%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : NUM926^2 : TPTP v7.0.0. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n036.star.cs.uiowa.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz % Memory : 32218.625MB % OS : Linux 3.10.0-693.2.2.el7.x86_64 % CPULimit : 300s % DateTime : Mon Jan 8 13:12:06 EST 2018 % Result : Timeout 300.02s % Output : None % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.04 % Problem : NUM926^2 : TPTP v7.0.0. Released v5.3.0. % 0.00/0.05 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % 0.02/0.24 % Computer : n036.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 16:04:50 CST 2018 % 0.02/0.24 % CPUTime : % 0.02/0.26 Python 2.7.13 % 0.09/0.51 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/'] % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0dbd8>, <kernel.Type object at 0x2ba153e0ddd0>) of role type named ty_ty_tc__Int__Oint % 0.09/0.51 Using role type % 0.09/0.51 Declaring int:Type % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153397710>, <kernel.Type object at 0x2ba153e0d4d0>) of role type named ty_ty_tc__Nat__Onat % 0.09/0.51 Using role type % 0.09/0.51 Declaring nat:Type % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0d680>, <kernel.Type object at 0x2ba153e0de18>) of role type named ty_ty_tc__RealDef__Oreal % 0.09/0.51 Using role type % 0.09/0.51 Declaring real:Type % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0ddd0>, <kernel.Type object at 0x2ba153e0d3b0>) of role type named ty_ty_tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J % 0.09/0.51 Using role type % 0.09/0.51 Declaring product_prod_int_int:Type % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0d5a8>, <kernel.DependentProduct object at 0x2ba153e0ddd0>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint % 0.09/0.51 Using role type % 0.09/0.51 Declaring minus_minus_int:(int->(int->int)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0d908>, <kernel.DependentProduct object at 0x2ba153e0d758>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat % 0.09/0.51 Using role type % 0.09/0.51 Declaring minus_minus_nat:(nat->(nat->nat)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0d200>, <kernel.DependentProduct object at 0x2ba153e0dd40>) of role type named sy_c_Groups_Ominus__class_Ominus_000tc__RealDef__Oreal % 0.09/0.51 Using role type % 0.09/0.51 Declaring minus_minus_real:(real->(real->real)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0ddd0>, <kernel.Constant object at 0x2ba153e0dd40>) of role type named sy_c_Groups_Oone__class_Oone_000tc__Int__Oint % 0.09/0.51 Using role type % 0.09/0.51 Declaring one_one_int:int % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0d908>, <kernel.Constant object at 0x2ba153e0dd40>) of role type named sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat % 0.09/0.51 Using role type % 0.09/0.51 Declaring one_one_nat:nat % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0d200>, <kernel.Constant object at 0x2ba153e0dd40>) of role type named sy_c_Groups_Oone__class_Oone_000tc__RealDef__Oreal % 0.09/0.51 Using role type % 0.09/0.51 Declaring one_one_real:real % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0ddd0>, <kernel.DependentProduct object at 0x2ba153e0dd88>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint % 0.09/0.51 Using role type % 0.09/0.51 Declaring plus_plus_int:(int->(int->int)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0d680>, <kernel.DependentProduct object at 0x2ba153e0db48>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat % 0.09/0.51 Using role type % 0.09/0.51 Declaring plus_plus_nat:(nat->(nat->nat)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0dd40>, <kernel.DependentProduct object at 0x2ba153e0dcb0>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__RealDef__Oreal % 0.09/0.51 Using role type % 0.09/0.51 Declaring plus_plus_real:(real->(real->real)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0dd88>, <kernel.DependentProduct object at 0x2ba153e0d908>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint % 0.09/0.51 Using role type % 0.09/0.51 Declaring times_times_int:(int->(int->int)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0db48>, <kernel.DependentProduct object at 0x2ba153e0d200>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__Nat__Onat % 0.09/0.51 Using role type % 0.09/0.51 Declaring times_times_nat:(nat->(nat->nat)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0dcb0>, <kernel.DependentProduct object at 0x2ba153e0ddd0>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__RealDef__Oreal % 0.09/0.51 Using role type % 0.09/0.51 Declaring times_times_real:(real->(real->real)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0d908>, <kernel.Constant object at 0x2ba153e0ddd0>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint % 0.09/0.51 Using role type % 0.09/0.51 Declaring zero_zero_int:int % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0db48>, <kernel.Constant object at 0x2ba153e0ddd0>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat % 0.09/0.51 Using role type % 0.09/0.51 Declaring zero_zero_nat:nat % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2ba153e0dcb0>, <kernel.Constant object at 0x2ba153e0ddd0>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__RealDef__Oreal % 0.35/0.52 Using role type % 0.35/0.52 Declaring zero_zero_real:real % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153e0d908>, <kernel.DependentProduct object at 0x2ba153e0d638>) of role type named sy_c_IntPrimes_Ozcong % 0.35/0.52 Using role type % 0.35/0.52 Declaring zcong:(int->(int->(int->Prop))) % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153e0dd40>, <kernel.DependentProduct object at 0x2ba153e0db48>) of role type named sy_c_IntPrimes_Ozprime % 0.35/0.52 Using role type % 0.35/0.52 Declaring zprime:(int->Prop) % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153e0ddd0>, <kernel.DependentProduct object at 0x2ba153e0dd88>) of role type named sy_c_Int_OBit0 % 0.35/0.52 Using role type % 0.35/0.52 Declaring bit0:(int->int) % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153e0d908>, <kernel.DependentProduct object at 0x2ba153e0d098>) of role type named sy_c_Int_OBit1 % 0.35/0.52 Using role type % 0.35/0.52 Declaring bit1:(int->int) % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153e0db48>, <kernel.Constant object at 0x2ba153e0d098>) of role type named sy_c_Int_OMin % 0.35/0.52 Using role type % 0.35/0.52 Declaring min:int % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153e0ddd0>, <kernel.Constant object at 0x2ba153e0d098>) of role type named sy_c_Int_OPls % 0.35/0.52 Using role type % 0.35/0.52 Declaring pls:int % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153e0d908>, <kernel.DependentProduct object at 0x2ba153392368>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint % 0.35/0.52 Using role type % 0.35/0.52 Declaring number_number_of_int:(int->int) % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153756b48>, <kernel.DependentProduct object at 0x2ba153392e60>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__Nat__Onat % 0.35/0.52 Using role type % 0.35/0.52 Declaring number_number_of_nat:(int->nat) % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153e0d098>, <kernel.DependentProduct object at 0x2ba153392cf8>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__RealDef__Oreal % 0.35/0.52 Using role type % 0.35/0.52 Declaring number267125858f_real:(int->real) % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153e0d5a8>, <kernel.DependentProduct object at 0x2ba153392368>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Int__Oint % 0.35/0.52 Using role type % 0.35/0.52 Declaring ord_less_int:(int->(int->Prop)) % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153e0d1b8>, <kernel.DependentProduct object at 0x2ba153392c68>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat % 0.35/0.52 Using role type % 0.35/0.52 Declaring ord_less_nat:(nat->(nat->Prop)) % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153e0d098>, <kernel.DependentProduct object at 0x2ba153392320>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__RealDef__Oreal % 0.35/0.52 Using role type % 0.35/0.52 Declaring ord_less_real:(real->(real->Prop)) % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153e0d1b8>, <kernel.DependentProduct object at 0x2ba153392a70>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Int__Oint % 0.35/0.52 Using role type % 0.35/0.52 Declaring ord_less_eq_int:(int->(int->Prop)) % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153e0d098>, <kernel.DependentProduct object at 0x2ba153392e60>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat % 0.35/0.52 Using role type % 0.35/0.52 Declaring ord_less_eq_nat:(nat->(nat->Prop)) % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153e0d5a8>, <kernel.DependentProduct object at 0x2ba153392368>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__RealDef__Oreal % 0.35/0.52 Using role type % 0.35/0.52 Declaring ord_less_eq_real:(real->(real->Prop)) % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153e0d5a8>, <kernel.DependentProduct object at 0x2ba153392128>) of role type named sy_c_Power_Opower__class_Opower_000tc__Int__Oint % 0.35/0.52 Using role type % 0.35/0.52 Declaring power_power_int:(int->(nat->int)) % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153392e60>, <kernel.DependentProduct object at 0x2ba153392c68>) of role type named sy_c_Power_Opower__class_Opower_000tc__Nat__Onat % 0.35/0.52 Using role type % 0.35/0.52 Declaring power_power_nat:(nat->(nat->nat)) % 0.35/0.52 FOF formula (<kernel.Constant object at 0x2ba153392368>, <kernel.DependentProduct object at 0x2ba153392488>) of role type named sy_c_Power_Opower__class_Opower_000tc__RealDef__Oreal % 0.35/0.53 Using role type % 0.35/0.53 Declaring power_power_real:(real->(nat->real)) % 0.35/0.53 FOF formula (<kernel.Constant object at 0x2ba153392128>, <kernel.DependentProduct object at 0x2ba153392320>) of role type named sy_c_Product__Type_OPair_000tc__Int__Oint_000tc__Int__Oint % 0.35/0.53 Using role type % 0.35/0.53 Declaring product_Pair_int_int:(int->(int->product_prod_int_int)) % 0.35/0.53 FOF formula (<kernel.Constant object at 0x2ba153392c68>, <kernel.DependentProduct object at 0x2ba153392a70>) of role type named sy_c_Residues_OLegendre % 0.35/0.53 Using role type % 0.35/0.53 Declaring legendre:(int->(int->int)) % 0.35/0.53 FOF formula (<kernel.Constant object at 0x2ba153392488>, <kernel.DependentProduct object at 0x2ba1533920e0>) of role type named sy_c_Residues_OQuadRes % 0.35/0.53 Using role type % 0.35/0.53 Declaring quadRes:(int->(int->Prop)) % 0.35/0.53 FOF formula (<kernel.Constant object at 0x2ba153392320>, <kernel.DependentProduct object at 0x2ba153392cf8>) of role type named sy_c_Rings_Odvd__class_Odvd_000tc__Int__Oint % 0.35/0.53 Using role type % 0.35/0.53 Declaring dvd_dvd_int:(int->(int->Prop)) % 0.35/0.53 FOF formula (<kernel.Constant object at 0x2ba153392a70>, <kernel.DependentProduct object at 0x2ba153392128>) of role type named sy_c_Rings_Odvd__class_Odvd_000tc__Nat__Onat % 0.35/0.53 Using role type % 0.35/0.53 Declaring dvd_dvd_nat:(nat->(nat->Prop)) % 0.35/0.53 FOF formula (<kernel.Constant object at 0x2ba1533920e0>, <kernel.DependentProduct object at 0x2ba153392c68>) of role type named sy_c_Rings_Odvd__class_Odvd_000tc__RealDef__Oreal % 0.35/0.53 Using role type % 0.35/0.53 Declaring dvd_dvd_real:(real->(real->Prop)) % 0.35/0.53 FOF formula (<kernel.Constant object at 0x2ba153392cf8>, <kernel.DependentProduct object at 0x2ba153392a28>) of role type named sy_c_TwoSquares__Mirabelle__hgbmwyaznu_Ois__sum2sq % 0.35/0.53 Using role type % 0.35/0.53 Declaring twoSqu362149276sum2sq:(int->Prop) % 0.35/0.53 FOF formula (<kernel.Constant object at 0x2ba153392128>, <kernel.DependentProduct object at 0x2ba153392098>) of role type named sy_c_TwoSquares__Mirabelle__hgbmwyaznu_Osum2sq % 0.35/0.53 Using role type % 0.35/0.53 Declaring twoSqu1078207634sum2sq:(product_prod_int_int->int) % 0.35/0.53 FOF formula (<kernel.Constant object at 0x2ba153392c68>, <kernel.Constant object at 0x2ba153392098>) of role type named sy_v_m % 0.35/0.53 Using role type % 0.35/0.53 Declaring m:int % 0.35/0.53 FOF formula (<kernel.Constant object at 0x2ba153392cf8>, <kernel.Constant object at 0x2ba153392098>) of role type named sy_v_s1____ % 0.35/0.53 Using role type % 0.35/0.53 Declaring s1:int % 0.35/0.53 FOF formula (<kernel.Constant object at 0x2ba153392128>, <kernel.Constant object at 0x2ba153392098>) of role type named sy_v_s____ % 0.35/0.53 Using role type % 0.35/0.53 Declaring s:int % 0.35/0.53 FOF formula (<kernel.Constant object at 0x2ba153392c68>, <kernel.Constant object at 0x2ba153392098>) of role type named sy_v_t____ % 0.35/0.53 Using role type % 0.35/0.53 Declaring t:int % 0.35/0.53 FOF formula ((ord_less_eq_int one_one_int) t) of role axiom named fact_0_tpos % 0.35/0.53 A new axiom: ((ord_less_eq_int one_one_int) t) % 0.35/0.53 FOF formula ((((eq int) t) one_one_int)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))) of role axiom named fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06 % 0.35/0.53 A new axiom: ((((eq int) t) one_one_int)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))) % 0.35/0.53 FOF formula (((ord_less_int one_one_int) t)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))) of role axiom named fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06 % 0.35/0.53 A new axiom: (((ord_less_int one_one_int) t)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))) % 0.35/0.55 FOF formula ((ord_less_int t) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) of role axiom named fact_3_t__l__p % 0.35/0.55 A new axiom: ((ord_less_int t) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) % 0.35/0.55 FOF formula (zprime ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) of role axiom named fact_4_p % 0.35/0.55 A new axiom: (zprime ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) % 0.35/0.55 FOF formula (((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)) of role axiom named fact_5_t % 0.35/0.55 A new axiom: (((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)) % 0.35/0.55 FOF formula (twoSqu362149276sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)) of role axiom named fact_6_qf1pt % 0.35/0.55 A new axiom: (twoSqu362149276sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)) % 0.35/0.55 FOF formula (forall (A:int) (B_1:int), (((eq int) ((power_power_int ((plus_plus_int A) B_1)) (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_1))) ((power_power_int B_1) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_7_zadd__power2 % 0.35/0.55 A new axiom: (forall (A:int) (B_1:int), (((eq int) ((power_power_int ((plus_plus_int A) B_1)) (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_1))) ((power_power_int B_1) (number_number_of_nat (bit0 (bit1 pls))))))) % 0.35/0.55 FOF formula (forall (A:int) (B_1:int), (((eq int) ((power_power_int ((plus_plus_int A) B_1)) (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_1))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) A)) ((power_power_int B_1) (number_number_of_nat (bit0 (bit1 pls))))))) ((power_power_int B_1) (number_number_of_nat (bit1 (bit1 pls))))))) of role axiom named fact_8_zadd__power3 % 0.35/0.55 A new axiom: (forall (A:int) (B_1:int), (((eq int) ((power_power_int ((plus_plus_int A) B_1)) (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_1))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) A)) ((power_power_int B_1) (number_number_of_nat (bit0 (bit1 pls))))))) ((power_power_int B_1) (number_number_of_nat (bit1 (bit1 pls))))))) % 0.35/0.55 FOF formula (forall (X_38:real) (Y_30:real), (((eq real) ((power_power_real ((plus_plus_real X_38) Y_30)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X_38) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_30) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_38)) Y_30)))) of role axiom named fact_9_power2__sum % 0.35/0.56 A new axiom: (forall (X_38:real) (Y_30:real), (((eq real) ((power_power_real ((plus_plus_real X_38) Y_30)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X_38) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_30) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_38)) Y_30)))) % 0.35/0.56 FOF formula (forall (X_38:nat) (Y_30:nat), (((eq nat) ((power_power_nat ((plus_plus_nat X_38) Y_30)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat ((plus_plus_nat ((power_power_nat X_38) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_30) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) X_38)) Y_30)))) of role axiom named fact_10_power2__sum % 0.35/0.56 A new axiom: (forall (X_38:nat) (Y_30:nat), (((eq nat) ((power_power_nat ((plus_plus_nat X_38) Y_30)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat ((plus_plus_nat ((power_power_nat X_38) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_30) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) X_38)) Y_30)))) % 0.35/0.56 FOF formula (forall (X_38:int) (Y_30:int), (((eq int) ((power_power_int ((plus_plus_int X_38) Y_30)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int X_38) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_30) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) X_38)) Y_30)))) of role axiom named fact_11_power2__sum % 0.35/0.56 A new axiom: (forall (X_38:int) (Y_30:int), (((eq int) ((power_power_int ((plus_plus_int X_38) Y_30)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int X_38) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_30) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) X_38)) Y_30)))) % 0.35/0.56 FOF formula (forall (W_18:int), (((eq nat) ((power_power_nat (number_number_of_nat W_18)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat (number_number_of_nat W_18)) (number_number_of_nat W_18)))) of role axiom named fact_12_power2__eq__square__number__of % 0.35/0.56 A new axiom: (forall (W_18:int), (((eq nat) ((power_power_nat (number_number_of_nat W_18)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat (number_number_of_nat W_18)) (number_number_of_nat W_18)))) % 0.35/0.56 FOF formula (forall (W_18:int), (((eq real) ((power_power_real (number267125858f_real W_18)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real (number267125858f_real W_18)) (number267125858f_real W_18)))) of role axiom named fact_13_power2__eq__square__number__of % 0.35/0.56 A new axiom: (forall (W_18:int), (((eq real) ((power_power_real (number267125858f_real W_18)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real (number267125858f_real W_18)) (number267125858f_real W_18)))) % 0.35/0.56 FOF formula (forall (W_18:int), (((eq int) ((power_power_int (number_number_of_int W_18)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int (number_number_of_int W_18)) (number_number_of_int W_18)))) of role axiom named fact_14_power2__eq__square__number__of % 0.35/0.56 A new axiom: (forall (W_18:int), (((eq int) ((power_power_int (number_number_of_int W_18)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int (number_number_of_int W_18)) (number_number_of_int W_18)))) % 0.35/0.56 FOF formula (forall (A:int), (((eq int) ((times_times_int A) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_int A) (number_number_of_nat (bit1 (bit1 pls)))))) of role axiom named fact_15_cube__square % 0.35/0.56 A new axiom: (forall (A:int), (((eq int) ((times_times_int A) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_int A) (number_number_of_nat (bit1 (bit1 pls)))))) % 0.35/0.58 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_16_one__power2 % 0.35/0.58 A new axiom: (((eq real) ((power_power_real one_one_real) (number_number_of_nat (bit0 (bit1 pls))))) one_one_real) % 0.35/0.58 FOF formula (((eq nat) ((power_power_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls))))) one_one_nat) of role axiom named fact_17_one__power2 % 0.35/0.58 A new axiom: (((eq nat) ((power_power_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls))))) one_one_nat) % 0.35/0.58 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_18_one__power2 % 0.35/0.58 A new axiom: (((eq int) ((power_power_int one_one_int) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int) % 0.35/0.58 FOF formula (forall (X_37:nat), (((eq nat) ((times_times_nat X_37) X_37)) ((power_power_nat X_37) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J % 0.35/0.58 A new axiom: (forall (X_37:nat), (((eq nat) ((times_times_nat X_37) X_37)) ((power_power_nat X_37) (number_number_of_nat (bit0 (bit1 pls)))))) % 0.35/0.58 FOF formula (forall (X_37:real), (((eq real) ((times_times_real X_37) X_37)) ((power_power_real X_37) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J % 0.35/0.58 A new axiom: (forall (X_37:real), (((eq real) ((times_times_real X_37) X_37)) ((power_power_real X_37) (number_number_of_nat (bit0 (bit1 pls)))))) % 0.35/0.58 FOF formula (forall (X_37:int), (((eq int) ((times_times_int X_37) X_37)) ((power_power_int X_37) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J % 0.35/0.58 A new axiom: (forall (X_37:int), (((eq int) ((times_times_int X_37) X_37)) ((power_power_int X_37) (number_number_of_nat (bit0 (bit1 pls)))))) % 0.35/0.58 FOF formula (forall (A_65:nat), (((eq nat) ((power_power_nat A_65) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat A_65) A_65))) of role axiom named fact_22_power2__eq__square % 0.35/0.58 A new axiom: (forall (A_65:nat), (((eq nat) ((power_power_nat A_65) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat A_65) A_65))) % 0.35/0.58 FOF formula (forall (A_65:real), (((eq real) ((power_power_real A_65) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real A_65) A_65))) of role axiom named fact_23_power2__eq__square % 0.35/0.58 A new axiom: (forall (A_65:real), (((eq real) ((power_power_real A_65) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real A_65) A_65))) % 0.35/0.58 FOF formula (forall (A_65:int), (((eq int) ((power_power_int A_65) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int A_65) A_65))) of role axiom named fact_24_power2__eq__square % 0.35/0.58 A new axiom: (forall (A_65:int), (((eq int) ((power_power_int A_65) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int A_65) A_65))) % 0.35/0.58 FOF formula (forall (X_36:nat) (N_39:nat), (((eq nat) ((power_power_nat X_36) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_39))) ((times_times_nat ((power_power_nat X_36) N_39)) ((power_power_nat X_36) N_39)))) of role axiom named fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J % 0.35/0.58 A new axiom: (forall (X_36:nat) (N_39:nat), (((eq nat) ((power_power_nat X_36) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_39))) ((times_times_nat ((power_power_nat X_36) N_39)) ((power_power_nat X_36) N_39)))) % 0.35/0.58 FOF formula (forall (X_36:real) (N_39:nat), (((eq real) ((power_power_real X_36) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_39))) ((times_times_real ((power_power_real X_36) N_39)) ((power_power_real