiom: (forall (A_64:nat), (((eq nat) ((power_power_nat A_64) zero_zero_nat)) one_one_nat))
% 1.14/1.39 FOF formula (forall (A_64:int), (((eq int) ((power_power_int A_64) zero_zero_nat)) one_one_int)) of role axiom named fact_546_power__0
% 1.14/1.39 A new axiom: (forall (A_64:int), (((eq int) ((power_power_int A_64) zero_zero_nat)) one_one_int))
% 1.14/1.39 FOF formula (((eq nat) (number_number_of_nat pls)) zero_zero_nat) of role axiom named fact_547_nat__number__of__Pls
% 1.14/1.39 A new axiom: (((eq nat) (number_number_of_nat pls)) zero_zero_nat)
% 1.14/1.39 FOF formula (((eq nat) zero_zero_nat) (number_number_of_nat pls)) of role axiom named fact_548_semiring__norm_I113_J
% 1.14/1.39 A new axiom: (((eq nat) zero_zero_nat) (number_number_of_nat pls))
% 1.14/1.39 FOF formula (forall (K:int), ((iff ((ord_less_eq_int min) (bit0 K))) ((ord_less_int min) K))) of role axiom named fact_549_rel__simps_I25_J
% 1.14/1.39 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int min) (bit0 K))) ((ord_less_int min) K)))
% 1.14/1.39 FOF formula (forall (K:int), ((iff ((ord_less_int (bit0 K)) min)) ((ord_less_eq_int K) min))) of role axiom named fact_550_rel__simps_I11_J
% 1.14/1.39 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit0 K)) min)) ((ord_less_eq_int K) min)))
% 1.14/1.39 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_551_pos__zmult__eq__1__iff__lemma
% 1.14/1.39 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)))))
% 1.14/1.39 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_552_zmult__eq__1__iff
% 1.14/1.39 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))))))
% 1.14/1.39 FOF formula (forall (N_5:nat) (A_63:real), (((ord_less_real one_one_real) A_63)->(((ord_less_nat zero_zero_nat) N_5)->((ord_less_real one_one_real) ((power_power_real A_63) N_5))))) of role axiom named fact_553_one__less__power
% 1.21/1.41 A new axiom: (forall (N_5:nat) (A_63:real), (((ord_less_real one_one_real) A_63)->(((ord_less_nat zero_zero_nat) N_5)->((ord_less_real one_one_real) ((power_power_real A_63) N_5)))))
% 1.21/1.41 FOF formula (forall (N_5:nat) (A_63:nat), (((ord_less_nat one_one_nat) A_63)->(((ord_less_nat zero_zero_nat) N_5)->((ord_less_nat one_one_nat) ((power_power_nat A_63) N_5))))) of role axiom named fact_554_one__less__power
% 1.21/1.41 A new axiom: (forall (N_5:nat) (A_63:nat), (((ord_less_nat one_one_nat) A_63)->(((ord_less_nat zero_zero_nat) N_5)->((ord_less_nat one_one_nat) ((power_power_nat A_63) N_5)))))
% 1.21/1.41 FOF formula (forall (N_5:nat) (A_63:int), (((ord_less_int one_one_int) A_63)->(((ord_less_nat zero_zero_nat) N_5)->((ord_less_int one_one_int) ((power_power_int A_63) N_5))))) of role axiom named fact_555_one__less__power
% 1.21/1.41 A new axiom: (forall (N_5:nat) (A_63:int), (((ord_less_int one_one_int) A_63)->(((ord_less_nat zero_zero_nat) N_5)->((ord_less_int one_one_int) ((power_power_int A_63) N_5)))))
% 1.21/1.41 FOF formula (forall (X_8:real) (N_4:nat), (((or ((ord_less_nat zero_zero_nat) N_4)) (((eq real) X_8) one_one_real))->((dvd_dvd_real X_8) ((power_power_real X_8) N_4)))) of role axiom named fact_556_dvd__power
% 1.21/1.41 A new axiom: (forall (X_8:real) (N_4:nat), (((or ((ord_less_nat zero_zero_nat) N_4)) (((eq real) X_8) one_one_real))->((dvd_dvd_real X_8) ((power_power_real X_8) N_4))))
% 1.21/1.41 FOF formula (forall (X_8:nat) (N_4:nat), (((or ((ord_less_nat zero_zero_nat) N_4)) (((eq nat) X_8) one_one_nat))->((dvd_dvd_nat X_8) ((power_power_nat X_8) N_4)))) of role axiom named fact_557_dvd__power
% 1.21/1.41 A new axiom: (forall (X_8:nat) (N_4:nat), (((or ((ord_less_nat zero_zero_nat) N_4)) (((eq nat) X_8) one_one_nat))->((dvd_dvd_nat X_8) ((power_power_nat X_8) N_4))))
% 1.21/1.41 FOF formula (forall (X_8:int) (N_4:nat), (((or ((ord_less_nat zero_zero_nat) N_4)) (((eq int) X_8) one_one_int))->((dvd_dvd_int X_8) ((power_power_int X_8) N_4)))) of role axiom named fact_558_dvd__power
% 1.21/1.41 A new axiom: (forall (X_8:int) (N_4:nat), (((or ((ord_less_nat zero_zero_nat) N_4)) (((eq int) X_8) one_one_int))->((dvd_dvd_int X_8) ((power_power_int X_8) N_4))))
% 1.21/1.41 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_559_less__0__number__of
% 1.21/1.41 A new axiom: (forall (V:int), ((iff ((ord_less_nat zero_zero_nat) (number_number_of_nat V))) ((ord_less_int pls) V)))
% 1.21/1.41 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_560_eq__number__of__0
% 1.21/1.41 A new axiom: (forall (V:int), ((iff (((eq nat) (number_number_of_nat V)) zero_zero_nat)) ((ord_less_eq_int V) pls)))
% 1.21/1.41 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_561_eq__0__number__of
% 1.21/1.41 A new axiom: (forall (V:int), ((iff (((eq nat) zero_zero_nat) (number_number_of_nat V))) ((ord_less_eq_int V) pls)))
% 1.21/1.41 FOF formula (forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) (((zcong B) A) M))) of role axiom named fact_562_zcong__sym
% 1.21/1.41 A new axiom: (forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) (((zcong B) A) M)))
% 1.21/1.41 FOF formula (forall (K:int) (M:int), (((zcong K) K) M)) of role axiom named fact_563_zcong__refl
% 1.21/1.41 A new axiom: (forall (K:int) (M:int), (((zcong K) K) M))
% 1.21/1.41 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_564_zcong__trans
% 1.21/1.41 A new axiom: (forall (C:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((zcong B) C) M)->(((zcong A) C) M))))
% 1.21/1.41 FOF formula ((ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls)))) of role axiom named fact_565_pos2
% 1.21/1.41 A new axiom: ((ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls))))
% 1.21/1.41 FOF formula (forall (V_6: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_6)) 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_6)) K))) ((times_times_nat (number_number_of_nat ((times_times_int V) V_6))) K))))) of role axiom named fact_566_nat__number__of__mult__left
% 1.21/1.43 A new axiom: (forall (V_6: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_6)) 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_6)) K))) ((times_times_nat (number_number_of_nat ((times_times_int V) V_6))) K)))))
% 1.21/1.43 FOF formula (forall (V_6:int) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((times_times_nat (number_number_of_nat V)) (number_number_of_nat V_6))) zero_zero_nat))) ((((ord_less_int V) pls)->False)->(((eq nat) ((times_times_nat (number_number_of_nat V)) (number_number_of_nat V_6))) (number_number_of_nat ((times_times_int V) V_6)))))) of role axiom named fact_567_mult__nat__number__of
% 1.21/1.43 A new axiom: (forall (V_6:int) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((times_times_nat (number_number_of_nat V)) (number_number_of_nat V_6))) zero_zero_nat))) ((((ord_less_int V) pls)->False)->(((eq nat) ((times_times_nat (number_number_of_nat V)) (number_number_of_nat V_6))) (number_number_of_nat ((times_times_int V) V_6))))))
% 1.21/1.43 FOF formula (forall (X_7:real) (Y_6:real), (((ord_less_eq_real X_7) Y_6)->((not (((eq real) X_7) Y_6))->((ord_less_real X_7) Y_6)))) of role axiom named fact_568_order__le__neq__implies__less
% 1.21/1.43 A new axiom: (forall (X_7:real) (Y_6:real), (((ord_less_eq_real X_7) Y_6)->((not (((eq real) X_7) Y_6))->((ord_less_real X_7) Y_6))))
% 1.21/1.43 FOF formula (forall (X_7:nat) (Y_6:nat), (((ord_less_eq_nat X_7) Y_6)->((not (((eq nat) X_7) Y_6))->((ord_less_nat X_7) Y_6)))) of role axiom named fact_569_order__le__neq__implies__less
% 1.21/1.43 A new axiom: (forall (X_7:nat) (Y_6:nat), (((ord_less_eq_nat X_7) Y_6)->((not (((eq nat) X_7) Y_6))->((ord_less_nat X_7) Y_6))))
% 1.21/1.43 FOF formula (forall (X_7:int) (Y_6:int), (((ord_less_eq_int X_7) Y_6)->((not (((eq int) X_7) Y_6))->((ord_less_int X_7) Y_6)))) of role axiom named fact_570_order__le__neq__implies__less
% 1.21/1.43 A new axiom: (forall (X_7:int) (Y_6:int), (((ord_less_eq_int X_7) Y_6)->((not (((eq int) X_7) Y_6))->((ord_less_int X_7) Y_6))))
% 1.21/1.43 FOF formula ((ord_less_eq_int zero_zero_int) zero_zero_int) of role axiom named fact_571_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J
% 1.21/1.43 A new axiom: ((ord_less_eq_int zero_zero_int) zero_zero_int)
% 1.21/1.43 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_572_Euler_Oaux2
% 1.21/1.43 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)))))
% 1.21/1.43 FOF formula (forall (A:int) (B:int), ((iff (((zcong A) B) zero_zero_int)) (((eq int) A) B))) of role axiom named fact_573_IntPrimes_Ozcong__zero
% 1.21/1.43 A new axiom: (forall (A:int) (B:int), ((iff (((zcong A) B) zero_zero_int)) (((eq int) A) B)))
% 1.21/1.43 FOF formula (forall (A:int) (B:int), (((zcong A) B) one_one_int)) of role axiom named fact_574_zcong__1
% 1.21/1.43 A new axiom: (forall (A:int) (B:int), (((zcong A) B) one_one_int))
% 1.21/1.43 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_575_zcong__zmult
% 1.21/1.43 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))))
% 1.21/1.43 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_576_zcong__scalar2
% 1.21/1.43 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)))
% 1.21/1.43 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_577_zcong__scalar
% 1.21/1.45 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)))
% 1.21/1.45 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_578_zcong__zmult__self
% 1.21/1.45 A new axiom: (forall (A:int) (M:int) (B:int), (((zcong ((times_times_int A) M)) ((times_times_int B) M)) M))
% 1.21/1.45 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_579_zcong__zadd
% 1.21/1.45 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))))
% 1.21/1.45 FOF formula (forall (N_3:nat), (((eq real) ((power_power_real (number267125858f_real min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_3))) one_one_real)) of role axiom named fact_580_power__m1__even
% 1.21/1.45 A new axiom: (forall (N_3:nat), (((eq real) ((power_power_real (number267125858f_real min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_3))) one_one_real))
% 1.21/1.45 FOF formula (forall (N_3:nat), (((eq int) ((power_power_int (number_number_of_int min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_3))) one_one_int)) of role axiom named fact_581_power__m1__even
% 1.21/1.45 A new axiom: (forall (N_3:nat), (((eq int) ((power_power_int (number_number_of_int min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_3))) one_one_int))
% 1.21/1.45 FOF formula (forall (A_62:real) (W_4:int), ((iff (((eq real) ((power_power_real A_62) (number_number_of_nat W_4))) zero_zero_real)) ((and (((eq real) A_62) zero_zero_real)) (not (((eq nat) (number_number_of_nat W_4)) zero_zero_nat))))) of role axiom named fact_582_power__eq__0__iff__number__of
% 1.21/1.45 A new axiom: (forall (A_62:real) (W_4:int), ((iff (((eq real) ((power_power_real A_62) (number_number_of_nat W_4))) zero_zero_real)) ((and (((eq real) A_62) zero_zero_real)) (not (((eq nat) (number_number_of_nat W_4)) zero_zero_nat)))))
% 1.21/1.45 FOF formula (forall (A_62:nat) (W_4:int), ((iff (((eq nat) ((power_power_nat A_62) (number_number_of_nat W_4))) zero_zero_nat)) ((and (((eq nat) A_62) zero_zero_nat)) (not (((eq nat) (number_number_of_nat W_4)) zero_zero_nat))))) of role axiom named fact_583_power__eq__0__iff__number__of
% 1.21/1.45 A new axiom: (forall (A_62:nat) (W_4:int), ((iff (((eq nat) ((power_power_nat A_62) (number_number_of_nat W_4))) zero_zero_nat)) ((and (((eq nat) A_62) zero_zero_nat)) (not (((eq nat) (number_number_of_nat W_4)) zero_zero_nat)))))
% 1.21/1.45 FOF formula (forall (A_62:int) (W_4:int), ((iff (((eq int) ((power_power_int A_62) (number_number_of_nat W_4))) zero_zero_int)) ((and (((eq int) A_62) zero_zero_int)) (not (((eq nat) (number_number_of_nat W_4)) zero_zero_nat))))) of role axiom named fact_584_power__eq__0__iff__number__of
% 1.21/1.45 A new axiom: (forall (A_62:int) (W_4:int), ((iff (((eq int) ((power_power_int A_62) (number_number_of_nat W_4))) zero_zero_int)) ((and (((eq int) A_62) zero_zero_int)) (not (((eq nat) (number_number_of_nat W_4)) zero_zero_nat)))))
% 1.21/1.45 FOF formula ((ord_less_eq_int zero_zero_int) one_one_int) of role axiom named fact_585_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J
% 1.21/1.45 A new axiom: ((ord_less_eq_int zero_zero_int) one_one_int)
% 1.21/1.45 FOF formula (forall (Y_1:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_eq_int zero_zero_int) Y_1)->((ord_less_eq_int zero_zero_int) ((times_times_int X_1) Y_1))))) of role axiom named fact_586_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J
% 1.21/1.45 A new axiom: (forall (Y_1:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_eq_int zero_zero_int) Y_1)->((ord_less_eq_int zero_zero_int) ((times_times_int X_1) Y_1)))))
% 1.21/1.45 FOF formula (forall (Y_1:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_eq_int zero_zero_int) Y_1)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X_1) Y_1))))) of role axiom named fact_587_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J
% 1.21/1.46 A new axiom: (forall (Y_1:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_eq_int zero_zero_int) Y_1)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X_1) Y_1)))))
% 1.21/1.46 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_588_zcong__not
% 1.21/1.46 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))))))
% 1.21/1.46 FOF formula (forall (N:nat) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->((ord_less_eq_int zero_zero_int) ((power_power_int X_1) N)))) of role axiom named fact_589_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J
% 1.21/1.46 A new axiom: (forall (N:nat) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->((ord_less_eq_int zero_zero_int) ((power_power_int X_1) N))))
% 1.21/1.46 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_590_zcong__iff__lin
% 1.21/1.46 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)))))))
% 1.21/1.46 FOF formula (forall (W_3:int), ((and ((((eq nat) (number_number_of_nat W_3)) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_3))) one_one_real))) ((not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_3))) zero_zero_real)))) of role axiom named fact_591_power__0__left__number__of
% 1.21/1.46 A new axiom: (forall (W_3:int), ((and ((((eq nat) (number_number_of_nat W_3)) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_3))) one_one_real))) ((not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_3))) zero_zero_real))))
% 1.21/1.46 FOF formula (forall (W_3:int), ((and ((((eq nat) (number_number_of_nat W_3)) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_3))) one_one_nat))) ((not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_3))) zero_zero_nat)))) of role axiom named fact_592_power__0__left__number__of
% 1.21/1.46 A new axiom: (forall (W_3:int), ((and ((((eq nat) (number_number_of_nat W_3)) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_3))) one_one_nat))) ((not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_3))) zero_zero_nat))))
% 1.21/1.46 FOF formula (forall (W_3:int), ((and ((((eq nat) (number_number_of_nat W_3)) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_3))) one_one_int))) ((not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_3))) zero_zero_int)))) of role axiom named fact_593_power__0__left__number__of
% 1.21/1.46 A new axiom: (forall (W_3:int), ((and ((((eq nat) (number_number_of_nat W_3)) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_3))) one_one_int))) ((not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_3))) zero_zero_int))))
% 1.21/1.46 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_594_zcong__zless__imp__eq
% 1.21/1.46 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)))))))
% 1.29/1.49 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_595_zcong__zless__0
% 1.29/1.49 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)))))
% 1.29/1.49 FOF formula ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 (bit1 pls)))) of role axiom named fact_596_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J
% 1.29/1.49 A new axiom: ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 (bit1 pls))))
% 1.29/1.49 FOF formula (forall (B:int) (Q:int) (R:int) (B_54: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_54) Q_3)) R_2))->(((ord_less_int ((plus_plus_int ((times_times_int B_54) 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_54)->(((ord_less_eq_int B_54) B)->((ord_less_eq_int Q_3) Q)))))))) of role axiom named fact_597_zdiv__mono2__neg__lemma
% 1.29/1.49 A new axiom: (forall (B:int) (Q:int) (R:int) (B_54: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_54) Q_3)) R_2))->(((ord_less_int ((plus_plus_int ((times_times_int B_54) 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_54)->(((ord_less_eq_int B_54) B)->((ord_less_eq_int Q_3) Q))))))))
% 1.29/1.49 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_598_unique__quotient__lemma__neg
% 1.29/1.49 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))))))
% 1.29/1.49 FOF formula (forall (B:int) (Q:int) (R:int) (B_54: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_54) Q_3)) R_2))->(((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_54) Q_3)) R_2))->(((ord_less_int R_2) B_54)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int zero_zero_int) B_54)->(((ord_less_eq_int B_54) B)->((ord_less_eq_int Q) Q_3)))))))) of role axiom named fact_599_zdiv__mono2__lemma
% 1.29/1.49 A new axiom: (forall (B:int) (Q:int) (R:int) (B_54: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_54) Q_3)) R_2))->(((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_54) Q_3)) R_2))->(((ord_less_int R_2) B_54)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int zero_zero_int) B_54)->(((ord_less_eq_int B_54) B)->((ord_less_eq_int Q) Q_3))))))))
% 1.29/1.49 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_600_unique__quotient__lemma
% 1.29/1.49 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))))))
% 1.29/1.49 FOF formula (forall (B_54:int) (Q_3:int) (R_2:int), (((ord_less_int ((plus_plus_int ((times_times_int B_54) Q_3)) R_2)) zero_zero_int)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B_54)->((ord_less_eq_int Q_3) zero_zero_int))))) of role axiom named fact_601_q__neg__lemma
% 1.32/1.50 A new axiom: (forall (B_54:int) (Q_3:int) (R_2:int), (((ord_less_int ((plus_plus_int ((times_times_int B_54) Q_3)) R_2)) zero_zero_int)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B_54)->((ord_less_eq_int Q_3) zero_zero_int)))))
% 1.32/1.50 FOF formula (forall (B_54:int) (Q_3:int) (R_2:int), (((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_54) Q_3)) R_2))->(((ord_less_int R_2) B_54)->(((ord_less_int zero_zero_int) B_54)->((ord_less_eq_int zero_zero_int) Q_3))))) of role axiom named fact_602_q__pos__lemma
% 1.32/1.50 A new axiom: (forall (B_54:int) (Q_3:int) (R_2:int), (((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_54) Q_3)) R_2))->(((ord_less_int R_2) B_54)->(((ord_less_int zero_zero_int) B_54)->((ord_less_eq_int zero_zero_int) Q_3)))))
% 1.32/1.50 FOF formula (forall (N:int) (P:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->((zprime P)->(((dvd_dvd_int P) ((times_times_int M) N))->((or ((dvd_dvd_int P) M)) ((dvd_dvd_int P) N)))))) of role axiom named fact_603_zprime__zdvd__zmult
% 1.32/1.50 A new axiom: (forall (N:int) (P:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->((zprime P)->(((dvd_dvd_int P) ((times_times_int M) N))->((or ((dvd_dvd_int P) M)) ((dvd_dvd_int P) N))))))
% 1.32/1.50 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_604__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096
% 1.32/1.50 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))
% 1.32/1.50 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_605__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096
% 1.32/1.50 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)))
% 1.32/1.50 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_606_neg__one__power__eq__mod__m
% 1.32/1.50 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)))))
% 1.32/1.50 FOF formula (forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((((zcong X_1) (number_number_of_int min)) P)->((((zcong X_1) one_one_int) P)->False)))) of role axiom named fact_607_zcong__neg__1__impl__ne__1
% 1.32/1.50 A new axiom: (forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((((zcong X_1) (number_number_of_int min)) P)->((((zcong X_1) one_one_int) P)->False))))
% 1.32/1.50 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_608_one__not__neg__one__mod__m
% 1.32/1.50 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)))
% 1.32/1.50 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_609__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096
% 1.32/1.50 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))
% 1.34/1.52 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_610__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N
% 1.34/1.52 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)))
% 1.34/1.52 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_611_Int2_Oaux1
% 1.34/1.52 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))))
% 1.34/1.52 FOF formula (forall (V_5:int) (W_2:int), (((eq real) (number267125858f_real ((minus_minus_int V_5) W_2))) ((minus_minus_real (number267125858f_real V_5)) (number267125858f_real W_2)))) of role axiom named fact_612_number__of__diff
% 1.34/1.52 A new axiom: (forall (V_5:int) (W_2:int), (((eq real) (number267125858f_real ((minus_minus_int V_5) W_2))) ((minus_minus_real (number267125858f_real V_5)) (number267125858f_real W_2))))
% 1.34/1.52 FOF formula (forall (V_5:int) (W_2:int), (((eq int) (number_number_of_int ((minus_minus_int V_5) W_2))) ((minus_minus_int (number_number_of_int V_5)) (number_number_of_int W_2)))) of role axiom named fact_613_number__of__diff
% 1.34/1.52 A new axiom: (forall (V_5:int) (W_2:int), (((eq int) (number_number_of_int ((minus_minus_int V_5) W_2))) ((minus_minus_int (number_number_of_int V_5)) (number_number_of_int W_2))))
% 1.34/1.52 FOF formula (forall (K:int), (((eq int) ((minus_minus_int K) pls)) K)) of role axiom named fact_614_diff__bin__simps_I1_J
% 1.34/1.52 A new axiom: (forall (K:int), (((eq int) ((minus_minus_int K) pls)) K))
% 1.34/1.52 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_615_diff__bin__simps_I7_J
% 1.34/1.52 A new axiom: (forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit0 K)) (bit0 L))) (bit0 ((minus_minus_int K) L))))
% 1.34/1.52 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_616_zdiff__zmult__distrib2
% 1.34/1.52 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))))
% 1.34/1.52 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_617_zdiff__zmult__distrib
% 1.34/1.52 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))))
% 1.34/1.52 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_618_zcong__zdiff
% 1.34/1.52 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))))
% 1.34/1.52 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_619_zdvd__zdiffD
% 1.34/1.52 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))))
% 1.34/1.52 FOF formula (forall (V_4:int) (B_53:real) (C_29:real), (((eq real) ((times_times_real (number267125858f_real V_4)) ((minus_minus_real B_53) C_29))) ((minus_minus_real ((times_times_real (number267125858f_real V_4)) B_53)) ((times_times_real (number267125858f_real V_4)) C_29)))) of role axiom named fact_620_right__diff__distrib__number__of
% 1.34/1.54 A new axiom: (forall (V_4:int) (B_53:real) (C_29:real), (((eq real) ((times_times_real (number267125858f_real V_4)) ((minus_minus_real B_53) C_29))) ((minus_minus_real ((times_times_real (number267125858f_real V_4)) B_53)) ((times_times_real (number267125858f_real V_4)) C_29))))
% 1.34/1.54 FOF formula (forall (V_4:int) (B_53:int) (C_29:int), (((eq int) ((times_times_int (number_number_of_int V_4)) ((minus_minus_int B_53) C_29))) ((minus_minus_int ((times_times_int (number_number_of_int V_4)) B_53)) ((times_times_int (number_number_of_int V_4)) C_29)))) of role axiom named fact_621_right__diff__distrib__number__of
% 1.34/1.54 A new axiom: (forall (V_4:int) (B_53:int) (C_29:int), (((eq int) ((times_times_int (number_number_of_int V_4)) ((minus_minus_int B_53) C_29))) ((minus_minus_int ((times_times_int (number_number_of_int V_4)) B_53)) ((times_times_int (number_number_of_int V_4)) C_29))))
% 1.34/1.54 FOF formula (forall (A_61:real) (B_52:real) (V_3:int), (((eq real) ((times_times_real ((minus_minus_real A_61) B_52)) (number267125858f_real V_3))) ((minus_minus_real ((times_times_real A_61) (number267125858f_real V_3))) ((times_times_real B_52) (number267125858f_real V_3))))) of role axiom named fact_622_left__diff__distrib__number__of
% 1.34/1.54 A new axiom: (forall (A_61:real) (B_52:real) (V_3:int), (((eq real) ((times_times_real ((minus_minus_real A_61) B_52)) (number267125858f_real V_3))) ((minus_minus_real ((times_times_real A_61) (number267125858f_real V_3))) ((times_times_real B_52) (number267125858f_real V_3)))))
% 1.34/1.54 FOF formula (forall (A_61:int) (B_52:int) (V_3:int), (((eq int) ((times_times_int ((minus_minus_int A_61) B_52)) (number_number_of_int V_3))) ((minus_minus_int ((times_times_int A_61) (number_number_of_int V_3))) ((times_times_int B_52) (number_number_of_int V_3))))) of role axiom named fact_623_left__diff__distrib__number__of
% 1.34/1.54 A new axiom: (forall (A_61:int) (B_52:int) (V_3:int), (((eq int) ((times_times_int ((minus_minus_int A_61) B_52)) (number_number_of_int V_3))) ((minus_minus_int ((times_times_int A_61) (number_number_of_int V_3))) ((times_times_int B_52) (number_number_of_int V_3)))))
% 1.34/1.54 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_624_diff__bin__simps_I9_J
% 1.34/1.54 A new axiom: (forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit1 K)) (bit0 L))) (bit1 ((minus_minus_int K) L))))
% 1.34/1.54 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_625_diff__bin__simps_I10_J
% 1.34/1.54 A new axiom: (forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit1 K)) (bit1 L))) (bit0 ((minus_minus_int K) L))))
% 1.34/1.54 FOF formula (forall (L:int), (((eq int) ((minus_minus_int pls) (bit0 L))) (bit0 ((minus_minus_int pls) L)))) of role axiom named fact_626_diff__bin__simps_I3_J
% 1.34/1.54 A new axiom: (forall (L:int), (((eq int) ((minus_minus_int pls) (bit0 L))) (bit0 ((minus_minus_int pls) L))))
% 1.34/1.54 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_627_less__bin__lemma
% 1.34/1.54 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)))
% 1.34/1.54 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_628_xzgcda__linear__aux1
% 1.34/1.54 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))))))
% 1.34/1.56 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_629_zcong__def
% 1.34/1.56 A new axiom: (forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) ((dvd_dvd_int M) ((minus_minus_int A) B))))
% 1.34/1.56 FOF formula (forall (V_2:int) (W_1:int) (C_28:real), (((eq real) ((plus_plus_real (number267125858f_real V_2)) ((minus_minus_real (number267125858f_real W_1)) C_28))) ((minus_minus_real (number267125858f_real ((plus_plus_int V_2) W_1))) C_28))) of role axiom named fact_630_add__number__of__diff1
% 1.34/1.56 A new axiom: (forall (V_2:int) (W_1:int) (C_28:real), (((eq real) ((plus_plus_real (number267125858f_real V_2)) ((minus_minus_real (number267125858f_real W_1)) C_28))) ((minus_minus_real (number267125858f_real ((plus_plus_int V_2) W_1))) C_28)))
% 1.34/1.56 FOF formula (forall (V_2:int) (W_1:int) (C_28:int), (((eq int) ((plus_plus_int (number_number_of_int V_2)) ((minus_minus_int (number_number_of_int W_1)) C_28))) ((minus_minus_int (number_number_of_int ((plus_plus_int V_2) W_1))) C_28))) of role axiom named fact_631_add__number__of__diff1
% 1.34/1.56 A new axiom: (forall (V_2:int) (W_1:int) (C_28:int), (((eq int) ((plus_plus_int (number_number_of_int V_2)) ((minus_minus_int (number_number_of_int W_1)) C_28))) ((minus_minus_int (number_number_of_int ((plus_plus_int V_2) W_1))) C_28)))
% 1.34/1.56 FOF formula (forall (A:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int X_1) A)->((not (((eq int) X_1) ((minus_minus_int A) one_one_int)))->((ord_less_int X_1) ((minus_minus_int A) one_one_int)))))) of role axiom named fact_632_Euler_Oaux1
% 1.34/1.56 A new axiom: (forall (A:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int X_1) A)->((not (((eq int) X_1) ((minus_minus_int A) one_one_int)))->((ord_less_int X_1) ((minus_minus_int A) one_one_int))))))
% 1.34/1.56 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_633_zle__diff1__eq
% 1.34/1.56 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)))
% 1.34/1.56 FOF formula (forall (L:int), (((eq int) ((minus_minus_int pls) (bit1 L))) (bit1 ((minus_minus_int min) L)))) of role axiom named fact_634_diff__bin__simps_I4_J
% 1.34/1.56 A new axiom: (forall (L:int), (((eq int) ((minus_minus_int pls) (bit1 L))) (bit1 ((minus_minus_int min) L))))
% 1.34/1.56 FOF formula (forall (L:int), (((eq int) ((minus_minus_int min) (bit0 L))) (bit1 ((minus_minus_int min) L)))) of role axiom named fact_635_diff__bin__simps_I5_J
% 1.34/1.56 A new axiom: (forall (L:int), (((eq int) ((minus_minus_int min) (bit0 L))) (bit1 ((minus_minus_int min) L))))
% 1.34/1.56 FOF formula (forall (L:int), (((eq int) ((minus_minus_int min) (bit1 L))) (bit0 ((minus_minus_int min) L)))) of role axiom named fact_636_diff__bin__simps_I6_J
% 1.34/1.56 A new axiom: (forall (L:int), (((eq int) ((minus_minus_int min) (bit1 L))) (bit0 ((minus_minus_int min) L))))
% 1.34/1.56 FOF formula (forall (A:int) (P:int), ((iff (((zcong ((times_times_int A) ((minus_minus_int P) one_one_int))) one_one_int) P)) (((zcong A) ((minus_minus_int P) one_one_int)) P))) of role axiom named fact_637_inv__not__p__minus__1__aux
% 1.34/1.56 A new axiom: (forall (A:int) (P:int), ((iff (((zcong ((times_times_int A) ((minus_minus_int P) one_one_int))) one_one_int) P)) (((zcong A) ((minus_minus_int P) one_one_int)) P)))
% 1.34/1.56 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_638_zcong__eq__trans
% 1.34/1.56 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)))))
% 1.34/1.56 FOF formula (forall (A:int) (B:int) (P:int) (Q:int), (((eq int) ((times_times_int (twoSqu2057625106sum2sq ((product_Pair_int_int A) B))) (twoSqu2057625106sum2sq ((product_Pair_int_int P) Q)))) (twoSqu2057625106sum2sq ((product_Pair_int_int ((plus_plus_int ((times_times_int A) P)) ((times_times_int B) Q))) ((minus_minus_int ((times_times_int A) Q)) ((times_times_int B) P)))))) of role axiom named fact_639_mult__sum2sq
% 1.34/1.58 A new axiom: (forall (A:int) (B:int) (P:int) (Q:int), (((eq int) ((times_times_int (twoSqu2057625106sum2sq ((product_Pair_int_int A) B))) (twoSqu2057625106sum2sq ((product_Pair_int_int P) Q)))) (twoSqu2057625106sum2sq ((product_Pair_int_int ((plus_plus_int ((times_times_int A) P)) ((times_times_int B) Q))) ((minus_minus_int ((times_times_int A) Q)) ((times_times_int B) P))))))
% 1.34/1.58 FOF formula (forall (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) A)) one_one_int) P)->((or (((zcong A) one_one_int) P)) (((zcong A) ((minus_minus_int P) one_one_int)) P)))))) of role axiom named fact_640_zcong__square
% 1.34/1.58 A new axiom: (forall (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) A)) one_one_int) P)->((or (((zcong A) one_one_int) P)) (((zcong A) ((minus_minus_int P) one_one_int)) P))))))
% 1.34/1.58 FOF formula (forall (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P)->((((zcong ((times_times_int A) A)) one_one_int) P)->((or (((eq int) A) one_one_int)) (((eq int) A) ((minus_minus_int P) one_one_int)))))))) of role axiom named fact_641_zcong__square__zless
% 1.34/1.58 A new axiom: (forall (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P)->((((zcong ((times_times_int A) A)) one_one_int) P)->((or (((eq int) A) one_one_int)) (((eq int) A) ((minus_minus_int P) one_one_int))))))))
% 1.34/1.58 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_642_zspecial__product
% 1.34/1.58 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)))))))
% 1.34/1.58 FOF formula (forall (M:int), (((zcong M) zero_zero_int) M)) of role axiom named fact_643_zcong__id
% 1.34/1.58 A new axiom: (forall (M:int), (((zcong M) zero_zero_int) M))
% 1.34/1.58 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_644_zcong__zmult__prop1
% 1.34/1.58 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))))
% 1.34/1.58 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_645_zcong__zmult__prop2
% 1.34/1.58 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))))
% 1.34/1.58 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_646_zcong__shift
% 1.34/1.58 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)))
% 1.34/1.58 FOF formula (forall (Z:nat) (X_1:int) (Y_1:int) (M:int), ((((zcong X_1) Y_1) M)->(((zcong ((power_power_int X_1) Z)) ((power_power_int Y_1) Z)) M))) of role axiom named fact_647_zcong__zpower
% 1.34/1.58 A new axiom: (forall (Z:nat) (X_1:int) (Y_1:int) (M:int), ((((zcong X_1) Y_1) M)->(((zcong ((power_power_int X_1) Z)) ((power_power_int Y_1) Z)) M)))
% 1.34/1.58 FOF formula (forall (X_6:real) (Y_5:real), (((eq real) ((power_power_real ((minus_minus_real X_6) Y_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((minus_minus_real ((plus_plus_real ((power_power_real X_6) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_6)) Y_5)))) of role axiom named fact_648_power2__diff
% 1.34/1.60 A new axiom: (forall (X_6:real) (Y_5:real), (((eq real) ((power_power_real ((minus_minus_real X_6) Y_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((minus_minus_real ((plus_plus_real ((power_power_real X_6) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_6)) Y_5))))
% 1.34/1.60 FOF formula (forall (X_6:int) (Y_5:int), (((eq int) ((power_power_int ((minus_minus_int X_6) Y_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((minus_minus_int ((plus_plus_int ((power_power_int X_6) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) X_6)) Y_5)))) of role axiom named fact_649_power2__diff
% 1.34/1.60 A new axiom: (forall (X_6:int) (Y_5:int), (((eq int) ((power_power_int ((minus_minus_int X_6) Y_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((minus_minus_int ((plus_plus_int ((power_power_int X_6) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) X_6)) Y_5))))
% 1.34/1.60 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_650_zdiff__power2
% 1.34/1.60 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)))))))
% 1.34/1.60 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_651_zdiff__power3
% 1.34/1.60 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)))))))
% 1.34/1.60 FOF formula (forall (M:int) (Y_1:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int zero_zero_int) Y_1)->(((ord_less_int zero_zero_int) M)->((((zcong X_1) Y_1) M)->(((ord_less_int X_1) M)->(((ord_less_int Y_1) M)->(((eq int) X_1) Y_1)))))))) of role axiom named fact_652_zcong__less__eq
% 1.34/1.60 A new axiom: (forall (M:int) (Y_1:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int zero_zero_int) Y_1)->(((ord_less_int zero_zero_int) M)->((((zcong X_1) Y_1) M)->(((ord_less_int X_1) M)->(((ord_less_int Y_1) M)->(((eq int) X_1) Y_1))))))))
% 1.44/1.62 FOF formula (forall (M:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int X_1) M)->((((zcong X_1) zero_zero_int) M)->False)))) of role axiom named fact_653_zcong__not__zero
% 1.44/1.62 A new axiom: (forall (M:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int X_1) M)->((((zcong X_1) zero_zero_int) M)->False))))
% 1.44/1.62 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_654_zdvd__bounds
% 1.44/1.62 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))))
% 1.44/1.62 FOF formula (forall (X_1:int) (P:int), ((iff (((zcong X_1) zero_zero_int) P)) ((dvd_dvd_int P) X_1))) of role axiom named fact_655_zcong__eq__zdvd__prop
% 1.44/1.62 A new axiom: (forall (X_1:int) (P:int), ((iff (((zcong X_1) zero_zero_int) P)) ((dvd_dvd_int P) X_1)))
% 1.44/1.62 FOF formula (forall (A:int) (M:int), ((iff (((zcong A) zero_zero_int) M)) ((dvd_dvd_int M) A))) of role axiom named fact_656_zcong__zero__equiv__div
% 1.44/1.62 A new axiom: (forall (A:int) (M:int), ((iff (((zcong A) zero_zero_int) M)) ((dvd_dvd_int M) A)))
% 1.44/1.62 FOF formula (forall (M:int) (N:int) (P:int), ((zprime P)->(((dvd_dvd_int P) ((times_times_int M) N))->((or ((dvd_dvd_int P) M)) ((dvd_dvd_int P) N))))) of role axiom named fact_657_zprime__zdvd__zmult__better
% 1.44/1.62 A new axiom: (forall (M:int) (N:int) (P:int), ((zprime P)->(((dvd_dvd_int P) ((times_times_int M) N))->((or ((dvd_dvd_int P) M)) ((dvd_dvd_int P) N)))))
% 1.44/1.62 FOF formula (forall (M:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_int X_1) M)->((((zcong X_1) zero_zero_int) M)->(((eq int) X_1) zero_zero_int))))) of role axiom named fact_658_Int2_Ozcong__zero
% 1.44/1.62 A new axiom: (forall (M:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_int X_1) M)->((((zcong X_1) zero_zero_int) M)->(((eq int) X_1) zero_zero_int)))))
% 1.44/1.62 FOF formula (forall (P:int) (Y_1:int) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((dvd_dvd_int P) Y_1)->((dvd_dvd_int P) ((power_power_int Y_1) N))))) of role axiom named fact_659_zpower__zdvd__prop1
% 1.44/1.62 A new axiom: (forall (P:int) (Y_1:int) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((dvd_dvd_int P) Y_1)->((dvd_dvd_int P) ((power_power_int Y_1) N)))))
% 1.44/1.62 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_660_neg__one__power
% 1.44/1.62 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))))
% 1.44/1.62 FOF formula (forall (Y_1:int) (X_1:int) (P:int), ((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((((zcong Y_1) zero_zero_int) P)->False)->((((zcong ((times_times_int X_1) Y_1)) zero_zero_int) P)->False))))) of role axiom named fact_661_zcong__zmult__prop3
% 1.44/1.62 A new axiom: (forall (Y_1:int) (X_1:int) (P:int), ((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((((zcong Y_1) zero_zero_int) P)->False)->((((zcong ((times_times_int X_1) Y_1)) zero_zero_int) P)->False)))))
% 1.44/1.62 FOF formula (forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) B)) zero_zero_int) P)->((or (((zcong A) zero_zero_int) P)) (((zcong B) zero_zero_int) P)))))) of role axiom named fact_662_zcong__zprime__prod__zero
% 1.44/1.62 A new axiom: (forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) B)) zero_zero_int) P)->((or (((zcong A) zero_zero_int) P)) (((zcong B) zero_zero_int) P))))))
% 1.44/1.62 FOF formula (forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->(((and ((((zcong A) zero_zero_int) P)->False)) ((((zcong B) zero_zero_int) P)->False))->((((zcong ((times_times_int A) B)) zero_zero_int) P)->False))))) of role axiom named fact_663_zcong__zprime__prod__zero__contra
% 1.44/1.62 A new axiom: (forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->(((and ((((zcong A) zero_zero_int) P)->False)) ((((zcong B) zero_zero_int) P)->False))->((((zcong ((times_times_int A) B)) zero_zero_int) P)->False)))))
% 1.44/1.64 FOF formula (forall (Y_1:int) (N:nat) (P:int), ((zprime P)->(((dvd_dvd_int P) ((power_power_int Y_1) N))->(((ord_less_nat zero_zero_nat) N)->((dvd_dvd_int P) Y_1))))) of role axiom named fact_664_zpower__zdvd__prop2
% 1.44/1.64 A new axiom: (forall (Y_1:int) (N:nat) (P:int), ((zprime P)->(((dvd_dvd_int P) ((power_power_int Y_1) N))->(((ord_less_nat zero_zero_nat) N)->((dvd_dvd_int P) Y_1)))))
% 1.44/1.64 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_665_Legendre__1mod4
% 1.44/1.64 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)))
% 1.44/1.64 FOF formula (forall (A:int) (P:int), ((and ((((zcong A) zero_zero_int) P)->(((eq int) ((legendre A) P)) zero_zero_int))) (((((zcong A) zero_zero_int) P)->False)->((and (((quadRes P) A)->(((eq int) ((legendre A) P)) one_one_int))) ((((quadRes P) A)->False)->(((eq int) ((legendre A) P)) (number_number_of_int min))))))) of role axiom named fact_666_Legendre__def
% 1.44/1.64 A new axiom: (forall (A:int) (P:int), ((and ((((zcong A) zero_zero_int) P)->(((eq int) ((legendre A) P)) zero_zero_int))) (((((zcong A) zero_zero_int) P)->False)->((and (((quadRes P) A)->(((eq int) ((legendre A) P)) one_one_int))) ((((quadRes P) A)->False)->(((eq int) ((legendre A) P)) (number_number_of_int min)))))))
% 1.44/1.64 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_667_divides__cases
% 1.44/1.64 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))))
% 1.44/1.64 FOF formula (forall (M:int) (X_1:int), ((iff ((quadRes M) X_1)) ((ex int) (fun (Y:int)=> (((zcong ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls))))) X_1) M))))) of role axiom named fact_668_QuadRes__def
% 1.44/1.64 A new axiom: (forall (M:int) (X_1:int), ((iff ((quadRes M) X_1)) ((ex int) (fun (Y:int)=> (((zcong ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls))))) X_1) M)))))
% 1.44/1.64 FOF formula (forall (X_1:real) (Y_1:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_1) zero_zero_real)) (((eq real) Y_1) zero_zero_real)))) of role axiom named fact_669_realpow__two__sum__zero__iff
% 1.44/1.64 A new axiom: (forall (X_1:real) (Y_1:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_1) zero_zero_real)) (((eq real) Y_1) zero_zero_real))))
% 1.44/1.64 FOF formula (forall (V_1:real) (U_1:real) (Y_4:real) (X_5:real) (A_60:real), (((ord_less_real X_5) A_60)->(((ord_less_real Y_4) A_60)->(((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_5)) ((times_times_real V_1) Y_4))) A_60))))))) of role axiom named fact_670_convex__bound__lt
% 1.44/1.64 A new axiom: (forall (V_1:real) (U_1:real) (Y_4:real) (X_5:real) (A_60:real), (((ord_less_real X_5) A_60)->(((ord_less_real Y_4) A_60)->(((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_5)) ((times_times_real V_1) Y_4))) A_60)))))))
% 1.44/1.66 FOF formula (forall (V_1:int) (U_1:int) (Y_4:int) (X_5:int) (A_60:int), (((ord_less_int X_5) A_60)->(((ord_less_int Y_4) A_60)->(((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_5)) ((times_times_int V_1) Y_4))) A_60))))))) of role axiom named fact_671_convex__bound__lt
% 1.44/1.66 A new axiom: (forall (V_1:int) (U_1:int) (Y_4:int) (X_5:int) (A_60:int), (((ord_less_int X_5) A_60)->(((ord_less_int Y_4) A_60)->(((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_5)) ((times_times_int V_1) Y_4))) A_60)))))))
% 1.44/1.66 FOF formula (forall (A_59:real), ((dvd_dvd_real A_59) zero_zero_real)) of role axiom named fact_672_dvd__0__right
% 1.44/1.66 A new axiom: (forall (A_59:real), ((dvd_dvd_real A_59) zero_zero_real))
% 1.44/1.66 FOF formula (forall (A_59:nat), ((dvd_dvd_nat A_59) zero_zero_nat)) of role axiom named fact_673_dvd__0__right
% 1.44/1.66 A new axiom: (forall (A_59:nat), ((dvd_dvd_nat A_59) zero_zero_nat))
% 1.44/1.66 FOF formula (forall (A_59:int), ((dvd_dvd_int A_59) zero_zero_int)) of role axiom named fact_674_dvd__0__right
% 1.44/1.66 A new axiom: (forall (A_59:int), ((dvd_dvd_int A_59) zero_zero_int))
% 1.44/1.66 FOF formula (forall (X_1:real) (Y_1:real), ((iff ((ord_less_eq_real X_1) Y_1)) ((ord_less_eq_real ((minus_minus_real X_1) Y_1)) zero_zero_real))) of role axiom named fact_675_real__le__eq__diff
% 1.44/1.66 A new axiom: (forall (X_1:real) (Y_1:real), ((iff ((ord_less_eq_real X_1) Y_1)) ((ord_less_eq_real ((minus_minus_real X_1) Y_1)) zero_zero_real)))
% 1.44/1.66 FOF formula (forall (X_4:real) (Y_3:real), ((not (((eq real) X_4) Y_3))->((((ord_less_real X_4) Y_3)->False)->((ord_less_real Y_3) X_4)))) of role axiom named fact_676_linorder__neqE__linordered__idom
% 1.44/1.66 A new axiom: (forall (X_4:real) (Y_3:real), ((not (((eq real) X_4) Y_3))->((((ord_less_real X_4) Y_3)->False)->((ord_less_real Y_3) X_4))))
% 1.44/1.66 FOF formula (forall (X_4:int) (Y_3:int), ((not (((eq int) X_4) Y_3))->((((ord_less_int X_4) Y_3)->False)->((ord_less_int Y_3) X_4)))) of role axiom named fact_677_linorder__neqE__linordered__idom
% 1.44/1.66 A new axiom: (forall (X_4:int) (Y_3:int), ((not (((eq int) X_4) Y_3))->((((ord_less_int X_4) Y_3)->False)->((ord_less_int Y_3) X_4))))
% 1.44/1.66 FOF formula (forall (A_58:real), ((dvd_dvd_real A_58) A_58)) of role axiom named fact_678_dvd__refl
% 1.44/1.66 A new axiom: (forall (A_58:real), ((dvd_dvd_real A_58) A_58))
% 1.44/1.66 FOF formula (forall (A_58:nat), ((dvd_dvd_nat A_58) A_58)) of role axiom named fact_679_dvd__refl
% 1.44/1.66 A new axiom: (forall (A_58:nat), ((dvd_dvd_nat A_58) A_58))
% 1.44/1.66 FOF formula (forall (A_58:int), ((dvd_dvd_int A_58) A_58)) of role axiom named fact_680_dvd__refl
% 1.44/1.66 A new axiom: (forall (A_58:int), ((dvd_dvd_int A_58) A_58))
% 1.44/1.66 FOF formula (forall (C_27:real) (A_57:real) (B_51:real), (((dvd_dvd_real A_57) B_51)->(((dvd_dvd_real B_51) C_27)->((dvd_dvd_real A_57) C_27)))) of role axiom named fact_681_dvd__trans
% 1.44/1.66 A new axiom: (forall (C_27:real) (A_57:real) (B_51:real), (((dvd_dvd_real A_57) B_51)->(((dvd_dvd_real B_51) C_27)->((dvd_dvd_real A_57) C_27))))
% 1.44/1.66 FOF formula (forall (C_27:nat) (A_57:nat) (B_51:nat), (((dvd_dvd_nat A_57) B_51)->(((dvd_dvd_nat B_51) C_27)->((dvd_dvd_nat A_57) C_27)))) of role axiom named fact_682_dvd__trans
% 1.44/1.66 A new axiom: (forall (C_27:nat) (A_57:nat) (B_51:nat), (((dvd_dvd_nat A_57) B_51)->(((dvd_dvd_nat B_51) C_27)->((dvd_dvd_nat A_57) C_27))))
% 1.44/1.66 FOF formula (forall (C_27:int) (A_57:int) (B_51:int), (((dvd_dvd_int A_57) B_51)->(((dvd_dvd_int B_51) C_27)->((dvd_dvd_int A_57) C_27)))) of role axiom named fact_683_dvd__trans
% 1.44/1.66 A new axiom: (forall (C_27:int) (A_57:int) (B_51:int), (((dvd_dvd_int A_57) B_51)->(((dvd_dvd_int B_51) C_27)->((dvd_dvd_int A_57) C_27))))
% 1.44/1.66 FOF formula (not (((eq real) zero_zero_real) one_one_real)) of role axiom named fact_684_real__zero__not__eq__one
% 1.44/1.66 A new axiom: (not (((eq real) zero_zero_real) one_one_real))
% 1.44/1.68 FOF formula (forall (X_1:real) (Y_1:real), ((iff ((ord_less_eq_real X_1) Y_1)) ((or ((ord_less_real X_1) Y_1)) (((eq real) X_1) Y_1)))) of role axiom named fact_685_less__eq__real__def
% 1.44/1.68 A new axiom: (forall (X_1:real) (Y_1:real), ((iff ((ord_less_eq_real X_1) Y_1)) ((or ((ord_less_real X_1) Y_1)) (((eq real) X_1) Y_1))))
% 1.44/1.68 FOF formula (forall (X_1:real) (Y_1:real), ((iff ((ord_less_real X_1) Y_1)) ((and ((ord_less_eq_real X_1) Y_1)) (not (((eq real) X_1) Y_1))))) of role axiom named fact_686_real__less__def
% 1.44/1.68 A new axiom: (forall (X_1:real) (Y_1:real), ((iff ((ord_less_real X_1) Y_1)) ((and ((ord_less_eq_real X_1) Y_1)) (not (((eq real) X_1) Y_1)))))
% 1.44/1.68 FOF formula (forall (X_1:nat) (Y_1:nat), ((iff ((and ((dvd_dvd_nat X_1) Y_1)) ((dvd_dvd_nat Y_1) X_1))) (((eq nat) X_1) Y_1))) of role axiom named fact_687_divides__antisym
% 1.44/1.68 A new axiom: (forall (X_1:nat) (Y_1:nat), ((iff ((and ((dvd_dvd_nat X_1) Y_1)) ((dvd_dvd_nat Y_1) X_1))) (((eq nat) X_1) Y_1)))
% 1.44/1.68 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_688_real__mult__assoc
% 1.44/1.68 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))))
% 1.44/1.68 FOF formula (forall (Z:real) (W:real), (((eq real) ((times_times_real Z) W)) ((times_times_real W) Z))) of role axiom named fact_689_real__mult__commute
% 1.44/1.68 A new axiom: (forall (Z:real) (W:real), (((eq real) ((times_times_real Z) W)) ((times_times_real W) Z)))
% 1.44/1.68 FOF formula (forall (Z:real), (((eq real) ((times_times_real one_one_real) Z)) Z)) of role axiom named fact_690_real__mult__1
% 1.44/1.68 A new axiom: (forall (Z:real), (((eq real) ((times_times_real one_one_real) Z)) Z))
% 1.44/1.68 FOF formula (forall (Z:real) (X_1:real) (Y_1:real), (((ord_less_eq_real X_1) Y_1)->((ord_less_eq_real ((plus_plus_real Z) X_1)) ((plus_plus_real Z) Y_1)))) of role axiom named fact_691_real__add__left__mono
% 1.44/1.68 A new axiom: (forall (Z:real) (X_1:real) (Y_1:real), (((ord_less_eq_real X_1) Y_1)->((ord_less_eq_real ((plus_plus_real Z) X_1)) ((plus_plus_real Z) Y_1))))
% 1.44/1.68 FOF formula (forall (X_3:nat) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq nat) ((times_times_nat ((power_power_nat X_3) ((minus_minus_nat N_2) one_one_nat))) X_3)) ((power_power_nat X_3) N_2)))) of role axiom named fact_692_realpow__minus__mult
% 1.44/1.68 A new axiom: (forall (X_3:nat) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq nat) ((times_times_nat ((power_power_nat X_3) ((minus_minus_nat N_2) one_one_nat))) X_3)) ((power_power_nat X_3) N_2))))
% 1.44/1.68 FOF formula (forall (X_3:real) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq real) ((times_times_real ((power_power_real X_3) ((minus_minus_nat N_2) one_one_nat))) X_3)) ((power_power_real X_3) N_2)))) of role axiom named fact_693_realpow__minus__mult
% 1.44/1.68 A new axiom: (forall (X_3:real) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq real) ((times_times_real ((power_power_real X_3) ((minus_minus_nat N_2) one_one_nat))) X_3)) ((power_power_real X_3) N_2))))
% 1.44/1.68 FOF formula (forall (X_3:int) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq int) ((times_times_int ((power_power_int X_3) ((minus_minus_nat N_2) one_one_nat))) X_3)) ((power_power_int X_3) N_2)))) of role axiom named fact_694_realpow__minus__mult
% 1.44/1.68 A new axiom: (forall (X_3:int) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq int) ((times_times_int ((power_power_int X_3) ((minus_minus_nat N_2) one_one_nat))) X_3)) ((power_power_int X_3) N_2))))
% 1.44/1.68 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_695_mult__eq__if
% 1.44/1.68 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))))))
% 1.44/1.69 FOF formula (forall (P:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((power_power_nat P) M)) one_one_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((power_power_nat P) M)) ((times_times_nat P) ((power_power_nat P) ((minus_minus_nat M) one_one_nat))))))) of role axiom named fact_696_power__eq__if
% 1.44/1.69 A new axiom: (forall (P:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((power_power_nat P) M)) one_one_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((power_power_nat P) M)) ((times_times_nat P) ((power_power_nat P) ((minus_minus_nat M) one_one_nat)))))))
% 1.44/1.69 FOF formula (forall (X_1:nat) (Y_1:nat), (((eq nat) ((minus_minus_nat ((power_power_nat X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((plus_plus_nat X_1) Y_1)) ((minus_minus_nat X_1) Y_1)))) of role axiom named fact_697_diff__square
% 1.44/1.69 A new axiom: (forall (X_1:nat) (Y_1:nat), (((eq nat) ((minus_minus_nat ((power_power_nat X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((plus_plus_nat X_1) Y_1)) ((minus_minus_nat X_1) Y_1))))
% 1.44/1.69 FOF formula (forall (A_56:real) (B_50:real), ((((eq real) ((times_times_real A_56) B_50)) zero_zero_real)->((or (((eq real) A_56) zero_zero_real)) (((eq real) B_50) zero_zero_real)))) of role axiom named fact_698_divisors__zero
% 1.44/1.69 A new axiom: (forall (A_56:real) (B_50:real), ((((eq real) ((times_times_real A_56) B_50)) zero_zero_real)->((or (((eq real) A_56) zero_zero_real)) (((eq real) B_50) zero_zero_real))))
% 1.44/1.69 FOF formula (forall (A_56:nat) (B_50:nat), ((((eq nat) ((times_times_nat A_56) B_50)) zero_zero_nat)->((or (((eq nat) A_56) zero_zero_nat)) (((eq nat) B_50) zero_zero_nat)))) of role axiom named fact_699_divisors__zero
% 1.44/1.69 A new axiom: (forall (A_56:nat) (B_50:nat), ((((eq nat) ((times_times_nat A_56) B_50)) zero_zero_nat)->((or (((eq nat) A_56) zero_zero_nat)) (((eq nat) B_50) zero_zero_nat))))
% 1.44/1.69 FOF formula (forall (A_56:int) (B_50:int), ((((eq int) ((times_times_int A_56) B_50)) zero_zero_int)->((or (((eq int) A_56) zero_zero_int)) (((eq int) B_50) zero_zero_int)))) of role axiom named fact_700_divisors__zero
% 1.44/1.69 A new axiom: (forall (A_56:int) (B_50:int), ((((eq int) ((times_times_int A_56) B_50)) zero_zero_int)->((or (((eq int) A_56) zero_zero_int)) (((eq int) B_50) zero_zero_int))))
% 1.44/1.69 FOF formula (forall (B_49:real) (A_55:real), ((not (((eq real) A_55) zero_zero_real))->((not (((eq real) B_49) zero_zero_real))->(not (((eq real) ((times_times_real A_55) B_49)) zero_zero_real))))) of role axiom named fact_701_no__zero__divisors
% 1.44/1.69 A new axiom: (forall (B_49:real) (A_55:real), ((not (((eq real) A_55) zero_zero_real))->((not (((eq real) B_49) zero_zero_real))->(not (((eq real) ((times_times_real A_55) B_49)) zero_zero_real)))))
% 1.44/1.69 FOF formula (forall (B_49:nat) (A_55:nat), ((not (((eq nat) A_55) zero_zero_nat))->((not (((eq nat) B_49) zero_zero_nat))->(not (((eq nat) ((times_times_nat A_55) B_49)) zero_zero_nat))))) of role axiom named fact_702_no__zero__divisors
