TSTP Solution File: NUM925^3 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM925^3 : TPTP v7.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n121.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 13:12:04 EST 2018
% Result : Unknown 271.48s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM925^3 : TPTP v7.0.0. Released v5.3.0.
% 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.24 % Computer : n121.star.cs.uiowa.edu
% 0.02/0.24 % Model : x86_64 x86_64
% 0.02/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.24 % Memory : 32218.625MB
% 0.02/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.24 % CPULimit : 300
% 0.02/0.24 % DateTime : Fri Jan 5 16:01:34 CST 2018
% 0.02/0.24 % CPUTime :
% 0.02/0.26 Python 2.7.13
% 0.07/0.51 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox2/benchmark/', '/export/starexec/sandbox2/benchmark/']
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b2877d878>, <kernel.Type object at 0x2b1b2877d320>) of role type named ty_ty_tc__Int__Oint
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring int:Type
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b284967e8>, <kernel.Type object at 0x2b1b2877d5a8>) of role type named ty_ty_tc__Nat__Onat
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring nat:Type
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b2877d518>, <kernel.Type object at 0x2b1b2877da28>) of role type named ty_ty_tc__RealDef__Oreal
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring real:Type
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b2877dbd8>, <kernel.DependentProduct object at 0x2b1b2877d3f8>) of role type named sy_c_All
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring all:((nat->Prop)->Prop)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b2877dc20>, <kernel.DependentProduct object at 0x2b1b2877d758>) of role type named sy_c_Ex
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring _TPTP_ex:((nat->Prop)->Prop)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b2877da70>, <kernel.DependentProduct object at 0x2b1b2877d908>) of role type named sy_c_Groups_Oabs__class_Oabs_000tc__Int__Oint
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring abs_abs_int:(int->int)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b2877d8c0>, <kernel.DependentProduct object at 0x2b1b284927a0>) of role type named sy_c_Groups_Oabs__class_Oabs_000tc__RealDef__Oreal
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring abs_abs_real:(real->real)
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b2877d758>, <kernel.DependentProduct object at 0x2b1b2877d908>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring minus_minus_int:(int->(int->int))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b2877d518>, <kernel.DependentProduct object at 0x2b1b2877d8c0>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring minus_minus_nat:(nat->(nat->nat))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b2877dbd8>, <kernel.DependentProduct object at 0x2b1b2877d758>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__RealDef__Oreal
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring minus_minus_real:(real->(real->real))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b2877d8c0>, <kernel.Constant object at 0x2b1b2877d518>) of role type named sy_c_Groups_Oone__class_Oone_000tc__Int__Oint
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring one_one_int:int
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b2877dbd8>, <kernel.Constant object at 0x2b1b284920e0>) of role type named sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring one_one_nat:nat
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b2877d518>, <kernel.Constant object at 0x2b1b28492290>) of role type named sy_c_Groups_Oone__class_Oone_000tc__RealDef__Oreal
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring one_one_real:real
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b2877dbd8>, <kernel.DependentProduct object at 0x2b1b284927a0>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring plus_plus_int:(int->(int->int))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b2877d758>, <kernel.DependentProduct object at 0x2b1b28492680>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring plus_plus_nat:(nat->(nat->nat))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b2877d758>, <kernel.DependentProduct object at 0x2b1b28492758>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__RealDef__Oreal
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring plus_plus_real:(real->(real->real))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b284927a0>, <kernel.DependentProduct object at 0x2b1b28492320>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring times_times_int:(int->(int->int))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b28492680>, <kernel.DependentProduct object at 0x2b1b284920e0>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__Nat__Onat
% 0.07/0.51 Using role type
% 0.07/0.51 Declaring times_times_nat:(nat->(nat->nat))
% 0.07/0.51 FOF formula (<kernel.Constant object at 0x2b1b28492758>, <kernel.DependentProduct object at 0x2b1b284924d0>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__RealDef__Oreal
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring times_times_real:(real->(real->real))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b28492320>, <kernel.Constant object at 0x2b1b284924d0>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring zero_zero_int:int
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b28492680>, <kernel.Constant object at 0x2b1b284924d0>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring zero_zero_nat:nat
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b28492758>, <kernel.Constant object at 0x2b1b284924d0>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__RealDef__Oreal
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring zero_zero_real:real
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b28492320>, <kernel.DependentProduct object at 0x2b1b283b2098>) of role type named sy_c_If_000tc__Int__Oint
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring if_int:(Prop->(int->(int->int)))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b283b2f38>, <kernel.DependentProduct object at 0x2b1b284922d8>) of role type named sy_c_If_000tc__Nat__Onat
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring if_nat:(Prop->(nat->(nat->nat)))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b283b2098>, <kernel.DependentProduct object at 0x2b1b28492680>) of role type named sy_c_IntPrimes_Ozcong
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring zcong:(int->(int->(int->Prop)))
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b283b2f38>, <kernel.DependentProduct object at 0x2b1b284922d8>) of role type named sy_c_IntPrimes_Ozprime
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring zprime:(int->Prop)
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b283b2d40>, <kernel.DependentProduct object at 0x2b1b283a2098>) of role type named sy_c_Int_OBit0
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring bit0:(int->int)
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b283b2d40>, <kernel.DependentProduct object at 0x2b1b283a2248>) of role type named sy_c_Int_OBit1
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring bit1:(int->int)
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b284924d0>, <kernel.Constant object at 0x2b1b28492290>) of role type named sy_c_Int_OMin
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring min:int
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b28492758>, <kernel.Constant object at 0x2b1b28492290>) of role type named sy_c_Int_OPls
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring pls:int
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b284922d8>, <kernel.DependentProduct object at 0x2b1b283b5518>) of role type named sy_c_Int_Onat
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring nat_1:(int->nat)
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b283a2098>, <kernel.DependentProduct object at 0x2b1b283b54d0>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring number_number_of_int:(int->int)
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b283a22d8>, <kernel.DependentProduct object at 0x2b1b283b5368>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__Nat__Onat
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring number_number_of_nat:(int->nat)
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b283a22d8>, <kernel.DependentProduct object at 0x2b1b283b5320>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__RealDef__Oreal
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring number267125858f_real:(int->real)
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b28492290>, <kernel.DependentProduct object at 0x2b1b283b5878>) of role type named sy_c_Int_Osucc
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring succ:(int->int)
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b284922d8>, <kernel.DependentProduct object at 0x2b1b283b5830>) of role type named sy_c_Nat_Osemiring__1__class_Oof__nat_000tc__Int__Oint
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring semiri1621563631at_int:(nat->int)
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b28492290>, <kernel.DependentProduct object at 0x2b1b283b51b8>) of role type named sy_c_Nat_Osemiring__1__class_Oof__nat_000tc__Nat__Onat
% 0.07/0.52 Using role type
% 0.07/0.52 Declaring semiri984289939at_nat:(nat->nat)
% 0.07/0.52 FOF formula (<kernel.Constant object at 0x2b1b284924d0>, <kernel.DependentProduct object at 0x2b1b283b5170>) of role type named sy_c_Nat_Osemiring__1__class_Oof__nat_000tc__RealDef__Oreal
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring semiri132038758t_real:(nat->real)
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b1b28492290>, <kernel.DependentProduct object at 0x2b1b283b5320>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Int__Oint
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring ord_less_int:(int->(int->Prop))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b1b28492290>, <kernel.DependentProduct object at 0x2b1b283b5878>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring ord_less_nat:(nat->(nat->Prop))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b1b283b5170>, <kernel.DependentProduct object at 0x2b1b283b51b8>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__RealDef__Oreal
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring ord_less_real:(real->(real->Prop))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b1b283b5320>, <kernel.DependentProduct object at 0x2b1b283b54d0>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Int__Oint
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring ord_less_eq_int:(int->(int->Prop))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b1b283b5878>, <kernel.DependentProduct object at 0x2b1b283b5518>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring ord_less_eq_nat:(nat->(nat->Prop))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b1b283b51b8>, <kernel.DependentProduct object at 0x2b1b283b5830>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__RealDef__Oreal
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring ord_less_eq_real:(real->(real->Prop))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b1b283b54d0>, <kernel.DependentProduct object at 0x2b1b283b5170>) of role type named sy_c_Power_Opower__class_Opower_000tc__Int__Oint
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring power_power_int:(int->(nat->int))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b1b283b5518>, <kernel.DependentProduct object at 0x2b1b283b53f8>) of role type named sy_c_Power_Opower__class_Opower_000tc__Nat__Onat
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring power_power_nat:(nat->(nat->nat))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b1b283b5830>, <kernel.DependentProduct object at 0x2b1b283b5950>) of role type named sy_c_Power_Opower__class_Opower_000tc__RealDef__Oreal
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring power_power_real:(real->(nat->real))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b1b283b5170>, <kernel.DependentProduct object at 0x2b1b283b5878>) of role type named sy_c_Residues_OLegendre
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring legendre:(int->(int->int))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b1b283b53f8>, <kernel.DependentProduct object at 0x2b1b283b51b8>) of role type named sy_c_Residues_OQuadRes
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring quadRes:(int->(int->Prop))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b1b283b5950>, <kernel.DependentProduct object at 0x2b1b283b5320>) of role type named sy_c_Rings_Odvd__class_Odvd_000tc__Int__Oint
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring dvd_dvd_int:(int->(int->Prop))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b1b283b5878>, <kernel.DependentProduct object at 0x2b1b283b5830>) of role type named sy_c_Rings_Odvd__class_Odvd_000tc__Nat__Onat
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring dvd_dvd_nat:(nat->(nat->Prop))
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b1b283b51b8>, <kernel.DependentProduct object at 0x2b1b283b5440>) of role type named sy_c_TwoSquares__Mirabelle__dzzvbppuls_Ois__sum2sq
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring twoSqu919416604sum2sq:(int->Prop)
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b1b283b5320>, <kernel.Constant object at 0x2b1b283b5440>) 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 0x2b1b283b5878>, <kernel.Constant object at 0x2b1b283b5440>) of role type named sy_v_m1____
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring m1:int
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b1b283b51b8>, <kernel.Constant object at 0x2b1b283b5440>) of role type named sy_v_n____
% 0.07/0.53 Using role type
% 0.07/0.53 Declaring n:nat
% 0.07/0.53 FOF formula (<kernel.Constant object at 0x2b1b283b5320>, <kernel.Constant object at 0x2b1b283b5440>) 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 0x2b1b283b5878>, <kernel.Constant object at 0x2b1b283b5440>) of role type named sy_v_s____
% 0.07/0.54 Using role type
% 0.07/0.54 Declaring s:int
% 0.07/0.54 FOF formula (<kernel.Constant object at 0x2b1b283b51b8>, <kernel.Constant object at 0x2b1b283b5320>) of role type named sy_v_t____
% 0.07/0.54 Using role type
% 0.07/0.54 Declaring t:int
% 0.07/0.54 FOF formula (<kernel.Constant object at 0x2b1b283b5878>, <kernel.Constant object at 0x2b1b283aef38>) of role type named sy_v_tn____
% 0.07/0.54 Using role type
% 0.07/0.54 Declaring tn:nat
% 0.07/0.54 FOF formula (<kernel.Constant object at 0x2b1b283b5320>, <kernel.Constant object at 0x2b1b283ae9e0>) of role type named sy_v_x____
% 0.07/0.54 Using role type
% 0.07/0.54 Declaring x:int
% 0.07/0.54 FOF formula (<kernel.Constant object at 0x2b1b283b5878>, <kernel.Constant object at 0x2b1b283ae440>) of role type named sy_v_y____
% 0.07/0.54 Using role type
% 0.07/0.54 Declaring y:int
% 0.07/0.54 FOF formula ((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) (semiri1621563631at_int n))) of role axiom named fact_0_n1pos
% 0.07/0.54 A new axiom: ((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) (semiri1621563631at_int n)))
% 0.07/0.54 FOF formula ((ord_less_int one_one_int) t) of role axiom named fact_1_t1
% 0.07/0.54 A new axiom: ((ord_less_int one_one_int) t)
% 0.07/0.54 FOF formula (forall (X:int) (Y:int), ((iff (((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)))))) zero_zero_int)) ((and (((eq int) X) zero_zero_int)) (((eq int) Y) zero_zero_int)))) of role axiom named fact_2_sum__power2__eq__zero__iff
% 0.07/0.54 A new axiom: (forall (X:int) (Y:int), ((iff (((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)))))) zero_zero_int)) ((and (((eq int) X) zero_zero_int)) (((eq int) Y) zero_zero_int))))
% 0.07/0.54 FOF formula (forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real)))) of role axiom named fact_3_sum__power2__eq__zero__iff
% 0.07/0.54 A new axiom: (forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real))))
% 0.07/0.54 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_4_one__power2
% 0.07/0.54 A new axiom: (((eq int) ((power_power_int one_one_int) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)
% 0.07/0.54 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_5_one__power2
% 0.07/0.54 A new axiom: (((eq nat) ((power_power_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls))))) one_one_nat)
% 0.07/0.54 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_6_one__power2
% 0.07/0.54 A new axiom: (((eq real) ((power_power_real one_one_real) (number_number_of_nat (bit0 (bit1 pls))))) one_one_real)
% 0.07/0.54 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_7_zero__power2
% 0.07/0.54 A new axiom: (((eq int) ((power_power_int zero_zero_int) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)
% 0.07/0.54 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_8_zero__power2
% 0.07/0.54 A new axiom: (((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_nat)
% 0.07/0.54 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_9_zero__power2
% 0.07/0.54 A new axiom: (((eq real) ((power_power_real zero_zero_real) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)
% 0.07/0.54 FOF formula (forall (A_136:int), ((iff (((eq int) ((power_power_int A_136) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)) (((eq int) A_136) zero_zero_int))) of role axiom named fact_10_zero__eq__power2
% 0.07/0.55 A new axiom: (forall (A_136:int), ((iff (((eq int) ((power_power_int A_136) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)) (((eq int) A_136) zero_zero_int)))
% 0.07/0.55 FOF formula (forall (A_136:real), ((iff (((eq real) ((power_power_real A_136) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)) (((eq real) A_136) zero_zero_real))) of role axiom named fact_11_zero__eq__power2
% 0.07/0.55 A new axiom: (forall (A_136:real), ((iff (((eq real) ((power_power_real A_136) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)) (((eq real) A_136) zero_zero_real)))
% 0.07/0.55 FOF formula (forall (W_16:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_16))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_16)))) of role axiom named fact_12_add__special_I2_J
% 0.07/0.55 A new axiom: (forall (W_16:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_16))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_16))))
% 0.07/0.55 FOF formula (forall (W_16:int), (((eq real) ((plus_plus_real one_one_real) (number267125858f_real W_16))) (number267125858f_real ((plus_plus_int (bit1 pls)) W_16)))) of role axiom named fact_13_add__special_I2_J
% 0.07/0.55 A new axiom: (forall (W_16:int), (((eq real) ((plus_plus_real one_one_real) (number267125858f_real W_16))) (number267125858f_real ((plus_plus_int (bit1 pls)) W_16))))
% 0.07/0.55 FOF formula (forall (V_16:int), (((eq int) ((plus_plus_int (number_number_of_int V_16)) one_one_int)) (number_number_of_int ((plus_plus_int V_16) (bit1 pls))))) of role axiom named fact_14_add__special_I3_J
% 0.07/0.55 A new axiom: (forall (V_16:int), (((eq int) ((plus_plus_int (number_number_of_int V_16)) one_one_int)) (number_number_of_int ((plus_plus_int V_16) (bit1 pls)))))
% 0.07/0.55 FOF formula (forall (V_16:int), (((eq real) ((plus_plus_real (number267125858f_real V_16)) one_one_real)) (number267125858f_real ((plus_plus_int V_16) (bit1 pls))))) of role axiom named fact_15_add__special_I3_J
% 0.07/0.55 A new axiom: (forall (V_16:int), (((eq real) ((plus_plus_real (number267125858f_real V_16)) one_one_real)) (number267125858f_real ((plus_plus_int V_16) (bit1 pls)))))
% 0.07/0.55 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_16_one__add__one__is__two
% 0.07/0.55 A new axiom: (((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls))))
% 0.07/0.55 FOF formula (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))) of role axiom named fact_17_one__add__one__is__two
% 0.07/0.55 A new axiom: (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls))))
% 0.07/0.55 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_18_semiring__one__add__one__is__two
% 0.07/0.55 A new axiom: (((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls))))
% 0.07/0.55 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_19_semiring__one__add__one__is__two
% 0.07/0.55 A new axiom: (((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls))))
% 0.07/0.55 FOF formula (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))) of role axiom named fact_20_semiring__one__add__one__is__two
% 0.07/0.55 A new axiom: (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls))))
% 0.07/0.55 FOF formula (forall (X:int), (((eq int) ((power_power_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int X) (number_number_of_nat (bit0 (bit0 (bit1 pls))))))) of role axiom named fact_21_quartic__square__square
% 0.07/0.55 A new axiom: (forall (X:int), (((eq int) ((power_power_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int X) (number_number_of_nat (bit0 (bit0 (bit1 pls)))))))
% 0.07/0.55 FOF formula (forall (W_15:int), ((and ((((eq nat) (number_number_of_nat W_15)) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_15))) one_one_int))) ((not (((eq nat) (number_number_of_nat W_15)) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_15))) zero_zero_int)))) of role axiom named fact_22_power__0__left__number__of
% 0.07/0.57 A new axiom: (forall (W_15:int), ((and ((((eq nat) (number_number_of_nat W_15)) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_15))) one_one_int))) ((not (((eq nat) (number_number_of_nat W_15)) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_15))) zero_zero_int))))
% 0.07/0.57 FOF formula (forall (W_15:int), ((and ((((eq nat) (number_number_of_nat W_15)) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_15))) one_one_nat))) ((not (((eq nat) (number_number_of_nat W_15)) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_15))) zero_zero_nat)))) of role axiom named fact_23_power__0__left__number__of
% 0.07/0.57 A new axiom: (forall (W_15:int), ((and ((((eq nat) (number_number_of_nat W_15)) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_15))) one_one_nat))) ((not (((eq nat) (number_number_of_nat W_15)) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_15))) zero_zero_nat))))
% 0.07/0.57 FOF formula (forall (W_15:int), ((and ((((eq nat) (number_number_of_nat W_15)) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_15))) one_one_real))) ((not (((eq nat) (number_number_of_nat W_15)) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_15))) zero_zero_real)))) of role axiom named fact_24_power__0__left__number__of
% 0.07/0.57 A new axiom: (forall (W_15:int), ((and ((((eq nat) (number_number_of_nat W_15)) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_15))) one_one_real))) ((not (((eq nat) (number_number_of_nat W_15)) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_15))) zero_zero_real))))
% 0.07/0.57 FOF formula (((eq int) one_one_int) (number_number_of_int (bit1 pls))) of role axiom named fact_25_semiring__norm_I110_J
% 0.07/0.57 A new axiom: (((eq int) one_one_int) (number_number_of_int (bit1 pls)))
% 0.07/0.57 FOF formula (((eq real) one_one_real) (number267125858f_real (bit1 pls))) of role axiom named fact_26_semiring__norm_I110_J
% 0.07/0.57 A new axiom: (((eq real) one_one_real) (number267125858f_real (bit1 pls)))
% 0.07/0.57 FOF formula (((eq int) (number_number_of_int (bit1 pls))) one_one_int) of role axiom named fact_27_numeral__1__eq__1
% 0.07/0.57 A new axiom: (((eq int) (number_number_of_int (bit1 pls))) one_one_int)
% 0.07/0.57 FOF formula (((eq real) (number267125858f_real (bit1 pls))) one_one_real) of role axiom named fact_28_numeral__1__eq__1
% 0.07/0.57 A new axiom: (((eq real) (number267125858f_real (bit1 pls))) one_one_real)
% 0.07/0.57 FOF formula ((ord_less_nat zero_zero_nat) n) of role axiom named fact_29_n0
% 0.07/0.57 A new axiom: ((ord_less_nat zero_zero_nat) n)
% 0.07/0.57 FOF formula (forall (X:int) (Y:int), ((or ((or ((ord_less_int X) Y)) (((eq int) X) Y))) ((ord_less_int Y) X))) of role axiom named fact_30_zless__linear
% 0.07/0.57 A new axiom: (forall (X:int) (Y:int), ((or ((or ((ord_less_int X) Y)) (((eq int) X) Y))) ((ord_less_int Y) X)))
% 0.07/0.57 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_31_less__number__of__int__code
% 0.07/0.57 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)))
% 0.07/0.57 FOF formula (forall (V_1:int) (W:int), (((eq int) ((plus_plus_int (number_number_of_int V_1)) (number_number_of_int W))) (number_number_of_int ((plus_plus_int V_1) W)))) of role axiom named fact_32_plus__numeral__code_I9_J
% 0.07/0.57 A new axiom: (forall (V_1:int) (W:int), (((eq int) ((plus_plus_int (number_number_of_int V_1)) (number_number_of_int W))) (number_number_of_int ((plus_plus_int V_1) W))))
% 0.07/0.57 FOF formula (forall (X_30:int) (Y_23:int), ((iff ((ord_less_int (number_number_of_int X_30)) (number_number_of_int Y_23))) ((ord_less_int X_30) Y_23))) of role axiom named fact_33_less__number__of
% 0.07/0.58 A new axiom: (forall (X_30:int) (Y_23:int), ((iff ((ord_less_int (number_number_of_int X_30)) (number_number_of_int Y_23))) ((ord_less_int X_30) Y_23)))
% 0.07/0.58 FOF formula (forall (X_30:int) (Y_23:int), ((iff ((ord_less_real (number267125858f_real X_30)) (number267125858f_real Y_23))) ((ord_less_int X_30) Y_23))) of role axiom named fact_34_less__number__of
% 0.07/0.58 A new axiom: (forall (X_30:int) (Y_23:int), ((iff ((ord_less_real (number267125858f_real X_30)) (number267125858f_real Y_23))) ((ord_less_int X_30) Y_23)))
% 0.07/0.58 FOF formula (((eq int) zero_zero_int) (number_number_of_int pls)) of role axiom named fact_35_zero__is__num__zero
% 0.07/0.58 A new axiom: (((eq int) zero_zero_int) (number_number_of_int pls))
% 0.07/0.58 FOF formula (forall (M:nat) (N:nat), (((eq int) ((power_power_int (semiri1621563631at_int M)) N)) (semiri1621563631at_int ((power_power_nat M) N)))) of role axiom named fact_36_zpower__int
% 0.07/0.58 A new axiom: (forall (M:nat) (N:nat), (((eq int) ((power_power_int (semiri1621563631at_int M)) N)) (semiri1621563631at_int ((power_power_nat M) N))))
% 0.07/0.58 FOF formula (forall (M:nat) (N:nat), (((eq int) (semiri1621563631at_int ((power_power_nat M) N))) ((power_power_int (semiri1621563631at_int M)) N))) of role axiom named fact_37_int__power
% 0.07/0.58 A new axiom: (forall (M:nat) (N:nat), (((eq int) (semiri1621563631at_int ((power_power_nat M) N))) ((power_power_int (semiri1621563631at_int M)) N)))
% 0.07/0.58 FOF formula (forall (M:nat) (N:nat) (Z:int), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) ((plus_plus_int (semiri1621563631at_int N)) Z))) ((plus_plus_int (semiri1621563631at_int ((plus_plus_nat M) N))) Z))) of role axiom named fact_38_zadd__int__left
% 0.07/0.58 A new axiom: (forall (M:nat) (N:nat) (Z:int), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) ((plus_plus_int (semiri1621563631at_int N)) Z))) ((plus_plus_int (semiri1621563631at_int ((plus_plus_nat M) N))) Z)))
% 0.07/0.58 FOF formula (forall (M:nat) (N:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((plus_plus_nat M) N)))) of role axiom named fact_39_zadd__int
% 0.07/0.58 A new axiom: (forall (M:nat) (N:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((plus_plus_nat M) N))))
% 0.07/0.58 FOF formula (((eq int) (semiri1621563631at_int one_one_nat)) one_one_int) of role axiom named fact_40_int__1
% 0.07/0.58 A new axiom: (((eq int) (semiri1621563631at_int one_one_nat)) one_one_int)
% 0.07/0.58 FOF formula (((eq nat) (number_number_of_nat pls)) zero_zero_nat) of role axiom named fact_41_nat__number__of__Pls
% 0.07/0.58 A new axiom: (((eq nat) (number_number_of_nat pls)) zero_zero_nat)
% 0.07/0.58 FOF formula (((eq nat) zero_zero_nat) (number_number_of_nat pls)) of role axiom named fact_42_semiring__norm_I113_J
% 0.07/0.58 A new axiom: (((eq nat) zero_zero_nat) (number_number_of_nat pls))
% 0.07/0.58 FOF formula (forall (N:nat), ((iff (((eq int) (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat))) of role axiom named fact_43_int__eq__0__conv
% 0.07/0.58 A new axiom: (forall (N:nat), ((iff (((eq int) (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat)))
% 0.07/0.58 FOF formula (((eq int) (semiri1621563631at_int zero_zero_nat)) zero_zero_int) of role axiom named fact_44_int__0
% 0.07/0.58 A new axiom: (((eq int) (semiri1621563631at_int zero_zero_nat)) zero_zero_int)
% 0.07/0.58 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_45_nat__1__add__1
% 0.07/0.58 A new axiom: (((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls))))
% 0.07/0.58 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_46_less__int__code_I16_J
% 0.07/0.58 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2)))
% 0.07/0.58 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_47_rel__simps_I17_J
% 0.07/0.58 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L)))
% 0.39/0.60 FOF formula (((ord_less_int pls) pls)->False) of role axiom named fact_48_rel__simps_I2_J
% 0.39/0.60 A new axiom: (((ord_less_int pls) pls)->False)
% 0.39/0.60 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_49_less__int__code_I13_J
% 0.39/0.60 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit0 K2))) ((ord_less_int K1) K2)))
% 0.39/0.60 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_50_rel__simps_I14_J
% 0.39/0.60 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit0 L))) ((ord_less_int K) L)))
% 0.39/0.60 FOF formula (forall (K:int) (I_1:int) (J:int), (((ord_less_int I_1) J)->((ord_less_int ((plus_plus_int I_1) K)) ((plus_plus_int J) K)))) of role axiom named fact_51_zadd__strict__right__mono
% 0.39/0.60 A new axiom: (forall (K:int) (I_1:int) (J:int), (((ord_less_int I_1) J)->((ord_less_int ((plus_plus_int I_1) K)) ((plus_plus_int J) K))))
% 0.39/0.60 FOF formula (forall (V_2:int) (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) (number_number_of_nat V_2)))) ((((ord_less_int V_1) pls)->False)->((and (((ord_less_int V_2) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) (number_number_of_nat V_1)))) ((((ord_less_int V_2) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) (number_number_of_nat ((plus_plus_int V_1) V_2)))))))) of role axiom named fact_52_add__nat__number__of
% 0.39/0.60 A new axiom: (forall (V_2:int) (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) (number_number_of_nat V_2)))) ((((ord_less_int V_1) pls)->False)->((and (((ord_less_int V_2) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) (number_number_of_nat V_1)))) ((((ord_less_int V_2) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) (number_number_of_nat ((plus_plus_int V_1) V_2))))))))
% 0.39/0.60 FOF formula (((eq int) one_one_int) (number_number_of_int (bit1 pls))) of role axiom named fact_53_one__is__num__one
% 0.39/0.60 A new axiom: (((eq int) one_one_int) (number_number_of_int (bit1 pls)))
% 0.39/0.60 FOF formula (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat) of role axiom named fact_54_nat__numeral__1__eq__1
% 0.39/0.60 A new axiom: (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat)
% 0.39/0.60 FOF formula (((eq nat) one_one_nat) (number_number_of_nat (bit1 pls))) of role axiom named fact_55_Numeral1__eq1__nat
% 0.39/0.60 A new axiom: (((eq nat) one_one_nat) (number_number_of_nat (bit1 pls)))
% 0.39/0.60 FOF formula (forall (X_29:int) (Y_22:int), ((iff (((eq int) (number_number_of_int X_29)) (number_number_of_int Y_22))) (((eq int) X_29) Y_22))) of role axiom named fact_56_eq__number__of
% 0.39/0.60 A new axiom: (forall (X_29:int) (Y_22:int), ((iff (((eq int) (number_number_of_int X_29)) (number_number_of_int Y_22))) (((eq int) X_29) Y_22)))
% 0.39/0.60 FOF formula (forall (X_29:int) (Y_22:int), ((iff (((eq real) (number267125858f_real X_29)) (number267125858f_real Y_22))) (((eq int) X_29) Y_22))) of role axiom named fact_57_eq__number__of
% 0.39/0.60 A new axiom: (forall (X_29:int) (Y_22:int), ((iff (((eq real) (number267125858f_real X_29)) (number267125858f_real Y_22))) (((eq int) X_29) Y_22)))
% 0.39/0.60 FOF formula (forall (W_14:int) (X_28:nat), ((iff (((eq nat) (number_number_of_nat W_14)) X_28)) (((eq nat) X_28) (number_number_of_nat W_14)))) of role axiom named fact_58_number__of__reorient
% 0.39/0.60 A new axiom: (forall (W_14:int) (X_28:nat), ((iff (((eq nat) (number_number_of_nat W_14)) X_28)) (((eq nat) X_28) (number_number_of_nat W_14))))
% 0.39/0.60 FOF formula (forall (W_14:int) (X_28:int), ((iff (((eq int) (number_number_of_int W_14)) X_28)) (((eq int) X_28) (number_number_of_int W_14)))) of role axiom named fact_59_number__of__reorient
% 0.39/0.60 A new axiom: (forall (W_14:int) (X_28:int), ((iff (((eq int) (number_number_of_int W_14)) X_28)) (((eq int) X_28) (number_number_of_int W_14))))
% 0.41/0.62 FOF formula (forall (W_14:int) (X_28:real), ((iff (((eq real) (number267125858f_real W_14)) X_28)) (((eq real) X_28) (number267125858f_real W_14)))) of role axiom named fact_60_number__of__reorient
% 0.41/0.62 A new axiom: (forall (W_14:int) (X_28:real), ((iff (((eq real) (number267125858f_real W_14)) X_28)) (((eq real) X_28) (number267125858f_real W_14))))
% 0.41/0.62 FOF formula (forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L))) of role axiom named fact_61_rel__simps_I51_J
% 0.41/0.62 A new axiom: (forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L)))
% 0.41/0.62 FOF formula (forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L))) of role axiom named fact_62_rel__simps_I48_J
% 0.41/0.62 A new axiom: (forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L)))
% 0.41/0.62 FOF formula (forall (A_135:int), ((iff ((ord_less_int ((plus_plus_int A_135) A_135)) zero_zero_int)) ((ord_less_int A_135) zero_zero_int))) of role axiom named fact_63_even__less__0__iff
% 0.41/0.62 A new axiom: (forall (A_135:int), ((iff ((ord_less_int ((plus_plus_int A_135) A_135)) zero_zero_int)) ((ord_less_int A_135) zero_zero_int)))
% 0.41/0.62 FOF formula (forall (A_135:real), ((iff ((ord_less_real ((plus_plus_real A_135) A_135)) zero_zero_real)) ((ord_less_real A_135) zero_zero_real))) of role axiom named fact_64_even__less__0__iff
% 0.41/0.62 A new axiom: (forall (A_135:real), ((iff ((ord_less_real ((plus_plus_real A_135) A_135)) zero_zero_real)) ((ord_less_real A_135) zero_zero_real)))
% 0.41/0.62 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_65_zadd__assoc
% 0.41/0.62 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))))
% 0.41/0.62 FOF formula (forall (X:int) (Y:int) (Z:int), (((eq int) ((plus_plus_int X) ((plus_plus_int Y) Z))) ((plus_plus_int Y) ((plus_plus_int X) Z)))) of role axiom named fact_66_zadd__left__commute
% 0.41/0.62 A new axiom: (forall (X:int) (Y:int) (Z:int), (((eq int) ((plus_plus_int X) ((plus_plus_int Y) Z))) ((plus_plus_int Y) ((plus_plus_int X) Z))))
% 0.41/0.62 FOF formula (forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z))) of role axiom named fact_67_zadd__commute
% 0.41/0.62 A new axiom: (forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z)))
% 0.41/0.62 FOF formula (forall (M:nat) (N:nat), ((iff (((eq int) (semiri1621563631at_int M)) (semiri1621563631at_int N))) (((eq nat) M) N))) of role axiom named fact_68_int__int__eq
% 0.41/0.62 A new axiom: (forall (M:nat) (N:nat), ((iff (((eq int) (semiri1621563631at_int M)) (semiri1621563631at_int N))) (((eq nat) M) N)))
% 0.41/0.62 FOF formula (forall (X_27:int), ((iff ((ord_less_int (number_number_of_int X_27)) zero_zero_int)) ((ord_less_int X_27) pls))) of role axiom named fact_69_less__special_I3_J
% 0.41/0.62 A new axiom: (forall (X_27:int), ((iff ((ord_less_int (number_number_of_int X_27)) zero_zero_int)) ((ord_less_int X_27) pls)))
% 0.41/0.62 FOF formula (forall (X_27:int), ((iff ((ord_less_real (number267125858f_real X_27)) zero_zero_real)) ((ord_less_int X_27) pls))) of role axiom named fact_70_less__special_I3_J
% 0.41/0.62 A new axiom: (forall (X_27:int), ((iff ((ord_less_real (number267125858f_real X_27)) zero_zero_real)) ((ord_less_int X_27) pls)))
% 0.41/0.62 FOF formula (forall (Y_21:int), ((iff ((ord_less_int zero_zero_int) (number_number_of_int Y_21))) ((ord_less_int pls) Y_21))) of role axiom named fact_71_less__special_I1_J
% 0.41/0.62 A new axiom: (forall (Y_21:int), ((iff ((ord_less_int zero_zero_int) (number_number_of_int Y_21))) ((ord_less_int pls) Y_21)))
% 0.41/0.62 FOF formula (forall (Y_21:int), ((iff ((ord_less_real zero_zero_real) (number267125858f_real Y_21))) ((ord_less_int pls) Y_21))) of role axiom named fact_72_less__special_I1_J
% 0.41/0.62 A new axiom: (forall (Y_21:int), ((iff ((ord_less_real zero_zero_real) (number267125858f_real Y_21))) ((ord_less_int pls) Y_21)))
% 0.41/0.62 FOF formula (forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_73_rel__simps_I12_J
% 0.41/0.62 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls)))
% 0.42/0.63 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_74_less__int__code_I15_J
% 0.42/0.63 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2)))
% 0.42/0.63 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_75_rel__simps_I16_J
% 0.42/0.63 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit0 L))) ((ord_less_int K) L)))
% 0.42/0.63 FOF formula (forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_76_rel__simps_I10_J
% 0.42/0.63 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls)))
% 0.42/0.63 FOF formula (forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K))) of role axiom named fact_77_rel__simps_I4_J
% 0.42/0.63 A new axiom: (forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K)))
% 0.42/0.63 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_78_bin__less__0__simps_I4_J
% 0.42/0.63 A new axiom: (forall (W:int), ((iff ((ord_less_int (bit1 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int)))
% 0.42/0.63 FOF formula (((ord_less_int pls) zero_zero_int)->False) of role axiom named fact_79_bin__less__0__simps_I1_J
% 0.42/0.63 A new axiom: (((ord_less_int pls) zero_zero_int)->False)
% 0.42/0.63 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_80_bin__less__0__simps_I3_J
% 0.42/0.63 A new axiom: (forall (W:int), ((iff ((ord_less_int (bit0 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int)))
% 0.42/0.63 FOF formula ((ord_less_int zero_zero_int) one_one_int) of role axiom named fact_81_int__0__less__1
% 0.42/0.63 A new axiom: ((ord_less_int zero_zero_int) one_one_int)
% 0.42/0.63 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_82_zless__add1__eq
% 0.42/0.63 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))))
% 0.42/0.63 FOF formula (forall (K:nat), (((ord_less_int (semiri1621563631at_int K)) zero_zero_int)->False)) of role axiom named fact_83_int__less__0__conv
% 0.42/0.63 A new axiom: (forall (K:nat), (((ord_less_int (semiri1621563631at_int K)) zero_zero_int)->False))
% 0.42/0.63 FOF formula (forall (X_26:int), ((iff ((ord_less_int (number_number_of_int X_26)) one_one_int)) ((ord_less_int X_26) (bit1 pls)))) of role axiom named fact_84_less__special_I4_J
% 0.42/0.63 A new axiom: (forall (X_26:int), ((iff ((ord_less_int (number_number_of_int X_26)) one_one_int)) ((ord_less_int X_26) (bit1 pls))))
% 0.42/0.63 FOF formula (forall (X_26:int), ((iff ((ord_less_real (number267125858f_real X_26)) one_one_real)) ((ord_less_int X_26) (bit1 pls)))) of role axiom named fact_85_less__special_I4_J
% 0.42/0.63 A new axiom: (forall (X_26:int), ((iff ((ord_less_real (number267125858f_real X_26)) one_one_real)) ((ord_less_int X_26) (bit1 pls))))
% 0.42/0.63 FOF formula (forall (Y_20:int), ((iff ((ord_less_int one_one_int) (number_number_of_int Y_20))) ((ord_less_int (bit1 pls)) Y_20))) of role axiom named fact_86_less__special_I2_J
% 0.42/0.63 A new axiom: (forall (Y_20:int), ((iff ((ord_less_int one_one_int) (number_number_of_int Y_20))) ((ord_less_int (bit1 pls)) Y_20)))
% 0.42/0.63 FOF formula (forall (Y_20:int), ((iff ((ord_less_real one_one_real) (number267125858f_real Y_20))) ((ord_less_int (bit1 pls)) Y_20))) of role axiom named fact_87_less__special_I2_J
% 0.42/0.63 A new axiom: (forall (Y_20:int), ((iff ((ord_less_real one_one_real) (number267125858f_real Y_20))) ((ord_less_int (bit1 pls)) Y_20)))
% 0.42/0.63 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_88_odd__less__0
% 0.42/0.63 A new axiom: (forall (Z:int), ((iff ((ord_less_int ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int)) ((ord_less_int Z) zero_zero_int)))
% 0.42/0.65 FOF formula (forall (A_134:int), ((iff (((eq int) ((plus_plus_int A_134) A_134)) zero_zero_int)) (((eq int) A_134) zero_zero_int))) of role axiom named fact_89_double__eq__0__iff
% 0.42/0.65 A new axiom: (forall (A_134:int), ((iff (((eq int) ((plus_plus_int A_134) A_134)) zero_zero_int)) (((eq int) A_134) zero_zero_int)))
% 0.42/0.65 FOF formula (forall (A_134:real), ((iff (((eq real) ((plus_plus_real A_134) A_134)) zero_zero_real)) (((eq real) A_134) zero_zero_real))) of role axiom named fact_90_double__eq__0__iff
% 0.42/0.65 A new axiom: (forall (A_134:real), ((iff (((eq real) ((plus_plus_real A_134) A_134)) zero_zero_real)) (((eq real) A_134) zero_zero_real)))
% 0.42/0.65 FOF formula (forall (K:int), (not (((eq int) (bit1 K)) pls))) of role axiom named fact_91_rel__simps_I46_J
% 0.42/0.65 A new axiom: (forall (K:int), (not (((eq int) (bit1 K)) pls)))
% 0.42/0.65 FOF formula (forall (L:int), (not (((eq int) pls) (bit1 L)))) of role axiom named fact_92_rel__simps_I39_J
% 0.42/0.65 A new axiom: (forall (L:int), (not (((eq int) pls) (bit1 L))))
% 0.42/0.65 FOF formula (forall (K:int) (L:int), (not (((eq int) (bit1 K)) (bit0 L)))) of role axiom named fact_93_rel__simps_I50_J
% 0.42/0.65 A new axiom: (forall (K:int) (L:int), (not (((eq int) (bit1 K)) (bit0 L))))
% 0.42/0.65 FOF formula (forall (K:int) (L:int), (not (((eq int) (bit0 K)) (bit1 L)))) of role axiom named fact_94_rel__simps_I49_J
% 0.42/0.65 A new axiom: (forall (K:int) (L:int), (not (((eq int) (bit0 K)) (bit1 L))))
% 0.42/0.65 FOF formula (forall (K:int), ((iff (((eq int) (bit0 K)) pls)) (((eq int) K) pls))) of role axiom named fact_95_rel__simps_I44_J
% 0.42/0.65 A new axiom: (forall (K:int), ((iff (((eq int) (bit0 K)) pls)) (((eq int) K) pls)))
% 0.42/0.65 FOF formula (forall (L:int), ((iff (((eq int) pls) (bit0 L))) (((eq int) pls) L))) of role axiom named fact_96_rel__simps_I38_J
% 0.42/0.65 A new axiom: (forall (L:int), ((iff (((eq int) pls) (bit0 L))) (((eq int) pls) L)))
% 0.42/0.65 FOF formula (((eq int) (bit0 pls)) pls) of role axiom named fact_97_Bit0__Pls
% 0.42/0.65 A new axiom: (((eq int) (bit0 pls)) pls)
% 0.42/0.65 FOF formula (((eq int) pls) zero_zero_int) of role axiom named fact_98_Pls__def
% 0.42/0.65 A new axiom: (((eq int) pls) zero_zero_int)
% 0.42/0.65 FOF formula (not (((eq int) zero_zero_int) one_one_int)) of role axiom named fact_99_int__0__neq__1
% 0.42/0.65 A new axiom: (not (((eq int) zero_zero_int) one_one_int))
% 0.42/0.65 FOF formula (forall (K:int), (((eq int) ((plus_plus_int K) pls)) K)) of role axiom named fact_100_add__Pls__right
% 0.42/0.65 A new axiom: (forall (K:int), (((eq int) ((plus_plus_int K) pls)) K))
% 0.42/0.65 FOF formula (forall (K:int), (((eq int) ((plus_plus_int pls) K)) K)) of role axiom named fact_101_add__Pls
% 0.42/0.65 A new axiom: (forall (K:int), (((eq int) ((plus_plus_int pls) K)) K))
% 0.42/0.65 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_102_add__Bit0__Bit0
% 0.42/0.65 A new axiom: (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit0 L))) (bit0 ((plus_plus_int K) L))))
% 0.42/0.65 FOF formula (forall (K:int), (((eq int) (bit0 K)) ((plus_plus_int K) K))) of role axiom named fact_103_Bit0__def
% 0.42/0.65 A new axiom: (forall (K:int), (((eq int) (bit0 K)) ((plus_plus_int K) K)))
% 0.42/0.65 FOF formula (forall (Z:int), (((eq int) ((plus_plus_int Z) zero_zero_int)) Z)) of role axiom named fact_104_zadd__0__right
% 0.42/0.65 A new axiom: (forall (Z:int), (((eq int) ((plus_plus_int Z) zero_zero_int)) Z))
% 0.42/0.65 FOF formula (forall (Z:int), (((eq int) ((plus_plus_int zero_zero_int) Z)) Z)) of role axiom named fact_105_zadd__0
% 0.42/0.65 A new axiom: (forall (Z:int), (((eq int) ((plus_plus_int zero_zero_int) Z)) Z))
% 0.42/0.65 FOF formula (((eq int) (number_number_of_int pls)) zero_zero_int) of role axiom named fact_106_semiring__numeral__0__eq__0
% 0.42/0.65 A new axiom: (((eq int) (number_number_of_int pls)) zero_zero_int)
% 0.42/0.65 FOF formula (((eq nat) (number_number_of_nat pls)) zero_zero_nat) of role axiom named fact_107_semiring__numeral__0__eq__0
% 0.42/0.65 A new axiom: (((eq nat) (number_number_of_nat pls)) zero_zero_nat)
% 0.42/0.65 FOF formula (((eq real) (number267125858f_real pls)) zero_zero_real) of role axiom named fact_108_semiring__numeral__0__eq__0
% 0.42/0.65 A new axiom: (((eq real) (number267125858f_real pls)) zero_zero_real)
% 0.42/0.65 FOF formula (((eq int) (number_number_of_int pls)) zero_zero_int) of role axiom named fact_109_number__of__Pls
% 0.42/0.66 A new axiom: (((eq int) (number_number_of_int pls)) zero_zero_int)
% 0.42/0.66 FOF formula (((eq real) (number267125858f_real pls)) zero_zero_real) of role axiom named fact_110_number__of__Pls
% 0.42/0.66 A new axiom: (((eq real) (number267125858f_real pls)) zero_zero_real)
% 0.42/0.66 FOF formula (((eq int) zero_zero_int) (number_number_of_int pls)) of role axiom named fact_111_semiring__norm_I112_J
% 0.42/0.66 A new axiom: (((eq int) zero_zero_int) (number_number_of_int pls))
% 0.42/0.66 FOF formula (((eq real) zero_zero_real) (number267125858f_real pls)) of role axiom named fact_112_semiring__norm_I112_J
% 0.42/0.66 A new axiom: (((eq real) zero_zero_real) (number267125858f_real pls))
% 0.42/0.66 FOF formula (forall (A_133:int), (((eq int) ((plus_plus_int (number_number_of_int pls)) A_133)) A_133)) of role axiom named fact_113_add__numeral__0
% 0.42/0.66 A new axiom: (forall (A_133:int), (((eq int) ((plus_plus_int (number_number_of_int pls)) A_133)) A_133))
% 0.42/0.66 FOF formula (forall (A_133:real), (((eq real) ((plus_plus_real (number267125858f_real pls)) A_133)) A_133)) of role axiom named fact_114_add__numeral__0
% 0.42/0.66 A new axiom: (forall (A_133:real), (((eq real) ((plus_plus_real (number267125858f_real pls)) A_133)) A_133))
% 0.42/0.66 FOF formula (forall (A_132:int), (((eq int) ((plus_plus_int A_132) (number_number_of_int pls))) A_132)) of role axiom named fact_115_add__numeral__0__right
% 0.42/0.66 A new axiom: (forall (A_132:int), (((eq int) ((plus_plus_int A_132) (number_number_of_int pls))) A_132))
% 0.42/0.66 FOF formula (forall (A_132:real), (((eq real) ((plus_plus_real A_132) (number267125858f_real pls))) A_132)) of role axiom named fact_116_add__numeral__0__right
% 0.42/0.66 A new axiom: (forall (A_132:real), (((eq real) ((plus_plus_real A_132) (number267125858f_real pls))) A_132))
% 0.42/0.66 FOF formula (forall (A_131:int) (W_13:int), ((iff (((eq int) ((power_power_int A_131) (number_number_of_nat W_13))) zero_zero_int)) ((and (((eq int) A_131) zero_zero_int)) (not (((eq nat) (number_number_of_nat W_13)) zero_zero_nat))))) of role axiom named fact_117_power__eq__0__iff__number__of
% 0.42/0.66 A new axiom: (forall (A_131:int) (W_13:int), ((iff (((eq int) ((power_power_int A_131) (number_number_of_nat W_13))) zero_zero_int)) ((and (((eq int) A_131) zero_zero_int)) (not (((eq nat) (number_number_of_nat W_13)) zero_zero_nat)))))
% 0.42/0.66 FOF formula (forall (A_131:nat) (W_13:int), ((iff (((eq nat) ((power_power_nat A_131) (number_number_of_nat W_13))) zero_zero_nat)) ((and (((eq nat) A_131) zero_zero_nat)) (not (((eq nat) (number_number_of_nat W_13)) zero_zero_nat))))) of role axiom named fact_118_power__eq__0__iff__number__of
% 0.42/0.66 A new axiom: (forall (A_131:nat) (W_13:int), ((iff (((eq nat) ((power_power_nat A_131) (number_number_of_nat W_13))) zero_zero_nat)) ((and (((eq nat) A_131) zero_zero_nat)) (not (((eq nat) (number_number_of_nat W_13)) zero_zero_nat)))))
% 0.42/0.66 FOF formula (forall (A_131:real) (W_13:int), ((iff (((eq real) ((power_power_real A_131) (number_number_of_nat W_13))) zero_zero_real)) ((and (((eq real) A_131) zero_zero_real)) (not (((eq nat) (number_number_of_nat W_13)) zero_zero_nat))))) of role axiom named fact_119_power__eq__0__iff__number__of
% 0.42/0.66 A new axiom: (forall (A_131:real) (W_13:int), ((iff (((eq real) ((power_power_real A_131) (number_number_of_nat W_13))) zero_zero_real)) ((and (((eq real) A_131) zero_zero_real)) (not (((eq nat) (number_number_of_nat W_13)) zero_zero_nat)))))
% 0.42/0.66 FOF formula (forall (V_15:int) (W_12:int) (Z_5:int), (((eq int) ((plus_plus_int (number_number_of_int V_15)) ((plus_plus_int (number_number_of_int W_12)) Z_5))) ((plus_plus_int (number_number_of_int ((plus_plus_int V_15) W_12))) Z_5))) of role axiom named fact_120_add__number__of__left
% 0.42/0.66 A new axiom: (forall (V_15:int) (W_12:int) (Z_5:int), (((eq int) ((plus_plus_int (number_number_of_int V_15)) ((plus_plus_int (number_number_of_int W_12)) Z_5))) ((plus_plus_int (number_number_of_int ((plus_plus_int V_15) W_12))) Z_5)))
% 0.42/0.66 FOF formula (forall (V_15:int) (W_12:int) (Z_5:real), (((eq real) ((plus_plus_real (number267125858f_real V_15)) ((plus_plus_real (number267125858f_real W_12)) Z_5))) ((plus_plus_real (number267125858f_real ((plus_plus_int V_15) W_12))) Z_5))) of role axiom named fact_121_add__number__of__left
% 0.42/0.68 A new axiom: (forall (V_15:int) (W_12:int) (Z_5:real), (((eq real) ((plus_plus_real (number267125858f_real V_15)) ((plus_plus_real (number267125858f_real W_12)) Z_5))) ((plus_plus_real (number267125858f_real ((plus_plus_int V_15) W_12))) Z_5)))
% 0.42/0.68 FOF formula (forall (V_14:int) (W_11:int), (((eq int) ((plus_plus_int (number_number_of_int V_14)) (number_number_of_int W_11))) (number_number_of_int ((plus_plus_int V_14) W_11)))) of role axiom named fact_122_add__number__of__eq
% 0.42/0.68 A new axiom: (forall (V_14:int) (W_11:int), (((eq int) ((plus_plus_int (number_number_of_int V_14)) (number_number_of_int W_11))) (number_number_of_int ((plus_plus_int V_14) W_11))))
% 0.42/0.68 FOF formula (forall (V_14:int) (W_11:int), (((eq real) ((plus_plus_real (number267125858f_real V_14)) (number267125858f_real W_11))) (number267125858f_real ((plus_plus_int V_14) W_11)))) of role axiom named fact_123_add__number__of__eq
% 0.42/0.68 A new axiom: (forall (V_14:int) (W_11:int), (((eq real) ((plus_plus_real (number267125858f_real V_14)) (number267125858f_real W_11))) (number267125858f_real ((plus_plus_int V_14) W_11))))
% 0.42/0.68 FOF formula (forall (V_13:int) (W_10:int), (((eq int) (number_number_of_int ((plus_plus_int V_13) W_10))) ((plus_plus_int (number_number_of_int V_13)) (number_number_of_int W_10)))) of role axiom named fact_124_number__of__add
% 0.42/0.68 A new axiom: (forall (V_13:int) (W_10:int), (((eq int) (number_number_of_int ((plus_plus_int V_13) W_10))) ((plus_plus_int (number_number_of_int V_13)) (number_number_of_int W_10))))
% 0.42/0.68 FOF formula (forall (V_13:int) (W_10:int), (((eq real) (number267125858f_real ((plus_plus_int V_13) W_10))) ((plus_plus_real (number267125858f_real V_13)) (number267125858f_real W_10)))) of role axiom named fact_125_number__of__add
% 0.42/0.68 A new axiom: (forall (V_13:int) (W_10:int), (((eq real) (number267125858f_real ((plus_plus_int V_13) W_10))) ((plus_plus_real (number267125858f_real V_13)) (number267125858f_real W_10))))
% 0.42/0.68 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_126_add__Bit1__Bit0
% 0.42/0.68 A new axiom: (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit0 L))) (bit1 ((plus_plus_int K) L))))
% 0.42/0.68 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_127_add__Bit0__Bit1
% 0.42/0.68 A new axiom: (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit1 L))) (bit1 ((plus_plus_int K) L))))
% 0.42/0.68 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_128_Bit1__def
% 0.42/0.68 A new axiom: (forall (K:int), (((eq int) (bit1 K)) ((plus_plus_int ((plus_plus_int one_one_int) K)) K)))
% 0.42/0.68 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_129_odd__nonzero
% 0.42/0.68 A new axiom: (forall (Z:int), (not (((eq int) ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int)))
% 0.42/0.68 FOF formula (forall (N_32:nat), (((eq nat) (number_number_of_nat (semiri1621563631at_int N_32))) (semiri984289939at_nat N_32))) of role axiom named fact_130_number__of__int
% 0.42/0.68 A new axiom: (forall (N_32:nat), (((eq nat) (number_number_of_nat (semiri1621563631at_int N_32))) (semiri984289939at_nat N_32)))
% 0.42/0.68 FOF formula (forall (N_32:nat), (((eq int) (number_number_of_int (semiri1621563631at_int N_32))) (semiri1621563631at_int N_32))) of role axiom named fact_131_number__of__int
% 0.42/0.68 A new axiom: (forall (N_32:nat), (((eq int) (number_number_of_int (semiri1621563631at_int N_32))) (semiri1621563631at_int N_32)))
% 0.42/0.68 FOF formula (forall (N_32:nat), (((eq real) (number267125858f_real (semiri1621563631at_int N_32))) (semiri132038758t_real N_32))) of role axiom named fact_132_number__of__int
% 0.42/0.68 A new axiom: (forall (N_32:nat), (((eq real) (number267125858f_real (semiri1621563631at_int N_32))) (semiri132038758t_real N_32)))
% 0.42/0.68 FOF formula (forall (A_130:int), ((iff ((ord_less_int zero_zero_int) ((power_power_int A_130) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq int) A_130) zero_zero_int)))) of role axiom named fact_133_zero__less__power2
% 0.42/0.69 A new axiom: (forall (A_130:int), ((iff ((ord_less_int zero_zero_int) ((power_power_int A_130) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq int) A_130) zero_zero_int))))
% 0.42/0.69 FOF formula (forall (A_130:real), ((iff ((ord_less_real zero_zero_real) ((power_power_real A_130) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq real) A_130) zero_zero_real)))) of role axiom named fact_134_zero__less__power2
% 0.42/0.69 A new axiom: (forall (A_130:real), ((iff ((ord_less_real zero_zero_real) ((power_power_real A_130) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq real) A_130) zero_zero_real))))
% 0.42/0.69 FOF formula (forall (A_129:int), (((ord_less_int ((power_power_int A_129) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)->False)) of role axiom named fact_135_power2__less__0
% 0.42/0.69 A new axiom: (forall (A_129:int), (((ord_less_int ((power_power_int A_129) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)->False))
% 0.42/0.69 FOF formula (forall (A_129:real), (((ord_less_real ((power_power_real A_129) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)->False)) of role axiom named fact_136_power2__less__0
% 0.42/0.69 A new axiom: (forall (A_129:real), (((ord_less_real ((power_power_real A_129) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)->False))
% 0.42/0.69 FOF formula (forall (X_25:int) (Y_19:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((power_power_int X_25) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_19) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq int) X_25) zero_zero_int))) (not (((eq int) Y_19) zero_zero_int))))) of role axiom named fact_137_sum__power2__gt__zero__iff
% 0.42/0.69 A new axiom: (forall (X_25:int) (Y_19:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((power_power_int X_25) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_19) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq int) X_25) zero_zero_int))) (not (((eq int) Y_19) zero_zero_int)))))
% 0.42/0.69 FOF formula (forall (X_25:real) (Y_19:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((power_power_real X_25) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_19) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq real) X_25) zero_zero_real))) (not (((eq real) Y_19) zero_zero_real))))) of role axiom named fact_138_sum__power2__gt__zero__iff
% 0.42/0.69 A new axiom: (forall (X_25:real) (Y_19:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((power_power_real X_25) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_19) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq real) X_25) zero_zero_real))) (not (((eq real) Y_19) zero_zero_real)))))
% 0.42/0.69 FOF formula (forall (X_24:int) (Y_18:int), (((ord_less_int ((plus_plus_int ((power_power_int X_24) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_18) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)->False)) of role axiom named fact_139_not__sum__power2__lt__zero
% 0.42/0.69 A new axiom: (forall (X_24:int) (Y_18:int), (((ord_less_int ((plus_plus_int ((power_power_int X_24) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_18) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)->False))
% 0.42/0.69 FOF formula (forall (X_24:real) (Y_18:real), (((ord_less_real ((plus_plus_real ((power_power_real X_24) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_18) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)->False)) of role axiom named fact_140_not__sum__power2__lt__zero
% 0.42/0.69 A new axiom: (forall (X_24:real) (Y_18:real), (((ord_less_real ((plus_plus_real ((power_power_real X_24) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_18) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)->False))
% 0.42/0.69 FOF formula (forall (W_9:int), (((eq int) (number_number_of_int (bit0 W_9))) ((plus_plus_int ((plus_plus_int zero_zero_int) (number_number_of_int W_9))) (number_number_of_int W_9)))) of role axiom named fact_141_number__of__Bit0
% 0.42/0.69 A new axiom: (forall (W_9:int), (((eq int) (number_number_of_int (bit0 W_9))) ((plus_plus_int ((plus_plus_int zero_zero_int) (number_number_of_int W_9))) (number_number_of_int W_9))))
% 0.50/0.70 FOF formula (forall (W_9:int), (((eq real) (number267125858f_real (bit0 W_9))) ((plus_plus_real ((plus_plus_real zero_zero_real) (number267125858f_real W_9))) (number267125858f_real W_9)))) of role axiom named fact_142_number__of__Bit0
% 0.50/0.70 A new axiom: (forall (W_9:int), (((eq real) (number267125858f_real (bit0 W_9))) ((plus_plus_real ((plus_plus_real zero_zero_real) (number267125858f_real W_9))) (number267125858f_real W_9))))
% 0.50/0.70 FOF formula (forall (W_8:int), (((eq int) (number_number_of_int (bit1 W_8))) ((plus_plus_int ((plus_plus_int one_one_int) (number_number_of_int W_8))) (number_number_of_int W_8)))) of role axiom named fact_143_number__of__Bit1
% 0.50/0.70 A new axiom: (forall (W_8:int), (((eq int) (number_number_of_int (bit1 W_8))) ((plus_plus_int ((plus_plus_int one_one_int) (number_number_of_int W_8))) (number_number_of_int W_8))))
% 0.50/0.70 FOF formula (forall (W_8:int), (((eq real) (number267125858f_real (bit1 W_8))) ((plus_plus_real ((plus_plus_real one_one_real) (number267125858f_real W_8))) (number267125858f_real W_8)))) of role axiom named fact_144_number__of__Bit1
% 0.50/0.70 A new axiom: (forall (W_8:int), (((eq real) (number267125858f_real (bit1 W_8))) ((plus_plus_real ((plus_plus_real one_one_real) (number267125858f_real W_8))) (number267125858f_real W_8))))
% 0.50/0.70 FOF formula (((eq int) (number_number_of_int (bit1 pls))) one_one_int) of role axiom named fact_145_semiring__numeral__1__eq__1
% 0.50/0.70 A new axiom: (((eq int) (number_number_of_int (bit1 pls))) one_one_int)
% 0.50/0.70 FOF formula (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat) of role axiom named fact_146_semiring__numeral__1__eq__1
% 0.50/0.70 A new axiom: (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat)
% 0.50/0.70 FOF formula (((eq real) (number267125858f_real (bit1 pls))) one_one_real) of role axiom named fact_147_semiring__numeral__1__eq__1
% 0.50/0.70 A new axiom: (((eq real) (number267125858f_real (bit1 pls))) one_one_real)
% 0.50/0.70 FOF formula ((ord_less_int m1) ((plus_plus_int one_one_int) (semiri1621563631at_int n))) of role axiom named fact_148_mn
% 0.50/0.70 A new axiom: ((ord_less_int m1) ((plus_plus_int one_one_int) (semiri1621563631at_int n)))
% 0.50/0.70 FOF formula (forall (N_31:nat), ((ord_less_int (semiri1621563631at_int N_31)) ((power_power_int (number_number_of_int (bit0 (bit1 pls)))) N_31))) of role axiom named fact_149_of__nat__less__two__power
% 0.50/0.70 A new axiom: (forall (N_31:nat), ((ord_less_int (semiri1621563631at_int N_31)) ((power_power_int (number_number_of_int (bit0 (bit1 pls)))) N_31)))
% 0.50/0.70 FOF formula (forall (N_31:nat), ((ord_less_real (semiri132038758t_real N_31)) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N_31))) of role axiom named fact_150_of__nat__less__two__power
% 0.50/0.70 A new axiom: (forall (N_31:nat), ((ord_less_real (semiri132038758t_real N_31)) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N_31)))
% 0.50/0.70 FOF formula (((eq int) (number_number_of_int (bit0 (bit1 pls)))) (semiri1621563631at_int (number_number_of_nat (bit0 (bit1 pls))))) of role axiom named fact_151_transfer__int__nat__numerals_I3_J
% 0.50/0.70 A new axiom: (((eq int) (number_number_of_int (bit0 (bit1 pls)))) (semiri1621563631at_int (number_number_of_nat (bit0 (bit1 pls)))))
% 0.50/0.70 FOF formula (((eq int) (number_number_of_int (bit1 (bit1 pls)))) (semiri1621563631at_int (number_number_of_nat (bit1 (bit1 pls))))) of role axiom named fact_152_transfer__int__nat__numerals_I4_J
% 0.50/0.70 A new axiom: (((eq int) (number_number_of_int (bit1 (bit1 pls)))) (semiri1621563631at_int (number_number_of_nat (bit1 (bit1 pls)))))
% 0.50/0.70 FOF formula (forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real)))) of role axiom named fact_153_realpow__two__sum__zero__iff
% 0.50/0.70 A new axiom: (forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real))))
% 0.50/0.72 FOF formula (forall (N_30:nat), ((iff ((ord_less_int zero_zero_int) (semiri1621563631at_int N_30))) ((ord_less_nat zero_zero_nat) N_30))) of role axiom named fact_154_of__nat__0__less__iff
% 0.50/0.72 A new axiom: (forall (N_30:nat), ((iff ((ord_less_int zero_zero_int) (semiri1621563631at_int N_30))) ((ord_less_nat zero_zero_nat) N_30)))
% 0.50/0.72 FOF formula (forall (N_30:nat), ((iff ((ord_less_nat zero_zero_nat) (semiri984289939at_nat N_30))) ((ord_less_nat zero_zero_nat) N_30))) of role axiom named fact_155_of__nat__0__less__iff
% 0.50/0.72 A new axiom: (forall (N_30:nat), ((iff ((ord_less_nat zero_zero_nat) (semiri984289939at_nat N_30))) ((ord_less_nat zero_zero_nat) N_30)))
% 0.50/0.72 FOF formula (forall (N_30:nat), ((iff ((ord_less_real zero_zero_real) (semiri132038758t_real N_30))) ((ord_less_nat zero_zero_nat) N_30))) of role axiom named fact_156_of__nat__0__less__iff
% 0.50/0.72 A new axiom: (forall (N_30:nat), ((iff ((ord_less_real zero_zero_real) (semiri132038758t_real N_30))) ((ord_less_nat zero_zero_nat) N_30)))
% 0.50/0.72 FOF formula (forall (N_29:nat) (A_128:int), (((ord_less_int one_one_int) A_128)->(((ord_less_nat zero_zero_nat) N_29)->((ord_less_int one_one_int) ((power_power_int A_128) N_29))))) of role axiom named fact_157_one__less__power
% 0.50/0.72 A new axiom: (forall (N_29:nat) (A_128:int), (((ord_less_int one_one_int) A_128)->(((ord_less_nat zero_zero_nat) N_29)->((ord_less_int one_one_int) ((power_power_int A_128) N_29)))))
% 0.50/0.72 FOF formula (forall (N_29:nat) (A_128:nat), (((ord_less_nat one_one_nat) A_128)->(((ord_less_nat zero_zero_nat) N_29)->((ord_less_nat one_one_nat) ((power_power_nat A_128) N_29))))) of role axiom named fact_158_one__less__power
% 0.50/0.72 A new axiom: (forall (N_29:nat) (A_128:nat), (((ord_less_nat one_one_nat) A_128)->(((ord_less_nat zero_zero_nat) N_29)->((ord_less_nat one_one_nat) ((power_power_nat A_128) N_29)))))
% 0.50/0.72 FOF formula (forall (N_29:nat) (A_128:real), (((ord_less_real one_one_real) A_128)->(((ord_less_nat zero_zero_nat) N_29)->((ord_less_real one_one_real) ((power_power_real A_128) N_29))))) of role axiom named fact_159_one__less__power
% 0.50/0.72 A new axiom: (forall (N_29:nat) (A_128:real), (((ord_less_real one_one_real) A_128)->(((ord_less_nat zero_zero_nat) N_29)->((ord_less_real one_one_real) ((power_power_real A_128) N_29)))))
% 0.50/0.72 FOF formula (forall (N_28:nat), ((and ((((eq nat) N_28) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) N_28)) one_one_int))) ((not (((eq nat) N_28) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) N_28)) zero_zero_int)))) of role axiom named fact_160_power__0__left
% 0.50/0.72 A new axiom: (forall (N_28:nat), ((and ((((eq nat) N_28) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) N_28)) one_one_int))) ((not (((eq nat) N_28) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) N_28)) zero_zero_int))))
% 0.50/0.72 FOF formula (forall (N_28:nat), ((and ((((eq nat) N_28) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) N_28)) one_one_nat))) ((not (((eq nat) N_28) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) N_28)) zero_zero_nat)))) of role axiom named fact_161_power__0__left
% 0.50/0.72 A new axiom: (forall (N_28:nat), ((and ((((eq nat) N_28) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) N_28)) one_one_nat))) ((not (((eq nat) N_28) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) N_28)) zero_zero_nat))))
% 0.50/0.72 FOF formula (forall (N_28:nat), ((and ((((eq nat) N_28) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) N_28)) one_one_real))) ((not (((eq nat) N_28) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) N_28)) zero_zero_real)))) of role axiom named fact_162_power__0__left
% 0.50/0.72 A new axiom: (forall (N_28:nat), ((and ((((eq nat) N_28) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) N_28)) one_one_real))) ((not (((eq nat) N_28) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) N_28)) zero_zero_real))))
% 0.50/0.72 FOF formula (forall (A_127:int) (N_27:nat) (N_26:nat), (((ord_less_nat N_27) N_26)->(((ord_less_int zero_zero_int) A_127)->(((ord_less_int A_127) one_one_int)->((ord_less_int ((power_power_int A_127) N_26)) ((power_power_int A_127) N_27)))))) of role axiom named fact_163_power__strict__decreasing
% 0.50/0.74 A new axiom: (forall (A_127:int) (N_27:nat) (N_26:nat), (((ord_less_nat N_27) N_26)->(((ord_less_int zero_zero_int) A_127)->(((ord_less_int A_127) one_one_int)->((ord_less_int ((power_power_int A_127) N_26)) ((power_power_int A_127) N_27))))))
% 0.50/0.74 FOF formula (forall (A_127:nat) (N_27:nat) (N_26:nat), (((ord_less_nat N_27) N_26)->(((ord_less_nat zero_zero_nat) A_127)->(((ord_less_nat A_127) one_one_nat)->((ord_less_nat ((power_power_nat A_127) N_26)) ((power_power_nat A_127) N_27)))))) of role axiom named fact_164_power__strict__decreasing
% 0.50/0.74 A new axiom: (forall (A_127:nat) (N_27:nat) (N_26:nat), (((ord_less_nat N_27) N_26)->(((ord_less_nat zero_zero_nat) A_127)->(((ord_less_nat A_127) one_one_nat)->((ord_less_nat ((power_power_nat A_127) N_26)) ((power_power_nat A_127) N_27))))))
% 0.50/0.74 FOF formula (forall (A_127:real) (N_27:nat) (N_26:nat), (((ord_less_nat N_27) N_26)->(((ord_less_real zero_zero_real) A_127)->(((ord_less_real A_127) one_one_real)->((ord_less_real ((power_power_real A_127) N_26)) ((power_power_real A_127) N_27)))))) of role axiom named fact_165_power__strict__decreasing
% 0.50/0.74 A new axiom: (forall (A_127:real) (N_27:nat) (N_26:nat), (((ord_less_nat N_27) N_26)->(((ord_less_real zero_zero_real) A_127)->(((ord_less_real A_127) one_one_real)->((ord_less_real ((power_power_real A_127) N_26)) ((power_power_real A_127) N_27))))))
% 0.50/0.74 FOF formula ((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) one_one_int)) of role axiom named fact_166_zero__less__two
% 0.50/0.74 A new axiom: ((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) one_one_int))
% 0.50/0.74 FOF formula ((ord_less_nat zero_zero_nat) ((plus_plus_nat one_one_nat) one_one_nat)) of role axiom named fact_167_zero__less__two
% 0.50/0.74 A new axiom: ((ord_less_nat zero_zero_nat) ((plus_plus_nat one_one_nat) one_one_nat))
% 0.50/0.74 FOF formula ((ord_less_real zero_zero_real) ((plus_plus_real one_one_real) one_one_real)) of role axiom named fact_168_zero__less__two
% 0.50/0.74 A new axiom: ((ord_less_real zero_zero_real) ((plus_plus_real one_one_real) one_one_real))
% 0.50/0.74 FOF formula (forall (P:(int->Prop)) (K:int) (I_1:int), (((ord_less_int K) I_1)->((P ((plus_plus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->(P I_1))))) of role axiom named fact_169_int__gr__induct
% 0.50/0.74 A new axiom: (forall (P:(int->Prop)) (K:int) (I_1:int), (((ord_less_int K) I_1)->((P ((plus_plus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->(P I_1)))))
% 0.50/0.74 FOF formula (((eq int) zero_zero_int) (semiri1621563631at_int zero_zero_nat)) of role axiom named fact_170_transfer__int__nat__numerals_I1_J
% 0.50/0.74 A new axiom: (((eq int) zero_zero_int) (semiri1621563631at_int zero_zero_nat))
% 0.50/0.74 FOF formula ((ord_less_nat zero_zero_nat) tn) of role axiom named fact_171_tn0
% 0.50/0.74 A new axiom: ((ord_less_nat zero_zero_nat) tn)
% 0.50/0.74 FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_172_less__zeroE
% 0.50/0.74 A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False))
% 0.50/0.74 FOF formula (not (((eq real) zero_zero_real) one_one_real)) of role axiom named fact_173_real__zero__not__eq__one
% 0.50/0.74 A new axiom: (not (((eq real) zero_zero_real) one_one_real))
% 0.50/0.74 FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_174_less__not__refl
% 0.50/0.74 A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False))
% 0.50/0.74 FOF formula (forall (I_1:nat) (J:nat), (((ord_less_nat ((plus_plus_nat I_1) J)) I_1)->False)) of role axiom named fact_175_not__add__less1
% 0.50/0.74 A new axiom: (forall (I_1:nat) (J:nat), (((ord_less_nat ((plus_plus_nat I_1) J)) I_1)->False))
% 0.50/0.74 FOF formula (forall (J:nat) (I_1:nat), (((ord_less_nat ((plus_plus_nat J) I_1)) I_1)->False)) of role axiom named fact_176_not__add__less2
% 0.50/0.74 A new axiom: (forall (J:nat) (I_1:nat), (((ord_less_nat ((plus_plus_nat J) I_1)) I_1)->False))
% 0.50/0.74 FOF formula (forall (K:int), (((eq int) (number_number_of_int K)) K)) of role axiom named fact_177_number__of__is__id
% 0.50/0.76 A new axiom: (forall (K:int), (((eq int) (number_number_of_int K)) K))
% 0.50/0.76 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_178_nat__neq__iff
% 0.50/0.76 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))))
% 0.50/0.76 FOF formula (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) N)) ((plus_plus_nat N) M))) of role axiom named fact_179_nat__add__commute
% 0.50/0.76 A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) N)) ((plus_plus_nat N) M)))
% 0.50/0.76 FOF formula (forall (X:nat) (Y:nat) (Z:nat), (((eq nat) ((plus_plus_nat X) ((plus_plus_nat Y) Z))) ((plus_plus_nat Y) ((plus_plus_nat X) Z)))) of role axiom named fact_180_nat__add__left__commute
% 0.50/0.76 A new axiom: (forall (X:nat) (Y:nat) (Z:nat), (((eq nat) ((plus_plus_nat X) ((plus_plus_nat Y) Z))) ((plus_plus_nat Y) ((plus_plus_nat X) Z))))
% 0.50/0.76 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_181_nat__add__assoc
% 0.50/0.76 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))))
% 0.50/0.76 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_182_nat__add__left__cancel
% 0.50/0.76 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)))
% 0.50/0.76 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_183_nat__add__right__cancel
% 0.50/0.76 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)))
% 0.50/0.76 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_184_nat__add__left__cancel__less
% 0.50/0.76 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)))
% 0.50/0.76 FOF formula (forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X)))) of role axiom named fact_185_linorder__neqE__nat
% 0.50/0.76 A new axiom: (forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X))))
% 0.50/0.76 FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_186_less__irrefl__nat
% 0.50/0.76 A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False))
% 0.50/0.76 FOF formula (forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N)))) of role axiom named fact_187_less__not__refl2
% 0.50/0.76 A new axiom: (forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N))))
% 0.50/0.76 FOF formula (forall (S_1:nat) (T:nat), (((ord_less_nat S_1) T)->(not (((eq nat) S_1) T)))) of role axiom named fact_188_less__not__refl3
% 0.50/0.76 A new axiom: (forall (S_1:nat) (T:nat), (((ord_less_nat S_1) T)->(not (((eq nat) S_1) T))))
% 0.50/0.76 FOF formula (forall (M:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat I_1) ((plus_plus_nat J) M)))) of role axiom named fact_189_trans__less__add1
% 0.50/0.76 A new axiom: (forall (M:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat I_1) ((plus_plus_nat J) M))))
% 0.50/0.76 FOF formula (forall (M:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat I_1) ((plus_plus_nat M) J)))) of role axiom named fact_190_trans__less__add2
% 0.50/0.76 A new axiom: (forall (M:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat I_1) ((plus_plus_nat M) J))))
% 0.50/0.76 FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) K)))) of role axiom named fact_191_add__less__mono1
% 0.50/0.76 A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) K))))
% 0.50/0.76 FOF formula (forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) L))))) of role axiom named fact_192_add__less__mono
% 0.50/0.78 A new axiom: (forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) L)))))
% 0.50/0.78 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_193_less__add__eq__less
% 0.50/0.78 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))))
% 0.50/0.78 FOF formula (forall (I_1:nat) (J:nat) (K:nat), (((ord_less_nat ((plus_plus_nat I_1) J)) K)->((ord_less_nat I_1) K))) of role axiom named fact_194_add__lessD1
% 0.50/0.78 A new axiom: (forall (I_1:nat) (J:nat) (K:nat), (((ord_less_nat ((plus_plus_nat I_1) J)) K)->((ord_less_nat I_1) K)))
% 0.50/0.78 FOF formula (forall (P:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P N) M))->(((((eq nat) M) N)->((P N) M))->((((ord_less_nat N) M)->((P N) M))->((P N) M))))) of role axiom named fact_195_nat__less__cases
% 0.50/0.78 A new axiom: (forall (P:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P N) M))->(((((eq nat) M) N)->((P N) M))->((((ord_less_nat N) M)->((P N) M))->((P N) M)))))
% 0.50/0.78 FOF formula (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N))) of role axiom named fact_196_gr0I
% 0.50/0.78 A new axiom: (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N)))
% 0.50/0.78 FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->(not (((eq nat) N) zero_zero_nat)))) of role axiom named fact_197_gr__implies__not0
% 0.50/0.78 A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->(not (((eq nat) N) zero_zero_nat))))
% 0.50/0.78 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_198_nat__power__less__imp__less
% 0.50/0.78 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))))
% 0.50/0.78 FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_199_less__nat__zero__code
% 0.50/0.78 A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False))
% 0.50/0.78 FOF formula (forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or ((ord_less_nat zero_zero_nat) X)) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_200_nat__zero__less__power__iff
% 0.50/0.78 A new axiom: (forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or ((ord_less_nat zero_zero_nat) X)) (((eq nat) N) zero_zero_nat))))
% 0.50/0.78 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_201_add__gr__0
% 0.50/0.78 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))))
% 0.50/0.78 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_202_neq0__conv
% 0.50/0.78 A new axiom: (forall (N:nat), ((iff (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N)))
% 0.50/0.78 FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_203_not__less0
% 0.50/0.78 A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False))
% 0.50/0.78 FOF formula (forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or (((eq nat) N) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X)))) of role axiom named fact_204_zero__less__power__nat__eq
% 0.50/0.78 A new axiom: (forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or (((eq nat) N) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X))))
% 0.50/0.78 FOF formula (forall (X:nat) (Y:nat), ((iff ((ord_less_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_nat X) Y))) of role axiom named fact_205_Nat__Transfer_Otransfer__int__nat__relations_I2_J
% 0.58/0.79 A new axiom: (forall (X:nat) (Y:nat), ((iff ((ord_less_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_nat X) Y)))
% 0.58/0.79 FOF formula (forall (X:nat) (W:int), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) (number_number_of_nat W)))) ((or (((eq nat) (number_number_of_nat W)) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X)))) of role axiom named fact_206_zero__less__power__nat__eq__number__of
% 0.58/0.79 A new axiom: (forall (X:nat) (W:int), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) (number_number_of_nat W)))) ((or (((eq nat) (number_number_of_nat W)) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X))))
% 0.58/0.79 FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_nat M) N))) of role axiom named fact_207_zless__int
% 0.58/0.79 A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_nat M) N)))
% 0.58/0.79 FOF formula (forall (V_1:int) (V_2:int), ((iff ((ord_less_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) ((and (((ord_less_int V_1) V_2)->((ord_less_int pls) V_2))) ((ord_less_int V_1) V_2)))) of role axiom named fact_208_less__nat__number__of
% 0.58/0.79 A new axiom: (forall (V_1:int) (V_2:int), ((iff ((ord_less_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) ((and (((ord_less_int V_1) V_2)->((ord_less_int pls) V_2))) ((ord_less_int V_1) V_2))))
% 0.58/0.79 FOF formula (forall (X_23:int) (Y_17:int), ((not (((eq int) X_23) Y_17))->((((ord_less_int X_23) Y_17)->False)->((ord_less_int Y_17) X_23)))) of role axiom named fact_209_linorder__neqE__linordered__idom
% 0.58/0.79 A new axiom: (forall (X_23:int) (Y_17:int), ((not (((eq int) X_23) Y_17))->((((ord_less_int X_23) Y_17)->False)->((ord_less_int Y_17) X_23))))
% 0.58/0.79 FOF formula (forall (X_23:real) (Y_17:real), ((not (((eq real) X_23) Y_17))->((((ord_less_real X_23) Y_17)->False)->((ord_less_real Y_17) X_23)))) of role axiom named fact_210_linorder__neqE__linordered__idom
% 0.58/0.79 A new axiom: (forall (X_23:real) (Y_17:real), ((not (((eq real) X_23) Y_17))->((((ord_less_real X_23) Y_17)->False)->((ord_less_real Y_17) X_23))))
% 0.58/0.79 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_211_add__eq__self__zero
% 0.58/0.79 A new axiom: (forall (M:nat) (N:nat), ((((eq nat) ((plus_plus_nat M) N)) M)->(((eq nat) N) zero_zero_nat)))
% 0.58/0.79 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_212_add__is__0
% 0.58/0.79 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))))
% 0.58/0.79 FOF formula (forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M)) of role axiom named fact_213_Nat_Oadd__0__right
% 0.58/0.79 A new axiom: (forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M))
% 0.58/0.79 FOF formula (forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N)) of role axiom named fact_214_plus__nat_Oadd__0
% 0.58/0.79 A new axiom: (forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N))
% 0.58/0.79 FOF formula (forall (A_126:int), (((eq int) ((power_power_int A_126) one_one_nat)) A_126)) of role axiom named fact_215_power__one__right
% 0.58/0.79 A new axiom: (forall (A_126:int), (((eq int) ((power_power_int A_126) one_one_nat)) A_126))
% 0.58/0.79 FOF formula (forall (A_126:nat), (((eq nat) ((power_power_nat A_126) one_one_nat)) A_126)) of role axiom named fact_216_power__one__right
% 0.58/0.79 A new axiom: (forall (A_126:nat), (((eq nat) ((power_power_nat A_126) one_one_nat)) A_126))
% 0.58/0.79 FOF formula (forall (A_126:real), (((eq real) ((power_power_real A_126) one_one_nat)) A_126)) of role axiom named fact_217_power__one__right
% 0.58/0.79 A new axiom: (forall (A_126:real), (((eq real) ((power_power_real A_126) one_one_nat)) A_126))
% 0.58/0.79 FOF formula (forall (M_14:nat) (N_25:nat), ((iff (((eq real) (semiri132038758t_real M_14)) (semiri132038758t_real N_25))) (((eq nat) M_14) N_25))) of role axiom named fact_218_of__nat__eq__iff
% 0.58/0.81 A new axiom: (forall (M_14:nat) (N_25:nat), ((iff (((eq real) (semiri132038758t_real M_14)) (semiri132038758t_real N_25))) (((eq nat) M_14) N_25)))
% 0.58/0.81 FOF formula (forall (M_14:nat) (N_25:nat), ((iff (((eq nat) (semiri984289939at_nat M_14)) (semiri984289939at_nat N_25))) (((eq nat) M_14) N_25))) of role axiom named fact_219_of__nat__eq__iff
% 0.58/0.81 A new axiom: (forall (M_14:nat) (N_25:nat), ((iff (((eq nat) (semiri984289939at_nat M_14)) (semiri984289939at_nat N_25))) (((eq nat) M_14) N_25)))
% 0.58/0.81 FOF formula (forall (M_14:nat) (N_25:nat), ((iff (((eq int) (semiri1621563631at_int M_14)) (semiri1621563631at_int N_25))) (((eq nat) M_14) N_25))) of role axiom named fact_220_of__nat__eq__iff
% 0.58/0.81 A new axiom: (forall (M_14:nat) (N_25:nat), ((iff (((eq int) (semiri1621563631at_int M_14)) (semiri1621563631at_int N_25))) (((eq nat) M_14) N_25)))
% 0.58/0.81 FOF formula (forall (X:nat) (Y:nat), ((iff (((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (((eq nat) X) Y))) of role axiom named fact_221_Nat__Transfer_Otransfer__int__nat__relations_I1_J
% 0.58/0.81 A new axiom: (forall (X:nat) (Y:nat), ((iff (((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (((eq nat) X) Y)))
% 0.58/0.81 FOF formula (forall (X:nat) (Y:nat) (P:Prop), ((and (P->(((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int (((if_nat P) X) Y))))) ((P->False)->(((eq int) (semiri1621563631at_int Y)) (semiri1621563631at_int (((if_nat P) X) Y)))))) of role axiom named fact_222_int__if__cong
% 0.58/0.81 A new axiom: (forall (X:nat) (Y:nat) (P:Prop), ((and (P->(((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int (((if_nat P) X) Y))))) ((P->False)->(((eq int) (semiri1621563631at_int Y)) (semiri1621563631at_int (((if_nat P) X) Y))))))
% 0.58/0.81 FOF formula (forall (V_1:int), ((iff ((ord_less_nat zero_zero_nat) (number_number_of_nat V_1))) ((ord_less_int pls) V_1))) of role axiom named fact_223_less__0__number__of
% 0.58/0.81 A new axiom: (forall (V_1:int), ((iff ((ord_less_nat zero_zero_nat) (number_number_of_nat V_1))) ((ord_less_int pls) V_1)))
% 0.58/0.81 FOF formula (forall (N:nat), ((iff ((ord_less_int zero_zero_int) (semiri1621563631at_int N))) ((ord_less_nat zero_zero_nat) N))) of role axiom named fact_224_zero__less__int__conv
% 0.58/0.81 A new axiom: (forall (N:nat), ((iff ((ord_less_int zero_zero_int) (semiri1621563631at_int N))) ((ord_less_nat zero_zero_nat) N)))
% 0.58/0.81 FOF formula (not (((eq int) one_one_int) zero_zero_int)) of role axiom named fact_225_one__neq__zero
% 0.58/0.81 A new axiom: (not (((eq int) one_one_int) zero_zero_int))
% 0.58/0.81 FOF formula (not (((eq nat) one_one_nat) zero_zero_nat)) of role axiom named fact_226_one__neq__zero
% 0.58/0.81 A new axiom: (not (((eq nat) one_one_nat) zero_zero_nat))
% 0.58/0.81 FOF formula (not (((eq real) one_one_real) zero_zero_real)) of role axiom named fact_227_one__neq__zero
% 0.58/0.81 A new axiom: (not (((eq real) one_one_real) zero_zero_real))
% 0.58/0.81 FOF formula (not (((eq int) zero_zero_int) one_one_int)) of role axiom named fact_228_zero__neq__one
% 0.58/0.81 A new axiom: (not (((eq int) zero_zero_int) one_one_int))
% 0.58/0.81 FOF formula (not (((eq nat) zero_zero_nat) one_one_nat)) of role axiom named fact_229_zero__neq__one
% 0.58/0.81 A new axiom: (not (((eq nat) zero_zero_nat) one_one_nat))
% 0.58/0.81 FOF formula (not (((eq real) zero_zero_real) one_one_real)) of role axiom named fact_230_zero__neq__one
% 0.58/0.81 A new axiom: (not (((eq real) zero_zero_real) one_one_real))
% 0.58/0.81 FOF formula (forall (N_24:nat) (A_125:int), ((not (((eq int) A_125) zero_zero_int))->(not (((eq int) ((power_power_int A_125) N_24)) zero_zero_int)))) of role axiom named fact_231_field__power__not__zero
% 0.58/0.81 A new axiom: (forall (N_24:nat) (A_125:int), ((not (((eq int) A_125) zero_zero_int))->(not (((eq int) ((power_power_int A_125) N_24)) zero_zero_int))))
% 0.58/0.81 FOF formula (forall (N_24:nat) (A_125:real), ((not (((eq real) A_125) zero_zero_real))->(not (((eq real) ((power_power_real A_125) N_24)) zero_zero_real)))) of role axiom named fact_232_field__power__not__zero
% 0.58/0.81 A new axiom: (forall (N_24:nat) (A_125:real), ((not (((eq real) A_125) zero_zero_real))->(not (((eq real) ((power_power_real A_125) N_24)) zero_zero_real))))
% 0.58/0.82 FOF formula (forall (N_23:nat), (((eq int) ((power_power_int one_one_int) N_23)) one_one_int)) of role axiom named fact_233_power__one
% 0.58/0.82 A new axiom: (forall (N_23:nat), (((eq int) ((power_power_int one_one_int) N_23)) one_one_int))
% 0.58/0.82 FOF formula (forall (N_23:nat), (((eq nat) ((power_power_nat one_one_nat) N_23)) one_one_nat)) of role axiom named fact_234_power__one
% 0.58/0.82 A new axiom: (forall (N_23:nat), (((eq nat) ((power_power_nat one_one_nat) N_23)) one_one_nat))
% 0.58/0.82 FOF formula (forall (N_23:nat), (((eq real) ((power_power_real one_one_real) N_23)) one_one_real)) of role axiom named fact_235_power__one
% 0.58/0.82 A new axiom: (forall (N_23:nat), (((eq real) ((power_power_real one_one_real) N_23)) one_one_real))
% 0.58/0.82 FOF formula (forall (M_13:nat) (N_22:nat), ((iff ((ord_less_int (semiri1621563631at_int M_13)) (semiri1621563631at_int N_22))) ((ord_less_nat M_13) N_22))) of role axiom named fact_236_of__nat__less__iff
% 0.58/0.82 A new axiom: (forall (M_13:nat) (N_22:nat), ((iff ((ord_less_int (semiri1621563631at_int M_13)) (semiri1621563631at_int N_22))) ((ord_less_nat M_13) N_22)))
% 0.58/0.82 FOF formula (forall (M_13:nat) (N_22:nat), ((iff ((ord_less_nat (semiri984289939at_nat M_13)) (semiri984289939at_nat N_22))) ((ord_less_nat M_13) N_22))) of role axiom named fact_237_of__nat__less__iff
% 0.58/0.82 A new axiom: (forall (M_13:nat) (N_22:nat), ((iff ((ord_less_nat (semiri984289939at_nat M_13)) (semiri984289939at_nat N_22))) ((ord_less_nat M_13) N_22)))
% 0.58/0.82 FOF formula (forall (M_13:nat) (N_22:nat), ((iff ((ord_less_real (semiri132038758t_real M_13)) (semiri132038758t_real N_22))) ((ord_less_nat M_13) N_22))) of role axiom named fact_238_of__nat__less__iff
% 0.58/0.82 A new axiom: (forall (M_13:nat) (N_22:nat), ((iff ((ord_less_real (semiri132038758t_real M_13)) (semiri132038758t_real N_22))) ((ord_less_nat M_13) N_22)))
% 0.58/0.82 FOF formula (forall (M_12:nat) (N_21:nat), (((ord_less_nat M_12) N_21)->((ord_less_int (semiri1621563631at_int M_12)) (semiri1621563631at_int N_21)))) of role axiom named fact_239_less__imp__of__nat__less
% 0.58/0.82 A new axiom: (forall (M_12:nat) (N_21:nat), (((ord_less_nat M_12) N_21)->((ord_less_int (semiri1621563631at_int M_12)) (semiri1621563631at_int N_21))))
% 0.58/0.82 FOF formula (forall (M_12:nat) (N_21:nat), (((ord_less_nat M_12) N_21)->((ord_less_nat (semiri984289939at_nat M_12)) (semiri984289939at_nat N_21)))) of role axiom named fact_240_less__imp__of__nat__less