X_36) N_39)))) of role axiom named fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J % 0.35/0.58 A new axiom: (forall (X_36:real) (N_39:nat), (((eq real) ((power_power_real X_36) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_39))) ((times_times_real ((power_power_real X_36) N_39)) ((power_power_real X_36) N_39)))) % 0.35/0.58 FOF formula (forall (X_36:int) (N_39:nat), (((eq int) ((power_power_int X_36) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_39))) ((times_times_int ((power_power_int X_36) N_39)) ((power_power_int X_36) N_39)))) of role axiom named fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J % 0.35/0.59 A new axiom: (forall (X_36:int) (N_39:nat), (((eq int) ((power_power_int X_36) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_39))) ((times_times_int ((power_power_int X_36) N_39)) ((power_power_int X_36) N_39)))) % 0.35/0.59 FOF formula (forall (W_17:int), (((eq real) ((plus_plus_real one_one_real) (number267125858f_real W_17))) (number267125858f_real ((plus_plus_int (bit1 pls)) W_17)))) of role axiom named fact_28_add__special_I2_J % 0.35/0.59 A new axiom: (forall (W_17:int), (((eq real) ((plus_plus_real one_one_real) (number267125858f_real W_17))) (number267125858f_real ((plus_plus_int (bit1 pls)) W_17)))) % 0.35/0.59 FOF formula (forall (W_17:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_17))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_17)))) of role axiom named fact_29_add__special_I2_J % 0.35/0.59 A new axiom: (forall (W_17:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_17))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_17)))) % 0.35/0.59 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_30_add__special_I3_J % 0.35/0.59 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))))) % 0.35/0.59 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_31_add__special_I3_J % 0.35/0.59 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))))) % 0.35/0.59 FOF formula (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))) of role axiom named fact_32_one__add__one__is__two % 0.35/0.59 A new axiom: (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))) % 0.35/0.59 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_33_one__add__one__is__two % 0.35/0.59 A new axiom: (((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))) % 0.35/0.59 FOF formula ((forall (T_1:int), (not (((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) T_1))))->False) of role axiom named fact_34__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_ % 0.35/0.59 A new axiom: ((forall (T_1:int), (not (((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) T_1))))->False) % 0.35/0.59 FOF formula (forall (W:int), ((ord_less_eq_int W) W)) of role axiom named fact_35_zle__refl % 0.35/0.59 A new axiom: (forall (W:int), ((ord_less_eq_int W) W)) % 0.35/0.59 FOF formula (forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z))) of role axiom named fact_36_zle__linear % 0.35/0.59 A new axiom: (forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z))) % 0.35/0.59 FOF formula (forall (Z:int) (W:int), ((iff ((ord_less_int Z) W)) ((and ((ord_less_eq_int Z) W)) (not (((eq int) Z) W))))) of role axiom named fact_37_zless__le % 0.35/0.59 A new axiom: (forall (Z:int) (W:int), ((iff ((ord_less_int Z) W)) ((and ((ord_less_eq_int Z) W)) (not (((eq int) Z) W))))) % 0.35/0.59 FOF formula (forall (X_1:int) (Y_1:int), ((or ((or ((ord_less_int X_1) Y_1)) (((eq int) X_1) Y_1))) ((ord_less_int Y_1) X_1))) of role axiom named fact_38_zless__linear % 0.35/0.59 A new axiom: (forall (X_1:int) (Y_1:int), ((or ((or ((ord_less_int X_1) Y_1)) (((eq int) X_1) Y_1))) ((ord_less_int Y_1) X_1))) % 0.43/0.61 FOF formula (forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_eq_int _TPTP_I) J)->(((ord_less_eq_int J) K)->((ord_less_eq_int _TPTP_I) K)))) of role axiom named fact_39_zle__trans % 0.43/0.61 A new axiom: (forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_eq_int _TPTP_I) J)->(((ord_less_eq_int J) K)->((ord_less_eq_int _TPTP_I) K)))) % 0.43/0.61 FOF formula (forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W)))) of role axiom named fact_40_zle__antisym % 0.43/0.61 A new axiom: (forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W)))) % 0.43/0.61 FOF formula (forall (X_35:nat) (P_2:nat) (Q_4:nat), (((eq nat) ((power_power_nat ((power_power_nat X_35) P_2)) Q_4)) ((power_power_nat X_35) ((times_times_nat P_2) Q_4)))) of role axiom named fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J % 0.43/0.61 A new axiom: (forall (X_35:nat) (P_2:nat) (Q_4:nat), (((eq nat) ((power_power_nat ((power_power_nat X_35) P_2)) Q_4)) ((power_power_nat X_35) ((times_times_nat P_2) Q_4)))) % 0.43/0.61 FOF formula (forall (X_35:real) (P_2:nat) (Q_4:nat), (((eq real) ((power_power_real ((power_power_real X_35) P_2)) Q_4)) ((power_power_real X_35) ((times_times_nat P_2) Q_4)))) of role axiom named fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J % 0.43/0.61 A new axiom: (forall (X_35:real) (P_2:nat) (Q_4:nat), (((eq real) ((power_power_real ((power_power_real X_35) P_2)) Q_4)) ((power_power_real X_35) ((times_times_nat P_2) Q_4)))) % 0.43/0.61 FOF formula (forall (X_35:int) (P_2:nat) (Q_4:nat), (((eq int) ((power_power_int ((power_power_int X_35) P_2)) Q_4)) ((power_power_int X_35) ((times_times_nat P_2) Q_4)))) of role axiom named fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J % 0.43/0.61 A new axiom: (forall (X_35:int) (P_2:nat) (Q_4:nat), (((eq int) ((power_power_int ((power_power_int X_35) P_2)) Q_4)) ((power_power_int X_35) ((times_times_nat P_2) Q_4)))) % 0.43/0.61 FOF formula (forall (X_34:nat), (((eq nat) ((power_power_nat X_34) one_one_nat)) X_34)) of role axiom named fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J % 0.43/0.61 A new axiom: (forall (X_34:nat), (((eq nat) ((power_power_nat X_34) one_one_nat)) X_34)) % 0.43/0.61 FOF formula (forall (X_34:real), (((eq real) ((power_power_real X_34) one_one_nat)) X_34)) of role axiom named fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J % 0.43/0.61 A new axiom: (forall (X_34:real), (((eq real) ((power_power_real X_34) one_one_nat)) X_34)) % 0.43/0.61 FOF formula (forall (X_34:int), (((eq int) ((power_power_int X_34) one_one_nat)) X_34)) of role axiom named fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J % 0.43/0.61 A new axiom: (forall (X_34:int), (((eq int) ((power_power_int X_34) one_one_nat)) X_34)) % 0.43/0.61 FOF formula (forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int ((power_power_int X_1) Y_1)) Z)) ((power_power_int X_1) ((times_times_nat Y_1) Z)))) of role axiom named fact_47_zpower__zpower % 0.43/0.61 A new axiom: (forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int ((power_power_int X_1) Y_1)) Z)) ((power_power_int X_1) ((times_times_nat Y_1) Z)))) % 0.43/0.61 FOF formula (forall (V_15:int) (W_16:int), ((iff ((ord_less_eq_real (number267125858f_real V_15)) (number267125858f_real W_16))) (((ord_less_real (number267125858f_real W_16)) (number267125858f_real V_15))->False))) of role axiom named fact_48_le__number__of__eq__not__less % 0.43/0.61 A new axiom: (forall (V_15:int) (W_16:int), ((iff ((ord_less_eq_real (number267125858f_real V_15)) (number267125858f_real W_16))) (((ord_less_real (number267125858f_real W_16)) (number267125858f_real V_15))->False))) % 0.43/0.61 FOF formula (forall (V_15:int) (W_16:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_15)) (number_number_of_nat W_16))) (((ord_less_nat (number_number_of_nat W_16)) (number_number_of_nat V_15))->False))) of role axiom named fact_49_le__number__of__eq__not__less % 0.43/0.61 A new axiom: (forall (V_15:int) (W_16:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_15)) (number_number_of_nat W_16))) (((ord_less_nat (number_number_of_nat W_16)) (number_number_of_nat V_15))->False))) % 0.43/0.62 FOF formula (forall (V_15:int) (W_16:int), ((iff ((ord_less_eq_int (number_number_of_int V_15)) (number_number_of_int W_16))) (((ord_less_int (number_number_of_int W_16)) (number_number_of_int V_15))->False))) of role axiom named fact_50_le__number__of__eq__not__less % 0.43/0.62 A new axiom: (forall (V_15:int) (W_16:int), ((iff ((ord_less_eq_int (number_number_of_int V_15)) (number_number_of_int W_16))) (((ord_less_int (number_number_of_int W_16)) (number_number_of_int V_15))->False))) % 0.43/0.62 FOF formula (forall (X_33:int) (Y_29:int), ((iff ((ord_less_real (number267125858f_real X_33)) (number267125858f_real Y_29))) ((ord_less_int X_33) Y_29))) of role axiom named fact_51_less__number__of % 0.43/0.62 A new axiom: (forall (X_33:int) (Y_29:int), ((iff ((ord_less_real (number267125858f_real X_33)) (number267125858f_real Y_29))) ((ord_less_int X_33) Y_29))) % 0.43/0.62 FOF formula (forall (X_33:int) (Y_29:int), ((iff ((ord_less_int (number_number_of_int X_33)) (number_number_of_int Y_29))) ((ord_less_int X_33) Y_29))) of role axiom named fact_52_less__number__of % 0.43/0.62 A new axiom: (forall (X_33:int) (Y_29:int), ((iff ((ord_less_int (number_number_of_int X_33)) (number_number_of_int Y_29))) ((ord_less_int X_33) Y_29))) % 0.43/0.62 FOF formula (forall (X_32:int) (Y_28:int), ((iff ((ord_less_eq_real (number267125858f_real X_32)) (number267125858f_real Y_28))) ((ord_less_eq_int X_32) Y_28))) of role axiom named fact_53_le__number__of % 0.43/0.62 A new axiom: (forall (X_32:int) (Y_28:int), ((iff ((ord_less_eq_real (number267125858f_real X_32)) (number267125858f_real Y_28))) ((ord_less_eq_int X_32) Y_28))) % 0.43/0.62 FOF formula (forall (X_32:int) (Y_28:int), ((iff ((ord_less_eq_int (number_number_of_int X_32)) (number_number_of_int Y_28))) ((ord_less_eq_int X_32) Y_28))) of role axiom named fact_54_le__number__of % 0.43/0.62 A new axiom: (forall (X_32:int) (Y_28:int), ((iff ((ord_less_eq_int (number_number_of_int X_32)) (number_number_of_int Y_28))) ((ord_less_eq_int X_32) Y_28))) % 0.43/0.62 FOF formula (forall (Z_9:int) (Z:int) (W_15:int) (W:int), (((ord_less_int W_15) W)->(((ord_less_eq_int Z_9) Z)->((ord_less_int ((plus_plus_int W_15) Z_9)) ((plus_plus_int W) Z))))) of role axiom named fact_55_zadd__zless__mono % 0.43/0.62 A new axiom: (forall (Z_9:int) (Z:int) (W_15:int) (W:int), (((ord_less_int W_15) W)->(((ord_less_eq_int Z_9) Z)->((ord_less_int ((plus_plus_int W_15) Z_9)) ((plus_plus_int W) Z))))) % 0.43/0.62 FOF formula (forall (X_31:nat) (P_1:nat) (Q_3:nat), (((eq nat) ((times_times_nat ((power_power_nat X_31) P_1)) ((power_power_nat X_31) Q_3))) ((power_power_nat X_31) ((plus_plus_nat P_1) Q_3)))) of role axiom named fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J % 0.43/0.62 A new axiom: (forall (X_31:nat) (P_1:nat) (Q_3:nat), (((eq nat) ((times_times_nat ((power_power_nat X_31) P_1)) ((power_power_nat X_31) Q_3))) ((power_power_nat X_31) ((plus_plus_nat P_1) Q_3)))) % 0.43/0.62 FOF formula (forall (X_31:real) (P_1:nat) (Q_3:nat), (((eq real) ((times_times_real ((power_power_real X_31) P_1)) ((power_power_real X_31) Q_3))) ((power_power_real X_31) ((plus_plus_nat P_1) Q_3)))) of role axiom named fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J % 0.43/0.62 A new axiom: (forall (X_31:real) (P_1:nat) (Q_3:nat), (((eq real) ((times_times_real ((power_power_real X_31) P_1)) ((power_power_real X_31) Q_3))) ((power_power_real X_31) ((plus_plus_nat P_1) Q_3)))) % 0.43/0.62 FOF formula (forall (X_31:int) (P_1:nat) (Q_3:nat), (((eq int) ((times_times_int ((power_power_int X_31) P_1)) ((power_power_int X_31) Q_3))) ((power_power_int X_31) ((plus_plus_nat P_1) Q_3)))) of role axiom named fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J % 0.43/0.62 A new axiom: (forall (X_31:int) (P_1:nat) (Q_3:nat), (((eq int) ((times_times_int ((power_power_int X_31) P_1)) ((power_power_int X_31) Q_3))) ((power_power_int X_31) ((plus_plus_nat P_1) Q_3)))) % 0.43/0.62 FOF formula (forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int X_1) ((plus_plus_nat Y_1) Z))) ((times_times_int ((power_power_int X_1) Y_1)) ((power_power_int X_1) Z)))) of role axiom named fact_59_zpower__zadd__distrib % 0.43/0.62 A new axiom: (forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int X_1) ((plus_plus_nat Y_1) Z))) ((times_times_int ((power_power_int X_1) Y_1)) ((power_power_int X_1) Z)))) % 0.43/0.64 FOF formula (forall (Z:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z)) ((plus_plus_nat Z) Z))) of role axiom named fact_60_nat__mult__2 % 0.43/0.64 A new axiom: (forall (Z:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z)) ((plus_plus_nat Z) Z))) % 0.43/0.64 FOF formula (forall (Z:nat), (((eq nat) ((times_times_nat Z) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z) Z))) of role axiom named fact_61_nat__mult__2__right % 0.43/0.64 A new axiom: (forall (Z:nat), (((eq nat) ((times_times_nat Z) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z) Z))) % 0.43/0.64 FOF formula (((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))) of role axiom named fact_62_nat__1__add__1 % 0.43/0.64 A new axiom: (((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))) % 0.43/0.64 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2))) of role axiom named fact_63_less__int__code_I16_J % 0.43/0.64 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2))) % 0.43/0.64 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L))) of role axiom named fact_64_rel__simps_I17_J % 0.43/0.64 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L))) % 0.43/0.64 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))) of role axiom named fact_65_less__eq__int__code_I16_J % 0.43/0.64 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))) % 0.43/0.64 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit1 L))) ((ord_less_eq_int K) L))) of role axiom named fact_66_rel__simps_I34_J % 0.43/0.64 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit1 L))) ((ord_less_eq_int K) L))) % 0.43/0.64 FOF formula (((ord_less_int pls) pls)->False) of role axiom named fact_67_rel__simps_I2_J % 0.43/0.64 A new axiom: (((ord_less_int pls) pls)->False) % 0.43/0.64 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit0 K2))) ((ord_less_int K1) K2))) of role axiom named fact_68_less__int__code_I13_J % 0.43/0.64 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit0 K2))) ((ord_less_int K1) K2))) % 0.43/0.64 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit0 L))) ((ord_less_int K) L))) of role axiom named fact_69_rel__simps_I14_J % 0.43/0.64 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit0 L))) ((ord_less_int K) L))) % 0.43/0.64 FOF formula ((ord_less_eq_int pls) pls) of role axiom named fact_70_rel__simps_I19_J % 0.43/0.64 A new axiom: ((ord_less_eq_int pls) pls) % 0.43/0.64 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit0 K2))) ((ord_less_eq_int K1) K2))) of role axiom named fact_71_less__eq__int__code_I13_J % 0.43/0.64 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit0 K2))) ((ord_less_eq_int K1) K2))) % 0.43/0.64 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit0 L))) ((ord_less_eq_int K) L))) of role axiom named fact_72_rel__simps_I31_J % 0.43/0.64 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit0 L))) ((ord_less_eq_int K) L))) % 0.43/0.64 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_int K) L))) of role axiom named fact_73_less__number__of__int__code % 0.43/0.64 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_int K) L))) % 0.43/0.64 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_eq_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_eq_int K) L))) of role axiom named fact_74_less__eq__number__of__int__code % 0.43/0.64 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_eq_int K) L))) % 0.43/0.64 FOF formula (forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_int _TPTP_I) J)->((ord_less_int ((plus_plus_int _TPTP_I) K)) ((plus_plus_int J) K)))) of role axiom named fact_75_zadd__strict__right__mono % 0.43/0.66 A new axiom: (forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_int _TPTP_I) J)->((ord_less_int ((plus_plus_int _TPTP_I) K)) ((plus_plus_int J) K)))) % 0.43/0.66 FOF formula (forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_eq_int _TPTP_I) J)->((ord_less_eq_int ((plus_plus_int K) _TPTP_I)) ((plus_plus_int K) J)))) of role axiom named fact_76_zadd__left__mono % 0.43/0.66 A new axiom: (forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_eq_int _TPTP_I) J)->((ord_less_eq_int ((plus_plus_int K) _TPTP_I)) ((plus_plus_int K) J)))) % 0.43/0.66 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_77_add__nat__number__of % 0.43/0.66 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)))))))) % 0.43/0.66 FOF formula (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat) of role axiom named fact_78_nat__numeral__1__eq__1 % 0.43/0.66 A new axiom: (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat) % 0.43/0.66 FOF formula (((eq nat) one_one_nat) (number_number_of_nat (bit1 pls))) of role axiom named fact_79_Numeral1__eq1__nat % 0.43/0.66 A new axiom: (((eq nat) one_one_nat) (number_number_of_nat (bit1 pls))) % 0.43/0.66 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_80_rel__simps_I29_J % 0.43/0.66 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls))) % 0.43/0.66 FOF formula (forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_81_rel__simps_I5_J % 0.43/0.66 A new axiom: (forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) % 0.43/0.66 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2))) of role axiom named fact_82_less__eq__int__code_I15_J % 0.43/0.66 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2))) % 0.43/0.66 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))) of role axiom named fact_83_rel__simps_I33_J % 0.43/0.66 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))) % 0.43/0.66 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))) of role axiom named fact_84_less__int__code_I14_J % 0.43/0.66 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))) % 0.43/0.66 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))) of role axiom named fact_85_rel__simps_I15_J % 0.43/0.66 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))) % 0.43/0.66 FOF formula (forall (W:int) (Z:int), (((ord_less_int W) Z)->((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z))) of role axiom named fact_86_zless__imp__add1__zle % 0.43/0.66 A new axiom: (forall (W:int) (Z:int), (((ord_less_int W) Z)->((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z))) % 0.43/0.66 FOF formula (forall (W:int) (Z:int), ((iff ((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z)) ((ord_less_int W) Z))) of role axiom named fact_87_add1__zle__eq % 0.43/0.68 A new axiom: (forall (W:int) (Z:int), ((iff ((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z)) ((ord_less_int W) Z))) % 0.43/0.68 FOF formula (forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((ord_less_eq_int W) Z))) of role axiom named fact_88_zle__add1__eq__le % 0.43/0.68 A new axiom: (forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((ord_less_eq_int W) Z))) % 0.43/0.68 FOF formula (zprime (number_number_of_int (bit0 (bit1 pls)))) of role axiom named fact_89_zprime__2 % 0.43/0.68 A new axiom: (zprime (number_number_of_int (bit0 (bit1 pls)))) % 0.43/0.68 FOF formula (forall (Y_1:int) (X_1:int), ((twoSqu362149276sum2sq X_1)->((twoSqu362149276sum2sq Y_1)->(twoSqu362149276sum2sq ((times_times_int X_1) Y_1))))) of role axiom named fact_90_is__mult__sum2sq % 0.43/0.68 A new axiom: (forall (Y_1:int) (X_1:int), ((twoSqu362149276sum2sq X_1)->((twoSqu362149276sum2sq Y_1)->(twoSqu362149276sum2sq ((times_times_int X_1) Y_1))))) % 0.43/0.68 FOF formula (forall (Lx_6:real) (Ly_4:real) (Rx_6:real) (Ry_4:real), (((eq real) ((times_times_real ((times_times_real Lx_6) Ly_4)) ((times_times_real Rx_6) Ry_4))) ((times_times_real ((times_times_real Lx_6) Rx_6)) ((times_times_real Ly_4) Ry_4)))) of role axiom named fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J % 0.43/0.68 A new axiom: (forall (Lx_6:real) (Ly_4:real) (Rx_6:real) (Ry_4:real), (((eq real) ((times_times_real ((times_times_real Lx_6) Ly_4)) ((times_times_real Rx_6) Ry_4))) ((times_times_real ((times_times_real Lx_6) Rx_6)) ((times_times_real Ly_4) Ry_4)))) % 0.43/0.68 FOF formula (forall (Lx_6:nat) (Ly_4:nat) (Rx_6:nat) (Ry_4:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_6) Ly_4)) ((times_times_nat Rx_6) Ry_4))) ((times_times_nat ((times_times_nat Lx_6) Rx_6)) ((times_times_nat Ly_4) Ry_4)))) of role axiom named fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J % 0.43/0.68 A new axiom: (forall (Lx_6:nat) (Ly_4:nat) (Rx_6:nat) (Ry_4:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_6) Ly_4)) ((times_times_nat Rx_6) Ry_4))) ((times_times_nat ((times_times_nat Lx_6) Rx_6)) ((times_times_nat Ly_4) Ry_4)))) % 0.43/0.68 FOF formula (forall (Lx_6:int) (Ly_4:int) (Rx_6:int) (Ry_4:int), (((eq int) ((times_times_int ((times_times_int Lx_6) Ly_4)) ((times_times_int Rx_6) Ry_4))) ((times_times_int ((times_times_int Lx_6) Rx_6)) ((times_times_int Ly_4) Ry_4)))) of role axiom named fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J % 0.43/0.68 A new axiom: (forall (Lx_6:int) (Ly_4:int) (Rx_6:int) (Ry_4:int), (((eq int) ((times_times_int ((times_times_int Lx_6) Ly_4)) ((times_times_int Rx_6) Ry_4))) ((times_times_int ((times_times_int Lx_6) Rx_6)) ((times_times_int Ly_4) Ry_4)))) % 0.43/0.68 FOF formula (forall (Lx_5:real) (Ly_3:real) (Rx_5:real) (Ry_3:real), (((eq real) ((times_times_real ((times_times_real Lx_5) Ly_3)) ((times_times_real Rx_5) Ry_3))) ((times_times_real Rx_5) ((times_times_real ((times_times_real Lx_5) Ly_3)) Ry_3)))) of role axiom named fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J % 0.43/0.68 A new axiom: (forall (Lx_5:real) (Ly_3:real) (Rx_5:real) (Ry_3:real), (((eq real) ((times_times_real ((times_times_real Lx_5) Ly_3)) ((times_times_real Rx_5) Ry_3))) ((times_times_real Rx_5) ((times_times_real ((times_times_real Lx_5) Ly_3)) Ry_3)))) % 0.43/0.68 FOF formula (forall (Lx_5:nat) (Ly_3:nat) (Rx_5:nat) (Ry_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) ((times_times_nat Rx_5) Ry_3))) ((times_times_nat Rx_5) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) Ry_3)))) of role axiom named fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J % 0.43/0.68 A new axiom: (forall (Lx_5:nat) (Ly_3:nat) (Rx_5:nat) (Ry_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) ((times_times_nat Rx_5) Ry_3))) ((times_times_nat Rx_5) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) Ry_3)))) % 0.43/0.68 FOF formula (forall (Lx_5:int) (Ly_3:int) (Rx_5:int) (Ry_3:int), (((eq int) ((times_times_int ((times_times_int Lx_5) Ly_3)) ((times_times_int Rx_5) Ry_3))) ((times_times_int Rx_5) ((times_times_int ((times_times_int Lx_5) Ly_3)) Ry_3)))) of role axiom named fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J % 0.51/0.69 A new axiom: (forall (Lx_5:int) (Ly_3:int) (Rx_5:int) (Ry_3:int), (((eq int) ((times_times_int ((times_times_int Lx_5) Ly_3)) ((times_times_int Rx_5) Ry_3))) ((times_times_int Rx_5) ((times_times_int ((times_times_int Lx_5) Ly_3)) Ry_3)))) % 0.51/0.69 FOF formula (forall (Lx_4:real) (Ly_2:real) (Rx_4:real) (Ry_2:real), (((eq real) ((times_times_real ((times_times_real Lx_4) Ly_2)) ((times_times_real Rx_4) Ry_2))) ((times_times_real Lx_4) ((times_times_real Ly_2) ((times_times_real Rx_4) Ry_2))))) of role axiom named fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J % 0.51/0.69 A new axiom: (forall (Lx_4:real) (Ly_2:real) (Rx_4:real) (Ry_2:real), (((eq real) ((times_times_real ((times_times_real Lx_4) Ly_2)) ((times_times_real Rx_4) Ry_2))) ((times_times_real Lx_4) ((times_times_real Ly_2) ((times_times_real Rx_4) Ry_2))))) % 0.51/0.69 FOF formula (forall (Lx_4:nat) (Ly_2:nat) (Rx_4:nat) (Ry_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_4) Ly_2)) ((times_times_nat Rx_4) Ry_2))) ((times_times_nat Lx_4) ((times_times_nat Ly_2) ((times_times_nat Rx_4) Ry_2))))) of role axiom named fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J % 0.51/0.69 A new axiom: (forall (Lx_4:nat) (Ly_2:nat) (Rx_4:nat) (Ry_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_4) Ly_2)) ((times_times_nat Rx_4) Ry_2))) ((times_times_nat Lx_4) ((times_times_nat Ly_2) ((times_times_nat Rx_4) Ry_2))))) % 0.51/0.69 FOF formula (forall (Lx_4:int) (Ly_2:int) (Rx_4:int) (Ry_2:int), (((eq int) ((times_times_int ((times_times_int Lx_4) Ly_2)) ((times_times_int Rx_4) Ry_2))) ((times_times_int Lx_4) ((times_times_int Ly_2) ((times_times_int Rx_4) Ry_2))))) of role axiom named fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J % 0.51/0.69 A new axiom: (forall (Lx_4:int) (Ly_2:int) (Rx_4:int) (Ry_2:int), (((eq int) ((times_times_int ((times_times_int Lx_4) Ly_2)) ((times_times_int Rx_4) Ry_2))) ((times_times_int Lx_4) ((times_times_int Ly_2) ((times_times_int Rx_4) Ry_2))))) % 0.51/0.69 FOF formula (forall (Lx_3:real) (Ly_1:real) (Rx_3:real), (((eq real) ((times_times_real ((times_times_real Lx_3) Ly_1)) Rx_3)) ((times_times_real ((times_times_real Lx_3) Rx_3)) Ly_1))) of role axiom named fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J % 0.51/0.69 A new axiom: (forall (Lx_3:real) (Ly_1:real) (Rx_3:real), (((eq real) ((times_times_real ((times_times_real Lx_3) Ly_1)) Rx_3)) ((times_times_real ((times_times_real Lx_3) Rx_3)) Ly_1))) % 0.51/0.69 FOF formula (forall (Lx_3:nat) (Ly_1:nat) (Rx_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_3) Ly_1)) Rx_3)) ((times_times_nat ((times_times_nat Lx_3) Rx_3)) Ly_1))) of role axiom named fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J % 0.51/0.69 A new axiom: (forall (Lx_3:nat) (Ly_1:nat) (Rx_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_3) Ly_1)) Rx_3)) ((times_times_nat ((times_times_nat Lx_3) Rx_3)) Ly_1))) % 0.51/0.69 FOF formula (forall (Lx_3:int) (Ly_1:int) (Rx_3:int), (((eq int) ((times_times_int ((times_times_int Lx_3) Ly_1)) Rx_3)) ((times_times_int ((times_times_int Lx_3) Rx_3)) Ly_1))) of role axiom named fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J % 0.51/0.69 A new axiom: (forall (Lx_3:int) (Ly_1:int) (Rx_3:int), (((eq int) ((times_times_int ((times_times_int Lx_3) Ly_1)) Rx_3)) ((times_times_int ((times_times_int Lx_3) Rx_3)) Ly_1))) % 0.51/0.69 FOF formula (forall (Lx_2:real) (Ly:real) (Rx_2:real), (((eq real) ((times_times_real ((times_times_real Lx_2) Ly)) Rx_2)) ((times_times_real Lx_2) ((times_times_real Ly) Rx_2)))) of role axiom named fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J % 0.51/0.69 A new axiom: (forall (Lx_2:real) (Ly:real) (Rx_2:real), (((eq real) ((times_times_real ((times_times_real Lx_2) Ly)) Rx_2)) ((times_times_real Lx_2) ((times_times_real Ly) Rx_2)))) % 0.51/0.69 FOF formula (forall (Lx_2:nat) (Ly:nat) (Rx_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_2) Ly)) Rx_2)) ((times_times_nat Lx_2) ((times_times_nat Ly) Rx_2)))) of role axiom named fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J % 0.51/0.71 A new axiom: (forall (Lx_2:nat) (Ly:nat) (Rx_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_2) Ly)) Rx_2)) ((times_times_nat Lx_2) ((times_times_nat Ly) Rx_2)))) % 0.51/0.71 FOF formula (forall (Lx_2:int) (Ly:int) (Rx_2:int), (((eq int) ((times_times_int ((times_times_int Lx_2) Ly)) Rx_2)) ((times_times_int Lx_2) ((times_times_int Ly) Rx_2)))) of role axiom named fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J % 0.51/0.71 A new axiom: (forall (Lx_2:int) (Ly:int) (Rx_2:int), (((eq int) ((times_times_int ((times_times_int Lx_2) Ly)) Rx_2)) ((times_times_int Lx_2) ((times_times_int Ly) Rx_2)))) % 0.51/0.71 FOF formula (forall (Lx_1:real) (Rx_1:real) (Ry_1:real), (((eq real) ((times_times_real Lx_1) ((times_times_real Rx_1) Ry_1))) ((times_times_real ((times_times_real Lx_1) Rx_1)) Ry_1))) of role axiom named fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J % 0.51/0.71 A new axiom: (forall (Lx_1:real) (Rx_1:real) (Ry_1:real), (((eq real) ((times_times_real Lx_1) ((times_times_real Rx_1) Ry_1))) ((times_times_real ((times_times_real Lx_1) Rx_1)) Ry_1))) % 0.51/0.71 FOF formula (forall (Lx_1:nat) (Rx_1:nat) (Ry_1:nat), (((eq nat) ((times_times_nat Lx_1) ((times_times_nat Rx_1) Ry_1))) ((times_times_nat ((times_times_nat Lx_1) Rx_1)) Ry_1))) of role axiom named fact_107_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J % 0.51/0.71 A new axiom: (forall (Lx_1:nat) (Rx_1:nat) (Ry_1:nat), (((eq nat) ((times_times_nat Lx_1) ((times_times_nat Rx_1) Ry_1))) ((times_times_nat ((times_times_nat Lx_1) Rx_1)) Ry_1))) % 0.51/0.71 FOF formula (forall (Lx_1:int) (Rx_1:int) (Ry_1:int), (((eq int) ((times_times_int Lx_1) ((times_times_int Rx_1) Ry_1))) ((times_times_int ((times_times_int Lx_1) Rx_1)) Ry_1))) of role axiom named fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J % 0.51/0.71 A new axiom: (forall (Lx_1:int) (Rx_1:int) (Ry_1:int), (((eq int) ((times_times_int Lx_1) ((times_times_int Rx_1) Ry_1))) ((times_times_int ((times_times_int Lx_1) Rx_1)) Ry_1))) % 0.51/0.71 FOF formula (forall (Lx:real) (Rx:real) (Ry:real), (((eq real) ((times_times_real Lx) ((times_times_real Rx) Ry))) ((times_times_real Rx) ((times_times_real Lx) Ry)))) of role axiom named fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J % 0.51/0.71 A new axiom: (forall (Lx:real) (Rx:real) (Ry:real), (((eq real) ((times_times_real Lx) ((times_times_real Rx) Ry))) ((times_times_real Rx) ((times_times_real Lx) Ry)))) % 0.51/0.71 FOF formula (forall (Lx:nat) (Rx:nat) (Ry:nat), (((eq nat) ((times_times_nat Lx) ((times_times_nat Rx) Ry))) ((times_times_nat Rx) ((times_times_nat Lx) Ry)))) of role axiom named fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J % 0.51/0.71 A new axiom: (forall (Lx:nat) (Rx:nat) (Ry:nat), (((eq nat) ((times_times_nat Lx) ((times_times_nat Rx) Ry))) ((times_times_nat Rx) ((times_times_nat Lx) Ry)))) % 0.51/0.71 FOF formula (forall (Lx:int) (Rx:int) (Ry:int), (((eq int) ((times_times_int Lx) ((times_times_int Rx) Ry))) ((times_times_int Rx) ((times_times_int Lx) Ry)))) of role axiom named fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J % 0.51/0.71 A new axiom: (forall (Lx:int) (Rx:int) (Ry:int), (((eq int) ((times_times_int Lx) ((times_times_int Rx) Ry))) ((times_times_int Rx) ((times_times_int Lx) Ry)))) % 0.51/0.71 FOF formula (forall (A_64:real) (B_20:real), (((eq real) ((times_times_real A_64) B_20)) ((times_times_real B_20) A_64))) of role axiom named fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J % 0.51/0.71 A new axiom: (forall (A_64:real) (B_20:real), (((eq real) ((times_times_real A_64) B_20)) ((times_times_real B_20) A_64))) % 0.51/0.71 FOF formula (forall (A_64:nat) (B_20:nat), (((eq nat) ((times_times_nat A_64) B_20)) ((times_times_nat B_20) A_64))) of role axiom named fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J % 0.51/0.71 A new axiom: (forall (A_64:nat) (B_20:nat), (((eq nat) ((times_times_nat A_64) B_20)) ((times_times_nat B_20) A_64))) % 0.51/0.71 FOF formula (forall (A_64:int) (B_20:int), (((eq int) ((times_times_int A_64) B_20)) ((times_times_int B_20) A_64))) of role axiom named fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J % 0.51/0.73 A new axiom: (forall (A_64:int) (B_20:int), (((eq int) ((times_times_int A_64) B_20)) ((times_times_int B_20) A_64))) % 0.51/0.73 FOF formula (forall (A_63:real) (B_19:real) (C_10:real) (D_5:real), (((eq real) ((plus_plus_real ((plus_plus_real A_63) B_19)) ((plus_plus_real C_10) D_5))) ((plus_plus_real ((plus_plus_real A_63) C_10)) ((plus_plus_real B_19) D_5)))) of role axiom named fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J % 0.51/0.73 A new axiom: (forall (A_63:real) (B_19:real) (C_10:real) (D_5:real), (((eq real) ((plus_plus_real ((plus_plus_real A_63) B_19)) ((plus_plus_real C_10) D_5))) ((plus_plus_real ((plus_plus_real A_63) C_10)) ((plus_plus_real B_19) D_5)))) % 0.51/0.73 FOF formula (forall (A_63:nat) (B_19:nat) (C_10:nat) (D_5:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_63) B_19)) ((plus_plus_nat C_10) D_5))) ((plus_plus_nat ((plus_plus_nat A_63) C_10)) ((plus_plus_nat B_19) D_5)))) of role axiom named fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J % 0.51/0.73 A new axiom: (forall (A_63:nat) (B_19:nat) (C_10:nat) (D_5:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_63) B_19)) ((plus_plus_nat C_10) D_5))) ((plus_plus_nat ((plus_plus_nat A_63) C_10)) ((plus_plus_nat B_19) D_5)))) % 0.51/0.73 FOF formula (forall (A_63:int) (B_19:int) (C_10:int) (D_5:int), (((eq int) ((plus_plus_int ((plus_plus_int A_63) B_19)) ((plus_plus_int C_10) D_5))) ((plus_plus_int ((plus_plus_int A_63) C_10)) ((plus_plus_int B_19) D_5)))) of role axiom named fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J % 0.51/0.73 A new axiom: (forall (A_63:int) (B_19:int) (C_10:int) (D_5:int), (((eq int) ((plus_plus_int ((plus_plus_int A_63) B_19)) ((plus_plus_int C_10) D_5))) ((plus_plus_int ((plus_plus_int A_63) C_10)) ((plus_plus_int B_19) D_5)))) % 0.51/0.73 FOF formula (forall (A_62:real) (B_18:real) (C_9:real), (((eq real) ((plus_plus_real ((plus_plus_real A_62) B_18)) C_9)) ((plus_plus_real ((plus_plus_real A_62) C_9)) B_18))) of role axiom named fact_118_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J % 0.51/0.73 A new axiom: (forall (A_62:real) (B_18:real) (C_9:real), (((eq real) ((plus_plus_real ((plus_plus_real A_62) B_18)) C_9)) ((plus_plus_real ((plus_plus_real A_62) C_9)) B_18))) % 0.51/0.73 FOF formula (forall (A_62:nat) (B_18:nat) (C_9:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_62) B_18)) C_9)) ((plus_plus_nat ((plus_plus_nat A_62) C_9)) B_18))) of role axiom named fact_119_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J % 0.51/0.73 A new axiom: (forall (A_62:nat) (B_18:nat) (C_9:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_62) B_18)) C_9)) ((plus_plus_nat ((plus_plus_nat A_62) C_9)) B_18))) % 0.51/0.73 FOF formula (forall (A_62:int) (B_18:int) (C_9:int), (((eq int) ((plus_plus_int ((plus_plus_int A_62) B_18)) C_9)) ((plus_plus_int ((plus_plus_int A_62) C_9)) B_18))) of role axiom named fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J % 0.51/0.73 A new axiom: (forall (A_62:int) (B_18:int) (C_9:int), (((eq int) ((plus_plus_int ((plus_plus_int A_62) B_18)) C_9)) ((plus_plus_int ((plus_plus_int A_62) C_9)) B_18))) % 0.51/0.73 FOF formula (forall (A_61:real) (B_17:real) (C_8:real), (((eq real) ((plus_plus_real ((plus_plus_real A_61) B_17)) C_8)) ((plus_plus_real A_61) ((plus_plus_real B_17) C_8)))) of role axiom named fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J % 0.51/0.73 A new axiom: (forall (A_61:real) (B_17:real) (C_8:real), (((eq real) ((plus_plus_real ((plus_plus_real A_61) B_17)) C_8)) ((plus_plus_real A_61) ((plus_plus_real B_17) C_8)))) % 0.51/0.73 FOF formula (forall (A_61:nat) (B_17:nat) (C_8:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_61) B_17)) C_8)) ((plus_plus_nat A_61) ((plus_plus_nat B_17) C_8)))) of role axiom named fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J % 0.51/0.73 A new axiom: (forall (A_61:nat) (B_17:nat) (C_8:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_61) B_17)) C_8)) ((plus_plus_nat A_61) ((plus_plus_nat B_17) C_8)))) % 0.51/0.73 FOF formula (forall (A_61:int) (B_17:int) (C_8:int), (((eq int) ((plus_plus_int ((plus_plus_int A_61) B_17)) C_8)) ((plus_plus_int A_61) ((plus_plus_int B_17) C_8)))) of role axiom named fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J % 0.51/0.74 A new axiom: (forall (A_61:int) (B_17:int) (C_8:int), (((eq int) ((plus_plus_int ((plus_plus_int A_61) B_17)) C_8)) ((plus_plus_int A_61) ((plus_plus_int B_17) C_8)))) % 0.51/0.74 FOF formula (forall (A_60:real) (C_7:real) (D_4:real), (((eq real) ((plus_plus_real A_60) ((plus_plus_real C_7) D_4))) ((plus_plus_real ((plus_plus_real A_60) C_7)) D_4))) of role axiom named fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J % 0.51/0.74 A new axiom: (forall (A_60:real) (C_7:real) (D_4:real), (((eq real) ((plus_plus_real A_60) ((plus_plus_real C_7) D_4))) ((plus_plus_real ((plus_plus_real A_60) C_7)) D_4))) % 0.51/0.74 FOF formula (forall (A_60:nat) (C_7:nat) (D_4:nat), (((eq nat) ((plus_plus_nat A_60) ((plus_plus_nat C_7) D_4))) ((plus_plus_nat ((plus_plus_nat A_60) C_7)) D_4))) of role axiom named fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J % 0.51/0.74 A new axiom: (forall (A_60:nat) (C_7:nat) (D_4:nat), (((eq nat) ((plus_plus_nat A_60) ((plus_plus_nat C_7) D_4))) ((plus_plus_nat ((plus_plus_nat A_60) C_7)) D_4))) % 0.51/0.74 FOF formula (forall (A_60:int) (C_7:int) (D_4:int), (((eq int) ((plus_plus_int A_60) ((plus_plus_int C_7) D_4))) ((plus_plus_int ((plus_plus_int A_60) C_7)) D_4))) of role axiom named fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J % 0.51/0.74 A new axiom: (forall (A_60:int) (C_7:int) (D_4:int), (((eq int) ((plus_plus_int A_60) ((plus_plus_int C_7) D_4))) ((plus_plus_int ((plus_plus_int A_60) C_7)) D_4))) % 0.51/0.74 FOF formula (forall (A_59:real) (C_6:real) (D_3:real), (((eq real) ((plus_plus_real A_59) ((plus_plus_real C_6) D_3))) ((plus_plus_real C_6) ((plus_plus_real A_59) D_3)))) of role axiom named fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J % 0.51/0.74 A new axiom: (forall (A_59:real) (C_6:real) (D_3:real), (((eq real) ((plus_plus_real A_59) ((plus_plus_real C_6) D_3))) ((plus_plus_real C_6) ((plus_plus_real A_59) D_3)))) % 0.51/0.74 FOF formula (forall (A_59:nat) (C_6:nat) (D_3:nat), (((eq nat) ((plus_plus_nat A_59) ((plus_plus_nat C_6) D_3))) ((plus_plus_nat C_6) ((plus_plus_nat A_59) D_3)))) of role axiom named fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J % 0.51/0.74 A new axiom: (forall (A_59:nat) (C_6:nat) (D_3:nat), (((eq nat) ((plus_plus_nat A_59) ((plus_plus_nat C_6) D_3))) ((plus_plus_nat C_6) ((plus_plus_nat A_59) D_3)))) % 0.51/0.74 FOF formula (forall (A_59:int) (C_6:int) (D_3:int), (((eq int) ((plus_plus_int A_59) ((plus_plus_int C_6) D_3))) ((plus_plus_int C_6) ((plus_plus_int A_59) D_3)))) of role axiom named fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J % 0.51/0.74 A new axiom: (forall (A_59:int) (C_6:int) (D_3:int), (((eq int) ((plus_plus_int A_59) ((plus_plus_int C_6) D_3))) ((plus_plus_int C_6) ((plus_plus_int A_59) D_3)))) % 0.51/0.74 FOF formula (forall (A_58:real) (C_5:real), (((eq real) ((plus_plus_real A_58) C_5)) ((plus_plus_real C_5) A_58))) of role axiom named fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J % 0.51/0.74 A new axiom: (forall (A_58:real) (C_5:real), (((eq real) ((plus_plus_real A_58) C_5)) ((plus_plus_real C_5) A_58))) % 0.51/0.74 FOF formula (forall (A_58:nat) (C_5:nat), (((eq nat) ((plus_plus_nat A_58) C_5)) ((plus_plus_nat C_5) A_58))) of role axiom named fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J % 0.51/0.74 A new axiom: (forall (A_58:nat) (C_5:nat), (((eq nat) ((plus_plus_nat A_58) C_5)) ((plus_plus_nat C_5) A_58))) % 0.51/0.74 FOF formula (forall (A_58:int) (C_5:int), (((eq int) ((plus_plus_int A_58) C_5)) ((plus_plus_int C_5) A_58))) of role axiom named fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J % 0.51/0.74 A new axiom: (forall (A_58:int) (C_5:int), (((eq int) ((plus_plus_int A_58) C_5)) ((plus_plus_int C_5) A_58))) % 0.51/0.74 FOF formula (forall (X_30:int) (Y_27:int), ((iff (((eq real) (number267125858f_real X_30)) (number267125858f_real Y_27))) (((eq int) X_30) Y_27))) of role axiom named fact_133_eq__number__of % 0.51/0.74 A new axiom: (forall (X_30:int) (Y_27:int), ((iff (((eq real) (number267125858f_real X_30)) (number267125858f_real Y_27))) (((eq int) X_30) Y_27))) % 0.51/0.76 FOF formula (forall (X_30:int) (Y_27:int), ((iff (((eq int) (number_number_of_int X_30)) (number_number_of_int Y_27))) (((eq int) X_30) Y_27))) of role axiom named fact_134_eq__number__of % 0.51/0.76 A new axiom: (forall (X_30:int) (Y_27:int), ((iff (((eq int) (number_number_of_int X_30)) (number_number_of_int Y_27))) (((eq int) X_30) Y_27))) % 0.51/0.76 FOF formula (forall (W_14:int) (X_29:real), ((iff (((eq real) (number267125858f_real W_14)) X_29)) (((eq real) X_29) (number267125858f_real W_14)))) of role axiom named fact_135_number__of__reorient % 0.51/0.76 A new axiom: (forall (W_14:int) (X_29:real), ((iff (((eq real) (number267125858f_real W_14)) X_29)) (((eq real) X_29) (number267125858f_real W_14)))) % 0.51/0.76 FOF formula (forall (W_14:int) (X_29:int), ((iff (((eq int) (number_number_of_int W_14)) X_29)) (((eq int) X_29) (number_number_of_int W_14)))) of role axiom named fact_136_number__of__reorient % 0.51/0.76 A new axiom: (forall (W_14:int) (X_29:int), ((iff (((eq int) (number_number_of_int W_14)) X_29)) (((eq int) X_29) (number_number_of_int W_14)))) % 0.51/0.76 FOF formula (forall (W_14:int) (X_29:nat), ((iff (((eq nat) (number_number_of_nat W_14)) X_29)) (((eq nat) X_29) (number_number_of_nat W_14)))) of role axiom named fact_137_number__of__reorient % 0.51/0.76 A new axiom: (forall (W_14:int) (X_29:nat), ((iff (((eq nat) (number_number_of_nat W_14)) X_29)) (((eq nat) X_29) (number_number_of_nat W_14)))) % 0.51/0.76 FOF formula (forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L))) of role axiom named fact_138_rel__simps_I51_J % 0.51/0.76 A new axiom: (forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L))) % 0.51/0.76 FOF formula (forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L))) of role axiom named fact_139_rel__simps_I48_J % 0.51/0.76 A new axiom: (forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L))) % 0.51/0.76 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_140_zmult__assoc % 0.51/0.76 A new axiom: (forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((times_times_int ((times_times_int Z1) Z2)) Z3)) ((times_times_int Z1) ((times_times_int Z2) Z3)))) % 0.51/0.76 FOF formula (forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z))) of role axiom named fact_141_zmult__commute % 0.51/0.76 A new axiom: (forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z))) % 0.51/0.76 FOF formula (forall (K:int), (((eq int) (number_number_of_int K)) K)) of role axiom named fact_142_number__of__is__id % 0.51/0.76 A new axiom: (forall (K:int), (((eq int) (number_number_of_int K)) K)) % 0.51/0.76 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_143_zadd__assoc % 0.51/0.76 A new axiom: (forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((plus_plus_int ((plus_plus_int Z1) Z2)) Z3)) ((plus_plus_int Z1) ((plus_plus_int Z2) Z3)))) % 0.51/0.76 FOF formula (forall (X_1:int) (Y_1:int) (Z:int), (((eq int) ((plus_plus_int X_1) ((plus_plus_int Y_1) Z))) ((plus_plus_int Y_1) ((plus_plus_int X_1) Z)))) of role axiom named fact_144_zadd__left__commute % 0.51/0.76 A new axiom: (forall (X_1:int) (Y_1:int) (Z:int), (((eq int) ((plus_plus_int X_1) ((plus_plus_int Y_1) Z))) ((plus_plus_int Y_1) ((plus_plus_int X_1) Z)))) % 0.51/0.76 FOF formula (forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z))) of role axiom named fact_145_zadd__commute % 0.51/0.76 A new axiom: (forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z))) % 0.51/0.76 FOF formula (forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_146_rel__simps_I12_J % 0.51/0.76 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls))) % 0.51/0.76 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_147_less__int__code_I15_J % 0.51/0.76 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2))) % 0.51/0.76 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_148_rel__simps_I16_J % 0.60/0.78 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))) % 0.60/0.78 FOF formula (forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_149_rel__simps_I10_J % 0.60/0.78 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls))) % 0.60/0.78 FOF formula (forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K))) of role axiom named fact_150_rel__simps_I4_J % 0.60/0.78 A new axiom: (forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K))) % 0.60/0.78 FOF formula (forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_151_rel__simps_I22_J % 0.60/0.78 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) % 0.60/0.78 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_152_less__eq__int__code_I14_J % 0.60/0.78 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))) % 0.60/0.78 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_153_rel__simps_I32_J % 0.60/0.78 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))) % 0.60/0.78 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) pls)) ((ord_less_eq_int K) pls))) of role axiom named fact_154_rel__simps_I27_J % 0.60/0.78 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) pls)) ((ord_less_eq_int K) pls))) % 0.60/0.78 FOF formula (forall (K:int), ((iff ((ord_less_eq_int pls) (bit0 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_155_rel__simps_I21_J % 0.60/0.78 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int pls) (bit0 K))) ((ord_less_eq_int pls) K))) % 0.60/0.78 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_156_zless__add1__eq % 0.60/0.78 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)))) % 0.60/0.78 FOF formula (forall (A_57:nat) (N_38:nat), (((eq nat) ((power_power_nat A_57) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_38))) ((power_power_nat ((power_power_nat A_57) N_38)) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_157_power__even__eq % 0.60/0.78 A new axiom: (forall (A_57:nat) (N_38:nat), (((eq nat) ((power_power_nat A_57) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_38))) ((power_power_nat ((power_power_nat A_57) N_38)) (number_number_of_nat (bit0 (bit1 pls)))))) % 0.60/0.78 FOF formula (forall (A_57:real) (N_38:nat), (((eq real) ((power_power_real A_57) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_38))) ((power_power_real ((power_power_real A_57) N_38)) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_158_power__even__eq % 0.60/0.78 A new axiom: (forall (A_57:real) (N_38:nat), (((eq real) ((power_power_real A_57) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_38))) ((power_power_real ((power_power_real A_57) N_38)) (number_number_of_nat (bit0 (bit1 pls)))))) % 