% 1.44/1.69 A new axiom: (forall (B_49:nat) (A_55:nat), ((not (((eq nat) A_55) zero_zero_nat))->((not (((eq nat) B_49) zero_zero_nat))->(not (((eq nat) ((times_times_nat A_55) B_49)) zero_zero_nat)))))
% 1.44/1.69 FOF formula (forall (B_49:int) (A_55:int), ((not (((eq int) A_55) zero_zero_int))->((not (((eq int) B_49) zero_zero_int))->(not (((eq int) ((times_times_int A_55) B_49)) zero_zero_int))))) of role axiom named fact_703_no__zero__divisors
% 1.44/1.69 A new axiom: (forall (B_49:int) (A_55:int), ((not (((eq int) A_55) zero_zero_int))->((not (((eq int) B_49) zero_zero_int))->(not (((eq int) ((times_times_int A_55) B_49)) zero_zero_int)))))
% 1.44/1.69 FOF formula (forall (A_54:real) (B_48:real), ((iff (((eq real) ((times_times_real A_54) B_48)) zero_zero_real)) ((or (((eq real) A_54) zero_zero_real)) (((eq real) B_48) zero_zero_real)))) of role axiom named fact_704_mult__eq__0__iff
% 1.44/1.69 A new axiom: (forall (A_54:real) (B_48:real), ((iff (((eq real) ((times_times_real A_54) B_48)) zero_zero_real)) ((or (((eq real) A_54) zero_zero_real)) (((eq real) B_48) zero_zero_real))))
% 1.52/1.71 FOF formula (forall (A_54:int) (B_48:int), ((iff (((eq int) ((times_times_int A_54) B_48)) zero_zero_int)) ((or (((eq int) A_54) zero_zero_int)) (((eq int) B_48) zero_zero_int)))) of role axiom named fact_705_mult__eq__0__iff
% 1.52/1.71 A new axiom: (forall (A_54:int) (B_48:int), ((iff (((eq int) ((times_times_int A_54) B_48)) zero_zero_int)) ((or (((eq int) A_54) zero_zero_int)) (((eq int) B_48) zero_zero_int))))
% 1.52/1.71 FOF formula (forall (A_53:real), (((eq real) ((times_times_real A_53) zero_zero_real)) zero_zero_real)) of role axiom named fact_706_mult__zero__right
% 1.52/1.71 A new axiom: (forall (A_53:real), (((eq real) ((times_times_real A_53) zero_zero_real)) zero_zero_real))
% 1.52/1.71 FOF formula (forall (A_53:nat), (((eq nat) ((times_times_nat A_53) zero_zero_nat)) zero_zero_nat)) of role axiom named fact_707_mult__zero__right
% 1.52/1.71 A new axiom: (forall (A_53:nat), (((eq nat) ((times_times_nat A_53) zero_zero_nat)) zero_zero_nat))
% 1.52/1.71 FOF formula (forall (A_53:int), (((eq int) ((times_times_int A_53) zero_zero_int)) zero_zero_int)) of role axiom named fact_708_mult__zero__right
% 1.52/1.71 A new axiom: (forall (A_53:int), (((eq int) ((times_times_int A_53) zero_zero_int)) zero_zero_int))
% 1.52/1.71 FOF formula (forall (A_52:real), (((eq real) ((times_times_real zero_zero_real) A_52)) zero_zero_real)) of role axiom named fact_709_mult__zero__left
% 1.52/1.71 A new axiom: (forall (A_52:real), (((eq real) ((times_times_real zero_zero_real) A_52)) zero_zero_real))
% 1.52/1.71 FOF formula (forall (A_52:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_52)) zero_zero_nat)) of role axiom named fact_710_mult__zero__left
% 1.52/1.71 A new axiom: (forall (A_52:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_52)) zero_zero_nat))
% 1.52/1.71 FOF formula (forall (A_52:int), (((eq int) ((times_times_int zero_zero_int) A_52)) zero_zero_int)) of role axiom named fact_711_mult__zero__left
% 1.52/1.71 A new axiom: (forall (A_52:int), (((eq int) ((times_times_int zero_zero_int) A_52)) zero_zero_int))
% 1.52/1.71 FOF formula (not (((eq real) zero_zero_real) one_one_real)) of role axiom named fact_712_zero__neq__one
% 1.52/1.71 A new axiom: (not (((eq real) zero_zero_real) one_one_real))
% 1.52/1.71 FOF formula (not (((eq nat) zero_zero_nat) one_one_nat)) of role axiom named fact_713_zero__neq__one
% 1.52/1.71 A new axiom: (not (((eq nat) zero_zero_nat) one_one_nat))
% 1.52/1.71 FOF formula (not (((eq int) zero_zero_int) one_one_int)) of role axiom named fact_714_zero__neq__one
% 1.52/1.71 A new axiom: (not (((eq int) zero_zero_int) one_one_int))
% 1.52/1.71 FOF formula (not (((eq real) one_one_real) zero_zero_real)) of role axiom named fact_715_one__neq__zero
% 1.52/1.71 A new axiom: (not (((eq real) one_one_real) zero_zero_real))
% 1.52/1.71 FOF formula (not (((eq nat) one_one_nat) zero_zero_nat)) of role axiom named fact_716_one__neq__zero
% 1.52/1.71 A new axiom: (not (((eq nat) one_one_nat) zero_zero_nat))
% 1.52/1.71 FOF formula (not (((eq int) one_one_int) zero_zero_int)) of role axiom named fact_717_one__neq__zero
% 1.52/1.71 A new axiom: (not (((eq int) one_one_int) zero_zero_int))
% 1.52/1.71 FOF formula (forall (A_51:real) (E:real) (B_47:real) (C_26:real), (((eq real) ((plus_plus_real ((times_times_real A_51) E)) ((plus_plus_real ((times_times_real B_47) E)) C_26))) ((plus_plus_real ((times_times_real ((plus_plus_real A_51) B_47)) E)) C_26))) of role axiom named fact_718_combine__common__factor
% 1.52/1.71 A new axiom: (forall (A_51:real) (E:real) (B_47:real) (C_26:real), (((eq real) ((plus_plus_real ((times_times_real A_51) E)) ((plus_plus_real ((times_times_real B_47) E)) C_26))) ((plus_plus_real ((times_times_real ((plus_plus_real A_51) B_47)) E)) C_26)))
% 1.52/1.71 FOF formula (forall (A_51:nat) (E:nat) (B_47:nat) (C_26:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_51) E)) ((plus_plus_nat ((times_times_nat B_47) E)) C_26))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat A_51) B_47)) E)) C_26))) of role axiom named fact_719_combine__common__factor
% 1.52/1.71 A new axiom: (forall (A_51:nat) (E:nat) (B_47:nat) (C_26:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_51) E)) ((plus_plus_nat ((times_times_nat B_47) E)) C_26))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat A_51) B_47)) E)) C_26)))
% 1.52/1.72 FOF formula (forall (A_51:int) (E:int) (B_47:int) (C_26:int), (((eq int) ((plus_plus_int ((times_times_int A_51) E)) ((plus_plus_int ((times_times_int B_47) E)) C_26))) ((plus_plus_int ((times_times_int ((plus_plus_int A_51) B_47)) E)) C_26))) of role axiom named fact_720_combine__common__factor
% 1.52/1.72 A new axiom: (forall (A_51:int) (E:int) (B_47:int) (C_26:int), (((eq int) ((plus_plus_int ((times_times_int A_51) E)) ((plus_plus_int ((times_times_int B_47) E)) C_26))) ((plus_plus_int ((times_times_int ((plus_plus_int A_51) B_47)) E)) C_26)))
% 1.52/1.72 FOF formula (forall (A_50:real) (B_46:real) (C_25:real), (((eq real) ((times_times_real ((plus_plus_real A_50) B_46)) C_25)) ((plus_plus_real ((times_times_real A_50) C_25)) ((times_times_real B_46) C_25)))) of role axiom named fact_721_comm__semiring__class_Odistrib
% 1.52/1.72 A new axiom: (forall (A_50:real) (B_46:real) (C_25:real), (((eq real) ((times_times_real ((plus_plus_real A_50) B_46)) C_25)) ((plus_plus_real ((times_times_real A_50) C_25)) ((times_times_real B_46) C_25))))
% 1.52/1.72 FOF formula (forall (A_50:nat) (B_46:nat) (C_25:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_50) B_46)) C_25)) ((plus_plus_nat ((times_times_nat A_50) C_25)) ((times_times_nat B_46) C_25)))) of role axiom named fact_722_comm__semiring__class_Odistrib
% 1.52/1.72 A new axiom: (forall (A_50:nat) (B_46:nat) (C_25:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_50) B_46)) C_25)) ((plus_plus_nat ((times_times_nat A_50) C_25)) ((times_times_nat B_46) C_25))))
% 1.52/1.72 FOF formula (forall (A_50:int) (B_46:int) (C_25:int), (((eq int) ((times_times_int ((plus_plus_int A_50) B_46)) C_25)) ((plus_plus_int ((times_times_int A_50) C_25)) ((times_times_int B_46) C_25)))) of role axiom named fact_723_comm__semiring__class_Odistrib
% 1.52/1.72 A new axiom: (forall (A_50:int) (B_46:int) (C_25:int), (((eq int) ((times_times_int ((plus_plus_int A_50) B_46)) C_25)) ((plus_plus_int ((times_times_int A_50) C_25)) ((times_times_int B_46) C_25))))
% 1.52/1.72 FOF formula (forall (A_49:real), (((dvd_dvd_real zero_zero_real) A_49)->(((eq real) A_49) zero_zero_real))) of role axiom named fact_724_dvd__0__left
% 1.52/1.72 A new axiom: (forall (A_49:real), (((dvd_dvd_real zero_zero_real) A_49)->(((eq real) A_49) zero_zero_real)))
% 1.52/1.72 FOF formula (forall (A_49:nat), (((dvd_dvd_nat zero_zero_nat) A_49)->(((eq nat) A_49) zero_zero_nat))) of role axiom named fact_725_dvd__0__left
% 1.52/1.72 A new axiom: (forall (A_49:nat), (((dvd_dvd_nat zero_zero_nat) A_49)->(((eq nat) A_49) zero_zero_nat)))
% 1.52/1.72 FOF formula (forall (A_49:int), (((dvd_dvd_int zero_zero_int) A_49)->(((eq int) A_49) zero_zero_int))) of role axiom named fact_726_dvd__0__left
% 1.52/1.72 A new axiom: (forall (A_49:int), (((dvd_dvd_int zero_zero_int) A_49)->(((eq int) A_49) zero_zero_int)))
% 1.52/1.72 FOF formula (forall (A_48:real) (C_24:real) (B_45:real) (D_6:real), (((eq real) ((minus_minus_real ((plus_plus_real A_48) C_24)) ((plus_plus_real B_45) D_6))) ((plus_plus_real ((minus_minus_real A_48) B_45)) ((minus_minus_real C_24) D_6)))) of role axiom named fact_727_add__diff__add
% 1.52/1.72 A new axiom: (forall (A_48:real) (C_24:real) (B_45:real) (D_6:real), (((eq real) ((minus_minus_real ((plus_plus_real A_48) C_24)) ((plus_plus_real B_45) D_6))) ((plus_plus_real ((minus_minus_real A_48) B_45)) ((minus_minus_real C_24) D_6))))
% 1.52/1.72 FOF formula (forall (A_48:int) (C_24:int) (B_45:int) (D_6:int), (((eq int) ((minus_minus_int ((plus_plus_int A_48) C_24)) ((plus_plus_int B_45) D_6))) ((plus_plus_int ((minus_minus_int A_48) B_45)) ((minus_minus_int C_24) D_6)))) of role axiom named fact_728_add__diff__add
% 1.52/1.72 A new axiom: (forall (A_48:int) (C_24:int) (B_45:int) (D_6:int), (((eq int) ((minus_minus_int ((plus_plus_int A_48) C_24)) ((plus_plus_int B_45) D_6))) ((plus_plus_int ((minus_minus_int A_48) B_45)) ((minus_minus_int C_24) D_6))))
% 1.52/1.72 FOF formula (forall (A_47:real) (B_44:real) (C_23:real), (((dvd_dvd_real ((times_times_real A_47) B_44)) C_23)->((dvd_dvd_real B_44) C_23))) of role axiom named fact_729_dvd__mult__right
% 1.52/1.72 A new axiom: (forall (A_47:real) (B_44:real) (C_23:real), (((dvd_dvd_real ((times_times_real A_47) B_44)) C_23)->((dvd_dvd_real B_44) C_23)))
% 1.52/1.72 FOF formula (forall (A_47:nat) (B_44:nat) (C_23:nat), (((dvd_dvd_nat ((times_times_nat A_47) B_44)) C_23)->((dvd_dvd_nat B_44) C_23))) of role axiom named fact_730_dvd__mult__right
% 1.52/1.74 A new axiom: (forall (A_47:nat) (B_44:nat) (C_23:nat), (((dvd_dvd_nat ((times_times_nat A_47) B_44)) C_23)->((dvd_dvd_nat B_44) C_23)))
% 1.52/1.74 FOF formula (forall (A_47:int) (B_44:int) (C_23:int), (((dvd_dvd_int ((times_times_int A_47) B_44)) C_23)->((dvd_dvd_int B_44) C_23))) of role axiom named fact_731_dvd__mult__right
% 1.52/1.74 A new axiom: (forall (A_47:int) (B_44:int) (C_23:int), (((dvd_dvd_int ((times_times_int A_47) B_44)) C_23)->((dvd_dvd_int B_44) C_23)))
% 1.52/1.74 FOF formula (forall (A_46:real) (B_43:real) (C_22:real), (((dvd_dvd_real ((times_times_real A_46) B_43)) C_22)->((dvd_dvd_real A_46) C_22))) of role axiom named fact_732_dvd__mult__left
% 1.52/1.74 A new axiom: (forall (A_46:real) (B_43:real) (C_22:real), (((dvd_dvd_real ((times_times_real A_46) B_43)) C_22)->((dvd_dvd_real A_46) C_22)))
% 1.52/1.74 FOF formula (forall (A_46:nat) (B_43:nat) (C_22:nat), (((dvd_dvd_nat ((times_times_nat A_46) B_43)) C_22)->((dvd_dvd_nat A_46) C_22))) of role axiom named fact_733_dvd__mult__left
% 1.52/1.74 A new axiom: (forall (A_46:nat) (B_43:nat) (C_22:nat), (((dvd_dvd_nat ((times_times_nat A_46) B_43)) C_22)->((dvd_dvd_nat A_46) C_22)))
% 1.52/1.74 FOF formula (forall (A_46:int) (B_43:int) (C_22:int), (((dvd_dvd_int ((times_times_int A_46) B_43)) C_22)->((dvd_dvd_int A_46) C_22))) of role axiom named fact_734_dvd__mult__left
% 1.52/1.74 A new axiom: (forall (A_46:int) (B_43:int) (C_22:int), (((dvd_dvd_int ((times_times_int A_46) B_43)) C_22)->((dvd_dvd_int A_46) C_22)))
% 1.52/1.74 FOF formula (forall (A_45:real) (B_42:real) (K_2:real), ((((eq real) A_45) ((times_times_real B_42) K_2))->((dvd_dvd_real B_42) A_45))) of role axiom named fact_735_dvdI
% 1.52/1.74 A new axiom: (forall (A_45:real) (B_42:real) (K_2:real), ((((eq real) A_45) ((times_times_real B_42) K_2))->((dvd_dvd_real B_42) A_45)))
% 1.52/1.74 FOF formula (forall (A_45:nat) (B_42:nat) (K_2:nat), ((((eq nat) A_45) ((times_times_nat B_42) K_2))->((dvd_dvd_nat B_42) A_45))) of role axiom named fact_736_dvdI
% 1.52/1.74 A new axiom: (forall (A_45:nat) (B_42:nat) (K_2:nat), ((((eq nat) A_45) ((times_times_nat B_42) K_2))->((dvd_dvd_nat B_42) A_45)))
% 1.52/1.74 FOF formula (forall (A_45:int) (B_42:int) (K_2:int), ((((eq int) A_45) ((times_times_int B_42) K_2))->((dvd_dvd_int B_42) A_45))) of role axiom named fact_737_dvdI
% 1.52/1.74 A new axiom: (forall (A_45:int) (B_42:int) (K_2:int), ((((eq int) A_45) ((times_times_int B_42) K_2))->((dvd_dvd_int B_42) A_45)))
% 1.52/1.74 FOF formula (forall (C_21:real) (D_5:real) (A_44:real) (B_41:real), (((dvd_dvd_real A_44) B_41)->(((dvd_dvd_real C_21) D_5)->((dvd_dvd_real ((times_times_real A_44) C_21)) ((times_times_real B_41) D_5))))) of role axiom named fact_738_mult__dvd__mono
% 1.52/1.74 A new axiom: (forall (C_21:real) (D_5:real) (A_44:real) (B_41:real), (((dvd_dvd_real A_44) B_41)->(((dvd_dvd_real C_21) D_5)->((dvd_dvd_real ((times_times_real A_44) C_21)) ((times_times_real B_41) D_5)))))
% 1.52/1.74 FOF formula (forall (C_21:nat) (D_5:nat) (A_44:nat) (B_41:nat), (((dvd_dvd_nat A_44) B_41)->(((dvd_dvd_nat C_21) D_5)->((dvd_dvd_nat ((times_times_nat A_44) C_21)) ((times_times_nat B_41) D_5))))) of role axiom named fact_739_mult__dvd__mono
% 1.52/1.74 A new axiom: (forall (C_21:nat) (D_5:nat) (A_44:nat) (B_41:nat), (((dvd_dvd_nat A_44) B_41)->(((dvd_dvd_nat C_21) D_5)->((dvd_dvd_nat ((times_times_nat A_44) C_21)) ((times_times_nat B_41) D_5)))))
% 1.52/1.74 FOF formula (forall (C_21:int) (D_5:int) (A_44:int) (B_41:int), (((dvd_dvd_int A_44) B_41)->(((dvd_dvd_int C_21) D_5)->((dvd_dvd_int ((times_times_int A_44) C_21)) ((times_times_int B_41) D_5))))) of role axiom named fact_740_mult__dvd__mono
% 1.52/1.74 A new axiom: (forall (C_21:int) (D_5:int) (A_44:int) (B_41:int), (((dvd_dvd_int A_44) B_41)->(((dvd_dvd_int C_21) D_5)->((dvd_dvd_int ((times_times_int A_44) C_21)) ((times_times_int B_41) D_5)))))
% 1.52/1.74 FOF formula (forall (B_40:real) (A_43:real) (C_20:real), (((dvd_dvd_real A_43) C_20)->((dvd_dvd_real A_43) ((times_times_real B_40) C_20)))) of role axiom named fact_741_dvd__mult
% 1.52/1.74 A new axiom: (forall (B_40:real) (A_43:real) (C_20:real), (((dvd_dvd_real A_43) C_20)->((dvd_dvd_real A_43) ((times_times_real B_40) C_20))))
% 1.52/1.76 FOF formula (forall (B_40:nat) (A_43:nat) (C_20:nat), (((dvd_dvd_nat A_43) C_20)->((dvd_dvd_nat A_43) ((times_times_nat B_40) C_20)))) of role axiom named fact_742_dvd__mult
% 1.52/1.76 A new axiom: (forall (B_40:nat) (A_43:nat) (C_20:nat), (((dvd_dvd_nat A_43) C_20)->((dvd_dvd_nat A_43) ((times_times_nat B_40) C_20))))
% 1.52/1.76 FOF formula (forall (B_40:int) (A_43:int) (C_20:int), (((dvd_dvd_int A_43) C_20)->((dvd_dvd_int A_43) ((times_times_int B_40) C_20)))) of role axiom named fact_743_dvd__mult
% 1.52/1.76 A new axiom: (forall (B_40:int) (A_43:int) (C_20:int), (((dvd_dvd_int A_43) C_20)->((dvd_dvd_int A_43) ((times_times_int B_40) C_20))))
% 1.52/1.76 FOF formula (forall (C_19:real) (A_42:real) (B_39:real), (((dvd_dvd_real A_42) B_39)->((dvd_dvd_real A_42) ((times_times_real B_39) C_19)))) of role axiom named fact_744_dvd__mult2
% 1.52/1.76 A new axiom: (forall (C_19:real) (A_42:real) (B_39:real), (((dvd_dvd_real A_42) B_39)->((dvd_dvd_real A_42) ((times_times_real B_39) C_19))))
% 1.52/1.76 FOF formula (forall (C_19:nat) (A_42:nat) (B_39:nat), (((dvd_dvd_nat A_42) B_39)->((dvd_dvd_nat A_42) ((times_times_nat B_39) C_19)))) of role axiom named fact_745_dvd__mult2
% 1.52/1.76 A new axiom: (forall (C_19:nat) (A_42:nat) (B_39:nat), (((dvd_dvd_nat A_42) B_39)->((dvd_dvd_nat A_42) ((times_times_nat B_39) C_19))))
% 1.52/1.76 FOF formula (forall (C_19:int) (A_42:int) (B_39:int), (((dvd_dvd_int A_42) B_39)->((dvd_dvd_int A_42) ((times_times_int B_39) C_19)))) of role axiom named fact_746_dvd__mult2
% 1.52/1.76 A new axiom: (forall (C_19:int) (A_42:int) (B_39:int), (((dvd_dvd_int A_42) B_39)->((dvd_dvd_int A_42) ((times_times_int B_39) C_19))))
% 1.52/1.76 FOF formula (forall (A_41:real) (B_38:real), ((dvd_dvd_real A_41) ((times_times_real B_38) A_41))) of role axiom named fact_747_dvd__triv__right
% 1.52/1.76 A new axiom: (forall (A_41:real) (B_38:real), ((dvd_dvd_real A_41) ((times_times_real B_38) A_41)))
% 1.52/1.76 FOF formula (forall (A_41:nat) (B_38:nat), ((dvd_dvd_nat A_41) ((times_times_nat B_38) A_41))) of role axiom named fact_748_dvd__triv__right
% 1.52/1.76 A new axiom: (forall (A_41:nat) (B_38:nat), ((dvd_dvd_nat A_41) ((times_times_nat B_38) A_41)))
% 1.52/1.76 FOF formula (forall (A_41:int) (B_38:int), ((dvd_dvd_int A_41) ((times_times_int B_38) A_41))) of role axiom named fact_749_dvd__triv__right
% 1.52/1.76 A new axiom: (forall (A_41:int) (B_38:int), ((dvd_dvd_int A_41) ((times_times_int B_38) A_41)))
% 1.52/1.76 FOF formula (forall (A_40:real) (B_37:real), ((dvd_dvd_real A_40) ((times_times_real A_40) B_37))) of role axiom named fact_750_dvd__triv__left
% 1.52/1.76 A new axiom: (forall (A_40:real) (B_37:real), ((dvd_dvd_real A_40) ((times_times_real A_40) B_37)))
% 1.52/1.76 FOF formula (forall (A_40:nat) (B_37:nat), ((dvd_dvd_nat A_40) ((times_times_nat A_40) B_37))) of role axiom named fact_751_dvd__triv__left
% 1.52/1.76 A new axiom: (forall (A_40:nat) (B_37:nat), ((dvd_dvd_nat A_40) ((times_times_nat A_40) B_37)))
% 1.52/1.76 FOF formula (forall (A_40:int) (B_37:int), ((dvd_dvd_int A_40) ((times_times_int A_40) B_37))) of role axiom named fact_752_dvd__triv__left
% 1.52/1.76 A new axiom: (forall (A_40:int) (B_37:int), ((dvd_dvd_int A_40) ((times_times_int A_40) B_37)))
% 1.52/1.76 FOF formula (forall (C_18:real) (A_39:real) (B_36:real), (((dvd_dvd_real A_39) B_36)->(((dvd_dvd_real A_39) C_18)->((dvd_dvd_real A_39) ((plus_plus_real B_36) C_18))))) of role axiom named fact_753_dvd__add
% 1.52/1.76 A new axiom: (forall (C_18:real) (A_39:real) (B_36:real), (((dvd_dvd_real A_39) B_36)->(((dvd_dvd_real A_39) C_18)->((dvd_dvd_real A_39) ((plus_plus_real B_36) C_18)))))
% 1.52/1.76 FOF formula (forall (C_18:nat) (A_39:nat) (B_36:nat), (((dvd_dvd_nat A_39) B_36)->(((dvd_dvd_nat A_39) C_18)->((dvd_dvd_nat A_39) ((plus_plus_nat B_36) C_18))))) of role axiom named fact_754_dvd__add
% 1.52/1.76 A new axiom: (forall (C_18:nat) (A_39:nat) (B_36:nat), (((dvd_dvd_nat A_39) B_36)->(((dvd_dvd_nat A_39) C_18)->((dvd_dvd_nat A_39) ((plus_plus_nat B_36) C_18)))))
% 1.52/1.76 FOF formula (forall (C_18:int) (A_39:int) (B_36:int), (((dvd_dvd_int A_39) B_36)->(((dvd_dvd_int A_39) C_18)->((dvd_dvd_int A_39) ((plus_plus_int B_36) C_18))))) of role axiom named fact_755_dvd__add
% 1.52/1.76 A new axiom: (forall (C_18:int) (A_39:int) (B_36:int), (((dvd_dvd_int A_39) B_36)->(((dvd_dvd_int A_39) C_18)->((dvd_dvd_int A_39) ((plus_plus_int B_36) C_18)))))
% 1.60/1.78 FOF formula (forall (A_38:real), ((dvd_dvd_real one_one_real) A_38)) of role axiom named fact_756_one__dvd
% 1.60/1.78 A new axiom: (forall (A_38:real), ((dvd_dvd_real one_one_real) A_38))
% 1.60/1.78 FOF formula (forall (A_38:nat), ((dvd_dvd_nat one_one_nat) A_38)) of role axiom named fact_757_one__dvd
% 1.60/1.78 A new axiom: (forall (A_38:nat), ((dvd_dvd_nat one_one_nat) A_38))
% 1.60/1.78 FOF formula (forall (A_38:int), ((dvd_dvd_int one_one_int) A_38)) of role axiom named fact_758_one__dvd
% 1.60/1.78 A new axiom: (forall (A_38:int), ((dvd_dvd_int one_one_int) A_38))
% 1.60/1.78 FOF formula (forall (Z_1:real) (X_2:real) (Y_2:real), (((dvd_dvd_real X_2) Y_2)->(((dvd_dvd_real X_2) Z_1)->((dvd_dvd_real X_2) ((minus_minus_real Y_2) Z_1))))) of role axiom named fact_759_dvd__diff
% 1.60/1.78 A new axiom: (forall (Z_1:real) (X_2:real) (Y_2:real), (((dvd_dvd_real X_2) Y_2)->(((dvd_dvd_real X_2) Z_1)->((dvd_dvd_real X_2) ((minus_minus_real Y_2) Z_1)))))
% 1.60/1.78 FOF formula (forall (Z_1:int) (X_2:int) (Y_2:int), (((dvd_dvd_int X_2) Y_2)->(((dvd_dvd_int X_2) Z_1)->((dvd_dvd_int X_2) ((minus_minus_int Y_2) Z_1))))) of role axiom named fact_760_dvd__diff
% 1.60/1.78 A new axiom: (forall (Z_1:int) (X_2:int) (Y_2:int), (((dvd_dvd_int X_2) Y_2)->(((dvd_dvd_int X_2) Z_1)->((dvd_dvd_int X_2) ((minus_minus_int Y_2) Z_1)))))
% 1.60/1.78 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_761_real__mult__right__cancel
% 1.60/1.78 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))))
% 1.60/1.78 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_762_real__mult__left__cancel
% 1.60/1.78 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))))
% 1.60/1.78 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_763_divides__add__revr
% 1.60/1.78 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))))
% 1.60/1.78 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_764_divides__mul__l
% 1.60/1.78 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))))
% 1.60/1.78 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_765_divides__mul__r
% 1.60/1.78 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))))
% 1.60/1.78 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_766_nat__mult__eq__one
% 1.60/1.78 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))))
% 1.60/1.78 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_767_real__add__mult__distrib
% 1.60/1.78 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))))
% 1.60/1.78 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_768_nat__power__eq__0__iff
% 1.60/1.78 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))))
% 1.62/1.80 FOF formula (forall (N:nat) (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->((dvd_dvd_nat ((power_power_nat X_1) N)) ((power_power_nat Y_1) N)))) of role axiom named fact_769_divides__exp
% 1.62/1.80 A new axiom: (forall (N:nat) (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->((dvd_dvd_nat ((power_power_nat X_1) N)) ((power_power_nat Y_1) N))))
% 1.62/1.80 FOF formula (forall (B_35:real) (A_37:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_37)) ((ord_less_eq_real B_35) zero_zero_real))) ((and ((ord_less_eq_real A_37) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_35)))->((ord_less_eq_real ((times_times_real A_37) B_35)) zero_zero_real))) of role axiom named fact_770_split__mult__neg__le
% 1.62/1.80 A new axiom: (forall (B_35:real) (A_37:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_37)) ((ord_less_eq_real B_35) zero_zero_real))) ((and ((ord_less_eq_real A_37) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_35)))->((ord_less_eq_real ((times_times_real A_37) B_35)) zero_zero_real)))
% 1.62/1.80 FOF formula (forall (B_35:nat) (A_37:nat), (((or ((and ((ord_less_eq_nat zero_zero_nat) A_37)) ((ord_less_eq_nat B_35) zero_zero_nat))) ((and ((ord_less_eq_nat A_37) zero_zero_nat)) ((ord_less_eq_nat zero_zero_nat) B_35)))->((ord_less_eq_nat ((times_times_nat A_37) B_35)) zero_zero_nat))) of role axiom named fact_771_split__mult__neg__le
% 1.62/1.80 A new axiom: (forall (B_35:nat) (A_37:nat), (((or ((and ((ord_less_eq_nat zero_zero_nat) A_37)) ((ord_less_eq_nat B_35) zero_zero_nat))) ((and ((ord_less_eq_nat A_37) zero_zero_nat)) ((ord_less_eq_nat zero_zero_nat) B_35)))->((ord_less_eq_nat ((times_times_nat A_37) B_35)) zero_zero_nat)))
% 1.62/1.80 FOF formula (forall (B_35:int) (A_37:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_37)) ((ord_less_eq_int B_35) zero_zero_int))) ((and ((ord_less_eq_int A_37) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_35)))->((ord_less_eq_int ((times_times_int A_37) B_35)) zero_zero_int))) of role axiom named fact_772_split__mult__neg__le
% 1.62/1.80 A new axiom: (forall (B_35:int) (A_37:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_37)) ((ord_less_eq_int B_35) zero_zero_int))) ((and ((ord_less_eq_int A_37) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_35)))->((ord_less_eq_int ((times_times_int A_37) B_35)) zero_zero_int)))
% 1.62/1.80 FOF formula (forall (B_34:real) (A_36:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_36)) ((ord_less_eq_real zero_zero_real) B_34))) ((and ((ord_less_eq_real A_36) zero_zero_real)) ((ord_less_eq_real B_34) zero_zero_real)))->((ord_less_eq_real zero_zero_real) ((times_times_real A_36) B_34)))) of role axiom named fact_773_split__mult__pos__le
% 1.62/1.80 A new axiom: (forall (B_34:real) (A_36:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_36)) ((ord_less_eq_real zero_zero_real) B_34))) ((and ((ord_less_eq_real A_36) zero_zero_real)) ((ord_less_eq_real B_34) zero_zero_real)))->((ord_less_eq_real zero_zero_real) ((times_times_real A_36) B_34))))
% 1.62/1.80 FOF formula (forall (B_34:int) (A_36:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_36)) ((ord_less_eq_int zero_zero_int) B_34))) ((and ((ord_less_eq_int A_36) zero_zero_int)) ((ord_less_eq_int B_34) zero_zero_int)))->((ord_less_eq_int zero_zero_int) ((times_times_int A_36) B_34)))) of role axiom named fact_774_split__mult__pos__le
% 1.62/1.80 A new axiom: (forall (B_34:int) (A_36:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_36)) ((ord_less_eq_int zero_zero_int) B_34))) ((and ((ord_less_eq_int A_36) zero_zero_int)) ((ord_less_eq_int B_34) zero_zero_int)))->((ord_less_eq_int zero_zero_int) ((times_times_int A_36) B_34))))
% 1.62/1.80 FOF formula (forall (C_17:real) (D_4:real) (A_35:real) (B_33:real), (((ord_less_eq_real A_35) B_33)->(((ord_less_eq_real C_17) D_4)->(((ord_less_eq_real zero_zero_real) B_33)->(((ord_less_eq_real zero_zero_real) C_17)->((ord_less_eq_real ((times_times_real A_35) C_17)) ((times_times_real B_33) D_4))))))) of role axiom named fact_775_mult__mono
% 1.62/1.80 A new axiom: (forall (C_17:real) (D_4:real) (A_35:real) (B_33:real), (((ord_less_eq_real A_35) B_33)->(((ord_less_eq_real C_17) D_4)->(((ord_less_eq_real zero_zero_real) B_33)->(((ord_less_eq_real zero_zero_real) C_17)->((ord_less_eq_real ((times_times_real A_35) C_17)) ((times_times_real B_33) D_4)))))))
% 1.63/1.82 FOF formula (forall (C_17:nat) (D_4:nat) (A_35:nat) (B_33:nat), (((ord_less_eq_nat A_35) B_33)->(((ord_less_eq_nat C_17) D_4)->(((ord_less_eq_nat zero_zero_nat) B_33)->(((ord_less_eq_nat zero_zero_nat) C_17)->((ord_less_eq_nat ((times_times_nat A_35) C_17)) ((times_times_nat B_33) D_4))))))) of role axiom named fact_776_mult__mono
% 1.63/1.82 A new axiom: (forall (C_17:nat) (D_4:nat) (A_35:nat) (B_33:nat), (((ord_less_eq_nat A_35) B_33)->(((ord_less_eq_nat C_17) D_4)->(((ord_less_eq_nat zero_zero_nat) B_33)->(((ord_less_eq_nat zero_zero_nat) C_17)->((ord_less_eq_nat ((times_times_nat A_35) C_17)) ((times_times_nat B_33) D_4)))))))
% 1.63/1.82 FOF formula (forall (C_17:int) (D_4:int) (A_35:int) (B_33:int), (((ord_less_eq_int A_35) B_33)->(((ord_less_eq_int C_17) D_4)->(((ord_less_eq_int zero_zero_int) B_33)->(((ord_less_eq_int zero_zero_int) C_17)->((ord_less_eq_int ((times_times_int A_35) C_17)) ((times_times_int B_33) D_4))))))) of role axiom named fact_777_mult__mono
% 1.63/1.82 A new axiom: (forall (C_17:int) (D_4:int) (A_35:int) (B_33:int), (((ord_less_eq_int A_35) B_33)->(((ord_less_eq_int C_17) D_4)->(((ord_less_eq_int zero_zero_int) B_33)->(((ord_less_eq_int zero_zero_int) C_17)->((ord_less_eq_int ((times_times_int A_35) C_17)) ((times_times_int B_33) D_4)))))))
% 1.63/1.82 FOF formula (forall (C_16:real) (D_3:real) (A_34:real) (B_32:real), (((ord_less_eq_real A_34) B_32)->(((ord_less_eq_real C_16) D_3)->(((ord_less_eq_real zero_zero_real) A_34)->(((ord_less_eq_real zero_zero_real) C_16)->((ord_less_eq_real ((times_times_real A_34) C_16)) ((times_times_real B_32) D_3))))))) of role axiom named fact_778_mult__mono_H
% 1.63/1.82 A new axiom: (forall (C_16:real) (D_3:real) (A_34:real) (B_32:real), (((ord_less_eq_real A_34) B_32)->(((ord_less_eq_real C_16) D_3)->(((ord_less_eq_real zero_zero_real) A_34)->(((ord_less_eq_real zero_zero_real) C_16)->((ord_less_eq_real ((times_times_real A_34) C_16)) ((times_times_real B_32) D_3)))))))
% 1.63/1.82 FOF formula (forall (C_16:nat) (D_3:nat) (A_34:nat) (B_32:nat), (((ord_less_eq_nat A_34) B_32)->(((ord_less_eq_nat C_16) D_3)->(((ord_less_eq_nat zero_zero_nat) A_34)->(((ord_less_eq_nat zero_zero_nat) C_16)->((ord_less_eq_nat ((times_times_nat A_34) C_16)) ((times_times_nat B_32) D_3))))))) of role axiom named fact_779_mult__mono_H
% 1.63/1.82 A new axiom: (forall (C_16:nat) (D_3:nat) (A_34:nat) (B_32:nat), (((ord_less_eq_nat A_34) B_32)->(((ord_less_eq_nat C_16) D_3)->(((ord_less_eq_nat zero_zero_nat) A_34)->(((ord_less_eq_nat zero_zero_nat) C_16)->((ord_less_eq_nat ((times_times_nat A_34) C_16)) ((times_times_nat B_32) D_3)))))))
% 1.63/1.82 FOF formula (forall (C_16:int) (D_3:int) (A_34:int) (B_32:int), (((ord_less_eq_int A_34) B_32)->(((ord_less_eq_int C_16) D_3)->(((ord_less_eq_int zero_zero_int) A_34)->(((ord_less_eq_int zero_zero_int) C_16)->((ord_less_eq_int ((times_times_int A_34) C_16)) ((times_times_int B_32) D_3))))))) of role axiom named fact_780_mult__mono_H
% 1.63/1.82 A new axiom: (forall (C_16:int) (D_3:int) (A_34:int) (B_32:int), (((ord_less_eq_int A_34) B_32)->(((ord_less_eq_int C_16) D_3)->(((ord_less_eq_int zero_zero_int) A_34)->(((ord_less_eq_int zero_zero_int) C_16)->((ord_less_eq_int ((times_times_int A_34) C_16)) ((times_times_int B_32) D_3)))))))
% 1.63/1.82 FOF formula (forall (C_15:real) (B_31:real) (A_33:real), (((ord_less_eq_real B_31) A_33)->(((ord_less_eq_real C_15) zero_zero_real)->((ord_less_eq_real ((times_times_real C_15) A_33)) ((times_times_real C_15) B_31))))) of role axiom named fact_781_mult__left__mono__neg
% 1.63/1.82 A new axiom: (forall (C_15:real) (B_31:real) (A_33:real), (((ord_less_eq_real B_31) A_33)->(((ord_less_eq_real C_15) zero_zero_real)->((ord_less_eq_real ((times_times_real C_15) A_33)) ((times_times_real C_15) B_31)))))
% 1.63/1.82 FOF formula (forall (C_15:int) (B_31:int) (A_33:int), (((ord_less_eq_int B_31) A_33)->(((ord_less_eq_int C_15) zero_zero_int)->((ord_less_eq_int ((times_times_int C_15) A_33)) ((times_times_int C_15) B_31))))) of role axiom named fact_782_mult__left__mono__neg
% 1.63/1.84 A new axiom: (forall (C_15:int) (B_31:int) (A_33:int), (((ord_less_eq_int B_31) A_33)->(((ord_less_eq_int C_15) zero_zero_int)->((ord_less_eq_int ((times_times_int C_15) A_33)) ((times_times_int C_15) B_31)))))
% 1.63/1.84 FOF formula (forall (C_14:real) (B_30:real) (A_32:real), (((ord_less_eq_real B_30) A_32)->(((ord_less_eq_real C_14) zero_zero_real)->((ord_less_eq_real ((times_times_real A_32) C_14)) ((times_times_real B_30) C_14))))) of role axiom named fact_783_mult__right__mono__neg
% 1.63/1.84 A new axiom: (forall (C_14:real) (B_30:real) (A_32:real), (((ord_less_eq_real B_30) A_32)->(((ord_less_eq_real C_14) zero_zero_real)->((ord_less_eq_real ((times_times_real A_32) C_14)) ((times_times_real B_30) C_14)))))
% 1.63/1.84 FOF formula (forall (C_14:int) (B_30:int) (A_32:int), (((ord_less_eq_int B_30) A_32)->(((ord_less_eq_int C_14) zero_zero_int)->((ord_less_eq_int ((times_times_int A_32) C_14)) ((times_times_int B_30) C_14))))) of role axiom named fact_784_mult__right__mono__neg
% 1.63/1.84 A new axiom: (forall (C_14:int) (B_30:int) (A_32:int), (((ord_less_eq_int B_30) A_32)->(((ord_less_eq_int C_14) zero_zero_int)->((ord_less_eq_int ((times_times_int A_32) C_14)) ((times_times_int B_30) C_14)))))
% 1.63/1.84 FOF formula (forall (C_13:real) (A_31:real) (B_29:real), (((ord_less_eq_real A_31) B_29)->(((ord_less_eq_real zero_zero_real) C_13)->((ord_less_eq_real ((times_times_real C_13) A_31)) ((times_times_real C_13) B_29))))) of role axiom named fact_785_comm__mult__left__mono
% 1.63/1.84 A new axiom: (forall (C_13:real) (A_31:real) (B_29:real), (((ord_less_eq_real A_31) B_29)->(((ord_less_eq_real zero_zero_real) C_13)->((ord_less_eq_real ((times_times_real C_13) A_31)) ((times_times_real C_13) B_29)))))
% 1.63/1.84 FOF formula (forall (C_13:nat) (A_31:nat) (B_29:nat), (((ord_less_eq_nat A_31) B_29)->(((ord_less_eq_nat zero_zero_nat) C_13)->((ord_less_eq_nat ((times_times_nat C_13) A_31)) ((times_times_nat C_13) B_29))))) of role axiom named fact_786_comm__mult__left__mono
% 1.63/1.84 A new axiom: (forall (C_13:nat) (A_31:nat) (B_29:nat), (((ord_less_eq_nat A_31) B_29)->(((ord_less_eq_nat zero_zero_nat) C_13)->((ord_less_eq_nat ((times_times_nat C_13) A_31)) ((times_times_nat C_13) B_29)))))
% 1.63/1.84 FOF formula (forall (C_13:int) (A_31:int) (B_29:int), (((ord_less_eq_int A_31) B_29)->(((ord_less_eq_int zero_zero_int) C_13)->((ord_less_eq_int ((times_times_int C_13) A_31)) ((times_times_int C_13) B_29))))) of role axiom named fact_787_comm__mult__left__mono
% 1.63/1.84 A new axiom: (forall (C_13:int) (A_31:int) (B_29:int), (((ord_less_eq_int A_31) B_29)->(((ord_less_eq_int zero_zero_int) C_13)->((ord_less_eq_int ((times_times_int C_13) A_31)) ((times_times_int C_13) B_29)))))
% 1.63/1.84 FOF formula (forall (C_12:real) (A_30:real) (B_28:real), (((ord_less_eq_real A_30) B_28)->(((ord_less_eq_real zero_zero_real) C_12)->((ord_less_eq_real ((times_times_real C_12) A_30)) ((times_times_real C_12) B_28))))) of role axiom named fact_788_mult__left__mono
% 1.63/1.84 A new axiom: (forall (C_12:real) (A_30:real) (B_28:real), (((ord_less_eq_real A_30) B_28)->(((ord_less_eq_real zero_zero_real) C_12)->((ord_less_eq_real ((times_times_real C_12) A_30)) ((times_times_real C_12) B_28)))))
% 1.63/1.84 FOF formula (forall (C_12:nat) (A_30:nat) (B_28:nat), (((ord_less_eq_nat A_30) B_28)->(((ord_less_eq_nat zero_zero_nat) C_12)->((ord_less_eq_nat ((times_times_nat C_12) A_30)) ((times_times_nat C_12) B_28))))) of role axiom named fact_789_mult__left__mono
% 1.63/1.84 A new axiom: (forall (C_12:nat) (A_30:nat) (B_28:nat), (((ord_less_eq_nat A_30) B_28)->(((ord_less_eq_nat zero_zero_nat) C_12)->((ord_less_eq_nat ((times_times_nat C_12) A_30)) ((times_times_nat C_12) B_28)))))
% 1.63/1.84 FOF formula (forall (C_12:int) (A_30:int) (B_28:int), (((ord_less_eq_int A_30) B_28)->(((ord_less_eq_int zero_zero_int) C_12)->((ord_less_eq_int ((times_times_int C_12) A_30)) ((times_times_int C_12) B_28))))) of role axiom named fact_790_mult__left__mono
% 1.63/1.84 A new axiom: (forall (C_12:int) (A_30:int) (B_28:int), (((ord_less_eq_int A_30) B_28)->(((ord_less_eq_int zero_zero_int) C_12)->((ord_less_eq_int ((times_times_int C_12) A_30)) ((times_times_int C_12) B_28)))))
% 1.63/1.84 FOF formula (forall (C_11:real) (A_29:real) (B_27:real), (((ord_less_eq_real A_29) B_27)->(((ord_less_eq_real zero_zero_real) C_11)->((ord_less_eq_real ((times_times_real A_29) C_11)) ((times_times_real B_27) C_11))))) of role axiom named fact_791_mult__right__mono
% 1.63/1.85 A new axiom: (forall (C_11:real) (A_29:real) (B_27:real), (((ord_less_eq_real A_29) B_27)->(((ord_less_eq_real zero_zero_real) C_11)->((ord_less_eq_real ((times_times_real A_29) C_11)) ((times_times_real B_27) C_11)))))
% 1.63/1.85 FOF formula (forall (C_11:nat) (A_29:nat) (B_27:nat), (((ord_less_eq_nat A_29) B_27)->(((ord_less_eq_nat zero_zero_nat) C_11)->((ord_less_eq_nat ((times_times_nat A_29) C_11)) ((times_times_nat B_27) C_11))))) of role axiom named fact_792_mult__right__mono
% 1.63/1.85 A new axiom: (forall (C_11:nat) (A_29:nat) (B_27:nat), (((ord_less_eq_nat A_29) B_27)->(((ord_less_eq_nat zero_zero_nat) C_11)->((ord_less_eq_nat ((times_times_nat A_29) C_11)) ((times_times_nat B_27) C_11)))))
% 1.63/1.85 FOF formula (forall (C_11:int) (A_29:int) (B_27:int), (((ord_less_eq_int A_29) B_27)->(((ord_less_eq_int zero_zero_int) C_11)->((ord_less_eq_int ((times_times_int A_29) C_11)) ((times_times_int B_27) C_11))))) of role axiom named fact_793_mult__right__mono
% 1.63/1.85 A new axiom: (forall (C_11:int) (A_29:int) (B_27:int), (((ord_less_eq_int A_29) B_27)->(((ord_less_eq_int zero_zero_int) C_11)->((ord_less_eq_int ((times_times_int A_29) C_11)) ((times_times_int B_27) C_11)))))
% 1.63/1.85 FOF formula (forall (B_26:real) (A_28:real), (((ord_less_eq_real A_28) zero_zero_real)->(((ord_less_eq_real B_26) zero_zero_real)->((ord_less_eq_real zero_zero_real) ((times_times_real A_28) B_26))))) of role axiom named fact_794_mult__nonpos__nonpos
% 1.63/1.85 A new axiom: (forall (B_26:real) (A_28:real), (((ord_less_eq_real A_28) zero_zero_real)->(((ord_less_eq_real B_26) zero_zero_real)->((ord_less_eq_real zero_zero_real) ((times_times_real A_28) B_26)))))
% 1.63/1.85 FOF formula (forall (B_26:int) (A_28:int), (((ord_less_eq_int A_28) zero_zero_int)->(((ord_less_eq_int B_26) zero_zero_int)->((ord_less_eq_int zero_zero_int) ((times_times_int A_28) B_26))))) of role axiom named fact_795_mult__nonpos__nonpos
% 1.63/1.85 A new axiom: (forall (B_26:int) (A_28:int), (((ord_less_eq_int A_28) zero_zero_int)->(((ord_less_eq_int B_26) zero_zero_int)->((ord_less_eq_int zero_zero_int) ((times_times_int A_28) B_26)))))
% 1.63/1.85 FOF formula (forall (B_25:real) (A_27:real), (((ord_less_eq_real A_27) zero_zero_real)->(((ord_less_eq_real zero_zero_real) B_25)->((ord_less_eq_real ((times_times_real A_27) B_25)) zero_zero_real)))) of role axiom named fact_796_mult__nonpos__nonneg
% 1.63/1.85 A new axiom: (forall (B_25:real) (A_27:real), (((ord_less_eq_real A_27) zero_zero_real)->(((ord_less_eq_real zero_zero_real) B_25)->((ord_less_eq_real ((times_times_real A_27) B_25)) zero_zero_real))))
% 1.63/1.85 FOF formula (forall (B_25:nat) (A_27:nat), (((ord_less_eq_nat A_27) zero_zero_nat)->(((ord_less_eq_nat zero_zero_nat) B_25)->((ord_less_eq_nat ((times_times_nat A_27) B_25)) zero_zero_nat)))) of role axiom named fact_797_mult__nonpos__nonneg
% 1.63/1.85 A new axiom: (forall (B_25:nat) (A_27:nat), (((ord_less_eq_nat A_27) zero_zero_nat)->(((ord_less_eq_nat zero_zero_nat) B_25)->((ord_less_eq_nat ((times_times_nat A_27) B_25)) zero_zero_nat))))
% 1.63/1.85 FOF formula (forall (B_25:int) (A_27:int), (((ord_less_eq_int A_27) zero_zero_int)->(((ord_less_eq_int zero_zero_int) B_25)->((ord_less_eq_int ((times_times_int A_27) B_25)) zero_zero_int)))) of role axiom named fact_798_mult__nonpos__nonneg
% 1.63/1.85 A new axiom: (forall (B_25:int) (A_27:int), (((ord_less_eq_int A_27) zero_zero_int)->(((ord_less_eq_int zero_zero_int) B_25)->((ord_less_eq_int ((times_times_int A_27) B_25)) zero_zero_int))))
% 1.63/1.85 FOF formula (forall (B_24:real) (A_26:real), (((ord_less_eq_real zero_zero_real) A_26)->(((ord_less_eq_real B_24) zero_zero_real)->((ord_less_eq_real ((times_times_real B_24) A_26)) zero_zero_real)))) of role axiom named fact_799_mult__nonneg__nonpos2
% 1.63/1.85 A new axiom: (forall (B_24:real) (A_26:real), (((ord_less_eq_real zero_zero_real) A_26)->(((ord_less_eq_real B_24) zero_zero_real)->((ord_less_eq_real ((times_times_real B_24) A_26)) zero_zero_real))))
% 1.63/1.85 FOF formula (forall (B_24:nat) (A_26:nat), (((ord_less_eq_nat zero_zero_nat) A_26)->(((ord_less_eq_nat B_24) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat B_24) A_26)) zero_zero_nat)))) of role axiom named fact_800_mult__nonneg__nonpos2
% 1.63/1.87 A new axiom: (forall (B_24:nat) (A_26:nat), (((ord_less_eq_nat zero_zero_nat) A_26)->(((ord_less_eq_nat B_24) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat B_24) A_26)) zero_zero_nat))))
% 1.63/1.87 FOF formula (forall (B_24:int) (A_26:int), (((ord_less_eq_int zero_zero_int) A_26)->(((ord_less_eq_int B_24) zero_zero_int)->((ord_less_eq_int ((times_times_int B_24) A_26)) zero_zero_int)))) of role axiom named fact_801_mult__nonneg__nonpos2
% 1.63/1.87 A new axiom: (forall (B_24:int) (A_26:int), (((ord_less_eq_int zero_zero_int) A_26)->(((ord_less_eq_int B_24) zero_zero_int)->((ord_less_eq_int ((times_times_int B_24) A_26)) zero_zero_int))))
% 1.63/1.87 FOF formula (forall (B_23:real) (A_25:real), (((ord_less_eq_real zero_zero_real) A_25)->(((ord_less_eq_real B_23) zero_zero_real)->((ord_less_eq_real ((times_times_real A_25) B_23)) zero_zero_real)))) of role axiom named fact_802_mult__nonneg__nonpos
% 1.63/1.87 A new axiom: (forall (B_23:real) (A_25:real), (((ord_less_eq_real zero_zero_real) A_25)->(((ord_less_eq_real B_23) zero_zero_real)->((ord_less_eq_real ((times_times_real A_25) B_23)) zero_zero_real))))
% 1.63/1.87 FOF formula (forall (B_23:nat) (A_25:nat), (((ord_less_eq_nat zero_zero_nat) A_25)->(((ord_less_eq_nat B_23) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat A_25) B_23)) zero_zero_nat)))) of role axiom named fact_803_mult__nonneg__nonpos
% 1.63/1.87 A new axiom: (forall (B_23:nat) (A_25:nat), (((ord_less_eq_nat zero_zero_nat) A_25)->(((ord_less_eq_nat B_23) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat A_25) B_23)) zero_zero_nat))))
% 1.63/1.87 FOF formula (forall (B_23:int) (A_25:int), (((ord_less_eq_int zero_zero_int) A_25)->(((ord_less_eq_int B_23) zero_zero_int)->((ord_less_eq_int ((times_times_int A_25) B_23)) zero_zero_int)))) of role axiom named fact_804_mult__nonneg__nonpos
% 1.63/1.87 A new axiom: (forall (B_23:int) (A_25:int), (((ord_less_eq_int zero_zero_int) A_25)->(((ord_less_eq_int B_23) zero_zero_int)->((ord_less_eq_int ((times_times_int A_25) B_23)) zero_zero_int))))
% 1.63/1.87 FOF formula (forall (B_22:real) (A_24:real), (((ord_less_eq_real zero_zero_real) A_24)->(((ord_less_eq_real zero_zero_real) B_22)->((ord_less_eq_real zero_zero_real) ((times_times_real A_24) B_22))))) of role axiom named fact_805_mult__nonneg__nonneg
% 1.63/1.87 A new axiom: (forall (B_22:real) (A_24:real), (((ord_less_eq_real zero_zero_real) A_24)->(((ord_less_eq_real zero_zero_real) B_22)->((ord_less_eq_real zero_zero_real) ((times_times_real A_24) B_22)))))
% 1.63/1.87 FOF formula (forall (B_22:nat) (A_24:nat), (((ord_less_eq_nat zero_zero_nat) A_24)->(((ord_less_eq_nat zero_zero_nat) B_22)->((ord_less_eq_nat zero_zero_nat) ((times_times_nat A_24) B_22))))) of role axiom named fact_806_mult__nonneg__nonneg
% 1.63/1.87 A new axiom: (forall (B_22:nat) (A_24:nat), (((ord_less_eq_nat zero_zero_nat) A_24)->(((ord_less_eq_nat zero_zero_nat) B_22)->((ord_less_eq_nat zero_zero_nat) ((times_times_nat A_24) B_22)))))
% 1.63/1.87 FOF formula (forall (B_22:int) (A_24:int), (((ord_less_eq_int zero_zero_int) A_24)->(((ord_less_eq_int zero_zero_int) B_22)->((ord_less_eq_int zero_zero_int) ((times_times_int A_24) B_22))))) of role axiom named fact_807_mult__nonneg__nonneg
% 1.63/1.87 A new axiom: (forall (B_22:int) (A_24:int), (((ord_less_eq_int zero_zero_int) A_24)->(((ord_less_eq_int zero_zero_int) B_22)->((ord_less_eq_int zero_zero_int) ((times_times_int A_24) B_22)))))
% 1.63/1.87 FOF formula (forall (A_23:real) (B_21:real), ((iff ((ord_less_eq_real ((times_times_real A_23) B_21)) zero_zero_real)) ((or ((and ((ord_less_eq_real zero_zero_real) A_23)) ((ord_less_eq_real B_21) zero_zero_real))) ((and ((ord_less_eq_real A_23) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_21))))) of role axiom named fact_808_mult__le__0__iff
% 1.63/1.87 A new axiom: (forall (A_23:real) (B_21:real), ((iff ((ord_less_eq_real ((times_times_real A_23) B_21)) zero_zero_real)) ((or ((and ((ord_less_eq_real zero_zero_real) A_23)) ((ord_less_eq_real B_21) zero_zero_real))) ((and ((ord_less_eq_real A_23) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_21)))))
% 1.63/1.88 FOF formula (forall (A_23:int) (B_21:int), ((iff ((ord_less_eq_int ((times_times_int A_23) B_21)) zero_zero_int)) ((or ((and ((ord_less_eq_int zero_zero_int) A_23)) ((ord_less_eq_int B_21) zero_zero_int))) ((and ((ord_less_eq_int A_23) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_21))))) of role axiom named fact_809_mult__le__0__iff
% 1.63/1.88 A new axiom: (forall (A_23:int) (B_21:int), ((iff ((ord_less_eq_int ((times_times_int A_23) B_21)) zero_zero_int)) ((or ((and ((ord_less_eq_int zero_zero_int) A_23)) ((ord_less_eq_int B_21) zero_zero_int))) ((and ((ord_less_eq_int A_23) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_21)))))
% 1.63/1.88 FOF formula (forall (A_22:real) (B_20:real), ((iff ((ord_less_eq_real zero_zero_real) ((times_times_real A_22) B_20))) ((or ((and ((ord_less_eq_real zero_zero_real) A_22)) ((ord_less_eq_real zero_zero_real) B_20))) ((and ((ord_less_eq_real A_22) zero_zero_real)) ((ord_less_eq_real B_20) zero_zero_real))))) of role axiom named fact_810_zero__le__mult__iff
% 1.63/1.88 A new axiom: (forall (A_22:real) (B_20:real), ((iff ((ord_less_eq_real zero_zero_real) ((times_times_real A_22) B_20))) ((or ((and ((ord_less_eq_real zero_zero_real) A_22)) ((ord_less_eq_real zero_zero_real) B_20))) ((and ((ord_less_eq_real A_22) zero_zero_real)) ((ord_less_eq_real B_20) zero_zero_real)))))
% 1.63/1.88 FOF formula (forall (A_22:int) (B_20:int), ((iff ((ord_less_eq_int zero_zero_int) ((times_times_int A_22) B_20))) ((or ((and ((ord_less_eq_int zero_zero_int) A_22)) ((ord_less_eq_int zero_zero_int) B_20))) ((and ((ord_less_eq_int A_22) zero_zero_int)) ((ord_less_eq_int B_20) zero_zero_int))))) of role axiom named fact_811_zero__le__mult__iff
% 1.63/1.88 A new axiom: (forall (A_22:int) (B_20:int), ((iff ((ord_less_eq_int zero_zero_int) ((times_times_int A_22) B_20))) ((or ((and ((ord_less_eq_int zero_zero_int) A_22)) ((ord_less_eq_int zero_zero_int) B_20))) ((and ((ord_less_eq_int A_22) zero_zero_int)) ((ord_less_eq_int B_20) zero_zero_int)))))
% 1.63/1.88 FOF formula (forall (A_21:real), ((ord_less_eq_real zero_zero_real) ((times_times_real A_21) A_21))) of role axiom named fact_812_zero__le__square
% 1.63/1.88 A new axiom: (forall (A_21:real), ((ord_less_eq_real zero_zero_real) ((times_times_real A_21) A_21)))
% 1.63/1.88 FOF formula (forall (A_21:int), ((ord_less_eq_int zero_zero_int) ((times_times_int A_21) A_21))) of role axiom named fact_813_zero__le__square
% 1.63/1.88 A new axiom: (forall (A_21:int), ((ord_less_eq_int zero_zero_int) ((times_times_int A_21) A_21)))
% 1.63/1.88 FOF formula (forall (C_10:real) (B_19:real) (A_20:real), (((ord_less_real B_19) A_20)->(((ord_less_real C_10) zero_zero_real)->((ord_less_real ((times_times_real C_10) A_20)) ((times_times_real C_10) B_19))))) of role axiom named fact_814_mult__strict__left__mono__neg
% 1.63/1.88 A new axiom: (forall (C_10:real) (B_19:real) (A_20:real), (((ord_less_real B_19) A_20)->(((ord_less_real C_10) zero_zero_real)->((ord_less_real ((times_times_real C_10) A_20)) ((times_times_real C_10) B_19)))))
% 1.63/1.88 FOF formula (forall (C_10:int) (B_19:int) (A_20:int), (((ord_less_int B_19) A_20)->(((ord_less_int C_10) zero_zero_int)->((ord_less_int ((times_times_int C_10) A_20)) ((times_times_int C_10) B_19))))) of role axiom named fact_815_mult__strict__left__mono__neg
% 1.63/1.88 A new axiom: (forall (C_10:int) (B_19:int) (A_20:int), (((ord_less_int B_19) A_20)->(((ord_less_int C_10) zero_zero_int)->((ord_less_int ((times_times_int C_10) A_20)) ((times_times_int C_10) B_19)))))
% 1.63/1.88 FOF formula (forall (C_9:real) (B_18:real) (A_19:real), (((ord_less_real B_18) A_19)->(((ord_less_real C_9) zero_zero_real)->((ord_less_real ((times_times_real A_19) C_9)) ((times_times_real B_18) C_9))))) of role axiom named fact_816_mult__strict__right__mono__neg
% 1.63/1.88 A new axiom: (forall (C_9:real) (B_18:real) (A_19:real), (((ord_less_real B_18) A_19)->(((ord_less_real C_9) zero_zero_real)->((ord_less_real ((times_times_real A_19) C_9)) ((times_times_real B_18) C_9)))))
% 1.63/1.88 FOF formula (forall (C_9:int) (B_18:int) (A_19:int), (((ord_less_int B_18) A_19)->(((ord_less_int C_9) zero_zero_int)->((ord_less_int ((times_times_int A_19) C_9)) ((times_times_int B_18) C_9))))) of role axiom named fact_817_mult__strict__right__mono__neg
% 1.63/1.90 A new axiom: (forall (C_9:int) (B_18:int) (A_19:int), (((ord_less_int B_18) A_19)->(((ord_less_int C_9) zero_zero_int)->((ord_less_int ((times_times_int A_19) C_9)) ((times_times_int B_18) C_9)))))
% 1.63/1.90 FOF formula (forall (C_8:real) (A_18:real) (B_17:real), (((ord_less_real A_18) B_17)->(((ord_less_real zero_zero_real) C_8)->((ord_less_real ((times_times_real C_8) A_18)) ((times_times_real C_8) B_17))))) of role axiom named fact_818_comm__mult__strict__left__mono
% 1.63/1.90 A new axiom: (forall (C_8:real) (A_18:real) (B_17:real), (((ord_less_real A_18) B_17)->(((ord_less_real zero_zero_real) C_8)->((ord_less_real ((times_times_real C_8) A_18)) ((times_times_real C_8) B_17)))))
% 1.63/1.90 FOF formula (forall (C_8:nat) (A_18:nat) (B_17:nat), (((ord_less_nat A_18) B_17)->(((ord_less_nat zero_zero_nat) C_8)->((ord_less_nat ((times_times_nat C_8) A_18)) ((times_times_nat C_8) B_17))))) of role axiom named fact_819_comm__mult__strict__left__mono
% 1.63/1.90 A new axiom: (forall (C_8:nat) (A_18:nat) (B_17:nat), (((ord_less_nat A_18) B_17)->(((ord_less_nat zero_zero_nat) C_8)->((ord_less_nat ((times_times_nat C_8) A_18)) ((times_times_nat C_8) B_17)))))
% 1.63/1.90 FOF formula (forall (C_8:int) (A_18:int) (B_17:int), (((ord_less_int A_18) B_17)->(((ord_less_int zero_zero_int) C_8)->((ord_less_int ((times_times_int C_8) A_18)) ((times_times_int C_8) B_17))))) of role axiom named fact_820_comm__mult__strict__left__mono
% 1.63/1.90 A new axiom: (forall (C_8:int) (A_18:int) (B_17:int), (((ord_less_int A_18) B_17)->(((ord_less_int zero_zero_int) C_8)->((ord_less_int ((times_times_int C_8) A_18)) ((times_times_int C_8) B_17)))))
% 1.63/1.90 FOF formula (forall (C_7:real) (A_17:real) (B_16:real), (((ord_less_real A_17) B_16)->(((ord_less_real zero_zero_real) C_7)->((ord_less_real ((times_times_real C_7) A_17)) ((times_times_real C_7) B_16))))) of role axiom named fact_821_mult__strict__left__mono
% 1.63/1.90 A new axiom: (forall (C_7:real) (A_17:real) (B_16:real), (((ord_less_real A_17) B_16)->(((ord_less_real zero_zero_real) C_7)->((ord_less_real ((times_times_real C_7) A_17)) ((times_times_real C_7) B_16)))))
% 1.63/1.90 FOF formula (forall (C_7:nat) (A_17:nat) (B_16:nat), (((ord_less_nat A_17) B_16)->(((ord_less_nat zero_zero_nat) C_7)->((ord_less_nat ((times_times_nat C_7) A_17)) ((times_times_nat C_7) B_16))))) of role axiom named fact_822_mult__strict__left__mono
% 1.63/1.90 A new axiom: (forall (C_7:nat) (A_17:nat) (B_16:nat), (((ord_less_nat A_17) B_16)->(((ord_less_nat zero_zero_nat) C_7)->((ord_less_nat ((times_times_nat C_7) A_17)) ((times_times_nat C_7) B_16)))))
% 1.63/1.90 FOF formula (forall (C_7:int) (A_17:int) (B_16:int), (((ord_less_int A_17) B_16)->(((ord_less_int zero_zero_int) C_7)->((ord_less_int ((times_times_int C_7) A_17)) ((times_times_int C_7) B_16))))) of role axiom named fact_823_mult__strict__left__mono
% 1.63/1.90 A new axiom: (forall (C_7:int) (A_17:int) (B_16:int), (((ord_less_int A_17) B_16)->(((ord_less_int zero_zero_int) C_7)->((ord_less_int ((times_times_int C_7) A_17)) ((times_times_int C_7) B_16)))))
% 1.63/1.90 FOF formula (forall (C_6:real) (A_16:real) (B_15:real), (((ord_less_real A_16) B_15)->(((ord_less_real zero_zero_real) C_6)->((ord_less_real ((times_times_real A_16) C_6)) ((times_times_real B_15) C_6))))) of role axiom named fact_824_mult__strict__right__mono
% 1.63/1.90 A new axiom: (forall (C_6:real) (A_16:real) (B_15:real), (((ord_less_real A_16) B_15)->(((ord_less_real zero_zero_real) C_6)->((ord_less_real ((times_times_real A_16) C_6)) ((times_times_real B_15) C_6)))))
% 1.63/1.90 FOF formula (forall (C_6:nat) (A_16:nat) (B_15:nat), (((ord_less_nat A_16) B_15)->(((ord_less_nat zero_zero_nat) C_6)->((ord_less_nat ((times_times_nat A_16) C_6)) ((times_times_nat B_15) C_6))))) of role axiom named fact_825_mult__strict__right__mono
% 1.63/1.90 A new axiom: (forall (C_6:nat) (A_16:nat) (B_15:nat), (((ord_less_nat A_16) B_15)->(((ord_less_nat zero_zero_nat) C_6)->((ord_less_nat ((times_times_nat A_16) C_6)) ((times_times_nat B_15) C_6)))))
% 1.63/1.90 FOF formula (forall (C_6:int) (A_16:int) (B_15:int), (((ord_less_int A_16) B_15)->(((ord_less_int zero_zero_int) C_6)->((ord_less_int ((times_times_int A_16) C_6)) ((times_times_int B_15) C_6))))) of role axiom named fact_826_mult__strict__right__mono
% 1.73/1.92 A new axiom: (forall (C_6:int) (A_16:int) (B_15:int), (((ord_less_int A_16) B_15)->(((ord_less_int zero_zero_int) C_6)->((ord_less_int ((times_times_int A_16) C_6)) ((times_times_int B_15) C_6)))))
% 1.73/1.92 FOF formula (forall (B_14:real) (A_15:real), (((ord_less_real A_15) zero_zero_real)->(((ord_less_real B_14) zero_zero_real)->((ord_less_real zero_zero_real) ((times_times_real A_15) B_14))))) of role axiom named fact_827_mult__neg__neg
% 1.73/1.92 A new axiom: (forall (B_14:real) (A_15:real), (((ord_less_real A_15) zero_zero_real)->(((ord_less_real B_14) zero_zero_real)->((ord_less_real zero_zero_real) ((times_times_real A_15) B_14)))))
% 1.73/1.92 FOF formula (forall (B_14:int) (A_15:int), (((ord_less_int A_15) zero_zero_int)->(((ord_less_int B_14) zero_zero_int)->((ord_less_int zero_zero_int) ((times_times_int A_15) B_14))))) of role axiom named fact_828_mult__neg__neg
% 1.73/1.92 A new axiom: (forall (B_14:int) (A_15:int), (((ord_less_int A_15) zero_zero_int)->(((ord_less_int B_14) zero_zero_int)->((ord_less_int zero_zero_int) ((times_times_int A_15) B_14)))))
% 1.73/1.92 FOF formula (forall (B_13:real) (A_14:real), (((ord_less_real A_14) zero_zero_real)->(((ord_less_real zero_zero_real) B_13)->((ord_less_real ((times_times_real A_14) B_13)) zero_zero_real)))) of role axiom named fact_829_mult__neg__pos