% 0.58/0.82 A new axiom: (forall (M_12:nat) (N_21:nat), (((ord_less_nat M_12) N_21)->((ord_less_nat (semiri984289939at_nat M_12)) (semiri984289939at_nat N_21))))
% 0.58/0.82 FOF formula (forall (M_12:nat) (N_21:nat), (((ord_less_nat M_12) N_21)->((ord_less_real (semiri132038758t_real M_12)) (semiri132038758t_real N_21)))) of role axiom named fact_241_less__imp__of__nat__less
% 0.58/0.82 A new axiom: (forall (M_12:nat) (N_21:nat), (((ord_less_nat M_12) N_21)->((ord_less_real (semiri132038758t_real M_12)) (semiri132038758t_real N_21))))
% 0.58/0.82 FOF formula (forall (M_11:nat) (N_20:nat), (((ord_less_int (semiri1621563631at_int M_11)) (semiri1621563631at_int N_20))->((ord_less_nat M_11) N_20))) of role axiom named fact_242_of__nat__less__imp__less
% 0.58/0.82 A new axiom: (forall (M_11:nat) (N_20:nat), (((ord_less_int (semiri1621563631at_int M_11)) (semiri1621563631at_int N_20))->((ord_less_nat M_11) N_20)))
% 0.58/0.82 FOF formula (forall (M_11:nat) (N_20:nat), (((ord_less_nat (semiri984289939at_nat M_11)) (semiri984289939at_nat N_20))->((ord_less_nat M_11) N_20))) of role axiom named fact_243_of__nat__less__imp__less
% 0.58/0.82 A new axiom: (forall (M_11:nat) (N_20:nat), (((ord_less_nat (semiri984289939at_nat M_11)) (semiri984289939at_nat N_20))->((ord_less_nat M_11) N_20)))
% 0.58/0.82 FOF formula (forall (M_11:nat) (N_20:nat), (((ord_less_real (semiri132038758t_real M_11)) (semiri132038758t_real N_20))->((ord_less_nat M_11) N_20))) of role axiom named fact_244_of__nat__less__imp__less
% 0.58/0.82 A new axiom: (forall (M_11:nat) (N_20:nat), (((ord_less_real (semiri132038758t_real M_11)) (semiri132038758t_real N_20))->((ord_less_nat M_11) N_20)))
% 0.58/0.82 FOF formula (forall (M_10:nat) (N_19:nat), (((eq int) (semiri1621563631at_int ((plus_plus_nat M_10) N_19))) ((plus_plus_int (semiri1621563631at_int M_10)) (semiri1621563631at_int N_19)))) of role axiom named fact_245_of__nat__add
% 0.58/0.84 A new axiom: (forall (M_10:nat) (N_19:nat), (((eq int) (semiri1621563631at_int ((plus_plus_nat M_10) N_19))) ((plus_plus_int (semiri1621563631at_int M_10)) (semiri1621563631at_int N_19))))
% 0.58/0.84 FOF formula (forall (M_10:nat) (N_19:nat), (((eq nat) (semiri984289939at_nat ((plus_plus_nat M_10) N_19))) ((plus_plus_nat (semiri984289939at_nat M_10)) (semiri984289939at_nat N_19)))) of role axiom named fact_246_of__nat__add
% 0.58/0.84 A new axiom: (forall (M_10:nat) (N_19:nat), (((eq nat) (semiri984289939at_nat ((plus_plus_nat M_10) N_19))) ((plus_plus_nat (semiri984289939at_nat M_10)) (semiri984289939at_nat N_19))))
% 0.58/0.84 FOF formula (forall (M_10:nat) (N_19:nat), (((eq real) (semiri132038758t_real ((plus_plus_nat M_10) N_19))) ((plus_plus_real (semiri132038758t_real M_10)) (semiri132038758t_real N_19)))) of role axiom named fact_247_of__nat__add
% 0.58/0.84 A new axiom: (forall (M_10:nat) (N_19:nat), (((eq real) (semiri132038758t_real ((plus_plus_nat M_10) N_19))) ((plus_plus_real (semiri132038758t_real M_10)) (semiri132038758t_real N_19))))
% 0.58/0.84 FOF formula (((eq int) (semiri1621563631at_int one_one_nat)) one_one_int) of role axiom named fact_248_of__nat__1
% 0.58/0.84 A new axiom: (((eq int) (semiri1621563631at_int one_one_nat)) one_one_int)
% 0.58/0.84 FOF formula (((eq nat) (semiri984289939at_nat one_one_nat)) one_one_nat) of role axiom named fact_249_of__nat__1
% 0.58/0.84 A new axiom: (((eq nat) (semiri984289939at_nat one_one_nat)) one_one_nat)
% 0.58/0.84 FOF formula (((eq real) (semiri132038758t_real one_one_nat)) one_one_real) of role axiom named fact_250_of__nat__1
% 0.58/0.84 A new axiom: (((eq real) (semiri132038758t_real one_one_nat)) one_one_real)
% 0.58/0.84 FOF formula (forall (M_9:nat) (N_18:nat), (((eq int) (semiri1621563631at_int ((power_power_nat M_9) N_18))) ((power_power_int (semiri1621563631at_int M_9)) N_18))) of role axiom named fact_251_of__nat__power
% 0.58/0.84 A new axiom: (forall (M_9:nat) (N_18:nat), (((eq int) (semiri1621563631at_int ((power_power_nat M_9) N_18))) ((power_power_int (semiri1621563631at_int M_9)) N_18)))
% 0.58/0.84 FOF formula (forall (M_9:nat) (N_18:nat), (((eq nat) (semiri984289939at_nat ((power_power_nat M_9) N_18))) ((power_power_nat (semiri984289939at_nat M_9)) N_18))) of role axiom named fact_252_of__nat__power
% 0.58/0.84 A new axiom: (forall (M_9:nat) (N_18:nat), (((eq nat) (semiri984289939at_nat ((power_power_nat M_9) N_18))) ((power_power_nat (semiri984289939at_nat M_9)) N_18)))
% 0.58/0.84 FOF formula (forall (M_9:nat) (N_18:nat), (((eq real) (semiri132038758t_real ((power_power_nat M_9) N_18))) ((power_power_real (semiri132038758t_real M_9)) N_18))) of role axiom named fact_253_of__nat__power
% 0.58/0.84 A new axiom: (forall (M_9:nat) (N_18:nat), (((eq real) (semiri132038758t_real ((power_power_nat M_9) N_18))) ((power_power_real (semiri132038758t_real M_9)) N_18)))
% 0.58/0.84 FOF formula (((eq int) one_one_int) (semiri1621563631at_int one_one_nat)) of role axiom named fact_254_transfer__int__nat__numerals_I2_J
% 0.58/0.84 A new axiom: (((eq int) one_one_int) (semiri1621563631at_int one_one_nat))
% 0.58/0.84 FOF formula (forall (X:nat) (Y:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((plus_plus_nat X) Y)))) of role axiom named fact_255_Nat__Transfer_Otransfer__int__nat__functions_I1_J
% 0.58/0.84 A new axiom: (forall (X:nat) (Y:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((plus_plus_nat X) Y))))
% 0.58/0.84 FOF formula (forall (X:nat) (N:nat), (((eq int) ((power_power_int (semiri1621563631at_int X)) N)) (semiri1621563631at_int ((power_power_nat X) N)))) of role axiom named fact_256_Nat__Transfer_Otransfer__int__nat__functions_I4_J
% 0.58/0.84 A new axiom: (forall (X:nat) (N:nat), (((eq int) ((power_power_int (semiri1621563631at_int X)) N)) (semiri1621563631at_int ((power_power_nat X) N))))
% 0.58/0.84 FOF formula (forall (B_89:int) (C_63:int) (A_124:int), (((ord_less_int zero_zero_int) A_124)->(((ord_less_int B_89) C_63)->((ord_less_int B_89) ((plus_plus_int A_124) C_63))))) of role axiom named fact_257_pos__add__strict
% 0.58/0.84 A new axiom: (forall (B_89:int) (C_63:int) (A_124:int), (((ord_less_int zero_zero_int) A_124)->(((ord_less_int B_89) C_63)->((ord_less_int B_89) ((plus_plus_int A_124) C_63)))))
% 0.58/0.85 FOF formula (forall (B_89:nat) (C_63:nat) (A_124:nat), (((ord_less_nat zero_zero_nat) A_124)->(((ord_less_nat B_89) C_63)->((ord_less_nat B_89) ((plus_plus_nat A_124) C_63))))) of role axiom named fact_258_pos__add__strict
% 0.58/0.85 A new axiom: (forall (B_89:nat) (C_63:nat) (A_124:nat), (((ord_less_nat zero_zero_nat) A_124)->(((ord_less_nat B_89) C_63)->((ord_less_nat B_89) ((plus_plus_nat A_124) C_63)))))
% 0.58/0.85 FOF formula (forall (B_89:real) (C_63:real) (A_124:real), (((ord_less_real zero_zero_real) A_124)->(((ord_less_real B_89) C_63)->((ord_less_real B_89) ((plus_plus_real A_124) C_63))))) of role axiom named fact_259_pos__add__strict
% 0.58/0.85 A new axiom: (forall (B_89:real) (C_63:real) (A_124:real), (((ord_less_real zero_zero_real) A_124)->(((ord_less_real B_89) C_63)->((ord_less_real B_89) ((plus_plus_real A_124) C_63)))))
% 0.58/0.85 FOF formula (((ord_less_int one_one_int) zero_zero_int)->False) of role axiom named fact_260_not__one__less__zero
% 0.58/0.85 A new axiom: (((ord_less_int one_one_int) zero_zero_int)->False)
% 0.58/0.85 FOF formula (((ord_less_nat one_one_nat) zero_zero_nat)->False) of role axiom named fact_261_not__one__less__zero
% 0.58/0.85 A new axiom: (((ord_less_nat one_one_nat) zero_zero_nat)->False)
% 0.58/0.85 FOF formula (((ord_less_real one_one_real) zero_zero_real)->False) of role axiom named fact_262_not__one__less__zero
% 0.58/0.85 A new axiom: (((ord_less_real one_one_real) zero_zero_real)->False)
% 0.58/0.85 FOF formula ((ord_less_int zero_zero_int) one_one_int) of role axiom named fact_263_zero__less__one
% 0.58/0.85 A new axiom: ((ord_less_int zero_zero_int) one_one_int)
% 0.58/0.85 FOF formula ((ord_less_nat zero_zero_nat) one_one_nat) of role axiom named fact_264_zero__less__one
% 0.58/0.85 A new axiom: ((ord_less_nat zero_zero_nat) one_one_nat)
% 0.58/0.85 FOF formula ((ord_less_real zero_zero_real) one_one_real) of role axiom named fact_265_zero__less__one
% 0.58/0.85 A new axiom: ((ord_less_real zero_zero_real) one_one_real)
% 0.58/0.85 FOF formula (forall (N_17:nat) (A_123:int), (((ord_less_int zero_zero_int) A_123)->((ord_less_int zero_zero_int) ((power_power_int A_123) N_17)))) of role axiom named fact_266_zero__less__power
% 0.58/0.85 A new axiom: (forall (N_17:nat) (A_123:int), (((ord_less_int zero_zero_int) A_123)->((ord_less_int zero_zero_int) ((power_power_int A_123) N_17))))
% 0.58/0.85 FOF formula (forall (N_17:nat) (A_123:nat), (((ord_less_nat zero_zero_nat) A_123)->((ord_less_nat zero_zero_nat) ((power_power_nat A_123) N_17)))) of role axiom named fact_267_zero__less__power
% 0.58/0.85 A new axiom: (forall (N_17:nat) (A_123:nat), (((ord_less_nat zero_zero_nat) A_123)->((ord_less_nat zero_zero_nat) ((power_power_nat A_123) N_17))))
% 0.58/0.85 FOF formula (forall (N_17:nat) (A_123:real), (((ord_less_real zero_zero_real) A_123)->((ord_less_real zero_zero_real) ((power_power_real A_123) N_17)))) of role axiom named fact_268_zero__less__power
% 0.58/0.85 A new axiom: (forall (N_17:nat) (A_123:real), (((ord_less_real zero_zero_real) A_123)->((ord_less_real zero_zero_real) ((power_power_real A_123) N_17))))
% 0.58/0.85 FOF formula (forall (A_122:int), ((ord_less_int A_122) ((plus_plus_int A_122) one_one_int))) of role axiom named fact_269_less__add__one
% 0.58/0.85 A new axiom: (forall (A_122:int), ((ord_less_int A_122) ((plus_plus_int A_122) one_one_int)))
% 0.58/0.85 FOF formula (forall (A_122:nat), ((ord_less_nat A_122) ((plus_plus_nat A_122) one_one_nat))) of role axiom named fact_270_less__add__one
% 0.58/0.85 A new axiom: (forall (A_122:nat), ((ord_less_nat A_122) ((plus_plus_nat A_122) one_one_nat)))
% 0.58/0.85 FOF formula (forall (A_122:real), ((ord_less_real A_122) ((plus_plus_real A_122) one_one_real))) of role axiom named fact_271_less__add__one
% 0.58/0.85 A new axiom: (forall (A_122:real), ((ord_less_real A_122) ((plus_plus_real A_122) one_one_real)))
% 0.58/0.85 FOF formula (forall (M_8:nat) (N_16:nat) (A_121:int), (((ord_less_int one_one_int) A_121)->((iff (((eq int) ((power_power_int A_121) M_8)) ((power_power_int A_121) N_16))) (((eq nat) M_8) N_16)))) of role axiom named fact_272_power__inject__exp
% 0.58/0.85 A new axiom: (forall (M_8:nat) (N_16:nat) (A_121:int), (((ord_less_int one_one_int) A_121)->((iff (((eq int) ((power_power_int A_121) M_8)) ((power_power_int A_121) N_16))) (((eq nat) M_8) N_16))))
% 0.58/0.87 FOF formula (forall (M_8:nat) (N_16:nat) (A_121:nat), (((ord_less_nat one_one_nat) A_121)->((iff (((eq nat) ((power_power_nat A_121) M_8)) ((power_power_nat A_121) N_16))) (((eq nat) M_8) N_16)))) of role axiom named fact_273_power__inject__exp
% 0.58/0.87 A new axiom: (forall (M_8:nat) (N_16:nat) (A_121:nat), (((ord_less_nat one_one_nat) A_121)->((iff (((eq nat) ((power_power_nat A_121) M_8)) ((power_power_nat A_121) N_16))) (((eq nat) M_8) N_16))))
% 0.58/0.87 FOF formula (forall (M_8:nat) (N_16:nat) (A_121:real), (((ord_less_real one_one_real) A_121)->((iff (((eq real) ((power_power_real A_121) M_8)) ((power_power_real A_121) N_16))) (((eq nat) M_8) N_16)))) of role axiom named fact_274_power__inject__exp
% 0.58/0.87 A new axiom: (forall (M_8:nat) (N_16:nat) (A_121:real), (((ord_less_real one_one_real) A_121)->((iff (((eq real) ((power_power_real A_121) M_8)) ((power_power_real A_121) N_16))) (((eq nat) M_8) N_16))))
% 0.58/0.87 FOF formula (forall (X_22:nat) (Y_16:nat) (B_88:int), (((ord_less_int one_one_int) B_88)->((iff ((ord_less_int ((power_power_int B_88) X_22)) ((power_power_int B_88) Y_16))) ((ord_less_nat X_22) Y_16)))) of role axiom named fact_275_power__strict__increasing__iff
% 0.58/0.87 A new axiom: (forall (X_22:nat) (Y_16:nat) (B_88:int), (((ord_less_int one_one_int) B_88)->((iff ((ord_less_int ((power_power_int B_88) X_22)) ((power_power_int B_88) Y_16))) ((ord_less_nat X_22) Y_16))))
% 0.58/0.87 FOF formula (forall (X_22:nat) (Y_16:nat) (B_88:nat), (((ord_less_nat one_one_nat) B_88)->((iff ((ord_less_nat ((power_power_nat B_88) X_22)) ((power_power_nat B_88) Y_16))) ((ord_less_nat X_22) Y_16)))) of role axiom named fact_276_power__strict__increasing__iff
% 0.58/0.87 A new axiom: (forall (X_22:nat) (Y_16:nat) (B_88:nat), (((ord_less_nat one_one_nat) B_88)->((iff ((ord_less_nat ((power_power_nat B_88) X_22)) ((power_power_nat B_88) Y_16))) ((ord_less_nat X_22) Y_16))))
% 0.58/0.87 FOF formula (forall (X_22:nat) (Y_16:nat) (B_88:real), (((ord_less_real one_one_real) B_88)->((iff ((ord_less_real ((power_power_real B_88) X_22)) ((power_power_real B_88) Y_16))) ((ord_less_nat X_22) Y_16)))) of role axiom named fact_277_power__strict__increasing__iff
% 0.58/0.87 A new axiom: (forall (X_22:nat) (Y_16:nat) (B_88:real), (((ord_less_real one_one_real) B_88)->((iff ((ord_less_real ((power_power_real B_88) X_22)) ((power_power_real B_88) Y_16))) ((ord_less_nat X_22) Y_16))))
% 0.58/0.87 FOF formula (forall (M_7:nat) (N_15:nat) (A_120:int), (((ord_less_int one_one_int) A_120)->(((ord_less_int ((power_power_int A_120) M_7)) ((power_power_int A_120) N_15))->((ord_less_nat M_7) N_15)))) of role axiom named fact_278_power__less__imp__less__exp
% 0.58/0.87 A new axiom: (forall (M_7:nat) (N_15:nat) (A_120:int), (((ord_less_int one_one_int) A_120)->(((ord_less_int ((power_power_int A_120) M_7)) ((power_power_int A_120) N_15))->((ord_less_nat M_7) N_15))))
% 0.58/0.87 FOF formula (forall (M_7:nat) (N_15:nat) (A_120:nat), (((ord_less_nat one_one_nat) A_120)->(((ord_less_nat ((power_power_nat A_120) M_7)) ((power_power_nat A_120) N_15))->((ord_less_nat M_7) N_15)))) of role axiom named fact_279_power__less__imp__less__exp
% 0.58/0.87 A new axiom: (forall (M_7:nat) (N_15:nat) (A_120:nat), (((ord_less_nat one_one_nat) A_120)->(((ord_less_nat ((power_power_nat A_120) M_7)) ((power_power_nat A_120) N_15))->((ord_less_nat M_7) N_15))))
% 0.58/0.87 FOF formula (forall (M_7:nat) (N_15:nat) (A_120:real), (((ord_less_real one_one_real) A_120)->(((ord_less_real ((power_power_real A_120) M_7)) ((power_power_real A_120) N_15))->((ord_less_nat M_7) N_15)))) of role axiom named fact_280_power__less__imp__less__exp
% 0.58/0.87 A new axiom: (forall (M_7:nat) (N_15:nat) (A_120:real), (((ord_less_real one_one_real) A_120)->(((ord_less_real ((power_power_real A_120) M_7)) ((power_power_real A_120) N_15))->((ord_less_nat M_7) N_15))))
% 0.58/0.87 FOF formula (forall (A_119:int) (N_14:nat) (N_13:nat), (((ord_less_nat N_14) N_13)->(((ord_less_int one_one_int) A_119)->((ord_less_int ((power_power_int A_119) N_14)) ((power_power_int A_119) N_13))))) of role axiom named fact_281_power__strict__increasing
% 0.58/0.87 A new axiom: (forall (A_119:int) (N_14:nat) (N_13:nat), (((ord_less_nat N_14) N_13)->(((ord_less_int one_one_int) A_119)->((ord_less_int ((power_power_int A_119) N_14)) ((power_power_int A_119) N_13)))))
% 0.68/0.88 FOF formula (forall (A_119:nat) (N_14:nat) (N_13:nat), (((ord_less_nat N_14) N_13)->(((ord_less_nat one_one_nat) A_119)->((ord_less_nat ((power_power_nat A_119) N_14)) ((power_power_nat A_119) N_13))))) of role axiom named fact_282_power__strict__increasing
% 0.68/0.88 A new axiom: (forall (A_119:nat) (N_14:nat) (N_13:nat), (((ord_less_nat N_14) N_13)->(((ord_less_nat one_one_nat) A_119)->((ord_less_nat ((power_power_nat A_119) N_14)) ((power_power_nat A_119) N_13)))))
% 0.68/0.88 FOF formula (forall (A_119:real) (N_14:nat) (N_13:nat), (((ord_less_nat N_14) N_13)->(((ord_less_real one_one_real) A_119)->((ord_less_real ((power_power_real A_119) N_14)) ((power_power_real A_119) N_13))))) of role axiom named fact_283_power__strict__increasing
% 0.68/0.88 A new axiom: (forall (A_119:real) (N_14:nat) (N_13:nat), (((ord_less_nat N_14) N_13)->(((ord_less_real one_one_real) A_119)->((ord_less_real ((power_power_real A_119) N_14)) ((power_power_real A_119) N_13)))))
% 0.68/0.88 FOF formula (forall (A_118:int) (N_12:nat), ((iff (((eq int) ((power_power_int A_118) N_12)) zero_zero_int)) ((and (((eq int) A_118) zero_zero_int)) (not (((eq nat) N_12) zero_zero_nat))))) of role axiom named fact_284_power__eq__0__iff
% 0.68/0.88 A new axiom: (forall (A_118:int) (N_12:nat), ((iff (((eq int) ((power_power_int A_118) N_12)) zero_zero_int)) ((and (((eq int) A_118) zero_zero_int)) (not (((eq nat) N_12) zero_zero_nat)))))
% 0.68/0.88 FOF formula (forall (A_118:nat) (N_12:nat), ((iff (((eq nat) ((power_power_nat A_118) N_12)) zero_zero_nat)) ((and (((eq nat) A_118) zero_zero_nat)) (not (((eq nat) N_12) zero_zero_nat))))) of role axiom named fact_285_power__eq__0__iff
% 0.68/0.88 A new axiom: (forall (A_118:nat) (N_12:nat), ((iff (((eq nat) ((power_power_nat A_118) N_12)) zero_zero_nat)) ((and (((eq nat) A_118) zero_zero_nat)) (not (((eq nat) N_12) zero_zero_nat)))))
% 0.68/0.88 FOF formula (forall (A_118:real) (N_12:nat), ((iff (((eq real) ((power_power_real A_118) N_12)) zero_zero_real)) ((and (((eq real) A_118) zero_zero_real)) (not (((eq nat) N_12) zero_zero_nat))))) of role axiom named fact_286_power__eq__0__iff
% 0.68/0.88 A new axiom: (forall (A_118:real) (N_12:nat), ((iff (((eq real) ((power_power_real A_118) N_12)) zero_zero_real)) ((and (((eq real) A_118) zero_zero_real)) (not (((eq nat) N_12) zero_zero_nat)))))
% 0.68/0.88 FOF formula (forall (M_6:nat), (((ord_less_int (semiri1621563631at_int M_6)) zero_zero_int)->False)) of role axiom named fact_287_of__nat__less__0__iff
% 0.68/0.88 A new axiom: (forall (M_6:nat), (((ord_less_int (semiri1621563631at_int M_6)) zero_zero_int)->False))
% 0.68/0.88 FOF formula (forall (M_6:nat), (((ord_less_nat (semiri984289939at_nat M_6)) zero_zero_nat)->False)) of role axiom named fact_288_of__nat__less__0__iff
% 0.68/0.88 A new axiom: (forall (M_6:nat), (((ord_less_nat (semiri984289939at_nat M_6)) zero_zero_nat)->False))
% 0.68/0.88 FOF formula (forall (M_6:nat), (((ord_less_real (semiri132038758t_real M_6)) zero_zero_real)->False)) of role axiom named fact_289_of__nat__less__0__iff
% 0.68/0.88 A new axiom: (forall (M_6:nat), (((ord_less_real (semiri132038758t_real M_6)) zero_zero_real)->False))
% 0.68/0.88 FOF formula (forall (A_117:int), (((eq int) ((power_power_int A_117) zero_zero_nat)) one_one_int)) of role axiom named fact_290_power__0
% 0.68/0.88 A new axiom: (forall (A_117:int), (((eq int) ((power_power_int A_117) zero_zero_nat)) one_one_int))
% 0.68/0.88 FOF formula (forall (A_117:nat), (((eq nat) ((power_power_nat A_117) zero_zero_nat)) one_one_nat)) of role axiom named fact_291_power__0
% 0.68/0.88 A new axiom: (forall (A_117:nat), (((eq nat) ((power_power_nat A_117) zero_zero_nat)) one_one_nat))
% 0.68/0.88 FOF formula (forall (A_117:real), (((eq real) ((power_power_real A_117) zero_zero_nat)) one_one_real)) of role axiom named fact_292_power__0
% 0.68/0.88 A new axiom: (forall (A_117:real), (((eq real) ((power_power_real A_117) zero_zero_nat)) one_one_real))
% 0.68/0.88 FOF formula (((eq int) (semiri1621563631at_int zero_zero_nat)) zero_zero_int) of role axiom named fact_293_of__nat__0
% 0.68/0.88 A new axiom: (((eq int) (semiri1621563631at_int zero_zero_nat)) zero_zero_int)
% 0.68/0.88 FOF formula (((eq nat) (semiri984289939at_nat zero_zero_nat)) zero_zero_nat) of role axiom named fact_294_of__nat__0
% 0.69/0.90 A new axiom: (((eq nat) (semiri984289939at_nat zero_zero_nat)) zero_zero_nat)
% 0.69/0.90 FOF formula (((eq real) (semiri132038758t_real zero_zero_nat)) zero_zero_real) of role axiom named fact_295_of__nat__0
% 0.69/0.90 A new axiom: (((eq real) (semiri132038758t_real zero_zero_nat)) zero_zero_real)
% 0.69/0.90 FOF formula ((ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls)))) of role axiom named fact_296_pos2
% 0.69/0.90 A new axiom: ((ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls))))
% 0.69/0.90 FOF formula (forall (K:int), (((ord_less_int zero_zero_int) K)->((ex nat) (fun (N_1:nat)=> ((and ((ord_less_nat zero_zero_nat) N_1)) (((eq int) K) (semiri1621563631at_int N_1))))))) of role axiom named fact_297_zero__less__imp__eq__int
% 0.69/0.90 A new axiom: (forall (K:int), (((ord_less_int zero_zero_int) K)->((ex nat) (fun (N_1:nat)=> ((and ((ord_less_nat zero_zero_nat) N_1)) (((eq int) K) (semiri1621563631at_int N_1)))))))
% 0.69/0.90 FOF formula (forall (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((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)))))) of role axiom named fact_298_less__imp__add__positive
% 0.69/0.90 A new axiom: (forall (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((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))))))
% 0.69/0.90 FOF formula (forall (X:nat) (N:nat), ((iff (((eq nat) ((power_power_nat X) N)) one_one_nat)) ((or (((eq nat) X) one_one_nat)) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_299_exp__eq__1
% 0.69/0.90 A new axiom: (forall (X:nat) (N:nat), ((iff (((eq nat) ((power_power_nat X) N)) one_one_nat)) ((or (((eq nat) X) one_one_nat)) (((eq nat) N) zero_zero_nat))))
% 0.69/0.90 FOF formula (forall (X_21:int), (((eq int) ((power_power_int X_21) zero_zero_nat)) one_one_int)) of role axiom named fact_300_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J
% 0.69/0.90 A new axiom: (forall (X_21:int), (((eq int) ((power_power_int X_21) zero_zero_nat)) one_one_int))
% 0.69/0.90 FOF formula (forall (X_21:nat), (((eq nat) ((power_power_nat X_21) zero_zero_nat)) one_one_nat)) of role axiom named fact_301_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J
% 0.69/0.90 A new axiom: (forall (X_21:nat), (((eq nat) ((power_power_nat X_21) zero_zero_nat)) one_one_nat))
% 0.69/0.90 FOF formula (forall (X_21:real), (((eq real) ((power_power_real X_21) zero_zero_nat)) one_one_real)) of role axiom named fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J
% 0.69/0.90 A new axiom: (forall (X_21:real), (((eq real) ((power_power_real X_21) zero_zero_nat)) one_one_real))
% 0.69/0.90 FOF formula (forall (A_116:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int A_116) A_116))) ((ord_less_int zero_zero_int) A_116))) of role axiom named fact_303_zero__less__double__add__iff__zero__less__single__add
% 0.69/0.90 A new axiom: (forall (A_116:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int A_116) A_116))) ((ord_less_int zero_zero_int) A_116)))
% 0.69/0.90 FOF formula (forall (A_116:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real A_116) A_116))) ((ord_less_real zero_zero_real) A_116))) of role axiom named fact_304_zero__less__double__add__iff__zero__less__single__add
% 0.69/0.90 A new axiom: (forall (A_116:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real A_116) A_116))) ((ord_less_real zero_zero_real) A_116)))
% 0.69/0.90 FOF formula (forall (A_115:int), ((iff ((ord_less_int ((plus_plus_int A_115) A_115)) zero_zero_int)) ((ord_less_int A_115) zero_zero_int))) of role axiom named fact_305_double__add__less__zero__iff__single__add__less__zero
% 0.69/0.90 A new axiom: (forall (A_115:int), ((iff ((ord_less_int ((plus_plus_int A_115) A_115)) zero_zero_int)) ((ord_less_int A_115) zero_zero_int)))
% 0.69/0.90 FOF formula (forall (A_115:real), ((iff ((ord_less_real ((plus_plus_real A_115) A_115)) zero_zero_real)) ((ord_less_real A_115) zero_zero_real))) of role axiom named fact_306_double__add__less__zero__iff__single__add__less__zero
% 0.69/0.90 A new axiom: (forall (A_115:real), ((iff ((ord_less_real ((plus_plus_real A_115) A_115)) zero_zero_real)) ((ord_less_real A_115) zero_zero_real)))
% 0.69/0.90 FOF formula (forall (B_87:int) (A_114:int), (((ord_less_int zero_zero_int) A_114)->(((ord_less_int zero_zero_int) B_87)->((ord_less_int zero_zero_int) ((plus_plus_int A_114) B_87))))) of role axiom named fact_307_add__pos__pos
% 0.71/0.91 A new axiom: (forall (B_87:int) (A_114:int), (((ord_less_int zero_zero_int) A_114)->(((ord_less_int zero_zero_int) B_87)->((ord_less_int zero_zero_int) ((plus_plus_int A_114) B_87)))))
% 0.71/0.91 FOF formula (forall (B_87:nat) (A_114:nat), (((ord_less_nat zero_zero_nat) A_114)->(((ord_less_nat zero_zero_nat) B_87)->((ord_less_nat zero_zero_nat) ((plus_plus_nat A_114) B_87))))) of role axiom named fact_308_add__pos__pos
% 0.71/0.91 A new axiom: (forall (B_87:nat) (A_114:nat), (((ord_less_nat zero_zero_nat) A_114)->(((ord_less_nat zero_zero_nat) B_87)->((ord_less_nat zero_zero_nat) ((plus_plus_nat A_114) B_87)))))
% 0.71/0.91 FOF formula (forall (B_87:real) (A_114:real), (((ord_less_real zero_zero_real) A_114)->(((ord_less_real zero_zero_real) B_87)->((ord_less_real zero_zero_real) ((plus_plus_real A_114) B_87))))) of role axiom named fact_309_add__pos__pos
% 0.71/0.91 A new axiom: (forall (B_87:real) (A_114:real), (((ord_less_real zero_zero_real) A_114)->(((ord_less_real zero_zero_real) B_87)->((ord_less_real zero_zero_real) ((plus_plus_real A_114) B_87)))))
% 0.71/0.91 FOF formula (forall (B_86:int) (A_113:int), (((ord_less_int A_113) zero_zero_int)->(((ord_less_int B_86) zero_zero_int)->((ord_less_int ((plus_plus_int A_113) B_86)) zero_zero_int)))) of role axiom named fact_310_add__neg__neg
% 0.71/0.91 A new axiom: (forall (B_86:int) (A_113:int), (((ord_less_int A_113) zero_zero_int)->(((ord_less_int B_86) zero_zero_int)->((ord_less_int ((plus_plus_int A_113) B_86)) zero_zero_int))))
% 0.71/0.91 FOF formula (forall (B_86:nat) (A_113:nat), (((ord_less_nat A_113) zero_zero_nat)->(((ord_less_nat B_86) zero_zero_nat)->((ord_less_nat ((plus_plus_nat A_113) B_86)) zero_zero_nat)))) of role axiom named fact_311_add__neg__neg
% 0.71/0.91 A new axiom: (forall (B_86:nat) (A_113:nat), (((ord_less_nat A_113) zero_zero_nat)->(((ord_less_nat B_86) zero_zero_nat)->((ord_less_nat ((plus_plus_nat A_113) B_86)) zero_zero_nat))))
% 0.71/0.91 FOF formula (forall (B_86:real) (A_113:real), (((ord_less_real A_113) zero_zero_real)->(((ord_less_real B_86) zero_zero_real)->((ord_less_real ((plus_plus_real A_113) B_86)) zero_zero_real)))) of role axiom named fact_312_add__neg__neg
% 0.71/0.91 A new axiom: (forall (B_86:real) (A_113:real), (((ord_less_real A_113) zero_zero_real)->(((ord_less_real B_86) zero_zero_real)->((ord_less_real ((plus_plus_real A_113) B_86)) zero_zero_real))))
% 0.71/0.91 FOF formula (forall (X_20:int), ((iff (((eq int) zero_zero_int) X_20)) (((eq int) X_20) zero_zero_int))) of role axiom named fact_313_zero__reorient
% 0.71/0.91 A new axiom: (forall (X_20:int), ((iff (((eq int) zero_zero_int) X_20)) (((eq int) X_20) zero_zero_int)))
% 0.71/0.91 FOF formula (forall (X_20:nat), ((iff (((eq nat) zero_zero_nat) X_20)) (((eq nat) X_20) zero_zero_nat))) of role axiom named fact_314_zero__reorient
% 0.71/0.91 A new axiom: (forall (X_20:nat), ((iff (((eq nat) zero_zero_nat) X_20)) (((eq nat) X_20) zero_zero_nat)))
% 0.71/0.91 FOF formula (forall (X_20:real), ((iff (((eq real) zero_zero_real) X_20)) (((eq real) X_20) zero_zero_real))) of role axiom named fact_315_zero__reorient
% 0.71/0.91 A new axiom: (forall (X_20:real), ((iff (((eq real) zero_zero_real) X_20)) (((eq real) X_20) zero_zero_real)))
% 0.71/0.91 FOF formula (forall (B_85:int) (A_112:int) (C_62:int), ((((eq int) ((plus_plus_int B_85) A_112)) ((plus_plus_int C_62) A_112))->(((eq int) B_85) C_62))) of role axiom named fact_316_add__right__imp__eq
% 0.71/0.91 A new axiom: (forall (B_85:int) (A_112:int) (C_62:int), ((((eq int) ((plus_plus_int B_85) A_112)) ((plus_plus_int C_62) A_112))->(((eq int) B_85) C_62)))
% 0.71/0.91 FOF formula (forall (B_85:nat) (A_112:nat) (C_62:nat), ((((eq nat) ((plus_plus_nat B_85) A_112)) ((plus_plus_nat C_62) A_112))->(((eq nat) B_85) C_62))) of role axiom named fact_317_add__right__imp__eq
% 0.71/0.91 A new axiom: (forall (B_85:nat) (A_112:nat) (C_62:nat), ((((eq nat) ((plus_plus_nat B_85) A_112)) ((plus_plus_nat C_62) A_112))->(((eq nat) B_85) C_62)))
% 0.71/0.91 FOF formula (forall (B_85:real) (A_112:real) (C_62:real), ((((eq real) ((plus_plus_real B_85) A_112)) ((plus_plus_real C_62) A_112))->(((eq real) B_85) C_62))) of role axiom named fact_318_add__right__imp__eq
% 0.72/0.93 A new axiom: (forall (B_85:real) (A_112:real) (C_62:real), ((((eq real) ((plus_plus_real B_85) A_112)) ((plus_plus_real C_62) A_112))->(((eq real) B_85) C_62)))
% 0.72/0.93 FOF formula (forall (A_111:int) (B_84:int) (C_61:int), ((((eq int) ((plus_plus_int A_111) B_84)) ((plus_plus_int A_111) C_61))->(((eq int) B_84) C_61))) of role axiom named fact_319_add__imp__eq
% 0.72/0.93 A new axiom: (forall (A_111:int) (B_84:int) (C_61:int), ((((eq int) ((plus_plus_int A_111) B_84)) ((plus_plus_int A_111) C_61))->(((eq int) B_84) C_61)))
% 0.72/0.93 FOF formula (forall (A_111:nat) (B_84:nat) (C_61:nat), ((((eq nat) ((plus_plus_nat A_111) B_84)) ((plus_plus_nat A_111) C_61))->(((eq nat) B_84) C_61))) of role axiom named fact_320_add__imp__eq
% 0.72/0.93 A new axiom: (forall (A_111:nat) (B_84:nat) (C_61:nat), ((((eq nat) ((plus_plus_nat A_111) B_84)) ((plus_plus_nat A_111) C_61))->(((eq nat) B_84) C_61)))
% 0.72/0.93 FOF formula (forall (A_111:real) (B_84:real) (C_61:real), ((((eq real) ((plus_plus_real A_111) B_84)) ((plus_plus_real A_111) C_61))->(((eq real) B_84) C_61))) of role axiom named fact_321_add__imp__eq
% 0.72/0.93 A new axiom: (forall (A_111:real) (B_84:real) (C_61:real), ((((eq real) ((plus_plus_real A_111) B_84)) ((plus_plus_real A_111) C_61))->(((eq real) B_84) C_61)))
% 0.72/0.93 FOF formula (forall (A_110:int) (B_83:int) (C_60:int), ((((eq int) ((plus_plus_int A_110) B_83)) ((plus_plus_int A_110) C_60))->(((eq int) B_83) C_60))) of role axiom named fact_322_add__left__imp__eq
% 0.72/0.93 A new axiom: (forall (A_110:int) (B_83:int) (C_60:int), ((((eq int) ((plus_plus_int A_110) B_83)) ((plus_plus_int A_110) C_60))->(((eq int) B_83) C_60)))
% 0.72/0.93 FOF formula (forall (A_110:nat) (B_83:nat) (C_60:nat), ((((eq nat) ((plus_plus_nat A_110) B_83)) ((plus_plus_nat A_110) C_60))->(((eq nat) B_83) C_60))) of role axiom named fact_323_add__left__imp__eq
% 0.72/0.93 A new axiom: (forall (A_110:nat) (B_83:nat) (C_60:nat), ((((eq nat) ((plus_plus_nat A_110) B_83)) ((plus_plus_nat A_110) C_60))->(((eq nat) B_83) C_60)))
% 0.72/0.93 FOF formula (forall (A_110:real) (B_83:real) (C_60:real), ((((eq real) ((plus_plus_real A_110) B_83)) ((plus_plus_real A_110) C_60))->(((eq real) B_83) C_60))) of role axiom named fact_324_add__left__imp__eq
% 0.72/0.93 A new axiom: (forall (A_110:real) (B_83:real) (C_60:real), ((((eq real) ((plus_plus_real A_110) B_83)) ((plus_plus_real A_110) C_60))->(((eq real) B_83) C_60)))
% 0.72/0.93 FOF formula (forall (A_109:int) (B_82:int) (C_59:int) (D_23:int), (((eq int) ((plus_plus_int ((plus_plus_int A_109) B_82)) ((plus_plus_int C_59) D_23))) ((plus_plus_int ((plus_plus_int A_109) C_59)) ((plus_plus_int B_82) D_23)))) of role axiom named fact_325_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J
% 0.72/0.93 A new axiom: (forall (A_109:int) (B_82:int) (C_59:int) (D_23:int), (((eq int) ((plus_plus_int ((plus_plus_int A_109) B_82)) ((plus_plus_int C_59) D_23))) ((plus_plus_int ((plus_plus_int A_109) C_59)) ((plus_plus_int B_82) D_23))))
% 0.72/0.93 FOF formula (forall (A_109:nat) (B_82:nat) (C_59:nat) (D_23:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_109) B_82)) ((plus_plus_nat C_59) D_23))) ((plus_plus_nat ((plus_plus_nat A_109) C_59)) ((plus_plus_nat B_82) D_23)))) of role axiom named fact_326_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J
% 0.72/0.93 A new axiom: (forall (A_109:nat) (B_82:nat) (C_59:nat) (D_23:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_109) B_82)) ((plus_plus_nat C_59) D_23))) ((plus_plus_nat ((plus_plus_nat A_109) C_59)) ((plus_plus_nat B_82) D_23))))
% 0.72/0.93 FOF formula (forall (A_109:real) (B_82:real) (C_59:real) (D_23:real), (((eq real) ((plus_plus_real ((plus_plus_real A_109) B_82)) ((plus_plus_real C_59) D_23))) ((plus_plus_real ((plus_plus_real A_109) C_59)) ((plus_plus_real B_82) D_23)))) of role axiom named fact_327_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J
% 0.72/0.93 A new axiom: (forall (A_109:real) (B_82:real) (C_59:real) (D_23:real), (((eq real) ((plus_plus_real ((plus_plus_real A_109) B_82)) ((plus_plus_real C_59) D_23))) ((plus_plus_real ((plus_plus_real A_109) C_59)) ((plus_plus_real B_82) D_23))))
% 0.72/0.93 FOF formula (forall (B_81:int) (A_108:int) (C_58:int), ((iff (((eq int) ((plus_plus_int B_81) A_108)) ((plus_plus_int C_58) A_108))) (((eq int) B_81) C_58))) of role axiom named fact_328_add__right__cancel
% 0.72/0.95 A new axiom: (forall (B_81:int) (A_108:int) (C_58:int), ((iff (((eq int) ((plus_plus_int B_81) A_108)) ((plus_plus_int C_58) A_108))) (((eq int) B_81) C_58)))
% 0.72/0.95 FOF formula (forall (B_81:nat) (A_108:nat) (C_58:nat), ((iff (((eq nat) ((plus_plus_nat B_81) A_108)) ((plus_plus_nat C_58) A_108))) (((eq nat) B_81) C_58))) of role axiom named fact_329_add__right__cancel
% 0.72/0.95 A new axiom: (forall (B_81:nat) (A_108:nat) (C_58:nat), ((iff (((eq nat) ((plus_plus_nat B_81) A_108)) ((plus_plus_nat C_58) A_108))) (((eq nat) B_81) C_58)))
% 0.72/0.95 FOF formula (forall (B_81:real) (A_108:real) (C_58:real), ((iff (((eq real) ((plus_plus_real B_81) A_108)) ((plus_plus_real C_58) A_108))) (((eq real) B_81) C_58))) of role axiom named fact_330_add__right__cancel
% 0.72/0.95 A new axiom: (forall (B_81:real) (A_108:real) (C_58:real), ((iff (((eq real) ((plus_plus_real B_81) A_108)) ((plus_plus_real C_58) A_108))) (((eq real) B_81) C_58)))
% 0.72/0.95 FOF formula (forall (A_107:int) (B_80:int) (C_57:int), ((iff (((eq int) ((plus_plus_int A_107) B_80)) ((plus_plus_int A_107) C_57))) (((eq int) B_80) C_57))) of role axiom named fact_331_add__left__cancel
% 0.72/0.95 A new axiom: (forall (A_107:int) (B_80:int) (C_57:int), ((iff (((eq int) ((plus_plus_int A_107) B_80)) ((plus_plus_int A_107) C_57))) (((eq int) B_80) C_57)))
% 0.72/0.95 FOF formula (forall (A_107:nat) (B_80:nat) (C_57:nat), ((iff (((eq nat) ((plus_plus_nat A_107) B_80)) ((plus_plus_nat A_107) C_57))) (((eq nat) B_80) C_57))) of role axiom named fact_332_add__left__cancel
% 0.72/0.95 A new axiom: (forall (A_107:nat) (B_80:nat) (C_57:nat), ((iff (((eq nat) ((plus_plus_nat A_107) B_80)) ((plus_plus_nat A_107) C_57))) (((eq nat) B_80) C_57)))
% 0.72/0.95 FOF formula (forall (A_107:real) (B_80:real) (C_57:real), ((iff (((eq real) ((plus_plus_real A_107) B_80)) ((plus_plus_real A_107) C_57))) (((eq real) B_80) C_57))) of role axiom named fact_333_add__left__cancel
% 0.72/0.95 A new axiom: (forall (A_107:real) (B_80:real) (C_57:real), ((iff (((eq real) ((plus_plus_real A_107) B_80)) ((plus_plus_real A_107) C_57))) (((eq real) B_80) C_57)))
% 0.72/0.95 FOF formula (forall (A_106:int) (B_79:int) (C_56:int), (((eq int) ((plus_plus_int ((plus_plus_int A_106) B_79)) C_56)) ((plus_plus_int ((plus_plus_int A_106) C_56)) B_79))) of role axiom named fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J
% 0.72/0.95 A new axiom: (forall (A_106:int) (B_79:int) (C_56:int), (((eq int) ((plus_plus_int ((plus_plus_int A_106) B_79)) C_56)) ((plus_plus_int ((plus_plus_int A_106) C_56)) B_79)))
% 0.72/0.95 FOF formula (forall (A_106:nat) (B_79:nat) (C_56:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_106) B_79)) C_56)) ((plus_plus_nat ((plus_plus_nat A_106) C_56)) B_79))) of role axiom named fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J
% 0.72/0.95 A new axiom: (forall (A_106:nat) (B_79:nat) (C_56:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_106) B_79)) C_56)) ((plus_plus_nat ((plus_plus_nat A_106) C_56)) B_79)))
% 0.72/0.95 FOF formula (forall (A_106:real) (B_79:real) (C_56:real), (((eq real) ((plus_plus_real ((plus_plus_real A_106) B_79)) C_56)) ((plus_plus_real ((plus_plus_real A_106) C_56)) B_79))) of role axiom named fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J
% 0.72/0.95 A new axiom: (forall (A_106:real) (B_79:real) (C_56:real), (((eq real) ((plus_plus_real ((plus_plus_real A_106) B_79)) C_56)) ((plus_plus_real ((plus_plus_real A_106) C_56)) B_79)))
% 0.72/0.95 FOF formula (forall (A_105:int) (B_78:int) (C_55:int), (((eq int) ((plus_plus_int ((plus_plus_int A_105) B_78)) C_55)) ((plus_plus_int A_105) ((plus_plus_int B_78) C_55)))) of role axiom named fact_337_ab__semigroup__add__class_Oadd__ac_I1_J
% 0.72/0.95 A new axiom: (forall (A_105:int) (B_78:int) (C_55:int), (((eq int) ((plus_plus_int ((plus_plus_int A_105) B_78)) C_55)) ((plus_plus_int A_105) ((plus_plus_int B_78) C_55))))
% 0.72/0.95 FOF formula (forall (A_105:nat) (B_78:nat) (C_55:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_105) B_78)) C_55)) ((plus_plus_nat A_105) ((plus_plus_nat B_78) C_55)))) of role axiom named fact_338_ab__semigroup__add__class_Oadd__ac_I1_J
% 0.72/0.97 A new axiom: (forall (A_105:nat) (B_78:nat) (C_55:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_105) B_78)) C_55)) ((plus_plus_nat A_105) ((plus_plus_nat B_78) C_55))))
% 0.72/0.97 FOF formula (forall (A_105:real) (B_78:real) (C_55:real), (((eq real) ((plus_plus_real ((plus_plus_real A_105) B_78)) C_55)) ((plus_plus_real A_105) ((plus_plus_real B_78) C_55)))) of role axiom named fact_339_ab__semigroup__add__class_Oadd__ac_I1_J
% 0.72/0.97 A new axiom: (forall (A_105:real) (B_78:real) (C_55:real), (((eq real) ((plus_plus_real ((plus_plus_real A_105) B_78)) C_55)) ((plus_plus_real A_105) ((plus_plus_real B_78) C_55))))
% 0.72/0.97 FOF formula (forall (A_104:int) (B_77:int) (C_54:int), (((eq int) ((plus_plus_int ((plus_plus_int A_104) B_77)) C_54)) ((plus_plus_int A_104) ((plus_plus_int B_77) C_54)))) of role axiom named fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J
% 0.72/0.97 A new axiom: (forall (A_104:int) (B_77:int) (C_54:int), (((eq int) ((plus_plus_int ((plus_plus_int A_104) B_77)) C_54)) ((plus_plus_int A_104) ((plus_plus_int B_77) C_54))))
% 0.72/0.97 FOF formula (forall (A_104:nat) (B_77:nat) (C_54:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_104) B_77)) C_54)) ((plus_plus_nat A_104) ((plus_plus_nat B_77) C_54)))) of role axiom named fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J
% 0.72/0.97 A new axiom: (forall (A_104:nat) (B_77:nat) (C_54:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_104) B_77)) C_54)) ((plus_plus_nat A_104) ((plus_plus_nat B_77) C_54))))
% 0.72/0.97 FOF formula (forall (A_104:real) (B_77:real) (C_54:real), (((eq real) ((plus_plus_real ((plus_plus_real A_104) B_77)) C_54)) ((plus_plus_real A_104) ((plus_plus_real B_77) C_54)))) of role axiom named fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J
% 0.72/0.97 A new axiom: (forall (A_104:real) (B_77:real) (C_54:real), (((eq real) ((plus_plus_real ((plus_plus_real A_104) B_77)) C_54)) ((plus_plus_real A_104) ((plus_plus_real B_77) C_54))))
% 0.72/0.97 FOF formula (forall (A_103:int) (C_53:int) (D_22:int), (((eq int) ((plus_plus_int A_103) ((plus_plus_int C_53) D_22))) ((plus_plus_int ((plus_plus_int A_103) C_53)) D_22))) of role axiom named fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J
% 0.72/0.97 A new axiom: (forall (A_103:int) (C_53:int) (D_22:int), (((eq int) ((plus_plus_int A_103) ((plus_plus_int C_53) D_22))) ((plus_plus_int ((plus_plus_int A_103) C_53)) D_22)))
% 0.72/0.97 FOF formula (forall (A_103:nat) (C_53:nat) (D_22:nat), (((eq nat) ((plus_plus_nat A_103) ((plus_plus_nat C_53) D_22))) ((plus_plus_nat ((plus_plus_nat A_103) C_53)) D_22))) of role axiom named fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J
% 0.72/0.97 A new axiom: (forall (A_103:nat) (C_53:nat) (D_22:nat), (((eq nat) ((plus_plus_nat A_103) ((plus_plus_nat C_53) D_22))) ((plus_plus_nat ((plus_plus_nat A_103) C_53)) D_22)))
% 0.72/0.97 FOF formula (forall (A_103:real) (C_53:real) (D_22:real), (((eq real) ((plus_plus_real A_103) ((plus_plus_real C_53) D_22))) ((plus_plus_real ((plus_plus_real A_103) C_53)) D_22))) of role axiom named fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J
% 0.72/0.97 A new axiom: (forall (A_103:real) (C_53:real) (D_22:real), (((eq real) ((plus_plus_real A_103) ((plus_plus_real C_53) D_22))) ((plus_plus_real ((plus_plus_real A_103) C_53)) D_22)))
% 0.72/0.97 FOF formula (forall (A_102:int) (C_52:int) (D_21:int), (((eq int) ((plus_plus_int A_102) ((plus_plus_int C_52) D_21))) ((plus_plus_int C_52) ((plus_plus_int A_102) D_21)))) of role axiom named fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J
% 0.72/0.97 A new axiom: (forall (A_102:int) (C_52:int) (D_21:int), (((eq int) ((plus_plus_int A_102) ((plus_plus_int C_52) D_21))) ((plus_plus_int C_52) ((plus_plus_int A_102) D_21))))
% 0.72/0.97 FOF formula (forall (A_102:nat) (C_52:nat) (D_21:nat), (((eq nat) ((plus_plus_nat A_102) ((plus_plus_nat C_52) D_21))) ((plus_plus_nat C_52) ((plus_plus_nat A_102) D_21)))) of role axiom named fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J
% 0.72/0.97 A new axiom: (forall (A_102:nat) (C_52:nat) (D_21:nat), (((eq nat) ((plus_plus_nat A_102) ((plus_plus_nat C_52) D_21))) ((plus_plus_nat C_52) ((plus_plus_nat A_102) D_21))))
% 0.72/0.98 FOF formula (forall (A_102:real) (C_52:real) (D_21:real), (((eq real) ((plus_plus_real A_102) ((plus_plus_real C_52) D_21))) ((plus_plus_real C_52) ((plus_plus_real A_102) D_21)))) of role axiom named fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J
% 0.72/0.98 A new axiom: (forall (A_102:real) (C_52:real) (D_21:real), (((eq real) ((plus_plus_real A_102) ((plus_plus_real C_52) D_21))) ((plus_plus_real C_52) ((plus_plus_real A_102) D_21))))
% 0.72/0.98 FOF formula (forall (A_101:int) (C_51:int), (((eq int) ((plus_plus_int A_101) C_51)) ((plus_plus_int C_51) A_101))) of role axiom named fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J
% 0.72/0.98 A new axiom: (forall (A_101:int) (C_51:int), (((eq int) ((plus_plus_int A_101) C_51)) ((plus_plus_int C_51) A_101)))
% 0.72/0.98 FOF formula (forall (A_101:nat) (C_51:nat), (((eq nat) ((plus_plus_nat A_101) C_51)) ((plus_plus_nat C_51) A_101))) of role axiom named fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J
% 0.72/0.98 A new axiom: (forall (A_101:nat) (C_51:nat), (((eq nat) ((plus_plus_nat A_101) C_51)) ((plus_plus_nat C_51) A_101)))
% 0.72/0.98 FOF formula (forall (A_101:real) (C_51:real), (((eq real) ((plus_plus_real A_101) C_51)) ((plus_plus_real C_51) A_101))) of role axiom named fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J
% 0.72/0.98 A new axiom: (forall (A_101:real) (C_51:real), (((eq real) ((plus_plus_real A_101) C_51)) ((plus_plus_real C_51) A_101)))
% 0.72/0.98 FOF formula (forall (X_19:int), ((iff (((eq int) one_one_int) X_19)) (((eq int) X_19) one_one_int))) of role axiom named fact_352_one__reorient
% 0.72/0.98 A new axiom: (forall (X_19:int), ((iff (((eq int) one_one_int) X_19)) (((eq int) X_19) one_one_int)))
% 0.72/0.98 FOF formula (forall (X_19:nat), ((iff (((eq nat) one_one_nat) X_19)) (((eq nat) X_19) one_one_nat))) of role axiom named fact_353_one__reorient
% 0.72/0.98 A new axiom: (forall (X_19:nat), ((iff (((eq nat) one_one_nat) X_19)) (((eq nat) X_19) one_one_nat)))
% 0.72/0.98 FOF formula (forall (X_19:real), ((iff (((eq real) one_one_real) X_19)) (((eq real) X_19) one_one_real))) of role axiom named fact_354_one__reorient
% 0.72/0.98 A new axiom: (forall (X_19:real), ((iff (((eq real) one_one_real) X_19)) (((eq real) X_19) one_one_real)))
% 0.72/0.98 FOF formula (forall (B_76:int) (A_100:int), ((iff (((eq int) B_76) ((plus_plus_int B_76) A_100))) (((eq int) A_100) zero_zero_int))) of role axiom named fact_355_add__0__iff
% 0.72/0.98 A new axiom: (forall (B_76:int) (A_100:int), ((iff (((eq int) B_76) ((plus_plus_int B_76) A_100))) (((eq int) A_100) zero_zero_int)))
% 0.72/0.98 FOF formula (forall (B_76:nat) (A_100:nat), ((iff (((eq nat) B_76) ((plus_plus_nat B_76) A_100))) (((eq nat) A_100) zero_zero_nat))) of role axiom named fact_356_add__0__iff
% 0.72/0.98 A new axiom: (forall (B_76:nat) (A_100:nat), ((iff (((eq nat) B_76) ((plus_plus_nat B_76) A_100))) (((eq nat) A_100) zero_zero_nat)))
% 0.72/0.98 FOF formula (forall (B_76:real) (A_100:real), ((iff (((eq real) B_76) ((plus_plus_real B_76) A_100))) (((eq real) A_100) zero_zero_real))) of role axiom named fact_357_add__0__iff
% 0.72/0.98 A new axiom: (forall (B_76:real) (A_100:real), ((iff (((eq real) B_76) ((plus_plus_real B_76) A_100))) (((eq real) A_100) zero_zero_real)))
% 0.72/0.98 FOF formula (forall (A_99:int), (((eq int) ((plus_plus_int A_99) zero_zero_int)) A_99)) of role axiom named fact_358_add_Ocomm__neutral
% 0.72/0.98 A new axiom: (forall (A_99:int), (((eq int) ((plus_plus_int A_99) zero_zero_int)) A_99))
% 0.72/0.98 FOF formula (forall (A_99:nat), (((eq nat) ((plus_plus_nat A_99) zero_zero_nat)) A_99)) of role axiom named fact_359_add_Ocomm__neutral
% 0.72/0.98 A new axiom: (forall (A_99:nat), (((eq nat) ((plus_plus_nat A_99) zero_zero_nat)) A_99))
% 0.72/0.98 FOF formula (forall (A_99:real), (((eq real) ((plus_plus_real A_99) zero_zero_real)) A_99)) of role axiom named fact_360_add_Ocomm__neutral
% 0.72/0.98 A new axiom: (forall (A_99:real), (((eq real) ((plus_plus_real A_99) zero_zero_real)) A_99))
% 0.72/0.98 FOF formula (forall (A_98:int), (((eq int) ((plus_plus_int A_98) zero_zero_int)) A_98)) of role axiom named fact_361_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J
% 0.72/0.98 A new axiom: (forall (A_98:int), (((eq int) ((plus_plus_int A_98) zero_zero_int)) A_98))
% 0.72/0.99 FOF formula (forall (A_98:nat), (((eq nat) ((plus_plus_nat A_98) zero_zero_nat)) A_98)) of role axiom named fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J
% 0.72/0.99 A new axiom: (forall (A_98:nat), (((eq nat) ((plus_plus_nat A_98) zero_zero_nat)) A_98))
% 0.72/0.99 FOF formula (forall (A_98:real), (((eq real) ((plus_plus_real A_98) zero_zero_real)) A_98)) of role axiom named fact_363_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J
% 0.72/0.99 A new axiom: (forall (A_98:real), (((eq real) ((plus_plus_real A_98) zero_zero_real)) A_98))
% 0.72/0.99 FOF formula (forall (A_97:int), (((eq int) ((plus_plus_int A_97) zero_zero_int)) A_97)) of role axiom named fact_364_add__0__right
% 0.72/0.99 A new axiom: (forall (A_97:int), (((eq int) ((plus_plus_int A_97) zero_zero_int)) A_97))
% 0.72/0.99 FOF formula (forall (A_97:nat), (((eq nat) ((plus_plus_nat A_97) zero_zero_nat)) A_97)) of role axiom named fact_365_add__0__right
% 0.72/0.99 A new axiom: (forall (A_97:nat), (((eq nat) ((plus_plus_nat A_97) zero_zero_nat)) A_97))
% 0.72/0.99 FOF formula (forall (A_97:real), (((eq real) ((plus_plus_real A_97) zero_zero_real)) A_97)) of role axiom named fact_366_add__0__right
% 0.72/0.99 A new axiom: (forall (A_97:real), (((eq real) ((plus_plus_real A_97) zero_zero_real)) A_97))
% 0.72/0.99 FOF formula (forall (A_96:int), ((iff (((eq int) zero_zero_int) ((plus_plus_int A_96) A_96))) (((eq int) A_96) zero_zero_int))) of role axiom named fact_367_double__zero__sym
% 0.72/0.99 A new axiom: (forall (A_96:int), ((iff (((eq int) zero_zero_int) ((plus_plus_int A_96) A_96))) (((eq int) A_96) zero_zero_int)))
% 0.72/0.99 FOF formula (forall (A_96:real), ((iff (((eq real) zero_zero_real) ((plus_plus_real A_96) A_96))) (((eq real) A_96) zero_zero_real))) of role axiom named fact_368_double__zero__sym
% 0.72/0.99 A new axiom: (forall (A_96:real), ((iff (((eq real) zero_zero_real) ((plus_plus_real A_96) A_96))) (((eq real) A_96) zero_zero_real)))
% 0.72/0.99 FOF formula (forall (A_95:int), (((eq int) ((plus_plus_int zero_zero_int) A_95)) A_95)) of role axiom named fact_369_add__0
% 0.72/0.99 A new axiom: (forall (A_95:int), (((eq int) ((plus_plus_int zero_zero_int) A_95)) A_95))
% 0.72/0.99 FOF formula (forall (A_95:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_95)) A_95)) of role axiom named fact_370_add__0
% 0.72/0.99 A new axiom: (forall (A_95:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_95)) A_95))
% 0.72/0.99 FOF formula (forall (A_95:real), (((eq real) ((plus_plus_real zero_zero_real) A_95)) A_95)) of role axiom named fact_371_add__0
% 0.72/0.99 A new axiom: (forall (A_95:real), (((eq real) ((plus_plus_real zero_zero_real) A_95)) A_95))
% 0.72/0.99 FOF formula (forall (A_94:int), (((eq int) ((plus_plus_int zero_zero_int) A_94)) A_94)) of role axiom named fact_372_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J
% 0.72/0.99 A new axiom: (forall (A_94:int), (((eq int) ((plus_plus_int zero_zero_int) A_94)) A_94))
% 0.72/0.99 FOF formula (forall (A_94:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_94)) A_94)) of role axiom named fact_373_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J
% 0.72/0.99 A new axiom: (forall (A_94:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_94)) A_94))
% 0.72/0.99 FOF formula (forall (A_94:real), (((eq real) ((plus_plus_real zero_zero_real) A_94)) A_94)) of role axiom named fact_374_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J
% 0.72/0.99 A new axiom: (forall (A_94:real), (((eq real) ((plus_plus_real zero_zero_real) A_94)) A_94))
% 0.72/0.99 FOF formula (forall (A_93:int), (((eq int) ((plus_plus_int zero_zero_int) A_93)) A_93)) of role axiom named fact_375_add__0__left
% 0.72/0.99 A new axiom: (forall (A_93:int), (((eq int) ((plus_plus_int zero_zero_int) A_93)) A_93))
% 0.72/0.99 FOF formula (forall (A_93:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_93)) A_93)) of role axiom named fact_376_add__0__left
% 0.72/0.99 A new axiom: (forall (A_93:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_93)) A_93))
% 0.72/0.99 FOF formula (forall (A_93:real), (((eq real) ((plus_plus_real zero_zero_real) A_93)) A_93)) of role axiom named fact_377_add__0__left
% 0.72/0.99 A new axiom: (forall (A_93:real), (((eq real) ((plus_plus_real zero_zero_real) A_93)) A_93))
% 0.72/0.99 FOF formula (forall (C_50:int) (A_92:int) (B_75:int), (((ord_less_int ((plus_plus_int C_50) A_92)) ((plus_plus_int C_50) B_75))->((ord_less_int A_92) B_75))) of role axiom named fact_378_add__less__imp__less__left
% 0.80/1.01 A new axiom: (forall (C_50:int) (A_92:int) (B_75:int), (((ord_less_int ((plus_plus_int C_50) A_92)) ((plus_plus_int C_50) B_75))->((ord_less_int A_92) B_75)))
% 0.80/1.01 FOF formula (forall (C_50:nat) (A_92:nat) (B_75:nat), (((ord_less_nat ((plus_plus_nat C_50) A_92)) ((plus_plus_nat C_50) B_75))->((ord_less_nat A_92) B_75))) of role axiom named fact_379_add__less__imp__less__left
% 0.80/1.01 A new axiom: (forall (C_50:nat) (A_92:nat) (B_75:nat), (((ord_less_nat ((plus_plus_nat C_50) A_92)) ((plus_plus_nat C_50) B_75))->((ord_less_nat A_92) B_75)))
% 0.80/1.01 FOF formula (forall (C_50:real) (A_92:real) (B_75:real), (((ord_less_real ((plus_plus_real C_50) A_92)) ((plus_plus_real C_50) B_75))->((ord_less_real A_92) B_75))) of role axiom named fact_380_add__less__imp__less__left
% 0.80/1.01 A new axiom: (forall (C_50:real) (A_92:real) (B_75:real), (((ord_less_real ((plus_plus_real C_50) A_92)) ((plus_plus_real C_50) B_75))->((ord_less_real A_92) B_75)))
% 0.80/1.01 FOF formula (forall (A_91:int) (C_49:int) (B_74:int), (((ord_less_int ((plus_plus_int A_91) C_49)) ((plus_plus_int B_74) C_49))->((ord_less_int A_91) B_74))) of role axiom named fact_381_add__less__imp__less__right
% 0.80/1.01 A new axiom: (forall (A_91:int) (C_49:int) (B_74:int), (((ord_less_int ((plus_plus_int A_91) C_49)) ((plus_plus_int B_74) C_49))->((ord_less_int A_91) B_74)))
% 0.80/1.01 FOF formula (forall (A_91:nat) (C_49:nat) (B_74:nat), (((ord_less_nat ((plus_plus_nat A_91) C_49)) ((plus_plus_nat B_74) C_49))->((ord_less_nat A_91) B_74))) of role axiom named fact_382_add__less__imp__less__right
% 0.80/1.01 A new axiom: (forall (A_91:nat) (C_49:nat) (B_74:nat), (((ord_less_nat ((plus_plus_nat A_91) C_49)) ((plus_plus_nat B_74) C_49))->((ord_less_nat A_91) B_74)))
% 0.80/1.01 FOF formula (forall (A_91:real) (C_49:real) (B_74:real), (((ord_less_real ((plus_plus_real A_91) C_49)) ((plus_plus_real B_74) C_49))->((ord_less_real A_91) B_74))) of role axiom named fact_383_add__less__imp__less__right
% 0.80/1.01 A new axiom: (forall (A_91:real) (C_49:real) (B_74:real), (((ord_less_real ((plus_plus_real A_91) C_49)) ((plus_plus_real B_74) C_49))->((ord_less_real A_91) B_74)))
% 0.80/1.01 FOF formula (forall (C_48:int) (D_20:int) (A_90:int) (B_73:int), (((ord_less_int A_90) B_73)->(((ord_less_int C_48) D_20)->((ord_less_int ((plus_plus_int A_90) C_48)) ((plus_plus_int B_73) D_20))))) of role axiom named fact_384_add__strict__mono
% 0.80/1.01 A new axiom: (forall (C_48:int) (D_20:int) (A_90:int) (B_73:int), (((ord_less_int A_90) B_73)->(((ord_less_int C_48) D_20)->((ord_less_int ((plus_plus_int A_90) C_48)) ((plus_plus_int B_73) D_20)))))
% 0.80/1.01 FOF formula (forall (C_48:nat) (D_20:nat) (A_90:nat) (B_73:nat), (((ord_less_nat A_90) B_73)->(((ord_less_nat C_48) D_20)->((ord_less_nat ((plus_plus_nat A_90) C_48)) ((plus_plus_nat B_73) D_20))))) of role axiom named fact_385_add__strict__mono
% 0.80/1.01 A new axiom: (forall (C_48:nat) (D_20:nat) (A_90:nat) (B_73:nat), (((ord_less_nat A_90) B_73)->(((ord_less_nat C_48) D_20)->((ord_less_nat ((plus_plus_nat A_90) C_48)) ((plus_plus_nat B_73) D_20)))))
% 0.80/1.01 FOF formula (forall (C_48:real) (D_20:real) (A_90:real) (B_73:real), (((ord_less_real A_90) B_73)->(((ord_less_real C_48) D_20)->((ord_less_real ((plus_plus_real A_90) C_48)) ((plus_plus_real B_73) D_20))))) of role axiom named fact_386_add__strict__mono
% 0.80/1.01 A new axiom: (forall (C_48:real) (D_20:real) (A_90:real) (B_73:real), (((ord_less_real A_90) B_73)->(((ord_less_real C_48) D_20)->((ord_less_real ((plus_plus_real A_90) C_48)) ((plus_plus_real B_73) D_20)))))
% 0.80/1.01 FOF formula (forall (C_47:int) (A_89:int) (B_72:int), (((ord_less_int A_89) B_72)->((ord_less_int ((plus_plus_int C_47) A_89)) ((plus_plus_int C_47) B_72)))) of role axiom named fact_387_add__strict__left__mono
% 0.80/1.01 A new axiom: (forall (C_47:int) (A_89:int) (B_72:int), (((ord_less_int A_89) B_72)->((ord_less_int ((plus_plus_int C_47) A_89)) ((plus_plus_int C_47) B_72))))
% 0.80/1.01 FOF formula (forall (C_47:nat) (A_89:nat) (B_72:nat), (((ord_less_nat A_89) B_72)->((ord_less_nat ((plus_plus_nat C_47) A_89)) ((plus_plus_nat C_47) B_72)))) of role axiom named fact_388_add__strict__left__mono
% 0.80/1.03 A new axiom: (forall (C_47:nat) (A_89:nat) (B_72:nat), (((ord_less_nat A_89) B_72)->((ord_less_nat ((plus_plus_nat C_47) A_89)) ((plus_plus_nat C_47) B_72))))
% 0.80/1.03 FOF formula (forall (C_47:real) (A_89:real) (B_72:real), (((ord_less_real A_89) B_72)->((ord_less_real ((plus_plus_real C_47) A_89)) ((plus_plus_real C_47) B_72)))) of role axiom named fact_389_add__strict__left__mono
% 0.80/1.03 A new axiom: (forall (C_47:real) (A_89:real) (B_72:real), (((ord_less_real A_89) B_72)->((ord_less_real ((plus_plus_real C_47) A_89)) ((plus_plus_real C_47) B_72))))
% 0.80/1.03 FOF formula (forall (C_46:int) (A_88:int) (B_71:int), (((ord_less_int A_88) B_71)->((ord_less_int ((plus_plus_int A_88) C_46)) ((plus_plus_int B_71) C_46)))) of role axiom named fact_390_add__strict__right__mono
% 0.80/1.03 A new axiom: (forall (C_46:int) (A_88:int) (B_71:int), (((ord_less_int A_88) B_71)->((ord_less_int ((plus_plus_int A_88) C_46)) ((plus_plus_int B_71) C_46))))
% 0.80/1.03 FOF formula (forall (C_46:nat) (A_88:nat) (B_71:nat), (((ord_less_nat A_88) B_71)->((ord_less_nat ((plus_plus_nat A_88) C_46)) ((plus_plus_nat B_71) C_46)))) of role axiom named fact_391_add__strict__right__mono
% 0.80/1.03 A new axiom: (forall (C_46:nat) (A_88:nat) (B_71:nat), (((ord_less_nat A_88) B_71)->((ord_less_nat ((plus_plus_nat A_88) C_46)) ((plus_plus_nat B_71) C_46))))
% 0.80/1.03 FOF formula (forall (C_46:real) (A_88:real) (B_71:real), (((ord_less_real A_88) B_71)->((ord_less_real ((plus_plus_real A_88) C_46)) ((plus_plus_real B_71) C_46)))) of role axiom named fact_392_add__strict__right__mono
% 0.80/1.03 A new axiom: (forall (C_46:real) (A_88:real) (B_71:real), (((ord_less_real A_88) B_71)->((ord_less_real ((plus_plus_real A_88) C_46)) ((plus_plus_real B_71) C_46))))
% 0.80/1.03 FOF formula (forall (C_45:int) (A_87:int) (B_70:int), ((iff ((ord_less_int ((plus_plus_int C_45) A_87)) ((plus_plus_int C_45) B_70))) ((ord_less_int A_87) B_70))) of role axiom named fact_393_add__less__cancel__left
% 0.80/1.03 A new axiom: (forall (C_45:int) (A_87:int) (B_70:int), ((iff ((ord_less_int ((plus_plus_int C_45) A_87)) ((plus_plus_int C_45) B_70))) ((ord_less_int A_87) B_70)))
% 0.80/1.03 FOF formula (forall (C_45:nat) (A_87:nat) (B_70:nat), ((iff ((ord_less_nat ((plus_plus_nat C_45) A_87)) ((plus_plus_nat C_45) B_70))) ((ord_less_nat A_87) B_70))) of role axiom named fact_394_add__less__cancel__left
% 0.80/1.03 A new axiom: (forall (C_45:nat) (A_87:nat) (B_70:nat), ((iff ((ord_less_nat ((plus_plus_nat C_45) A_87)) ((plus_plus_nat C_45) B_70))) ((ord_less_nat A_87) B_70)))
% 0.80/1.03 FOF formula (forall (C_45:real) (A_87:real) (B_70:real), ((iff ((ord_less_real ((plus_plus_real C_45) A_87)) ((plus_plus_real C_45) B_70))) ((ord_less_real A_87) B_70))) of role axiom named fact_395_add__less__cancel__left
% 0.80/1.03 A new axiom: (forall (C_45:real) (A_87:real) (B_70:real), ((iff ((ord_less_real ((plus_plus_real C_45) A_87)) ((plus_plus_real C_45) B_70))) ((ord_less_real A_87) B_70)))
% 0.80/1.03 FOF formula (forall (A_86:int) (C_44:int) (B_69:int), ((iff ((ord_less_int ((plus_plus_int A_86) C_44)) ((plus_plus_int B_69) C_44))) ((ord_less_int A_86) B_69))) of role axiom named fact_396_add__less__cancel__right
% 0.80/1.03 A new axiom: (forall (A_86:int) (C_44:int) (B_69:int), ((iff ((ord_less_int ((plus_plus_int A_86) C_44)) ((plus_plus_int B_69) C_44))) ((ord_less_int A_86) B_69)))
% 0.80/1.03 FOF formula (forall (A_86:nat) (C_44:nat) (B_69:nat), ((iff ((ord_less_nat ((plus_plus_nat A_86) C_44)) ((plus_plus_nat B_69) C_44))) ((ord_less_nat A_86) B_69))) of role axiom named fact_397_add__less__cancel__right
% 0.80/1.03 A new axiom: (forall (A_86:nat) (C_44:nat) (B_69:nat), ((iff ((ord_less_nat ((plus_plus_nat A_86) C_44)) ((plus_plus_nat B_69) C_44))) ((ord_less_nat A_86) B_69)))
% 0.80/1.03 FOF formula (forall (A_86:real) (C_44:real) (B_69:real), ((iff ((ord_less_real ((plus_plus_real A_86) C_44)) ((plus_plus_real B_69) C_44))) ((ord_less_real A_86) B_69))) of role axiom named fact_398_add__less__cancel__right
% 0.80/1.03 A new axiom: (forall (A_86:real) (C_44:real) (B_69:real), ((iff ((ord_less_real ((plus_plus_real A_86) C_44)) ((plus_plus_real B_69) C_44))) ((ord_less_real A_86) B_69)))
% 0.80/1.03 FOF formula (forall (X_18:int), (((eq int) ((power_power_int X_18) one_one_nat)) X_18)) of role axiom named fact_399_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J
% 0.80/1.05 A new axiom: (forall (X_18:int), (((eq int) ((power_power_int X_18) one_one_nat)) X_18))
% 0.80/1.05 FOF formula (forall (X_18:nat), (((eq nat) ((power_power_nat X_18) one_one_nat)) X_18)) of role axiom named fact_400_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J
% 0.80/1.05 A new axiom: (forall (X_18:nat), (((eq nat) ((power_power_nat X_18) one_one_nat)) X_18))
% 0.80/1.05 FOF formula (forall (X_18:real), (((eq real) ((power_power_real X_18) one_one_nat)) X_18)) of role axiom named fact_401_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J
% 0.80/1.05 A new axiom: (forall (X_18:real), (((eq real) ((power_power_real X_18) one_one_nat)) X_18))
% 0.80/1.05 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_402_nat__power__eq__0__iff
% 0.80/1.05 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))))
% 0.80/1.05 FOF formula (forall (A:real) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_real zero_zero_real) A)->((ex real) (fun (X_1:real)=> ((and ((and ((ord_less_real zero_zero_real) X_1)) (((eq real) ((power_power_real X_1) N)) A))) (forall (Y_1:real), (((and ((ord_less_real zero_zero_real) Y_1)) (((eq real) ((power_power_real Y_1) N)) A))->(((eq real) Y_1) X_1))))))))) of role axiom named fact_403_realpow__pos__nth__unique
% 0.80/1.05 A new axiom: (forall (A:real) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_real zero_zero_real) A)->((ex real) (fun (X_1:real)=> ((and ((and ((ord_less_real zero_zero_real) X_1)) (((eq real) ((power_power_real X_1) N)) A))) (forall (Y_1:real), (((and ((ord_less_real zero_zero_real) Y_1)) (((eq real) ((power_power_real Y_1) N)) A))->(((eq real) Y_1) X_1)))))))))
% 0.80/1.05 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:real)=> ((and ((ord_less_real zero_zero_real) R)) (((eq real) ((power_power_real R) N)) A))))))) of role axiom named fact_404_realpow__pos__nth
% 0.80/1.05 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:real)=> ((and ((ord_less_real zero_zero_real) R)) (((eq real) ((power_power_real R) N)) A)))))))
% 0.80/1.05 FOF formula ((ord_less_eq_int one_one_int) t) of role axiom named fact_405_tpos
% 0.80/1.05 A new axiom: ((ord_less_eq_int one_one_int) t)
% 0.80/1.05 FOF formula (forall (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) one_one_nat)) one_one_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) one_one_nat)) (number_number_of_nat (succ V_1)))))) of role axiom named fact_406_nat__number__of__add__1
% 0.80/1.05 A new axiom: (forall (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) one_one_nat)) one_one_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) one_one_nat)) (number_number_of_nat (succ V_1))))))
% 0.80/1.05 FOF formula (forall (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V_1))) one_one_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V_1))) (number_number_of_nat (succ V_1)))))) of role axiom named fact_407_nat__1__add__number__of
% 0.80/1.05 A new axiom: (forall (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V_1))) one_one_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V_1))) (number_number_of_nat (succ V_1))))))
% 0.80/1.05 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_408_zadd__power3
% 0.80/1.06 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)))))))
% 0.80/1.06 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_409_zadd__power2
% 0.80/1.06 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)))))))
% 0.80/1.06 FOF formula (((eq nat) tn) ((minus_minus_nat (nat_1 t)) one_one_nat)) of role axiom named fact_410_tn
% 0.80/1.06 A new axiom: (((eq nat) tn) ((minus_minus_nat (nat_1 t)) one_one_nat))
% 0.80/1.06 FOF formula ((ord_less_nat zero_zero_nat) ((minus_minus_nat (nat_1 t)) one_one_nat)) of role axiom named fact_411__096_B_Bthesis_O_A_I_B_Btn_O_A_091_124_Atn_A_061_Anat_At_A_N_A1_059_A0_
% 0.80/1.06 A new axiom: ((ord_less_nat zero_zero_nat) ((minus_minus_nat (nat_1 t)) one_one_nat))
% 0.80/1.06 FOF formula (forall (A_85:int) (B_68:int), ((iff ((ord_less_eq_int A_85) B_68)) ((ord_less_eq_int ((minus_minus_int A_85) B_68)) zero_zero_int))) of role axiom named fact_412_le__iff__diff__le__0
% 0.80/1.06 A new axiom: (forall (A_85:int) (B_68:int), ((iff ((ord_less_eq_int A_85) B_68)) ((ord_less_eq_int ((minus_minus_int A_85) B_68)) zero_zero_int)))
% 0.80/1.06 FOF formula (forall (A_85:real) (B_68:real), ((iff ((ord_less_eq_real A_85) B_68)) ((ord_less_eq_real ((minus_minus_real A_85) B_68)) zero_zero_real))) of role axiom named fact_413_le__iff__diff__le__0
% 0.80/1.06 A new axiom: (forall (A_85:real) (B_68:real), ((iff ((ord_less_eq_real A_85) B_68)) ((ord_less_eq_real ((minus_minus_real A_85) B_68)) zero_zero_real)))
% 0.80/1.06 FOF formula (forall (A_84:int) (B_67:int), (((eq int) ((times_times_int A_84) B_67)) ((times_times_int B_67) A_84))) of role axiom named fact_414_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J
% 0.80/1.06 A new axiom: (forall (A_84:int) (B_67:int), (((eq int) ((times_times_int A_84) B_67)) ((times_times_int B_67) A_84)))
% 0.80/1.06 FOF formula (forall (A_84:nat) (B_67:nat), (((eq nat) ((times_times_nat A_84) B_67)) ((times_times_nat B_67) A_84))) of role axiom named fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J
% 0.80/1.06 A new axiom: (forall (A_84:nat) (B_67:nat), (((eq nat) ((times_times_nat A_84) B_67)) ((times_times_nat B_67) A_84)))
% 0.80/1.06 FOF formula (forall (A_84:real) (B_67:real), (((eq real) ((times_times_real A_84) B_67)) ((times_times_real B_67) A_84))) of role axiom named fact_416_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J
% 0.80/1.06 A new axiom: (forall (A_84:real) (B_67:real), (((eq real) ((times_times_real A_84) B_67)) ((times_times_real B_67) A_84)))
% 0.80/1.06 FOF formula (forall (Lx_6:int) (Rx_6:int) (Ry_4:int), (((eq int) ((times_times_int Lx_6) ((times_times_int Rx_6) Ry_4))) ((times_times_int Rx_6) ((times_times_int Lx_6) Ry_4)))) of role axiom named fact_417_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J
% 0.80/1.08 A new axiom: (forall (Lx_6:int) (Rx_6:int) (Ry_4:int), (((eq int) ((times_times_int Lx_6) ((times_times_int Rx_6) Ry_4))) ((times_times_int Rx_6) ((times_times_int Lx_6) Ry_4))))
% 0.80/1.08 FOF formula (forall (Lx_6:nat) (Rx_6:nat) (Ry_4:nat), (((eq nat) ((times_times_nat Lx_6) ((times_times_nat Rx_6) Ry_4))) ((times_times_nat Rx_6) ((times_times_nat Lx_6) Ry_4)))) of role axiom named fact_418_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J
% 0.80/1.08 A new axiom: (forall (Lx_6:nat) (Rx_6:nat) (Ry_4:nat), (((eq nat) ((times_times_nat Lx_6) ((times_times_nat Rx_6) Ry_4))) ((times_times_nat Rx_6) ((times_times_nat Lx_6) Ry_4))))
% 0.80/1.08 FOF formula (forall (Lx_6:real) (Rx_6:real) (Ry_4:real), (((eq real) ((times_times_real Lx_6) ((times_times_real Rx_6) Ry_4))) ((times_times_real Rx_6) ((times_times_real Lx_6) Ry_4)))) of role axiom named fact_419_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J
% 0.80/1.08 A new axiom: (forall (Lx_6:real) (Rx_6:real) (Ry_4:real), (((eq real) ((times_times_real Lx_6) ((times_times_real Rx_6) Ry_4))) ((times_times_real Rx_6) ((times_times_real Lx_6) Ry_4))))
% 0.80/1.08 FOF formula (forall (Lx_5:int) (Rx_5:int) (Ry_3:int), (((eq int) ((times_times_int Lx_5) ((times_times_int Rx_5) Ry_3))) ((times_times_int ((times_times_int Lx_5) Rx_5)) Ry_3))) of role axiom named fact_420_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J
% 0.80/1.08 A new axiom: (forall (Lx_5:int) (Rx_5:int) (Ry_3:int), (((eq int) ((times_times_int Lx_5) ((times_times_int Rx_5) Ry_3))) ((times_times_int ((times_times_int Lx_5) Rx_5)) Ry_3)))
% 0.80/1.08 FOF formula (forall (Lx_5:nat) (Rx_5:nat) (Ry_3:nat), (((eq nat) ((times_times_nat Lx_5) ((times_times_nat Rx_5) Ry_3))) ((times_times_nat ((times_times_nat Lx_5) Rx_5)) Ry_3))) of role axiom named fact_421_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J
% 0.80/1.08 A new axiom: (forall (Lx_5:nat) (Rx_5:nat) (Ry_3:nat), (((eq nat) ((times_times_nat Lx_5) ((times_times_nat Rx_5) Ry_3))) ((times_times_nat ((times_times_nat Lx_5) Rx_5)) Ry_3)))
% 0.80/1.08 FOF formula (forall (Lx_5:real) (Rx_5:real) (Ry_3:real), (((eq real) ((times_times_real Lx_5) ((times_times_real Rx_5) Ry_3))) ((times_times_real ((times_times_real Lx_5) Rx_5)) Ry_3))) of role axiom named fact_422_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J
% 0.80/1.08 A new axiom: (forall (Lx_5:real) (Rx_5:real) (Ry_3:real), (((eq real) ((times_times_real Lx_5) ((times_times_real Rx_5) Ry_3))) ((times_times_real ((times_times_real Lx_5) Rx_5)) Ry_3)))
% 0.80/1.08 FOF formula (forall (A_83:int) (B_66:int) (C_43:int), (((eq int) ((times_times_int ((times_times_int A_83) B_66)) C_43)) ((times_times_int A_83) ((times_times_int B_66) C_43)))) of role axiom named fact_423_ab__semigroup__mult__class_Omult__ac_I1_J
% 0.80/1.08 A new axiom: (forall (A_83:int) (B_66:int) (C_43:int), (((eq int) ((times_times_int ((times_times_int A_83) B_66)) C_43)) ((times_times_int A_83) ((times_times_int B_66) C_43))))
% 0.80/1.08 FOF formula (forall (A_83:nat) (B_66:nat) (C_43:nat), (((eq nat) ((times_times_nat ((times_times_nat A_83) B_66)) C_43)) ((times_times_nat A_83) ((times_times_nat B_66) C_43)))) of role axiom named fact_424_ab__semigroup__mult__class_Omult__ac_I1_J
% 0.80/1.08 A new axiom: (forall (A_83:nat) (B_66:nat) (C_43:nat), (((eq nat) ((times_times_nat ((times_times_nat A_83) B_66)) C_43)) ((times_times_nat A_83) ((times_times_nat B_66) C_43))))
% 0.80/1.08 FOF formula (forall (A_83:real) (B_66:real) (C_43:real), (((eq real) ((times_times_real ((times_times_real A_83) B_66)) C_43)) ((times_times_real A_83) ((times_times_real B_66) C_43)))) of role axiom named fact_425_ab__semigroup__mult__class_Omult__ac_I1_J
% 0.80/1.08 A new axiom: (forall (A_83:real) (B_66:real) (C_43:real), (((eq real) ((times_times_real ((times_times_real A_83) B_66)) C_43)) ((times_times_real A_83) ((times_times_real B_66) C_43))))
% 0.80/1.08 FOF formula (forall (Lx_4:int) (Ly_4:int) (Rx_4:int), (((eq int) ((times_times_int ((times_times_int Lx_4) Ly_4)) Rx_4)) ((times_times_int Lx_4) ((times_times_int Ly_4) Rx_4)))) of role axiom named fact_426_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J
% 0.80/1.08 A new axiom: (forall (Lx_4:int) (Ly_4:int) (Rx_4:int), (((eq int) ((times_times_int ((times_times_int Lx_4) Ly_4)) Rx_4)) ((times_times_int Lx_4) ((times_times_int Ly_4) Rx_4))))
% 0.89/1.10 FOF formula (forall (Lx_4:nat) (Ly_4:nat) (Rx_4:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_4) Ly_4)) Rx_4)) ((times_times_nat Lx_4) ((times_times_nat Ly_4) Rx_4)))) of role axiom named fact_427_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J
% 0.89/1.10 A new axiom: (forall (Lx_4:nat) (Ly_4:nat) (Rx_4:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_4) Ly_4)) Rx_4)) ((times_times_nat Lx_4) ((times_times_nat Ly_4) Rx_4))))
% 0.89/1.10 FOF formula (forall (Lx_4:real) (Ly_4:real) (Rx_4:real), (((eq real) ((times_times_real ((times_times_real Lx_4) Ly_4)) Rx_4)) ((times_times_real Lx_4) ((times_times_real Ly_4) Rx_4)))) of role axiom named fact_428_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J
% 0.89/1.10 A new axiom: (forall (Lx_4:real) (Ly_4:real) (Rx_4:real), (((eq real) ((times_times_real ((times_times_real Lx_4) Ly_4)) Rx_4)) ((times_times_real Lx_4) ((times_times_real Ly_4) Rx_4))))
% 0.89/1.10 FOF formula (forall (Lx_3:int) (Ly_3:int) (Rx_3:int), (((eq int) ((times_times_int ((times_times_int Lx_3) Ly_3)) Rx_3)) ((times_times_int ((times_times_int Lx_3) Rx_3)) Ly_3))) of role axiom named fact_429_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J
% 0.89/1.10 A new axiom: (forall (Lx_3:int) (Ly_3:int) (Rx_3:int), (((eq int) ((times_times_int ((times_times_int Lx_3) Ly_3)) Rx_3)) ((times_times_int ((times_times_int Lx_3) Rx_3)) Ly_3)))
% 0.89/1.10 FOF formula (forall (Lx_3:nat) (Ly_3:nat) (Rx_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_3) Ly_3)) Rx_3)) ((times_times_nat ((times_times_nat Lx_3) Rx_3)) Ly_3))) of role axiom named fact_430_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J
% 0.89/1.10 A new axiom: (forall (Lx_3:nat) (Ly_3:nat) (Rx_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_3) Ly_3)) Rx_3)) ((times_times_nat ((times_times_nat Lx_3) Rx_3)) Ly_3)))
% 0.89/1.10 FOF formula (forall (Lx_3:real) (Ly_3:real) (Rx_3:real), (((eq real) ((times_times_real ((times_times_real Lx_3) Ly_3)) Rx_3)) ((times_times_real ((times_times_real Lx_3) Rx_3)) Ly_3))) of role axiom named fact_431_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J
% 0.89/1.10 A new axiom: (forall (Lx_3:real) (Ly_3:real) (Rx_3:real), (((eq real) ((times_times_real ((times_times_real Lx_3) Ly_3)) Rx_3)) ((times_times_real ((times_times_real Lx_3) Rx_3)) Ly_3)))
% 0.89/1.10 FOF formula (forall (Lx_2:int) (Ly_2:int) (Rx_2:int) (Ry_2:int), (((eq int) ((times_times_int ((times_times_int Lx_2) Ly_2)) ((times_times_int Rx_2) Ry_2))) ((times_times_int Lx_2) ((times_times_int Ly_2) ((times_times_int Rx_2) Ry_2))))) of role axiom named fact_432_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J
% 0.89/1.10 A new axiom: (forall (Lx_2:int) (Ly_2:int) (Rx_2:int) (Ry_2:int), (((eq int) ((times_times_int ((times_times_int Lx_2) Ly_2)) ((times_times_int Rx_2) Ry_2))) ((times_times_int Lx_2) ((times_times_int Ly_2) ((times_times_int Rx_2) Ry_2)))))
% 0.89/1.10 FOF formula (forall (Lx_2:nat) (Ly_2:nat) (Rx_2:nat) (Ry_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_2) Ly_2)) ((times_times_nat Rx_2) Ry_2))) ((times_times_nat Lx_2) ((times_times_nat Ly_2) ((times_times_nat Rx_2) Ry_2))))) of role axiom named fact_433_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J
% 0.89/1.10 A new axiom: (forall (Lx_2:nat) (Ly_2:nat) (Rx_2:nat) (Ry_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_2) Ly_2)) ((times_times_nat Rx_2) Ry_2))) ((times_times_nat Lx_2) ((times_times_nat Ly_2) ((times_times_nat Rx_2) Ry_2)))))
% 0.89/1.10 FOF formula (forall (Lx_2:real) (Ly_2:real) (Rx_2:real) (Ry_2:real), (((eq real) ((times_times_real ((times_times_real Lx_2) Ly_2)) ((times_times_real Rx_2) Ry_2))) ((times_times_real Lx_2) ((times_times_real Ly_2) ((times_times_real Rx_2) Ry_2))))) of role axiom named fact_434_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J
% 0.89/1.10 A new axiom: (forall (Lx_2:real) (Ly_2:real) (Rx_2:real) (Ry_2:real), (((eq real) ((times_times_real ((times_times_real Lx_2) Ly_2)) ((times_times_real Rx_2) Ry_2))) ((times_times_real Lx_2) ((times_times_real Ly_2) ((times_times_real Rx_2) Ry_2)))))
% 0.89/1.11 FOF formula (forall (Lx_1:real) (Ly_1:real) (Rx_1:real) (Ry_1:real), (((eq real) ((times_times_real ((times_times_real Lx_1) Ly_1)) ((times_times_real Rx_1) Ry_1))) ((times_times_real Rx_1) ((times_times_real ((times_times_real Lx_1) Ly_1)) Ry_1)))) of role axiom named fact_435_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J
% 0.89/1.11 A new axiom: (forall (Lx_1:real) (Ly_1:real) (Rx_1:real) (Ry_1:real), (((eq real) ((times_times_real ((times_times_real Lx_1) Ly_1)) ((times_times_real Rx_1) Ry_1))) ((times_times_real Rx_1) ((times_times_real ((times_times_real Lx_1) Ly_1)) Ry_1))))
% 0.89/1.11 FOF formula (forall (Lx_1:nat) (Ly_1:nat) (Rx_1:nat) (Ry_1:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_1) Ly_1)) ((times_times_nat Rx_1) Ry_1))) ((times_times_nat Rx_1) ((times_times_nat ((times_times_nat Lx_1) Ly_1)) Ry_1)))) of role axiom named fact_436_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J
% 0.89/1.11 A new axiom: (forall (Lx_1:nat) (Ly_1:nat) (Rx_1:nat) (Ry_1:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_1) Ly_1)) ((times_times_nat Rx_1) Ry_1))) ((times_times_nat Rx_1) ((times_times_nat ((times_times_nat Lx_1) Ly_1)) Ry_1))))
% 0.89/1.11 FOF formula (forall (Lx_1:int) (Ly_1:int) (Rx_1:int) (Ry_1:int), (((eq int) ((times_times_int ((times_times_int Lx_1) Ly_1)) ((times_times_int Rx_1) Ry_1))) ((times_times_int Rx_1) ((times_times_int ((times_times_int Lx_1) Ly_1)) Ry_1)))) of role axiom named fact_437_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J
% 0.89/1.11 A new axiom: (forall (Lx_1:int) (Ly_1:int) (Rx_1:int) (Ry_1:int), (((eq int) ((times_times_int ((times_times_int Lx_1) Ly_1)) ((times_times_int Rx_1) Ry_1))) ((times_times_int Rx_1) ((times_times_int ((times_times_int Lx_1) Ly_1)) Ry_1))))
% 0.89/1.11 FOF formula (forall (Lx:real) (Ly:real) (Rx:real) (Ry:real), (((eq real) ((times_times_real ((times_times_real Lx) Ly)) ((times_times_real Rx) Ry))) ((times_times_real ((times_times_real Lx) Rx)) ((times_times_real Ly) Ry)))) of role axiom named fact_438_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J
% 0.89/1.11 A new axiom: (forall (Lx:real) (Ly:real) (Rx:real) (Ry:real), (((eq real) ((times_times_real ((times_times_real Lx) Ly)) ((times_times_real Rx) Ry))) ((times_times_real ((times_times_real Lx) Rx)) ((times_times_real Ly) Ry))))
% 0.89/1.11 FOF formula (forall (Lx:nat) (Ly:nat) (Rx:nat) (Ry:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx) Ly)) ((times_times_nat Rx) Ry))) ((times_times_nat ((times_times_nat Lx) Rx)) ((times_times_nat Ly) Ry)))) of role axiom named fact_439_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J
% 0.89/1.11 A new axiom: (forall (Lx:nat) (Ly:nat) (Rx:nat) (Ry:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx) Ly)) ((times_times_nat Rx) Ry))) ((times_times_nat ((times_times_nat Lx) Rx)) ((times_times_nat Ly) Ry))))
% 0.89/1.11 FOF formula (forall (Lx:int) (Ly:int) (Rx:int) (Ry:int), (((eq int) ((times_times_int ((times_times_int Lx) Ly)) ((times_times_int Rx) Ry))) ((times_times_int ((times_times_int Lx) Rx)) ((times_times_int Ly) Ry)))) of role axiom named fact_440_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J
% 0.89/1.11 A new axiom: (forall (Lx:int) (Ly:int) (Rx:int) (Ry:int), (((eq int) ((times_times_int ((times_times_int Lx) Ly)) ((times_times_int Rx) Ry))) ((times_times_int ((times_times_int Lx) Rx)) ((times_times_int Ly) Ry))))
% 0.89/1.11 FOF formula (forall (A_82:int) (B_65:int) (C_42:int) (D_19:int), ((((eq int) ((minus_minus_int A_82) B_65)) ((minus_minus_int C_42) D_19))->((iff (((eq int) A_82) B_65)) (((eq int) C_42) D_19)))) of role axiom named fact_441_diff__eq__diff__eq
% 0.89/1.11 A new axiom: (forall (A_82:int) (B_65:int) (C_42:int) (D_19:int), ((((eq int) ((minus_minus_int A_82) B_65)) ((minus_minus_int C_42) D_19))->((iff (((eq int) A_82) B_65)) (((eq int) C_42) D_19))))
% 0.89/1.11 FOF formula (forall (A_82:real) (B_65:real) (C_42:real) (D_19:real), ((((eq real) ((minus_minus_real A_82) B_65)) ((minus_minus_real C_42) D_19))->((iff (((eq real) A_82) B_65)) (((eq real) C_42) D_19)))) of role axiom named fact_442_diff__eq__diff__eq
% 0.89/1.11 A new axiom: (forall (A_82:real) (B_65:real) (C_42:real) (D_19:real), ((((eq real) ((minus_minus_real A_82) B_65)) ((minus_minus_real C_42) D_19))->((iff (((eq real) A_82) B_65)) (((eq real) C_42) D_19))))
% 0.89/1.13 FOF formula (forall (A_81:int) (B_64:int) (C_41:int) (D_18:int), ((((eq int) ((minus_minus_int A_81) B_64)) ((minus_minus_int C_41) D_18))->((iff ((ord_less_eq_int A_81) B_64)) ((ord_less_eq_int C_41) D_18)))) of role axiom named fact_443_diff__eq__diff__less__eq
% 0.89/1.13 A new axiom: (forall (A_81:int) (B_64:int) (C_41:int) (D_18:int), ((((eq int) ((minus_minus_int A_81) B_64)) ((minus_minus_int C_41) D_18))->((iff ((ord_less_eq_int A_81) B_64)) ((ord_less_eq_int C_41) D_18))))
% 0.89/1.13 FOF formula (forall (A_81:real) (B_64:real) (C_41:real) (D_18:real), ((((eq real) ((minus_minus_real A_81) B_64)) ((minus_minus_real C_41) D_18))->((iff ((ord_less_eq_real A_81) B_64)) ((ord_less_eq_real C_41) D_18)))) of role axiom named fact_444_diff__eq__diff__less__eq
% 0.89/1.13 A new axiom: (forall (A_81:real) (B_64:real) (C_41:real) (D_18:real), ((((eq real) ((minus_minus_real A_81) B_64)) ((minus_minus_real C_41) D_18))->((iff ((ord_less_eq_real A_81) B_64)) ((ord_less_eq_real C_41) D_18))))
% 0.89/1.13 FOF formula (forall (V_12:int) (V_11:int), (((ord_less_eq_int pls) V_11)->(((ord_less_eq_int pls) V_12)->(((eq real) ((times_times_real (number267125858f_real V_11)) (number267125858f_real V_12))) (number267125858f_real ((times_times_int V_11) V_12)))))) of role axiom named fact_445_semiring__mult__number__of
% 0.89/1.13 A new axiom: (forall (V_12:int) (V_11:int), (((ord_less_eq_int pls) V_11)->(((ord_less_eq_int pls) V_12)->(((eq real) ((times_times_real (number267125858f_real V_11)) (number267125858f_real V_12))) (number267125858f_real ((times_times_int V_11) V_12))))))
% 0.89/1.13 FOF formula (forall (V_12:int) (V_11:int), (((ord_less_eq_int pls) V_11)->(((ord_less_eq_int pls) V_12)->(((eq nat) ((times_times_nat (number_number_of_nat V_11)) (number_number_of_nat V_12))) (number_number_of_nat ((times_times_int V_11) V_12)))))) of role axiom named fact_446_semiring__mult__number__of
% 0.89/1.13 A new axiom: (forall (V_12:int) (V_11:int), (((ord_less_eq_int pls) V_11)->(((ord_less_eq_int pls) V_12)->(((eq nat) ((times_times_nat (number_number_of_nat V_11)) (number_number_of_nat V_12))) (number_number_of_nat ((times_times_int V_11) V_12))))))
% 0.89/1.13 FOF formula (forall (V_12:int) (V_11:int), (((ord_less_eq_int pls) V_11)->(((ord_less_eq_int pls) V_12)->(((eq int) ((times_times_int (number_number_of_int V_11)) (number_number_of_int V_12))) (number_number_of_int ((times_times_int V_11) V_12)))))) of role axiom named fact_447_semiring__mult__number__of
% 0.89/1.13 A new axiom: (forall (V_12:int) (V_11:int), (((ord_less_eq_int pls) V_11)->(((ord_less_eq_int pls) V_12)->(((eq int) ((times_times_int (number_number_of_int V_11)) (number_number_of_int V_12))) (number_number_of_int ((times_times_int V_11) V_12))))))
% 0.89/1.13 FOF formula (forall (W:int), ((ord_less_eq_int W) W)) of role axiom named fact_448_zle__refl
% 0.89/1.13 A new axiom: (forall (W:int), ((ord_less_eq_int W) W))
% 0.89/1.13 FOF formula (forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z))) of role axiom named fact_449_zmult__commute
% 0.89/1.13 A new axiom: (forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z)))
% 0.89/1.13 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_450_zle__linear
% 0.89/1.13 A new axiom: (forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z)))
% 0.89/1.13 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_451_zmult__assoc
% 0.89/1.13 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))))
% 0.89/1.13 FOF formula (forall (K:int) (I_1:int) (J:int), (((ord_less_eq_int I_1) J)->(((ord_less_eq_int J) K)->((ord_less_eq_int I_1) K)))) of role axiom named fact_452_zle__trans
% 0.89/1.13 A new axiom: (forall (K:int) (I_1:int) (J:int), (((ord_less_eq_int I_1) J)->(((ord_less_eq_int J) K)->((ord_less_eq_int I_1) K))))
% 0.89/1.15 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_453_zle__antisym
% 0.89/1.15 A new axiom: (forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W))))
% 0.89/1.15 FOF formula (forall (X_17:int) (Y_15:int), ((iff ((ord_less_eq_real (number267125858f_real X_17)) (number267125858f_real Y_15))) ((ord_less_eq_int X_17) Y_15))) of role axiom named fact_454_le__number__of
% 0.89/1.15 A new axiom: (forall (X_17:int) (Y_15:int), ((iff ((ord_less_eq_real (number267125858f_real X_17)) (number267125858f_real Y_15))) ((ord_less_eq_int X_17) Y_15)))
% 0.89/1.15 FOF formula (forall (X_17:int) (Y_15:int), ((iff ((ord_less_eq_int (number_number_of_int X_17)) (number_number_of_int Y_15))) ((ord_less_eq_int X_17) Y_15))) of role axiom named fact_455_le__number__of
% 0.89/1.15 A new axiom: (forall (X_17:int) (Y_15:int), ((iff ((ord_less_eq_int (number_number_of_int X_17)) (number_number_of_int Y_15))) ((ord_less_eq_int X_17) Y_15)))
% 0.89/1.15 FOF formula (forall (V_10:int) (W_7:int), (((eq real) (number267125858f_real ((times_times_int V_10) W_7))) ((times_times_real (number267125858f_real V_10)) (number267125858f_real W_7)))) of role axiom named fact_456_number__of__mult
% 0.89/1.15 A new axiom: (forall (V_10:int) (W_7:int), (((eq real) (number267125858f_real ((times_times_int V_10) W_7))) ((times_times_real (number267125858f_real V_10)) (number267125858f_real W_7))))
% 0.89/1.15 FOF formula (forall (V_10:int) (W_7:int), (((eq int) (number_number_of_int ((times_times_int V_10) W_7))) ((times_times_int (number_number_of_int V_10)) (number_number_of_int W_7)))) of role axiom named fact_457_number__of__mult
% 0.89/1.15 A new axiom: (forall (V_10:int) (W_7:int), (((eq int) (number_number_of_int ((times_times_int V_10) W_7))) ((times_times_int (number_number_of_int V_10)) (number_number_of_int W_7))))
% 0.89/1.15 FOF formula (forall (V_9:int) (W_6:int), (((eq real) ((times_times_real (number267125858f_real V_9)) (number267125858f_real W_6))) (number267125858f_real ((times_times_int V_9) W_6)))) of role axiom named fact_458_arith__simps_I32_J
% 0.89/1.15 A new axiom: (forall (V_9:int) (W_6:int), (((eq real) ((times_times_real (number267125858f_real V_9)) (number267125858f_real W_6))) (number267125858f_real ((times_times_int V_9) W_6))))
% 0.89/1.15 FOF formula (forall (V_9:int) (W_6:int), (((eq int) ((times_times_int (number_number_of_int V_9)) (number_number_of_int W_6))) (number_number_of_int ((times_times_int V_9) W_6)))) of role axiom named fact_459_arith__simps_I32_J
% 0.89/1.15 A new axiom: (forall (V_9:int) (W_6:int), (((eq int) ((times_times_int (number_number_of_int V_9)) (number_number_of_int W_6))) (number_number_of_int ((times_times_int V_9) W_6))))
% 0.89/1.15 FOF formula (forall (V_8:int) (W_5:int) (Z_4:real), (((eq real) ((times_times_real (number267125858f_real V_8)) ((times_times_real (number267125858f_real W_5)) Z_4))) ((times_times_real (number267125858f_real ((times_times_int V_8) W_5))) Z_4))) of role axiom named fact_460_mult__number__of__left
% 0.89/1.15 A new axiom: (forall (V_8:int) (W_5:int) (Z_4:real), (((eq real) ((times_times_real (number267125858f_real V_8)) ((times_times_real (number267125858f_real W_5)) Z_4))) ((times_times_real (number267125858f_real ((times_times_int V_8) W_5))) Z_4)))
% 0.89/1.15 FOF formula (forall (V_8:int) (W_5:int) (Z_4:int), (((eq int) ((times_times_int (number_number_of_int V_8)) ((times_times_int (number_number_of_int W_5)) Z_4))) ((times_times_int (number_number_of_int ((times_times_int V_8) W_5))) Z_4))) of role axiom named fact_461_mult__number__of__left
% 0.89/1.15 A new axiom: (forall (V_8:int) (W_5:int) (Z_4:int), (((eq int) ((times_times_int (number_number_of_int V_8)) ((times_times_int (number_number_of_int W_5)) Z_4))) ((times_times_int (number_number_of_int ((times_times_int V_8) W_5))) Z_4)))
% 0.89/1.15 FOF formula (forall (Z_1:int) (Z:int), (((ord_less_eq_int zero_zero_int) Z)->(((ord_less_eq_int zero_zero_int) Z_1)->((iff (((eq nat) (nat_1 Z)) (nat_1 Z_1))) (((eq int) Z) Z_1))))) of role axiom named fact_462_eq__nat__nat__iff
% 0.89/1.15 A new axiom: (forall (Z_1:int) (Z:int), (((ord_less_eq_int zero_zero_int) Z)->(((ord_less_eq_int zero_zero_int) Z_1)->((iff (((eq nat) (nat_1 Z)) (nat_1 Z_1))) (((eq int) Z) Z_1)))))
% 0.89/1.16 FOF formula (forall (V_7:int) (B_63:int) (C_40:int), (((eq int) ((times_times_int (number_number_of_int V_7)) ((minus_minus_int B_63) C_40))) ((minus_minus_int ((times_times_int (number_number_of_int V_7)) B_63)) ((times_times_int (number_number_of_int V_7)) C_40)))) of role axiom named fact_463_right__diff__distrib__number__of
% 0.89/1.16 A new axiom: (forall (V_7:int) (B_63:int) (C_40:int), (((eq int) ((times_times_int (number_number_of_int V_7)) ((minus_minus_int B_63) C_40))) ((minus_minus_int ((times_times_int (number_number_of_int V_7)) B_63)) ((times_times_int (number_number_of_int V_7)) C_40))))
% 0.89/1.16 FOF formula (forall (V_7:int) (B_63:real) (C_40:real), (((eq real) ((times_times_real (number267125858f_real V_7)) ((minus_minus_real B_63) C_40))) ((minus_minus_real ((times_times_real (number267125858f_real V_7)) B_63)) ((times_times_real (number267125858f_real V_7)) C_40)))) of role axiom named fact_464_right__diff__distrib__number__of
% 0.89/1.16 A new axiom: (forall (V_7:int) (B_63:real) (C_40:real), (((eq real) ((times_times_real (number267125858f_real V_7)) ((minus_minus_real B_63) C_40))) ((minus_minus_real ((times_times_real (number267125858f_real V_7)) B_63)) ((times_times_real (number267125858f_real V_7)) C_40))))
% 0.89/1.16 FOF formula (forall (A_80:int) (B_62:int) (V_6:int), (((eq int) ((times_times_int ((minus_minus_int A_80) B_62)) (number_number_of_int V_6))) ((minus_minus_int ((times_times_int A_80) (number_number_of_int V_6))) ((times_times_int B_62) (number_number_of_int V_6))))) of role axiom named fact_465_left__diff__distrib__number__of
% 0.89/1.16 A new axiom: (forall (A_80:int) (B_62:int) (V_6:int), (((eq int) ((times_times_int ((minus_minus_int A_80) B_62)) (number_number_of_int V_6))) ((minus_minus_int ((times_times_int A_80) (number_number_of_int V_6))) ((times_times_int B_62) (number_number_of_int V_6)))))