0.60/0.78 FOF formula (forall (A_57:int) (N_38:nat), (((eq int) ((power_power_int A_57) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_38))) ((power_power_int ((power_power_int A_57) N_38)) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_159_power__even__eq % 0.60/0.78 A new axiom: (forall (A_57:int) (N_38:nat), (((eq int) ((power_power_int A_57) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_38))) ((power_power_int ((power_power_int A_57) N_38)) (number_number_of_nat (bit0 (bit1 pls)))))) % 0.60/0.78 FOF formula (forall (X_28:int), ((iff ((ord_less_real (number267125858f_real X_28)) one_one_real)) ((ord_less_int X_28) (bit1 pls)))) of role axiom named fact_160_less__special_I4_J % 0.60/0.78 A new axiom: (forall (X_28:int), ((iff ((ord_less_real (number267125858f_real X_28)) one_one_real)) ((ord_less_int X_28) (bit1 pls)))) % 0.61/0.80 FOF formula (forall (X_28:int), ((iff ((ord_less_int (number_number_of_int X_28)) one_one_int)) ((ord_less_int X_28) (bit1 pls)))) of role axiom named fact_161_less__special_I4_J % 0.61/0.80 A new axiom: (forall (X_28:int), ((iff ((ord_less_int (number_number_of_int X_28)) one_one_int)) ((ord_less_int X_28) (bit1 pls)))) % 0.61/0.80 FOF formula (forall (Y_26:int), ((iff ((ord_less_real one_one_real) (number267125858f_real Y_26))) ((ord_less_int (bit1 pls)) Y_26))) of role axiom named fact_162_less__special_I2_J % 0.61/0.80 A new axiom: (forall (Y_26:int), ((iff ((ord_less_real one_one_real) (number267125858f_real Y_26))) ((ord_less_int (bit1 pls)) Y_26))) % 0.61/0.80 FOF formula (forall (Y_26:int), ((iff ((ord_less_int one_one_int) (number_number_of_int Y_26))) ((ord_less_int (bit1 pls)) Y_26))) of role axiom named fact_163_less__special_I2_J % 0.61/0.80 A new axiom: (forall (Y_26:int), ((iff ((ord_less_int one_one_int) (number_number_of_int Y_26))) ((ord_less_int (bit1 pls)) Y_26))) % 0.61/0.80 FOF formula (forall (X_27:int), ((iff ((ord_less_eq_real (number267125858f_real X_27)) one_one_real)) ((ord_less_eq_int X_27) (bit1 pls)))) of role axiom named fact_164_le__special_I4_J % 0.61/0.80 A new axiom: (forall (X_27:int), ((iff ((ord_less_eq_real (number267125858f_real X_27)) one_one_real)) ((ord_less_eq_int X_27) (bit1 pls)))) % 0.61/0.80 FOF formula (forall (X_27:int), ((iff ((ord_less_eq_int (number_number_of_int X_27)) one_one_int)) ((ord_less_eq_int X_27) (bit1 pls)))) of role axiom named fact_165_le__special_I4_J % 0.61/0.80 A new axiom: (forall (X_27:int), ((iff ((ord_less_eq_int (number_number_of_int X_27)) one_one_int)) ((ord_less_eq_int X_27) (bit1 pls)))) % 0.61/0.80 FOF formula (forall (Y_25:int), ((iff ((ord_less_eq_real one_one_real) (number267125858f_real Y_25))) ((ord_less_eq_int (bit1 pls)) Y_25))) of role axiom named fact_166_le__special_I2_J % 0.61/0.80 A new axiom: (forall (Y_25:int), ((iff ((ord_less_eq_real one_one_real) (number267125858f_real Y_25))) ((ord_less_eq_int (bit1 pls)) Y_25))) % 0.61/0.80 FOF formula (forall (Y_25:int), ((iff ((ord_less_eq_int one_one_int) (number_number_of_int Y_25))) ((ord_less_eq_int (bit1 pls)) Y_25))) of role axiom named fact_167_le__special_I2_J % 0.61/0.80 A new axiom: (forall (Y_25:int), ((iff ((ord_less_eq_int one_one_int) (number_number_of_int Y_25))) ((ord_less_eq_int (bit1 pls)) Y_25))) % 0.61/0.80 FOF formula (forall (W_13:real) (Y_24:real) (X_26:real) (Z_8:real), ((iff (((eq real) ((plus_plus_real ((times_times_real W_13) Y_24)) ((times_times_real X_26) Z_8))) ((plus_plus_real ((times_times_real W_13) Z_8)) ((times_times_real X_26) Y_24)))) ((or (((eq real) W_13) X_26)) (((eq real) Y_24) Z_8)))) of role axiom named fact_168_crossproduct__eq % 0.61/0.80 A new axiom: (forall (W_13:real) (Y_24:real) (X_26:real) (Z_8:real), ((iff (((eq real) ((plus_plus_real ((times_times_real W_13) Y_24)) ((times_times_real X_26) Z_8))) ((plus_plus_real ((times_times_real W_13) Z_8)) ((times_times_real X_26) Y_24)))) ((or (((eq real) W_13) X_26)) (((eq real) Y_24) Z_8)))) % 0.61/0.80 FOF formula (forall (W_13:nat) (Y_24:nat) (X_26:nat) (Z_8:nat), ((iff (((eq nat) ((plus_plus_nat ((times_times_nat W_13) Y_24)) ((times_times_nat X_26) Z_8))) ((plus_plus_nat ((times_times_nat W_13) Z_8)) ((times_times_nat X_26) Y_24)))) ((or (((eq nat) W_13) X_26)) (((eq nat) Y_24) Z_8)))) of role axiom named fact_169_crossproduct__eq % 0.61/0.80 A new axiom: (forall (W_13:nat) (Y_24:nat) (X_26:nat) (Z_8:nat), ((iff (((eq nat) ((plus_plus_nat ((times_times_nat W_13) Y_24)) ((times_times_nat X_26) Z_8))) ((plus_plus_nat ((times_times_nat W_13) Z_8)) ((times_times_nat X_26) Y_24)))) ((or (((eq nat) W_13) X_26)) (((eq nat) Y_24) Z_8)))) % 0.61/0.80 FOF formula (forall (W_13:int) (Y_24:int) (X_26:int) (Z_8:int), ((iff (((eq int) ((plus_plus_int ((times_times_int W_13) Y_24)) ((times_times_int X_26) Z_8))) ((plus_plus_int ((times_times_int W_13) Z_8)) ((times_times_int X_26) Y_24)))) ((or (((eq int) W_13) X_26)) (((eq int) Y_24) Z_8)))) of role axiom named fact_170_crossproduct__eq % 0.61/0.80 A new axiom: (forall (W_13:int) (Y_24:int) (X_26:int) (Z_8:int), ((iff (((eq int) ((plus_plus_int ((times_times_int W_13) Y_24)) ((times_times_int X_26) Z_8))) ((plus_plus_int ((times_times_int W_13) Z_8)) ((times_times_int X_26) Y_24)))) ((or (((eq int) W_13) X_26)) (((eq int) Y_24) Z_8)))) % 0.63/0.82 FOF formula (forall (A_56:real) (M_13:real) (B_16:real), (((eq real) ((plus_plus_real ((times_times_real A_56) M_13)) ((times_times_real B_16) M_13))) ((times_times_real ((plus_plus_real A_56) B_16)) M_13))) of role axiom named fact_171_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J % 0.63/0.82 A new axiom: (forall (A_56:real) (M_13:real) (B_16:real), (((eq real) ((plus_plus_real ((times_times_real A_56) M_13)) ((times_times_real B_16) M_13))) ((times_times_real ((plus_plus_real A_56) B_16)) M_13))) % 0.63/0.82 FOF formula (forall (A_56:nat) (M_13:nat) (B_16:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_56) M_13)) ((times_times_nat B_16) M_13))) ((times_times_nat ((plus_plus_nat A_56) B_16)) M_13))) of role axiom named fact_172_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J % 0.63/0.82 A new axiom: (forall (A_56:nat) (M_13:nat) (B_16:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_56) M_13)) ((times_times_nat B_16) M_13))) ((times_times_nat ((plus_plus_nat A_56) B_16)) M_13))) % 0.63/0.82 FOF formula (forall (A_56:int) (M_13:int) (B_16:int), (((eq int) ((plus_plus_int ((times_times_int A_56) M_13)) ((times_times_int B_16) M_13))) ((times_times_int ((plus_plus_int A_56) B_16)) M_13))) of role axiom named fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J % 0.63/0.82 A new axiom: (forall (A_56:int) (M_13:int) (B_16:int), (((eq int) ((plus_plus_int ((times_times_int A_56) M_13)) ((times_times_int B_16) M_13))) ((times_times_int ((plus_plus_int A_56) B_16)) M_13))) % 0.63/0.82 FOF formula (forall (A_55:real) (B_15:real) (C_4:real), (((eq real) ((times_times_real ((plus_plus_real A_55) B_15)) C_4)) ((plus_plus_real ((times_times_real A_55) C_4)) ((times_times_real B_15) C_4)))) of role axiom named fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J % 0.63/0.82 A new axiom: (forall (A_55:real) (B_15:real) (C_4:real), (((eq real) ((times_times_real ((plus_plus_real A_55) B_15)) C_4)) ((plus_plus_real ((times_times_real A_55) C_4)) ((times_times_real B_15) C_4)))) % 0.63/0.82 FOF formula (forall (A_55:nat) (B_15:nat) (C_4:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_55) B_15)) C_4)) ((plus_plus_nat ((times_times_nat A_55) C_4)) ((times_times_nat B_15) C_4)))) of role axiom named fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J % 0.63/0.82 A new axiom: (forall (A_55:nat) (B_15:nat) (C_4:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_55) B_15)) C_4)) ((plus_plus_nat ((times_times_nat A_55) C_4)) ((times_times_nat B_15) C_4)))) % 0.63/0.82 FOF formula (forall (A_55:int) (B_15:int) (C_4:int), (((eq int) ((times_times_int ((plus_plus_int A_55) B_15)) C_4)) ((plus_plus_int ((times_times_int A_55) C_4)) ((times_times_int B_15) C_4)))) of role axiom named fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J % 0.63/0.82 A new axiom: (forall (A_55:int) (B_15:int) (C_4:int), (((eq int) ((times_times_int ((plus_plus_int A_55) B_15)) C_4)) ((plus_plus_int ((times_times_int A_55) C_4)) ((times_times_int B_15) C_4)))) % 0.63/0.82 FOF formula (forall (C_3:real) (D_2:real) (A_54:real) (B_14:real), ((iff ((and (not (((eq real) A_54) B_14))) (not (((eq real) C_3) D_2)))) (not (((eq real) ((plus_plus_real ((times_times_real A_54) C_3)) ((times_times_real B_14) D_2))) ((plus_plus_real ((times_times_real A_54) D_2)) ((times_times_real B_14) C_3)))))) of role axiom named fact_177_crossproduct__noteq % 0.63/0.82 A new axiom: (forall (C_3:real) (D_2:real) (A_54:real) (B_14:real), ((iff ((and (not (((eq real) A_54) B_14))) (not (((eq real) C_3) D_2)))) (not (((eq real) ((plus_plus_real ((times_times_real A_54) C_3)) ((times_times_real B_14) D_2))) ((plus_plus_real ((times_times_real A_54) D_2)) ((times_times_real B_14) C_3)))))) % 0.63/0.82 FOF formula (forall (C_3:nat) (D_2:nat) (A_54:nat) (B_14:nat), ((iff ((and (not (((eq nat) A_54) B_14))) (not (((eq nat) C_3) D_2)))) (not (((eq nat) ((plus_plus_nat ((times_times_nat A_54) C_3)) ((times_times_nat B_14) D_2))) ((plus_plus_nat ((times_times_nat A_54) D_2)) ((times_times_nat B_14) C_3)))))) of role axiom named fact_178_crossproduct__noteq % 0.65/0.83 A new axiom: (forall (C_3:nat) (D_2:nat) (A_54:nat) (B_14:nat), ((iff ((and (not (((eq nat) A_54) B_14))) (not (((eq nat) C_3) D_2)))) (not (((eq nat) ((plus_plus_nat ((times_times_nat A_54) C_3)) ((times_times_nat B_14) D_2))) ((plus_plus_nat ((times_times_nat A_54) D_2)) ((times_times_nat B_14) C_3)))))) % 0.65/0.83 FOF formula (forall (C_3:int) (D_2:int) (A_54:int) (B_14:int), ((iff ((and (not (((eq int) A_54) B_14))) (not (((eq int) C_3) D_2)))) (not (((eq int) ((plus_plus_int ((times_times_int A_54) C_3)) ((times_times_int B_14) D_2))) ((plus_plus_int ((times_times_int A_54) D_2)) ((times_times_int B_14) C_3)))))) of role axiom named fact_179_crossproduct__noteq % 0.65/0.83 A new axiom: (forall (C_3:int) (D_2:int) (A_54:int) (B_14:int), ((iff ((and (not (((eq int) A_54) B_14))) (not (((eq int) C_3) D_2)))) (not (((eq int) ((plus_plus_int ((times_times_int A_54) C_3)) ((times_times_int B_14) D_2))) ((plus_plus_int ((times_times_int A_54) D_2)) ((times_times_int B_14) C_3)))))) % 0.65/0.83 FOF formula (forall (X_25:real) (Y_23:real) (Z_7:real), (((eq real) ((times_times_real X_25) ((plus_plus_real Y_23) Z_7))) ((plus_plus_real ((times_times_real X_25) Y_23)) ((times_times_real X_25) Z_7)))) of role axiom named fact_180_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J % 0.65/0.83 A new axiom: (forall (X_25:real) (Y_23:real) (Z_7:real), (((eq real) ((times_times_real X_25) ((plus_plus_real Y_23) Z_7))) ((plus_plus_real ((times_times_real X_25) Y_23)) ((times_times_real X_25) Z_7)))) % 0.65/0.83 FOF formula (forall (X_25:nat) (Y_23:nat) (Z_7:nat), (((eq nat) ((times_times_nat X_25) ((plus_plus_nat Y_23) Z_7))) ((plus_plus_nat ((times_times_nat X_25) Y_23)) ((times_times_nat X_25) Z_7)))) of role axiom named fact_181_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J % 0.65/0.83 A new axiom: (forall (X_25:nat) (Y_23:nat) (Z_7:nat), (((eq nat) ((times_times_nat X_25) ((plus_plus_nat Y_23) Z_7))) ((plus_plus_nat ((times_times_nat X_25) Y_23)) ((times_times_nat X_25) Z_7)))) % 0.65/0.83 FOF formula (forall (X_25:int) (Y_23:int) (Z_7:int), (((eq int) ((times_times_int X_25) ((plus_plus_int Y_23) Z_7))) ((plus_plus_int ((times_times_int X_25) Y_23)) ((times_times_int X_25) Z_7)))) of role axiom named fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J % 0.65/0.83 A new axiom: (forall (X_25:int) (Y_23:int) (Z_7:int), (((eq int) ((times_times_int X_25) ((plus_plus_int Y_23) Z_7))) ((plus_plus_int ((times_times_int X_25) Y_23)) ((times_times_int X_25) Z_7)))) % 0.65/0.83 FOF formula (forall (A_53:real), (((eq real) ((times_times_real A_53) one_one_real)) A_53)) of role axiom named fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J % 0.65/0.83 A new axiom: (forall (A_53:real), (((eq real) ((times_times_real A_53) one_one_real)) A_53)) % 0.65/0.83 FOF formula (forall (A_53:nat), (((eq nat) ((times_times_nat A_53) one_one_nat)) A_53)) of role axiom named fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J % 0.65/0.83 A new axiom: (forall (A_53:nat), (((eq nat) ((times_times_nat A_53) one_one_nat)) A_53)) % 0.65/0.83 FOF formula (forall (A_53:int), (((eq int) ((times_times_int A_53) one_one_int)) A_53)) of role axiom named fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J % 0.65/0.83 A new axiom: (forall (A_53:int), (((eq int) ((times_times_int A_53) one_one_int)) A_53)) % 0.65/0.83 FOF formula (forall (A_52:real), (((eq real) ((times_times_real one_one_real) A_52)) A_52)) of role axiom named fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J % 0.65/0.83 A new axiom: (forall (A_52:real), (((eq real) ((times_times_real one_one_real) A_52)) A_52)) % 0.65/0.83 FOF formula (forall (A_52:nat), (((eq nat) ((times_times_nat one_one_nat) A_52)) A_52)) of role axiom named fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J % 0.65/0.83 A new axiom: (forall (A_52:nat), (((eq nat) ((times_times_nat one_one_nat) A_52)) A_52)) % 0.65/0.83 FOF formula (forall (A_52:int), (((eq int) ((times_times_int one_one_int) A_52)) A_52)) of role axiom named fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J % 0.65/0.83 A new axiom: (forall (A_52:int), (((eq int) ((times_times_int one_one_int) A_52)) A_52)) % 0.65/0.85 FOF formula (forall (X_24:nat) (Y_22:nat) (Q_2:nat), (((eq nat) ((power_power_nat ((times_times_nat X_24) Y_22)) Q_2)) ((times_times_nat ((power_power_nat X_24) Q_2)) ((power_power_nat Y_22) Q_2)))) of role axiom named fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J % 0.65/0.85 A new axiom: (forall (X_24:nat) (Y_22:nat) (Q_2:nat), (((eq nat) ((power_power_nat ((times_times_nat X_24) Y_22)) Q_2)) ((times_times_nat ((power_power_nat X_24) Q_2)) ((power_power_nat Y_22) Q_2)))) % 0.65/0.85 FOF formula (forall (X_24:real) (Y_22:real) (Q_2:nat), (((eq real) ((power_power_real ((times_times_real X_24) Y_22)) Q_2)) ((times_times_real ((power_power_real X_24) Q_2)) ((power_power_real Y_22) Q_2)))) of role axiom named fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J % 0.65/0.85 A new axiom: (forall (X_24:real) (Y_22:real) (Q_2:nat), (((eq real) ((power_power_real ((times_times_real X_24) Y_22)) Q_2)) ((times_times_real ((power_power_real X_24) Q_2)) ((power_power_real Y_22) Q_2)))) % 0.65/0.85 FOF formula (forall (X_24:int) (Y_22:int) (Q_2:nat), (((eq int) ((power_power_int ((times_times_int X_24) Y_22)) Q_2)) ((times_times_int ((power_power_int X_24) Q_2)) ((power_power_int Y_22) Q_2)))) of role axiom named fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J % 0.65/0.85 A new axiom: (forall (X_24:int) (Y_22:int) (Q_2:nat), (((eq int) ((power_power_int ((times_times_int X_24) Y_22)) Q_2)) ((times_times_int ((power_power_int X_24) Q_2)) ((power_power_int Y_22) Q_2)))) % 0.65/0.85 FOF formula (forall (K:int), (not (((eq int) (bit1 K)) pls))) of role axiom named fact_192_rel__simps_I46_J % 0.65/0.85 A new axiom: (forall (K:int), (not (((eq int) (bit1 K)) pls))) % 0.65/0.85 FOF formula (forall (L:int), (not (((eq int) pls) (bit1 L)))) of role axiom named fact_193_rel__simps_I39_J % 0.65/0.85 A new axiom: (forall (L:int), (not (((eq int) pls) (bit1 L)))) % 0.65/0.85 FOF formula (forall (K:int) (L:int), (not (((eq int) (bit1 K)) (bit0 L)))) of role axiom named fact_194_rel__simps_I50_J % 0.65/0.85 A new axiom: (forall (K:int) (L:int), (not (((eq int) (bit1 K)) (bit0 L)))) % 0.65/0.85 FOF formula (forall (K:int) (L:int), (not (((eq int) (bit0 K)) (bit1 L)))) of role axiom named fact_195_rel__simps_I49_J % 0.65/0.85 A new axiom: (forall (K:int) (L:int), (not (((eq int) (bit0 K)) (bit1 L)))) % 0.65/0.85 FOF formula (forall (K:int), ((iff (((eq int) (bit0 K)) pls)) (((eq int) K) pls))) of role axiom named fact_196_rel__simps_I44_J % 0.65/0.85 A new axiom: (forall (K:int), ((iff (((eq int) (bit0 K)) pls)) (((eq int) K) pls))) % 0.65/0.85 FOF formula (forall (L:int), ((iff (((eq int) pls) (bit0 L))) (((eq int) pls) L))) of role axiom named fact_197_rel__simps_I38_J % 0.65/0.85 A new axiom: (forall (L:int), ((iff (((eq int) pls) (bit0 L))) (((eq int) pls) L))) % 0.65/0.85 FOF formula (((eq int) (bit0 pls)) pls) of role axiom named fact_198_Bit0__Pls % 0.65/0.85 A new axiom: (((eq int) (bit0 pls)) pls) % 0.65/0.85 FOF formula (forall (W:int), (((eq int) ((times_times_int pls) W)) pls)) of role axiom named fact_199_mult__Pls % 0.65/0.85 A new axiom: (forall (W:int), (((eq int) ((times_times_int pls) W)) pls)) % 0.65/0.85 FOF formula (forall (K:int) (L:int), (((eq int) ((times_times_int (bit0 K)) L)) (bit0 ((times_times_int K) L)))) of role axiom named fact_200_mult__Bit0 % 0.65/0.85 A new axiom: (forall (K:int) (L:int), (((eq int) ((times_times_int (bit0 K)) L)) (bit0 ((times_times_int K) L)))) % 0.65/0.85 FOF formula (forall (K:int), (((eq int) ((plus_plus_int K) pls)) K)) of role axiom named fact_201_add__Pls__right % 0.65/0.85 A new axiom: (forall (K:int), (((eq int) ((plus_plus_int K) pls)) K)) % 0.65/0.85 FOF formula (forall (K:int), (((eq int) ((plus_plus_int pls) K)) K)) of role axiom named fact_202_add__Pls % 0.65/0.85 A new axiom: (forall (K:int), (((eq int) ((plus_plus_int pls) K)) K)) % 0.65/0.85 FOF formula (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit0 L))) (bit0 ((plus_plus_int K) L)))) of role axiom named fact_203_add__Bit0__Bit0 % 0.65/0.85 A new axiom: (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit0 L))) (bit0 ((plus_plus_int K) L)))) % 0.65/0.85 FOF formula (forall (K:int), (((eq int) (bit0 K)) ((plus_plus_int K) K))) of role axiom named fact_204_Bit0__def % 0.65/0.85 A new axiom: (forall (K:int), (((eq int) (bit0 K)) ((plus_plus_int K) K))) % 0.65/0.85 FOF formula (forall (Z:int), (((eq int) ((times_times_int Z) one_one_int)) Z)) of role axiom named fact_205_zmult__1__right % 0.65/0.86 A new axiom: (forall (Z:int), (((eq int) ((times_times_int Z) one_one_int)) Z)) % 0.65/0.86 FOF formula (forall (Z:int), (((eq int) ((times_times_int one_one_int) Z)) Z)) of role axiom named fact_206_zmult__1 % 0.65/0.86 A new axiom: (forall (Z:int), (((eq int) ((times_times_int one_one_int) Z)) Z)) % 0.65/0.86 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_207_times__numeral__code_I5_J % 0.65/0.86 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)))) % 0.65/0.86 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_208_zadd__zmult__distrib % 0.65/0.86 A new axiom: (forall (Z1:int) (Z2:int) (W:int), (((eq int) ((times_times_int ((plus_plus_int Z1) Z2)) W)) ((plus_plus_int ((times_times_int Z1) W)) ((times_times_int Z2) W)))) % 0.65/0.86 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_209_zadd__zmult__distrib2 % 0.65/0.86 A new axiom: (forall (W:int) (Z1:int) (Z2:int), (((eq int) ((times_times_int W) ((plus_plus_int Z1) Z2))) ((plus_plus_int ((times_times_int W) Z1)) ((times_times_int W) Z2)))) % 0.65/0.86 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_210_plus__numeral__code_I9_J % 0.65/0.86 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)))) % 0.65/0.86 FOF formula (forall (V_14:int) (V_13:int), (((ord_less_eq_int pls) V_13)->(((ord_less_eq_int pls) V_14)->(((eq real) ((times_times_real (number267125858f_real V_13)) (number267125858f_real V_14))) (number267125858f_real ((times_times_int V_13) V_14)))))) of role axiom named fact_211_semiring__mult__number__of % 0.65/0.86 A new axiom: (forall (V_14:int) (V_13:int), (((ord_less_eq_int pls) V_13)->(((ord_less_eq_int pls) V_14)->(((eq real) ((times_times_real (number267125858f_real V_13)) (number267125858f_real V_14))) (number267125858f_real ((times_times_int V_13) V_14)))))) % 0.65/0.86 FOF formula (forall (V_14:int) (V_13:int), (((ord_less_eq_int pls) V_13)->(((ord_less_eq_int pls) V_14)->(((eq nat) ((times_times_nat (number_number_of_nat V_13)) (number_number_of_nat V_14))) (number_number_of_nat ((times_times_int V_13) V_14)))))) of role axiom named fact_212_semiring__mult__number__of % 0.65/0.86 A new axiom: (forall (V_14:int) (V_13:int), (((ord_less_eq_int pls) V_13)->(((ord_less_eq_int pls) V_14)->(((eq nat) ((times_times_nat (number_number_of_nat V_13)) (number_number_of_nat V_14))) (number_number_of_nat ((times_times_int V_13) V_14)))))) % 0.65/0.86 FOF formula (forall (V_14:int) (V_13:int), (((ord_less_eq_int pls) V_13)->(((ord_less_eq_int pls) V_14)->(((eq int) ((times_times_int (number_number_of_int V_13)) (number_number_of_int V_14))) (number_number_of_int ((times_times_int V_13) V_14)))))) of role axiom named fact_213_semiring__mult__number__of % 0.65/0.86 A new axiom: (forall (V_14:int) (V_13:int), (((ord_less_eq_int pls) V_13)->(((ord_less_eq_int pls) V_14)->(((eq int) ((times_times_int (number_number_of_int V_13)) (number_number_of_int V_14))) (number_number_of_int ((times_times_int V_13) V_14)))))) % 0.65/0.86 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) ((plus_plus_real (number267125858f_real V_11)) (number267125858f_real V_12))) (number267125858f_real ((plus_plus_int V_11) V_12)))))) of role axiom named fact_214_semiring__add__number__of % 0.65/0.86 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) ((plus_plus_real (number267125858f_real V_11)) (number267125858f_real V_12))) (number267125858f_real ((plus_plus_int V_11) V_12)))))) % 0.65/0.88 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) ((plus_plus_nat (number_number_of_nat V_11)) (number_number_of_nat V_12))) (number_number_of_nat ((plus_plus_int V_11) V_12)))))) of role axiom named fact_215_semiring__add__number__of % 0.65/0.88 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) ((plus_plus_nat (number_number_of_nat V_11)) (number_number_of_nat V_12))) (number_number_of_nat ((plus_plus_int V_11) V_12)))))) % 0.65/0.88 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) ((plus_plus_int (number_number_of_int V_11)) (number_number_of_int V_12))) (number_number_of_int ((plus_plus_int V_11) V_12)))))) of role axiom named fact_216_semiring__add__number__of % 0.65/0.88 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) ((plus_plus_int (number_number_of_int V_11)) (number_number_of_int V_12))) (number_number_of_int ((plus_plus_int V_11) V_12)))))) % 0.65/0.88 FOF formula (forall (X_1:int), ((ord_less_eq_int X_1) ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_217_power2__ge__self % 0.65/0.88 A new axiom: (forall (X_1:int), ((ord_less_eq_int X_1) ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls)))))) % 0.65/0.88 FOF formula (forall (A_51:real) (B_13:real) (V_10:int), (((eq real) ((times_times_real ((plus_plus_real A_51) B_13)) (number267125858f_real V_10))) ((plus_plus_real ((times_times_real A_51) (number267125858f_real V_10))) ((times_times_real B_13) (number267125858f_real V_10))))) of role axiom named fact_218_left__distrib__number__of % 0.65/0.88 A new axiom: (forall (A_51:real) (B_13:real) (V_10:int), (((eq real) ((times_times_real ((plus_plus_real A_51) B_13)) (number267125858f_real V_10))) ((plus_plus_real ((times_times_real A_51) (number267125858f_real V_10))) ((times_times_real B_13) (number267125858f_real V_10))))) % 0.65/0.88 FOF formula (forall (A_51:nat) (B_13:nat) (V_10:int), (((eq nat) ((times_times_nat ((plus_plus_nat A_51) B_13)) (number_number_of_nat V_10))) ((plus_plus_nat ((times_times_nat A_51) (number_number_of_nat V_10))) ((times_times_nat B_13) (number_number_of_nat V_10))))) of role axiom named fact_219_left__distrib__number__of % 0.65/0.88 A new axiom: (forall (A_51:nat) (B_13:nat) (V_10:int), (((eq nat) ((times_times_nat ((plus_plus_nat A_51) B_13)) (number_number_of_nat V_10))) ((plus_plus_nat ((times_times_nat A_51) (number_number_of_nat V_10))) ((times_times_nat B_13) (number_number_of_nat V_10))))) % 0.65/0.88 FOF formula (forall (A_51:int) (B_13:int) (V_10:int), (((eq int) ((times_times_int ((plus_plus_int A_51) B_13)) (number_number_of_int V_10))) ((plus_plus_int ((times_times_int A_51) (number_number_of_int V_10))) ((times_times_int B_13) (number_number_of_int V_10))))) of role axiom named fact_220_left__distrib__number__of % 0.65/0.88 A new axiom: (forall (A_51:int) (B_13:int) (V_10:int), (((eq int) ((times_times_int ((plus_plus_int A_51) B_13)) (number_number_of_int V_10))) ((plus_plus_int ((times_times_int A_51) (number_number_of_int V_10))) ((times_times_int B_13) (number_number_of_int V_10))))) % 0.65/0.88 FOF formula (forall (V_9:int) (B_12:real) (C_2:real), (((eq real) ((times_times_real (number267125858f_real V_9)) ((plus_plus_real B_12) C_2))) ((plus_plus_real ((times_times_real (number267125858f_real V_9)) B_12)) ((times_times_real (number267125858f_real V_9)) C_2)))) of role axiom named fact_221_right__distrib__number__of % 0.65/0.88 A new axiom: (forall (V_9:int) (B_12:real) (C_2:real), (((eq real) ((times_times_real (number267125858f_real V_9)) ((plus_plus_real B_12) C_2))) ((plus_plus_real ((times_times_real (number267125858f_real V_9)) B_12)) ((times_times_real (number267125858f_real V_9)) C_2)))) % 0.65/0.88 FOF formula (forall (V_9:int) (B_12:nat) (C_2:nat), (((eq nat) ((times_times_nat (number_number_of_nat V_9)) ((plus_plus_nat B_12) C_2))) ((plus_plus_nat ((times_times_nat (number_number_of_nat V_9)) B_12)) ((times_times_nat (number_number_of_nat V_9)) C_2)))) of role axiom named fact_222_right__distrib__number__of % 0.65/0.89 A new axiom: (forall (V_9:int) (B_12:nat) (C_2:nat), (((eq nat) ((times_times_nat (number_number_of_nat V_9)) ((plus_plus_nat B_12) C_2))) ((plus_plus_nat ((times_times_nat (number_number_of_nat V_9)) B_12)) ((times_times_nat (number_number_of_nat V_9)) C_2)))) % 0.65/0.89 FOF formula (forall (V_9:int) (B_12:int) (C_2:int), (((eq int) ((times_times_int (number_number_of_int V_9)) ((plus_plus_int B_12) C_2))) ((plus_plus_int ((times_times_int (number_number_of_int V_9)) B_12)) ((times_times_int (number_number_of_int V_9)) C_2)))) of role axiom named fact_223_right__distrib__number__of % 0.65/0.89 A new axiom: (forall (V_9:int) (B_12:int) (C_2:int), (((eq int) ((times_times_int (number_number_of_int V_9)) ((plus_plus_int B_12) C_2))) ((plus_plus_int ((times_times_int (number_number_of_int V_9)) B_12)) ((times_times_int (number_number_of_int V_9)) C_2)))) % 0.65/0.89 FOF formula (forall (A_50:real) (M_12:real), (((eq real) ((plus_plus_real ((times_times_real A_50) M_12)) M_12)) ((times_times_real ((plus_plus_real A_50) one_one_real)) M_12))) of role axiom named fact_224_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J % 0.65/0.89 A new axiom: (forall (A_50:real) (M_12:real), (((eq real) ((plus_plus_real ((times_times_real A_50) M_12)) M_12)) ((times_times_real ((plus_plus_real A_50) one_one_real)) M_12))) % 0.65/0.89 FOF formula (forall (A_50:nat) (M_12:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_50) M_12)) M_12)) ((times_times_nat ((plus_plus_nat A_50) one_one_nat)) M_12))) of role axiom named fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J % 0.65/0.89 A new axiom: (forall (A_50:nat) (M_12:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_50) M_12)) M_12)) ((times_times_nat ((plus_plus_nat A_50) one_one_nat)) M_12))) % 0.65/0.89 FOF formula (forall (A_50:int) (M_12:int), (((eq int) ((plus_plus_int ((times_times_int A_50) M_12)) M_12)) ((times_times_int ((plus_plus_int A_50) one_one_int)) M_12))) of role axiom named fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J % 0.65/0.89 A new axiom: (forall (A_50:int) (M_12:int), (((eq int) ((plus_plus_int ((times_times_int A_50) M_12)) M_12)) ((times_times_int ((plus_plus_int A_50) one_one_int)) M_12))) % 0.65/0.89 FOF formula (forall (M_11:real) (A_49:real), (((eq real) ((plus_plus_real M_11) ((times_times_real A_49) M_11))) ((times_times_real ((plus_plus_real A_49) one_one_real)) M_11))) of role axiom named fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J % 0.65/0.89 A new axiom: (forall (M_11:real) (A_49:real), (((eq real) ((plus_plus_real M_11) ((times_times_real A_49) M_11))) ((times_times_real ((plus_plus_real A_49) one_one_real)) M_11))) % 0.65/0.89 FOF formula (forall (M_11:nat) (A_49:nat), (((eq nat) ((plus_plus_nat M_11) ((times_times_nat A_49) M_11))) ((times_times_nat ((plus_plus_nat A_49) one_one_nat)) M_11))) of role axiom named fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J % 0.65/0.89 A new axiom: (forall (M_11:nat) (A_49:nat), (((eq nat) ((plus_plus_nat M_11) ((times_times_nat A_49) M_11))) ((times_times_nat ((plus_plus_nat A_49) one_one_nat)) M_11))) % 0.65/0.89 FOF formula (forall (M_11:int) (A_49:int), (((eq int) ((plus_plus_int M_11) ((times_times_int A_49) M_11))) ((times_times_int ((plus_plus_int A_49) one_one_int)) M_11))) of role axiom named fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J % 0.65/0.89 A new axiom: (forall (M_11:int) (A_49:int), (((eq int) ((plus_plus_int M_11) ((times_times_int A_49) M_11))) ((times_times_int ((plus_plus_int A_49) one_one_int)) M_11))) % 0.65/0.89 FOF formula (forall (M_10:real), (((eq real) ((plus_plus_real M_10) M_10)) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) M_10))) of role axiom named fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J % 0.65/0.89 A new axiom: (forall (M_10:real), (((eq real) ((plus_plus_real M_10) M_10)) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) M_10))) % 0.65/0.89 FOF formula (forall (M_10:nat), (((eq nat) ((plus_plus_nat M_10) M_10)) ((times_times_nat ((plus_plus_nat one_one_nat) one_one_nat)) M_10))) of role axiom named fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J % 0.73/0.91 A new axiom: (forall (M_10:nat), (((eq nat) ((plus_plus_nat M_10) M_10)) ((times_times_nat ((plus_plus_nat one_one_nat) one_one_nat)) M_10))) % 0.73/0.91 FOF formula (forall (M_10:int), (((eq int) ((plus_plus_int M_10) M_10)) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) M_10))) of role axiom named fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J % 0.73/0.91 A new axiom: (forall (M_10:int), (((eq int) ((plus_plus_int M_10) M_10)) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) M_10))) % 0.73/0.91 FOF formula (forall (A_48:real), (((eq real) ((plus_plus_real (number267125858f_real pls)) A_48)) A_48)) of role axiom named fact_233_add__numeral__0 % 0.73/0.91 A new axiom: (forall (A_48:real), (((eq real) ((plus_plus_real (number267125858f_real pls)) A_48)) A_48)) % 0.73/0.91 FOF formula (forall (A_48:int), (((eq int) ((plus_plus_int (number_number_of_int pls)) A_48)) A_48)) of role axiom named fact_234_add__numeral__0 % 0.73/0.91 A new axiom: (forall (A_48:int), (((eq int) ((plus_plus_int (number_number_of_int pls)) A_48)) A_48)) % 0.73/0.91 FOF formula (forall (A_47:real), (((eq real) ((plus_plus_real A_47) (number267125858f_real pls))) A_47)) of role axiom named fact_235_add__numeral__0__right % 0.73/0.91 A new axiom: (forall (A_47:real), (((eq real) ((plus_plus_real A_47) (number267125858f_real pls))) A_47)) % 0.73/0.91 FOF formula (forall (A_47:int), (((eq int) ((plus_plus_int A_47) (number_number_of_int pls))) A_47)) of role axiom named fact_236_add__numeral__0__right % 0.73/0.91 A new axiom: (forall (A_47:int), (((eq int) ((plus_plus_int A_47) (number_number_of_int pls))) A_47)) % 0.73/0.91 FOF formula (forall (V_8:int) (W_12:int) (Z_6:real), (((eq real) ((times_times_real (number267125858f_real V_8)) ((times_times_real (number267125858f_real W_12)) Z_6))) ((times_times_real (number267125858f_real ((times_times_int V_8) W_12))) Z_6))) of role axiom named fact_237_mult__number__of__left % 0.73/0.91 A new axiom: (forall (V_8:int) (W_12:int) (Z_6:real), (((eq real) ((times_times_real (number267125858f_real V_8)) ((times_times_real (number267125858f_real W_12)) Z_6))) ((times_times_real (number267125858f_real ((times_times_int V_8) W_12))) Z_6))) % 0.73/0.91 FOF formula (forall (V_8:int) (W_12:int) (Z_6:int), (((eq int) ((times_times_int (number_number_of_int V_8)) ((times_times_int (number_number_of_int W_12)) Z_6))) ((times_times_int (number_number_of_int ((times_times_int V_8) W_12))) Z_6))) of role axiom named fact_238_mult__number__of__left % 0.73/0.91 A new axiom: (forall (V_8:int) (W_12:int) (Z_6:int), (((eq int) ((times_times_int (number_number_of_int V_8)) ((times_times_int (number_number_of_int W_12)) Z_6))) ((times_times_int (number_number_of_int ((times_times_int V_8) W_12))) Z_6))) % 0.73/0.91 FOF formula (forall (V_7:int) (W_11:int), (((eq real) ((times_times_real (number267125858f_real V_7)) (number267125858f_real W_11))) (number267125858f_real ((times_times_int V_7) W_11)))) of role axiom named fact_239_arith__simps_I32_J % 0.73/0.91 A new axiom: (forall (V_7:int) (W_11:int), (((eq real) ((times_times_real (number267125858f_real V_7)) (number267125858f_real W_11))) (number267125858f_real ((times_times_int V_7) W_11)))) % 0.73/0.91 FOF formula (forall (V_7:int) (W_11:int), (((eq int) ((times_times_int (number_number_of_int V_7)) (number_number_of_int W_11))) (number_number_of_int ((times_times_int V_7) W_11)))) of role axiom named fact_240_arith__simps_I32_J % 0.73/0.91 A new axiom: (forall (V_7:int) (W_11:int), (((eq int) ((times_times_int (number_number_of_int V_7)) (number_number_of_int W_11))) (number_number_of_int ((times_times_int V_7) W_11)))) % 0.73/0.91 FOF formula (forall (V_6:int) (W_10:int), (((eq real) (number267125858f_real ((times_times_int V_6) W_10))) ((times_times_real (number267125858f_real V_6)) (number267125858f_real W_10)))) of role axiom named fact_241_number__of__mult % 0.73/0.91 A new axiom: (forall (V_6:int) (W_10:int), (((eq real) (number267125858f_real ((times_times_int V_6) W_10))) ((times_times_real (number267125858f_real V_6)) (number267125858f_real W_10)))) % 0.73/0.91 FOF formula (forall (V_6:int) (W_10:int), (((eq int) (number_number_of_int ((times_times_int V_6) W_10))) ((times_times_int (number_number_of_int V_6)) (number_number_of_int W_10)))) of role axiom named fact_242_number__of__mult % 0.73/0.93 A new axiom: (forall (V_6:int) (W_10:int), (((eq int) (number_number_of_int ((times_times_int V_6) W_10))) ((times_times_int (number_number_of_int V_6)) (number_number_of_int W_10)))) % 0.73/0.93 FOF formula (forall (V_5:int) (W_9:int) (Z_5:real), (((eq real) ((plus_plus_real (number267125858f_real V_5)) ((plus_plus_real (number267125858f_real W_9)) Z_5))) ((plus_plus_real (number267125858f_real ((plus_plus_int V_5) W_9))) Z_5))) of role axiom named fact_243_add__number__of__left % 0.73/0.93 A new axiom: (forall (V_5:int) (W_9:int) (Z_5:real), (((eq real) ((plus_plus_real (number267125858f_real V_5)) ((plus_plus_real (number267125858f_real W_9)) Z_5))) ((plus_plus_real (number267125858f_real ((plus_plus_int V_5) W_9))) Z_5))) % 0.73/0.93 FOF formula (forall (V_5:int) (W_9:int) (Z_5:int), (((eq int) ((plus_plus_int (number_number_of_int V_5)) ((plus_plus_int (number_number_of_int W_9)) Z_5))) ((plus_plus_int (number_number_of_int ((plus_plus_int V_5) W_9))) Z_5))) of role axiom named fact_244_add__number__of__left % 0.73/0.93 A new axiom: (forall (V_5:int) (W_9:int) (Z_5:int), (((eq int) ((plus_plus_int (number_number_of_int V_5)) ((plus_plus_int (number_number_of_int W_9)) Z_5))) ((plus_plus_int (number_number_of_int ((plus_plus_int V_5) W_9))) Z_5))) % 0.73/0.93 FOF formula (forall (V_4:int) (W_8:int), (((eq real) ((plus_plus_real (number267125858f_real V_4)) (number267125858f_real W_8))) (number267125858f_real ((plus_plus_int V_4) W_8)))) of role axiom named fact_245_add__number__of__eq % 0.73/0.93 A new axiom: (forall (V_4:int) (W_8:int), (((eq real) ((plus_plus_real (number267125858f_real V_4)) (number267125858f_real W_8))) (number267125858f_real ((plus_plus_int V_4) W_8)))) % 0.73/0.93 FOF formula (forall (V_4:int) (W_8:int), (((eq int) ((plus_plus_int (number_number_of_int V_4)) (number_number_of_int W_8))) (number_number_of_int ((plus_plus_int V_4) W_8)))) of role axiom named fact_246_add__number__of__eq % 0.73/0.93 A new axiom: (forall (V_4:int) (W_8:int), (((eq int) ((plus_plus_int (number_number_of_int V_4)) (number_number_of_int W_8))) (number_number_of_int ((plus_plus_int V_4) W_8)))) % 0.73/0.93 FOF formula (forall (V_3:int) (W_7:int), (((eq real) (number267125858f_real ((plus_plus_int V_3) W_7))) ((plus_plus_real (number267125858f_real V_3)) (number267125858f_real W_7)))) of role axiom named fact_247_number__of__add % 0.73/0.93 A new axiom: (forall (V_3:int) (W_7:int), (((eq real) (number267125858f_real ((plus_plus_int V_3) W_7))) ((plus_plus_real (number267125858f_real V_3)) (number267125858f_real W_7)))) % 0.73/0.93 FOF formula (forall (V_3:int) (W_7:int), (((eq int) (number_number_of_int ((plus_plus_int V_3) W_7))) ((plus_plus_int (number_number_of_int V_3)) (number_number_of_int W_7)))) of role axiom named fact_248_number__of__add % 0.73/0.93 A new axiom: (forall (V_3:int) (W_7:int), (((eq int) (number_number_of_int ((plus_plus_int V_3) W_7))) ((plus_plus_int (number_number_of_int V_3)) (number_number_of_int W_7)))) % 0.73/0.93 FOF formula (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit0 L))) (bit1 ((plus_plus_int K) L)))) of role axiom named fact_249_add__Bit1__Bit0 % 0.73/0.93 A new axiom: (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit0 L))) (bit1 ((plus_plus_int K) L)))) % 0.73/0.93 FOF formula (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit1 L))) (bit1 ((plus_plus_int K) L)))) of role axiom named fact_250_add__Bit0__Bit1 % 0.73/0.93 A new axiom: (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit1 L))) (bit1 ((plus_plus_int K) L)))) % 0.73/0.93 FOF formula (forall (K:int), (((eq int) (bit1 K)) ((plus_plus_int ((plus_plus_int one_one_int) K)) K))) of role axiom named fact_251_Bit1__def % 0.73/0.93 A new axiom: (forall (K:int), (((eq int) (bit1 K)) ((plus_plus_int ((plus_plus_int one_one_int) K)) K))) % 0.73/0.93 FOF formula (forall (W_6:int), (((eq real) (number267125858f_real (bit1 W_6))) ((plus_plus_real ((plus_plus_real one_one_real) (number267125858f_real W_6))) (number267125858f_real W_6)))) of role axiom named fact_252_number__of__Bit1 % 0.73/0.93 A new axiom: (forall (W_6:int), (((eq real) (number267125858f_real (bit1 W_6))) ((plus_plus_real ((plus_plus_real one_one_real) (number267125858f_real W_6))) (number267125858f_real W_6)))) % 0.73/0.94 FOF formula (forall (W_6:int), (((eq int) (number_number_of_int (bit1 W_6))) ((plus_plus_int ((plus_plus_int one_one_int) (number_number_of_int W_6))) (number_number_of_int W_6)))) of role axiom named fact_253_number__of__Bit1 % 0.73/0.94 A new axiom: (forall (W_6:int), (((eq int) (number_number_of_int (bit1 W_6))) ((plus_plus_int ((plus_plus_int one_one_int) (number_number_of_int W_6))) (number_number_of_int W_6)))) % 0.73/0.94 FOF formula (forall (A_46:real), (((eq real) ((times_times_real (number267125858f_real (bit1 pls))) A_46)) A_46)) of role axiom named fact_254_mult__numeral__1 % 0.73/0.94 A new axiom: (forall (A_46:real), (((eq real) ((times_times_real (number267125858f_real (bit1 pls))) A_46)) A_46)) % 0.73/0.94 FOF formula (forall (A_46:int), (((eq int) ((times_times_int (number_number_of_int (bit1 pls))) A_46)) A_46)) of role axiom named fact_255_mult__numeral__1 % 0.73/0.94 A new axiom: (forall (A_46:int), (((eq int) ((times_times_int (number_number_of_int (bit1 pls))) A_46)) A_46)) % 0.73/0.94 FOF formula (forall (A_45:real), (((eq real) ((times_times_real A_45) (number267125858f_real (bit1 pls)))) A_45)) of role axiom named fact_256_mult__numeral__1__right % 0.73/0.94 A new axiom: (forall (A_45:real), (((eq real) ((times_times_real A_45) (number267125858f_real (bit1 pls)))) A_45)) % 0.73/0.94 FOF formula (forall (A_45:int), (((eq int) ((times_times_int A_45) (number_number_of_int (bit1 pls)))) A_45)) of role axiom named fact_257_mult__numeral__1__right % 0.73/0.94 A new axiom: (forall (A_45:int), (((eq int) ((times_times_int A_45) (number_number_of_int (bit1 pls)))) A_45)) % 0.73/0.94 FOF formula (((eq real) (number267125858f_real (bit1 pls))) one_one_real) of role axiom named fact_258_semiring__numeral__1__eq__1 % 0.73/0.94 A new axiom: (((eq real) (number267125858f_real (bit1 pls))) one_one_real) % 0.73/0.94 FOF formula (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat) of role axiom named fact_259_semiring__numeral__1__eq__1 % 0.73/0.94 A new axiom: (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat) % 0.73/0.94 FOF formula (((eq int) (number_number_of_int (bit1 pls))) one_one_int) of role axiom named fact_260_semiring__numeral__1__eq__1 % 0.73/0.94 A new axiom: (((eq int) (number_number_of_int (bit1 pls))) one_one_int) % 0.73/0.94 FOF formula (((eq real) (number267125858f_real (bit1 pls))) one_one_real) of role axiom named fact_261_numeral__1__eq__1 % 0.73/0.94 A new axiom: (((eq real) (number267125858f_real (bit1 pls))) one_one_real) % 0.73/0.94 FOF formula (((eq int) (number_number_of_int (bit1 pls))) one_one_int) of role axiom named fact_262_numeral__1__eq__1 % 0.73/0.94 A new axiom: (((eq int) (number_number_of_int (bit1 pls))) one_one_int) % 0.73/0.94 FOF formula (((eq real) one_one_real) (number267125858f_real (bit1 pls))) of role axiom named fact_263_semiring__norm_I110_J % 0.73/0.94 A new axiom: (((eq real) one_one_real) (number267125858f_real (bit1 pls))) % 0.73/0.94 FOF formula (((eq int) one_one_int) (number_number_of_int (bit1 pls))) of role axiom named fact_264_semiring__norm_I110_J % 0.73/0.94 A new axiom: (((eq int) one_one_int) (number_number_of_int (bit1 pls))) % 0.73/0.94 FOF formula (((eq int) one_one_int) (number_number_of_int (bit1 pls))) of role axiom named fact_265_one__is__num__one % 0.73/0.94 A new axiom: (((eq int) one_one_int) (number_number_of_int (bit1 pls))) % 0.73/0.94 FOF formula (forall (K:int) (L:int), (((eq int) ((times_times_int (bit1 K)) L)) ((plus_plus_int (bit0 ((times_times_int K) L))) L))) of role axiom named fact_266_mult__Bit1 % 0.73/0.94 A new axiom: (forall (K:int) (L:int), (((eq int) ((times_times_int (bit1 K)) L)) ((plus_plus_int (bit0 ((times_times_int K) L))) L))) % 0.73/0.94 FOF formula (forall (W_5:int), (((eq real) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real W_5))) (number267125858f_real (bit0 W_5)))) of role axiom named fact_267_double__number__of__Bit0 % 0.73/0.94 A new axiom: (forall (W_5:int), (((eq real) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real W_5))) (number267125858f_real (bit0 W_5)))) % 0.73/0.94 FOF formula (forall (W_5:int), (((eq int) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int W_5))) (number_number_of_int (bit0 W_5)))) of role axiom named fact_268_double__number__of__Bit0 % 0.73/0.94 A new axiom: (forall (W_5:int), (((eq int) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int W_5))) (number_number_of_int (bit0 W_5)))) % 0.73/0.96 FOF formula (forall (A_44:nat), (((eq nat) ((power_power_nat A_44) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_nat ((times_times_nat A_44) A_44)) A_44))) of role axiom named fact_269_power3__eq__cube % 0.73/0.96 A new axiom: (forall (A_44:nat), (((eq nat) ((power_power_nat A_44) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_nat ((times_times_nat A_44) A_44)) A_44))) % 0.73/0.96 FOF formula (forall (A_44:real), (((eq real) ((power_power_real A_44) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_real ((times_times_real A_44) A_44)) A_44))) of role axiom named fact_270_power3__eq__cube % 0.73/0.96 A new axiom: (forall (A_44:real), (((eq real) ((power_power_real A_44) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_real ((times_times_real A_44) A_44)) A_44))) % 0.73/0.96 FOF formula (forall (A_44:int), (((eq int) ((power_power_int A_44) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int A_44) A_44)) A_44))) of role axiom named fact_271_power3__eq__cube % 0.73/0.96 A new axiom: (forall (A_44:int), (((eq int) ((power_power_int A_44) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int A_44) A_44)) A_44))) % 0.73/0.96 FOF formula (forall (X_1:int), (((eq int) ((power_power_int ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int X_1) (number_number_of_nat (bit0 (bit0 (bit1 pls))))))) of role axiom named fact_272_quartic__square__square % 0.73/0.96 A new axiom: (forall (X_1:int), (((eq int) ((power_power_int ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int X_1) (number_number_of_nat (bit0 (bit0 (bit1 pls))))))) % 0.73/0.96 FOF formula (forall (Z_4:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_4)) ((plus_plus_real Z_4) Z_4))) of role axiom named fact_273_semiring__mult__2 % 0.73/0.96 A new axiom: (forall (Z_4:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_4)) ((plus_plus_real Z_4) Z_4))) % 0.73/0.96 FOF formula (forall (Z_4:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z_4)) ((plus_plus_nat Z_4) Z_4))) of role axiom named fact_274_semiring__mult__2 % 0.73/0.96 A new axiom: (forall (Z_4:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z_4)) ((plus_plus_nat Z_4) Z_4))) % 0.73/0.96 FOF formula (forall (Z_4:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_4)) ((plus_plus_int Z_4) Z_4))) of role axiom named fact_275_semiring__mult__2 % 0.73/0.96 A new axiom: (forall (Z_4:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_4)) ((plus_plus_int Z_4) Z_4))) % 0.73/0.96 FOF formula (forall (Z_3:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_3)) ((plus_plus_real Z_3) Z_3))) of role axiom named fact_276_mult__2 % 0.73/0.96 A new axiom: (forall (Z_3:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_3)) ((plus_plus_real Z_3) Z_3))) % 0.73/0.96 FOF formula (forall (Z_3:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_3)) ((plus_plus_int Z_3) Z_3))) of role axiom named fact_277_mult__2 % 0.73/0.96 A new axiom: (forall (Z_3:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_3)) ((plus_plus_int Z_3) Z_3))) % 0.73/0.96 FOF formula (forall (Z_2:real), (((eq real) ((times_times_real Z_2) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_2) Z_2))) of role axiom named fact_278_semiring__mult__2__right % 0.73/0.96 A new axiom: (forall (Z_2:real), (((eq real) ((times_times_real