% 1.73/1.92 A new axiom: (forall (B_13:real) (A_14:real), (((ord_less_real A_14) zero_zero_real)->(((ord_less_real zero_zero_real) B_13)->((ord_less_real ((times_times_real A_14) B_13)) zero_zero_real))))
% 1.73/1.92 FOF formula (forall (B_13:nat) (A_14:nat), (((ord_less_nat A_14) zero_zero_nat)->(((ord_less_nat zero_zero_nat) B_13)->((ord_less_nat ((times_times_nat A_14) B_13)) zero_zero_nat)))) of role axiom named fact_830_mult__neg__pos
% 1.73/1.92 A new axiom: (forall (B_13:nat) (A_14:nat), (((ord_less_nat A_14) zero_zero_nat)->(((ord_less_nat zero_zero_nat) B_13)->((ord_less_nat ((times_times_nat A_14) B_13)) zero_zero_nat))))
% 1.73/1.92 FOF formula (forall (B_13:int) (A_14:int), (((ord_less_int A_14) zero_zero_int)->(((ord_less_int zero_zero_int) B_13)->((ord_less_int ((times_times_int A_14) B_13)) zero_zero_int)))) of role axiom named fact_831_mult__neg__pos
% 1.73/1.92 A new axiom: (forall (B_13:int) (A_14:int), (((ord_less_int A_14) zero_zero_int)->(((ord_less_int zero_zero_int) B_13)->((ord_less_int ((times_times_int A_14) B_13)) zero_zero_int))))
% 1.73/1.92 FOF formula (forall (A_13:real) (B_12:real) (C_5:real), (((ord_less_real C_5) zero_zero_real)->((iff ((ord_less_real ((times_times_real C_5) A_13)) ((times_times_real C_5) B_12))) ((ord_less_real B_12) A_13)))) of role axiom named fact_832_mult__less__cancel__left__neg
% 1.73/1.92 A new axiom: (forall (A_13:real) (B_12:real) (C_5:real), (((ord_less_real C_5) zero_zero_real)->((iff ((ord_less_real ((times_times_real C_5) A_13)) ((times_times_real C_5) B_12))) ((ord_less_real B_12) A_13))))
% 1.73/1.92 FOF formula (forall (A_13:int) (B_12:int) (C_5:int), (((ord_less_int C_5) zero_zero_int)->((iff ((ord_less_int ((times_times_int C_5) A_13)) ((times_times_int C_5) B_12))) ((ord_less_int B_12) A_13)))) of role axiom named fact_833_mult__less__cancel__left__neg
% 1.73/1.92 A new axiom: (forall (A_13:int) (B_12:int) (C_5:int), (((ord_less_int C_5) zero_zero_int)->((iff ((ord_less_int ((times_times_int C_5) A_13)) ((times_times_int C_5) B_12))) ((ord_less_int B_12) A_13))))
% 1.73/1.92 FOF formula (forall (B_11:real) (A_12:real), (((ord_less_real zero_zero_real) ((times_times_real B_11) A_12))->(((ord_less_real zero_zero_real) A_12)->((ord_less_real zero_zero_real) B_11)))) of role axiom named fact_834_zero__less__mult__pos2
% 1.73/1.92 A new axiom: (forall (B_11:real) (A_12:real), (((ord_less_real zero_zero_real) ((times_times_real B_11) A_12))->(((ord_less_real zero_zero_real) A_12)->((ord_less_real zero_zero_real) B_11))))
% 1.73/1.92 FOF formula (forall (B_11:nat) (A_12:nat), (((ord_less_nat zero_zero_nat) ((times_times_nat B_11) A_12))->(((ord_less_nat zero_zero_nat) A_12)->((ord_less_nat zero_zero_nat) B_11)))) of role axiom named fact_835_zero__less__mult__pos2
% 1.73/1.92 A new axiom: (forall (B_11:nat) (A_12:nat), (((ord_less_nat zero_zero_nat) ((times_times_nat B_11) A_12))->(((ord_less_nat zero_zero_nat) A_12)->((ord_less_nat zero_zero_nat) B_11))))
% 1.73/1.93 FOF formula (forall (B_11:int) (A_12:int), (((ord_less_int zero_zero_int) ((times_times_int B_11) A_12))->(((ord_less_int zero_zero_int) A_12)->((ord_less_int zero_zero_int) B_11)))) of role axiom named fact_836_zero__less__mult__pos2
% 1.73/1.93 A new axiom: (forall (B_11:int) (A_12:int), (((ord_less_int zero_zero_int) ((times_times_int B_11) A_12))->(((ord_less_int zero_zero_int) A_12)->((ord_less_int zero_zero_int) B_11))))
% 1.73/1.93 FOF formula (forall (A_11:real) (B_10:real), (((ord_less_real zero_zero_real) ((times_times_real A_11) B_10))->(((ord_less_real zero_zero_real) A_11)->((ord_less_real zero_zero_real) B_10)))) of role axiom named fact_837_zero__less__mult__pos
% 1.73/1.93 A new axiom: (forall (A_11:real) (B_10:real), (((ord_less_real zero_zero_real) ((times_times_real A_11) B_10))->(((ord_less_real zero_zero_real) A_11)->((ord_less_real zero_zero_real) B_10))))
% 1.73/1.93 FOF formula (forall (A_11:nat) (B_10:nat), (((ord_less_nat zero_zero_nat) ((times_times_nat A_11) B_10))->(((ord_less_nat zero_zero_nat) A_11)->((ord_less_nat zero_zero_nat) B_10)))) of role axiom named fact_838_zero__less__mult__pos
% 1.73/1.93 A new axiom: (forall (A_11:nat) (B_10:nat), (((ord_less_nat zero_zero_nat) ((times_times_nat A_11) B_10))->(((ord_less_nat zero_zero_nat) A_11)->((ord_less_nat zero_zero_nat) B_10))))
% 1.73/1.93 FOF formula (forall (A_11:int) (B_10:int), (((ord_less_int zero_zero_int) ((times_times_int A_11) B_10))->(((ord_less_int zero_zero_int) A_11)->((ord_less_int zero_zero_int) B_10)))) of role axiom named fact_839_zero__less__mult__pos
% 1.73/1.93 A new axiom: (forall (A_11:int) (B_10:int), (((ord_less_int zero_zero_int) ((times_times_int A_11) B_10))->(((ord_less_int zero_zero_int) A_11)->((ord_less_int zero_zero_int) B_10))))
% 1.73/1.93 FOF formula (forall (B_9:real) (A_10:real), (((ord_less_real zero_zero_real) A_10)->(((ord_less_real B_9) zero_zero_real)->((ord_less_real ((times_times_real B_9) A_10)) zero_zero_real)))) of role axiom named fact_840_mult__pos__neg2
% 1.73/1.93 A new axiom: (forall (B_9:real) (A_10:real), (((ord_less_real zero_zero_real) A_10)->(((ord_less_real B_9) zero_zero_real)->((ord_less_real ((times_times_real B_9) A_10)) zero_zero_real))))
% 1.73/1.93 FOF formula (forall (B_9:nat) (A_10:nat), (((ord_less_nat zero_zero_nat) A_10)->(((ord_less_nat B_9) zero_zero_nat)->((ord_less_nat ((times_times_nat B_9) A_10)) zero_zero_nat)))) of role axiom named fact_841_mult__pos__neg2
% 1.73/1.93 A new axiom: (forall (B_9:nat) (A_10:nat), (((ord_less_nat zero_zero_nat) A_10)->(((ord_less_nat B_9) zero_zero_nat)->((ord_less_nat ((times_times_nat B_9) A_10)) zero_zero_nat))))
% 1.73/1.93 FOF formula (forall (B_9:int) (A_10:int), (((ord_less_int zero_zero_int) A_10)->(((ord_less_int B_9) zero_zero_int)->((ord_less_int ((times_times_int B_9) A_10)) zero_zero_int)))) of role axiom named fact_842_mult__pos__neg2
% 1.73/1.93 A new axiom: (forall (B_9:int) (A_10:int), (((ord_less_int zero_zero_int) A_10)->(((ord_less_int B_9) zero_zero_int)->((ord_less_int ((times_times_int B_9) A_10)) zero_zero_int))))
% 1.73/1.93 FOF formula (forall (B_8:real) (A_9:real), (((ord_less_real zero_zero_real) A_9)->(((ord_less_real B_8) zero_zero_real)->((ord_less_real ((times_times_real A_9) B_8)) zero_zero_real)))) of role axiom named fact_843_mult__pos__neg
% 1.73/1.93 A new axiom: (forall (B_8:real) (A_9:real), (((ord_less_real zero_zero_real) A_9)->(((ord_less_real B_8) zero_zero_real)->((ord_less_real ((times_times_real A_9) B_8)) zero_zero_real))))
% 1.73/1.93 FOF formula (forall (B_8:nat) (A_9:nat), (((ord_less_nat zero_zero_nat) A_9)->(((ord_less_nat B_8) zero_zero_nat)->((ord_less_nat ((times_times_nat A_9) B_8)) zero_zero_nat)))) of role axiom named fact_844_mult__pos__neg
% 1.73/1.93 A new axiom: (forall (B_8:nat) (A_9:nat), (((ord_less_nat zero_zero_nat) A_9)->(((ord_less_nat B_8) zero_zero_nat)->((ord_less_nat ((times_times_nat A_9) B_8)) zero_zero_nat))))
% 1.73/1.93 FOF formula (forall (B_8:int) (A_9:int), (((ord_less_int zero_zero_int) A_9)->(((ord_less_int B_8) zero_zero_int)->((ord_less_int ((times_times_int A_9) B_8)) zero_zero_int)))) of role axiom named fact_845_mult__pos__neg
% 1.73/1.93 A new axiom: (forall (B_8:int) (A_9:int), (((ord_less_int zero_zero_int) A_9)->(((ord_less_int B_8) zero_zero_int)->((ord_less_int ((times_times_int A_9) B_8)) zero_zero_int))))
% 1.73/1.95 FOF formula (forall (B_7:real) (A_8:real), (((ord_less_real zero_zero_real) A_8)->(((ord_less_real zero_zero_real) B_7)->((ord_less_real zero_zero_real) ((times_times_real A_8) B_7))))) of role axiom named fact_846_mult__pos__pos
% 1.73/1.95 A new axiom: (forall (B_7:real) (A_8:real), (((ord_less_real zero_zero_real) A_8)->(((ord_less_real zero_zero_real) B_7)->((ord_less_real zero_zero_real) ((times_times_real A_8) B_7)))))
% 1.73/1.95 FOF formula (forall (B_7:nat) (A_8:nat), (((ord_less_nat zero_zero_nat) A_8)->(((ord_less_nat zero_zero_nat) B_7)->((ord_less_nat zero_zero_nat) ((times_times_nat A_8) B_7))))) of role axiom named fact_847_mult__pos__pos
% 1.73/1.95 A new axiom: (forall (B_7:nat) (A_8:nat), (((ord_less_nat zero_zero_nat) A_8)->(((ord_less_nat zero_zero_nat) B_7)->((ord_less_nat zero_zero_nat) ((times_times_nat A_8) B_7)))))
% 1.73/1.95 FOF formula (forall (B_7:int) (A_8:int), (((ord_less_int zero_zero_int) A_8)->(((ord_less_int zero_zero_int) B_7)->((ord_less_int zero_zero_int) ((times_times_int A_8) B_7))))) of role axiom named fact_848_mult__pos__pos
% 1.73/1.95 A new axiom: (forall (B_7:int) (A_8:int), (((ord_less_int zero_zero_int) A_8)->(((ord_less_int zero_zero_int) B_7)->((ord_less_int zero_zero_int) ((times_times_int A_8) B_7)))))
% 1.73/1.95 FOF formula (forall (A_7:real) (B_6:real) (C_4:real), (((ord_less_real zero_zero_real) C_4)->((iff ((ord_less_real ((times_times_real C_4) A_7)) ((times_times_real C_4) B_6))) ((ord_less_real A_7) B_6)))) of role axiom named fact_849_mult__less__cancel__left__pos
% 1.73/1.95 A new axiom: (forall (A_7:real) (B_6:real) (C_4:real), (((ord_less_real zero_zero_real) C_4)->((iff ((ord_less_real ((times_times_real C_4) A_7)) ((times_times_real C_4) B_6))) ((ord_less_real A_7) B_6))))
% 1.73/1.95 FOF formula (forall (A_7:int) (B_6:int) (C_4:int), (((ord_less_int zero_zero_int) C_4)->((iff ((ord_less_int ((times_times_int C_4) A_7)) ((times_times_int C_4) B_6))) ((ord_less_int A_7) B_6)))) of role axiom named fact_850_mult__less__cancel__left__pos
% 1.73/1.95 A new axiom: (forall (A_7:int) (B_6:int) (C_4:int), (((ord_less_int zero_zero_int) C_4)->((iff ((ord_less_int ((times_times_int C_4) A_7)) ((times_times_int C_4) B_6))) ((ord_less_int A_7) B_6))))
% 1.73/1.95 FOF formula (forall (C_3:real) (A_6:real) (B_5:real), ((iff ((ord_less_real ((times_times_real C_3) A_6)) ((times_times_real C_3) B_5))) ((or ((and ((ord_less_real zero_zero_real) C_3)) ((ord_less_real A_6) B_5))) ((and ((ord_less_real C_3) zero_zero_real)) ((ord_less_real B_5) A_6))))) of role axiom named fact_851_mult__less__cancel__left__disj
% 1.73/1.95 A new axiom: (forall (C_3:real) (A_6:real) (B_5:real), ((iff ((ord_less_real ((times_times_real C_3) A_6)) ((times_times_real C_3) B_5))) ((or ((and ((ord_less_real zero_zero_real) C_3)) ((ord_less_real A_6) B_5))) ((and ((ord_less_real C_3) zero_zero_real)) ((ord_less_real B_5) A_6)))))
% 1.73/1.95 FOF formula (forall (C_3:int) (A_6:int) (B_5:int), ((iff ((ord_less_int ((times_times_int C_3) A_6)) ((times_times_int C_3) B_5))) ((or ((and ((ord_less_int zero_zero_int) C_3)) ((ord_less_int A_6) B_5))) ((and ((ord_less_int C_3) zero_zero_int)) ((ord_less_int B_5) A_6))))) of role axiom named fact_852_mult__less__cancel__left__disj
% 1.73/1.95 A new axiom: (forall (C_3:int) (A_6:int) (B_5:int), ((iff ((ord_less_int ((times_times_int C_3) A_6)) ((times_times_int C_3) B_5))) ((or ((and ((ord_less_int zero_zero_int) C_3)) ((ord_less_int A_6) B_5))) ((and ((ord_less_int C_3) zero_zero_int)) ((ord_less_int B_5) A_6)))))
% 1.73/1.95 FOF formula (forall (A_5:real) (C_2:real) (B_4:real), ((iff ((ord_less_real ((times_times_real A_5) C_2)) ((times_times_real B_4) C_2))) ((or ((and ((ord_less_real zero_zero_real) C_2)) ((ord_less_real A_5) B_4))) ((and ((ord_less_real C_2) zero_zero_real)) ((ord_less_real B_4) A_5))))) of role axiom named fact_853_mult__less__cancel__right__disj
% 1.73/1.95 A new axiom: (forall (A_5:real) (C_2:real) (B_4:real), ((iff ((ord_less_real ((times_times_real A_5) C_2)) ((times_times_real B_4) C_2))) ((or ((and ((ord_less_real zero_zero_real) C_2)) ((ord_less_real A_5) B_4))) ((and ((ord_less_real C_2) zero_zero_real)) ((ord_less_real B_4) A_5)))))
% 1.73/1.97 FOF formula (forall (A_5:int) (C_2:int) (B_4:int), ((iff ((ord_less_int ((times_times_int A_5) C_2)) ((times_times_int B_4) C_2))) ((or ((and ((ord_less_int zero_zero_int) C_2)) ((ord_less_int A_5) B_4))) ((and ((ord_less_int C_2) zero_zero_int)) ((ord_less_int B_4) A_5))))) of role axiom named fact_854_mult__less__cancel__right__disj
% 1.73/1.97 A new axiom: (forall (A_5:int) (C_2:int) (B_4:int), ((iff ((ord_less_int ((times_times_int A_5) C_2)) ((times_times_int B_4) C_2))) ((or ((and ((ord_less_int zero_zero_int) C_2)) ((ord_less_int A_5) B_4))) ((and ((ord_less_int C_2) zero_zero_int)) ((ord_less_int B_4) A_5)))))
% 1.73/1.97 FOF formula (forall (A_4:real), (((ord_less_real ((times_times_real A_4) A_4)) zero_zero_real)->False)) of role axiom named fact_855_not__square__less__zero
% 1.73/1.97 A new axiom: (forall (A_4:real), (((ord_less_real ((times_times_real A_4) A_4)) zero_zero_real)->False))
% 1.73/1.97 FOF formula (forall (A_4:int), (((ord_less_int ((times_times_int A_4) A_4)) zero_zero_int)->False)) of role axiom named fact_856_not__square__less__zero
% 1.73/1.97 A new axiom: (forall (A_4:int), (((ord_less_int ((times_times_int A_4) A_4)) zero_zero_int)->False))
% 1.73/1.97 FOF formula (forall (B_3:nat) (C_1:nat) (A_3:nat), (((ord_less_nat zero_zero_nat) A_3)->(((ord_less_nat B_3) C_1)->((ord_less_nat B_3) ((plus_plus_nat A_3) C_1))))) of role axiom named fact_857_pos__add__strict
% 1.73/1.97 A new axiom: (forall (B_3:nat) (C_1:nat) (A_3:nat), (((ord_less_nat zero_zero_nat) A_3)->(((ord_less_nat B_3) C_1)->((ord_less_nat B_3) ((plus_plus_nat A_3) C_1)))))
% 1.73/1.97 FOF formula (forall (B_3:int) (C_1:int) (A_3:int), (((ord_less_int zero_zero_int) A_3)->(((ord_less_int B_3) C_1)->((ord_less_int B_3) ((plus_plus_int A_3) C_1))))) of role axiom named fact_858_pos__add__strict
% 1.73/1.97 A new axiom: (forall (B_3:int) (C_1:int) (A_3:int), (((ord_less_int zero_zero_int) A_3)->(((ord_less_int B_3) C_1)->((ord_less_int B_3) ((plus_plus_int A_3) C_1)))))
% 1.73/1.97 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_859_divides__ge
% 1.73/1.97 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))))
% 1.73/1.97 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_860_nat__mult__dvd__cancel__disj_H
% 1.73/1.97 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))))
% 1.73/1.97 FOF formula (forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_real ((times_times_real X_1) Z)) ((times_times_real Y_1) Z))) ((ord_less_real X_1) Y_1)))) of role axiom named fact_861_real__mult__less__iff1
% 1.73/1.97 A new axiom: (forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_real ((times_times_real X_1) Z)) ((times_times_real Y_1) Z))) ((ord_less_real X_1) Y_1))))
% 1.73/1.97 FOF formula (forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real X_1) Z)) ((times_times_real Y_1) Z))) ((ord_less_eq_real X_1) Y_1)))) of role axiom named fact_862_real__mult__le__cancel__iff1
% 1.73/1.97 A new axiom: (forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real X_1) Z)) ((times_times_real Y_1) Z))) ((ord_less_eq_real X_1) Y_1))))
% 1.73/1.97 FOF formula (forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real Z) X_1)) ((times_times_real Z) Y_1))) ((ord_less_eq_real X_1) Y_1)))) of role axiom named fact_863_real__mult__le__cancel__iff2
% 1.73/1.97 A new axiom: (forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real Z) X_1)) ((times_times_real Z) Y_1))) ((ord_less_eq_real X_1) Y_1))))
% 1.73/1.97 FOF formula (forall (Y_1:real) (X_1:real), (((ord_less_real zero_zero_real) X_1)->(((ord_less_real zero_zero_real) Y_1)->((ord_less_real zero_zero_real) ((times_times_real X_1) Y_1))))) of role axiom named fact_864_real__mult__order
% 1.73/1.99 A new axiom: (forall (Y_1:real) (X_1:real), (((ord_less_real zero_zero_real) X_1)->(((ord_less_real zero_zero_real) Y_1)->((ord_less_real zero_zero_real) ((times_times_real X_1) Y_1)))))
% 1.73/1.99 FOF formula (forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->(((ord_less_real X_1) Y_1)->((ord_less_real ((times_times_real Z) X_1)) ((times_times_real Z) Y_1))))) of role axiom named fact_865_real__mult__less__mono2
% 1.73/1.99 A new axiom: (forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->(((ord_less_real X_1) Y_1)->((ord_less_real ((times_times_real Z) X_1)) ((times_times_real Z) Y_1)))))
% 1.73/1.99 FOF formula (forall (X_1:real) (Y_1:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X_1) X_1)) ((times_times_real Y_1) Y_1))) zero_zero_real)) ((and (((eq real) X_1) zero_zero_real)) (((eq real) Y_1) zero_zero_real)))) of role axiom named fact_866_real__two__squares__add__zero__iff
% 1.73/1.99 A new axiom: (forall (X_1:real) (Y_1:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X_1) X_1)) ((times_times_real Y_1) Y_1))) zero_zero_real)) ((and (((eq real) X_1) zero_zero_real)) (((eq real) Y_1) zero_zero_real))))
% 1.73/1.99 FOF formula (forall (X_1:nat) (Y_1:nat) (N:nat), ((not (((eq nat) N) zero_zero_nat))->(((dvd_dvd_nat ((power_power_nat X_1) N)) Y_1)->((dvd_dvd_nat X_1) Y_1)))) of role axiom named fact_867_divides__exp2
% 1.73/1.99 A new axiom: (forall (X_1:nat) (Y_1:nat) (N:nat), ((not (((eq nat) N) zero_zero_nat))->(((dvd_dvd_nat ((power_power_nat X_1) N)) Y_1)->((dvd_dvd_nat X_1) Y_1))))
% 1.73/1.99 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_868_divides__rev
% 1.73/1.99 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))))
% 1.73/1.99 FOF formula (forall (X_1:nat) (N:nat), ((iff (((eq nat) ((power_power_nat X_1) N)) one_one_nat)) ((or (((eq nat) X_1) one_one_nat)) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_869_exp__eq__1
% 1.73/1.99 A new axiom: (forall (X_1:nat) (N:nat), ((iff (((eq nat) ((power_power_nat X_1) N)) one_one_nat)) ((or (((eq nat) X_1) one_one_nat)) (((eq nat) N) zero_zero_nat))))
% 1.73/1.99 FOF formula (forall (X_1:nat) (Q:nat) (N:nat) (R:nat), ((((eq nat) X_1) ((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_1)->False))))) of role axiom named fact_870_divides__div__not
% 1.73/1.99 A new axiom: (forall (X_1:nat) (Q:nat) (N:nat) (R:nat), ((((eq nat) X_1) ((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_1)->False)))))
% 1.73/1.99 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_871_two__realpow__ge__one
% 1.73/1.99 A new axiom: (forall (N:nat), ((ord_less_eq_real one_one_real) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N)))
% 1.73/1.99 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_872_realpow__pos__nth
% 1.73/1.99 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)))))))
% 1.73/1.99 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:real)=> ((and ((and ((ord_less_real zero_zero_real) X)) (((eq real) ((power_power_real X) N)) A))) (forall (Y:real), (((and ((ord_less_real zero_zero_real) Y)) (((eq real) ((power_power_real Y) N)) A))->(((eq real) Y) X))))))))) of role axiom named fact_873_realpow__pos__nth__unique
% 1.73/1.99 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:real)=> ((and ((and ((ord_less_real zero_zero_real) X)) (((eq real) ((power_power_real X) N)) A))) (forall (Y:real), (((and ((ord_less_real zero_zero_real) Y)) (((eq real) ((power_power_real Y) N)) A))->(((eq real) Y) X)))))))))
% 1.81/2.01 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_874_dvd__mult__cancel2
% 1.81/2.01 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))))
% 1.81/2.01 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_875_dvd__mult__cancel1
% 1.81/2.01 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))))
% 1.81/2.01 FOF formula (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) of role axiom named fact_876_le0
% 1.81/2.01 A new axiom: (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N))
% 1.81/2.01 FOF formula (forall (X_1:nat), ((dvd_dvd_nat X_1) X_1)) of role axiom named fact_877_dvd_Oorder__refl
% 1.81/2.01 A new axiom: (forall (X_1:nat), ((dvd_dvd_nat X_1) X_1))
% 1.81/2.01 FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_878_less__zeroE
% 1.81/2.01 A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False))
% 1.81/2.01 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_879_diff__commute
% 1.81/2.01 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)))
% 1.81/2.01 FOF formula (forall (W:real), ((ord_less_eq_real W) W)) of role axiom named fact_880_real__le__refl
% 1.81/2.01 A new axiom: (forall (W:real), ((ord_less_eq_real W) W))
% 1.81/2.01 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_881_real__le__linear
% 1.81/2.01 A new axiom: (forall (Z:real) (W:real), ((or ((ord_less_eq_real Z) W)) ((ord_less_eq_real W) Z)))
% 1.81/2.01 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_882_real__le__trans
% 1.81/2.01 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))))
% 1.81/2.01 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_883_real__le__antisym
% 1.81/2.01 A new axiom: (forall (Z:real) (W:real), (((ord_less_eq_real Z) W)->(((ord_less_eq_real W) Z)->(((eq real) Z) W))))
% 1.81/2.01 FOF formula (forall (N:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N)) zero_zero_nat)) of role axiom named fact_884_diff__0__eq__0
% 1.81/2.01 A new axiom: (forall (N:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N)) zero_zero_nat))
% 1.81/2.01 FOF formula (forall (M:nat), (((eq nat) ((minus_minus_nat M) zero_zero_nat)) M)) of role axiom named fact_885_minus__nat_Odiff__0
% 1.81/2.01 A new axiom: (forall (M:nat), (((eq nat) ((minus_minus_nat M) zero_zero_nat)) M))
% 1.81/2.01 FOF formula (forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat)) of role axiom named fact_886_diff__self__eq__0
% 1.81/2.01 A new axiom: (forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat))
% 1.81/2.01 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_887_diffs0__imp__equal
% 1.81/2.01 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))))
% 1.81/2.01 FOF formula (forall (P_1:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P_1 N) M))->(((((eq nat) M) N)->((P_1 N) M))->((((ord_less_nat N) M)->((P_1 N) M))->((P_1 N) M))))) of role axiom named fact_888_nat__less__cases
% 1.81/2.03 A new axiom: (forall (P_1:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P_1 N) M))->(((((eq nat) M) N)->((P_1 N) M))->((((ord_less_nat N) M)->((P_1 N) M))->((P_1 N) M)))))
% 1.81/2.03 FOF formula (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))) of role axiom named fact_889_less__not__refl3
% 1.81/2.03 A new axiom: (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T))))
% 1.81/2.03 FOF formula (forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N)))) of role axiom named fact_890_less__not__refl2
% 1.81/2.03 A new axiom: (forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N))))
% 1.81/2.03 FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_891_less__irrefl__nat
% 1.81/2.03 A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False))
% 1.81/2.03 FOF formula (forall (X_1:nat) (Y_1:nat), ((not (((eq nat) X_1) Y_1))->((((ord_less_nat X_1) Y_1)->False)->((ord_less_nat Y_1) X_1)))) of role axiom named fact_892_linorder__neqE__nat
% 1.81/2.03 A new axiom: (forall (X_1:nat) (Y_1:nat), ((not (((eq nat) X_1) Y_1))->((((ord_less_nat X_1) Y_1)->False)->((ord_less_nat Y_1) X_1))))
% 1.81/2.03 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_893_nat__neq__iff
% 1.81/2.03 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))))
% 1.81/2.03 FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_894_less__not__refl
% 1.81/2.03 A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False))
% 1.81/2.03 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_895_diff__less__mono2
% 1.81/2.03 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)))))
% 1.81/2.03 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_896_less__imp__diff__less
% 1.81/2.03 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)))
% 1.81/2.03 FOF formula (forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((and ((dvd_dvd_nat Y_1) X_1)) (((dvd_dvd_nat X_1) Y_1)->False))->False))) of role axiom named fact_897_dvd_Oless__asym
% 1.81/2.03 A new axiom: (forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((and ((dvd_dvd_nat Y_1) X_1)) (((dvd_dvd_nat X_1) Y_1)->False))->False)))
% 1.81/2.03 FOF formula (forall (Z:nat) (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((and ((dvd_dvd_nat Y_1) Z)) (((dvd_dvd_nat Z) Y_1)->False))->((and ((dvd_dvd_nat X_1) Z)) (((dvd_dvd_nat Z) X_1)->False))))) of role axiom named fact_898_dvd_Oless__trans
% 1.81/2.03 A new axiom: (forall (Z:nat) (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((and ((dvd_dvd_nat Y_1) Z)) (((dvd_dvd_nat Z) Y_1)->False))->((and ((dvd_dvd_nat X_1) Z)) (((dvd_dvd_nat Z) X_1)->False)))))
% 1.81/2.03 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_899_dvd_Oless__asym_H
% 1.81/2.03 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)))
% 1.81/2.03 FOF formula (forall (Z:nat) (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((dvd_dvd_nat Y_1) Z)->((and ((dvd_dvd_nat X_1) Z)) (((dvd_dvd_nat Z) X_1)->False))))) of role axiom named fact_900_dvd_Oless__le__trans
% 1.81/2.03 A new axiom: (forall (Z:nat) (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((dvd_dvd_nat Y_1) Z)->((and ((dvd_dvd_nat X_1) Z)) (((dvd_dvd_nat Z) X_1)->False)))))
% 1.81/2.05 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_901_dvd_Oord__less__eq__trans
% 1.81/2.05 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)))))
% 1.81/2.05 FOF formula (forall (P_1:Prop) (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((and ((dvd_dvd_nat Y_1) X_1)) (((dvd_dvd_nat X_1) Y_1)->False))->P_1))) of role axiom named fact_902_dvd_Oless__imp__triv
% 1.81/2.05 A new axiom: (forall (P_1:Prop) (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((and ((dvd_dvd_nat Y_1) X_1)) (((dvd_dvd_nat X_1) Y_1)->False))->P_1)))
% 1.81/2.05 FOF formula (forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(not (((eq nat) Y_1) X_1)))) of role axiom named fact_903_dvd_Oless__imp__not__eq2
% 1.81/2.05 A new axiom: (forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(not (((eq nat) Y_1) X_1))))
% 1.81/2.05 FOF formula (forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(not (((eq nat) X_1) Y_1)))) of role axiom named fact_904_dvd_Oless__imp__not__eq
% 1.81/2.05 A new axiom: (forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(not (((eq nat) X_1) Y_1))))
% 1.81/2.05 FOF formula (forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((and ((dvd_dvd_nat Y_1) X_1)) (((dvd_dvd_nat X_1) Y_1)->False))->False))) of role axiom named fact_905_dvd_Oless__imp__not__less
% 1.81/2.05 A new axiom: (forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((and ((dvd_dvd_nat Y_1) X_1)) (((dvd_dvd_nat X_1) Y_1)->False))->False)))
% 1.81/2.05 FOF formula (forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->((dvd_dvd_nat X_1) Y_1))) of role axiom named fact_906_dvd_Oless__imp__le
% 1.81/2.05 A new axiom: (forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->((dvd_dvd_nat X_1) Y_1)))
% 1.81/2.05 FOF formula (forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((and ((dvd_dvd_nat Y_1) X_1)) (((dvd_dvd_nat X_1) Y_1)->False))->False))) of role axiom named fact_907_dvd_Oless__not__sym
% 1.81/2.05 A new axiom: (forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((and ((dvd_dvd_nat Y_1) X_1)) (((dvd_dvd_nat X_1) Y_1)->False))->False)))
% 1.81/2.05 FOF formula (forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(not (((eq nat) X_1) Y_1)))) of role axiom named fact_908_dvd_Oless__imp__neq
% 1.81/2.05 A new axiom: (forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(not (((eq nat) X_1) Y_1))))
% 1.81/2.05 FOF formula (forall (Z:nat) (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->(((and ((dvd_dvd_nat Y_1) Z)) (((dvd_dvd_nat Z) Y_1)->False))->((and ((dvd_dvd_nat X_1) Z)) (((dvd_dvd_nat Z) X_1)->False))))) of role axiom named fact_909_dvd_Ole__less__trans
% 1.81/2.05 A new axiom: (forall (Z:nat) (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->(((and ((dvd_dvd_nat Y_1) Z)) (((dvd_dvd_nat Z) Y_1)->False))->((and ((dvd_dvd_nat X_1) Z)) (((dvd_dvd_nat Z) X_1)->False)))))
% 1.81/2.05 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_910_dvd_Oord__eq__less__trans
% 1.81/2.05 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)))))
% 1.81/2.05 FOF formula (forall (Z:nat) (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->(((dvd_dvd_nat Y_1) Z)->((dvd_dvd_nat X_1) Z)))) of role axiom named fact_911_dvd_Oorder__trans
% 1.81/2.05 A new axiom: (forall (Z:nat) (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->(((dvd_dvd_nat Y_1) Z)->((dvd_dvd_nat X_1) Z))))
% 1.81/2.07 FOF formula (forall (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->(((dvd_dvd_nat Y_1) X_1)->(((eq nat) X_1) Y_1)))) of role axiom named fact_912_dvd_Oantisym
% 1.81/2.07 A new axiom: (forall (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->(((dvd_dvd_nat Y_1) X_1)->(((eq nat) X_1) Y_1))))
% 1.81/2.07 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_913_dvd__antisym
% 1.81/2.07 A new axiom: (forall (M:nat) (N:nat), (((dvd_dvd_nat M) N)->(((dvd_dvd_nat N) M)->(((eq nat) M) N))))
% 1.81/2.07 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_914_dvd_Oord__le__eq__trans
% 1.81/2.07 A new axiom: (forall (C:nat) (A:nat) (B:nat), (((dvd_dvd_nat A) B)->((((eq nat) B) C)->((dvd_dvd_nat A) C))))
% 1.81/2.07 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_915_dvd_Oord__eq__le__trans
% 1.81/2.07 A new axiom: (forall (C:nat) (A:nat) (B:nat), ((((eq nat) A) B)->(((dvd_dvd_nat B) C)->((dvd_dvd_nat A) C))))
% 1.81/2.07 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_916_dvd_Ole__neq__trans
% 1.81/2.07 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)))))
% 1.81/2.07 FOF formula (forall (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->((or ((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))) (((eq nat) X_1) Y_1)))) of role axiom named fact_917_dvd_Ole__imp__less__or__eq
% 1.81/2.07 A new axiom: (forall (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->((or ((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))) (((eq nat) X_1) Y_1))))
% 1.81/2.07 FOF formula (forall (Y_1:nat) (X_1:nat), (((dvd_dvd_nat Y_1) X_1)->((iff ((dvd_dvd_nat X_1) Y_1)) (((eq nat) X_1) Y_1)))) of role axiom named fact_918_dvd_Oantisym__conv
% 1.81/2.07 A new axiom: (forall (Y_1:nat) (X_1:nat), (((dvd_dvd_nat Y_1) X_1)->((iff ((dvd_dvd_nat X_1) Y_1)) (((eq nat) X_1) Y_1))))
% 1.81/2.07 FOF formula (forall (X_1:nat) (Y_1:nat), ((((eq nat) X_1) Y_1)->((dvd_dvd_nat X_1) Y_1))) of role axiom named fact_919_dvd_Oeq__refl
% 1.81/2.07 A new axiom: (forall (X_1:nat) (Y_1:nat), ((((eq nat) X_1) Y_1)->((dvd_dvd_nat X_1) Y_1)))
% 1.81/2.07 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_920_dvd_Oneq__le__trans
% 1.81/2.07 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)))))
% 1.81/2.07 FOF formula (forall (X_1:nat) (Y_1:nat), ((iff ((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))) ((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False)))) of role axiom named fact_921_dvd_Oless__le__not__le
% 1.81/2.07 A new axiom: (forall (X_1:nat) (Y_1:nat), ((iff ((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))) ((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))))
% 1.81/2.07 FOF formula (forall (X_1:nat) (Y_1:nat), ((iff ((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))) ((and ((dvd_dvd_nat X_1) Y_1)) (not (((eq nat) X_1) Y_1))))) of role axiom named fact_922_dvd_Oless__le
% 1.81/2.07 A new axiom: (forall (X_1:nat) (Y_1:nat), ((iff ((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))) ((and ((dvd_dvd_nat X_1) Y_1)) (not (((eq nat) X_1) Y_1)))))
% 1.81/2.07 FOF formula (forall (X_1:nat) (Y_1:nat), ((iff ((dvd_dvd_nat X_1) Y_1)) ((or ((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))) (((eq nat) X_1) Y_1)))) of role axiom named fact_923_dvd_Ole__less
% 1.81/2.07 A new axiom: (forall (X_1:nat) (Y_1:nat), ((iff ((dvd_dvd_nat X_1) Y_1)) ((or ((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))) (((eq nat) X_1) Y_1))))
% 1.81/2.07 FOF formula (forall (X_1:nat) (Y_1:nat), ((iff (((eq nat) X_1) Y_1)) ((and ((dvd_dvd_nat X_1) Y_1)) ((dvd_dvd_nat Y_1) X_1)))) of role axiom named fact_924_dvd_Oeq__iff
% 1.81/2.07 A new axiom: (forall (X_1:nat) (Y_1:nat), ((iff (((eq nat) X_1) Y_1)) ((and ((dvd_dvd_nat X_1) Y_1)) ((dvd_dvd_nat Y_1) X_1))))
% 1.90/2.09 FOF formula (forall (X_1:nat), (((and ((dvd_dvd_nat X_1) X_1)) (((dvd_dvd_nat X_1) X_1)->False))->False)) of role axiom named fact_925_dvd_Oless__irrefl
% 1.90/2.09 A new axiom: (forall (X_1:nat), (((and ((dvd_dvd_nat X_1) X_1)) (((dvd_dvd_nat X_1) X_1)->False))->False))
% 1.90/2.09 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_926_dvd__diff__nat
% 1.90/2.09 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)))))
% 1.90/2.09 FOF formula (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) N)) ((plus_plus_nat N) M))) of role axiom named fact_927_nat__add__commute
% 1.90/2.09 A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) N)) ((plus_plus_nat N) M)))
% 1.90/2.09 FOF formula (forall (X_1:nat) (Y_1:nat) (Z:nat), (((eq nat) ((plus_plus_nat X_1) ((plus_plus_nat Y_1) Z))) ((plus_plus_nat Y_1) ((plus_plus_nat X_1) Z)))) of role axiom named fact_928_nat__add__left__commute
% 1.90/2.09 A new axiom: (forall (X_1:nat) (Y_1:nat) (Z:nat), (((eq nat) ((plus_plus_nat X_1) ((plus_plus_nat Y_1) Z))) ((plus_plus_nat Y_1) ((plus_plus_nat X_1) Z))))
% 1.90/2.09 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_929_nat__add__assoc
% 1.90/2.09 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))))
% 1.90/2.09 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_930_nat__add__left__cancel
% 1.90/2.09 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)))
% 1.90/2.09 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_931_nat__add__right__cancel
% 1.90/2.09 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)))
% 1.90/2.09 FOF formula (forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) N)) N)) M)) of role axiom named fact_932_diff__add__inverse2
% 1.90/2.09 A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) N)) N)) M))
% 1.90/2.09 FOF formula (forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat N) M)) N)) M)) of role axiom named fact_933_diff__add__inverse
% 1.90/2.09 A new axiom: (forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat N) M)) N)) M))
% 1.90/2.09 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_934_diff__diff__left
% 1.90/2.09 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))))
% 1.90/2.09 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_935_Nat_Odiff__cancel
% 1.90/2.09 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)))
% 1.90/2.09 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_936_diff__cancel2
% 1.90/2.09 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)))
% 1.90/2.09 FOF formula (forall (N:nat), ((ord_less_eq_nat N) N)) of role axiom named fact_937_le__refl
% 1.90/2.09 A new axiom: (forall (N:nat), ((ord_less_eq_nat N) N))
% 1.90/2.09 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_938_nat__le__linear
% 1.90/2.09 A new axiom: (forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M)))
% 1.93/2.12 FOF formula (forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N))) of role axiom named fact_939_eq__imp__le
% 1.93/2.12 A new axiom: (forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N)))
% 1.93/2.12 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_940_le__trans
% 1.93/2.12 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))))
% 1.93/2.12 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_941_le__antisym
% 1.93/2.12 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N))))
% 1.93/2.12 FOF formula (forall (M:nat) (N:nat), ((ord_less_eq_nat ((minus_minus_nat M) N)) M)) of role axiom named fact_942_Nat_Odiff__le__self
% 1.93/2.12 A new axiom: (forall (M:nat) (N:nat), ((ord_less_eq_nat ((minus_minus_nat M) N)) M))
% 1.93/2.12 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_943_diff__le__mono2
% 1.93/2.12 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))))
% 1.93/2.12 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_944_diff__le__mono
% 1.93/2.12 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))))
% 1.93/2.12 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_945_diff__diff__cancel
% 1.93/2.12 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)))
% 1.93/2.12 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_946_eq__diff__iff
% 1.93/2.12 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)))))
% 1.93/2.12 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_947_Nat_Odiff__diff__eq
% 1.93/2.12 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)))))
% 1.93/2.12 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_948_le__diff__iff
% 1.93/2.12 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)))))
% 1.93/2.12 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_949_nat__mult__assoc
% 1.93/2.12 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))))
% 1.93/2.12 FOF formula (forall (M:nat) (N:nat), (((eq nat) ((times_times_nat M) N)) ((times_times_nat N) M))) of role axiom named fact_950_nat__mult__commute
% 1.93/2.12 A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((times_times_nat M) N)) ((times_times_nat N) M)))
% 1.93/2.12 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_951_diff__mult__distrib
% 1.93/2.13 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))))
% 1.93/2.13 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_952_diff__mult__distrib2
% 1.93/2.13 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))))
% 1.93/2.13 FOF formula (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N))) of role axiom named fact_953_gr0I
% 1.93/2.13 A new axiom: (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N)))
% 1.93/2.13 FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->(not (((eq nat) N) zero_zero_nat)))) of role axiom named fact_954_gr__implies__not0
% 1.93/2.13 A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->(not (((eq nat) N) zero_zero_nat))))
% 1.93/2.13 FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_955_less__nat__zero__code
% 1.93/2.13 A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False))
% 1.93/2.13 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_956_neq0__conv
% 1.93/2.13 A new axiom: (forall (N:nat), ((iff (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N)))
% 1.93/2.13 FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_957_not__less0
% 1.93/2.13 A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False))
% 1.93/2.13 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_958_diff__less
% 1.93/2.13 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))))
% 1.93/2.13 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_959_zero__less__diff
% 1.93/2.13 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)))
% 1.93/2.13 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_960_add__eq__self__zero
% 1.93/2.13 A new axiom: (forall (M:nat) (N:nat), ((((eq nat) ((plus_plus_nat M) N)) M)->(((eq nat) N) zero_zero_nat)))
% 1.93/2.13 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_961_add__is__0
% 1.93/2.13 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))))
% 1.93/2.13 FOF formula (forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M)) of role axiom named fact_962_Nat_Oadd__0__right
% 1.93/2.13 A new axiom: (forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M))
% 1.93/2.13 FOF formula (forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N)) of role axiom named fact_963_plus__nat_Oadd__0
% 1.93/2.13 A new axiom: (forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N))
% 1.93/2.13 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_964_diff__add__0
% 1.93/2.13 A new axiom: (forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat N) ((plus_plus_nat N) M))) zero_zero_nat))
% 1.93/2.13 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_965_le__0__eq
% 1.93/2.13 A new axiom: (forall (N:nat), ((iff ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))
% 1.93/2.13 FOF formula (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) of role axiom named fact_966_less__eq__nat_Osimps_I1_J
% 1.93/2.13 A new axiom: (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N))
% 1.93/2.15 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_967_diff__is__0__eq_H
% 1.93/2.15 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)))
% 1.93/2.15 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_968_diff__is__0__eq
% 1.93/2.15 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)))
% 1.93/2.15 FOF formula (forall (N:nat), (((eq nat) ((times_times_nat zero_zero_nat) N)) zero_zero_nat)) of role axiom named fact_969_mult__0
% 1.93/2.15 A new axiom: (forall (N:nat), (((eq nat) ((times_times_nat zero_zero_nat) N)) zero_zero_nat))
% 1.93/2.15 FOF formula (forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat)) of role axiom named fact_970_mult__0__right
% 1.93/2.15 A new axiom: (forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat))
% 1.93/2.15 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_971_mult__is__0
% 1.93/2.15 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))))
% 1.93/2.15 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_972_mult__cancel1
% 1.93/2.15 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))))
% 1.93/2.15 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_973_mult__cancel2
% 1.93/2.15 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))))
% 1.93/2.15 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_974_not__add__less1
% 1.93/2.15 A new axiom: (forall (I_1:nat) (J_1:nat), (((ord_less_nat ((plus_plus_nat I_1) J_1)) I_1)->False))
% 1.93/2.15 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_975_not__add__less2
% 1.93/2.15 A new axiom: (forall (J_1:nat) (I_1:nat), (((ord_less_nat ((plus_plus_nat J_1) I_1)) I_1)->False))
% 1.93/2.15 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_976_nat__add__left__cancel__less
% 1.93/2.15 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)))
% 1.93/2.15 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_977_trans__less__add1
% 1.93/2.15 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))))
% 1.93/2.15 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_978_trans__less__add2
% 1.93/2.15 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))))
% 1.93/2.15 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_979_add__less__mono1
% 1.93/2.15 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))))
% 1.93/2.15 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_980_add__less__mono
% 1.93/2.17 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)))))
% 1.93/2.17 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_981_less__add__eq__less
% 1.93/2.17 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))))
% 1.93/2.17 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_982_add__lessD1
% 1.93/2.17 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)))
% 1.93/2.17 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_983_add__diff__inverse
% 1.93/2.17 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)))
% 1.93/2.17 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_984_less__diff__conv
% 1.93/2.17 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)))
% 1.93/2.17 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_985_nat__less__le
% 1.93/2.17 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)))))
% 1.93/2.17 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_986_le__eq__less__or__eq
% 1.93/2.17 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))))
% 1.93/2.17 FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N))) of role axiom named fact_987_less__imp__le__nat
% 1.93/2.17 A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N)))
% 1.93/2.17 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_988_le__neq__implies__less
% 1.93/2.17 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((not (((eq nat) M) N))->((ord_less_nat M) N))))
% 1.93/2.17 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_989_less__or__eq__imp__le
% 1.93/2.17 A new axiom: (forall (M:nat) (N:nat), (((or ((ord_less_nat M) N)) (((eq nat) M) N))->((ord_less_eq_nat M) N)))
% 1.93/2.17 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_990_less__diff__iff
% 1.93/2.17 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)))))
% 1.93/2.17 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_991_diff__less__mono
% 1.93/2.17 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)))))
% 1.93/2.17 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_992_dvd__reduce
% 1.93/2.17 A new axiom: (forall (K:nat) (N:nat), ((iff ((dvd_dvd_nat K) ((plus_plus_nat N) K))) ((dvd_dvd_nat K) N)))
% 1.93/2.17 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_993_dvd__diffD1
% 1.93/2.20 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)))))
% 1.93/2.20 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_994_dvd__diffD
% 1.93/2.20 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)))))
% 1.93/2.20 FOF formula (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat M) N))) of role axiom named fact_995_le__add2
% 1.93/2.20 A new axiom: (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat M) N)))
% 1.93/2.20 FOF formula (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M))) of role axiom named fact_996_le__add1
% 1.93/2.20 A new axiom: (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M)))
% 1.93/2.20 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_997_le__iff__add
% 1.93/2.20 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))))))
% 1.93/2.20 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_998_nat__add__left__cancel__le
% 1.93/2.20 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)))
% 1.93/2.20 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_999_trans__le__add1
% 1.93/2.20 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))))
% 1.93/2.20 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_1000_trans__le__add2
% 1.93/2.20 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))))
% 1.93/2.20 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_1001_add__le__mono1
% 1.93/2.20 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))))
% 1.93/2.20 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_1002_add__le__mono
% 1.93/2.20 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)))))
% 1.93/2.20 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_1003_add__leD2
% 1.93/2.20 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)))
% 1.93/2.20 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_1004_add__leD1
% 1.93/2.20 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)))
% 1.93/2.20 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_1005_add__leE
% 1.93/2.20 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)))
% 1.93/2.20 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_1006_diff__diff__right
% 2.03/2.22 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))))
% 2.03/2.22 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_1007_le__diff__conv
% 2.03/2.22 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))))
% 2.03/2.22 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_1008_le__add__diff
% 2.03/2.22 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))))
% 2.03/2.22 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_1009_le__add__diff__inverse
% 2.03/2.22 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)))
% 2.03/2.22 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_1010_add__diff__assoc
% 2.03/2.22 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))))
% 2.03/2.22 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_1011_le__diff__conv2
% 2.03/2.22 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))))
% 2.03/2.22 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_1012_le__add__diff__inverse2
% 2.03/2.22 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)))
% 2.03/2.22 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_1013_le__imp__diff__is__add
% 2.03/2.22 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)))))
% 2.03/2.22 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_1014_diff__add__assoc
% 2.03/2.22 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)))))
% 2.03/2.22 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_1015_add__diff__assoc2
% 2.03/2.22 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))))
% 2.03/2.22 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_1016_diff__add__assoc2
% 2.03/2.22 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))))
% 2.03/2.22 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_1017_add__mult__distrib
% 2.03/2.24 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))))
% 2.03/2.24 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_1018_add__mult__distrib2
% 2.03/2.24 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))))
% 2.03/2.24 FOF formula (forall (M:nat), ((iff ((dvd_dvd_nat M) one_one_nat)) (((eq nat) M) one_one_nat))) of role axiom named fact_1019_nat__dvd__1__iff__1
% 2.03/2.24 A new axiom: (forall (M:nat), ((iff ((dvd_dvd_nat M) one_one_nat)) (((eq nat) M) one_one_nat)))
% 2.03/2.24 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_1020_mult__le__mono
% 2.03/2.24 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)))))
% 2.03/2.24 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_1021_mult__le__mono2
% 2.03/2.24 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))))
% 2.03/2.24 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_1022_mult__le__mono1
% 2.03/2.24 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))))
% 2.03/2.24 FOF formula (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) ((times_times_nat M) M)))) of role axiom named fact_1023_le__cube
% 2.03/2.24 A new axiom: (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) ((times_times_nat M) M))))
% 2.03/2.24 FOF formula (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) M))) of role axiom named fact_1024_le__square
% 2.03/2.24 A new axiom: (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) M)))
% 2.03/2.24 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_1025_nat__mult__eq__1__iff
% 2.03/2.24 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))))
% 2.03/2.24 FOF formula (forall (N:nat), (((eq nat) ((times_times_nat N) one_one_nat)) N)) of role axiom named fact_1026_nat__mult__1__right
% 2.03/2.24 A new axiom: (forall (N:nat), (((eq nat) ((times_times_nat N) one_one_nat)) N))
% 2.03/2.24 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_1027_nat__1__eq__mult__iff
% 2.03/2.24 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))))
% 2.03/2.24 FOF formula (forall (N:nat), (((eq nat) ((times_times_nat one_one_nat) N)) N)) of role axiom named fact_1028_nat__mult__1
% 2.03/2.24 A new axiom: (forall (N:nat), (((eq nat) ((times_times_nat one_one_nat) N)) N))
% 2.03/2.24 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_1029_nat__dvd__not__less
% 2.03/2.24 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))))
% 2.03/2.24 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_1030_add__gr__0
% 2.03/2.26 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))))
% 2.03/2.26 FOF formula (forall (P_1:(nat->Prop)) (A:nat) (B:nat), ((iff (P_1 ((minus_minus_nat A) B))) ((and (((ord_less_nat A) B)->(P_1 zero_zero_nat))) (forall (D_2:nat), ((((eq nat) A) ((plus_plus_nat B) D_2))->(P_1 D_2)))))) of role axiom named fact_1031_nat__diff__split
% 2.03/2.26 A new axiom: (forall (P_1:(nat->Prop)) (A:nat) (B:nat), ((iff (P_1 ((minus_minus_nat A) B))) ((and (((ord_less_nat A) B)->(P_1 zero_zero_nat))) (forall (D_2:nat), ((((eq nat) A) ((plus_plus_nat B) D_2))->(P_1 D_2))))))
% 2.03/2.26 FOF formula (forall (P_1:(nat->Prop)) (A:nat) (B:nat), ((iff (P_1 ((minus_minus_nat A) B))) (((or ((and ((ord_less_nat A) B)) ((P_1 zero_zero_nat)->False))) ((ex nat) (fun (D_2:nat)=> ((and (((eq nat) A) ((plus_plus_nat B) D_2))) ((P_1 D_2)->False)))))->False))) of role axiom named fact_1032_nat__diff__split__asm
% 2.03/2.26 A new axiom: (forall (P_1:(nat->Prop)) (A:nat) (B:nat), ((iff (P_1 ((minus_minus_nat A) B))) (((or ((and ((ord_less_nat A) B)) ((P_1 zero_zero_nat)->False))) ((ex nat) (fun (D_2:nat)=> ((and (((eq nat) A) ((plus_plus_nat B) D_2))) ((P_1 D_2)->False)))))->False)))
% 2.03/2.26 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_1033_mult__less__mono2
% 2.03/2.26 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)))))
% 2.03/2.26 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_1034_mult__less__mono1
% 2.03/2.26 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)))))
% 2.03/2.26 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_1035_mult__less__cancel2
% 2.03/2.26 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))))