% 0.89/1.16 FOF formula (forall (A_80:real) (B_62:real) (V_6:int), (((eq real) ((times_times_real ((minus_minus_real A_80) B_62)) (number267125858f_real V_6))) ((minus_minus_real ((times_times_real A_80) (number267125858f_real V_6))) ((times_times_real B_62) (number267125858f_real V_6))))) of role axiom named fact_466_left__diff__distrib__number__of
% 0.89/1.16 A new axiom: (forall (A_80:real) (B_62:real) (V_6:int), (((eq real) ((times_times_real ((minus_minus_real A_80) B_62)) (number267125858f_real V_6))) ((minus_minus_real ((times_times_real A_80) (number267125858f_real V_6))) ((times_times_real B_62) (number267125858f_real V_6)))))
% 0.89/1.16 FOF formula (forall (V_5:int) (W_4:int), (((eq int) (number_number_of_int ((minus_minus_int V_5) W_4))) ((minus_minus_int (number_number_of_int V_5)) (number_number_of_int W_4)))) of role axiom named fact_467_number__of__diff
% 0.89/1.16 A new axiom: (forall (V_5:int) (W_4:int), (((eq int) (number_number_of_int ((minus_minus_int V_5) W_4))) ((minus_minus_int (number_number_of_int V_5)) (number_number_of_int W_4))))
% 0.89/1.16 FOF formula (forall (V_5:int) (W_4:int), (((eq real) (number267125858f_real ((minus_minus_int V_5) W_4))) ((minus_minus_real (number267125858f_real V_5)) (number267125858f_real W_4)))) of role axiom named fact_468_number__of__diff
% 0.89/1.16 A new axiom: (forall (V_5:int) (W_4:int), (((eq real) (number267125858f_real ((minus_minus_int V_5) W_4))) ((minus_minus_real (number267125858f_real V_5)) (number267125858f_real W_4))))
% 0.89/1.16 FOF formula (forall (M_5:nat) (N_11:nat), (((eq real) (semiri132038758t_real ((times_times_nat M_5) N_11))) ((times_times_real (semiri132038758t_real M_5)) (semiri132038758t_real N_11)))) of role axiom named fact_469_of__nat__mult
% 0.89/1.16 A new axiom: (forall (M_5:nat) (N_11:nat), (((eq real) (semiri132038758t_real ((times_times_nat M_5) N_11))) ((times_times_real (semiri132038758t_real M_5)) (semiri132038758t_real N_11))))
% 0.89/1.16 FOF formula (forall (M_5:nat) (N_11:nat), (((eq nat) (semiri984289939at_nat ((times_times_nat M_5) N_11))) ((times_times_nat (semiri984289939at_nat M_5)) (semiri984289939at_nat N_11)))) of role axiom named fact_470_of__nat__mult
% 0.89/1.16 A new axiom: (forall (M_5:nat) (N_11:nat), (((eq nat) (semiri984289939at_nat ((times_times_nat M_5) N_11))) ((times_times_nat (semiri984289939at_nat M_5)) (semiri984289939at_nat N_11))))
% 0.89/1.18 FOF formula (forall (M_5:nat) (N_11:nat), (((eq int) (semiri1621563631at_int ((times_times_nat M_5) N_11))) ((times_times_int (semiri1621563631at_int M_5)) (semiri1621563631at_int N_11)))) of role axiom named fact_471_of__nat__mult
% 0.89/1.18 A new axiom: (forall (M_5:nat) (N_11:nat), (((eq int) (semiri1621563631at_int ((times_times_nat M_5) N_11))) ((times_times_int (semiri1621563631at_int M_5)) (semiri1621563631at_int N_11))))
% 0.89/1.18 FOF formula (forall (M_4:nat) (N_10:nat), ((iff ((ord_less_eq_real (semiri132038758t_real M_4)) (semiri132038758t_real N_10))) ((ord_less_eq_nat M_4) N_10))) of role axiom named fact_472_of__nat__le__iff
% 0.89/1.18 A new axiom: (forall (M_4:nat) (N_10:nat), ((iff ((ord_less_eq_real (semiri132038758t_real M_4)) (semiri132038758t_real N_10))) ((ord_less_eq_nat M_4) N_10)))
% 0.89/1.18 FOF formula (forall (M_4:nat) (N_10:nat), ((iff ((ord_less_eq_nat (semiri984289939at_nat M_4)) (semiri984289939at_nat N_10))) ((ord_less_eq_nat M_4) N_10))) of role axiom named fact_473_of__nat__le__iff
% 0.89/1.18 A new axiom: (forall (M_4:nat) (N_10:nat), ((iff ((ord_less_eq_nat (semiri984289939at_nat M_4)) (semiri984289939at_nat N_10))) ((ord_less_eq_nat M_4) N_10)))
% 0.89/1.18 FOF formula (forall (M_4:nat) (N_10:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int M_4)) (semiri1621563631at_int N_10))) ((ord_less_eq_nat M_4) N_10))) of role axiom named fact_474_of__nat__le__iff
% 0.89/1.18 A new axiom: (forall (M_4:nat) (N_10:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int M_4)) (semiri1621563631at_int N_10))) ((ord_less_eq_nat M_4) N_10)))
% 0.89/1.18 FOF formula (forall (I_1:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J)) K)) ((minus_minus_nat ((minus_minus_nat I_1) K)) J))) of role axiom named fact_475_diff__commute
% 0.89/1.18 A new axiom: (forall (I_1:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J)) K)) ((minus_minus_nat ((minus_minus_nat I_1) K)) J)))
% 0.89/1.18 FOF formula (forall (X:int) (Y:int) (P:Prop), ((and (P->(((eq nat) (nat_1 X)) (nat_1 (((if_int P) X) Y))))) ((P->False)->(((eq nat) (nat_1 Y)) (nat_1 (((if_int P) X) Y)))))) of role axiom named fact_476_nat__if__cong
% 0.89/1.18 A new axiom: (forall (X:int) (Y:int) (P:Prop), ((and (P->(((eq nat) (nat_1 X)) (nat_1 (((if_int P) X) Y))))) ((P->False)->(((eq nat) (nat_1 Y)) (nat_1 (((if_int P) X) Y))))))
% 0.89/1.18 FOF formula (forall (B_61:real) (A_79:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_79)) ((ord_less_eq_real B_61) zero_zero_real))) ((and ((ord_less_eq_real A_79) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_61)))->((ord_less_eq_real ((times_times_real A_79) B_61)) zero_zero_real))) of role axiom named fact_477_split__mult__neg__le
% 0.89/1.18 A new axiom: (forall (B_61:real) (A_79:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_79)) ((ord_less_eq_real B_61) zero_zero_real))) ((and ((ord_less_eq_real A_79) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_61)))->((ord_less_eq_real ((times_times_real A_79) B_61)) zero_zero_real)))
% 0.89/1.18 FOF formula (forall (B_61:nat) (A_79:nat), (((or ((and ((ord_less_eq_nat zero_zero_nat) A_79)) ((ord_less_eq_nat B_61) zero_zero_nat))) ((and ((ord_less_eq_nat A_79) zero_zero_nat)) ((ord_less_eq_nat zero_zero_nat) B_61)))->((ord_less_eq_nat ((times_times_nat A_79) B_61)) zero_zero_nat))) of role axiom named fact_478_split__mult__neg__le
% 0.89/1.18 A new axiom: (forall (B_61:nat) (A_79:nat), (((or ((and ((ord_less_eq_nat zero_zero_nat) A_79)) ((ord_less_eq_nat B_61) zero_zero_nat))) ((and ((ord_less_eq_nat A_79) zero_zero_nat)) ((ord_less_eq_nat zero_zero_nat) B_61)))->((ord_less_eq_nat ((times_times_nat A_79) B_61)) zero_zero_nat)))
% 0.89/1.18 FOF formula (forall (B_61:int) (A_79:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_79)) ((ord_less_eq_int B_61) zero_zero_int))) ((and ((ord_less_eq_int A_79) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_61)))->((ord_less_eq_int ((times_times_int A_79) B_61)) zero_zero_int))) of role axiom named fact_479_split__mult__neg__le
% 0.89/1.18 A new axiom: (forall (B_61:int) (A_79:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_79)) ((ord_less_eq_int B_61) zero_zero_int))) ((and ((ord_less_eq_int A_79) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_61)))->((ord_less_eq_int ((times_times_int A_79) B_61)) zero_zero_int)))
% 1.00/1.20 FOF formula (forall (B_60:real) (A_78:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_78)) ((ord_less_eq_real zero_zero_real) B_60))) ((and ((ord_less_eq_real A_78) zero_zero_real)) ((ord_less_eq_real B_60) zero_zero_real)))->((ord_less_eq_real zero_zero_real) ((times_times_real A_78) B_60)))) of role axiom named fact_480_split__mult__pos__le
% 1.00/1.20 A new axiom: (forall (B_60:real) (A_78:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_78)) ((ord_less_eq_real zero_zero_real) B_60))) ((and ((ord_less_eq_real A_78) zero_zero_real)) ((ord_less_eq_real B_60) zero_zero_real)))->((ord_less_eq_real zero_zero_real) ((times_times_real A_78) B_60))))
% 1.00/1.20 FOF formula (forall (B_60:int) (A_78:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_78)) ((ord_less_eq_int zero_zero_int) B_60))) ((and ((ord_less_eq_int A_78) zero_zero_int)) ((ord_less_eq_int B_60) zero_zero_int)))->((ord_less_eq_int zero_zero_int) ((times_times_int A_78) B_60)))) of role axiom named fact_481_split__mult__pos__le
% 1.00/1.20 A new axiom: (forall (B_60:int) (A_78:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_78)) ((ord_less_eq_int zero_zero_int) B_60))) ((and ((ord_less_eq_int A_78) zero_zero_int)) ((ord_less_eq_int B_60) zero_zero_int)))->((ord_less_eq_int zero_zero_int) ((times_times_int A_78) B_60))))
% 1.00/1.20 FOF formula (forall (C_39:real) (D_17:real) (A_77:real) (B_59:real), (((ord_less_eq_real A_77) B_59)->(((ord_less_eq_real C_39) D_17)->(((ord_less_eq_real zero_zero_real) B_59)->(((ord_less_eq_real zero_zero_real) C_39)->((ord_less_eq_real ((times_times_real A_77) C_39)) ((times_times_real B_59) D_17))))))) of role axiom named fact_482_mult__mono
% 1.00/1.20 A new axiom: (forall (C_39:real) (D_17:real) (A_77:real) (B_59:real), (((ord_less_eq_real A_77) B_59)->(((ord_less_eq_real C_39) D_17)->(((ord_less_eq_real zero_zero_real) B_59)->(((ord_less_eq_real zero_zero_real) C_39)->((ord_less_eq_real ((times_times_real A_77) C_39)) ((times_times_real B_59) D_17)))))))
% 1.00/1.20 FOF formula (forall (C_39:nat) (D_17:nat) (A_77:nat) (B_59:nat), (((ord_less_eq_nat A_77) B_59)->(((ord_less_eq_nat C_39) D_17)->(((ord_less_eq_nat zero_zero_nat) B_59)->(((ord_less_eq_nat zero_zero_nat) C_39)->((ord_less_eq_nat ((times_times_nat A_77) C_39)) ((times_times_nat B_59) D_17))))))) of role axiom named fact_483_mult__mono
% 1.00/1.20 A new axiom: (forall (C_39:nat) (D_17:nat) (A_77:nat) (B_59:nat), (((ord_less_eq_nat A_77) B_59)->(((ord_less_eq_nat C_39) D_17)->(((ord_less_eq_nat zero_zero_nat) B_59)->(((ord_less_eq_nat zero_zero_nat) C_39)->((ord_less_eq_nat ((times_times_nat A_77) C_39)) ((times_times_nat B_59) D_17)))))))
% 1.00/1.20 FOF formula (forall (C_39:int) (D_17:int) (A_77:int) (B_59:int), (((ord_less_eq_int A_77) B_59)->(((ord_less_eq_int C_39) D_17)->(((ord_less_eq_int zero_zero_int) B_59)->(((ord_less_eq_int zero_zero_int) C_39)->((ord_less_eq_int ((times_times_int A_77) C_39)) ((times_times_int B_59) D_17))))))) of role axiom named fact_484_mult__mono
% 1.00/1.20 A new axiom: (forall (C_39:int) (D_17:int) (A_77:int) (B_59:int), (((ord_less_eq_int A_77) B_59)->(((ord_less_eq_int C_39) D_17)->(((ord_less_eq_int zero_zero_int) B_59)->(((ord_less_eq_int zero_zero_int) C_39)->((ord_less_eq_int ((times_times_int A_77) C_39)) ((times_times_int B_59) D_17)))))))
% 1.00/1.20 FOF formula (forall (C_38:real) (D_16:real) (A_76:real) (B_58:real), (((ord_less_eq_real A_76) B_58)->(((ord_less_eq_real C_38) D_16)->(((ord_less_eq_real zero_zero_real) A_76)->(((ord_less_eq_real zero_zero_real) C_38)->((ord_less_eq_real ((times_times_real A_76) C_38)) ((times_times_real B_58) D_16))))))) of role axiom named fact_485_mult__mono_H
% 1.00/1.20 A new axiom: (forall (C_38:real) (D_16:real) (A_76:real) (B_58:real), (((ord_less_eq_real A_76) B_58)->(((ord_less_eq_real C_38) D_16)->(((ord_less_eq_real zero_zero_real) A_76)->(((ord_less_eq_real zero_zero_real) C_38)->((ord_less_eq_real ((times_times_real A_76) C_38)) ((times_times_real B_58) D_16)))))))
% 1.00/1.20 FOF formula (forall (C_38:nat) (D_16:nat) (A_76:nat) (B_58:nat), (((ord_less_eq_nat A_76) B_58)->(((ord_less_eq_nat C_38) D_16)->(((ord_less_eq_nat zero_zero_nat) A_76)->(((ord_less_eq_nat zero_zero_nat) C_38)->((ord_less_eq_nat ((times_times_nat A_76) C_38)) ((times_times_nat B_58) D_16))))))) of role axiom named fact_486_mult__mono_H
% 1.01/1.22 A new axiom: (forall (C_38:nat) (D_16:nat) (A_76:nat) (B_58:nat), (((ord_less_eq_nat A_76) B_58)->(((ord_less_eq_nat C_38) D_16)->(((ord_less_eq_nat zero_zero_nat) A_76)->(((ord_less_eq_nat zero_zero_nat) C_38)->((ord_less_eq_nat ((times_times_nat A_76) C_38)) ((times_times_nat B_58) D_16)))))))
% 1.01/1.22 FOF formula (forall (C_38:int) (D_16:int) (A_76:int) (B_58:int), (((ord_less_eq_int A_76) B_58)->(((ord_less_eq_int C_38) D_16)->(((ord_less_eq_int zero_zero_int) A_76)->(((ord_less_eq_int zero_zero_int) C_38)->((ord_less_eq_int ((times_times_int A_76) C_38)) ((times_times_int B_58) D_16))))))) of role axiom named fact_487_mult__mono_H
% 1.01/1.22 A new axiom: (forall (C_38:int) (D_16:int) (A_76:int) (B_58:int), (((ord_less_eq_int A_76) B_58)->(((ord_less_eq_int C_38) D_16)->(((ord_less_eq_int zero_zero_int) A_76)->(((ord_less_eq_int zero_zero_int) C_38)->((ord_less_eq_int ((times_times_int A_76) C_38)) ((times_times_int B_58) D_16)))))))
% 1.01/1.22 FOF formula (forall (C_37:real) (B_57:real) (A_75:real), (((ord_less_eq_real B_57) A_75)->(((ord_less_eq_real C_37) zero_zero_real)->((ord_less_eq_real ((times_times_real C_37) A_75)) ((times_times_real C_37) B_57))))) of role axiom named fact_488_mult__left__mono__neg
% 1.01/1.22 A new axiom: (forall (C_37:real) (B_57:real) (A_75:real), (((ord_less_eq_real B_57) A_75)->(((ord_less_eq_real C_37) zero_zero_real)->((ord_less_eq_real ((times_times_real C_37) A_75)) ((times_times_real C_37) B_57)))))
% 1.01/1.22 FOF formula (forall (C_37:int) (B_57:int) (A_75:int), (((ord_less_eq_int B_57) A_75)->(((ord_less_eq_int C_37) zero_zero_int)->((ord_less_eq_int ((times_times_int C_37) A_75)) ((times_times_int C_37) B_57))))) of role axiom named fact_489_mult__left__mono__neg
% 1.01/1.22 A new axiom: (forall (C_37:int) (B_57:int) (A_75:int), (((ord_less_eq_int B_57) A_75)->(((ord_less_eq_int C_37) zero_zero_int)->((ord_less_eq_int ((times_times_int C_37) A_75)) ((times_times_int C_37) B_57)))))
% 1.01/1.22 FOF formula (forall (C_36:real) (B_56:real) (A_74:real), (((ord_less_eq_real B_56) A_74)->(((ord_less_eq_real C_36) zero_zero_real)->((ord_less_eq_real ((times_times_real A_74) C_36)) ((times_times_real B_56) C_36))))) of role axiom named fact_490_mult__right__mono__neg
% 1.01/1.22 A new axiom: (forall (C_36:real) (B_56:real) (A_74:real), (((ord_less_eq_real B_56) A_74)->(((ord_less_eq_real C_36) zero_zero_real)->((ord_less_eq_real ((times_times_real A_74) C_36)) ((times_times_real B_56) C_36)))))
% 1.01/1.22 FOF formula (forall (C_36:int) (B_56:int) (A_74:int), (((ord_less_eq_int B_56) A_74)->(((ord_less_eq_int C_36) zero_zero_int)->((ord_less_eq_int ((times_times_int A_74) C_36)) ((times_times_int B_56) C_36))))) of role axiom named fact_491_mult__right__mono__neg
% 1.01/1.22 A new axiom: (forall (C_36:int) (B_56:int) (A_74:int), (((ord_less_eq_int B_56) A_74)->(((ord_less_eq_int C_36) zero_zero_int)->((ord_less_eq_int ((times_times_int A_74) C_36)) ((times_times_int B_56) C_36)))))
% 1.01/1.22 FOF formula (forall (C_35:real) (A_73:real) (B_55:real), (((ord_less_eq_real A_73) B_55)->(((ord_less_eq_real zero_zero_real) C_35)->((ord_less_eq_real ((times_times_real C_35) A_73)) ((times_times_real C_35) B_55))))) of role axiom named fact_492_comm__mult__left__mono
% 1.01/1.22 A new axiom: (forall (C_35:real) (A_73:real) (B_55:real), (((ord_less_eq_real A_73) B_55)->(((ord_less_eq_real zero_zero_real) C_35)->((ord_less_eq_real ((times_times_real C_35) A_73)) ((times_times_real C_35) B_55)))))
% 1.01/1.22 FOF formula (forall (C_35:nat) (A_73:nat) (B_55:nat), (((ord_less_eq_nat A_73) B_55)->(((ord_less_eq_nat zero_zero_nat) C_35)->((ord_less_eq_nat ((times_times_nat C_35) A_73)) ((times_times_nat C_35) B_55))))) of role axiom named fact_493_comm__mult__left__mono
% 1.01/1.22 A new axiom: (forall (C_35:nat) (A_73:nat) (B_55:nat), (((ord_less_eq_nat A_73) B_55)->(((ord_less_eq_nat zero_zero_nat) C_35)->((ord_less_eq_nat ((times_times_nat C_35) A_73)) ((times_times_nat C_35) B_55)))))
% 1.01/1.22 FOF formula (forall (C_35:int) (A_73:int) (B_55:int), (((ord_less_eq_int A_73) B_55)->(((ord_less_eq_int zero_zero_int) C_35)->((ord_less_eq_int ((times_times_int C_35) A_73)) ((times_times_int C_35) B_55))))) of role axiom named fact_494_comm__mult__left__mono
% 1.01/1.23 A new axiom: (forall (C_35:int) (A_73:int) (B_55:int), (((ord_less_eq_int A_73) B_55)->(((ord_less_eq_int zero_zero_int) C_35)->((ord_less_eq_int ((times_times_int C_35) A_73)) ((times_times_int C_35) B_55)))))
% 1.01/1.23 FOF formula (forall (C_34:real) (A_72:real) (B_54:real), (((ord_less_eq_real A_72) B_54)->(((ord_less_eq_real zero_zero_real) C_34)->((ord_less_eq_real ((times_times_real C_34) A_72)) ((times_times_real C_34) B_54))))) of role axiom named fact_495_mult__left__mono
% 1.01/1.23 A new axiom: (forall (C_34:real) (A_72:real) (B_54:real), (((ord_less_eq_real A_72) B_54)->(((ord_less_eq_real zero_zero_real) C_34)->((ord_less_eq_real ((times_times_real C_34) A_72)) ((times_times_real C_34) B_54)))))
% 1.01/1.23 FOF formula (forall (C_34:nat) (A_72:nat) (B_54:nat), (((ord_less_eq_nat A_72) B_54)->(((ord_less_eq_nat zero_zero_nat) C_34)->((ord_less_eq_nat ((times_times_nat C_34) A_72)) ((times_times_nat C_34) B_54))))) of role axiom named fact_496_mult__left__mono
% 1.01/1.23 A new axiom: (forall (C_34:nat) (A_72:nat) (B_54:nat), (((ord_less_eq_nat A_72) B_54)->(((ord_less_eq_nat zero_zero_nat) C_34)->((ord_less_eq_nat ((times_times_nat C_34) A_72)) ((times_times_nat C_34) B_54)))))
% 1.01/1.23 FOF formula (forall (C_34:int) (A_72:int) (B_54:int), (((ord_less_eq_int A_72) B_54)->(((ord_less_eq_int zero_zero_int) C_34)->((ord_less_eq_int ((times_times_int C_34) A_72)) ((times_times_int C_34) B_54))))) of role axiom named fact_497_mult__left__mono
% 1.01/1.23 A new axiom: (forall (C_34:int) (A_72:int) (B_54:int), (((ord_less_eq_int A_72) B_54)->(((ord_less_eq_int zero_zero_int) C_34)->((ord_less_eq_int ((times_times_int C_34) A_72)) ((times_times_int C_34) B_54)))))
% 1.01/1.23 FOF formula (forall (C_33:real) (A_71:real) (B_53:real), (((ord_less_eq_real A_71) B_53)->(((ord_less_eq_real zero_zero_real) C_33)->((ord_less_eq_real ((times_times_real A_71) C_33)) ((times_times_real B_53) C_33))))) of role axiom named fact_498_mult__right__mono
% 1.01/1.23 A new axiom: (forall (C_33:real) (A_71:real) (B_53:real), (((ord_less_eq_real A_71) B_53)->(((ord_less_eq_real zero_zero_real) C_33)->((ord_less_eq_real ((times_times_real A_71) C_33)) ((times_times_real B_53) C_33)))))
% 1.01/1.23 FOF formula (forall (C_33:nat) (A_71:nat) (B_53:nat), (((ord_less_eq_nat A_71) B_53)->(((ord_less_eq_nat zero_zero_nat) C_33)->((ord_less_eq_nat ((times_times_nat A_71) C_33)) ((times_times_nat B_53) C_33))))) of role axiom named fact_499_mult__right__mono
% 1.01/1.23 A new axiom: (forall (C_33:nat) (A_71:nat) (B_53:nat), (((ord_less_eq_nat A_71) B_53)->(((ord_less_eq_nat zero_zero_nat) C_33)->((ord_less_eq_nat ((times_times_nat A_71) C_33)) ((times_times_nat B_53) C_33)))))
% 1.01/1.23 FOF formula (forall (C_33:int) (A_71:int) (B_53:int), (((ord_less_eq_int A_71) B_53)->(((ord_less_eq_int zero_zero_int) C_33)->((ord_less_eq_int ((times_times_int A_71) C_33)) ((times_times_int B_53) C_33))))) of role axiom named fact_500_mult__right__mono
% 1.01/1.23 A new axiom: (forall (C_33:int) (A_71:int) (B_53:int), (((ord_less_eq_int A_71) B_53)->(((ord_less_eq_int zero_zero_int) C_33)->((ord_less_eq_int ((times_times_int A_71) C_33)) ((times_times_int B_53) C_33)))))
% 1.01/1.23 FOF formula (forall (B_52:real) (A_70:real), (((ord_less_eq_real A_70) zero_zero_real)->(((ord_less_eq_real B_52) zero_zero_real)->((ord_less_eq_real zero_zero_real) ((times_times_real A_70) B_52))))) of role axiom named fact_501_mult__nonpos__nonpos
% 1.01/1.23 A new axiom: (forall (B_52:real) (A_70:real), (((ord_less_eq_real A_70) zero_zero_real)->(((ord_less_eq_real B_52) zero_zero_real)->((ord_less_eq_real zero_zero_real) ((times_times_real A_70) B_52)))))
% 1.01/1.23 FOF formula (forall (B_52:int) (A_70:int), (((ord_less_eq_int A_70) zero_zero_int)->(((ord_less_eq_int B_52) zero_zero_int)->((ord_less_eq_int zero_zero_int) ((times_times_int A_70) B_52))))) of role axiom named fact_502_mult__nonpos__nonpos
% 1.01/1.23 A new axiom: (forall (B_52:int) (A_70:int), (((ord_less_eq_int A_70) zero_zero_int)->(((ord_less_eq_int B_52) zero_zero_int)->((ord_less_eq_int zero_zero_int) ((times_times_int A_70) B_52)))))
% 1.01/1.25 FOF formula (forall (B_51:real) (A_69:real), (((ord_less_eq_real A_69) zero_zero_real)->(((ord_less_eq_real zero_zero_real) B_51)->((ord_less_eq_real ((times_times_real A_69) B_51)) zero_zero_real)))) of role axiom named fact_503_mult__nonpos__nonneg
% 1.01/1.25 A new axiom: (forall (B_51:real) (A_69:real), (((ord_less_eq_real A_69) zero_zero_real)->(((ord_less_eq_real zero_zero_real) B_51)->((ord_less_eq_real ((times_times_real A_69) B_51)) zero_zero_real))))
% 1.01/1.25 FOF formula (forall (B_51:nat) (A_69:nat), (((ord_less_eq_nat A_69) zero_zero_nat)->(((ord_less_eq_nat zero_zero_nat) B_51)->((ord_less_eq_nat ((times_times_nat A_69) B_51)) zero_zero_nat)))) of role axiom named fact_504_mult__nonpos__nonneg
% 1.01/1.25 A new axiom: (forall (B_51:nat) (A_69:nat), (((ord_less_eq_nat A_69) zero_zero_nat)->(((ord_less_eq_nat zero_zero_nat) B_51)->((ord_less_eq_nat ((times_times_nat A_69) B_51)) zero_zero_nat))))
% 1.01/1.25 FOF formula (forall (B_51:int) (A_69:int), (((ord_less_eq_int A_69) zero_zero_int)->(((ord_less_eq_int zero_zero_int) B_51)->((ord_less_eq_int ((times_times_int A_69) B_51)) zero_zero_int)))) of role axiom named fact_505_mult__nonpos__nonneg
% 1.01/1.25 A new axiom: (forall (B_51:int) (A_69:int), (((ord_less_eq_int A_69) zero_zero_int)->(((ord_less_eq_int zero_zero_int) B_51)->((ord_less_eq_int ((times_times_int A_69) B_51)) zero_zero_int))))
% 1.01/1.25 FOF formula (forall (B_50:real) (A_68:real), (((ord_less_eq_real zero_zero_real) A_68)->(((ord_less_eq_real B_50) zero_zero_real)->((ord_less_eq_real ((times_times_real B_50) A_68)) zero_zero_real)))) of role axiom named fact_506_mult__nonneg__nonpos2
% 1.01/1.25 A new axiom: (forall (B_50:real) (A_68:real), (((ord_less_eq_real zero_zero_real) A_68)->(((ord_less_eq_real B_50) zero_zero_real)->((ord_less_eq_real ((times_times_real B_50) A_68)) zero_zero_real))))
% 1.01/1.25 FOF formula (forall (B_50:nat) (A_68:nat), (((ord_less_eq_nat zero_zero_nat) A_68)->(((ord_less_eq_nat B_50) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat B_50) A_68)) zero_zero_nat)))) of role axiom named fact_507_mult__nonneg__nonpos2
% 1.01/1.25 A new axiom: (forall (B_50:nat) (A_68:nat), (((ord_less_eq_nat zero_zero_nat) A_68)->(((ord_less_eq_nat B_50) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat B_50) A_68)) zero_zero_nat))))
% 1.01/1.25 FOF formula (forall (B_50:int) (A_68:int), (((ord_less_eq_int zero_zero_int) A_68)->(((ord_less_eq_int B_50) zero_zero_int)->((ord_less_eq_int ((times_times_int B_50) A_68)) zero_zero_int)))) of role axiom named fact_508_mult__nonneg__nonpos2
% 1.01/1.25 A new axiom: (forall (B_50:int) (A_68:int), (((ord_less_eq_int zero_zero_int) A_68)->(((ord_less_eq_int B_50) zero_zero_int)->((ord_less_eq_int ((times_times_int B_50) A_68)) zero_zero_int))))
% 1.01/1.25 FOF formula (forall (B_49:real) (A_67:real), (((ord_less_eq_real zero_zero_real) A_67)->(((ord_less_eq_real B_49) zero_zero_real)->((ord_less_eq_real ((times_times_real A_67) B_49)) zero_zero_real)))) of role axiom named fact_509_mult__nonneg__nonpos
% 1.01/1.25 A new axiom: (forall (B_49:real) (A_67:real), (((ord_less_eq_real zero_zero_real) A_67)->(((ord_less_eq_real B_49) zero_zero_real)->((ord_less_eq_real ((times_times_real A_67) B_49)) zero_zero_real))))
% 1.01/1.25 FOF formula (forall (B_49:nat) (A_67:nat), (((ord_less_eq_nat zero_zero_nat) A_67)->(((ord_less_eq_nat B_49) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat A_67) B_49)) zero_zero_nat)))) of role axiom named fact_510_mult__nonneg__nonpos
% 1.01/1.25 A new axiom: (forall (B_49:nat) (A_67:nat), (((ord_less_eq_nat zero_zero_nat) A_67)->(((ord_less_eq_nat B_49) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat A_67) B_49)) zero_zero_nat))))
% 1.01/1.25 FOF formula (forall (B_49:int) (A_67:int), (((ord_less_eq_int zero_zero_int) A_67)->(((ord_less_eq_int B_49) zero_zero_int)->((ord_less_eq_int ((times_times_int A_67) B_49)) zero_zero_int)))) of role axiom named fact_511_mult__nonneg__nonpos
% 1.01/1.25 A new axiom: (forall (B_49:int) (A_67:int), (((ord_less_eq_int zero_zero_int) A_67)->(((ord_less_eq_int B_49) zero_zero_int)->((ord_less_eq_int ((times_times_int A_67) B_49)) zero_zero_int))))
% 1.01/1.25 FOF formula (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((iff (((eq nat) (nat_1 X)) (nat_1 Y))) (((eq int) X) Y))))) of role axiom named fact_512_transfer__nat__int__relations_I1_J
% 1.01/1.26 A new axiom: (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((iff (((eq nat) (nat_1 X)) (nat_1 Y))) (((eq int) X) Y)))))
% 1.01/1.26 FOF formula (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((times_times_int X) Y))))) of role axiom named fact_513_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J
% 1.01/1.26 A new axiom: (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((times_times_int X) Y)))))
% 1.01/1.26 FOF formula (forall (B_48:real) (A_66:real), (((ord_less_eq_real zero_zero_real) A_66)->(((ord_less_eq_real zero_zero_real) B_48)->((ord_less_eq_real zero_zero_real) ((times_times_real A_66) B_48))))) of role axiom named fact_514_mult__nonneg__nonneg
% 1.01/1.26 A new axiom: (forall (B_48:real) (A_66:real), (((ord_less_eq_real zero_zero_real) A_66)->(((ord_less_eq_real zero_zero_real) B_48)->((ord_less_eq_real zero_zero_real) ((times_times_real A_66) B_48)))))
% 1.01/1.26 FOF formula (forall (B_48:nat) (A_66:nat), (((ord_less_eq_nat zero_zero_nat) A_66)->(((ord_less_eq_nat zero_zero_nat) B_48)->((ord_less_eq_nat zero_zero_nat) ((times_times_nat A_66) B_48))))) of role axiom named fact_515_mult__nonneg__nonneg
% 1.01/1.26 A new axiom: (forall (B_48:nat) (A_66:nat), (((ord_less_eq_nat zero_zero_nat) A_66)->(((ord_less_eq_nat zero_zero_nat) B_48)->((ord_less_eq_nat zero_zero_nat) ((times_times_nat A_66) B_48)))))
% 1.01/1.26 FOF formula (forall (B_48:int) (A_66:int), (((ord_less_eq_int zero_zero_int) A_66)->(((ord_less_eq_int zero_zero_int) B_48)->((ord_less_eq_int zero_zero_int) ((times_times_int A_66) B_48))))) of role axiom named fact_516_mult__nonneg__nonneg
% 1.01/1.26 A new axiom: (forall (B_48:int) (A_66:int), (((ord_less_eq_int zero_zero_int) A_66)->(((ord_less_eq_int zero_zero_int) B_48)->((ord_less_eq_int zero_zero_int) ((times_times_int A_66) B_48)))))
% 1.01/1.26 FOF formula (forall (A_65:real) (E_6:real) (C_32:real) (B_47:real) (D_15:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real A_65) E_6)) C_32)) ((plus_plus_real ((times_times_real B_47) E_6)) D_15))) ((ord_less_eq_real ((plus_plus_real ((times_times_real ((minus_minus_real A_65) B_47)) E_6)) C_32)) D_15))) of role axiom named fact_517_le__add__iff1
% 1.01/1.26 A new axiom: (forall (A_65:real) (E_6:real) (C_32:real) (B_47:real) (D_15:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real A_65) E_6)) C_32)) ((plus_plus_real ((times_times_real B_47) E_6)) D_15))) ((ord_less_eq_real ((plus_plus_real ((times_times_real ((minus_minus_real A_65) B_47)) E_6)) C_32)) D_15)))
% 1.01/1.26 FOF formula (forall (A_65:int) (E_6:int) (C_32:int) (B_47:int) (D_15:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int A_65) E_6)) C_32)) ((plus_plus_int ((times_times_int B_47) E_6)) D_15))) ((ord_less_eq_int ((plus_plus_int ((times_times_int ((minus_minus_int A_65) B_47)) E_6)) C_32)) D_15))) of role axiom named fact_518_le__add__iff1
% 1.01/1.26 A new axiom: (forall (A_65:int) (E_6:int) (C_32:int) (B_47:int) (D_15:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int A_65) E_6)) C_32)) ((plus_plus_int ((times_times_int B_47) E_6)) D_15))) ((ord_less_eq_int ((plus_plus_int ((times_times_int ((minus_minus_int A_65) B_47)) E_6)) C_32)) D_15)))
% 1.01/1.26 FOF formula (forall (A_64:real) (E_5:real) (C_31:real) (B_46:real) (D_14:real), ((iff (((eq real) ((plus_plus_real ((times_times_real A_64) E_5)) C_31)) ((plus_plus_real ((times_times_real B_46) E_5)) D_14))) (((eq real) ((plus_plus_real ((times_times_real ((minus_minus_real A_64) B_46)) E_5)) C_31)) D_14))) of role axiom named fact_519_eq__add__iff1
% 1.01/1.26 A new axiom: (forall (A_64:real) (E_5:real) (C_31:real) (B_46:real) (D_14:real), ((iff (((eq real) ((plus_plus_real ((times_times_real A_64) E_5)) C_31)) ((plus_plus_real ((times_times_real B_46) E_5)) D_14))) (((eq real) ((plus_plus_real ((times_times_real ((minus_minus_real A_64) B_46)) E_5)) C_31)) D_14)))
% 1.01/1.29 FOF formula (forall (A_64:int) (E_5:int) (C_31:int) (B_46:int) (D_14:int), ((iff (((eq int) ((plus_plus_int ((times_times_int A_64) E_5)) C_31)) ((plus_plus_int ((times_times_int B_46) E_5)) D_14))) (((eq int) ((plus_plus_int ((times_times_int ((minus_minus_int A_64) B_46)) E_5)) C_31)) D_14))) of role axiom named fact_520_eq__add__iff1
% 1.01/1.29 A new axiom: (forall (A_64:int) (E_5:int) (C_31:int) (B_46:int) (D_14:int), ((iff (((eq int) ((plus_plus_int ((times_times_int A_64) E_5)) C_31)) ((plus_plus_int ((times_times_int B_46) E_5)) D_14))) (((eq int) ((plus_plus_int ((times_times_int ((minus_minus_int A_64) B_46)) E_5)) C_31)) D_14)))
% 1.01/1.29 FOF formula (forall (A_63:real) (E_4:real) (C_30:real) (B_45:real) (D_13:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real A_63) E_4)) C_30)) ((plus_plus_real ((times_times_real B_45) E_4)) D_13))) ((ord_less_eq_real C_30) ((plus_plus_real ((times_times_real ((minus_minus_real B_45) A_63)) E_4)) D_13)))) of role axiom named fact_521_le__add__iff2
% 1.01/1.29 A new axiom: (forall (A_63:real) (E_4:real) (C_30:real) (B_45:real) (D_13:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real A_63) E_4)) C_30)) ((plus_plus_real ((times_times_real B_45) E_4)) D_13))) ((ord_less_eq_real C_30) ((plus_plus_real ((times_times_real ((minus_minus_real B_45) A_63)) E_4)) D_13))))
% 1.01/1.29 FOF formula (forall (A_63:int) (E_4:int) (C_30:int) (B_45:int) (D_13:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int A_63) E_4)) C_30)) ((plus_plus_int ((times_times_int B_45) E_4)) D_13))) ((ord_less_eq_int C_30) ((plus_plus_int ((times_times_int ((minus_minus_int B_45) A_63)) E_4)) D_13)))) of role axiom named fact_522_le__add__iff2
% 1.01/1.29 A new axiom: (forall (A_63:int) (E_4:int) (C_30:int) (B_45:int) (D_13:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int A_63) E_4)) C_30)) ((plus_plus_int ((times_times_int B_45) E_4)) D_13))) ((ord_less_eq_int C_30) ((plus_plus_int ((times_times_int ((minus_minus_int B_45) A_63)) E_4)) D_13))))
% 1.01/1.29 FOF formula (forall (A_62:real) (E_3:real) (C_29:real) (B_44:real) (D_12:real), ((iff (((eq real) ((plus_plus_real ((times_times_real A_62) E_3)) C_29)) ((plus_plus_real ((times_times_real B_44) E_3)) D_12))) (((eq real) C_29) ((plus_plus_real ((times_times_real ((minus_minus_real B_44) A_62)) E_3)) D_12)))) of role axiom named fact_523_eq__add__iff2
% 1.01/1.29 A new axiom: (forall (A_62:real) (E_3:real) (C_29:real) (B_44:real) (D_12:real), ((iff (((eq real) ((plus_plus_real ((times_times_real A_62) E_3)) C_29)) ((plus_plus_real ((times_times_real B_44) E_3)) D_12))) (((eq real) C_29) ((plus_plus_real ((times_times_real ((minus_minus_real B_44) A_62)) E_3)) D_12))))
% 1.01/1.29 FOF formula (forall (A_62:int) (E_3:int) (C_29:int) (B_44:int) (D_12:int), ((iff (((eq int) ((plus_plus_int ((times_times_int A_62) E_3)) C_29)) ((plus_plus_int ((times_times_int B_44) E_3)) D_12))) (((eq int) C_29) ((plus_plus_int ((times_times_int ((minus_minus_int B_44) A_62)) E_3)) D_12)))) of role axiom named fact_524_eq__add__iff2
% 1.01/1.29 A new axiom: (forall (A_62:int) (E_3:int) (C_29:int) (B_44:int) (D_12:int), ((iff (((eq int) ((plus_plus_int ((times_times_int A_62) E_3)) C_29)) ((plus_plus_int ((times_times_int B_44) E_3)) D_12))) (((eq int) C_29) ((plus_plus_int ((times_times_int ((minus_minus_int B_44) A_62)) E_3)) D_12))))
% 1.01/1.29 FOF formula (forall (X_16:real) (Y_14:real) (A_61:real) (B_43:real), (((eq real) ((minus_minus_real ((times_times_real X_16) Y_14)) ((times_times_real A_61) B_43))) ((plus_plus_real ((times_times_real X_16) ((minus_minus_real Y_14) B_43))) ((times_times_real ((minus_minus_real X_16) A_61)) B_43)))) of role axiom named fact_525_mult__diff__mult
% 1.01/1.29 A new axiom: (forall (X_16:real) (Y_14:real) (A_61:real) (B_43:real), (((eq real) ((minus_minus_real ((times_times_real X_16) Y_14)) ((times_times_real A_61) B_43))) ((plus_plus_real ((times_times_real X_16) ((minus_minus_real Y_14) B_43))) ((times_times_real ((minus_minus_real X_16) A_61)) B_43))))
% 1.01/1.29 FOF formula (forall (X_16:int) (Y_14:int) (A_61:int) (B_43:int), (((eq int) ((minus_minus_int ((times_times_int X_16) Y_14)) ((times_times_int A_61) B_43))) ((plus_plus_int ((times_times_int X_16) ((minus_minus_int Y_14) B_43))) ((times_times_int ((minus_minus_int X_16) A_61)) B_43)))) of role axiom named fact_526_mult__diff__mult
% 1.01/1.30 A new axiom: (forall (X_16:int) (Y_14:int) (A_61:int) (B_43:int), (((eq int) ((minus_minus_int ((times_times_int X_16) Y_14)) ((times_times_int A_61) B_43))) ((plus_plus_int ((times_times_int X_16) ((minus_minus_int Y_14) B_43))) ((times_times_int ((minus_minus_int X_16) A_61)) B_43))))
% 1.01/1.30 FOF formula (forall (A_60:real) (B_42:real), ((iff ((ord_less_eq_real ((times_times_real A_60) B_42)) zero_zero_real)) ((or ((and ((ord_less_eq_real zero_zero_real) A_60)) ((ord_less_eq_real B_42) zero_zero_real))) ((and ((ord_less_eq_real A_60) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_42))))) of role axiom named fact_527_mult__le__0__iff
% 1.01/1.30 A new axiom: (forall (A_60:real) (B_42:real), ((iff ((ord_less_eq_real ((times_times_real A_60) B_42)) zero_zero_real)) ((or ((and ((ord_less_eq_real zero_zero_real) A_60)) ((ord_less_eq_real B_42) zero_zero_real))) ((and ((ord_less_eq_real A_60) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_42)))))
% 1.01/1.30 FOF formula (forall (A_60:int) (B_42:int), ((iff ((ord_less_eq_int ((times_times_int A_60) B_42)) zero_zero_int)) ((or ((and ((ord_less_eq_int zero_zero_int) A_60)) ((ord_less_eq_int B_42) zero_zero_int))) ((and ((ord_less_eq_int A_60) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_42))))) of role axiom named fact_528_mult__le__0__iff
% 1.01/1.30 A new axiom: (forall (A_60:int) (B_42:int), ((iff ((ord_less_eq_int ((times_times_int A_60) B_42)) zero_zero_int)) ((or ((and ((ord_less_eq_int zero_zero_int) A_60)) ((ord_less_eq_int B_42) zero_zero_int))) ((and ((ord_less_eq_int A_60) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_42)))))
% 1.01/1.30 FOF formula (forall (A_59:real) (B_41:real), ((iff ((ord_less_eq_real zero_zero_real) ((times_times_real A_59) B_41))) ((or ((and ((ord_less_eq_real zero_zero_real) A_59)) ((ord_less_eq_real zero_zero_real) B_41))) ((and ((ord_less_eq_real A_59) zero_zero_real)) ((ord_less_eq_real B_41) zero_zero_real))))) of role axiom named fact_529_zero__le__mult__iff
% 1.01/1.30 A new axiom: (forall (A_59:real) (B_41:real), ((iff ((ord_less_eq_real zero_zero_real) ((times_times_real A_59) B_41))) ((or ((and ((ord_less_eq_real zero_zero_real) A_59)) ((ord_less_eq_real zero_zero_real) B_41))) ((and ((ord_less_eq_real A_59) zero_zero_real)) ((ord_less_eq_real B_41) zero_zero_real)))))
% 1.01/1.30 FOF formula (forall (A_59:int) (B_41:int), ((iff ((ord_less_eq_int zero_zero_int) ((times_times_int A_59) B_41))) ((or ((and ((ord_less_eq_int zero_zero_int) A_59)) ((ord_less_eq_int zero_zero_int) B_41))) ((and ((ord_less_eq_int A_59) zero_zero_int)) ((ord_less_eq_int B_41) zero_zero_int))))) of role axiom named fact_530_zero__le__mult__iff
% 1.01/1.30 A new axiom: (forall (A_59:int) (B_41:int), ((iff ((ord_less_eq_int zero_zero_int) ((times_times_int A_59) B_41))) ((or ((and ((ord_less_eq_int zero_zero_int) A_59)) ((ord_less_eq_int zero_zero_int) B_41))) ((and ((ord_less_eq_int A_59) zero_zero_int)) ((ord_less_eq_int B_41) zero_zero_int)))))
% 1.01/1.30 FOF formula (forall (P:(nat->Prop)), ((iff (all P)) (forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(P (nat_1 X_1)))))) of role axiom named fact_531_all__nat
% 1.01/1.30 A new axiom: (forall (P:(nat->Prop)), ((iff (all P)) (forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(P (nat_1 X_1))))))
% 1.01/1.30 FOF formula (forall (P:(nat->Prop)), ((iff (_TPTP_ex P)) ((ex int) (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P (nat_1 X_1))))))) of role axiom named fact_532_ex__nat
% 1.01/1.30 A new axiom: (forall (P:(nat->Prop)), ((iff (_TPTP_ex P)) ((ex int) (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P (nat_1 X_1)))))))
% 1.01/1.30 FOF formula (forall (A_58:real), ((ord_less_eq_real zero_zero_real) ((times_times_real A_58) A_58))) of role axiom named fact_533_zero__le__square
% 1.01/1.30 A new axiom: (forall (A_58:real), ((ord_less_eq_real zero_zero_real) ((times_times_real A_58) A_58)))
% 1.01/1.30 FOF formula (forall (A_58:int), ((ord_less_eq_int zero_zero_int) ((times_times_int A_58) A_58))) of role axiom named fact_534_zero__le__square
% 1.11/1.32 A new axiom: (forall (A_58:int), ((ord_less_eq_int zero_zero_int) ((times_times_int A_58) A_58)))
% 1.11/1.32 FOF formula (forall (A_57:real) (E_2:real) (C_28:real) (B_40:real) (D_11:real), ((iff ((ord_less_real ((plus_plus_real ((times_times_real A_57) E_2)) C_28)) ((plus_plus_real ((times_times_real B_40) E_2)) D_11))) ((ord_less_real ((plus_plus_real ((times_times_real ((minus_minus_real A_57) B_40)) E_2)) C_28)) D_11))) of role axiom named fact_535_less__add__iff1
% 1.11/1.32 A new axiom: (forall (A_57:real) (E_2:real) (C_28:real) (B_40:real) (D_11:real), ((iff ((ord_less_real ((plus_plus_real ((times_times_real A_57) E_2)) C_28)) ((plus_plus_real ((times_times_real B_40) E_2)) D_11))) ((ord_less_real ((plus_plus_real ((times_times_real ((minus_minus_real A_57) B_40)) E_2)) C_28)) D_11)))
% 1.11/1.32 FOF formula (forall (A_57:int) (E_2:int) (C_28:int) (B_40:int) (D_11:int), ((iff ((ord_less_int ((plus_plus_int ((times_times_int A_57) E_2)) C_28)) ((plus_plus_int ((times_times_int B_40) E_2)) D_11))) ((ord_less_int ((plus_plus_int ((times_times_int ((minus_minus_int A_57) B_40)) E_2)) C_28)) D_11))) of role axiom named fact_536_less__add__iff1
% 1.11/1.32 A new axiom: (forall (A_57:int) (E_2:int) (C_28:int) (B_40:int) (D_11:int), ((iff ((ord_less_int ((plus_plus_int ((times_times_int A_57) E_2)) C_28)) ((plus_plus_int ((times_times_int B_40) E_2)) D_11))) ((ord_less_int ((plus_plus_int ((times_times_int ((minus_minus_int A_57) B_40)) E_2)) C_28)) D_11)))
% 1.11/1.32 FOF formula (forall (A_56:real) (E_1:real) (C_27:real) (B_39:real) (D_10:real), ((iff ((ord_less_real ((plus_plus_real ((times_times_real A_56) E_1)) C_27)) ((plus_plus_real ((times_times_real B_39) E_1)) D_10))) ((ord_less_real C_27) ((plus_plus_real ((times_times_real ((minus_minus_real B_39) A_56)) E_1)) D_10)))) of role axiom named fact_537_less__add__iff2
% 1.11/1.32 A new axiom: (forall (A_56:real) (E_1:real) (C_27:real) (B_39:real) (D_10:real), ((iff ((ord_less_real ((plus_plus_real ((times_times_real A_56) E_1)) C_27)) ((plus_plus_real ((times_times_real B_39) E_1)) D_10))) ((ord_less_real C_27) ((plus_plus_real ((times_times_real ((minus_minus_real B_39) A_56)) E_1)) D_10))))
% 1.11/1.32 FOF formula (forall (A_56:int) (E_1:int) (C_27:int) (B_39:int) (D_10:int), ((iff ((ord_less_int ((plus_plus_int ((times_times_int A_56) E_1)) C_27)) ((plus_plus_int ((times_times_int B_39) E_1)) D_10))) ((ord_less_int C_27) ((plus_plus_int ((times_times_int ((minus_minus_int B_39) A_56)) E_1)) D_10)))) of role axiom named fact_538_less__add__iff2
% 1.11/1.32 A new axiom: (forall (A_56:int) (E_1:int) (C_27:int) (B_39:int) (D_10:int), ((iff ((ord_less_int ((plus_plus_int ((times_times_int A_56) E_1)) C_27)) ((plus_plus_int ((times_times_int B_39) E_1)) D_10))) ((ord_less_int C_27) ((plus_plus_int ((times_times_int ((minus_minus_int B_39) A_56)) E_1)) D_10))))
% 1.11/1.32 FOF formula (forall (X_15:real), (((eq real) ((minus_minus_real ((times_times_real X_15) X_15)) one_one_real)) ((times_times_real ((plus_plus_real X_15) one_one_real)) ((minus_minus_real X_15) one_one_real)))) of role axiom named fact_539_real__squared__diff__one__factored
% 1.11/1.32 A new axiom: (forall (X_15:real), (((eq real) ((minus_minus_real ((times_times_real X_15) X_15)) one_one_real)) ((times_times_real ((plus_plus_real X_15) one_one_real)) ((minus_minus_real X_15) one_one_real))))
% 1.11/1.32 FOF formula (forall (X_15:int), (((eq int) ((minus_minus_int ((times_times_int X_15) X_15)) one_one_int)) ((times_times_int ((plus_plus_int X_15) one_one_int)) ((minus_minus_int X_15) one_one_int)))) of role axiom named fact_540_real__squared__diff__one__factored
% 1.11/1.32 A new axiom: (forall (X_15:int), (((eq int) ((minus_minus_int ((times_times_int X_15) X_15)) one_one_int)) ((times_times_int ((plus_plus_int X_15) one_one_int)) ((minus_minus_int X_15) one_one_int))))
% 1.11/1.32 FOF formula (forall (C_26:real) (A_55:real) (B_38:real), (((ord_less_eq_real ((times_times_real C_26) A_55)) ((times_times_real C_26) B_38))->(((ord_less_real zero_zero_real) C_26)->((ord_less_eq_real A_55) B_38)))) of role axiom named fact_541_mult__left__le__imp__le
% 1.11/1.32 A new axiom: (forall (C_26:real) (A_55:real) (B_38:real), (((ord_less_eq_real ((times_times_real C_26) A_55)) ((times_times_real C_26) B_38))->(((ord_less_real zero_zero_real) C_26)->((ord_less_eq_real A_55) B_38))))
% 1.11/1.34 FOF formula (forall (C_26:nat) (A_55:nat) (B_38:nat), (((ord_less_eq_nat ((times_times_nat C_26) A_55)) ((times_times_nat C_26) B_38))->(((ord_less_nat zero_zero_nat) C_26)->((ord_less_eq_nat A_55) B_38)))) of role axiom named fact_542_mult__left__le__imp__le
% 1.11/1.34 A new axiom: (forall (C_26:nat) (A_55:nat) (B_38:nat), (((ord_less_eq_nat ((times_times_nat C_26) A_55)) ((times_times_nat C_26) B_38))->(((ord_less_nat zero_zero_nat) C_26)->((ord_less_eq_nat A_55) B_38))))
% 1.11/1.34 FOF formula (forall (C_26:int) (A_55:int) (B_38:int), (((ord_less_eq_int ((times_times_int C_26) A_55)) ((times_times_int C_26) B_38))->(((ord_less_int zero_zero_int) C_26)->((ord_less_eq_int A_55) B_38)))) of role axiom named fact_543_mult__left__le__imp__le
% 1.11/1.34 A new axiom: (forall (C_26:int) (A_55:int) (B_38:int), (((ord_less_eq_int ((times_times_int C_26) A_55)) ((times_times_int C_26) B_38))->(((ord_less_int zero_zero_int) C_26)->((ord_less_eq_int A_55) B_38))))
% 1.11/1.34 FOF formula (forall (A_54:real) (C_25:real) (B_37:real), (((ord_less_eq_real ((times_times_real A_54) C_25)) ((times_times_real B_37) C_25))->(((ord_less_real zero_zero_real) C_25)->((ord_less_eq_real A_54) B_37)))) of role axiom named fact_544_mult__right__le__imp__le
% 1.11/1.34 A new axiom: (forall (A_54:real) (C_25:real) (B_37:real), (((ord_less_eq_real ((times_times_real A_54) C_25)) ((times_times_real B_37) C_25))->(((ord_less_real zero_zero_real) C_25)->((ord_less_eq_real A_54) B_37))))
% 1.11/1.34 FOF formula (forall (A_54:nat) (C_25:nat) (B_37:nat), (((ord_less_eq_nat ((times_times_nat A_54) C_25)) ((times_times_nat B_37) C_25))->(((ord_less_nat zero_zero_nat) C_25)->((ord_less_eq_nat A_54) B_37)))) of role axiom named fact_545_mult__right__le__imp__le
% 1.11/1.34 A new axiom: (forall (A_54:nat) (C_25:nat) (B_37:nat), (((ord_less_eq_nat ((times_times_nat A_54) C_25)) ((times_times_nat B_37) C_25))->(((ord_less_nat zero_zero_nat) C_25)->((ord_less_eq_nat A_54) B_37))))
% 1.11/1.34 FOF formula (forall (A_54:int) (C_25:int) (B_37:int), (((ord_less_eq_int ((times_times_int A_54) C_25)) ((times_times_int B_37) C_25))->(((ord_less_int zero_zero_int) C_25)->((ord_less_eq_int A_54) B_37)))) of role axiom named fact_546_mult__right__le__imp__le
% 1.11/1.34 A new axiom: (forall (A_54:int) (C_25:int) (B_37:int), (((ord_less_eq_int ((times_times_int A_54) C_25)) ((times_times_int B_37) C_25))->(((ord_less_int zero_zero_int) C_25)->((ord_less_eq_int A_54) B_37))))
% 1.11/1.34 FOF formula (forall (C_24:real) (A_53:real) (B_36:real), (((ord_less_real ((times_times_real C_24) A_53)) ((times_times_real C_24) B_36))->(((ord_less_eq_real zero_zero_real) C_24)->((ord_less_real A_53) B_36)))) of role axiom named fact_547_mult__less__imp__less__left
% 1.11/1.34 A new axiom: (forall (C_24:real) (A_53:real) (B_36:real), (((ord_less_real ((times_times_real C_24) A_53)) ((times_times_real C_24) B_36))->(((ord_less_eq_real zero_zero_real) C_24)->((ord_less_real A_53) B_36))))
% 1.11/1.34 FOF formula (forall (C_24:nat) (A_53:nat) (B_36:nat), (((ord_less_nat ((times_times_nat C_24) A_53)) ((times_times_nat C_24) B_36))->(((ord_less_eq_nat zero_zero_nat) C_24)->((ord_less_nat A_53) B_36)))) of role axiom named fact_548_mult__less__imp__less__left
% 1.11/1.34 A new axiom: (forall (C_24:nat) (A_53:nat) (B_36:nat), (((ord_less_nat ((times_times_nat C_24) A_53)) ((times_times_nat C_24) B_36))->(((ord_less_eq_nat zero_zero_nat) C_24)->((ord_less_nat A_53) B_36))))
% 1.11/1.34 FOF formula (forall (C_24:int) (A_53:int) (B_36:int), (((ord_less_int ((times_times_int C_24) A_53)) ((times_times_int C_24) B_36))->(((ord_less_eq_int zero_zero_int) C_24)->((ord_less_int A_53) B_36)))) of role axiom named fact_549_mult__less__imp__less__left
% 1.11/1.34 A new axiom: (forall (C_24:int) (A_53:int) (B_36:int), (((ord_less_int ((times_times_int C_24) A_53)) ((times_times_int C_24) B_36))->(((ord_less_eq_int zero_zero_int) C_24)->((ord_less_int A_53) B_36))))
% 1.11/1.34 FOF formula (forall (C_23:real) (A_52:real) (B_35:real), (((ord_less_real ((times_times_real C_23) A_52)) ((times_times_real C_23) B_35))->(((ord_less_eq_real zero_zero_real) C_23)->((ord_less_real A_52) B_35)))) of role axiom named fact_550_mult__left__less__imp__less
% 1.11/1.35 A new axiom: (forall (C_23:real) (A_52:real) (B_35:real), (((ord_less_real ((times_times_real C_23) A_52)) ((times_times_real C_23) B_35))->(((ord_less_eq_real zero_zero_real) C_23)->((ord_less_real A_52) B_35))))
% 1.11/1.35 FOF formula (forall (C_23:nat) (A_52:nat) (B_35:nat), (((ord_less_nat ((times_times_nat C_23) A_52)) ((times_times_nat C_23) B_35))->(((ord_less_eq_nat zero_zero_nat) C_23)->((ord_less_nat A_52) B_35)))) of role axiom named fact_551_mult__left__less__imp__less
% 1.11/1.35 A new axiom: (forall (C_23:nat) (A_52:nat) (B_35:nat), (((ord_less_nat ((times_times_nat C_23) A_52)) ((times_times_nat C_23) B_35))->(((ord_less_eq_nat zero_zero_nat) C_23)->((ord_less_nat A_52) B_35))))
% 1.11/1.35 FOF formula (forall (C_23:int) (A_52:int) (B_35:int), (((ord_less_int ((times_times_int C_23) A_52)) ((times_times_int C_23) B_35))->(((ord_less_eq_int zero_zero_int) C_23)->((ord_less_int A_52) B_35)))) of role axiom named fact_552_mult__left__less__imp__less
% 1.11/1.35 A new axiom: (forall (C_23:int) (A_52:int) (B_35:int), (((ord_less_int ((times_times_int C_23) A_52)) ((times_times_int C_23) B_35))->(((ord_less_eq_int zero_zero_int) C_23)->((ord_less_int A_52) B_35))))
% 1.11/1.35 FOF formula (forall (A_51:real) (C_22:real) (B_34:real), (((ord_less_real ((times_times_real A_51) C_22)) ((times_times_real B_34) C_22))->(((ord_less_eq_real zero_zero_real) C_22)->((ord_less_real A_51) B_34)))) of role axiom named fact_553_mult__less__imp__less__right
% 1.11/1.35 A new axiom: (forall (A_51:real) (C_22:real) (B_34:real), (((ord_less_real ((times_times_real A_51) C_22)) ((times_times_real B_34) C_22))->(((ord_less_eq_real zero_zero_real) C_22)->((ord_less_real A_51) B_34))))
% 1.11/1.35 FOF formula (forall (A_51:nat) (C_22:nat) (B_34:nat), (((ord_less_nat ((times_times_nat A_51) C_22)) ((times_times_nat B_34) C_22))->(((ord_less_eq_nat zero_zero_nat) C_22)->((ord_less_nat A_51) B_34)))) of role axiom named fact_554_mult__less__imp__less__right
% 1.11/1.35 A new axiom: (forall (A_51:nat) (C_22:nat) (B_34:nat), (((ord_less_nat ((times_times_nat A_51) C_22)) ((times_times_nat B_34) C_22))->(((ord_less_eq_nat zero_zero_nat) C_22)->((ord_less_nat A_51) B_34))))
% 1.11/1.35 FOF formula (forall (A_51:int) (C_22:int) (B_34:int), (((ord_less_int ((times_times_int A_51) C_22)) ((times_times_int B_34) C_22))->(((ord_less_eq_int zero_zero_int) C_22)->((ord_less_int A_51) B_34)))) of role axiom named fact_555_mult__less__imp__less__right
% 1.11/1.35 A new axiom: (forall (A_51:int) (C_22:int) (B_34:int), (((ord_less_int ((times_times_int A_51) C_22)) ((times_times_int B_34) C_22))->(((ord_less_eq_int zero_zero_int) C_22)->((ord_less_int A_51) B_34))))
% 1.11/1.35 FOF formula (forall (A_50:real) (C_21:real) (B_33:real), (((ord_less_real ((times_times_real A_50) C_21)) ((times_times_real B_33) C_21))->(((ord_less_eq_real zero_zero_real) C_21)->((ord_less_real A_50) B_33)))) of role axiom named fact_556_mult__right__less__imp__less
% 1.11/1.35 A new axiom: (forall (A_50:real) (C_21:real) (B_33:real), (((ord_less_real ((times_times_real A_50) C_21)) ((times_times_real B_33) C_21))->(((ord_less_eq_real zero_zero_real) C_21)->((ord_less_real A_50) B_33))))
% 1.11/1.35 FOF formula (forall (A_50:nat) (C_21:nat) (B_33:nat), (((ord_less_nat ((times_times_nat A_50) C_21)) ((times_times_nat B_33) C_21))->(((ord_less_eq_nat zero_zero_nat) C_21)->((ord_less_nat A_50) B_33)))) of role axiom named fact_557_mult__right__less__imp__less
% 1.11/1.35 A new axiom: (forall (A_50:nat) (C_21:nat) (B_33:nat), (((ord_less_nat ((times_times_nat A_50) C_21)) ((times_times_nat B_33) C_21))->(((ord_less_eq_nat zero_zero_nat) C_21)->((ord_less_nat A_50) B_33))))
% 1.11/1.35 FOF formula (forall (A_50:int) (C_21:int) (B_33:int), (((ord_less_int ((times_times_int A_50) C_21)) ((times_times_int B_33) C_21))->(((ord_less_eq_int zero_zero_int) C_21)->((ord_less_int A_50) B_33)))) of role axiom named fact_558_mult__right__less__imp__less
% 1.11/1.35 A new axiom: (forall (A_50:int) (C_21:int) (B_33:int), (((ord_less_int ((times_times_int A_50) C_21)) ((times_times_int B_33) C_21))->(((ord_less_eq_int zero_zero_int) C_21)->((ord_less_int A_50) B_33))))
% 1.11/1.37 FOF formula (forall (C_20:real) (D_9:real) (A_49:real) (B_32:real), (((ord_less_eq_real A_49) B_32)->(((ord_less_real C_20) D_9)->(((ord_less_real zero_zero_real) A_49)->(((ord_less_eq_real zero_zero_real) C_20)->((ord_less_real ((times_times_real A_49) C_20)) ((times_times_real B_32) D_9))))))) of role axiom named fact_559_mult__le__less__imp__less
% 1.11/1.37 A new axiom: (forall (C_20:real) (D_9:real) (A_49:real) (B_32:real), (((ord_less_eq_real A_49) B_32)->(((ord_less_real C_20) D_9)->(((ord_less_real zero_zero_real) A_49)->(((ord_less_eq_real zero_zero_real) C_20)->((ord_less_real ((times_times_real A_49) C_20)) ((times_times_real B_32) D_9)))))))
% 1.11/1.37 FOF formula (forall (C_20:nat) (D_9:nat) (A_49:nat) (B_32:nat), (((ord_less_eq_nat A_49) B_32)->(((ord_less_nat C_20) D_9)->(((ord_less_nat zero_zero_nat) A_49)->(((ord_less_eq_nat zero_zero_nat) C_20)->((ord_less_nat ((times_times_nat A_49) C_20)) ((times_times_nat B_32) D_9))))))) of role axiom named fact_560_mult__le__less__imp__less
% 1.11/1.37 A new axiom: (forall (C_20:nat) (D_9:nat) (A_49:nat) (B_32:nat), (((ord_less_eq_nat A_49) B_32)->(((ord_less_nat C_20) D_9)->(((ord_less_nat zero_zero_nat) A_49)->(((ord_less_eq_nat zero_zero_nat) C_20)->((ord_less_nat ((times_times_nat A_49) C_20)) ((times_times_nat B_32) D_9)))))))
% 1.11/1.37 FOF formula (forall (C_20:int) (D_9:int) (A_49:int) (B_32:int), (((ord_less_eq_int A_49) B_32)->(((ord_less_int C_20) D_9)->(((ord_less_int zero_zero_int) A_49)->(((ord_less_eq_int zero_zero_int) C_20)->((ord_less_int ((times_times_int A_49) C_20)) ((times_times_int B_32) D_9))))))) of role axiom named fact_561_mult__le__less__imp__less
% 1.11/1.37 A new axiom: (forall (C_20:int) (D_9:int) (A_49:int) (B_32:int), (((ord_less_eq_int A_49) B_32)->(((ord_less_int C_20) D_9)->(((ord_less_int zero_zero_int) A_49)->(((ord_less_eq_int zero_zero_int) C_20)->((ord_less_int ((times_times_int A_49) C_20)) ((times_times_int B_32) D_9)))))))
% 1.11/1.37 FOF formula (forall (C_19:real) (D_8:real) (A_48:real) (B_31:real), (((ord_less_real A_48) B_31)->(((ord_less_eq_real C_19) D_8)->(((ord_less_eq_real zero_zero_real) A_48)->(((ord_less_real zero_zero_real) C_19)->((ord_less_real ((times_times_real A_48) C_19)) ((times_times_real B_31) D_8))))))) of role axiom named fact_562_mult__less__le__imp__less
% 1.11/1.37 A new axiom: (forall (C_19:real) (D_8:real) (A_48:real) (B_31:real), (((ord_less_real A_48) B_31)->(((ord_less_eq_real C_19) D_8)->(((ord_less_eq_real zero_zero_real) A_48)->(((ord_less_real zero_zero_real) C_19)->((ord_less_real ((times_times_real A_48) C_19)) ((times_times_real B_31) D_8)))))))
% 1.11/1.37 FOF formula (forall (C_19:nat) (D_8:nat) (A_48:nat) (B_31:nat), (((ord_less_nat A_48) B_31)->(((ord_less_eq_nat C_19) D_8)->(((ord_less_eq_nat zero_zero_nat) A_48)->(((ord_less_nat zero_zero_nat) C_19)->((ord_less_nat ((times_times_nat A_48) C_19)) ((times_times_nat B_31) D_8))))))) of role axiom named fact_563_mult__less__le__imp__less
% 1.11/1.37 A new axiom: (forall (C_19:nat) (D_8:nat) (A_48:nat) (B_31:nat), (((ord_less_nat A_48) B_31)->(((ord_less_eq_nat C_19) D_8)->(((ord_less_eq_nat zero_zero_nat) A_48)->(((ord_less_nat zero_zero_nat) C_19)->((ord_less_nat ((times_times_nat A_48) C_19)) ((times_times_nat B_31) D_8)))))))
% 1.11/1.37 FOF formula (forall (C_19:int) (D_8:int) (A_48:int) (B_31:int), (((ord_less_int A_48) B_31)->(((ord_less_eq_int C_19) D_8)->(((ord_less_eq_int zero_zero_int) A_48)->(((ord_less_int zero_zero_int) C_19)->((ord_less_int ((times_times_int A_48) C_19)) ((times_times_int B_31) D_8))))))) of role axiom named fact_564_mult__less__le__imp__less
% 1.11/1.37 A new axiom: (forall (C_19:int) (D_8:int) (A_48:int) (B_31:int), (((ord_less_int A_48) B_31)->(((ord_less_eq_int C_19) D_8)->(((ord_less_eq_int zero_zero_int) A_48)->(((ord_less_int zero_zero_int) C_19)->((ord_less_int ((times_times_int A_48) C_19)) ((times_times_int B_31) D_8)))))))
% 1.11/1.37 FOF formula (forall (C_18:real) (D_7:real) (A_47:real) (B_30:real), (((ord_less_real A_47) B_30)->(((ord_less_real C_18) D_7)->(((ord_less_eq_real zero_zero_real) A_47)->(((ord_less_eq_real zero_zero_real) C_18)->((ord_less_real ((times_times_real A_47) C_18)) ((times_times_real B_30) D_7))))))) of role axiom named fact_565_mult__strict__mono_H
% 1.11/1.39 A new axiom: (forall (C_18:real) (D_7:real) (A_47:real) (B_30:real), (((ord_less_real A_47) B_30)->(((ord_less_real C_18) D_7)->(((ord_less_eq_real zero_zero_real) A_47)->(((ord_less_eq_real zero_zero_real) C_18)->((ord_less_real ((times_times_real A_47) C_18)) ((times_times_real B_30) D_7)))))))
% 1.11/1.39 FOF formula (forall (C_18:nat) (D_7:nat) (A_47:nat) (B_30:nat), (((ord_less_nat A_47) B_30)->(((ord_less_nat C_18) D_7)->(((ord_less_eq_nat zero_zero_nat) A_47)->(((ord_less_eq_nat zero_zero_nat) C_18)->((ord_less_nat ((times_times_nat A_47) C_18)) ((times_times_nat B_30) D_7))))))) of role axiom named fact_566_mult__strict__mono_H
% 1.11/1.39 A new axiom: (forall (C_18:nat) (D_7:nat) (A_47:nat) (B_30:nat), (((ord_less_nat A_47) B_30)->(((ord_less_nat C_18) D_7)->(((ord_less_eq_nat zero_zero_nat) A_47)->(((ord_less_eq_nat zero_zero_nat) C_18)->((ord_less_nat ((times_times_nat A_47) C_18)) ((times_times_nat B_30) D_7)))))))
% 1.11/1.39 FOF formula (forall (C_18:int) (D_7:int) (A_47:int) (B_30:int), (((ord_less_int A_47) B_30)->(((ord_less_int C_18) D_7)->(((ord_less_eq_int zero_zero_int) A_47)->(((ord_less_eq_int zero_zero_int) C_18)->((ord_less_int ((times_times_int A_47) C_18)) ((times_times_int B_30) D_7))))))) of role axiom named fact_567_mult__strict__mono_H
% 1.11/1.39 A new axiom: (forall (C_18:int) (D_7:int) (A_47:int) (B_30:int), (((ord_less_int A_47) B_30)->(((ord_less_int C_18) D_7)->(((ord_less_eq_int zero_zero_int) A_47)->(((ord_less_eq_int zero_zero_int) C_18)->((ord_less_int ((times_times_int A_47) C_18)) ((times_times_int B_30) D_7)))))))
% 1.11/1.39 FOF formula (forall (C_17:real) (D_6:real) (A_46:real) (B_29:real), (((ord_less_real A_46) B_29)->(((ord_less_real C_17) D_6)->(((ord_less_real zero_zero_real) B_29)->(((ord_less_eq_real zero_zero_real) C_17)->((ord_less_real ((times_times_real A_46) C_17)) ((times_times_real B_29) D_6))))))) of role axiom named fact_568_mult__strict__mono
% 1.11/1.39 A new axiom: (forall (C_17:real) (D_6:real) (A_46:real) (B_29:real), (((ord_less_real A_46) B_29)->(((ord_less_real C_17) D_6)->(((ord_less_real zero_zero_real) B_29)->(((ord_less_eq_real zero_zero_real) C_17)->((ord_less_real ((times_times_real A_46) C_17)) ((times_times_real B_29) D_6)))))))
% 1.11/1.39 FOF formula (forall (C_17:nat) (D_6:nat) (A_46:nat) (B_29:nat), (((ord_less_nat A_46) B_29)->(((ord_less_nat C_17) D_6)->(((ord_less_nat zero_zero_nat) B_29)->(((ord_less_eq_nat zero_zero_nat) C_17)->((ord_less_nat ((times_times_nat A_46) C_17)) ((times_times_nat B_29) D_6))))))) of role axiom named fact_569_mult__strict__mono
% 1.11/1.39 A new axiom: (forall (C_17:nat) (D_6:nat) (A_46:nat) (B_29:nat), (((ord_less_nat A_46) B_29)->(((ord_less_nat C_17) D_6)->(((ord_less_nat zero_zero_nat) B_29)->(((ord_less_eq_nat zero_zero_nat) C_17)->((ord_less_nat ((times_times_nat A_46) C_17)) ((times_times_nat B_29) D_6)))))))
% 1.11/1.39 FOF formula (forall (C_17:int) (D_6:int) (A_46:int) (B_29:int), (((ord_less_int A_46) B_29)->(((ord_less_int C_17) D_6)->(((ord_less_int zero_zero_int) B_29)->(((ord_less_eq_int zero_zero_int) C_17)->((ord_less_int ((times_times_int A_46) C_17)) ((times_times_int B_29) D_6))))))) of role axiom named fact_570_mult__strict__mono
% 1.11/1.39 A new axiom: (forall (C_17:int) (D_6:int) (A_46:int) (B_29:int), (((ord_less_int A_46) B_29)->(((ord_less_int C_17) D_6)->(((ord_less_int zero_zero_int) B_29)->(((ord_less_eq_int zero_zero_int) C_17)->((ord_less_int ((times_times_int A_46) C_17)) ((times_times_int B_29) D_6)))))))
% 1.11/1.39 FOF formula (forall (A_45:real) (B_28:real) (C_16:real), (((ord_less_real C_16) zero_zero_real)->((iff ((ord_less_eq_real ((times_times_real C_16) A_45)) ((times_times_real C_16) B_28))) ((ord_less_eq_real B_28) A_45)))) of role axiom named fact_571_mult__le__cancel__left__neg
% 1.11/1.39 A new axiom: (forall (A_45:real) (B_28:real) (C_16:real), (((ord_less_real C_16) zero_zero_real)->((iff ((ord_less_eq_real ((times_times_real C_16) A_45)) ((times_times_real C_16) B_28))) ((ord_less_eq_real B_28) A_45))))
% 1.11/1.39 FOF formula (forall (A_45:int) (B_28:int) (C_16:int), (((ord_less_int C_16) zero_zero_int)->((iff ((ord_less_eq_int ((times_times_int C_16) A_45)) ((times_times_int C_16) B_28))) ((ord_less_eq_int B_28) A_45)))) of role axiom named fact_572_mult__le__cancel__left__neg
% 1.20/1.41 A new axiom: (forall (A_45:int) (B_28:int) (C_16:int), (((ord_less_int C_16) zero_zero_int)->((iff ((ord_less_eq_int ((times_times_int C_16) A_45)) ((times_times_int C_16) B_28))) ((ord_less_eq_int B_28) A_45))))
% 1.20/1.41 FOF formula (forall (A_44:real) (B_27:real) (C_15:real), (((ord_less_real zero_zero_real) C_15)->((iff ((ord_less_eq_real ((times_times_real C_15) A_44)) ((times_times_real C_15) B_27))) ((ord_less_eq_real A_44) B_27)))) of role axiom named fact_573_mult__le__cancel__left__pos
% 1.20/1.41 A new axiom: (forall (A_44:real) (B_27:real) (C_15:real), (((ord_less_real zero_zero_real) C_15)->((iff ((ord_less_eq_real ((times_times_real C_15) A_44)) ((times_times_real C_15) B_27))) ((ord_less_eq_real A_44) B_27))))
% 1.20/1.41 FOF formula (forall (A_44:int) (B_27:int) (C_15:int), (((ord_less_int zero_zero_int) C_15)->((iff ((ord_less_eq_int ((times_times_int C_15) A_44)) ((times_times_int C_15) B_27))) ((ord_less_eq_int A_44) B_27)))) of role axiom named fact_574_mult__le__cancel__left__pos
% 1.20/1.41 A new axiom: (forall (A_44:int) (B_27:int) (C_15:int), (((ord_less_int zero_zero_int) C_15)->((iff ((ord_less_eq_int ((times_times_int C_15) A_44)) ((times_times_int C_15) B_27))) ((ord_less_eq_int A_44) B_27))))
% 1.20/1.41 FOF formula (forall (X_14:real) (Y_13:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((times_times_real X_14) X_14)) ((times_times_real Y_13) Y_13)))) of role axiom named fact_575_sum__squares__ge__zero
% 1.20/1.41 A new axiom: (forall (X_14:real) (Y_13:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((times_times_real X_14) X_14)) ((times_times_real Y_13) Y_13))))
% 1.20/1.41 FOF formula (forall (X_14:int) (Y_13:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int X_14) X_14)) ((times_times_int Y_13) Y_13)))) of role axiom named fact_576_sum__squares__ge__zero
% 1.20/1.41 A new axiom: (forall (X_14:int) (Y_13:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int X_14) X_14)) ((times_times_int Y_13) Y_13))))
% 1.20/1.41 FOF formula (forall (X_13:real) (Y_12:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real X_13) X_13)) ((times_times_real Y_12) Y_12))) zero_zero_real)) ((and (((eq real) X_13) zero_zero_real)) (((eq real) Y_12) zero_zero_real)))) of role axiom named fact_577_sum__squares__le__zero__iff
% 1.20/1.41 A new axiom: (forall (X_13:real) (Y_12:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real X_13) X_13)) ((times_times_real Y_12) Y_12))) zero_zero_real)) ((and (((eq real) X_13) zero_zero_real)) (((eq real) Y_12) zero_zero_real))))
% 1.20/1.41 FOF formula (forall (X_13:int) (Y_12:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int X_13) X_13)) ((times_times_int Y_12) Y_12))) zero_zero_int)) ((and (((eq int) X_13) zero_zero_int)) (((eq int) Y_12) zero_zero_int)))) of role axiom named fact_578_sum__squares__le__zero__iff
% 1.20/1.41 A new axiom: (forall (X_13:int) (Y_12:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int X_13) X_13)) ((times_times_int Y_12) Y_12))) zero_zero_int)) ((and (((eq int) X_13) zero_zero_int)) (((eq int) Y_12) zero_zero_int))))
% 1.20/1.41 FOF formula (forall (Y_11:real) (X_12:real), (((ord_less_eq_real zero_zero_real) X_12)->(((ord_less_eq_real zero_zero_real) Y_11)->(((ord_less_eq_real Y_11) one_one_real)->((ord_less_eq_real ((times_times_real X_12) Y_11)) X_12))))) of role axiom named fact_579_mult__right__le__one__le
% 1.20/1.41 A new axiom: (forall (Y_11:real) (X_12:real), (((ord_less_eq_real zero_zero_real) X_12)->(((ord_less_eq_real zero_zero_real) Y_11)->(((ord_less_eq_real Y_11) one_one_real)->((ord_less_eq_real ((times_times_real X_12) Y_11)) X_12)))))
% 1.20/1.41 FOF formula (forall (Y_11:int) (X_12:int), (((ord_less_eq_int zero_zero_int) X_12)->(((ord_less_eq_int zero_zero_int) Y_11)->(((ord_less_eq_int Y_11) one_one_int)->((ord_less_eq_int ((times_times_int X_12) Y_11)) X_12))))) of role axiom named fact_580_mult__right__le__one__le
% 1.20/1.41 A new axiom: (forall (Y_11:int) (X_12:int), (((ord_less_eq_int zero_zero_int) X_12)->(((ord_less_eq_int zero_zero_int) Y_11)->(((ord_less_eq_int Y_11) one_one_int)->((ord_less_eq_int ((times_times_int X_12) Y_11)) X_12)))))
% 1.20/1.42 FOF formula (forall (Y_10:real) (X_11:real), (((ord_less_eq_real zero_zero_real) X_11)->(((ord_less_eq_real zero_zero_real) Y_10)->(((ord_less_eq_real Y_10) one_one_real)->((ord_less_eq_real ((times_times_real Y_10) X_11)) X_11))))) of role axiom named fact_581_mult__left__le__one__le
% 1.20/1.42 A new axiom: (forall (Y_10:real) (X_11:real), (((ord_less_eq_real zero_zero_real) X_11)->(((ord_less_eq_real zero_zero_real) Y_10)->(((ord_less_eq_real Y_10) one_one_real)->((ord_less_eq_real ((times_times_real Y_10) X_11)) X_11)))))
% 1.20/1.42 FOF formula (forall (Y_10:int) (X_11:int), (((ord_less_eq_int zero_zero_int) X_11)->(((ord_less_eq_int zero_zero_int) Y_10)->(((ord_less_eq_int Y_10) one_one_int)->((ord_less_eq_int ((times_times_int Y_10) X_11)) X_11))))) of role axiom named fact_582_mult__left__le__one__le
% 1.20/1.42 A new axiom: (forall (Y_10:int) (X_11:int), (((ord_less_eq_int zero_zero_int) X_11)->(((ord_less_eq_int zero_zero_int) Y_10)->(((ord_less_eq_int Y_10) one_one_int)->((ord_less_eq_int ((times_times_int Y_10) X_11)) X_11)))))
% 1.20/1.42 FOF formula (forall (Z:int), (((ord_less_eq_int Z) zero_zero_int)->(((eq nat) (nat_1 Z)) zero_zero_nat))) of role axiom named fact_583_nat__le__0
% 1.20/1.42 A new axiom: (forall (Z:int), (((ord_less_eq_int Z) zero_zero_int)->(((eq nat) (nat_1 Z)) zero_zero_nat)))
% 1.20/1.42 FOF formula (forall (I_1:int), ((iff (((eq nat) (nat_1 I_1)) zero_zero_nat)) ((ord_less_eq_int I_1) zero_zero_int))) of role axiom named fact_584_nat__0__iff
% 1.20/1.42 A new axiom: (forall (I_1:int), ((iff (((eq nat) (nat_1 I_1)) zero_zero_nat)) ((ord_less_eq_int I_1) zero_zero_int)))
% 1.20/1.42 FOF formula (forall (A_43:real) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_real one_one_real) A_43)->((ord_less_eq_real ((power_power_real A_43) N_9)) ((power_power_real A_43) N_8))))) of role axiom named fact_585_power__increasing
% 1.20/1.42 A new axiom: (forall (A_43:real) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_real one_one_real) A_43)->((ord_less_eq_real ((power_power_real A_43) N_9)) ((power_power_real A_43) N_8)))))
% 1.20/1.42 FOF formula (forall (A_43:nat) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_nat one_one_nat) A_43)->((ord_less_eq_nat ((power_power_nat A_43) N_9)) ((power_power_nat A_43) N_8))))) of role axiom named fact_586_power__increasing
% 1.20/1.42 A new axiom: (forall (A_43:nat) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_nat one_one_nat) A_43)->((ord_less_eq_nat ((power_power_nat A_43) N_9)) ((power_power_nat A_43) N_8)))))
% 1.20/1.42 FOF formula (forall (A_43:int) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_int one_one_int) A_43)->((ord_less_eq_int ((power_power_int A_43) N_9)) ((power_power_int A_43) N_8))))) of role axiom named fact_587_power__increasing
% 1.20/1.42 A new axiom: (forall (A_43:int) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_int one_one_int) A_43)->((ord_less_eq_int ((power_power_int A_43) N_9)) ((power_power_int A_43) N_8)))))
% 1.20/1.42 FOF formula (forall (Z:int), ((and (((ord_less_eq_int zero_zero_int) Z)->(((eq int) (semiri1621563631at_int (nat_1 Z))) Z))) ((((ord_less_eq_int zero_zero_int) Z)->False)->(((eq int) (semiri1621563631at_int (nat_1 Z))) zero_zero_int)))) of role axiom named fact_588_int__nat__eq
% 1.20/1.42 A new axiom: (forall (Z:int), ((and (((ord_less_eq_int zero_zero_int) Z)->(((eq int) (semiri1621563631at_int (nat_1 Z))) Z))) ((((ord_less_eq_int zero_zero_int) Z)->False)->(((eq int) (semiri1621563631at_int (nat_1 Z))) zero_zero_int))))
% 1.20/1.42 FOF formula (forall (M:nat) (Z:int), ((iff (((eq int) (semiri1621563631at_int M)) Z)) ((and (((eq nat) M) (nat_1 Z))) ((ord_less_eq_int zero_zero_int) Z)))) of role axiom named fact_589_int__eq__iff
% 1.20/1.42 A new axiom: (forall (M:nat) (Z:int), ((iff (((eq int) (semiri1621563631at_int M)) Z)) ((and (((eq nat) M) (nat_1 Z))) ((ord_less_eq_int zero_zero_int) Z))))
% 1.20/1.42 FOF formula (forall (Z:int), (((ord_less_eq_int zero_zero_int) Z)->(((eq int) (semiri1621563631at_int (nat_1 Z))) Z))) of role axiom named fact_590_nat__0__le
% 1.20/1.42 A new axiom: (forall (Z:int), (((ord_less_eq_int zero_zero_int) Z)->(((eq int) (semiri1621563631at_int (nat_1 Z))) Z)))
% 1.20/1.44 FOF formula (forall (A_42:real) (B_26:real), ((iff (((eq real) ((minus_minus_real A_42) B_26)) zero_zero_real)) (((eq real) A_42) B_26))) of role axiom named fact_591_right__minus__eq
% 1.20/1.44 A new axiom: (forall (A_42:real) (B_26:real), ((iff (((eq real) ((minus_minus_real A_42) B_26)) zero_zero_real)) (((eq real) A_42) B_26)))
% 1.20/1.44 FOF formula (forall (A_42:int) (B_26:int), ((iff (((eq int) ((minus_minus_int A_42) B_26)) zero_zero_int)) (((eq int) A_42) B_26))) of role axiom named fact_592_right__minus__eq
% 1.20/1.44 A new axiom: (forall (A_42:int) (B_26:int), ((iff (((eq int) ((minus_minus_int A_42) B_26)) zero_zero_int)) (((eq int) A_42) B_26)))
% 1.20/1.44 FOF formula (forall (A_41:real) (B_25:real), ((iff (((eq real) A_41) B_25)) (((eq real) ((minus_minus_real A_41) B_25)) zero_zero_real))) of role axiom named fact_593_eq__iff__diff__eq__0
% 1.20/1.44 A new axiom: (forall (A_41:real) (B_25:real), ((iff (((eq real) A_41) B_25)) (((eq real) ((minus_minus_real A_41) B_25)) zero_zero_real)))
% 1.20/1.44 FOF formula (forall (A_41:int) (B_25:int), ((iff (((eq int) A_41) B_25)) (((eq int) ((minus_minus_int A_41) B_25)) zero_zero_int))) of role axiom named fact_594_eq__iff__diff__eq__0
% 1.20/1.44 A new axiom: (forall (A_41:int) (B_25:int), ((iff (((eq int) A_41) B_25)) (((eq int) ((minus_minus_int A_41) B_25)) zero_zero_int)))
% 1.20/1.44 FOF formula (forall (A_40:real), (((eq real) ((minus_minus_real A_40) A_40)) zero_zero_real)) of role axiom named fact_595_diff__self
% 1.20/1.44 A new axiom: (forall (A_40:real), (((eq real) ((minus_minus_real A_40) A_40)) zero_zero_real))
% 1.20/1.44 FOF formula (forall (A_40:int), (((eq int) ((minus_minus_int A_40) A_40)) zero_zero_int)) of role axiom named fact_596_diff__self
% 1.20/1.44 A new axiom: (forall (A_40:int), (((eq int) ((minus_minus_int A_40) A_40)) zero_zero_int))
% 1.20/1.44 FOF formula (forall (A_39:real), (((eq real) ((minus_minus_real A_39) zero_zero_real)) A_39)) of role axiom named fact_597_diff__0__right
% 1.20/1.44 A new axiom: (forall (A_39:real), (((eq real) ((minus_minus_real A_39) zero_zero_real)) A_39))
% 1.20/1.44 FOF formula (forall (A_39:int), (((eq int) ((minus_minus_int A_39) zero_zero_int)) A_39)) of role axiom named fact_598_diff__0__right
% 1.20/1.44 A new axiom: (forall (A_39:int), (((eq int) ((minus_minus_int A_39) zero_zero_int)) A_39))
% 1.20/1.44 FOF formula (forall (A_38:int) (B_24:int) (C_14:int) (D_5:int), ((((eq int) ((minus_minus_int A_38) B_24)) ((minus_minus_int C_14) D_5))->((iff ((ord_less_int A_38) B_24)) ((ord_less_int C_14) D_5)))) of role axiom named fact_599_diff__eq__diff__less
% 1.20/1.44 A new axiom: (forall (A_38:int) (B_24:int) (C_14:int) (D_5:int), ((((eq int) ((minus_minus_int A_38) B_24)) ((minus_minus_int C_14) D_5))->((iff ((ord_less_int A_38) B_24)) ((ord_less_int C_14) D_5))))
% 1.20/1.44 FOF formula (forall (A_38:real) (B_24:real) (C_14:real) (D_5:real), ((((eq real) ((minus_minus_real A_38) B_24)) ((minus_minus_real C_14) D_5))->((iff ((ord_less_real A_38) B_24)) ((ord_less_real C_14) D_5)))) of role axiom named fact_600_diff__eq__diff__less
% 1.20/1.44 A new axiom: (forall (A_38:real) (B_24:real) (C_14:real) (D_5:real), ((((eq real) ((minus_minus_real A_38) B_24)) ((minus_minus_real C_14) D_5))->((iff ((ord_less_real A_38) B_24)) ((ord_less_real C_14) D_5))))
% 1.20/1.44 FOF formula (forall (A_37:real) (C_13:real) (B_23:real) (D_4:real), (((eq real) ((minus_minus_real ((plus_plus_real A_37) C_13)) ((plus_plus_real B_23) D_4))) ((plus_plus_real ((minus_minus_real A_37) B_23)) ((minus_minus_real C_13) D_4)))) of role axiom named fact_601_add__diff__add
% 1.20/1.44 A new axiom: (forall (A_37:real) (C_13:real) (B_23:real) (D_4:real), (((eq real) ((minus_minus_real ((plus_plus_real A_37) C_13)) ((plus_plus_real B_23) D_4))) ((plus_plus_real ((minus_minus_real A_37) B_23)) ((minus_minus_real C_13) D_4))))
% 1.20/1.44 FOF formula (forall (A_37:int) (C_13:int) (B_23:int) (D_4:int), (((eq int) ((minus_minus_int ((plus_plus_int A_37) C_13)) ((plus_plus_int B_23) D_4))) ((plus_plus_int ((minus_minus_int A_37) B_23)) ((minus_minus_int C_13) D_4)))) of role axiom named fact_602_add__diff__add
% 1.20/1.44 A new axiom: (forall (A_37:int) (C_13:int) (B_23:int) (D_4:int), (((eq int) ((minus_minus_int ((plus_plus_int A_37) C_13)) ((plus_plus_int B_23) D_4))) ((plus_plus_int ((minus_minus_int A_37) B_23)) ((minus_minus_int C_13) D_4))))
% 1.20/1.46 FOF formula (forall (A_36:real) (B_22:real), (((eq real) ((minus_minus_real ((plus_plus_real A_36) B_22)) B_22)) A_36)) of role axiom named fact_603_add__diff__cancel
% 1.20/1.46 A new axiom: (forall (A_36:real) (B_22:real), (((eq real) ((minus_minus_real ((plus_plus_real A_36) B_22)) B_22)) A_36))
% 1.20/1.46 FOF formula (forall (A_36:int) (B_22:int), (((eq int) ((minus_minus_int ((plus_plus_int A_36) B_22)) B_22)) A_36)) of role axiom named fact_604_add__diff__cancel
% 1.20/1.46 A new axiom: (forall (A_36:int) (B_22:int), (((eq int) ((minus_minus_int ((plus_plus_int A_36) B_22)) B_22)) A_36))
% 1.20/1.46 FOF formula (forall (A_35:real) (B_21:real), (((eq real) ((plus_plus_real ((minus_minus_real A_35) B_21)) B_21)) A_35)) of role axiom named fact_605_diff__add__cancel
% 1.20/1.46 A new axiom: (forall (A_35:real) (B_21:real), (((eq real) ((plus_plus_real ((minus_minus_real A_35) B_21)) B_21)) A_35))
% 1.20/1.46 FOF formula (forall (A_35:int) (B_21:int), (((eq int) ((plus_plus_int ((minus_minus_int A_35) B_21)) B_21)) A_35)) of role axiom named fact_606_diff__add__cancel
% 1.20/1.46 A new axiom: (forall (A_35:int) (B_21:int), (((eq int) ((plus_plus_int ((minus_minus_int A_35) B_21)) B_21)) A_35))
% 1.20/1.46 FOF formula (forall (A_34:real), (((eq real) ((times_times_real zero_zero_real) A_34)) zero_zero_real)) of role axiom named fact_607_mult__zero__left
% 1.20/1.46 A new axiom: (forall (A_34:real), (((eq real) ((times_times_real zero_zero_real) A_34)) zero_zero_real))
% 1.20/1.46 FOF formula (forall (A_34:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_34)) zero_zero_nat)) of role axiom named fact_608_mult__zero__left
% 1.20/1.46 A new axiom: (forall (A_34:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_34)) zero_zero_nat))
% 1.20/1.46 FOF formula (forall (A_34:int), (((eq int) ((times_times_int zero_zero_int) A_34)) zero_zero_int)) of role axiom named fact_609_mult__zero__left
% 1.20/1.46 A new axiom: (forall (A_34:int), (((eq int) ((times_times_int zero_zero_int) A_34)) zero_zero_int))
% 1.20/1.46 FOF formula (forall (A_33:real), (((eq real) ((times_times_real A_33) zero_zero_real)) zero_zero_real)) of role axiom named fact_610_mult__zero__right
% 1.20/1.46 A new axiom: (forall (A_33:real), (((eq real) ((times_times_real A_33) zero_zero_real)) zero_zero_real))
% 1.20/1.46 FOF formula (forall (A_33:nat), (((eq nat) ((times_times_nat A_33) zero_zero_nat)) zero_zero_nat)) of role axiom named fact_611_mult__zero__right
% 1.20/1.46 A new axiom: (forall (A_33:nat), (((eq nat) ((times_times_nat A_33) zero_zero_nat)) zero_zero_nat))
% 1.20/1.46 FOF formula (forall (A_33:int), (((eq int) ((times_times_int A_33) zero_zero_int)) zero_zero_int)) of role axiom named fact_612_mult__zero__right
% 1.20/1.46 A new axiom: (forall (A_33:int), (((eq int) ((times_times_int A_33) zero_zero_int)) zero_zero_int))
% 1.20/1.46 FOF formula (forall (A_32:real) (B_20:real), ((iff (((eq real) ((times_times_real A_32) B_20)) zero_zero_real)) ((or (((eq real) A_32) zero_zero_real)) (((eq real) B_20) zero_zero_real)))) of role axiom named fact_613_mult__eq__0__iff
% 1.20/1.46 A new axiom: (forall (A_32:real) (B_20:real), ((iff (((eq real) ((times_times_real A_32) B_20)) zero_zero_real)) ((or (((eq real) A_32) zero_zero_real)) (((eq real) B_20) zero_zero_real))))
% 1.20/1.46 FOF formula (forall (A_32:int) (B_20:int), ((iff (((eq int) ((times_times_int A_32) B_20)) zero_zero_int)) ((or (((eq int) A_32) zero_zero_int)) (((eq int) B_20) zero_zero_int)))) of role axiom named fact_614_mult__eq__0__iff
% 1.20/1.46 A new axiom: (forall (A_32:int) (B_20:int), ((iff (((eq int) ((times_times_int A_32) B_20)) zero_zero_int)) ((or (((eq int) A_32) zero_zero_int)) (((eq int) B_20) zero_zero_int))))
% 1.20/1.46 FOF formula (forall (B_19:real) (A_31:real), ((not (((eq real) A_31) zero_zero_real))->((not (((eq real) B_19) zero_zero_real))->(not (((eq real) ((times_times_real A_31) B_19)) zero_zero_real))))) of role axiom named fact_615_no__zero__divisors
% 1.20/1.46 A new axiom: (forall (B_19:real) (A_31:real), ((not (((eq real) A_31) zero_zero_real))->((not (((eq real) B_19) zero_zero_real))->(not (((eq real) ((times_times_real A_31) B_19)) zero_zero_real)))))
% 1.20/1.46 FOF formula (forall (B_19:nat) (A_31:nat), ((not (((eq nat) A_31) zero_zero_nat))->((not (((eq nat) B_19) zero_zero_nat))->(not (((eq nat) ((times_times_nat A_31) B_19)) zero_zero_nat))))) of role axiom named fact_616_no__zero__divisors
% 1.20/1.47 A new axiom: (forall (B_19:nat) (A_31:nat), ((not (((eq nat) A_31) zero_zero_nat))->((not (((eq nat) B_19) zero_zero_nat))->(not (((eq nat) ((times_times_nat A_31) B_19)) zero_zero_nat)))))
% 1.20/1.47 FOF formula (forall (B_19:int) (A_31:int), ((not (((eq int) A_31) zero_zero_int))->((not (((eq int) B_19) zero_zero_int))->(not (((eq int) ((times_times_int A_31) B_19)) zero_zero_int))))) of role axiom named fact_617_no__zero__divisors
% 1.20/1.47 A new axiom: (forall (B_19:int) (A_31:int), ((not (((eq int) A_31) zero_zero_int))->((not (((eq int) B_19) zero_zero_int))->(not (((eq int) ((times_times_int A_31) B_19)) zero_zero_int)))))
% 1.20/1.47 FOF formula (forall (A_30:real) (B_18:real), ((((eq real) ((times_times_real A_30) B_18)) zero_zero_real)->((or (((eq real) A_30) zero_zero_real)) (((eq real) B_18) zero_zero_real)))) of role axiom named fact_618_divisors__zero
% 1.20/1.47 A new axiom: (forall (A_30:real) (B_18:real), ((((eq real) ((times_times_real A_30) B_18)) zero_zero_real)->((or (((eq real) A_30) zero_zero_real)) (((eq real) B_18) zero_zero_real))))
% 1.20/1.47 FOF formula (forall (A_30:nat) (B_18:nat), ((((eq nat) ((times_times_nat A_30) B_18)) zero_zero_nat)->((or (((eq nat) A_30) zero_zero_nat)) (((eq nat) B_18) zero_zero_nat)))) of role axiom named fact_619_divisors__zero
% 1.20/1.47 A new axiom: (forall (A_30:nat) (B_18:nat), ((((eq nat) ((times_times_nat A_30) B_18)) zero_zero_nat)->((or (((eq nat) A_30) zero_zero_nat)) (((eq nat) B_18) zero_zero_nat))))
% 1.20/1.47 FOF formula (forall (A_30:int) (B_18:int), ((((eq int) ((times_times_int A_30) B_18)) zero_zero_int)->((or (((eq int) A_30) zero_zero_int)) (((eq int) B_18) zero_zero_int)))) of role axiom named fact_620_divisors__zero
% 1.20/1.47 A new axiom: (forall (A_30:int) (B_18:int), ((((eq int) ((times_times_int A_30) B_18)) zero_zero_int)->((or (((eq int) A_30) zero_zero_int)) (((eq int) B_18) zero_zero_int))))
% 1.20/1.47 FOF formula (forall (A_29:real), (((eq real) ((times_times_real A_29) zero_zero_real)) zero_zero_real)) of role axiom named fact_621_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J
% 1.20/1.47 A new axiom: (forall (A_29:real), (((eq real) ((times_times_real A_29) zero_zero_real)) zero_zero_real))
% 1.20/1.47 FOF formula (forall (A_29:nat), (((eq nat) ((times_times_nat A_29) zero_zero_nat)) zero_zero_nat)) of role axiom named fact_622_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J
% 1.20/1.47 A new axiom: (forall (A_29:nat), (((eq nat) ((times_times_nat A_29) zero_zero_nat)) zero_zero_nat))
% 1.20/1.47 FOF formula (forall (A_29:int), (((eq int) ((times_times_int A_29) zero_zero_int)) zero_zero_int)) of role axiom named fact_623_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J
% 1.20/1.47 A new axiom: (forall (A_29:int), (((eq int) ((times_times_int A_29) zero_zero_int)) zero_zero_int))
% 1.20/1.47 FOF formula (forall (A_28:real), (((eq real) ((times_times_real zero_zero_real) A_28)) zero_zero_real)) of role axiom named fact_624_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J
% 1.20/1.47 A new axiom: (forall (A_28:real), (((eq real) ((times_times_real zero_zero_real) A_28)) zero_zero_real))
% 1.20/1.47 FOF formula (forall (A_28:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_28)) zero_zero_nat)) of role axiom named fact_625_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J
% 1.20/1.47 A new axiom: (forall (A_28:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_28)) zero_zero_nat))
% 1.20/1.47 FOF formula (forall (A_28:int), (((eq int) ((times_times_int zero_zero_int) A_28)) zero_zero_int)) of role axiom named fact_626_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J
% 1.20/1.47 A new axiom: (forall (A_28:int), (((eq int) ((times_times_int zero_zero_int) A_28)) zero_zero_int))
% 1.20/1.47 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_627_diffs0__imp__equal
% 1.20/1.47 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))))
% 1.20/1.47 FOF formula (forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat)) of role axiom named fact_628_diff__self__eq__0
% 1.28/1.49 A new axiom: (forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat))
% 1.28/1.49 FOF formula (forall (M:nat), (((eq nat) ((minus_minus_nat M) zero_zero_nat)) M)) of role axiom named fact_629_minus__nat_Odiff__0
% 1.28/1.49 A new axiom: (forall (M:nat), (((eq nat) ((minus_minus_nat M) zero_zero_nat)) M))
% 1.28/1.49 FOF formula (forall (N:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N)) zero_zero_nat)) of role axiom named fact_630_diff__0__eq__0
% 1.28/1.49 A new axiom: (forall (N:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N)) zero_zero_nat))
% 1.28/1.49 FOF formula (forall (A_27:real) (B_17:real) (C_12:real), (((eq real) ((times_times_real ((plus_plus_real A_27) B_17)) C_12)) ((plus_plus_real ((times_times_real A_27) C_12)) ((times_times_real B_17) C_12)))) of role axiom named fact_631_comm__semiring__class_Odistrib
% 1.28/1.49 A new axiom: (forall (A_27:real) (B_17:real) (C_12:real), (((eq real) ((times_times_real ((plus_plus_real A_27) B_17)) C_12)) ((plus_plus_real ((times_times_real A_27) C_12)) ((times_times_real B_17) C_12))))
% 1.28/1.49 FOF formula (forall (A_27:nat) (B_17:nat) (C_12:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_27) B_17)) C_12)) ((plus_plus_nat ((times_times_nat A_27) C_12)) ((times_times_nat B_17) C_12)))) of role axiom named fact_632_comm__semiring__class_Odistrib
% 1.28/1.49 A new axiom: (forall (A_27:nat) (B_17:nat) (C_12:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_27) B_17)) C_12)) ((plus_plus_nat ((times_times_nat A_27) C_12)) ((times_times_nat B_17) C_12))))
% 1.28/1.49 FOF formula (forall (A_27:int) (B_17:int) (C_12:int), (((eq int) ((times_times_int ((plus_plus_int A_27) B_17)) C_12)) ((plus_plus_int ((times_times_int A_27) C_12)) ((times_times_int B_17) C_12)))) of role axiom named fact_633_comm__semiring__class_Odistrib
% 1.28/1.49 A new axiom: (forall (A_27:int) (B_17:int) (C_12:int), (((eq int) ((times_times_int ((plus_plus_int A_27) B_17)) C_12)) ((plus_plus_int ((times_times_int A_27) C_12)) ((times_times_int B_17) C_12))))
% 1.28/1.49 FOF formula (forall (A_26:real) (E:real) (B_16:real) (C_11:real), (((eq real) ((plus_plus_real ((times_times_real A_26) E)) ((plus_plus_real ((times_times_real B_16) E)) C_11))) ((plus_plus_real ((times_times_real ((plus_plus_real A_26) B_16)) E)) C_11))) of role axiom named fact_634_combine__common__factor
% 1.28/1.49 A new axiom: (forall (A_26:real) (E:real) (B_16:real) (C_11:real), (((eq real) ((plus_plus_real ((times_times_real A_26) E)) ((plus_plus_real ((times_times_real B_16) E)) C_11))) ((plus_plus_real ((times_times_real ((plus_plus_real A_26) B_16)) E)) C_11)))
% 1.28/1.49 FOF formula (forall (A_26:nat) (E:nat) (B_16:nat) (C_11:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_26) E)) ((plus_plus_nat ((times_times_nat B_16) E)) C_11))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat A_26) B_16)) E)) C_11))) of role axiom named fact_635_combine__common__factor
% 1.28/1.49 A new axiom: (forall (A_26:nat) (E:nat) (B_16:nat) (C_11:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_26) E)) ((plus_plus_nat ((times_times_nat B_16) E)) C_11))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat A_26) B_16)) E)) C_11)))
% 1.28/1.49 FOF formula (forall (A_26:int) (E:int) (B_16:int) (C_11:int), (((eq int) ((plus_plus_int ((times_times_int A_26) E)) ((plus_plus_int ((times_times_int B_16) E)) C_11))) ((plus_plus_int ((times_times_int ((plus_plus_int A_26) B_16)) E)) C_11))) of role axiom named fact_636_combine__common__factor
% 1.28/1.49 A new axiom: (forall (A_26:int) (E:int) (B_16:int) (C_11:int), (((eq int) ((plus_plus_int ((times_times_int A_26) E)) ((plus_plus_int ((times_times_int B_16) E)) C_11))) ((plus_plus_int ((times_times_int ((plus_plus_int A_26) B_16)) E)) C_11)))
% 1.28/1.49 FOF formula (forall (W_3:real) (Y_9:real) (X_10:real) (Z_3:real), ((iff (((eq real) ((plus_plus_real ((times_times_real W_3) Y_9)) ((times_times_real X_10) Z_3))) ((plus_plus_real ((times_times_real W_3) Z_3)) ((times_times_real X_10) Y_9)))) ((or (((eq real) W_3) X_10)) (((eq real) Y_9) Z_3)))) of role axiom named fact_637_crossproduct__eq
% 1.28/1.49 A new axiom: (forall (W_3:real) (Y_9:real) (X_10:real) (Z_3:real), ((iff (((eq real) ((plus_plus_real ((times_times_real W_3) Y_9)) ((times_times_real X_10) Z_3))) ((plus_plus_real ((times_times_real W_3) Z_3)) ((times_times_real X_10) Y_9)))) ((or (((eq real) W_3) X_10)) (((eq real) Y_9) Z_3))))
% 1.28/1.51 FOF formula (forall (W_3:nat) (Y_9:nat) (X_10:nat) (Z_3:nat), ((iff (((eq nat) ((plus_plus_nat ((times_times_nat W_3) Y_9)) ((times_times_nat X_10) Z_3))) ((plus_plus_nat ((times_times_nat W_3) Z_3)) ((times_times_nat X_10) Y_9)))) ((or (((eq nat) W_3) X_10)) (((eq nat) Y_9) Z_3)))) of role axiom named fact_638_crossproduct__eq
% 1.28/1.51 A new axiom: (forall (W_3:nat) (Y_9:nat) (X_10:nat) (Z_3:nat), ((iff (((eq nat) ((plus_plus_nat ((times_times_nat W_3) Y_9)) ((times_times_nat X_10) Z_3))) ((plus_plus_nat ((times_times_nat W_3) Z_3)) ((times_times_nat X_10) Y_9)))) ((or (((eq nat) W_3) X_10)) (((eq nat) Y_9) Z_3))))
% 1.28/1.51 FOF formula (forall (W_3:int) (Y_9:int) (X_10:int) (Z_3:int), ((iff (((eq int) ((plus_plus_int ((times_times_int W_3) Y_9)) ((times_times_int X_10) Z_3))) ((plus_plus_int ((times_times_int W_3) Z_3)) ((times_times_int X_10) Y_9)))) ((or (((eq int) W_3) X_10)) (((eq int) Y_9) Z_3)))) of role axiom named fact_639_crossproduct__eq
% 1.28/1.51 A new axiom: (forall (W_3:int) (Y_9:int) (X_10:int) (Z_3:int), ((iff (((eq int) ((plus_plus_int ((times_times_int W_3) Y_9)) ((times_times_int X_10) Z_3))) ((plus_plus_int ((times_times_int W_3) Z_3)) ((times_times_int X_10) Y_9)))) ((or (((eq int) W_3) X_10)) (((eq int) Y_9) Z_3))))
% 1.28/1.51 FOF formula (forall (A_25:real) (M_3:real) (B_15:real), (((eq real) ((plus_plus_real ((times_times_real A_25) M_3)) ((times_times_real B_15) M_3))) ((times_times_real ((plus_plus_real A_25) B_15)) M_3))) of role axiom named fact_640_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J
% 1.28/1.51 A new axiom: (forall (A_25:real) (M_3:real) (B_15:real), (((eq real) ((plus_plus_real ((times_times_real A_25) M_3)) ((times_times_real B_15) M_3))) ((times_times_real ((plus_plus_real A_25) B_15)) M_3)))
% 1.28/1.51 FOF formula (forall (A_25:nat) (M_3:nat) (B_15:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_25) M_3)) ((times_times_nat B_15) M_3))) ((times_times_nat ((plus_plus_nat A_25) B_15)) M_3))) of role axiom named fact_641_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J
% 1.28/1.51 A new axiom: (forall (A_25:nat) (M_3:nat) (B_15:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_25) M_3)) ((times_times_nat B_15) M_3))) ((times_times_nat ((plus_plus_nat A_25) B_15)) M_3)))
% 1.28/1.51 FOF formula (forall (A_25:int) (M_3:int) (B_15:int), (((eq int) ((plus_plus_int ((times_times_int A_25) M_3)) ((times_times_int B_15) M_3))) ((times_times_int ((plus_plus_int A_25) B_15)) M_3))) of role axiom named fact_642_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J
% 1.28/1.51 A new axiom: (forall (A_25:int) (M_3:int) (B_15:int), (((eq int) ((plus_plus_int ((times_times_int A_25) M_3)) ((times_times_int B_15) M_3))) ((times_times_int ((plus_plus_int A_25) B_15)) M_3)))
% 1.28/1.51 FOF formula (forall (A_24:real) (B_14:real) (C_10:real), (((eq real) ((times_times_real ((plus_plus_real A_24) B_14)) C_10)) ((plus_plus_real ((times_times_real A_24) C_10)) ((times_times_real B_14) C_10)))) of role axiom named fact_643_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J
% 1.28/1.51 A new axiom: (forall (A_24:real) (B_14:real) (C_10:real), (((eq real) ((times_times_real ((plus_plus_real A_24) B_14)) C_10)) ((plus_plus_real ((times_times_real A_24) C_10)) ((times_times_real B_14) C_10))))
% 1.28/1.51 FOF formula (forall (A_24:nat) (B_14:nat) (C_10:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_24) B_14)) C_10)) ((plus_plus_nat ((times_times_nat A_24) C_10)) ((times_times_nat B_14) C_10)))) of role axiom named fact_644_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J