Z_2) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_2) Z_2))) % 0.73/0.96 FOF formula (forall (Z_2:nat), (((eq nat) ((times_times_nat Z_2) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z_2) Z_2))) of role axiom named fact_279_semiring__mult__2__right % 0.73/0.96 A new axiom: (forall (Z_2:nat), (((eq nat) ((times_times_nat Z_2) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z_2) Z_2))) % 0.73/0.97 FOF formula (forall (Z_2:int), (((eq int) ((times_times_int Z_2) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_2) Z_2))) of role axiom named fact_280_semiring__mult__2__right % 0.73/0.97 A new axiom: (forall (Z_2:int), (((eq int) ((times_times_int Z_2) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_2) Z_2))) % 0.73/0.97 FOF formula (forall (Z_1:real), (((eq real) ((times_times_real Z_1) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_1) Z_1))) of role axiom named fact_281_mult__2__right % 0.73/0.97 A new axiom: (forall (Z_1:real), (((eq real) ((times_times_real Z_1) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_1) Z_1))) % 0.73/0.97 FOF formula (forall (Z_1:int), (((eq int) ((times_times_int Z_1) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_1) Z_1))) of role axiom named fact_282_mult__2__right % 0.73/0.97 A new axiom: (forall (Z_1:int), (((eq int) ((times_times_int Z_1) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_1) Z_1))) % 0.73/0.97 FOF formula (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))) of role axiom named fact_283_semiring__one__add__one__is__two % 0.73/0.97 A new axiom: (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))) % 0.73/0.97 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_284_semiring__one__add__one__is__two % 0.73/0.97 A new axiom: (((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))) % 0.73/0.97 FOF formula (((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))) of role axiom named fact_285_semiring__one__add__one__is__two % 0.73/0.97 A new axiom: (((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))) % 0.73/0.97 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_286_p0 % 0.73/0.97 A new axiom: ((ord_less_int zero_zero_int) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) % 0.73/0.97 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_287__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096 % 0.73/0.97 A new axiom: ((dvd_dvd_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) % 0.73/0.97 FOF formula (forall (P:int), ((zprime P)->((not (((eq int) P) (number_number_of_int (bit0 (bit1 pls)))))->((not (((eq int) P) (number_number_of_int (bit1 (bit1 pls)))))->((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P))))) of role axiom named fact_288_prime__g__5 % 0.73/0.97 A new axiom: (forall (P:int), ((zprime P)->((not (((eq int) P) (number_number_of_int (bit0 (bit1 pls)))))->((not (((eq int) P) (number_number_of_int (bit1 (bit1 pls)))))->((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P))))) % 0.73/0.97 FOF formula (((eq int) (twoSqu1078207634sum2sq ((product_Pair_int_int s) one_one_int))) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)) of role axiom named fact_289__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096 % 0.73/0.97 A new axiom: (((eq int) (twoSqu1078207634sum2sq ((product_Pair_int_int s) one_one_int))) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)) % 0.73/0.97 FOF formula (forall (X_1:real) (Y_1:real), (((eq real) ((power_power_real ((plus_plus_real X_1) Y_1)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_1)) Y_1)))) of role axiom named fact_290_real__sum__squared__expand % 0.81/0.99 A new axiom: (forall (X_1:real) (Y_1:real), (((eq real) ((power_power_real ((plus_plus_real X_1) Y_1)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_1)) Y_1)))) % 0.81/0.99 FOF formula (forall (X_1:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit0 (bit1 pls))))) ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_1)) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_291_four__x__squared % 0.81/0.99 A new axiom: (forall (X_1:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit0 (bit1 pls))))) ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_1)) (number_number_of_nat (bit0 (bit1 pls)))))) % 0.81/0.99 FOF formula (forall (N_37:nat) (A_43:real), (((ord_less_real one_one_real) A_43)->((ord_less_real ((power_power_real A_43) N_37)) ((times_times_real A_43) ((power_power_real A_43) N_37))))) of role axiom named fact_292_power__less__power__Suc % 0.81/0.99 A new axiom: (forall (N_37:nat) (A_43:real), (((ord_less_real one_one_real) A_43)->((ord_less_real ((power_power_real A_43) N_37)) ((times_times_real A_43) ((power_power_real A_43) N_37))))) % 0.81/0.99 FOF formula (forall (N_37:nat) (A_43:nat), (((ord_less_nat one_one_nat) A_43)->((ord_less_nat ((power_power_nat A_43) N_37)) ((times_times_nat A_43) ((power_power_nat A_43) N_37))))) of role axiom named fact_293_power__less__power__Suc % 0.81/0.99 A new axiom: (forall (N_37:nat) (A_43:nat), (((ord_less_nat one_one_nat) A_43)->((ord_less_nat ((power_power_nat A_43) N_37)) ((times_times_nat A_43) ((power_power_nat A_43) N_37))))) % 0.81/0.99 FOF formula (forall (N_37:nat) (A_43:int), (((ord_less_int one_one_int) A_43)->((ord_less_int ((power_power_int A_43) N_37)) ((times_times_int A_43) ((power_power_int A_43) N_37))))) of role axiom named fact_294_power__less__power__Suc % 0.81/0.99 A new axiom: (forall (N_37:nat) (A_43:int), (((ord_less_int one_one_int) A_43)->((ord_less_int ((power_power_int A_43) N_37)) ((times_times_int A_43) ((power_power_int A_43) N_37))))) % 0.81/0.99 FOF formula (forall (N_36:nat) (A_42:real), (((ord_less_real one_one_real) A_42)->((ord_less_real one_one_real) ((times_times_real A_42) ((power_power_real A_42) N_36))))) of role axiom named fact_295_power__gt1__lemma % 0.81/0.99 A new axiom: (forall (N_36:nat) (A_42:real), (((ord_less_real one_one_real) A_42)->((ord_less_real one_one_real) ((times_times_real A_42) ((power_power_real A_42) N_36))))) % 0.81/0.99 FOF formula (forall (N_36:nat) (A_42:nat), (((ord_less_nat one_one_nat) A_42)->((ord_less_nat one_one_nat) ((times_times_nat A_42) ((power_power_nat A_42) N_36))))) of role axiom named fact_296_power__gt1__lemma % 0.81/0.99 A new axiom: (forall (N_36:nat) (A_42:nat), (((ord_less_nat one_one_nat) A_42)->((ord_less_nat one_one_nat) ((times_times_nat A_42) ((power_power_nat A_42) N_36))))) % 0.81/0.99 FOF formula (forall (N_36:nat) (A_42:int), (((ord_less_int one_one_int) A_42)->((ord_less_int one_one_int) ((times_times_int A_42) ((power_power_int A_42) N_36))))) of role axiom named fact_297_power__gt1__lemma % 0.81/0.99 A new axiom: (forall (N_36:nat) (A_42:int), (((ord_less_int one_one_int) A_42)->((ord_less_int one_one_int) ((times_times_int A_42) ((power_power_int A_42) N_36))))) % 0.81/0.99 FOF formula (forall (M_9:nat) (N_35:nat) (A_41:real), (((ord_less_real one_one_real) A_41)->(((ord_less_eq_real ((power_power_real A_41) M_9)) ((power_power_real A_41) N_35))->((ord_less_eq_nat M_9) N_35)))) of role axiom named fact_298_power__le__imp__le__exp % 0.81/0.99 A new axiom: (forall (M_9:nat) (N_35:nat) (A_41:real), (((ord_less_real one_one_real) A_41)->(((ord_less_eq_real ((power_power_real A_41) M_9)) ((power_power_real A_41) N_35))->((ord_less_eq_nat M_9) N_35)))) % 0.81/0.99 FOF formula (forall (M_9:nat) (N_35:nat) (A_41:nat), (((ord_less_nat one_one_nat) A_41)->(((ord_less_eq_nat ((power_power_nat A_41) M_9)) ((power_power_nat A_41) N_35))->((ord_less_eq_nat M_9) N_35)))) of role axiom named fact_299_power__le__imp__le__exp % 0.81/1.01 A new axiom: (forall (M_9:nat) (N_35:nat) (A_41:nat), (((ord_less_nat one_one_nat) A_41)->(((ord_less_eq_nat ((power_power_nat A_41) M_9)) ((power_power_nat A_41) N_35))->((ord_less_eq_nat M_9) N_35)))) % 0.81/1.01 FOF formula (forall (M_9:nat) (N_35:nat) (A_41:int), (((ord_less_int one_one_int) A_41)->(((ord_less_eq_int ((power_power_int A_41) M_9)) ((power_power_int A_41) N_35))->((ord_less_eq_nat M_9) N_35)))) of role axiom named fact_300_power__le__imp__le__exp % 0.81/1.01 A new axiom: (forall (M_9:nat) (N_35:nat) (A_41:int), (((ord_less_int one_one_int) A_41)->(((ord_less_eq_int ((power_power_int A_41) M_9)) ((power_power_int A_41) N_35))->((ord_less_eq_nat M_9) N_35)))) % 0.81/1.01 FOF formula (forall (X_23:nat) (Y_21:nat) (B_11:real), (((ord_less_real one_one_real) B_11)->((iff ((ord_less_eq_real ((power_power_real B_11) X_23)) ((power_power_real B_11) Y_21))) ((ord_less_eq_nat X_23) Y_21)))) of role axiom named fact_301_power__increasing__iff % 0.81/1.01 A new axiom: (forall (X_23:nat) (Y_21:nat) (B_11:real), (((ord_less_real one_one_real) B_11)->((iff ((ord_less_eq_real ((power_power_real B_11) X_23)) ((power_power_real B_11) Y_21))) ((ord_less_eq_nat X_23) Y_21)))) % 0.81/1.01 FOF formula (forall (X_23:nat) (Y_21:nat) (B_11:nat), (((ord_less_nat one_one_nat) B_11)->((iff ((ord_less_eq_nat ((power_power_nat B_11) X_23)) ((power_power_nat B_11) Y_21))) ((ord_less_eq_nat X_23) Y_21)))) of role axiom named fact_302_power__increasing__iff % 0.81/1.01 A new axiom: (forall (X_23:nat) (Y_21:nat) (B_11:nat), (((ord_less_nat one_one_nat) B_11)->((iff ((ord_less_eq_nat ((power_power_nat B_11) X_23)) ((power_power_nat B_11) Y_21))) ((ord_less_eq_nat X_23) Y_21)))) % 0.81/1.01 FOF formula (forall (X_23:nat) (Y_21:nat) (B_11:int), (((ord_less_int one_one_int) B_11)->((iff ((ord_less_eq_int ((power_power_int B_11) X_23)) ((power_power_int B_11) Y_21))) ((ord_less_eq_nat X_23) Y_21)))) of role axiom named fact_303_power__increasing__iff % 0.81/1.01 A new axiom: (forall (X_23:nat) (Y_21:nat) (B_11:int), (((ord_less_int one_one_int) B_11)->((iff ((ord_less_eq_int ((power_power_int B_11) X_23)) ((power_power_int B_11) Y_21))) ((ord_less_eq_nat X_23) Y_21)))) % 0.81/1.01 FOF formula (((zcong ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int s1) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) of role axiom named fact_304__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096 % 0.81/1.01 A new axiom: (((zcong ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int s1) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) % 0.81/1.01 FOF formula ((and ((and ((ord_less_eq_int zero_zero_int) s)) ((ord_less_int s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) of role axiom named fact_305_s0p % 0.81/1.01 A new axiom: ((and ((and ((ord_less_eq_int zero_zero_int) s)) ((ord_less_int s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) s) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) % 0.81/1.01 FOF formula ((ex int) (fun (X:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X)) ((ord_less_int X) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) X) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (forall (Y:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y)) ((ord_less_int Y) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) Y) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))->(((eq int) Y) X)))))) of role axiom named fact_306__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1 % 0.81/1.02 A new axiom: ((ex int) (fun (X:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X)) ((ord_less_int X) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) X) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (forall (Y:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y)) ((ord_less_int Y) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) Y) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))->(((eq int) Y) X)))))) % 0.81/1.02 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_307__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_ % 0.81/1.02 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) % 0.81/1.02 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_308_s1 % 0.81/1.02 A new axiom: (((zcong ((power_power_int s1) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) % 0.81/1.02 FOF formula (forall (A_40:real) (N_34:nat), ((iff (((eq real) ((power_power_real A_40) N_34)) zero_zero_real)) ((and (((eq real) A_40) zero_zero_real)) (not (((eq nat) N_34) zero_zero_nat))))) of role axiom named fact_309_power__eq__0__iff % 0.81/1.02 A new axiom: (forall (A_40:real) (N_34:nat), ((iff (((eq real) ((power_power_real A_40) N_34)) zero_zero_real)) ((and (((eq real) A_40) zero_zero_real)) (not (((eq nat) N_34) zero_zero_nat))))) % 0.81/1.02 FOF formula (forall (A_40:nat) (N_34:nat), ((iff (((eq nat) ((power_power_nat A_40) N_34)) zero_zero_nat)) ((and (((eq nat) A_40) zero_zero_nat)) (not (((eq nat) N_34) zero_zero_nat))))) of role axiom named fact_310_power__eq__0__iff % 0.81/1.02 A new axiom: (forall (A_40:nat) (N_34:nat), ((iff (((eq nat) ((power_power_nat A_40) N_34)) zero_zero_nat)) ((and (((eq nat) A_40) zero_zero_nat)) (not (((eq nat) N_34) zero_zero_nat))))) % 0.81/1.02 FOF formula (forall (A_40:int) (N_34:nat), ((iff (((eq int) ((power_power_int A_40) N_34)) zero_zero_int)) ((and (((eq int) A_40) zero_zero_int)) (not (((eq nat) N_34) zero_zero_nat))))) of role axiom named fact_311_power__eq__0__iff % 0.81/1.02 A new axiom: (forall (A_40:int) (N_34:nat), ((iff (((eq int) ((power_power_int A_40) N_34)) zero_zero_int)) ((and (((eq int) A_40) zero_zero_int)) (not (((eq nat) N_34) zero_zero_nat))))) % 0.81/1.02 FOF formula (forall (A_39:nat) (M_8:nat) (N_33:nat), (((ord_less_eq_nat M_8) N_33)->((dvd_dvd_nat ((power_power_nat A_39) M_8)) ((power_power_nat A_39) N_33)))) of role axiom named fact_312_le__imp__power__dvd % 0.81/1.02 A new axiom: (forall (A_39:nat) (M_8:nat) (N_33:nat), (((ord_less_eq_nat M_8) N_33)->((dvd_dvd_nat ((power_power_nat A_39) M_8)) ((power_power_nat A_39) N_33)))) % 0.81/1.02 FOF formula (forall (A_39:int) (M_8:nat) (N_33:nat), (((ord_less_eq_nat M_8) N_33)->((dvd_dvd_int ((power_power_int A_39) M_8)) ((power_power_int A_39) N_33)))) of role axiom named fact_313_le__imp__power__dvd % 0.81/1.02 A new axiom: (forall (A_39:int) (M_8:nat) (N_33:nat), (((ord_less_eq_nat M_8) N_33)->((dvd_dvd_int ((power_power_int A_39) M_8)) ((power_power_int A_39) N_33)))) % 0.81/1.04 FOF formula (forall (A_39:real) (M_8:nat) (N_33:nat), (((ord_less_eq_nat M_8) N_33)->((dvd_dvd_real ((power_power_real A_39) M_8)) ((power_power_real A_39) N_33)))) of role axiom named fact_314_le__imp__power__dvd % 0.81/1.04 A new axiom: (forall (A_39:real) (M_8:nat) (N_33:nat), (((ord_less_eq_nat M_8) N_33)->((dvd_dvd_real ((power_power_real A_39) M_8)) ((power_power_real A_39) N_33)))) % 0.81/1.04 FOF formula (forall (N_32:nat) (M_7:nat) (X_22:nat) (Y_20:nat), (((dvd_dvd_nat X_22) Y_20)->(((ord_less_eq_nat N_32) M_7)->((dvd_dvd_nat ((power_power_nat X_22) N_32)) ((power_power_nat Y_20) M_7))))) of role axiom named fact_315_dvd__power__le % 0.81/1.04 A new axiom: (forall (N_32:nat) (M_7:nat) (X_22:nat) (Y_20:nat), (((dvd_dvd_nat X_22) Y_20)->(((ord_less_eq_nat N_32) M_7)->((dvd_dvd_nat ((power_power_nat X_22) N_32)) ((power_power_nat Y_20) M_7))))) % 0.81/1.04 FOF formula (forall (N_32:nat) (M_7:nat) (X_22:int) (Y_20:int), (((dvd_dvd_int X_22) Y_20)->(((ord_less_eq_nat N_32) M_7)->((dvd_dvd_int ((power_power_int X_22) N_32)) ((power_power_int Y_20) M_7))))) of role axiom named fact_316_dvd__power__le % 0.81/1.04 A new axiom: (forall (N_32:nat) (M_7:nat) (X_22:int) (Y_20:int), (((dvd_dvd_int X_22) Y_20)->(((ord_less_eq_nat N_32) M_7)->((dvd_dvd_int ((power_power_int X_22) N_32)) ((power_power_int Y_20) M_7))))) % 0.81/1.04 FOF formula (forall (N_32:nat) (M_7:nat) (X_22:real) (Y_20:real), (((dvd_dvd_real X_22) Y_20)->(((ord_less_eq_nat N_32) M_7)->((dvd_dvd_real ((power_power_real X_22) N_32)) ((power_power_real Y_20) M_7))))) of role axiom named fact_317_dvd__power__le % 0.81/1.04 A new axiom: (forall (N_32:nat) (M_7:nat) (X_22:real) (Y_20:real), (((dvd_dvd_real X_22) Y_20)->(((ord_less_eq_nat N_32) M_7)->((dvd_dvd_real ((power_power_real X_22) N_32)) ((power_power_real Y_20) M_7))))) % 0.81/1.04 FOF formula (forall (M_6:nat) (A_38:nat) (N_31:nat) (B_10:nat), (((dvd_dvd_nat ((power_power_nat A_38) N_31)) B_10)->(((ord_less_eq_nat M_6) N_31)->((dvd_dvd_nat ((power_power_nat A_38) M_6)) B_10)))) of role axiom named fact_318_power__le__dvd % 0.81/1.04 A new axiom: (forall (M_6:nat) (A_38:nat) (N_31:nat) (B_10:nat), (((dvd_dvd_nat ((power_power_nat A_38) N_31)) B_10)->(((ord_less_eq_nat M_6) N_31)->((dvd_dvd_nat ((power_power_nat A_38) M_6)) B_10)))) % 0.81/1.04 FOF formula (forall (M_6:nat) (A_38:int) (N_31:nat) (B_10:int), (((dvd_dvd_int ((power_power_int A_38) N_31)) B_10)->(((ord_less_eq_nat M_6) N_31)->((dvd_dvd_int ((power_power_int A_38) M_6)) B_10)))) of role axiom named fact_319_power__le__dvd % 0.81/1.04 A new axiom: (forall (M_6:nat) (A_38:int) (N_31:nat) (B_10:int), (((dvd_dvd_int ((power_power_int A_38) N_31)) B_10)->(((ord_less_eq_nat M_6) N_31)->((dvd_dvd_int ((power_power_int A_38) M_6)) B_10)))) % 0.81/1.04 FOF formula (forall (M_6:nat) (A_38:real) (N_31:nat) (B_10:real), (((dvd_dvd_real ((power_power_real A_38) N_31)) B_10)->(((ord_less_eq_nat M_6) N_31)->((dvd_dvd_real ((power_power_real A_38) M_6)) B_10)))) of role axiom named fact_320_power__le__dvd % 0.81/1.04 A new axiom: (forall (M_6:nat) (A_38:real) (N_31:nat) (B_10:real), (((dvd_dvd_real ((power_power_real A_38) N_31)) B_10)->(((ord_less_eq_nat M_6) N_31)->((dvd_dvd_real ((power_power_real A_38) M_6)) B_10)))) % 0.81/1.04 FOF formula (forall (A_37:real) (N_30:nat) (B_9:real), ((((eq real) ((power_power_real A_37) N_30)) ((power_power_real B_9) N_30))->(((ord_less_eq_real zero_zero_real) A_37)->(((ord_less_eq_real zero_zero_real) B_9)->(((ord_less_nat zero_zero_nat) N_30)->(((eq real) A_37) B_9)))))) of role axiom named fact_321_power__eq__imp__eq__base % 0.81/1.04 A new axiom: (forall (A_37:real) (N_30:nat) (B_9:real), ((((eq real) ((power_power_real A_37) N_30)) ((power_power_real B_9) N_30))->(((ord_less_eq_real zero_zero_real) A_37)->(((ord_less_eq_real zero_zero_real) B_9)->(((ord_less_nat zero_zero_nat) N_30)->(((eq real) A_37) B_9)))))) % 0.81/1.04 FOF formula (forall (A_37:nat) (N_30:nat) (B_9:nat), ((((eq nat) ((power_power_nat A_37) N_30)) ((power_power_nat B_9) N_30))->(((ord_less_eq_nat zero_zero_nat) A_37)->(((ord_less_eq_nat zero_zero_nat) B_9)->(((ord_less_nat zero_zero_nat) N_30)->(((eq nat) A_37) B_9)))))) of role axiom named fact_322_power__eq__imp__eq__base % 0.81/1.04 A new axiom: (forall (A_37:nat) (N_30:nat) (B_9:nat), ((((eq nat) ((power_power_nat A_37) N_30)) ((power_power_nat B_9) N_30))->(((ord_less_eq_nat zero_zero_nat) A_37)->(((ord_less_eq_nat zero_zero_nat) B_9)->(((ord_less_nat zero_zero_nat) N_30)->(((eq nat) A_37) B_9)))))) % 0.81/1.06 FOF formula (forall (A_37:int) (N_30:nat) (B_9:int), ((((eq int) ((power_power_int A_37) N_30)) ((power_power_int B_9) N_30))->(((ord_less_eq_int zero_zero_int) A_37)->(((ord_less_eq_int zero_zero_int) B_9)->(((ord_less_nat zero_zero_nat) N_30)->(((eq int) A_37) B_9)))))) of role axiom named fact_323_power__eq__imp__eq__base % 0.81/1.06 A new axiom: (forall (A_37:int) (N_30:nat) (B_9:int), ((((eq int) ((power_power_int A_37) N_30)) ((power_power_int B_9) N_30))->(((ord_less_eq_int zero_zero_int) A_37)->(((ord_less_eq_int zero_zero_int) B_9)->(((ord_less_nat zero_zero_nat) N_30)->(((eq int) A_37) B_9)))))) % 0.81/1.06 FOF formula (forall (N:int) (M:int), (((ord_less_int zero_zero_int) M)->(((ord_less_int M) N)->(((dvd_dvd_int N) M)->False)))) of role axiom named fact_324_zdvd__not__zless % 0.81/1.06 A new axiom: (forall (N:int) (M:int), (((ord_less_int zero_zero_int) M)->(((ord_less_int M) N)->(((dvd_dvd_int N) M)->False)))) % 0.81/1.06 FOF formula (forall (N:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->(((ord_less_eq_int zero_zero_int) N)->(((dvd_dvd_int M) N)->(((dvd_dvd_int N) M)->(((eq int) M) N)))))) of role axiom named fact_325_zdvd__antisym__nonneg % 0.81/1.06 A new axiom: (forall (N:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->(((ord_less_eq_int zero_zero_int) N)->(((dvd_dvd_int M) N)->(((dvd_dvd_int N) M)->(((eq int) M) N)))))) % 0.81/1.06 FOF formula (forall (K:int) (M:int) (N:int), (((dvd_dvd_int ((times_times_int K) M)) ((times_times_int K) N))->((not (((eq int) K) zero_zero_int))->((dvd_dvd_int M) N)))) of role axiom named fact_326_zdvd__mult__cancel % 0.81/1.06 A new axiom: (forall (K:int) (M:int) (N:int), (((dvd_dvd_int ((times_times_int K) M)) ((times_times_int K) N))->((not (((eq int) K) zero_zero_int))->((dvd_dvd_int M) N)))) % 0.81/1.06 FOF formula (forall (N_29:nat) (X_21:nat) (Y_19:nat), (((dvd_dvd_nat X_21) Y_19)->((dvd_dvd_nat ((power_power_nat X_21) N_29)) ((power_power_nat Y_19) N_29)))) of role axiom named fact_327_dvd__power__same % 0.81/1.06 A new axiom: (forall (N_29:nat) (X_21:nat) (Y_19:nat), (((dvd_dvd_nat X_21) Y_19)->((dvd_dvd_nat ((power_power_nat X_21) N_29)) ((power_power_nat Y_19) N_29)))) % 0.81/1.06 FOF formula (forall (N_29:nat) (X_21:int) (Y_19:int), (((dvd_dvd_int X_21) Y_19)->((dvd_dvd_int ((power_power_int X_21) N_29)) ((power_power_int Y_19) N_29)))) of role axiom named fact_328_dvd__power__same % 0.81/1.06 A new axiom: (forall (N_29:nat) (X_21:int) (Y_19:int), (((dvd_dvd_int X_21) Y_19)->((dvd_dvd_int ((power_power_int X_21) N_29)) ((power_power_int Y_19) N_29)))) % 0.81/1.06 FOF formula (forall (N_29:nat) (X_21:real) (Y_19:real), (((dvd_dvd_real X_21) Y_19)->((dvd_dvd_real ((power_power_real X_21) N_29)) ((power_power_real Y_19) N_29)))) of role axiom named fact_329_dvd__power__same % 0.81/1.06 A new axiom: (forall (N_29:nat) (X_21:real) (Y_19:real), (((dvd_dvd_real X_21) Y_19)->((dvd_dvd_real ((power_power_real X_21) N_29)) ((power_power_real Y_19) N_29)))) % 0.81/1.06 FOF formula (forall (N_28:nat) (A_36:real), ((not (((eq real) A_36) zero_zero_real))->(not (((eq real) ((power_power_real A_36) N_28)) zero_zero_real)))) of role axiom named fact_330_field__power__not__zero % 0.81/1.06 A new axiom: (forall (N_28:nat) (A_36:real), ((not (((eq real) A_36) zero_zero_real))->(not (((eq real) ((power_power_real A_36) N_28)) zero_zero_real)))) % 0.81/1.06 FOF formula (forall (N_28:nat) (A_36:int), ((not (((eq int) A_36) zero_zero_int))->(not (((eq int) ((power_power_int A_36) N_28)) zero_zero_int)))) of role axiom named fact_331_field__power__not__zero % 0.81/1.06 A new axiom: (forall (N_28:nat) (A_36:int), ((not (((eq int) A_36) zero_zero_int))->(not (((eq int) ((power_power_int A_36) N_28)) zero_zero_int)))) % 0.81/1.06 FOF formula (forall (N_27:nat), ((and ((((eq nat) N_27) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) N_27)) one_one_real))) ((not (((eq nat) N_27) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) N_27)) zero_zero_real)))) of role axiom named fact_332_power__0__left % 0.81/1.06 A new axiom: (forall (N_27:nat), ((and ((((eq nat) N_27) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) N_27)) one_one_real))) ((not (((eq nat) N_27) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) N_27)) zero_zero_real)))) % 0.90/1.07 FOF formula (forall (N_27:nat), ((and ((((eq nat) N_27) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) N_27)) one_one_nat))) ((not (((eq