% 2.03/2.26 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_1036_mult__less__cancel1
% 2.03/2.26 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))))
% 2.03/2.26 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_1037_nat__0__less__mult__iff
% 2.03/2.26 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))))
% 2.03/2.26 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_1038_mult__eq__self__implies__10
% 2.03/2.26 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))))
% 2.03/2.26 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_1039_dvd__imp__le
% 2.03/2.26 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))))
% 2.03/2.26 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_1040_dvd__mult__cancel
% 2.03/2.28 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))))
% 2.03/2.28 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_1041_mult__le__cancel1
% 2.03/2.28 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))))
% 2.03/2.28 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_1042_mult__le__cancel2
% 2.03/2.28 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))))
% 2.03/2.28 FOF formula (forall (N:nat) (P_1:(nat->Prop)), (((P_1 zero_zero_nat)->False)->((P_1 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_1 _TPTP_I)->False))))) (P_1 ((plus_plus_nat K_1) one_one_nat)))))))) of role axiom named fact_1043_ex__least__nat__less
% 2.03/2.28 A new axiom: (forall (N:nat) (P_1:(nat->Prop)), (((P_1 zero_zero_nat)->False)->((P_1 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_1 _TPTP_I)->False))))) (P_1 ((plus_plus_nat K_1) one_one_nat))))))))
% 2.03/2.28 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_1044_nat__less__add__iff2
% 2.03/2.28 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)))))
% 2.03/2.28 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_1045_nat__mult__eq__cancel__disj
% 2.03/2.28 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))))
% 2.03/2.28 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_1046_left__add__mult__distrib
% 2.03/2.28 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)))
% 2.03/2.28 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_1047_nat__mult__eq__cancel1
% 2.03/2.28 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))))
% 2.03/2.28 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
% 2.03/2.28 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))))
% 2.03/2.30 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_1049_nat__mult__dvd__cancel__disj
% 2.03/2.30 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))))
% 2.03/2.30 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_1050_nat__mult__dvd__cancel1
% 2.03/2.30 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))))
% 2.03/2.30 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_1051_nat__mult__le__cancel1
% 2.03/2.30 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))))
% 2.03/2.30 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_1052_nat__le__add__iff1
% 2.03/2.30 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))))
% 2.03/2.30 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_1053_nat__diff__add__eq1
% 2.03/2.30 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))))
% 2.03/2.30 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_1054_nat__eq__add__iff1
% 2.03/2.30 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))))
% 2.03/2.30 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_1055_nat__le__add__iff2
% 2.03/2.30 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)))))
% 2.03/2.30 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_1056_nat__diff__add__eq2
% 2.12/2.32 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)))))
% 2.12/2.32 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_1057_nat__eq__add__iff2
% 2.12/2.32 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)))))
% 2.12/2.32 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_1058_nat__less__add__iff1
% 2.12/2.32 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))))
% 2.12/2.32 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
% 2.12/2.32 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))))))
% 2.12/2.32 FOF formula (forall (X_1:int), ((iff (twoSqu919416604sum2sq X_1)) ((ex int) (fun (A_2:int)=> ((ex int) (fun (B_2:int)=> (((eq int) (twoSqu2057625106sum2sq ((product_Pair_int_int A_2) B_2))) X_1))))))) of role axiom named fact_1060_is__sum2sq__def
% 2.12/2.32 A new axiom: (forall (X_1:int), ((iff (twoSqu919416604sum2sq X_1)) ((ex int) (fun (A_2:int)=> ((ex int) (fun (B_2:int)=> (((eq int) (twoSqu2057625106sum2sq ((product_Pair_int_int A_2) B_2))) X_1)))))))
% 2.12/2.32 FOF formula (forall (P_3:Prop) (P_1:Prop) (X_1:int), ((((ord_less_eq_int zero_zero_int) X_1)->((iff P_1) P_3))->((iff (((ord_less_eq_int zero_zero_int) X_1)->P_1)) (((ord_less_eq_int zero_zero_int) X_1)->P_3)))) of role axiom named fact_1061_imp__le__cong
% 2.12/2.32 A new axiom: (forall (P_3:Prop) (P_1:Prop) (X_1:int), ((((ord_less_eq_int zero_zero_int) X_1)->((iff P_1) P_3))->((iff (((ord_less_eq_int zero_zero_int) X_1)->P_1)) (((ord_less_eq_int zero_zero_int) X_1)->P_3))))
% 2.12/2.32 FOF formula (forall (P_3:Prop) (P_1:Prop) (X_1:int), ((((ord_less_eq_int zero_zero_int) X_1)->((iff P_1) P_3))->((iff ((and ((ord_less_eq_int zero_zero_int) X_1)) P_1)) ((and ((ord_less_eq_int zero_zero_int) X_1)) P_3)))) of role axiom named fact_1062_conj__le__cong
% 2.12/2.32 A new axiom: (forall (P_3:Prop) (P_1:Prop) (X_1:int), ((((ord_less_eq_int zero_zero_int) X_1)->((iff P_1) P_3))->((iff ((and ((ord_less_eq_int zero_zero_int) X_1)) P_1)) ((and ((ord_less_eq_int zero_zero_int) X_1)) P_3))))
% 2.12/2.32 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
% 2.12/2.32 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)))))
% 2.12/2.32 FOF formula ((ord_less_eq_int zero_zero_int) (number_number_of_int pls)) of role axiom named fact_1064_number__of2
% 2.12/2.34 A new axiom: ((ord_less_eq_int zero_zero_int) (number_number_of_int pls))
% 2.12/2.34 FOF formula (forall (K:int) (P_1:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X:int), ((P_1 X)->(P_1 ((minus_minus_int X) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X:int), ((P_1 X)->(P_1 ((minus_minus_int X) ((times_times_int K) D))))))))) of role axiom named fact_1065_decr__mult__lemma
% 2.12/2.34 A new axiom: (forall (K:int) (P_1:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X:int), ((P_1 X)->(P_1 ((minus_minus_int X) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X:int), ((P_1 X)->(P_1 ((minus_minus_int X) ((times_times_int K) D)))))))))
% 2.12/2.34 FOF formula (forall (K:int) (P_1:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X:int), ((P_1 X)->(P_1 ((plus_plus_int X) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X:int), ((P_1 X)->(P_1 ((plus_plus_int X) ((times_times_int K) D))))))))) of role axiom named fact_1066_incr__mult__lemma
% 2.12/2.34 A new axiom: (forall (K:int) (P_1:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X:int), ((P_1 X)->(P_1 ((plus_plus_int X) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X:int), ((P_1 X)->(P_1 ((plus_plus_int X) ((times_times_int K) D)))))))))
% 2.12/2.34 FOF formula (forall (A:int), (((ord_less_int one_one_int) A)->((ex int) (fun (P_2:int)=> ((and (zprime P_2)) ((dvd_dvd_int P_2) A)))))) of role axiom named fact_1067_zprime__factor__exists
% 2.12/2.34 A new axiom: (forall (A:int), (((ord_less_int one_one_int) A)->((ex int) (fun (P_2:int)=> ((and (zprime P_2)) ((dvd_dvd_int P_2) A))))))
% 2.12/2.34 FOF formula (forall (A:int) (M:int), (((ord_less_int zero_zero_int) M)->((ex int) (fun (X:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X)) ((ord_less_int X) M))) (((zcong A) X) M))) (forall (Y:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y)) ((ord_less_int Y) M))) (((zcong A) Y) M))->(((eq int) Y) X)))))))) of role axiom named fact_1068_zcong__zless__unique
% 2.12/2.34 A new axiom: (forall (A:int) (M:int), (((ord_less_int zero_zero_int) M)->((ex int) (fun (X:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X)) ((ord_less_int X) M))) (((zcong A) X) M))) (forall (Y:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y)) ((ord_less_int Y) M))) (((zcong A) Y) M))->(((eq int) Y) X))))))))
% 2.12/2.34 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_1069_norR__mem__unique__aux
% 2.12/2.34 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)))
% 2.12/2.34 FOF formula (forall (P:int), ((zprime P)->(((zcong (zfact ((minus_minus_int P) one_one_int))) (number_number_of_int min)) P))) of role axiom named fact_1070_Wilson__Russ
% 2.12/2.34 A new axiom: (forall (P:int), ((zprime P)->(((zcong (zfact ((minus_minus_int P) one_one_int))) (number_number_of_int min)) P)))
% 2.12/2.34 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_1071_zfact_Osimps
% 2.12/2.34 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)))))))
% 2.12/2.34 FOF formula (forall (A:int) (P:int), ((zprime P)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P)->(((eq int) ((inv P) ((inv P) A))) A)))))) of role axiom named fact_1072_inv__inv
% 2.12/2.34 A new axiom: (forall (A:int) (P:int), ((zprime P)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P)->(((eq int) ((inv P) ((inv P) A))) A))))))
% 2.12/2.34 FOF formula (forall (J_1:int) (A:int) (P:int), ((zprime P)->(((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->(((((zcong A) zero_zero_int) P)->False)->(((((zcong J_1) zero_zero_int) P)->False)->((((quadRes P) A)->False)->((((zcong J_1) ((times_times_int A) ((multInv P) J_1))) P)->False))))))) of role axiom named fact_1073_MultInvPair__distinct
% 2.12/2.36 A new axiom: (forall (J_1:int) (A:int) (P:int), ((zprime P)->(((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->(((((zcong A) zero_zero_int) P)->False)->(((((zcong J_1) zero_zero_int) P)->False)->((((quadRes P) A)->False)->((((zcong J_1) ((times_times_int A) ((multInv P) J_1))) P)->False)))))))
% 2.12/2.36 FOF formula (forall (J_1:int) (K:int) (A:int) (P:int), ((((zcong ((times_times_int J_1) K)) A) P)->(((zcong ((times_times_int ((times_times_int ((multInv P) J_1)) J_1)) K)) ((times_times_int ((multInv P) J_1)) A)) P))) of role axiom named fact_1074_aux______3
% 2.12/2.36 A new axiom: (forall (J_1:int) (K:int) (A:int) (P:int), ((((zcong ((times_times_int J_1) K)) A) P)->(((zcong ((times_times_int ((times_times_int ((multInv P) J_1)) J_1)) K)) ((times_times_int ((multInv P) J_1)) A)) P)))
% 2.12/2.36 FOF formula (forall (J_1:int) (A:int) (P:int) (K:int), ((((zcong J_1) ((times_times_int A) ((multInv P) K))) P)->(((zcong ((times_times_int J_1) K)) ((times_times_int ((times_times_int A) ((multInv P) K))) K)) P))) of role axiom named fact_1075_aux______1
% 2.12/2.36 A new axiom: (forall (J_1:int) (A:int) (P:int) (K:int), ((((zcong J_1) ((times_times_int A) ((multInv P) K))) P)->(((zcong ((times_times_int J_1) K)) ((times_times_int ((times_times_int A) ((multInv P) K))) K)) P)))
% 2.12/2.36 FOF formula (forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(not (((eq int) A) ((inv P) A))))))) of role axiom named fact_1076_inv__distinct
% 2.12/2.36 A new axiom: (forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(not (((eq int) A) ((inv P) A)))))))
% 2.12/2.36 FOF formula (forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(not (((eq int) ((inv P) A)) one_one_int)))))) of role axiom named fact_1077_inv__not__1
% 2.12/2.36 A new axiom: (forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(not (((eq int) ((inv P) A)) one_one_int))))))
% 2.12/2.36 FOF formula (forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(not (((eq int) ((inv P) A)) ((minus_minus_int P) one_one_int))))))) of role axiom named fact_1078_inv__not__p__minus__1
% 2.12/2.36 A new axiom: (forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(not (((eq int) ((inv P) A)) ((minus_minus_int P) one_one_int)))))))
% 2.12/2.36 FOF formula (forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->((ord_less_int one_one_int) ((inv P) A)))))) of role axiom named fact_1079_inv__g__1
% 2.12/2.36 A new axiom: (forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->((ord_less_int one_one_int) ((inv P) A))))))
% 2.12/2.36 FOF formula (forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->((ord_less_int ((inv P) A)) ((minus_minus_int P) one_one_int)))))) of role axiom named fact_1080_inv__less__p__minus__1
% 2.12/2.36 A new axiom: (forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->((ord_less_int ((inv P) A)) ((minus_minus_int P) one_one_int))))))
% 2.12/2.36 FOF formula (forall (X_1:int) (Y_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((((zcong X_1) Y_1) P)->(((zcong ((multInv P) X_1)) ((multInv P) Y_1)) P)))) of role axiom named fact_1081_MultInv__prop1
% 2.12/2.36 A new axiom: (forall (X_1:int) (Y_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((((zcong X_1) Y_1) P)->(((zcong ((multInv P) X_1)) ((multInv P) Y_1)) P))))
% 2.12/2.36 FOF formula (forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(not (((eq int) ((inv P) A)) zero_zero_int)))))) of role axiom named fact_1082_inv__not__0
% 2.12/2.39 A new axiom: (forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(not (((eq int) ((inv P) A)) zero_zero_int))))))
% 2.12/2.39 FOF formula (forall (A:int) (J_1:int) (K:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((((zcong J_1) K) P)->(((zcong ((times_times_int A) ((multInv P) J_1))) ((times_times_int A) ((multInv P) K))) P)))) of role axiom named fact_1083_MultInv__zcong__prop1
% 2.12/2.39 A new axiom: (forall (A:int) (J_1:int) (K:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((((zcong J_1) K) P)->(((zcong ((times_times_int A) ((multInv P) J_1))) ((times_times_int A) ((multInv P) K))) P))))
% 2.12/2.39 FOF formula (forall (Y_1:int) (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((((zcong Y_1) zero_zero_int) P)->False)->((((zcong ((multInv P) X_1)) ((multInv P) Y_1)) P)->(((zcong X_1) Y_1) P))))))) of role axiom named fact_1084_MultInv__prop5
% 2.12/2.39 A new axiom: (forall (Y_1:int) (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((((zcong Y_1) zero_zero_int) P)->False)->((((zcong ((multInv P) X_1)) ((multInv P) Y_1)) P)->(((zcong X_1) Y_1) P)))))))
% 2.12/2.39 FOF formula (forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((zcong ((multInv P) ((multInv P) X_1))) X_1) P))))) of role axiom named fact_1085_MultInv__prop4
% 2.12/2.39 A new axiom: (forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((zcong ((multInv P) ((multInv P) X_1))) X_1) P)))))
% 2.12/2.39 FOF formula (forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->((((zcong ((multInv P) X_1)) zero_zero_int) P)->False))))) of role axiom named fact_1086_MultInv__prop3
% 2.12/2.39 A new axiom: (forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->((((zcong ((multInv P) X_1)) zero_zero_int) P)->False)))))
% 2.12/2.39 FOF formula (forall (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P)->(((zcong ((times_times_int A) ((inv P) A))) one_one_int) P))))) of role axiom named fact_1087_inv__is__inv
% 2.12/2.39 A new axiom: (forall (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P)->(((zcong ((times_times_int A) ((inv P) A))) one_one_int) P)))))
% 2.12/2.39 FOF formula (forall (K:int) (A:int) (J_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong J_1) zero_zero_int) P)->False)->((((zcong ((times_times_int ((times_times_int ((multInv P) J_1)) J_1)) K)) ((times_times_int ((multInv P) J_1)) A)) P)->(((zcong K) ((times_times_int A) ((multInv P) J_1))) P)))))) of role axiom named fact_1088_aux______4
% 2.12/2.39 A new axiom: (forall (K:int) (A:int) (J_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong J_1) zero_zero_int) P)->False)->((((zcong ((times_times_int ((times_times_int ((multInv P) J_1)) J_1)) K)) ((times_times_int ((multInv P) J_1)) A)) P)->(((zcong K) ((times_times_int A) ((multInv P) J_1))) P))))))
% 2.12/2.39 FOF formula (forall (J_1:int) (A:int) (K:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong K) zero_zero_int) P)->False)->((((zcong ((times_times_int J_1) K)) ((times_times_int ((times_times_int A) ((multInv P) K))) K)) P)->(((zcong ((times_times_int J_1) K)) A) P)))))) of role axiom named fact_1089_aux______2
% 2.12/2.39 A new axiom: (forall (J_1:int) (A:int) (K:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong K) zero_zero_int) P)->False)->((((zcong ((times_times_int J_1) K)) ((times_times_int ((times_times_int A) ((multInv P) K))) K)) P)->(((zcong ((times_times_int J_1) K)) A) P))))))
% 2.21/2.41 FOF formula (forall (A:int) (J_1:int) (K:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong K) zero_zero_int) P)->False)->(((((zcong J_1) zero_zero_int) P)->False)->((((zcong J_1) ((times_times_int A) ((multInv P) K))) P)->(((zcong K) ((times_times_int A) ((multInv P) J_1))) P))))))) of role axiom named fact_1090_MultInv__zcong__prop2
% 2.21/2.41 A new axiom: (forall (A:int) (J_1:int) (K:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong K) zero_zero_int) P)->False)->(((((zcong J_1) zero_zero_int) P)->False)->((((zcong J_1) ((times_times_int A) ((multInv P) K))) P)->(((zcong K) ((times_times_int A) ((multInv P) J_1))) P)))))))
% 2.21/2.41 FOF formula (forall (J_1:int) (K:int) (A:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong A) zero_zero_int) P)->False)->(((((zcong K) zero_zero_int) P)->False)->(((((zcong J_1) zero_zero_int) P)->False)->((((zcong ((times_times_int A) ((multInv P) J_1))) ((times_times_int A) ((multInv P) K))) P)->(((zcong J_1) K) P)))))))) of role axiom named fact_1091_MultInv__zcong__prop3
% 2.21/2.41 A new axiom: (forall (J_1:int) (K:int) (A:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong A) zero_zero_int) P)->False)->(((((zcong K) zero_zero_int) P)->False)->(((((zcong J_1) zero_zero_int) P)->False)->((((zcong ((times_times_int A) ((multInv P) J_1))) ((times_times_int A) ((multInv P) K))) P)->(((zcong J_1) K) P))))))))
% 2.21/2.41 FOF formula (forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((zcong ((times_times_int ((times_times_int X_1) ((multInv P) X_1))) ((multInv P) ((multInv P) X_1)))) X_1) P))))) of role axiom named fact_1092_Int2_Oaux____2
% 2.21/2.41 A new axiom: (forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((zcong ((times_times_int ((times_times_int X_1) ((multInv P) X_1))) ((multInv P) ((multInv P) X_1)))) X_1) P)))))
% 2.21/2.41 FOF formula (forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((zcong ((multInv P) ((multInv P) X_1))) ((times_times_int ((times_times_int X_1) ((multInv P) X_1))) ((multInv P) ((multInv P) X_1)))) P))))) of role axiom named fact_1093_Int2_Oaux____1
% 2.21/2.41 A new axiom: (forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((zcong ((multInv P) ((multInv P) X_1))) ((times_times_int ((times_times_int X_1) ((multInv P) X_1))) ((multInv P) ((multInv P) X_1)))) P)))))
% 2.21/2.41 FOF formula (forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((zcong ((times_times_int ((multInv P) X_1)) X_1)) one_one_int) P))))) of role axiom named fact_1094_MultInv__prop2a
% 2.21/2.41 A new axiom: (forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((zcong ((times_times_int ((multInv P) X_1)) X_1)) one_one_int) P)))))
% 2.21/2.41 FOF formula (forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((zcong ((times_times_int X_1) ((multInv P) X_1))) one_one_int) P))))) of role axiom named fact_1095_MultInv__prop2
% 2.21/2.41 A new axiom: (forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((zcong ((times_times_int X_1) ((multInv P) X_1))) one_one_int) P)))))
% 2.21/2.41 FOF formula (forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(((member_int B) ((wset A) P))->((member_int ((inv P) B)) ((wset A) P))))))) of role axiom named fact_1096_wset__mem__inv__mem
% 2.21/2.43 A new axiom: (forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(((member_int B) ((wset A) P))->((member_int ((inv P) B)) ((wset A) P)))))))
% 2.21/2.43 FOF formula (forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(((ord_less_int one_one_int) B)->(((ord_less_int B) ((minus_minus_int P) one_one_int))->(((member_int ((inv P) B)) ((wset A) P))->((member_int B) ((wset A) P))))))))) of role axiom named fact_1097_wset__inv__mem__mem
% 2.21/2.43 A new axiom: (forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(((ord_less_int one_one_int) B)->(((ord_less_int B) ((minus_minus_int P) one_one_int))->(((member_int ((inv P) B)) ((wset A) P))->((member_int B) ((wset A) P)))))))))
% 2.21/2.43 FOF formula (forall (P:int) (A:int), (((ord_less_int one_one_int) A)->((member_int A) ((wset A) P)))) of role axiom named fact_1098_wset__mem__mem
% 2.21/2.43 A new axiom: (forall (P:int) (A:int), (((ord_less_int one_one_int) A)->((member_int A) ((wset A) P))))
% 2.21/2.43 FOF formula (forall (B:int) (P:int) (A:int), (((ord_less_int one_one_int) A)->(((member_int B) ((wset ((minus_minus_int A) one_one_int)) P))->((member_int B) ((wset A) P))))) of role axiom named fact_1099_wset__subset
% 2.21/2.43 A new axiom: (forall (B:int) (P:int) (A:int), (((ord_less_int one_one_int) A)->(((member_int B) ((wset ((minus_minus_int A) one_one_int)) P))->((member_int B) ((wset A) P)))))
% 2.21/2.43 FOF formula (forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(((member_int B) ((wset A) P))->((ord_less_int B) ((minus_minus_int P) one_one_int)))))) of role axiom named fact_1100_wset__less
% 2.21/2.43 A new axiom: (forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(((member_int B) ((wset A) P))->((ord_less_int B) ((minus_minus_int P) one_one_int))))))
% 2.21/2.43 FOF formula (forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(((member_int B) ((wset A) P))->((ord_less_int one_one_int) B))))) of role axiom named fact_1101_wset__g__1
% 2.21/2.43 A new axiom: (forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(((member_int B) ((wset A) P))->((ord_less_int one_one_int) B)))))
% 2.21/2.43 FOF formula (forall (B:int) (P:int) (A:int), (((ord_less_int one_one_int) A)->((((member_int B) ((wset ((minus_minus_int A) one_one_int)) P))->False)->(((member_int B) ((wset A) P))->((or (((eq int) B) A)) (((eq int) B) ((inv P) A))))))) of role axiom named fact_1102_wset__mem__imp__or
% 2.21/2.43 A new axiom: (forall (B:int) (P:int) (A:int), (((ord_less_int one_one_int) A)->((((member_int B) ((wset ((minus_minus_int A) one_one_int)) P))->False)->(((member_int B) ((wset A) P))->((or (((eq int) B) A)) (((eq int) B) ((inv P) A)))))))
% 2.21/2.43 FOF formula (forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(((ord_less_int one_one_int) B)->(((ord_less_eq_int B) A)->((member_int B) ((wset A) P))))))) of role axiom named fact_1103_wset__mem
% 2.21/2.43 A new axiom: (forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(((ord_less_int one_one_int) B)->(((ord_less_eq_int B) A)->((member_int B) ((wset A) P)))))))
% 2.21/2.43 FOF formula (forall (P_1:(int->Prop)) (I_1:int) (K:int), (((ord_less_eq_int I_1) K)->((P_1 K)->((forall (_TPTP_I:int), (((ord_less_eq_int _TPTP_I) K)->((P_1 _TPTP_I)->(P_1 ((minus_minus_int _TPTP_I) one_one_int)))))->(P_1 I_1))))) of role axiom named fact_1104_int__le__induct
% 2.21/2.43 A new axiom: (forall (P_1:(int->Prop)) (I_1:int) (K:int), (((ord_less_eq_int I_1) K)->((P_1 K)->((forall (_TPTP_I:int), (((ord_less_eq_int _TPTP_I) K)->((P_1 _TPTP_I)->(P_1 ((minus_minus_int _TPTP_I) one_one_int)))))->(P_1 I_1)))))
% 2.21/2.46 FOF formula (forall (P_1:(int->Prop)) (I_1:int) (K:int), (((ord_less_int I_1) K)->((P_1 ((minus_minus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int _TPTP_I) K)->((P_1 _TPTP_I)->(P_1 ((minus_minus_int _TPTP_I) one_one_int)))))->(P_1 I_1))))) of role axiom named fact_1105_int__less__induct
% 2.21/2.46 A new axiom: (forall (P_1:(int->Prop)) (I_1:int) (K:int), (((ord_less_int I_1) K)->((P_1 ((minus_minus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int _TPTP_I) K)->((P_1 _TPTP_I)->(P_1 ((minus_minus_int _TPTP_I) one_one_int)))))->(P_1 I_1)))))
% 2.21/2.46 FOF formula (forall (X_1:int) (P_1:(int->Prop)), ((forall (A_2:int), ((((ord_less_int one_one_int) A_2)->(P_1 ((minus_minus_int A_2) one_one_int)))->(P_1 A_2)))->(P_1 X_1))) of role axiom named fact_1106_d22set__induct__old
% 2.21/2.46 A new axiom: (forall (X_1:int) (P_1:(int->Prop)), ((forall (A_2:int), ((((ord_less_int one_one_int) A_2)->(P_1 ((minus_minus_int A_2) one_one_int)))->(P_1 A_2)))->(P_1 X_1)))
% 2.21/2.46 FOF formula (forall (P_1:(int->Prop)) (K:int) (I_1:int), (((ord_less_eq_int K) I_1)->((P_1 K)->((forall (_TPTP_I:int), (((ord_less_eq_int K) _TPTP_I)->((P_1 _TPTP_I)->(P_1 ((plus_plus_int _TPTP_I) one_one_int)))))->(P_1 I_1))))) of role axiom named fact_1107_int__ge__induct
% 2.21/2.46 A new axiom: (forall (P_1:(int->Prop)) (K:int) (I_1:int), (((ord_less_eq_int K) I_1)->((P_1 K)->((forall (_TPTP_I:int), (((ord_less_eq_int K) _TPTP_I)->((P_1 _TPTP_I)->(P_1 ((plus_plus_int _TPTP_I) one_one_int)))))->(P_1 I_1)))))
% 2.21/2.46 FOF formula (forall (P_1:(int->Prop)) (K:int) (I_1:int), (((ord_less_int K) I_1)->((P_1 ((plus_plus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int K) _TPTP_I)->((P_1 _TPTP_I)->(P_1 ((plus_plus_int _TPTP_I) one_one_int)))))->(P_1 I_1))))) of role axiom named fact_1108_int__gr__induct
% 2.21/2.46 A new axiom: (forall (P_1:(int->Prop)) (K:int) (I_1:int), (((ord_less_int K) I_1)->((P_1 ((plus_plus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int K) _TPTP_I)->((P_1 _TPTP_I)->(P_1 ((plus_plus_int _TPTP_I) one_one_int)))))->(P_1 I_1)))))
% 2.21/2.46 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_1109_mono__nat__linear__lb
% 2.21/2.46 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)))))
% 2.21/2.46 FOF formula (forall (P:int), ((zprime P)->(((eq (int->Prop)) (d22set ((minus_minus_int P) (number_number_of_int (bit0 (bit1 pls)))))) ((wset ((minus_minus_int P) (number_number_of_int (bit0 (bit1 pls))))) P)))) of role axiom named fact_1110_d22set__eq__wset
% 2.21/2.46 A new axiom: (forall (P:int), ((zprime P)->(((eq (int->Prop)) (d22set ((minus_minus_int P) (number_number_of_int (bit0 (bit1 pls)))))) ((wset ((minus_minus_int P) (number_number_of_int (bit0 (bit1 pls))))) P))))
% 2.21/2.46 FOF formula (forall (N:nat) (P_1:(nat->Prop)), (((P_1 zero_zero_nat)->False)->((P_1 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_1 _TPTP_I)->False))))) (P_1 K_1))))))) of role axiom named fact_1111_ex__least__nat__le
% 2.21/2.46 A new axiom: (forall (N:nat) (P_1:(nat->Prop)), (((P_1 zero_zero_nat)->False)->((P_1 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_1 _TPTP_I)->False))))) (P_1 K_1)))))))
% 2.21/2.46 FOF formula (forall (B:int) (A:int), (((member_int B) (d22set A))->((ord_less_eq_int B) A))) of role axiom named fact_1112_d22set__le
% 2.21/2.46 A new axiom: (forall (B:int) (A:int), (((member_int B) (d22set A))->((ord_less_eq_int B) A)))
% 2.21/2.46 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
% 2.21/2.46 A new axiom: (forall (A:int) (B:int), (((ord_less_int A) B)->(((member_int B) (d22set A))->False)))
% 2.21/2.47 FOF formula (forall (B:int) (A:int), (((member_int B) (d22set A))->((ord_less_int one_one_int) B))) of role axiom named fact_1114_d22set__g__1
% 2.21/2.47 A new axiom: (forall (B:int) (A:int), (((member_int B) (d22set A))->((ord_less_int one_one_int) B)))
% 2.21/2.47 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_1115_d22set__mem
% 2.21/2.47 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)))))
% 2.21/2.47 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_1116_less__imp__add__positive
% 2.21/2.47 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))))))
% 2.21/2.47 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_1117_pow__divides__eq__int
% 2.21/2.47 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))))
% 2.21/2.47 FOF formula (forall (A:nat), (((dvd_dvd_nat zero_zero_nat) A)->(((eq nat) A) zero_zero_nat))) of role axiom named fact_1118_gcd__lcm__complete__lattice__nat_Otop__le
% 2.21/2.47 A new axiom: (forall (A:nat), (((dvd_dvd_nat zero_zero_nat) A)->(((eq nat) A) zero_zero_nat)))
% 2.21/2.47 FOF formula (forall (A:nat), ((iff ((dvd_dvd_nat zero_zero_nat) A)) (((eq nat) A) zero_zero_nat))) of role axiom named fact_1119_gcd__lcm__complete__lattice__nat_Otop__unique
% 2.21/2.47 A new axiom: (forall (A:nat), ((iff ((dvd_dvd_nat zero_zero_nat) A)) (((eq nat) A) zero_zero_nat)))
% 2.21/2.47 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_1120_gcd__lcm__complete__lattice__nat_Oless__top
% 2.21/2.47 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))))
% 2.21/2.47 FOF formula (forall (A:nat), ((dvd_dvd_nat A) zero_zero_nat)) of role axiom named fact_1121_gcd__lcm__complete__lattice__nat_Otop__greatest
% 2.21/2.47 A new axiom: (forall (A:nat), ((dvd_dvd_nat A) zero_zero_nat))
% 2.21/2.47 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_1122_gcd__lcm__complete__lattice__nat_Onot__top__less
% 2.21/2.47 A new axiom: (forall (A:nat), (((and ((dvd_dvd_nat zero_zero_nat) A)) (((dvd_dvd_nat A) zero_zero_nat)->False))->False))
% 2.21/2.47 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_1123_gcd__lcm__complete__lattice__nat_Onot__less__bot
% 2.21/2.47 A new axiom: (forall (A:nat), (((and ((dvd_dvd_nat A) one_one_nat)) (((dvd_dvd_nat one_one_nat) A)->False))->False))
% 2.21/2.47 FOF formula (forall (A:nat), ((dvd_dvd_nat one_one_nat) A)) of role axiom named fact_1124_gcd__lcm__complete__lattice__nat_Obot__least
% 2.21/2.47 A new axiom: (forall (A:nat), ((dvd_dvd_nat one_one_nat) A))
% 2.21/2.47 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_1125_gcd__lcm__complete__lattice__nat_Obot__less
% 2.21/2.47 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))))
% 2.21/2.47 FOF formula (forall (A:nat), ((iff ((dvd_dvd_nat A) one_one_nat)) (((eq nat) A) one_one_nat))) of role axiom named fact_1126_gcd__lcm__complete__lattice__nat_Obot__unique
% 2.21/2.47 A new axiom: (forall (A:nat), ((iff ((dvd_dvd_nat A) one_one_nat)) (((eq nat) A) one_one_nat)))
% 2.21/2.47 FOF formula (forall (A:nat), (((dvd_dvd_nat A) one_one_nat)->(((eq nat) A) one_one_nat))) of role axiom named fact_1127_gcd__lcm__complete__lattice__nat_Ole__bot
% 2.31/2.49 A new axiom: (forall (A:nat), (((dvd_dvd_nat A) one_one_nat)->(((eq nat) A) one_one_nat)))
% 2.31/2.49 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_1128_dvd__pos__nat
% 2.31/2.49 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))))
% 2.31/2.49 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_1129_pow__divides__eq__nat
% 2.31/2.49 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))))
% 2.31/2.49 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_1130_pow__divides__pow__int
% 2.31/2.49 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))))
% 2.31/2.49 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_1131_divides__le
% 2.31/2.49 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))))
% 2.31/2.49 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_1132_mult__left__cancel
% 2.31/2.49 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))))
% 2.31/2.49 FOF formula (forall (P:int), (((eq (int->Prop)) (sr P)) (collect_int (fun (X:int)=> ((and ((ord_less_eq_int zero_zero_int) X)) ((ord_less_int X) P)))))) of role axiom named fact_1133_SR__def
% 2.31/2.49 A new axiom: (forall (P:int), (((eq (int->Prop)) (sr P)) (collect_int (fun (X:int)=> ((and ((ord_less_eq_int zero_zero_int) X)) ((ord_less_int X) P))))))
% 2.31/2.49 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_1134_neg__zmod__mult__2
% 2.31/2.49 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))))
% 2.31/2.49 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_1135_zmod__number__of__Bit1
% 2.31/2.49 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)))))
% 2.33/2.51 FOF formula (forall (X_1:int) (Y_1:int), ((iff ((dvd_dvd_int (number_number_of_int X_1)) (number_number_of_int Y_1))) (((eq int) ((div_mod_int (number_number_of_int Y_1)) (number_number_of_int X_1))) zero_zero_int))) of role axiom named fact_1136_zdvd__iff__zmod__eq__0__number__of
% 2.33/2.51 A new axiom: (forall (X_1:int) (Y_1:int), ((iff ((dvd_dvd_int (number_number_of_int X_1)) (number_number_of_int Y_1))) (((eq int) ((div_mod_int (number_number_of_int Y_1)) (number_number_of_int X_1))) zero_zero_int)))
% 2.33/2.51 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_1137_neg__mod__bound
% 2.33/2.51 A new axiom: (forall (A:int) (B:int), (((ord_less_int B) zero_zero_int)->((ord_less_int B) ((div_mod_int A) B))))
% 2.33/2.51 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_1138_pos__mod__bound
% 2.33/2.51 A new axiom: (forall (A:int) (B:int), (((ord_less_int zero_zero_int) B)->((ord_less_int ((div_mod_int A) B)) B)))
% 2.33/2.51 FOF formula (forall (Y_1:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_eq_int zero_zero_int) Y_1)->((ord_less_eq_int zero_zero_int) ((div_mod_int X_1) Y_1))))) of role axiom named fact_1139_Divides_Otransfer__nat__int__function__closures_I2_J
% 2.33/2.51 A new axiom: (forall (Y_1:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_eq_int zero_zero_int) Y_1)->((ord_less_eq_int zero_zero_int) ((div_mod_int X_1) Y_1)))))
% 2.33/2.51 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_1140_zmod__le__nonneg__dividend
% 2.33/2.51 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)))
% 2.33/2.51 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_1141_zmod__eq__0__iff
% 2.33/2.51 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))))))
% 2.33/2.51 FOF formula (forall (X_1:int) (N:int) (Y_1:int), ((iff (((eq int) ((div_mod_int X_1) N)) ((div_mod_int Y_1) N))) ((dvd_dvd_int N) ((minus_minus_int X_1) Y_1)))) of role axiom named fact_1142_zmod__eq__dvd__iff
% 2.33/2.51 A new axiom: (forall (X_1:int) (N:int) (Y_1:int), ((iff (((eq int) ((div_mod_int X_1) N)) ((div_mod_int Y_1) N))) ((dvd_dvd_int N) ((minus_minus_int X_1) Y_1))))
% 2.33/2.51 FOF formula (forall (X_1:int) (M:int) (Y_1:int), ((((eq int) ((div_mod_int X_1) M)) ((div_mod_int Y_1) M))->(((zcong X_1) Y_1) M))) of role axiom named fact_1143_Residues_Oaux
% 2.33/2.51 A new axiom: (forall (X_1:int) (M:int) (Y_1:int), ((((eq int) ((div_mod_int X_1) M)) ((div_mod_int Y_1) M))->(((zcong X_1) Y_1) M)))
% 2.33/2.51 FOF formula (forall (X_1:int) (M:int), (((zcong X_1) ((div_mod_int X_1) M)) M)) of role axiom named fact_1144_mod__mod__is__mod
% 2.33/2.51 A new axiom: (forall (X_1:int) (M:int), (((zcong X_1) ((div_mod_int X_1) M)) M))
% 2.33/2.51 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_1145_zcong__zmod
% 2.33/2.51 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)))
% 2.33/2.51 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_1146_zdvd__zmod__imp__zdvd
% 2.33/2.51 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))))
% 2.33/2.53 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_1147_zdvd__zmod
% 2.33/2.53 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)))))
% 2.33/2.53 FOF formula (forall (X_1:int) (M:int) (Y_1:nat), (((eq int) ((div_mod_int ((power_power_int ((div_mod_int X_1) M)) Y_1)) M)) ((div_mod_int ((power_power_int X_1) Y_1)) M))) of role axiom named fact_1148_zpower__zmod
% 2.33/2.53 A new axiom: (forall (X_1:int) (M:int) (Y_1:nat), (((eq int) ((div_mod_int ((power_power_int ((div_mod_int X_1) M)) Y_1)) M)) ((div_mod_int ((power_power_int X_1) Y_1)) M)))
% 2.33/2.53 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_1149_zmod__zmult1__eq
% 2.33/2.53 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)))
% 2.33/2.53 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_1150_zmod__simps_I3_J
% 2.33/2.53 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)))
% 2.33/2.53 FOF formula (forall (A:int), (((eq int) ((div_mod_int A) A)) zero_zero_int)) of role axiom named fact_1151_zmod__self
% 2.33/2.53 A new axiom: (forall (A:int), (((eq int) ((div_mod_int A) A)) zero_zero_int))
% 2.33/2.53 FOF formula (forall (B:int), (((eq int) ((div_mod_int zero_zero_int) B)) zero_zero_int)) of role axiom named fact_1152_zmod__zero
% 2.33/2.53 A new axiom: (forall (B:int), (((eq int) ((div_mod_int zero_zero_int) B)) zero_zero_int))
% 2.33/2.53 FOF formula (forall (X_1:int) (Y_1:int) (M:int), (((eq int) ((div_mod_int ((minus_minus_int X_1) ((div_mod_int Y_1) M))) M)) ((div_mod_int ((minus_minus_int X_1) Y_1)) M))) of role axiom named fact_1153_zdiff__zmod__right
% 2.33/2.53 A new axiom: (forall (X_1:int) (Y_1:int) (M:int), (((eq int) ((div_mod_int ((minus_minus_int X_1) ((div_mod_int Y_1) M))) M)) ((div_mod_int ((minus_minus_int X_1) Y_1)) M)))
% 2.33/2.53 FOF formula (forall (X_1:int) (M:int) (Y_1:int), (((eq int) ((div_mod_int ((minus_minus_int ((div_mod_int X_1) M)) Y_1)) M)) ((div_mod_int ((minus_minus_int X_1) Y_1)) M))) of role axiom named fact_1154_zdiff__zmod__left
% 2.33/2.53 A new axiom: (forall (X_1:int) (M:int) (Y_1:int), (((eq int) ((div_mod_int ((minus_minus_int ((div_mod_int X_1) M)) Y_1)) M)) ((div_mod_int ((minus_minus_int X_1) Y_1)) M)))
% 2.33/2.53 FOF formula (forall (A:int), (((eq int) ((div_mod_int A) (number_number_of_int min))) zero_zero_int)) of role axiom named fact_1155_zmod__minus1__right
% 2.33/2.53 A new axiom: (forall (A:int), (((eq int) ((div_mod_int A) (number_number_of_int min))) zero_zero_int))
% 2.33/2.53 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_1156_zmod__zdvd__zmod
% 2.33/2.53 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)))))
% 2.33/2.53 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_1157_zcong__zmod__eq
% 2.33/2.53 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)))))
% 2.33/2.53 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_1158_pos__mod__sign
% 2.33/2.53 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))))
% 2.33/2.53 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_1159_pos__mod__conj
% 2.33/2.55 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))))
% 2.33/2.55 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_1160_mod__pos__pos__trivial
% 2.33/2.55 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))))
% 2.33/2.55 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_1161_neg__mod__sign
% 2.33/2.55 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)))
% 2.33/2.55 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_1162_neg__mod__conj
% 2.33/2.55 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)))))
% 2.33/2.55 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_1163_mod__neg__neg__trivial
% 2.33/2.55 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))))
% 2.33/2.55 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_1164_mod__pos__neg__trivial
% 2.33/2.55 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)))))
% 2.33/2.55 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_1165_zmod__number__of__Bit0
% 2.33/2.55 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)))))
% 2.33/2.55 FOF formula (forall (P_1:(int->Prop)) (N:int) (K:int), ((iff (P_1 ((div_mod_int N) K))) ((and ((and ((((eq int) K) zero_zero_int)->(P_1 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_1 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_1 J))))))) of role axiom named fact_1166_split__zmod
% 2.33/2.55 A new axiom: (forall (P_1:(int->Prop)) (N:int) (K:int), ((iff (P_1 ((div_mod_int N) K))) ((and ((and ((((eq int) K) zero_zero_int)->(P_1 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_1 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_1 J)))))))
% 2.33/2.55 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_1167_zmult2__lemma__aux3
% 2.33/2.57 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))))))
% 2.33/2.57 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_1168_zmult2__lemma__aux4
% 2.33/2.57 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))))))
% 2.33/2.57 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_1169_zmult2__lemma__aux1
% 2.33/2.57 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))))))
% 2.33/2.57 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_1170_zmult2__lemma__aux2
% 2.33/2.57 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)))))
% 2.33/2.57 FOF formula (forall (A_1:int) (B_1:int) (Q_2:int) (Y_1:int), ((((eq int) A_1) ((plus_plus_int ((times_times_int B_1) Q_2)) Y_1))->(((and (((ord_less_int zero_zero_int) B_1)->((and ((ord_less_eq_int zero_zero_int) Y_1)) ((ord_less_int Y_1) B_1)))) ((((ord_less_int zero_zero_int) B_1)->False)->((and ((ord_less_int B_1) Y_1)) ((ord_less_eq_int Y_1) zero_zero_int))))->((not (((eq int) B_1) zero_zero_int))->(((eq int) ((div_mod_int A_1) B_1)) Y_1))))) of role axiom named fact_1171_divmod__int__rel__mod__eq
% 2.33/2.57 A new axiom: (forall (A_1:int) (B_1:int) (Q_2:int) (Y_1:int), ((((eq int) A_1) ((plus_plus_int ((times_times_int B_1) Q_2)) Y_1))->(((and (((ord_less_int zero_zero_int) B_1)->((and ((ord_less_eq_int zero_zero_int) Y_1)) ((ord_less_int Y_1) B_1)))) ((((ord_less_int zero_zero_int) B_1)->False)->((and ((ord_less_int B_1) Y_1)) ((ord_less_eq_int Y_1) zero_zero_int))))->((not (((eq int) B_1) zero_zero_int))->(((eq int) ((div_mod_int A_1) B_1)) Y_1)))))
% 2.33/2.57 FOF formula (forall (X_1:int), ((iff (not (((eq int) ((div_mod_int X_1) (number_number_of_int (bit0 (bit1 pls))))) zero_zero_int))) (((eq int) ((div_mod_int X_1) (number_number_of_int (bit0 (bit1 pls))))) one_one_int))) of role axiom named fact_1172_neq__one__mod__two
% 2.33/2.57 A new axiom: (forall (X_1:int), ((iff (not (((eq int) ((div_mod_int X_1) (number_number_of_int (bit0 (bit1 pls))))) zero_zero_int))) (((eq int) ((div_mod_int X_1) (number_number_of_int (bit0 (bit1 pls))))) one_one_int)))
% 2.33/2.57 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_1173_zmod__minus1
% 2.33/2.57 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))))
% 2.33/2.57 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_1174_pos__zmod__mult__2
% 2.33/2.59 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))))))
% 2.33/2.59 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_1175_zmod__eq__0D
% 2.33/2.59 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))))))
% 2.33/2.59 FOF formula (forall (X_1:int) (Y_1:int) (M:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) M)->(((zcong ((times_times_int ((standardRes M) X_1)) ((standardRes M) Y_1))) ((times_times_int X_1) Y_1)) M))) of role axiom named fact_1176_StandardRes__prop4
% 2.33/2.59 A new axiom: (forall (X_1:int) (Y_1:int) (M:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) M)->(((zcong ((times_times_int ((standardRes M) X_1)) ((standardRes M) Y_1))) ((times_times_int X_1) Y_1)) M)))
% 2.33/2.59 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_1177_mod__le__divisor
% 2.33/2.59 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)))
% 2.33/2.59 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_1178_mod__less__divisor
% 2.33/2.59 A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->((ord_less_nat ((div_mod_nat M) N)) N)))
% 2.33/2.59 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_1179_mod__eq__0__iff
% 2.33/2.59 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))))))
% 2.33/2.59 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_1180_mod__geq
% 2.33/2.59 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))))
% 2.33/2.59 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_1181_mod__if
% 2.33/2.59 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)))))
% 2.33/2.59 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_1182_mod__mult__self3
% 2.33/2.59 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)))
% 2.33/2.59 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_1183_le__mod__geq
% 2.33/2.59 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))))
% 2.33/2.59 FOF formula (forall (M:int) (X_1:int), (((eq int) ((standardRes M) X_1)) ((div_mod_int X_1) M))) of role axiom named fact_1184_StandardRes__def
% 2.33/2.59 A new axiom: (forall (M:int) (X_1:int), (((eq int) ((standardRes M) X_1)) ((div_mod_int X_1) M)))
% 2.33/2.59 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_1185_mod__mult__distrib
% 2.42/2.61 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))))
% 2.42/2.61 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_1186_mod__mult__distrib2
% 2.42/2.61 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))))
% 2.42/2.61 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_1187_mod__less
% 2.42/2.61 A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->(((eq nat) ((div_mod_nat M) N)) M)))
% 2.42/2.61 FOF formula (forall (M:nat) (N:nat), ((ord_less_eq_nat ((div_mod_nat M) N)) M)) of role axiom named fact_1188_mod__less__eq__dividend
% 2.42/2.61 A new axiom: (forall (M:nat) (N:nat), ((ord_less_eq_nat ((div_mod_nat M) N)) M))
% 2.42/2.61 FOF formula (forall (M:int) (X_1:int), ((iff (((eq int) ((standardRes M) X_1)) zero_zero_int)) (((zcong X_1) zero_zero_int) M))) of role axiom named fact_1189_StandardRes__eq__zcong
% 2.42/2.61 A new axiom: (forall (M:int) (X_1:int), ((iff (((eq int) ((standardRes M) X_1)) zero_zero_int)) (((zcong X_1) zero_zero_int) M)))
% 2.42/2.61 FOF formula (forall (X_1:int) (P:int), ((iff ((((zcong X_1) zero_zero_int) P)->False)) (not (((eq int) ((standardRes P) X_1)) zero_zero_int)))) of role axiom named fact_1190_StandardRes__prop3
% 2.42/2.61 A new axiom: (forall (X_1:int) (P:int), ((iff ((((zcong X_1) zero_zero_int) P)->False)) (not (((eq int) ((standardRes P) X_1)) zero_zero_int))))
% 2.42/2.61 FOF formula (forall (X_1:int) (M:int), (((zcong X_1) ((standardRes M) X_1)) M)) of role axiom named fact_1191_StandardRes__prop1
% 2.42/2.61 A new axiom: (forall (X_1:int) (M:int), (((zcong X_1) ((standardRes M) X_1)) M))
% 2.42/2.61 FOF formula (forall (X_1:int) (P:int), (((ord_less_int zero_zero_int) P)->((ord_less_int ((standardRes P) X_1)) P))) of role axiom named fact_1192_StandardRes__ubound
% 2.42/2.61 A new axiom: (forall (X_1:int) (P:int), (((ord_less_int zero_zero_int) P)->((ord_less_int ((standardRes P) X_1)) P)))
% 2.42/2.61 FOF formula (forall (X_1:int) (P:int), (((member_int X_1) (sr P))->(((eq int) ((standardRes P) X_1)) X_1))) of role axiom named fact_1193_StandardRes__SR__prop
% 2.42/2.61 A new axiom: (forall (X_1:int) (P:int), (((member_int X_1) (sr P))->(((eq int) ((standardRes P) X_1)) X_1)))
% 2.42/2.61 FOF formula (forall (P_1:(nat->Prop)) (N:nat) (K:nat), ((iff (P_1 ((div_mod_nat N) K))) ((and ((((eq nat) K) zero_zero_nat)->(P_1 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_1 J)))))))) of role axiom named fact_1194_split__mod
% 2.42/2.61 A new axiom: (forall (P_1:(nat->Prop)) (N:nat) (K:nat), ((iff (P_1 ((div_mod_nat N) K))) ((and ((((eq nat) K) zero_zero_nat)->(P_1 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_1 J))))))))
% 2.42/2.61 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_1195_mod__lemma
% 2.42/2.61 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)))))
% 2.42/2.61 FOF formula (forall (X_1:int) (P:int), (((ord_less_int zero_zero_int) P)->((ord_less_eq_int zero_zero_int) ((standardRes P) X_1)))) of role axiom named fact_1196_StandardRes__lbound
% 2.42/2.61 A new axiom: (forall (X_1:int) (P:int), (((ord_less_int zero_zero_int) P)->((ord_less_eq_int zero_zero_int) ((standardRes P) X_1))))
% 2.42/2.61 FOF formula (forall (X1:int) (X2:int) (M:int), (((ord_less_int zero_zero_int) M)->((iff (((eq int) ((standardRes M) X1)) ((standardRes M) X2))) (((zcong X1) X2) M)))) of role axiom named fact_1197_StandardRes__prop2
% 2.42/2.63 A new axiom: (forall (X1:int) (X2:int) (M:int), (((ord_less_int zero_zero_int) M)->((iff (((eq int) ((standardRes M) X1)) ((standardRes M) X2))) (((zcong X1) X2) M))))
% 2.42/2.63 FOF formula ((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq 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)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))))) of role conjecture named conj_0
% 2.42/2.63 Conjecture to prove = ((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq 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)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))))):Prop
% 2.42/2.63 Parameter product_prod_int_int_DUMMY:product_prod_int_int.
% 2.42/2.63 We need to prove ['((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq 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)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))']
% 2.42/2.63 Parameter int:Type.
% 2.42/2.63 Parameter nat:Type.
% 2.42/2.63 Parameter real:Type.
% 2.42/2.63 Parameter product_prod_int_int:Type.
% 2.42/2.63 Parameter div_mod_int:(int->(int->int)).
% 2.42/2.63 Parameter div_mod_nat:(nat->(nat->nat)).
% 2.42/2.63 Parameter minus_minus_int:(int->(int->int)).
% 2.42/2.63 Parameter minus_minus_nat:(nat->(nat->nat)).
% 2.42/2.63 Parameter minus_minus_real:(real->(real->real)).
% 2.42/2.63 Parameter one_one_int:int.
% 2.42/2.63 Parameter one_one_nat:nat.
% 2.42/2.63 Parameter one_one_real:real.
% 2.42/2.63 Parameter plus_plus_int:(int->(int->int)).
% 2.42/2.63 Parameter plus_plus_nat:(nat->(nat->nat)).
% 2.42/2.63 Parameter plus_plus_real:(real->(real->real)).
% 2.42/2.63 Parameter times_times_int:(int->(int->int)).
% 2.42/2.63 Parameter times_times_nat:(nat->(nat->nat)).
% 2.42/2.63 Parameter times_times_real:(real->(real->real)).
% 2.42/2.63 Parameter zero_zero_int:int.
% 2.42/2.63 Parameter zero_zero_nat:nat.
% 2.42/2.63 Parameter zero_zero_real:real.
% 2.42/2.63 Parameter multInv:(int->(int->int)).
% 2.42/2.63 Parameter d22set:(int->(int->Prop)).
% 2.42/2.63 Parameter zfact:(int->int).
% 2.42/2.63 Parameter zcong:(int->(int->(int->Prop))).
% 2.42/2.63 Parameter zprime:(int->Prop).
% 2.42/2.63 Parameter bit0:(int->int).
% 2.42/2.63 Parameter bit1:(int->int).
% 2.42/2.63 Parameter min:int.
% 2.42/2.63 Parameter pls:int.
% 2.42/2.63 Parameter number_number_of_int:(int->int).
% 2.42/2.63 Parameter number_number_of_nat:(int->nat).
% 2.42/2.63 Parameter number267125858f_real:(int->real).
% 2.42/2.63 Parameter ord_less_int:(int->(int->Prop)).
% 2.42/2.63 Parameter ord_less_nat:(nat->(nat->Prop)).
% 2.42/2.63 Parameter ord_less_real:(real->(real->Prop)).
% 2.42/2.63 Parameter ord_less_eq_int:(int->(int->Prop)).
% 2.42/2.63 Parameter ord_less_eq_nat:(nat->(nat->Prop)).
% 2.42/2.63 Parameter ord_less_eq_real:(real->(real->Prop)).
% 2.42/2.63 Parameter power_power_int:(int->(nat->int)).
% 2.42/2.63 Parameter power_power_nat:(nat->(nat->nat)).
% 2.42/2.63 Parameter power_power_real:(real->(nat->real)).
% 2.42/2.63 Parameter product_Pair_int_int:(int->(int->product_prod_int_int)).
% 2.42/2.63 Parameter legendre:(int->(int->int)).
% 2.42/2.63 Parameter quadRes:(int->(int->Prop)).
% 2.42/2.63 Parameter sr:(int->(int->Prop)).
% 2.42/2.63 Parameter standardRes:(int->(int->int)).
% 2.42/2.63 Parameter dvd_dvd_int:(int->(int->Prop)).
% 2.42/2.63 Parameter dvd_dvd_nat:(nat->(nat->Prop)).
% 2.42/2.63 Parameter dvd_dvd_real:(real->(real->Prop)).
% 2.42/2.63 Parameter collect_int:((int->Prop)->(int->Prop)).
% 2.42/2.63 Parameter twoSqu919416604sum2sq:(int->Prop).
% 2.42/2.63 Parameter twoSqu2057625106sum2sq:(product_prod_int_int->int).
% 2.42/2.63 Parameter inv:(int->(int->int)).
% 2.42/2.63 Parameter wset:(int->(int->(int->Prop))).
% 2.42/2.63 Parameter member_int:(int->((int->Prop)->Prop)).
% 2.42/2.63 Parameter m:int.
% 2.42/2.63 Parameter s1:int.
% 2.42/2.63 Parameter s:int.
% 2.42/2.63 Parameter t:int.
% 2.42/2.63 Axiom fact_0_tpos:((ord_less_eq_int one_one_int) t).
% 2.42/2.63 Axiom fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06:((((eq int) t) one_one_int)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq 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)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))).
% 2.42/2.63 Axiom fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06:(((ord_less_int one_one_int) t)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq 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)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))).
% 2.42/2.63 Axiom fact_3_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)).
% 2.42/2.63 Axiom fact_4_p:(zprime ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)).
% 2.42/2.63 Axiom fact_5_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)).
% 2.42/2.63 Axiom fact_6_qf1pt:(twoSqu919416604sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)).
% 2.42/2.63 Axiom fact_7_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))))))).
% 2.42/2.63 Axiom fact_8_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))))))).
% 2.42/2.63 Axiom fact_9_power2__sum:(forall (X_44:int) (Y_34:int), (((eq int) ((power_power_int ((plus_plus_int X_44) Y_34)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int X_44) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_34) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) X_44)) Y_34)))).