% 1.28/1.51 A new axiom: (forall (A_24:nat) (B_14:nat) (C_10:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_24) B_14)) C_10)) ((plus_plus_nat ((times_times_nat A_24) C_10)) ((times_times_nat B_14) C_10))))
% 1.28/1.51 FOF formula (forall (A_24:int) (B_14:int) (C_10:int), (((eq int) ((times_times_int ((plus_plus_int A_24) B_14)) C_10)) ((plus_plus_int ((times_times_int A_24) C_10)) ((times_times_int B_14) C_10)))) of role axiom named fact_645_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J
% 1.28/1.52 A new axiom: (forall (A_24:int) (B_14:int) (C_10:int), (((eq int) ((times_times_int ((plus_plus_int A_24) B_14)) C_10)) ((plus_plus_int ((times_times_int A_24) C_10)) ((times_times_int B_14) C_10))))
% 1.28/1.52 FOF formula (forall (C_9:real) (D_3:real) (A_23:real) (B_13:real), ((iff ((and (not (((eq real) A_23) B_13))) (not (((eq real) C_9) D_3)))) (not (((eq real) ((plus_plus_real ((times_times_real A_23) C_9)) ((times_times_real B_13) D_3))) ((plus_plus_real ((times_times_real A_23) D_3)) ((times_times_real B_13) C_9)))))) of role axiom named fact_646_crossproduct__noteq
% 1.28/1.52 A new axiom: (forall (C_9:real) (D_3:real) (A_23:real) (B_13:real), ((iff ((and (not (((eq real) A_23) B_13))) (not (((eq real) C_9) D_3)))) (not (((eq real) ((plus_plus_real ((times_times_real A_23) C_9)) ((times_times_real B_13) D_3))) ((plus_plus_real ((times_times_real A_23) D_3)) ((times_times_real B_13) C_9))))))
% 1.28/1.52 FOF formula (forall (C_9:nat) (D_3:nat) (A_23:nat) (B_13:nat), ((iff ((and (not (((eq nat) A_23) B_13))) (not (((eq nat) C_9) D_3)))) (not (((eq nat) ((plus_plus_nat ((times_times_nat A_23) C_9)) ((times_times_nat B_13) D_3))) ((plus_plus_nat ((times_times_nat A_23) D_3)) ((times_times_nat B_13) C_9)))))) of role axiom named fact_647_crossproduct__noteq
% 1.28/1.52 A new axiom: (forall (C_9:nat) (D_3:nat) (A_23:nat) (B_13:nat), ((iff ((and (not (((eq nat) A_23) B_13))) (not (((eq nat) C_9) D_3)))) (not (((eq nat) ((plus_plus_nat ((times_times_nat A_23) C_9)) ((times_times_nat B_13) D_3))) ((plus_plus_nat ((times_times_nat A_23) D_3)) ((times_times_nat B_13) C_9))))))
% 1.28/1.52 FOF formula (forall (C_9:int) (D_3:int) (A_23:int) (B_13:int), ((iff ((and (not (((eq int) A_23) B_13))) (not (((eq int) C_9) D_3)))) (not (((eq int) ((plus_plus_int ((times_times_int A_23) C_9)) ((times_times_int B_13) D_3))) ((plus_plus_int ((times_times_int A_23) D_3)) ((times_times_int B_13) C_9)))))) of role axiom named fact_648_crossproduct__noteq
% 1.28/1.52 A new axiom: (forall (C_9:int) (D_3:int) (A_23:int) (B_13:int), ((iff ((and (not (((eq int) A_23) B_13))) (not (((eq int) C_9) D_3)))) (not (((eq int) ((plus_plus_int ((times_times_int A_23) C_9)) ((times_times_int B_13) D_3))) ((plus_plus_int ((times_times_int A_23) D_3)) ((times_times_int B_13) C_9))))))
% 1.28/1.52 FOF formula (forall (X_9:real) (Y_8:real) (Z_2:real), (((eq real) ((times_times_real X_9) ((plus_plus_real Y_8) Z_2))) ((plus_plus_real ((times_times_real X_9) Y_8)) ((times_times_real X_9) Z_2)))) of role axiom named fact_649_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J
% 1.28/1.52 A new axiom: (forall (X_9:real) (Y_8:real) (Z_2:real), (((eq real) ((times_times_real X_9) ((plus_plus_real Y_8) Z_2))) ((plus_plus_real ((times_times_real X_9) Y_8)) ((times_times_real X_9) Z_2))))
% 1.28/1.52 FOF formula (forall (X_9:nat) (Y_8:nat) (Z_2:nat), (((eq nat) ((times_times_nat X_9) ((plus_plus_nat Y_8) Z_2))) ((plus_plus_nat ((times_times_nat X_9) Y_8)) ((times_times_nat X_9) Z_2)))) of role axiom named fact_650_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J
% 1.28/1.52 A new axiom: (forall (X_9:nat) (Y_8:nat) (Z_2:nat), (((eq nat) ((times_times_nat X_9) ((plus_plus_nat Y_8) Z_2))) ((plus_plus_nat ((times_times_nat X_9) Y_8)) ((times_times_nat X_9) Z_2))))
% 1.28/1.52 FOF formula (forall (X_9:int) (Y_8:int) (Z_2:int), (((eq int) ((times_times_int X_9) ((plus_plus_int Y_8) Z_2))) ((plus_plus_int ((times_times_int X_9) Y_8)) ((times_times_int X_9) Z_2)))) of role axiom named fact_651_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J
% 1.28/1.52 A new axiom: (forall (X_9:int) (Y_8:int) (Z_2:int), (((eq int) ((times_times_int X_9) ((plus_plus_int Y_8) Z_2))) ((plus_plus_int ((times_times_int X_9) Y_8)) ((times_times_int X_9) Z_2))))
% 1.28/1.52 FOF formula (forall (N:nat), (((eq nat) (nat_1 (semiri1621563631at_int N))) N)) of role axiom named fact_652_nat__int
% 1.28/1.52 A new axiom: (forall (N:nat), (((eq nat) (nat_1 (semiri1621563631at_int N))) N))
% 1.28/1.52 FOF formula (forall (A_22:real), (((eq real) ((times_times_real A_22) one_one_real)) A_22)) of role axiom named fact_653_mult_Ocomm__neutral
% 1.28/1.52 A new axiom: (forall (A_22:real), (((eq real) ((times_times_real A_22) one_one_real)) A_22))
% 1.28/1.53 FOF formula (forall (A_22:nat), (((eq nat) ((times_times_nat A_22) one_one_nat)) A_22)) of role axiom named fact_654_mult_Ocomm__neutral
% 1.28/1.53 A new axiom: (forall (A_22:nat), (((eq nat) ((times_times_nat A_22) one_one_nat)) A_22))
% 1.28/1.53 FOF formula (forall (A_22:int), (((eq int) ((times_times_int A_22) one_one_int)) A_22)) of role axiom named fact_655_mult_Ocomm__neutral
% 1.28/1.53 A new axiom: (forall (A_22:int), (((eq int) ((times_times_int A_22) one_one_int)) A_22))
% 1.28/1.53 FOF formula (forall (A_21:real), (((eq real) ((times_times_real A_21) one_one_real)) A_21)) of role axiom named fact_656_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J
% 1.28/1.53 A new axiom: (forall (A_21:real), (((eq real) ((times_times_real A_21) one_one_real)) A_21))
% 1.28/1.53 FOF formula (forall (A_21:nat), (((eq nat) ((times_times_nat A_21) one_one_nat)) A_21)) of role axiom named fact_657_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J
% 1.28/1.53 A new axiom: (forall (A_21:nat), (((eq nat) ((times_times_nat A_21) one_one_nat)) A_21))
% 1.28/1.54 FOF formula (forall (A_21:int), (((eq int) ((times_times_int A_21) one_one_int)) A_21)) of role axiom named fact_658_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J
% 1.28/1.54 A new axiom: (forall (A_21:int), (((eq int) ((times_times_int A_21) one_one_int)) A_21))
% 1.28/1.54 FOF formula (forall (A_20:real), (((eq real) ((times_times_real A_20) one_one_real)) A_20)) of role axiom named fact_659_mult__1__right
% 1.28/1.54 A new axiom: (forall (A_20:real), (((eq real) ((times_times_real A_20) one_one_real)) A_20))
% 1.28/1.54 FOF formula (forall (A_20:nat), (((eq nat) ((times_times_nat A_20) one_one_nat)) A_20)) of role axiom named fact_660_mult__1__right
% 1.28/1.54 A new axiom: (forall (A_20:nat), (((eq nat) ((times_times_nat A_20) one_one_nat)) A_20))
% 1.28/1.54 FOF formula (forall (A_20:int), (((eq int) ((times_times_int A_20) one_one_int)) A_20)) of role axiom named fact_661_mult__1__right
% 1.28/1.54 A new axiom: (forall (A_20:int), (((eq int) ((times_times_int A_20) one_one_int)) A_20))
% 1.28/1.54 FOF formula (forall (A_19:real), (((eq real) ((times_times_real one_one_real) A_19)) A_19)) of role axiom named fact_662_mult__1
% 1.28/1.54 A new axiom: (forall (A_19:real), (((eq real) ((times_times_real one_one_real) A_19)) A_19))
% 1.28/1.54 FOF formula (forall (A_19:nat), (((eq nat) ((times_times_nat one_one_nat) A_19)) A_19)) of role axiom named fact_663_mult__1
% 1.28/1.54 A new axiom: (forall (A_19:nat), (((eq nat) ((times_times_nat one_one_nat) A_19)) A_19))
% 1.28/1.54 FOF formula (forall (A_19:int), (((eq int) ((times_times_int one_one_int) A_19)) A_19)) of role axiom named fact_664_mult__1
% 1.28/1.54 A new axiom: (forall (A_19:int), (((eq int) ((times_times_int one_one_int) A_19)) A_19))
% 1.28/1.54 FOF formula (forall (A_18:real), (((eq real) ((times_times_real one_one_real) A_18)) A_18)) of role axiom named fact_665_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J
% 1.28/1.54 A new axiom: (forall (A_18:real), (((eq real) ((times_times_real one_one_real) A_18)) A_18))
% 1.28/1.54 FOF formula (forall (A_18:nat), (((eq nat) ((times_times_nat one_one_nat) A_18)) A_18)) of role axiom named fact_666_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J
% 1.28/1.54 A new axiom: (forall (A_18:nat), (((eq nat) ((times_times_nat one_one_nat) A_18)) A_18))
% 1.28/1.54 FOF formula (forall (A_18:int), (((eq int) ((times_times_int one_one_int) A_18)) A_18)) of role axiom named fact_667_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J
% 1.28/1.54 A new axiom: (forall (A_18:int), (((eq int) ((times_times_int one_one_int) A_18)) A_18))
% 1.28/1.54 FOF formula (forall (A_17:real), (((eq real) ((times_times_real one_one_real) A_17)) A_17)) of role axiom named fact_668_mult__1__left
% 1.28/1.54 A new axiom: (forall (A_17:real), (((eq real) ((times_times_real one_one_real) A_17)) A_17))
% 1.28/1.54 FOF formula (forall (A_17:nat), (((eq nat) ((times_times_nat one_one_nat) A_17)) A_17)) of role axiom named fact_669_mult__1__left
% 1.28/1.54 A new axiom: (forall (A_17:nat), (((eq nat) ((times_times_nat one_one_nat) A_17)) A_17))
% 1.28/1.54 FOF formula (forall (A_17:int), (((eq int) ((times_times_int one_one_int) A_17)) A_17)) of role axiom named fact_670_mult__1__left
% 1.28/1.54 A new axiom: (forall (A_17:int), (((eq int) ((times_times_int one_one_int) A_17)) A_17))
% 1.28/1.56 FOF formula (forall (C_8:real) (A_16:real) (B_12:real), (((ord_less_eq_real ((plus_plus_real C_8) A_16)) ((plus_plus_real C_8) B_12))->((ord_less_eq_real A_16) B_12))) of role axiom named fact_671_add__le__imp__le__left
% 1.28/1.56 A new axiom: (forall (C_8:real) (A_16:real) (B_12:real), (((ord_less_eq_real ((plus_plus_real C_8) A_16)) ((plus_plus_real C_8) B_12))->((ord_less_eq_real A_16) B_12)))
% 1.28/1.56 FOF formula (forall (C_8:nat) (A_16:nat) (B_12:nat), (((ord_less_eq_nat ((plus_plus_nat C_8) A_16)) ((plus_plus_nat C_8) B_12))->((ord_less_eq_nat A_16) B_12))) of role axiom named fact_672_add__le__imp__le__left
% 1.28/1.56 A new axiom: (forall (C_8:nat) (A_16:nat) (B_12:nat), (((ord_less_eq_nat ((plus_plus_nat C_8) A_16)) ((plus_plus_nat C_8) B_12))->((ord_less_eq_nat A_16) B_12)))
% 1.28/1.56 FOF formula (forall (C_8:int) (A_16:int) (B_12:int), (((ord_less_eq_int ((plus_plus_int C_8) A_16)) ((plus_plus_int C_8) B_12))->((ord_less_eq_int A_16) B_12))) of role axiom named fact_673_add__le__imp__le__left
% 1.28/1.56 A new axiom: (forall (C_8:int) (A_16:int) (B_12:int), (((ord_less_eq_int ((plus_plus_int C_8) A_16)) ((plus_plus_int C_8) B_12))->((ord_less_eq_int A_16) B_12)))
% 1.28/1.56 FOF formula (forall (A_15:real) (C_7:real) (B_11:real), (((ord_less_eq_real ((plus_plus_real A_15) C_7)) ((plus_plus_real B_11) C_7))->((ord_less_eq_real A_15) B_11))) of role axiom named fact_674_add__le__imp__le__right
% 1.28/1.56 A new axiom: (forall (A_15:real) (C_7:real) (B_11:real), (((ord_less_eq_real ((plus_plus_real A_15) C_7)) ((plus_plus_real B_11) C_7))->((ord_less_eq_real A_15) B_11)))
% 1.28/1.56 FOF formula (forall (A_15:nat) (C_7:nat) (B_11:nat), (((ord_less_eq_nat ((plus_plus_nat A_15) C_7)) ((plus_plus_nat B_11) C_7))->((ord_less_eq_nat A_15) B_11))) of role axiom named fact_675_add__le__imp__le__right
% 1.28/1.56 A new axiom: (forall (A_15:nat) (C_7:nat) (B_11:nat), (((ord_less_eq_nat ((plus_plus_nat A_15) C_7)) ((plus_plus_nat B_11) C_7))->((ord_less_eq_nat A_15) B_11)))
% 1.28/1.56 FOF formula (forall (A_15:int) (C_7:int) (B_11:int), (((ord_less_eq_int ((plus_plus_int A_15) C_7)) ((plus_plus_int B_11) C_7))->((ord_less_eq_int A_15) B_11))) of role axiom named fact_676_add__le__imp__le__right
% 1.28/1.56 A new axiom: (forall (A_15:int) (C_7:int) (B_11:int), (((ord_less_eq_int ((plus_plus_int A_15) C_7)) ((plus_plus_int B_11) C_7))->((ord_less_eq_int A_15) B_11)))
% 1.28/1.56 FOF formula (forall (C_6:real) (D_2:real) (A_14:real) (B_10:real), (((ord_less_eq_real A_14) B_10)->(((ord_less_eq_real C_6) D_2)->((ord_less_eq_real ((plus_plus_real A_14) C_6)) ((plus_plus_real B_10) D_2))))) of role axiom named fact_677_add__mono
% 1.28/1.56 A new axiom: (forall (C_6:real) (D_2:real) (A_14:real) (B_10:real), (((ord_less_eq_real A_14) B_10)->(((ord_less_eq_real C_6) D_2)->((ord_less_eq_real ((plus_plus_real A_14) C_6)) ((plus_plus_real B_10) D_2)))))
% 1.28/1.56 FOF formula (forall (C_6:nat) (D_2:nat) (A_14:nat) (B_10:nat), (((ord_less_eq_nat A_14) B_10)->(((ord_less_eq_nat C_6) D_2)->((ord_less_eq_nat ((plus_plus_nat A_14) C_6)) ((plus_plus_nat B_10) D_2))))) of role axiom named fact_678_add__mono
% 1.28/1.56 A new axiom: (forall (C_6:nat) (D_2:nat) (A_14:nat) (B_10:nat), (((ord_less_eq_nat A_14) B_10)->(((ord_less_eq_nat C_6) D_2)->((ord_less_eq_nat ((plus_plus_nat A_14) C_6)) ((plus_plus_nat B_10) D_2)))))
% 1.28/1.56 FOF formula (forall (C_6:int) (D_2:int) (A_14:int) (B_10:int), (((ord_less_eq_int A_14) B_10)->(((ord_less_eq_int C_6) D_2)->((ord_less_eq_int ((plus_plus_int A_14) C_6)) ((plus_plus_int B_10) D_2))))) of role axiom named fact_679_add__mono
% 1.28/1.56 A new axiom: (forall (C_6:int) (D_2:int) (A_14:int) (B_10:int), (((ord_less_eq_int A_14) B_10)->(((ord_less_eq_int C_6) D_2)->((ord_less_eq_int ((plus_plus_int A_14) C_6)) ((plus_plus_int B_10) D_2)))))
% 1.28/1.56 FOF formula (forall (C_5:real) (A_13:real) (B_9:real), (((ord_less_eq_real A_13) B_9)->((ord_less_eq_real ((plus_plus_real C_5) A_13)) ((plus_plus_real C_5) B_9)))) of role axiom named fact_680_add__left__mono
% 1.28/1.56 A new axiom: (forall (C_5:real) (A_13:real) (B_9:real), (((ord_less_eq_real A_13) B_9)->((ord_less_eq_real ((plus_plus_real C_5) A_13)) ((plus_plus_real C_5) B_9))))
% 1.28/1.56 FOF formula (forall (C_5:nat) (A_13:nat) (B_9:nat), (((ord_less_eq_nat A_13) B_9)->((ord_less_eq_nat ((plus_plus_nat C_5) A_13)) ((plus_plus_nat C_5) B_9)))) of role axiom named fact_681_add__left__mono
% 1.28/1.57 A new axiom: (forall (C_5:nat) (A_13:nat) (B_9:nat), (((ord_less_eq_nat A_13) B_9)->((ord_less_eq_nat ((plus_plus_nat C_5) A_13)) ((plus_plus_nat C_5) B_9))))
% 1.28/1.57 FOF formula (forall (C_5:int) (A_13:int) (B_9:int), (((ord_less_eq_int A_13) B_9)->((ord_less_eq_int ((plus_plus_int C_5) A_13)) ((plus_plus_int C_5) B_9)))) of role axiom named fact_682_add__left__mono
% 1.28/1.57 A new axiom: (forall (C_5:int) (A_13:int) (B_9:int), (((ord_less_eq_int A_13) B_9)->((ord_less_eq_int ((plus_plus_int C_5) A_13)) ((plus_plus_int C_5) B_9))))
% 1.28/1.57 FOF formula (forall (C_4:real) (A_12:real) (B_8:real), (((ord_less_eq_real A_12) B_8)->((ord_less_eq_real ((plus_plus_real A_12) C_4)) ((plus_plus_real B_8) C_4)))) of role axiom named fact_683_add__right__mono
% 1.28/1.57 A new axiom: (forall (C_4:real) (A_12:real) (B_8:real), (((ord_less_eq_real A_12) B_8)->((ord_less_eq_real ((plus_plus_real A_12) C_4)) ((plus_plus_real B_8) C_4))))
% 1.28/1.57 FOF formula (forall (C_4:nat) (A_12:nat) (B_8:nat), (((ord_less_eq_nat A_12) B_8)->((ord_less_eq_nat ((plus_plus_nat A_12) C_4)) ((plus_plus_nat B_8) C_4)))) of role axiom named fact_684_add__right__mono
% 1.28/1.57 A new axiom: (forall (C_4:nat) (A_12:nat) (B_8:nat), (((ord_less_eq_nat A_12) B_8)->((ord_less_eq_nat ((plus_plus_nat A_12) C_4)) ((plus_plus_nat B_8) C_4))))
% 1.28/1.57 FOF formula (forall (C_4:int) (A_12:int) (B_8:int), (((ord_less_eq_int A_12) B_8)->((ord_less_eq_int ((plus_plus_int A_12) C_4)) ((plus_plus_int B_8) C_4)))) of role axiom named fact_685_add__right__mono
% 1.28/1.57 A new axiom: (forall (C_4:int) (A_12:int) (B_8:int), (((ord_less_eq_int A_12) B_8)->((ord_less_eq_int ((plus_plus_int A_12) C_4)) ((plus_plus_int B_8) C_4))))
% 1.28/1.57 FOF formula (forall (C_3:real) (A_11:real) (B_7:real), ((iff ((ord_less_eq_real ((plus_plus_real C_3) A_11)) ((plus_plus_real C_3) B_7))) ((ord_less_eq_real A_11) B_7))) of role axiom named fact_686_add__le__cancel__left
% 1.28/1.57 A new axiom: (forall (C_3:real) (A_11:real) (B_7:real), ((iff ((ord_less_eq_real ((plus_plus_real C_3) A_11)) ((plus_plus_real C_3) B_7))) ((ord_less_eq_real A_11) B_7)))
% 1.28/1.57 FOF formula (forall (C_3:nat) (A_11:nat) (B_7:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat C_3) A_11)) ((plus_plus_nat C_3) B_7))) ((ord_less_eq_nat A_11) B_7))) of role axiom named fact_687_add__le__cancel__left
% 1.28/1.57 A new axiom: (forall (C_3:nat) (A_11:nat) (B_7:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat C_3) A_11)) ((plus_plus_nat C_3) B_7))) ((ord_less_eq_nat A_11) B_7)))
% 1.28/1.57 FOF formula (forall (C_3:int) (A_11:int) (B_7:int), ((iff ((ord_less_eq_int ((plus_plus_int C_3) A_11)) ((plus_plus_int C_3) B_7))) ((ord_less_eq_int A_11) B_7))) of role axiom named fact_688_add__le__cancel__left
% 1.28/1.57 A new axiom: (forall (C_3:int) (A_11:int) (B_7:int), ((iff ((ord_less_eq_int ((plus_plus_int C_3) A_11)) ((plus_plus_int C_3) B_7))) ((ord_less_eq_int A_11) B_7)))
% 1.28/1.57 FOF formula (forall (A_10:real) (C_2:real) (B_6:real), ((iff ((ord_less_eq_real ((plus_plus_real A_10) C_2)) ((plus_plus_real B_6) C_2))) ((ord_less_eq_real A_10) B_6))) of role axiom named fact_689_add__le__cancel__right
% 1.28/1.57 A new axiom: (forall (A_10:real) (C_2:real) (B_6:real), ((iff ((ord_less_eq_real ((plus_plus_real A_10) C_2)) ((plus_plus_real B_6) C_2))) ((ord_less_eq_real A_10) B_6)))
% 1.28/1.57 FOF formula (forall (A_10:nat) (C_2:nat) (B_6:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat A_10) C_2)) ((plus_plus_nat B_6) C_2))) ((ord_less_eq_nat A_10) B_6))) of role axiom named fact_690_add__le__cancel__right
% 1.28/1.57 A new axiom: (forall (A_10:nat) (C_2:nat) (B_6:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat A_10) C_2)) ((plus_plus_nat B_6) C_2))) ((ord_less_eq_nat A_10) B_6)))
% 1.28/1.57 FOF formula (forall (A_10:int) (C_2:int) (B_6:int), ((iff ((ord_less_eq_int ((plus_plus_int A_10) C_2)) ((plus_plus_int B_6) C_2))) ((ord_less_eq_int A_10) B_6))) of role axiom named fact_691_add__le__cancel__right
% 1.28/1.57 A new axiom: (forall (A_10:int) (C_2:int) (B_6:int), ((iff ((ord_less_eq_int ((plus_plus_int A_10) C_2)) ((plus_plus_int B_6) C_2))) ((ord_less_eq_int A_10) B_6)))
% 1.28/1.57 FOF formula (forall (N:nat) (J:nat) (K:nat), (((ord_less_nat J) K)->((ord_less_nat ((minus_minus_nat J) N)) K))) of role axiom named fact_692_less__imp__diff__less
% 1.38/1.59 A new axiom: (forall (N:nat) (J:nat) (K:nat), (((ord_less_nat J) K)->((ord_less_nat ((minus_minus_nat J) N)) K)))
% 1.38/1.59 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_693_diff__less__mono2
% 1.38/1.59 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)))))
% 1.38/1.59 FOF formula (forall (A_9:real) (N_7:nat), (((eq real) ((times_times_real ((power_power_real A_9) N_7)) A_9)) ((times_times_real A_9) ((power_power_real A_9) N_7)))) of role axiom named fact_694_power__commutes
% 1.38/1.59 A new axiom: (forall (A_9:real) (N_7:nat), (((eq real) ((times_times_real ((power_power_real A_9) N_7)) A_9)) ((times_times_real A_9) ((power_power_real A_9) N_7))))
% 1.38/1.59 FOF formula (forall (A_9:nat) (N_7:nat), (((eq nat) ((times_times_nat ((power_power_nat A_9) N_7)) A_9)) ((times_times_nat A_9) ((power_power_nat A_9) N_7)))) of role axiom named fact_695_power__commutes
% 1.38/1.59 A new axiom: (forall (A_9:nat) (N_7:nat), (((eq nat) ((times_times_nat ((power_power_nat A_9) N_7)) A_9)) ((times_times_nat A_9) ((power_power_nat A_9) N_7))))
% 1.38/1.59 FOF formula (forall (A_9:int) (N_7:nat), (((eq int) ((times_times_int ((power_power_int A_9) N_7)) A_9)) ((times_times_int A_9) ((power_power_int A_9) N_7)))) of role axiom named fact_696_power__commutes
% 1.38/1.59 A new axiom: (forall (A_9:int) (N_7:nat), (((eq int) ((times_times_int ((power_power_int A_9) N_7)) A_9)) ((times_times_int A_9) ((power_power_int A_9) N_7))))
% 1.38/1.59 FOF formula (forall (A_8:real) (B_5:real) (N_6:nat), (((eq real) ((power_power_real ((times_times_real A_8) B_5)) N_6)) ((times_times_real ((power_power_real A_8) N_6)) ((power_power_real B_5) N_6)))) of role axiom named fact_697_power__mult__distrib
% 1.38/1.59 A new axiom: (forall (A_8:real) (B_5:real) (N_6:nat), (((eq real) ((power_power_real ((times_times_real A_8) B_5)) N_6)) ((times_times_real ((power_power_real A_8) N_6)) ((power_power_real B_5) N_6))))
% 1.38/1.59 FOF formula (forall (A_8:nat) (B_5:nat) (N_6:nat), (((eq nat) ((power_power_nat ((times_times_nat A_8) B_5)) N_6)) ((times_times_nat ((power_power_nat A_8) N_6)) ((power_power_nat B_5) N_6)))) of role axiom named fact_698_power__mult__distrib
% 1.38/1.59 A new axiom: (forall (A_8:nat) (B_5:nat) (N_6:nat), (((eq nat) ((power_power_nat ((times_times_nat A_8) B_5)) N_6)) ((times_times_nat ((power_power_nat A_8) N_6)) ((power_power_nat B_5) N_6))))
% 1.38/1.59 FOF formula (forall (A_8:int) (B_5:int) (N_6:nat), (((eq int) ((power_power_int ((times_times_int A_8) B_5)) N_6)) ((times_times_int ((power_power_int A_8) N_6)) ((power_power_int B_5) N_6)))) of role axiom named fact_699_power__mult__distrib
% 1.38/1.59 A new axiom: (forall (A_8:int) (B_5:int) (N_6:nat), (((eq int) ((power_power_int ((times_times_int A_8) B_5)) N_6)) ((times_times_int ((power_power_int A_8) N_6)) ((power_power_int B_5) N_6))))
% 1.38/1.59 FOF formula (forall (X_8:real) (Y_7:real) (Q_2:nat), (((eq real) ((power_power_real ((times_times_real X_8) Y_7)) Q_2)) ((times_times_real ((power_power_real X_8) Q_2)) ((power_power_real Y_7) Q_2)))) of role axiom named fact_700_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J
% 1.38/1.59 A new axiom: (forall (X_8:real) (Y_7:real) (Q_2:nat), (((eq real) ((power_power_real ((times_times_real X_8) Y_7)) Q_2)) ((times_times_real ((power_power_real X_8) Q_2)) ((power_power_real Y_7) Q_2))))
% 1.38/1.59 FOF formula (forall (X_8:nat) (Y_7:nat) (Q_2:nat), (((eq nat) ((power_power_nat ((times_times_nat X_8) Y_7)) Q_2)) ((times_times_nat ((power_power_nat X_8) Q_2)) ((power_power_nat Y_7) Q_2)))) of role axiom named fact_701_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J
% 1.38/1.59 A new axiom: (forall (X_8:nat) (Y_7:nat) (Q_2:nat), (((eq nat) ((power_power_nat ((times_times_nat X_8) Y_7)) Q_2)) ((times_times_nat ((power_power_nat X_8) Q_2)) ((power_power_nat Y_7) Q_2))))
% 1.38/1.59 FOF formula (forall (X_8:int) (Y_7:int) (Q_2:nat), (((eq int) ((power_power_int ((times_times_int X_8) Y_7)) Q_2)) ((times_times_int ((power_power_int X_8) Q_2)) ((power_power_int Y_7) Q_2)))) of role axiom named fact_702_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J
% 1.41/1.61 A new axiom: (forall (X_8:int) (Y_7:int) (Q_2:nat), (((eq int) ((power_power_int ((times_times_int X_8) Y_7)) Q_2)) ((times_times_int ((power_power_int X_8) Q_2)) ((power_power_int Y_7) Q_2))))
% 1.41/1.61 FOF formula (forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) N)) N)) M)) of role axiom named fact_703_diff__add__inverse2
% 1.41/1.61 A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) N)) N)) M))
% 1.41/1.61 FOF formula (forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat N) M)) N)) M)) of role axiom named fact_704_diff__add__inverse
% 1.41/1.61 A new axiom: (forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat N) M)) N)) M))
% 1.41/1.61 FOF formula (forall (I_1:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J)) K)) ((minus_minus_nat I_1) ((plus_plus_nat J) K)))) of role axiom named fact_705_diff__diff__left
% 1.41/1.61 A new axiom: (forall (I_1:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J)) K)) ((minus_minus_nat I_1) ((plus_plus_nat J) K))))
% 1.41/1.61 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_706_Nat_Odiff__cancel
% 1.41/1.61 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)))
% 1.41/1.61 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_707_diff__cancel2
% 1.41/1.61 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)))
% 1.41/1.61 FOF formula (forall (W:int), (((eq int) ((times_times_int pls) W)) pls)) of role axiom named fact_708_mult__Pls
% 1.41/1.61 A new axiom: (forall (W:int), (((eq int) ((times_times_int pls) W)) pls))
% 1.41/1.61 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_709_mult__Bit0
% 1.41/1.61 A new axiom: (forall (K:int) (L:int), (((eq int) ((times_times_int (bit0 K)) L)) (bit0 ((times_times_int K) L))))
% 1.41/1.61 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_710_rel__simps_I34_J
% 1.41/1.61 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit1 L))) ((ord_less_eq_int K) L)))
% 1.41/1.61 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_711_less__eq__int__code_I16_J
% 1.41/1.61 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2)))
% 1.41/1.61 FOF formula ((ord_less_eq_int pls) pls) of role axiom named fact_712_rel__simps_I19_J
% 1.41/1.61 A new axiom: ((ord_less_eq_int pls) pls)
% 1.41/1.61 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_713_rel__simps_I31_J
% 1.41/1.61 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit0 L))) ((ord_less_eq_int K) L)))
% 1.41/1.61 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_714_less__eq__int__code_I13_J
% 1.41/1.61 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit0 K2))) ((ord_less_eq_int K1) K2)))
% 1.41/1.61 FOF formula ((ord_less_eq_int zero_zero_int) zero_zero_int) of role axiom named fact_715_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J
% 1.41/1.61 A new axiom: ((ord_less_eq_int zero_zero_int) zero_zero_int)
% 1.41/1.61 FOF formula (forall (Z:int), (((eq int) ((times_times_int one_one_int) Z)) Z)) of role axiom named fact_716_zmult__1
% 1.41/1.61 A new axiom: (forall (Z:int), (((eq int) ((times_times_int one_one_int) Z)) Z))
% 1.41/1.61 FOF formula (forall (Z:int), (((eq int) ((times_times_int Z) one_one_int)) Z)) of role axiom named fact_717_zmult__1__right
% 1.41/1.63 A new axiom: (forall (Z:int), (((eq int) ((times_times_int Z) one_one_int)) Z))
% 1.41/1.63 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_718_zless__le
% 1.41/1.63 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)))))
% 1.41/1.63 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_719_zadd__zmult__distrib2
% 1.41/1.63 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))))
% 1.41/1.63 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_720_zadd__zmult__distrib
% 1.41/1.63 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))))
% 1.41/1.63 FOF formula (forall (K:int) (I_1:int) (J:int), (((ord_less_eq_int I_1) J)->((ord_less_eq_int ((plus_plus_int K) I_1)) ((plus_plus_int K) J)))) of role axiom named fact_721_zadd__left__mono
% 1.41/1.63 A new axiom: (forall (K:int) (I_1:int) (J:int), (((ord_less_eq_int I_1) J)->((ord_less_eq_int ((plus_plus_int K) I_1)) ((plus_plus_int K) J))))
% 1.41/1.63 FOF formula (forall (V_1:int) (W:int), (((eq int) ((times_times_int (number_number_of_int V_1)) (number_number_of_int W))) (number_number_of_int ((times_times_int V_1) W)))) of role axiom named fact_722_times__numeral__code_I5_J
% 1.41/1.63 A new axiom: (forall (V_1:int) (W:int), (((eq int) ((times_times_int (number_number_of_int V_1)) (number_number_of_int W))) (number_number_of_int ((times_times_int V_1) W))))
% 1.41/1.63 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_723_less__eq__number__of__int__code
% 1.41/1.63 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)))
% 1.41/1.63 FOF formula (forall (V_4:real) (U_2:real) (Y_6:real) (X_7:real) (A_7:real), (((ord_less_eq_real X_7) A_7)->(((ord_less_eq_real Y_6) A_7)->(((ord_less_eq_real zero_zero_real) U_2)->(((ord_less_eq_real zero_zero_real) V_4)->((((eq real) ((plus_plus_real U_2) V_4)) one_one_real)->((ord_less_eq_real ((plus_plus_real ((times_times_real U_2) X_7)) ((times_times_real V_4) Y_6))) A_7))))))) of role axiom named fact_724_convex__bound__le
% 1.41/1.63 A new axiom: (forall (V_4:real) (U_2:real) (Y_6:real) (X_7:real) (A_7:real), (((ord_less_eq_real X_7) A_7)->(((ord_less_eq_real Y_6) A_7)->(((ord_less_eq_real zero_zero_real) U_2)->(((ord_less_eq_real zero_zero_real) V_4)->((((eq real) ((plus_plus_real U_2) V_4)) one_one_real)->((ord_less_eq_real ((plus_plus_real ((times_times_real U_2) X_7)) ((times_times_real V_4) Y_6))) A_7)))))))
% 1.41/1.63 FOF formula (forall (V_4:int) (U_2:int) (Y_6:int) (X_7:int) (A_7:int), (((ord_less_eq_int X_7) A_7)->(((ord_less_eq_int Y_6) A_7)->(((ord_less_eq_int zero_zero_int) U_2)->(((ord_less_eq_int zero_zero_int) V_4)->((((eq int) ((plus_plus_int U_2) V_4)) one_one_int)->((ord_less_eq_int ((plus_plus_int ((times_times_int U_2) X_7)) ((times_times_int V_4) Y_6))) A_7))))))) of role axiom named fact_725_convex__bound__le
% 1.41/1.63 A new axiom: (forall (V_4:int) (U_2:int) (Y_6:int) (X_7:int) (A_7:int), (((ord_less_eq_int X_7) A_7)->(((ord_less_eq_int Y_6) A_7)->(((ord_less_eq_int zero_zero_int) U_2)->(((ord_less_eq_int zero_zero_int) V_4)->((((eq int) ((plus_plus_int U_2) V_4)) one_one_int)->((ord_less_eq_int ((plus_plus_int ((times_times_int U_2) X_7)) ((times_times_int V_4) Y_6))) A_7)))))))
% 1.41/1.63 FOF formula (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((iff ((ord_less_nat (nat_1 X)) (nat_1 Y))) ((ord_less_int X) Y))))) of role axiom named fact_726_transfer__nat__int__relations_I2_J
% 1.41/1.65 A new axiom: (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((iff ((ord_less_nat (nat_1 X)) (nat_1 Y))) ((ord_less_int X) Y)))))
% 1.41/1.65 FOF formula (forall (Z:int) (W:int), (((ord_less_eq_int zero_zero_int) W)->((iff ((ord_less_nat (nat_1 W)) (nat_1 Z))) ((ord_less_int W) Z)))) of role axiom named fact_727_nat__less__eq__zless
% 1.41/1.65 A new axiom: (forall (Z:int) (W:int), (((ord_less_eq_int zero_zero_int) W)->((iff ((ord_less_nat (nat_1 W)) (nat_1 Z))) ((ord_less_int W) Z))))
% 1.41/1.65 FOF formula (forall (Y_5:int), ((iff ((ord_less_eq_real zero_zero_real) (number267125858f_real Y_5))) ((ord_less_eq_int pls) Y_5))) of role axiom named fact_728_le__special_I1_J
% 1.41/1.65 A new axiom: (forall (Y_5:int), ((iff ((ord_less_eq_real zero_zero_real) (number267125858f_real Y_5))) ((ord_less_eq_int pls) Y_5)))
% 1.41/1.65 FOF formula (forall (Y_5:int), ((iff ((ord_less_eq_int zero_zero_int) (number_number_of_int Y_5))) ((ord_less_eq_int pls) Y_5))) of role axiom named fact_729_le__special_I1_J
% 1.41/1.65 A new axiom: (forall (Y_5:int), ((iff ((ord_less_eq_int zero_zero_int) (number_number_of_int Y_5))) ((ord_less_eq_int pls) Y_5)))
% 1.41/1.65 FOF formula (forall (X_6:int), ((iff ((ord_less_eq_real (number267125858f_real X_6)) zero_zero_real)) ((ord_less_eq_int X_6) pls))) of role axiom named fact_730_le__special_I3_J
% 1.41/1.65 A new axiom: (forall (X_6:int), ((iff ((ord_less_eq_real (number267125858f_real X_6)) zero_zero_real)) ((ord_less_eq_int X_6) pls)))
% 1.41/1.65 FOF formula (forall (X_6:int), ((iff ((ord_less_eq_int (number_number_of_int X_6)) zero_zero_int)) ((ord_less_eq_int X_6) pls))) of role axiom named fact_731_le__special_I3_J
% 1.41/1.65 A new axiom: (forall (X_6:int), ((iff ((ord_less_eq_int (number_number_of_int X_6)) zero_zero_int)) ((ord_less_eq_int X_6) pls)))
% 1.41/1.65 FOF formula (forall (A_6:real) (N_5:nat) (N_4:nat), (((ord_less_eq_nat N_5) N_4)->(((ord_less_eq_real zero_zero_real) A_6)->(((ord_less_eq_real A_6) one_one_real)->((ord_less_eq_real ((power_power_real A_6) N_4)) ((power_power_real A_6) N_5)))))) of role axiom named fact_732_power__decreasing
% 1.41/1.65 A new axiom: (forall (A_6:real) (N_5:nat) (N_4:nat), (((ord_less_eq_nat N_5) N_4)->(((ord_less_eq_real zero_zero_real) A_6)->(((ord_less_eq_real A_6) one_one_real)->((ord_less_eq_real ((power_power_real A_6) N_4)) ((power_power_real A_6) N_5))))))
% 1.41/1.65 FOF formula (forall (A_6:nat) (N_5:nat) (N_4:nat), (((ord_less_eq_nat N_5) N_4)->(((ord_less_eq_nat zero_zero_nat) A_6)->(((ord_less_eq_nat A_6) one_one_nat)->((ord_less_eq_nat ((power_power_nat A_6) N_4)) ((power_power_nat A_6) N_5)))))) of role axiom named fact_733_power__decreasing
% 1.41/1.65 A new axiom: (forall (A_6:nat) (N_5:nat) (N_4:nat), (((ord_less_eq_nat N_5) N_4)->(((ord_less_eq_nat zero_zero_nat) A_6)->(((ord_less_eq_nat A_6) one_one_nat)->((ord_less_eq_nat ((power_power_nat A_6) N_4)) ((power_power_nat A_6) N_5))))))
% 1.41/1.65 FOF formula (forall (A_6:int) (N_5:nat) (N_4:nat), (((ord_less_eq_nat N_5) N_4)->(((ord_less_eq_int zero_zero_int) A_6)->(((ord_less_eq_int A_6) one_one_int)->((ord_less_eq_int ((power_power_int A_6) N_4)) ((power_power_int A_6) N_5)))))) of role axiom named fact_734_power__decreasing
% 1.41/1.65 A new axiom: (forall (A_6:int) (N_5:nat) (N_4:nat), (((ord_less_eq_nat N_5) N_4)->(((ord_less_eq_int zero_zero_int) A_6)->(((ord_less_eq_int A_6) one_one_int)->((ord_less_eq_int ((power_power_int A_6) N_4)) ((power_power_int A_6) N_5))))))
% 1.41/1.65 FOF formula (forall (X_5:nat) (Y_4:nat) (B_4:real), (((ord_less_real one_one_real) B_4)->((iff ((ord_less_eq_real ((power_power_real B_4) X_5)) ((power_power_real B_4) Y_4))) ((ord_less_eq_nat X_5) Y_4)))) of role axiom named fact_735_power__increasing__iff
% 1.41/1.65 A new axiom: (forall (X_5:nat) (Y_4:nat) (B_4:real), (((ord_less_real one_one_real) B_4)->((iff ((ord_less_eq_real ((power_power_real B_4) X_5)) ((power_power_real B_4) Y_4))) ((ord_less_eq_nat X_5) Y_4))))
% 1.41/1.65 FOF formula (forall (X_5:nat) (Y_4:nat) (B_4:nat), (((ord_less_nat one_one_nat) B_4)->((iff ((ord_less_eq_nat ((power_power_nat B_4) X_5)) ((power_power_nat B_4) Y_4))) ((ord_less_eq_nat X_5) Y_4)))) of role axiom named fact_736_power__increasing__iff
% 1.41/1.67 A new axiom: (forall (X_5:nat) (Y_4:nat) (B_4:nat), (((ord_less_nat one_one_nat) B_4)->((iff ((ord_less_eq_nat ((power_power_nat B_4) X_5)) ((power_power_nat B_4) Y_4))) ((ord_less_eq_nat X_5) Y_4))))
% 1.41/1.67 FOF formula (forall (X_5:nat) (Y_4:nat) (B_4:int), (((ord_less_int one_one_int) B_4)->((iff ((ord_less_eq_int ((power_power_int B_4) X_5)) ((power_power_int B_4) Y_4))) ((ord_less_eq_nat X_5) Y_4)))) of role axiom named fact_737_power__increasing__iff
% 1.41/1.67 A new axiom: (forall (X_5:nat) (Y_4:nat) (B_4:int), (((ord_less_int one_one_int) B_4)->((iff ((ord_less_eq_int ((power_power_int B_4) X_5)) ((power_power_int B_4) Y_4))) ((ord_less_eq_nat X_5) Y_4))))
% 1.41/1.67 FOF formula (forall (M_2:nat) (N_3:nat) (A_5:real), (((ord_less_real one_one_real) A_5)->(((ord_less_eq_real ((power_power_real A_5) M_2)) ((power_power_real A_5) N_3))->((ord_less_eq_nat M_2) N_3)))) of role axiom named fact_738_power__le__imp__le__exp
% 1.41/1.67 A new axiom: (forall (M_2:nat) (N_3:nat) (A_5:real), (((ord_less_real one_one_real) A_5)->(((ord_less_eq_real ((power_power_real A_5) M_2)) ((power_power_real A_5) N_3))->((ord_less_eq_nat M_2) N_3))))
% 1.41/1.67 FOF formula (forall (M_2:nat) (N_3:nat) (A_5:nat), (((ord_less_nat one_one_nat) A_5)->(((ord_less_eq_nat ((power_power_nat A_5) M_2)) ((power_power_nat A_5) N_3))->((ord_less_eq_nat M_2) N_3)))) of role axiom named fact_739_power__le__imp__le__exp
% 1.41/1.67 A new axiom: (forall (M_2:nat) (N_3:nat) (A_5:nat), (((ord_less_nat one_one_nat) A_5)->(((ord_less_eq_nat ((power_power_nat A_5) M_2)) ((power_power_nat A_5) N_3))->((ord_less_eq_nat M_2) N_3))))
% 1.41/1.67 FOF formula (forall (M_2:nat) (N_3:nat) (A_5:int), (((ord_less_int one_one_int) A_5)->(((ord_less_eq_int ((power_power_int A_5) M_2)) ((power_power_int A_5) N_3))->((ord_less_eq_nat M_2) N_3)))) of role axiom named fact_740_power__le__imp__le__exp
% 1.41/1.67 A new axiom: (forall (M_2:nat) (N_3:nat) (A_5:int), (((ord_less_int one_one_int) A_5)->(((ord_less_eq_int ((power_power_int A_5) M_2)) ((power_power_int A_5) N_3))->((ord_less_eq_nat M_2) N_3))))
% 1.41/1.67 FOF formula (forall (M:nat) (W:int), ((iff (((eq nat) M) (nat_1 W))) ((and (((ord_less_eq_int zero_zero_int) W)->(((eq int) W) (semiri1621563631at_int M)))) ((((ord_less_eq_int zero_zero_int) W)->False)->(((eq nat) M) zero_zero_nat))))) of role axiom named fact_741_nat__eq__iff2
% 1.41/1.67 A new axiom: (forall (M:nat) (W:int), ((iff (((eq nat) M) (nat_1 W))) ((and (((ord_less_eq_int zero_zero_int) W)->(((eq int) W) (semiri1621563631at_int M)))) ((((ord_less_eq_int zero_zero_int) W)->False)->(((eq nat) M) zero_zero_nat)))))
% 1.41/1.67 FOF formula (forall (W:int) (M:nat), ((iff (((eq nat) (nat_1 W)) M)) ((and (((ord_less_eq_int zero_zero_int) W)->(((eq int) W) (semiri1621563631at_int M)))) ((((ord_less_eq_int zero_zero_int) W)->False)->(((eq nat) M) zero_zero_nat))))) of role axiom named fact_742_nat__eq__iff
% 1.41/1.67 A new axiom: (forall (W:int) (M:nat), ((iff (((eq nat) (nat_1 W)) M)) ((and (((ord_less_eq_int zero_zero_int) W)->(((eq int) W) (semiri1621563631at_int M)))) ((((ord_less_eq_int zero_zero_int) W)->False)->(((eq nat) M) zero_zero_nat)))))
% 1.41/1.67 FOF formula (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->(((eq nat) ((plus_plus_nat (nat_1 X)) (nat_1 Y))) (nat_1 ((plus_plus_int X) Y)))))) of role axiom named fact_743_Nat__Transfer_Otransfer__nat__int__functions_I1_J
% 1.41/1.67 A new axiom: (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->(((eq nat) ((plus_plus_nat (nat_1 X)) (nat_1 Y))) (nat_1 ((plus_plus_int X) Y))))))
% 1.41/1.67 FOF formula (forall (Z_1:int) (Z:int), (((ord_less_eq_int zero_zero_int) Z)->(((ord_less_eq_int zero_zero_int) Z_1)->(((eq nat) (nat_1 ((plus_plus_int Z) Z_1))) ((plus_plus_nat (nat_1 Z)) (nat_1 Z_1)))))) of role axiom named fact_744_nat__add__distrib
% 1.41/1.67 A new axiom: (forall (Z_1:int) (Z:int), (((ord_less_eq_int zero_zero_int) Z)->(((ord_less_eq_int zero_zero_int) Z_1)->(((eq nat) (nat_1 ((plus_plus_int Z) Z_1))) ((plus_plus_nat (nat_1 Z)) (nat_1 Z_1))))))
% 1.41/1.67 FOF formula (forall (M:nat) (V_1:int), ((iff (((eq int) (semiri1621563631at_int M)) (number_number_of_int V_1))) ((and (((eq nat) M) (nat_1 (number_number_of_int V_1)))) ((ord_less_eq_int zero_zero_int) (number_number_of_int V_1))))) of role axiom named fact_745_int__eq__iff__number__of
% 1.41/1.68 A new axiom: (forall (M:nat) (V_1:int), ((iff (((eq int) (semiri1621563631at_int M)) (number_number_of_int V_1))) ((and (((eq nat) M) (nat_1 (number_number_of_int V_1)))) ((ord_less_eq_int zero_zero_int) (number_number_of_int V_1)))))
% 1.41/1.68 FOF formula (forall (N:nat) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((eq nat) ((power_power_nat (nat_1 X)) N)) (nat_1 ((power_power_int X) N))))) of role axiom named fact_746_Nat__Transfer_Otransfer__nat__int__functions_I4_J
% 1.41/1.68 A new axiom: (forall (N:nat) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((eq nat) ((power_power_nat (nat_1 X)) N)) (nat_1 ((power_power_int X) N)))))
% 1.41/1.68 FOF formula (forall (N:nat) (Z:int), (((ord_less_eq_int zero_zero_int) Z)->(((eq nat) (nat_1 ((power_power_int Z) N))) ((power_power_nat (nat_1 Z)) N)))) of role axiom named fact_747_nat__power__eq
% 1.41/1.68 A new axiom: (forall (N:nat) (Z:int), (((ord_less_eq_int zero_zero_int) Z)->(((eq nat) (nat_1 ((power_power_int Z) N))) ((power_power_nat (nat_1 Z)) N))))
% 1.41/1.68 FOF formula (forall (V_3:real) (U_1:real) (Y_3:real) (X_4:real) (A_4:real), (((ord_less_real X_4) A_4)->(((ord_less_real Y_3) A_4)->(((ord_less_eq_real zero_zero_real) U_1)->(((ord_less_eq_real zero_zero_real) V_3)->((((eq real) ((plus_plus_real U_1) V_3)) one_one_real)->((ord_less_real ((plus_plus_real ((times_times_real U_1) X_4)) ((times_times_real V_3) Y_3))) A_4))))))) of role axiom named fact_748_convex__bound__lt
% 1.41/1.68 A new axiom: (forall (V_3:real) (U_1:real) (Y_3:real) (X_4:real) (A_4:real), (((ord_less_real X_4) A_4)->(((ord_less_real Y_3) A_4)->(((ord_less_eq_real zero_zero_real) U_1)->(((ord_less_eq_real zero_zero_real) V_3)->((((eq real) ((plus_plus_real U_1) V_3)) one_one_real)->((ord_less_real ((plus_plus_real ((times_times_real U_1) X_4)) ((times_times_real V_3) Y_3))) A_4)))))))
% 1.41/1.68 FOF formula (forall (V_3:int) (U_1:int) (Y_3:int) (X_4:int) (A_4:int), (((ord_less_int X_4) A_4)->(((ord_less_int Y_3) A_4)->(((ord_less_eq_int zero_zero_int) U_1)->(((ord_less_eq_int zero_zero_int) V_3)->((((eq int) ((plus_plus_int U_1) V_3)) one_one_int)->((ord_less_int ((plus_plus_int ((times_times_int U_1) X_4)) ((times_times_int V_3) Y_3))) A_4))))))) of role axiom named fact_749_convex__bound__lt
% 1.41/1.68 A new axiom: (forall (V_3:int) (U_1:int) (Y_3:int) (X_4:int) (A_4:int), (((ord_less_int X_4) A_4)->(((ord_less_int Y_3) A_4)->(((ord_less_eq_int zero_zero_int) U_1)->(((ord_less_eq_int zero_zero_int) V_3)->((((eq int) ((plus_plus_int U_1) V_3)) one_one_int)->((ord_less_int ((plus_plus_int ((times_times_int U_1) X_4)) ((times_times_int V_3) Y_3))) A_4)))))))
% 1.41/1.68 FOF formula (forall (M:nat) (W:int), (((ord_less_eq_int zero_zero_int) W)->((iff ((ord_less_nat (nat_1 W)) M)) ((ord_less_int W) (semiri1621563631at_int M))))) of role axiom named fact_750_nat__less__iff
% 1.41/1.68 A new axiom: (forall (M:nat) (W:int), (((ord_less_eq_int zero_zero_int) W)->((iff ((ord_less_nat (nat_1 W)) M)) ((ord_less_int W) (semiri1621563631at_int M)))))
% 1.41/1.68 FOF formula (forall (Y_2:int), ((iff ((ord_less_eq_real one_one_real) (number267125858f_real Y_2))) ((ord_less_eq_int (bit1 pls)) Y_2))) of role axiom named fact_751_le__special_I2_J
% 1.41/1.68 A new axiom: (forall (Y_2:int), ((iff ((ord_less_eq_real one_one_real) (number267125858f_real Y_2))) ((ord_less_eq_int (bit1 pls)) Y_2)))
% 1.41/1.68 FOF formula (forall (Y_2:int), ((iff ((ord_less_eq_int one_one_int) (number_number_of_int Y_2))) ((ord_less_eq_int (bit1 pls)) Y_2))) of role axiom named fact_752_le__special_I2_J
% 1.41/1.68 A new axiom: (forall (Y_2:int), ((iff ((ord_less_eq_int one_one_int) (number_number_of_int Y_2))) ((ord_less_eq_int (bit1 pls)) Y_2)))
% 1.41/1.68 FOF formula (forall (X_3:int), ((iff ((ord_less_eq_real (number267125858f_real X_3)) one_one_real)) ((ord_less_eq_int X_3) (bit1 pls)))) of role axiom named fact_753_le__special_I4_J
% 1.41/1.68 A new axiom: (forall (X_3:int), ((iff ((ord_less_eq_real (number267125858f_real X_3)) one_one_real)) ((ord_less_eq_int X_3) (bit1 pls))))
% 1.41/1.68 FOF formula (forall (X_3:int), ((iff ((ord_less_eq_int (number_number_of_int X_3)) one_one_int)) ((ord_less_eq_int X_3) (bit1 pls)))) of role axiom named fact_754_le__special_I4_J
% 1.41/1.70 A new axiom: (forall (X_3:int), ((iff ((ord_less_eq_int (number_number_of_int X_3)) one_one_int)) ((ord_less_eq_int X_3) (bit1 pls))))
% 1.41/1.70 FOF formula (forall (X_2:real) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq real) ((times_times_real ((power_power_real X_2) ((minus_minus_nat N_2) one_one_nat))) X_2)) ((power_power_real X_2) N_2)))) of role axiom named fact_755_realpow__minus__mult
% 1.41/1.70 A new axiom: (forall (X_2:real) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq real) ((times_times_real ((power_power_real X_2) ((minus_minus_nat N_2) one_one_nat))) X_2)) ((power_power_real X_2) N_2))))
% 1.41/1.70 FOF formula (forall (X_2:nat) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq nat) ((times_times_nat ((power_power_nat X_2) ((minus_minus_nat N_2) one_one_nat))) X_2)) ((power_power_nat X_2) N_2)))) of role axiom named fact_756_realpow__minus__mult
% 1.41/1.70 A new axiom: (forall (X_2:nat) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq nat) ((times_times_nat ((power_power_nat X_2) ((minus_minus_nat N_2) one_one_nat))) X_2)) ((power_power_nat X_2) N_2))))
% 1.41/1.70 FOF formula (forall (X_2:int) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq int) ((times_times_int ((power_power_int X_2) ((minus_minus_nat N_2) one_one_nat))) X_2)) ((power_power_int X_2) N_2)))) of role axiom named fact_757_realpow__minus__mult
% 1.41/1.70 A new axiom: (forall (X_2:int) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq int) ((times_times_int ((power_power_int X_2) ((minus_minus_nat N_2) one_one_nat))) X_2)) ((power_power_int X_2) N_2))))
% 1.41/1.70 FOF formula (forall (A_3:real) (B_3:real), ((iff ((ord_less_real A_3) B_3)) ((ord_less_real ((minus_minus_real A_3) B_3)) zero_zero_real))) of role axiom named fact_758_less__iff__diff__less__0
% 1.41/1.70 A new axiom: (forall (A_3:real) (B_3:real), ((iff ((ord_less_real A_3) B_3)) ((ord_less_real ((minus_minus_real A_3) B_3)) zero_zero_real)))
% 1.41/1.70 FOF formula (forall (A_3:int) (B_3:int), ((iff ((ord_less_int A_3) B_3)) ((ord_less_int ((minus_minus_int A_3) B_3)) zero_zero_int))) of role axiom named fact_759_less__iff__diff__less__0
% 1.41/1.70 A new axiom: (forall (A_3:int) (B_3:int), ((iff ((ord_less_int A_3) B_3)) ((ord_less_int ((minus_minus_int A_3) B_3)) zero_zero_int)))
% 1.41/1.70 FOF formula (((eq nat) zero_zero_nat) (nat_1 zero_zero_int)) of role axiom named fact_760_transfer__nat__int__numerals_I1_J
% 1.41/1.70 A new axiom: (((eq nat) zero_zero_nat) (nat_1 zero_zero_int))
% 1.41/1.70 FOF formula (((eq nat) (nat_1 zero_zero_int)) zero_zero_nat) of role axiom named fact_761_nat__0
% 1.41/1.70 A new axiom: (((eq nat) (nat_1 zero_zero_int)) zero_zero_nat)
% 1.41/1.70 FOF formula (forall (A_2:real), (((ord_less_real ((times_times_real A_2) A_2)) zero_zero_real)->False)) of role axiom named fact_762_not__square__less__zero
% 1.41/1.70 A new axiom: (forall (A_2:real), (((ord_less_real ((times_times_real A_2) A_2)) zero_zero_real)->False))
% 1.41/1.70 FOF formula (forall (A_2:int), (((ord_less_int ((times_times_int A_2) A_2)) zero_zero_int)->False)) of role axiom named fact_763_not__square__less__zero
% 1.41/1.70 A new axiom: (forall (A_2:int), (((ord_less_int ((times_times_int A_2) A_2)) zero_zero_int)->False))
% 1.41/1.70 FOF formula (forall (A_1:real) (C_1:real) (B_2:real), ((iff ((ord_less_real ((times_times_real A_1) C_1)) ((times_times_real B_2) C_1))) ((or ((and ((ord_less_real zero_zero_real) C_1)) ((ord_less_real A_1) B_2))) ((and ((ord_less_real C_1) zero_zero_real)) ((ord_less_real B_2) A_1))))) of role axiom named fact_764_mult__less__cancel__right__disj
% 1.41/1.70 A new axiom: (forall (A_1:real) (C_1:real) (B_2:real), ((iff ((ord_less_real ((times_times_real A_1) C_1)) ((times_times_real B_2) C_1))) ((or ((and ((ord_less_real zero_zero_real) C_1)) ((ord_less_real A_1) B_2))) ((and ((ord_less_real C_1) zero_zero_real)) ((ord_less_real B_2) A_1)))))
% 1.41/1.70 FOF formula (forall (A_1:int) (C_1:int) (B_2:int), ((iff ((ord_less_int ((times_times_int A_1) C_1)) ((times_times_int B_2) C_1))) ((or ((and ((ord_less_int zero_zero_int) C_1)) ((ord_less_int A_1) B_2))) ((and ((ord_less_int C_1) zero_zero_int)) ((ord_less_int B_2) A_1))))) of role axiom named fact_765_mult__less__cancel__right__disj
% 1.50/1.72 A new axiom: (forall (A_1:int) (C_1:int) (B_2:int), ((iff ((ord_less_int ((times_times_int A_1) C_1)) ((times_times_int B_2) C_1))) ((or ((and ((ord_less_int zero_zero_int) C_1)) ((ord_less_int A_1) B_2))) ((and ((ord_less_int C_1) zero_zero_int)) ((ord_less_int B_2) A_1)))))
% 1.50/1.72 FOF formula (forall (W:int), (((eq nat) (nat_1 (number_number_of_int W))) (number_number_of_nat W))) of role axiom named fact_766_nat__number__of
% 1.50/1.72 A new axiom: (forall (W:int), (((eq nat) (nat_1 (number_number_of_int W))) (number_number_of_nat W)))
% 1.50/1.72 FOF formula (forall (V_1:int), (((eq nat) (number_number_of_nat V_1)) (nat_1 (number_number_of_int V_1)))) of role axiom named fact_767_nat__number__of__def
% 1.50/1.72 A new axiom: (forall (V_1:int), (((eq nat) (number_number_of_nat V_1)) (nat_1 (number_number_of_int V_1))))
% 1.50/1.72 FOF formula (((eq nat) one_one_nat) (nat_1 one_one_int)) of role axiom named fact_768_transfer__nat__int__numerals_I2_J
% 1.50/1.72 A new axiom: (((eq nat) one_one_nat) (nat_1 one_one_int))
% 1.50/1.72 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_769_zero__less__diff
% 1.50/1.72 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)))
% 1.50/1.72 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_770_diff__less
% 1.50/1.72 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))))
% 1.50/1.72 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_771_diff__add__0
% 1.50/1.72 A new axiom: (forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat N) ((plus_plus_nat N) M))) zero_zero_nat))
% 1.50/1.72 FOF formula (forall (I_1:nat) (J:nat) (K:nat), ((iff ((ord_less_nat I_1) ((minus_minus_nat J) K))) ((ord_less_nat ((plus_plus_nat I_1) K)) J))) of role axiom named fact_772_less__diff__conv
% 1.50/1.72 A new axiom: (forall (I_1:nat) (J:nat) (K:nat), ((iff ((ord_less_nat I_1) ((minus_minus_nat J) K))) ((ord_less_nat ((plus_plus_nat I_1) K)) J)))
% 1.50/1.72 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_773_add__diff__inverse
% 1.50/1.72 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)))
% 1.50/1.72 FOF formula (forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_774_rel__simps_I22_J
% 1.50/1.72 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K)))
% 1.50/1.72 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_775_rel__simps_I32_J
% 1.50/1.72 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L)))
% 1.50/1.72 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_776_less__eq__int__code_I14_J
% 1.50/1.72 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2)))
% 1.50/1.72 FOF formula (forall (K:int), ((iff ((ord_less_eq_int pls) (bit0 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_777_rel__simps_I21_J
% 1.50/1.72 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int pls) (bit0 K))) ((ord_less_eq_int pls) K)))
% 1.50/1.72 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) pls)) ((ord_less_eq_int K) pls))) of role axiom named fact_778_rel__simps_I27_J
% 1.50/1.72 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) pls)) ((ord_less_eq_int K) pls)))
% 1.50/1.72 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_779_pos__zmult__pos
% 1.50/1.72 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))))
% 1.50/1.74 FOF formula (forall (K:int) (I_1:int) (J:int), (((ord_less_int I_1) J)->(((ord_less_int zero_zero_int) K)->((ord_less_int ((times_times_int K) I_1)) ((times_times_int K) J))))) of role axiom named fact_780_zmult__zless__mono2
% 1.50/1.74 A new axiom: (forall (K:int) (I_1:int) (J:int), (((ord_less_int I_1) J)->(((ord_less_int zero_zero_int) K)->((ord_less_int ((times_times_int K) I_1)) ((times_times_int K) J)))))
% 1.50/1.74 FOF formula ((ord_less_eq_int zero_zero_int) one_one_int) of role axiom named fact_781_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J
% 1.50/1.74 A new axiom: ((ord_less_eq_int zero_zero_int) one_one_int)
% 1.50/1.74 FOF formula (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X) Y))))) of role axiom named fact_782_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J
% 1.50/1.74 A new axiom: (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X) Y)))))
% 1.50/1.74 FOF formula (forall (Z_1:int) (Z:int) (W_2:int) (W:int), (((ord_less_int W_2) W)->(((ord_less_eq_int Z_1) Z)->((ord_less_int ((plus_plus_int W_2) Z_1)) ((plus_plus_int W) Z))))) of role axiom named fact_783_zadd__zless__mono
% 1.50/1.74 A new axiom: (forall (Z_1:int) (Z:int) (W_2:int) (W:int), (((ord_less_int W_2) W)->(((ord_less_eq_int Z_1) Z)->((ord_less_int ((plus_plus_int W_2) Z_1)) ((plus_plus_int W) Z)))))
% 1.50/1.74 FOF formula (forall (Z:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int Z))) of role axiom named fact_784_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J
% 1.50/1.74 A new axiom: (forall (Z:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int Z)))
% 1.50/1.74 FOF formula (forall (P:(int->Prop)), ((iff ((ex int) (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P X_1))))) ((ex nat) (fun (X_1:nat)=> (P (semiri1621563631at_int X_1)))))) of role axiom named fact_785_transfer__int__nat__quantifiers_I2_J
% 1.50/1.74 A new axiom: (forall (P:(int->Prop)), ((iff ((ex int) (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P X_1))))) ((ex nat) (fun (X_1:nat)=> (P (semiri1621563631at_int X_1))))))
% 1.50/1.74 FOF formula (forall (P:(int->Prop)), ((iff (forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(P X_1)))) (forall (X_1:nat), (P (semiri1621563631at_int X_1))))) of role axiom named fact_786_transfer__int__nat__quantifiers_I1_J
% 1.50/1.74 A new axiom: (forall (P:(int->Prop)), ((iff (forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(P X_1)))) (forall (X_1:nat), (P (semiri1621563631at_int X_1)))))
% 1.50/1.74 FOF formula (forall (N:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int N))) of role axiom named fact_787_zero__zle__int
% 1.50/1.74 A new axiom: (forall (N:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int N)))
% 1.50/1.74 FOF formula (forall (N:nat) (X:int), (((ord_less_eq_int zero_zero_int) X)->((ord_less_eq_int zero_zero_int) ((power_power_int X) N)))) of role axiom named fact_788_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J
% 1.50/1.74 A new axiom: (forall (N:nat) (X:int), (((ord_less_eq_int zero_zero_int) X)->((ord_less_eq_int zero_zero_int) ((power_power_int X) N))))
% 1.50/1.74 FOF formula (forall (W:int) (Z:int), ((iff ((ord_less_eq_int W) Z)) ((ex nat) (fun (N_1:nat)=> (((eq int) Z) ((plus_plus_int W) (semiri1621563631at_int N_1))))))) of role axiom named fact_789_zle__iff__zadd
% 1.50/1.74 A new axiom: (forall (W:int) (Z:int), ((iff ((ord_less_eq_int W) Z)) ((ex nat) (fun (N_1:nat)=> (((eq int) Z) ((plus_plus_int W) (semiri1621563631at_int N_1)))))))
% 1.50/1.74 FOF formula (forall (X:int) (Y:nat) (Z:nat), (((eq int) ((power_power_int X) ((plus_plus_nat Y) Z))) ((times_times_int ((power_power_int X) Y)) ((power_power_int X) Z)))) of role axiom named fact_790_zpower__zadd__distrib
% 1.50/1.74 A new axiom: (forall (X:int) (Y:nat) (Z:nat), (((eq int) ((power_power_int X) ((plus_plus_nat Y) Z))) ((times_times_int ((power_power_int X) Y)) ((power_power_int X) Z))))
% 1.50/1.74 FOF formula (forall (W:int) (Z:int), (((ord_less_int zero_zero_int) Z)->((iff ((ord_less_nat (nat_1 W)) (nat_1 Z))) ((ord_less_int W) Z)))) of role axiom named fact_791_nat__mono__iff
% 1.50/1.76 A new axiom: (forall (W:int) (Z:int), (((ord_less_int zero_zero_int) Z)->((iff ((ord_less_nat (nat_1 W)) (nat_1 Z))) ((ord_less_int W) Z))))
% 1.50/1.76 FOF formula (forall (W:int) (Z:int), ((iff ((ord_less_nat (nat_1 W)) (nat_1 Z))) ((and ((ord_less_int zero_zero_int) Z)) ((ord_less_int W) Z)))) of role axiom named fact_792_zless__nat__conj
% 1.50/1.76 A new axiom: (forall (W:int) (Z:int), ((iff ((ord_less_nat (nat_1 W)) (nat_1 Z))) ((and ((ord_less_int zero_zero_int) Z)) ((ord_less_int W) Z))))
% 1.50/1.76 FOF formula (forall (M:nat) (Z:int), ((iff ((ord_less_nat M) (nat_1 Z))) ((ord_less_int (semiri1621563631at_int M)) Z))) of role axiom named fact_793_zless__nat__eq__int__zless
% 1.50/1.76 A new axiom: (forall (M:nat) (Z:int), ((iff ((ord_less_nat M) (nat_1 Z))) ((ord_less_int (semiri1621563631at_int M)) Z)))
% 1.50/1.76 FOF formula (forall (P:(nat->Prop)) (A:nat) (B:nat), ((iff (P ((minus_minus_nat A) B))) (((or ((and ((ord_less_nat A) B)) ((P zero_zero_nat)->False))) ((ex nat) (fun (D_1:nat)=> ((and (((eq nat) A) ((plus_plus_nat B) D_1))) ((P D_1)->False)))))->False))) of role axiom named fact_794_nat__diff__split__asm
% 1.50/1.76 A new axiom: (forall (P:(nat->Prop)) (A:nat) (B:nat), ((iff (P ((minus_minus_nat A) B))) (((or ((and ((ord_less_nat A) B)) ((P zero_zero_nat)->False))) ((ex nat) (fun (D_1:nat)=> ((and (((eq nat) A) ((plus_plus_nat B) D_1))) ((P D_1)->False)))))->False)))
% 1.50/1.76 FOF formula (forall (P:(nat->Prop)) (A:nat) (B:nat), ((iff (P ((minus_minus_nat A) B))) ((and (((ord_less_nat A) B)->(P zero_zero_nat))) (forall (D_1:nat), ((((eq nat) A) ((plus_plus_nat B) D_1))->(P D_1)))))) of role axiom named fact_795_nat__diff__split
% 1.50/1.76 A new axiom: (forall (P:(nat->Prop)) (A:nat) (B:nat), ((iff (P ((minus_minus_nat A) B))) ((and (((ord_less_nat A) B)->(P zero_zero_nat))) (forall (D_1:nat), ((((eq nat) A) ((plus_plus_nat B) D_1))->(P D_1))))))
% 1.50/1.76 FOF formula (forall (V_1:int), ((iff (((eq nat) zero_zero_nat) (number_number_of_nat V_1))) ((ord_less_eq_int V_1) pls))) of role axiom named fact_796_eq__0__number__of
% 1.50/1.76 A new axiom: (forall (V_1:int), ((iff (((eq nat) zero_zero_nat) (number_number_of_nat V_1))) ((ord_less_eq_int V_1) pls)))
% 1.50/1.76 FOF formula (forall (V_1:int), ((iff (((eq nat) (number_number_of_nat V_1)) zero_zero_nat)) ((ord_less_eq_int V_1) pls))) of role axiom named fact_797_eq__number__of__0
% 1.50/1.76 A new axiom: (forall (V_1:int), ((iff (((eq nat) (number_number_of_nat V_1)) zero_zero_nat)) ((ord_less_eq_int V_1) pls)))
% 1.50/1.76 FOF formula (forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_798_rel__simps_I5_J
% 1.50/1.76 A new axiom: (forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K)))
% 1.50/1.76 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_799_rel__simps_I29_J
% 1.50/1.76 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls)))
% 1.50/1.76 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_800_rel__simps_I15_J
% 1.50/1.76 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L)))
% 1.50/1.76 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_801_less__int__code_I14_J
% 1.50/1.76 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2)))
% 1.50/1.76 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_802_rel__simps_I33_J
% 1.50/1.76 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit0 L))) ((ord_less_int K) L)))
% 1.50/1.76 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_803_less__eq__int__code_I15_J
% 1.50/1.76 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2)))
% 1.50/1.76 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_804_mult__Bit1
% 1.50/1.77 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)))
% 1.50/1.77 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_805_pos__zmult__eq__1__iff
% 1.50/1.77 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)))))
% 1.50/1.77 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_806_int__one__le__iff__zero__less
% 1.50/1.77 A new axiom: (forall (Z:int), ((iff ((ord_less_eq_int one_one_int) Z)) ((ord_less_int zero_zero_int) Z)))
% 1.50/1.77 FOF formula (forall (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat))) of role axiom named fact_807_int__le__0__conv
% 1.50/1.77 A new axiom: (forall (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat)))
% 1.50/1.77 FOF formula (((eq int) (succ pls)) (bit1 pls)) of role axiom named fact_808_succ__Pls
% 1.50/1.77 A new axiom: (((eq int) (succ pls)) (bit1 pls))
% 1.50/1.77 FOF formula (forall (K:int), (((eq int) (succ (bit0 K))) (bit1 K))) of role axiom named fact_809_succ__Bit0
% 1.50/1.77 A new axiom: (forall (K:int), (((eq int) (succ (bit0 K))) (bit1 K)))
% 1.50/1.77 FOF formula (forall (K:int), (((eq int) (succ (bit1 K))) (bit0 (succ K)))) of role axiom named fact_810_succ__Bit1
% 1.50/1.77 A new axiom: (forall (K:int), (((eq int) (succ (bit1 K))) (bit0 (succ K))))
% 1.50/1.77 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_811_zle__add1__eq__le
% 1.50/1.77 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)))
% 1.50/1.77 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_812_add1__zle__eq
% 1.50/1.77 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)))
% 1.50/1.77 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_813_zless__imp__add1__zle
% 1.50/1.77 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)))
% 1.50/1.77 FOF formula (forall (K:int), (((eq int) (succ K)) ((plus_plus_int K) one_one_int))) of role axiom named fact_814_succ__def
% 1.50/1.77 A new axiom: (forall (K:int), (((eq int) (succ K)) ((plus_plus_int K) one_one_int)))
% 1.50/1.77 FOF formula (forall (Z:int), ((iff ((ord_less_nat zero_zero_nat) (nat_1 Z))) ((ord_less_int zero_zero_int) Z))) of role axiom named fact_815_zero__less__nat__eq
% 1.50/1.77 A new axiom: (forall (Z:int), ((iff ((ord_less_nat zero_zero_nat) (nat_1 Z))) ((ord_less_int zero_zero_int) Z)))
% 1.50/1.77 FOF formula (((eq nat) (number_number_of_nat (bit1 (bit1 pls)))) (nat_1 (number_number_of_int (bit1 (bit1 pls))))) of role axiom named fact_816_transfer__nat__int__numerals_I4_J
% 1.50/1.77 A new axiom: (((eq nat) (number_number_of_nat (bit1 (bit1 pls)))) (nat_1 (number_number_of_int (bit1 (bit1 pls)))))
% 1.50/1.77 FOF formula (forall (P:(nat->Prop)) (I_1:int), ((iff (P (nat_1 I_1))) ((and (forall (N_1:nat), ((((eq int) I_1) (semiri1621563631at_int N_1))->(P N_1)))) (((ord_less_int I_1) zero_zero_int)->(P zero_zero_nat))))) of role axiom named fact_817_split__nat
% 1.50/1.77 A new axiom: (forall (P:(nat->Prop)) (I_1:int), ((iff (P (nat_1 I_1))) ((and (forall (N_1:nat), ((((eq int) I_1) (semiri1621563631at_int N_1))->(P N_1)))) (((ord_less_int I_1) zero_zero_int)->(P zero_zero_nat)))))
% 1.50/1.77 FOF formula ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 (bit1 pls)))) of role axiom named fact_818_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J
% 1.50/1.77 A new axiom: ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 (bit1 pls))))
% 1.59/1.79 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_819_le__imp__0__less
% 1.59/1.79 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))))
% 1.59/1.79 FOF formula (forall (K:nat) (I_1:int) (J:int), (((ord_less_int I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_int ((times_times_int (semiri1621563631at_int K)) I_1)) ((times_times_int (semiri1621563631at_int K)) J))))) of role axiom named fact_820_zmult__zless__mono2__lemma
% 1.59/1.79 A new axiom: (forall (K:nat) (I_1:int) (J:int), (((ord_less_int I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_int ((times_times_int (semiri1621563631at_int K)) I_1)) ((times_times_int (semiri1621563631at_int K)) J)))))
% 1.59/1.79 FOF formula (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit1 L))) (bit0 ((plus_plus_int K) (succ L))))) of role axiom named fact_821_add__Bit1__Bit1
% 1.59/1.79 A new axiom: (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit1 L))) (bit0 ((plus_plus_int K) (succ L)))))
% 1.59/1.79 FOF formula (((eq nat) (number_number_of_nat (bit0 (bit1 pls)))) (nat_1 (number_number_of_int (bit0 (bit1 pls))))) of role axiom named fact_822_transfer__nat__int__numerals_I3_J
% 1.59/1.79 A new axiom: (((eq nat) (number_number_of_nat (bit0 (bit1 pls)))) (nat_1 (number_number_of_int (bit0 (bit1 pls)))))
% 1.59/1.79 FOF formula ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 (bit1 pls)))) of role axiom named fact_823_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J
% 1.59/1.79 A new axiom: ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 (bit1 pls))))
% 1.59/1.79 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_824_cube__square
% 1.59/1.79 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))))))
% 1.59/1.79 FOF formula (forall (X:int), ((ord_less_eq_int X) ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_825_power2__ge__self
% 1.59/1.79 A new axiom: (forall (X:int), ((ord_less_eq_int X) ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))))
% 1.59/1.79 FOF formula (forall (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_int X) (number_number_of_int (bit0 (bit1 pls))))->((or (((eq int) X) zero_zero_int)) (((eq int) X) one_one_int))))) of role axiom named fact_826_int__pos__lt__two__imp__zero__or__one
% 1.59/1.79 A new axiom: (forall (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_int X) (number_number_of_int (bit0 (bit1 pls))))->((or (((eq int) X) zero_zero_int)) (((eq int) X) one_one_int)))))
% 1.59/1.79 FOF formula (forall (A:int) (P_1:int), (((ord_less_int zero_zero_int) P_1)->(((eq int) ((power_power_int A) (nat_1 P_1))) ((times_times_int A) ((power_power_int A) ((minus_minus_nat (nat_1 P_1)) one_one_nat)))))) of role axiom named fact_827_Euler_Oaux__1
% 1.59/1.79 A new axiom: (forall (A:int) (P_1:int), (((ord_less_int zero_zero_int) P_1)->(((eq int) ((power_power_int A) (nat_1 P_1))) ((times_times_int A) ((power_power_int A) ((minus_minus_nat (nat_1 P_1)) one_one_nat))))))
% 1.59/1.79 FOF formula (forall (R_1:int) (Q:int) (A:int), (((ord_less_int zero_zero_int) A)->((((eq int) A) ((plus_plus_int R_1) ((times_times_int A) Q)))->(((ord_less_eq_int zero_zero_int) R_1)->((ord_less_eq_int Q) one_one_int))))) of role axiom named fact_828_self__quotient__aux2
% 1.59/1.79 A new axiom: (forall (R_1:int) (Q:int) (A:int), (((ord_less_int zero_zero_int) A)->((((eq int) A) ((plus_plus_int R_1) ((times_times_int A) Q)))->(((ord_less_eq_int zero_zero_int) R_1)->((ord_less_eq_int Q) one_one_int)))))
% 1.59/1.79 FOF formula (forall (R_1:int) (Q:int) (A:int), (((ord_less_int zero_zero_int) A)->((((eq int) A) ((plus_plus_int R_1) ((times_times_int A) Q)))->(((ord_less_int R_1) A)->((ord_less_eq_int one_one_int) Q))))) of role axiom named fact_829_self__quotient__aux1
% 1.59/1.79 A new axiom: (forall (R_1:int) (Q:int) (A:int), (((ord_less_int zero_zero_int) A)->((((eq int) A) ((plus_plus_int R_1) ((times_times_int A) Q)))->(((ord_less_int R_1) A)->((ord_less_eq_int one_one_int) Q)))))
% 1.59/1.81 FOF formula ((((ord_less_int ((plus_plus_int one_one_int) (semiri1621563631at_int n))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))->((twoSqu919416604sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))->False))->False) of role axiom named fact_830_smaller_I2_J
% 1.59/1.81 A new axiom: ((((ord_less_int ((plus_plus_int one_one_int) (semiri1621563631at_int n))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))->((twoSqu919416604sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))->False))->False)
% 1.59/1.81 FOF formula (forall (B_1:int) (Q_1:int) (R_2:int), (((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_1) Q_1)) R_2))->(((ord_less_int R_2) B_1)->(((ord_less_int zero_zero_int) B_1)->((ord_less_eq_int zero_zero_int) Q_1))))) of role axiom named fact_831_q__pos__lemma
% 1.59/1.81 A new axiom: (forall (B_1:int) (Q_1:int) (R_2:int), (((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_1) Q_1)) R_2))->(((ord_less_int R_2) B_1)->(((ord_less_int zero_zero_int) B_1)->((ord_less_eq_int zero_zero_int) Q_1)))))
% 1.59/1.81 FOF formula (forall (B_1:int) (Q_1:int) (R_2:int), (((ord_less_int ((plus_plus_int ((times_times_int B_1) Q_1)) R_2)) zero_zero_int)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B_1)->((ord_less_eq_int Q_1) zero_zero_int))))) of role axiom named fact_832_q__neg__lemma
% 1.59/1.81 A new axiom: (forall (B_1:int) (Q_1:int) (R_2:int), (((ord_less_int ((plus_plus_int ((times_times_int B_1) Q_1)) R_2)) zero_zero_int)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B_1)->((ord_less_eq_int Q_1) zero_zero_int)))))
% 1.59/1.81 FOF formula ((twoSqu919416604sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int zero_zero_nat))))->False) of role axiom named fact_833_nQ1
% 1.59/1.81 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)) ((plus_plus_int one_one_int) (semiri1621563631at_int zero_zero_nat))))->False)
% 1.59/1.81 FOF formula (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) of role axiom named fact_834_le0
% 1.59/1.81 A new axiom: (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N))
% 1.59/1.81 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_835_p0
% 1.59/1.81 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))
% 1.59/1.81 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_836_t__l__p
% 1.59/1.81 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))
% 1.59/1.81 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_837_qf1pt
% 1.59/1.81 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))
% 1.59/1.81 FOF formula ((and ((ord_less_int ((plus_plus_int one_one_int) (semiri1621563631at_int n))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) (twoSqu919416604sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))) of role axiom named fact_838_IH
% 1.59/1.82 A new axiom: ((and ((ord_less_int ((plus_plus_int one_one_int) (semiri1621563631at_int n))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) (twoSqu919416604sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int n)))))
% 1.59/1.82 FOF formula ((forall (X_1:int) (Y_1:int), (not (((eq int) ((plus_plus_int ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))))->False) of role axiom named fact_839__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_061_A_I4_A
% 1.59/1.82 A new axiom: ((forall (X_1:int) (Y_1:int), (not (((eq int) ((plus_plus_int ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))))->False)
% 1.59/1.82 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_840_t
% 1.59/1.82 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))
% 1.59/1.82 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_841_p
% 1.59/1.82 A new axiom: (zprime ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))
% 1.59/1.82 FOF formula ((((eq int) t) one_one_int)->((ex int) (fun (X_1:int)=> ((ex int) (fun (Y_1:int)=> (((eq int) ((plus_plus_int ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_1) (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_842__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_
% 1.59/1.82 A new axiom: ((((eq int) t) one_one_int)->((ex int) (fun (X_1:int)=> ((ex int) (fun (Y_1:int)=> (((eq int) ((plus_plus_int ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_1) (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)))))))
% 1.59/1.82 FOF formula (forall (N:nat), ((ord_less_eq_nat N) N)) of role axiom named fact_843_le__refl
% 1.59/1.82 A new axiom: (forall (N:nat), ((ord_less_eq_nat N) N))
% 1.59/1.82 FOF formula (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) M))) of role axiom named fact_844_le__square
% 1.59/1.82 A new axiom: (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) M)))
% 1.59/1.82 FOF formula (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) ((times_times_nat M) M)))) of role axiom named fact_845_le__cube
% 1.59/1.82 A new axiom: (forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) ((times_times_nat M) M))))
% 1.59/1.82 FOF formula (forall (M:nat) (N:nat), (((eq nat) ((times_times_nat M) N)) ((times_times_nat N) M))) of role axiom named fact_846_nat__mult__commute
% 1.59/1.82 A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((times_times_nat M) N)) ((times_times_nat N) M)))
% 1.59/1.82 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_847_nat__le__linear
% 1.59/1.82 A new axiom: (forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M)))
% 1.59/1.82 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_848_nat__mult__assoc
% 1.59/1.84 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))))
% 1.59/1.84 FOF formula (forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N))) of role axiom named fact_849_eq__imp__le
% 1.59/1.84 A new axiom: (forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N)))
% 1.59/1.84 FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J) K)))) of role axiom named fact_850_mult__le__mono1
% 1.59/1.84 A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J) K))))
% 1.59/1.84 FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((times_times_nat K) I_1)) ((times_times_nat K) J)))) of role axiom named fact_851_mult__le__mono2
% 1.59/1.84 A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((times_times_nat K) I_1)) ((times_times_nat K) J))))
% 1.59/1.84 FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat I_1) K)))) of role axiom named fact_852_le__trans
% 1.59/1.84 A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat I_1) K))))
% 1.59/1.84 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_853_le__antisym
% 1.59/1.84 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N))))
% 1.59/1.84 FOF formula (forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J) L))))) of role axiom named fact_854_mult__le__mono
% 1.59/1.84 A new axiom: (forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J) L)))))
% 1.59/1.84 FOF formula (forall (X:real) (Y:real), ((iff ((ord_less_eq_real X) Y)) ((ord_less_eq_real ((minus_minus_real X) Y)) zero_zero_real))) of role axiom named fact_855_real__le__eq__diff
% 1.59/1.84 A new axiom: (forall (X:real) (Y:real), ((iff ((ord_less_eq_real X) Y)) ((ord_less_eq_real ((minus_minus_real X) Y)) zero_zero_real)))
% 1.59/1.84 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_856_mult__le__cancel2
% 1.59/1.84 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))))
% 1.59/1.84 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_857_mult__le__cancel1
% 1.59/1.84 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))))
% 1.59/1.84 FOF formula (forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real X) Z)) ((times_times_real Y) Z))) ((ord_less_eq_real X) Y)))) of role axiom named fact_858_real__mult__le__cancel__iff1
% 1.59/1.84 A new axiom: (forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real X) Z)) ((times_times_real Y) Z))) ((ord_less_eq_real X) Y))))
% 1.59/1.84 FOF formula (forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real Z) X)) ((times_times_real Z) Y))) ((ord_less_eq_real X) Y)))) of role axiom named fact_859_real__mult__le__cancel__iff2
% 1.59/1.84 A new axiom: (forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real Z) X)) ((times_times_real Z) Y))) ((ord_less_eq_real X) Y))))
% 1.59/1.86 FOF formula (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq int) ((minus_minus_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((minus_minus_nat M) N))))) of role axiom named fact_860_zdiff__int
% 1.59/1.86 A new axiom: (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq int) ((minus_minus_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((minus_minus_nat M) N)))))
% 1.59/1.86 FOF formula (forall (K:int), (((eq int) ((minus_minus_int K) pls)) K)) of role axiom named fact_861_diff__bin__simps_I1_J
% 1.59/1.86 A new axiom: (forall (K:int), (((eq int) ((minus_minus_int K) pls)) K))
% 1.59/1.86 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_862_diff__bin__simps_I7_J
% 1.59/1.86 A new axiom: (forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit0 K)) (bit0 L))) (bit0 ((minus_minus_int K) L))))
% 1.59/1.86 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_863_zdiff__zmult__distrib
% 1.59/1.86 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))))
% 1.59/1.86 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_864_zdiff__zmult__distrib2
% 1.59/1.86 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))))
% 1.59/1.86 FOF formula (forall (N:nat), (((eq nat) ((times_times_nat zero_zero_nat) N)) zero_zero_nat)) of role axiom named fact_865_mult__0
% 1.59/1.86 A new axiom: (forall (N:nat), (((eq nat) ((times_times_nat zero_zero_nat) N)) zero_zero_nat))
% 1.59/1.86 FOF formula (forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat)) of role axiom named fact_866_mult__0__right
% 1.59/1.86 A new axiom: (forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat))
% 1.59/1.86 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_867_mult__is__0
% 1.59/1.86 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))))
% 1.59/1.86 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_868_mult__cancel1
% 1.59/1.86 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))))
% 1.59/1.86 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_869_mult__cancel2
% 1.59/1.86 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))))
% 1.59/1.86 FOF formula (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) of role axiom named fact_870_less__eq__nat_Osimps_I1_J
% 1.59/1.86 A new axiom: (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N))
% 1.59/1.86 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_871_le__0__eq
% 1.59/1.86 A new axiom: (forall (N:nat), ((iff ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))
% 1.59/1.86 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_872_real__mult__left__cancel
% 1.59/1.88 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))))
% 1.59/1.88 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_873_real__mult__right__cancel
% 1.59/1.88 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))))
% 1.59/1.88 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_874_less__or__eq__imp__le
% 1.59/1.88 A new axiom: (forall (M:nat) (N:nat), (((or ((ord_less_nat M) N)) (((eq nat) M) N))->((ord_less_eq_nat M) N)))
% 1.59/1.88 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_875_le__neq__implies__less
% 1.59/1.88 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((not (((eq nat) M) N))->((ord_less_nat M) N))))
% 1.59/1.88 FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N))) of role axiom named fact_876_less__imp__le__nat
% 1.59/1.88 A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N)))
% 1.59/1.88 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_877_le__eq__less__or__eq
% 1.59/1.88 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))))
% 1.59/1.88 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_878_nat__less__le
% 1.59/1.88 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)))))
% 1.59/1.88 FOF formula (forall (X:real) (Y:real), ((iff ((ord_less_real X) Y)) ((and ((ord_less_eq_real X) Y)) (not (((eq real) X) Y))))) of role axiom named fact_879_real__less__def
% 1.59/1.88 A new axiom: (forall (X:real) (Y:real), ((iff ((ord_less_real X) Y)) ((and ((ord_less_eq_real X) Y)) (not (((eq real) X) Y)))))
% 1.59/1.88 FOF formula (forall (X:real) (Y:real), ((iff ((ord_less_eq_real X) Y)) ((or ((ord_less_real X) Y)) (((eq real) X) Y)))) of role axiom named fact_880_less__eq__real__def
% 1.59/1.88 A new axiom: (forall (X:real) (Y:real), ((iff ((ord_less_eq_real X) Y)) ((or ((ord_less_real X) Y)) (((eq real) X) Y))))
% 1.59/1.88 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_881_add__mult__distrib
% 1.59/1.88 A new axiom: (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((times_times_nat ((plus_plus_nat M) N)) K)) ((plus_plus_nat ((times_times_nat M) K)) ((times_times_nat N) K))))
% 1.59/1.88 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_882_add__mult__distrib2
% 1.59/1.88 A new axiom: (forall (K:nat) (M:nat) (N:nat), (((eq nat) ((times_times_nat K) ((plus_plus_nat M) N))) ((plus_plus_nat ((times_times_nat K) M)) ((times_times_nat K) N))))
% 1.59/1.88 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_883_add__leE
% 1.59/1.88 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)))
% 1.59/1.88 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_884_add__leD1
% 1.59/1.88 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)))
% 1.59/1.88 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_885_add__leD2
% 1.59/1.88 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)))
% 1.70/1.90 FOF formula (forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) L))))) of role axiom named fact_886_add__le__mono
% 1.70/1.90 A new axiom: (forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) L)))))
% 1.70/1.90 FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) K)))) of role axiom named fact_887_add__le__mono1
% 1.70/1.90 A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) K))))
% 1.70/1.90 FOF formula (forall (M:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat I_1) ((plus_plus_nat M) J)))) of role axiom named fact_888_trans__le__add2
% 1.70/1.90 A new axiom: (forall (M:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat I_1) ((plus_plus_nat M) J))))
% 1.70/1.90 FOF formula (forall (M:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat I_1) ((plus_plus_nat J) M)))) of role axiom named fact_889_trans__le__add1
% 1.70/1.90 A new axiom: (forall (M:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat I_1) ((plus_plus_nat J) M))))
% 1.70/1.90 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_890_nat__add__left__cancel__le
% 1.70/1.90 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)))
% 1.70/1.90 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_891_le__iff__add
% 1.70/1.90 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))))))
% 1.70/1.90 FOF formula (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M))) of role axiom named fact_892_le__add1
% 1.70/1.90 A new axiom: (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M)))
% 1.70/1.90 FOF formula (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat M) N))) of role axiom named fact_893_le__add2
% 1.70/1.90 A new axiom: (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat M) N)))
% 1.70/1.90 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_894_nat__mult__eq__one
% 1.70/1.90 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))))
% 1.70/1.90 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_895_nat__mult__eq__1__iff
% 1.70/1.90 A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) ((times_times_nat M) N)) one_one_nat)) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat))))
% 1.70/1.90 FOF formula (forall (N:nat), (((eq nat) ((times_times_nat N) one_one_nat)) N)) of role axiom named fact_896_nat__mult__1__right
% 1.70/1.90 A new axiom: (forall (N:nat), (((eq nat) ((times_times_nat N) one_one_nat)) N))
% 1.70/1.90 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_897_nat__1__eq__mult__iff
% 1.70/1.90 A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) one_one_nat) ((times_times_nat M) N))) ((and (((eq nat) M) one_one_nat)) (((eq nat) N) one_one_nat))))
% 1.70/1.90 FOF formula (forall (N:nat), (((eq nat) ((times_times_nat one_one_nat) N)) N)) of role axiom named fact_898_nat__mult__1
% 1.70/1.90 A new axiom: (forall (N:nat), (((eq nat) ((times_times_nat one_one_nat) N)) N))
% 1.70/1.90 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_899_diff__mult__distrib
% 1.70/1.92 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))))
% 1.70/1.92 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_900_diff__mult__distrib2
% 1.70/1.92 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))))
% 1.70/1.92 FOF formula (forall (Z:real), (((eq real) ((times_times_real one_one_real) Z)) Z)) of role axiom named fact_901_real__mult__1
% 1.70/1.92 A new axiom: (forall (Z:real), (((eq real) ((times_times_real one_one_real) Z)) Z))
% 1.70/1.92 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_902_le__diff__iff
% 1.70/1.92 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)))))
% 1.70/1.92 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_903_Nat_Odiff__diff__eq
% 1.70/1.92 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)))))
% 1.70/1.92 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_904_eq__diff__iff
% 1.70/1.92 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)))))
% 1.70/1.92 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_905_diff__diff__cancel
% 1.70/1.92 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)))
% 1.70/1.92 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_906_diff__le__mono
% 1.70/1.92 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))))
% 1.70/1.92 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_907_diff__le__mono2
% 1.70/1.92 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))))
% 1.70/1.92 FOF formula (forall (M:nat) (N:nat), ((ord_less_eq_nat ((minus_minus_nat M) N)) M)) of role axiom named fact_908_Nat_Odiff__le__self
% 1.70/1.92 A new axiom: (forall (M:nat) (N:nat), ((ord_less_eq_nat ((minus_minus_nat M) N)) M))
% 1.70/1.92 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_909_real__add__mult__distrib
% 1.70/1.92 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))))
% 1.70/1.92 FOF formula (forall (X:int) (Y:nat) (Z:nat), (((eq int) ((power_power_int ((power_power_int X) Y)) Z)) ((power_power_int X) ((times_times_nat Y) Z)))) of role axiom named fact_910_zpower__zpower
% 1.70/1.92 A new axiom: (forall (X:int) (Y:nat) (Z:nat), (((eq int) ((power_power_int ((power_power_int X) Y)) Z)) ((power_power_int X) ((times_times_nat Y) Z))))
% 1.70/1.94 FOF formula (forall (Z:real) (X:real) (Y:real), (((ord_less_eq_real X) Y)->((ord_less_eq_real ((plus_plus_real Z) X)) ((plus_plus_real Z) Y)))) of role axiom named fact_911_real__add__left__mono
% 1.70/1.94 A new axiom: (forall (Z:real) (X:real) (Y:real), (((ord_less_eq_real X) Y)->((ord_less_eq_real ((plus_plus_real Z) X)) ((plus_plus_real Z) Y))))
% 1.70/1.94 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_912_diff__bin__simps_I10_J
% 1.70/1.94 A new axiom: (forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit1 K)) (bit1 L))) (bit0 ((minus_minus_int K) L))))
% 1.70/1.94 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_913_diff__bin__simps_I9_J
% 1.70/1.94 A new axiom: (forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit1 K)) (bit0 L))) (bit1 ((minus_minus_int K) L))))
% 1.70/1.94 FOF formula (forall (L:int), (((eq int) ((minus_minus_int pls) (bit0 L))) (bit0 ((minus_minus_int pls) L)))) of role axiom named fact_914_diff__bin__simps_I3_J
% 1.70/1.94 A new axiom: (forall (L:int), (((eq int) ((minus_minus_int pls) (bit0 L))) (bit0 ((minus_minus_int pls) L))))
% 1.70/1.94 FOF formula (forall (A:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int X) A)->((not (((eq int) X) ((minus_minus_int A) one_one_int)))->((ord_less_int X) ((minus_minus_int A) one_one_int)))))) of role axiom named fact_915_Euler_Oaux1
% 1.70/1.94 A new axiom: (forall (A:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int X) A)->((not (((eq int) X) ((minus_minus_int A) one_one_int)))->((ord_less_int X) ((minus_minus_int A) one_one_int))))))
% 1.70/1.94 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_916_less__bin__lemma
% 1.70/1.94 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)))
% 1.70/1.94 FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat K) I_1)) ((times_times_nat K) J))))) of role axiom named fact_917_mult__less__mono2
% 1.70/1.94 A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat K) I_1)) ((times_times_nat K) J)))))
% 1.70/1.94 FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat I_1) K)) ((times_times_nat J) K))))) of role axiom named fact_918_mult__less__mono1
% 1.70/1.94 A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat I_1) K)) ((times_times_nat J) K)))))
% 1.70/1.94 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_919_mult__less__cancel2
% 1.70/1.94 A new axiom: (forall (M:nat) (K:nat) (N:nat), ((iff ((ord_less_nat ((times_times_nat M) K)) ((times_times_nat N) K))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M) N))))
% 1.70/1.94 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_920_mult__less__cancel1
% 1.70/1.94 A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((times_times_nat K) M)) ((times_times_nat K) N))) ((and ((ord_less_nat zero_zero_nat) K)) ((ord_less_nat M) N))))
% 1.70/1.94 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_921_nat__0__less__mult__iff
% 1.70/1.94 A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((times_times_nat M) N))) ((and ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N))))
% 1.70/1.94 FOF formula (forall (X:real), ((iff (((ord_less_real zero_zero_real) ((times_times_real X) X))->False)) (((eq real) X) zero_zero_real))) of role axiom named fact_922_not__real__square__gt__zero
% 1.70/1.96 A new axiom: (forall (X:real), ((iff (((ord_less_real zero_zero_real) ((times_times_real X) X))->False)) (((eq real) X) zero_zero_real)))
% 1.70/1.96 FOF formula (forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->(((ord_less_real X) Y)->((ord_less_real ((times_times_real Z) X)) ((times_times_real Z) Y))))) of role axiom named fact_923_real__mult__less__mono2
% 1.70/1.96 A new axiom: (forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->(((ord_less_real X) Y)->((ord_less_real ((times_times_real Z) X)) ((times_times_real Z) Y)))))
% 1.70/1.96 FOF formula (forall (Y:real) (X:real), (((ord_less_real zero_zero_real) X)->(((ord_less_real zero_zero_real) Y)->((ord_less_real zero_zero_real) ((times_times_real X) Y))))) of role axiom named fact_924_real__mult__order