nat) N_27) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) N_27)) zero_zero_nat)))) of role axiom named fact_333_power__0__left % 0.90/1.07 A new axiom: (forall (N_27:nat), ((and ((((eq nat) N_27) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) N_27)) one_one_nat))) ((not (((eq nat) N_27) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) N_27)) zero_zero_nat)))) % 0.90/1.07 FOF formula (forall (N_27:nat), ((and ((((eq nat) N_27) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) N_27)) one_one_int))) ((not (((eq nat) N_27) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) N_27)) zero_zero_int)))) of role axiom named fact_334_power__0__left % 0.90/1.07 A new axiom: (forall (N_27:nat), ((and ((((eq nat) N_27) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) N_27)) one_one_int))) ((not (((eq nat) N_27) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) N_27)) zero_zero_int)))) % 0.90/1.07 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_335_zdvd__imp__le % 0.90/1.07 A new axiom: (forall (Z:int) (N:int), (((dvd_dvd_int Z) N)->(((ord_less_int zero_zero_int) N)->((ord_less_eq_int Z) N)))) % 0.90/1.07 FOF formula (forall (N_26:nat) (A_35:real) (B_8:real), (((ord_less_real A_35) B_8)->(((ord_less_eq_real zero_zero_real) A_35)->(((ord_less_nat zero_zero_nat) N_26)->((ord_less_real ((power_power_real A_35) N_26)) ((power_power_real B_8) N_26)))))) of role axiom named fact_336_power__strict__mono % 0.90/1.07 A new axiom: (forall (N_26:nat) (A_35:real) (B_8:real), (((ord_less_real A_35) B_8)->(((ord_less_eq_real zero_zero_real) A_35)->(((ord_less_nat zero_zero_nat) N_26)->((ord_less_real ((power_power_real A_35) N_26)) ((power_power_real B_8) N_26)))))) % 0.90/1.07 FOF formula (forall (N_26:nat) (A_35:nat) (B_8:nat), (((ord_less_nat A_35) B_8)->(((ord_less_eq_nat zero_zero_nat) A_35)->(((ord_less_nat zero_zero_nat) N_26)->((ord_less_nat ((power_power_nat A_35) N_26)) ((power_power_nat B_8) N_26)))))) of role axiom named fact_337_power__strict__mono % 0.90/1.07 A new axiom: (forall (N_26:nat) (A_35:nat) (B_8:nat), (((ord_less_nat A_35) B_8)->(((ord_less_eq_nat zero_zero_nat) A_35)->(((ord_less_nat zero_zero_nat) N_26)->((ord_less_nat ((power_power_nat A_35) N_26)) ((power_power_nat B_8) N_26)))))) % 0.90/1.07 FOF formula (forall (N_26:nat) (A_35:int) (B_8:int), (((ord_less_int A_35) B_8)->(((ord_less_eq_int zero_zero_int) A_35)->(((ord_less_nat zero_zero_nat) N_26)->((ord_less_int ((power_power_int A_35) N_26)) ((power_power_int B_8) N_26)))))) of role axiom named fact_338_power__strict__mono % 0.90/1.07 A new axiom: (forall (N_26:nat) (A_35:int) (B_8:int), (((ord_less_int A_35) B_8)->(((ord_less_eq_int zero_zero_int) A_35)->(((ord_less_nat zero_zero_nat) N_26)->((ord_less_int ((power_power_int A_35) N_26)) ((power_power_int B_8) N_26)))))) % 0.90/1.07 FOF formula (forall (A_34:real), (((eq real) ((times_times_real zero_zero_real) A_34)) zero_zero_real)) of role axiom named fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J % 0.90/1.07 A new axiom: (forall (A_34:real), (((eq real) ((times_times_real zero_zero_real) A_34)) zero_zero_real)) % 0.90/1.07 FOF formula (forall (A_34:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_34)) zero_zero_nat)) of role axiom named fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J % 0.90/1.07 A new axiom: (forall (A_34:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_34)) zero_zero_nat)) % 0.90/1.07 FOF formula (forall (A_34:int), (((eq int) ((times_times_int zero_zero_int) A_34)) zero_zero_int)) of role axiom named fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J % 0.90/1.07 A new axiom: (forall (A_34:int), (((eq int) ((times_times_int zero_zero_int) A_34)) zero_zero_int)) % 0.90/1.07 FOF formula (forall (A_33:real), (((eq real) ((times_times_real A_33) zero_zero_real)) zero_zero_real)) of role axiom named fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J % 0.90/1.09 A new axiom: (forall (A_33:real), (((eq real) ((times_times_real A_33) zero_zero_real)) zero_zero_real)) % 0.90/1.09 FOF formula (forall (A_33:nat), (((eq nat) ((times_times_nat A_33) zero_zero_nat)) zero_zero_nat)) of role axiom named fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J % 0.90/1.09 A new axiom: (forall (A_33:nat), (((eq nat) ((times_times_nat A_33) zero_zero_nat)) zero_zero_nat)) % 0.90/1.09 FOF formula (forall (A_33:int), (((eq int) ((times_times_int A_33) zero_zero_int)) zero_zero_int)) of role axiom named fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J % 0.90/1.09 A new axiom: (forall (A_33:int), (((eq int) ((times_times_int A_33) zero_zero_int)) zero_zero_int)) % 0.90/1.09 FOF formula (forall (A_32:real), (((eq real) ((plus_plus_real zero_zero_real) A_32)) A_32)) of role axiom named fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J % 0.90/1.09 A new axiom: (forall (A_32:real), (((eq real) ((plus_plus_real zero_zero_real) A_32)) A_32)) % 0.90/1.09 FOF formula (forall (A_32:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_32)) A_32)) of role axiom named fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J % 0.90/1.09 A new axiom: (forall (A_32:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_32)) A_32)) % 0.90/1.09 FOF formula (forall (A_32:int), (((eq int) ((plus_plus_int zero_zero_int) A_32)) A_32)) of role axiom named fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J % 0.90/1.09 A new axiom: (forall (A_32:int), (((eq int) ((plus_plus_int zero_zero_int) A_32)) A_32)) % 0.90/1.09 FOF formula (forall (A_31:real), (((eq real) ((plus_plus_real A_31) zero_zero_real)) A_31)) of role axiom named fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J % 0.90/1.09 A new axiom: (forall (A_31:real), (((eq real) ((plus_plus_real A_31) zero_zero_real)) A_31)) % 0.90/1.09 FOF formula (forall (A_31:nat), (((eq nat) ((plus_plus_nat A_31) zero_zero_nat)) A_31)) of role axiom named fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J % 0.90/1.09 A new axiom: (forall (A_31:nat), (((eq nat) ((plus_plus_nat A_31) zero_zero_nat)) A_31)) % 0.90/1.09 FOF formula (forall (A_31:int), (((eq int) ((plus_plus_int A_31) zero_zero_int)) A_31)) of role axiom named fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J % 0.90/1.09 A new axiom: (forall (A_31:int), (((eq int) ((plus_plus_int A_31) zero_zero_int)) A_31)) % 0.90/1.09 FOF formula (forall (B_7:real) (A_30:real), ((iff (((eq real) B_7) ((plus_plus_real B_7) A_30))) (((eq real) A_30) zero_zero_real))) of role axiom named fact_351_add__0__iff % 0.90/1.09 A new axiom: (forall (B_7:real) (A_30:real), ((iff (((eq real) B_7) ((plus_plus_real B_7) A_30))) (((eq real) A_30) zero_zero_real))) % 0.90/1.09 FOF formula (forall (B_7:nat) (A_30:nat), ((iff (((eq nat) B_7) ((plus_plus_nat B_7) A_30))) (((eq nat) A_30) zero_zero_nat))) of role axiom named fact_352_add__0__iff % 0.90/1.09 A new axiom: (forall (B_7:nat) (A_30:nat), ((iff (((eq nat) B_7) ((plus_plus_nat B_7) A_30))) (((eq nat) A_30) zero_zero_nat))) % 0.90/1.09 FOF formula (forall (B_7:int) (A_30:int), ((iff (((eq int) B_7) ((plus_plus_int B_7) A_30))) (((eq int) A_30) zero_zero_int))) of role axiom named fact_353_add__0__iff % 0.90/1.09 A new axiom: (forall (B_7:int) (A_30:int), ((iff (((eq int) B_7) ((plus_plus_int B_7) A_30))) (((eq int) A_30) zero_zero_int))) % 0.90/1.09 FOF formula (forall (A_29:real), ((iff (((eq real) ((plus_plus_real A_29) A_29)) zero_zero_real)) (((eq real) A_29) zero_zero_real))) of role axiom named fact_354_double__eq__0__iff % 0.90/1.09 A new axiom: (forall (A_29:real), ((iff (((eq real) ((plus_plus_real A_29) A_29)) zero_zero_real)) (((eq real) A_29) zero_zero_real))) % 0.90/1.09 FOF formula (forall (A_29:int), ((iff (((eq int) ((plus_plus_int A_29) A_29)) zero_zero_int)) (((eq int) A_29) zero_zero_int))) of role axiom named fact_355_double__eq__0__iff % 0.90/1.09 A new axiom: (forall (A_29:int), ((iff (((eq int) ((plus_plus_int A_29) A_29)) zero_zero_int)) (((eq int) A_29) zero_zero_int))) % 0.90/1.09 FOF formula (((eq int) pls) zero_zero_int) of role axiom named fact_356_Pls__def % 0.90/1.09 A new axiom: (((eq int) pls) zero_zero_int) % 0.92/1.11 FOF formula (not (((eq int) zero_zero_int) one_one_int)) of role axiom named fact_357_int__0__neq__1 % 0.92/1.11 A new axiom: (not (((eq int) zero_zero_int) one_one_int)) % 0.92/1.11 FOF formula (forall (Z:int), (((eq int) ((plus_plus_int zero_zero_int) Z)) Z)) of role axiom named fact_358_zadd__0 % 0.92/1.11 A new axiom: (forall (Z:int), (((eq int) ((plus_plus_int zero_zero_int) Z)) Z)) % 0.92/1.11 FOF formula (forall (Z:int), (((eq int) ((plus_plus_int Z) zero_zero_int)) Z)) of role axiom named fact_359_zadd__0__right % 0.92/1.11 A new axiom: (forall (Z:int), (((eq int) ((plus_plus_int Z) zero_zero_int)) Z)) % 0.92/1.11 FOF formula (forall (N_25:nat) (A_28:real), (((ord_less_eq_real zero_zero_real) A_28)->((ord_less_eq_real zero_zero_real) ((power_power_real A_28) N_25)))) of role axiom named fact_360_zero__le__power % 0.92/1.11 A new axiom: (forall (N_25:nat) (A_28:real), (((ord_less_eq_real zero_zero_real) A_28)->((ord_less_eq_real zero_zero_real) ((power_power_real A_28) N_25)))) % 0.92/1.11 FOF formula (forall (N_25:nat) (A_28:nat), (((ord_less_eq_nat zero_zero_nat) A_28)->((ord_less_eq_nat zero_zero_nat) ((power_power_nat A_28) N_25)))) of role axiom named fact_361_zero__le__power % 0.92/1.11 A new axiom: (forall (N_25:nat) (A_28:nat), (((ord_less_eq_nat zero_zero_nat) A_28)->((ord_less_eq_nat zero_zero_nat) ((power_power_nat A_28) N_25)))) % 0.92/1.11 FOF formula (forall (N_25:nat) (A_28:int), (((ord_less_eq_int zero_zero_int) A_28)->((ord_less_eq_int zero_zero_int) ((power_power_int A_28) N_25)))) of role axiom named fact_362_zero__le__power % 0.92/1.11 A new axiom: (forall (N_25:nat) (A_28:int), (((ord_less_eq_int zero_zero_int) A_28)->((ord_less_eq_int zero_zero_int) ((power_power_int A_28) N_25)))) % 0.92/1.11 FOF formula (forall (N_24:nat) (A_27:real) (B_6:real), (((ord_less_eq_real A_27) B_6)->(((ord_less_eq_real zero_zero_real) A_27)->((ord_less_eq_real ((power_power_real A_27) N_24)) ((power_power_real B_6) N_24))))) of role axiom named fact_363_power__mono % 0.92/1.11 A new axiom: (forall (N_24:nat) (A_27:real) (B_6:real), (((ord_less_eq_real A_27) B_6)->(((ord_less_eq_real zero_zero_real) A_27)->((ord_less_eq_real ((power_power_real A_27) N_24)) ((power_power_real B_6) N_24))))) % 0.92/1.11 FOF formula (forall (N_24:nat) (A_27:nat) (B_6:nat), (((ord_less_eq_nat A_27) B_6)->(((ord_less_eq_nat zero_zero_nat) A_27)->((ord_less_eq_nat ((power_power_nat A_27) N_24)) ((power_power_nat B_6) N_24))))) of role axiom named fact_364_power__mono % 0.92/1.11 A new axiom: (forall (N_24:nat) (A_27:nat) (B_6:nat), (((ord_less_eq_nat A_27) B_6)->(((ord_less_eq_nat zero_zero_nat) A_27)->((ord_less_eq_nat ((power_power_nat A_27) N_24)) ((power_power_nat B_6) N_24))))) % 0.92/1.11 FOF formula (forall (N_24:nat) (A_27:int) (B_6:int), (((ord_less_eq_int A_27) B_6)->(((ord_less_eq_int zero_zero_int) A_27)->((ord_less_eq_int ((power_power_int A_27) N_24)) ((power_power_int B_6) N_24))))) of role axiom named fact_365_power__mono % 0.92/1.11 A new axiom: (forall (N_24:nat) (A_27:int) (B_6:int), (((ord_less_eq_int A_27) B_6)->(((ord_less_eq_int zero_zero_int) A_27)->((ord_less_eq_int ((power_power_int A_27) N_24)) ((power_power_int B_6) N_24))))) % 0.92/1.11 FOF formula (forall (N_23:nat) (A_26:real), (((ord_less_real zero_zero_real) A_26)->((ord_less_real zero_zero_real) ((power_power_real A_26) N_23)))) of role axiom named fact_366_zero__less__power % 0.92/1.11 A new axiom: (forall (N_23:nat) (A_26:real), (((ord_less_real zero_zero_real) A_26)->((ord_less_real zero_zero_real) ((power_power_real A_26) N_23)))) % 0.92/1.11 FOF formula (forall (N_23:nat) (A_26:nat), (((ord_less_nat zero_zero_nat) A_26)->((ord_less_nat zero_zero_nat) ((power_power_nat A_26) N_23)))) of role axiom named fact_367_zero__less__power % 0.92/1.11 A new axiom: (forall (N_23:nat) (A_26:nat), (((ord_less_nat zero_zero_nat) A_26)->((ord_less_nat zero_zero_nat) ((power_power_nat A_26) N_23)))) % 0.92/1.11 FOF formula (forall (N_23:nat) (A_26:int), (((ord_less_int zero_zero_int) A_26)->((ord_less_int zero_zero_int) ((power_power_int A_26) N_23)))) of role axiom named fact_368_zero__less__power % 0.92/1.11 A new axiom: (forall (N_23:nat) (A_26:int), (((ord_less_int zero_zero_int) A_26)->((ord_less_int zero_zero_int) ((power_power_int A_26) N_23)))) % 0.92/1.11 FOF formula (forall (Z:nat) (X_1:int) (Y_1:nat) (P:int), ((((zcong ((power_power_int X_1) Y_1)) one_one_int) P)->(((zcong ((power_power_int X_1) ((times_times_nat Y_1) Z))) one_one_int) P))) of role axiom named fact_369_zcong__zpower__zmult % 0.94/1.12 A new axiom: (forall (Z:nat) (X_1:int) (Y_1:nat) (P:int), ((((zcong ((power_power_int X_1) Y_1)) one_one_int) P)->(((zcong ((power_power_int X_1) ((times_times_nat Y_1) Z))) one_one_int) P))) % 0.94/1.12 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_370_zdvd__reduce % 0.94/1.12 A new axiom: (forall (K:int) (N:int) (M:int), ((iff ((dvd_dvd_int K) ((plus_plus_int N) ((times_times_int K) M)))) ((dvd_dvd_int K) N))) % 0.94/1.12 FOF formula (forall (C:int) (X_1:int) (T:int) (A:int) (D:int), (((dvd_dvd_int A) D)->((iff ((dvd_dvd_int A) ((plus_plus_int X_1) T))) ((dvd_dvd_int A) ((plus_plus_int ((plus_plus_int X_1) ((times_times_int C) D))) T))))) of role axiom named fact_371_zdvd__period % 0.94/1.12 A new axiom: (forall (C:int) (X_1:int) (T:int) (A:int) (D:int), (((dvd_dvd_int A) D)->((iff ((dvd_dvd_int A) ((plus_plus_int X_1) T))) ((dvd_dvd_int A) ((plus_plus_int ((plus_plus_int X_1) ((times_times_int C) D))) T))))) % 0.94/1.12 FOF formula (forall (A_25:real) (N_22:nat) (B_5:real), (((ord_less_real ((power_power_real A_25) N_22)) ((power_power_real B_5) N_22))->(((ord_less_eq_real zero_zero_real) B_5)->((ord_less_real A_25) B_5)))) of role axiom named fact_372_power__less__imp__less__base % 0.94/1.12 A new axiom: (forall (A_25:real) (N_22:nat) (B_5:real), (((ord_less_real ((power_power_real A_25) N_22)) ((power_power_real B_5) N_22))->(((ord_less_eq_real zero_zero_real) B_5)->((ord_less_real A_25) B_5)))) % 0.94/1.12 FOF formula (forall (A_25:nat) (N_22:nat) (B_5:nat), (((ord_less_nat ((power_power_nat A_25) N_22)) ((power_power_nat B_5) N_22))->(((ord_less_eq_nat zero_zero_nat) B_5)->((ord_less_nat A_25) B_5)))) of role axiom named fact_373_power__less__imp__less__base % 0.94/1.12 A new axiom: (forall (A_25:nat) (N_22:nat) (B_5:nat), (((ord_less_nat ((power_power_nat A_25) N_22)) ((power_power_nat B_5) N_22))->(((ord_less_eq_nat zero_zero_nat) B_5)->((ord_less_nat A_25) B_5)))) % 0.94/1.12 FOF formula (forall (A_25:int) (N_22:nat) (B_5:int), (((ord_less_int ((power_power_int A_25) N_22)) ((power_power_int B_5) N_22))->(((ord_less_eq_int zero_zero_int) B_5)->((ord_less_int A_25) B_5)))) of role axiom named fact_374_power__less__imp__less__base % 0.94/1.12 A new axiom: (forall (A_25:int) (N_22:nat) (B_5:int), (((ord_less_int ((power_power_int A_25) N_22)) ((power_power_int B_5) N_22))->(((ord_less_eq_int zero_zero_int) B_5)->((ord_less_int A_25) B_5)))) % 0.94/1.12 FOF formula (forall (A_24:real) (N_21:nat) (N_20:nat), (((ord_less_eq_nat N_21) N_20)->(((ord_less_eq_real zero_zero_real) A_24)->(((ord_less_eq_real A_24) one_one_real)->((ord_less_eq_real ((power_power_real A_24) N_20)) ((power_power_real A_24) N_21)))))) of role axiom named fact_375_power__decreasing % 0.94/1.12 A new axiom: (forall (A_24:real) (N_21:nat) (N_20:nat), (((ord_less_eq_nat N_21) N_20)->(((ord_less_eq_real zero_zero_real) A_24)->(((ord_less_eq_real A_24) one_one_real)->((ord_less_eq_real ((power_power_real A_24) N_20)) ((power_power_real A_24) N_21)))))) % 0.94/1.12 FOF formula (forall (A_24:nat) (N_21:nat) (N_20:nat), (((ord_less_eq_nat N_21) N_20)->(((ord_less_eq_nat zero_zero_nat) A_24)->(((ord_less_eq_nat A_24) one_one_nat)->((ord_less_eq_nat ((power_power_nat A_24) N_20)) ((power_power_nat A_24) N_21)))))) of role axiom named fact_376_power__decreasing % 0.94/1.12 A new axiom: (forall (A_24:nat) (N_21:nat) (N_20:nat), (((ord_less_eq_nat N_21) N_20)->(((ord_less_eq_nat zero_zero_nat) A_24)->(((ord_less_eq_nat A_24) one_one_nat)->((ord_less_eq_nat ((power_power_nat A_24) N_20)) ((power_power_nat A_24) N_21)))))) % 0.94/1.12 FOF formula (forall (A_24:int) (N_21:nat) (N_20:nat), (((ord_less_eq_nat N_21) N_20)->(((ord_less_eq_int zero_zero_int) A_24)->(((ord_less_eq_int A_24) one_one_int)->((ord_less_eq_int ((power_power_int A_24) N_20)) ((power_power_int A_24) N_21)))))) of role axiom named fact_377_power__decreasing % 0.94/1.12 A new axiom: (forall (A_24:int) (N_21:nat) (N_20:nat), (((ord_less_eq_nat N_21) N_20)->(((ord_less_eq_int zero_zero_int) A_24)->(((ord_less_eq_int A_24) one_one_int)->((ord_less_eq_int ((power_power_int A_24) N_20)) ((power_power_int A_24) N_21)))))) % 0.95/1.14 FOF formula (forall (A_23:real) (N_19:nat) (N_18:nat), (((ord_less_nat N_19) N_18)->(((ord_less_real zero_zero_real) A_23)->(((ord_less_real A_23) one_one_real)->((ord_less_real ((power_power_real A_23) N_18)) ((power_power_real A_23) N_19)))))) of role axiom named fact_378_power__strict__decreasing % 0.95/1.14 A new axiom: (forall (A_23:real) (N_19:nat) (N_18:nat), (((ord_less_nat N_19) N_18)->(((ord_less_real zero_zero_real) A_23)->(((ord_less_real A_23) one_one_real)->((ord_less_real ((power_power_real A_23) N_18)) ((power_power_real A_23) N_19)))))) % 0.95/1.14 FOF formula (forall (A_23:nat) (N_19:nat) (N_18:nat), (((ord_less_nat N_19) N_18)->(((ord_less_nat zero_zero_nat) A_23)->(((ord_less_nat A_23) one_one_nat)->((ord_less_nat ((power_power_nat A_23) N_18)) ((power_power_nat A_23) N_19)))))) of role axiom named fact_379_power__strict__decreasing % 0.95/1.14 A new axiom: (forall (A_23:nat) (N_19:nat) (N_18:nat), (((ord_less_nat N_19) N_18)->(((ord_less_nat zero_zero_nat) A_23)->(((ord_less_nat A_23) one_one_nat)->((ord_less_nat ((power_power_nat A_23) N_18)) ((power_power_nat A_23) N_19)))))) % 0.95/1.14 FOF formula (forall (A_23:int) (N_19:nat) (N_18:nat), (((ord_less_nat N_19) N_18)->(((ord_less_int zero_zero_int) A_23)->(((ord_less_int A_23) one_one_int)->((ord_less_int ((power_power_int A_23) N_18)) ((power_power_int A_23) N_19)))))) of role axiom named fact_380_power__strict__decreasing % 0.95/1.14 A new axiom: (forall (A_23:int) (N_19:nat) (N_18:nat), (((ord_less_nat N_19) N_18)->(((ord_less_int zero_zero_int) A_23)->(((ord_less_int A_23) one_one_int)->((ord_less_int ((power_power_int A_23) N_18)) ((power_power_int A_23) N_19)))))) % 0.95/1.14 FOF formula (forall (A_22:real), ((iff ((ord_less_real ((plus_plus_real A_22) A_22)) zero_zero_real)) ((ord_less_real A_22) zero_zero_real))) of role axiom named fact_381_even__less__0__iff % 0.95/1.14 A new axiom: (forall (A_22:real), ((iff ((ord_less_real ((plus_plus_real A_22) A_22)) zero_zero_real)) ((ord_less_real A_22) zero_zero_real))) % 0.95/1.14 FOF formula (forall (A_22:int), ((iff ((ord_less_int ((plus_plus_int A_22) A_22)) zero_zero_int)) ((ord_less_int A_22) zero_zero_int))) of role axiom named fact_382_even__less__0__iff % 0.95/1.14 A new axiom: (forall (A_22:int), ((iff ((ord_less_int ((plus_plus_int A_22) A_22)) zero_zero_int)) ((ord_less_int A_22) zero_zero_int))) % 0.95/1.14 FOF formula (forall (X_20:real) (Y_18:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X_20) X_20)) ((times_times_real Y_18) Y_18))) zero_zero_real)) ((and (((eq real) X_20) zero_zero_real)) (((eq real) Y_18) zero_zero_real)))) of role axiom named fact_383_sum__squares__eq__zero__iff % 0.95/1.14 A new axiom: (forall (X_20:real) (Y_18:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X_20) X_20)) ((times_times_real Y_18) Y_18))) zero_zero_real)) ((and (((eq real) X_20) zero_zero_real)) (((eq real) Y_18) zero_zero_real)))) % 0.95/1.14 FOF formula (forall (X_20:int) (Y_18:int), ((iff (((eq int) ((plus_plus_int ((times_times_int X_20) X_20)) ((times_times_int Y_18) Y_18))) zero_zero_int)) ((and (((eq int) X_20) zero_zero_int)) (((eq int) Y_18) zero_zero_int)))) of role axiom named fact_384_sum__squares__eq__zero__iff % 0.95/1.14 A new axiom: (forall (X_20:int) (Y_18:int), ((iff (((eq int) ((plus_plus_int ((times_times_int X_20) X_20)) ((times_times_int Y_18) Y_18))) zero_zero_int)) ((and (((eq int) X_20) zero_zero_int)) (((eq int) Y_18) zero_zero_int)))) % 0.95/1.14 FOF formula (forall (C_1:real) (D_1:real) (A_21:real) (B_4:real) (R_3:real), ((not (((eq real) R_3) zero_zero_real))->(((and (((eq real) A_21) B_4)) (not (((eq real) C_1) D_1)))->(not (((eq real) ((plus_plus_real A_21) ((times_times_real R_3) C_1))) ((plus_plus_real B_4) ((times_times_real R_3) D_1))))))) of role axiom named fact_385_add__scale__eq__noteq % 0.95/1.14 A new axiom: (forall (C_1:real) (D_1:real) (A_21:real) (B_4:real) (R_3:real), ((not (((eq real) R_3) zero_zero_real))->(((and (((eq real) A_21) B_4)) (not (((eq real) C_1) D_1)))->(not (((eq real) ((plus_plus_real A_21) ((times_times_real R_3) C_1))) ((plus_plus_real B_4) ((times_times_real R_3) D_1))))))) % 0.95/1.16 FOF formula (forall (C_1:nat) (D_1:nat) (A_21:nat) (B_4:nat) (R_3:nat), ((not (((eq nat) R_3) zero_zero_nat))->(((and (((eq nat) A_21) B_4)) (not (((eq nat) C_1) D_1)))->(not (((eq nat) ((plus_plus_nat A_21) ((times_times_nat R_3) C_1))) ((plus_plus_nat B_4) ((times_times_nat R_3) D_1))))))) of role axiom named fact_386_add__scale__eq__noteq % 0.95/1.16 A new axiom: (forall (C_1:nat) (D_1:nat) (A_21:nat) (B_4:nat) (R_3:nat), ((not (((eq nat) R_3) zero_zero_nat))->(((and (((eq nat) A_21) B_4)) (not (((eq nat) C_1) D_1)))->(not (((eq nat) ((plus_plus_nat A_21) ((times_times_nat R_3) C_1))) ((plus_plus_nat B_4) ((times_times_nat R_3) D_1))))))) % 0.95/1.16 FOF formula (forall (C_1:int) (D_1:int) (A_21:int) (B_4:int) (R_3:int), ((not (((eq int) R_3) zero_zero_int))->(((and (((eq int) A_21) B_4)) (not (((eq int) C_1) D_1)))->(not (((eq int) ((plus_plus_int A_21) ((times_times_int R_3) C_1))) ((plus_plus_int B_4) ((times_times_int R_3) D_1))))))) of role axiom named fact_387_add__scale__eq__noteq % 0.95/1.16 A new axiom: (forall (C_1:int) (D_1:int) (A_21:int) (B_4:int) (R_3:int), ((not (((eq int) R_3) zero_zero_int))->(((and (((eq int) A_21) B_4)) (not (((eq int) C_1) D_1)))->(not (((eq int) ((plus_plus_int A_21) ((times_times_int R_3) C_1))) ((plus_plus_int B_4) ((times_times_int R_3) D_1))))))) % 0.95/1.16 FOF formula (forall (A:int) (N:nat) (P:int), ((zprime P)->(((dvd_dvd_int P) ((power_power_int A) N))->((dvd_dvd_int P) A)))) of role axiom named fact_388_zprime__zdvd__power % 0.95/1.16 A new axiom: (forall (A:int) (N:nat) (P:int), ((zprime P)->(((dvd_dvd_int P) ((power_power_int A) N))->((dvd_dvd_int P) A)))) % 0.95/1.16 FOF formula (((eq real) zero_zero_real) (number267125858f_real pls)) of role axiom named fact_389_semiring__norm_I112_J % 0.95/1.16 A new axiom: (((eq real) zero_zero_real) (number267125858f_real pls)) % 0.95/1.16 FOF formula (((eq int) zero_zero_int) (number_number_of_int pls)) of role axiom named fact_390_semiring__norm_I112_J % 0.95/1.16 A new axiom: (((eq int) zero_zero_int) (number_number_of_int pls)) % 0.95/1.16 FOF formula (((eq