% 2.42/2.63 Axiom fact_10_power2__sum:(forall (X_44:nat) (Y_34:nat), (((eq nat) ((power_power_nat ((plus_plus_nat X_44) Y_34)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat ((plus_plus_nat ((power_power_nat X_44) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_34) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) X_44)) Y_34)))).
% 2.42/2.63 Axiom fact_11_power2__sum:(forall (X_44:real) (Y_34:real), (((eq real) ((power_power_real ((plus_plus_real X_44) Y_34)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X_44) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_34) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_44)) Y_34)))).
% 2.42/2.63 Axiom fact_12_power2__eq__square__number__of:(forall (W_19:int), (((eq int) ((power_power_int (number_number_of_int W_19)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int (number_number_of_int W_19)) (number_number_of_int W_19)))).
% 2.42/2.63 Axiom fact_13_power2__eq__square__number__of:(forall (W_19:int), (((eq real) ((power_power_real (number267125858f_real W_19)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real (number267125858f_real W_19)) (number267125858f_real W_19)))).
% 2.42/2.63 Axiom fact_14_power2__eq__square__number__of:(forall (W_19:int), (((eq nat) ((power_power_nat (number_number_of_nat W_19)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat (number_number_of_nat W_19)) (number_number_of_nat W_19)))).
% 2.42/2.63 Axiom fact_15_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)))))).
% 2.42/2.63 Axiom fact_16_one__power2:(((eq int) ((power_power_int one_one_int) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int).
% 2.42/2.63 Axiom fact_17_one__power2:(((eq nat) ((power_power_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls))))) one_one_nat).
% 2.42/2.63 Axiom fact_18_one__power2:(((eq real) ((power_power_real one_one_real) (number_number_of_nat (bit0 (bit1 pls))))) one_one_real).
% 2.42/2.63 Axiom fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J:(forall (X_43:int), (((eq int) ((times_times_int X_43) X_43)) ((power_power_int X_43) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.42/2.63 Axiom fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J:(forall (X_43:real), (((eq real) ((times_times_real X_43) X_43)) ((power_power_real X_43) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.42/2.63 Axiom fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J:(forall (X_43:nat), (((eq nat) ((times_times_nat X_43) X_43)) ((power_power_nat X_43) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.42/2.63 Axiom fact_22_power2__eq__square:(forall (A_127:int), (((eq int) ((power_power_int A_127) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int A_127) A_127))).
% 2.42/2.63 Axiom fact_23_power2__eq__square:(forall (A_127:real), (((eq real) ((power_power_real A_127) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real A_127) A_127))).
% 2.42/2.63 Axiom fact_24_power2__eq__square:(forall (A_127:nat), (((eq nat) ((power_power_nat A_127) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat A_127) A_127))).
% 2.42/2.63 Axiom fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J:(forall (X_42:int) (N_41:nat), (((eq int) ((power_power_int X_42) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_41))) ((times_times_int ((power_power_int X_42) N_41)) ((power_power_int X_42) N_41)))).
% 2.42/2.63 Axiom fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J:(forall (X_42:real) (N_41:nat), (((eq real) ((power_power_real X_42) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_41))) ((times_times_real ((power_power_real X_42) N_41)) ((power_power_real X_42) N_41)))).
% 2.42/2.63 Axiom fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J:(forall (X_42:nat) (N_41:nat), (((eq nat) ((power_power_nat X_42) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_41))) ((times_times_nat ((power_power_nat X_42) N_41)) ((power_power_nat X_42) N_41)))).
% 2.42/2.63 Axiom fact_28_add__special_I2_J:(forall (W_18:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_18))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_18)))).
% 2.42/2.63 Axiom fact_29_add__special_I2_J:(forall (W_18:int), (((eq real) ((plus_plus_real one_one_real) (number267125858f_real W_18))) (number267125858f_real ((plus_plus_int (bit1 pls)) W_18)))).
% 2.42/2.63 Axiom fact_30_add__special_I3_J:(forall (V_20:int), (((eq int) ((plus_plus_int (number_number_of_int V_20)) one_one_int)) (number_number_of_int ((plus_plus_int V_20) (bit1 pls))))).
% 2.42/2.63 Axiom fact_31_add__special_I3_J:(forall (V_20:int), (((eq real) ((plus_plus_real (number267125858f_real V_20)) one_one_real)) (number267125858f_real ((plus_plus_int V_20) (bit1 pls))))).
% 2.42/2.63 Axiom fact_32_one__add__one__is__two:(((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))).
% 2.42/2.63 Axiom fact_33_one__add__one__is__two:(((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))).
% 2.42/2.63 Axiom fact_34__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).
% 2.42/2.63 Axiom fact_35_zle__refl:(forall (W:int), ((ord_less_eq_int W) W)).
% 2.42/2.63 Axiom fact_36_zle__linear:(forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z))).
% 2.42/2.63 Axiom fact_37_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))))).
% 2.42/2.63 Axiom fact_38_zless__linear:(forall (X_1:int) (Y_1:int), ((or ((or ((ord_less_int X_1) Y_1)) (((eq int) X_1) Y_1))) ((ord_less_int Y_1) X_1))).
% 2.42/2.63 Axiom fact_39_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)))).
% 2.42/2.63 Axiom fact_40_zle__antisym:(forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W)))).
% 2.42/2.63 Axiom fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J:(forall (X_41:int) (P_6:nat) (Q_6:nat), (((eq int) ((power_power_int ((power_power_int X_41) P_6)) Q_6)) ((power_power_int X_41) ((times_times_nat P_6) Q_6)))).
% 2.42/2.63 Axiom fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J:(forall (X_41:real) (P_6:nat) (Q_6:nat), (((eq real) ((power_power_real ((power_power_real X_41) P_6)) Q_6)) ((power_power_real X_41) ((times_times_nat P_6) Q_6)))).
% 2.42/2.63 Axiom fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J:(forall (X_41:nat) (P_6:nat) (Q_6:nat), (((eq nat) ((power_power_nat ((power_power_nat X_41) P_6)) Q_6)) ((power_power_nat X_41) ((times_times_nat P_6) Q_6)))).
% 2.42/2.63 Axiom fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J:(forall (X_40:int), (((eq int) ((power_power_int X_40) one_one_nat)) X_40)).
% 2.42/2.63 Axiom fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J:(forall (X_40:real), (((eq real) ((power_power_real X_40) one_one_nat)) X_40)).
% 2.42/2.63 Axiom fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J:(forall (X_40:nat), (((eq nat) ((power_power_nat X_40) one_one_nat)) X_40)).
% 2.42/2.63 Axiom fact_47_zpower__zpower:(forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int ((power_power_int X_1) Y_1)) Z)) ((power_power_int X_1) ((times_times_nat Y_1) Z)))).
% 2.42/2.63 Axiom fact_48_le__number__of__eq__not__less:(forall (V_19:int) (W_17:int), ((iff ((ord_less_eq_int (number_number_of_int V_19)) (number_number_of_int W_17))) (((ord_less_int (number_number_of_int W_17)) (number_number_of_int V_19))->False))).
% 2.42/2.63 Axiom fact_49_le__number__of__eq__not__less:(forall (V_19:int) (W_17:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_19)) (number_number_of_nat W_17))) (((ord_less_nat (number_number_of_nat W_17)) (number_number_of_nat V_19))->False))).
% 2.42/2.63 Axiom fact_50_le__number__of__eq__not__less:(forall (V_19:int) (W_17:int), ((iff ((ord_less_eq_real (number267125858f_real V_19)) (number267125858f_real W_17))) (((ord_less_real (number267125858f_real W_17)) (number267125858f_real V_19))->False))).
% 2.42/2.63 Axiom fact_51_less__number__of:(forall (X_39:int) (Y_33:int), ((iff ((ord_less_int (number_number_of_int X_39)) (number_number_of_int Y_33))) ((ord_less_int X_39) Y_33))).
% 2.42/2.63 Axiom fact_52_less__number__of:(forall (X_39:int) (Y_33:int), ((iff ((ord_less_real (number267125858f_real X_39)) (number267125858f_real Y_33))) ((ord_less_int X_39) Y_33))).
% 2.42/2.63 Axiom fact_53_le__number__of:(forall (X_38:int) (Y_32:int), ((iff ((ord_less_eq_int (number_number_of_int X_38)) (number_number_of_int Y_32))) ((ord_less_eq_int X_38) Y_32))).
% 2.42/2.63 Axiom fact_54_le__number__of:(forall (X_38:int) (Y_32:int), ((iff ((ord_less_eq_real (number267125858f_real X_38)) (number267125858f_real Y_32))) ((ord_less_eq_int X_38) Y_32))).
% 2.42/2.63 Axiom fact_55_zadd__zless__mono:(forall (Z_10:int) (Z:int) (W_16:int) (W:int), (((ord_less_int W_16) W)->(((ord_less_eq_int Z_10) Z)->((ord_less_int ((plus_plus_int W_16) Z_10)) ((plus_plus_int W) Z))))).
% 2.42/2.63 Axiom fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J:(forall (X_37:int) (P_5:nat) (Q_5:nat), (((eq int) ((times_times_int ((power_power_int X_37) P_5)) ((power_power_int X_37) Q_5))) ((power_power_int X_37) ((plus_plus_nat P_5) Q_5)))).
% 2.42/2.63 Axiom fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J:(forall (X_37:real) (P_5:nat) (Q_5:nat), (((eq real) ((times_times_real ((power_power_real X_37) P_5)) ((power_power_real X_37) Q_5))) ((power_power_real X_37) ((plus_plus_nat P_5) Q_5)))).
% 2.42/2.63 Axiom fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J:(forall (X_37:nat) (P_5:nat) (Q_5:nat), (((eq nat) ((times_times_nat ((power_power_nat X_37) P_5)) ((power_power_nat X_37) Q_5))) ((power_power_nat X_37) ((plus_plus_nat P_5) Q_5)))).
% 2.42/2.63 Axiom fact_59_zpower__zadd__distrib:(forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int X_1) ((plus_plus_nat Y_1) Z))) ((times_times_int ((power_power_int X_1) Y_1)) ((power_power_int X_1) Z)))).
% 2.42/2.63 Axiom fact_60_nat__mult__2:(forall (Z:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z)) ((plus_plus_nat Z) Z))).
% 2.42/2.63 Axiom fact_61_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))).
% 2.42/2.63 Axiom fact_62_nat__1__add__1:(((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))).
% 2.42/2.63 Axiom fact_63_less__int__code_I16_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2))).
% 2.42/2.63 Axiom fact_64_rel__simps_I17_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L))).
% 2.42/2.63 Axiom fact_65_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))).
% 2.42/2.63 Axiom fact_66_rel__simps_I34_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit1 L))) ((ord_less_eq_int K) L))).
% 2.42/2.63 Axiom fact_67_rel__simps_I2_J:(((ord_less_int pls) pls)->False).
% 2.42/2.63 Axiom fact_68_less__int__code_I13_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit0 K2))) ((ord_less_int K1) K2))).
% 2.42/2.63 Axiom fact_69_rel__simps_I14_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit0 L))) ((ord_less_int K) L))).
% 2.42/2.63 Axiom fact_70_rel__simps_I19_J:((ord_less_eq_int pls) pls).
% 2.42/2.63 Axiom fact_71_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))).
% 2.42/2.63 Axiom fact_72_rel__simps_I31_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit0 L))) ((ord_less_eq_int K) L))).
% 2.42/2.63 Axiom fact_73_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))).
% 2.42/2.63 Axiom fact_74_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))).
% 2.42/2.63 Axiom fact_75_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)))).
% 2.42/2.63 Axiom fact_76_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)))).
% 2.42/2.63 Axiom fact_77_add__nat__number__of:(forall (V_6:int) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_6))) (number_number_of_nat V_6)))) ((((ord_less_int V) pls)->False)->((and (((ord_less_int V_6) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_6))) (number_number_of_nat V)))) ((((ord_less_int V_6) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_6))) (number_number_of_nat ((plus_plus_int V) V_6)))))))).
% 2.42/2.63 Axiom fact_78_nat__numeral__1__eq__1:(((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat).
% 2.42/2.63 Axiom fact_79_Numeral1__eq1__nat:(((eq nat) one_one_nat) (number_number_of_nat (bit1 pls))).
% 2.42/2.63 Axiom fact_80_rel__simps_I29_J:(forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls))).
% 2.42/2.63 Axiom fact_81_rel__simps_I5_J:(forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K))).
% 2.42/2.63 Axiom fact_82_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))).
% 2.42/2.63 Axiom fact_83_rel__simps_I33_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))).
% 2.42/2.63 Axiom fact_84_less__int__code_I14_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))).
% 2.42/2.64 Axiom fact_85_rel__simps_I15_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))).
% 2.42/2.64 Axiom fact_86_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))).
% 2.42/2.64 Axiom fact_87_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))).
% 2.42/2.64 Axiom fact_88_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))).
% 2.42/2.64 Axiom fact_89_zprime__2:(zprime (number_number_of_int (bit0 (bit1 pls)))).
% 2.42/2.64 Axiom fact_90_is__mult__sum2sq:(forall (Y_1:int) (X_1:int), ((twoSqu919416604sum2sq X_1)->((twoSqu919416604sum2sq Y_1)->(twoSqu919416604sum2sq ((times_times_int X_1) Y_1))))).
% 2.42/2.64 Axiom fact_91_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)))).
% 2.42/2.64 Axiom fact_92_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)))).
% 2.42/2.64 Axiom fact_93_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)))).
% 2.42/2.64 Axiom fact_94_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)))).
% 2.42/2.64 Axiom fact_95_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)))).
% 2.42/2.64 Axiom fact_96_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)))).
% 2.42/2.64 Axiom fact_97_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))))).
% 2.42/2.64 Axiom fact_98_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))))).
% 2.42/2.64 Axiom fact_99_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))))).
% 2.42/2.64 Axiom fact_100_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))).
% 2.42/2.64 Axiom fact_101_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))).
% 2.42/2.64 Axiom fact_102_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))).
% 2.42/2.64 Axiom fact_103_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)))).
% 2.42/2.64 Axiom fact_104_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)))).
% 2.42/2.64 Axiom fact_105_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)))).
% 2.42/2.64 Axiom fact_106_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))).
% 2.42/2.64 Axiom fact_107_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))).
% 2.42/2.64 Axiom fact_108_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))).
% 2.42/2.64 Axiom fact_109_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)))).
% 2.42/2.64 Axiom fact_110_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)))).
% 2.42/2.64 Axiom fact_111_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)))).
% 2.42/2.64 Axiom fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J:(forall (A_126:int) (B_73:int), (((eq int) ((times_times_int A_126) B_73)) ((times_times_int B_73) A_126))).
% 2.42/2.64 Axiom fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J:(forall (A_126:nat) (B_73:nat), (((eq nat) ((times_times_nat A_126) B_73)) ((times_times_nat B_73) A_126))).
% 2.42/2.64 Axiom fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J:(forall (A_126:real) (B_73:real), (((eq real) ((times_times_real A_126) B_73)) ((times_times_real B_73) A_126))).
% 2.42/2.64 Axiom fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_125:int) (B_72:int) (C_39:int) (D_11:int), (((eq int) ((plus_plus_int ((plus_plus_int A_125) B_72)) ((plus_plus_int C_39) D_11))) ((plus_plus_int ((plus_plus_int A_125) C_39)) ((plus_plus_int B_72) D_11)))).
% 2.42/2.64 Axiom fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_125:nat) (B_72:nat) (C_39:nat) (D_11:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_125) B_72)) ((plus_plus_nat C_39) D_11))) ((plus_plus_nat ((plus_plus_nat A_125) C_39)) ((plus_plus_nat B_72) D_11)))).
% 2.42/2.64 Axiom fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_125:real) (B_72:real) (C_39:real) (D_11:real), (((eq real) ((plus_plus_real ((plus_plus_real A_125) B_72)) ((plus_plus_real C_39) D_11))) ((plus_plus_real ((plus_plus_real A_125) C_39)) ((plus_plus_real B_72) D_11)))).
% 2.42/2.64 Axiom fact_118_mem__def:(forall (X_36:int) (A_124:(int->Prop)), ((iff ((member_int X_36) A_124)) (A_124 X_36))).
% 2.42/2.64 Axiom fact_119_Collect__def:(forall (P_4:(int->Prop)), (((eq (int->Prop)) (collect_int P_4)) P_4)).
% 2.42/2.64 Axiom fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_123:int) (B_71:int) (C_38:int), (((eq int) ((plus_plus_int ((plus_plus_int A_123) B_71)) C_38)) ((plus_plus_int ((plus_plus_int A_123) C_38)) B_71))).
% 2.42/2.64 Axiom fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_123:nat) (B_71:nat) (C_38:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_123) B_71)) C_38)) ((plus_plus_nat ((plus_plus_nat A_123) C_38)) B_71))).
% 2.42/2.64 Axiom fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_123:real) (B_71:real) (C_38:real), (((eq real) ((plus_plus_real ((plus_plus_real A_123) B_71)) C_38)) ((plus_plus_real ((plus_plus_real A_123) C_38)) B_71))).
% 2.42/2.64 Axiom fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_122:int) (B_70:int) (C_37:int), (((eq int) ((plus_plus_int ((plus_plus_int A_122) B_70)) C_37)) ((plus_plus_int A_122) ((plus_plus_int B_70) C_37)))).
% 2.42/2.64 Axiom fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_122:nat) (B_70:nat) (C_37:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_122) B_70)) C_37)) ((plus_plus_nat A_122) ((plus_plus_nat B_70) C_37)))).
% 2.42/2.64 Axiom fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_122:real) (B_70:real) (C_37:real), (((eq real) ((plus_plus_real ((plus_plus_real A_122) B_70)) C_37)) ((plus_plus_real A_122) ((plus_plus_real B_70) C_37)))).
% 2.42/2.64 Axiom fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_121:int) (C_36:int) (D_10:int), (((eq int) ((plus_plus_int A_121) ((plus_plus_int C_36) D_10))) ((plus_plus_int ((plus_plus_int A_121) C_36)) D_10))).
% 2.42/2.64 Axiom fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_121:nat) (C_36:nat) (D_10:nat), (((eq nat) ((plus_plus_nat A_121) ((plus_plus_nat C_36) D_10))) ((plus_plus_nat ((plus_plus_nat A_121) C_36)) D_10))).
% 2.42/2.64 Axiom fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_121:real) (C_36:real) (D_10:real), (((eq real) ((plus_plus_real A_121) ((plus_plus_real C_36) D_10))) ((plus_plus_real ((plus_plus_real A_121) C_36)) D_10))).
% 2.42/2.64 Axiom fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_120:int) (C_35:int) (D_9:int), (((eq int) ((plus_plus_int A_120) ((plus_plus_int C_35) D_9))) ((plus_plus_int C_35) ((plus_plus_int A_120) D_9)))).
% 2.42/2.64 Axiom fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_120:nat) (C_35:nat) (D_9:nat), (((eq nat) ((plus_plus_nat A_120) ((plus_plus_nat C_35) D_9))) ((plus_plus_nat C_35) ((plus_plus_nat A_120) D_9)))).
% 2.42/2.64 Axiom fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_120:real) (C_35:real) (D_9:real), (((eq real) ((plus_plus_real A_120) ((plus_plus_real C_35) D_9))) ((plus_plus_real C_35) ((plus_plus_real A_120) D_9)))).
% 2.42/2.64 Axiom fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A_119:int) (C_34:int), (((eq int) ((plus_plus_int A_119) C_34)) ((plus_plus_int C_34) A_119))).
% 2.42/2.64 Axiom fact_133_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A_119:nat) (C_34:nat), (((eq nat) ((plus_plus_nat A_119) C_34)) ((plus_plus_nat C_34) A_119))).
% 2.42/2.64 Axiom fact_134_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A_119:real) (C_34:real), (((eq real) ((plus_plus_real A_119) C_34)) ((plus_plus_real C_34) A_119))).
% 2.42/2.64 Axiom fact_135_eq__number__of:(forall (X_35:int) (Y_31:int), ((iff (((eq int) (number_number_of_int X_35)) (number_number_of_int Y_31))) (((eq int) X_35) Y_31))).
% 2.42/2.64 Axiom fact_136_eq__number__of:(forall (X_35:int) (Y_31:int), ((iff (((eq real) (number267125858f_real X_35)) (number267125858f_real Y_31))) (((eq int) X_35) Y_31))).
% 2.42/2.64 Axiom fact_137_number__of__reorient:(forall (W_15:int) (X_34:nat), ((iff (((eq nat) (number_number_of_nat W_15)) X_34)) (((eq nat) X_34) (number_number_of_nat W_15)))).
% 2.42/2.64 Axiom fact_138_number__of__reorient:(forall (W_15:int) (X_34:int), ((iff (((eq int) (number_number_of_int W_15)) X_34)) (((eq int) X_34) (number_number_of_int W_15)))).
% 2.42/2.64 Axiom fact_139_number__of__reorient:(forall (W_15:int) (X_34:real), ((iff (((eq real) (number267125858f_real W_15)) X_34)) (((eq real) X_34) (number267125858f_real W_15)))).
% 2.42/2.64 Axiom fact_140_rel__simps_I51_J:(forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L))).
% 2.42/2.64 Axiom fact_141_rel__simps_I48_J:(forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L))).
% 2.42/2.64 Axiom fact_142_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)))).
% 2.42/2.64 Axiom fact_143_zmult__commute:(forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z))).
% 2.42/2.64 Axiom fact_144_number__of__is__id:(forall (K:int), (((eq int) (number_number_of_int K)) K)).
% 2.42/2.64 Axiom fact_145_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)))).
% 2.42/2.64 Axiom fact_146_zadd__left__commute:(forall (X_1:int) (Y_1:int) (Z:int), (((eq int) ((plus_plus_int X_1) ((plus_plus_int Y_1) Z))) ((plus_plus_int Y_1) ((plus_plus_int X_1) Z)))).
% 2.42/2.64 Axiom fact_147_zadd__commute:(forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z))).
% 2.42/2.64 Axiom fact_148_rel__simps_I12_J:(forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls))).
% 2.42/2.64 Axiom fact_149_less__int__code_I15_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2))).
% 2.42/2.64 Axiom fact_150_rel__simps_I16_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))).
% 2.42/2.64 Axiom fact_151_rel__simps_I10_J:(forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls))).
% 2.42/2.64 Axiom fact_152_rel__simps_I4_J:(forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K))).
% 2.42/2.64 Axiom fact_153_rel__simps_I22_J:(forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K))).
% 2.42/2.64 Axiom fact_154_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))).
% 2.42/2.64 Axiom fact_155_rel__simps_I32_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))).
% 2.42/2.64 Axiom fact_156_rel__simps_I27_J:(forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) pls)) ((ord_less_eq_int K) pls))).
% 2.42/2.64 Axiom fact_157_rel__simps_I21_J:(forall (K:int), ((iff ((ord_less_eq_int pls) (bit0 K))) ((ord_less_eq_int pls) K))).
% 2.42/2.64 Axiom fact_158_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)))).
% 2.42/2.64 Axiom fact_159_power__even__eq:(forall (A_118:int) (N_40:nat), (((eq int) ((power_power_int A_118) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_40))) ((power_power_int ((power_power_int A_118) N_40)) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.42/2.64 Axiom fact_160_power__even__eq:(forall (A_118:real) (N_40:nat), (((eq real) ((power_power_real A_118) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_40))) ((power_power_real ((power_power_real A_118) N_40)) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.42/2.64 Axiom fact_161_power__even__eq:(forall (A_118:nat) (N_40:nat), (((eq nat) ((power_power_nat A_118) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_40))) ((power_power_nat ((power_power_nat A_118) N_40)) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.42/2.64 Axiom fact_162_less__special_I4_J:(forall (X_33:int), ((iff ((ord_less_int (number_number_of_int X_33)) one_one_int)) ((ord_less_int X_33) (bit1 pls)))).
% 2.42/2.64 Axiom fact_163_less__special_I4_J:(forall (X_33:int), ((iff ((ord_less_real (number267125858f_real X_33)) one_one_real)) ((ord_less_int X_33) (bit1 pls)))).
% 2.42/2.64 Axiom fact_164_less__special_I2_J:(forall (Y_30:int), ((iff ((ord_less_int one_one_int) (number_number_of_int Y_30))) ((ord_less_int (bit1 pls)) Y_30))).
% 2.42/2.64 Axiom fact_165_less__special_I2_J:(forall (Y_30:int), ((iff ((ord_less_real one_one_real) (number267125858f_real Y_30))) ((ord_less_int (bit1 pls)) Y_30))).
% 2.42/2.64 Axiom fact_166_le__special_I4_J:(forall (X_32:int), ((iff ((ord_less_eq_int (number_number_of_int X_32)) one_one_int)) ((ord_less_eq_int X_32) (bit1 pls)))).
% 2.42/2.64 Axiom fact_167_le__special_I4_J:(forall (X_32:int), ((iff ((ord_less_eq_real (number267125858f_real X_32)) one_one_real)) ((ord_less_eq_int X_32) (bit1 pls)))).
% 2.42/2.64 Axiom fact_168_le__special_I2_J:(forall (Y_29:int), ((iff ((ord_less_eq_int one_one_int) (number_number_of_int Y_29))) ((ord_less_eq_int (bit1 pls)) Y_29))).
% 2.42/2.64 Axiom fact_169_le__special_I2_J:(forall (Y_29:int), ((iff ((ord_less_eq_real one_one_real) (number267125858f_real Y_29))) ((ord_less_eq_int (bit1 pls)) Y_29))).
% 2.42/2.64 Axiom fact_170_crossproduct__eq:(forall (W_14:int) (Y_28:int) (X_31:int) (Z_9:int), ((iff (((eq int) ((plus_plus_int ((times_times_int W_14) Y_28)) ((times_times_int X_31) Z_9))) ((plus_plus_int ((times_times_int W_14) Z_9)) ((times_times_int X_31) Y_28)))) ((or (((eq int) W_14) X_31)) (((eq int) Y_28) Z_9)))).
% 2.42/2.64 Axiom fact_171_crossproduct__eq:(forall (W_14:nat) (Y_28:nat) (X_31:nat) (Z_9:nat), ((iff (((eq nat) ((plus_plus_nat ((times_times_nat W_14) Y_28)) ((times_times_nat X_31) Z_9))) ((plus_plus_nat ((times_times_nat W_14) Z_9)) ((times_times_nat X_31) Y_28)))) ((or (((eq nat) W_14) X_31)) (((eq nat) Y_28) Z_9)))).
% 2.42/2.64 Axiom fact_172_crossproduct__eq:(forall (W_14:real) (Y_28:real) (X_31:real) (Z_9:real), ((iff (((eq real) ((plus_plus_real ((times_times_real W_14) Y_28)) ((times_times_real X_31) Z_9))) ((plus_plus_real ((times_times_real W_14) Z_9)) ((times_times_real X_31) Y_28)))) ((or (((eq real) W_14) X_31)) (((eq real) Y_28) Z_9)))).
% 2.42/2.64 Axiom fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J:(forall (A_117:int) (M_14:int) (B_69:int), (((eq int) ((plus_plus_int ((times_times_int A_117) M_14)) ((times_times_int B_69) M_14))) ((times_times_int ((plus_plus_int A_117) B_69)) M_14))).
% 2.42/2.64 Axiom fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J:(forall (A_117:nat) (M_14:nat) (B_69:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_117) M_14)) ((times_times_nat B_69) M_14))) ((times_times_nat ((plus_plus_nat A_117) B_69)) M_14))).
% 2.42/2.64 Axiom fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J:(forall (A_117:real) (M_14:real) (B_69:real), (((eq real) ((plus_plus_real ((times_times_real A_117) M_14)) ((times_times_real B_69) M_14))) ((times_times_real ((plus_plus_real A_117) B_69)) M_14))).
% 2.42/2.64 Axiom fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J:(forall (A_116:int) (B_68:int) (C_33:int), (((eq int) ((times_times_int ((plus_plus_int A_116) B_68)) C_33)) ((plus_plus_int ((times_times_int A_116) C_33)) ((times_times_int B_68) C_33)))).
% 2.42/2.64 Axiom fact_177_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J:(forall (A_116:nat) (B_68:nat) (C_33:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_116) B_68)) C_33)) ((plus_plus_nat ((times_times_nat A_116) C_33)) ((times_times_nat B_68) C_33)))).
% 2.42/2.64 Axiom fact_178_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J:(forall (A_116:real) (B_68:real) (C_33:real), (((eq real) ((times_times_real ((plus_plus_real A_116) B_68)) C_33)) ((plus_plus_real ((times_times_real A_116) C_33)) ((times_times_real B_68) C_33)))).
% 2.42/2.64 Axiom fact_179_crossproduct__noteq:(forall (C_32:int) (D_8:int) (A_115:int) (B_67:int), ((iff ((and (not (((eq int) A_115) B_67))) (not (((eq int) C_32) D_8)))) (not (((eq int) ((plus_plus_int ((times_times_int A_115) C_32)) ((times_times_int B_67) D_8))) ((plus_plus_int ((times_times_int A_115) D_8)) ((times_times_int B_67) C_32)))))).
% 2.42/2.64 Axiom fact_180_crossproduct__noteq:(forall (C_32:nat) (D_8:nat) (A_115:nat) (B_67:nat), ((iff ((and (not (((eq nat) A_115) B_67))) (not (((eq nat) C_32) D_8)))) (not (((eq nat) ((plus_plus_nat ((times_times_nat A_115) C_32)) ((times_times_nat B_67) D_8))) ((plus_plus_nat ((times_times_nat A_115) D_8)) ((times_times_nat B_67) C_32)))))).
% 2.42/2.64 Axiom fact_181_crossproduct__noteq:(forall (C_32:real) (D_8:real) (A_115:real) (B_67:real), ((iff ((and (not (((eq real) A_115) B_67))) (not (((eq real) C_32) D_8)))) (not (((eq real) ((plus_plus_real ((times_times_real A_115) C_32)) ((times_times_real B_67) D_8))) ((plus_plus_real ((times_times_real A_115) D_8)) ((times_times_real B_67) C_32)))))).
% 2.42/2.64 Axiom fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J:(forall (X_30:int) (Y_27:int) (Z_8:int), (((eq int) ((times_times_int X_30) ((plus_plus_int Y_27) Z_8))) ((plus_plus_int ((times_times_int X_30) Y_27)) ((times_times_int X_30) Z_8)))).
% 2.42/2.64 Axiom fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J:(forall (X_30:nat) (Y_27:nat) (Z_8:nat), (((eq nat) ((times_times_nat X_30) ((plus_plus_nat Y_27) Z_8))) ((plus_plus_nat ((times_times_nat X_30) Y_27)) ((times_times_nat X_30) Z_8)))).
% 2.42/2.64 Axiom fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J:(forall (X_30:real) (Y_27:real) (Z_8:real), (((eq real) ((times_times_real X_30) ((plus_plus_real Y_27) Z_8))) ((plus_plus_real ((times_times_real X_30) Y_27)) ((times_times_real X_30) Z_8)))).
% 2.42/2.64 Axiom fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J:(forall (A_114:int), (((eq int) ((times_times_int A_114) one_one_int)) A_114)).
% 2.42/2.64 Axiom fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J:(forall (A_114:nat), (((eq nat) ((times_times_nat A_114) one_one_nat)) A_114)).
% 2.42/2.64 Axiom fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J:(forall (A_114:real), (((eq real) ((times_times_real A_114) one_one_real)) A_114)).
% 2.42/2.64 Axiom fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J:(forall (A_113:int), (((eq int) ((times_times_int one_one_int) A_113)) A_113)).
% 2.42/2.64 Axiom fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J:(forall (A_113:nat), (((eq nat) ((times_times_nat one_one_nat) A_113)) A_113)).
% 2.42/2.64 Axiom fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J:(forall (A_113:real), (((eq real) ((times_times_real one_one_real) A_113)) A_113)).
% 2.42/2.64 Axiom fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J:(forall (X_29:int) (Y_26:int) (Q_4:nat), (((eq int) ((power_power_int ((times_times_int X_29) Y_26)) Q_4)) ((times_times_int ((power_power_int X_29) Q_4)) ((power_power_int Y_26) Q_4)))).
% 2.42/2.64 Axiom fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J:(forall (X_29:real) (Y_26:real) (Q_4:nat), (((eq real) ((power_power_real ((times_times_real X_29) Y_26)) Q_4)) ((times_times_real ((power_power_real X_29) Q_4)) ((power_power_real Y_26) Q_4)))).
% 2.42/2.64 Axiom fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J:(forall (X_29:nat) (Y_26:nat) (Q_4:nat), (((eq nat) ((power_power_nat ((times_times_nat X_29) Y_26)) Q_4)) ((times_times_nat ((power_power_nat X_29) Q_4)) ((power_power_nat Y_26) Q_4)))).
% 2.42/2.64 Axiom fact_194_rel__simps_I46_J:(forall (K:int), (not (((eq int) (bit1 K)) pls))).
% 2.42/2.64 Axiom fact_195_rel__simps_I39_J:(forall (L:int), (not (((eq int) pls) (bit1 L)))).
% 2.42/2.64 Axiom fact_196_rel__simps_I50_J:(forall (K:int) (L:int), (not (((eq int) (bit1 K)) (bit0 L)))).
% 2.42/2.64 Axiom fact_197_rel__simps_I49_J:(forall (K:int) (L:int), (not (((eq int) (bit0 K)) (bit1 L)))).
% 2.42/2.64 Axiom fact_198_rel__simps_I44_J:(forall (K:int), ((iff (((eq int) (bit0 K)) pls)) (((eq int) K) pls))).
% 2.42/2.64 Axiom fact_199_rel__simps_I38_J:(forall (L:int), ((iff (((eq int) pls) (bit0 L))) (((eq int) pls) L))).
% 2.42/2.64 Axiom fact_200_Bit0__Pls:(((eq int) (bit0 pls)) pls).
% 2.42/2.64 Axiom fact_201_mult__Pls:(forall (W:int), (((eq int) ((times_times_int pls) W)) pls)).
% 2.42/2.64 Axiom fact_202_mult__Bit0:(forall (K:int) (L:int), (((eq int) ((times_times_int (bit0 K)) L)) (bit0 ((times_times_int K) L)))).
% 2.42/2.64 Axiom fact_203_add__Pls__right:(forall (K:int), (((eq int) ((plus_plus_int K) pls)) K)).
% 2.42/2.64 Axiom fact_204_add__Pls:(forall (K:int), (((eq int) ((plus_plus_int pls) K)) K)).
% 2.42/2.64 Axiom fact_205_add__Bit0__Bit0:(forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit0 L))) (bit0 ((plus_plus_int K) L)))).
% 2.42/2.64 Axiom fact_206_Bit0__def:(forall (K:int), (((eq int) (bit0 K)) ((plus_plus_int K) K))).
% 2.42/2.64 Axiom fact_207_zmult__1__right:(forall (Z:int), (((eq int) ((times_times_int Z) one_one_int)) Z)).
% 2.42/2.64 Axiom fact_208_zmult__1:(forall (Z:int), (((eq int) ((times_times_int one_one_int) Z)) Z)).
% 2.42/2.64 Axiom fact_209_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)))).
% 2.42/2.65 Axiom fact_210_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)))).
% 2.42/2.65 Axiom fact_211_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)))).
% 2.42/2.65 Axiom fact_212_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)))).
% 2.42/2.65 Axiom fact_213_semiring__mult__number__of:(forall (V_18:int) (V_17:int), (((ord_less_eq_int pls) V_17)->(((ord_less_eq_int pls) V_18)->(((eq int) ((times_times_int (number_number_of_int V_17)) (number_number_of_int V_18))) (number_number_of_int ((times_times_int V_17) V_18)))))).
% 2.42/2.65 Axiom fact_214_semiring__mult__number__of:(forall (V_18:int) (V_17:int), (((ord_less_eq_int pls) V_17)->(((ord_less_eq_int pls) V_18)->(((eq nat) ((times_times_nat (number_number_of_nat V_17)) (number_number_of_nat V_18))) (number_number_of_nat ((times_times_int V_17) V_18)))))).
% 2.42/2.65 Axiom fact_215_semiring__mult__number__of:(forall (V_18:int) (V_17:int), (((ord_less_eq_int pls) V_17)->(((ord_less_eq_int pls) V_18)->(((eq real) ((times_times_real (number267125858f_real V_17)) (number267125858f_real V_18))) (number267125858f_real ((times_times_int V_17) V_18)))))).
% 2.42/2.65 Axiom fact_216_semiring__add__number__of:(forall (V_16:int) (V_15:int), (((ord_less_eq_int pls) V_15)->(((ord_less_eq_int pls) V_16)->(((eq int) ((plus_plus_int (number_number_of_int V_15)) (number_number_of_int V_16))) (number_number_of_int ((plus_plus_int V_15) V_16)))))).
% 2.42/2.65 Axiom fact_217_semiring__add__number__of:(forall (V_16:int) (V_15:int), (((ord_less_eq_int pls) V_15)->(((ord_less_eq_int pls) V_16)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_15)) (number_number_of_nat V_16))) (number_number_of_nat ((plus_plus_int V_15) V_16)))))).
% 2.42/2.65 Axiom fact_218_semiring__add__number__of:(forall (V_16:int) (V_15:int), (((ord_less_eq_int pls) V_15)->(((ord_less_eq_int pls) V_16)->(((eq real) ((plus_plus_real (number267125858f_real V_15)) (number267125858f_real V_16))) (number267125858f_real ((plus_plus_int V_15) V_16)))))).
% 2.42/2.65 Axiom fact_219_power2__ge__self:(forall (X_1:int), ((ord_less_eq_int X_1) ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.42/2.65 Axiom fact_220_left__distrib__number__of:(forall (A_112:int) (B_66:int) (V_14:int), (((eq int) ((times_times_int ((plus_plus_int A_112) B_66)) (number_number_of_int V_14))) ((plus_plus_int ((times_times_int A_112) (number_number_of_int V_14))) ((times_times_int B_66) (number_number_of_int V_14))))).
% 2.42/2.65 Axiom fact_221_left__distrib__number__of:(forall (A_112:nat) (B_66:nat) (V_14:int), (((eq nat) ((times_times_nat ((plus_plus_nat A_112) B_66)) (number_number_of_nat V_14))) ((plus_plus_nat ((times_times_nat A_112) (number_number_of_nat V_14))) ((times_times_nat B_66) (number_number_of_nat V_14))))).
% 2.42/2.65 Axiom fact_222_left__distrib__number__of:(forall (A_112:real) (B_66:real) (V_14:int), (((eq real) ((times_times_real ((plus_plus_real A_112) B_66)) (number267125858f_real V_14))) ((plus_plus_real ((times_times_real A_112) (number267125858f_real V_14))) ((times_times_real B_66) (number267125858f_real V_14))))).
% 2.42/2.65 Axiom fact_223_right__distrib__number__of:(forall (V_13:int) (B_65:int) (C_31:int), (((eq int) ((times_times_int (number_number_of_int V_13)) ((plus_plus_int B_65) C_31))) ((plus_plus_int ((times_times_int (number_number_of_int V_13)) B_65)) ((times_times_int (number_number_of_int V_13)) C_31)))).
% 2.42/2.65 Axiom fact_224_right__distrib__number__of:(forall (V_13:int) (B_65:nat) (C_31:nat), (((eq nat) ((times_times_nat (number_number_of_nat V_13)) ((plus_plus_nat B_65) C_31))) ((plus_plus_nat ((times_times_nat (number_number_of_nat V_13)) B_65)) ((times_times_nat (number_number_of_nat V_13)) C_31)))).
% 2.42/2.65 Axiom fact_225_right__distrib__number__of:(forall (V_13:int) (B_65:real) (C_31:real), (((eq real) ((times_times_real (number267125858f_real V_13)) ((plus_plus_real B_65) C_31))) ((plus_plus_real ((times_times_real (number267125858f_real V_13)) B_65)) ((times_times_real (number267125858f_real V_13)) C_31)))).
% 2.42/2.65 Axiom fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J:(forall (A_111:int) (M_13:int), (((eq int) ((plus_plus_int ((times_times_int A_111) M_13)) M_13)) ((times_times_int ((plus_plus_int A_111) one_one_int)) M_13))).
% 2.42/2.65 Axiom fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J:(forall (A_111:nat) (M_13:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_111) M_13)) M_13)) ((times_times_nat ((plus_plus_nat A_111) one_one_nat)) M_13))).
% 2.42/2.65 Axiom fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J:(forall (A_111:real) (M_13:real), (((eq real) ((plus_plus_real ((times_times_real A_111) M_13)) M_13)) ((times_times_real ((plus_plus_real A_111) one_one_real)) M_13))).
% 2.42/2.65 Axiom fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J:(forall (M_12:int) (A_110:int), (((eq int) ((plus_plus_int M_12) ((times_times_int A_110) M_12))) ((times_times_int ((plus_plus_int A_110) one_one_int)) M_12))).
% 2.42/2.65 Axiom fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J:(forall (M_12:nat) (A_110:nat), (((eq nat) ((plus_plus_nat M_12) ((times_times_nat A_110) M_12))) ((times_times_nat ((plus_plus_nat A_110) one_one_nat)) M_12))).
% 2.42/2.65 Axiom fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J:(forall (M_12:real) (A_110:real), (((eq real) ((plus_plus_real M_12) ((times_times_real A_110) M_12))) ((times_times_real ((plus_plus_real A_110) one_one_real)) M_12))).
% 2.42/2.65 Axiom fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J:(forall (M_11:int), (((eq int) ((plus_plus_int M_11) M_11)) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) M_11))).
% 2.42/2.65 Axiom fact_233_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J:(forall (M_11:nat), (((eq nat) ((plus_plus_nat M_11) M_11)) ((times_times_nat ((plus_plus_nat one_one_nat) one_one_nat)) M_11))).
% 2.42/2.65 Axiom fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J:(forall (M_11:real), (((eq real) ((plus_plus_real M_11) M_11)) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) M_11))).
% 2.42/2.65 Axiom fact_235_add__numeral__0:(forall (A_109:int), (((eq int) ((plus_plus_int (number_number_of_int pls)) A_109)) A_109)).
% 2.42/2.65 Axiom fact_236_add__numeral__0:(forall (A_109:real), (((eq real) ((plus_plus_real (number267125858f_real pls)) A_109)) A_109)).
% 2.42/2.65 Axiom fact_237_add__numeral__0__right:(forall (A_108:int), (((eq int) ((plus_plus_int A_108) (number_number_of_int pls))) A_108)).
% 2.42/2.65 Axiom fact_238_add__numeral__0__right:(forall (A_108:real), (((eq real) ((plus_plus_real A_108) (number267125858f_real pls))) A_108)).
% 2.42/2.65 Axiom fact_239_mult__number__of__left:(forall (V_12:int) (W_13:int) (Z_7:int), (((eq int) ((times_times_int (number_number_of_int V_12)) ((times_times_int (number_number_of_int W_13)) Z_7))) ((times_times_int (number_number_of_int ((times_times_int V_12) W_13))) Z_7))).
% 2.42/2.65 Axiom fact_240_mult__number__of__left:(forall (V_12:int) (W_13:int) (Z_7:real), (((eq real) ((times_times_real (number267125858f_real V_12)) ((times_times_real (number267125858f_real W_13)) Z_7))) ((times_times_real (number267125858f_real ((times_times_int V_12) W_13))) Z_7))).
% 2.42/2.65 Axiom fact_241_arith__simps_I32_J:(forall (V_11:int) (W_12:int), (((eq int) ((times_times_int (number_number_of_int V_11)) (number_number_of_int W_12))) (number_number_of_int ((times_times_int V_11) W_12)))).
% 2.42/2.65 Axiom fact_242_arith__simps_I32_J:(forall (V_11:int) (W_12:int), (((eq real) ((times_times_real (number267125858f_real V_11)) (number267125858f_real W_12))) (number267125858f_real ((times_times_int V_11) W_12)))).
% 2.42/2.65 Axiom fact_243_number__of__mult:(forall (V_10:int) (W_11:int), (((eq int) (number_number_of_int ((times_times_int V_10) W_11))) ((times_times_int (number_number_of_int V_10)) (number_number_of_int W_11)))).
% 2.42/2.65 Axiom fact_244_number__of__mult:(forall (V_10:int) (W_11:int), (((eq real) (number267125858f_real ((times_times_int V_10) W_11))) ((times_times_real (number267125858f_real V_10)) (number267125858f_real W_11)))).
% 2.42/2.65 Axiom fact_245_add__number__of__left:(forall (V_9:int) (W_10:int) (Z_6:int), (((eq int) ((plus_plus_int (number_number_of_int V_9)) ((plus_plus_int (number_number_of_int W_10)) Z_6))) ((plus_plus_int (number_number_of_int ((plus_plus_int V_9) W_10))) Z_6))).
% 2.42/2.65 Axiom fact_246_add__number__of__left:(forall (V_9:int) (W_10:int) (Z_6:real), (((eq real) ((plus_plus_real (number267125858f_real V_9)) ((plus_plus_real (number267125858f_real W_10)) Z_6))) ((plus_plus_real (number267125858f_real ((plus_plus_int V_9) W_10))) Z_6))).
% 2.42/2.65 Axiom fact_247_add__number__of__eq:(forall (V_8:int) (W_9:int), (((eq int) ((plus_plus_int (number_number_of_int V_8)) (number_number_of_int W_9))) (number_number_of_int ((plus_plus_int V_8) W_9)))).
% 2.42/2.65 Axiom fact_248_add__number__of__eq:(forall (V_8:int) (W_9:int), (((eq real) ((plus_plus_real (number267125858f_real V_8)) (number267125858f_real W_9))) (number267125858f_real ((plus_plus_int V_8) W_9)))).
% 2.42/2.65 Axiom fact_249_number__of__add:(forall (V_7:int) (W_8:int), (((eq int) (number_number_of_int ((plus_plus_int V_7) W_8))) ((plus_plus_int (number_number_of_int V_7)) (number_number_of_int W_8)))).
% 2.42/2.65 Axiom fact_250_number__of__add:(forall (V_7:int) (W_8:int), (((eq real) (number267125858f_real ((plus_plus_int V_7) W_8))) ((plus_plus_real (number267125858f_real V_7)) (number267125858f_real W_8)))).
% 2.42/2.65 Axiom fact_251_add__Bit1__Bit0:(forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit0 L))) (bit1 ((plus_plus_int K) L)))).
% 2.42/2.65 Axiom fact_252_add__Bit0__Bit1:(forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit1 L))) (bit1 ((plus_plus_int K) L)))).
% 2.42/2.65 Axiom fact_253_Bit1__def:(forall (K:int), (((eq int) (bit1 K)) ((plus_plus_int ((plus_plus_int one_one_int) K)) K))).
% 2.42/2.65 Axiom fact_254_number__of__Bit1:(forall (W_7:int), (((eq int) (number_number_of_int (bit1 W_7))) ((plus_plus_int ((plus_plus_int one_one_int) (number_number_of_int W_7))) (number_number_of_int W_7)))).
% 2.42/2.65 Axiom fact_255_number__of__Bit1:(forall (W_7:int), (((eq real) (number267125858f_real (bit1 W_7))) ((plus_plus_real ((plus_plus_real one_one_real) (number267125858f_real W_7))) (number267125858f_real W_7)))).
% 2.42/2.65 Axiom fact_256_mult__numeral__1:(forall (A_107:int), (((eq int) ((times_times_int (number_number_of_int (bit1 pls))) A_107)) A_107)).
% 2.42/2.65 Axiom fact_257_mult__numeral__1:(forall (A_107:real), (((eq real) ((times_times_real (number267125858f_real (bit1 pls))) A_107)) A_107)).
% 2.42/2.65 Axiom fact_258_mult__numeral__1__right:(forall (A_106:int), (((eq int) ((times_times_int A_106) (number_number_of_int (bit1 pls)))) A_106)).
% 2.42/2.65 Axiom fact_259_mult__numeral__1__right:(forall (A_106:real), (((eq real) ((times_times_real A_106) (number267125858f_real (bit1 pls)))) A_106)).
% 2.42/2.65 Axiom fact_260_semiring__numeral__1__eq__1:(((eq int) (number_number_of_int (bit1 pls))) one_one_int).
% 2.42/2.65 Axiom fact_261_semiring__numeral__1__eq__1:(((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat).
% 2.42/2.65 Axiom fact_262_semiring__numeral__1__eq__1:(((eq real) (number267125858f_real (bit1 pls))) one_one_real).
% 2.42/2.65 Axiom fact_263_numeral__1__eq__1:(((eq int) (number_number_of_int (bit1 pls))) one_one_int).
% 2.42/2.65 Axiom fact_264_numeral__1__eq__1:(((eq real) (number267125858f_real (bit1 pls))) one_one_real).
% 2.42/2.65 Axiom fact_265_semiring__norm_I110_J:(((eq int) one_one_int) (number_number_of_int (bit1 pls))).
% 2.42/2.65 Axiom fact_266_semiring__norm_I110_J:(((eq real) one_one_real) (number267125858f_real (bit1 pls))).
% 2.42/2.65 Axiom fact_267_one__is__num__one:(((eq int) one_one_int) (number_number_of_int (bit1 pls))).
% 2.42/2.65 Axiom fact_268_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))).
% 2.42/2.65 Axiom fact_269_double__number__of__Bit0:(forall (W_6:int), (((eq int) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int W_6))) (number_number_of_int (bit0 W_6)))).
% 2.42/2.65 Axiom fact_270_double__number__of__Bit0:(forall (W_6:int), (((eq real) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real W_6))) (number267125858f_real (bit0 W_6)))).
% 2.42/2.65 Axiom fact_271_power3__eq__cube:(forall (A_105:int), (((eq int) ((power_power_int A_105) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int A_105) A_105)) A_105))).
% 2.42/2.65 Axiom fact_272_power3__eq__cube:(forall (A_105:real), (((eq real) ((power_power_real A_105) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_real ((times_times_real A_105) A_105)) A_105))).
% 2.42/2.65 Axiom fact_273_power3__eq__cube:(forall (A_105:nat), (((eq nat) ((power_power_nat A_105) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_nat ((times_times_nat A_105) A_105)) A_105))).
% 2.42/2.65 Axiom fact_274_quartic__square__square:(forall (X_1:int), (((eq int) ((power_power_int ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int X_1) (number_number_of_nat (bit0 (bit0 (bit1 pls))))))).
% 2.42/2.65 Axiom fact_275_semiring__mult__2:(forall (Z_5:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_5)) ((plus_plus_int Z_5) Z_5))).
% 2.42/2.65 Axiom fact_276_semiring__mult__2:(forall (Z_5:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z_5)) ((plus_plus_nat Z_5) Z_5))).
% 2.42/2.65 Axiom fact_277_semiring__mult__2:(forall (Z_5:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_5)) ((plus_plus_real Z_5) Z_5))).
% 2.42/2.65 Axiom fact_278_mult__2:(forall (Z_4:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_4)) ((plus_plus_int Z_4) Z_4))).
% 2.42/2.65 Axiom fact_279_mult__2:(forall (Z_4:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_4)) ((plus_plus_real Z_4) Z_4))).
% 2.42/2.65 Axiom fact_280_semiring__mult__2__right:(forall (Z_3:int), (((eq int) ((times_times_int Z_3) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_3) Z_3))).
% 2.42/2.65 Axiom fact_281_semiring__mult__2__right:(forall (Z_3:nat), (((eq nat) ((times_times_nat Z_3) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z_3) Z_3))).
% 2.42/2.65 Axiom fact_282_semiring__mult__2__right:(forall (Z_3:real), (((eq real) ((times_times_real Z_3) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_3) Z_3))).
% 2.42/2.65 Axiom fact_283_mult__2__right:(forall (Z_2:int), (((eq int) ((times_times_int Z_2) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_2) Z_2))).
% 2.42/2.65 Axiom fact_284_mult__2__right:(forall (Z_2:real), (((eq real) ((times_times_real Z_2) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_2) Z_2))).
% 2.42/2.65 Axiom fact_285_semiring__one__add__one__is__two:(((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))).
% 2.42/2.65 Axiom fact_286_semiring__one__add__one__is__two:(((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))).
% 2.42/2.65 Axiom fact_287_semiring__one__add__one__is__two:(((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))).
% 2.42/2.65 Axiom fact_288_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)).
% 2.42/2.65 Axiom fact_289__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)).
% 2.42/2.65 Axiom fact_290_prime__g__5:(forall (P:int), ((zprime P)->((not (((eq int) P) (number_number_of_int (bit0 (bit1 pls)))))->((not (((eq int) P) (number_number_of_int (bit1 (bit1 pls)))))->((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P))))).
% 2.42/2.65 Axiom fact_291__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)).
% 2.42/2.65 Axiom fact_292_real__sum__squared__expand:(forall (X_1:real) (Y_1:real), (((eq real) ((power_power_real ((plus_plus_real X_1) Y_1)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_1)) Y_1)))).
% 2.42/2.65 Axiom fact_293_four__x__squared:(forall (X_1:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit0 (bit1 pls))))) ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_1)) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.42/2.65 Axiom fact_294_power__less__power__Suc:(forall (N_39:nat) (A_104:int), (((ord_less_int one_one_int) A_104)->((ord_less_int ((power_power_int A_104) N_39)) ((times_times_int A_104) ((power_power_int A_104) N_39))))).
% 2.42/2.65 Axiom fact_295_power__less__power__Suc:(forall (N_39:nat) (A_104:nat), (((ord_less_nat one_one_nat) A_104)->((ord_less_nat ((power_power_nat A_104) N_39)) ((times_times_nat A_104) ((power_power_nat A_104) N_39))))).
% 2.42/2.65 Axiom fact_296_power__less__power__Suc:(forall (N_39:nat) (A_104:real), (((ord_less_real one_one_real) A_104)->((ord_less_real ((power_power_real A_104) N_39)) ((times_times_real A_104) ((power_power_real A_104) N_39))))).
% 2.42/2.65 Axiom fact_297_power__gt1__lemma:(forall (N_38:nat) (A_103:int), (((ord_less_int one_one_int) A_103)->((ord_less_int one_one_int) ((times_times_int A_103) ((power_power_int A_103) N_38))))).
% 2.42/2.65 Axiom fact_298_power__gt1__lemma:(forall (N_38:nat) (A_103:nat), (((ord_less_nat one_one_nat) A_103)->((ord_less_nat one_one_nat) ((times_times_nat A_103) ((power_power_nat A_103) N_38))))).
% 2.42/2.65 Axiom fact_299_power__gt1__lemma:(forall (N_38:nat) (A_103:real), (((ord_less_real one_one_real) A_103)->((ord_less_real one_one_real) ((times_times_real A_103) ((power_power_real A_103) N_38))))).
% 2.42/2.65 Axiom fact_300_power__le__imp__le__exp:(forall (M_10:nat) (N_37:nat) (A_102:int), (((ord_less_int one_one_int) A_102)->(((ord_less_eq_int ((power_power_int A_102) M_10)) ((power_power_int A_102) N_37))->((ord_less_eq_nat M_10) N_37)))).
% 2.42/2.65 Axiom fact_301_power__le__imp__le__exp:(forall (M_10:nat) (N_37:nat) (A_102:nat), (((ord_less_nat one_one_nat) A_102)->(((ord_less_eq_nat ((power_power_nat A_102) M_10)) ((power_power_nat A_102) N_37))->((ord_less_eq_nat M_10) N_37)))).
% 2.42/2.65 Axiom fact_302_power__le__imp__le__exp:(forall (M_10:nat) (N_37:nat) (A_102:real), (((ord_less_real one_one_real) A_102)->(((ord_less_eq_real ((power_power_real A_102) M_10)) ((power_power_real A_102) N_37))->((ord_less_eq_nat M_10) N_37)))).
% 2.42/2.65 Axiom fact_303_power__increasing__iff:(forall (X_28:nat) (Y_25:nat) (B_64:int), (((ord_less_int one_one_int) B_64)->((iff ((ord_less_eq_int ((power_power_int B_64) X_28)) ((power_power_int B_64) Y_25))) ((ord_less_eq_nat X_28) Y_25)))).
% 2.42/2.65 Axiom fact_304_power__increasing__iff:(forall (X_28:nat) (Y_25:nat) (B_64:nat), (((ord_less_nat one_one_nat) B_64)->((iff ((ord_less_eq_nat ((power_power_nat B_64) X_28)) ((power_power_nat B_64) Y_25))) ((ord_less_eq_nat X_28) Y_25)))).
% 2.42/2.65 Axiom fact_305_power__increasing__iff:(forall (X_28:nat) (Y_25:nat) (B_64:real), (((ord_less_real one_one_real) B_64)->((iff ((ord_less_eq_real ((power_power_real B_64) X_28)) ((power_power_real B_64) Y_25))) ((ord_less_eq_nat X_28) Y_25)))).
% 2.42/2.65 Axiom fact_306__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)).
% 2.42/2.65 Axiom fact_307_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))).
% 2.42/2.65 Axiom fact_308__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:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X)) ((ord_less_int X) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) X) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (forall (Y:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y)) ((ord_less_int Y) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) Y) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))->(((eq int) Y) X)))))).
% 2.42/2.65 Axiom fact_309__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).
% 2.42/2.65 Axiom fact_310_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)).
% 2.42/2.65 Axiom fact_311_power__eq__0__iff:(forall (A_101:int) (N_36:nat), ((iff (((eq int) ((power_power_int A_101) N_36)) zero_zero_int)) ((and (((eq int) A_101) zero_zero_int)) (not (((eq nat) N_36) zero_zero_nat))))).
% 2.42/2.65 Axiom fact_312_power__eq__0__iff:(forall (A_101:nat) (N_36:nat), ((iff (((eq nat) ((power_power_nat A_101) N_36)) zero_zero_nat)) ((and (((eq nat) A_101) zero_zero_nat)) (not (((eq nat) N_36) zero_zero_nat))))).
% 2.42/2.65 Axiom fact_313_power__eq__0__iff:(forall (A_101:real) (N_36:nat), ((iff (((eq real) ((power_power_real A_101) N_36)) zero_zero_real)) ((and (((eq real) A_101) zero_zero_real)) (not (((eq nat) N_36) zero_zero_nat))))).
% 2.42/2.65 Axiom fact_314_le__imp__power__dvd:(forall (A_100:real) (M_9:nat) (N_35:nat), (((ord_less_eq_nat M_9) N_35)->((dvd_dvd_real ((power_power_real A_100) M_9)) ((power_power_real A_100) N_35)))).
% 2.42/2.65 Axiom fact_315_le__imp__power__dvd:(forall (A_100:int) (M_9:nat) (N_35:nat), (((ord_less_eq_nat M_9) N_35)->((dvd_dvd_int ((power_power_int A_100) M_9)) ((power_power_int A_100) N_35)))).
% 2.42/2.65 Axiom fact_316_le__imp__power__dvd:(forall (A_100:nat) (M_9:nat) (N_35:nat), (((ord_less_eq_nat M_9) N_35)->((dvd_dvd_nat ((power_power_nat A_100) M_9)) ((power_power_nat A_100) N_35)))).