% 1.70/1.96 A new axiom: (forall (Y:real) (X:real), (((ord_less_real zero_zero_real) X)->(((ord_less_real zero_zero_real) Y)->((ord_less_real zero_zero_real) ((times_times_real X) Y)))))
% 1.70/1.96 FOF formula (forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_real ((times_times_real X) Z)) ((times_times_real Y) Z))) ((ord_less_real X) Y)))) of role axiom named fact_925_real__mult__less__iff1
% 1.70/1.96 A new axiom: (forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_real ((times_times_real X) Z)) ((times_times_real Y) Z))) ((ord_less_real X) Y))))
% 1.70/1.96 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_926_mult__eq__self__implies__10
% 1.70/1.96 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))))
% 1.70/1.96 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_927_diff__is__0__eq
% 1.70/1.96 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)))
% 1.70/1.96 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_928_diff__is__0__eq_H
% 1.70/1.96 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((eq nat) ((minus_minus_nat M) N)) zero_zero_nat)))
% 1.70/1.96 FOF formula (forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X) X)) ((times_times_real Y) Y))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real)))) of role axiom named fact_929_real__two__squares__add__zero__iff
% 1.70/1.96 A new axiom: (forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X) X)) ((times_times_real Y) Y))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real))))
% 1.70/1.96 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_930_diff__less__mono
% 1.70/1.96 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)))))
% 1.70/1.96 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_931_less__diff__iff
% 1.70/1.96 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)))))
% 1.70/1.96 FOF formula (forall (X:nat) (Y:nat), (((eq int) ((times_times_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((times_times_nat X) Y)))) of role axiom named fact_932_Nat__Transfer_Otransfer__int__nat__functions_I2_J
% 1.70/1.96 A new axiom: (forall (X:nat) (Y:nat), (((eq int) ((times_times_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((times_times_nat X) Y))))
% 1.70/1.98 FOF formula (forall (M:nat) (N:nat), (((eq int) ((times_times_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((times_times_nat M) N)))) of role axiom named fact_933_zmult__int
% 1.70/1.98 A new axiom: (forall (M:nat) (N:nat), (((eq int) ((times_times_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((times_times_nat M) N))))
% 1.70/1.98 FOF formula (forall (M:nat) (N:nat), (((eq int) (semiri1621563631at_int ((times_times_nat M) N))) ((times_times_int (semiri1621563631at_int M)) (semiri1621563631at_int N)))) of role axiom named fact_934_int__mult
% 1.70/1.98 A new axiom: (forall (M:nat) (N:nat), (((eq int) (semiri1621563631at_int ((times_times_nat M) N))) ((times_times_int (semiri1621563631at_int M)) (semiri1621563631at_int N))))
% 1.70/1.98 FOF formula (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat I_1) ((minus_minus_nat J) K))) ((minus_minus_nat ((plus_plus_nat I_1) K)) J)))) of role axiom named fact_935_diff__diff__right
% 1.70/1.98 A new axiom: (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat I_1) ((minus_minus_nat J) K))) ((minus_minus_nat ((plus_plus_nat I_1) K)) J))))
% 1.70/1.98 FOF formula (forall (J:nat) (K:nat) (I_1:nat), ((iff ((ord_less_eq_nat ((minus_minus_nat J) K)) I_1)) ((ord_less_eq_nat J) ((plus_plus_nat I_1) K)))) of role axiom named fact_936_le__diff__conv
% 1.70/1.98 A new axiom: (forall (J:nat) (K:nat) (I_1:nat), ((iff ((ord_less_eq_nat ((minus_minus_nat J) K)) I_1)) ((ord_less_eq_nat J) ((plus_plus_nat I_1) K))))
% 1.70/1.98 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_937_le__add__diff
% 1.70/1.98 A new axiom: (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat K) N)->((ord_less_eq_nat M) ((minus_minus_nat ((plus_plus_nat N) M)) K))))
% 1.70/1.98 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_938_le__add__diff__inverse
% 1.70/1.98 A new axiom: (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((plus_plus_nat N) ((minus_minus_nat M) N))) M)))
% 1.70/1.98 FOF formula (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((plus_plus_nat I_1) ((minus_minus_nat J) K))) ((minus_minus_nat ((plus_plus_nat I_1) J)) K)))) of role axiom named fact_939_add__diff__assoc
% 1.70/1.98 A new axiom: (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((plus_plus_nat I_1) ((minus_minus_nat J) K))) ((minus_minus_nat ((plus_plus_nat I_1) J)) K))))
% 1.70/1.98 FOF formula (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->((iff ((ord_less_eq_nat I_1) ((minus_minus_nat J) K))) ((ord_less_eq_nat ((plus_plus_nat I_1) K)) J)))) of role axiom named fact_940_le__diff__conv2
% 1.70/1.98 A new axiom: (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->((iff ((ord_less_eq_nat I_1) ((minus_minus_nat J) K))) ((ord_less_eq_nat ((plus_plus_nat I_1) K)) J))))
% 1.70/1.98 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_941_le__add__diff__inverse2
% 1.70/1.98 A new axiom: (forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq nat) ((plus_plus_nat ((minus_minus_nat M) N)) N)) M)))
% 1.70/1.98 FOF formula (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff (((eq nat) ((minus_minus_nat J) I_1)) K)) (((eq nat) J) ((plus_plus_nat K) I_1))))) of role axiom named fact_942_le__imp__diff__is__add
% 1.70/1.98 A new axiom: (forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff (((eq nat) ((minus_minus_nat J) I_1)) K)) (((eq nat) J) ((plus_plus_nat K) I_1)))))
% 1.70/1.98 FOF formula (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat I_1) J)) K)) ((plus_plus_nat I_1) ((minus_minus_nat J) K))))) of role axiom named fact_943_diff__add__assoc
% 1.70/1.98 A new axiom: (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat I_1) J)) K)) ((plus_plus_nat I_1) ((minus_minus_nat J) K)))))
% 1.80/2.00 FOF formula (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((plus_plus_nat ((minus_minus_nat J) K)) I_1)) ((minus_minus_nat ((plus_plus_nat J) I_1)) K)))) of role axiom named fact_944_add__diff__assoc2
% 1.80/2.00 A new axiom: (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((plus_plus_nat ((minus_minus_nat J) K)) I_1)) ((minus_minus_nat ((plus_plus_nat J) I_1)) K))))
% 1.80/2.00 FOF formula (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat J) I_1)) K)) ((plus_plus_nat ((minus_minus_nat J) K)) I_1)))) of role axiom named fact_945_diff__add__assoc2
% 1.80/2.00 A new axiom: (forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat J) I_1)) K)) ((plus_plus_nat ((minus_minus_nat J) K)) I_1))))
% 1.80/2.00 FOF formula (forall (X:nat) (Y:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_eq_nat X) Y))) of role axiom named fact_946_Nat__Transfer_Otransfer__int__nat__relations_I3_J
% 1.80/2.00 A new axiom: (forall (X:nat) (Y:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_eq_nat X) Y)))
% 1.80/2.00 FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_eq_nat M) N))) of role axiom named fact_947_zle__int
% 1.80/2.00 A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_eq_nat M) N)))
% 1.80/2.00 FOF formula (forall (Y:int) (X:int), ((twoSqu919416604sum2sq X)->((twoSqu919416604sum2sq Y)->(twoSqu919416604sum2sq ((times_times_int X) Y))))) of role axiom named fact_948_is__mult__sum2sq
% 1.80/2.00 A new axiom: (forall (Y:int) (X:int), ((twoSqu919416604sum2sq X)->((twoSqu919416604sum2sq Y)->(twoSqu919416604sum2sq ((times_times_int X) Y)))))
% 1.80/2.00 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_949_zle__diff1__eq
% 1.80/2.00 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)))
% 1.80/2.00 FOF formula (forall (V_1:int) (V_2:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) ((((ord_less_eq_int V_1) V_2)->False)->((ord_less_eq_int V_1) pls)))) of role axiom named fact_950_le__nat__number__of
% 1.80/2.00 A new axiom: (forall (V_1:int) (V_2:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) ((((ord_less_eq_int V_1) V_2)->False)->((ord_less_eq_int V_1) pls))))
% 1.80/2.00 FOF formula (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((iff ((ord_less_eq_nat (nat_1 X)) (nat_1 Y))) ((ord_less_eq_int X) Y))))) of role axiom named fact_951_transfer__nat__int__relations_I3_J
% 1.80/2.00 A new axiom: (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((iff ((ord_less_eq_nat (nat_1 X)) (nat_1 Y))) ((ord_less_eq_int X) Y)))))
% 1.80/2.00 FOF formula (forall (Z:int) (Z_1:int), (((ord_less_eq_int zero_zero_int) Z_1)->(((ord_less_eq_int Z_1) Z)->(((eq nat) (nat_1 ((minus_minus_int Z) Z_1))) ((minus_minus_nat (nat_1 Z)) (nat_1 Z_1)))))) of role axiom named fact_952_nat__diff__distrib
% 1.80/2.00 A new axiom: (forall (Z:int) (Z_1:int), (((ord_less_eq_int zero_zero_int) Z_1)->(((ord_less_eq_int Z_1) Z)->(((eq nat) (nat_1 ((minus_minus_int Z) Z_1))) ((minus_minus_nat (nat_1 Z)) (nat_1 Z_1))))))
% 1.80/2.00 FOF formula (forall (Z_1:int) (Z:int), (((ord_less_eq_int zero_zero_int) Z)->(((eq nat) (nat_1 ((times_times_int Z) Z_1))) ((times_times_nat (nat_1 Z)) (nat_1 Z_1))))) of role axiom named fact_953_nat__mult__distrib
% 1.80/2.00 A new axiom: (forall (Z_1:int) (Z:int), (((ord_less_eq_int zero_zero_int) Z)->(((eq nat) (nat_1 ((times_times_int Z) Z_1))) ((times_times_nat (nat_1 Z)) (nat_1 Z_1)))))
% 1.80/2.00 FOF formula (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->(((eq nat) ((times_times_nat (nat_1 X)) (nat_1 Y))) (nat_1 ((times_times_int X) Y)))))) of role axiom named fact_954_Nat__Transfer_Otransfer__nat__int__functions_I2_J
% 1.80/2.02 A new axiom: (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->(((eq nat) ((times_times_nat (nat_1 X)) (nat_1 Y))) (nat_1 ((times_times_int X) Y))))))
% 1.80/2.02 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_955_mult__eq__if
% 1.80/2.02 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))))))
% 1.80/2.02 FOF formula (forall (Z:int) (W:int), (((or ((ord_less_int zero_zero_int) W)) ((ord_less_eq_int zero_zero_int) Z))->((iff ((ord_less_eq_nat (nat_1 W)) (nat_1 Z))) ((ord_less_eq_int W) Z)))) of role axiom named fact_956_nat__le__eq__zle
% 1.80/2.02 A new axiom: (forall (Z:int) (W:int), (((or ((ord_less_int zero_zero_int) W)) ((ord_less_eq_int zero_zero_int) Z))->((iff ((ord_less_eq_nat (nat_1 W)) (nat_1 Z))) ((ord_less_eq_int W) Z))))
% 1.80/2.02 FOF formula (forall (P_1:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((power_power_nat P_1) M)) one_one_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((power_power_nat P_1) M)) ((times_times_nat P_1) ((power_power_nat P_1) ((minus_minus_nat M) one_one_nat))))))) of role axiom named fact_957_power__eq__if
% 1.80/2.02 A new axiom: (forall (P_1:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((power_power_nat P_1) M)) one_one_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((power_power_nat P_1) M)) ((times_times_nat P_1) ((power_power_nat P_1) ((minus_minus_nat M) one_one_nat)))))))
% 1.80/2.02 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_958_nat__mult__2
% 1.80/2.02 A new axiom: (forall (Z:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z)) ((plus_plus_nat Z) Z)))
% 1.80/2.02 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_959_nat__mult__2__right
% 1.80/2.02 A new axiom: (forall (Z:nat), (((eq nat) ((times_times_nat Z) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z) Z)))
% 1.80/2.02 FOF formula (forall (V_2:int) (K:nat) (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((times_times_nat (number_number_of_nat V_1)) ((times_times_nat (number_number_of_nat V_2)) K))) zero_zero_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((times_times_nat (number_number_of_nat V_1)) ((times_times_nat (number_number_of_nat V_2)) K))) ((times_times_nat (number_number_of_nat ((times_times_int V_1) V_2))) K))))) of role axiom named fact_960_nat__number__of__mult__left
% 1.80/2.02 A new axiom: (forall (V_2:int) (K:nat) (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((times_times_nat (number_number_of_nat V_1)) ((times_times_nat (number_number_of_nat V_2)) K))) zero_zero_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((times_times_nat (number_number_of_nat V_1)) ((times_times_nat (number_number_of_nat V_2)) K))) ((times_times_nat (number_number_of_nat ((times_times_int V_1) V_2))) K)))))
% 1.80/2.02 FOF formula (forall (V_2:int) (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((times_times_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) zero_zero_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((times_times_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) (number_number_of_nat ((times_times_int V_1) V_2)))))) of role axiom named fact_961_mult__nat__number__of
% 1.80/2.02 A new axiom: (forall (V_2:int) (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((times_times_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) zero_zero_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((times_times_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) (number_number_of_nat ((times_times_int V_1) V_2))))))
% 1.80/2.04 FOF formula (forall (X:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit0 (bit1 pls))))) ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X)) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_962_four__x__squared
% 1.80/2.04 A new axiom: (forall (X:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit0 (bit1 pls))))) ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X)) (number_number_of_nat (bit0 (bit1 pls))))))
% 1.80/2.04 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_963_two__realpow__ge__one
% 1.80/2.04 A new axiom: (forall (N:nat), ((ord_less_eq_real one_one_real) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N)))
% 1.80/2.04 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_964_Euler_Oaux2
% 1.80/2.04 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)))))
% 1.80/2.04 FOF formula (forall (A:int) (B:int), (((eq int) ((times_times_int ((plus_plus_int A) B)) ((minus_minus_int A) B))) ((minus_minus_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_965_zspecial__product
% 1.80/2.04 A new axiom: (forall (A:int) (B:int), (((eq int) ((times_times_int ((plus_plus_int A) B)) ((minus_minus_int A) B))) ((minus_minus_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls)))))))
% 1.80/2.04 FOF formula (forall (X:nat) (Y:nat), (((eq nat) ((minus_minus_nat ((power_power_nat X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((plus_plus_nat X) Y)) ((minus_minus_nat X) Y)))) of role axiom named fact_966_diff__square
% 1.80/2.04 A new axiom: (forall (X:nat) (Y:nat), (((eq nat) ((minus_minus_nat ((power_power_nat X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((plus_plus_nat X) Y)) ((minus_minus_nat X) Y))))
% 1.80/2.04 FOF formula (forall (A:int) (B:int), (((eq int) ((power_power_int ((minus_minus_int A) B)) (number_number_of_nat (bit1 (bit1 pls))))) ((minus_minus_int ((plus_plus_int ((minus_minus_int ((power_power_int A) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls)))))) B))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) A)) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))) ((power_power_int B) (number_number_of_nat (bit1 (bit1 pls))))))) of role axiom named fact_967_zdiff__power3
% 1.80/2.04 A new axiom: (forall (A:int) (B:int), (((eq int) ((power_power_int ((minus_minus_int A) B)) (number_number_of_nat (bit1 (bit1 pls))))) ((minus_minus_int ((plus_plus_int ((minus_minus_int ((power_power_int A) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls)))))) B))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) A)) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))) ((power_power_int B) (number_number_of_nat (bit1 (bit1 pls)))))))
% 1.80/2.04 FOF formula (forall (A:int) (B:int), (((eq int) ((power_power_int ((minus_minus_int A) B)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((minus_minus_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A)) B))) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_968_zdiff__power2
% 1.80/2.06 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)))))))
% 1.80/2.06 FOF formula (forall (B:int) (Q:int) (R_1:int) (B_1:int) (Q_1:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B) Q)) R_1)) ((plus_plus_int ((times_times_int B_1) Q_1)) R_2))->(((ord_less_int ((plus_plus_int ((times_times_int B_1) Q_1)) R_2)) zero_zero_int)->(((ord_less_int R_1) B)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B_1)->(((ord_less_eq_int B_1) B)->((ord_less_eq_int Q_1) Q)))))))) of role axiom named fact_969_zdiv__mono2__neg__lemma
% 1.80/2.06 A new axiom: (forall (B:int) (Q:int) (R_1:int) (B_1:int) (Q_1:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B) Q)) R_1)) ((plus_plus_int ((times_times_int B_1) Q_1)) R_2))->(((ord_less_int ((plus_plus_int ((times_times_int B_1) Q_1)) R_2)) zero_zero_int)->(((ord_less_int R_1) B)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B_1)->(((ord_less_eq_int B_1) B)->((ord_less_eq_int Q_1) Q))))))))
% 1.80/2.06 FOF formula (forall (B:int) (Q_1:int) (R_2:int) (Q:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B) Q_1)) R_2)) ((plus_plus_int ((times_times_int B) Q)) R_1))->(((ord_less_eq_int R_1) zero_zero_int)->(((ord_less_int B) R_1)->(((ord_less_int B) R_2)->((ord_less_eq_int Q) Q_1)))))) of role axiom named fact_970_unique__quotient__lemma__neg
% 1.80/2.06 A new axiom: (forall (B:int) (Q_1:int) (R_2:int) (Q:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B) Q_1)) R_2)) ((plus_plus_int ((times_times_int B) Q)) R_1))->(((ord_less_eq_int R_1) zero_zero_int)->(((ord_less_int B) R_1)->(((ord_less_int B) R_2)->((ord_less_eq_int Q) Q_1))))))
% 1.80/2.06 FOF formula (forall (B:int) (Q:int) (R_1:int) (B_1:int) (Q_1:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B) Q)) R_1)) ((plus_plus_int ((times_times_int B_1) Q_1)) R_2))->(((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_1) Q_1)) R_2))->(((ord_less_int R_2) B_1)->(((ord_less_eq_int zero_zero_int) R_1)->(((ord_less_int zero_zero_int) B_1)->(((ord_less_eq_int B_1) B)->((ord_less_eq_int Q) Q_1)))))))) of role axiom named fact_971_zdiv__mono2__lemma
% 1.80/2.06 A new axiom: (forall (B:int) (Q:int) (R_1:int) (B_1:int) (Q_1:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B) Q)) R_1)) ((plus_plus_int ((times_times_int B_1) Q_1)) R_2))->(((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_1) Q_1)) R_2))->(((ord_less_int R_2) B_1)->(((ord_less_eq_int zero_zero_int) R_1)->(((ord_less_int zero_zero_int) B_1)->(((ord_less_eq_int B_1) B)->((ord_less_eq_int Q) Q_1))))))))
% 1.80/2.06 FOF formula (forall (B:int) (Q_1:int) (R_2:int) (Q:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B) Q_1)) R_2)) ((plus_plus_int ((times_times_int B) Q)) R_1))->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int R_2) B)->(((ord_less_int R_1) B)->((ord_less_eq_int Q_1) Q)))))) of role axiom named fact_972_unique__quotient__lemma
% 1.80/2.06 A new axiom: (forall (B:int) (Q_1:int) (R_2:int) (Q:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B) Q_1)) R_2)) ((plus_plus_int ((times_times_int B) Q)) R_1))->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int R_2) B)->(((ord_less_int R_1) B)->((ord_less_eq_int Q_1) Q))))))
% 1.80/2.06 FOF formula (((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)))))) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int n)))) of role axiom named fact_973_xy
% 1.80/2.07 A new axiom: (((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)))))) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))
% 1.80/2.07 FOF formula (forall (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->(((eq nat) ((minus_minus_nat (nat_1 P_1)) (number_number_of_nat (bit0 (bit1 pls))))) (nat_1 ((minus_minus_int P_1) (number_number_of_int (bit0 (bit1 pls)))))))) of role axiom named fact_974_Int2_Oaux__1
% 1.80/2.07 A new axiom: (forall (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->(((eq nat) ((minus_minus_nat (nat_1 P_1)) (number_number_of_nat (bit0 (bit1 pls))))) (nat_1 ((minus_minus_int P_1) (number_number_of_int (bit0 (bit1 pls))))))))
% 1.80/2.07 FOF formula (forall (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((ord_less_nat zero_zero_nat) (nat_1 ((minus_minus_int P_1) (number_number_of_int (bit0 (bit1 pls)))))))) of role axiom named fact_975_Int2_Oaux__2
% 1.80/2.07 A new axiom: (forall (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((ord_less_nat zero_zero_nat) (nat_1 ((minus_minus_int P_1) (number_number_of_int (bit0 (bit1 pls))))))))
% 1.80/2.07 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_976__096_B_Bthesis_O_A_I_B_Bt_O_As_____A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_
% 1.80/2.07 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)
% 1.80/2.07 FOF formula (forall (W:real), ((ord_less_eq_real W) W)) of role axiom named fact_977_real__le__refl
% 1.80/2.07 A new axiom: (forall (W:real), ((ord_less_eq_real W) W))
% 1.80/2.07 FOF formula (forall (Z:real) (W:real), (((eq real) ((times_times_real Z) W)) ((times_times_real W) Z))) of role axiom named fact_978_real__mult__commute
% 1.80/2.07 A new axiom: (forall (Z:real) (W:real), (((eq real) ((times_times_real Z) W)) ((times_times_real W) Z)))
% 1.80/2.07 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_979_real__le__linear
% 1.80/2.07 A new axiom: (forall (Z:real) (W:real), ((or ((ord_less_eq_real Z) W)) ((ord_less_eq_real W) Z)))
% 1.80/2.07 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_980_real__mult__assoc
% 1.80/2.07 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))))
% 1.80/2.07 FOF formula (forall (K:real) (I_1:real) (J:real), (((ord_less_eq_real I_1) J)->(((ord_less_eq_real J) K)->((ord_less_eq_real I_1) K)))) of role axiom named fact_981_real__le__trans
% 1.80/2.07 A new axiom: (forall (K:real) (I_1:real) (J:real), (((ord_less_eq_real I_1) J)->(((ord_less_eq_real J) K)->((ord_less_eq_real I_1) K))))
% 1.80/2.07 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_982_real__le__antisym
% 1.80/2.07 A new axiom: (forall (Z:real) (W:real), (((ord_less_eq_real Z) W)->(((ord_less_eq_real W) Z)->(((eq real) Z) W))))
% 1.80/2.07 FOF formula (zprime (number_number_of_int (bit0 (bit1 pls)))) of role axiom named fact_983_zprime__2
% 1.80/2.07 A new axiom: (zprime (number_number_of_int (bit0 (bit1 pls))))
% 1.80/2.07 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_984_Int2_Oaux1
% 1.80/2.07 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))))
% 1.89/2.09 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_985__0964_A_K_Am_A_L_A1_Advd_As_____A_094_A2_A_L_A1_096
% 1.89/2.09 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))
% 1.89/2.09 FOF formula (forall (X:real) (Y:real), (((eq real) ((power_power_real ((plus_plus_real X) Y)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X)) Y)))) of role axiom named fact_986_real__sum__squared__expand
% 1.89/2.09 A new axiom: (forall (X:real) (Y:real), (((eq real) ((power_power_real ((plus_plus_real X) Y)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X)) Y))))
% 1.89/2.09 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_987__096s_____A_094_A2_A_N_A_N1_A_061_As_____A_094_A2_A_L_A1_096
% 1.89/2.09 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))
% 1.89/2.09 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_988__0964_A_K_Am_A_L_A1_Advd_As_____A_094_A2_A_N_A_N1_096
% 1.89/2.09 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)))
% 1.89/2.09 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_989__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096
% 1.89/2.09 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)
% 1.89/2.09 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_990_zdvd__zdiffD
% 1.89/2.09 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))))
% 1.89/2.09 FOF formula (forall (M:int) (N:int) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((times_times_int M) N))->((or ((dvd_dvd_int P_1) M)) ((dvd_dvd_int P_1) N))))) of role axiom named fact_991_zprime__zdvd__zmult__better
% 1.89/2.09 A new axiom: (forall (M:int) (N:int) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((times_times_int M) N))->((or ((dvd_dvd_int P_1) M)) ((dvd_dvd_int P_1) N)))))
% 1.89/2.09 FOF formula ((ord_less_eq_int min) min) of role axiom named fact_992_rel__simps_I24_J
% 1.89/2.09 A new axiom: ((ord_less_eq_int min) min)
% 1.89/2.09 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_993_zdvd__bounds
% 1.89/2.09 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))))
% 1.89/2.09 FOF formula (forall (A:int) (N:nat) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((power_power_int A) N))->((dvd_dvd_int P_1) A)))) of role axiom named fact_994_zprime__zdvd__power
% 1.89/2.11 A new axiom: (forall (A:int) (N:nat) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((power_power_int A) N))->((dvd_dvd_int P_1) A))))
% 1.89/2.11 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_995_zdvd__not__zless
% 1.89/2.11 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))))
% 1.89/2.11 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_996_zdvd__mult__cancel
% 1.89/2.11 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))))
% 1.89/2.11 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_997_zdvd__antisym__nonneg
% 1.89/2.11 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))))))
% 1.89/2.11 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_998_zdvd__reduce
% 1.89/2.11 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)))
% 1.89/2.11 FOF formula (forall (C:int) (X:int) (T:int) (A:int) (D:int), (((dvd_dvd_int A) D)->((iff ((dvd_dvd_int A) ((plus_plus_int X) T))) ((dvd_dvd_int A) ((plus_plus_int ((plus_plus_int X) ((times_times_int C) D))) T))))) of role axiom named fact_999_zdvd__period
% 1.89/2.11 A new axiom: (forall (C:int) (X:int) (T:int) (A:int) (D:int), (((dvd_dvd_int A) D)->((iff ((dvd_dvd_int A) ((plus_plus_int X) T))) ((dvd_dvd_int A) ((plus_plus_int ((plus_plus_int X) ((times_times_int C) D))) T)))))
% 1.89/2.11 FOF formula (forall (K:int), ((iff ((ord_less_int min) (bit1 K))) ((ord_less_int min) K))) of role axiom named fact_1000_rel__simps_I9_J
% 1.89/2.11 A new axiom: (forall (K:int), ((iff ((ord_less_int min) (bit1 K))) ((ord_less_int min) K)))
% 1.89/2.11 FOF formula (forall (K:int), ((iff ((ord_less_int (bit1 K)) min)) ((ord_less_int K) min))) of role axiom named fact_1001_rel__simps_I13_J
% 1.89/2.11 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit1 K)) min)) ((ord_less_int K) min)))
% 1.89/2.11 FOF formula ((ord_less_int min) pls) of role axiom named fact_1002_rel__simps_I6_J
% 1.89/2.11 A new axiom: ((ord_less_int min) pls)
% 1.89/2.11 FOF formula (((ord_less_int pls) min)->False) of role axiom named fact_1003_rel__simps_I3_J
% 1.89/2.11 A new axiom: (((ord_less_int pls) min)->False)
% 1.89/2.11 FOF formula (forall (K:int), ((iff ((ord_less_int min) (bit0 K))) ((ord_less_int min) K))) of role axiom named fact_1004_rel__simps_I8_J
% 1.89/2.11 A new axiom: (forall (K:int), ((iff ((ord_less_int min) (bit0 K))) ((ord_less_int min) K)))
% 1.89/2.11 FOF formula (forall (K:int), ((iff ((ord_less_eq_int min) (bit1 K))) ((ord_less_eq_int min) K))) of role axiom named fact_1005_rel__simps_I26_J
% 1.89/2.11 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int min) (bit1 K))) ((ord_less_eq_int min) K)))
% 1.89/2.11 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) min)) ((ord_less_eq_int K) min))) of role axiom named fact_1006_rel__simps_I30_J
% 1.89/2.11 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) min)) ((ord_less_eq_int K) min)))
% 1.89/2.11 FOF formula ((ord_less_int min) zero_zero_int) of role axiom named fact_1007_bin__less__0__simps_I2_J
% 1.89/2.11 A new axiom: ((ord_less_int min) zero_zero_int)
% 1.89/2.11 FOF formula ((ord_less_eq_int min) pls) of role axiom named fact_1008_rel__simps_I23_J
% 1.89/2.11 A new axiom: ((ord_less_eq_int min) pls)
% 1.89/2.11 FOF formula (((ord_less_eq_int pls) min)->False) of role axiom named fact_1009_rel__simps_I20_J
% 1.89/2.11 A new axiom: (((ord_less_eq_int pls) min)->False)
% 1.89/2.11 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) min)) ((ord_less_eq_int K) min))) of role axiom named fact_1010_rel__simps_I28_J
% 1.89/2.13 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) min)) ((ord_less_eq_int K) min)))
% 1.89/2.13 FOF formula (not (((eq int) (number_number_of_int pls)) (number_number_of_int min))) of role axiom named fact_1011_eq__number__of__Pls__Min
% 1.89/2.13 A new axiom: (not (((eq int) (number_number_of_int pls)) (number_number_of_int min)))
% 1.89/2.13 FOF formula (((ord_less_int min) min)->False) of role axiom named fact_1012_rel__simps_I7_J
% 1.89/2.13 A new axiom: (((ord_less_int min) min)->False)
% 1.89/2.13 FOF formula (forall (L:int), (not (((eq int) min) (bit0 L)))) of role axiom named fact_1013_rel__simps_I42_J
% 1.89/2.13 A new axiom: (forall (L:int), (not (((eq int) min) (bit0 L))))
% 1.89/2.13 FOF formula (forall (K:int), (not (((eq int) (bit0 K)) min))) of role axiom named fact_1014_rel__simps_I45_J
% 1.89/2.13 A new axiom: (forall (K:int), (not (((eq int) (bit0 K)) min)))
% 1.89/2.13 FOF formula (not (((eq int) min) pls)) of role axiom named fact_1015_rel__simps_I40_J
% 1.89/2.13 A new axiom: (not (((eq int) min) pls))
% 1.89/2.13 FOF formula (not (((eq int) pls) min)) of role axiom named fact_1016_rel__simps_I37_J
% 1.89/2.13 A new axiom: (not (((eq int) pls) min))
% 1.89/2.13 FOF formula (((eq int) (bit1 min)) min) of role axiom named fact_1017_Bit1__Min
% 1.89/2.13 A new axiom: (((eq int) (bit1 min)) min)
% 1.89/2.13 FOF formula (forall (L:int), ((iff (((eq int) min) (bit1 L))) (((eq int) min) L))) of role axiom named fact_1018_rel__simps_I43_J
% 1.89/2.13 A new axiom: (forall (L:int), ((iff (((eq int) min) (bit1 L))) (((eq int) min) L)))
% 1.89/2.13 FOF formula (forall (K:int), ((iff (((eq int) (bit1 K)) min)) (((eq int) K) min))) of role axiom named fact_1019_rel__simps_I47_J
% 1.89/2.13 A new axiom: (forall (K:int), ((iff (((eq int) (bit1 K)) min)) (((eq int) K) min)))
% 1.89/2.13 FOF formula (((eq int) (succ min)) pls) of role axiom named fact_1020_succ__Min
% 1.89/2.13 A new axiom: (((eq int) (succ min)) pls)
% 1.89/2.13 FOF formula (forall (K:int), (((eq int) ((minus_minus_int K) min)) (succ K))) of role axiom named fact_1021_diff__bin__simps_I2_J
% 1.89/2.13 A new axiom: (forall (K:int), (((eq int) ((minus_minus_int K) min)) (succ K)))
% 1.89/2.13 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_1022_zdvd__imp__le
% 1.89/2.13 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))))
% 1.89/2.13 FOF formula (forall (P_1:int) (Y:int) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((dvd_dvd_int P_1) Y)->((dvd_dvd_int P_1) ((power_power_int Y) N))))) of role axiom named fact_1023_zpower__zdvd__prop1
% 1.89/2.13 A new axiom: (forall (P_1:int) (Y:int) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((dvd_dvd_int P_1) Y)->((dvd_dvd_int P_1) ((power_power_int Y) N)))))
% 1.89/2.13 FOF formula (forall (K:int), ((iff ((ord_less_eq_int min) (bit0 K))) ((ord_less_int min) K))) of role axiom named fact_1024_rel__simps_I25_J
% 1.89/2.13 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int min) (bit0 K))) ((ord_less_int min) K)))
% 1.89/2.13 FOF formula (forall (K:int), ((iff ((ord_less_int (bit0 K)) min)) ((ord_less_eq_int K) min))) of role axiom named fact_1025_rel__simps_I11_J
% 1.89/2.13 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit0 K)) min)) ((ord_less_eq_int K) min)))
% 1.89/2.13 FOF formula (forall (L:int), (((eq int) ((minus_minus_int pls) (bit1 L))) (bit1 ((minus_minus_int min) L)))) of role axiom named fact_1026_diff__bin__simps_I4_J
% 1.89/2.13 A new axiom: (forall (L:int), (((eq int) ((minus_minus_int pls) (bit1 L))) (bit1 ((minus_minus_int min) L))))
% 1.89/2.13 FOF formula (forall (L:int), (((eq int) ((minus_minus_int min) (bit1 L))) (bit0 ((minus_minus_int min) L)))) of role axiom named fact_1027_diff__bin__simps_I6_J
% 1.89/2.13 A new axiom: (forall (L:int), (((eq int) ((minus_minus_int min) (bit1 L))) (bit0 ((minus_minus_int min) L))))
% 1.89/2.13 FOF formula (forall (L:int), (((eq int) ((minus_minus_int min) (bit0 L))) (bit1 ((minus_minus_int min) L)))) of role axiom named fact_1028_diff__bin__simps_I5_J
% 1.89/2.13 A new axiom: (forall (L:int), (((eq int) ((minus_minus_int min) (bit0 L))) (bit1 ((minus_minus_int min) L))))
% 1.89/2.13 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_1029_zmult__eq__1__iff
% 1.89/2.14 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))))))
% 1.89/2.14 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_1030_pos__zmult__eq__1__iff__lemma
% 1.89/2.14 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)))))
% 1.89/2.14 FOF formula (forall (N:nat) (A:int) (B:int) (P_1:int), ((zprime P_1)->((((dvd_dvd_int P_1) B)->False)->(((dvd_dvd_int ((power_power_int P_1) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P_1) N)) A))))) of role axiom named fact_1031_zprime__power__zdvd__cancel__right
% 1.89/2.14 A new axiom: (forall (N:nat) (A:int) (B:int) (P_1:int), ((zprime P_1)->((((dvd_dvd_int P_1) B)->False)->(((dvd_dvd_int ((power_power_int P_1) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P_1) N)) A)))))
% 1.89/2.14 FOF formula (forall (N:nat) (B:int) (A:int) (P_1:int), ((zprime P_1)->((((dvd_dvd_int P_1) A)->False)->(((dvd_dvd_int ((power_power_int P_1) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P_1) N)) B))))) of role axiom named fact_1032_zprime__power__zdvd__cancel__left
% 1.89/2.14 A new axiom: (forall (N:nat) (B:int) (A:int) (P_1:int), ((zprime P_1)->((((dvd_dvd_int P_1) A)->False)->(((dvd_dvd_int ((power_power_int P_1) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P_1) N)) B)))))
% 1.89/2.14 FOF formula (forall (Y:int) (N:nat) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((power_power_int Y) N))->(((ord_less_nat zero_zero_nat) N)->((dvd_dvd_int P_1) Y))))) of role axiom named fact_1033_zpower__zdvd__prop2
% 1.89/2.14 A new axiom: (forall (Y:int) (N:nat) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((power_power_int Y) N))->(((ord_less_nat zero_zero_nat) N)->((dvd_dvd_int P_1) Y)))))
% 1.89/2.14 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_1034__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096
% 1.89/2.14 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))
% 1.89/2.14 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_1035_s
% 1.89/2.14 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))
% 1.89/2.14 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_1036__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_
% 1.89/2.14 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)))
% 1.89/2.14 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_1037_s1
% 1.89/2.14 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))
% 1.89/2.16 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_1038_s0p
% 1.89/2.16 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)))
% 1.89/2.16 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_1039__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4
% 1.89/2.16 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)
% 1.89/2.16 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_1040_divides__mul__r
% 1.89/2.16 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))))
% 1.89/2.16 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_1041_divides__mul__l
% 1.89/2.16 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))))
% 1.89/2.16 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_1042_dvd__diff__nat
% 1.89/2.16 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)))))
% 1.89/2.16 FOF formula (forall (X:int) (P_1:int), ((iff (((zcong X) zero_zero_int) P_1)) ((dvd_dvd_int P_1) X))) of role axiom named fact_1043_zcong__eq__zdvd__prop
% 1.89/2.16 A new axiom: (forall (X:int) (P_1:int), ((iff (((zcong X) zero_zero_int) P_1)) ((dvd_dvd_int P_1) X)))
% 1.89/2.16 FOF formula (forall (A:int) (M:int), ((iff (((zcong A) zero_zero_int) M)) ((dvd_dvd_int M) A))) of role axiom named fact_1044_zcong__zero__equiv__div
% 1.89/2.16 A new axiom: (forall (A:int) (M:int), ((iff (((zcong A) zero_zero_int) M)) ((dvd_dvd_int M) A)))
% 1.89/2.16 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_1045_nat__dvd__not__less
% 1.89/2.16 A new axiom: (forall (N:nat) (M:nat), (((ord_less_nat zero_zero_nat) M)->(((ord_less_nat M) N)->(((dvd_dvd_nat N) M)->False))))
% 1.89/2.16 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_1046_divides__ge
% 1.89/2.16 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))))
% 1.89/2.16 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_1047_nat__mult__dvd__cancel__disj_H
% 1.89/2.16 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))))
% 1.89/2.16 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_1048_dvd__diffD
% 1.89/2.16 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)))))
% 1.99/2.19 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_1049_dvd__diffD1
% 1.99/2.19 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)))))
% 1.99/2.19 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_1050_divides__rev
% 1.99/2.19 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))))
% 1.99/2.19 FOF formula (forall (X:nat) (Y:nat) (N:nat), ((not (((eq nat) N) zero_zero_nat))->(((dvd_dvd_nat ((power_power_nat X) N)) Y)->((dvd_dvd_nat X) Y)))) of role axiom named fact_1051_divides__exp2
% 1.99/2.19 A new axiom: (forall (X:nat) (Y:nat) (N:nat), ((not (((eq nat) N) zero_zero_nat))->(((dvd_dvd_nat ((power_power_nat X) N)) Y)->((dvd_dvd_nat X) Y))))
% 1.99/2.19 FOF formula (forall (X:nat) (Y:nat), ((iff ((dvd_dvd_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((dvd_dvd_nat X) Y))) of role axiom named fact_1052_Nat__Transfer_Otransfer__int__nat__relations_I4_J
% 1.99/2.19 A new axiom: (forall (X:nat) (Y:nat), ((iff ((dvd_dvd_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((dvd_dvd_nat X) Y)))
% 1.99/2.19 FOF formula (forall (X:nat) (Y:nat), ((iff ((dvd_dvd_nat X) Y)) ((dvd_dvd_int (semiri1621563631at_int X)) (semiri1621563631at_int Y)))) of role axiom named fact_1053_zdvd__int
% 1.99/2.19 A new axiom: (forall (X:nat) (Y:nat), ((iff ((dvd_dvd_nat X) Y)) ((dvd_dvd_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))))
% 1.99/2.19 FOF formula (forall (N:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->((dvd_dvd_nat ((power_power_nat X) N)) ((power_power_nat Y) N)))) of role axiom named fact_1054_divides__exp
% 1.99/2.19 A new axiom: (forall (N:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->((dvd_dvd_nat ((power_power_nat X) N)) ((power_power_nat Y) N))))
% 1.99/2.19 FOF formula (forall (M:nat), ((iff ((dvd_dvd_nat M) one_one_nat)) (((eq nat) M) one_one_nat))) of role axiom named fact_1055_nat__dvd__1__iff__1
% 1.99/2.19 A new axiom: (forall (M:nat), ((iff ((dvd_dvd_nat M) one_one_nat)) (((eq nat) M) one_one_nat)))
% 1.99/2.19 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_1056_dvd__reduce
% 1.99/2.19 A new axiom: (forall (K:nat) (N:nat), ((iff ((dvd_dvd_nat K) ((plus_plus_nat N) K))) ((dvd_dvd_nat K) N)))
% 1.99/2.19 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_1057_divides__add__revr
% 1.99/2.19 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))))
% 1.99/2.19 FOF formula (forall (M:int), (((zcong M) zero_zero_int) M)) of role axiom named fact_1058_zcong__id
% 1.99/2.19 A new axiom: (forall (M:int), (((zcong M) zero_zero_int) M))
% 1.99/2.19 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_1059_zcong__shift
% 1.99/2.19 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)))
% 1.99/2.19 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_1060_zcong__eq__trans
% 1.99/2.19 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)))))
% 1.99/2.19 FOF formula (forall (Z:nat) (X:int) (Y:int) (M:int), ((((zcong X) Y) M)->(((zcong ((power_power_int X) Z)) ((power_power_int Y) Z)) M))) of role axiom named fact_1061_zcong__zpower
% 1.99/2.19 A new axiom: (forall (Z:nat) (X:int) (Y:int) (M:int), ((((zcong X) Y) M)->(((zcong ((power_power_int X) Z)) ((power_power_int Y) Z)) M)))
% 1.99/2.19 FOF formula (forall (M:int) (Y:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int zero_zero_int) Y)->(((ord_less_int zero_zero_int) M)->((((zcong X) Y) M)->(((ord_less_int X) M)->(((ord_less_int Y) M)->(((eq int) X) Y)))))))) of role axiom named fact_1062_zcong__less__eq
% 2.00/2.21 A new axiom: (forall (M:int) (Y:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int zero_zero_int) Y)->(((ord_less_int zero_zero_int) M)->((((zcong X) Y) M)->(((ord_less_int X) M)->(((ord_less_int Y) M)->(((eq int) X) Y))))))))
% 2.00/2.21 FOF formula (forall (M:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int X) M)->((((zcong X) zero_zero_int) M)->False)))) of role axiom named fact_1063_zcong__not__zero
% 2.00/2.21 A new axiom: (forall (M:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int X) M)->((((zcong X) zero_zero_int) M)->False))))
% 2.00/2.21 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_1064_zcong__zmult__prop1
% 2.00/2.21 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))))
% 2.00/2.21 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_1065_zcong__zmult__prop2
% 2.00/2.21 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))))
% 2.00/2.21 FOF formula (forall (M:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_int X) M)->((((zcong X) zero_zero_int) M)->(((eq int) X) zero_zero_int))))) of role axiom named fact_1066_Int2_Ozcong__zero
% 2.00/2.21 A new axiom: (forall (M:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_int X) M)->((((zcong X) zero_zero_int) M)->(((eq int) X) zero_zero_int)))))
% 2.00/2.21 FOF formula (forall (Y:int) (X:int) (P_1:int), ((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((((zcong Y) zero_zero_int) P_1)->False)->((((zcong ((times_times_int X) Y)) zero_zero_int) P_1)->False))))) of role axiom named fact_1067_zcong__zmult__prop3
% 2.00/2.21 A new axiom: (forall (Y:int) (X:int) (P_1:int), ((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((((zcong Y) zero_zero_int) P_1)->False)->((((zcong ((times_times_int X) Y)) zero_zero_int) P_1)->False)))))
% 2.00/2.21 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_1068_dvd__imp__le
% 2.00/2.21 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))))
% 2.00/2.21 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_1069_dvd__mult__cancel
% 2.00/2.21 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))))
% 2.00/2.21 FOF formula (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) B)) zero_zero_int) P_1)->((or (((zcong A) zero_zero_int) P_1)) (((zcong B) zero_zero_int) P_1)))))) of role axiom named fact_1070_zcong__zprime__prod__zero
% 2.00/2.21 A new axiom: (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) B)) zero_zero_int) P_1)->((or (((zcong A) zero_zero_int) P_1)) (((zcong B) zero_zero_int) P_1))))))
% 2.00/2.21 FOF formula (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->(((and ((((zcong A) zero_zero_int) P_1)->False)) ((((zcong B) zero_zero_int) P_1)->False))->((((zcong ((times_times_int A) B)) zero_zero_int) P_1)->False))))) of role axiom named fact_1071_zcong__zprime__prod__zero__contra
% 2.00/2.21 A new axiom: (forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->(((and ((((zcong A) zero_zero_int) P_1)->False)) ((((zcong B) zero_zero_int) P_1)->False))->((((zcong ((times_times_int A) B)) zero_zero_int) P_1)->False)))))
% 2.01/2.23 FOF formula (forall (X:nat) (Q:nat) (N:nat) (R_1:nat), ((((eq nat) X) ((plus_plus_nat ((times_times_nat Q) N)) R_1))->(((ord_less_nat zero_zero_nat) R_1)->(((ord_less_nat R_1) N)->(((dvd_dvd_nat N) X)->False))))) of role axiom named fact_1072_divides__div__not
% 2.01/2.23 A new axiom: (forall (X:nat) (Q:nat) (N:nat) (R_1:nat), ((((eq nat) X) ((plus_plus_nat ((times_times_nat Q) N)) R_1))->(((ord_less_nat zero_zero_nat) R_1)->(((ord_less_nat R_1) N)->(((dvd_dvd_nat N) X)->False)))))
% 2.01/2.23 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_1073_dvd__mult__cancel1
% 2.01/2.23 A new axiom: (forall (N:nat) (M:nat), (((ord_less_nat zero_zero_nat) M)->((iff ((dvd_dvd_nat ((times_times_nat M) N)) M)) (((eq nat) N) one_one_nat))))
% 2.01/2.23 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_1074_dvd__mult__cancel2
% 2.01/2.23 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))))
% 2.01/2.23 FOF formula (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((iff ((dvd_dvd_nat (nat_1 X)) (nat_1 Y))) ((dvd_dvd_int X) Y))))) of role axiom named fact_1075_transfer__nat__int__relations_I4_J
% 2.01/2.23 A new axiom: (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((iff ((dvd_dvd_nat (nat_1 X)) (nat_1 Y))) ((dvd_dvd_int X) Y)))))
% 2.01/2.23 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_1076_power__dvd__imp__le
% 2.01/2.23 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))))
% 2.01/2.23 FOF formula (forall (Z:int) (M:nat), ((iff ((dvd_dvd_nat (nat_1 Z)) M)) ((and (((ord_less_eq_int zero_zero_int) Z)->((dvd_dvd_int Z) (semiri1621563631at_int M)))) ((((ord_less_eq_int zero_zero_int) Z)->False)->(((eq nat) M) zero_zero_nat))))) of role axiom named fact_1077_nat__dvd__iff
% 2.01/2.23 A new axiom: (forall (Z:int) (M:nat), ((iff ((dvd_dvd_nat (nat_1 Z)) M)) ((and (((ord_less_eq_int zero_zero_int) Z)->((dvd_dvd_int Z) (semiri1621563631at_int M)))) ((((ord_less_eq_int zero_zero_int) Z)->False)->(((eq nat) M) zero_zero_nat)))))
% 2.01/2.23 FOF formula (forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((((zcong X) (number_number_of_int min)) P_1)->((((zcong X) one_one_int) P_1)->False)))) of role axiom named fact_1078_zcong__neg__1__impl__ne__1
% 2.01/2.23 A new axiom: (forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((((zcong X) (number_number_of_int min)) P_1)->((((zcong X) one_one_int) P_1)->False))))
% 2.01/2.23 FOF formula (forall (Y:int) (X:int) (P_1:int), (((((zcong X) zero_zero_int) P_1)->False)->((((zcong ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls))))) X) P_1)->(((dvd_dvd_int P_1) Y)->False)))) of role axiom named fact_1079_Euler_Oaux____1
% 2.01/2.23 A new axiom: (forall (Y:int) (X:int) (P_1:int), (((((zcong X) zero_zero_int) P_1)->False)->((((zcong ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls))))) X) P_1)->(((dvd_dvd_int P_1) Y)->False))))
% 2.01/2.23 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_1080_divides__cases
% 2.01/2.23 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))))
% 2.01/2.23 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_1081_Legendre__1mod4
% 2.01/2.25 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)))
% 2.01/2.25 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_1082__096_091s_____A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_
% 2.01/2.25 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))
% 2.01/2.25 FOF formula ((ex int) (fun (X_1:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X_1)) ((ord_less_int X_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) X_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (forall (Y_1:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y_1)) ((ord_less_int Y_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) Y_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))->(((eq int) Y_1) X_1)))))) of role axiom named fact_1083__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s
% 2.01/2.25 A new axiom: ((ex int) (fun (X_1:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X_1)) ((ord_less_int X_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) X_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (forall (Y_1:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y_1)) ((ord_less_int Y_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) Y_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))->(((eq int) Y_1) X_1))))))
% 2.01/2.25 FOF formula (forall (X:nat), ((dvd_dvd_nat X) X)) of role axiom named fact_1084_dvd_Oorder__refl
% 2.01/2.25 A new axiom: (forall (X:nat), ((dvd_dvd_nat X) X))
% 2.01/2.25 FOF formula ((forall (S:int), (((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)))->False))->False) of role axiom named fact_1085__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
% 2.01/2.25 A new axiom: ((forall (S:int), (((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)))->False))->False)
% 2.01/2.25 FOF formula (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False))) of role axiom named fact_1086_dvd_Oless__asym
% 2.01/2.25 A new axiom: (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False)))
% 2.01/2.25 FOF formula (forall (Z:nat) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) Z)) (((dvd_dvd_nat Z) Y)->False))->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False))))) of role axiom named fact_1087_dvd_Oless__trans
% 2.01/2.27 A new axiom: (forall (Z:nat) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) Z)) (((dvd_dvd_nat Z) Y)->False))->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False)))))
% 2.01/2.27 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_1088_dvd_Oless__asym_H
% 2.01/2.27 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)))
% 2.01/2.27 FOF formula (forall (Z:nat) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((dvd_dvd_nat Y) Z)->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False))))) of role axiom named fact_1089_dvd_Oless__le__trans
% 2.01/2.27 A new axiom: (forall (Z:nat) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((dvd_dvd_nat Y) Z)->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False)))))
% 2.01/2.27 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_1090_dvd_Oord__less__eq__trans
% 2.01/2.27 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)))))
% 2.01/2.27 FOF formula (forall (P:Prop) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->P))) of role axiom named fact_1091_dvd_Oless__imp__triv
% 2.01/2.27 A new axiom: (forall (P:Prop) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->P)))
% 2.01/2.27 FOF formula (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) Y) X)))) of role axiom named fact_1092_dvd_Oless__imp__not__eq2
% 2.01/2.27 A new axiom: (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) Y) X))))
% 2.01/2.27 FOF formula (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) X) Y)))) of role axiom named fact_1093_dvd_Oless__imp__not__eq
% 2.01/2.27 A new axiom: (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) X) Y))))
% 2.01/2.27 FOF formula (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False))) of role axiom named fact_1094_dvd_Oless__imp__not__less
% 2.01/2.27 A new axiom: (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False)))
% 2.01/2.27 FOF formula (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->((dvd_dvd_nat X) Y))) of role axiom named fact_1095_dvd_Oless__imp__le
% 2.01/2.27 A new axiom: (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->((dvd_dvd_nat X) Y)))
% 2.01/2.27 FOF formula (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False))) of role axiom named fact_1096_dvd_Oless__not__sym
% 2.01/2.27 A new axiom: (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False)))
% 2.01/2.27 FOF formula (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) X) Y)))) of role axiom named fact_1097_dvd_Oless__imp__neq
% 2.01/2.27 A new axiom: (forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) X) Y))))
% 2.01/2.27 FOF formula (forall (Z:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((and ((dvd_dvd_nat Y) Z)) (((dvd_dvd_nat Z) Y)->False))->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False))))) of role axiom named fact_1098_dvd_Ole__less__trans
% 2.01/2.29 A new axiom: (forall (Z:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((and ((dvd_dvd_nat Y) Z)) (((dvd_dvd_nat Z) Y)->False))->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False)))))
% 2.01/2.29 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_1099_dvd_Oord__eq__less__trans
% 2.01/2.29 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)))))
% 2.01/2.29 FOF formula (forall (Z:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((dvd_dvd_nat Y) Z)->((dvd_dvd_nat X) Z)))) of role axiom named fact_1100_dvd_Oorder__trans
% 2.01/2.29 A new axiom: (forall (Z:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((dvd_dvd_nat Y) Z)->((dvd_dvd_nat X) Z))))
% 2.01/2.29 FOF formula (forall (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((dvd_dvd_nat Y) X)->(((eq nat) X) Y)))) of role axiom named fact_1101_dvd_Oantisym
% 2.01/2.29 A new axiom: (forall (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((dvd_dvd_nat Y) X)->(((eq nat) X) Y))))
% 2.01/2.29 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_1102_dvd__antisym
% 2.01/2.29 A new axiom: (forall (M:nat) (N:nat), (((dvd_dvd_nat M) N)->(((dvd_dvd_nat N) M)->(((eq nat) M) N))))
% 2.01/2.29 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_1103_dvd_Oord__le__eq__trans
% 2.01/2.29 A new axiom: (forall (C:nat) (A:nat) (B:nat), (((dvd_dvd_nat A) B)->((((eq nat) B) C)->((dvd_dvd_nat A) C))))
% 2.01/2.29 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_1104_dvd_Oord__eq__le__trans
% 2.01/2.29 A new axiom: (forall (C:nat) (A:nat) (B:nat), ((((eq nat) A) B)->(((dvd_dvd_nat B) C)->((dvd_dvd_nat A) C))))
% 2.01/2.29 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_1105_dvd_Ole__neq__trans
% 2.01/2.29 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)))))
% 2.01/2.29 FOF formula (forall (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->((or ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) (((eq nat) X) Y)))) of role axiom named fact_1106_dvd_Ole__imp__less__or__eq
% 2.01/2.29 A new axiom: (forall (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->((or ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) (((eq nat) X) Y))))
% 2.01/2.29 FOF formula (forall (Y:nat) (X:nat), (((dvd_dvd_nat Y) X)->((iff ((dvd_dvd_nat X) Y)) (((eq nat) X) Y)))) of role axiom named fact_1107_dvd_Oantisym__conv
% 2.01/2.29 A new axiom: (forall (Y:nat) (X:nat), (((dvd_dvd_nat Y) X)->((iff ((dvd_dvd_nat X) Y)) (((eq nat) X) Y))))
% 2.01/2.29 FOF formula (forall (X:nat) (Y:nat), ((((eq nat) X) Y)->((dvd_dvd_nat X) Y))) of role axiom named fact_1108_dvd_Oeq__refl
% 2.01/2.29 A new axiom: (forall (X:nat) (Y:nat), ((((eq nat) X) Y)->((dvd_dvd_nat X) Y)))
% 2.01/2.29 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_1109_dvd_Oneq__le__trans
% 2.01/2.29 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)))))
% 2.01/2.29 FOF formula (forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False)))) of role axiom named fact_1110_dvd_Oless__le__not__le
% 2.01/2.29 A new axiom: (forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))))
% 2.01/2.29 FOF formula (forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) ((and ((dvd_dvd_nat X) Y)) (not (((eq nat) X) Y))))) of role axiom named fact_1111_dvd_Oless__le
% 2.01/2.29 A new axiom: (forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) ((and ((dvd_dvd_nat X) Y)) (not (((eq nat) X) Y)))))
% 2.10/2.31 FOF formula (forall (X:nat) (Y:nat), ((iff ((dvd_dvd_nat X) Y)) ((or ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) (((eq nat) X) Y)))) of role axiom named fact_1112_dvd_Ole__less
% 2.10/2.31 A new axiom: (forall (X:nat) (Y:nat), ((iff ((dvd_dvd_nat X) Y)) ((or ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) (((eq nat) X) Y))))
% 2.10/2.31 FOF formula (forall (X:nat) (Y:nat), ((iff (((eq nat) X) Y)) ((and ((dvd_dvd_nat X) Y)) ((dvd_dvd_nat Y) X)))) of role axiom named fact_1113_dvd_Oeq__iff
% 2.10/2.31 A new axiom: (forall (X:nat) (Y:nat), ((iff (((eq nat) X) Y)) ((and ((dvd_dvd_nat X) Y)) ((dvd_dvd_nat Y) X))))
% 2.10/2.31 FOF formula (forall (X:nat), (((and ((dvd_dvd_nat X) X)) (((dvd_dvd_nat X) X)->False))->False)) of role axiom named fact_1114_dvd_Oless__irrefl
% 2.10/2.31 A new axiom: (forall (X:nat), (((and ((dvd_dvd_nat X) X)) (((dvd_dvd_nat X) X)->False))->False))
% 2.10/2.31 FOF formula (forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) ((dvd_dvd_nat Y) X))) (((eq nat) X) Y))) of role axiom named fact_1115_divides__antisym
% 2.10/2.31 A new axiom: (forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) ((dvd_dvd_nat Y) X))) (((eq nat) X) Y)))
% 2.10/2.31 FOF formula (forall (J: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)) ((power_power_int (number_number_of_int min)) K)) M)->(((eq int) ((power_power_int (number_number_of_int min)) J)) ((power_power_int (number_number_of_int min)) K))))) of role axiom named fact_1116_neg__one__power__eq__mod__m
% 2.10/2.31 A new axiom: (forall (J: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)) ((power_power_int (number_number_of_int min)) K)) M)->(((eq int) ((power_power_int (number_number_of_int min)) J)) ((power_power_int (number_number_of_int min)) K)))))
% 2.10/2.31 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_1117_one__not__neg__one__mod__m
% 2.10/2.31 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)))
% 2.10/2.31 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_1118_neg__one__power
% 2.10/2.31 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))))
% 2.10/2.31 FOF formula (forall (A:int) (P_1:int), ((and ((((zcong A) zero_zero_int) P_1)->(((eq int) ((legendre A) P_1)) zero_zero_int))) (((((zcong A) zero_zero_int) P_1)->False)->((and (((quadRes P_1) A)->(((eq int) ((legendre A) P_1)) one_one_int))) ((((quadRes P_1) A)->False)->(((eq int) ((legendre A) P_1)) (number_number_of_int min))))))) of role axiom named fact_1119_Legendre__def
% 2.10/2.31 A new axiom: (forall (A:int) (P_1:int), ((and ((((zcong A) zero_zero_int) P_1)->(((eq int) ((legendre A) P_1)) zero_zero_int))) (((((zcong A) zero_zero_int) P_1)->False)->((and (((quadRes P_1) A)->(((eq int) ((legendre A) P_1)) one_one_int))) ((((quadRes P_1) A)->False)->(((eq int) ((legendre A) P_1)) (number_number_of_int min)))))))
% 2.10/2.31 FOF formula (forall (M:int) (X:int), ((iff ((quadRes M) X)) ((ex int) (fun (Y_1:int)=> (((zcong ((power_power_int Y_1) (number_number_of_nat (bit0 (bit1 pls))))) X) M))))) of role axiom named fact_1120_QuadRes__def
% 2.10/2.31 A new axiom: (forall (M:int) (X:int), ((iff ((quadRes M) X)) ((ex int) (fun (Y_1:int)=> (((zcong ((power_power_int Y_1) (number_number_of_nat (bit0 (bit1 pls))))) X) M)))))
% 2.10/2.31 FOF formula (forall (X:int) (P_1:int), ((zprime P_1)->((((dvd_dvd_int P_1) X)->False)->(((zcong ((power_power_int X) (nat_1 ((minus_minus_int P_1) one_one_int)))) one_one_int) P_1)))) of role axiom named fact_1121_Little__Fermat
% 2.10/2.34 A new axiom: (forall (X:int) (P_1:int), ((zprime P_1)->((((dvd_dvd_int P_1) X)->False)->(((zcong ((power_power_int X) (nat_1 ((minus_minus_int P_1) one_one_int)))) one_one_int) P_1))))
% 2.10/2.34 FOF formula (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P_1)->((((zcong ((times_times_int A) A)) one_one_int) P_1)->((or (((eq int) A) one_one_int)) (((eq int) A) ((minus_minus_int P_1) one_one_int)))))))) of role axiom named fact_1122_zcong__square__zless
% 2.10/2.34 A new axiom: (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P_1)->((((zcong ((times_times_int A) A)) one_one_int) P_1)->((or (((eq int) A) one_one_int)) (((eq int) A) ((minus_minus_int P_1) one_one_int))))))))
% 2.10/2.34 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_1123_zcong__trans
% 2.10/2.34 A new axiom: (forall (C:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((zcong B) C) M)->(((zcong A) C) M))))
% 2.10/2.34 FOF formula (forall (K:int) (M:int), (((zcong K) K) M)) of role axiom named fact_1124_zcong__refl
% 2.10/2.34 A new axiom: (forall (K:int) (M:int), (((zcong K) K) M))
% 2.10/2.34 FOF formula (forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) (((zcong B) A) M))) of role axiom named fact_1125_zcong__sym
% 2.10/2.34 A new axiom: (forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) (((zcong B) A) M)))
% 2.10/2.34 FOF formula (forall (A:int) (B:int), ((iff (((zcong A) B) zero_zero_int)) (((eq int) A) B))) of role axiom named fact_1126_IntPrimes_Ozcong__zero
% 2.10/2.34 A new axiom: (forall (A:int) (B:int), ((iff (((zcong A) B) zero_zero_int)) (((eq int) A) B)))
% 2.10/2.34 FOF formula (forall (A:int) (B:int), (((zcong A) B) one_one_int)) of role axiom named fact_1127_zcong__1
% 2.10/2.34 A new axiom: (forall (A:int) (B:int), (((zcong A) B) one_one_int))
% 2.10/2.34 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_1128_zcong__zmult__self
% 2.10/2.34 A new axiom: (forall (A:int) (M:int) (B:int), (((zcong ((times_times_int A) M)) ((times_times_int B) M)) M))
% 2.10/2.34 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_1129_zcong__scalar
% 2.10/2.34 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)))
% 2.10/2.34 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_1130_zcong__scalar2
% 2.10/2.34 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)))
% 2.10/2.34 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_1131_zcong__zmult
% 2.10/2.34 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))))
% 2.10/2.34 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_1132_zcong__zadd
% 2.10/2.34 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))))
% 2.10/2.34 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_1133_zcong__zdiff
% 2.10/2.34 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))))
% 2.10/2.34 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_1134_zcong__not
% 2.10/2.34 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))))))
% 2.10/2.36 FOF formula (forall (A:int) (R_1: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_1) B))) M)) ((times_times_int ((minus_minus_int C) ((times_times_int R_1) D))) N))) ((minus_minus_int ((plus_plus_int ((times_times_int A) M)) ((times_times_int C) N))) ((times_times_int R_1) ((plus_plus_int ((times_times_int B) M)) ((times_times_int D) N)))))) of role axiom named fact_1135_xzgcda__linear__aux1
% 2.10/2.36 A new axiom: (forall (A:int) (R_1: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_1) B))) M)) ((times_times_int ((minus_minus_int C) ((times_times_int R_1) D))) N))) ((minus_minus_int ((plus_plus_int ((times_times_int A) M)) ((times_times_int C) N))) ((times_times_int R_1) ((plus_plus_int ((times_times_int B) M)) ((times_times_int D) N))))))
% 2.10/2.36 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_1136_zcong__iff__lin
% 2.10/2.36 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)))))))
% 2.10/2.36 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_1137_zcong__def
% 2.10/2.36 A new axiom: (forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) ((dvd_dvd_int M) ((minus_minus_int A) B))))
% 2.10/2.36 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_1138_norR__mem__unique__aux
% 2.10/2.36 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)))
% 2.10/2.36 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_1139_zcong__zless__0
% 2.10/2.36 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)))))
% 2.10/2.36 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_1140_zcong__zless__imp__eq
% 2.10/2.36 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)))))))
% 2.10/2.36 FOF formula (forall (N:int) (P_1:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->((zprime P_1)->(((dvd_dvd_int P_1) ((times_times_int M) N))->((or ((dvd_dvd_int P_1) M)) ((dvd_dvd_int P_1) N)))))) of role axiom named fact_1141_zprime__zdvd__zmult
% 2.10/2.36 A new axiom: (forall (N:int) (P_1:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->((zprime P_1)->(((dvd_dvd_int P_1) ((times_times_int M) N))->((or ((dvd_dvd_int P_1) M)) ((dvd_dvd_int P_1) N))))))
% 2.10/2.36 FOF formula (forall (P_1:int), ((iff (zprime P_1)) ((and ((ord_less_int one_one_int) P_1)) (forall (M_1:int), (((and ((ord_less_eq_int zero_zero_int) M_1)) ((dvd_dvd_int M_1) P_1))->((or (((eq int) M_1) one_one_int)) (((eq int) M_1) P_1))))))) of role axiom named fact_1142_zprime__def
% 2.10/2.36 A new axiom: (forall (P_1:int), ((iff (zprime P_1)) ((and ((ord_less_int one_one_int) P_1)) (forall (M_1:int), (((and ((ord_less_eq_int zero_zero_int) M_1)) ((dvd_dvd_int M_1) P_1))->((or (((eq int) M_1) one_one_int)) (((eq int) M_1) P_1)))))))
% 2.10/2.36 FOF formula (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) A)) one_one_int) P_1)->((or (((zcong A) one_one_int) P_1)) (((zcong A) ((minus_minus_int P_1) one_one_int)) P_1)))))) of role axiom named fact_1143_zcong__square
% 2.10/2.38 A new axiom: (forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) A)) one_one_int) P_1)->((or (((zcong A) one_one_int) P_1)) (((zcong A) ((minus_minus_int P_1) one_one_int)) P_1))))))
% 2.10/2.38 FOF formula (forall (P:(int->Prop)) (X:nat) (Y:nat), ((iff (P (semiri1621563631at_int ((minus_minus_nat X) Y)))) ((and (((ord_less_eq_nat Y) X)->(P ((minus_minus_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))))) (((ord_less_nat X) Y)->(P zero_zero_int))))) of role axiom named fact_1144_zdiff__int__split
% 2.10/2.38 A new axiom: (forall (P:(int->Prop)) (X:nat) (Y:nat), ((iff (P (semiri1621563631at_int ((minus_minus_nat X) Y)))) ((and (((ord_less_eq_nat Y) X)->(P ((minus_minus_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))))) (((ord_less_nat X) Y)->(P zero_zero_int)))))
% 2.10/2.38 FOF formula (forall (P_1:int), ((zprime P_1)->((not (((eq int) P_1) (number_number_of_int (bit0 (bit1 pls)))))->((not (((eq int) P_1) (number_number_of_int (bit1 (bit1 pls)))))->((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P_1))))) of role axiom named fact_1145_prime__g__5
% 2.10/2.38 A new axiom: (forall (P_1:int), ((zprime P_1)->((not (((eq int) P_1) (number_number_of_int (bit0 (bit1 pls)))))->((not (((eq int) P_1) (number_number_of_int (bit1 (bit1 pls)))))->((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P_1)))))
% 2.10/2.38 FOF formula (forall (P_2:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_2))->((iff ((and ((ord_less_eq_int zero_zero_int) X)) P)) ((and ((ord_less_eq_int zero_zero_int) X)) P_2)))) of role axiom named fact_1146_conj__le__cong
% 2.10/2.38 A new axiom: (forall (P_2:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_2))->((iff ((and ((ord_less_eq_int zero_zero_int) X)) P)) ((and ((ord_less_eq_int zero_zero_int) X)) P_2))))
% 2.10/2.38 FOF formula (forall (P_2:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_2))->((iff (((ord_less_eq_int zero_zero_int) X)->P)) (((ord_less_eq_int zero_zero_int) X)->P_2)))) of role axiom named fact_1147_imp__le__cong
% 2.10/2.38 A new axiom: (forall (P_2:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_2))->((iff (((ord_less_eq_int zero_zero_int) X)->P)) (((ord_less_eq_int zero_zero_int) X)->P_2))))
% 2.10/2.38 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_1148_zdvd__mono
% 2.10/2.38 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)))))
% 2.10/2.38 FOF formula ((ord_less_eq_int zero_zero_int) (number_number_of_int pls)) of role axiom named fact_1149_number__of2
% 2.10/2.38 A new axiom: ((ord_less_eq_int zero_zero_int) (number_number_of_int pls))
% 2.10/2.38 FOF formula (forall (A:int) (P_1:int), ((iff (((zcong ((times_times_int A) ((minus_minus_int P_1) one_one_int))) one_one_int) P_1)) (((zcong A) ((minus_minus_int P_1) one_one_int)) P_1))) of role axiom named fact_1150_inv__not__p__minus__1__aux
% 2.10/2.38 A new axiom: (forall (A:int) (P_1:int), ((iff (((zcong ((times_times_int A) ((minus_minus_int P_1) one_one_int))) one_one_int) P_1)) (((zcong A) ((minus_minus_int P_1) one_one_int)) P_1)))
% 2.10/2.38 FOF formula (forall (Z:nat) (X:int) (Y:nat) (P_1:int), ((((zcong ((power_power_int X) Y)) one_one_int) P_1)->(((zcong ((power_power_int X) ((times_times_nat Y) Z))) one_one_int) P_1))) of role axiom named fact_1151_zcong__zpower__zmult
% 2.10/2.38 A new axiom: (forall (Z:nat) (X:int) (Y:nat) (P_1:int), ((((zcong ((power_power_int X) Y)) one_one_int) P_1)->(((zcong ((power_power_int X) ((times_times_nat Y) Z))) one_one_int) P_1)))
% 2.10/2.38 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_1152_number__of1
% 2.10/2.38 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))))))
% 2.10/2.39 FOF formula ((forall (S:int) (W_1:int), (((and (((eq int) W_1) ((minus_minus_int y) ((times_times_int S) ((plus_plus_int one_one_int) (semiri1621563631at_int n)))))) ((ord_less_eq_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) (abs_abs_int W_1))) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))->False))->False) of role axiom named fact_1153__096_B_Bthesis_O_A_I_B_Bs_Aw_O_Aw_A_061_Ay_A_N_As_A_K_A_I1_A_L_Aint_An
% 2.10/2.39 A new axiom: ((forall (S:int) (W_1:int), (((and (((eq int) W_1) ((minus_minus_int y) ((times_times_int S) ((plus_plus_int one_one_int) (semiri1621563631at_int n)))))) ((ord_less_eq_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) (abs_abs_int W_1))) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))->False))->False)
% 2.10/2.39 FOF formula ((forall (R:int) (V:int), (((and (((eq int) V) ((minus_minus_int x) ((times_times_int R) ((plus_plus_int one_one_int) (semiri1621563631at_int n)))))) ((ord_less_eq_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) (abs_abs_int V))) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))->False))->False) of role axiom named fact_1154__096_B_Bthesis_O_A_I_B_Br_Av_O_Av_A_061_Ax_A_N_Ar_A_K_A_I1_A_L_Aint_An
% 2.10/2.39 A new axiom: ((forall (R:int) (V:int), (((and (((eq int) V) ((minus_minus_int x) ((times_times_int R) ((plus_plus_int one_one_int) (semiri1621563631at_int n)))))) ((ord_less_eq_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) (abs_abs_int V))) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))->False))->False)
% 2.10/2.39 FOF formula (forall (D:int) (I_1:int), ((not (((eq int) I_1) zero_zero_int))->(((dvd_dvd_int D) I_1)->((ord_less_eq_int (abs_abs_int D)) (abs_abs_int I_1))))) of role axiom named fact_1155_dvd__imp__le__int
% 2.10/2.39 A new axiom: (forall (D:int) (I_1:int), ((not (((eq int) I_1) zero_zero_int))->(((dvd_dvd_int D) I_1)->((ord_less_eq_int (abs_abs_int D)) (abs_abs_int I_1)))))
% 2.10/2.39 FOF formula (forall (W:int) (Z:int), (((eq nat) (nat_1 (abs_abs_int ((times_times_int W) Z)))) ((times_times_nat (nat_1 (abs_abs_int W))) (nat_1 (abs_abs_int Z))))) of role axiom named fact_1156_nat__abs__mult__distrib
% 2.10/2.39 A new axiom: (forall (W:int) (Z:int), (((eq nat) (nat_1 (abs_abs_int ((times_times_int W) Z)))) ((times_times_nat (nat_1 (abs_abs_int W))) (nat_1 (abs_abs_int Z)))))
% 2.10/2.39 FOF formula (forall (A:int) (B:int), (((dvd_dvd_int A) B)->(((dvd_dvd_int B) A)->(((eq int) (abs_abs_int A)) (abs_abs_int B))))) of role axiom named fact_1157_zdvd__antisym__abs
% 2.10/2.39 A new axiom: (forall (A:int) (B:int), (((dvd_dvd_int A) B)->(((dvd_dvd_int B) A)->(((eq int) (abs_abs_int A)) (abs_abs_int B)))))
% 2.10/2.39 FOF formula (forall (X:int), ((iff ((dvd_dvd_int X) one_one_int)) (((eq int) (abs_abs_int X)) one_one_int))) of role axiom named fact_1158_zdvd1__eq
% 2.10/2.39 A new axiom: (forall (X:int), ((iff ((dvd_dvd_int X) one_one_int)) (((eq int) (abs_abs_int X)) one_one_int)))
% 2.10/2.39 FOF formula (forall (M:nat), (((eq int) (abs_abs_int (semiri1621563631at_int M))) (semiri1621563631at_int M))) of role axiom named fact_1159_abs__int__eq
% 2.10/2.39 A new axiom: (forall (M:nat), (((eq int) (abs_abs_int (semiri1621563631at_int M))) (semiri1621563631at_int M)))
% 2.10/2.39 FOF formula (forall (M:int) (N:int), ((((eq int) (abs_abs_int ((times_times_int M) N))) one_one_int)->(((eq int) (abs_abs_int M)) one_one_int))) of role axiom named fact_1160_abs__zmult__eq__1
% 2.10/2.39 A new axiom: (forall (M:int) (N:int), ((((eq int) (abs_abs_int ((times_times_int M) N))) one_one_int)->(((eq int) (abs_abs_int M)) one_one_int)))
% 2.10/2.39 FOF formula (forall (X:int) (N:nat), ((ord_less_eq_int zero_zero_int) ((power_power_int (abs_abs_int X)) N))) of role axiom named fact_1161_zero__le__zpower__abs
% 2.10/2.39 A new axiom: (forall (X:int) (N:nat), ((ord_less_eq_int zero_zero_int) ((power_power_int (abs_abs_int X)) N)))
% 2.10/2.39 FOF formula (forall (Z:int), ((iff ((ord_less_int (abs_abs_int Z)) one_one_int)) (((eq int) Z) zero_zero_int))) of role axiom named fact_1162_zabs__less__one__iff
% 2.10/2.39 A new axiom: (forall (Z:int), ((iff ((ord_less_int (abs_abs_int Z)) one_one_int)) (((eq int) Z) zero_zero_int)))
% 2.19/2.41 FOF formula (forall (Z:int), ((iff (((eq int) (abs_abs_int Z)) one_one_int)) ((or (((eq int) Z) one_one_int)) (((eq int) Z) (number_number_of_int min))))) of role axiom named fact_1163_abs__eq__1__iff
% 2.19/2.41 A new axiom: (forall (Z:int), ((iff (((eq int) (abs_abs_int Z)) one_one_int)) ((or (((eq int) Z) one_one_int)) (((eq int) Z) (number_number_of_int min)))))
% 2.19/2.41 FOF formula (forall (X:int), (((eq int) (abs_abs_int ((power_power_int X) (number_number_of_nat (bit1 (bit1 pls)))))) ((power_power_int (abs_abs_int X)) (number_number_of_nat (bit1 (bit1 pls)))))) of role axiom named fact_1164_abs__power3__distrib
% 2.19/2.41 A new axiom: (forall (X:int), (((eq int) (abs_abs_int ((power_power_int X) (number_number_of_nat (bit1 (bit1 pls)))))) ((power_power_int (abs_abs_int X)) (number_number_of_nat (bit1 (bit1 pls))))))
% 2.19/2.41 FOF formula (forall (X:int) (N:nat), ((iff ((ord_less_int zero_zero_int) ((power_power_int (abs_abs_int X)) N))) ((or (not (((eq int) X) zero_zero_int))) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_1165_zero__less__zpower__abs__iff
% 2.19/2.41 A new axiom: (forall (X:int) (N:nat), ((iff ((ord_less_int zero_zero_int) ((power_power_int (abs_abs_int X)) N))) ((or (not (((eq int) X) zero_zero_int))) (((eq nat) N) zero_zero_nat))))
% 2.19/2.41 FOF formula (forall (N:int) (M:int), ((not (((eq int) M) zero_zero_int))->((iff ((dvd_dvd_int ((times_times_int M) N)) M)) (((eq int) (abs_abs_int N)) one_one_int)))) of role axiom named fact_1166_zdvd__mult__cancel1
% 2.19/2.41 A new axiom: (forall (N:int) (M:int), ((not (((eq int) M) zero_zero_int))->((iff ((dvd_dvd_int ((times_times_int M) N)) M)) (((eq int) (abs_abs_int N)) one_one_int))))
% 2.19/2.41 FOF formula (forall (M:nat) (Z:int), ((iff ((dvd_dvd_int (semiri1621563631at_int M)) Z)) ((dvd_dvd_nat M) (nat_1 (abs_abs_int Z))))) of role axiom named fact_1167_int__dvd__iff
% 2.19/2.41 A new axiom: (forall (M:nat) (Z:int), ((iff ((dvd_dvd_int (semiri1621563631at_int M)) Z)) ((dvd_dvd_nat M) (nat_1 (abs_abs_int Z)))))
% 2.19/2.41 FOF formula (forall (Z:int) (M:nat), ((iff ((dvd_dvd_int Z) (semiri1621563631at_int M))) ((dvd_dvd_nat (nat_1 (abs_abs_int Z))) M))) of role axiom named fact_1168_dvd__int__iff
% 2.19/2.41 A new axiom: (forall (Z:int) (M:nat), ((iff ((dvd_dvd_int Z) (semiri1621563631at_int M))) ((dvd_dvd_nat (nat_1 (abs_abs_int Z))) M)))
% 2.19/2.41 FOF formula (forall (A:int), (((eq int) (abs_abs_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_int (abs_abs_int A)) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_1169_abs__power2__distrib
% 2.19/2.41 A new axiom: (forall (A:int), (((eq int) (abs_abs_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_int (abs_abs_int A)) (number_number_of_nat (bit0 (bit1 pls))))))
% 2.19/2.41 FOF formula (forall (A:int) (B:int), ((iff (((eq int) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls)))))) (((eq int) (abs_abs_int A)) (abs_abs_int B)))) of role axiom named fact_1170_power2__eq__iff__abs__eq
% 2.19/2.41 A new axiom: (forall (A:int) (B:int), ((iff (((eq int) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls)))))) (((eq int) (abs_abs_int A)) (abs_abs_int B))))
% 2.19/2.41 FOF formula (forall (A:int), ((((eq int) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)->(((eq int) (abs_abs_int A)) one_one_int))) of role axiom named fact_1171_power2__eq1__iff
% 2.19/2.41 A new axiom: (forall (A:int), ((((eq int) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)->(((eq int) (abs_abs_int A)) one_one_int)))
% 2.19/2.41 FOF formula (forall (Z:int) (X:int) (D:int), (((ord_less_int zero_zero_int) D)->((ord_less_int Z) ((plus_plus_int X) ((times_times_int ((plus_plus_int (abs_abs_int ((minus_minus_int X) Z))) one_one_int)) D))))) of role axiom named fact_1172_incr__lemma
% 2.19/2.41 A new axiom: (forall (Z:int) (X:int) (D:int), (((ord_less_int zero_zero_int) D)->((ord_less_int Z) ((plus_plus_int X) ((times_times_int ((plus_plus_int (abs_abs_int ((minus_minus_int X) Z))) one_one_int)) D)))))
% 2.19/2.43 FOF formula (forall (X:int) (Z:int) (D:int), (((ord_less_int zero_zero_int) D)->((ord_less_int ((minus_minus_int X) ((times_times_int ((plus_plus_int (abs_abs_int ((minus_minus_int X) Z))) one_one_int)) D))) Z))) of role axiom named fact_1173_decr__lemma
% 2.19/2.43 A new axiom: (forall (X:int) (Z:int) (D:int), (((ord_less_int zero_zero_int) D)->((ord_less_int ((minus_minus_int X) ((times_times_int ((plus_plus_int (abs_abs_int ((minus_minus_int X) Z))) one_one_int)) D))) Z)))
% 2.19/2.43 FOF formula (forall (Y:int) (X:int), (((ord_less_int zero_zero_int) X)->((ex int) (fun (N_1:int)=> ((ord_less_eq_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) (abs_abs_int ((minus_minus_int Y) ((times_times_int N_1) X))))) X))))) of role axiom named fact_1174_best__division__abs
% 2.19/2.43 A new axiom: (forall (Y:int) (X:int), (((ord_less_int zero_zero_int) X)->((ex int) (fun (N_1:int)=> ((ord_less_eq_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) (abs_abs_int ((minus_minus_int Y) ((times_times_int N_1) X))))) X)))))
% 2.19/2.43 FOF formula (forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) ((times_times_int K) D))))))))) of role axiom named fact_1175_decr__mult__lemma
% 2.19/2.43 A new axiom: (forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) ((times_times_int K) D)))))))))
% 2.19/2.43 FOF formula (forall (X:real), (((ord_less_real ((plus_plus_real (abs_abs_real X)) one_one_real)) X)->False)) of role axiom named fact_1176_abs__add__one__not__less__self
% 2.19/2.43 A new axiom: (forall (X:real), (((ord_less_real ((plus_plus_real (abs_abs_real X)) one_one_real)) X)->False))
% 2.19/2.43 FOF formula (forall (X:real), ((ord_less_real zero_zero_real) ((plus_plus_real one_one_real) (abs_abs_real X)))) of role axiom named fact_1177_abs__add__one__gt__zero
% 2.19/2.43 A new axiom: (forall (X:real), ((ord_less_real zero_zero_real) ((plus_plus_real one_one_real) (abs_abs_real X))))
% 2.19/2.43 FOF formula (forall (X:real), (((ord_less_real (abs_abs_real X)) one_one_real)->((ord_less_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) one_one_real))) of role axiom named fact_1178_less__one__imp__sqr__less__one
% 2.19/2.43 A new axiom: (forall (X:real), (((ord_less_real (abs_abs_real X)) one_one_real)->((ord_less_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) one_one_real)))
% 2.19/2.43 FOF formula (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N)) (forall (_TPTP_I:nat), (((ord_less_eq_nat _TPTP_I) K_1)->((P _TPTP_I)->False))))) (P ((plus_plus_nat K_1) one_one_nat)))))))) of role axiom named fact_1179_ex__least__nat__less
% 2.19/2.43 A new axiom: (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N)) (forall (_TPTP_I:nat), (((ord_less_eq_nat _TPTP_I) K_1)->((P _TPTP_I)->False))))) (P ((plus_plus_nat K_1) one_one_nat))))))))
% 2.19/2.43 FOF formula (forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) ((times_times_int K) D))))))))) of role axiom named fact_1180_incr__mult__lemma
% 2.19/2.43 A new axiom: (forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) ((times_times_int K) D)))))))))
% 2.19/2.43 FOF formula (forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))) of role axiom named fact_1181_nat__less__add__iff1
% 2.19/2.45 A new axiom: (forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N))))
% 2.19/2.45 FOF formula (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))) of role axiom named fact_1182_nat__less__add__iff2
% 2.19/2.45 A new axiom: (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N)))))
% 2.19/2.45 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_1183_nat__mult__eq__cancel__disj
% 2.19/2.45 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))))
% 2.19/2.45 FOF formula (forall (I_1:nat) (U:nat) (J:nat) (K:nat), (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) ((plus_plus_nat ((times_times_nat J) U)) K))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat I_1) J)) U)) K))) of role axiom named fact_1184_left__add__mult__distrib
% 2.19/2.45 A new axiom: (forall (I_1:nat) (U:nat) (J:nat) (K:nat), (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) ((plus_plus_nat ((times_times_nat J) U)) K))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat I_1) J)) U)) K)))
% 2.19/2.45 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_1185_nat__mult__less__cancel1
% 2.19/2.45 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))))
% 2.19/2.45 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_1186_nat__mult__eq__cancel1
% 2.19/2.45 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))))
% 2.19/2.45 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_1187_nat__mult__dvd__cancel__disj
% 2.19/2.45 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))))
% 2.19/2.45 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_1188_nat__mult__dvd__cancel1
% 2.19/2.45 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))))
% 2.19/2.45 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_1189_nat__mult__le__cancel1
% 2.19/2.45 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))))
% 2.19/2.45 FOF formula (forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))) of role axiom named fact_1190_nat__le__add__iff1
% 2.19/2.48 A new axiom: (forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N))))
% 2.19/2.48 FOF formula (forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((minus_minus_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))) of role axiom named fact_1191_nat__diff__add__eq1
% 2.19/2.48 A new axiom: (forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((minus_minus_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N))))
% 2.19/2.48 FOF formula (forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) (((eq nat) ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))) of role axiom named fact_1192_nat__eq__add__iff1
% 2.19/2.48 A new axiom: (forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) (((eq nat) ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N))))
% 2.19/2.48 FOF formula (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_eq_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))) of role axiom named fact_1193_nat__le__add__iff2
% 2.19/2.48 A new axiom: (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_eq_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N)))))
% 2.19/2.48 FOF formula (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((minus_minus_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))) of role axiom named fact_1194_nat__diff__add__eq2
% 2.19/2.48 A new axiom: (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((minus_minus_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N)))))
% 2.19/2.48 FOF formula (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) (((eq nat) M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))) of role axiom named fact_1195_nat__eq__add__iff2
% 2.19/2.48 A new axiom: (forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) (((eq nat) M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N)))))
% 2.19/2.48 FOF formula (forall (K:int) (F:(nat->int)) (N:nat), ((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) N)->((ord_less_eq_int (abs_abs_int ((minus_minus_int (F ((plus_plus_nat _TPTP_I) one_one_nat))) (F _TPTP_I)))) one_one_int)))->(((ord_less_eq_int (F zero_zero_nat)) K)->(((ord_less_eq_int K) (F N))->((ex nat) (fun (_TPTP_I:nat)=> ((and ((ord_less_eq_nat _TPTP_I) N)) (((eq int) (F _TPTP_I)) K)))))))) of role axiom named fact_1196_nat0__intermed__int__val
% 2.30/2.50 A new axiom: (forall (K:int) (F:(nat->int)) (N:nat), ((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) N)->((ord_less_eq_int (abs_abs_int ((minus_minus_int (F ((plus_plus_nat _TPTP_I) one_one_nat))) (F _TPTP_I)))) one_one_int)))->(((ord_less_eq_int (F zero_zero_nat)) K)->(((ord_less_eq_int K) (F N))->((ex nat) (fun (_TPTP_I:nat)=> ((and ((ord_less_eq_nat _TPTP_I) N)) (((eq int) (F _TPTP_I)) K))))))))
% 2.30/2.50 FOF formula (forall (K:int) (F:(nat->int)) (N:nat), ((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) N)->((ord_less_eq_int (abs_abs_int ((minus_minus_int (F ((plus_plus_nat _TPTP_I) one_one_nat))) (F _TPTP_I)))) one_one_int)))->(((ord_less_eq_int (F zero_zero_nat)) K)->(((ord_less_eq_int K) (F N))->((ex nat) (fun (_TPTP_I:nat)=> ((and ((ord_less_eq_nat _TPTP_I) N)) (((eq int) (F _TPTP_I)) K)))))))) of role axiom named fact_1197_int__val__lemma
% 2.30/2.50 A new axiom: (forall (K:int) (F:(nat->int)) (N:nat), ((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) N)->((ord_less_eq_int (abs_abs_int ((minus_minus_int (F ((plus_plus_nat _TPTP_I) one_one_nat))) (F _TPTP_I)))) one_one_int)))->(((ord_less_eq_int (F zero_zero_nat)) K)->(((ord_less_eq_int K) (F N))->((ex nat) (fun (_TPTP_I:nat)=> ((and ((ord_less_eq_nat _TPTP_I) N)) (((eq int) (F _TPTP_I)) K))))))))
% 2.30/2.50 FOF formula (forall (X:int) (Y:int), (((eq int) (((if_int True) X) Y)) X)) of role axiom named help_If_1_1_If_000tc__Int__Oint_T
% 2.30/2.50 A new axiom: (forall (X:int) (Y:int), (((eq int) (((if_int True) X) Y)) X))
% 2.30/2.50 FOF formula (forall (X:int) (Y:int), (((eq int) (((if_int False) X) Y)) Y)) of role axiom named help_If_2_1_If_000tc__Int__Oint_T
% 2.30/2.50 A new axiom: (forall (X:int) (Y:int), (((eq int) (((if_int False) X) Y)) Y))
% 2.30/2.50 FOF formula (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))) of role axiom named help_If_3_1_If_000tc__Int__Oint_T
% 2.30/2.50 A new axiom: (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False)))
% 2.30/2.50 FOF formula (forall (X:nat) (Y:nat), (((eq nat) (((if_nat True) X) Y)) X)) of role axiom named help_If_1_1_If_000tc__Nat__Onat_T
% 2.30/2.50 A new axiom: (forall (X:nat) (Y:nat), (((eq nat) (((if_nat True) X) Y)) X))
% 2.30/2.50 FOF formula (forall (X:nat) (Y:nat), (((eq nat) (((if_nat False) X) Y)) Y)) of role axiom named help_If_2_1_If_000tc__Nat__Onat_T
% 2.30/2.50 A new axiom: (forall (X:nat) (Y:nat), (((eq nat) (((if_nat False) X) Y)) Y))
% 2.30/2.50 FOF formula (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))) of role axiom named help_If_3_1_If_000tc__Nat__Onat_T
% 2.30/2.50 A new axiom: (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False)))
% 2.30/2.50 FOF formula (not (((eq int) ((power_power_int ((plus_plus_int one_one_int) (semiri1621563631at_int n))) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)) of role conjecture named conj_0
% 2.30/2.50 Conjecture to prove = (not (((eq int) ((power_power_int ((plus_plus_int one_one_int) (semiri1621563631at_int n))) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)):Prop
% 2.30/2.50 We need to prove ['(not (((eq int) ((power_power_int ((plus_plus_int one_one_int) (semiri1621563631at_int n))) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int))']
% 2.30/2.50 Parameter int:Type.