% 2.42/2.65 Axiom fact_317_dvd__power__le:(forall (N_34:nat) (M_8:nat) (X_27:real) (Y_24:real), (((dvd_dvd_real X_27) Y_24)->(((ord_less_eq_nat N_34) M_8)->((dvd_dvd_real ((power_power_real X_27) N_34)) ((power_power_real Y_24) M_8))))).
% 2.42/2.65 Axiom fact_318_dvd__power__le:(forall (N_34:nat) (M_8:nat) (X_27:int) (Y_24:int), (((dvd_dvd_int X_27) Y_24)->(((ord_less_eq_nat N_34) M_8)->((dvd_dvd_int ((power_power_int X_27) N_34)) ((power_power_int Y_24) M_8))))).
% 2.42/2.65 Axiom fact_319_dvd__power__le:(forall (N_34:nat) (M_8:nat) (X_27:nat) (Y_24:nat), (((dvd_dvd_nat X_27) Y_24)->(((ord_less_eq_nat N_34) M_8)->((dvd_dvd_nat ((power_power_nat X_27) N_34)) ((power_power_nat Y_24) M_8))))).
% 2.42/2.65 Axiom fact_320_power__le__dvd:(forall (M_7:nat) (A_99:real) (N_33:nat) (B_63:real), (((dvd_dvd_real ((power_power_real A_99) N_33)) B_63)->(((ord_less_eq_nat M_7) N_33)->((dvd_dvd_real ((power_power_real A_99) M_7)) B_63)))).
% 2.42/2.65 Axiom fact_321_power__le__dvd:(forall (M_7:nat) (A_99:int) (N_33:nat) (B_63:int), (((dvd_dvd_int ((power_power_int A_99) N_33)) B_63)->(((ord_less_eq_nat M_7) N_33)->((dvd_dvd_int ((power_power_int A_99) M_7)) B_63)))).
% 2.42/2.65 Axiom fact_322_power__le__dvd:(forall (M_7:nat) (A_99:nat) (N_33:nat) (B_63:nat), (((dvd_dvd_nat ((power_power_nat A_99) N_33)) B_63)->(((ord_less_eq_nat M_7) N_33)->((dvd_dvd_nat ((power_power_nat A_99) M_7)) B_63)))).
% 2.42/2.65 Axiom fact_323_power__eq__imp__eq__base:(forall (A_98:int) (N_32:nat) (B_62:int), ((((eq int) ((power_power_int A_98) N_32)) ((power_power_int B_62) N_32))->(((ord_less_eq_int zero_zero_int) A_98)->(((ord_less_eq_int zero_zero_int) B_62)->(((ord_less_nat zero_zero_nat) N_32)->(((eq int) A_98) B_62)))))).
% 2.42/2.65 Axiom fact_324_power__eq__imp__eq__base:(forall (A_98:nat) (N_32:nat) (B_62:nat), ((((eq nat) ((power_power_nat A_98) N_32)) ((power_power_nat B_62) N_32))->(((ord_less_eq_nat zero_zero_nat) A_98)->(((ord_less_eq_nat zero_zero_nat) B_62)->(((ord_less_nat zero_zero_nat) N_32)->(((eq nat) A_98) B_62)))))).
% 2.42/2.66 Axiom fact_325_power__eq__imp__eq__base:(forall (A_98:real) (N_32:nat) (B_62:real), ((((eq real) ((power_power_real A_98) N_32)) ((power_power_real B_62) N_32))->(((ord_less_eq_real zero_zero_real) A_98)->(((ord_less_eq_real zero_zero_real) B_62)->(((ord_less_nat zero_zero_nat) N_32)->(((eq real) A_98) B_62)))))).
% 2.42/2.66 Axiom fact_326_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)))).
% 2.42/2.66 Axiom fact_327_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)))))).
% 2.42/2.66 Axiom fact_328_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)))).
% 2.42/2.66 Axiom fact_329_dvd__power__same:(forall (N_31:nat) (X_26:real) (Y_23:real), (((dvd_dvd_real X_26) Y_23)->((dvd_dvd_real ((power_power_real X_26) N_31)) ((power_power_real Y_23) N_31)))).
% 2.42/2.66 Axiom fact_330_dvd__power__same:(forall (N_31:nat) (X_26:int) (Y_23:int), (((dvd_dvd_int X_26) Y_23)->((dvd_dvd_int ((power_power_int X_26) N_31)) ((power_power_int Y_23) N_31)))).
% 2.42/2.66 Axiom fact_331_dvd__power__same:(forall (N_31:nat) (X_26:nat) (Y_23:nat), (((dvd_dvd_nat X_26) Y_23)->((dvd_dvd_nat ((power_power_nat X_26) N_31)) ((power_power_nat Y_23) N_31)))).
% 2.42/2.66 Axiom fact_332_field__power__not__zero:(forall (N_30:nat) (A_97:int), ((not (((eq int) A_97) zero_zero_int))->(not (((eq int) ((power_power_int A_97) N_30)) zero_zero_int)))).
% 2.42/2.66 Axiom fact_333_field__power__not__zero:(forall (N_30:nat) (A_97:real), ((not (((eq real) A_97) zero_zero_real))->(not (((eq real) ((power_power_real A_97) N_30)) zero_zero_real)))).
% 2.42/2.66 Axiom fact_334_power__0__left:(forall (N_29:nat), ((and ((((eq nat) N_29) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) N_29)) one_one_int))) ((not (((eq nat) N_29) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) N_29)) zero_zero_int)))).
% 2.42/2.66 Axiom fact_335_power__0__left:(forall (N_29:nat), ((and ((((eq nat) N_29) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) N_29)) one_one_nat))) ((not (((eq nat) N_29) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) N_29)) zero_zero_nat)))).
% 2.42/2.66 Axiom fact_336_power__0__left:(forall (N_29:nat), ((and ((((eq nat) N_29) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) N_29)) one_one_real))) ((not (((eq nat) N_29) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) N_29)) zero_zero_real)))).
% 2.42/2.66 Axiom fact_337_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)))).
% 2.42/2.66 Axiom fact_338_power__strict__mono:(forall (N_28:nat) (A_96:int) (B_61:int), (((ord_less_int A_96) B_61)->(((ord_less_eq_int zero_zero_int) A_96)->(((ord_less_nat zero_zero_nat) N_28)->((ord_less_int ((power_power_int A_96) N_28)) ((power_power_int B_61) N_28)))))).
% 2.42/2.66 Axiom fact_339_power__strict__mono:(forall (N_28:nat) (A_96:nat) (B_61:nat), (((ord_less_nat A_96) B_61)->(((ord_less_eq_nat zero_zero_nat) A_96)->(((ord_less_nat zero_zero_nat) N_28)->((ord_less_nat ((power_power_nat A_96) N_28)) ((power_power_nat B_61) N_28)))))).
% 2.42/2.66 Axiom fact_340_power__strict__mono:(forall (N_28:nat) (A_96:real) (B_61:real), (((ord_less_real A_96) B_61)->(((ord_less_eq_real zero_zero_real) A_96)->(((ord_less_nat zero_zero_nat) N_28)->((ord_less_real ((power_power_real A_96) N_28)) ((power_power_real B_61) N_28)))))).
% 2.42/2.66 Axiom fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J:(forall (A_95:int), (((eq int) ((times_times_int zero_zero_int) A_95)) zero_zero_int)).
% 2.42/2.66 Axiom fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J:(forall (A_95:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_95)) zero_zero_nat)).
% 2.42/2.66 Axiom fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J:(forall (A_95:real), (((eq real) ((times_times_real zero_zero_real) A_95)) zero_zero_real)).
% 2.42/2.66 Axiom fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J:(forall (A_94:int), (((eq int) ((times_times_int A_94) zero_zero_int)) zero_zero_int)).
% 2.42/2.66 Axiom fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J:(forall (A_94:nat), (((eq nat) ((times_times_nat A_94) zero_zero_nat)) zero_zero_nat)).
% 2.42/2.66 Axiom fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J:(forall (A_94:real), (((eq real) ((times_times_real A_94) zero_zero_real)) zero_zero_real)).
% 2.42/2.66 Axiom fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J:(forall (A_93:int), (((eq int) ((plus_plus_int zero_zero_int) A_93)) A_93)).
% 2.42/2.66 Axiom fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J:(forall (A_93:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_93)) A_93)).
% 2.42/2.66 Axiom fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J:(forall (A_93:real), (((eq real) ((plus_plus_real zero_zero_real) A_93)) A_93)).
% 2.42/2.66 Axiom fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J:(forall (A_92:int), (((eq int) ((plus_plus_int A_92) zero_zero_int)) A_92)).
% 2.42/2.66 Axiom fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J:(forall (A_92:nat), (((eq nat) ((plus_plus_nat A_92) zero_zero_nat)) A_92)).
% 2.42/2.66 Axiom fact_352_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J:(forall (A_92:real), (((eq real) ((plus_plus_real A_92) zero_zero_real)) A_92)).
% 2.42/2.66 Axiom fact_353_add__0__iff:(forall (B_60:int) (A_91:int), ((iff (((eq int) B_60) ((plus_plus_int B_60) A_91))) (((eq int) A_91) zero_zero_int))).
% 2.42/2.66 Axiom fact_354_add__0__iff:(forall (B_60:nat) (A_91:nat), ((iff (((eq nat) B_60) ((plus_plus_nat B_60) A_91))) (((eq nat) A_91) zero_zero_nat))).
% 2.42/2.66 Axiom fact_355_add__0__iff:(forall (B_60:real) (A_91:real), ((iff (((eq real) B_60) ((plus_plus_real B_60) A_91))) (((eq real) A_91) zero_zero_real))).
% 2.42/2.66 Axiom fact_356_double__eq__0__iff:(forall (A_90:int), ((iff (((eq int) ((plus_plus_int A_90) A_90)) zero_zero_int)) (((eq int) A_90) zero_zero_int))).
% 2.42/2.66 Axiom fact_357_double__eq__0__iff:(forall (A_90:real), ((iff (((eq real) ((plus_plus_real A_90) A_90)) zero_zero_real)) (((eq real) A_90) zero_zero_real))).
% 2.42/2.66 Axiom fact_358_Pls__def:(((eq int) pls) zero_zero_int).
% 2.42/2.66 Axiom fact_359_int__0__neq__1:(not (((eq int) zero_zero_int) one_one_int)).
% 2.42/2.66 Axiom fact_360_zadd__0:(forall (Z:int), (((eq int) ((plus_plus_int zero_zero_int) Z)) Z)).
% 2.42/2.66 Axiom fact_361_zadd__0__right:(forall (Z:int), (((eq int) ((plus_plus_int Z) zero_zero_int)) Z)).
% 2.42/2.66 Axiom fact_362_zero__le__power:(forall (N_27:nat) (A_89:int), (((ord_less_eq_int zero_zero_int) A_89)->((ord_less_eq_int zero_zero_int) ((power_power_int A_89) N_27)))).
% 2.42/2.66 Axiom fact_363_zero__le__power:(forall (N_27:nat) (A_89:nat), (((ord_less_eq_nat zero_zero_nat) A_89)->((ord_less_eq_nat zero_zero_nat) ((power_power_nat A_89) N_27)))).
% 2.42/2.66 Axiom fact_364_zero__le__power:(forall (N_27:nat) (A_89:real), (((ord_less_eq_real zero_zero_real) A_89)->((ord_less_eq_real zero_zero_real) ((power_power_real A_89) N_27)))).
% 2.42/2.66 Axiom fact_365_power__mono:(forall (N_26:nat) (A_88:int) (B_59:int), (((ord_less_eq_int A_88) B_59)->(((ord_less_eq_int zero_zero_int) A_88)->((ord_less_eq_int ((power_power_int A_88) N_26)) ((power_power_int B_59) N_26))))).
% 2.42/2.66 Axiom fact_366_power__mono:(forall (N_26:nat) (A_88:nat) (B_59:nat), (((ord_less_eq_nat A_88) B_59)->(((ord_less_eq_nat zero_zero_nat) A_88)->((ord_less_eq_nat ((power_power_nat A_88) N_26)) ((power_power_nat B_59) N_26))))).
% 2.42/2.66 Axiom fact_367_power__mono:(forall (N_26:nat) (A_88:real) (B_59:real), (((ord_less_eq_real A_88) B_59)->(((ord_less_eq_real zero_zero_real) A_88)->((ord_less_eq_real ((power_power_real A_88) N_26)) ((power_power_real B_59) N_26))))).
% 2.42/2.66 Axiom fact_368_zero__less__power:(forall (N_25:nat) (A_87:int), (((ord_less_int zero_zero_int) A_87)->((ord_less_int zero_zero_int) ((power_power_int A_87) N_25)))).
% 2.42/2.66 Axiom fact_369_zero__less__power:(forall (N_25:nat) (A_87:nat), (((ord_less_nat zero_zero_nat) A_87)->((ord_less_nat zero_zero_nat) ((power_power_nat A_87) N_25)))).
% 2.42/2.66 Axiom fact_370_zero__less__power:(forall (N_25:nat) (A_87:real), (((ord_less_real zero_zero_real) A_87)->((ord_less_real zero_zero_real) ((power_power_real A_87) N_25)))).
% 2.42/2.66 Axiom fact_371_zcong__zpower__zmult:(forall (Z:nat) (X_1:int) (Y_1:nat) (P:int), ((((zcong ((power_power_int X_1) Y_1)) one_one_int) P)->(((zcong ((power_power_int X_1) ((times_times_nat Y_1) Z))) one_one_int) P))).
% 2.42/2.66 Axiom fact_372_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))).
% 2.42/2.66 Axiom fact_373_zdvd__period:(forall (C:int) (X_1:int) (T:int) (A:int) (D:int), (((dvd_dvd_int A) D)->((iff ((dvd_dvd_int A) ((plus_plus_int X_1) T))) ((dvd_dvd_int A) ((plus_plus_int ((plus_plus_int X_1) ((times_times_int C) D))) T))))).
% 2.42/2.66 Axiom fact_374_power__less__imp__less__base:(forall (A_86:int) (N_24:nat) (B_58:int), (((ord_less_int ((power_power_int A_86) N_24)) ((power_power_int B_58) N_24))->(((ord_less_eq_int zero_zero_int) B_58)->((ord_less_int A_86) B_58)))).
% 2.42/2.66 Axiom fact_375_power__less__imp__less__base:(forall (A_86:nat) (N_24:nat) (B_58:nat), (((ord_less_nat ((power_power_nat A_86) N_24)) ((power_power_nat B_58) N_24))->(((ord_less_eq_nat zero_zero_nat) B_58)->((ord_less_nat A_86) B_58)))).
% 2.42/2.66 Axiom fact_376_power__less__imp__less__base:(forall (A_86:real) (N_24:nat) (B_58:real), (((ord_less_real ((power_power_real A_86) N_24)) ((power_power_real B_58) N_24))->(((ord_less_eq_real zero_zero_real) B_58)->((ord_less_real A_86) B_58)))).
% 2.42/2.66 Axiom fact_377_power__decreasing:(forall (A_85:int) (N_23:nat) (N_22:nat), (((ord_less_eq_nat N_23) N_22)->(((ord_less_eq_int zero_zero_int) A_85)->(((ord_less_eq_int A_85) one_one_int)->((ord_less_eq_int ((power_power_int A_85) N_22)) ((power_power_int A_85) N_23)))))).
% 2.42/2.66 Axiom fact_378_power__decreasing:(forall (A_85:nat) (N_23:nat) (N_22:nat), (((ord_less_eq_nat N_23) N_22)->(((ord_less_eq_nat zero_zero_nat) A_85)->(((ord_less_eq_nat A_85) one_one_nat)->((ord_less_eq_nat ((power_power_nat A_85) N_22)) ((power_power_nat A_85) N_23)))))).
% 2.42/2.66 Axiom fact_379_power__decreasing:(forall (A_85:real) (N_23:nat) (N_22:nat), (((ord_less_eq_nat N_23) N_22)->(((ord_less_eq_real zero_zero_real) A_85)->(((ord_less_eq_real A_85) one_one_real)->((ord_less_eq_real ((power_power_real A_85) N_22)) ((power_power_real A_85) N_23)))))).
% 2.42/2.66 Axiom fact_380_power__strict__decreasing:(forall (A_84:int) (N_21:nat) (N_20:nat), (((ord_less_nat N_21) N_20)->(((ord_less_int zero_zero_int) A_84)->(((ord_less_int A_84) one_one_int)->((ord_less_int ((power_power_int A_84) N_20)) ((power_power_int A_84) N_21)))))).
% 2.42/2.66 Axiom fact_381_power__strict__decreasing:(forall (A_84:nat) (N_21:nat) (N_20:nat), (((ord_less_nat N_21) N_20)->(((ord_less_nat zero_zero_nat) A_84)->(((ord_less_nat A_84) one_one_nat)->((ord_less_nat ((power_power_nat A_84) N_20)) ((power_power_nat A_84) N_21)))))).
% 2.42/2.66 Axiom fact_382_power__strict__decreasing:(forall (A_84:real) (N_21:nat) (N_20:nat), (((ord_less_nat N_21) N_20)->(((ord_less_real zero_zero_real) A_84)->(((ord_less_real A_84) one_one_real)->((ord_less_real ((power_power_real A_84) N_20)) ((power_power_real A_84) N_21)))))).
% 2.42/2.66 Axiom fact_383_even__less__0__iff:(forall (A_83:int), ((iff ((ord_less_int ((plus_plus_int A_83) A_83)) zero_zero_int)) ((ord_less_int A_83) zero_zero_int))).
% 2.42/2.66 Axiom fact_384_even__less__0__iff:(forall (A_83:real), ((iff ((ord_less_real ((plus_plus_real A_83) A_83)) zero_zero_real)) ((ord_less_real A_83) zero_zero_real))).
% 2.42/2.66 Axiom fact_385_sum__squares__eq__zero__iff:(forall (X_25:int) (Y_22:int), ((iff (((eq int) ((plus_plus_int ((times_times_int X_25) X_25)) ((times_times_int Y_22) Y_22))) zero_zero_int)) ((and (((eq int) X_25) zero_zero_int)) (((eq int) Y_22) zero_zero_int)))).
% 2.42/2.66 Axiom fact_386_sum__squares__eq__zero__iff:(forall (X_25:real) (Y_22:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X_25) X_25)) ((times_times_real Y_22) Y_22))) zero_zero_real)) ((and (((eq real) X_25) zero_zero_real)) (((eq real) Y_22) zero_zero_real)))).
% 2.42/2.66 Axiom fact_387_add__scale__eq__noteq:(forall (C_30:int) (D_7:int) (A_82:int) (B_57:int) (R_3:int), ((not (((eq int) R_3) zero_zero_int))->(((and (((eq int) A_82) B_57)) (not (((eq int) C_30) D_7)))->(not (((eq int) ((plus_plus_int A_82) ((times_times_int R_3) C_30))) ((plus_plus_int B_57) ((times_times_int R_3) D_7))))))).
% 2.42/2.66 Axiom fact_388_add__scale__eq__noteq:(forall (C_30:nat) (D_7:nat) (A_82:nat) (B_57:nat) (R_3:nat), ((not (((eq nat) R_3) zero_zero_nat))->(((and (((eq nat) A_82) B_57)) (not (((eq nat) C_30) D_7)))->(not (((eq nat) ((plus_plus_nat A_82) ((times_times_nat R_3) C_30))) ((plus_plus_nat B_57) ((times_times_nat R_3) D_7))))))).
% 2.42/2.66 Axiom fact_389_add__scale__eq__noteq:(forall (C_30:real) (D_7:real) (A_82:real) (B_57:real) (R_3:real), ((not (((eq real) R_3) zero_zero_real))->(((and (((eq real) A_82) B_57)) (not (((eq real) C_30) D_7)))->(not (((eq real) ((plus_plus_real A_82) ((times_times_real R_3) C_30))) ((plus_plus_real B_57) ((times_times_real R_3) D_7))))))).
% 2.42/2.66 Axiom fact_390_zprime__zdvd__power:(forall (A:int) (N:nat) (P:int), ((zprime P)->(((dvd_dvd_int P) ((power_power_int A) N))->((dvd_dvd_int P) A)))).
% 2.42/2.66 Axiom fact_391_semiring__norm_I112_J:(((eq int) zero_zero_int) (number_number_of_int pls)).
% 2.42/2.66 Axiom fact_392_semiring__norm_I112_J:(((eq real) zero_zero_real) (number267125858f_real pls)).
% 2.42/2.66 Axiom fact_393_number__of__Pls:(((eq int) (number_number_of_int pls)) zero_zero_int).
% 2.42/2.66 Axiom fact_394_number__of__Pls:(((eq real) (number267125858f_real pls)) zero_zero_real).
% 2.42/2.66 Axiom fact_395_semiring__numeral__0__eq__0:(((eq int) (number_number_of_int pls)) zero_zero_int).
% 2.42/2.66 Axiom fact_396_semiring__numeral__0__eq__0:(((eq nat) (number_number_of_nat pls)) zero_zero_nat).
% 2.42/2.66 Axiom fact_397_semiring__numeral__0__eq__0:(((eq real) (number267125858f_real pls)) zero_zero_real).
% 2.42/2.66 Axiom fact_398_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))).
% 2.42/2.66 Axiom fact_399_bin__less__0__simps_I1_J:(((ord_less_int pls) zero_zero_int)->False).
% 2.42/2.66 Axiom fact_400_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))).
% 2.42/2.66 Axiom fact_401_zero__is__num__zero:(((eq int) zero_zero_int) (number_number_of_int pls)).
% 2.42/2.66 Axiom fact_402_int__0__less__1:((ord_less_int zero_zero_int) one_one_int).
% 2.42/2.66 Axiom fact_403_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)))).
% 2.42/2.66 Axiom fact_404_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))))).
% 2.42/2.66 Axiom fact_405_odd__nonzero:(forall (Z:int), (not (((eq int) ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int))).
% 2.42/2.66 Axiom fact_406_power__Suc__less:(forall (N_19:nat) (A_81:int), (((ord_less_int zero_zero_int) A_81)->(((ord_less_int A_81) one_one_int)->((ord_less_int ((times_times_int A_81) ((power_power_int A_81) N_19))) ((power_power_int A_81) N_19))))).
% 2.42/2.66 Axiom fact_407_power__Suc__less:(forall (N_19:nat) (A_81:nat), (((ord_less_nat zero_zero_nat) A_81)->(((ord_less_nat A_81) one_one_nat)->((ord_less_nat ((times_times_nat A_81) ((power_power_nat A_81) N_19))) ((power_power_nat A_81) N_19))))).
% 2.42/2.66 Axiom fact_408_power__Suc__less:(forall (N_19:nat) (A_81:real), (((ord_less_real zero_zero_real) A_81)->(((ord_less_real A_81) one_one_real)->((ord_less_real ((times_times_real A_81) ((power_power_real A_81) N_19))) ((power_power_real A_81) N_19))))).
% 2.42/2.66 Axiom fact_409_zprime__power__zdvd__cancel__left:(forall (N:nat) (B:int) (A:int) (P:int), ((zprime P)->((((dvd_dvd_int P) A)->False)->(((dvd_dvd_int ((power_power_int P) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P) N)) B))))).
% 2.42/2.66 Axiom fact_410_zprime__power__zdvd__cancel__right:(forall (N:nat) (A:int) (B:int) (P:int), ((zprime P)->((((dvd_dvd_int P) B)->False)->(((dvd_dvd_int ((power_power_int P) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P) N)) A))))).
% 2.42/2.66 Axiom fact_411_sum__squares__ge__zero:(forall (X_24:int) (Y_21:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int X_24) X_24)) ((times_times_int Y_21) Y_21)))).
% 2.42/2.66 Axiom fact_412_sum__squares__ge__zero:(forall (X_24:real) (Y_21:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((times_times_real X_24) X_24)) ((times_times_real Y_21) Y_21)))).
% 2.42/2.66 Axiom fact_413_sum__squares__le__zero__iff:(forall (X_23:int) (Y_20:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int X_23) X_23)) ((times_times_int Y_20) Y_20))) zero_zero_int)) ((and (((eq int) X_23) zero_zero_int)) (((eq int) Y_20) zero_zero_int)))).
% 2.42/2.66 Axiom fact_414_sum__squares__le__zero__iff:(forall (X_23:real) (Y_20:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real X_23) X_23)) ((times_times_real Y_20) Y_20))) zero_zero_real)) ((and (((eq real) X_23) zero_zero_real)) (((eq real) Y_20) zero_zero_real)))).
% 2.42/2.66 Axiom fact_415_less__nat__number__of:(forall (V:int) (V_6:int), ((iff ((ord_less_nat (number_number_of_nat V)) (number_number_of_nat V_6))) ((and (((ord_less_int V) V_6)->((ord_less_int pls) V_6))) ((ord_less_int V) V_6)))).
% 2.42/2.66 Axiom fact_416_not__sum__squares__lt__zero:(forall (X_22:int) (Y_19:int), (((ord_less_int ((plus_plus_int ((times_times_int X_22) X_22)) ((times_times_int Y_19) Y_19))) zero_zero_int)->False)).
% 2.42/2.66 Axiom fact_417_not__sum__squares__lt__zero:(forall (X_22:real) (Y_19:real), (((ord_less_real ((plus_plus_real ((times_times_real X_22) X_22)) ((times_times_real Y_19) Y_19))) zero_zero_real)->False)).
% 2.42/2.66 Axiom fact_418_sum__squares__gt__zero__iff:(forall (X_21:int) (Y_18:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((times_times_int X_21) X_21)) ((times_times_int Y_18) Y_18)))) ((or (not (((eq int) X_21) zero_zero_int))) (not (((eq int) Y_18) zero_zero_int))))).
% 2.42/2.66 Axiom fact_419_sum__squares__gt__zero__iff:(forall (X_21:real) (Y_18:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((times_times_real X_21) X_21)) ((times_times_real Y_18) Y_18)))) ((or (not (((eq real) X_21) zero_zero_real))) (not (((eq real) Y_18) zero_zero_real))))).
% 2.42/2.66 Axiom fact_420_le__nat__number__of:(forall (V:int) (V_6:int), ((iff ((ord_less_eq_nat (number_number_of_nat V)) (number_number_of_nat V_6))) ((((ord_less_eq_int V) V_6)->False)->((ord_less_eq_int V) pls)))).
% 2.42/2.66 Axiom fact_421_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)))).
% 2.42/2.66 Axiom fact_422_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)))).
% 2.42/2.66 Axiom fact_423_power__one__right:(forall (A_80:int), (((eq int) ((power_power_int A_80) one_one_nat)) A_80)).
% 2.42/2.66 Axiom fact_424_power__one__right:(forall (A_80:real), (((eq real) ((power_power_real A_80) one_one_nat)) A_80)).
% 2.42/2.66 Axiom fact_425_power__one__right:(forall (A_80:nat), (((eq nat) ((power_power_nat A_80) one_one_nat)) A_80)).
% 2.42/2.66 Axiom fact_426_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))).
% 2.42/2.66 Axiom fact_427_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))))).
% 2.42/2.66 Axiom fact_428_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))).
% 2.42/2.66 Axiom fact_429_less__special_I1_J:(forall (Y_17:int), ((iff ((ord_less_int zero_zero_int) (number_number_of_int Y_17))) ((ord_less_int pls) Y_17))).
% 2.42/2.66 Axiom fact_430_less__special_I1_J:(forall (Y_17:int), ((iff ((ord_less_real zero_zero_real) (number267125858f_real Y_17))) ((ord_less_int pls) Y_17))).
% 2.42/2.66 Axiom fact_431_less__special_I3_J:(forall (X_20:int), ((iff ((ord_less_int (number_number_of_int X_20)) zero_zero_int)) ((ord_less_int X_20) pls))).
% 2.42/2.66 Axiom fact_432_less__special_I3_J:(forall (X_20:int), ((iff ((ord_less_real (number267125858f_real X_20)) zero_zero_real)) ((ord_less_int X_20) pls))).
% 2.42/2.67 Axiom fact_433_le__special_I1_J:(forall (Y_16:int), ((iff ((ord_less_eq_real zero_zero_real) (number267125858f_real Y_16))) ((ord_less_eq_int pls) Y_16))).
% 2.42/2.67 Axiom fact_434_le__special_I1_J:(forall (Y_16:int), ((iff ((ord_less_eq_int zero_zero_int) (number_number_of_int Y_16))) ((ord_less_eq_int pls) Y_16))).
% 2.42/2.67 Axiom fact_435_le__special_I3_J:(forall (X_19:int), ((iff ((ord_less_eq_real (number267125858f_real X_19)) zero_zero_real)) ((ord_less_eq_int X_19) pls))).
% 2.42/2.67 Axiom fact_436_le__special_I3_J:(forall (X_19:int), ((iff ((ord_less_eq_int (number_number_of_int X_19)) zero_zero_int)) ((ord_less_eq_int X_19) pls))).
% 2.42/2.67 Axiom fact_437_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)))).
% 2.42/2.67 Axiom fact_438_zero__power2:(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real).
% 2.42/2.67 Axiom fact_439_zero__power2:(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_nat).
% 2.42/2.67 Axiom fact_440_zero__power2:(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int).
% 2.42/2.67 Axiom fact_441_zero__eq__power2:(forall (A_79:real), ((iff (((eq real) ((power_power_real A_79) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)) (((eq real) A_79) zero_zero_real))).
% 2.42/2.67 Axiom fact_442_zero__eq__power2:(forall (A_79:int), ((iff (((eq int) ((power_power_int A_79) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)) (((eq int) A_79) zero_zero_int))).
% 2.42/2.67 Axiom fact_443_zero__le__power2:(forall (A_78:real), ((ord_less_eq_real zero_zero_real) ((power_power_real A_78) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.42/2.67 Axiom fact_444_zero__le__power2:(forall (A_78:int), ((ord_less_eq_int zero_zero_int) ((power_power_int A_78) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.42/2.67 Axiom fact_445_power2__le__imp__le:(forall (X_18:real) (Y_15:real), (((ord_less_eq_real ((power_power_real X_18) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_15) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_15)->((ord_less_eq_real X_18) Y_15)))).
% 2.42/2.67 Axiom fact_446_power2__le__imp__le:(forall (X_18:nat) (Y_15:nat), (((ord_less_eq_nat ((power_power_nat X_18) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_15) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_15)->((ord_less_eq_nat X_18) Y_15)))).
% 2.42/2.67 Axiom fact_447_power2__le__imp__le:(forall (X_18:int) (Y_15:int), (((ord_less_eq_int ((power_power_int X_18) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_15) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_15)->((ord_less_eq_int X_18) Y_15)))).
% 2.42/2.67 Axiom fact_448_power2__eq__imp__eq:(forall (X_17:real) (Y_14:real), ((((eq real) ((power_power_real X_17) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_14) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) X_17)->(((ord_less_eq_real zero_zero_real) Y_14)->(((eq real) X_17) Y_14))))).
% 2.42/2.67 Axiom fact_449_power2__eq__imp__eq:(forall (X_17:nat) (Y_14:nat), ((((eq nat) ((power_power_nat X_17) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_14) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) X_17)->(((ord_less_eq_nat zero_zero_nat) Y_14)->(((eq nat) X_17) Y_14))))).
% 2.42/2.67 Axiom fact_450_power2__eq__imp__eq:(forall (X_17:int) (Y_14:int), ((((eq int) ((power_power_int X_17) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_14) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) X_17)->(((ord_less_eq_int zero_zero_int) Y_14)->(((eq int) X_17) Y_14))))).
% 2.42/2.67 Axiom fact_451_power2__less__0:(forall (A_77:real), (((ord_less_real ((power_power_real A_77) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)->False)).
% 2.42/2.67 Axiom fact_452_power2__less__0:(forall (A_77:int), (((ord_less_int ((power_power_int A_77) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)->False)).
% 2.42/2.67 Axiom fact_453_zero__less__power2:(forall (A_76:real), ((iff ((ord_less_real zero_zero_real) ((power_power_real A_76) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq real) A_76) zero_zero_real)))).
% 2.42/2.67 Axiom fact_454_zero__less__power2:(forall (A_76:int), ((iff ((ord_less_int zero_zero_int) ((power_power_int A_76) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq int) A_76) zero_zero_int)))).
% 2.42/2.67 Axiom fact_455_sum__power2__eq__zero__iff:(forall (X_16:real) (Y_13:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X_16) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_13) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_16) zero_zero_real)) (((eq real) Y_13) zero_zero_real)))).
% 2.42/2.67 Axiom fact_456_sum__power2__eq__zero__iff:(forall (X_16:int) (Y_13:int), ((iff (((eq int) ((plus_plus_int ((power_power_int X_16) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_13) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_16) zero_zero_int)) (((eq int) Y_13) zero_zero_int)))).
% 2.42/2.67 Axiom fact_457_power__commutes:(forall (A_75:nat) (N_18:nat), (((eq nat) ((times_times_nat ((power_power_nat A_75) N_18)) A_75)) ((times_times_nat A_75) ((power_power_nat A_75) N_18)))).
% 2.42/2.67 Axiom fact_458_power__commutes:(forall (A_75:real) (N_18:nat), (((eq real) ((times_times_real ((power_power_real A_75) N_18)) A_75)) ((times_times_real A_75) ((power_power_real A_75) N_18)))).
% 2.42/2.67 Axiom fact_459_power__commutes:(forall (A_75:int) (N_18:nat), (((eq int) ((times_times_int ((power_power_int A_75) N_18)) A_75)) ((times_times_int A_75) ((power_power_int A_75) N_18)))).
% 2.42/2.67 Axiom fact_460_power__mult__distrib:(forall (A_74:nat) (B_56:nat) (N_17:nat), (((eq nat) ((power_power_nat ((times_times_nat A_74) B_56)) N_17)) ((times_times_nat ((power_power_nat A_74) N_17)) ((power_power_nat B_56) N_17)))).
% 2.42/2.67 Axiom fact_461_power__mult__distrib:(forall (A_74:real) (B_56:real) (N_17:nat), (((eq real) ((power_power_real ((times_times_real A_74) B_56)) N_17)) ((times_times_real ((power_power_real A_74) N_17)) ((power_power_real B_56) N_17)))).
% 2.42/2.67 Axiom fact_462_power__mult__distrib:(forall (A_74:int) (B_56:int) (N_17:nat), (((eq int) ((power_power_int ((times_times_int A_74) B_56)) N_17)) ((times_times_int ((power_power_int A_74) N_17)) ((power_power_int B_56) N_17)))).
% 2.42/2.67 Axiom fact_463_power__add:(forall (A_73:nat) (M_6:nat) (N_16:nat), (((eq nat) ((power_power_nat A_73) ((plus_plus_nat M_6) N_16))) ((times_times_nat ((power_power_nat A_73) M_6)) ((power_power_nat A_73) N_16)))).
% 2.42/2.67 Axiom fact_464_power__add:(forall (A_73:real) (M_6:nat) (N_16:nat), (((eq real) ((power_power_real A_73) ((plus_plus_nat M_6) N_16))) ((times_times_real ((power_power_real A_73) M_6)) ((power_power_real A_73) N_16)))).
% 2.42/2.67 Axiom fact_465_power__add:(forall (A_73:int) (M_6:nat) (N_16:nat), (((eq int) ((power_power_int A_73) ((plus_plus_nat M_6) N_16))) ((times_times_int ((power_power_int A_73) M_6)) ((power_power_int A_73) N_16)))).
% 2.42/2.67 Axiom fact_466_power__one:(forall (N_15:nat), (((eq real) ((power_power_real one_one_real) N_15)) one_one_real)).
% 2.42/2.67 Axiom fact_467_power__one:(forall (N_15:nat), (((eq nat) ((power_power_nat one_one_nat) N_15)) one_one_nat)).
% 2.42/2.67 Axiom fact_468_power__one:(forall (N_15:nat), (((eq int) ((power_power_int one_one_int) N_15)) one_one_int)).
% 2.42/2.67 Axiom fact_469_power__mult:(forall (A_72:nat) (M_5:nat) (N_14:nat), (((eq nat) ((power_power_nat A_72) ((times_times_nat M_5) N_14))) ((power_power_nat ((power_power_nat A_72) M_5)) N_14))).
% 2.42/2.67 Axiom fact_470_power__mult:(forall (A_72:real) (M_5:nat) (N_14:nat), (((eq real) ((power_power_real A_72) ((times_times_nat M_5) N_14))) ((power_power_real ((power_power_real A_72) M_5)) N_14))).
% 2.42/2.67 Axiom fact_471_power__mult:(forall (A_72:int) (M_5:nat) (N_14:nat), (((eq int) ((power_power_int A_72) ((times_times_nat M_5) N_14))) ((power_power_int ((power_power_int A_72) M_5)) N_14))).
% 2.42/2.67 Axiom fact_472_power2__less__imp__less:(forall (X_15:real) (Y_12:real), (((ord_less_real ((power_power_real X_15) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_12)->((ord_less_real X_15) Y_12)))).
% 2.42/2.67 Axiom fact_473_power2__less__imp__less:(forall (X_15:nat) (Y_12:nat), (((ord_less_nat ((power_power_nat X_15) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_12)->((ord_less_nat X_15) Y_12)))).
% 2.42/2.67 Axiom fact_474_power2__less__imp__less:(forall (X_15:int) (Y_12:int), (((ord_less_int ((power_power_int X_15) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_12)->((ord_less_int X_15) Y_12)))).
% 2.42/2.67 Axiom fact_475_sum__power2__ge__zero:(forall (X_14:real) (Y_11:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((power_power_real X_14) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_11) (number_number_of_nat (bit0 (bit1 pls))))))).
% 2.42/2.67 Axiom fact_476_sum__power2__ge__zero:(forall (X_14:int) (Y_11:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((power_power_int X_14) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_11) (number_number_of_nat (bit0 (bit1 pls))))))).
% 2.42/2.67 Axiom fact_477_sum__power2__le__zero__iff:(forall (X_13:real) (Y_10:real), ((iff ((ord_less_eq_real ((plus_plus_real ((power_power_real X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_10) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_13) zero_zero_real)) (((eq real) Y_10) zero_zero_real)))).
% 2.42/2.67 Axiom fact_478_sum__power2__le__zero__iff:(forall (X_13:int) (Y_10:int), ((iff ((ord_less_eq_int ((plus_plus_int ((power_power_int X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_10) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_13) zero_zero_int)) (((eq int) Y_10) zero_zero_int)))).
% 2.42/2.67 Axiom fact_479_not__sum__power2__lt__zero:(forall (X_12:real) (Y_9:real), (((ord_less_real ((plus_plus_real ((power_power_real X_12) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_9) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)->False)).
% 2.42/2.67 Axiom fact_480_not__sum__power2__lt__zero:(forall (X_12:int) (Y_9:int), (((ord_less_int ((plus_plus_int ((power_power_int X_12) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_9) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)->False)).
% 2.42/2.67 Axiom fact_481_sum__power2__gt__zero__iff:(forall (X_11:real) (Y_8:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((power_power_real X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_8) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq real) X_11) zero_zero_real))) (not (((eq real) Y_8) zero_zero_real))))).
% 2.42/2.67 Axiom fact_482_sum__power2__gt__zero__iff:(forall (X_11:int) (Y_8:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((power_power_int X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_8) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq int) X_11) zero_zero_int))) (not (((eq int) Y_8) zero_zero_int))))).
% 2.42/2.67 Axiom fact_483_zero__le__even__power_H:(forall (A_71:real) (N_13:nat), ((ord_less_eq_real zero_zero_real) ((power_power_real A_71) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_13)))).
% 2.42/2.67 Axiom fact_484_zero__le__even__power_H:(forall (A_71:int) (N_13:nat), ((ord_less_eq_int zero_zero_int) ((power_power_int A_71) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_13)))).
% 2.42/2.67 Axiom fact_485_one__le__power:(forall (N_12:nat) (A_70:real), (((ord_less_eq_real one_one_real) A_70)->((ord_less_eq_real one_one_real) ((power_power_real A_70) N_12)))).
% 2.42/2.67 Axiom fact_486_one__le__power:(forall (N_12:nat) (A_70:nat), (((ord_less_eq_nat one_one_nat) A_70)->((ord_less_eq_nat one_one_nat) ((power_power_nat A_70) N_12)))).
% 2.42/2.67 Axiom fact_487_one__le__power:(forall (N_12:nat) (A_70:int), (((ord_less_eq_int one_one_int) A_70)->((ord_less_eq_int one_one_int) ((power_power_int A_70) N_12)))).
% 2.42/2.67 Axiom fact_488_power__increasing:(forall (A_69:real) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_real one_one_real) A_69)->((ord_less_eq_real ((power_power_real A_69) N_11)) ((power_power_real A_69) N_10))))).
% 2.42/2.67 Axiom fact_489_power__increasing:(forall (A_69:nat) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_nat one_one_nat) A_69)->((ord_less_eq_nat ((power_power_nat A_69) N_11)) ((power_power_nat A_69) N_10))))).
% 2.42/2.67 Axiom fact_490_power__increasing:(forall (A_69:int) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_int one_one_int) A_69)->((ord_less_eq_int ((power_power_int A_69) N_11)) ((power_power_int A_69) N_10))))).
% 2.42/2.67 Axiom fact_491_power__inject__exp:(forall (M_4:nat) (N_9:nat) (A_68:real), (((ord_less_real one_one_real) A_68)->((iff (((eq real) ((power_power_real A_68) M_4)) ((power_power_real A_68) N_9))) (((eq nat) M_4) N_9)))).
% 2.42/2.67 Axiom fact_492_power__inject__exp:(forall (M_4:nat) (N_9:nat) (A_68:nat), (((ord_less_nat one_one_nat) A_68)->((iff (((eq nat) ((power_power_nat A_68) M_4)) ((power_power_nat A_68) N_9))) (((eq nat) M_4) N_9)))).
% 2.42/2.67 Axiom fact_493_power__inject__exp:(forall (M_4:nat) (N_9:nat) (A_68:int), (((ord_less_int one_one_int) A_68)->((iff (((eq int) ((power_power_int A_68) M_4)) ((power_power_int A_68) N_9))) (((eq nat) M_4) N_9)))).
% 2.42/2.67 Axiom fact_494_power__strict__increasing__iff:(forall (X_10:nat) (Y_7:nat) (B_55:real), (((ord_less_real one_one_real) B_55)->((iff ((ord_less_real ((power_power_real B_55) X_10)) ((power_power_real B_55) Y_7))) ((ord_less_nat X_10) Y_7)))).
% 2.42/2.67 Axiom fact_495_power__strict__increasing__iff:(forall (X_10:nat) (Y_7:nat) (B_55:nat), (((ord_less_nat one_one_nat) B_55)->((iff ((ord_less_nat ((power_power_nat B_55) X_10)) ((power_power_nat B_55) Y_7))) ((ord_less_nat X_10) Y_7)))).
% 2.42/2.67 Axiom fact_496_power__strict__increasing__iff:(forall (X_10:nat) (Y_7:nat) (B_55:int), (((ord_less_int one_one_int) B_55)->((iff ((ord_less_int ((power_power_int B_55) X_10)) ((power_power_int B_55) Y_7))) ((ord_less_nat X_10) Y_7)))).
% 2.42/2.67 Axiom fact_497_power__less__imp__less__exp:(forall (M_3:nat) (N_8:nat) (A_67:real), (((ord_less_real one_one_real) A_67)->(((ord_less_real ((power_power_real A_67) M_3)) ((power_power_real A_67) N_8))->((ord_less_nat M_3) N_8)))).
% 2.42/2.67 Axiom fact_498_power__less__imp__less__exp:(forall (M_3:nat) (N_8:nat) (A_67:nat), (((ord_less_nat one_one_nat) A_67)->(((ord_less_nat ((power_power_nat A_67) M_3)) ((power_power_nat A_67) N_8))->((ord_less_nat M_3) N_8)))).
% 2.42/2.67 Axiom fact_499_power__less__imp__less__exp:(forall (M_3:nat) (N_8:nat) (A_67:int), (((ord_less_int one_one_int) A_67)->(((ord_less_int ((power_power_int A_67) M_3)) ((power_power_int A_67) N_8))->((ord_less_nat M_3) N_8)))).
% 2.42/2.67 Axiom fact_500_power__strict__increasing:(forall (A_66:real) (N_7:nat) (N_6:nat), (((ord_less_nat N_7) N_6)->(((ord_less_real one_one_real) A_66)->((ord_less_real ((power_power_real A_66) N_7)) ((power_power_real A_66) N_6))))).
% 2.42/2.67 Axiom fact_501_power__strict__increasing:(forall (A_66:nat) (N_7:nat) (N_6:nat), (((ord_less_nat N_7) N_6)->(((ord_less_nat one_one_nat) A_66)->((ord_less_nat ((power_power_nat A_66) N_7)) ((power_power_nat A_66) N_6))))).
% 2.42/2.67 Axiom fact_502_power__strict__increasing:(forall (A_66:int) (N_7:nat) (N_6:nat), (((ord_less_nat N_7) N_6)->(((ord_less_int one_one_int) A_66)->((ord_less_int ((power_power_int A_66) N_7)) ((power_power_int A_66) N_6))))).
% 2.42/2.67 Axiom fact_503_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)).
% 2.42/2.67 Axiom fact_504_Euler_Oaux____1:(forall (Y_1:int) (X_1:int) (P:int), (((((zcong X_1) zero_zero_int) P)->False)->((((zcong ((power_power_int Y_1) (number_number_of_nat (bit0 (bit1 pls))))) X_1) P)->(((dvd_dvd_int P) Y_1)->False)))).
% 2.42/2.67 Axiom fact_505_int__pos__lt__two__imp__zero__or__one:(forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_int X_1) (number_number_of_int (bit0 (bit1 pls))))->((or (((eq int) X_1) zero_zero_int)) (((eq int) X_1) one_one_int))))).
% 2.42/2.67 Axiom fact_506_even__power__le__0__imp__0:(forall (A_65:real) (K_3:nat), (((ord_less_eq_real ((power_power_real A_65) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_3))) zero_zero_real)->(((eq real) A_65) zero_zero_real))).
% 2.42/2.67 Axiom fact_507_even__power__le__0__imp__0:(forall (A_65:int) (K_3:nat), (((ord_less_eq_int ((power_power_int A_65) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_3))) zero_zero_int)->(((eq int) A_65) zero_zero_int))).
% 2.42/2.67 Axiom fact_508_zprime__def:(forall (P:int), ((iff (zprime P)) ((and ((ord_less_int one_one_int) P)) (forall (M_2:int), (((and ((ord_less_eq_int zero_zero_int) M_2)) ((dvd_dvd_int M_2) P))->((or (((eq int) M_2) one_one_int)) (((eq int) M_2) P))))))).
% 2.42/2.67 Axiom fact_509_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))))).
% 2.42/2.67 Axiom fact_510_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))))).
% 2.42/2.67 Axiom fact_511_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J:((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 (bit1 pls)))).
% 2.42/2.67 Axiom fact_512__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).
% 2.42/2.67 Axiom fact_513__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).
% 2.42/2.67 Axiom fact_514_nat__zero__less__power__iff:(forall (X_1:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) N))) ((or ((ord_less_nat zero_zero_nat) X_1)) (((eq nat) N) zero_zero_nat)))).
% 2.42/2.67 Axiom fact_515_zero__less__power__nat__eq:(forall (X_1:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) N))) ((or (((eq nat) N) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X_1)))).
% 2.42/2.67 Axiom fact_516_zero__less__power__nat__eq__number__of:(forall (X_1:nat) (W:int), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) (number_number_of_nat W)))) ((or (((eq nat) (number_number_of_nat W)) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X_1)))).
% 2.42/2.67 Axiom fact_517_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)))).
% 2.42/2.67 Axiom fact_518_rel__simps_I47_J:(forall (K:int), ((iff (((eq int) (bit1 K)) min)) (((eq int) K) min))).
% 2.42/2.67 Axiom fact_519_rel__simps_I43_J:(forall (L:int), ((iff (((eq int) min) (bit1 L))) (((eq int) min) L))).
% 2.42/2.67 Axiom fact_520_Bit1__Min:(((eq int) (bit1 min)) min).
% 2.42/2.67 Axiom fact_521_rel__simps_I37_J:(not (((eq int) pls) min)).
% 2.42/2.67 Axiom fact_522_rel__simps_I40_J:(not (((eq int) min) pls)).
% 2.42/2.67 Axiom fact_523_rel__simps_I45_J:(forall (K:int), (not (((eq int) (bit0 K)) min))).
% 2.42/2.67 Axiom fact_524_rel__simps_I42_J:(forall (L:int), (not (((eq int) min) (bit0 L)))).
% 2.42/2.67 Axiom fact_525_rel__simps_I7_J:(((ord_less_int min) min)->False).
% 2.42/2.67 Axiom fact_526_rel__simps_I24_J:((ord_less_eq_int min) min).
% 2.42/2.67 Axiom fact_527_not__real__square__gt__zero:(forall (X_1:real), ((iff (((ord_less_real zero_zero_real) ((times_times_real X_1) X_1))->False)) (((eq real) X_1) zero_zero_real))).
% 2.42/2.67 Axiom fact_528_rel__simps_I13_J:(forall (K:int), ((iff ((ord_less_int (bit1 K)) min)) ((ord_less_int K) min))).
% 2.42/2.67 Axiom fact_529_rel__simps_I9_J:(forall (K:int), ((iff ((ord_less_int min) (bit1 K))) ((ord_less_int min) K))).
% 2.42/2.67 Axiom fact_530_rel__simps_I3_J:(((ord_less_int pls) min)->False).
% 2.42/2.67 Axiom fact_531_rel__simps_I6_J:((ord_less_int min) pls).
% 2.42/2.67 Axiom fact_532_rel__simps_I8_J:(forall (K:int), ((iff ((ord_less_int min) (bit0 K))) ((ord_less_int min) K))).
% 2.42/2.67 Axiom fact_533_bin__less__0__simps_I2_J:((ord_less_int min) zero_zero_int).
% 2.42/2.67 Axiom fact_534_rel__simps_I30_J:(forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) min)) ((ord_less_eq_int K) min))).
% 2.42/2.67 Axiom fact_535_rel__simps_I26_J:(forall (K:int), ((iff ((ord_less_eq_int min) (bit1 K))) ((ord_less_eq_int min) K))).
% 2.42/2.67 Axiom fact_536_rel__simps_I20_J:(((ord_less_eq_int pls) min)->False).
% 2.42/2.67 Axiom fact_537_rel__simps_I23_J:((ord_less_eq_int min) pls).
% 2.42/2.67 Axiom fact_538_rel__simps_I28_J:(forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) min)) ((ord_less_eq_int K) min))).
% 2.42/2.67 Axiom fact_539_eq__number__of__Pls__Min:(not (((eq int) (number_number_of_int pls)) (number_number_of_int min))).
% 2.42/2.67 Axiom fact_540_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)))).
% 2.42/2.67 Axiom fact_541_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)).
% 2.42/2.67 Axiom fact_542_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)).
% 2.42/2.67 Axiom fact_543_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)).
% 2.42/2.67 Axiom fact_544_power__0:(forall (A_64:real), (((eq real) ((power_power_real A_64) zero_zero_nat)) one_one_real)).
% 2.42/2.67 Axiom fact_545_power__0:(forall (A_64:nat), (((eq nat) ((power_power_nat A_64) zero_zero_nat)) one_one_nat)).
% 2.42/2.67 Axiom fact_546_power__0:(forall (A_64:int), (((eq int) ((power_power_int A_64) zero_zero_nat)) one_one_int)).
% 2.42/2.67 Axiom fact_547_nat__number__of__Pls:(((eq nat) (number_number_of_nat pls)) zero_zero_nat).
% 2.42/2.67 Axiom fact_548_semiring__norm_I113_J:(((eq nat) zero_zero_nat) (number_number_of_nat pls)).
% 2.42/2.67 Axiom fact_549_rel__simps_I25_J:(forall (K:int), ((iff ((ord_less_eq_int min) (bit0 K))) ((ord_less_int min) K))).
% 2.42/2.67 Axiom fact_550_rel__simps_I11_J:(forall (K:int), ((iff ((ord_less_int (bit0 K)) min)) ((ord_less_eq_int K) min))).
% 2.42/2.67 Axiom fact_551_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))))).
% 2.42/2.67 Axiom fact_552_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)))))).
% 2.42/2.67 Axiom fact_553_one__less__power:(forall (N_5:nat) (A_63:real), (((ord_less_real one_one_real) A_63)->(((ord_less_nat zero_zero_nat) N_5)->((ord_less_real one_one_real) ((power_power_real A_63) N_5))))).
% 2.42/2.67 Axiom fact_554_one__less__power:(forall (N_5:nat) (A_63:nat), (((ord_less_nat one_one_nat) A_63)->(((ord_less_nat zero_zero_nat) N_5)->((ord_less_nat one_one_nat) ((power_power_nat A_63) N_5))))).
% 2.42/2.67 Axiom fact_555_one__less__power:(forall (N_5:nat) (A_63:int), (((ord_less_int one_one_int) A_63)->(((ord_less_nat zero_zero_nat) N_5)->((ord_less_int one_one_int) ((power_power_int A_63) N_5))))).
% 2.42/2.67 Axiom fact_556_dvd__power:(forall (X_8:real) (N_4:nat), (((or ((ord_less_nat zero_zero_nat) N_4)) (((eq real) X_8) one_one_real))->((dvd_dvd_real X_8) ((power_power_real X_8) N_4)))).
% 2.42/2.67 Axiom fact_557_dvd__power:(forall (X_8:nat) (N_4:nat), (((or ((ord_less_nat zero_zero_nat) N_4)) (((eq nat) X_8) one_one_nat))->((dvd_dvd_nat X_8) ((power_power_nat X_8) N_4)))).
% 2.42/2.67 Axiom fact_558_dvd__power:(forall (X_8:int) (N_4:nat), (((or ((ord_less_nat zero_zero_nat) N_4)) (((eq int) X_8) one_one_int))->((dvd_dvd_int X_8) ((power_power_int X_8) N_4)))).
% 2.42/2.67 Axiom fact_559_less__0__number__of:(forall (V:int), ((iff ((ord_less_nat zero_zero_nat) (number_number_of_nat V))) ((ord_less_int pls) V))).
% 2.42/2.67 Axiom fact_560_eq__number__of__0:(forall (V:int), ((iff (((eq nat) (number_number_of_nat V)) zero_zero_nat)) ((ord_less_eq_int V) pls))).
% 2.42/2.67 Axiom fact_561_eq__0__number__of:(forall (V:int), ((iff (((eq nat) zero_zero_nat) (number_number_of_nat V))) ((ord_less_eq_int V) pls))).
% 2.42/2.68 Axiom fact_562_zcong__sym:(forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) (((zcong B) A) M))).
% 2.42/2.68 Axiom fact_563_zcong__refl:(forall (K:int) (M:int), (((zcong K) K) M)).
% 2.42/2.68 Axiom fact_564_zcong__trans:(forall (C:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((zcong B) C) M)->(((zcong A) C) M)))).
% 2.42/2.68 Axiom fact_565_pos2:((ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls)))).
% 2.42/2.68 Axiom fact_566_nat__number__of__mult__left:(forall (V_6: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_6)) 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_6)) K))) ((times_times_nat (number_number_of_nat ((times_times_int V) V_6))) K))))).
% 2.42/2.68 Axiom fact_567_mult__nat__number__of:(forall (V_6:int) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((times_times_nat (number_number_of_nat V)) (number_number_of_nat V_6))) zero_zero_nat))) ((((ord_less_int V) pls)->False)->(((eq nat) ((times_times_nat (number_number_of_nat V)) (number_number_of_nat V_6))) (number_number_of_nat ((times_times_int V) V_6)))))).
% 2.42/2.68 Axiom fact_568_order__le__neq__implies__less:(forall (X_7:real) (Y_6:real), (((ord_less_eq_real X_7) Y_6)->((not (((eq real) X_7) Y_6))->((ord_less_real X_7) Y_6)))).
% 2.42/2.68 Axiom fact_569_order__le__neq__implies__less:(forall (X_7:nat) (Y_6:nat), (((ord_less_eq_nat X_7) Y_6)->((not (((eq nat) X_7) Y_6))->((ord_less_nat X_7) Y_6)))).
% 2.42/2.68 Axiom fact_570_order__le__neq__implies__less:(forall (X_7:int) (Y_6:int), (((ord_less_eq_int X_7) Y_6)->((not (((eq int) X_7) Y_6))->((ord_less_int X_7) Y_6)))).
% 2.42/2.68 Axiom fact_571_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J:((ord_less_eq_int zero_zero_int) zero_zero_int).
% 2.42/2.68 Axiom fact_572_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))))).
% 2.42/2.68 Axiom fact_573_IntPrimes_Ozcong__zero:(forall (A:int) (B:int), ((iff (((zcong A) B) zero_zero_int)) (((eq int) A) B))).
% 2.42/2.68 Axiom fact_574_zcong__1:(forall (A:int) (B:int), (((zcong A) B) one_one_int)).
% 2.42/2.68 Axiom fact_575_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)))).
% 2.42/2.68 Axiom fact_576_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))).
% 2.42/2.68 Axiom fact_577_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))).
% 2.42/2.68 Axiom fact_578_zcong__zmult__self:(forall (A:int) (M:int) (B:int), (((zcong ((times_times_int A) M)) ((times_times_int B) M)) M)).
% 2.42/2.68 Axiom fact_579_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)))).
% 2.42/2.68 Axiom fact_580_power__m1__even:(forall (N_3:nat), (((eq real) ((power_power_real (number267125858f_real min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_3))) one_one_real)).
% 2.42/2.68 Axiom fact_581_power__m1__even:(forall (N_3:nat), (((eq int) ((power_power_int (number_number_of_int min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_3))) one_one_int)).
% 2.42/2.68 Axiom fact_582_power__eq__0__iff__number__of:(forall (A_62:real) (W_4:int), ((iff (((eq real) ((power_power_real A_62) (number_number_of_nat W_4))) zero_zero_real)) ((and (((eq real) A_62) zero_zero_real)) (not (((eq nat) (number_number_of_nat W_4)) zero_zero_nat))))).
% 2.42/2.68 Axiom fact_583_power__eq__0__iff__number__of:(forall (A_62:nat) (W_4:int), ((iff (((eq nat) ((power_power_nat A_62) (number_number_of_nat W_4))) zero_zero_nat)) ((and (((eq nat) A_62) zero_zero_nat)) (not (((eq nat) (number_number_of_nat W_4)) zero_zero_nat))))).
% 2.42/2.68 Axiom fact_584_power__eq__0__iff__number__of:(forall (A_62:int) (W_4:int), ((iff (((eq int) ((power_power_int A_62) (number_number_of_nat W_4))) zero_zero_int)) ((and (((eq int) A_62) zero_zero_int)) (not (((eq nat) (number_number_of_nat W_4)) zero_zero_nat))))).
% 2.42/2.68 Axiom fact_585_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J:((ord_less_eq_int zero_zero_int) one_one_int).
% 2.42/2.68 Axiom fact_586_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J:(forall (Y_1:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_eq_int zero_zero_int) Y_1)->((ord_less_eq_int zero_zero_int) ((times_times_int X_1) Y_1))))).
% 2.42/2.68 Axiom fact_587_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J:(forall (Y_1:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_eq_int zero_zero_int) Y_1)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X_1) Y_1))))).
% 2.42/2.68 Axiom fact_588_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)))))).
% 2.42/2.68 Axiom fact_589_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J:(forall (N:nat) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->((ord_less_eq_int zero_zero_int) ((power_power_int X_1) N)))).
% 2.42/2.68 Axiom fact_590_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))))))).
% 2.42/2.68 Axiom fact_591_power__0__left__number__of:(forall (W_3:int), ((and ((((eq nat) (number_number_of_nat W_3)) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_3))) one_one_real))) ((not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_3))) zero_zero_real)))).
% 2.42/2.68 Axiom fact_592_power__0__left__number__of:(forall (W_3:int), ((and ((((eq nat) (number_number_of_nat W_3)) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_3))) one_one_nat))) ((not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_3))) zero_zero_nat)))).
% 2.42/2.68 Axiom fact_593_power__0__left__number__of:(forall (W_3:int), ((and ((((eq nat) (number_number_of_nat W_3)) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_3))) one_one_int))) ((not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_3))) zero_zero_int)))).
% 2.42/2.68 Axiom fact_594_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))))))).
% 2.42/2.68 Axiom fact_595_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))))).
% 2.42/2.68 Axiom fact_596_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J:((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 (bit1 pls)))).
% 2.42/2.68 Axiom fact_597_zdiv__mono2__neg__lemma:(forall (B:int) (Q:int) (R:int) (B_54: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_54) Q_3)) R_2))->(((ord_less_int ((plus_plus_int ((times_times_int B_54) 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_54)->(((ord_less_eq_int B_54) B)->((ord_less_eq_int Q_3) Q)))))))).
% 2.42/2.68 Axiom fact_598_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)))))).
% 2.42/2.68 Axiom fact_599_zdiv__mono2__lemma:(forall (B:int) (Q:int) (R:int) (B_54: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_54) Q_3)) R_2))->(((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_54) Q_3)) R_2))->(((ord_less_int R_2) B_54)->(((ord_less_eq_int zero_zero_int) R)->(((ord_less_int zero_zero_int) B_54)->(((ord_less_eq_int B_54) B)->((ord_less_eq_int Q) Q_3)))))))).
% 2.42/2.68 Axiom fact_600_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)))))).
% 2.42/2.68 Axiom fact_601_q__neg__lemma:(forall (B_54:int) (Q_3:int) (R_2:int), (((ord_less_int ((plus_plus_int ((times_times_int B_54) Q_3)) R_2)) zero_zero_int)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B_54)->((ord_less_eq_int Q_3) zero_zero_int))))).
% 2.42/2.68 Axiom fact_602_q__pos__lemma:(forall (B_54:int) (Q_3:int) (R_2:int), (((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_54) Q_3)) R_2))->(((ord_less_int R_2) B_54)->(((ord_less_int zero_zero_int) B_54)->((ord_less_eq_int zero_zero_int) Q_3))))).
% 2.42/2.68 Axiom fact_603_zprime__zdvd__zmult:(forall (N:int) (P:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->((zprime P)->(((dvd_dvd_int P) ((times_times_int M) N))->((or ((dvd_dvd_int P) M)) ((dvd_dvd_int P) N)))))).
% 2.42/2.68 Axiom fact_604__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)).
% 2.42/2.68 Axiom fact_605__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))).
% 2.42/2.68 Axiom fact_606_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))))).
% 2.42/2.68 Axiom fact_607_zcong__neg__1__impl__ne__1:(forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((((zcong X_1) (number_number_of_int min)) P)->((((zcong X_1) one_one_int) P)->False)))).
% 2.42/2.68 Axiom fact_608_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))).
% 2.42/2.68 Axiom fact_609__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)).
% 2.42/2.68 Axiom fact_610__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))).
% 2.42/2.68 Axiom fact_611_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)))).
% 2.42/2.68 Axiom fact_612_number__of__diff:(forall (V_5:int) (W_2:int), (((eq real) (number267125858f_real ((minus_minus_int V_5) W_2))) ((minus_minus_real (number267125858f_real V_5)) (number267125858f_real W_2)))).
% 2.42/2.68 Axiom fact_613_number__of__diff:(forall (V_5:int) (W_2:int), (((eq int) (number_number_of_int ((minus_minus_int V_5) W_2))) ((minus_minus_int (number_number_of_int V_5)) (number_number_of_int W_2)))).
% 2.42/2.68 Axiom fact_614_diff__bin__simps_I1_J:(forall (K:int), (((eq int) ((minus_minus_int K) pls)) K)).
% 2.42/2.68 Axiom fact_615_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)))).
% 2.42/2.68 Axiom fact_616_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)))).
% 2.42/2.68 Axiom fact_617_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)))).
% 2.42/2.68 Axiom fact_618_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)))).
% 2.42/2.68 Axiom fact_619_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)))).
% 2.42/2.68 Axiom fact_620_right__diff__distrib__number__of:(forall (V_4:int) (B_53:real) (C_29:real), (((eq real) ((times_times_real (number267125858f_real V_4)) ((minus_minus_real B_53) C_29))) ((minus_minus_real ((times_times_real (number267125858f_real V_4)) B_53)) ((times_times_real (number267125858f_real V_4)) C_29)))).
% 2.42/2.68 Axiom fact_621_right__diff__distrib__number__of:(forall (V_4:int) (B_53:int) (C_29:int), (((eq int) ((times_times_int (number_number_of_int V_4)) ((minus_minus_int B_53) C_29))) ((minus_minus_int ((times_times_int (number_number_of_int V_4)) B_53)) ((times_times_int (number_number_of_int V_4)) C_29)))).
% 2.42/2.68 Axiom fact_622_left__diff__distrib__number__of:(forall (A_61:real) (B_52:real) (V_3:int), (((eq real) ((times_times_real ((minus_minus_real A_61) B_52)) (number267125858f_real V_3))) ((minus_minus_real ((times_times_real A_61) (number267125858f_real V_3))) ((times_times_real B_52) (number267125858f_real V_3))))).
% 2.42/2.68 Axiom fact_623_left__diff__distrib__number__of:(forall (A_61:int) (B_52:int) (V_3:int), (((eq int) ((times_times_int ((minus_minus_int A_61) B_52)) (number_number_of_int V_3))) ((minus_minus_int ((times_times_int A_61) (number_number_of_int V_3))) ((times_times_int B_52) (number_number_of_int V_3))))).
% 2.42/2.68 Axiom fact_624_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)))).
% 2.42/2.68 Axiom fact_625_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)))).
% 2.42/2.68 Axiom fact_626_diff__bin__simps_I3_J:(forall (L:int), (((eq int) ((minus_minus_int pls) (bit0 L))) (bit0 ((minus_minus_int pls) L)))).
% 2.42/2.68 Axiom fact_627_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))).
% 2.42/2.68 Axiom fact_628_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)))))).
% 2.42/2.68 Axiom fact_629_zcong__def:(forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) ((dvd_dvd_int M) ((minus_minus_int A) B)))).
% 2.42/2.68 Axiom fact_630_add__number__of__diff1:(forall (V_2:int) (W_1:int) (C_28:real), (((eq real) ((plus_plus_real (number267125858f_real V_2)) ((minus_minus_real (number267125858f_real W_1)) C_28))) ((minus_minus_real (number267125858f_real ((plus_plus_int V_2) W_1))) C_28))).
% 2.42/2.68 Axiom fact_631_add__number__of__diff1:(forall (V_2:int) (W_1:int) (C_28:int), (((eq int) ((plus_plus_int (number_number_of_int V_2)) ((minus_minus_int (number_number_of_int W_1)) C_28))) ((minus_minus_int (number_number_of_int ((plus_plus_int V_2) W_1))) C_28))).
% 2.42/2.68 Axiom fact_632_Euler_Oaux1:(forall (A:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int X_1) A)->((not (((eq int) X_1) ((minus_minus_int A) one_one_int)))->((ord_less_int X_1) ((minus_minus_int A) one_one_int)))))).
% 2.42/2.68 Axiom fact_633_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))).
% 2.42/2.68 Axiom fact_634_diff__bin__simps_I4_J:(forall (L:int), (((eq int) ((minus_minus_int pls) (bit1 L))) (bit1 ((minus_minus_int min) L)))).
% 2.42/2.68 Axiom fact_635_diff__bin__simps_I5_J:(forall (L:int), (((eq int) ((minus_minus_int min) (bit0 L))) (bit1 ((minus_minus_int min) L)))).
% 2.42/2.68 Axiom fact_636_diff__bin__simps_I6_J:(forall (L:int), (((eq int) ((minus_minus_int min) (bit1 L))) (bit0 ((minus_minus_int min) L)))).
% 2.42/2.68 Axiom fact_637_inv__not__p__minus__1__aux:(forall (A:int) (P:int), ((iff (((zcong ((times_times_int A) ((minus_minus_int P) one_one_int))) one_one_int) P)) (((zcong A) ((minus_minus_int P) one_one_int)) P))).
% 2.42/2.68 Axiom fact_638_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))))).
% 2.42/2.68 Axiom fact_639_mult__sum2sq:(forall (A:int) (B:int) (P:int) (Q:int), (((eq int) ((times_times_int (twoSqu2057625106sum2sq ((product_Pair_int_int A) B))) (twoSqu2057625106sum2sq ((product_Pair_int_int P) Q)))) (twoSqu2057625106sum2sq ((product_Pair_int_int ((plus_plus_int ((times_times_int A) P)) ((times_times_int B) Q))) ((minus_minus_int ((times_times_int A) Q)) ((times_times_int B) P)))))).
% 2.42/2.68 Axiom fact_640_zcong__square:(forall (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) A)) one_one_int) P)->((or (((zcong A) one_one_int) P)) (((zcong A) ((minus_minus_int P) one_one_int)) P)))))).
% 2.42/2.68 Axiom fact_641_zcong__square__zless:(forall (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P)->((((zcong ((times_times_int A) A)) one_one_int) P)->((or (((eq int) A) one_one_int)) (((eq int) A) ((minus_minus_int P) one_one_int)))))))).
% 2.42/2.68 Axiom fact_642_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))))))).
% 2.42/2.68 Axiom fact_643_zcong__id:(forall (M:int), (((zcong M) zero_zero_int) M)).
% 2.42/2.68 Axiom fact_644_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)))).
% 2.42/2.68 Axiom fact_645_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)))).
% 2.42/2.68 Axiom fact_646_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))).
% 2.42/2.68 Axiom fact_647_zcong__zpower:(forall (Z:nat) (X_1:int) (Y_1:int) (M:int), ((((zcong X_1) Y_1) M)->(((zcong ((power_power_int X_1) Z)) ((power_power_int Y_1) Z)) M))).
% 2.42/2.68 Axiom fact_648_power2__diff:(forall (X_6:real) (Y_5:real), (((eq real) ((power_power_real ((minus_minus_real X_6) Y_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((minus_minus_real ((plus_plus_real ((power_power_real X_6) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_6)) Y_5)))).
% 2.42/2.68 Axiom fact_649_power2__diff:(forall (X_6:int) (Y_5:int), (((eq int) ((power_power_int ((minus_minus_int X_6) Y_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((minus_minus_int ((plus_plus_int ((power_power_int X_6) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) X_6)) Y_5)))).
% 2.42/2.68 Axiom fact_650_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))))))).
% 2.42/2.68 Axiom fact_651_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))))))).
% 2.42/2.69 Axiom fact_652_zcong__less__eq:(forall (M:int) (Y_1:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int zero_zero_int) Y_1)->(((ord_less_int zero_zero_int) M)->((((zcong X_1) Y_1) M)->(((ord_less_int X_1) M)->(((ord_less_int Y_1) M)->(((eq int) X_1) Y_1)))))))).
% 2.42/2.69 Axiom fact_653_zcong__not__zero:(forall (M:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int X_1) M)->((((zcong X_1) zero_zero_int) M)->False)))).
% 2.42/2.69 Axiom fact_654_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)))).
% 2.42/2.69 Axiom fact_655_zcong__eq__zdvd__prop:(forall (X_1:int) (P:int), ((iff (((zcong X_1) zero_zero_int) P)) ((dvd_dvd_int P) X_1))).
% 2.42/2.69 Axiom fact_656_zcong__zero__equiv__div:(forall (A:int) (M:int), ((iff (((zcong A) zero_zero_int) M)) ((dvd_dvd_int M) A))).
% 2.42/2.69 Axiom fact_657_zprime__zdvd__zmult__better:(forall (M:int) (N:int) (P:int), ((zprime P)->(((dvd_dvd_int P) ((times_times_int M) N))->((or ((dvd_dvd_int P) M)) ((dvd_dvd_int P) N))))).
% 2.42/2.69 Axiom fact_658_Int2_Ozcong__zero:(forall (M:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_int X_1) M)->((((zcong X_1) zero_zero_int) M)->(((eq int) X_1) zero_zero_int))))).
% 2.42/2.69 Axiom fact_659_zpower__zdvd__prop1:(forall (P:int) (Y_1:int) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((dvd_dvd_int P) Y_1)->((dvd_dvd_int P) ((power_power_int Y_1) N))))).
% 2.42/2.69 Axiom fact_660_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)))).
% 2.42/2.69 Axiom fact_661_zcong__zmult__prop3:(forall (Y_1:int) (X_1:int) (P:int), ((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((((zcong Y_1) zero_zero_int) P)->False)->((((zcong ((times_times_int X_1) Y_1)) zero_zero_int) P)->False))))).
% 2.42/2.69 Axiom fact_662_zcong__zprime__prod__zero:(forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) B)) zero_zero_int) P)->((or (((zcong A) zero_zero_int) P)) (((zcong B) zero_zero_int) P)))))).
% 2.42/2.69 Axiom fact_663_zcong__zprime__prod__zero__contra:(forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->(((and ((((zcong A) zero_zero_int) P)->False)) ((((zcong B) zero_zero_int) P)->False))->((((zcong ((times_times_int A) B)) zero_zero_int) P)->False))))).
% 2.42/2.69 Axiom fact_664_zpower__zdvd__prop2:(forall (Y_1:int) (N:nat) (P:int), ((zprime P)->(((dvd_dvd_int P) ((power_power_int Y_1) N))->(((ord_less_nat zero_zero_nat) N)->((dvd_dvd_int P) Y_1))))).
% 2.42/2.69 Axiom fact_665_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))).
% 2.42/2.69 Axiom fact_666_Legendre__def:(forall (A:int) (P:int), ((and ((((zcong A) zero_zero_int) P)->(((eq int) ((legendre A) P)) zero_zero_int))) (((((zcong A) zero_zero_int) P)->False)->((and (((quadRes P) A)->(((eq int) ((legendre A) P)) one_one_int))) ((((quadRes P) A)->False)->(((eq int) ((legendre A) P)) (number_number_of_int min))))))).
% 2.42/2.69 Axiom fact_667_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)))).
% 2.42/2.69 Axiom fact_668_QuadRes__def:(forall (M:int) (X_1:int), ((iff ((quadRes M) X_1)) ((ex int) (fun (Y:int)=> (((zcong ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls))))) X_1) M))))).
% 2.42/2.69 Axiom fact_669_realpow__two__sum__zero__iff:(forall (X_1:real) (Y_1:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_1) zero_zero_real)) (((eq real) Y_1) zero_zero_real)))).
% 2.51/2.69 Axiom fact_670_convex__bound__lt:(forall (V_1:real) (U_1:real) (Y_4:real) (X_5:real) (A_60:real), (((ord_less_real X_5) A_60)->(((ord_less_real Y_4) A_60)->(((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_5)) ((times_times_real V_1) Y_4))) A_60))))))).
% 2.51/2.69 Axiom fact_671_convex__bound__lt:(forall (V_1:int) (U_1:int) (Y_4:int) (X_5:int) (A_60:int), (((ord_less_int X_5) A_60)->(((ord_less_int Y_4) A_60)->(((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_5)) ((times_times_int V_1) Y_4))) A_60))))))).
% 2.51/2.69 Axiom fact_672_dvd__0__right:(forall (A_59:real), ((dvd_dvd_real A_59) zero_zero_real)).
% 2.51/2.69 Axiom fact_673_dvd__0__right:(forall (A_59:nat), ((dvd_dvd_nat A_59) zero_zero_nat)).
% 2.51/2.69 Axiom fact_674_dvd__0__right:(forall (A_59:int), ((dvd_dvd_int A_59) zero_zero_int)).
% 2.51/2.69 Axiom fact_675_real__le__eq__diff:(forall (X_1:real) (Y_1:real), ((iff ((ord_less_eq_real X_1) Y_1)) ((ord_less_eq_real ((minus_minus_real X_1) Y_1)) zero_zero_real))).
% 2.51/2.69 Axiom fact_676_linorder__neqE__linordered__idom:(forall (X_4:real) (Y_3:real), ((not (((eq real) X_4) Y_3))->((((ord_less_real X_4) Y_3)->False)->((ord_less_real Y_3) X_4)))).
% 2.51/2.69 Axiom fact_677_linorder__neqE__linordered__idom:(forall (X_4:int) (Y_3:int), ((not (((eq int) X_4) Y_3))->((((ord_less_int X_4) Y_3)->False)->((ord_less_int Y_3) X_4)))).
% 2.51/2.69 Axiom fact_678_dvd__refl:(forall (A_58:real), ((dvd_dvd_real A_58) A_58)).
% 2.51/2.69 Axiom fact_679_dvd__refl:(forall (A_58:nat), ((dvd_dvd_nat A_58) A_58)).
% 2.51/2.69 Axiom fact_680_dvd__refl:(forall (A_58:int), ((dvd_dvd_int A_58) A_58)).
% 2.51/2.69 Axiom fact_681_dvd__trans:(forall (C_27:real) (A_57:real) (B_51:real), (((dvd_dvd_real A_57) B_51)->(((dvd_dvd_real B_51) C_27)->((dvd_dvd_real A_57) C_27)))).
% 2.51/2.69 Axiom fact_682_dvd__trans:(forall (C_27:nat) (A_57:nat) (B_51:nat), (((dvd_dvd_nat A_57) B_51)->(((dvd_dvd_nat B_51) C_27)->((dvd_dvd_nat A_57) C_27)))).
% 2.51/2.69 Axiom fact_683_dvd__trans:(forall (C_27:int) (A_57:int) (B_51:int), (((dvd_dvd_int A_57) B_51)->(((dvd_dvd_int B_51) C_27)->((dvd_dvd_int A_57) C_27)))).
% 2.51/2.69 Axiom fact_684_real__zero__not__eq__one:(not (((eq real) zero_zero_real) one_one_real)).
% 2.51/2.69 Axiom fact_685_less__eq__real__def:(forall (X_1:real) (Y_1:real), ((iff ((ord_less_eq_real X_1) Y_1)) ((or ((ord_less_real X_1) Y_1)) (((eq real) X_1) Y_1)))).
% 2.51/2.69 Axiom fact_686_real__less__def:(forall (X_1:real) (Y_1:real), ((iff ((ord_less_real X_1) Y_1)) ((and ((ord_less_eq_real X_1) Y_1)) (not (((eq real) X_1) Y_1))))).
% 2.51/2.69 Axiom fact_687_divides__antisym:(forall (X_1:nat) (Y_1:nat), ((iff ((and ((dvd_dvd_nat X_1) Y_1)) ((dvd_dvd_nat Y_1) X_1))) (((eq nat) X_1) Y_1))).
% 2.51/2.69 Axiom fact_688_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)))).
% 2.51/2.69 Axiom fact_689_real__mult__commute:(forall (Z:real) (W:real), (((eq real) ((times_times_real Z) W)) ((times_times_real W) Z))).
% 2.51/2.69 Axiom fact_690_real__mult__1:(forall (Z:real), (((eq real) ((times_times_real one_one_real) Z)) Z)).
% 2.51/2.69 Axiom fact_691_real__add__left__mono:(forall (Z:real) (X_1:real) (Y_1:real), (((ord_less_eq_real X_1) Y_1)->((ord_less_eq_real ((plus_plus_real Z) X_1)) ((plus_plus_real Z) Y_1)))).
% 2.51/2.69 Axiom fact_692_realpow__minus__mult:(forall (X_3:nat) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq nat) ((times_times_nat ((power_power_nat X_3) ((minus_minus_nat N_2) one_one_nat))) X_3)) ((power_power_nat X_3) N_2)))).
% 2.51/2.69 Axiom fact_693_realpow__minus__mult:(forall (X_3:real) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq real) ((times_times_real ((power_power_real X_3) ((minus_minus_nat N_2) one_one_nat))) X_3)) ((power_power_real X_3) N_2)))).
% 2.51/2.69 Axiom fact_694_realpow__minus__mult:(forall (X_3:int) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq int) ((times_times_int ((power_power_int X_3) ((minus_minus_nat N_2) one_one_nat))) X_3)) ((power_power_int X_3) N_2)))).
% 2.51/2.69 Axiom fact_695_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)))))).
% 2.51/2.69 Axiom fact_696_power__eq__if:(forall (P:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((power_power_nat P) M)) one_one_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((power_power_nat P) M)) ((times_times_nat P) ((power_power_nat P) ((minus_minus_nat M) one_one_nat))))))).
% 2.51/2.69 Axiom fact_697_diff__square:(forall (X_1:nat) (Y_1:nat), (((eq nat) ((minus_minus_nat ((power_power_nat X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((plus_plus_nat X_1) Y_1)) ((minus_minus_nat X_1) Y_1)))).
% 2.51/2.69 Axiom fact_698_divisors__zero:(forall (A_56:real) (B_50:real), ((((eq real) ((times_times_real A_56) B_50)) zero_zero_real)->((or (((eq real) A_56) zero_zero_real)) (((eq real) B_50) zero_zero_real)))).
% 2.51/2.69 Axiom fact_699_divisors__zero:(forall (A_56:nat) (B_50:nat), ((((eq nat) ((times_times_nat A_56) B_50)) zero_zero_nat)->((or (((eq nat) A_56) zero_zero_nat)) (((eq nat) B_50) zero_zero_nat)))).
% 2.51/2.69 Axiom fact_700_divisors__zero:(forall (A_56:int) (B_50:int), ((((eq int) ((times_times_int A_56) B_50)) zero_zero_int)->((or (((eq int) A_56) zero_zero_int)) (((eq int) B_50) zero_zero_int)))).
% 2.51/2.69 Axiom fact_701_no__zero__divisors:(forall (B_49:real) (A_55:real), ((not (((eq real) A_55) zero_zero_real))->((not (((eq real) B_49) zero_zero_real))->(not (((eq real) ((times_times_real A_55) B_49)) zero_zero_real))))).
% 2.51/2.69 Axiom fact_702_no__zero__divisors:(forall (B_49:nat) (A_55:nat), ((not (((eq nat) A_55) zero_zero_nat))->((not (((eq nat) B_49) zero_zero_nat))->(not (((eq nat) ((times_times_nat A_55) B_49)) zero_zero_nat))))).
% 2.51/2.69 Axiom fact_703_no__zero__divisors:(forall (B_49:int) (A_55:int), ((not (((eq int) A_55) zero_zero_int))->((not (((eq int) B_49) zero_zero_int))->(not (((eq int) ((times_times_int A_55) B_49)) zero_zero_int))))).
% 2.51/2.69 Axiom fact_704_mult__eq__0__iff:(forall (A_54:real) (B_48:real), ((iff (((eq real) ((times_times_real A_54) B_48)) zero_zero_real)) ((or (((eq real) A_54) zero_zero_real)) (((eq real) B_48) zero_zero_real)))).
% 2.51/2.69 Axiom fact_705_mult__eq__0__iff:(forall (A_54:int) (B_48:int), ((iff (((eq int) ((times_times_int A_54) B_48)) zero_zero_int)) ((or (((eq int) A_54) zero_zero_int)) (((eq int) B_48) zero_zero_int)))).
% 2.51/2.69 Axiom fact_706_mult__zero__right:(forall (A_53:real), (((eq real) ((times_times_real A_53) zero_zero_real)) zero_zero_real)).
% 2.51/2.69 Axiom fact_707_mult__zero__right:(forall (A_53:nat), (((eq nat) ((times_times_nat A_53) zero_zero_nat)) zero_zero_nat)).
% 2.51/2.69 Axiom fact_708_mult__zero__right:(forall (A_53:int), (((eq int) ((times_times_int A_53) zero_zero_int)) zero_zero_int)).
% 2.51/2.69 Axiom fact_709_mult__zero__left:(forall (A_52:real), (((eq real) ((times_times_real zero_zero_real) A_52)) zero_zero_real)).
% 2.51/2.69 Axiom fact_710_mult__zero__left:(forall (A_52:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_52)) zero_zero_nat)).
% 2.51/2.69 Axiom fact_711_mult__zero__left:(forall (A_52:int), (((eq int) ((times_times_int zero_zero_int) A_52)) zero_zero_int)).
% 2.51/2.69 Axiom fact_712_zero__neq__one:(not (((eq real) zero_zero_real) one_one_real)).
% 2.51/2.69 Axiom fact_713_zero__neq__one:(not (((eq nat) zero_zero_nat) one_one_nat)).
% 2.51/2.69 Axiom fact_714_zero__neq__one:(not (((eq int) zero_zero_int) one_one_int)).
% 2.51/2.69 Axiom fact_715_one__neq__zero:(not (((eq real) one_one_real) zero_zero_real)).
% 2.51/2.69 Axiom fact_716_one__neq__zero:(not (((eq nat) one_one_nat) zero_zero_nat)).
% 2.51/2.69 Axiom fact_717_one__neq__zero:(not (((eq int) one_one_int) zero_zero_int)).
% 2.51/2.69 Axiom fact_718_combine__common__factor:(forall (A_51:real) (E:real) (B_47:real) (C_26:real), (((eq real) ((plus_plus_real ((times_times_real A_51) E)) ((plus_plus_real ((times_times_real B_47) E)) C_26))) ((plus_plus_real ((times_times_real ((plus_plus_real A_51) B_47)) E)) C_26))).
% 2.51/2.69 Axiom fact_719_combine__common__factor:(forall (A_51:nat) (E:nat) (B_47:nat) (C_26:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_51) E)) ((plus_plus_nat ((times_times_nat B_47) E)) C_26))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat A_51) B_47)) E)) C_26))).
% 2.51/2.69 Axiom fact_720_combine__common__factor:(forall (A_51:int) (E:int) (B_47:int) (C_26:int), (((eq int) ((plus_plus_int ((times_times_int A_51) E)) ((plus_plus_int ((times_times_int B_47) E)) C_26))) ((plus_plus_int ((times_times_int ((plus_plus_int A_51) B_47)) E)) C_26))).
% 2.51/2.69 Axiom fact_721_comm__semiring__class_Odistrib:(forall (A_50:real) (B_46:real) (C_25:real), (((eq real) ((times_times_real ((plus_plus_real A_50) B_46)) C_25)) ((plus_plus_real ((times_times_real A_50) C_25)) ((times_times_real B_46) C_25)))).
% 2.51/2.69 Axiom fact_722_comm__semiring__class_Odistrib:(forall (A_50:nat) (B_46:nat) (C_25:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_50) B_46)) C_25)) ((plus_plus_nat ((times_times_nat A_50) C_25)) ((times_times_nat B_46) C_25)))).
% 2.51/2.69 Axiom fact_723_comm__semiring__class_Odistrib:(forall (A_50:int) (B_46:int) (C_25:int), (((eq int) ((times_times_int ((plus_plus_int A_50) B_46)) C_25)) ((plus_plus_int ((times_times_int A_50) C_25)) ((times_times_int B_46) C_25)))).
% 2.51/2.69 Axiom fact_724_dvd__0__left:(forall (A_49:real), (((dvd_dvd_real zero_zero_real) A_49)->(((eq real) A_49) zero_zero_real))).
% 2.51/2.69 Axiom fact_725_dvd__0__left:(forall (A_49:nat), (((dvd_dvd_nat zero_zero_nat) A_49)->(((eq nat) A_49) zero_zero_nat))).
% 2.51/2.69 Axiom fact_726_dvd__0__left:(forall (A_49:int), (((dvd_dvd_int zero_zero_int) A_49)->(((eq int) A_49) zero_zero_int))).
% 2.51/2.69 Axiom fact_727_add__diff__add:(forall (A_48:real) (C_24:real) (B_45:real) (D_6:real), (((eq real) ((minus_minus_real ((plus_plus_real A_48) C_24)) ((plus_plus_real B_45) D_6))) ((plus_plus_real ((minus_minus_real A_48) B_45)) ((minus_minus_real C_24) D_6)))).
% 2.51/2.69 Axiom fact_728_add__diff__add:(forall (A_48:int) (C_24:int) (B_45:int) (D_6:int), (((eq int) ((minus_minus_int ((plus_plus_int A_48) C_24)) ((plus_plus_int B_45) D_6))) ((plus_plus_int ((minus_minus_int A_48) B_45)) ((minus_minus_int C_24) D_6)))).
% 2.51/2.69 Axiom fact_729_dvd__mult__right:(forall (A_47:real) (B_44:real) (C_23:real), (((dvd_dvd_real ((times_times_real A_47) B_44)) C_23)->((dvd_dvd_real B_44) C_23))).
% 2.51/2.69 Axiom fact_730_dvd__mult__right:(forall (A_47:nat) (B_44:nat) (C_23:nat), (((dvd_dvd_nat ((times_times_nat A_47) B_44)) C_23)->((dvd_dvd_nat B_44) C_23))).
% 2.51/2.69 Axiom fact_731_dvd__mult__right:(forall (A_47:int) (B_44:int) (C_23:int), (((dvd_dvd_int ((times_times_int A_47) B_44)) C_23)->((dvd_dvd_int B_44) C_23))).
% 2.51/2.69 Axiom fact_732_dvd__mult__left:(forall (A_46:real) (B_43:real) (C_22:real), (((dvd_dvd_real ((times_times_real A_46) B_43)) C_22)->((dvd_dvd_real A_46) C_22))).
% 2.51/2.69 Axiom fact_733_dvd__mult__left:(forall (A_46:nat) (B_43:nat) (C_22:nat), (((dvd_dvd_nat ((times_times_nat A_46) B_43)) C_22)->((dvd_dvd_nat A_46) C_22))).
% 2.51/2.69 Axiom fact_734_dvd__mult__left:(forall (A_46:int) (B_43:int) (C_22:int), (((dvd_dvd_int ((times_times_int A_46) B_43)) C_22)->((dvd_dvd_int A_46) C_22))).
% 2.51/2.69 Axiom fact_735_dvdI:(forall (A_45:real) (B_42:real) (K_2:real), ((((eq real) A_45) ((times_times_real B_42) K_2))->((dvd_dvd_real B_42) A_45))).
% 2.51/2.69 Axiom fact_736_dvdI:(forall (A_45:nat) (B_42:nat) (K_2:nat), ((((eq nat) A_45) ((times_times_nat B_42) K_2))->((dvd_dvd_nat B_42) A_45))).
% 2.51/2.69 Axiom fact_737_dvdI:(forall (A_45:int) (B_42:int) (K_2:int), ((((eq int) A_45) ((times_times_int B_42) K_2))->((dvd_dvd_int B_42) A_45))).
% 2.51/2.69 Axiom fact_738_mult__dvd__mono:(forall (C_21:real) (D_5:real) (A_44:real) (B_41:real), (((dvd_dvd_real A_44) B_41)->(((dvd_dvd_real C_21) D_5)->((dvd_dvd_real ((times_times_real A_44) C_21)) ((times_times_real B_41) D_5))))).
% 2.51/2.69 Axiom fact_739_mult__dvd__mono:(forall (C_21:nat) (D_5:nat) (A_44:nat) (B_41:nat), (((dvd_dvd_nat A_44) B_41)->(((dvd_dvd_nat C_21) D_5)->((dvd_dvd_nat ((times_times_nat A_44) C_21)) ((times_times_nat B_41) D_5))))).
% 2.51/2.70 Axiom fact_740_mult__dvd__mono:(forall (C_21:int) (D_5:int) (A_44:int) (B_41:int), (((dvd_dvd_int A_44) B_41)->(((dvd_dvd_int C_21) D_5)->((dvd_dvd_int ((times_times_int A_44) C_21)) ((times_times_int B_41) D_5))))).
% 2.51/2.70 Axiom fact_741_dvd__mult:(forall (B_40:real) (A_43:real) (C_20:real), (((dvd_dvd_real A_43) C_20)->((dvd_dvd_real A_43) ((times_times_real B_40) C_20)))).
% 2.51/2.70 Axiom fact_742_dvd__mult:(forall (B_40:nat) (A_43:nat) (C_20:nat), (((dvd_dvd_nat A_43) C_20)->((dvd_dvd_nat A_43) ((times_times_nat B_40) C_20)))).
% 2.51/2.70 Axiom fact_743_dvd__mult:(forall (B_40:int) (A_43:int) (C_20:int), (((dvd_dvd_int A_43) C_20)->((dvd_dvd_int A_43) ((times_times_int B_40) C_20)))).
% 2.51/2.70 Axiom fact_744_dvd__mult2:(forall (C_19:real) (A_42:real) (B_39:real), (((dvd_dvd_real A_42) B_39)->((dvd_dvd_real A_42) ((times_times_real B_39) C_19)))).
% 2.51/2.70 Axiom fact_745_dvd__mult2:(forall (C_19:nat) (A_42:nat) (B_39:nat), (((dvd_dvd_nat A_42) B_39)->((dvd_dvd_nat A_42) ((times_times_nat B_39) C_19)))).
% 2.51/2.70 Axiom fact_746_dvd__mult2:(forall (C_19:int) (A_42:int) (B_39:int), (((dvd_dvd_int A_42) B_39)->((dvd_dvd_int A_42) ((times_times_int B_39) C_19)))).
% 2.51/2.70 Axiom fact_747_dvd__triv__right:(forall (A_41:real) (B_38:real), ((dvd_dvd_real A_41) ((times_times_real B_38) A_41))).
% 2.51/2.70 Axiom fact_748_dvd__triv__right:(forall (A_41:nat) (B_38:nat), ((dvd_dvd_nat A_41) ((times_times_nat B_38) A_41))).
% 2.51/2.70 Axiom fact_749_dvd__triv__right:(forall (A_41:int) (B_38:int), ((dvd_dvd_int A_41) ((times_times_int B_38) A_41))).
% 2.51/2.70 Axiom fact_750_dvd__triv__left:(forall (A_40:real) (B_37:real), ((dvd_dvd_real A_40) ((times_times_real A_40) B_37))).
% 2.51/2.70 Axiom fact_751_dvd__triv__left:(forall (A_40:nat) (B_37:nat), ((dvd_dvd_nat A_40) ((times_times_nat A_40) B_37))).
% 2.51/2.70 Axiom fact_752_dvd__triv__left:(forall (A_40:int) (B_37:int), ((dvd_dvd_int A_40) ((times_times_int A_40) B_37))).
% 2.51/2.70 Axiom fact_753_dvd__add:(forall (C_18:real) (A_39:real) (B_36:real), (((dvd_dvd_real A_39) B_36)->(((dvd_dvd_real A_39) C_18)->((dvd_dvd_real A_39) ((plus_plus_real B_36) C_18))))).
% 2.51/2.70 Axiom fact_754_dvd__add:(forall (C_18:nat) (A_39:nat) (B_36:nat), (((dvd_dvd_nat A_39) B_36)->(((dvd_dvd_nat A_39) C_18)->((dvd_dvd_nat A_39) ((plus_plus_nat B_36) C_18))))).
% 2.51/2.70 Axiom fact_755_dvd__add:(forall (C_18:int) (A_39:int) (B_36:int), (((dvd_dvd_int A_39) B_36)->(((dvd_dvd_int A_39) C_18)->((dvd_dvd_int A_39) ((plus_plus_int B_36) C_18))))).
% 2.51/2.70 Axiom fact_756_one__dvd:(forall (A_38:real), ((dvd_dvd_real one_one_real) A_38)).
% 2.51/2.70 Axiom fact_757_one__dvd:(forall (A_38:nat), ((dvd_dvd_nat one_one_nat) A_38)).
% 2.51/2.70 Axiom fact_758_one__dvd:(forall (A_38:int), ((dvd_dvd_int one_one_int) A_38)).
% 2.51/2.70 Axiom fact_759_dvd__diff:(forall (Z_1:real) (X_2:real) (Y_2:real), (((dvd_dvd_real X_2) Y_2)->(((dvd_dvd_real X_2) Z_1)->((dvd_dvd_real X_2) ((minus_minus_real Y_2) Z_1))))).
% 2.51/2.70 Axiom fact_760_dvd__diff:(forall (Z_1:int) (X_2:int) (Y_2:int), (((dvd_dvd_int X_2) Y_2)->(((dvd_dvd_int X_2) Z_1)->((dvd_dvd_int X_2) ((minus_minus_int Y_2) Z_1))))).
% 2.51/2.70 Axiom fact_761_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)))).
% 2.51/2.70 Axiom fact_762_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)))).
% 2.51/2.70 Axiom fact_763_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)))).
% 2.51/2.70 Axiom fact_764_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)))).
% 2.51/2.70 Axiom fact_765_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)))).
% 2.51/2.70 Axiom fact_766_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)))).
% 2.51/2.70 Axiom fact_767_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)))).
% 2.51/2.70 Axiom fact_768_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)))).
% 2.51/2.70 Axiom fact_769_divides__exp:(forall (N:nat) (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->((dvd_dvd_nat ((power_power_nat X_1) N)) ((power_power_nat Y_1) N)))).
% 2.51/2.70 Axiom fact_770_split__mult__neg__le:(forall (B_35:real) (A_37:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_37)) ((ord_less_eq_real B_35) zero_zero_real))) ((and ((ord_less_eq_real A_37) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_35)))->((ord_less_eq_real ((times_times_real A_37) B_35)) zero_zero_real))).
% 2.51/2.70 Axiom fact_771_split__mult__neg__le:(forall (B_35:nat) (A_37:nat), (((or ((and ((ord_less_eq_nat zero_zero_nat) A_37)) ((ord_less_eq_nat B_35) zero_zero_nat))) ((and ((ord_less_eq_nat A_37) zero_zero_nat)) ((ord_less_eq_nat zero_zero_nat) B_35)))->((ord_less_eq_nat ((times_times_nat A_37) B_35)) zero_zero_nat))).
% 2.51/2.70 Axiom fact_772_split__mult__neg__le:(forall (B_35:int) (A_37:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_37)) ((ord_less_eq_int B_35) zero_zero_int))) ((and ((ord_less_eq_int A_37) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_35)))->((ord_less_eq_int ((times_times_int A_37) B_35)) zero_zero_int))).
% 2.51/2.70 Axiom fact_773_split__mult__pos__le:(forall (B_34:real) (A_36:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_36)) ((ord_less_eq_real zero_zero_real) B_34))) ((and ((ord_less_eq_real A_36) zero_zero_real)) ((ord_less_eq_real B_34) zero_zero_real)))->((ord_less_eq_real zero_zero_real) ((times_times_real A_36) B_34)))).
% 2.51/2.70 Axiom fact_774_split__mult__pos__le:(forall (B_34:int) (A_36:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_36)) ((ord_less_eq_int zero_zero_int) B_34))) ((and ((ord_less_eq_int A_36) zero_zero_int)) ((ord_less_eq_int B_34) zero_zero_int)))->((ord_less_eq_int zero_zero_int) ((times_times_int A_36) B_34)))).
% 2.51/2.70 Axiom fact_775_mult__mono:(forall (C_17:real) (D_4:real) (A_35:real) (B_33:real), (((ord_less_eq_real A_35) B_33)->(((ord_less_eq_real C_17) D_4)->(((ord_less_eq_real zero_zero_real) B_33)->(((ord_less_eq_real zero_zero_real) C_17)->((ord_less_eq_real ((times_times_real A_35) C_17)) ((times_times_real B_33) D_4))))))).
% 2.51/2.70 Axiom fact_776_mult__mono:(forall (C_17:nat) (D_4:nat) (A_35:nat) (B_33:nat), (((ord_less_eq_nat A_35) B_33)->(((ord_less_eq_nat C_17) D_4)->(((ord_less_eq_nat zero_zero_nat) B_33)->(((ord_less_eq_nat zero_zero_nat) C_17)->((ord_less_eq_nat ((times_times_nat A_35) C_17)) ((times_times_nat B_33) D_4))))))).
% 2.51/2.70 Axiom fact_777_mult__mono:(forall (C_17:int) (D_4:int) (A_35:int) (B_33:int), (((ord_less_eq_int A_35) B_33)->(((ord_less_eq_int C_17) D_4)->(((ord_less_eq_int zero_zero_int) B_33)->(((ord_less_eq_int zero_zero_int) C_17)->((ord_less_eq_int ((times_times_int A_35) C_17)) ((times_times_int B_33) D_4))))))).
% 2.51/2.70 Axiom fact_778_mult__mono_H:(forall (C_16:real) (D_3:real) (A_34:real) (B_32:real), (((ord_less_eq_real A_34) B_32)->(((ord_less_eq_real C_16) D_3)->(((ord_less_eq_real zero_zero_real) A_34)->(((ord_less_eq_real zero_zero_real) C_16)->((ord_less_eq_real ((times_times_real A_34) C_16)) ((times_times_real B_32) D_3))))))).
% 2.51/2.70 Axiom fact_779_mult__mono_H:(forall (C_16:nat) (D_3:nat) (A_34:nat) (B_32:nat), (((ord_less_eq_nat A_34) B_32)->(((ord_less_eq_nat C_16) D_3)->(((ord_less_eq_nat zero_zero_nat) A_34)->(((ord_less_eq_nat zero_zero_nat) C_16)->((ord_less_eq_nat ((times_times_nat A_34) C_16)) ((times_times_nat B_32) D_3))))))).
% 2.51/2.70 Axiom fact_780_mult__mono_H:(forall (C_16:int) (D_3:int) (A_34:int) (B_32:int), (((ord_less_eq_int A_34) B_32)->(((ord_less_eq_int C_16) D_3)->(((ord_less_eq_int zero_zero_int) A_34)->(((ord_less_eq_int zero_zero_int) C_16)->((ord_less_eq_int ((times_times_int A_34) C_16)) ((times_times_int B_32) D_3))))))).
% 2.51/2.70 Axiom fact_781_mult__left__mono__neg:(forall (C_15:real) (B_31:real) (A_33:real), (((ord_less_eq_real B_31) A_33)->(((ord_less_eq_real C_15) zero_zero_real)->((ord_less_eq_real ((times_times_real C_15) A_33)) ((times_times_real C_15) B_31))))).
% 2.51/2.70 Axiom fact_782_mult__left__mono__neg:(forall (C_15:int) (B_31:int) (A_33:int), (((ord_less_eq_int B_31) A_33)->(((ord_less_eq_int C_15) zero_zero_int)->((ord_less_eq_int ((times_times_int C_15) A_33)) ((times_times_int C_15) B_31))))).
% 2.51/2.70 Axiom fact_783_mult__right__mono__neg:(forall (C_14:real) (B_30:real) (A_32:real), (((ord_less_eq_real B_30) A_32)->(((ord_less_eq_real C_14) zero_zero_real)->((ord_less_eq_real ((times_times_real A_32) C_14)) ((times_times_real B_30) C_14))))).
% 2.51/2.70 Axiom fact_784_mult__right__mono__neg:(forall (C_14:int) (B_30:int) (A_32:int), (((ord_less_eq_int B_30) A_32)->(((ord_less_eq_int C_14) zero_zero_int)->((ord_less_eq_int ((times_times_int A_32) C_14)) ((times_times_int B_30) C_14))))).
% 2.51/2.70 Axiom fact_785_comm__mult__left__mono:(forall (C_13:real) (A_31:real) (B_29:real), (((ord_less_eq_real A_31) B_29)->(((ord_less_eq_real zero_zero_real) C_13)->((ord_less_eq_real ((times_times_real C_13) A_31)) ((times_times_real C_13) B_29))))).
% 2.51/2.70 Axiom fact_786_comm__mult__left__mono:(forall (C_13:nat) (A_31:nat) (B_29:nat), (((ord_less_eq_nat A_31) B_29)->(((ord_less_eq_nat zero_zero_nat) C_13)->((ord_less_eq_nat ((times_times_nat C_13) A_31)) ((times_times_nat C_13) B_29))))).
% 2.51/2.70 Axiom fact_787_comm__mult__left__mono:(forall (C_13:int) (A_31:int) (B_29:int), (((ord_less_eq_int A_31) B_29)->(((ord_less_eq_int zero_zero_int) C_13)->((ord_less_eq_int ((times_times_int C_13) A_31)) ((times_times_int C_13) B_29))))).
% 2.51/2.70 Axiom fact_788_mult__left__mono:(forall (C_12:real) (A_30:real) (B_28:real), (((ord_less_eq_real A_30) B_28)->(((ord_less_eq_real zero_zero_real) C_12)->((ord_less_eq_real ((times_times_real C_12) A_30)) ((times_times_real C_12) B_28))))).
% 2.51/2.70 Axiom fact_789_mult__left__mono:(forall (C_12:nat) (A_30:nat) (B_28:nat), (((ord_less_eq_nat A_30) B_28)->(((ord_less_eq_nat zero_zero_nat) C_12)->((ord_less_eq_nat ((times_times_nat C_12) A_30)) ((times_times_nat C_12) B_28))))).
% 2.51/2.70 Axiom fact_790_mult__left__mono:(forall (C_12:int) (A_30:int) (B_28:int), (((ord_less_eq_int A_30) B_28)->(((ord_less_eq_int zero_zero_int) C_12)->((ord_less_eq_int ((times_times_int C_12) A_30)) ((times_times_int C_12) B_28))))).
% 2.51/2.70 Axiom fact_791_mult__right__mono:(forall (C_11:real) (A_29:real) (B_27:real), (((ord_less_eq_real A_29) B_27)->(((ord_less_eq_real zero_zero_real) C_11)->((ord_less_eq_real ((times_times_real A_29) C_11)) ((times_times_real B_27) C_11))))).
% 2.51/2.70 Axiom fact_792_mult__right__mono:(forall (C_11:nat) (A_29:nat) (B_27:nat), (((ord_less_eq_nat A_29) B_27)->(((ord_less_eq_nat zero_zero_nat) C_11)->((ord_less_eq_nat ((times_times_nat A_29) C_11)) ((times_times_nat B_27) C_11))))).
% 2.51/2.70 Axiom fact_793_mult__right__mono:(forall (C_11:int) (A_29:int) (B_27:int), (((ord_less_eq_int A_29) B_27)->(((ord_less_eq_int zero_zero_int) C_11)->((ord_less_eq_int ((times_times_int A_29) C_11)) ((times_times_int B_27) C_11))))).
% 2.51/2.70 Axiom fact_794_mult__nonpos__nonpos:(forall (B_26:real) (A_28:real), (((ord_less_eq_real A_28) zero_zero_real)->(((ord_less_eq_real B_26) zero_zero_real)->((ord_less_eq_real zero_zero_real) ((times_times_real A_28) B_26))))).
% 2.51/2.70 Axiom fact_795_mult__nonpos__nonpos:(forall (B_26:int) (A_28:int), (((ord_less_eq_int A_28) zero_zero_int)->(((ord_less_eq_int B_26) zero_zero_int)->((ord_less_eq_int zero_zero_int) ((times_times_int A_28) B_26))))).
% 2.51/2.70 Axiom fact_796_mult__nonpos__nonneg:(forall (B_25:real) (A_27:real), (((ord_less_eq_real A_27) zero_zero_real)->(((ord_less_eq_real zero_zero_real) B_25)->((ord_less_eq_real ((times_times_real A_27) B_25)) zero_zero_real)))).
% 2.51/2.70 Axiom fact_797_mult__nonpos__nonneg:(forall (B_25:nat) (A_27:nat), (((ord_less_eq_nat A_27) zero_zero_nat)->(((ord_less_eq_nat zero_zero_nat) B_25)->((ord_less_eq_nat ((times_times_nat A_27) B_25)) zero_zero_nat)))).
% 2.51/2.70 Axiom fact_798_mult__nonpos__nonneg:(forall (B_25:int) (A_27:int), (((ord_less_eq_int A_27) zero_zero_int)->(((ord_less_eq_int zero_zero_int) B_25)->((ord_less_eq_int ((times_times_int A_27) B_25)) zero_zero_int)))).
% 2.51/2.70 Axiom fact_799_mult__nonneg__nonpos2:(forall (B_24:real) (A_26:real), (((ord_less_eq_real zero_zero_real) A_26)->(((ord_less_eq_real B_24) zero_zero_real)->((ord_less_eq_real ((times_times_real B_24) A_26)) zero_zero_real)))).
% 2.51/2.70 Axiom fact_800_mult__nonneg__nonpos2:(forall (B_24:nat) (A_26:nat), (((ord_less_eq_nat zero_zero_nat) A_26)->(((ord_less_eq_nat B_24) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat B_24) A_26)) zero_zero_nat)))).
% 2.51/2.70 Axiom fact_801_mult__nonneg__nonpos2:(forall (B_24:int) (A_26:int), (((ord_less_eq_int zero_zero_int) A_26)->(((ord_less_eq_int B_24) zero_zero_int)->((ord_less_eq_int ((times_times_int B_24) A_26)) zero_zero_int)))).
% 2.51/2.70 Axiom fact_802_mult__nonneg__nonpos:(forall (B_23:real) (A_25:real), (((ord_less_eq_real zero_zero_real) A_25)->(((ord_less_eq_real B_23) zero_zero_real)->((ord_less_eq_real ((times_times_real A_25) B_23)) zero_zero_real)))).
% 2.51/2.70 Axiom fact_803_mult__nonneg__nonpos:(forall (B_23:nat) (A_25:nat), (((ord_less_eq_nat zero_zero_nat) A_25)->(((ord_less_eq_nat B_23) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat A_25) B_23)) zero_zero_nat)))).
% 2.51/2.70 Axiom fact_804_mult__nonneg__nonpos:(forall (B_23:int) (A_25:int), (((ord_less_eq_int zero_zero_int) A_25)->(((ord_less_eq_int B_23) zero_zero_int)->((ord_less_eq_int ((times_times_int A_25) B_23)) zero_zero_int)))).
% 2.51/2.70 Axiom fact_805_mult__nonneg__nonneg:(forall (B_22:real) (A_24:real), (((ord_less_eq_real zero_zero_real) A_24)->(((ord_less_eq_real zero_zero_real) B_22)->((ord_less_eq_real zero_zero_real) ((times_times_real A_24) B_22))))).
% 2.51/2.70 Axiom fact_806_mult__nonneg__nonneg:(forall (B_22:nat) (A_24:nat), (((ord_less_eq_nat zero_zero_nat) A_24)->(((ord_less_eq_nat zero_zero_nat) B_22)->((ord_less_eq_nat zero_zero_nat) ((times_times_nat A_24) B_22))))).
% 2.51/2.70 Axiom fact_807_mult__nonneg__nonneg:(forall (B_22:int) (A_24:int), (((ord_less_eq_int zero_zero_int) A_24)->(((ord_less_eq_int zero_zero_int) B_22)->((ord_less_eq_int zero_zero_int) ((times_times_int A_24) B_22))))).
% 2.51/2.70 Axiom fact_808_mult__le__0__iff:(forall (A_23:real) (B_21:real), ((iff ((ord_less_eq_real ((times_times_real A_23) B_21)) zero_zero_real)) ((or ((and ((ord_less_eq_real zero_zero_real) A_23)) ((ord_less_eq_real B_21) zero_zero_real))) ((and ((ord_less_eq_real A_23) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_21))))).
% 2.51/2.70 Axiom fact_809_mult__le__0__iff:(forall (A_23:int) (B_21:int), ((iff ((ord_less_eq_int ((times_times_int A_23) B_21)) zero_zero_int)) ((or ((and ((ord_less_eq_int zero_zero_int) A_23)) ((ord_less_eq_int B_21) zero_zero_int))) ((and ((ord_less_eq_int A_23) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_21))))).
% 2.51/2.70 Axiom fact_810_zero__le__mult__iff:(forall (A_22:real) (B_20:real), ((iff ((ord_less_eq_real zero_zero_real) ((times_times_real A_22) B_20))) ((or ((and ((ord_less_eq_real zero_zero_real) A_22)) ((ord_less_eq_real zero_zero_real) B_20))) ((and ((ord_less_eq_real A_22) zero_zero_real)) ((ord_less_eq_real B_20) zero_zero_real))))).
% 2.51/2.70 Axiom fact_811_zero__le__mult__iff:(forall (A_22:int) (B_20:int), ((iff ((ord_less_eq_int zero_zero_int) ((times_times_int A_22) B_20))) ((or ((and ((ord_less_eq_int zero_zero_int) A_22)) ((ord_less_eq_int zero_zero_int) B_20))) ((and ((ord_less_eq_int A_22) zero_zero_int)) ((ord_less_eq_int B_20) zero_zero_int))))).
% 2.51/2.70 Axiom fact_812_zero__le__square:(forall (A_21:real), ((ord_less_eq_real zero_zero_real) ((times_times_real A_21) A_21))).
% 2.51/2.70 Axiom fact_813_zero__le__square:(forall (A_21:int), ((ord_less_eq_int zero_zero_int) ((times_times_int A_21) A_21))).
% 2.51/2.70 Axiom fact_814_mult__strict__left__mono__neg:(forall (C_10:real) (B_19:real) (A_20:real), (((ord_less_real B_19) A_20)->(((ord_less_real C_10) zero_zero_real)->((ord_less_real ((times_times_real C_10) A_20)) ((times_times_real C_10) B_19))))).
% 2.51/2.70 Axiom fact_815_mult__strict__left__mono__neg:(forall (C_10:int) (B_19:int) (A_20:int), (((ord_less_int B_19) A_20)->(((ord_less_int C_10) zero_zero_int)->((ord_less_int ((times_times_int C_10) A_20)) ((times_times_int C_10) B_19))))).
% 2.51/2.70 Axiom fact_816_mult__strict__right__mono__neg:(forall (C_9:real) (B_18:real) (A_19:real), (((ord_less_real B_18) A_19)->(((ord_less_real C_9) zero_zero_real)->((ord_less_real ((times_times_real A_19) C_9)) ((times_times_real B_18) C_9))))).
% 2.51/2.70 Axiom fact_817_mult__strict__right__mono__neg:(forall (C_9:int) (B_18:int) (A_19:int), (((ord_less_int B_18) A_19)->(((ord_less_int C_9) zero_zero_int)->((ord_less_int ((times_times_int A_19) C_9)) ((times_times_int B_18) C_9))))).
% 2.51/2.70 Axiom fact_818_comm__mult__strict__left__mono:(forall (C_8:real) (A_18:real) (B_17:real), (((ord_less_real A_18) B_17)->(((ord_less_real zero_zero_real) C_8)->((ord_less_real ((times_times_real C_8) A_18)) ((times_times_real C_8) B_17))))).
% 2.51/2.70 Axiom fact_819_comm__mult__strict__left__mono:(forall (C_8:nat) (A_18:nat) (B_17:nat), (((ord_less_nat A_18) B_17)->(((ord_less_nat zero_zero_nat) C_8)->((ord_less_nat ((times_times_nat C_8) A_18)) ((times_times_nat C_8) B_17))))).
% 2.51/2.70 Axiom fact_820_comm__mult__strict__left__mono:(forall (C_8:int) (A_18:int) (B_17:int), (((ord_less_int A_18) B_17)->(((ord_less_int zero_zero_int) C_8)->((ord_less_int ((times_times_int C_8) A_18)) ((times_times_int C_8) B_17))))).
% 2.51/2.70 Axiom fact_821_mult__strict__left__mono:(forall (C_7:real) (A_17:real) (B_16:real), (((ord_less_real A_17) B_16)->(((ord_less_real zero_zero_real) C_7)->((ord_less_real ((times_times_real C_7) A_17)) ((times_times_real C_7) B_16))))).
% 2.51/2.70 Axiom fact_822_mult__strict__left__mono:(forall (C_7:nat) (A_17:nat) (B_16:nat), (((ord_less_nat A_17) B_16)->(((ord_less_nat zero_zero_nat) C_7)->((ord_less_nat ((times_times_nat C_7) A_17)) ((times_times_nat C_7) B_16))))).
% 2.51/2.70 Axiom fact_823_mult__strict__left__mono:(forall (C_7:int) (A_17:int) (B_16:int), (((ord_less_int A_17) B_16)->(((ord_less_int zero_zero_int) C_7)->((ord_less_int ((times_times_int C_7) A_17)) ((times_times_int C_7) B_16))))).
% 2.51/2.70 Axiom fact_824_mult__strict__right__mono:(forall (C_6:real) (A_16:real) (B_15:real), (((ord_less_real A_16) B_15)->(((ord_less_real zero_zero_real) C_6)->((ord_less_real ((times_times_real A_16) C_6)) ((times_times_real B_15) C_6))))).
% 2.51/2.70 Axiom fact_825_mult__strict__right__mono:(forall (C_6:nat) (A_16:nat) (B_15:nat), (((ord_less_nat A_16) B_15)->(((ord_less_nat zero_zero_nat) C_6)->((ord_less_nat ((times_times_nat A_16) C_6)) ((times_times_nat B_15) C_6))))).
% 2.51/2.70 Axiom fact_826_mult__strict__right__mono:(forall (C_6:int) (A_16:int) (B_15:int), (((ord_less_int A_16) B_15)->(((ord_less_int zero_zero_int) C_6)->((ord_less_int ((times_times_int A_16) C_6)) ((times_times_int B_15) C_6))))).
% 2.51/2.70 Axiom fact_827_mult__neg__neg:(forall (B_14:real) (A_15:real), (((ord_less_real A_15) zero_zero_real)->(((ord_less_real B_14) zero_zero_real)->((ord_less_real zero_zero_real) ((times_times_real A_15) B_14))))).
% 2.51/2.70 Axiom fact_828_mult__neg__neg:(forall (B_14:int) (A_15:int), (((ord_less_int A_15) zero_zero_int)->(((ord_less_int B_14) zero_zero_int)->((ord_less_int zero_zero_int) ((times_times_int A_15) B_14))))).
% 2.51/2.70 Axiom fact_829_mult__neg__pos:(forall (B_13:real) (A_14:real), (((ord_less_real A_14) zero_zero_real)->(((ord_less_real zero_zero_real) B_13)->((ord_less_real ((times_times_real A_14) B_13)) zero_zero_real)))).
% 2.51/2.70 Axiom fact_830_mult__neg__pos:(forall (B_13:nat) (A_14:nat), (((ord_less_nat A_14) zero_zero_nat)->(((ord_less_nat zero_zero_nat) B_13)->((ord_less_nat ((times_times_nat A_14) B_13)) zero_zero_nat)))).