% 2.30/2.50 Parameter nat:Type.
% 2.30/2.50 Parameter real:Type.
% 2.30/2.50 Parameter all:((nat->Prop)->Prop).
% 2.30/2.50 Parameter _TPTP_ex:((nat->Prop)->Prop).
% 2.30/2.50 Parameter abs_abs_int:(int->int).
% 2.30/2.50 Parameter abs_abs_real:(real->real).
% 2.30/2.50 Parameter minus_minus_int:(int->(int->int)).
% 2.30/2.50 Parameter minus_minus_nat:(nat->(nat->nat)).
% 2.30/2.50 Parameter minus_minus_real:(real->(real->real)).
% 2.30/2.50 Parameter one_one_int:int.
% 2.30/2.50 Parameter one_one_nat:nat.
% 2.30/2.50 Parameter one_one_real:real.
% 2.30/2.50 Parameter plus_plus_int:(int->(int->int)).
% 2.30/2.50 Parameter plus_plus_nat:(nat->(nat->nat)).
% 2.30/2.50 Parameter plus_plus_real:(real->(real->real)).
% 2.30/2.50 Parameter times_times_int:(int->(int->int)).
% 2.30/2.50 Parameter times_times_nat:(nat->(nat->nat)).
% 2.30/2.50 Parameter times_times_real:(real->(real->real)).
% 2.30/2.50 Parameter zero_zero_int:int.
% 2.30/2.50 Parameter zero_zero_nat:nat.
% 2.30/2.50 Parameter zero_zero_real:real.
% 2.30/2.50 Parameter if_int:(Prop->(int->(int->int))).
% 2.30/2.50 Parameter if_nat:(Prop->(nat->(nat->nat))).
% 2.30/2.50 Parameter zcong:(int->(int->(int->Prop))).
% 2.30/2.50 Parameter zprime:(int->Prop).
% 2.30/2.50 Parameter bit0:(int->int).
% 2.30/2.50 Parameter bit1:(int->int).
% 2.30/2.50 Parameter min:int.
% 2.30/2.50 Parameter pls:int.
% 2.30/2.50 Parameter nat_1:(int->nat).
% 2.30/2.50 Parameter number_number_of_int:(int->int).
% 2.30/2.50 Parameter number_number_of_nat:(int->nat).
% 2.30/2.50 Parameter number267125858f_real:(int->real).
% 2.30/2.50 Parameter succ:(int->int).
% 2.30/2.50 Parameter semiri1621563631at_int:(nat->int).
% 2.30/2.50 Parameter semiri984289939at_nat:(nat->nat).
% 2.30/2.50 Parameter semiri132038758t_real:(nat->real).
% 2.30/2.50 Parameter ord_less_int:(int->(int->Prop)).
% 2.30/2.50 Parameter ord_less_nat:(nat->(nat->Prop)).
% 2.30/2.50 Parameter ord_less_real:(real->(real->Prop)).
% 2.30/2.50 Parameter ord_less_eq_int:(int->(int->Prop)).
% 2.30/2.50 Parameter ord_less_eq_nat:(nat->(nat->Prop)).
% 2.30/2.50 Parameter ord_less_eq_real:(real->(real->Prop)).
% 2.30/2.50 Parameter power_power_int:(int->(nat->int)).
% 2.30/2.50 Parameter power_power_nat:(nat->(nat->nat)).
% 2.30/2.50 Parameter power_power_real:(real->(nat->real)).
% 2.30/2.50 Parameter legendre:(int->(int->int)).
% 2.30/2.50 Parameter quadRes:(int->(int->Prop)).
% 2.30/2.50 Parameter dvd_dvd_int:(int->(int->Prop)).
% 2.30/2.50 Parameter dvd_dvd_nat:(nat->(nat->Prop)).
% 2.30/2.50 Parameter twoSqu919416604sum2sq:(int->Prop).
% 2.30/2.50 Parameter m:int.
% 2.30/2.50 Parameter m1:int.
% 2.30/2.50 Parameter n:nat.
% 2.30/2.50 Parameter s1:int.
% 2.30/2.50 Parameter s:int.
% 2.30/2.50 Parameter t:int.
% 2.30/2.50 Parameter tn:nat.
% 2.30/2.50 Parameter x:int.
% 2.30/2.50 Parameter y:int.
% 2.30/2.50 Axiom fact_0_n1pos:((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) (semiri1621563631at_int n))).
% 2.30/2.50 Axiom fact_1_t1:((ord_less_int one_one_int) t).
% 2.30/2.50 Axiom fact_2_sum__power2__eq__zero__iff:(forall (X:int) (Y:int), ((iff (((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)))))) zero_zero_int)) ((and (((eq int) X) zero_zero_int)) (((eq int) Y) zero_zero_int)))).
% 2.30/2.50 Axiom fact_3_sum__power2__eq__zero__iff:(forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real)))).
% 2.30/2.50 Axiom fact_4_one__power2:(((eq int) ((power_power_int one_one_int) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int).
% 2.30/2.50 Axiom fact_5_one__power2:(((eq nat) ((power_power_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls))))) one_one_nat).
% 2.30/2.50 Axiom fact_6_one__power2:(((eq real) ((power_power_real one_one_real) (number_number_of_nat (bit0 (bit1 pls))))) one_one_real).
% 2.30/2.50 Axiom fact_7_zero__power2:(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int).
% 2.30/2.50 Axiom fact_8_zero__power2:(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_nat).
% 2.30/2.50 Axiom fact_9_zero__power2:(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real).
% 2.30/2.50 Axiom fact_10_zero__eq__power2:(forall (A_136:int), ((iff (((eq int) ((power_power_int A_136) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)) (((eq int) A_136) zero_zero_int))).
% 2.30/2.50 Axiom fact_11_zero__eq__power2:(forall (A_136:real), ((iff (((eq real) ((power_power_real A_136) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)) (((eq real) A_136) zero_zero_real))).
% 2.30/2.50 Axiom fact_12_add__special_I2_J:(forall (W_16:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_16))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_16)))).
% 2.30/2.50 Axiom fact_13_add__special_I2_J:(forall (W_16:int), (((eq real) ((plus_plus_real one_one_real) (number267125858f_real W_16))) (number267125858f_real ((plus_plus_int (bit1 pls)) W_16)))).
% 2.30/2.50 Axiom fact_14_add__special_I3_J:(forall (V_16:int), (((eq int) ((plus_plus_int (number_number_of_int V_16)) one_one_int)) (number_number_of_int ((plus_plus_int V_16) (bit1 pls))))).
% 2.30/2.50 Axiom fact_15_add__special_I3_J:(forall (V_16:int), (((eq real) ((plus_plus_real (number267125858f_real V_16)) one_one_real)) (number267125858f_real ((plus_plus_int V_16) (bit1 pls))))).
% 2.30/2.50 Axiom fact_16_one__add__one__is__two:(((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))).
% 2.30/2.50 Axiom fact_17_one__add__one__is__two:(((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))).
% 2.30/2.50 Axiom fact_18_semiring__one__add__one__is__two:(((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))).
% 2.30/2.50 Axiom fact_19_semiring__one__add__one__is__two:(((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))).
% 2.30/2.50 Axiom fact_20_semiring__one__add__one__is__two:(((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))).
% 2.30/2.50 Axiom fact_21_quartic__square__square:(forall (X:int), (((eq int) ((power_power_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int X) (number_number_of_nat (bit0 (bit0 (bit1 pls))))))).
% 2.30/2.50 Axiom fact_22_power__0__left__number__of:(forall (W_15:int), ((and ((((eq nat) (number_number_of_nat W_15)) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_15))) one_one_int))) ((not (((eq nat) (number_number_of_nat W_15)) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_15))) zero_zero_int)))).
% 2.30/2.50 Axiom fact_23_power__0__left__number__of:(forall (W_15:int), ((and ((((eq nat) (number_number_of_nat W_15)) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_15))) one_one_nat))) ((not (((eq nat) (number_number_of_nat W_15)) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_15))) zero_zero_nat)))).
% 2.30/2.50 Axiom fact_24_power__0__left__number__of:(forall (W_15:int), ((and ((((eq nat) (number_number_of_nat W_15)) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_15))) one_one_real))) ((not (((eq nat) (number_number_of_nat W_15)) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_15))) zero_zero_real)))).
% 2.30/2.50 Axiom fact_25_semiring__norm_I110_J:(((eq int) one_one_int) (number_number_of_int (bit1 pls))).
% 2.30/2.50 Axiom fact_26_semiring__norm_I110_J:(((eq real) one_one_real) (number267125858f_real (bit1 pls))).
% 2.30/2.50 Axiom fact_27_numeral__1__eq__1:(((eq int) (number_number_of_int (bit1 pls))) one_one_int).
% 2.30/2.50 Axiom fact_28_numeral__1__eq__1:(((eq real) (number267125858f_real (bit1 pls))) one_one_real).
% 2.30/2.50 Axiom fact_29_n0:((ord_less_nat zero_zero_nat) n).
% 2.30/2.50 Axiom fact_30_zless__linear:(forall (X:int) (Y:int), ((or ((or ((ord_less_int X) Y)) (((eq int) X) Y))) ((ord_less_int Y) X))).
% 2.30/2.50 Axiom fact_31_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))).
% 2.30/2.50 Axiom fact_32_plus__numeral__code_I9_J:(forall (V_1:int) (W:int), (((eq int) ((plus_plus_int (number_number_of_int V_1)) (number_number_of_int W))) (number_number_of_int ((plus_plus_int V_1) W)))).
% 2.30/2.50 Axiom fact_33_less__number__of:(forall (X_30:int) (Y_23:int), ((iff ((ord_less_int (number_number_of_int X_30)) (number_number_of_int Y_23))) ((ord_less_int X_30) Y_23))).
% 2.30/2.50 Axiom fact_34_less__number__of:(forall (X_30:int) (Y_23:int), ((iff ((ord_less_real (number267125858f_real X_30)) (number267125858f_real Y_23))) ((ord_less_int X_30) Y_23))).
% 2.30/2.50 Axiom fact_35_zero__is__num__zero:(((eq int) zero_zero_int) (number_number_of_int pls)).
% 2.30/2.50 Axiom fact_36_zpower__int:(forall (M:nat) (N:nat), (((eq int) ((power_power_int (semiri1621563631at_int M)) N)) (semiri1621563631at_int ((power_power_nat M) N)))).
% 2.30/2.50 Axiom fact_37_int__power:(forall (M:nat) (N:nat), (((eq int) (semiri1621563631at_int ((power_power_nat M) N))) ((power_power_int (semiri1621563631at_int M)) N))).
% 2.30/2.50 Axiom fact_38_zadd__int__left:(forall (M:nat) (N:nat) (Z:int), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) ((plus_plus_int (semiri1621563631at_int N)) Z))) ((plus_plus_int (semiri1621563631at_int ((plus_plus_nat M) N))) Z))).
% 2.30/2.50 Axiom fact_39_zadd__int:(forall (M:nat) (N:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((plus_plus_nat M) N)))).
% 2.30/2.50 Axiom fact_40_int__1:(((eq int) (semiri1621563631at_int one_one_nat)) one_one_int).
% 2.30/2.50 Axiom fact_41_nat__number__of__Pls:(((eq nat) (number_number_of_nat pls)) zero_zero_nat).
% 2.30/2.50 Axiom fact_42_semiring__norm_I113_J:(((eq nat) zero_zero_nat) (number_number_of_nat pls)).
% 2.30/2.50 Axiom fact_43_int__eq__0__conv:(forall (N:nat), ((iff (((eq int) (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat))).
% 2.30/2.50 Axiom fact_44_int__0:(((eq int) (semiri1621563631at_int zero_zero_nat)) zero_zero_int).
% 2.30/2.50 Axiom fact_45_nat__1__add__1:(((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))).
% 2.30/2.50 Axiom fact_46_less__int__code_I16_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2))).
% 2.30/2.50 Axiom fact_47_rel__simps_I17_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L))).
% 2.30/2.50 Axiom fact_48_rel__simps_I2_J:(((ord_less_int pls) pls)->False).
% 2.30/2.50 Axiom fact_49_less__int__code_I13_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit0 K2))) ((ord_less_int K1) K2))).
% 2.30/2.50 Axiom fact_50_rel__simps_I14_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit0 L))) ((ord_less_int K) L))).
% 2.30/2.50 Axiom fact_51_zadd__strict__right__mono:(forall (K:int) (I_1:int) (J:int), (((ord_less_int I_1) J)->((ord_less_int ((plus_plus_int I_1) K)) ((plus_plus_int J) K)))).
% 2.30/2.50 Axiom fact_52_add__nat__number__of:(forall (V_2:int) (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) (number_number_of_nat V_2)))) ((((ord_less_int V_1) pls)->False)->((and (((ord_less_int V_2) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) (number_number_of_nat V_1)))) ((((ord_less_int V_2) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) (number_number_of_nat ((plus_plus_int V_1) V_2)))))))).
% 2.30/2.50 Axiom fact_53_one__is__num__one:(((eq int) one_one_int) (number_number_of_int (bit1 pls))).
% 2.30/2.50 Axiom fact_54_nat__numeral__1__eq__1:(((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat).
% 2.30/2.50 Axiom fact_55_Numeral1__eq1__nat:(((eq nat) one_one_nat) (number_number_of_nat (bit1 pls))).
% 2.30/2.50 Axiom fact_56_eq__number__of:(forall (X_29:int) (Y_22:int), ((iff (((eq int) (number_number_of_int X_29)) (number_number_of_int Y_22))) (((eq int) X_29) Y_22))).
% 2.30/2.50 Axiom fact_57_eq__number__of:(forall (X_29:int) (Y_22:int), ((iff (((eq real) (number267125858f_real X_29)) (number267125858f_real Y_22))) (((eq int) X_29) Y_22))).
% 2.30/2.50 Axiom fact_58_number__of__reorient:(forall (W_14:int) (X_28:nat), ((iff (((eq nat) (number_number_of_nat W_14)) X_28)) (((eq nat) X_28) (number_number_of_nat W_14)))).
% 2.30/2.50 Axiom fact_59_number__of__reorient:(forall (W_14:int) (X_28:int), ((iff (((eq int) (number_number_of_int W_14)) X_28)) (((eq int) X_28) (number_number_of_int W_14)))).
% 2.30/2.50 Axiom fact_60_number__of__reorient:(forall (W_14:int) (X_28:real), ((iff (((eq real) (number267125858f_real W_14)) X_28)) (((eq real) X_28) (number267125858f_real W_14)))).
% 2.30/2.50 Axiom fact_61_rel__simps_I51_J:(forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L))).
% 2.30/2.50 Axiom fact_62_rel__simps_I48_J:(forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L))).
% 2.30/2.50 Axiom fact_63_even__less__0__iff:(forall (A_135:int), ((iff ((ord_less_int ((plus_plus_int A_135) A_135)) zero_zero_int)) ((ord_less_int A_135) zero_zero_int))).
% 2.30/2.50 Axiom fact_64_even__less__0__iff:(forall (A_135:real), ((iff ((ord_less_real ((plus_plus_real A_135) A_135)) zero_zero_real)) ((ord_less_real A_135) zero_zero_real))).
% 2.30/2.50 Axiom fact_65_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)))).
% 2.30/2.50 Axiom fact_66_zadd__left__commute:(forall (X:int) (Y:int) (Z:int), (((eq int) ((plus_plus_int X) ((plus_plus_int Y) Z))) ((plus_plus_int Y) ((plus_plus_int X) Z)))).
% 2.30/2.50 Axiom fact_67_zadd__commute:(forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z))).
% 2.30/2.50 Axiom fact_68_int__int__eq:(forall (M:nat) (N:nat), ((iff (((eq int) (semiri1621563631at_int M)) (semiri1621563631at_int N))) (((eq nat) M) N))).
% 2.30/2.50 Axiom fact_69_less__special_I3_J:(forall (X_27:int), ((iff ((ord_less_int (number_number_of_int X_27)) zero_zero_int)) ((ord_less_int X_27) pls))).
% 2.30/2.50 Axiom fact_70_less__special_I3_J:(forall (X_27:int), ((iff ((ord_less_real (number267125858f_real X_27)) zero_zero_real)) ((ord_less_int X_27) pls))).
% 2.30/2.50 Axiom fact_71_less__special_I1_J:(forall (Y_21:int), ((iff ((ord_less_int zero_zero_int) (number_number_of_int Y_21))) ((ord_less_int pls) Y_21))).
% 2.30/2.50 Axiom fact_72_less__special_I1_J:(forall (Y_21:int), ((iff ((ord_less_real zero_zero_real) (number267125858f_real Y_21))) ((ord_less_int pls) Y_21))).
% 2.30/2.50 Axiom fact_73_rel__simps_I12_J:(forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls))).
% 2.30/2.50 Axiom fact_74_less__int__code_I15_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2))).
% 2.30/2.50 Axiom fact_75_rel__simps_I16_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))).
% 2.30/2.50 Axiom fact_76_rel__simps_I10_J:(forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls))).
% 2.30/2.50 Axiom fact_77_rel__simps_I4_J:(forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K))).
% 2.30/2.50 Axiom fact_78_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))).
% 2.30/2.50 Axiom fact_79_bin__less__0__simps_I1_J:(((ord_less_int pls) zero_zero_int)->False).
% 2.30/2.50 Axiom fact_80_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))).
% 2.30/2.50 Axiom fact_81_int__0__less__1:((ord_less_int zero_zero_int) one_one_int).
% 2.30/2.50 Axiom fact_82_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)))).
% 2.30/2.50 Axiom fact_83_int__less__0__conv:(forall (K:nat), (((ord_less_int (semiri1621563631at_int K)) zero_zero_int)->False)).
% 2.30/2.50 Axiom fact_84_less__special_I4_J:(forall (X_26:int), ((iff ((ord_less_int (number_number_of_int X_26)) one_one_int)) ((ord_less_int X_26) (bit1 pls)))).
% 2.30/2.50 Axiom fact_85_less__special_I4_J:(forall (X_26:int), ((iff ((ord_less_real (number267125858f_real X_26)) one_one_real)) ((ord_less_int X_26) (bit1 pls)))).
% 2.30/2.50 Axiom fact_86_less__special_I2_J:(forall (Y_20:int), ((iff ((ord_less_int one_one_int) (number_number_of_int Y_20))) ((ord_less_int (bit1 pls)) Y_20))).
% 2.30/2.50 Axiom fact_87_less__special_I2_J:(forall (Y_20:int), ((iff ((ord_less_real one_one_real) (number267125858f_real Y_20))) ((ord_less_int (bit1 pls)) Y_20))).
% 2.30/2.50 Axiom fact_88_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))).
% 2.30/2.50 Axiom fact_89_double__eq__0__iff:(forall (A_134:int), ((iff (((eq int) ((plus_plus_int A_134) A_134)) zero_zero_int)) (((eq int) A_134) zero_zero_int))).
% 2.30/2.50 Axiom fact_90_double__eq__0__iff:(forall (A_134:real), ((iff (((eq real) ((plus_plus_real A_134) A_134)) zero_zero_real)) (((eq real) A_134) zero_zero_real))).
% 2.30/2.50 Axiom fact_91_rel__simps_I46_J:(forall (K:int), (not (((eq int) (bit1 K)) pls))).
% 2.30/2.50 Axiom fact_92_rel__simps_I39_J:(forall (L:int), (not (((eq int) pls) (bit1 L)))).
% 2.30/2.50 Axiom fact_93_rel__simps_I50_J:(forall (K:int) (L:int), (not (((eq int) (bit1 K)) (bit0 L)))).
% 2.30/2.50 Axiom fact_94_rel__simps_I49_J:(forall (K:int) (L:int), (not (((eq int) (bit0 K)) (bit1 L)))).
% 2.30/2.50 Axiom fact_95_rel__simps_I44_J:(forall (K:int), ((iff (((eq int) (bit0 K)) pls)) (((eq int) K) pls))).
% 2.30/2.50 Axiom fact_96_rel__simps_I38_J:(forall (L:int), ((iff (((eq int) pls) (bit0 L))) (((eq int) pls) L))).
% 2.30/2.50 Axiom fact_97_Bit0__Pls:(((eq int) (bit0 pls)) pls).
% 2.30/2.50 Axiom fact_98_Pls__def:(((eq int) pls) zero_zero_int).
% 2.30/2.50 Axiom fact_99_int__0__neq__1:(not (((eq int) zero_zero_int) one_one_int)).
% 2.30/2.50 Axiom fact_100_add__Pls__right:(forall (K:int), (((eq int) ((plus_plus_int K) pls)) K)).
% 2.30/2.50 Axiom fact_101_add__Pls:(forall (K:int), (((eq int) ((plus_plus_int pls) K)) K)).
% 2.30/2.50 Axiom fact_102_add__Bit0__Bit0:(forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit0 L))) (bit0 ((plus_plus_int K) L)))).
% 2.30/2.50 Axiom fact_103_Bit0__def:(forall (K:int), (((eq int) (bit0 K)) ((plus_plus_int K) K))).
% 2.30/2.51 Axiom fact_104_zadd__0__right:(forall (Z:int), (((eq int) ((plus_plus_int Z) zero_zero_int)) Z)).
% 2.30/2.51 Axiom fact_105_zadd__0:(forall (Z:int), (((eq int) ((plus_plus_int zero_zero_int) Z)) Z)).
% 2.30/2.51 Axiom fact_106_semiring__numeral__0__eq__0:(((eq int) (number_number_of_int pls)) zero_zero_int).
% 2.30/2.51 Axiom fact_107_semiring__numeral__0__eq__0:(((eq nat) (number_number_of_nat pls)) zero_zero_nat).
% 2.30/2.51 Axiom fact_108_semiring__numeral__0__eq__0:(((eq real) (number267125858f_real pls)) zero_zero_real).
% 2.30/2.51 Axiom fact_109_number__of__Pls:(((eq int) (number_number_of_int pls)) zero_zero_int).
% 2.30/2.51 Axiom fact_110_number__of__Pls:(((eq real) (number267125858f_real pls)) zero_zero_real).
% 2.30/2.51 Axiom fact_111_semiring__norm_I112_J:(((eq int) zero_zero_int) (number_number_of_int pls)).
% 2.30/2.51 Axiom fact_112_semiring__norm_I112_J:(((eq real) zero_zero_real) (number267125858f_real pls)).
% 2.30/2.51 Axiom fact_113_add__numeral__0:(forall (A_133:int), (((eq int) ((plus_plus_int (number_number_of_int pls)) A_133)) A_133)).
% 2.30/2.51 Axiom fact_114_add__numeral__0:(forall (A_133:real), (((eq real) ((plus_plus_real (number267125858f_real pls)) A_133)) A_133)).
% 2.30/2.51 Axiom fact_115_add__numeral__0__right:(forall (A_132:int), (((eq int) ((plus_plus_int A_132) (number_number_of_int pls))) A_132)).
% 2.30/2.51 Axiom fact_116_add__numeral__0__right:(forall (A_132:real), (((eq real) ((plus_plus_real A_132) (number267125858f_real pls))) A_132)).
% 2.30/2.51 Axiom fact_117_power__eq__0__iff__number__of:(forall (A_131:int) (W_13:int), ((iff (((eq int) ((power_power_int A_131) (number_number_of_nat W_13))) zero_zero_int)) ((and (((eq int) A_131) zero_zero_int)) (not (((eq nat) (number_number_of_nat W_13)) zero_zero_nat))))).
% 2.30/2.51 Axiom fact_118_power__eq__0__iff__number__of:(forall (A_131:nat) (W_13:int), ((iff (((eq nat) ((power_power_nat A_131) (number_number_of_nat W_13))) zero_zero_nat)) ((and (((eq nat) A_131) zero_zero_nat)) (not (((eq nat) (number_number_of_nat W_13)) zero_zero_nat))))).
% 2.30/2.51 Axiom fact_119_power__eq__0__iff__number__of:(forall (A_131:real) (W_13:int), ((iff (((eq real) ((power_power_real A_131) (number_number_of_nat W_13))) zero_zero_real)) ((and (((eq real) A_131) zero_zero_real)) (not (((eq nat) (number_number_of_nat W_13)) zero_zero_nat))))).
% 2.30/2.51 Axiom fact_120_add__number__of__left:(forall (V_15:int) (W_12:int) (Z_5:int), (((eq int) ((plus_plus_int (number_number_of_int V_15)) ((plus_plus_int (number_number_of_int W_12)) Z_5))) ((plus_plus_int (number_number_of_int ((plus_plus_int V_15) W_12))) Z_5))).
% 2.30/2.51 Axiom fact_121_add__number__of__left:(forall (V_15:int) (W_12:int) (Z_5:real), (((eq real) ((plus_plus_real (number267125858f_real V_15)) ((plus_plus_real (number267125858f_real W_12)) Z_5))) ((plus_plus_real (number267125858f_real ((plus_plus_int V_15) W_12))) Z_5))).
% 2.30/2.51 Axiom fact_122_add__number__of__eq:(forall (V_14:int) (W_11:int), (((eq int) ((plus_plus_int (number_number_of_int V_14)) (number_number_of_int W_11))) (number_number_of_int ((plus_plus_int V_14) W_11)))).
% 2.30/2.51 Axiom fact_123_add__number__of__eq:(forall (V_14:int) (W_11:int), (((eq real) ((plus_plus_real (number267125858f_real V_14)) (number267125858f_real W_11))) (number267125858f_real ((plus_plus_int V_14) W_11)))).
% 2.30/2.51 Axiom fact_124_number__of__add:(forall (V_13:int) (W_10:int), (((eq int) (number_number_of_int ((plus_plus_int V_13) W_10))) ((plus_plus_int (number_number_of_int V_13)) (number_number_of_int W_10)))).
% 2.30/2.51 Axiom fact_125_number__of__add:(forall (V_13:int) (W_10:int), (((eq real) (number267125858f_real ((plus_plus_int V_13) W_10))) ((plus_plus_real (number267125858f_real V_13)) (number267125858f_real W_10)))).
% 2.30/2.51 Axiom fact_126_add__Bit1__Bit0:(forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit0 L))) (bit1 ((plus_plus_int K) L)))).
% 2.30/2.51 Axiom fact_127_add__Bit0__Bit1:(forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit1 L))) (bit1 ((plus_plus_int K) L)))).
% 2.30/2.51 Axiom fact_128_Bit1__def:(forall (K:int), (((eq int) (bit1 K)) ((plus_plus_int ((plus_plus_int one_one_int) K)) K))).
% 2.30/2.51 Axiom fact_129_odd__nonzero:(forall (Z:int), (not (((eq int) ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int))).
% 2.30/2.51 Axiom fact_130_number__of__int:(forall (N_32:nat), (((eq nat) (number_number_of_nat (semiri1621563631at_int N_32))) (semiri984289939at_nat N_32))).
% 2.30/2.51 Axiom fact_131_number__of__int:(forall (N_32:nat), (((eq int) (number_number_of_int (semiri1621563631at_int N_32))) (semiri1621563631at_int N_32))).
% 2.30/2.51 Axiom fact_132_number__of__int:(forall (N_32:nat), (((eq real) (number267125858f_real (semiri1621563631at_int N_32))) (semiri132038758t_real N_32))).
% 2.30/2.51 Axiom fact_133_zero__less__power2:(forall (A_130:int), ((iff ((ord_less_int zero_zero_int) ((power_power_int A_130) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq int) A_130) zero_zero_int)))).
% 2.30/2.51 Axiom fact_134_zero__less__power2:(forall (A_130:real), ((iff ((ord_less_real zero_zero_real) ((power_power_real A_130) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq real) A_130) zero_zero_real)))).
% 2.30/2.51 Axiom fact_135_power2__less__0:(forall (A_129:int), (((ord_less_int ((power_power_int A_129) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)->False)).
% 2.30/2.51 Axiom fact_136_power2__less__0:(forall (A_129:real), (((ord_less_real ((power_power_real A_129) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)->False)).
% 2.30/2.51 Axiom fact_137_sum__power2__gt__zero__iff:(forall (X_25:int) (Y_19:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((power_power_int X_25) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_19) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq int) X_25) zero_zero_int))) (not (((eq int) Y_19) zero_zero_int))))).
% 2.30/2.51 Axiom fact_138_sum__power2__gt__zero__iff:(forall (X_25:real) (Y_19:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((power_power_real X_25) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_19) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq real) X_25) zero_zero_real))) (not (((eq real) Y_19) zero_zero_real))))).
% 2.30/2.51 Axiom fact_139_not__sum__power2__lt__zero:(forall (X_24:int) (Y_18:int), (((ord_less_int ((plus_plus_int ((power_power_int X_24) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_18) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)->False)).
% 2.30/2.51 Axiom fact_140_not__sum__power2__lt__zero:(forall (X_24:real) (Y_18:real), (((ord_less_real ((plus_plus_real ((power_power_real X_24) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_18) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)->False)).
% 2.30/2.51 Axiom fact_141_number__of__Bit0:(forall (W_9:int), (((eq int) (number_number_of_int (bit0 W_9))) ((plus_plus_int ((plus_plus_int zero_zero_int) (number_number_of_int W_9))) (number_number_of_int W_9)))).
% 2.30/2.51 Axiom fact_142_number__of__Bit0:(forall (W_9:int), (((eq real) (number267125858f_real (bit0 W_9))) ((plus_plus_real ((plus_plus_real zero_zero_real) (number267125858f_real W_9))) (number267125858f_real W_9)))).
% 2.30/2.51 Axiom fact_143_number__of__Bit1:(forall (W_8:int), (((eq int) (number_number_of_int (bit1 W_8))) ((plus_plus_int ((plus_plus_int one_one_int) (number_number_of_int W_8))) (number_number_of_int W_8)))).
% 2.30/2.51 Axiom fact_144_number__of__Bit1:(forall (W_8:int), (((eq real) (number267125858f_real (bit1 W_8))) ((plus_plus_real ((plus_plus_real one_one_real) (number267125858f_real W_8))) (number267125858f_real W_8)))).
% 2.30/2.51 Axiom fact_145_semiring__numeral__1__eq__1:(((eq int) (number_number_of_int (bit1 pls))) one_one_int).
% 2.30/2.51 Axiom fact_146_semiring__numeral__1__eq__1:(((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat).
% 2.30/2.51 Axiom fact_147_semiring__numeral__1__eq__1:(((eq real) (number267125858f_real (bit1 pls))) one_one_real).
% 2.30/2.51 Axiom fact_148_mn:((ord_less_int m1) ((plus_plus_int one_one_int) (semiri1621563631at_int n))).
% 2.30/2.51 Axiom fact_149_of__nat__less__two__power:(forall (N_31:nat), ((ord_less_int (semiri1621563631at_int N_31)) ((power_power_int (number_number_of_int (bit0 (bit1 pls)))) N_31))).
% 2.30/2.51 Axiom fact_150_of__nat__less__two__power:(forall (N_31:nat), ((ord_less_real (semiri132038758t_real N_31)) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N_31))).
% 2.30/2.51 Axiom fact_151_transfer__int__nat__numerals_I3_J:(((eq int) (number_number_of_int (bit0 (bit1 pls)))) (semiri1621563631at_int (number_number_of_nat (bit0 (bit1 pls))))).
% 2.30/2.51 Axiom fact_152_transfer__int__nat__numerals_I4_J:(((eq int) (number_number_of_int (bit1 (bit1 pls)))) (semiri1621563631at_int (number_number_of_nat (bit1 (bit1 pls))))).
% 2.30/2.51 Axiom fact_153_realpow__two__sum__zero__iff:(forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real)))).
% 2.30/2.51 Axiom fact_154_of__nat__0__less__iff:(forall (N_30:nat), ((iff ((ord_less_int zero_zero_int) (semiri1621563631at_int N_30))) ((ord_less_nat zero_zero_nat) N_30))).
% 2.30/2.51 Axiom fact_155_of__nat__0__less__iff:(forall (N_30:nat), ((iff ((ord_less_nat zero_zero_nat) (semiri984289939at_nat N_30))) ((ord_less_nat zero_zero_nat) N_30))).
% 2.30/2.51 Axiom fact_156_of__nat__0__less__iff:(forall (N_30:nat), ((iff ((ord_less_real zero_zero_real) (semiri132038758t_real N_30))) ((ord_less_nat zero_zero_nat) N_30))).
% 2.30/2.51 Axiom fact_157_one__less__power:(forall (N_29:nat) (A_128:int), (((ord_less_int one_one_int) A_128)->(((ord_less_nat zero_zero_nat) N_29)->((ord_less_int one_one_int) ((power_power_int A_128) N_29))))).
% 2.30/2.51 Axiom fact_158_one__less__power:(forall (N_29:nat) (A_128:nat), (((ord_less_nat one_one_nat) A_128)->(((ord_less_nat zero_zero_nat) N_29)->((ord_less_nat one_one_nat) ((power_power_nat A_128) N_29))))).
% 2.30/2.51 Axiom fact_159_one__less__power:(forall (N_29:nat) (A_128:real), (((ord_less_real one_one_real) A_128)->(((ord_less_nat zero_zero_nat) N_29)->((ord_less_real one_one_real) ((power_power_real A_128) N_29))))).
% 2.30/2.51 Axiom fact_160_power__0__left:(forall (N_28:nat), ((and ((((eq nat) N_28) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) N_28)) one_one_int))) ((not (((eq nat) N_28) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) N_28)) zero_zero_int)))).
% 2.30/2.51 Axiom fact_161_power__0__left:(forall (N_28:nat), ((and ((((eq nat) N_28) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) N_28)) one_one_nat))) ((not (((eq nat) N_28) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) N_28)) zero_zero_nat)))).
% 2.30/2.51 Axiom fact_162_power__0__left:(forall (N_28:nat), ((and ((((eq nat) N_28) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) N_28)) one_one_real))) ((not (((eq nat) N_28) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) N_28)) zero_zero_real)))).
% 2.30/2.51 Axiom fact_163_power__strict__decreasing:(forall (A_127:int) (N_27:nat) (N_26:nat), (((ord_less_nat N_27) N_26)->(((ord_less_int zero_zero_int) A_127)->(((ord_less_int A_127) one_one_int)->((ord_less_int ((power_power_int A_127) N_26)) ((power_power_int A_127) N_27)))))).
% 2.30/2.51 Axiom fact_164_power__strict__decreasing:(forall (A_127:nat) (N_27:nat) (N_26:nat), (((ord_less_nat N_27) N_26)->(((ord_less_nat zero_zero_nat) A_127)->(((ord_less_nat A_127) one_one_nat)->((ord_less_nat ((power_power_nat A_127) N_26)) ((power_power_nat A_127) N_27)))))).
% 2.30/2.51 Axiom fact_165_power__strict__decreasing:(forall (A_127:real) (N_27:nat) (N_26:nat), (((ord_less_nat N_27) N_26)->(((ord_less_real zero_zero_real) A_127)->(((ord_less_real A_127) one_one_real)->((ord_less_real ((power_power_real A_127) N_26)) ((power_power_real A_127) N_27)))))).
% 2.30/2.51 Axiom fact_166_zero__less__two:((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) one_one_int)).
% 2.30/2.51 Axiom fact_167_zero__less__two:((ord_less_nat zero_zero_nat) ((plus_plus_nat one_one_nat) one_one_nat)).
% 2.30/2.51 Axiom fact_168_zero__less__two:((ord_less_real zero_zero_real) ((plus_plus_real one_one_real) one_one_real)).
% 2.30/2.51 Axiom fact_169_int__gr__induct:(forall (P:(int->Prop)) (K:int) (I_1:int), (((ord_less_int K) I_1)->((P ((plus_plus_int K) one_one_int))->((forall (_TPTP_I:int), (((ord_less_int K) _TPTP_I)->((P _TPTP_I)->(P ((plus_plus_int _TPTP_I) one_one_int)))))->(P I_1))))).
% 2.30/2.51 Axiom fact_170_transfer__int__nat__numerals_I1_J:(((eq int) zero_zero_int) (semiri1621563631at_int zero_zero_nat)).
% 2.30/2.51 Axiom fact_171_tn0:((ord_less_nat zero_zero_nat) tn).
% 2.30/2.51 Axiom fact_172_less__zeroE:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)).
% 2.30/2.51 Axiom fact_173_real__zero__not__eq__one:(not (((eq real) zero_zero_real) one_one_real)).
% 2.30/2.51 Axiom fact_174_less__not__refl:(forall (N:nat), (((ord_less_nat N) N)->False)).
% 2.30/2.51 Axiom fact_175_not__add__less1:(forall (I_1:nat) (J:nat), (((ord_less_nat ((plus_plus_nat I_1) J)) I_1)->False)).
% 2.30/2.51 Axiom fact_176_not__add__less2:(forall (J:nat) (I_1:nat), (((ord_less_nat ((plus_plus_nat J) I_1)) I_1)->False)).
% 2.30/2.51 Axiom fact_177_number__of__is__id:(forall (K:int), (((eq int) (number_number_of_int K)) K)).
% 2.30/2.51 Axiom fact_178_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)))).
% 2.30/2.51 Axiom fact_179_nat__add__commute:(forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) N)) ((plus_plus_nat N) M))).
% 2.30/2.51 Axiom fact_180_nat__add__left__commute:(forall (X:nat) (Y:nat) (Z:nat), (((eq nat) ((plus_plus_nat X) ((plus_plus_nat Y) Z))) ((plus_plus_nat Y) ((plus_plus_nat X) Z)))).
% 2.30/2.51 Axiom fact_181_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)))).
% 2.30/2.51 Axiom fact_182_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))).
% 2.30/2.51 Axiom fact_183_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))).
% 2.30/2.51 Axiom fact_184_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))).
% 2.30/2.51 Axiom fact_185_linorder__neqE__nat:(forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X)))).
% 2.30/2.51 Axiom fact_186_less__irrefl__nat:(forall (N:nat), (((ord_less_nat N) N)->False)).
% 2.30/2.51 Axiom fact_187_less__not__refl2:(forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N)))).
% 2.30/2.51 Axiom fact_188_less__not__refl3:(forall (S_1:nat) (T:nat), (((ord_less_nat S_1) T)->(not (((eq nat) S_1) T)))).
% 2.30/2.51 Axiom fact_189_trans__less__add1:(forall (M:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat I_1) ((plus_plus_nat J) M)))).
% 2.30/2.51 Axiom fact_190_trans__less__add2:(forall (M:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat I_1) ((plus_plus_nat M) J)))).
% 2.30/2.51 Axiom fact_191_add__less__mono1:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) K)))).
% 2.30/2.51 Axiom fact_192_add__less__mono:(forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) L))))).
% 2.30/2.51 Axiom fact_193_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)))).
% 2.30/2.51 Axiom fact_194_add__lessD1:(forall (I_1:nat) (J:nat) (K:nat), (((ord_less_nat ((plus_plus_nat I_1) J)) K)->((ord_less_nat I_1) K))).
% 2.30/2.51 Axiom fact_195_nat__less__cases:(forall (P:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P N) M))->(((((eq nat) M) N)->((P N) M))->((((ord_less_nat N) M)->((P N) M))->((P N) M))))).
% 2.30/2.51 Axiom fact_196_gr0I:(forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N))).
% 2.30/2.51 Axiom fact_197_gr__implies__not0:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->(not (((eq nat) N) zero_zero_nat)))).
% 2.30/2.51 Axiom fact_198_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)))).
% 2.30/2.51 Axiom fact_199_less__nat__zero__code:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)).
% 2.30/2.51 Axiom fact_200_nat__zero__less__power__iff:(forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or ((ord_less_nat zero_zero_nat) X)) (((eq nat) N) zero_zero_nat)))).
% 2.30/2.51 Axiom fact_201_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)))).
% 2.30/2.51 Axiom fact_202_neq0__conv:(forall (N:nat), ((iff (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N))).
% 2.30/2.51 Axiom fact_203_not__less0:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)).
% 2.30/2.51 Axiom fact_204_zero__less__power__nat__eq:(forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or (((eq nat) N) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X)))).
% 2.30/2.51 Axiom fact_205_Nat__Transfer_Otransfer__int__nat__relations_I2_J:(forall (X:nat) (Y:nat), ((iff ((ord_less_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_nat X) Y))).
% 2.30/2.51 Axiom fact_206_zero__less__power__nat__eq__number__of:(forall (X:nat) (W:int), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) (number_number_of_nat W)))) ((or (((eq nat) (number_number_of_nat W)) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X)))).
% 2.30/2.51 Axiom fact_207_zless__int:(forall (M:nat) (N:nat), ((iff ((ord_less_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_nat M) N))).
% 2.30/2.51 Axiom fact_208_less__nat__number__of:(forall (V_1:int) (V_2:int), ((iff ((ord_less_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) ((and (((ord_less_int V_1) V_2)->((ord_less_int pls) V_2))) ((ord_less_int V_1) V_2)))).
% 2.30/2.51 Axiom fact_209_linorder__neqE__linordered__idom:(forall (X_23:int) (Y_17:int), ((not (((eq int) X_23) Y_17))->((((ord_less_int X_23) Y_17)->False)->((ord_less_int Y_17) X_23)))).
% 2.30/2.51 Axiom fact_210_linorder__neqE__linordered__idom:(forall (X_23:real) (Y_17:real), ((not (((eq real) X_23) Y_17))->((((ord_less_real X_23) Y_17)->False)->((ord_less_real Y_17) X_23)))).
% 2.30/2.51 Axiom fact_211_add__eq__self__zero:(forall (M:nat) (N:nat), ((((eq nat) ((plus_plus_nat M) N)) M)->(((eq nat) N) zero_zero_nat))).
% 2.30/2.51 Axiom fact_212_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)))).
% 2.30/2.51 Axiom fact_213_Nat_Oadd__0__right:(forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M)).
% 2.30/2.51 Axiom fact_214_plus__nat_Oadd__0:(forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N)).
% 2.30/2.51 Axiom fact_215_power__one__right:(forall (A_126:int), (((eq int) ((power_power_int A_126) one_one_nat)) A_126)).
% 2.30/2.51 Axiom fact_216_power__one__right:(forall (A_126:nat), (((eq nat) ((power_power_nat A_126) one_one_nat)) A_126)).
% 2.30/2.51 Axiom fact_217_power__one__right:(forall (A_126:real), (((eq real) ((power_power_real A_126) one_one_nat)) A_126)).
% 2.30/2.51 Axiom fact_218_of__nat__eq__iff:(forall (M_14:nat) (N_25:nat), ((iff (((eq real) (semiri132038758t_real M_14)) (semiri132038758t_real N_25))) (((eq nat) M_14) N_25))).
% 2.30/2.51 Axiom fact_219_of__nat__eq__iff:(forall (M_14:nat) (N_25:nat), ((iff (((eq nat) (semiri984289939at_nat M_14)) (semiri984289939at_nat N_25))) (((eq nat) M_14) N_25))).
% 2.30/2.51 Axiom fact_220_of__nat__eq__iff:(forall (M_14:nat) (N_25:nat), ((iff (((eq int) (semiri1621563631at_int M_14)) (semiri1621563631at_int N_25))) (((eq nat) M_14) N_25))).
% 2.30/2.51 Axiom fact_221_Nat__Transfer_Otransfer__int__nat__relations_I1_J:(forall (X:nat) (Y:nat), ((iff (((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (((eq nat) X) Y))).
% 2.30/2.51 Axiom fact_222_int__if__cong:(forall (X:nat) (Y:nat) (P:Prop), ((and (P->(((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int (((if_nat P) X) Y))))) ((P->False)->(((eq int) (semiri1621563631at_int Y)) (semiri1621563631at_int (((if_nat P) X) Y)))))).
% 2.30/2.51 Axiom fact_223_less__0__number__of:(forall (V_1:int), ((iff ((ord_less_nat zero_zero_nat) (number_number_of_nat V_1))) ((ord_less_int pls) V_1))).
% 2.30/2.51 Axiom fact_224_zero__less__int__conv:(forall (N:nat), ((iff ((ord_less_int zero_zero_int) (semiri1621563631at_int N))) ((ord_less_nat zero_zero_nat) N))).
% 2.30/2.51 Axiom fact_225_one__neq__zero:(not (((eq int) one_one_int) zero_zero_int)).
% 2.30/2.51 Axiom fact_226_one__neq__zero:(not (((eq nat) one_one_nat) zero_zero_nat)).
% 2.30/2.51 Axiom fact_227_one__neq__zero:(not (((eq real) one_one_real) zero_zero_real)).
% 2.30/2.51 Axiom fact_228_zero__neq__one:(not (((eq int) zero_zero_int) one_one_int)).
% 2.30/2.51 Axiom fact_229_zero__neq__one:(not (((eq nat) zero_zero_nat) one_one_nat)).
% 2.30/2.52 Axiom fact_230_zero__neq__one:(not (((eq real) zero_zero_real) one_one_real)).
% 2.30/2.52 Axiom fact_231_field__power__not__zero:(forall (N_24:nat) (A_125:int), ((not (((eq int) A_125) zero_zero_int))->(not (((eq int) ((power_power_int A_125) N_24)) zero_zero_int)))).
% 2.30/2.52 Axiom fact_232_field__power__not__zero:(forall (N_24:nat) (A_125:real), ((not (((eq real) A_125) zero_zero_real))->(not (((eq real) ((power_power_real A_125) N_24)) zero_zero_real)))).
% 2.30/2.52 Axiom fact_233_power__one:(forall (N_23:nat), (((eq int) ((power_power_int one_one_int) N_23)) one_one_int)).
% 2.30/2.52 Axiom fact_234_power__one:(forall (N_23:nat), (((eq nat) ((power_power_nat one_one_nat) N_23)) one_one_nat)).
% 2.30/2.52 Axiom fact_235_power__one:(forall (N_23:nat), (((eq real) ((power_power_real one_one_real) N_23)) one_one_real)).
% 2.30/2.52 Axiom fact_236_of__nat__less__iff:(forall (M_13:nat) (N_22:nat), ((iff ((ord_less_int (semiri1621563631at_int M_13)) (semiri1621563631at_int N_22))) ((ord_less_nat M_13) N_22))).
% 2.30/2.52 Axiom fact_237_of__nat__less__iff:(forall (M_13:nat) (N_22:nat), ((iff ((ord_less_nat (semiri984289939at_nat M_13)) (semiri984289939at_nat N_22))) ((ord_less_nat M_13) N_22))).
% 2.30/2.52 Axiom fact_238_of__nat__less__iff:(forall (M_13:nat) (N_22:nat), ((iff ((ord_less_real (semiri132038758t_real M_13)) (semiri132038758t_real N_22))) ((ord_less_nat M_13) N_22))).
% 2.30/2.52 Axiom fact_239_less__imp__of__nat__less:(forall (M_12:nat) (N_21:nat), (((ord_less_nat M_12) N_21)->((ord_less_int (semiri1621563631at_int M_12)) (semiri1621563631at_int N_21)))).
% 2.30/2.52 Axiom fact_240_less__imp__of__nat__less:(forall (M_12:nat) (N_21:nat), (((ord_less_nat M_12) N_21)->((ord_less_nat (semiri984289939at_nat M_12)) (semiri984289939at_nat N_21)))).
% 2.30/2.52 Axiom fact_241_less__imp__of__nat__less:(forall (M_12:nat) (N_21:nat), (((ord_less_nat M_12) N_21)->((ord_less_real (semiri132038758t_real M_12)) (semiri132038758t_real N_21)))).
% 2.30/2.52 Axiom fact_242_of__nat__less__imp__less:(forall (M_11:nat) (N_20:nat), (((ord_less_int (semiri1621563631at_int M_11)) (semiri1621563631at_int N_20))->((ord_less_nat M_11) N_20))).
% 2.30/2.52 Axiom fact_243_of__nat__less__imp__less:(forall (M_11:nat) (N_20:nat), (((ord_less_nat (semiri984289939at_nat M_11)) (semiri984289939at_nat N_20))->((ord_less_nat M_11) N_20))).
% 2.30/2.52 Axiom fact_244_of__nat__less__imp__less:(forall (M_11:nat) (N_20:nat), (((ord_less_real (semiri132038758t_real M_11)) (semiri132038758t_real N_20))->((ord_less_nat M_11) N_20))).
% 2.30/2.52 Axiom fact_245_of__nat__add:(forall (M_10:nat) (N_19:nat), (((eq int) (semiri1621563631at_int ((plus_plus_nat M_10) N_19))) ((plus_plus_int (semiri1621563631at_int M_10)) (semiri1621563631at_int N_19)))).
% 2.30/2.52 Axiom fact_246_of__nat__add:(forall (M_10:nat) (N_19:nat), (((eq nat) (semiri984289939at_nat ((plus_plus_nat M_10) N_19))) ((plus_plus_nat (semiri984289939at_nat M_10)) (semiri984289939at_nat N_19)))).
% 2.30/2.52 Axiom fact_247_of__nat__add:(forall (M_10:nat) (N_19:nat), (((eq real) (semiri132038758t_real ((plus_plus_nat M_10) N_19))) ((plus_plus_real (semiri132038758t_real M_10)) (semiri132038758t_real N_19)))).
% 2.30/2.52 Axiom fact_248_of__nat__1:(((eq int) (semiri1621563631at_int one_one_nat)) one_one_int).
% 2.30/2.52 Axiom fact_249_of__nat__1:(((eq nat) (semiri984289939at_nat one_one_nat)) one_one_nat).
% 2.30/2.52 Axiom fact_250_of__nat__1:(((eq real) (semiri132038758t_real one_one_nat)) one_one_real).
% 2.30/2.52 Axiom fact_251_of__nat__power:(forall (M_9:nat) (N_18:nat), (((eq int) (semiri1621563631at_int ((power_power_nat M_9) N_18))) ((power_power_int (semiri1621563631at_int M_9)) N_18))).
% 2.30/2.52 Axiom fact_252_of__nat__power:(forall (M_9:nat) (N_18:nat), (((eq nat) (semiri984289939at_nat ((power_power_nat M_9) N_18))) ((power_power_nat (semiri984289939at_nat M_9)) N_18))).
% 2.30/2.52 Axiom fact_253_of__nat__power:(forall (M_9:nat) (N_18:nat), (((eq real) (semiri132038758t_real ((power_power_nat M_9) N_18))) ((power_power_real (semiri132038758t_real M_9)) N_18))).
% 2.30/2.52 Axiom fact_254_transfer__int__nat__numerals_I2_J:(((eq int) one_one_int) (semiri1621563631at_int one_one_nat)).
% 2.30/2.52 Axiom fact_255_Nat__Transfer_Otransfer__int__nat__functions_I1_J:(forall (X:nat) (Y:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((plus_plus_nat X) Y)))).
% 2.30/2.52 Axiom fact_256_Nat__Transfer_Otransfer__int__nat__functions_I4_J:(forall (X:nat) (N:nat), (((eq int) ((power_power_int (semiri1621563631at_int X)) N)) (semiri1621563631at_int ((power_power_nat X) N)))).
% 2.30/2.52 Axiom fact_257_pos__add__strict:(forall (B_89:int) (C_63:int) (A_124:int), (((ord_less_int zero_zero_int) A_124)->(((ord_less_int B_89) C_63)->((ord_less_int B_89) ((plus_plus_int A_124) C_63))))).
% 2.30/2.52 Axiom fact_258_pos__add__strict:(forall (B_89:nat) (C_63:nat) (A_124:nat), (((ord_less_nat zero_zero_nat) A_124)->(((ord_less_nat B_89) C_63)->((ord_less_nat B_89) ((plus_plus_nat A_124) C_63))))).
% 2.30/2.52 Axiom fact_259_pos__add__strict:(forall (B_89:real) (C_63:real) (A_124:real), (((ord_less_real zero_zero_real) A_124)->(((ord_less_real B_89) C_63)->((ord_less_real B_89) ((plus_plus_real A_124) C_63))))).
% 2.30/2.52 Axiom fact_260_not__one__less__zero:(((ord_less_int one_one_int) zero_zero_int)->False).
% 2.30/2.52 Axiom fact_261_not__one__less__zero:(((ord_less_nat one_one_nat) zero_zero_nat)->False).
% 2.30/2.52 Axiom fact_262_not__one__less__zero:(((ord_less_real one_one_real) zero_zero_real)->False).
% 2.30/2.52 Axiom fact_263_zero__less__one:((ord_less_int zero_zero_int) one_one_int).
% 2.30/2.52 Axiom fact_264_zero__less__one:((ord_less_nat zero_zero_nat) one_one_nat).
% 2.30/2.52 Axiom fact_265_zero__less__one:((ord_less_real zero_zero_real) one_one_real).
% 2.30/2.52 Axiom fact_266_zero__less__power:(forall (N_17:nat) (A_123:int), (((ord_less_int zero_zero_int) A_123)->((ord_less_int zero_zero_int) ((power_power_int A_123) N_17)))).
% 2.30/2.52 Axiom fact_267_zero__less__power:(forall (N_17:nat) (A_123:nat), (((ord_less_nat zero_zero_nat) A_123)->((ord_less_nat zero_zero_nat) ((power_power_nat A_123) N_17)))).
% 2.30/2.52 Axiom fact_268_zero__less__power:(forall (N_17:nat) (A_123:real), (((ord_less_real zero_zero_real) A_123)->((ord_less_real zero_zero_real) ((power_power_real A_123) N_17)))).
% 2.30/2.52 Axiom fact_269_less__add__one:(forall (A_122:int), ((ord_less_int A_122) ((plus_plus_int A_122) one_one_int))).
% 2.30/2.52 Axiom fact_270_less__add__one:(forall (A_122:nat), ((ord_less_nat A_122) ((plus_plus_nat A_122) one_one_nat))).
% 2.30/2.52 Axiom fact_271_less__add__one:(forall (A_122:real), ((ord_less_real A_122) ((plus_plus_real A_122) one_one_real))).
% 2.30/2.52 Axiom fact_272_power__inject__exp:(forall (M_8:nat) (N_16:nat) (A_121:int), (((ord_less_int one_one_int) A_121)->((iff (((eq int) ((power_power_int A_121) M_8)) ((power_power_int A_121) N_16))) (((eq nat) M_8) N_16)))).
% 2.30/2.52 Axiom fact_273_power__inject__exp:(forall (M_8:nat) (N_16:nat) (A_121:nat), (((ord_less_nat one_one_nat) A_121)->((iff (((eq nat) ((power_power_nat A_121) M_8)) ((power_power_nat A_121) N_16))) (((eq nat) M_8) N_16)))).
% 2.30/2.52 Axiom fact_274_power__inject__exp:(forall (M_8:nat) (N_16:nat) (A_121:real), (((ord_less_real one_one_real) A_121)->((iff (((eq real) ((power_power_real A_121) M_8)) ((power_power_real A_121) N_16))) (((eq nat) M_8) N_16)))).
% 2.30/2.52 Axiom fact_275_power__strict__increasing__iff:(forall (X_22:nat) (Y_16:nat) (B_88:int), (((ord_less_int one_one_int) B_88)->((iff ((ord_less_int ((power_power_int B_88) X_22)) ((power_power_int B_88) Y_16))) ((ord_less_nat X_22) Y_16)))).
% 2.30/2.52 Axiom fact_276_power__strict__increasing__iff:(forall (X_22:nat) (Y_16:nat) (B_88:nat), (((ord_less_nat one_one_nat) B_88)->((iff ((ord_less_nat ((power_power_nat B_88) X_22)) ((power_power_nat B_88) Y_16))) ((ord_less_nat X_22) Y_16)))).
% 2.30/2.52 Axiom fact_277_power__strict__increasing__iff:(forall (X_22:nat) (Y_16:nat) (B_88:real), (((ord_less_real one_one_real) B_88)->((iff ((ord_less_real ((power_power_real B_88) X_22)) ((power_power_real B_88) Y_16))) ((ord_less_nat X_22) Y_16)))).
% 2.30/2.52 Axiom fact_278_power__less__imp__less__exp:(forall (M_7:nat) (N_15:nat) (A_120:int), (((ord_less_int one_one_int) A_120)->(((ord_less_int ((power_power_int A_120) M_7)) ((power_power_int A_120) N_15))->((ord_less_nat M_7) N_15)))).
% 2.30/2.52 Axiom fact_279_power__less__imp__less__exp:(forall (M_7:nat) (N_15:nat) (A_120:nat), (((ord_less_nat one_one_nat) A_120)->(((ord_less_nat ((power_power_nat A_120) M_7)) ((power_power_nat A_120) N_15))->((ord_less_nat M_7) N_15)))).
% 2.30/2.52 Axiom fact_280_power__less__imp__less__exp:(forall (M_7:nat) (N_15:nat) (A_120:real), (((ord_less_real one_one_real) A_120)->(((ord_less_real ((power_power_real A_120) M_7)) ((power_power_real A_120) N_15))->((ord_less_nat M_7) N_15)))).
% 2.30/2.52 Axiom fact_281_power__strict__increasing:(forall (A_119:int) (N_14:nat) (N_13:nat), (((ord_less_nat N_14) N_13)->(((ord_less_int one_one_int) A_119)->((ord_less_int ((power_power_int A_119) N_14)) ((power_power_int A_119) N_13))))).
% 2.30/2.52 Axiom fact_282_power__strict__increasing:(forall (A_119:nat) (N_14:nat) (N_13:nat), (((ord_less_nat N_14) N_13)->(((ord_less_nat one_one_nat) A_119)->((ord_less_nat ((power_power_nat A_119) N_14)) ((power_power_nat A_119) N_13))))).
% 2.30/2.52 Axiom fact_283_power__strict__increasing:(forall (A_119:real) (N_14:nat) (N_13:nat), (((ord_less_nat N_14) N_13)->(((ord_less_real one_one_real) A_119)->((ord_less_real ((power_power_real A_119) N_14)) ((power_power_real A_119) N_13))))).
% 2.30/2.52 Axiom fact_284_power__eq__0__iff:(forall (A_118:int) (N_12:nat), ((iff (((eq int) ((power_power_int A_118) N_12)) zero_zero_int)) ((and (((eq int) A_118) zero_zero_int)) (not (((eq nat) N_12) zero_zero_nat))))).
% 2.30/2.52 Axiom fact_285_power__eq__0__iff:(forall (A_118:nat) (N_12:nat), ((iff (((eq nat) ((power_power_nat A_118) N_12)) zero_zero_nat)) ((and (((eq nat) A_118) zero_zero_nat)) (not (((eq nat) N_12) zero_zero_nat))))).
% 2.30/2.52 Axiom fact_286_power__eq__0__iff:(forall (A_118:real) (N_12:nat), ((iff (((eq real) ((power_power_real A_118) N_12)) zero_zero_real)) ((and (((eq real) A_118) zero_zero_real)) (not (((eq nat) N_12) zero_zero_nat))))).
% 2.30/2.52 Axiom fact_287_of__nat__less__0__iff:(forall (M_6:nat), (((ord_less_int (semiri1621563631at_int M_6)) zero_zero_int)->False)).
% 2.30/2.52 Axiom fact_288_of__nat__less__0__iff:(forall (M_6:nat), (((ord_less_nat (semiri984289939at_nat M_6)) zero_zero_nat)->False)).
% 2.30/2.52 Axiom fact_289_of__nat__less__0__iff:(forall (M_6:nat), (((ord_less_real (semiri132038758t_real M_6)) zero_zero_real)->False)).
% 2.30/2.52 Axiom fact_290_power__0:(forall (A_117:int), (((eq int) ((power_power_int A_117) zero_zero_nat)) one_one_int)).
% 2.30/2.52 Axiom fact_291_power__0:(forall (A_117:nat), (((eq nat) ((power_power_nat A_117) zero_zero_nat)) one_one_nat)).
% 2.30/2.52 Axiom fact_292_power__0:(forall (A_117:real), (((eq real) ((power_power_real A_117) zero_zero_nat)) one_one_real)).
% 2.30/2.52 Axiom fact_293_of__nat__0:(((eq int) (semiri1621563631at_int zero_zero_nat)) zero_zero_int).
% 2.30/2.52 Axiom fact_294_of__nat__0:(((eq nat) (semiri984289939at_nat zero_zero_nat)) zero_zero_nat).
% 2.30/2.52 Axiom fact_295_of__nat__0:(((eq real) (semiri132038758t_real zero_zero_nat)) zero_zero_real).
% 2.30/2.52 Axiom fact_296_pos2:((ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls)))).
% 2.30/2.52 Axiom fact_297_zero__less__imp__eq__int:(forall (K:int), (((ord_less_int zero_zero_int) K)->((ex nat) (fun (N_1:nat)=> ((and ((ord_less_nat zero_zero_nat) N_1)) (((eq int) K) (semiri1621563631at_int N_1))))))).
% 2.30/2.52 Axiom fact_298_less__imp__add__positive:(forall (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->((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)))))).
% 2.30/2.52 Axiom fact_299_exp__eq__1:(forall (X:nat) (N:nat), ((iff (((eq nat) ((power_power_nat X) N)) one_one_nat)) ((or (((eq nat) X) one_one_nat)) (((eq nat) N) zero_zero_nat)))).
% 2.30/2.52 Axiom fact_300_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J:(forall (X_21:int), (((eq int) ((power_power_int X_21) zero_zero_nat)) one_one_int)).
% 2.30/2.52 Axiom fact_301_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J:(forall (X_21:nat), (((eq nat) ((power_power_nat X_21) zero_zero_nat)) one_one_nat)).
% 2.30/2.52 Axiom fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J:(forall (X_21:real), (((eq real) ((power_power_real X_21) zero_zero_nat)) one_one_real)).
% 2.30/2.52 Axiom fact_303_zero__less__double__add__iff__zero__less__single__add:(forall (A_116:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int A_116) A_116))) ((ord_less_int zero_zero_int) A_116))).
% 2.30/2.52 Axiom fact_304_zero__less__double__add__iff__zero__less__single__add:(forall (A_116:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real A_116) A_116))) ((ord_less_real zero_zero_real) A_116))).
% 2.30/2.52 Axiom fact_305_double__add__less__zero__iff__single__add__less__zero:(forall (A_115:int), ((iff ((ord_less_int ((plus_plus_int A_115) A_115)) zero_zero_int)) ((ord_less_int A_115) zero_zero_int))).
% 2.30/2.52 Axiom fact_306_double__add__less__zero__iff__single__add__less__zero:(forall (A_115:real), ((iff ((ord_less_real ((plus_plus_real A_115) A_115)) zero_zero_real)) ((ord_less_real A_115) zero_zero_real))).
% 2.30/2.52 Axiom fact_307_add__pos__pos:(forall (B_87:int) (A_114:int), (((ord_less_int zero_zero_int) A_114)->(((ord_less_int zero_zero_int) B_87)->((ord_less_int zero_zero_int) ((plus_plus_int A_114) B_87))))).
% 2.30/2.52 Axiom fact_308_add__pos__pos:(forall (B_87:nat) (A_114:nat), (((ord_less_nat zero_zero_nat) A_114)->(((ord_less_nat zero_zero_nat) B_87)->((ord_less_nat zero_zero_nat) ((plus_plus_nat A_114) B_87))))).
% 2.30/2.52 Axiom fact_309_add__pos__pos:(forall (B_87:real) (A_114:real), (((ord_less_real zero_zero_real) A_114)->(((ord_less_real zero_zero_real) B_87)->((ord_less_real zero_zero_real) ((plus_plus_real A_114) B_87))))).
% 2.30/2.52 Axiom fact_310_add__neg__neg:(forall (B_86:int) (A_113:int), (((ord_less_int A_113) zero_zero_int)->(((ord_less_int B_86) zero_zero_int)->((ord_less_int ((plus_plus_int A_113) B_86)) zero_zero_int)))).
% 2.30/2.52 Axiom fact_311_add__neg__neg:(forall (B_86:nat) (A_113:nat), (((ord_less_nat A_113) zero_zero_nat)->(((ord_less_nat B_86) zero_zero_nat)->((ord_less_nat ((plus_plus_nat A_113) B_86)) zero_zero_nat)))).
% 2.30/2.52 Axiom fact_312_add__neg__neg:(forall (B_86:real) (A_113:real), (((ord_less_real A_113) zero_zero_real)->(((ord_less_real B_86) zero_zero_real)->((ord_less_real ((plus_plus_real A_113) B_86)) zero_zero_real)))).
% 2.30/2.52 Axiom fact_313_zero__reorient:(forall (X_20:int), ((iff (((eq int) zero_zero_int) X_20)) (((eq int) X_20) zero_zero_int))).
% 2.30/2.52 Axiom fact_314_zero__reorient:(forall (X_20:nat), ((iff (((eq nat) zero_zero_nat) X_20)) (((eq nat) X_20) zero_zero_nat))).
% 2.30/2.52 Axiom fact_315_zero__reorient:(forall (X_20:real), ((iff (((eq real) zero_zero_real) X_20)) (((eq real) X_20) zero_zero_real))).
% 2.30/2.52 Axiom fact_316_add__right__imp__eq:(forall (B_85:int) (A_112:int) (C_62:int), ((((eq int) ((plus_plus_int B_85) A_112)) ((plus_plus_int C_62) A_112))->(((eq int) B_85) C_62))).
% 2.30/2.52 Axiom fact_317_add__right__imp__eq:(forall (B_85:nat) (A_112:nat) (C_62:nat), ((((eq nat) ((plus_plus_nat B_85) A_112)) ((plus_plus_nat C_62) A_112))->(((eq nat) B_85) C_62))).
% 2.30/2.52 Axiom fact_318_add__right__imp__eq:(forall (B_85:real) (A_112:real) (C_62:real), ((((eq real) ((plus_plus_real B_85) A_112)) ((plus_plus_real C_62) A_112))->(((eq real) B_85) C_62))).
% 2.30/2.52 Axiom fact_319_add__imp__eq:(forall (A_111:int) (B_84:int) (C_61:int), ((((eq int) ((plus_plus_int A_111) B_84)) ((plus_plus_int A_111) C_61))->(((eq int) B_84) C_61))).
% 2.30/2.52 Axiom fact_320_add__imp__eq:(forall (A_111:nat) (B_84:nat) (C_61:nat), ((((eq nat) ((plus_plus_nat A_111) B_84)) ((plus_plus_nat A_111) C_61))->(((eq nat) B_84) C_61))).
% 2.30/2.52 Axiom fact_321_add__imp__eq:(forall (A_111:real) (B_84:real) (C_61:real), ((((eq real) ((plus_plus_real A_111) B_84)) ((plus_plus_real A_111) C_61))->(((eq real) B_84) C_61))).
% 2.30/2.52 Axiom fact_322_add__left__imp__eq:(forall (A_110:int) (B_83:int) (C_60:int), ((((eq int) ((plus_plus_int A_110) B_83)) ((plus_plus_int A_110) C_60))->(((eq int) B_83) C_60))).
% 2.30/2.52 Axiom fact_323_add__left__imp__eq:(forall (A_110:nat) (B_83:nat) (C_60:nat), ((((eq nat) ((plus_plus_nat A_110) B_83)) ((plus_plus_nat A_110) C_60))->(((eq nat) B_83) C_60))).
% 2.30/2.52 Axiom fact_324_add__left__imp__eq:(forall (A_110:real) (B_83:real) (C_60:real), ((((eq real) ((plus_plus_real A_110) B_83)) ((plus_plus_real A_110) C_60))->(((eq real) B_83) C_60))).
% 2.30/2.52 Axiom fact_325_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_109:int) (B_82:int) (C_59:int) (D_23:int), (((eq int) ((plus_plus_int ((plus_plus_int A_109) B_82)) ((plus_plus_int C_59) D_23))) ((plus_plus_int ((plus_plus_int A_109) C_59)) ((plus_plus_int B_82) D_23)))).
% 2.30/2.52 Axiom fact_326_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_109:nat) (B_82:nat) (C_59:nat) (D_23:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_109) B_82)) ((plus_plus_nat C_59) D_23))) ((plus_plus_nat ((plus_plus_nat A_109) C_59)) ((plus_plus_nat B_82) D_23)))).
% 2.30/2.52 Axiom fact_327_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_109:real) (B_82:real) (C_59:real) (D_23:real), (((eq real) ((plus_plus_real ((plus_plus_real A_109) B_82)) ((plus_plus_real C_59) D_23))) ((plus_plus_real ((plus_plus_real A_109) C_59)) ((plus_plus_real B_82) D_23)))).
% 2.30/2.52 Axiom fact_328_add__right__cancel:(forall (B_81:int) (A_108:int) (C_58:int), ((iff (((eq int) ((plus_plus_int B_81) A_108)) ((plus_plus_int C_58) A_108))) (((eq int) B_81) C_58))).
% 2.30/2.52 Axiom fact_329_add__right__cancel:(forall (B_81:nat) (A_108:nat) (C_58:nat), ((iff (((eq nat) ((plus_plus_nat B_81) A_108)) ((plus_plus_nat C_58) A_108))) (((eq nat) B_81) C_58))).
% 2.30/2.52 Axiom fact_330_add__right__cancel:(forall (B_81:real) (A_108:real) (C_58:real), ((iff (((eq real) ((plus_plus_real B_81) A_108)) ((plus_plus_real C_58) A_108))) (((eq real) B_81) C_58))).
% 2.30/2.52 Axiom fact_331_add__left__cancel:(forall (A_107:int) (B_80:int) (C_57:int), ((iff (((eq int) ((plus_plus_int A_107) B_80)) ((plus_plus_int A_107) C_57))) (((eq int) B_80) C_57))).
% 2.30/2.52 Axiom fact_332_add__left__cancel:(forall (A_107:nat) (B_80:nat) (C_57:nat), ((iff (((eq nat) ((plus_plus_nat A_107) B_80)) ((plus_plus_nat A_107) C_57))) (((eq nat) B_80) C_57))).
% 2.30/2.52 Axiom fact_333_add__left__cancel:(forall (A_107:real) (B_80:real) (C_57:real), ((iff (((eq real) ((plus_plus_real A_107) B_80)) ((plus_plus_real A_107) C_57))) (((eq real) B_80) C_57))).
% 2.30/2.52 Axiom fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_106:int) (B_79:int) (C_56:int), (((eq int) ((plus_plus_int ((plus_plus_int A_106) B_79)) C_56)) ((plus_plus_int ((plus_plus_int A_106) C_56)) B_79))).
% 2.30/2.52 Axiom fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_106:nat) (B_79:nat) (C_56:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_106) B_79)) C_56)) ((plus_plus_nat ((plus_plus_nat A_106) C_56)) B_79))).
% 2.30/2.52 Axiom fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_106:real) (B_79:real) (C_56:real), (((eq real) ((plus_plus_real ((plus_plus_real A_106) B_79)) C_56)) ((plus_plus_real ((plus_plus_real A_106) C_56)) B_79))).
% 2.30/2.52 Axiom fact_337_ab__semigroup__add__class_Oadd__ac_I1_J:(forall (A_105:int) (B_78:int) (C_55:int), (((eq int) ((plus_plus_int ((plus_plus_int A_105) B_78)) C_55)) ((plus_plus_int A_105) ((plus_plus_int B_78) C_55)))).
% 2.30/2.52 Axiom fact_338_ab__semigroup__add__class_Oadd__ac_I1_J:(forall (A_105:nat) (B_78:nat) (C_55:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_105) B_78)) C_55)) ((plus_plus_nat A_105) ((plus_plus_nat B_78) C_55)))).
% 2.30/2.52 Axiom fact_339_ab__semigroup__add__class_Oadd__ac_I1_J:(forall (A_105:real) (B_78:real) (C_55:real), (((eq real) ((plus_plus_real ((plus_plus_real A_105) B_78)) C_55)) ((plus_plus_real A_105) ((plus_plus_real B_78) C_55)))).
% 2.30/2.52 Axiom fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_104:int) (B_77:int) (C_54:int), (((eq int) ((plus_plus_int ((plus_plus_int A_104) B_77)) C_54)) ((plus_plus_int A_104) ((plus_plus_int B_77) C_54)))).
% 2.30/2.52 Axiom fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_104:nat) (B_77:nat) (C_54:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_104) B_77)) C_54)) ((plus_plus_nat A_104) ((plus_plus_nat B_77) C_54)))).
% 2.30/2.52 Axiom fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_104:real) (B_77:real) (C_54:real), (((eq real) ((plus_plus_real ((plus_plus_real A_104) B_77)) C_54)) ((plus_plus_real A_104) ((plus_plus_real B_77) C_54)))).
% 2.30/2.52 Axiom fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_103:int) (C_53:int) (D_22:int), (((eq int) ((plus_plus_int A_103) ((plus_plus_int C_53) D_22))) ((plus_plus_int ((plus_plus_int A_103) C_53)) D_22))).
% 2.30/2.52 Axiom fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_103:nat) (C_53:nat) (D_22:nat), (((eq nat) ((plus_plus_nat A_103) ((plus_plus_nat C_53) D_22))) ((plus_plus_nat ((plus_plus_nat A_103) C_53)) D_22))).
% 2.30/2.52 Axiom fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_103:real) (C_53:real) (D_22:real), (((eq real) ((plus_plus_real A_103) ((plus_plus_real C_53) D_22))) ((plus_plus_real ((plus_plus_real A_103) C_53)) D_22))).
% 2.30/2.52 Axiom fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_102:int) (C_52:int) (D_21:int), (((eq int) ((plus_plus_int A_102) ((plus_plus_int C_52) D_21))) ((plus_plus_int C_52) ((plus_plus_int A_102) D_21)))).
% 2.30/2.52 Axiom fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_102:nat) (C_52:nat) (D_21:nat), (((eq nat) ((plus_plus_nat A_102) ((plus_plus_nat C_52) D_21))) ((plus_plus_nat C_52) ((plus_plus_nat A_102) D_21)))).
% 2.30/2.52 Axiom fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_102:real) (C_52:real) (D_21:real), (((eq real) ((plus_plus_real A_102) ((plus_plus_real C_52) D_21))) ((plus_plus_real C_52) ((plus_plus_real A_102) D_21)))).
% 2.30/2.52 Axiom fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A_101:int) (C_51:int), (((eq int) ((plus_plus_int A_101) C_51)) ((plus_plus_int C_51) A_101))).
% 2.30/2.52 Axiom fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A_101:nat) (C_51:nat), (((eq nat) ((plus_plus_nat A_101) C_51)) ((plus_plus_nat C_51) A_101))).
% 2.30/2.52 Axiom fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A_101:real) (C_51:real), (((eq real) ((plus_plus_real A_101) C_51)) ((plus_plus_real C_51) A_101))).
% 2.30/2.52 Axiom fact_352_one__reorient:(forall (X_19:int), ((iff (((eq int) one_one_int) X_19)) (((eq int) X_19) one_one_int))).
% 2.30/2.52 Axiom fact_353_one__reorient:(forall (X_19:nat), ((iff (((eq nat) one_one_nat) X_19)) (((eq nat) X_19) one_one_nat))).
% 2.30/2.52 Axiom fact_354_one__reorient:(forall (X_19:real), ((iff (((eq real) one_one_real) X_19)) (((eq real) X_19) one_one_real))).
% 2.30/2.52 Axiom fact_355_add__0__iff:(forall (B_76:int) (A_100:int), ((iff (((eq int) B_76) ((plus_plus_int B_76) A_100))) (((eq int) A_100) zero_zero_int))).
% 2.30/2.52 Axiom fact_356_add__0__iff:(forall (B_76:nat) (A_100:nat), ((iff (((eq nat) B_76) ((plus_plus_nat B_76) A_100))) (((eq nat) A_100) zero_zero_nat))).
% 2.30/2.52 Axiom fact_357_add__0__iff:(forall (B_76:real) (A_100:real), ((iff (((eq real) B_76) ((plus_plus_real B_76) A_100))) (((eq real) A_100) zero_zero_real))).