% 2.51/2.70 Axiom fact_831_mult__neg__pos:(forall (B_13:int) (A_14:int), (((ord_less_int A_14) zero_zero_int)->(((ord_less_int zero_zero_int) B_13)->((ord_less_int ((times_times_int A_14) B_13)) zero_zero_int)))).
% 2.51/2.70 Axiom fact_832_mult__less__cancel__left__neg:(forall (A_13:real) (B_12:real) (C_5:real), (((ord_less_real C_5) zero_zero_real)->((iff ((ord_less_real ((times_times_real C_5) A_13)) ((times_times_real C_5) B_12))) ((ord_less_real B_12) A_13)))).
% 2.51/2.70 Axiom fact_833_mult__less__cancel__left__neg:(forall (A_13:int) (B_12:int) (C_5:int), (((ord_less_int C_5) zero_zero_int)->((iff ((ord_less_int ((times_times_int C_5) A_13)) ((times_times_int C_5) B_12))) ((ord_less_int B_12) A_13)))).
% 2.51/2.70 Axiom fact_834_zero__less__mult__pos2:(forall (B_11:real) (A_12:real), (((ord_less_real zero_zero_real) ((times_times_real B_11) A_12))->(((ord_less_real zero_zero_real) A_12)->((ord_less_real zero_zero_real) B_11)))).
% 2.51/2.70 Axiom fact_835_zero__less__mult__pos2:(forall (B_11:nat) (A_12:nat), (((ord_less_nat zero_zero_nat) ((times_times_nat B_11) A_12))->(((ord_less_nat zero_zero_nat) A_12)->((ord_less_nat zero_zero_nat) B_11)))).
% 2.51/2.70 Axiom fact_836_zero__less__mult__pos2:(forall (B_11:int) (A_12:int), (((ord_less_int zero_zero_int) ((times_times_int B_11) A_12))->(((ord_less_int zero_zero_int) A_12)->((ord_less_int zero_zero_int) B_11)))).
% 2.51/2.70 Axiom fact_837_zero__less__mult__pos:(forall (A_11:real) (B_10:real), (((ord_less_real zero_zero_real) ((times_times_real A_11) B_10))->(((ord_less_real zero_zero_real) A_11)->((ord_less_real zero_zero_real) B_10)))).
% 2.51/2.70 Axiom fact_838_zero__less__mult__pos:(forall (A_11:nat) (B_10:nat), (((ord_less_nat zero_zero_nat) ((times_times_nat A_11) B_10))->(((ord_less_nat zero_zero_nat) A_11)->((ord_less_nat zero_zero_nat) B_10)))).
% 2.51/2.70 Axiom fact_839_zero__less__mult__pos:(forall (A_11:int) (B_10:int), (((ord_less_int zero_zero_int) ((times_times_int A_11) B_10))->(((ord_less_int zero_zero_int) A_11)->((ord_less_int zero_zero_int) B_10)))).
% 2.51/2.70 Axiom fact_840_mult__pos__neg2:(forall (B_9:real) (A_10:real), (((ord_less_real zero_zero_real) A_10)->(((ord_less_real B_9) zero_zero_real)->((ord_less_real ((times_times_real B_9) A_10)) zero_zero_real)))).
% 2.51/2.70 Axiom fact_841_mult__pos__neg2:(forall (B_9:nat) (A_10:nat), (((ord_less_nat zero_zero_nat) A_10)->(((ord_less_nat B_9) zero_zero_nat)->((ord_less_nat ((times_times_nat B_9) A_10)) zero_zero_nat)))).
% 2.51/2.70 Axiom fact_842_mult__pos__neg2:(forall (B_9:int) (A_10:int), (((ord_less_int zero_zero_int) A_10)->(((ord_less_int B_9) zero_zero_int)->((ord_less_int ((times_times_int B_9) A_10)) zero_zero_int)))).
% 2.51/2.70 Axiom fact_843_mult__pos__neg:(forall (B_8:real) (A_9:real), (((ord_less_real zero_zero_real) A_9)->(((ord_less_real B_8) zero_zero_real)->((ord_less_real ((times_times_real A_9) B_8)) zero_zero_real)))).
% 2.51/2.70 Axiom fact_844_mult__pos__neg:(forall (B_8:nat) (A_9:nat), (((ord_less_nat zero_zero_nat) A_9)->(((ord_less_nat B_8) zero_zero_nat)->((ord_less_nat ((times_times_nat A_9) B_8)) zero_zero_nat)))).
% 2.51/2.70 Axiom fact_845_mult__pos__neg:(forall (B_8:int) (A_9:int), (((ord_less_int zero_zero_int) A_9)->(((ord_less_int B_8) zero_zero_int)->((ord_less_int ((times_times_int A_9) B_8)) zero_zero_int)))).
% 2.51/2.70 Axiom fact_846_mult__pos__pos:(forall (B_7:real) (A_8:real), (((ord_less_real zero_zero_real) A_8)->(((ord_less_real zero_zero_real) B_7)->((ord_less_real zero_zero_real) ((times_times_real A_8) B_7))))).
% 2.51/2.70 Axiom fact_847_mult__pos__pos:(forall (B_7:nat) (A_8:nat), (((ord_less_nat zero_zero_nat) A_8)->(((ord_less_nat zero_zero_nat) B_7)->((ord_less_nat zero_zero_nat) ((times_times_nat A_8) B_7))))).
% 2.51/2.70 Axiom fact_848_mult__pos__pos:(forall (B_7:int) (A_8:int), (((ord_less_int zero_zero_int) A_8)->(((ord_less_int zero_zero_int) B_7)->((ord_less_int zero_zero_int) ((times_times_int A_8) B_7))))).
% 2.51/2.70 Axiom fact_849_mult__less__cancel__left__pos:(forall (A_7:real) (B_6:real) (C_4:real), (((ord_less_real zero_zero_real) C_4)->((iff ((ord_less_real ((times_times_real C_4) A_7)) ((times_times_real C_4) B_6))) ((ord_less_real A_7) B_6)))).
% 2.51/2.70 Axiom fact_850_mult__less__cancel__left__pos:(forall (A_7:int) (B_6:int) (C_4:int), (((ord_less_int zero_zero_int) C_4)->((iff ((ord_less_int ((times_times_int C_4) A_7)) ((times_times_int C_4) B_6))) ((ord_less_int A_7) B_6)))).
% 2.51/2.70 Axiom fact_851_mult__less__cancel__left__disj:(forall (C_3:real) (A_6:real) (B_5:real), ((iff ((ord_less_real ((times_times_real C_3) A_6)) ((times_times_real C_3) B_5))) ((or ((and ((ord_less_real zero_zero_real) C_3)) ((ord_less_real A_6) B_5))) ((and ((ord_less_real C_3) zero_zero_real)) ((ord_less_real B_5) A_6))))).
% 2.51/2.70 Axiom fact_852_mult__less__cancel__left__disj:(forall (C_3:int) (A_6:int) (B_5:int), ((iff ((ord_less_int ((times_times_int C_3) A_6)) ((times_times_int C_3) B_5))) ((or ((and ((ord_less_int zero_zero_int) C_3)) ((ord_less_int A_6) B_5))) ((and ((ord_less_int C_3) zero_zero_int)) ((ord_less_int B_5) A_6))))).
% 2.51/2.70 Axiom fact_853_mult__less__cancel__right__disj:(forall (A_5:real) (C_2:real) (B_4:real), ((iff ((ord_less_real ((times_times_real A_5) C_2)) ((times_times_real B_4) C_2))) ((or ((and ((ord_less_real zero_zero_real) C_2)) ((ord_less_real A_5) B_4))) ((and ((ord_less_real C_2) zero_zero_real)) ((ord_less_real B_4) A_5))))).
% 2.51/2.71 Axiom fact_854_mult__less__cancel__right__disj:(forall (A_5:int) (C_2:int) (B_4:int), ((iff ((ord_less_int ((times_times_int A_5) C_2)) ((times_times_int B_4) C_2))) ((or ((and ((ord_less_int zero_zero_int) C_2)) ((ord_less_int A_5) B_4))) ((and ((ord_less_int C_2) zero_zero_int)) ((ord_less_int B_4) A_5))))).
% 2.51/2.71 Axiom fact_855_not__square__less__zero:(forall (A_4:real), (((ord_less_real ((times_times_real A_4) A_4)) zero_zero_real)->False)).
% 2.51/2.71 Axiom fact_856_not__square__less__zero:(forall (A_4:int), (((ord_less_int ((times_times_int A_4) A_4)) zero_zero_int)->False)).
% 2.51/2.71 Axiom fact_857_pos__add__strict:(forall (B_3:nat) (C_1:nat) (A_3:nat), (((ord_less_nat zero_zero_nat) A_3)->(((ord_less_nat B_3) C_1)->((ord_less_nat B_3) ((plus_plus_nat A_3) C_1))))).
% 2.51/2.71 Axiom fact_858_pos__add__strict:(forall (B_3:int) (C_1:int) (A_3:int), (((ord_less_int zero_zero_int) A_3)->(((ord_less_int B_3) C_1)->((ord_less_int B_3) ((plus_plus_int A_3) C_1))))).
% 2.51/2.71 Axiom fact_859_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)))).
% 2.51/2.71 Axiom fact_860_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)))).
% 2.51/2.71 Axiom fact_861_real__mult__less__iff1:(forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_real ((times_times_real X_1) Z)) ((times_times_real Y_1) Z))) ((ord_less_real X_1) Y_1)))).
% 2.51/2.71 Axiom fact_862_real__mult__le__cancel__iff1:(forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real X_1) Z)) ((times_times_real Y_1) Z))) ((ord_less_eq_real X_1) Y_1)))).
% 2.51/2.71 Axiom fact_863_real__mult__le__cancel__iff2:(forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real Z) X_1)) ((times_times_real Z) Y_1))) ((ord_less_eq_real X_1) Y_1)))).
% 2.51/2.71 Axiom fact_864_real__mult__order:(forall (Y_1:real) (X_1:real), (((ord_less_real zero_zero_real) X_1)->(((ord_less_real zero_zero_real) Y_1)->((ord_less_real zero_zero_real) ((times_times_real X_1) Y_1))))).
% 2.51/2.71 Axiom fact_865_real__mult__less__mono2:(forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->(((ord_less_real X_1) Y_1)->((ord_less_real ((times_times_real Z) X_1)) ((times_times_real Z) Y_1))))).
% 2.51/2.71 Axiom fact_866_real__two__squares__add__zero__iff:(forall (X_1:real) (Y_1:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X_1) X_1)) ((times_times_real Y_1) Y_1))) zero_zero_real)) ((and (((eq real) X_1) zero_zero_real)) (((eq real) Y_1) zero_zero_real)))).
% 2.51/2.71 Axiom fact_867_divides__exp2:(forall (X_1:nat) (Y_1:nat) (N:nat), ((not (((eq nat) N) zero_zero_nat))->(((dvd_dvd_nat ((power_power_nat X_1) N)) Y_1)->((dvd_dvd_nat X_1) Y_1)))).
% 2.51/2.71 Axiom fact_868_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)))).
% 2.51/2.71 Axiom fact_869_exp__eq__1:(forall (X_1:nat) (N:nat), ((iff (((eq nat) ((power_power_nat X_1) N)) one_one_nat)) ((or (((eq nat) X_1) one_one_nat)) (((eq nat) N) zero_zero_nat)))).
% 2.51/2.71 Axiom fact_870_divides__div__not:(forall (X_1:nat) (Q:nat) (N:nat) (R:nat), ((((eq nat) X_1) ((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_1)->False))))).
% 2.51/2.71 Axiom fact_871_two__realpow__ge__one:(forall (N:nat), ((ord_less_eq_real one_one_real) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N))).
% 2.51/2.71 Axiom fact_872_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))))))).
% 2.51/2.71 Axiom fact_873_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:real)=> ((and ((and ((ord_less_real zero_zero_real) X)) (((eq real) ((power_power_real X) N)) A))) (forall (Y:real), (((and ((ord_less_real zero_zero_real) Y)) (((eq real) ((power_power_real Y) N)) A))->(((eq real) Y) X))))))))).
% 2.51/2.71 Axiom fact_874_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)))).
% 2.51/2.71 Axiom fact_875_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)))).
% 2.51/2.71 Axiom fact_876_le0:(forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)).
% 2.51/2.71 Axiom fact_877_dvd_Oorder__refl:(forall (X_1:nat), ((dvd_dvd_nat X_1) X_1)).
% 2.51/2.71 Axiom fact_878_less__zeroE:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)).
% 2.51/2.71 Axiom fact_879_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))).
% 2.51/2.71 Axiom fact_880_real__le__refl:(forall (W:real), ((ord_less_eq_real W) W)).
% 2.51/2.71 Axiom fact_881_real__le__linear:(forall (Z:real) (W:real), ((or ((ord_less_eq_real Z) W)) ((ord_less_eq_real W) Z))).
% 2.51/2.71 Axiom fact_882_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)))).
% 2.51/2.71 Axiom fact_883_real__le__antisym:(forall (Z:real) (W:real), (((ord_less_eq_real Z) W)->(((ord_less_eq_real W) Z)->(((eq real) Z) W)))).
% 2.51/2.71 Axiom fact_884_diff__0__eq__0:(forall (N:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N)) zero_zero_nat)).
% 2.51/2.71 Axiom fact_885_minus__nat_Odiff__0:(forall (M:nat), (((eq nat) ((minus_minus_nat M) zero_zero_nat)) M)).
% 2.51/2.71 Axiom fact_886_diff__self__eq__0:(forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat)).
% 2.51/2.71 Axiom fact_887_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)))).
% 2.51/2.71 Axiom fact_888_nat__less__cases:(forall (P_1:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P_1 N) M))->(((((eq nat) M) N)->((P_1 N) M))->((((ord_less_nat N) M)->((P_1 N) M))->((P_1 N) M))))).
% 2.51/2.71 Axiom fact_889_less__not__refl3:(forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))).
% 2.51/2.71 Axiom fact_890_less__not__refl2:(forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N)))).
% 2.51/2.71 Axiom fact_891_less__irrefl__nat:(forall (N:nat), (((ord_less_nat N) N)->False)).
% 2.51/2.71 Axiom fact_892_linorder__neqE__nat:(forall (X_1:nat) (Y_1:nat), ((not (((eq nat) X_1) Y_1))->((((ord_less_nat X_1) Y_1)->False)->((ord_less_nat Y_1) X_1)))).
% 2.51/2.71 Axiom fact_893_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)))).
% 2.51/2.71 Axiom fact_894_less__not__refl:(forall (N:nat), (((ord_less_nat N) N)->False)).
% 2.51/2.71 Axiom fact_895_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))))).
% 2.51/2.71 Axiom fact_896_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))).
% 2.51/2.71 Axiom fact_897_dvd_Oless__asym:(forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((and ((dvd_dvd_nat Y_1) X_1)) (((dvd_dvd_nat X_1) Y_1)->False))->False))).
% 2.51/2.71 Axiom fact_898_dvd_Oless__trans:(forall (Z:nat) (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((and ((dvd_dvd_nat Y_1) Z)) (((dvd_dvd_nat Z) Y_1)->False))->((and ((dvd_dvd_nat X_1) Z)) (((dvd_dvd_nat Z) X_1)->False))))).
% 2.51/2.71 Axiom fact_899_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))).
% 2.51/2.71 Axiom fact_900_dvd_Oless__le__trans:(forall (Z:nat) (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((dvd_dvd_nat Y_1) Z)->((and ((dvd_dvd_nat X_1) Z)) (((dvd_dvd_nat Z) X_1)->False))))).
% 2.51/2.71 Axiom fact_901_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))))).
% 2.51/2.71 Axiom fact_902_dvd_Oless__imp__triv:(forall (P_1:Prop) (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((and ((dvd_dvd_nat Y_1) X_1)) (((dvd_dvd_nat X_1) Y_1)->False))->P_1))).
% 2.51/2.71 Axiom fact_903_dvd_Oless__imp__not__eq2:(forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(not (((eq nat) Y_1) X_1)))).
% 2.51/2.71 Axiom fact_904_dvd_Oless__imp__not__eq:(forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(not (((eq nat) X_1) Y_1)))).
% 2.51/2.71 Axiom fact_905_dvd_Oless__imp__not__less:(forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((and ((dvd_dvd_nat Y_1) X_1)) (((dvd_dvd_nat X_1) Y_1)->False))->False))).
% 2.51/2.71 Axiom fact_906_dvd_Oless__imp__le:(forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->((dvd_dvd_nat X_1) Y_1))).
% 2.51/2.71 Axiom fact_907_dvd_Oless__not__sym:(forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((and ((dvd_dvd_nat Y_1) X_1)) (((dvd_dvd_nat X_1) Y_1)->False))->False))).
% 2.51/2.71 Axiom fact_908_dvd_Oless__imp__neq:(forall (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(not (((eq nat) X_1) Y_1)))).
% 2.51/2.71 Axiom fact_909_dvd_Ole__less__trans:(forall (Z:nat) (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->(((and ((dvd_dvd_nat Y_1) Z)) (((dvd_dvd_nat Z) Y_1)->False))->((and ((dvd_dvd_nat X_1) Z)) (((dvd_dvd_nat Z) X_1)->False))))).
% 2.51/2.71 Axiom fact_910_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))))).
% 2.51/2.71 Axiom fact_911_dvd_Oorder__trans:(forall (Z:nat) (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->(((dvd_dvd_nat Y_1) Z)->((dvd_dvd_nat X_1) Z)))).
% 2.51/2.71 Axiom fact_912_dvd_Oantisym:(forall (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->(((dvd_dvd_nat Y_1) X_1)->(((eq nat) X_1) Y_1)))).
% 2.51/2.71 Axiom fact_913_dvd__antisym:(forall (M:nat) (N:nat), (((dvd_dvd_nat M) N)->(((dvd_dvd_nat N) M)->(((eq nat) M) N)))).
% 2.51/2.71 Axiom fact_914_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)))).
% 2.51/2.71 Axiom fact_915_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)))).
% 2.51/2.71 Axiom fact_916_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))))).
% 2.51/2.71 Axiom fact_917_dvd_Ole__imp__less__or__eq:(forall (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->((or ((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))) (((eq nat) X_1) Y_1)))).
% 2.51/2.71 Axiom fact_918_dvd_Oantisym__conv:(forall (Y_1:nat) (X_1:nat), (((dvd_dvd_nat Y_1) X_1)->((iff ((dvd_dvd_nat X_1) Y_1)) (((eq nat) X_1) Y_1)))).
% 2.51/2.71 Axiom fact_919_dvd_Oeq__refl:(forall (X_1:nat) (Y_1:nat), ((((eq nat) X_1) Y_1)->((dvd_dvd_nat X_1) Y_1))).
% 2.51/2.71 Axiom fact_920_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))))).
% 2.51/2.71 Axiom fact_921_dvd_Oless__le__not__le:(forall (X_1:nat) (Y_1:nat), ((iff ((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))) ((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False)))).
% 2.51/2.71 Axiom fact_922_dvd_Oless__le:(forall (X_1:nat) (Y_1:nat), ((iff ((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))) ((and ((dvd_dvd_nat X_1) Y_1)) (not (((eq nat) X_1) Y_1))))).
% 2.51/2.71 Axiom fact_923_dvd_Ole__less:(forall (X_1:nat) (Y_1:nat), ((iff ((dvd_dvd_nat X_1) Y_1)) ((or ((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))) (((eq nat) X_1) Y_1)))).
% 2.51/2.71 Axiom fact_924_dvd_Oeq__iff:(forall (X_1:nat) (Y_1:nat), ((iff (((eq nat) X_1) Y_1)) ((and ((dvd_dvd_nat X_1) Y_1)) ((dvd_dvd_nat Y_1) X_1)))).
% 2.51/2.71 Axiom fact_925_dvd_Oless__irrefl:(forall (X_1:nat), (((and ((dvd_dvd_nat X_1) X_1)) (((dvd_dvd_nat X_1) X_1)->False))->False)).
% 2.51/2.71 Axiom fact_926_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))))).
% 2.51/2.71 Axiom fact_927_nat__add__commute:(forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) N)) ((plus_plus_nat N) M))).
% 2.51/2.71 Axiom fact_928_nat__add__left__commute:(forall (X_1:nat) (Y_1:nat) (Z:nat), (((eq nat) ((plus_plus_nat X_1) ((plus_plus_nat Y_1) Z))) ((plus_plus_nat Y_1) ((plus_plus_nat X_1) Z)))).
% 2.51/2.71 Axiom fact_929_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)))).
% 2.51/2.71 Axiom fact_930_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))).
% 2.51/2.71 Axiom fact_931_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))).
% 2.51/2.71 Axiom fact_932_diff__add__inverse2:(forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) N)) N)) M)).
% 2.51/2.71 Axiom fact_933_diff__add__inverse:(forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat N) M)) N)) M)).
% 2.51/2.71 Axiom fact_934_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)))).
% 2.51/2.71 Axiom fact_935_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))).
% 2.51/2.71 Axiom fact_936_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))).
% 2.51/2.71 Axiom fact_937_le__refl:(forall (N:nat), ((ord_less_eq_nat N) N)).
% 2.51/2.71 Axiom fact_938_nat__le__linear:(forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M))).
% 2.51/2.71 Axiom fact_939_eq__imp__le:(forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N))).
% 2.51/2.71 Axiom fact_940_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)))).
% 2.51/2.71 Axiom fact_941_le__antisym:(forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N)))).
% 2.51/2.71 Axiom fact_942_Nat_Odiff__le__self:(forall (M:nat) (N:nat), ((ord_less_eq_nat ((minus_minus_nat M) N)) M)).
% 2.51/2.71 Axiom fact_943_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)))).
% 2.51/2.71 Axiom fact_944_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)))).
% 2.51/2.71 Axiom fact_945_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))).
% 2.51/2.71 Axiom fact_946_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))))).
% 2.51/2.71 Axiom fact_947_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))))).
% 2.51/2.71 Axiom fact_948_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))))).
% 2.51/2.71 Axiom fact_949_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)))).
% 2.51/2.71 Axiom fact_950_nat__mult__commute:(forall (M:nat) (N:nat), (((eq nat) ((times_times_nat M) N)) ((times_times_nat N) M))).
% 2.51/2.72 Axiom fact_951_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)))).
% 2.51/2.72 Axiom fact_952_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)))).
% 2.51/2.72 Axiom fact_953_gr0I:(forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N))).
% 2.51/2.72 Axiom fact_954_gr__implies__not0:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->(not (((eq nat) N) zero_zero_nat)))).
% 2.51/2.72 Axiom fact_955_less__nat__zero__code:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)).
% 2.51/2.72 Axiom fact_956_neq0__conv:(forall (N:nat), ((iff (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N))).
% 2.51/2.72 Axiom fact_957_not__less0:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)).
% 2.51/2.72 Axiom fact_958_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)))).
% 2.51/2.72 Axiom fact_959_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))).
% 2.51/2.72 Axiom fact_960_add__eq__self__zero:(forall (M:nat) (N:nat), ((((eq nat) ((plus_plus_nat M) N)) M)->(((eq nat) N) zero_zero_nat))).
% 2.51/2.72 Axiom fact_961_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)))).
% 2.51/2.72 Axiom fact_962_Nat_Oadd__0__right:(forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M)).
% 2.51/2.72 Axiom fact_963_plus__nat_Oadd__0:(forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N)).
% 2.51/2.72 Axiom fact_964_diff__add__0:(forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat N) ((plus_plus_nat N) M))) zero_zero_nat)).
% 2.51/2.72 Axiom fact_965_le__0__eq:(forall (N:nat), ((iff ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat))).
% 2.51/2.72 Axiom fact_966_less__eq__nat_Osimps_I1_J:(forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)).
% 2.51/2.72 Axiom fact_967_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))).
% 2.51/2.72 Axiom fact_968_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))).
% 2.51/2.72 Axiom fact_969_mult__0:(forall (N:nat), (((eq nat) ((times_times_nat zero_zero_nat) N)) zero_zero_nat)).
% 2.51/2.72 Axiom fact_970_mult__0__right:(forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat)).
% 2.51/2.72 Axiom fact_971_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)))).
% 2.51/2.72 Axiom fact_972_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)))).
% 2.51/2.72 Axiom fact_973_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)))).
% 2.51/2.72 Axiom fact_974_not__add__less1:(forall (I_1:nat) (J_1:nat), (((ord_less_nat ((plus_plus_nat I_1) J_1)) I_1)->False)).
% 2.51/2.72 Axiom fact_975_not__add__less2:(forall (J_1:nat) (I_1:nat), (((ord_less_nat ((plus_plus_nat J_1) I_1)) I_1)->False)).
% 2.51/2.72 Axiom fact_976_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))).
% 2.51/2.72 Axiom fact_977_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)))).
% 2.51/2.72 Axiom fact_978_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)))).
% 2.51/2.72 Axiom fact_979_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)))).
% 2.51/2.72 Axiom fact_980_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))))).
% 2.51/2.72 Axiom fact_981_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)))).
% 2.51/2.72 Axiom fact_982_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))).
% 2.51/2.72 Axiom fact_983_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))).
% 2.51/2.72 Axiom fact_984_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))).
% 2.51/2.72 Axiom fact_985_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))))).
% 2.51/2.72 Axiom fact_986_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)))).
% 2.51/2.72 Axiom fact_987_less__imp__le__nat:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N))).
% 2.51/2.72 Axiom fact_988_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)))).
% 2.51/2.72 Axiom fact_989_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))).
% 2.51/2.72 Axiom fact_990_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))))).
% 2.51/2.72 Axiom fact_991_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))))).
% 2.51/2.72 Axiom fact_992_dvd__reduce:(forall (K:nat) (N:nat), ((iff ((dvd_dvd_nat K) ((plus_plus_nat N) K))) ((dvd_dvd_nat K) N))).
% 2.51/2.72 Axiom fact_993_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))))).
% 2.51/2.72 Axiom fact_994_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))))).
% 2.51/2.72 Axiom fact_995_le__add2:(forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat M) N))).
% 2.51/2.72 Axiom fact_996_le__add1:(forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M))).
% 2.51/2.72 Axiom fact_997_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)))))).
% 2.51/2.72 Axiom fact_998_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))).
% 2.51/2.72 Axiom fact_999_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)))).
% 2.51/2.72 Axiom fact_1000_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)))).
% 2.51/2.72 Axiom fact_1001_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)))).
% 2.51/2.72 Axiom fact_1002_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))))).
% 2.51/2.72 Axiom fact_1003_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))).
% 2.51/2.72 Axiom fact_1004_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))).
% 2.51/2.72 Axiom fact_1005_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))).
% 2.51/2.72 Axiom fact_1006_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)))).
% 2.51/2.72 Axiom fact_1007_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)))).
% 2.51/2.72 Axiom fact_1008_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)))).
% 2.51/2.72 Axiom fact_1009_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))).
% 2.51/2.72 Axiom fact_1010_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)))).
% 2.51/2.72 Axiom fact_1011_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)))).
% 2.51/2.72 Axiom fact_1012_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))).
% 2.51/2.72 Axiom fact_1013_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))))).
% 2.51/2.72 Axiom fact_1014_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))))).
% 2.51/2.72 Axiom fact_1015_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)))).
% 2.51/2.72 Axiom fact_1016_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)))).
% 2.51/2.72 Axiom fact_1017_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)))).
% 2.51/2.72 Axiom fact_1018_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)))).
% 2.51/2.72 Axiom fact_1019_nat__dvd__1__iff__1:(forall (M:nat), ((iff ((dvd_dvd_nat M) one_one_nat)) (((eq nat) M) one_one_nat))).
% 2.51/2.72 Axiom fact_1020_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))))).
% 2.51/2.72 Axiom fact_1021_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)))).
% 2.51/2.72 Axiom fact_1022_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)))).
% 2.51/2.72 Axiom fact_1023_le__cube:(forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) ((times_times_nat M) M)))).
% 2.51/2.72 Axiom fact_1024_le__square:(forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) M))).
% 2.51/2.72 Axiom fact_1025_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)))).
% 2.51/2.72 Axiom fact_1026_nat__mult__1__right:(forall (N:nat), (((eq nat) ((times_times_nat N) one_one_nat)) N)).
% 2.51/2.72 Axiom fact_1027_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)))).
% 2.51/2.72 Axiom fact_1028_nat__mult__1:(forall (N:nat), (((eq nat) ((times_times_nat one_one_nat) N)) N)).
% 2.51/2.72 Axiom fact_1029_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)))).
% 2.51/2.72 Axiom fact_1030_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)))).
% 2.51/2.72 Axiom fact_1031_nat__diff__split:(forall (P_1:(nat->Prop)) (A:nat) (B:nat), ((iff (P_1 ((minus_minus_nat A) B))) ((and (((ord_less_nat A) B)->(P_1 zero_zero_nat))) (forall (D_2:nat), ((((eq nat) A) ((plus_plus_nat B) D_2))->(P_1 D_2)))))).
% 2.51/2.72 Axiom fact_1032_nat__diff__split__asm:(forall (P_1:(nat->Prop)) (A:nat) (B:nat), ((iff (P_1 ((minus_minus_nat A) B))) (((or ((and ((ord_less_nat A) B)) ((P_1 zero_zero_nat)->False))) ((ex nat) (fun (D_2:nat)=> ((and (((eq nat) A) ((plus_plus_nat B) D_2))) ((P_1 D_2)->False)))))->False))).
% 2.51/2.72 Axiom fact_1033_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))))).
% 2.51/2.72 Axiom fact_1034_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))))).
% 2.51/2.72 Axiom fact_1035_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)))).
% 2.51/2.72 Axiom fact_1036_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)))).
% 2.51/2.72 Axiom fact_1037_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)))).
% 2.51/2.72 Axiom fact_1038_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)))).
% 2.51/2.72 Axiom fact_1039_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)))).
% 2.51/2.72 Axiom fact_1040_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)))).
% 2.51/2.72 Axiom fact_1041_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)))).
% 2.51/2.72 Axiom fact_1042_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)))).
% 2.51/2.72 Axiom fact_1043_ex__least__nat__less:(forall (N:nat) (P_1:(nat->Prop)), (((P_1 zero_zero_nat)->False)->((P_1 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_1 _TPTP_I)->False))))) (P_1 ((plus_plus_nat K_1) one_one_nat)))))))).
% 2.51/2.72 Axiom fact_1044_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))))).
% 2.51/2.72 Axiom fact_1045_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)))).
% 2.51/2.72 Axiom fact_1046_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))).
% 2.51/2.72 Axiom fact_1047_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)))).
% 2.51/2.72 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)))).
% 2.51/2.72 Axiom fact_1049_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)))).
% 2.51/2.72 Axiom fact_1050_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)))).
% 2.51/2.72 Axiom fact_1051_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)))).
% 2.51/2.72 Axiom fact_1052_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)))).
% 2.51/2.72 Axiom fact_1053_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)))).
% 2.51/2.72 Axiom fact_1054_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)))).
% 2.51/2.72 Axiom fact_1055_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))))).
% 2.51/2.72 Axiom fact_1056_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))))).
% 2.51/2.72 Axiom fact_1057_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))))).
% 2.51/2.72 Axiom fact_1058_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)))).
% 2.51/2.72 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)))))).
% 2.51/2.72 Axiom fact_1060_is__sum2sq__def:(forall (X_1:int), ((iff (twoSqu919416604sum2sq X_1)) ((ex int) (fun (A_2:int)=> ((ex int) (fun (B_2:int)=> (((eq int) (twoSqu2057625106sum2sq ((product_Pair_int_int A_2) B_2))) X_1))))))).
% 2.51/2.72 Axiom fact_1061_imp__le__cong:(forall (P_3:Prop) (P_1:Prop) (X_1:int), ((((ord_less_eq_int zero_zero_int) X_1)->((iff P_1) P_3))->((iff (((ord_less_eq_int zero_zero_int) X_1)->P_1)) (((ord_less_eq_int zero_zero_int) X_1)->P_3)))).
% 2.51/2.72 Axiom fact_1062_conj__le__cong:(forall (P_3:Prop) (P_1:Prop) (X_1:int), ((((ord_less_eq_int zero_zero_int) X_1)->((iff P_1) P_3))->((iff ((and ((ord_less_eq_int zero_zero_int) X_1)) P_1)) ((and ((ord_less_eq_int zero_zero_int) X_1)) P_3)))).
% 2.51/2.72 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))))).
% 2.51/2.72 Axiom fact_1064_number__of2:((ord_less_eq_int zero_zero_int) (number_number_of_int pls)).
% 2.51/2.72 Axiom fact_1065_decr__mult__lemma:(forall (K:int) (P_1:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X:int), ((P_1 X)->(P_1 ((minus_minus_int X) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X:int), ((P_1 X)->(P_1 ((minus_minus_int X) ((times_times_int K) D))))))))).
% 2.51/2.73 Axiom fact_1066_incr__mult__lemma:(forall (K:int) (P_1:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X:int), ((P_1 X)->(P_1 ((plus_plus_int X) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X:int), ((P_1 X)->(P_1 ((plus_plus_int X) ((times_times_int K) D))))))))).
% 2.51/2.73 Axiom fact_1067_zprime__factor__exists:(forall (A:int), (((ord_less_int one_one_int) A)->((ex int) (fun (P_2:int)=> ((and (zprime P_2)) ((dvd_dvd_int P_2) A)))))).
% 2.51/2.73 Axiom fact_1068_zcong__zless__unique:(forall (A:int) (M:int), (((ord_less_int zero_zero_int) M)->((ex int) (fun (X:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X)) ((ord_less_int X) M))) (((zcong A) X) M))) (forall (Y:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y)) ((ord_less_int Y) M))) (((zcong A) Y) M))->(((eq int) Y) X)))))))).
% 2.51/2.73 Axiom fact_1069_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))).
% 2.51/2.73 Axiom fact_1070_Wilson__Russ:(forall (P:int), ((zprime P)->(((zcong (zfact ((minus_minus_int P) one_one_int))) (number_number_of_int min)) P))).
% 2.51/2.73 Axiom fact_1071_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))))))).
% 2.51/2.73 Axiom fact_1072_inv__inv:(forall (A:int) (P:int), ((zprime P)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P)->(((eq int) ((inv P) ((inv P) A))) A)))))).
% 2.51/2.73 Axiom fact_1073_MultInvPair__distinct:(forall (J_1:int) (A:int) (P:int), ((zprime P)->(((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->(((((zcong A) zero_zero_int) P)->False)->(((((zcong J_1) zero_zero_int) P)->False)->((((quadRes P) A)->False)->((((zcong J_1) ((times_times_int A) ((multInv P) J_1))) P)->False))))))).
% 2.51/2.73 Axiom fact_1074_aux______3:(forall (J_1:int) (K:int) (A:int) (P:int), ((((zcong ((times_times_int J_1) K)) A) P)->(((zcong ((times_times_int ((times_times_int ((multInv P) J_1)) J_1)) K)) ((times_times_int ((multInv P) J_1)) A)) P))).
% 2.51/2.73 Axiom fact_1075_aux______1:(forall (J_1:int) (A:int) (P:int) (K:int), ((((zcong J_1) ((times_times_int A) ((multInv P) K))) P)->(((zcong ((times_times_int J_1) K)) ((times_times_int ((times_times_int A) ((multInv P) K))) K)) P))).
% 2.51/2.73 Axiom fact_1076_inv__distinct:(forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(not (((eq int) A) ((inv P) A))))))).
% 2.51/2.73 Axiom fact_1077_inv__not__1:(forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(not (((eq int) ((inv P) A)) one_one_int)))))).
% 2.51/2.73 Axiom fact_1078_inv__not__p__minus__1:(forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(not (((eq int) ((inv P) A)) ((minus_minus_int P) one_one_int))))))).
% 2.51/2.73 Axiom fact_1079_inv__g__1:(forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->((ord_less_int one_one_int) ((inv P) A)))))).
% 2.51/2.73 Axiom fact_1080_inv__less__p__minus__1:(forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->((ord_less_int ((inv P) A)) ((minus_minus_int P) one_one_int)))))).
% 2.51/2.73 Axiom fact_1081_MultInv__prop1:(forall (X_1:int) (Y_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((((zcong X_1) Y_1) P)->(((zcong ((multInv P) X_1)) ((multInv P) Y_1)) P)))).
% 2.51/2.73 Axiom fact_1082_inv__not__0:(forall (A:int) (P:int), ((zprime P)->(((ord_less_int one_one_int) A)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(not (((eq int) ((inv P) A)) zero_zero_int)))))).
% 2.51/2.73 Axiom fact_1083_MultInv__zcong__prop1:(forall (A:int) (J_1:int) (K:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((((zcong J_1) K) P)->(((zcong ((times_times_int A) ((multInv P) J_1))) ((times_times_int A) ((multInv P) K))) P)))).
% 2.51/2.73 Axiom fact_1084_MultInv__prop5:(forall (Y_1:int) (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((((zcong Y_1) zero_zero_int) P)->False)->((((zcong ((multInv P) X_1)) ((multInv P) Y_1)) P)->(((zcong X_1) Y_1) P))))))).
% 2.51/2.73 Axiom fact_1085_MultInv__prop4:(forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((zcong ((multInv P) ((multInv P) X_1))) X_1) P))))).
% 2.51/2.73 Axiom fact_1086_MultInv__prop3:(forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->((((zcong ((multInv P) X_1)) zero_zero_int) P)->False))))).
% 2.51/2.73 Axiom fact_1087_inv__is__inv:(forall (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P)->(((zcong ((times_times_int A) ((inv P) A))) one_one_int) P))))).
% 2.51/2.73 Axiom fact_1088_aux______4:(forall (K:int) (A:int) (J_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong J_1) zero_zero_int) P)->False)->((((zcong ((times_times_int ((times_times_int ((multInv P) J_1)) J_1)) K)) ((times_times_int ((multInv P) J_1)) A)) P)->(((zcong K) ((times_times_int A) ((multInv P) J_1))) P)))))).
% 2.51/2.73 Axiom fact_1089_aux______2:(forall (J_1:int) (A:int) (K:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong K) zero_zero_int) P)->False)->((((zcong ((times_times_int J_1) K)) ((times_times_int ((times_times_int A) ((multInv P) K))) K)) P)->(((zcong ((times_times_int J_1) K)) A) P)))))).
% 2.51/2.73 Axiom fact_1090_MultInv__zcong__prop2:(forall (A:int) (J_1:int) (K:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong K) zero_zero_int) P)->False)->(((((zcong J_1) zero_zero_int) P)->False)->((((zcong J_1) ((times_times_int A) ((multInv P) K))) P)->(((zcong K) ((times_times_int A) ((multInv P) J_1))) P))))))).
% 2.51/2.73 Axiom fact_1091_MultInv__zcong__prop3:(forall (J_1:int) (K:int) (A:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong A) zero_zero_int) P)->False)->(((((zcong K) zero_zero_int) P)->False)->(((((zcong J_1) zero_zero_int) P)->False)->((((zcong ((times_times_int A) ((multInv P) J_1))) ((times_times_int A) ((multInv P) K))) P)->(((zcong J_1) K) P)))))))).
% 2.51/2.73 Axiom fact_1092_Int2_Oaux____2:(forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((zcong ((times_times_int ((times_times_int X_1) ((multInv P) X_1))) ((multInv P) ((multInv P) X_1)))) X_1) P))))).
% 2.51/2.73 Axiom fact_1093_Int2_Oaux____1:(forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((zcong ((multInv P) ((multInv P) X_1))) ((times_times_int ((times_times_int X_1) ((multInv P) X_1))) ((multInv P) ((multInv P) X_1)))) P))))).
% 2.51/2.73 Axiom fact_1094_MultInv__prop2a:(forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((zcong ((times_times_int ((multInv P) X_1)) X_1)) one_one_int) P))))).
% 2.51/2.73 Axiom fact_1095_MultInv__prop2:(forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((zcong ((times_times_int X_1) ((multInv P) X_1))) one_one_int) P))))).
% 2.51/2.73 Axiom fact_1096_wset__mem__inv__mem:(forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(((member_int B) ((wset A) P))->((member_int ((inv P) B)) ((wset A) P))))))).
% 2.51/2.73 Axiom fact_1097_wset__inv__mem__mem:(forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(((ord_less_int one_one_int) B)->(((ord_less_int B) ((minus_minus_int P) one_one_int))->(((member_int ((inv P) B)) ((wset A) P))->((member_int B) ((wset A) P))))))))).
% 2.51/2.73 Axiom fact_1098_wset__mem__mem:(forall (P:int) (A:int), (((ord_less_int one_one_int) A)->((member_int A) ((wset A) P)))).
% 2.51/2.73 Axiom fact_1099_wset__subset:(forall (B:int) (P:int) (A:int), (((ord_less_int one_one_int) A)->(((member_int B) ((wset ((minus_minus_int A) one_one_int)) P))->((member_int B) ((wset A) P))))).
% 2.51/2.73 Axiom fact_1100_wset__less:(forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(((member_int B) ((wset A) P))->((ord_less_int B) ((minus_minus_int P) one_one_int)))))).
% 2.51/2.73 Axiom fact_1101_wset__g__1:(forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(((member_int B) ((wset A) P))->((ord_less_int one_one_int) B))))).
% 2.51/2.73 Axiom fact_1102_wset__mem__imp__or:(forall (B:int) (P:int) (A:int), (((ord_less_int one_one_int) A)->((((member_int B) ((wset ((minus_minus_int A) one_one_int)) P))->False)->(((member_int B) ((wset A) P))->((or (((eq int) B) A)) (((eq int) B) ((inv P) A))))))).
% 2.51/2.73 Axiom fact_1103_wset__mem:(forall (B:int) (A:int) (P:int), ((zprime P)->(((ord_less_int A) ((minus_minus_int P) one_one_int))->(((ord_less_int one_one_int) B)->(((ord_less_eq_int B) A)->((member_int B) ((wset A) P))))))).
% 2.51/2.73 Axiom fact_1104_int__le__induct:(forall (P_1:(int->Prop)) (I_1:int) (K:int), (((ord_less_eq_int I_1) K)->((P_1 K)->((forall (_TPTP_I:int), (((ord_less_eq_int _TPTP_I) K)->((P_1 _TPTP_I)->(P_1 ((minus_minus_int _TPTP_I) one_one_int)))))->(P_1 I_1))))).
% 2.51/2.73 Axiom fact_1105_int__less__induct:(forall (P_1:(int->Prop)) (I_1:int) (K:int), (((ord_less_int I_1) K)->((P_1 ((minus_minus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int _TPTP_I) K)->((P_1 _TPTP_I)->(P_1 ((minus_minus_int _TPTP_I) one_one_int)))))->(P_1 I_1))))).
% 2.51/2.73 Axiom fact_1106_d22set__induct__old:(forall (X_1:int) (P_1:(int->Prop)), ((forall (A_2:int), ((((ord_less_int one_one_int) A_2)->(P_1 ((minus_minus_int A_2) one_one_int)))->(P_1 A_2)))->(P_1 X_1))).
% 2.51/2.73 Axiom fact_1107_int__ge__induct:(forall (P_1:(int->Prop)) (K:int) (I_1:int), (((ord_less_eq_int K) I_1)->((P_1 K)->((forall (_TPTP_I:int), (((ord_less_eq_int K) _TPTP_I)->((P_1 _TPTP_I)->(P_1 ((plus_plus_int _TPTP_I) one_one_int)))))->(P_1 I_1))))).
% 2.51/2.73 Axiom fact_1108_int__gr__induct:(forall (P_1:(int->Prop)) (K:int) (I_1:int), (((ord_less_int K) I_1)->((P_1 ((plus_plus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int K) _TPTP_I)->((P_1 _TPTP_I)->(P_1 ((plus_plus_int _TPTP_I) one_one_int)))))->(P_1 I_1))))).
% 2.51/2.73 Axiom fact_1109_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))))).
% 2.51/2.73 Axiom fact_1110_d22set__eq__wset:(forall (P:int), ((zprime P)->(((eq (int->Prop)) (d22set ((minus_minus_int P) (number_number_of_int (bit0 (bit1 pls)))))) ((wset ((minus_minus_int P) (number_number_of_int (bit0 (bit1 pls))))) P)))).
% 2.51/2.73 Axiom fact_1111_ex__least__nat__le:(forall (N:nat) (P_1:(nat->Prop)), (((P_1 zero_zero_nat)->False)->((P_1 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_1 _TPTP_I)->False))))) (P_1 K_1))))))).
% 2.51/2.73 Axiom fact_1112_d22set__le:(forall (B:int) (A:int), (((member_int B) (d22set A))->((ord_less_eq_int B) A))).
% 2.51/2.73 Axiom fact_1113_d22set__le__swap:(forall (A:int) (B:int), (((ord_less_int A) B)->(((member_int B) (d22set A))->False))).
% 2.51/2.73 Axiom fact_1114_d22set__g__1:(forall (B:int) (A:int), (((member_int B) (d22set A))->((ord_less_int one_one_int) B))).
% 2.51/2.73 Axiom fact_1115_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))))).
% 2.51/2.73 Axiom fact_1116_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)))))).
% 2.51/2.73 Axiom fact_1117_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)))).
% 2.51/2.73 Axiom fact_1118_gcd__lcm__complete__lattice__nat_Otop__le:(forall (A:nat), (((dvd_dvd_nat zero_zero_nat) A)->(((eq nat) A) zero_zero_nat))).
% 2.51/2.73 Axiom fact_1119_gcd__lcm__complete__lattice__nat_Otop__unique:(forall (A:nat), ((iff ((dvd_dvd_nat zero_zero_nat) A)) (((eq nat) A) zero_zero_nat))).
% 2.51/2.73 Axiom fact_1120_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)))).
% 2.51/2.73 Axiom fact_1121_gcd__lcm__complete__lattice__nat_Otop__greatest:(forall (A:nat), ((dvd_dvd_nat A) zero_zero_nat)).
% 2.51/2.73 Axiom fact_1122_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)).
% 2.51/2.73 Axiom fact_1123_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)).
% 2.51/2.73 Axiom fact_1124_gcd__lcm__complete__lattice__nat_Obot__least:(forall (A:nat), ((dvd_dvd_nat one_one_nat) A)).
% 2.51/2.73 Axiom fact_1125_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)))).
% 2.51/2.73 Axiom fact_1126_gcd__lcm__complete__lattice__nat_Obot__unique:(forall (A:nat), ((iff ((dvd_dvd_nat A) one_one_nat)) (((eq nat) A) one_one_nat))).
% 2.51/2.73 Axiom fact_1127_gcd__lcm__complete__lattice__nat_Ole__bot:(forall (A:nat), (((dvd_dvd_nat A) one_one_nat)->(((eq nat) A) one_one_nat))).
% 2.51/2.73 Axiom fact_1128_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)))).
% 2.51/2.73 Axiom fact_1129_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)))).
% 2.51/2.73 Axiom fact_1130_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)))).
% 2.51/2.73 Axiom fact_1131_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)))).
% 2.51/2.73 Axiom fact_1132_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)))).
% 2.51/2.73 Axiom fact_1133_SR__def:(forall (P:int), (((eq (int->Prop)) (sr P)) (collect_int (fun (X:int)=> ((and ((ord_less_eq_int zero_zero_int) X)) ((ord_less_int X) P)))))).
% 2.51/2.73 Axiom fact_1134_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)))).
% 2.51/2.73 Axiom fact_1135_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))))).
% 2.51/2.74 Axiom fact_1136_zdvd__iff__zmod__eq__0__number__of:(forall (X_1:int) (Y_1:int), ((iff ((dvd_dvd_int (number_number_of_int X_1)) (number_number_of_int Y_1))) (((eq int) ((div_mod_int (number_number_of_int Y_1)) (number_number_of_int X_1))) zero_zero_int))).
% 2.51/2.74 Axiom fact_1137_neg__mod__bound:(forall (A:int) (B:int), (((ord_less_int B) zero_zero_int)->((ord_less_int B) ((div_mod_int A) B)))).
% 2.51/2.74 Axiom fact_1138_pos__mod__bound:(forall (A:int) (B:int), (((ord_less_int zero_zero_int) B)->((ord_less_int ((div_mod_int A) B)) B))).
% 2.51/2.74 Axiom fact_1139_Divides_Otransfer__nat__int__function__closures_I2_J:(forall (Y_1:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_eq_int zero_zero_int) Y_1)->((ord_less_eq_int zero_zero_int) ((div_mod_int X_1) Y_1))))).
% 2.51/2.74 Axiom fact_1140_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))).
% 2.51/2.74 Axiom fact_1141_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)))))).
% 2.51/2.74 Axiom fact_1142_zmod__eq__dvd__iff:(forall (X_1:int) (N:int) (Y_1:int), ((iff (((eq int) ((div_mod_int X_1) N)) ((div_mod_int Y_1) N))) ((dvd_dvd_int N) ((minus_minus_int X_1) Y_1)))).
% 2.51/2.74 Axiom fact_1143_Residues_Oaux:(forall (X_1:int) (M:int) (Y_1:int), ((((eq int) ((div_mod_int X_1) M)) ((div_mod_int Y_1) M))->(((zcong X_1) Y_1) M))).
% 2.51/2.74 Axiom fact_1144_mod__mod__is__mod:(forall (X_1:int) (M:int), (((zcong X_1) ((div_mod_int X_1) M)) M)).
% 2.51/2.74 Axiom fact_1145_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))).
% 2.51/2.74 Axiom fact_1146_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)))).
% 2.51/2.74 Axiom fact_1147_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))))).
% 2.51/2.74 Axiom fact_1148_zpower__zmod:(forall (X_1:int) (M:int) (Y_1:nat), (((eq int) ((div_mod_int ((power_power_int ((div_mod_int X_1) M)) Y_1)) M)) ((div_mod_int ((power_power_int X_1) Y_1)) M))).
% 2.51/2.74 Axiom fact_1149_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))).
% 2.51/2.74 Axiom fact_1150_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))).
% 2.51/2.74 Axiom fact_1151_zmod__self:(forall (A:int), (((eq int) ((div_mod_int A) A)) zero_zero_int)).
% 2.51/2.74 Axiom fact_1152_zmod__zero:(forall (B:int), (((eq int) ((div_mod_int zero_zero_int) B)) zero_zero_int)).
% 2.51/2.74 Axiom fact_1153_zdiff__zmod__right:(forall (X_1:int) (Y_1:int) (M:int), (((eq int) ((div_mod_int ((minus_minus_int X_1) ((div_mod_int Y_1) M))) M)) ((div_mod_int ((minus_minus_int X_1) Y_1)) M))).
% 2.51/2.74 Axiom fact_1154_zdiff__zmod__left:(forall (X_1:int) (M:int) (Y_1:int), (((eq int) ((div_mod_int ((minus_minus_int ((div_mod_int X_1) M)) Y_1)) M)) ((div_mod_int ((minus_minus_int X_1) Y_1)) M))).
% 2.51/2.74 Axiom fact_1155_zmod__minus1__right:(forall (A:int), (((eq int) ((div_mod_int A) (number_number_of_int min))) zero_zero_int)).
% 2.51/2.74 Axiom fact_1156_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))))).
% 2.51/2.74 Axiom fact_1157_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))))).
% 2.51/2.74 Axiom fact_1158_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)))).
% 2.51/2.74 Axiom fact_1159_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)))).
% 2.51/2.74 Axiom fact_1160_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)))).
% 2.51/2.74 Axiom fact_1161_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))).
% 2.51/2.74 Axiom fact_1162_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))))).
% 2.51/2.74 Axiom fact_1163_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)))).
% 2.51/2.74 Axiom fact_1164_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))))).
% 2.51/2.74 Axiom fact_1165_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))))).
% 2.51/2.74 Axiom fact_1166_split__zmod:(forall (P_1:(int->Prop)) (N:int) (K:int), ((iff (P_1 ((div_mod_int N) K))) ((and ((and ((((eq int) K) zero_zero_int)->(P_1 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_1 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_1 J))))))).
% 2.51/2.74 Axiom fact_1167_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)))))).
% 2.51/2.74 Axiom fact_1168_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)))))).
% 2.51/2.74 Axiom fact_1169_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)))))).
% 2.51/2.74 Axiom fact_1170_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))))).
% 2.51/2.74 Axiom fact_1171_divmod__int__rel__mod__eq:(forall (A_1:int) (B_1:int) (Q_2:int) (Y_1:int), ((((eq int) A_1) ((plus_plus_int ((times_times_int B_1) Q_2)) Y_1))->(((and (((ord_less_int zero_zero_int) B_1)->((and ((ord_less_eq_int zero_zero_int) Y_1)) ((ord_less_int Y_1) B_1)))) ((((ord_less_int zero_zero_int) B_1)->False)->((and ((ord_less_int B_1) Y_1)) ((ord_less_eq_int Y_1) zero_zero_int))))->((not (((eq int) B_1) zero_zero_int))->(((eq int) ((div_mod_int A_1) B_1)) Y_1))))).
% 2.51/2.74 Axiom fact_1172_neq__one__mod__two:(forall (X_1:int), ((iff (not (((eq int) ((div_mod_int X_1) (number_number_of_int (bit0 (bit1 pls))))) zero_zero_int))) (((eq int) ((div_mod_int X_1) (number_number_of_int (bit0 (bit1 pls))))) one_one_int))).
% 2.51/2.74 Axiom fact_1173_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)))).
% 2.51/2.74 Axiom fact_1174_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)))))).
% 2.63/2.90 Axiom fact_1175_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)))))).
% 2.63/2.90 Axiom fact_1176_StandardRes__prop4:(forall (X_1:int) (Y_1:int) (M:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) M)->(((zcong ((times_times_int ((standardRes M) X_1)) ((standardRes M) Y_1))) ((times_times_int X_1) Y_1)) M))).
% 2.63/2.90 Axiom fact_1177_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))).
% 2.63/2.90 Axiom fact_1178_mod__less__divisor:(forall (M:nat) (N:nat), (((ord_less_nat zero_zero_nat) N)->((ord_less_nat ((div_mod_nat M) N)) N))).
% 2.63/2.90 Axiom fact_1179_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)))))).
% 2.63/2.90 Axiom fact_1180_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)))).
% 2.63/2.90 Axiom fact_1181_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))))).
% 2.63/2.90 Axiom fact_1182_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))).
% 2.63/2.90 Axiom fact_1183_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)))).
% 2.63/2.90 Axiom fact_1184_StandardRes__def:(forall (M:int) (X_1:int), (((eq int) ((standardRes M) X_1)) ((div_mod_int X_1) M))).
% 2.63/2.90 Axiom fact_1185_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)))).
% 2.63/2.90 Axiom fact_1186_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)))).
% 2.63/2.90 Axiom fact_1187_mod__less:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->(((eq nat) ((div_mod_nat M) N)) M))).
% 2.63/2.90 Axiom fact_1188_mod__less__eq__dividend:(forall (M:nat) (N:nat), ((ord_less_eq_nat ((div_mod_nat M) N)) M)).
% 2.63/2.90 Axiom fact_1189_StandardRes__eq__zcong:(forall (M:int) (X_1:int), ((iff (((eq int) ((standardRes M) X_1)) zero_zero_int)) (((zcong X_1) zero_zero_int) M))).
% 2.63/2.90 Axiom fact_1190_StandardRes__prop3:(forall (X_1:int) (P:int), ((iff ((((zcong X_1) zero_zero_int) P)->False)) (not (((eq int) ((standardRes P) X_1)) zero_zero_int)))).
% 2.63/2.90 Axiom fact_1191_StandardRes__prop1:(forall (X_1:int) (M:int), (((zcong X_1) ((standardRes M) X_1)) M)).
% 2.63/2.90 Axiom fact_1192_StandardRes__ubound:(forall (X_1:int) (P:int), (((ord_less_int zero_zero_int) P)->((ord_less_int ((standardRes P) X_1)) P))).
% 2.63/2.90 Axiom fact_1193_StandardRes__SR__prop:(forall (X_1:int) (P:int), (((member_int X_1) (sr P))->(((eq int) ((standardRes P) X_1)) X_1))).
% 2.63/2.90 Axiom fact_1194_split__mod:(forall (P_1:(nat->Prop)) (N:nat) (K:nat), ((iff (P_1 ((div_mod_nat N) K))) ((and ((((eq nat) K) zero_zero_nat)->(P_1 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_1 J)))))))).
% 2.63/2.90 Axiom fact_1195_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))))).
% 2.63/2.90 Axiom fact_1196_StandardRes__lbound:(forall (X_1:int) (P:int), (((ord_less_int zero_zero_int) P)->((ord_less_eq_int zero_zero_int) ((standardRes P) X_1)))).
% 2.63/2.90 Axiom fact_1197_StandardRes__prop2:(forall (X1:int) (X2:int) (M:int), (((ord_less_int zero_zero_int) M)->((iff (((eq int) ((standardRes M) X1)) ((standardRes M) X2))) (((zcong X1) X2) M)))).
% 2.63/2.90 Trying to prove ((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq 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)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))
% 178.75/178.96 Unexpected exception Unexpected matching of length 0 when specializating fact_902_dvd_Oless__imp__triv:(forall (P_1:Prop) (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((and ((dvd_dvd_nat Y_1) X_1)) (((dvd_dvd_nat X_1) Y_1)->False))->P_1))) with fact_307_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_307_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 X_10) Y_10)) (((dvd_dvd_nat Y_10) X_10)->False)))
% 178.75/178.96 Traceback (most recent call last):
% 178.75/178.96 File "CASC.py", line 80, in <module>
% 178.75/178.96 proof=problem.solve()
% 178.75/178.96 File "/export/starexec/sandbox/solver/bin/TPTP.py", line 95, in solve
% 178.75/178.96 for x in self.solveyielding():
% 178.75/178.96 File "/export/starexec/sandbox/solver/bin/TPTP.py", line 83, in solveyielding
% 178.75/178.96 for proof in proofgen: yield proof
% 178.75/178.96 File "/export/starexec/sandbox/solver/bin/prover.py", line 422, in proveyielding
% 178.75/178.96 results=node.look() #Can add nodes
% 178.75/178.96 File "/export/starexec/sandbox/solver/bin/prover.py", line 1705, in look
% 178.75/178.96 dt=destructor_ass.x.boundingspecialization(self.context,assump.x,destructor.destroyingpos)
% 178.75/178.96 File "/export/starexec/sandbox/solver/bin/kernel.py", line 1057, in boundingspecialization
% 178.75/178.96 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))
% 178.75/178.96 kernel.SpecializationError: Unexpected matching of length 0 when specializating fact_902_dvd_Oless__imp__triv:(forall (P_1:Prop) (X_1:nat) (Y_1:nat), (((and ((dvd_dvd_nat X_1) Y_1)) (((dvd_dvd_nat Y_1) X_1)->False))->(((and ((dvd_dvd_nat Y_1) X_1)) (((dvd_dvd_nat X_1) Y_1)->False))->P_1))) with fact_307_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_307_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 X_10) Y_10)) (((dvd_dvd_nat Y_10) X_10)->False)))
%------------------------------------------------------------------------------