% 2.30/2.52 Axiom fact_358_add_Ocomm__neutral:(forall (A_99:int), (((eq int) ((plus_plus_int A_99) zero_zero_int)) A_99)).
% 2.30/2.52 Axiom fact_359_add_Ocomm__neutral:(forall (A_99:nat), (((eq nat) ((plus_plus_nat A_99) zero_zero_nat)) A_99)).
% 2.30/2.52 Axiom fact_360_add_Ocomm__neutral:(forall (A_99:real), (((eq real) ((plus_plus_real A_99) zero_zero_real)) A_99)).
% 2.30/2.52 Axiom fact_361_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J:(forall (A_98:int), (((eq int) ((plus_plus_int A_98) zero_zero_int)) A_98)).
% 2.30/2.52 Axiom fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J:(forall (A_98:nat), (((eq nat) ((plus_plus_nat A_98) zero_zero_nat)) A_98)).
% 2.30/2.52 Axiom fact_363_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J:(forall (A_98:real), (((eq real) ((plus_plus_real A_98) zero_zero_real)) A_98)).
% 2.30/2.52 Axiom fact_364_add__0__right:(forall (A_97:int), (((eq int) ((plus_plus_int A_97) zero_zero_int)) A_97)).
% 2.30/2.52 Axiom fact_365_add__0__right:(forall (A_97:nat), (((eq nat) ((plus_plus_nat A_97) zero_zero_nat)) A_97)).
% 2.30/2.52 Axiom fact_366_add__0__right:(forall (A_97:real), (((eq real) ((plus_plus_real A_97) zero_zero_real)) A_97)).
% 2.30/2.52 Axiom fact_367_double__zero__sym:(forall (A_96:int), ((iff (((eq int) zero_zero_int) ((plus_plus_int A_96) A_96))) (((eq int) A_96) zero_zero_int))).
% 2.30/2.52 Axiom fact_368_double__zero__sym:(forall (A_96:real), ((iff (((eq real) zero_zero_real) ((plus_plus_real A_96) A_96))) (((eq real) A_96) zero_zero_real))).
% 2.30/2.52 Axiom fact_369_add__0:(forall (A_95:int), (((eq int) ((plus_plus_int zero_zero_int) A_95)) A_95)).
% 2.30/2.52 Axiom fact_370_add__0:(forall (A_95:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_95)) A_95)).
% 2.30/2.52 Axiom fact_371_add__0:(forall (A_95:real), (((eq real) ((plus_plus_real zero_zero_real) A_95)) A_95)).
% 2.30/2.52 Axiom fact_372_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J:(forall (A_94:int), (((eq int) ((plus_plus_int zero_zero_int) A_94)) A_94)).
% 2.30/2.53 Axiom fact_373_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J:(forall (A_94:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_94)) A_94)).
% 2.30/2.53 Axiom fact_374_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J:(forall (A_94:real), (((eq real) ((plus_plus_real zero_zero_real) A_94)) A_94)).
% 2.30/2.53 Axiom fact_375_add__0__left:(forall (A_93:int), (((eq int) ((plus_plus_int zero_zero_int) A_93)) A_93)).
% 2.30/2.53 Axiom fact_376_add__0__left:(forall (A_93:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_93)) A_93)).
% 2.30/2.53 Axiom fact_377_add__0__left:(forall (A_93:real), (((eq real) ((plus_plus_real zero_zero_real) A_93)) A_93)).
% 2.30/2.53 Axiom fact_378_add__less__imp__less__left:(forall (C_50:int) (A_92:int) (B_75:int), (((ord_less_int ((plus_plus_int C_50) A_92)) ((plus_plus_int C_50) B_75))->((ord_less_int A_92) B_75))).
% 2.30/2.53 Axiom fact_379_add__less__imp__less__left:(forall (C_50:nat) (A_92:nat) (B_75:nat), (((ord_less_nat ((plus_plus_nat C_50) A_92)) ((plus_plus_nat C_50) B_75))->((ord_less_nat A_92) B_75))).
% 2.30/2.53 Axiom fact_380_add__less__imp__less__left:(forall (C_50:real) (A_92:real) (B_75:real), (((ord_less_real ((plus_plus_real C_50) A_92)) ((plus_plus_real C_50) B_75))->((ord_less_real A_92) B_75))).
% 2.30/2.53 Axiom fact_381_add__less__imp__less__right:(forall (A_91:int) (C_49:int) (B_74:int), (((ord_less_int ((plus_plus_int A_91) C_49)) ((plus_plus_int B_74) C_49))->((ord_less_int A_91) B_74))).
% 2.30/2.53 Axiom fact_382_add__less__imp__less__right:(forall (A_91:nat) (C_49:nat) (B_74:nat), (((ord_less_nat ((plus_plus_nat A_91) C_49)) ((plus_plus_nat B_74) C_49))->((ord_less_nat A_91) B_74))).
% 2.30/2.53 Axiom fact_383_add__less__imp__less__right:(forall (A_91:real) (C_49:real) (B_74:real), (((ord_less_real ((plus_plus_real A_91) C_49)) ((plus_plus_real B_74) C_49))->((ord_less_real A_91) B_74))).
% 2.30/2.53 Axiom fact_384_add__strict__mono:(forall (C_48:int) (D_20:int) (A_90:int) (B_73:int), (((ord_less_int A_90) B_73)->(((ord_less_int C_48) D_20)->((ord_less_int ((plus_plus_int A_90) C_48)) ((plus_plus_int B_73) D_20))))).
% 2.30/2.53 Axiom fact_385_add__strict__mono:(forall (C_48:nat) (D_20:nat) (A_90:nat) (B_73:nat), (((ord_less_nat A_90) B_73)->(((ord_less_nat C_48) D_20)->((ord_less_nat ((plus_plus_nat A_90) C_48)) ((plus_plus_nat B_73) D_20))))).
% 2.30/2.53 Axiom fact_386_add__strict__mono:(forall (C_48:real) (D_20:real) (A_90:real) (B_73:real), (((ord_less_real A_90) B_73)->(((ord_less_real C_48) D_20)->((ord_less_real ((plus_plus_real A_90) C_48)) ((plus_plus_real B_73) D_20))))).
% 2.30/2.53 Axiom fact_387_add__strict__left__mono:(forall (C_47:int) (A_89:int) (B_72:int), (((ord_less_int A_89) B_72)->((ord_less_int ((plus_plus_int C_47) A_89)) ((plus_plus_int C_47) B_72)))).
% 2.30/2.53 Axiom fact_388_add__strict__left__mono:(forall (C_47:nat) (A_89:nat) (B_72:nat), (((ord_less_nat A_89) B_72)->((ord_less_nat ((plus_plus_nat C_47) A_89)) ((plus_plus_nat C_47) B_72)))).
% 2.30/2.53 Axiom fact_389_add__strict__left__mono:(forall (C_47:real) (A_89:real) (B_72:real), (((ord_less_real A_89) B_72)->((ord_less_real ((plus_plus_real C_47) A_89)) ((plus_plus_real C_47) B_72)))).
% 2.30/2.53 Axiom fact_390_add__strict__right__mono:(forall (C_46:int) (A_88:int) (B_71:int), (((ord_less_int A_88) B_71)->((ord_less_int ((plus_plus_int A_88) C_46)) ((plus_plus_int B_71) C_46)))).
% 2.30/2.53 Axiom fact_391_add__strict__right__mono:(forall (C_46:nat) (A_88:nat) (B_71:nat), (((ord_less_nat A_88) B_71)->((ord_less_nat ((plus_plus_nat A_88) C_46)) ((plus_plus_nat B_71) C_46)))).
% 2.30/2.53 Axiom fact_392_add__strict__right__mono:(forall (C_46:real) (A_88:real) (B_71:real), (((ord_less_real A_88) B_71)->((ord_less_real ((plus_plus_real A_88) C_46)) ((plus_plus_real B_71) C_46)))).
% 2.30/2.53 Axiom fact_393_add__less__cancel__left:(forall (C_45:int) (A_87:int) (B_70:int), ((iff ((ord_less_int ((plus_plus_int C_45) A_87)) ((plus_plus_int C_45) B_70))) ((ord_less_int A_87) B_70))).
% 2.30/2.53 Axiom fact_394_add__less__cancel__left:(forall (C_45:nat) (A_87:nat) (B_70:nat), ((iff ((ord_less_nat ((plus_plus_nat C_45) A_87)) ((plus_plus_nat C_45) B_70))) ((ord_less_nat A_87) B_70))).
% 2.30/2.53 Axiom fact_395_add__less__cancel__left:(forall (C_45:real) (A_87:real) (B_70:real), ((iff ((ord_less_real ((plus_plus_real C_45) A_87)) ((plus_plus_real C_45) B_70))) ((ord_less_real A_87) B_70))).
% 2.30/2.53 Axiom fact_396_add__less__cancel__right:(forall (A_86:int) (C_44:int) (B_69:int), ((iff ((ord_less_int ((plus_plus_int A_86) C_44)) ((plus_plus_int B_69) C_44))) ((ord_less_int A_86) B_69))).
% 2.30/2.53 Axiom fact_397_add__less__cancel__right:(forall (A_86:nat) (C_44:nat) (B_69:nat), ((iff ((ord_less_nat ((plus_plus_nat A_86) C_44)) ((plus_plus_nat B_69) C_44))) ((ord_less_nat A_86) B_69))).
% 2.30/2.53 Axiom fact_398_add__less__cancel__right:(forall (A_86:real) (C_44:real) (B_69:real), ((iff ((ord_less_real ((plus_plus_real A_86) C_44)) ((plus_plus_real B_69) C_44))) ((ord_less_real A_86) B_69))).
% 2.30/2.53 Axiom fact_399_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J:(forall (X_18:int), (((eq int) ((power_power_int X_18) one_one_nat)) X_18)).
% 2.30/2.53 Axiom fact_400_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J:(forall (X_18:nat), (((eq nat) ((power_power_nat X_18) one_one_nat)) X_18)).
% 2.30/2.53 Axiom fact_401_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J:(forall (X_18:real), (((eq real) ((power_power_real X_18) one_one_nat)) X_18)).
% 2.30/2.53 Axiom fact_402_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)))).
% 2.30/2.53 Axiom fact_403_realpow__pos__nth__unique:(forall (A:real) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_real zero_zero_real) A)->((ex real) (fun (X_1:real)=> ((and ((and ((ord_less_real zero_zero_real) X_1)) (((eq real) ((power_power_real X_1) N)) A))) (forall (Y_1:real), (((and ((ord_less_real zero_zero_real) Y_1)) (((eq real) ((power_power_real Y_1) N)) A))->(((eq real) Y_1) X_1))))))))).
% 2.30/2.53 Axiom fact_404_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:real)=> ((and ((ord_less_real zero_zero_real) R)) (((eq real) ((power_power_real R) N)) A))))))).
% 2.30/2.53 Axiom fact_405_tpos:((ord_less_eq_int one_one_int) t).
% 2.30/2.53 Axiom fact_406_nat__number__of__add__1:(forall (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) one_one_nat)) one_one_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) one_one_nat)) (number_number_of_nat (succ V_1)))))).
% 2.30/2.53 Axiom fact_407_nat__1__add__number__of:(forall (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V_1))) one_one_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V_1))) (number_number_of_nat (succ V_1)))))).
% 2.30/2.53 Axiom fact_408_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))))))).
% 2.30/2.53 Axiom fact_409_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))))))).
% 2.30/2.53 Axiom fact_410_tn:(((eq nat) tn) ((minus_minus_nat (nat_1 t)) one_one_nat)).
% 2.30/2.53 Axiom fact_411__096_B_Bthesis_O_A_I_B_Btn_O_A_091_124_Atn_A_061_Anat_At_A_N_A1_059_A0_:((ord_less_nat zero_zero_nat) ((minus_minus_nat (nat_1 t)) one_one_nat)).
% 2.30/2.53 Axiom fact_412_le__iff__diff__le__0:(forall (A_85:int) (B_68:int), ((iff ((ord_less_eq_int A_85) B_68)) ((ord_less_eq_int ((minus_minus_int A_85) B_68)) zero_zero_int))).
% 2.30/2.53 Axiom fact_413_le__iff__diff__le__0:(forall (A_85:real) (B_68:real), ((iff ((ord_less_eq_real A_85) B_68)) ((ord_less_eq_real ((minus_minus_real A_85) B_68)) zero_zero_real))).
% 2.30/2.53 Axiom fact_414_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J:(forall (A_84:int) (B_67:int), (((eq int) ((times_times_int A_84) B_67)) ((times_times_int B_67) A_84))).
% 2.30/2.53 Axiom fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J:(forall (A_84:nat) (B_67:nat), (((eq nat) ((times_times_nat A_84) B_67)) ((times_times_nat B_67) A_84))).
% 2.30/2.53 Axiom fact_416_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J:(forall (A_84:real) (B_67:real), (((eq real) ((times_times_real A_84) B_67)) ((times_times_real B_67) A_84))).
% 2.30/2.53 Axiom fact_417_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J:(forall (Lx_6:int) (Rx_6:int) (Ry_4:int), (((eq int) ((times_times_int Lx_6) ((times_times_int Rx_6) Ry_4))) ((times_times_int Rx_6) ((times_times_int Lx_6) Ry_4)))).
% 2.30/2.53 Axiom fact_418_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J:(forall (Lx_6:nat) (Rx_6:nat) (Ry_4:nat), (((eq nat) ((times_times_nat Lx_6) ((times_times_nat Rx_6) Ry_4))) ((times_times_nat Rx_6) ((times_times_nat Lx_6) Ry_4)))).
% 2.30/2.53 Axiom fact_419_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J:(forall (Lx_6:real) (Rx_6:real) (Ry_4:real), (((eq real) ((times_times_real Lx_6) ((times_times_real Rx_6) Ry_4))) ((times_times_real Rx_6) ((times_times_real Lx_6) Ry_4)))).
% 2.30/2.53 Axiom fact_420_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J:(forall (Lx_5:int) (Rx_5:int) (Ry_3:int), (((eq int) ((times_times_int Lx_5) ((times_times_int Rx_5) Ry_3))) ((times_times_int ((times_times_int Lx_5) Rx_5)) Ry_3))).
% 2.30/2.53 Axiom fact_421_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J:(forall (Lx_5:nat) (Rx_5:nat) (Ry_3:nat), (((eq nat) ((times_times_nat Lx_5) ((times_times_nat Rx_5) Ry_3))) ((times_times_nat ((times_times_nat Lx_5) Rx_5)) Ry_3))).
% 2.30/2.53 Axiom fact_422_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J:(forall (Lx_5:real) (Rx_5:real) (Ry_3:real), (((eq real) ((times_times_real Lx_5) ((times_times_real Rx_5) Ry_3))) ((times_times_real ((times_times_real Lx_5) Rx_5)) Ry_3))).
% 2.30/2.53 Axiom fact_423_ab__semigroup__mult__class_Omult__ac_I1_J:(forall (A_83:int) (B_66:int) (C_43:int), (((eq int) ((times_times_int ((times_times_int A_83) B_66)) C_43)) ((times_times_int A_83) ((times_times_int B_66) C_43)))).
% 2.30/2.53 Axiom fact_424_ab__semigroup__mult__class_Omult__ac_I1_J:(forall (A_83:nat) (B_66:nat) (C_43:nat), (((eq nat) ((times_times_nat ((times_times_nat A_83) B_66)) C_43)) ((times_times_nat A_83) ((times_times_nat B_66) C_43)))).
% 2.30/2.53 Axiom fact_425_ab__semigroup__mult__class_Omult__ac_I1_J:(forall (A_83:real) (B_66:real) (C_43:real), (((eq real) ((times_times_real ((times_times_real A_83) B_66)) C_43)) ((times_times_real A_83) ((times_times_real B_66) C_43)))).
% 2.30/2.53 Axiom fact_426_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J:(forall (Lx_4:int) (Ly_4:int) (Rx_4:int), (((eq int) ((times_times_int ((times_times_int Lx_4) Ly_4)) Rx_4)) ((times_times_int Lx_4) ((times_times_int Ly_4) Rx_4)))).
% 2.30/2.53 Axiom fact_427_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J:(forall (Lx_4:nat) (Ly_4:nat) (Rx_4:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_4) Ly_4)) Rx_4)) ((times_times_nat Lx_4) ((times_times_nat Ly_4) Rx_4)))).
% 2.30/2.53 Axiom fact_428_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J:(forall (Lx_4:real) (Ly_4:real) (Rx_4:real), (((eq real) ((times_times_real ((times_times_real Lx_4) Ly_4)) Rx_4)) ((times_times_real Lx_4) ((times_times_real Ly_4) Rx_4)))).
% 2.30/2.53 Axiom fact_429_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J:(forall (Lx_3:int) (Ly_3:int) (Rx_3:int), (((eq int) ((times_times_int ((times_times_int Lx_3) Ly_3)) Rx_3)) ((times_times_int ((times_times_int Lx_3) Rx_3)) Ly_3))).
% 2.30/2.53 Axiom fact_430_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J:(forall (Lx_3:nat) (Ly_3:nat) (Rx_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_3) Ly_3)) Rx_3)) ((times_times_nat ((times_times_nat Lx_3) Rx_3)) Ly_3))).
% 2.30/2.53 Axiom fact_431_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J:(forall (Lx_3:real) (Ly_3:real) (Rx_3:real), (((eq real) ((times_times_real ((times_times_real Lx_3) Ly_3)) Rx_3)) ((times_times_real ((times_times_real Lx_3) Rx_3)) Ly_3))).
% 2.30/2.53 Axiom fact_432_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J:(forall (Lx_2:int) (Ly_2:int) (Rx_2:int) (Ry_2:int), (((eq int) ((times_times_int ((times_times_int Lx_2) Ly_2)) ((times_times_int Rx_2) Ry_2))) ((times_times_int Lx_2) ((times_times_int Ly_2) ((times_times_int Rx_2) Ry_2))))).
% 2.30/2.53 Axiom fact_433_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J:(forall (Lx_2:nat) (Ly_2:nat) (Rx_2:nat) (Ry_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_2) Ly_2)) ((times_times_nat Rx_2) Ry_2))) ((times_times_nat Lx_2) ((times_times_nat Ly_2) ((times_times_nat Rx_2) Ry_2))))).
% 2.30/2.53 Axiom fact_434_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J:(forall (Lx_2:real) (Ly_2:real) (Rx_2:real) (Ry_2:real), (((eq real) ((times_times_real ((times_times_real Lx_2) Ly_2)) ((times_times_real Rx_2) Ry_2))) ((times_times_real Lx_2) ((times_times_real Ly_2) ((times_times_real Rx_2) Ry_2))))).
% 2.30/2.53 Axiom fact_435_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J:(forall (Lx_1:real) (Ly_1:real) (Rx_1:real) (Ry_1:real), (((eq real) ((times_times_real ((times_times_real Lx_1) Ly_1)) ((times_times_real Rx_1) Ry_1))) ((times_times_real Rx_1) ((times_times_real ((times_times_real Lx_1) Ly_1)) Ry_1)))).
% 2.30/2.53 Axiom fact_436_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J:(forall (Lx_1:nat) (Ly_1:nat) (Rx_1:nat) (Ry_1:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_1) Ly_1)) ((times_times_nat Rx_1) Ry_1))) ((times_times_nat Rx_1) ((times_times_nat ((times_times_nat Lx_1) Ly_1)) Ry_1)))).
% 2.30/2.53 Axiom fact_437_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J:(forall (Lx_1:int) (Ly_1:int) (Rx_1:int) (Ry_1:int), (((eq int) ((times_times_int ((times_times_int Lx_1) Ly_1)) ((times_times_int Rx_1) Ry_1))) ((times_times_int Rx_1) ((times_times_int ((times_times_int Lx_1) Ly_1)) Ry_1)))).
% 2.30/2.53 Axiom fact_438_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J:(forall (Lx:real) (Ly:real) (Rx:real) (Ry:real), (((eq real) ((times_times_real ((times_times_real Lx) Ly)) ((times_times_real Rx) Ry))) ((times_times_real ((times_times_real Lx) Rx)) ((times_times_real Ly) Ry)))).
% 2.30/2.53 Axiom fact_439_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J:(forall (Lx:nat) (Ly:nat) (Rx:nat) (Ry:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx) Ly)) ((times_times_nat Rx) Ry))) ((times_times_nat ((times_times_nat Lx) Rx)) ((times_times_nat Ly) Ry)))).
% 2.30/2.53 Axiom fact_440_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J:(forall (Lx:int) (Ly:int) (Rx:int) (Ry:int), (((eq int) ((times_times_int ((times_times_int Lx) Ly)) ((times_times_int Rx) Ry))) ((times_times_int ((times_times_int Lx) Rx)) ((times_times_int Ly) Ry)))).
% 2.30/2.53 Axiom fact_441_diff__eq__diff__eq:(forall (A_82:int) (B_65:int) (C_42:int) (D_19:int), ((((eq int) ((minus_minus_int A_82) B_65)) ((minus_minus_int C_42) D_19))->((iff (((eq int) A_82) B_65)) (((eq int) C_42) D_19)))).
% 2.30/2.53 Axiom fact_442_diff__eq__diff__eq:(forall (A_82:real) (B_65:real) (C_42:real) (D_19:real), ((((eq real) ((minus_minus_real A_82) B_65)) ((minus_minus_real C_42) D_19))->((iff (((eq real) A_82) B_65)) (((eq real) C_42) D_19)))).
% 2.30/2.53 Axiom fact_443_diff__eq__diff__less__eq:(forall (A_81:int) (B_64:int) (C_41:int) (D_18:int), ((((eq int) ((minus_minus_int A_81) B_64)) ((minus_minus_int C_41) D_18))->((iff ((ord_less_eq_int A_81) B_64)) ((ord_less_eq_int C_41) D_18)))).
% 2.30/2.53 Axiom fact_444_diff__eq__diff__less__eq:(forall (A_81:real) (B_64:real) (C_41:real) (D_18:real), ((((eq real) ((minus_minus_real A_81) B_64)) ((minus_minus_real C_41) D_18))->((iff ((ord_less_eq_real A_81) B_64)) ((ord_less_eq_real C_41) D_18)))).
% 2.30/2.53 Axiom fact_445_semiring__mult__number__of:(forall (V_12:int) (V_11:int), (((ord_less_eq_int pls) V_11)->(((ord_less_eq_int pls) V_12)->(((eq real) ((times_times_real (number267125858f_real V_11)) (number267125858f_real V_12))) (number267125858f_real ((times_times_int V_11) V_12)))))).
% 2.30/2.53 Axiom fact_446_semiring__mult__number__of:(forall (V_12:int) (V_11:int), (((ord_less_eq_int pls) V_11)->(((ord_less_eq_int pls) V_12)->(((eq nat) ((times_times_nat (number_number_of_nat V_11)) (number_number_of_nat V_12))) (number_number_of_nat ((times_times_int V_11) V_12)))))).
% 2.30/2.53 Axiom fact_447_semiring__mult__number__of:(forall (V_12:int) (V_11:int), (((ord_less_eq_int pls) V_11)->(((ord_less_eq_int pls) V_12)->(((eq int) ((times_times_int (number_number_of_int V_11)) (number_number_of_int V_12))) (number_number_of_int ((times_times_int V_11) V_12)))))).
% 2.30/2.53 Axiom fact_448_zle__refl:(forall (W:int), ((ord_less_eq_int W) W)).
% 2.30/2.53 Axiom fact_449_zmult__commute:(forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z))).
% 2.30/2.53 Axiom fact_450_zle__linear:(forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z))).
% 2.30/2.53 Axiom fact_451_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)))).
% 2.30/2.53 Axiom fact_452_zle__trans:(forall (K:int) (I_1:int) (J:int), (((ord_less_eq_int I_1) J)->(((ord_less_eq_int J) K)->((ord_less_eq_int I_1) K)))).
% 2.30/2.53 Axiom fact_453_zle__antisym:(forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W)))).
% 2.30/2.53 Axiom fact_454_le__number__of:(forall (X_17:int) (Y_15:int), ((iff ((ord_less_eq_real (number267125858f_real X_17)) (number267125858f_real Y_15))) ((ord_less_eq_int X_17) Y_15))).
% 2.30/2.53 Axiom fact_455_le__number__of:(forall (X_17:int) (Y_15:int), ((iff ((ord_less_eq_int (number_number_of_int X_17)) (number_number_of_int Y_15))) ((ord_less_eq_int X_17) Y_15))).
% 2.30/2.53 Axiom fact_456_number__of__mult:(forall (V_10:int) (W_7:int), (((eq real) (number267125858f_real ((times_times_int V_10) W_7))) ((times_times_real (number267125858f_real V_10)) (number267125858f_real W_7)))).
% 2.30/2.53 Axiom fact_457_number__of__mult:(forall (V_10:int) (W_7:int), (((eq int) (number_number_of_int ((times_times_int V_10) W_7))) ((times_times_int (number_number_of_int V_10)) (number_number_of_int W_7)))).
% 2.30/2.53 Axiom fact_458_arith__simps_I32_J:(forall (V_9:int) (W_6:int), (((eq real) ((times_times_real (number267125858f_real V_9)) (number267125858f_real W_6))) (number267125858f_real ((times_times_int V_9) W_6)))).
% 2.30/2.53 Axiom fact_459_arith__simps_I32_J:(forall (V_9:int) (W_6:int), (((eq int) ((times_times_int (number_number_of_int V_9)) (number_number_of_int W_6))) (number_number_of_int ((times_times_int V_9) W_6)))).
% 2.30/2.53 Axiom fact_460_mult__number__of__left:(forall (V_8:int) (W_5:int) (Z_4:real), (((eq real) ((times_times_real (number267125858f_real V_8)) ((times_times_real (number267125858f_real W_5)) Z_4))) ((times_times_real (number267125858f_real ((times_times_int V_8) W_5))) Z_4))).
% 2.30/2.53 Axiom fact_461_mult__number__of__left:(forall (V_8:int) (W_5:int) (Z_4:int), (((eq int) ((times_times_int (number_number_of_int V_8)) ((times_times_int (number_number_of_int W_5)) Z_4))) ((times_times_int (number_number_of_int ((times_times_int V_8) W_5))) Z_4))).
% 2.30/2.53 Axiom fact_462_eq__nat__nat__iff:(forall (Z_1:int) (Z:int), (((ord_less_eq_int zero_zero_int) Z)->(((ord_less_eq_int zero_zero_int) Z_1)->((iff (((eq nat) (nat_1 Z)) (nat_1 Z_1))) (((eq int) Z) Z_1))))).
% 2.30/2.53 Axiom fact_463_right__diff__distrib__number__of:(forall (V_7:int) (B_63:int) (C_40:int), (((eq int) ((times_times_int (number_number_of_int V_7)) ((minus_minus_int B_63) C_40))) ((minus_minus_int ((times_times_int (number_number_of_int V_7)) B_63)) ((times_times_int (number_number_of_int V_7)) C_40)))).
% 2.30/2.53 Axiom fact_464_right__diff__distrib__number__of:(forall (V_7:int) (B_63:real) (C_40:real), (((eq real) ((times_times_real (number267125858f_real V_7)) ((minus_minus_real B_63) C_40))) ((minus_minus_real ((times_times_real (number267125858f_real V_7)) B_63)) ((times_times_real (number267125858f_real V_7)) C_40)))).
% 2.30/2.53 Axiom fact_465_left__diff__distrib__number__of:(forall (A_80:int) (B_62:int) (V_6:int), (((eq int) ((times_times_int ((minus_minus_int A_80) B_62)) (number_number_of_int V_6))) ((minus_minus_int ((times_times_int A_80) (number_number_of_int V_6))) ((times_times_int B_62) (number_number_of_int V_6))))).
% 2.30/2.53 Axiom fact_466_left__diff__distrib__number__of:(forall (A_80:real) (B_62:real) (V_6:int), (((eq real) ((times_times_real ((minus_minus_real A_80) B_62)) (number267125858f_real V_6))) ((minus_minus_real ((times_times_real A_80) (number267125858f_real V_6))) ((times_times_real B_62) (number267125858f_real V_6))))).
% 2.30/2.53 Axiom fact_467_number__of__diff:(forall (V_5:int) (W_4:int), (((eq int) (number_number_of_int ((minus_minus_int V_5) W_4))) ((minus_minus_int (number_number_of_int V_5)) (number_number_of_int W_4)))).
% 2.30/2.53 Axiom fact_468_number__of__diff:(forall (V_5:int) (W_4:int), (((eq real) (number267125858f_real ((minus_minus_int V_5) W_4))) ((minus_minus_real (number267125858f_real V_5)) (number267125858f_real W_4)))).
% 2.30/2.53 Axiom fact_469_of__nat__mult:(forall (M_5:nat) (N_11:nat), (((eq real) (semiri132038758t_real ((times_times_nat M_5) N_11))) ((times_times_real (semiri132038758t_real M_5)) (semiri132038758t_real N_11)))).
% 2.30/2.53 Axiom fact_470_of__nat__mult:(forall (M_5:nat) (N_11:nat), (((eq nat) (semiri984289939at_nat ((times_times_nat M_5) N_11))) ((times_times_nat (semiri984289939at_nat M_5)) (semiri984289939at_nat N_11)))).
% 2.30/2.53 Axiom fact_471_of__nat__mult:(forall (M_5:nat) (N_11:nat), (((eq int) (semiri1621563631at_int ((times_times_nat M_5) N_11))) ((times_times_int (semiri1621563631at_int M_5)) (semiri1621563631at_int N_11)))).
% 2.30/2.53 Axiom fact_472_of__nat__le__iff:(forall (M_4:nat) (N_10:nat), ((iff ((ord_less_eq_real (semiri132038758t_real M_4)) (semiri132038758t_real N_10))) ((ord_less_eq_nat M_4) N_10))).
% 2.30/2.53 Axiom fact_473_of__nat__le__iff:(forall (M_4:nat) (N_10:nat), ((iff ((ord_less_eq_nat (semiri984289939at_nat M_4)) (semiri984289939at_nat N_10))) ((ord_less_eq_nat M_4) N_10))).
% 2.30/2.53 Axiom fact_474_of__nat__le__iff:(forall (M_4:nat) (N_10:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int M_4)) (semiri1621563631at_int N_10))) ((ord_less_eq_nat M_4) N_10))).
% 2.30/2.53 Axiom fact_475_diff__commute:(forall (I_1:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J)) K)) ((minus_minus_nat ((minus_minus_nat I_1) K)) J))).
% 2.30/2.53 Axiom fact_476_nat__if__cong:(forall (X:int) (Y:int) (P:Prop), ((and (P->(((eq nat) (nat_1 X)) (nat_1 (((if_int P) X) Y))))) ((P->False)->(((eq nat) (nat_1 Y)) (nat_1 (((if_int P) X) Y)))))).
% 2.30/2.53 Axiom fact_477_split__mult__neg__le:(forall (B_61:real) (A_79:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_79)) ((ord_less_eq_real B_61) zero_zero_real))) ((and ((ord_less_eq_real A_79) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_61)))->((ord_less_eq_real ((times_times_real A_79) B_61)) zero_zero_real))).
% 2.30/2.53 Axiom fact_478_split__mult__neg__le:(forall (B_61:nat) (A_79:nat), (((or ((and ((ord_less_eq_nat zero_zero_nat) A_79)) ((ord_less_eq_nat B_61) zero_zero_nat))) ((and ((ord_less_eq_nat A_79) zero_zero_nat)) ((ord_less_eq_nat zero_zero_nat) B_61)))->((ord_less_eq_nat ((times_times_nat A_79) B_61)) zero_zero_nat))).
% 2.30/2.53 Axiom fact_479_split__mult__neg__le:(forall (B_61:int) (A_79:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_79)) ((ord_less_eq_int B_61) zero_zero_int))) ((and ((ord_less_eq_int A_79) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_61)))->((ord_less_eq_int ((times_times_int A_79) B_61)) zero_zero_int))).
% 2.30/2.53 Axiom fact_480_split__mult__pos__le:(forall (B_60:real) (A_78:real), (((or ((and ((ord_less_eq_real zero_zero_real) A_78)) ((ord_less_eq_real zero_zero_real) B_60))) ((and ((ord_less_eq_real A_78) zero_zero_real)) ((ord_less_eq_real B_60) zero_zero_real)))->((ord_less_eq_real zero_zero_real) ((times_times_real A_78) B_60)))).
% 2.30/2.53 Axiom fact_481_split__mult__pos__le:(forall (B_60:int) (A_78:int), (((or ((and ((ord_less_eq_int zero_zero_int) A_78)) ((ord_less_eq_int zero_zero_int) B_60))) ((and ((ord_less_eq_int A_78) zero_zero_int)) ((ord_less_eq_int B_60) zero_zero_int)))->((ord_less_eq_int zero_zero_int) ((times_times_int A_78) B_60)))).
% 2.30/2.54 Axiom fact_482_mult__mono:(forall (C_39:real) (D_17:real) (A_77:real) (B_59:real), (((ord_less_eq_real A_77) B_59)->(((ord_less_eq_real C_39) D_17)->(((ord_less_eq_real zero_zero_real) B_59)->(((ord_less_eq_real zero_zero_real) C_39)->((ord_less_eq_real ((times_times_real A_77) C_39)) ((times_times_real B_59) D_17))))))).
% 2.30/2.54 Axiom fact_483_mult__mono:(forall (C_39:nat) (D_17:nat) (A_77:nat) (B_59:nat), (((ord_less_eq_nat A_77) B_59)->(((ord_less_eq_nat C_39) D_17)->(((ord_less_eq_nat zero_zero_nat) B_59)->(((ord_less_eq_nat zero_zero_nat) C_39)->((ord_less_eq_nat ((times_times_nat A_77) C_39)) ((times_times_nat B_59) D_17))))))).
% 2.30/2.54 Axiom fact_484_mult__mono:(forall (C_39:int) (D_17:int) (A_77:int) (B_59:int), (((ord_less_eq_int A_77) B_59)->(((ord_less_eq_int C_39) D_17)->(((ord_less_eq_int zero_zero_int) B_59)->(((ord_less_eq_int zero_zero_int) C_39)->((ord_less_eq_int ((times_times_int A_77) C_39)) ((times_times_int B_59) D_17))))))).
% 2.30/2.54 Axiom fact_485_mult__mono_H:(forall (C_38:real) (D_16:real) (A_76:real) (B_58:real), (((ord_less_eq_real A_76) B_58)->(((ord_less_eq_real C_38) D_16)->(((ord_less_eq_real zero_zero_real) A_76)->(((ord_less_eq_real zero_zero_real) C_38)->((ord_less_eq_real ((times_times_real A_76) C_38)) ((times_times_real B_58) D_16))))))).
% 2.30/2.54 Axiom fact_486_mult__mono_H:(forall (C_38:nat) (D_16:nat) (A_76:nat) (B_58:nat), (((ord_less_eq_nat A_76) B_58)->(((ord_less_eq_nat C_38) D_16)->(((ord_less_eq_nat zero_zero_nat) A_76)->(((ord_less_eq_nat zero_zero_nat) C_38)->((ord_less_eq_nat ((times_times_nat A_76) C_38)) ((times_times_nat B_58) D_16))))))).
% 2.30/2.54 Axiom fact_487_mult__mono_H:(forall (C_38:int) (D_16:int) (A_76:int) (B_58:int), (((ord_less_eq_int A_76) B_58)->(((ord_less_eq_int C_38) D_16)->(((ord_less_eq_int zero_zero_int) A_76)->(((ord_less_eq_int zero_zero_int) C_38)->((ord_less_eq_int ((times_times_int A_76) C_38)) ((times_times_int B_58) D_16))))))).
% 2.30/2.54 Axiom fact_488_mult__left__mono__neg:(forall (C_37:real) (B_57:real) (A_75:real), (((ord_less_eq_real B_57) A_75)->(((ord_less_eq_real C_37) zero_zero_real)->((ord_less_eq_real ((times_times_real C_37) A_75)) ((times_times_real C_37) B_57))))).
% 2.30/2.54 Axiom fact_489_mult__left__mono__neg:(forall (C_37:int) (B_57:int) (A_75:int), (((ord_less_eq_int B_57) A_75)->(((ord_less_eq_int C_37) zero_zero_int)->((ord_less_eq_int ((times_times_int C_37) A_75)) ((times_times_int C_37) B_57))))).
% 2.30/2.54 Axiom fact_490_mult__right__mono__neg:(forall (C_36:real) (B_56:real) (A_74:real), (((ord_less_eq_real B_56) A_74)->(((ord_less_eq_real C_36) zero_zero_real)->((ord_less_eq_real ((times_times_real A_74) C_36)) ((times_times_real B_56) C_36))))).
% 2.30/2.54 Axiom fact_491_mult__right__mono__neg:(forall (C_36:int) (B_56:int) (A_74:int), (((ord_less_eq_int B_56) A_74)->(((ord_less_eq_int C_36) zero_zero_int)->((ord_less_eq_int ((times_times_int A_74) C_36)) ((times_times_int B_56) C_36))))).
% 2.30/2.54 Axiom fact_492_comm__mult__left__mono:(forall (C_35:real) (A_73:real) (B_55:real), (((ord_less_eq_real A_73) B_55)->(((ord_less_eq_real zero_zero_real) C_35)->((ord_less_eq_real ((times_times_real C_35) A_73)) ((times_times_real C_35) B_55))))).
% 2.30/2.54 Axiom fact_493_comm__mult__left__mono:(forall (C_35:nat) (A_73:nat) (B_55:nat), (((ord_less_eq_nat A_73) B_55)->(((ord_less_eq_nat zero_zero_nat) C_35)->((ord_less_eq_nat ((times_times_nat C_35) A_73)) ((times_times_nat C_35) B_55))))).
% 2.30/2.54 Axiom fact_494_comm__mult__left__mono:(forall (C_35:int) (A_73:int) (B_55:int), (((ord_less_eq_int A_73) B_55)->(((ord_less_eq_int zero_zero_int) C_35)->((ord_less_eq_int ((times_times_int C_35) A_73)) ((times_times_int C_35) B_55))))).
% 2.30/2.54 Axiom fact_495_mult__left__mono:(forall (C_34:real) (A_72:real) (B_54:real), (((ord_less_eq_real A_72) B_54)->(((ord_less_eq_real zero_zero_real) C_34)->((ord_less_eq_real ((times_times_real C_34) A_72)) ((times_times_real C_34) B_54))))).
% 2.30/2.54 Axiom fact_496_mult__left__mono:(forall (C_34:nat) (A_72:nat) (B_54:nat), (((ord_less_eq_nat A_72) B_54)->(((ord_less_eq_nat zero_zero_nat) C_34)->((ord_less_eq_nat ((times_times_nat C_34) A_72)) ((times_times_nat C_34) B_54))))).
% 2.30/2.54 Axiom fact_497_mult__left__mono:(forall (C_34:int) (A_72:int) (B_54:int), (((ord_less_eq_int A_72) B_54)->(((ord_less_eq_int zero_zero_int) C_34)->((ord_less_eq_int ((times_times_int C_34) A_72)) ((times_times_int C_34) B_54))))).
% 2.30/2.54 Axiom fact_498_mult__right__mono:(forall (C_33:real) (A_71:real) (B_53:real), (((ord_less_eq_real A_71) B_53)->(((ord_less_eq_real zero_zero_real) C_33)->((ord_less_eq_real ((times_times_real A_71) C_33)) ((times_times_real B_53) C_33))))).
% 2.30/2.54 Axiom fact_499_mult__right__mono:(forall (C_33:nat) (A_71:nat) (B_53:nat), (((ord_less_eq_nat A_71) B_53)->(((ord_less_eq_nat zero_zero_nat) C_33)->((ord_less_eq_nat ((times_times_nat A_71) C_33)) ((times_times_nat B_53) C_33))))).
% 2.30/2.54 Axiom fact_500_mult__right__mono:(forall (C_33:int) (A_71:int) (B_53:int), (((ord_less_eq_int A_71) B_53)->(((ord_less_eq_int zero_zero_int) C_33)->((ord_less_eq_int ((times_times_int A_71) C_33)) ((times_times_int B_53) C_33))))).
% 2.30/2.54 Axiom fact_501_mult__nonpos__nonpos:(forall (B_52:real) (A_70:real), (((ord_less_eq_real A_70) zero_zero_real)->(((ord_less_eq_real B_52) zero_zero_real)->((ord_less_eq_real zero_zero_real) ((times_times_real A_70) B_52))))).
% 2.30/2.54 Axiom fact_502_mult__nonpos__nonpos:(forall (B_52:int) (A_70:int), (((ord_less_eq_int A_70) zero_zero_int)->(((ord_less_eq_int B_52) zero_zero_int)->((ord_less_eq_int zero_zero_int) ((times_times_int A_70) B_52))))).
% 2.30/2.54 Axiom fact_503_mult__nonpos__nonneg:(forall (B_51:real) (A_69:real), (((ord_less_eq_real A_69) zero_zero_real)->(((ord_less_eq_real zero_zero_real) B_51)->((ord_less_eq_real ((times_times_real A_69) B_51)) zero_zero_real)))).
% 2.30/2.54 Axiom fact_504_mult__nonpos__nonneg:(forall (B_51:nat) (A_69:nat), (((ord_less_eq_nat A_69) zero_zero_nat)->(((ord_less_eq_nat zero_zero_nat) B_51)->((ord_less_eq_nat ((times_times_nat A_69) B_51)) zero_zero_nat)))).
% 2.30/2.54 Axiom fact_505_mult__nonpos__nonneg:(forall (B_51:int) (A_69:int), (((ord_less_eq_int A_69) zero_zero_int)->(((ord_less_eq_int zero_zero_int) B_51)->((ord_less_eq_int ((times_times_int A_69) B_51)) zero_zero_int)))).
% 2.30/2.54 Axiom fact_506_mult__nonneg__nonpos2:(forall (B_50:real) (A_68:real), (((ord_less_eq_real zero_zero_real) A_68)->(((ord_less_eq_real B_50) zero_zero_real)->((ord_less_eq_real ((times_times_real B_50) A_68)) zero_zero_real)))).
% 2.30/2.54 Axiom fact_507_mult__nonneg__nonpos2:(forall (B_50:nat) (A_68:nat), (((ord_less_eq_nat zero_zero_nat) A_68)->(((ord_less_eq_nat B_50) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat B_50) A_68)) zero_zero_nat)))).
% 2.30/2.54 Axiom fact_508_mult__nonneg__nonpos2:(forall (B_50:int) (A_68:int), (((ord_less_eq_int zero_zero_int) A_68)->(((ord_less_eq_int B_50) zero_zero_int)->((ord_less_eq_int ((times_times_int B_50) A_68)) zero_zero_int)))).
% 2.30/2.54 Axiom fact_509_mult__nonneg__nonpos:(forall (B_49:real) (A_67:real), (((ord_less_eq_real zero_zero_real) A_67)->(((ord_less_eq_real B_49) zero_zero_real)->((ord_less_eq_real ((times_times_real A_67) B_49)) zero_zero_real)))).
% 2.30/2.54 Axiom fact_510_mult__nonneg__nonpos:(forall (B_49:nat) (A_67:nat), (((ord_less_eq_nat zero_zero_nat) A_67)->(((ord_less_eq_nat B_49) zero_zero_nat)->((ord_less_eq_nat ((times_times_nat A_67) B_49)) zero_zero_nat)))).
% 2.30/2.54 Axiom fact_511_mult__nonneg__nonpos:(forall (B_49:int) (A_67:int), (((ord_less_eq_int zero_zero_int) A_67)->(((ord_less_eq_int B_49) zero_zero_int)->((ord_less_eq_int ((times_times_int A_67) B_49)) zero_zero_int)))).
% 2.30/2.54 Axiom fact_512_transfer__nat__int__relations_I1_J:(forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((iff (((eq nat) (nat_1 X)) (nat_1 Y))) (((eq int) X) Y))))).
% 2.30/2.54 Axiom fact_513_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J:(forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((times_times_int X) Y))))).
% 2.30/2.54 Axiom fact_514_mult__nonneg__nonneg:(forall (B_48:real) (A_66:real), (((ord_less_eq_real zero_zero_real) A_66)->(((ord_less_eq_real zero_zero_real) B_48)->((ord_less_eq_real zero_zero_real) ((times_times_real A_66) B_48))))).
% 2.30/2.54 Axiom fact_515_mult__nonneg__nonneg:(forall (B_48:nat) (A_66:nat), (((ord_less_eq_nat zero_zero_nat) A_66)->(((ord_less_eq_nat zero_zero_nat) B_48)->((ord_less_eq_nat zero_zero_nat) ((times_times_nat A_66) B_48))))).
% 2.30/2.54 Axiom fact_516_mult__nonneg__nonneg:(forall (B_48:int) (A_66:int), (((ord_less_eq_int zero_zero_int) A_66)->(((ord_less_eq_int zero_zero_int) B_48)->((ord_less_eq_int zero_zero_int) ((times_times_int A_66) B_48))))).
% 2.30/2.54 Axiom fact_517_le__add__iff1:(forall (A_65:real) (E_6:real) (C_32:real) (B_47:real) (D_15:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real A_65) E_6)) C_32)) ((plus_plus_real ((times_times_real B_47) E_6)) D_15))) ((ord_less_eq_real ((plus_plus_real ((times_times_real ((minus_minus_real A_65) B_47)) E_6)) C_32)) D_15))).
% 2.30/2.54 Axiom fact_518_le__add__iff1:(forall (A_65:int) (E_6:int) (C_32:int) (B_47:int) (D_15:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int A_65) E_6)) C_32)) ((plus_plus_int ((times_times_int B_47) E_6)) D_15))) ((ord_less_eq_int ((plus_plus_int ((times_times_int ((minus_minus_int A_65) B_47)) E_6)) C_32)) D_15))).
% 2.30/2.54 Axiom fact_519_eq__add__iff1:(forall (A_64:real) (E_5:real) (C_31:real) (B_46:real) (D_14:real), ((iff (((eq real) ((plus_plus_real ((times_times_real A_64) E_5)) C_31)) ((plus_plus_real ((times_times_real B_46) E_5)) D_14))) (((eq real) ((plus_plus_real ((times_times_real ((minus_minus_real A_64) B_46)) E_5)) C_31)) D_14))).
% 2.30/2.54 Axiom fact_520_eq__add__iff1:(forall (A_64:int) (E_5:int) (C_31:int) (B_46:int) (D_14:int), ((iff (((eq int) ((plus_plus_int ((times_times_int A_64) E_5)) C_31)) ((plus_plus_int ((times_times_int B_46) E_5)) D_14))) (((eq int) ((plus_plus_int ((times_times_int ((minus_minus_int A_64) B_46)) E_5)) C_31)) D_14))).
% 2.30/2.54 Axiom fact_521_le__add__iff2:(forall (A_63:real) (E_4:real) (C_30:real) (B_45:real) (D_13:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real A_63) E_4)) C_30)) ((plus_plus_real ((times_times_real B_45) E_4)) D_13))) ((ord_less_eq_real C_30) ((plus_plus_real ((times_times_real ((minus_minus_real B_45) A_63)) E_4)) D_13)))).
% 2.30/2.54 Axiom fact_522_le__add__iff2:(forall (A_63:int) (E_4:int) (C_30:int) (B_45:int) (D_13:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int A_63) E_4)) C_30)) ((plus_plus_int ((times_times_int B_45) E_4)) D_13))) ((ord_less_eq_int C_30) ((plus_plus_int ((times_times_int ((minus_minus_int B_45) A_63)) E_4)) D_13)))).
% 2.30/2.54 Axiom fact_523_eq__add__iff2:(forall (A_62:real) (E_3:real) (C_29:real) (B_44:real) (D_12:real), ((iff (((eq real) ((plus_plus_real ((times_times_real A_62) E_3)) C_29)) ((plus_plus_real ((times_times_real B_44) E_3)) D_12))) (((eq real) C_29) ((plus_plus_real ((times_times_real ((minus_minus_real B_44) A_62)) E_3)) D_12)))).
% 2.30/2.54 Axiom fact_524_eq__add__iff2:(forall (A_62:int) (E_3:int) (C_29:int) (B_44:int) (D_12:int), ((iff (((eq int) ((plus_plus_int ((times_times_int A_62) E_3)) C_29)) ((plus_plus_int ((times_times_int B_44) E_3)) D_12))) (((eq int) C_29) ((plus_plus_int ((times_times_int ((minus_minus_int B_44) A_62)) E_3)) D_12)))).
% 2.30/2.54 Axiom fact_525_mult__diff__mult:(forall (X_16:real) (Y_14:real) (A_61:real) (B_43:real), (((eq real) ((minus_minus_real ((times_times_real X_16) Y_14)) ((times_times_real A_61) B_43))) ((plus_plus_real ((times_times_real X_16) ((minus_minus_real Y_14) B_43))) ((times_times_real ((minus_minus_real X_16) A_61)) B_43)))).
% 2.30/2.54 Axiom fact_526_mult__diff__mult:(forall (X_16:int) (Y_14:int) (A_61:int) (B_43:int), (((eq int) ((minus_minus_int ((times_times_int X_16) Y_14)) ((times_times_int A_61) B_43))) ((plus_plus_int ((times_times_int X_16) ((minus_minus_int Y_14) B_43))) ((times_times_int ((minus_minus_int X_16) A_61)) B_43)))).
% 2.30/2.54 Axiom fact_527_mult__le__0__iff:(forall (A_60:real) (B_42:real), ((iff ((ord_less_eq_real ((times_times_real A_60) B_42)) zero_zero_real)) ((or ((and ((ord_less_eq_real zero_zero_real) A_60)) ((ord_less_eq_real B_42) zero_zero_real))) ((and ((ord_less_eq_real A_60) zero_zero_real)) ((ord_less_eq_real zero_zero_real) B_42))))).
% 2.30/2.54 Axiom fact_528_mult__le__0__iff:(forall (A_60:int) (B_42:int), ((iff ((ord_less_eq_int ((times_times_int A_60) B_42)) zero_zero_int)) ((or ((and ((ord_less_eq_int zero_zero_int) A_60)) ((ord_less_eq_int B_42) zero_zero_int))) ((and ((ord_less_eq_int A_60) zero_zero_int)) ((ord_less_eq_int zero_zero_int) B_42))))).
% 2.30/2.54 Axiom fact_529_zero__le__mult__iff:(forall (A_59:real) (B_41:real), ((iff ((ord_less_eq_real zero_zero_real) ((times_times_real A_59) B_41))) ((or ((and ((ord_less_eq_real zero_zero_real) A_59)) ((ord_less_eq_real zero_zero_real) B_41))) ((and ((ord_less_eq_real A_59) zero_zero_real)) ((ord_less_eq_real B_41) zero_zero_real))))).
% 2.30/2.54 Axiom fact_530_zero__le__mult__iff:(forall (A_59:int) (B_41:int), ((iff ((ord_less_eq_int zero_zero_int) ((times_times_int A_59) B_41))) ((or ((and ((ord_less_eq_int zero_zero_int) A_59)) ((ord_less_eq_int zero_zero_int) B_41))) ((and ((ord_less_eq_int A_59) zero_zero_int)) ((ord_less_eq_int B_41) zero_zero_int))))).
% 2.30/2.54 Axiom fact_531_all__nat:(forall (P:(nat->Prop)), ((iff (all P)) (forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(P (nat_1 X_1)))))).
% 2.30/2.54 Axiom fact_532_ex__nat:(forall (P:(nat->Prop)), ((iff (_TPTP_ex P)) ((ex int) (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P (nat_1 X_1))))))).
% 2.30/2.54 Axiom fact_533_zero__le__square:(forall (A_58:real), ((ord_less_eq_real zero_zero_real) ((times_times_real A_58) A_58))).
% 2.30/2.54 Axiom fact_534_zero__le__square:(forall (A_58:int), ((ord_less_eq_int zero_zero_int) ((times_times_int A_58) A_58))).
% 2.30/2.54 Axiom fact_535_less__add__iff1:(forall (A_57:real) (E_2:real) (C_28:real) (B_40:real) (D_11:real), ((iff ((ord_less_real ((plus_plus_real ((times_times_real A_57) E_2)) C_28)) ((plus_plus_real ((times_times_real B_40) E_2)) D_11))) ((ord_less_real ((plus_plus_real ((times_times_real ((minus_minus_real A_57) B_40)) E_2)) C_28)) D_11))).
% 2.30/2.54 Axiom fact_536_less__add__iff1:(forall (A_57:int) (E_2:int) (C_28:int) (B_40:int) (D_11:int), ((iff ((ord_less_int ((plus_plus_int ((times_times_int A_57) E_2)) C_28)) ((plus_plus_int ((times_times_int B_40) E_2)) D_11))) ((ord_less_int ((plus_plus_int ((times_times_int ((minus_minus_int A_57) B_40)) E_2)) C_28)) D_11))).
% 2.30/2.54 Axiom fact_537_less__add__iff2:(forall (A_56:real) (E_1:real) (C_27:real) (B_39:real) (D_10:real), ((iff ((ord_less_real ((plus_plus_real ((times_times_real A_56) E_1)) C_27)) ((plus_plus_real ((times_times_real B_39) E_1)) D_10))) ((ord_less_real C_27) ((plus_plus_real ((times_times_real ((minus_minus_real B_39) A_56)) E_1)) D_10)))).
% 2.30/2.54 Axiom fact_538_less__add__iff2:(forall (A_56:int) (E_1:int) (C_27:int) (B_39:int) (D_10:int), ((iff ((ord_less_int ((plus_plus_int ((times_times_int A_56) E_1)) C_27)) ((plus_plus_int ((times_times_int B_39) E_1)) D_10))) ((ord_less_int C_27) ((plus_plus_int ((times_times_int ((minus_minus_int B_39) A_56)) E_1)) D_10)))).
% 2.30/2.54 Axiom fact_539_real__squared__diff__one__factored:(forall (X_15:real), (((eq real) ((minus_minus_real ((times_times_real X_15) X_15)) one_one_real)) ((times_times_real ((plus_plus_real X_15) one_one_real)) ((minus_minus_real X_15) one_one_real)))).
% 2.30/2.54 Axiom fact_540_real__squared__diff__one__factored:(forall (X_15:int), (((eq int) ((minus_minus_int ((times_times_int X_15) X_15)) one_one_int)) ((times_times_int ((plus_plus_int X_15) one_one_int)) ((minus_minus_int X_15) one_one_int)))).
% 2.30/2.54 Axiom fact_541_mult__left__le__imp__le:(forall (C_26:real) (A_55:real) (B_38:real), (((ord_less_eq_real ((times_times_real C_26) A_55)) ((times_times_real C_26) B_38))->(((ord_less_real zero_zero_real) C_26)->((ord_less_eq_real A_55) B_38)))).
% 2.30/2.54 Axiom fact_542_mult__left__le__imp__le:(forall (C_26:nat) (A_55:nat) (B_38:nat), (((ord_less_eq_nat ((times_times_nat C_26) A_55)) ((times_times_nat C_26) B_38))->(((ord_less_nat zero_zero_nat) C_26)->((ord_less_eq_nat A_55) B_38)))).
% 2.30/2.54 Axiom fact_543_mult__left__le__imp__le:(forall (C_26:int) (A_55:int) (B_38:int), (((ord_less_eq_int ((times_times_int C_26) A_55)) ((times_times_int C_26) B_38))->(((ord_less_int zero_zero_int) C_26)->((ord_less_eq_int A_55) B_38)))).
% 2.30/2.54 Axiom fact_544_mult__right__le__imp__le:(forall (A_54:real) (C_25:real) (B_37:real), (((ord_less_eq_real ((times_times_real A_54) C_25)) ((times_times_real B_37) C_25))->(((ord_less_real zero_zero_real) C_25)->((ord_less_eq_real A_54) B_37)))).
% 2.30/2.54 Axiom fact_545_mult__right__le__imp__le:(forall (A_54:nat) (C_25:nat) (B_37:nat), (((ord_less_eq_nat ((times_times_nat A_54) C_25)) ((times_times_nat B_37) C_25))->(((ord_less_nat zero_zero_nat) C_25)->((ord_less_eq_nat A_54) B_37)))).
% 2.30/2.54 Axiom fact_546_mult__right__le__imp__le:(forall (A_54:int) (C_25:int) (B_37:int), (((ord_less_eq_int ((times_times_int A_54) C_25)) ((times_times_int B_37) C_25))->(((ord_less_int zero_zero_int) C_25)->((ord_less_eq_int A_54) B_37)))).
% 2.30/2.54 Axiom fact_547_mult__less__imp__less__left:(forall (C_24:real) (A_53:real) (B_36:real), (((ord_less_real ((times_times_real C_24) A_53)) ((times_times_real C_24) B_36))->(((ord_less_eq_real zero_zero_real) C_24)->((ord_less_real A_53) B_36)))).
% 2.30/2.54 Axiom fact_548_mult__less__imp__less__left:(forall (C_24:nat) (A_53:nat) (B_36:nat), (((ord_less_nat ((times_times_nat C_24) A_53)) ((times_times_nat C_24) B_36))->(((ord_less_eq_nat zero_zero_nat) C_24)->((ord_less_nat A_53) B_36)))).
% 2.30/2.54 Axiom fact_549_mult__less__imp__less__left:(forall (C_24:int) (A_53:int) (B_36:int), (((ord_less_int ((times_times_int C_24) A_53)) ((times_times_int C_24) B_36))->(((ord_less_eq_int zero_zero_int) C_24)->((ord_less_int A_53) B_36)))).
% 2.30/2.54 Axiom fact_550_mult__left__less__imp__less:(forall (C_23:real) (A_52:real) (B_35:real), (((ord_less_real ((times_times_real C_23) A_52)) ((times_times_real C_23) B_35))->(((ord_less_eq_real zero_zero_real) C_23)->((ord_less_real A_52) B_35)))).
% 2.30/2.54 Axiom fact_551_mult__left__less__imp__less:(forall (C_23:nat) (A_52:nat) (B_35:nat), (((ord_less_nat ((times_times_nat C_23) A_52)) ((times_times_nat C_23) B_35))->(((ord_less_eq_nat zero_zero_nat) C_23)->((ord_less_nat A_52) B_35)))).
% 2.30/2.54 Axiom fact_552_mult__left__less__imp__less:(forall (C_23:int) (A_52:int) (B_35:int), (((ord_less_int ((times_times_int C_23) A_52)) ((times_times_int C_23) B_35))->(((ord_less_eq_int zero_zero_int) C_23)->((ord_less_int A_52) B_35)))).
% 2.30/2.54 Axiom fact_553_mult__less__imp__less__right:(forall (A_51:real) (C_22:real) (B_34:real), (((ord_less_real ((times_times_real A_51) C_22)) ((times_times_real B_34) C_22))->(((ord_less_eq_real zero_zero_real) C_22)->((ord_less_real A_51) B_34)))).
% 2.30/2.54 Axiom fact_554_mult__less__imp__less__right:(forall (A_51:nat) (C_22:nat) (B_34:nat), (((ord_less_nat ((times_times_nat A_51) C_22)) ((times_times_nat B_34) C_22))->(((ord_less_eq_nat zero_zero_nat) C_22)->((ord_less_nat A_51) B_34)))).
% 2.30/2.54 Axiom fact_555_mult__less__imp__less__right:(forall (A_51:int) (C_22:int) (B_34:int), (((ord_less_int ((times_times_int A_51) C_22)) ((times_times_int B_34) C_22))->(((ord_less_eq_int zero_zero_int) C_22)->((ord_less_int A_51) B_34)))).
% 2.30/2.54 Axiom fact_556_mult__right__less__imp__less:(forall (A_50:real) (C_21:real) (B_33:real), (((ord_less_real ((times_times_real A_50) C_21)) ((times_times_real B_33) C_21))->(((ord_less_eq_real zero_zero_real) C_21)->((ord_less_real A_50) B_33)))).
% 2.30/2.54 Axiom fact_557_mult__right__less__imp__less:(forall (A_50:nat) (C_21:nat) (B_33:nat), (((ord_less_nat ((times_times_nat A_50) C_21)) ((times_times_nat B_33) C_21))->(((ord_less_eq_nat zero_zero_nat) C_21)->((ord_less_nat A_50) B_33)))).
% 2.30/2.54 Axiom fact_558_mult__right__less__imp__less:(forall (A_50:int) (C_21:int) (B_33:int), (((ord_less_int ((times_times_int A_50) C_21)) ((times_times_int B_33) C_21))->(((ord_less_eq_int zero_zero_int) C_21)->((ord_less_int A_50) B_33)))).
% 2.30/2.54 Axiom fact_559_mult__le__less__imp__less:(forall (C_20:real) (D_9:real) (A_49:real) (B_32:real), (((ord_less_eq_real A_49) B_32)->(((ord_less_real C_20) D_9)->(((ord_less_real zero_zero_real) A_49)->(((ord_less_eq_real zero_zero_real) C_20)->((ord_less_real ((times_times_real A_49) C_20)) ((times_times_real B_32) D_9))))))).
% 2.30/2.54 Axiom fact_560_mult__le__less__imp__less:(forall (C_20:nat) (D_9:nat) (A_49:nat) (B_32:nat), (((ord_less_eq_nat A_49) B_32)->(((ord_less_nat C_20) D_9)->(((ord_less_nat zero_zero_nat) A_49)->(((ord_less_eq_nat zero_zero_nat) C_20)->((ord_less_nat ((times_times_nat A_49) C_20)) ((times_times_nat B_32) D_9))))))).
% 2.30/2.54 Axiom fact_561_mult__le__less__imp__less:(forall (C_20:int) (D_9:int) (A_49:int) (B_32:int), (((ord_less_eq_int A_49) B_32)->(((ord_less_int C_20) D_9)->(((ord_less_int zero_zero_int) A_49)->(((ord_less_eq_int zero_zero_int) C_20)->((ord_less_int ((times_times_int A_49) C_20)) ((times_times_int B_32) D_9))))))).
% 2.30/2.55 Axiom fact_562_mult__less__le__imp__less:(forall (C_19:real) (D_8:real) (A_48:real) (B_31:real), (((ord_less_real A_48) B_31)->(((ord_less_eq_real C_19) D_8)->(((ord_less_eq_real zero_zero_real) A_48)->(((ord_less_real zero_zero_real) C_19)->((ord_less_real ((times_times_real A_48) C_19)) ((times_times_real B_31) D_8))))))).
% 2.30/2.55 Axiom fact_563_mult__less__le__imp__less:(forall (C_19:nat) (D_8:nat) (A_48:nat) (B_31:nat), (((ord_less_nat A_48) B_31)->(((ord_less_eq_nat C_19) D_8)->(((ord_less_eq_nat zero_zero_nat) A_48)->(((ord_less_nat zero_zero_nat) C_19)->((ord_less_nat ((times_times_nat A_48) C_19)) ((times_times_nat B_31) D_8))))))).
% 2.30/2.55 Axiom fact_564_mult__less__le__imp__less:(forall (C_19:int) (D_8:int) (A_48:int) (B_31:int), (((ord_less_int A_48) B_31)->(((ord_less_eq_int C_19) D_8)->(((ord_less_eq_int zero_zero_int) A_48)->(((ord_less_int zero_zero_int) C_19)->((ord_less_int ((times_times_int A_48) C_19)) ((times_times_int B_31) D_8))))))).
% 2.30/2.55 Axiom fact_565_mult__strict__mono_H:(forall (C_18:real) (D_7:real) (A_47:real) (B_30:real), (((ord_less_real A_47) B_30)->(((ord_less_real C_18) D_7)->(((ord_less_eq_real zero_zero_real) A_47)->(((ord_less_eq_real zero_zero_real) C_18)->((ord_less_real ((times_times_real A_47) C_18)) ((times_times_real B_30) D_7))))))).
% 2.30/2.55 Axiom fact_566_mult__strict__mono_H:(forall (C_18:nat) (D_7:nat) (A_47:nat) (B_30:nat), (((ord_less_nat A_47) B_30)->(((ord_less_nat C_18) D_7)->(((ord_less_eq_nat zero_zero_nat) A_47)->(((ord_less_eq_nat zero_zero_nat) C_18)->((ord_less_nat ((times_times_nat A_47) C_18)) ((times_times_nat B_30) D_7))))))).
% 2.30/2.55 Axiom fact_567_mult__strict__mono_H:(forall (C_18:int) (D_7:int) (A_47:int) (B_30:int), (((ord_less_int A_47) B_30)->(((ord_less_int C_18) D_7)->(((ord_less_eq_int zero_zero_int) A_47)->(((ord_less_eq_int zero_zero_int) C_18)->((ord_less_int ((times_times_int A_47) C_18)) ((times_times_int B_30) D_7))))))).
% 2.30/2.55 Axiom fact_568_mult__strict__mono:(forall (C_17:real) (D_6:real) (A_46:real) (B_29:real), (((ord_less_real A_46) B_29)->(((ord_less_real C_17) D_6)->(((ord_less_real zero_zero_real) B_29)->(((ord_less_eq_real zero_zero_real) C_17)->((ord_less_real ((times_times_real A_46) C_17)) ((times_times_real B_29) D_6))))))).
% 2.30/2.55 Axiom fact_569_mult__strict__mono:(forall (C_17:nat) (D_6:nat) (A_46:nat) (B_29:nat), (((ord_less_nat A_46) B_29)->(((ord_less_nat C_17) D_6)->(((ord_less_nat zero_zero_nat) B_29)->(((ord_less_eq_nat zero_zero_nat) C_17)->((ord_less_nat ((times_times_nat A_46) C_17)) ((times_times_nat B_29) D_6))))))).
% 2.30/2.55 Axiom fact_570_mult__strict__mono:(forall (C_17:int) (D_6:int) (A_46:int) (B_29:int), (((ord_less_int A_46) B_29)->(((ord_less_int C_17) D_6)->(((ord_less_int zero_zero_int) B_29)->(((ord_less_eq_int zero_zero_int) C_17)->((ord_less_int ((times_times_int A_46) C_17)) ((times_times_int B_29) D_6))))))).
% 2.30/2.55 Axiom fact_571_mult__le__cancel__left__neg:(forall (A_45:real) (B_28:real) (C_16:real), (((ord_less_real C_16) zero_zero_real)->((iff ((ord_less_eq_real ((times_times_real C_16) A_45)) ((times_times_real C_16) B_28))) ((ord_less_eq_real B_28) A_45)))).
% 2.30/2.55 Axiom fact_572_mult__le__cancel__left__neg:(forall (A_45:int) (B_28:int) (C_16:int), (((ord_less_int C_16) zero_zero_int)->((iff ((ord_less_eq_int ((times_times_int C_16) A_45)) ((times_times_int C_16) B_28))) ((ord_less_eq_int B_28) A_45)))).
% 2.30/2.55 Axiom fact_573_mult__le__cancel__left__pos:(forall (A_44:real) (B_27:real) (C_15:real), (((ord_less_real zero_zero_real) C_15)->((iff ((ord_less_eq_real ((times_times_real C_15) A_44)) ((times_times_real C_15) B_27))) ((ord_less_eq_real A_44) B_27)))).
% 2.30/2.55 Axiom fact_574_mult__le__cancel__left__pos:(forall (A_44:int) (B_27:int) (C_15:int), (((ord_less_int zero_zero_int) C_15)->((iff ((ord_less_eq_int ((times_times_int C_15) A_44)) ((times_times_int C_15) B_27))) ((ord_less_eq_int A_44) B_27)))).
% 2.30/2.55 Axiom fact_575_sum__squares__ge__zero:(forall (X_14:real) (Y_13:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((times_times_real X_14) X_14)) ((times_times_real Y_13) Y_13)))).
% 2.30/2.55 Axiom fact_576_sum__squares__ge__zero:(forall (X_14:int) (Y_13:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int X_14) X_14)) ((times_times_int Y_13) Y_13)))).
% 2.30/2.55 Axiom fact_577_sum__squares__le__zero__iff:(forall (X_13:real) (Y_12:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real X_13) X_13)) ((times_times_real Y_12) Y_12))) zero_zero_real)) ((and (((eq real) X_13) zero_zero_real)) (((eq real) Y_12) zero_zero_real)))).
% 2.30/2.55 Axiom fact_578_sum__squares__le__zero__iff:(forall (X_13:int) (Y_12:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int X_13) X_13)) ((times_times_int Y_12) Y_12))) zero_zero_int)) ((and (((eq int) X_13) zero_zero_int)) (((eq int) Y_12) zero_zero_int)))).
% 2.30/2.55 Axiom fact_579_mult__right__le__one__le:(forall (Y_11:real) (X_12:real), (((ord_less_eq_real zero_zero_real) X_12)->(((ord_less_eq_real zero_zero_real) Y_11)->(((ord_less_eq_real Y_11) one_one_real)->((ord_less_eq_real ((times_times_real X_12) Y_11)) X_12))))).
% 2.30/2.55 Axiom fact_580_mult__right__le__one__le:(forall (Y_11:int) (X_12:int), (((ord_less_eq_int zero_zero_int) X_12)->(((ord_less_eq_int zero_zero_int) Y_11)->(((ord_less_eq_int Y_11) one_one_int)->((ord_less_eq_int ((times_times_int X_12) Y_11)) X_12))))).
% 2.30/2.55 Axiom fact_581_mult__left__le__one__le:(forall (Y_10:real) (X_11:real), (((ord_less_eq_real zero_zero_real) X_11)->(((ord_less_eq_real zero_zero_real) Y_10)->(((ord_less_eq_real Y_10) one_one_real)->((ord_less_eq_real ((times_times_real Y_10) X_11)) X_11))))).
% 2.30/2.55 Axiom fact_582_mult__left__le__one__le:(forall (Y_10:int) (X_11:int), (((ord_less_eq_int zero_zero_int) X_11)->(((ord_less_eq_int zero_zero_int) Y_10)->(((ord_less_eq_int Y_10) one_one_int)->((ord_less_eq_int ((times_times_int Y_10) X_11)) X_11))))).
% 2.30/2.55 Axiom fact_583_nat__le__0:(forall (Z:int), (((ord_less_eq_int Z) zero_zero_int)->(((eq nat) (nat_1 Z)) zero_zero_nat))).
% 2.30/2.55 Axiom fact_584_nat__0__iff:(forall (I_1:int), ((iff (((eq nat) (nat_1 I_1)) zero_zero_nat)) ((ord_less_eq_int I_1) zero_zero_int))).
% 2.30/2.55 Axiom fact_585_power__increasing:(forall (A_43:real) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_real one_one_real) A_43)->((ord_less_eq_real ((power_power_real A_43) N_9)) ((power_power_real A_43) N_8))))).
% 2.30/2.55 Axiom fact_586_power__increasing:(forall (A_43:nat) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_nat one_one_nat) A_43)->((ord_less_eq_nat ((power_power_nat A_43) N_9)) ((power_power_nat A_43) N_8))))).
% 2.30/2.55 Axiom fact_587_power__increasing:(forall (A_43:int) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_int one_one_int) A_43)->((ord_less_eq_int ((power_power_int A_43) N_9)) ((power_power_int A_43) N_8))))).
% 2.30/2.55 Axiom fact_588_int__nat__eq:(forall (Z:int), ((and (((ord_less_eq_int zero_zero_int) Z)->(((eq int) (semiri1621563631at_int (nat_1 Z))) Z))) ((((ord_less_eq_int zero_zero_int) Z)->False)->(((eq int) (semiri1621563631at_int (nat_1 Z))) zero_zero_int)))).
% 2.30/2.55 Axiom fact_589_int__eq__iff:(forall (M:nat) (Z:int), ((iff (((eq int) (semiri1621563631at_int M)) Z)) ((and (((eq nat) M) (nat_1 Z))) ((ord_less_eq_int zero_zero_int) Z)))).
% 2.30/2.55 Axiom fact_590_nat__0__le:(forall (Z:int), (((ord_less_eq_int zero_zero_int) Z)->(((eq int) (semiri1621563631at_int (nat_1 Z))) Z))).
% 2.30/2.55 Axiom fact_591_right__minus__eq:(forall (A_42:real) (B_26:real), ((iff (((eq real) ((minus_minus_real A_42) B_26)) zero_zero_real)) (((eq real) A_42) B_26))).
% 2.30/2.55 Axiom fact_592_right__minus__eq:(forall (A_42:int) (B_26:int), ((iff (((eq int) ((minus_minus_int A_42) B_26)) zero_zero_int)) (((eq int) A_42) B_26))).
% 2.30/2.55 Axiom fact_593_eq__iff__diff__eq__0:(forall (A_41:real) (B_25:real), ((iff (((eq real) A_41) B_25)) (((eq real) ((minus_minus_real A_41) B_25)) zero_zero_real))).
% 2.30/2.55 Axiom fact_594_eq__iff__diff__eq__0:(forall (A_41:int) (B_25:int), ((iff (((eq int) A_41) B_25)) (((eq int) ((minus_minus_int A_41) B_25)) zero_zero_int))).
% 2.30/2.55 Axiom fact_595_diff__self:(forall (A_40:real), (((eq real) ((minus_minus_real A_40) A_40)) zero_zero_real)).
% 2.30/2.55 Axiom fact_596_diff__self:(forall (A_40:int), (((eq int) ((minus_minus_int A_40) A_40)) zero_zero_int)).
% 2.30/2.55 Axiom fact_597_diff__0__right:(forall (A_39:real), (((eq real) ((minus_minus_real A_39) zero_zero_real)) A_39)).
% 2.30/2.55 Axiom fact_598_diff__0__right:(forall (A_39:int), (((eq int) ((minus_minus_int A_39) zero_zero_int)) A_39)).
% 2.30/2.55 Axiom fact_599_diff__eq__diff__less:(forall (A_38:int) (B_24:int) (C_14:int) (D_5:int), ((((eq int) ((minus_minus_int A_38) B_24)) ((minus_minus_int C_14) D_5))->((iff ((ord_less_int A_38) B_24)) ((ord_less_int C_14) D_5)))).
% 2.30/2.55 Axiom fact_600_diff__eq__diff__less:(forall (A_38:real) (B_24:real) (C_14:real) (D_5:real), ((((eq real) ((minus_minus_real A_38) B_24)) ((minus_minus_real C_14) D_5))->((iff ((ord_less_real A_38) B_24)) ((ord_less_real C_14) D_5)))).
% 2.30/2.55 Axiom fact_601_add__diff__add:(forall (A_37:real) (C_13:real) (B_23:real) (D_4:real), (((eq real) ((minus_minus_real ((plus_plus_real A_37) C_13)) ((plus_plus_real B_23) D_4))) ((plus_plus_real ((minus_minus_real A_37) B_23)) ((minus_minus_real C_13) D_4)))).
% 2.30/2.55 Axiom fact_602_add__diff__add:(forall (A_37:int) (C_13:int) (B_23:int) (D_4:int), (((eq int) ((minus_minus_int ((plus_plus_int A_37) C_13)) ((plus_plus_int B_23) D_4))) ((plus_plus_int ((minus_minus_int A_37) B_23)) ((minus_minus_int C_13) D_4)))).
% 2.30/2.55 Axiom fact_603_add__diff__cancel:(forall (A_36:real) (B_22:real), (((eq real) ((minus_minus_real ((plus_plus_real A_36) B_22)) B_22)) A_36)).
% 2.30/2.55 Axiom fact_604_add__diff__cancel:(forall (A_36:int) (B_22:int), (((eq int) ((minus_minus_int ((plus_plus_int A_36) B_22)) B_22)) A_36)).
% 2.30/2.55 Axiom fact_605_diff__add__cancel:(forall (A_35:real) (B_21:real), (((eq real) ((plus_plus_real ((minus_minus_real A_35) B_21)) B_21)) A_35)).
% 2.30/2.55 Axiom fact_606_diff__add__cancel:(forall (A_35:int) (B_21:int), (((eq int) ((plus_plus_int ((minus_minus_int A_35) B_21)) B_21)) A_35)).
% 2.30/2.55 Axiom fact_607_mult__zero__left:(forall (A_34:real), (((eq real) ((times_times_real zero_zero_real) A_34)) zero_zero_real)).
% 2.30/2.55 Axiom fact_608_mult__zero__left:(forall (A_34:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_34)) zero_zero_nat)).
% 2.30/2.55 Axiom fact_609_mult__zero__left:(forall (A_34:int), (((eq int) ((times_times_int zero_zero_int) A_34)) zero_zero_int)).
% 2.30/2.55 Axiom fact_610_mult__zero__right:(forall (A_33:real), (((eq real) ((times_times_real A_33) zero_zero_real)) zero_zero_real)).
% 2.30/2.55 Axiom fact_611_mult__zero__right:(forall (A_33:nat), (((eq nat) ((times_times_nat A_33) zero_zero_nat)) zero_zero_nat)).
% 2.30/2.55 Axiom fact_612_mult__zero__right:(forall (A_33:int), (((eq int) ((times_times_int A_33) zero_zero_int)) zero_zero_int)).
% 2.30/2.55 Axiom fact_613_mult__eq__0__iff:(forall (A_32:real) (B_20:real), ((iff (((eq real) ((times_times_real A_32) B_20)) zero_zero_real)) ((or (((eq real) A_32) zero_zero_real)) (((eq real) B_20) zero_zero_real)))).
% 2.30/2.55 Axiom fact_614_mult__eq__0__iff:(forall (A_32:int) (B_20:int), ((iff (((eq int) ((times_times_int A_32) B_20)) zero_zero_int)) ((or (((eq int) A_32) zero_zero_int)) (((eq int) B_20) zero_zero_int)))).
% 2.30/2.55 Axiom fact_615_no__zero__divisors:(forall (B_19:real) (A_31:real), ((not (((eq real) A_31) zero_zero_real))->((not (((eq real) B_19) zero_zero_real))->(not (((eq real) ((times_times_real A_31) B_19)) zero_zero_real))))).
% 2.30/2.55 Axiom fact_616_no__zero__divisors:(forall (B_19:nat) (A_31:nat), ((not (((eq nat) A_31) zero_zero_nat))->((not (((eq nat) B_19) zero_zero_nat))->(not (((eq nat) ((times_times_nat A_31) B_19)) zero_zero_nat))))).
% 2.30/2.55 Axiom fact_617_no__zero__divisors:(forall (B_19:int) (A_31:int), ((not (((eq int) A_31) zero_zero_int))->((not (((eq int) B_19) zero_zero_int))->(not (((eq int) ((times_times_int A_31) B_19)) zero_zero_int))))).
% 2.30/2.55 Axiom fact_618_divisors__zero:(forall (A_30:real) (B_18:real), ((((eq real) ((times_times_real A_30) B_18)) zero_zero_real)->((or (((eq real) A_30) zero_zero_real)) (((eq real) B_18) zero_zero_real)))).
% 2.30/2.55 Axiom fact_619_divisors__zero:(forall (A_30:nat) (B_18:nat), ((((eq nat) ((times_times_nat A_30) B_18)) zero_zero_nat)->((or (((eq nat) A_30) zero_zero_nat)) (((eq nat) B_18) zero_zero_nat)))).
% 2.30/2.55 Axiom fact_620_divisors__zero:(forall (A_30:int) (B_18:int), ((((eq int) ((times_times_int A_30) B_18)) zero_zero_int)->((or (((eq int) A_30) zero_zero_int)) (((eq int) B_18) zero_zero_int)))).
% 2.30/2.55 Axiom fact_621_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J:(forall (A_29:real), (((eq real) ((times_times_real A_29) zero_zero_real)) zero_zero_real)).
% 2.30/2.55 Axiom fact_622_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J:(forall (A_29:nat), (((eq nat) ((times_times_nat A_29) zero_zero_nat)) zero_zero_nat)).
% 2.30/2.55 Axiom fact_623_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J:(forall (A_29:int), (((eq int) ((times_times_int A_29) zero_zero_int)) zero_zero_int)).
% 2.30/2.55 Axiom fact_624_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J:(forall (A_28:real), (((eq real) ((times_times_real zero_zero_real) A_28)) zero_zero_real)).
% 2.30/2.55 Axiom fact_625_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J:(forall (A_28:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_28)) zero_zero_nat)).
% 2.30/2.55 Axiom fact_626_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J:(forall (A_28:int), (((eq int) ((times_times_int zero_zero_int) A_28)) zero_zero_int)).
% 2.30/2.55 Axiom fact_627_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)))).
% 2.30/2.55 Axiom fact_628_diff__self__eq__0:(forall (M:nat), (((eq nat) ((minus_minus_nat M) M)) zero_zero_nat)).
% 2.30/2.55 Axiom fact_629_minus__nat_Odiff__0:(forall (M:nat), (((eq nat) ((minus_minus_nat M) zero_zero_nat)) M)).
% 2.30/2.55 Axiom fact_630_diff__0__eq__0:(forall (N:nat), (((eq nat) ((minus_minus_nat zero_zero_nat) N)) zero_zero_nat)).
% 2.30/2.55 Axiom fact_631_comm__semiring__class_Odistrib:(forall (A_27:real) (B_17:real) (C_12:real), (((eq real) ((times_times_real ((plus_plus_real A_27) B_17)) C_12)) ((plus_plus_real ((times_times_real A_27) C_12)) ((times_times_real B_17) C_12)))).
% 2.30/2.55 Axiom fact_632_comm__semiring__class_Odistrib:(forall (A_27:nat) (B_17:nat) (C_12:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_27) B_17)) C_12)) ((plus_plus_nat ((times_times_nat A_27) C_12)) ((times_times_nat B_17) C_12)))).
% 2.30/2.55 Axiom fact_633_comm__semiring__class_Odistrib:(forall (A_27:int) (B_17:int) (C_12:int), (((eq int) ((times_times_int ((plus_plus_int A_27) B_17)) C_12)) ((plus_plus_int ((times_times_int A_27) C_12)) ((times_times_int B_17) C_12)))).
% 2.30/2.55 Axiom fact_634_combine__common__factor:(forall (A_26:real) (E:real) (B_16:real) (C_11:real), (((eq real) ((plus_plus_real ((times_times_real A_26) E)) ((plus_plus_real ((times_times_real B_16) E)) C_11))) ((plus_plus_real ((times_times_real ((plus_plus_real A_26) B_16)) E)) C_11))).
% 2.30/2.55 Axiom fact_635_combine__common__factor:(forall (A_26:nat) (E:nat) (B_16:nat) (C_11:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_26) E)) ((plus_plus_nat ((times_times_nat B_16) E)) C_11))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat A_26) B_16)) E)) C_11))).
% 2.30/2.55 Axiom fact_636_combine__common__factor:(forall (A_26:int) (E:int) (B_16:int) (C_11:int), (((eq int) ((plus_plus_int ((times_times_int A_26) E)) ((plus_plus_int ((times_times_int B_16) E)) C_11))) ((plus_plus_int ((times_times_int ((plus_plus_int A_26) B_16)) E)) C_11))).
% 2.30/2.55 Axiom fact_637_crossproduct__eq:(forall (W_3:real) (Y_9:real) (X_10:real) (Z_3:real), ((iff (((eq real) ((plus_plus_real ((times_times_real W_3) Y_9)) ((times_times_real X_10) Z_3))) ((plus_plus_real ((times_times_real W_3) Z_3)) ((times_times_real X_10) Y_9)))) ((or (((eq real) W_3) X_10)) (((eq real) Y_9) Z_3)))).
% 2.30/2.55 Axiom fact_638_crossproduct__eq:(forall (W_3:nat) (Y_9:nat) (X_10:nat) (Z_3:nat), ((iff (((eq nat) ((plus_plus_nat ((times_times_nat W_3) Y_9)) ((times_times_nat X_10) Z_3))) ((plus_plus_nat ((times_times_nat W_3) Z_3)) ((times_times_nat X_10) Y_9)))) ((or (((eq nat) W_3) X_10)) (((eq nat) Y_9) Z_3)))).
% 2.30/2.55 Axiom fact_639_crossproduct__eq:(forall (W_3:int) (Y_9:int) (X_10:int) (Z_3:int), ((iff (((eq int) ((plus_plus_int ((times_times_int W_3) Y_9)) ((times_times_int X_10) Z_3))) ((plus_plus_int ((times_times_int W_3) Z_3)) ((times_times_int X_10) Y_9)))) ((or (((eq int) W_3) X_10)) (((eq int) Y_9) Z_3)))).
% 2.30/2.55 Axiom fact_640_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J:(forall (A_25:real) (M_3:real) (B_15:real), (((eq real) ((plus_plus_real ((times_times_real A_25) M_3)) ((times_times_real B_15) M_3))) ((times_times_real ((plus_plus_real A_25) B_15)) M_3))).
% 2.30/2.55 Axiom fact_641_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J:(forall (A_25:nat) (M_3:nat) (B_15:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_25) M_3)) ((times_times_nat B_15) M_3))) ((times_times_nat ((plus_plus_nat A_25) B_15)) M_3))).
% 2.30/2.55 Axiom fact_642_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J:(forall (A_25:int) (M_3:int) (B_15:int), (((eq int) ((plus_plus_int ((times_times_int A_25) M_3)) ((times_times_int B_15) M_3))) ((times_times_int ((plus_plus_int A_25) B_15)) M_3))).
% 2.30/2.55 Axiom fact_643_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J:(forall (A_24:real) (B_14:real) (C_10:real), (((eq real) ((times_times_real ((plus_plus_real A_24) B_14)) C_10)) ((plus_plus_real ((times_times_real A_24) C_10)) ((times_times_real B_14) C_10)))).
% 2.30/2.55 Axiom fact_644_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J:(forall (A_24:nat) (B_14:nat) (C_10:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_24) B_14)) C_10)) ((plus_plus_nat ((times_times_nat A_24) C_10)) ((times_times_nat B_14) C_10)))).
% 2.30/2.55 Axiom fact_645_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J:(forall (A_24:int) (B_14:int) (C_10:int), (((eq int) ((times_times_int ((plus_plus_int A_24) B_14)) C_10)) ((plus_plus_int ((times_times_int A_24) C_10)) ((times_times_int B_14) C_10)))).
% 2.30/2.55 Axiom fact_646_crossproduct__noteq:(forall (C_9:real) (D_3:real) (A_23:real) (B_13:real), ((iff ((and (not (((eq real) A_23) B_13))) (not (((eq real) C_9) D_3)))) (not (((eq real) ((plus_plus_real ((times_times_real A_23) C_9)) ((times_times_real B_13) D_3))) ((plus_plus_real ((times_times_real A_23) D_3)) ((times_times_real B_13) C_9)))))).
% 2.30/2.55 Axiom fact_647_crossproduct__noteq:(forall (C_9:nat) (D_3:nat) (A_23:nat) (B_13:nat), ((iff ((and (not (((eq nat) A_23) B_13))) (not (((eq nat) C_9) D_3)))) (not (((eq nat) ((plus_plus_nat ((times_times_nat A_23) C_9)) ((times_times_nat B_13) D_3))) ((plus_plus_nat ((times_times_nat A_23) D_3)) ((times_times_nat B_13) C_9)))))).
% 2.30/2.55 Axiom fact_648_crossproduct__noteq:(forall (C_9:int) (D_3:int) (A_23:int) (B_13:int), ((iff ((and (not (((eq int) A_23) B_13))) (not (((eq int) C_9) D_3)))) (not (((eq int) ((plus_plus_int ((times_times_int A_23) C_9)) ((times_times_int B_13) D_3))) ((plus_plus_int ((times_times_int A_23) D_3)) ((times_times_int B_13) C_9)))))).
% 2.30/2.55 Axiom fact_649_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J:(forall (X_9:real) (Y_8:real) (Z_2:real), (((eq real) ((times_times_real X_9) ((plus_plus_real Y_8) Z_2))) ((plus_plus_real ((times_times_real X_9) Y_8)) ((times_times_real X_9) Z_2)))).
% 2.30/2.55 Axiom fact_650_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J:(forall (X_9:nat) (Y_8:nat) (Z_2:nat), (((eq nat) ((times_times_nat X_9) ((plus_plus_nat Y_8) Z_2))) ((plus_plus_nat ((times_times_nat X_9) Y_8)) ((times_times_nat X_9) Z_2)))).
% 2.30/2.55 Axiom fact_651_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J:(forall (X_9:int) (Y_8:int) (Z_2:int), (((eq int) ((times_times_int X_9) ((plus_plus_int Y_8) Z_2))) ((plus_plus_int ((times_times_int X_9) Y_8)) ((times_times_int X_9) Z_2)))).
% 2.30/2.55 Axiom fact_652_nat__int:(forall (N:nat), (((eq nat) (nat_1 (semiri1621563631at_int N))) N)).
% 2.30/2.55 Axiom fact_653_mult_Ocomm__neutral:(forall (A_22:real), (((eq real) ((times_times_real A_22) one_one_real)) A_22)).
% 2.30/2.55 Axiom fact_654_mult_Ocomm__neutral:(forall (A_22:nat), (((eq nat) ((times_times_nat A_22) one_one_nat)) A_22)).
% 2.30/2.55 Axiom fact_655_mult_Ocomm__neutral:(forall (A_22:int), (((eq int) ((times_times_int A_22) one_one_int)) A_22)).
% 2.30/2.55 Axiom fact_656_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J:(forall (A_21:real), (((eq real) ((times_times_real A_21) one_one_real)) A_21)).
% 2.30/2.55 Axiom fact_657_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J:(forall (A_21:nat), (((eq nat) ((times_times_nat A_21) one_one_nat)) A_21)).
% 2.30/2.56 Axiom fact_658_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J:(forall (A_21:int), (((eq int) ((times_times_int A_21) one_one_int)) A_21)).
% 2.30/2.56 Axiom fact_659_mult__1__right:(forall (A_20:real), (((eq real) ((times_times_real A_20) one_one_real)) A_20)).
% 2.30/2.56 Axiom fact_660_mult__1__right:(forall (A_20:nat), (((eq nat) ((times_times_nat A_20) one_one_nat)) A_20)).
% 2.30/2.56 Axiom fact_661_mult__1__right:(forall (A_20:int), (((eq int) ((times_times_int A_20) one_one_int)) A_20)).
% 2.30/2.56 Axiom fact_662_mult__1:(forall (A_19:real), (((eq real) ((times_times_real one_one_real) A_19)) A_19)).
% 2.30/2.56 Axiom fact_663_mult__1:(forall (A_19:nat), (((eq nat) ((times_times_nat one_one_nat) A_19)) A_19)).
% 2.30/2.56 Axiom fact_664_mult__1:(forall (A_19:int), (((eq int) ((times_times_int one_one_int) A_19)) A_19)).
% 2.30/2.56 Axiom fact_665_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J:(forall (A_18:real), (((eq real) ((times_times_real one_one_real) A_18)) A_18)).
% 2.30/2.56 Axiom fact_666_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J:(forall (A_18:nat), (((eq nat) ((times_times_nat one_one_nat) A_18)) A_18)).
% 2.30/2.56 Axiom fact_667_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J:(forall (A_18:int), (((eq int) ((times_times_int one_one_int) A_18)) A_18)).
% 2.30/2.56 Axiom fact_668_mult__1__left:(forall (A_17:real), (((eq real) ((times_times_real one_one_real) A_17)) A_17)).
% 2.30/2.56 Axiom fact_669_mult__1__left:(forall (A_17:nat), (((eq nat) ((times_times_nat one_one_nat) A_17)) A_17)).
% 2.30/2.56 Axiom fact_670_mult__1__left:(forall (A_17:int), (((eq int) ((times_times_int one_one_int) A_17)) A_17)).
% 2.30/2.56 Axiom fact_671_add__le__imp__le__left:(forall (C_8:real) (A_16:real) (B_12:real), (((ord_less_eq_real ((plus_plus_real C_8) A_16)) ((plus_plus_real C_8) B_12))->((ord_less_eq_real A_16) B_12))).
% 2.30/2.56 Axiom fact_672_add__le__imp__le__left:(forall (C_8:nat) (A_16:nat) (B_12:nat), (((ord_less_eq_nat ((plus_plus_nat C_8) A_16)) ((plus_plus_nat C_8) B_12))->((ord_less_eq_nat A_16) B_12))).
% 2.30/2.56 Axiom fact_673_add__le__imp__le__left:(forall (C_8:int) (A_16:int) (B_12:int), (((ord_less_eq_int ((plus_plus_int C_8) A_16)) ((plus_plus_int C_8) B_12))->((ord_less_eq_int A_16) B_12))).
% 2.30/2.56 Axiom fact_674_add__le__imp__le__right:(forall (A_15:real) (C_7:real) (B_11:real), (((ord_less_eq_real ((plus_plus_real A_15) C_7)) ((plus_plus_real B_11) C_7))->((ord_less_eq_real A_15) B_11))).
% 2.30/2.56 Axiom fact_675_add__le__imp__le__right:(forall (A_15:nat) (C_7:nat) (B_11:nat), (((ord_less_eq_nat ((plus_plus_nat A_15) C_7)) ((plus_plus_nat B_11) C_7))->((ord_less_eq_nat A_15) B_11))).
% 2.30/2.56 Axiom fact_676_add__le__imp__le__right:(forall (A_15:int) (C_7:int) (B_11:int), (((ord_less_eq_int ((plus_plus_int A_15) C_7)) ((plus_plus_int B_11) C_7))->((ord_less_eq_int A_15) B_11))).
% 2.30/2.56 Axiom fact_677_add__mono:(forall (C_6:real) (D_2:real) (A_14:real) (B_10:real), (((ord_less_eq_real A_14) B_10)->(((ord_less_eq_real C_6) D_2)->((ord_less_eq_real ((plus_plus_real A_14) C_6)) ((plus_plus_real B_10) D_2))))).
% 2.30/2.56 Axiom fact_678_add__mono:(forall (C_6:nat) (D_2:nat) (A_14:nat) (B_10:nat), (((ord_less_eq_nat A_14) B_10)->(((ord_less_eq_nat C_6) D_2)->((ord_less_eq_nat ((plus_plus_nat A_14) C_6)) ((plus_plus_nat B_10) D_2))))).
% 2.30/2.56 Axiom fact_679_add__mono:(forall (C_6:int) (D_2:int) (A_14:int) (B_10:int), (((ord_less_eq_int A_14) B_10)->(((ord_less_eq_int C_6) D_2)->((ord_less_eq_int ((plus_plus_int A_14) C_6)) ((plus_plus_int B_10) D_2))))).
% 2.30/2.56 Axiom fact_680_add__left__mono:(forall (C_5:real) (A_13:real) (B_9:real), (((ord_less_eq_real A_13) B_9)->((ord_less_eq_real ((plus_plus_real C_5) A_13)) ((plus_plus_real C_5) B_9)))).
% 2.30/2.56 Axiom fact_681_add__left__mono:(forall (C_5:nat) (A_13:nat) (B_9:nat), (((ord_less_eq_nat A_13) B_9)->((ord_less_eq_nat ((plus_plus_nat C_5) A_13)) ((plus_plus_nat C_5) B_9)))).
% 2.30/2.56 Axiom fact_682_add__left__mono:(forall (C_5:int) (A_13:int) (B_9:int), (((ord_less_eq_int A_13) B_9)->((ord_less_eq_int ((plus_plus_int C_5) A_13)) ((plus_plus_int C_5) B_9)))).
% 2.30/2.56 Axiom fact_683_add__right__mono:(forall (C_4:real) (A_12:real) (B_8:real), (((ord_less_eq_real A_12) B_8)->((ord_less_eq_real ((plus_plus_real A_12) C_4)) ((plus_plus_real B_8) C_4)))).
% 2.30/2.56 Axiom fact_684_add__right__mono:(forall (C_4:nat) (A_12:nat) (B_8:nat), (((ord_less_eq_nat A_12) B_8)->((ord_less_eq_nat ((plus_plus_nat A_12) C_4)) ((plus_plus_nat B_8) C_4)))).
% 2.30/2.56 Axiom fact_685_add__right__mono:(forall (C_4:int) (A_12:int) (B_8:int), (((ord_less_eq_int A_12) B_8)->((ord_less_eq_int ((plus_plus_int A_12) C_4)) ((plus_plus_int B_8) C_4)))).
% 2.30/2.56 Axiom fact_686_add__le__cancel__left:(forall (C_3:real) (A_11:real) (B_7:real), ((iff ((ord_less_eq_real ((plus_plus_real C_3) A_11)) ((plus_plus_real C_3) B_7))) ((ord_less_eq_real A_11) B_7))).
% 2.30/2.56 Axiom fact_687_add__le__cancel__left:(forall (C_3:nat) (A_11:nat) (B_7:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat C_3) A_11)) ((plus_plus_nat C_3) B_7))) ((ord_less_eq_nat A_11) B_7))).
% 2.30/2.56 Axiom fact_688_add__le__cancel__left:(forall (C_3:int) (A_11:int) (B_7:int), ((iff ((ord_less_eq_int ((plus_plus_int C_3) A_11)) ((plus_plus_int C_3) B_7))) ((ord_less_eq_int A_11) B_7))).
% 2.30/2.56 Axiom fact_689_add__le__cancel__right:(forall (A_10:real) (C_2:real) (B_6:real), ((iff ((ord_less_eq_real ((plus_plus_real A_10) C_2)) ((plus_plus_real B_6) C_2))) ((ord_less_eq_real A_10) B_6))).
% 2.30/2.56 Axiom fact_690_add__le__cancel__right:(forall (A_10:nat) (C_2:nat) (B_6:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat A_10) C_2)) ((plus_plus_nat B_6) C_2))) ((ord_less_eq_nat A_10) B_6))).
% 2.30/2.56 Axiom fact_691_add__le__cancel__right:(forall (A_10:int) (C_2:int) (B_6:int), ((iff ((ord_less_eq_int ((plus_plus_int A_10) C_2)) ((plus_plus_int B_6) C_2))) ((ord_less_eq_int A_10) B_6))).
% 2.30/2.56 Axiom fact_692_less__imp__diff__less:(forall (N:nat) (J:nat) (K:nat), (((ord_less_nat J) K)->((ord_less_nat ((minus_minus_nat J) N)) K))).
% 2.30/2.56 Axiom fact_693_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))))).
% 2.30/2.56 Axiom fact_694_power__commutes:(forall (A_9:real) (N_7:nat), (((eq real) ((times_times_real ((power_power_real A_9) N_7)) A_9)) ((times_times_real A_9) ((power_power_real A_9) N_7)))).
% 2.30/2.56 Axiom fact_695_power__commutes:(forall (A_9:nat) (N_7:nat), (((eq nat) ((times_times_nat ((power_power_nat A_9) N_7)) A_9)) ((times_times_nat A_9) ((power_power_nat A_9) N_7)))).
% 2.30/2.56 Axiom fact_696_power__commutes:(forall (A_9:int) (N_7:nat), (((eq int) ((times_times_int ((power_power_int A_9) N_7)) A_9)) ((times_times_int A_9) ((power_power_int A_9) N_7)))).
% 2.30/2.56 Axiom fact_697_power__mult__distrib:(forall (A_8:real) (B_5:real) (N_6:nat), (((eq real) ((power_power_real ((times_times_real A_8) B_5)) N_6)) ((times_times_real ((power_power_real A_8) N_6)) ((power_power_real B_5) N_6)))).
% 2.30/2.56 Axiom fact_698_power__mult__distrib:(forall (A_8:nat) (B_5:nat) (N_6:nat), (((eq nat) ((power_power_nat ((times_times_nat A_8) B_5)) N_6)) ((times_times_nat ((power_power_nat A_8) N_6)) ((power_power_nat B_5) N_6)))).
% 2.30/2.56 Axiom fact_699_power__mult__distrib:(forall (A_8:int) (B_5:int) (N_6:nat), (((eq int) ((power_power_int ((times_times_int A_8) B_5)) N_6)) ((times_times_int ((power_power_int A_8) N_6)) ((power_power_int B_5) N_6)))).
% 2.30/2.56 Axiom fact_700_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J:(forall (X_8:real) (Y_7:real) (Q_2:nat), (((eq real) ((power_power_real ((times_times_real X_8) Y_7)) Q_2)) ((times_times_real ((power_power_real X_8) Q_2)) ((power_power_real Y_7) Q_2)))).
% 2.30/2.56 Axiom fact_701_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J:(forall (X_8:nat) (Y_7:nat) (Q_2:nat), (((eq nat) ((power_power_nat ((times_times_nat X_8) Y_7)) Q_2)) ((times_times_nat ((power_power_nat X_8) Q_2)) ((power_power_nat Y_7) Q_2)))).
% 2.30/2.56 Axiom fact_702_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J:(forall (X_8:int) (Y_7:int) (Q_2:nat), (((eq int) ((power_power_int ((times_times_int X_8) Y_7)) Q_2)) ((times_times_int ((power_power_int X_8) Q_2)) ((power_power_int Y_7) Q_2)))).
% 2.30/2.56 Axiom fact_703_diff__add__inverse2:(forall (M:nat) (N:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat M) N)) N)) M)).
% 2.30/2.56 Axiom fact_704_diff__add__inverse:(forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat ((plus_plus_nat N) M)) N)) M)).
% 2.30/2.56 Axiom fact_705_diff__diff__left:(forall (I_1:nat) (J:nat) (K:nat), (((eq nat) ((minus_minus_nat ((minus_minus_nat I_1) J)) K)) ((minus_minus_nat I_1) ((plus_plus_nat J) K)))).
% 2.30/2.56 Axiom fact_706_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))).
% 2.30/2.56 Axiom fact_707_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))).
% 2.30/2.56 Axiom fact_708_mult__Pls:(forall (W:int), (((eq int) ((times_times_int pls) W)) pls)).
% 2.30/2.56 Axiom fact_709_mult__Bit0:(forall (K:int) (L:int), (((eq int) ((times_times_int (bit0 K)) L)) (bit0 ((times_times_int K) L)))).
% 2.30/2.56 Axiom fact_710_rel__simps_I34_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit1 L))) ((ord_less_eq_int K) L))).
% 2.30/2.56 Axiom fact_711_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))).
% 2.30/2.56 Axiom fact_712_rel__simps_I19_J:((ord_less_eq_int pls) pls).
% 2.30/2.56 Axiom fact_713_rel__simps_I31_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit0 L))) ((ord_less_eq_int K) L))).
% 2.30/2.56 Axiom fact_714_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))).
% 2.30/2.56 Axiom fact_715_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J:((ord_less_eq_int zero_zero_int) zero_zero_int).
% 2.30/2.56 Axiom fact_716_zmult__1:(forall (Z:int), (((eq int) ((times_times_int one_one_int) Z)) Z)).
% 2.30/2.56 Axiom fact_717_zmult__1__right:(forall (Z:int), (((eq int) ((times_times_int Z) one_one_int)) Z)).
% 2.30/2.56 Axiom fact_718_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))))).
% 2.30/2.56 Axiom fact_719_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)))).
% 2.30/2.56 Axiom fact_720_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)))).
% 2.30/2.56 Axiom fact_721_zadd__left__mono:(forall (K:int) (I_1:int) (J:int), (((ord_less_eq_int I_1) J)->((ord_less_eq_int ((plus_plus_int K) I_1)) ((plus_plus_int K) J)))).
% 2.30/2.56 Axiom fact_722_times__numeral__code_I5_J:(forall (V_1:int) (W:int), (((eq int) ((times_times_int (number_number_of_int V_1)) (number_number_of_int W))) (number_number_of_int ((times_times_int V_1) W)))).
% 2.30/2.56 Axiom fact_723_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))).
% 2.30/2.56 Axiom fact_724_convex__bound__le:(forall (V_4:real) (U_2:real) (Y_6:real) (X_7:real) (A_7:real), (((ord_less_eq_real X_7) A_7)->(((ord_less_eq_real Y_6) A_7)->(((ord_less_eq_real zero_zero_real) U_2)->(((ord_less_eq_real zero_zero_real) V_4)->((((eq real) ((plus_plus_real U_2) V_4)) one_one_real)->((ord_less_eq_real ((plus_plus_real ((times_times_real U_2) X_7)) ((times_times_real V_4) Y_6))) A_7))))))).
% 2.30/2.56 Axiom fact_725_convex__bound__le:(forall (V_4:int) (U_2:int) (Y_6:int) (X_7:int) (A_7:int), (((ord_less_eq_int X_7) A_7)->(((ord_less_eq_int Y_6) A_7)->(((ord_less_eq_int zero_zero_int) U_2)->(((ord_less_eq_int zero_zero_int) V_4)->((((eq int) ((plus_plus_int U_2) V_4)) one_one_int)->((ord_less_eq_int ((plus_plus_int ((times_times_int U_2) X_7)) ((times_times_int V_4) Y_6))) A_7))))))).
% 2.30/2.56 Axiom fact_726_transfer__nat__int__relations_I2_J:(forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((iff ((ord_less_nat (nat_1 X)) (nat_1 Y))) ((ord_less_int X) Y))))).
% 2.30/2.56 Axiom fact_727_nat__less__eq__zless:(forall (Z:int) (W:int), (((ord_less_eq_int zero_zero_int) W)->((iff ((ord_less_nat (nat_1 W)) (nat_1 Z))) ((ord_less_int W) Z)))).
% 2.30/2.56 Axiom fact_728_le__special_I1_J:(forall (Y_5:int), ((iff ((ord_less_eq_real zero_zero_real) (number267125858f_real Y_5))) ((ord_less_eq_int pls) Y_5))).
% 2.30/2.56 Axiom fact_729_le__special_I1_J:(forall (Y_5:int), ((iff ((ord_less_eq_int zero_zero_int) (number_number_of_int Y_5))) ((ord_less_eq_int pls) Y_5))).
% 2.30/2.56 Axiom fact_730_le__special_I3_J:(forall (X_6:int), ((iff ((ord_less_eq_real (number267125858f_real X_6)) zero_zero_real)) ((ord_less_eq_int X_6) pls))).
% 2.30/2.56 Axiom fact_731_le__special_I3_J:(forall (X_6:int), ((iff ((ord_less_eq_int (number_number_of_int X_6)) zero_zero_int)) ((ord_less_eq_int X_6) pls))).
% 2.30/2.56 Axiom fact_732_power__decreasing:(forall (A_6:real) (N_5:nat) (N_4:nat), (((ord_less_eq_nat N_5) N_4)->(((ord_less_eq_real zero_zero_real) A_6)->(((ord_less_eq_real A_6) one_one_real)->((ord_less_eq_real ((power_power_real A_6) N_4)) ((power_power_real A_6) N_5)))))).
% 2.30/2.56 Axiom fact_733_power__decreasing:(forall (A_6:nat) (N_5:nat) (N_4:nat), (((ord_less_eq_nat N_5) N_4)->(((ord_less_eq_nat zero_zero_nat) A_6)->(((ord_less_eq_nat A_6) one_one_nat)->((ord_less_eq_nat ((power_power_nat A_6) N_4)) ((power_power_nat A_6) N_5)))))).
% 2.30/2.56 Axiom fact_734_power__decreasing:(forall (A_6:int) (N_5:nat) (N_4:nat), (((ord_less_eq_nat N_5) N_4)->(((ord_less_eq_int zero_zero_int) A_6)->(((ord_less_eq_int A_6) one_one_int)->((ord_less_eq_int ((power_power_int A_6) N_4)) ((power_power_int A_6) N_5)))))).
% 2.30/2.56 Axiom fact_735_power__increasing__iff:(forall (X_5:nat) (Y_4:nat) (B_4:real), (((ord_less_real one_one_real) B_4)->((iff ((ord_less_eq_real ((power_power_real B_4) X_5)) ((power_power_real B_4) Y_4))) ((ord_less_eq_nat X_5) Y_4)))).
% 2.30/2.56 Axiom fact_736_power__increasing__iff:(forall (X_5:nat) (Y_4:nat) (B_4:nat), (((ord_less_nat one_one_nat) B_4)->((iff ((ord_less_eq_nat ((power_power_nat B_4) X_5)) ((power_power_nat B_4) Y_4))) ((ord_less_eq_nat X_5) Y_4)))).
% 2.30/2.56 Axiom fact_737_power__increasing__iff:(forall (X_5:nat) (Y_4:nat) (B_4:int), (((ord_less_int one_one_int) B_4)->((iff ((ord_less_eq_int ((power_power_int B_4) X_5)) ((power_power_int B_4) Y_4))) ((ord_less_eq_nat X_5) Y_4)))).
% 2.30/2.56 Axiom fact_738_power__le__imp__le__exp:(forall (M_2:nat) (N_3:nat) (A_5:real), (((ord_less_real one_one_real) A_5)->(((ord_less_eq_real ((power_power_real A_5) M_2)) ((power_power_real A_5) N_3))->((ord_less_eq_nat M_2) N_3)))).
% 2.30/2.56 Axiom fact_739_power__le__imp__le__exp:(forall (M_2:nat) (N_3:nat) (A_5:nat), (((ord_less_nat one_one_nat) A_5)->(((ord_less_eq_nat ((power_power_nat A_5) M_2)) ((power_power_nat A_5) N_3))->((ord_less_eq_nat M_2) N_3)))).
% 2.30/2.56 Axiom fact_740_power__le__imp__le__exp:(forall (M_2:nat) (N_3:nat) (A_5:int), (((ord_less_int one_one_int) A_5)->(((ord_less_eq_int ((power_power_int A_5) M_2)) ((power_power_int A_5) N_3))->((ord_less_eq_nat M_2) N_3)))).
% 2.30/2.56 Axiom fact_741_nat__eq__iff2:(forall (M:nat) (W:int), ((iff (((eq nat) M) (nat_1 W))) ((and (((ord_less_eq_int zero_zero_int) W)->(((eq int) W) (semiri1621563631at_int M)))) ((((ord_less_eq_int zero_zero_int) W)->False)->(((eq nat) M) zero_zero_nat))))).
% 2.30/2.56 Axiom fact_742_nat__eq__iff:(forall (W:int) (M:nat), ((iff (((eq nat) (nat_1 W)) M)) ((and (((ord_less_eq_int zero_zero_int) W)->(((eq int) W) (semiri1621563631at_int M)))) ((((ord_less_eq_int zero_zero_int) W)->False)->(((eq nat) M) zero_zero_nat))))).
% 2.30/2.56 Axiom fact_743_Nat__Transfer_Otransfer__nat__int__functions_I1_J:(forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->(((eq nat) ((plus_plus_nat (nat_1 X)) (nat_1 Y))) (nat_1 ((plus_plus_int X) Y)))))).
% 2.30/2.56 Axiom fact_744_nat__add__distrib:(forall (Z_1:int) (Z:int), (((ord_less_eq_int zero_zero_int) Z)->(((ord_less_eq_int zero_zero_int) Z_1)->(((eq nat) (nat_1 ((plus_plus_int Z) Z_1))) ((plus_plus_nat (nat_1 Z)) (nat_1 Z_1)))))).
% 2.30/2.56 Axiom fact_745_int__eq__iff__number__of:(forall (M:nat) (V_1:int), ((iff (((eq int) (semiri1621563631at_int M)) (number_number_of_int V_1))) ((and (((eq nat) M) (nat_1 (number_number_of_int V_1)))) ((ord_less_eq_int zero_zero_int) (number_number_of_int V_1))))).
% 2.30/2.56 Axiom fact_746_Nat__Transfer_Otransfer__nat__int__functions_I4_J:(forall (N:nat) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((eq nat) ((power_power_nat (nat_1 X)) N)) (nat_1 ((power_power_int X) N))))).
% 2.30/2.56 Axiom fact_747_nat__power__eq:(forall (N:nat) (Z:int), (((ord_less_eq_int zero_zero_int) Z)->(((eq nat) (nat_1 ((power_power_int Z) N))) ((power_power_nat (nat_1 Z)) N)))).
% 2.30/2.56 Axiom fact_748_convex__bound__lt:(forall (V_3:real) (U_1:real) (Y_3:real) (X_4:real) (A_4:real), (((ord_less_real X_4) A_4)->(((ord_less_real Y_3) A_4)->(((ord_less_eq_real zero_zero_real) U_1)->(((ord_less_eq_real zero_zero_real) V_3)->((((eq real) ((plus_plus_real U_1) V_3)) one_one_real)->((ord_less_real ((plus_plus_real ((times_times_real U_1) X_4)) ((times_times_real V_3) Y_3))) A_4))))))).
% 2.30/2.56 Axiom fact_749_convex__bound__lt:(forall (V_3:int) (U_1:int) (Y_3:int) (X_4:int) (A_4:int), (((ord_less_int X_4) A_4)->(((ord_less_int Y_3) A_4)->(((ord_less_eq_int zero_zero_int) U_1)->(((ord_less_eq_int zero_zero_int) V_3)->((((eq int) ((plus_plus_int U_1) V_3)) one_one_int)->((ord_less_int ((plus_plus_int ((times_times_int U_1) X_4)) ((times_times_int V_3) Y_3))) A_4))))))).
% 2.30/2.56 Axiom fact_750_nat__less__iff:(forall (M:nat) (W:int), (((ord_less_eq_int zero_zero_int) W)->((iff ((ord_less_nat (nat_1 W)) M)) ((ord_less_int W) (semiri1621563631at_int M))))).
% 2.30/2.56 Axiom fact_751_le__special_I2_J:(forall (Y_2:int), ((iff ((ord_less_eq_real one_one_real) (number267125858f_real Y_2))) ((ord_less_eq_int (bit1 pls)) Y_2))).
% 2.30/2.56 Axiom fact_752_le__special_I2_J:(forall (Y_2:int), ((iff ((ord_less_eq_int one_one_int) (number_number_of_int Y_2))) ((ord_less_eq_int (bit1 pls)) Y_2))).
% 2.30/2.56 Axiom fact_753_le__special_I4_J:(forall (X_3:int), ((iff ((ord_less_eq_real (number267125858f_real X_3)) one_one_real)) ((ord_less_eq_int X_3) (bit1 pls)))).
% 2.30/2.56 Axiom fact_754_le__special_I4_J:(forall (X_3:int), ((iff ((ord_less_eq_int (number_number_of_int X_3)) one_one_int)) ((ord_less_eq_int X_3) (bit1 pls)))).
% 2.30/2.56 Axiom fact_755_realpow__minus__mult:(forall (X_2:real) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq real) ((times_times_real ((power_power_real X_2) ((minus_minus_nat N_2) one_one_nat))) X_2)) ((power_power_real X_2) N_2)))).
% 2.30/2.56 Axiom fact_756_realpow__minus__mult:(forall (X_2:nat) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq nat) ((times_times_nat ((power_power_nat X_2) ((minus_minus_nat N_2) one_one_nat))) X_2)) ((power_power_nat X_2) N_2)))).
% 2.30/2.56 Axiom fact_757_realpow__minus__mult:(forall (X_2:int) (N_2:nat), (((ord_less_nat zero_zero_nat) N_2)->(((eq int) ((times_times_int ((power_power_int X_2) ((minus_minus_nat N_2) one_one_nat))) X_2)) ((power_power_int X_2) N_2)))).
% 2.30/2.56 Axiom fact_758_less__iff__diff__less__0:(forall (A_3:real) (B_3:real), ((iff ((ord_less_real A_3) B_3)) ((ord_less_real ((minus_minus_real A_3) B_3)) zero_zero_real))).
% 2.30/2.56 Axiom fact_759_less__iff__diff__less__0:(forall (A_3:int) (B_3:int), ((iff ((ord_less_int A_3) B_3)) ((ord_less_int ((minus_minus_int A_3) B_3)) zero_zero_int))).
% 2.30/2.56 Axiom fact_760_transfer__nat__int__numerals_I1_J:(((eq nat) zero_zero_nat) (nat_1 zero_zero_int)).
% 2.30/2.56 Axiom fact_761_nat__0:(((eq nat) (nat_1 zero_zero_int)) zero_zero_nat).
% 2.30/2.56 Axiom fact_762_not__square__less__zero:(forall (A_2:real), (((ord_less_real ((times_times_real A_2) A_2)) zero_zero_real)->False)).
% 2.30/2.56 Axiom fact_763_not__square__less__zero:(forall (A_2:int), (((ord_less_int ((times_times_int A_2) A_2)) zero_zero_int)->False)).
% 2.30/2.56 Axiom fact_764_mult__less__cancel__right__disj:(forall (A_1:real) (C_1:real) (B_2:real), ((iff ((ord_less_real ((times_times_real A_1) C_1)) ((times_times_real B_2) C_1))) ((or ((and ((ord_less_real zero_zero_real) C_1)) ((ord_less_real A_1) B_2))) ((and ((ord_less_real C_1) zero_zero_real)) ((ord_less_real B_2) A_1))))).
% 2.30/2.56 Axiom fact_765_mult__less__cancel__right__disj:(forall (A_1:int) (C_1:int) (B_2:int), ((iff ((ord_less_int ((times_times_int A_1) C_1)) ((times_times_int B_2) C_1))) ((or ((and ((ord_less_int zero_zero_int) C_1)) ((ord_less_int A_1) B_2))) ((and ((ord_less_int C_1) zero_zero_int)) ((ord_less_int B_2) A_1))))).
% 2.30/2.56 Axiom fact_766_nat__number__of:(forall (W:int), (((eq nat) (nat_1 (number_number_of_int W))) (number_number_of_nat W))).
% 2.30/2.56 Axiom fact_767_nat__number__of__def:(forall (V_1:int), (((eq nat) (number_number_of_nat V_1)) (nat_1 (number_number_of_int V_1)))).
% 2.30/2.56 Axiom fact_768_transfer__nat__int__numerals_I2_J:(((eq nat) one_one_nat) (nat_1 one_one_int)).
% 2.30/2.57 Axiom fact_769_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))).
% 2.30/2.57 Axiom fact_770_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)))).
% 2.30/2.57 Axiom fact_771_diff__add__0:(forall (N:nat) (M:nat), (((eq nat) ((minus_minus_nat N) ((plus_plus_nat N) M))) zero_zero_nat)).
% 2.30/2.57 Axiom fact_772_less__diff__conv:(forall (I_1:nat) (J:nat) (K:nat), ((iff ((ord_less_nat I_1) ((minus_minus_nat J) K))) ((ord_less_nat ((plus_plus_nat I_1) K)) J))).
% 2.30/2.57 Axiom fact_773_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))).
% 2.30/2.57 Axiom fact_774_rel__simps_I22_J:(forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K))).
% 2.30/2.57 Axiom fact_775_rel__simps_I32_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))).
% 2.30/2.57 Axiom fact_776_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))).
% 2.30/2.57 Axiom fact_777_rel__simps_I21_J:(forall (K:int), ((iff ((ord_less_eq_int pls) (bit0 K))) ((ord_less_eq_int pls) K))).
% 2.30/2.57 Axiom fact_778_rel__simps_I27_J:(forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) pls)) ((ord_less_eq_int K) pls))).
% 2.30/2.57 Axiom fact_779_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)))).
% 2.30/2.57 Axiom fact_780_zmult__zless__mono2:(forall (K:int) (I_1:int) (J:int), (((ord_less_int I_1) J)->(((ord_less_int zero_zero_int) K)->((ord_less_int ((times_times_int K) I_1)) ((times_times_int K) J))))).
% 2.30/2.57 Axiom fact_781_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J:((ord_less_eq_int zero_zero_int) one_one_int).
% 2.30/2.57 Axiom fact_782_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J:(forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X) Y))))).
% 2.30/2.57 Axiom fact_783_zadd__zless__mono:(forall (Z_1:int) (Z:int) (W_2:int) (W:int), (((ord_less_int W_2) W)->(((ord_less_eq_int Z_1) Z)->((ord_less_int ((plus_plus_int W_2) Z_1)) ((plus_plus_int W) Z))))).
% 2.30/2.57 Axiom fact_784_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J:(forall (Z:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int Z))).
% 2.30/2.57 Axiom fact_785_transfer__int__nat__quantifiers_I2_J:(forall (P:(int->Prop)), ((iff ((ex int) (fun (X_1:int)=> ((and ((ord_less_eq_int zero_zero_int) X_1)) (P X_1))))) ((ex nat) (fun (X_1:nat)=> (P (semiri1621563631at_int X_1)))))).
% 2.30/2.57 Axiom fact_786_transfer__int__nat__quantifiers_I1_J:(forall (P:(int->Prop)), ((iff (forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(P X_1)))) (forall (X_1:nat), (P (semiri1621563631at_int X_1))))).
% 2.30/2.57 Axiom fact_787_zero__zle__int:(forall (N:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int N))).
% 2.30/2.57 Axiom fact_788_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J:(forall (N:nat) (X:int), (((ord_less_eq_int zero_zero_int) X)->((ord_less_eq_int zero_zero_int) ((power_power_int X) N)))).
% 2.30/2.57 Axiom fact_789_zle__iff__zadd:(forall (W:int) (Z:int), ((iff ((ord_less_eq_int W) Z)) ((ex nat) (fun (N_1:nat)=> (((eq int) Z) ((plus_plus_int W) (semiri1621563631at_int N_1))))))).
% 2.30/2.57 Axiom fact_790_zpower__zadd__distrib:(forall (X:int) (Y:nat) (Z:nat), (((eq int) ((power_power_int X) ((plus_plus_nat Y) Z))) ((times_times_int ((power_power_int X) Y)) ((power_power_int X) Z)))).
% 2.30/2.57 Axiom fact_791_nat__mono__iff:(forall (W:int) (Z:int), (((ord_less_int zero_zero_int) Z)->((iff ((ord_less_nat (nat_1 W)) (nat_1 Z))) ((ord_less_int W) Z)))).
% 2.30/2.57 Axiom fact_792_zless__nat__conj:(forall (W:int) (Z:int), ((iff ((ord_less_nat (nat_1 W)) (nat_1 Z))) ((and ((ord_less_int zero_zero_int) Z)) ((ord_less_int W) Z)))).
% 2.30/2.57 Axiom fact_793_zless__nat__eq__int__zless:(forall (M:nat) (Z:int), ((iff ((ord_less_nat M) (nat_1 Z))) ((ord_less_int (semiri1621563631at_int M)) Z))).
% 2.30/2.57 Axiom fact_794_nat__diff__split__asm:(forall (P:(nat->Prop)) (A:nat) (B:nat), ((iff (P ((minus_minus_nat A) B))) (((or ((and ((ord_less_nat A) B)) ((P zero_zero_nat)->False))) ((ex nat) (fun (D_1:nat)=> ((and (((eq nat) A) ((plus_plus_nat B) D_1))) ((P D_1)->False)))))->False))).
% 2.30/2.57 Axiom fact_795_nat__diff__split:(forall (P:(nat->Prop)) (A:nat) (B:nat), ((iff (P ((minus_minus_nat A) B))) ((and (((ord_less_nat A) B)->(P zero_zero_nat))) (forall (D_1:nat), ((((eq nat) A) ((plus_plus_nat B) D_1))->(P D_1)))))).
% 2.30/2.57 Axiom fact_796_eq__0__number__of:(forall (V_1:int), ((iff (((eq nat) zero_zero_nat) (number_number_of_nat V_1))) ((ord_less_eq_int V_1) pls))).
% 2.30/2.57 Axiom fact_797_eq__number__of__0:(forall (V_1:int), ((iff (((eq nat) (number_number_of_nat V_1)) zero_zero_nat)) ((ord_less_eq_int V_1) pls))).
% 2.30/2.57 Axiom fact_798_rel__simps_I5_J:(forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K))).
% 2.30/2.57 Axiom fact_799_rel__simps_I29_J:(forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls))).
% 2.30/2.57 Axiom fact_800_rel__simps_I15_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))).
% 2.30/2.57 Axiom fact_801_less__int__code_I14_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))).
% 2.30/2.57 Axiom fact_802_rel__simps_I33_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))).
% 2.30/2.57 Axiom fact_803_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))).
% 2.30/2.57 Axiom fact_804_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))).
% 2.30/2.57 Axiom fact_805_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))))).
% 2.30/2.57 Axiom fact_806_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))).
% 2.30/2.57 Axiom fact_807_int__le__0__conv:(forall (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat))).
% 2.30/2.57 Axiom fact_808_succ__Pls:(((eq int) (succ pls)) (bit1 pls)).
% 2.30/2.57 Axiom fact_809_succ__Bit0:(forall (K:int), (((eq int) (succ (bit0 K))) (bit1 K))).
% 2.30/2.57 Axiom fact_810_succ__Bit1:(forall (K:int), (((eq int) (succ (bit1 K))) (bit0 (succ K)))).
% 2.30/2.57 Axiom fact_811_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))).
% 2.30/2.57 Axiom fact_812_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))).
% 2.30/2.57 Axiom fact_813_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))).
% 2.30/2.57 Axiom fact_814_succ__def:(forall (K:int), (((eq int) (succ K)) ((plus_plus_int K) one_one_int))).
% 2.30/2.57 Axiom fact_815_zero__less__nat__eq:(forall (Z:int), ((iff ((ord_less_nat zero_zero_nat) (nat_1 Z))) ((ord_less_int zero_zero_int) Z))).
% 2.30/2.57 Axiom fact_816_transfer__nat__int__numerals_I4_J:(((eq nat) (number_number_of_nat (bit1 (bit1 pls)))) (nat_1 (number_number_of_int (bit1 (bit1 pls))))).
% 2.30/2.57 Axiom fact_817_split__nat:(forall (P:(nat->Prop)) (I_1:int), ((iff (P (nat_1 I_1))) ((and (forall (N_1:nat), ((((eq int) I_1) (semiri1621563631at_int N_1))->(P N_1)))) (((ord_less_int I_1) zero_zero_int)->(P zero_zero_nat))))).
% 2.30/2.57 Axiom fact_818_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J:((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 (bit1 pls)))).
% 2.30/2.57 Axiom fact_819_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)))).
% 2.30/2.57 Axiom fact_820_zmult__zless__mono2__lemma:(forall (K:nat) (I_1:int) (J:int), (((ord_less_int I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_int ((times_times_int (semiri1621563631at_int K)) I_1)) ((times_times_int (semiri1621563631at_int K)) J))))).
% 2.30/2.57 Axiom fact_821_add__Bit1__Bit1:(forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit1 L))) (bit0 ((plus_plus_int K) (succ L))))).
% 2.30/2.57 Axiom fact_822_transfer__nat__int__numerals_I3_J:(((eq nat) (number_number_of_nat (bit0 (bit1 pls)))) (nat_1 (number_number_of_int (bit0 (bit1 pls))))).
% 2.30/2.57 Axiom fact_823_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J:((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 (bit1 pls)))).
% 2.30/2.57 Axiom fact_824_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)))))).
% 2.30/2.57 Axiom fact_825_power2__ge__self:(forall (X:int), ((ord_less_eq_int X) ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.30/2.57 Axiom fact_826_int__pos__lt__two__imp__zero__or__one:(forall (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_int X) (number_number_of_int (bit0 (bit1 pls))))->((or (((eq int) X) zero_zero_int)) (((eq int) X) one_one_int))))).
% 2.30/2.57 Axiom fact_827_Euler_Oaux__1:(forall (A:int) (P_1:int), (((ord_less_int zero_zero_int) P_1)->(((eq int) ((power_power_int A) (nat_1 P_1))) ((times_times_int A) ((power_power_int A) ((minus_minus_nat (nat_1 P_1)) one_one_nat)))))).
% 2.30/2.57 Axiom fact_828_self__quotient__aux2:(forall (R_1:int) (Q:int) (A:int), (((ord_less_int zero_zero_int) A)->((((eq int) A) ((plus_plus_int R_1) ((times_times_int A) Q)))->(((ord_less_eq_int zero_zero_int) R_1)->((ord_less_eq_int Q) one_one_int))))).
% 2.30/2.57 Axiom fact_829_self__quotient__aux1:(forall (R_1:int) (Q:int) (A:int), (((ord_less_int zero_zero_int) A)->((((eq int) A) ((plus_plus_int R_1) ((times_times_int A) Q)))->(((ord_less_int R_1) A)->((ord_less_eq_int one_one_int) Q))))).
% 2.30/2.57 Axiom fact_830_smaller_I2_J:((((ord_less_int ((plus_plus_int one_one_int) (semiri1621563631at_int n))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))->((twoSqu919416604sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))->False))->False).
% 2.30/2.57 Axiom fact_831_q__pos__lemma:(forall (B_1:int) (Q_1:int) (R_2:int), (((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_1) Q_1)) R_2))->(((ord_less_int R_2) B_1)->(((ord_less_int zero_zero_int) B_1)->((ord_less_eq_int zero_zero_int) Q_1))))).
% 2.30/2.57 Axiom fact_832_q__neg__lemma:(forall (B_1:int) (Q_1:int) (R_2:int), (((ord_less_int ((plus_plus_int ((times_times_int B_1) Q_1)) R_2)) zero_zero_int)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B_1)->((ord_less_eq_int Q_1) zero_zero_int))))).
% 2.30/2.57 Axiom fact_833_nQ1:((twoSqu919416604sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int zero_zero_nat))))->False).
% 2.30/2.57 Axiom fact_834_le0:(forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)).
% 2.30/2.57 Axiom fact_835_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)).
% 2.30/2.57 Axiom fact_836_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)).
% 2.30/2.57 Axiom fact_837_qf1pt:(twoSqu919416604sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)).
% 2.30/2.57 Axiom fact_838_IH:((and ((ord_less_int ((plus_plus_int one_one_int) (semiri1621563631at_int n))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) (twoSqu919416604sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))).
% 2.30/2.57 Axiom fact_839__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_061_A_I4_A:((forall (X_1:int) (Y_1:int), (not (((eq int) ((plus_plus_int ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))))->False).
% 2.30/2.57 Axiom fact_840_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)).
% 2.30/2.57 Axiom fact_841_p:(zprime ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)).
% 2.30/2.57 Axiom fact_842__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_:((((eq int) t) one_one_int)->((ex int) (fun (X_1:int)=> ((ex int) (fun (Y_1:int)=> (((eq int) ((plus_plus_int ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_1) (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))))))).
% 2.30/2.57 Axiom fact_843_le__refl:(forall (N:nat), ((ord_less_eq_nat N) N)).
% 2.30/2.57 Axiom fact_844_le__square:(forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) M))).
% 2.30/2.57 Axiom fact_845_le__cube:(forall (M:nat), ((ord_less_eq_nat M) ((times_times_nat M) ((times_times_nat M) M)))).
% 2.30/2.57 Axiom fact_846_nat__mult__commute:(forall (M:nat) (N:nat), (((eq nat) ((times_times_nat M) N)) ((times_times_nat N) M))).
% 2.30/2.57 Axiom fact_847_nat__le__linear:(forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M))).
% 2.30/2.57 Axiom fact_848_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)))).
% 2.30/2.57 Axiom fact_849_eq__imp__le:(forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N))).
% 2.30/2.57 Axiom fact_850_mult__le__mono1:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J) K)))).
% 2.30/2.57 Axiom fact_851_mult__le__mono2:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((times_times_nat K) I_1)) ((times_times_nat K) J)))).
% 2.30/2.57 Axiom fact_852_le__trans:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat I_1) K)))).
% 2.30/2.57 Axiom fact_853_le__antisym:(forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N)))).
% 2.30/2.57 Axiom fact_854_mult__le__mono:(forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((times_times_nat I_1) K)) ((times_times_nat J) L))))).
% 2.30/2.57 Axiom fact_855_real__le__eq__diff:(forall (X:real) (Y:real), ((iff ((ord_less_eq_real X) Y)) ((ord_less_eq_real ((minus_minus_real X) Y)) zero_zero_real))).
% 2.30/2.57 Axiom fact_856_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)))).
% 2.30/2.57 Axiom fact_857_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)))).
% 2.30/2.57 Axiom fact_858_real__mult__le__cancel__iff1:(forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real X) Z)) ((times_times_real Y) Z))) ((ord_less_eq_real X) Y)))).
% 2.30/2.57 Axiom fact_859_real__mult__le__cancel__iff2:(forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real Z) X)) ((times_times_real Z) Y))) ((ord_less_eq_real X) Y)))).
% 2.30/2.57 Axiom fact_860_zdiff__int:(forall (N:nat) (M:nat), (((ord_less_eq_nat N) M)->(((eq int) ((minus_minus_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((minus_minus_nat M) N))))).
% 2.30/2.57 Axiom fact_861_diff__bin__simps_I1_J:(forall (K:int), (((eq int) ((minus_minus_int K) pls)) K)).
% 2.30/2.57 Axiom fact_862_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)))).
% 2.30/2.57 Axiom fact_863_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)))).
% 2.30/2.57 Axiom fact_864_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)))).
% 2.30/2.57 Axiom fact_865_mult__0:(forall (N:nat), (((eq nat) ((times_times_nat zero_zero_nat) N)) zero_zero_nat)).
% 2.30/2.57 Axiom fact_866_mult__0__right:(forall (M:nat), (((eq nat) ((times_times_nat M) zero_zero_nat)) zero_zero_nat)).
% 2.30/2.57 Axiom fact_867_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)))).
% 2.30/2.57 Axiom fact_868_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)))).
% 2.30/2.57 Axiom fact_869_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)))).
% 2.30/2.57 Axiom fact_870_less__eq__nat_Osimps_I1_J:(forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)).
% 2.30/2.57 Axiom fact_871_le__0__eq:(forall (N:nat), ((iff ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat))).
% 2.30/2.57 Axiom fact_872_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)))).
% 2.30/2.57 Axiom fact_873_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)))).
% 2.30/2.57 Axiom fact_874_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))).
% 2.30/2.57 Axiom fact_875_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)))).
% 2.30/2.57 Axiom fact_876_less__imp__le__nat:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N))).
% 2.30/2.57 Axiom fact_877_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)))).
% 2.30/2.57 Axiom fact_878_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))))).
% 2.30/2.57 Axiom fact_879_real__less__def:(forall (X:real) (Y:real), ((iff ((ord_less_real X) Y)) ((and ((ord_less_eq_real X) Y)) (not (((eq real) X) Y))))).
% 2.30/2.57 Axiom fact_880_less__eq__real__def:(forall (X:real) (Y:real), ((iff ((ord_less_eq_real X) Y)) ((or ((ord_less_real X) Y)) (((eq real) X) Y)))).
% 2.30/2.57 Axiom fact_881_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)))).
% 2.30/2.57 Axiom fact_882_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)))).
% 2.30/2.57 Axiom fact_883_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))).
% 2.30/2.57 Axiom fact_884_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))).
% 2.30/2.57 Axiom fact_885_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))).
% 2.30/2.57 Axiom fact_886_add__le__mono:(forall (K:nat) (L:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) L))))).
% 2.30/2.57 Axiom fact_887_add__le__mono1:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat ((plus_plus_nat I_1) K)) ((plus_plus_nat J) K)))).
% 2.30/2.57 Axiom fact_888_trans__le__add2:(forall (M:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat I_1) ((plus_plus_nat M) J)))).
% 2.30/2.57 Axiom fact_889_trans__le__add1:(forall (M:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((ord_less_eq_nat I_1) ((plus_plus_nat J) M)))).
% 2.30/2.58 Axiom fact_890_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))).
% 2.30/2.58 Axiom fact_891_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)))))).
% 2.30/2.58 Axiom fact_892_le__add1:(forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M))).
% 2.30/2.58 Axiom fact_893_le__add2:(forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat M) N))).
% 2.30/2.58 Axiom fact_894_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)))).
% 2.30/2.58 Axiom fact_895_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)))).
% 2.30/2.58 Axiom fact_896_nat__mult__1__right:(forall (N:nat), (((eq nat) ((times_times_nat N) one_one_nat)) N)).
% 2.30/2.58 Axiom fact_897_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)))).
% 2.30/2.58 Axiom fact_898_nat__mult__1:(forall (N:nat), (((eq nat) ((times_times_nat one_one_nat) N)) N)).
% 2.30/2.58 Axiom fact_899_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)))).
% 2.30/2.58 Axiom fact_900_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)))).
% 2.30/2.58 Axiom fact_901_real__mult__1:(forall (Z:real), (((eq real) ((times_times_real one_one_real) Z)) Z)).
% 2.30/2.58 Axiom fact_902_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))))).
% 2.30/2.58 Axiom fact_903_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))))).
% 2.30/2.58 Axiom fact_904_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))))).
% 2.30/2.58 Axiom fact_905_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))).
% 2.30/2.58 Axiom fact_906_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)))).
% 2.30/2.58 Axiom fact_907_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)))).
% 2.30/2.58 Axiom fact_908_Nat_Odiff__le__self:(forall (M:nat) (N:nat), ((ord_less_eq_nat ((minus_minus_nat M) N)) M)).
% 2.30/2.58 Axiom fact_909_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)))).
% 2.30/2.58 Axiom fact_910_zpower__zpower:(forall (X:int) (Y:nat) (Z:nat), (((eq int) ((power_power_int ((power_power_int X) Y)) Z)) ((power_power_int X) ((times_times_nat Y) Z)))).
% 2.30/2.58 Axiom fact_911_real__add__left__mono:(forall (Z:real) (X:real) (Y:real), (((ord_less_eq_real X) Y)->((ord_less_eq_real ((plus_plus_real Z) X)) ((plus_plus_real Z) Y)))).
% 2.30/2.58 Axiom fact_912_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)))).
% 2.30/2.58 Axiom fact_913_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)))).
% 2.30/2.58 Axiom fact_914_diff__bin__simps_I3_J:(forall (L:int), (((eq int) ((minus_minus_int pls) (bit0 L))) (bit0 ((minus_minus_int pls) L)))).
% 2.30/2.58 Axiom fact_915_Euler_Oaux1:(forall (A:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int X) A)->((not (((eq int) X) ((minus_minus_int A) one_one_int)))->((ord_less_int X) ((minus_minus_int A) one_one_int)))))).
% 2.30/2.58 Axiom fact_916_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))).
% 2.30/2.58 Axiom fact_917_mult__less__mono2:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat K) I_1)) ((times_times_nat K) J))))).
% 2.30/2.58 Axiom fact_918_mult__less__mono1:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_nat I_1) J)->(((ord_less_nat zero_zero_nat) K)->((ord_less_nat ((times_times_nat I_1) K)) ((times_times_nat J) K))))).
% 2.30/2.58 Axiom fact_919_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)))).
% 2.30/2.58 Axiom fact_920_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)))).
% 2.30/2.58 Axiom fact_921_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)))).
% 2.30/2.58 Axiom fact_922_not__real__square__gt__zero:(forall (X:real), ((iff (((ord_less_real zero_zero_real) ((times_times_real X) X))->False)) (((eq real) X) zero_zero_real))).
% 2.30/2.58 Axiom fact_923_real__mult__less__mono2:(forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->(((ord_less_real X) Y)->((ord_less_real ((times_times_real Z) X)) ((times_times_real Z) Y))))).
% 2.30/2.58 Axiom fact_924_real__mult__order:(forall (Y:real) (X:real), (((ord_less_real zero_zero_real) X)->(((ord_less_real zero_zero_real) Y)->((ord_less_real zero_zero_real) ((times_times_real X) Y))))).
% 2.30/2.58 Axiom fact_925_real__mult__less__iff1:(forall (X:real) (Y:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_real ((times_times_real X) Z)) ((times_times_real Y) Z))) ((ord_less_real X) Y)))).
% 2.30/2.58 Axiom fact_926_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)))).
% 2.30/2.58 Axiom fact_927_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))).
% 2.30/2.58 Axiom fact_928_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))).
% 2.30/2.58 Axiom fact_929_real__two__squares__add__zero__iff:(forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X) X)) ((times_times_real Y) Y))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real)))).
% 2.30/2.58 Axiom fact_930_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))))).
% 2.30/2.58 Axiom fact_931_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))))).
% 2.30/2.58 Axiom fact_932_Nat__Transfer_Otransfer__int__nat__functions_I2_J:(forall (X:nat) (Y:nat), (((eq int) ((times_times_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((times_times_nat X) Y)))).
% 2.30/2.58 Axiom fact_933_zmult__int:(forall (M:nat) (N:nat), (((eq int) ((times_times_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((times_times_nat M) N)))).
% 2.30/2.58 Axiom fact_934_int__mult:(forall (M:nat) (N:nat), (((eq int) (semiri1621563631at_int ((times_times_nat M) N))) ((times_times_int (semiri1621563631at_int M)) (semiri1621563631at_int N)))).
% 2.30/2.58 Axiom fact_935_diff__diff__right:(forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat I_1) ((minus_minus_nat J) K))) ((minus_minus_nat ((plus_plus_nat I_1) K)) J)))).
% 2.30/2.58 Axiom fact_936_le__diff__conv:(forall (J:nat) (K:nat) (I_1:nat), ((iff ((ord_less_eq_nat ((minus_minus_nat J) K)) I_1)) ((ord_less_eq_nat J) ((plus_plus_nat I_1) K)))).
% 2.30/2.58 Axiom fact_937_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)))).
% 2.30/2.58 Axiom fact_938_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))).
% 2.30/2.58 Axiom fact_939_add__diff__assoc:(forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((plus_plus_nat I_1) ((minus_minus_nat J) K))) ((minus_minus_nat ((plus_plus_nat I_1) J)) K)))).
% 2.30/2.58 Axiom fact_940_le__diff__conv2:(forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->((iff ((ord_less_eq_nat I_1) ((minus_minus_nat J) K))) ((ord_less_eq_nat ((plus_plus_nat I_1) K)) J)))).
% 2.30/2.58 Axiom fact_941_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))).
% 2.30/2.58 Axiom fact_942_le__imp__diff__is__add:(forall (K:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff (((eq nat) ((minus_minus_nat J) I_1)) K)) (((eq nat) J) ((plus_plus_nat K) I_1))))).
% 2.30/2.58 Axiom fact_943_diff__add__assoc:(forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat I_1) J)) K)) ((plus_plus_nat I_1) ((minus_minus_nat J) K))))).
% 2.30/2.58 Axiom fact_944_add__diff__assoc2:(forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((plus_plus_nat ((minus_minus_nat J) K)) I_1)) ((minus_minus_nat ((plus_plus_nat J) I_1)) K)))).
% 2.30/2.58 Axiom fact_945_diff__add__assoc2:(forall (I_1:nat) (K:nat) (J:nat), (((ord_less_eq_nat K) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat J) I_1)) K)) ((plus_plus_nat ((minus_minus_nat J) K)) I_1)))).
% 2.30/2.58 Axiom fact_946_Nat__Transfer_Otransfer__int__nat__relations_I3_J:(forall (X:nat) (Y:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_eq_nat X) Y))).
% 2.30/2.58 Axiom fact_947_zle__int:(forall (M:nat) (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_eq_nat M) N))).
% 2.30/2.58 Axiom fact_948_is__mult__sum2sq:(forall (Y:int) (X:int), ((twoSqu919416604sum2sq X)->((twoSqu919416604sum2sq Y)->(twoSqu919416604sum2sq ((times_times_int X) Y))))).
% 2.30/2.58 Axiom fact_949_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))).
% 2.30/2.58 Axiom fact_950_le__nat__number__of:(forall (V_1:int) (V_2:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) ((((ord_less_eq_int V_1) V_2)->False)->((ord_less_eq_int V_1) pls)))).
% 2.30/2.58 Axiom fact_951_transfer__nat__int__relations_I3_J:(forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((iff ((ord_less_eq_nat (nat_1 X)) (nat_1 Y))) ((ord_less_eq_int X) Y))))).
% 2.30/2.58 Axiom fact_952_nat__diff__distrib:(forall (Z:int) (Z_1:int), (((ord_less_eq_int zero_zero_int) Z_1)->(((ord_less_eq_int Z_1) Z)->(((eq nat) (nat_1 ((minus_minus_int Z) Z_1))) ((minus_minus_nat (nat_1 Z)) (nat_1 Z_1)))))).
% 2.30/2.58 Axiom fact_953_nat__mult__distrib:(forall (Z_1:int) (Z:int), (((ord_less_eq_int zero_zero_int) Z)->(((eq nat) (nat_1 ((times_times_int Z) Z_1))) ((times_times_nat (nat_1 Z)) (nat_1 Z_1))))).
% 2.30/2.58 Axiom fact_954_Nat__Transfer_Otransfer__nat__int__functions_I2_J:(forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->(((eq nat) ((times_times_nat (nat_1 X)) (nat_1 Y))) (nat_1 ((times_times_int X) Y)))))).
% 2.30/2.58 Axiom fact_955_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)))))).
% 2.30/2.58 Axiom fact_956_nat__le__eq__zle:(forall (Z:int) (W:int), (((or ((ord_less_int zero_zero_int) W)) ((ord_less_eq_int zero_zero_int) Z))->((iff ((ord_less_eq_nat (nat_1 W)) (nat_1 Z))) ((ord_less_eq_int W) Z)))).
% 2.30/2.58 Axiom fact_957_power__eq__if:(forall (P_1:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((power_power_nat P_1) M)) one_one_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((power_power_nat P_1) M)) ((times_times_nat P_1) ((power_power_nat P_1) ((minus_minus_nat M) one_one_nat))))))).
% 2.30/2.58 Axiom fact_958_nat__mult__2:(forall (Z:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z)) ((plus_plus_nat Z) Z))).
% 2.30/2.58 Axiom fact_959_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))).
% 2.30/2.58 Axiom fact_960_nat__number__of__mult__left:(forall (V_2:int) (K:nat) (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((times_times_nat (number_number_of_nat V_1)) ((times_times_nat (number_number_of_nat V_2)) K))) zero_zero_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((times_times_nat (number_number_of_nat V_1)) ((times_times_nat (number_number_of_nat V_2)) K))) ((times_times_nat (number_number_of_nat ((times_times_int V_1) V_2))) K))))).
% 2.30/2.58 Axiom fact_961_mult__nat__number__of:(forall (V_2:int) (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((times_times_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) zero_zero_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((times_times_nat (number_number_of_nat V_1)) (number_number_of_nat V_2))) (number_number_of_nat ((times_times_int V_1) V_2)))))).
% 2.30/2.58 Axiom fact_962_four__x__squared:(forall (X:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit0 (bit1 pls))))) ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X)) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.30/2.58 Axiom fact_963_two__realpow__ge__one:(forall (N:nat), ((ord_less_eq_real one_one_real) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N))).
% 2.30/2.58 Axiom fact_964_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))))).
% 2.30/2.58 Axiom fact_965_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))))))).
% 2.30/2.58 Axiom fact_966_diff__square:(forall (X:nat) (Y:nat), (((eq nat) ((minus_minus_nat ((power_power_nat X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((plus_plus_nat X) Y)) ((minus_minus_nat X) Y)))).
% 2.30/2.58 Axiom fact_967_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))))))).
% 2.30/2.58 Axiom fact_968_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))))))).
% 2.30/2.58 Axiom fact_969_zdiv__mono2__neg__lemma:(forall (B:int) (Q:int) (R_1:int) (B_1:int) (Q_1:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B) Q)) R_1)) ((plus_plus_int ((times_times_int B_1) Q_1)) R_2))->(((ord_less_int ((plus_plus_int ((times_times_int B_1) Q_1)) R_2)) zero_zero_int)->(((ord_less_int R_1) B)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B_1)->(((ord_less_eq_int B_1) B)->((ord_less_eq_int Q_1) Q)))))))).
% 2.30/2.58 Axiom fact_970_unique__quotient__lemma__neg:(forall (B:int) (Q_1:int) (R_2:int) (Q:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B) Q_1)) R_2)) ((plus_plus_int ((times_times_int B) Q)) R_1))->(((ord_less_eq_int R_1) zero_zero_int)->(((ord_less_int B) R_1)->(((ord_less_int B) R_2)->((ord_less_eq_int Q) Q_1)))))).
% 2.30/2.58 Axiom fact_971_zdiv__mono2__lemma:(forall (B:int) (Q:int) (R_1:int) (B_1:int) (Q_1:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B) Q)) R_1)) ((plus_plus_int ((times_times_int B_1) Q_1)) R_2))->(((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B_1) Q_1)) R_2))->(((ord_less_int R_2) B_1)->(((ord_less_eq_int zero_zero_int) R_1)->(((ord_less_int zero_zero_int) B_1)->(((ord_less_eq_int B_1) B)->((ord_less_eq_int Q) Q_1)))))))).
% 2.30/2.58 Axiom fact_972_unique__quotient__lemma:(forall (B:int) (Q_1:int) (R_2:int) (Q:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B) Q_1)) R_2)) ((plus_plus_int ((times_times_int B) Q)) R_1))->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int R_2) B)->(((ord_less_int R_1) B)->((ord_less_eq_int Q_1) Q)))))).
% 2.30/2.58 Axiom fact_973_xy:(((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)))))) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int n)))).
% 2.30/2.58 Axiom fact_974_Int2_Oaux__1:(forall (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->(((eq nat) ((minus_minus_nat (nat_1 P_1)) (number_number_of_nat (bit0 (bit1 pls))))) (nat_1 ((minus_minus_int P_1) (number_number_of_int (bit0 (bit1 pls)))))))).
% 2.30/2.58 Axiom fact_975_Int2_Oaux__2:(forall (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((ord_less_nat zero_zero_nat) (nat_1 ((minus_minus_int P_1) (number_number_of_int (bit0 (bit1 pls)))))))).
% 2.30/2.58 Axiom fact_976__096_B_Bthesis_O_A_I_B_Bt_O_As_____A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_:((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).
% 2.30/2.58 Axiom fact_977_real__le__refl:(forall (W:real), ((ord_less_eq_real W) W)).
% 2.30/2.58 Axiom fact_978_real__mult__commute:(forall (Z:real) (W:real), (((eq real) ((times_times_real Z) W)) ((times_times_real W) Z))).
% 2.30/2.58 Axiom fact_979_real__le__linear:(forall (Z:real) (W:real), ((or ((ord_less_eq_real Z) W)) ((ord_less_eq_real W) Z))).
% 2.30/2.58 Axiom fact_980_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)))).
% 2.30/2.58 Axiom fact_981_real__le__trans:(forall (K:real) (I_1:real) (J:real), (((ord_less_eq_real I_1) J)->(((ord_less_eq_real J) K)->((ord_less_eq_real I_1) K)))).
% 2.30/2.58 Axiom fact_982_real__le__antisym:(forall (Z:real) (W:real), (((ord_less_eq_real Z) W)->(((ord_less_eq_real W) Z)->(((eq real) Z) W)))).
% 2.30/2.58 Axiom fact_983_zprime__2:(zprime (number_number_of_int (bit0 (bit1 pls)))).
% 2.30/2.58 Axiom fact_984_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)))).
% 2.30/2.58 Axiom fact_985__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)).
% 2.30/2.58 Axiom fact_986_real__sum__squared__expand:(forall (X:real) (Y:real), (((eq real) ((power_power_real ((plus_plus_real X) Y)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X)) Y)))).
% 2.30/2.59 Axiom fact_987__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)).
% 2.30/2.59 Axiom fact_988__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))).
% 2.30/2.59 Axiom fact_989__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).
% 2.30/2.59 Axiom fact_990_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)))).
% 2.30/2.59 Axiom fact_991_zprime__zdvd__zmult__better:(forall (M:int) (N:int) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((times_times_int M) N))->((or ((dvd_dvd_int P_1) M)) ((dvd_dvd_int P_1) N))))).
% 2.30/2.59 Axiom fact_992_rel__simps_I24_J:((ord_less_eq_int min) min).
% 2.30/2.59 Axiom fact_993_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)))).
% 2.30/2.59 Axiom fact_994_zprime__zdvd__power:(forall (A:int) (N:nat) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((power_power_int A) N))->((dvd_dvd_int P_1) A)))).
% 2.30/2.59 Axiom fact_995_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)))).
% 2.30/2.59 Axiom fact_996_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)))).
% 2.30/2.59 Axiom fact_997_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)))))).
% 2.30/2.59 Axiom fact_998_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))).
% 2.30/2.59 Axiom fact_999_zdvd__period:(forall (C:int) (X:int) (T:int) (A:int) (D:int), (((dvd_dvd_int A) D)->((iff ((dvd_dvd_int A) ((plus_plus_int X) T))) ((dvd_dvd_int A) ((plus_plus_int ((plus_plus_int X) ((times_times_int C) D))) T))))).
% 2.30/2.59 Axiom fact_1000_rel__simps_I9_J:(forall (K:int), ((iff ((ord_less_int min) (bit1 K))) ((ord_less_int min) K))).
% 2.30/2.59 Axiom fact_1001_rel__simps_I13_J:(forall (K:int), ((iff ((ord_less_int (bit1 K)) min)) ((ord_less_int K) min))).
% 2.30/2.59 Axiom fact_1002_rel__simps_I6_J:((ord_less_int min) pls).
% 2.30/2.59 Axiom fact_1003_rel__simps_I3_J:(((ord_less_int pls) min)->False).
% 2.30/2.59 Axiom fact_1004_rel__simps_I8_J:(forall (K:int), ((iff ((ord_less_int min) (bit0 K))) ((ord_less_int min) K))).
% 2.30/2.59 Axiom fact_1005_rel__simps_I26_J:(forall (K:int), ((iff ((ord_less_eq_int min) (bit1 K))) ((ord_less_eq_int min) K))).
% 2.30/2.59 Axiom fact_1006_rel__simps_I30_J:(forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) min)) ((ord_less_eq_int K) min))).
% 2.30/2.59 Axiom fact_1007_bin__less__0__simps_I2_J:((ord_less_int min) zero_zero_int).
% 2.30/2.59 Axiom fact_1008_rel__simps_I23_J:((ord_less_eq_int min) pls).
% 2.30/2.59 Axiom fact_1009_rel__simps_I20_J:(((ord_less_eq_int pls) min)->False).
% 2.30/2.59 Axiom fact_1010_rel__simps_I28_J:(forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) min)) ((ord_less_eq_int K) min))).
% 2.30/2.59 Axiom fact_1011_eq__number__of__Pls__Min:(not (((eq int) (number_number_of_int pls)) (number_number_of_int min))).
% 2.30/2.59 Axiom fact_1012_rel__simps_I7_J:(((ord_less_int min) min)->False).
% 2.30/2.59 Axiom fact_1013_rel__simps_I42_J:(forall (L:int), (not (((eq int) min) (bit0 L)))).
% 2.30/2.59 Axiom fact_1014_rel__simps_I45_J:(forall (K:int), (not (((eq int) (bit0 K)) min))).
% 2.30/2.59 Axiom fact_1015_rel__simps_I40_J:(not (((eq int) min) pls)).
% 2.30/2.59 Axiom fact_1016_rel__simps_I37_J:(not (((eq int) pls) min)).
% 2.30/2.59 Axiom fact_1017_Bit1__Min:(((eq int) (bit1 min)) min).
% 2.30/2.59 Axiom fact_1018_rel__simps_I43_J:(forall (L:int), ((iff (((eq int) min) (bit1 L))) (((eq int) min) L))).
% 2.30/2.59 Axiom fact_1019_rel__simps_I47_J:(forall (K:int), ((iff (((eq int) (bit1 K)) min)) (((eq int) K) min))).
% 2.30/2.59 Axiom fact_1020_succ__Min:(((eq int) (succ min)) pls).
% 2.30/2.59 Axiom fact_1021_diff__bin__simps_I2_J:(forall (K:int), (((eq int) ((minus_minus_int K) min)) (succ K))).
% 2.30/2.59 Axiom fact_1022_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)))).
% 2.30/2.59 Axiom fact_1023_zpower__zdvd__prop1:(forall (P_1:int) (Y:int) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((dvd_dvd_int P_1) Y)->((dvd_dvd_int P_1) ((power_power_int Y) N))))).
% 2.30/2.59 Axiom fact_1024_rel__simps_I25_J:(forall (K:int), ((iff ((ord_less_eq_int min) (bit0 K))) ((ord_less_int min) K))).
% 2.30/2.59 Axiom fact_1025_rel__simps_I11_J:(forall (K:int), ((iff ((ord_less_int (bit0 K)) min)) ((ord_less_eq_int K) min))).
% 2.30/2.59 Axiom fact_1026_diff__bin__simps_I4_J:(forall (L:int), (((eq int) ((minus_minus_int pls) (bit1 L))) (bit1 ((minus_minus_int min) L)))).
% 2.30/2.59 Axiom fact_1027_diff__bin__simps_I6_J:(forall (L:int), (((eq int) ((minus_minus_int min) (bit1 L))) (bit0 ((minus_minus_int min) L)))).
% 2.30/2.59 Axiom fact_1028_diff__bin__simps_I5_J:(forall (L:int), (((eq int) ((minus_minus_int min) (bit0 L))) (bit1 ((minus_minus_int min) L)))).
% 2.30/2.59 Axiom fact_1029_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)))))).
% 2.30/2.59 Axiom fact_1030_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))))).
% 2.30/2.59 Axiom fact_1031_zprime__power__zdvd__cancel__right:(forall (N:nat) (A:int) (B:int) (P_1:int), ((zprime P_1)->((((dvd_dvd_int P_1) B)->False)->(((dvd_dvd_int ((power_power_int P_1) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P_1) N)) A))))).
% 2.30/2.59 Axiom fact_1032_zprime__power__zdvd__cancel__left:(forall (N:nat) (B:int) (A:int) (P_1:int), ((zprime P_1)->((((dvd_dvd_int P_1) A)->False)->(((dvd_dvd_int ((power_power_int P_1) N)) ((times_times_int A) B))->((dvd_dvd_int ((power_power_int P_1) N)) B))))).
% 2.30/2.59 Axiom fact_1033_zpower__zdvd__prop2:(forall (Y:int) (N:nat) (P_1:int), ((zprime P_1)->(((dvd_dvd_int P_1) ((power_power_int Y) N))->(((ord_less_nat zero_zero_nat) N)->((dvd_dvd_int P_1) Y))))).
% 2.30/2.59 Axiom fact_1034__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)).
% 2.30/2.59 Axiom fact_1035_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)).
% 2.30/2.59 Axiom fact_1036__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_:((((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))).
% 2.30/2.59 Axiom fact_1037_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)).
% 2.30/2.59 Axiom fact_1038_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))).
% 2.30/2.59 Axiom fact_1039__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).
% 2.30/2.59 Axiom fact_1040_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)))).
% 2.30/2.59 Axiom fact_1041_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)))).
% 2.30/2.59 Axiom fact_1042_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))))).
% 2.30/2.59 Axiom fact_1043_zcong__eq__zdvd__prop:(forall (X:int) (P_1:int), ((iff (((zcong X) zero_zero_int) P_1)) ((dvd_dvd_int P_1) X))).
% 2.30/2.59 Axiom fact_1044_zcong__zero__equiv__div:(forall (A:int) (M:int), ((iff (((zcong A) zero_zero_int) M)) ((dvd_dvd_int M) A))).
% 2.30/2.59 Axiom fact_1045_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)))).
% 2.30/2.59 Axiom fact_1046_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)))).
% 2.30/2.59 Axiom fact_1047_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)))).
% 2.30/2.59 Axiom fact_1048_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))))).
% 2.30/2.59 Axiom fact_1049_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))))).
% 2.30/2.59 Axiom fact_1050_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)))).
% 2.30/2.59 Axiom fact_1051_divides__exp2:(forall (X:nat) (Y:nat) (N:nat), ((not (((eq nat) N) zero_zero_nat))->(((dvd_dvd_nat ((power_power_nat X) N)) Y)->((dvd_dvd_nat X) Y)))).
% 2.30/2.59 Axiom fact_1052_Nat__Transfer_Otransfer__int__nat__relations_I4_J:(forall (X:nat) (Y:nat), ((iff ((dvd_dvd_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((dvd_dvd_nat X) Y))).
% 2.30/2.59 Axiom fact_1053_zdvd__int:(forall (X:nat) (Y:nat), ((iff ((dvd_dvd_nat X) Y)) ((dvd_dvd_int (semiri1621563631at_int X)) (semiri1621563631at_int Y)))).
% 2.30/2.59 Axiom fact_1054_divides__exp:(forall (N:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->((dvd_dvd_nat ((power_power_nat X) N)) ((power_power_nat Y) N)))).
% 2.30/2.59 Axiom fact_1055_nat__dvd__1__iff__1:(forall (M:nat), ((iff ((dvd_dvd_nat M) one_one_nat)) (((eq nat) M) one_one_nat))).
% 2.30/2.59 Axiom fact_1056_dvd__reduce:(forall (K:nat) (N:nat), ((iff ((dvd_dvd_nat K) ((plus_plus_nat N) K))) ((dvd_dvd_nat K) N))).
% 2.30/2.59 Axiom fact_1057_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)))).
% 2.30/2.59 Axiom fact_1058_zcong__id:(forall (M:int), (((zcong M) zero_zero_int) M)).
% 2.30/2.59 Axiom fact_1059_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))).
% 2.30/2.59 Axiom fact_1060_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))))).
% 2.30/2.59 Axiom fact_1061_zcong__zpower:(forall (Z:nat) (X:int) (Y:int) (M:int), ((((zcong X) Y) M)->(((zcong ((power_power_int X) Z)) ((power_power_int Y) Z)) M))).
% 2.30/2.59 Axiom fact_1062_zcong__less__eq:(forall (M:int) (Y:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int zero_zero_int) Y)->(((ord_less_int zero_zero_int) M)->((((zcong X) Y) M)->(((ord_less_int X) M)->(((ord_less_int Y) M)->(((eq int) X) Y)))))))).
% 2.30/2.59 Axiom fact_1063_zcong__not__zero:(forall (M:int) (X:int), (((ord_less_int zero_zero_int) X)->(((ord_less_int X) M)->((((zcong X) zero_zero_int) M)->False)))).
% 2.30/2.59 Axiom fact_1064_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)))).
% 2.30/2.59 Axiom fact_1065_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)))).
% 2.30/2.59 Axiom fact_1066_Int2_Ozcong__zero:(forall (M:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_int X) M)->((((zcong X) zero_zero_int) M)->(((eq int) X) zero_zero_int))))).
% 2.30/2.59 Axiom fact_1067_zcong__zmult__prop3:(forall (Y:int) (X:int) (P_1:int), ((zprime P_1)->(((((zcong X) zero_zero_int) P_1)->False)->(((((zcong Y) zero_zero_int) P_1)->False)->((((zcong ((times_times_int X) Y)) zero_zero_int) P_1)->False))))).
% 2.30/2.59 Axiom fact_1068_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)))).
% 2.30/2.59 Axiom fact_1069_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)))).
% 2.30/2.59 Axiom fact_1070_zcong__zprime__prod__zero:(forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) B)) zero_zero_int) P_1)->((or (((zcong A) zero_zero_int) P_1)) (((zcong B) zero_zero_int) P_1)))))).
% 2.30/2.59 Axiom fact_1071_zcong__zprime__prod__zero__contra:(forall (B:int) (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->(((and ((((zcong A) zero_zero_int) P_1)->False)) ((((zcong B) zero_zero_int) P_1)->False))->((((zcong ((times_times_int A) B)) zero_zero_int) P_1)->False))))).
% 2.30/2.59 Axiom fact_1072_divides__div__not:(forall (X:nat) (Q:nat) (N:nat) (R_1:nat), ((((eq nat) X) ((plus_plus_nat ((times_times_nat Q) N)) R_1))->(((ord_less_nat zero_zero_nat) R_1)->(((ord_less_nat R_1) N)->(((dvd_dvd_nat N) X)->False))))).
% 2.30/2.59 Axiom fact_1073_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)))).
% 2.30/2.59 Axiom fact_1074_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)))).
% 2.30/2.59 Axiom fact_1075_transfer__nat__int__relations_I4_J:(forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((iff ((dvd_dvd_nat (nat_1 X)) (nat_1 Y))) ((dvd_dvd_int X) Y))))).
% 2.30/2.59 Axiom fact_1076_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)))).
% 2.30/2.59 Axiom fact_1077_nat__dvd__iff:(forall (Z:int) (M:nat), ((iff ((dvd_dvd_nat (nat_1 Z)) M)) ((and (((ord_less_eq_int zero_zero_int) Z)->((dvd_dvd_int Z) (semiri1621563631at_int M)))) ((((ord_less_eq_int zero_zero_int) Z)->False)->(((eq nat) M) zero_zero_nat))))).
% 2.30/2.59 Axiom fact_1078_zcong__neg__1__impl__ne__1:(forall (X:int) (P_1:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P_1)->((((zcong X) (number_number_of_int min)) P_1)->((((zcong X) one_one_int) P_1)->False)))).
% 2.30/2.59 Axiom fact_1079_Euler_Oaux____1:(forall (Y:int) (X:int) (P_1:int), (((((zcong X) zero_zero_int) P_1)->False)->((((zcong ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls))))) X) P_1)->(((dvd_dvd_int P_1) Y)->False)))).
% 2.30/2.59 Axiom fact_1080_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)))).
% 2.30/2.59 Axiom fact_1081_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))).
% 2.30/2.59 Axiom fact_1082__096_091s_____A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_:(((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)).
% 2.30/2.59 Axiom fact_1083__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s:((ex int) (fun (X_1:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X_1)) ((ord_less_int X_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) X_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (forall (Y_1:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y_1)) ((ord_less_int Y_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) Y_1) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))->(((eq int) Y_1) X_1)))))).
% 2.30/2.59 Axiom fact_1084_dvd_Oorder__refl:(forall (X:nat), ((dvd_dvd_nat X) X)).
% 2.30/2.59 Axiom fact_1085__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:int), (((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)))->False))->False).
% 2.30/2.59 Axiom fact_1086_dvd_Oless__asym:(forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False))).
% 2.30/2.59 Axiom fact_1087_dvd_Oless__trans:(forall (Z:nat) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) Z)) (((dvd_dvd_nat Z) Y)->False))->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False))))).
% 2.30/2.59 Axiom fact_1088_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))).
% 2.30/2.59 Axiom fact_1089_dvd_Oless__le__trans:(forall (Z:nat) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((dvd_dvd_nat Y) Z)->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False))))).
% 2.30/2.59 Axiom fact_1090_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))))).
% 2.30/2.59 Axiom fact_1091_dvd_Oless__imp__triv:(forall (P:Prop) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->P))).
% 2.30/2.59 Axiom fact_1092_dvd_Oless__imp__not__eq2:(forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) Y) X)))).
% 2.30/2.59 Axiom fact_1093_dvd_Oless__imp__not__eq:(forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) X) Y)))).
% 2.30/2.59 Axiom fact_1094_dvd_Oless__imp__not__less:(forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False))).
% 2.30/2.59 Axiom fact_1095_dvd_Oless__imp__le:(forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->((dvd_dvd_nat X) Y))).
% 2.30/2.59 Axiom fact_1096_dvd_Oless__not__sym:(forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->False))).
% 2.30/2.59 Axiom fact_1097_dvd_Oless__imp__neq:(forall (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(not (((eq nat) X) Y)))).
% 2.30/2.59 Axiom fact_1098_dvd_Ole__less__trans:(forall (Z:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((and ((dvd_dvd_nat Y) Z)) (((dvd_dvd_nat Z) Y)->False))->((and ((dvd_dvd_nat X) Z)) (((dvd_dvd_nat Z) X)->False))))).
% 2.30/2.59 Axiom fact_1099_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))))).
% 2.30/2.59 Axiom fact_1100_dvd_Oorder__trans:(forall (Z:nat) (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((dvd_dvd_nat Y) Z)->((dvd_dvd_nat X) Z)))).
% 2.30/2.59 Axiom fact_1101_dvd_Oantisym:(forall (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->(((dvd_dvd_nat Y) X)->(((eq nat) X) Y)))).
% 2.30/2.59 Axiom fact_1102_dvd__antisym:(forall (M:nat) (N:nat), (((dvd_dvd_nat M) N)->(((dvd_dvd_nat N) M)->(((eq nat) M) N)))).
% 2.30/2.60 Axiom fact_1103_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)))).
% 2.30/2.60 Axiom fact_1104_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)))).
% 2.30/2.60 Axiom fact_1105_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))))).
% 2.30/2.60 Axiom fact_1106_dvd_Ole__imp__less__or__eq:(forall (X:nat) (Y:nat), (((dvd_dvd_nat X) Y)->((or ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) (((eq nat) X) Y)))).
% 2.30/2.60 Axiom fact_1107_dvd_Oantisym__conv:(forall (Y:nat) (X:nat), (((dvd_dvd_nat Y) X)->((iff ((dvd_dvd_nat X) Y)) (((eq nat) X) Y)))).
% 2.30/2.60 Axiom fact_1108_dvd_Oeq__refl:(forall (X:nat) (Y:nat), ((((eq nat) X) Y)->((dvd_dvd_nat X) Y))).
% 2.30/2.60 Axiom fact_1109_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))))).
% 2.30/2.60 Axiom fact_1110_dvd_Oless__le__not__le:(forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False)))).
% 2.30/2.60 Axiom fact_1111_dvd_Oless__le:(forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) ((and ((dvd_dvd_nat X) Y)) (not (((eq nat) X) Y))))).
% 2.30/2.60 Axiom fact_1112_dvd_Ole__less:(forall (X:nat) (Y:nat), ((iff ((dvd_dvd_nat X) Y)) ((or ((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))) (((eq nat) X) Y)))).
% 2.30/2.60 Axiom fact_1113_dvd_Oeq__iff:(forall (X:nat) (Y:nat), ((iff (((eq nat) X) Y)) ((and ((dvd_dvd_nat X) Y)) ((dvd_dvd_nat Y) X)))).
% 2.30/2.60 Axiom fact_1114_dvd_Oless__irrefl:(forall (X:nat), (((and ((dvd_dvd_nat X) X)) (((dvd_dvd_nat X) X)->False))->False)).
% 2.30/2.60 Axiom fact_1115_divides__antisym:(forall (X:nat) (Y:nat), ((iff ((and ((dvd_dvd_nat X) Y)) ((dvd_dvd_nat Y) X))) (((eq nat) X) Y))).
% 2.30/2.60 Axiom fact_1116_neg__one__power__eq__mod__m:(forall (J: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)) ((power_power_int (number_number_of_int min)) K)) M)->(((eq int) ((power_power_int (number_number_of_int min)) J)) ((power_power_int (number_number_of_int min)) K))))).
% 2.30/2.60 Axiom fact_1117_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))).
% 2.30/2.60 Axiom fact_1118_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)))).
% 2.30/2.60 Axiom fact_1119_Legendre__def:(forall (A:int) (P_1:int), ((and ((((zcong A) zero_zero_int) P_1)->(((eq int) ((legendre A) P_1)) zero_zero_int))) (((((zcong A) zero_zero_int) P_1)->False)->((and (((quadRes P_1) A)->(((eq int) ((legendre A) P_1)) one_one_int))) ((((quadRes P_1) A)->False)->(((eq int) ((legendre A) P_1)) (number_number_of_int min))))))).
% 2.30/2.60 Axiom fact_1120_QuadRes__def:(forall (M:int) (X:int), ((iff ((quadRes M) X)) ((ex int) (fun (Y_1:int)=> (((zcong ((power_power_int Y_1) (number_number_of_nat (bit0 (bit1 pls))))) X) M))))).
% 2.30/2.60 Axiom fact_1121_Little__Fermat:(forall (X:int) (P_1:int), ((zprime P_1)->((((dvd_dvd_int P_1) X)->False)->(((zcong ((power_power_int X) (nat_1 ((minus_minus_int P_1) one_one_int)))) one_one_int) P_1)))).
% 2.30/2.60 Axiom fact_1122_zcong__square__zless:(forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P_1)->((((zcong ((times_times_int A) A)) one_one_int) P_1)->((or (((eq int) A) one_one_int)) (((eq int) A) ((minus_minus_int P_1) one_one_int)))))))).
% 2.30/2.60 Axiom fact_1123_zcong__trans:(forall (C:int) (A:int) (B:int) (M:int), ((((zcong A) B) M)->((((zcong B) C) M)->(((zcong A) C) M)))).
% 2.30/2.60 Axiom fact_1124_zcong__refl:(forall (K:int) (M:int), (((zcong K) K) M)).
% 2.30/2.60 Axiom fact_1125_zcong__sym:(forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) (((zcong B) A) M))).
% 2.30/2.60 Axiom fact_1126_IntPrimes_Ozcong__zero:(forall (A:int) (B:int), ((iff (((zcong A) B) zero_zero_int)) (((eq int) A) B))).
% 2.30/2.60 Axiom fact_1127_zcong__1:(forall (A:int) (B:int), (((zcong A) B) one_one_int)).
% 2.30/2.60 Axiom fact_1128_zcong__zmult__self:(forall (A:int) (M:int) (B:int), (((zcong ((times_times_int A) M)) ((times_times_int B) M)) M)).
% 2.30/2.60 Axiom fact_1129_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))).
% 2.30/2.60 Axiom fact_1130_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))).
% 2.30/2.60 Axiom fact_1131_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)))).
% 2.30/2.60 Axiom fact_1132_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)))).
% 2.30/2.60 Axiom fact_1133_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)))).
% 2.30/2.60 Axiom fact_1134_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)))))).
% 2.30/2.60 Axiom fact_1135_xzgcda__linear__aux1:(forall (A:int) (R_1: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_1) B))) M)) ((times_times_int ((minus_minus_int C) ((times_times_int R_1) D))) N))) ((minus_minus_int ((plus_plus_int ((times_times_int A) M)) ((times_times_int C) N))) ((times_times_int R_1) ((plus_plus_int ((times_times_int B) M)) ((times_times_int D) N)))))).
% 2.30/2.60 Axiom fact_1136_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))))))).
% 2.30/2.60 Axiom fact_1137_zcong__def:(forall (A:int) (B:int) (M:int), ((iff (((zcong A) B) M)) ((dvd_dvd_int M) ((minus_minus_int A) B)))).
% 2.30/2.60 Axiom fact_1138_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))).
% 2.30/2.60 Axiom fact_1139_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))))).
% 2.30/2.60 Axiom fact_1140_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))))))).
% 2.30/2.60 Axiom fact_1141_zprime__zdvd__zmult:(forall (N:int) (P_1:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->((zprime P_1)->(((dvd_dvd_int P_1) ((times_times_int M) N))->((or ((dvd_dvd_int P_1) M)) ((dvd_dvd_int P_1) N)))))).
% 2.30/2.60 Axiom fact_1142_zprime__def:(forall (P_1:int), ((iff (zprime P_1)) ((and ((ord_less_int one_one_int) P_1)) (forall (M_1:int), (((and ((ord_less_eq_int zero_zero_int) M_1)) ((dvd_dvd_int M_1) P_1))->((or (((eq int) M_1) one_one_int)) (((eq int) M_1) P_1))))))).
% 2.30/2.60 Axiom fact_1143_zcong__square:(forall (A:int) (P_1:int), ((zprime P_1)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) A)) one_one_int) P_1)->((or (((zcong A) one_one_int) P_1)) (((zcong A) ((minus_minus_int P_1) one_one_int)) P_1)))))).
% 2.30/2.60 Axiom fact_1144_zdiff__int__split:(forall (P:(int->Prop)) (X:nat) (Y:nat), ((iff (P (semiri1621563631at_int ((minus_minus_nat X) Y)))) ((and (((ord_less_eq_nat Y) X)->(P ((minus_minus_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))))) (((ord_less_nat X) Y)->(P zero_zero_int))))).
% 2.30/2.60 Axiom fact_1145_prime__g__5:(forall (P_1:int), ((zprime P_1)->((not (((eq int) P_1) (number_number_of_int (bit0 (bit1 pls)))))->((not (((eq int) P_1) (number_number_of_int (bit1 (bit1 pls)))))->((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P_1))))).
% 2.30/2.60 Axiom fact_1146_conj__le__cong:(forall (P_2:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_2))->((iff ((and ((ord_less_eq_int zero_zero_int) X)) P)) ((and ((ord_less_eq_int zero_zero_int) X)) P_2)))).
% 2.30/2.60 Axiom fact_1147_imp__le__cong:(forall (P_2:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_2))->((iff (((ord_less_eq_int zero_zero_int) X)->P)) (((ord_less_eq_int zero_zero_int) X)->P_2)))).
% 2.30/2.60 Axiom fact_1148_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))))).
% 2.30/2.60 Axiom fact_1149_number__of2:((ord_less_eq_int zero_zero_int) (number_number_of_int pls)).
% 2.30/2.60 Axiom fact_1150_inv__not__p__minus__1__aux:(forall (A:int) (P_1:int), ((iff (((zcong ((times_times_int A) ((minus_minus_int P_1) one_one_int))) one_one_int) P_1)) (((zcong A) ((minus_minus_int P_1) one_one_int)) P_1))).
% 2.30/2.60 Axiom fact_1151_zcong__zpower__zmult:(forall (Z:nat) (X:int) (Y:nat) (P_1:int), ((((zcong ((power_power_int X) Y)) one_one_int) P_1)->(((zcong ((power_power_int X) ((times_times_nat Y) Z))) one_one_int) P_1))).
% 2.30/2.60 Axiom fact_1152_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)))))).
% 2.30/2.60 Axiom fact_1153__096_B_Bthesis_O_A_I_B_Bs_Aw_O_Aw_A_061_Ay_A_N_As_A_K_A_I1_A_L_Aint_An:((forall (S:int) (W_1:int), (((and (((eq int) W_1) ((minus_minus_int y) ((times_times_int S) ((plus_plus_int one_one_int) (semiri1621563631at_int n)))))) ((ord_less_eq_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) (abs_abs_int W_1))) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))->False))->False).
% 2.30/2.60 Axiom fact_1154__096_B_Bthesis_O_A_I_B_Br_Av_O_Av_A_061_Ax_A_N_Ar_A_K_A_I1_A_L_Aint_An:((forall (R:int) (V:int), (((and (((eq int) V) ((minus_minus_int x) ((times_times_int R) ((plus_plus_int one_one_int) (semiri1621563631at_int n)))))) ((ord_less_eq_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) (abs_abs_int V))) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))->False))->False).
% 2.30/2.60 Axiom fact_1155_dvd__imp__le__int:(forall (D:int) (I_1:int), ((not (((eq int) I_1) zero_zero_int))->(((dvd_dvd_int D) I_1)->((ord_less_eq_int (abs_abs_int D)) (abs_abs_int I_1))))).
% 2.30/2.60 Axiom fact_1156_nat__abs__mult__distrib:(forall (W:int) (Z:int), (((eq nat) (nat_1 (abs_abs_int ((times_times_int W) Z)))) ((times_times_nat (nat_1 (abs_abs_int W))) (nat_1 (abs_abs_int Z))))).
% 2.30/2.60 Axiom fact_1157_zdvd__antisym__abs:(forall (A:int) (B:int), (((dvd_dvd_int A) B)->(((dvd_dvd_int B) A)->(((eq int) (abs_abs_int A)) (abs_abs_int B))))).
% 2.30/2.60 Axiom fact_1158_zdvd1__eq:(forall (X:int), ((iff ((dvd_dvd_int X) one_one_int)) (((eq int) (abs_abs_int X)) one_one_int))).
% 2.30/2.60 Axiom fact_1159_abs__int__eq:(forall (M:nat), (((eq int) (abs_abs_int (semiri1621563631at_int M))) (semiri1621563631at_int M))).
% 2.30/2.60 Axiom fact_1160_abs__zmult__eq__1:(forall (M:int) (N:int), ((((eq int) (abs_abs_int ((times_times_int M) N))) one_one_int)->(((eq int) (abs_abs_int M)) one_one_int))).
% 2.30/2.60 Axiom fact_1161_zero__le__zpower__abs:(forall (X:int) (N:nat), ((ord_less_eq_int zero_zero_int) ((power_power_int (abs_abs_int X)) N))).
% 2.30/2.60 Axiom fact_1162_zabs__less__one__iff:(forall (Z:int), ((iff ((ord_less_int (abs_abs_int Z)) one_one_int)) (((eq int) Z) zero_zero_int))).
% 2.30/2.60 Axiom fact_1163_abs__eq__1__iff:(forall (Z:int), ((iff (((eq int) (abs_abs_int Z)) one_one_int)) ((or (((eq int) Z) one_one_int)) (((eq int) Z) (number_number_of_int min))))).
% 2.30/2.60 Axiom fact_1164_abs__power3__distrib:(forall (X:int), (((eq int) (abs_abs_int ((power_power_int X) (number_number_of_nat (bit1 (bit1 pls)))))) ((power_power_int (abs_abs_int X)) (number_number_of_nat (bit1 (bit1 pls)))))).
% 2.30/2.60 Axiom fact_1165_zero__less__zpower__abs__iff:(forall (X:int) (N:nat), ((iff ((ord_less_int zero_zero_int) ((power_power_int (abs_abs_int X)) N))) ((or (not (((eq int) X) zero_zero_int))) (((eq nat) N) zero_zero_nat)))).
% 2.30/2.60 Axiom fact_1166_zdvd__mult__cancel1:(forall (N:int) (M:int), ((not (((eq int) M) zero_zero_int))->((iff ((dvd_dvd_int ((times_times_int M) N)) M)) (((eq int) (abs_abs_int N)) one_one_int)))).
% 2.41/2.60 Axiom fact_1167_int__dvd__iff:(forall (M:nat) (Z:int), ((iff ((dvd_dvd_int (semiri1621563631at_int M)) Z)) ((dvd_dvd_nat M) (nat_1 (abs_abs_int Z))))).
% 2.41/2.60 Axiom fact_1168_dvd__int__iff:(forall (Z:int) (M:nat), ((iff ((dvd_dvd_int Z) (semiri1621563631at_int M))) ((dvd_dvd_nat (nat_1 (abs_abs_int Z))) M))).
% 2.41/2.60 Axiom fact_1169_abs__power2__distrib:(forall (A:int), (((eq int) (abs_abs_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_int (abs_abs_int A)) (number_number_of_nat (bit0 (bit1 pls)))))).
% 2.41/2.60 Axiom fact_1170_power2__eq__iff__abs__eq:(forall (A:int) (B:int), ((iff (((eq int) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls)))))) (((eq int) (abs_abs_int A)) (abs_abs_int B)))).
% 2.41/2.60 Axiom fact_1171_power2__eq1__iff:(forall (A:int), ((((eq int) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)->(((eq int) (abs_abs_int A)) one_one_int))).
% 2.41/2.60 Axiom fact_1172_incr__lemma:(forall (Z:int) (X:int) (D:int), (((ord_less_int zero_zero_int) D)->((ord_less_int Z) ((plus_plus_int X) ((times_times_int ((plus_plus_int (abs_abs_int ((minus_minus_int X) Z))) one_one_int)) D))))).
% 2.41/2.60 Axiom fact_1173_decr__lemma:(forall (X:int) (Z:int) (D:int), (((ord_less_int zero_zero_int) D)->((ord_less_int ((minus_minus_int X) ((times_times_int ((plus_plus_int (abs_abs_int ((minus_minus_int X) Z))) one_one_int)) D))) Z))).
% 2.41/2.60 Axiom fact_1174_best__division__abs:(forall (Y:int) (X:int), (((ord_less_int zero_zero_int) X)->((ex int) (fun (N_1:int)=> ((ord_less_eq_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) (abs_abs_int ((minus_minus_int Y) ((times_times_int N_1) X))))) X))))).
% 2.41/2.60 Axiom fact_1175_decr__mult__lemma:(forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((minus_minus_int X_1) ((times_times_int K) D))))))))).
% 2.41/2.60 Axiom fact_1176_abs__add__one__not__less__self:(forall (X:real), (((ord_less_real ((plus_plus_real (abs_abs_real X)) one_one_real)) X)->False)).
% 2.41/2.60 Axiom fact_1177_abs__add__one__gt__zero:(forall (X:real), ((ord_less_real zero_zero_real) ((plus_plus_real one_one_real) (abs_abs_real X)))).
% 2.41/2.60 Axiom fact_1178_less__one__imp__sqr__less__one:(forall (X:real), (((ord_less_real (abs_abs_real X)) one_one_real)->((ord_less_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) one_one_real))).
% 2.41/2.60 Axiom fact_1179_ex__least__nat__less:(forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N)) (forall (_TPTP_I:nat), (((ord_less_eq_nat _TPTP_I) K_1)->((P _TPTP_I)->False))))) (P ((plus_plus_nat K_1) one_one_nat)))))))).
% 2.41/2.60 Axiom fact_1180_incr__mult__lemma:(forall (K:int) (P:(int->Prop)) (D:int), (((ord_less_int zero_zero_int) D)->((forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) D))))->(((ord_less_eq_int zero_zero_int) K)->(forall (X_1:int), ((P X_1)->(P ((plus_plus_int X_1) ((times_times_int K) D))))))))).
% 2.41/2.60 Axiom fact_1181_nat__less__add__iff1:(forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))).
% 2.41/2.60 Axiom fact_1182_nat__less__add__iff2:(forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff ((ord_less_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))).
% 2.41/2.60 Axiom fact_1183_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)))).
% 2.41/2.60 Axiom fact_1184_left__add__mult__distrib:(forall (I_1:nat) (U:nat) (J:nat) (K:nat), (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) ((plus_plus_nat ((times_times_nat J) U)) K))) ((plus_plus_nat ((times_times_nat ((plus_plus_nat I_1) J)) U)) K))).
% 2.41/2.61 Axiom fact_1185_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)))).
% 2.41/2.61 Axiom fact_1186_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)))).
% 2.41/2.61 Axiom fact_1187_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)))).
% 2.41/2.61 Axiom fact_1188_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)))).
% 2.41/2.61 Axiom fact_1189_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)))).
% 2.41/2.61 Axiom fact_1190_nat__le__add__iff1:(forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))).
% 2.41/2.61 Axiom fact_1191_nat__diff__add__eq1:(forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((minus_minus_nat ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))).
% 2.41/2.61 Axiom fact_1192_nat__eq__add__iff1:(forall (U:nat) (M:nat) (N:nat) (J:nat) (I_1:nat), (((ord_less_eq_nat J) I_1)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) (((eq nat) ((plus_plus_nat ((times_times_nat ((minus_minus_nat I_1) J)) U)) M)) N)))).
% 2.41/2.61 Axiom fact_1193_nat__le__add__iff2:(forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff ((ord_less_eq_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((ord_less_eq_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))).
% 2.41/2.61 Axiom fact_1194_nat__diff__add__eq2:(forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->(((eq nat) ((minus_minus_nat ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) ((minus_minus_nat M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))).
% 2.41/2.61 Axiom fact_1195_nat__eq__add__iff2:(forall (U:nat) (M:nat) (N:nat) (I_1:nat) (J:nat), (((ord_less_eq_nat I_1) J)->((iff (((eq nat) ((plus_plus_nat ((times_times_nat I_1) U)) M)) ((plus_plus_nat ((times_times_nat J) U)) N))) (((eq nat) M) ((plus_plus_nat ((times_times_nat ((minus_minus_nat J) I_1)) U)) N))))).
% 2.41/2.61 Axiom fact_1196_nat0__intermed__int__val:(forall (K:int) (F:(nat->int)) (N:nat), ((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) N)->((ord_less_eq_int (abs_abs_int ((minus_minus_int (F ((plus_plus_nat _TPTP_I) one_one_nat))) (F _TPTP_I)))) one_one_int)))->(((ord_less_eq_int (F zero_zero_nat)) K)->(((ord_less_eq_int K) (F N))->((ex nat) (fun (_TPTP_I:nat)=> ((and ((ord_less_eq_nat _TPTP_I) N)) (((eq int) (F _TPTP_I)) K)))))))).
% 2.41/2.61 Axiom fact_1197_int__val__lemma:(forall (K:int) (F:(nat->int)) (N:nat), ((forall (_TPTP_I:nat), (((ord_less_nat _TPTP_I) N)->((ord_less_eq_int (abs_abs_int ((minus_minus_int (F ((plus_plus_nat _TPTP_I) one_one_nat))) (F _TPTP_I)))) one_one_int)))->(((ord_less_eq_int (F zero_zero_nat)) K)->(((ord_less_eq_int K) (F N))->((ex nat) (fun (_TPTP_I:nat)=> ((and ((ord_less_eq_nat _TPTP_I) N)) (((eq int) (F _TPTP_I)) K)))))))).
% 2.41/2.61 Axiom help_If_1_1_If_000tc__Int__Oint_T:(forall (X:int) (Y:int), (((eq int) (((if_int True) X) Y)) X)).
% 271.17/271.45 Axiom help_If_2_1_If_000tc__Int__Oint_T:(forall (X:int) (Y:int), (((eq int) (((if_int False) X) Y)) Y)).
% 271.17/271.45 Axiom help_If_3_1_If_000tc__Int__Oint_T:(forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))).
% 271.17/271.45 Axiom help_If_1_1_If_000tc__Nat__Onat_T:(forall (X:nat) (Y:nat), (((eq nat) (((if_nat True) X) Y)) X)).
% 271.17/271.45 Axiom help_If_2_1_If_000tc__Nat__Onat_T:(forall (X:nat) (Y:nat), (((eq nat) (((if_nat False) X) Y)) Y)).
% 271.17/271.45 Axiom help_If_3_1_If_000tc__Nat__Onat_T:(forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))).
% 271.17/271.45 Trying to prove (not (((eq int) ((power_power_int ((plus_plus_int one_one_int) (semiri1621563631at_int n))) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int))
% 271.17/271.45 Found fact_263_zero__less__one:((ord_less_int zero_zero_int) one_one_int)
% 271.17/271.45 Instantiate: K:=zero_zero_int:int
% 271.17/271.45 Found fact_263_zero__less__one as proof of ((ord_less_int K) one_one_int)
% 271.17/271.45 Found fact_1007_bin__less__0__simps_I2_J:((ord_less_int min) zero_zero_int)
% 271.17/271.45 Instantiate: K:=min:int
% 271.17/271.45 Found fact_1007_bin__less__0__simps_I2_J as proof of ((ord_less_int K) zero_zero_int)
% 271.17/271.45 Found fact_1002_rel__simps_I6_J:((ord_less_int min) pls)
% 271.17/271.45 Instantiate: K:=min:int
% 271.17/271.45 Found fact_1002_rel__simps_I6_J as proof of ((ord_less_int K) pls)
% 271.17/271.45 Unexpected exception Unexpected matching of length 0 when specializating fact_1091_dvd_Oless__imp__triv:(forall (P:Prop) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->P))) with fact_838_IH:((and ((ord_less_int ((plus_plus_int one_one_int) (semiri1621563631at_int n))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) (twoSqu919416604sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))) at 3 (i=3 v=fact_838_IH:((and ((ord_less_int ((plus_plus_int one_one_int) (semiri1621563631at_int n))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) (twoSqu919416604sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))) terms[i].vartype=((and ((dvd_dvd_nat X0) Y0)) (((dvd_dvd_nat Y0) X0)->False)))
% 271.17/271.45 Traceback (most recent call last):
% 271.17/271.45 File "CASC.py", line 80, in <module>
% 271.17/271.45 proof=problem.solve()
% 271.17/271.45 File "/export/starexec/sandbox2/solver/bin/TPTP.py", line 95, in solve
% 271.17/271.45 for x in self.solveyielding():
% 271.17/271.45 File "/export/starexec/sandbox2/solver/bin/TPTP.py", line 83, in solveyielding
% 271.17/271.45 for proof in proofgen: yield proof
% 271.17/271.45 File "/export/starexec/sandbox2/solver/bin/prover.py", line 422, in proveyielding
% 271.17/271.45 results=node.look() #Can add nodes
% 271.17/271.45 File "/export/starexec/sandbox2/solver/bin/prover.py", line 1705, in look
% 271.17/271.45 dt=destructor_ass.x.boundingspecialization(self.context,assump.x,destructor.destroyingpos)
% 271.17/271.45 File "/export/starexec/sandbox2/solver/bin/kernel.py", line 1057, in boundingspecialization
% 271.17/271.45 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))
% 271.17/271.45 kernel.SpecializationError: Unexpected matching of length 0 when specializating fact_1091_dvd_Oless__imp__triv:(forall (P:Prop) (X:nat) (Y:nat), (((and ((dvd_dvd_nat X) Y)) (((dvd_dvd_nat Y) X)->False))->(((and ((dvd_dvd_nat Y) X)) (((dvd_dvd_nat X) Y)->False))->P))) with fact_838_IH:((and ((ord_less_int ((plus_plus_int one_one_int) (semiri1621563631at_int n))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) (twoSqu919416604sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))) at 3 (i=3 v=fact_838_IH:((and ((ord_less_int ((plus_plus_int one_one_int) (semiri1621563631at_int n))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) (twoSqu919416604sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int one_one_int) (semiri1621563631at_int n))))) terms[i].vartype=((and ((dvd_dvd_nat X0) Y0)) (((dvd_dvd_nat Y0) X0)->False)))
%------------------------------------------------------------------------------