real) (number267125858f_real pls)) zero_zero_real) of role axiom named fact_391_number__of__Pls % 0.95/1.16 A new axiom: (((eq real) (number267125858f_real pls)) zero_zero_real) % 0.95/1.16 FOF formula (((eq int) (number_number_of_int pls)) zero_zero_int) of role axiom named fact_392_number__of__Pls % 0.95/1.16 A new axiom: (((eq int) (number_number_of_int pls)) zero_zero_int) % 0.95/1.16 FOF formula (((eq real) (number267125858f_real pls)) zero_zero_real) of role axiom named fact_393_semiring__numeral__0__eq__0 % 0.95/1.16 A new axiom: (((eq real) (number267125858f_real pls)) zero_zero_real) % 0.95/1.16 FOF formula (((eq nat) (number_number_of_nat pls)) zero_zero_nat) of role axiom named fact_394_semiring__numeral__0__eq__0 % 0.95/1.16 A new axiom: (((eq nat) (number_number_of_nat pls)) zero_zero_nat) % 0.95/1.16 FOF formula (((eq int) (number_number_of_int pls)) zero_zero_int) of role axiom named fact_395_semiring__numeral__0__eq__0 % 0.95/1.16 A new axiom: (((eq int) (number_number_of_int pls)) zero_zero_int) % 0.95/1.16 FOF formula (forall (W:int), ((iff ((ord_less_int (bit1 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int))) of role axiom named fact_396_bin__less__0__simps_I4_J % 0.95/1.16 A new axiom: (forall (W:int), ((iff ((ord_less_int (bit1 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int))) % 0.95/1.16 FOF formula (((ord_less_int pls) zero_zero_int)->False) of role axiom named fact_397_bin__less__0__simps_I1_J % 0.95/1.16 A new axiom: (((ord_less_int pls) zero_zero_int)->False) % 0.95/1.16 FOF formula (forall (W:int), ((iff ((ord_less_int (bit0 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int))) of role axiom named fact_398_bin__less__0__simps_I3_J % 0.95/1.16 A new axiom: (forall (W:int), ((iff ((ord_less_int (bit0 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int))) % 0.95/1.16 FOF formula (((eq int) zero_zero_int) (number_number_of_int pls)) of role axiom named fact_399_zero__is__num__zero % 0.95/1.16 A new axiom: (((eq int) zero_zero_int) (number_number_of_int pls)) % 0.95/1.16 FOF formula ((ord_less_int zero_zero_int) one_one_int) of role axiom named fact_400_int__0__less__1 % 0.95/1.16 A new axiom: ((ord_less_int zero_zero_int) one_one_int) % 0.95/1.16 FOF formula (forall (B_1:int) (A:int), (((ord_less_int zero_zero_int) A)->(((ord_less_int zero_zero_int) ((times_times_int A) B_1))->((ord_less_int zero_zero_int) B_1)))) of role axiom named fact_401_pos__zmult__pos % 0.95/1.17 A new axiom: (forall (B_1:int) (A:int), (((ord_less_int zero_zero_int) A)->(((ord_less_int zero_zero_int) ((times_times_int A) B_1))->((ord_less_int zero_zero_int) B_1)))) % 0.95/1.17 FOF formula (forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_int _TPTP_I) J)->(((ord_less_int zero_zero_int) K)->((ord_less_int ((times_times_int K) _TPTP_I)) ((times_times_int K) J))))) of role axiom named fact_402_zmult__zless__mono2 % 0.95/1.17 A new axiom: (forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_int _TPTP_I) J)->(((ord_less_int zero_zero_int) K)->((ord_less_int ((times_times_int K) _TPTP_I)) ((times_times_int K) J))))) % 0.95/1.17 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_403_odd__nonzero % 0.95/1.17 A new axiom: (forall (Z:int), (not (((eq int) ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int))) % 0.95/1.17 FOF formula (forall (N_17:nat) (A_20:real), (((ord_less_real zero_zero_real) A_20)->(((ord_less_real A_20) one_one_real)->((ord_less_real ((times_times_real A_20) ((power_power_real A_20) N_17))) ((power_power_real A_20) N_17))))) of role axiom named fact_404_power__Suc__less % 0.95/1.17 A new axiom: (forall (N_17:nat) (A_20:real), (((ord_less_real zero_zero_real) A_20)->(((ord_less_real A_20) one_one_real)->((ord_less_real ((times_times_real A_20) ((power_power_real A_20) N_17))) ((power_power_real A_20) N_17))))) % 0.95/1.17 FOF formula (forall (N_17:nat) (A_20:nat), (((ord_less_nat zero_zero_nat) A_20)->(((ord_less_nat A_20) one_one_nat)->((ord_less_nat ((times_times_nat A_20) ((power_power_nat A_20) N_17))) ((power_power_nat A_20) N_17))))) of role axiom named fact_405_power__Suc__less % 0.95/1.17 A new axiom: (forall (N_17:nat) (A_20:nat), (((ord_less_nat zero_zero_nat) A_20)->(((ord_less_nat A_20) one_one_nat)->((ord_less_nat ((times_times_nat A_20) ((power_power_nat A_20) N_17))) ((power_power_nat A_20) N_17))))) % 0.95/1.17 FOF formula (forall (N_17:nat) (A_20:int), (((ord_less_int zero_zero_int) A_20)->(((ord_less_int A_20) one_one_int)->((ord_less_int ((times_times_int A_20) ((power_power_int A_20) N_17))) ((power_power_int A_20) N_17))))) of role axiom named fact_406_power__Suc__less % 0.95/1.17 A new axiom: (forall (N_17:nat) (A_20:int), (((ord_less_int zero_zero_int) A_20)->(((ord_less_int A_20) one_one_int)->((ord_less_int ((times_times_int A_20) ((power_power_int A_20) N_17))) ((power_power_int A_20) N_17))))) % 0.95/1.17 FOF formula (forall (N:nat) (B_1:int) (A:int) (P:int), ((zprime P)->((((dvd_dvd_int P) A)->False)->(((dvd_dvd_int ((power_power_int P) N)) ((times_times_int A) B_1))->((dvd_dvd_int ((power_power_int P) N)) B_1))))) of role axiom named fact_407_zprime__power__zdvd__cancel__left % 0.95/1.17 A new axiom: (forall (N:nat) (B_1:int) (A:int) (P:int), ((zprime P)->((((dvd_dvd_int P) A)->False)->(((dvd_dvd_int ((power_power_int P) N)) ((times_times_int A) B_1))->((dvd_dvd_int ((power_power_int P) N)) B_1))))) % 0.95/1.17 FOF formula (forall (N:nat) (A:int) (B_1:int) (P:int), ((zprime P)->((((dvd_dvd_int P) B_1)->False)->(((dvd_dvd_int ((power_power_int P) N)) ((times_times_int A) B_1))->((dvd_dvd_int ((power_power_int P) N)) A))))) of role axiom named fact_408_zprime__power__zdvd__cancel__right % 0.95/1.17 A new axiom: (forall (N:nat) (A:int) (B_1:int) (P:int), ((zprime P)->((((dvd_dvd_int P) B_1)->False)->(((dvd_dvd_int ((power_power_int P) N)) ((times_times_int A) B_1))->((dvd_dvd_int ((power_power_int P) N)) A))))) % 0.95/1.17 FOF formula (forall (X_19:real) (Y_17:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((times_times_real X_19) X_19)) ((times_times_real Y_17) Y_17)))) of role axiom named fact_409_sum__squares__ge__zero % 0.95/1.17 A new axiom: (forall (X_19:real) (Y_17:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((times_times_real X_19) X_19)) ((times_times_real Y_17) Y_17)))) % 0.95/1.17 FOF formula (forall (X_19:int) (Y_17:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int X_19) X_19)) ((times_times_int Y_17) Y_17)))) of role axiom named fact_410_sum__squares__ge__zero % 0.95/1.17 A new axiom: (forall (X_19:int) (Y_17:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int X_19) X_19)) ((times_times_int Y_17) Y_17)))) % 0.95/1.19 FOF formula (forall (X_18:real) (Y_16:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real X_18) X_18)) ((times_times_real Y_16) Y_16))) zero_zero_real)) ((and (((eq real) X_18) zero_zero_real)) (((eq real) Y_16) zero_zero_real)))) of role axiom named fact_411_sum__squares__le__zero__iff % 0.95/1.19 A new axiom: (forall (X_18:real) (Y_16:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real X_18) X_18)) ((times_times_real Y_16) Y_16))) zero_zero_real)) ((and (((eq real) X_18) zero_zero_real)) (((eq real) Y_16) zero_zero_real)))) % 0.95/1.19 FOF formula (forall (X_18:int) (Y_16:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int X_18) X_18)) ((times_times_int Y_16) Y_16))) zero_zero_int)) ((and (((eq int) X_18) zero_zero_int)) (((eq int) Y_16) zero_zero_int)))) of role axiom named fact_412_sum__squares__le__zero__iff % 0.95/1.19 A new axiom: (forall (X_18:int) (Y_16:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int X_18) X_18)) ((times_times_int Y_16) Y_16))) zero_zero_int)) ((and (((eq int) X_18) zero_zero_int)) (((eq int) Y_16) zero_zero_int)))) % 0.95/1.19 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_413_less__nat__number__of % 0.95/1.19 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)))) % 0.95/1.19 FOF formula (forall (X_17:real) (Y_15:real), (((ord_less_real ((plus_plus_real ((times_times_real X_17) X_17)) ((times_times_real Y_15) Y_15))) zero_zero_real)->False)) of role axiom named fact_414_not__sum__squares__lt__zero % 0.95/1.19 A new axiom: (forall (X_17:real) (Y_15:real), (((ord_less_real ((plus_plus_real ((times_times_real X_17) X_17)) ((times_times_real Y_15) Y_15))) zero_zero_real)->False)) % 0.95/1.19 FOF formula (forall (X_17:int) (Y_15:int), (((ord_less_int ((plus_plus_int ((times_times_int X_17) X_17)) ((times_times_int Y_15) Y_15))) zero_zero_int)->False)) of role axiom named fact_415_not__sum__squares__lt__zero % 0.95/1.19 A new axiom: (forall (X_17:int) (Y_15:int), (((ord_less_int ((plus_plus_int ((times_times_int X_17) X_17)) ((times_times_int Y_15) Y_15))) zero_zero_int)->False)) % 0.95/1.19 FOF formula (forall (X_16:real) (Y_14:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((times_times_real X_16) X_16)) ((times_times_real Y_14) Y_14)))) ((or (not (((eq real) X_16) zero_zero_real))) (not (((eq real) Y_14) zero_zero_real))))) of role axiom named fact_416_sum__squares__gt__zero__iff % 0.95/1.19 A new axiom: (forall (X_16:real) (Y_14:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((times_times_real X_16) X_16)) ((times_times_real Y_14) Y_14)))) ((or (not (((eq real) X_16) zero_zero_real))) (not (((eq real) Y_14) zero_zero_real))))) % 0.95/1.19 FOF formula (forall (X_16:int) (Y_14:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((times_times_int X_16) X_16)) ((times_times_int Y_14) Y_14)))) ((or (not (((eq int) X_16) zero_zero_int))) (not (((eq int) Y_14) zero_zero_int))))) of role axiom named fact_417_sum__squares__gt__zero__iff % 0.95/1.19 A new axiom: (forall (X_16:int) (Y_14:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((times_times_int X_16) X_16)) ((times_times_int Y_14) Y_14)))) ((or (not (((eq int) X_16) zero_zero_int))) (not (((eq int) Y_14) zero_zero_int))))) % 0.95/1.19 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_418_le__nat__number__of % 0.95/1.19 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)))) % 0.95/1.19 FOF formula (forall (W_4:int), (((eq real) (number267125858f_real (bit0 W_4))) ((plus_plus_real ((plus_plus_real zero_zero_real) (number267125858f_real W_4))) (number267125858f_real W_4)))) of role axiom named fact_419_number__of__Bit0 % 0.95/1.20 A new axiom: (forall (W_4:int), (((eq real) (number267125858f_real (bit0 W_4))) ((plus_plus_real ((plus_plus_real zero_zero_real) (number267125858f_real W_4))) (number267125858f_real W_4)))) % 0.95/1.20 FOF formula (forall (W_4:int), (((eq int) (number_number_of_int (bit0 W_4))) ((plus_plus_int ((plus_plus_int zero_zero_int) (number_number_of_int W_4))) (number_number_of_int W_4)))) of role axiom named fact_420_number__of__Bit0 % 0.95/1.20 A new axiom: (forall (W_4:int), (((eq int) (number_number_of_int (bit0 W_4))) ((plus_plus_int ((plus_plus_int zero_zero_int) (number_number_of_int W_4))) (number_number_of_int W_4)))) % 0.95/1.20 FOF formula (forall (A_19:nat), (((eq nat) ((power_power_nat A_19) one_one_nat)) A_19)) of role axiom named fact_421_power__one__right % 0.95/1.20 A new axiom: (forall (A_19:nat), (((eq nat) ((power_power_nat A_19) one_one_nat)) A_19)) % 0.95/1.20 FOF formula (forall (A_19:real), (((eq real) ((power_power_real A_19) one_one_nat)) A_19)) of role axiom named fact_422_power__one__right % 0.95/1.20 A new axiom: (forall (A_19:real), (((eq real) ((power_power_real A_19) one_one_nat)) A_19)) % 0.95/1.20 FOF formula (forall (A_19:int), (((eq int) ((power_power_int A_19) one_one_nat)) A_19)) of role axiom named fact_423_power__one__right % 0.95/1.20 A new axiom: (forall (A_19:int), (((eq int) ((power_power_int A_19) one_one_nat)) A_19)) % 0.95/1.20 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_424_int__one__le__iff__zero__less % 0.95/1.20 A new axiom: (forall (Z:int), ((iff ((ord_less_eq_int one_one_int) Z)) ((ord_less_int zero_zero_int) Z))) % 0.95/1.20 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_425_pos__zmult__eq__1__iff % 0.95/1.20 A new axiom: (forall (N:int) (M:int), (((ord_less_int zero_zero_int) M)->((iff (((eq int) ((times_times_int M) N)) one_one_int)) ((and (((eq int) M) one_one_int)) (((eq int) N) one_one_int))))) % 0.95/1.20 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_426_odd__less__0 % 0.95/1.20 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))) % 0.95/1.20 FOF formula (forall (Y_13:int), ((iff ((ord_less_real zero_zero_real) (number267125858f_real Y_13))) ((ord_less_int pls) Y_13))) of role axiom named fact_427_less__special_I1_J % 0.95/1.20 A new axiom: (forall (Y_13:int), ((iff ((ord_less_real zero_zero_real) (number267125858f_real Y_13))) ((ord_less_int pls) Y_13))) % 0.95/1.20 FOF formula (forall (Y_13:int), ((iff ((ord_less_int zero_zero_int) (number_number_of_int Y_13))) ((ord_less_int pls) Y_13))) of role axiom named fact_428_less__special_I1_J % 0.95/1.20 A new axiom: (forall (Y_13:int), ((iff ((ord_less_int zero_zero_int) (number_number_of_int Y_13))) ((ord_less_int pls) Y_13))) % 0.95/1.20 FOF formula (forall (X_15:int), ((iff ((ord_less_real (number267125858f_real X_15)) zero_zero_real)) ((ord_less_int X_15) pls))) of role axiom named fact_429_less__special_I3_J % 0.95/1.20 A new axiom: (forall (X_15:int), ((iff ((ord_less_real (number267125858f_real X_15)) zero_zero_real)) ((ord_less_int X_15) pls))) % 0.95/1.20 FOF formula (forall (X_15:int), ((iff ((ord_less_int (number_number_of_int X_15)) zero_zero_int)) ((ord_less_int X_15) pls))) of role axiom named fact_430_less__special_I3_J % 0.95/1.20 A new axiom: (forall (X_15:int), ((iff ((ord_less_int (number_number_of_int X_15)) zero_zero_int)) ((ord_less_int X_15) pls))) % 0.95/1.20 FOF formula (forall (Y_12:int), ((iff ((ord_less_eq_real zero_zero_real) (number267125858f_real Y_12))) ((ord_less_eq_int pls) Y_12))) of role axiom named fact_431_le__special_I1_J % 0.95/1.20 A new axiom: (forall (Y_12:int), ((iff ((ord_less_eq_real zero_zero_real) (number267125858f_real Y_12))) ((ord_less_eq_int pls) Y_12))) % 0.95/1.20 FOF formula (forall (Y_12:int), ((iff ((ord_less_eq_int zero_zero_int) (number_number_of_int Y_12))) ((ord_less_eq_int pls) Y_12))) of role axiom named fact_432_le__special_I1_J % 1.03/1.22 A new axiom: (forall (Y_12:int), ((iff ((ord_less_eq_int zero_zero_int) (number_number_of_int Y_12))) ((ord_less_eq_int pls) Y_12))) % 1.03/1.22 FOF formula (forall (X_14:int), ((iff ((ord_less_eq_real (number267125858f_real X_14)) zero_zero_real)) ((ord_less_eq_int X_14) pls))) of role axiom named fact_433_le__special_I3_J % 1.03/1.22 A new axiom: (forall (X_14:int), ((iff ((ord_less_eq_real (number267125858f_real X_14)) zero_zero_real)) ((ord_less_eq_int X_14) pls))) % 1.03/1.22 FOF formula (forall (X_14:int), ((iff ((ord_less_eq_int (number_number_of_int X_14)) zero_zero_int)) ((ord_less_eq_int X_14) pls))) of role axiom named fact_434_le__special_I3_J % 1.03/1.22 A new axiom: (forall (X_14:int), ((iff ((ord_less_eq_int (number_number_of_int X_14)) zero_zero_int)) ((ord_less_eq_int X_14) pls))) % 1.03/1.22 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_435_le__imp__0__less % 1.03/1.22 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)))) % 1.03/1.22 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_436_zero__power2 % 1.03/1.22 A new axiom: (((eq real) ((power_power_real zero_zero_real) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real) % 1.03/1.22 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_437_zero__power2 % 1.03/1.22 A new axiom: (((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_nat) % 1.03/1.22 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_438_zero__power2 % 1.03/1.22 A new axiom: (((eq int) ((power_power_int zero_zero_int) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int) % 1.03/1.22 FOF formula (forall (A_18:real), ((iff (((eq real) ((power_power_real A_18) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)) (((eq real) A_18) zero_zero_real))) of role axiom named fact_439_zero__eq__power2 % 1.03/1.22 A new axiom: (forall (A_18:real), ((iff (((eq real) ((power_power_real A_18) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)) (((eq real) A_18) zero_zero_real))) % 1.03/1.22 FOF formula (forall (A_18:int), ((iff (((eq int) ((power_power_int A_18) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)) (((eq int) A_18) zero_zero_int))) of role axiom named fact_440_zero__eq__power2 % 1.03/1.22 A new axiom: (forall (A_18:int), ((iff (((eq int) ((power_power_int A_18) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)) (((eq int) A_18) zero_zero_int))) % 1.03/1.22 FOF formula (forall (A_17:real), ((ord_less_eq_real zero_zero_real) ((power_power_real A_17) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_441_zero__le__power2 % 1.03/1.22 A new axiom: (forall (A_17:real), ((ord_less_eq_real zero_zero_real) ((power_power_real A_17) (number_number_of_nat (bit0 (bit1 pls)))))) % 1.03/1.22 FOF formula (forall (A_17:int), ((ord_less_eq_int zero_zero_int) ((power_power_int A_17) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_442_zero__le__power2 % 1.03/1.22 A new axiom: (forall (A_17:int), ((ord_less_eq_int zero_zero_int) ((power_power_int A_17) (number_number_of_nat (bit0 (bit1 pls)))))) % 1.03/1.22 FOF formula (forall (X_13:real) (Y_11:real), (((ord_less_eq_real ((power_power_real X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_11) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_11)->((ord_less_eq_real X_13) Y_11)))) of role axiom named fact_443_power2__le__imp__le % 1.03/1.22 A new axiom: (forall (X_13:real) (Y_11:real), (((ord_less_eq_real ((power_power_real X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_11) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_11)->((ord_less_eq_real X_13) Y_11)))) % 1.03/1.22 FOF formula (forall (X_13:nat) (Y_11:nat), (((ord_less_eq_nat ((power_power_nat X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_11) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_11)->((ord_less_eq_nat X_13) Y_11)))) of role axiom named fact_444_power2__le__imp__le % 1.03/1.24 A new axiom: (forall (X_13:nat) (Y_11:nat), (((ord_less_eq_nat ((power_power_nat X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_11) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_11)->((ord_less_eq_nat X_13) Y_11)))) % 1.03/1.24 FOF formula (forall (X_13:int) (Y_11:int), (((ord_less_eq_int ((power_power_int X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_11) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_11)->((ord_less_eq_int X_13) Y_11)))) of role axiom named fact_445_power2__le__imp__le % 1.03/1.24 A new axiom: (forall (X_13:int) (Y_11:int), (((ord_less_eq_int ((power_power_int X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_11) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_11)->((ord_less_eq_int X_13) Y_11)))) % 1.03/1.24 FOF formula (forall (X_12:real) (Y_10:real), ((((eq real) ((power_power_real X_12) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_10) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) X_12)->(((ord_less_eq_real zero_zero_real) Y_10)->(((eq real) X_12) Y_10))))) of role axiom named fact_446_power2__eq__imp__eq % 1.03/1.24 A new axiom: (forall (X_12:real) (Y_10:real), ((((eq real) ((power_power_real X_12) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_10) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) X_12)->(((ord_less_eq_real zero_zero_real) Y_10)->(((eq real) X_12) Y_10))))) % 1.03/1.24 FOF formula (forall (X_12:nat) (Y_10:nat), ((((eq nat) ((power_power_nat X_12) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_10) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) X_12)->(((ord_less_eq_nat zero_zero_nat) Y_10)->(((eq nat) X_12) Y_10))))) of role axiom named fact_447_power2__eq__imp__eq % 1.03/1.24 A new axiom: (forall (X_12:nat) (Y_10:nat), ((((eq nat) ((power_power_nat X_12) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_10) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) X_12)->(((ord_less_eq_nat zero_zero_nat) Y_10)->(((eq nat) X_12) Y_10))))) % 1.03/1.24 FOF formula (forall (X_12:int) (Y_10:int), ((((eq int) ((power_power_int X_12) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_10) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) X_12)->(((ord_less_eq_int zero_zero_int) Y_10)->(((eq int) X_12) Y_10))))) of role axiom named fact_448_power2__eq__imp__eq % 1.03/1.24 A new axiom: (forall (X_12:int) (Y_10:int), ((((eq int) ((power_power_int X_12) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_10) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) X_12)->(((ord_less_eq_int zero_zero_int) Y_10)->(((eq int) X_12) Y_10))))) % 1.03/1.24 FOF formula (forall (A_16:real), (((ord_less_real ((power_power_real A_16) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)->False)) of role axiom named fact_449_power2__less__0 % 1.03/1.24 A new axiom: (forall (A_16:real), (((ord_less_real ((power_power_real A_16) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)->False)) % 1.03/1.24 FOF formula (forall (A_16:int), (((ord_less_int ((power_power_int A_16) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)->False)) of role axiom named fact_450_power2__less__0 % 1.03/1.24 A new axiom: (forall (A_16:int), (((ord_less_int ((power_power_int A_16) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)->False)) % 1.03/1.24 FOF formula (forall (A_15:real), ((iff ((ord_less_real zero_zero_real) ((power_power_real A_15) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq real) A_15) zero_zero_real)))) of role axiom named fact_451_zero__less__power2 % 1.03/1.24 A new axiom: (forall (A_15:real), ((iff ((ord_less_real zero_zero_real) ((power_power_real A_15) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq real) A_15) zero_zero_real)))) % 1.03/1.24 FOF formula (forall (A_15:int), ((iff ((ord_less_int zero_zero_int) ((power_power_int A_15) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq int) A_15) zero_zero_int)))) of role axiom named fact_452_zero__less__power2 % 1.03/1.25 A new axiom: (forall (A_15:int), ((iff ((ord_less_int zero_zero_int) ((power_power_int A_15) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq int) A_15) zero_zero_int)))) % 1.03/1.25 FOF formula (forall (X_11:real) (Y_9:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_9) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_11) zero_zero_real)) (((eq real) Y_9) zero_zero_real)))) of role axiom named fact_453_sum__power2__eq__zero__iff % 1.03/1.25 A new axiom: (forall (X_11:real) (Y_9:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_9) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_11) zero_zero_real)) (((eq real) Y_9) zero_zero_real)))) % 1.03/1.25 FOF formula (forall (X_11:int) (Y_9:int), ((iff (((eq int) ((plus_plus_int ((power_power_int X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_9) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_11) zero_zero_int)) (((eq int) Y_9) zero_zero_int)))) of role axiom named fact_454_sum__power2__eq__zero__iff % 1.03/1.25 A new axiom: (forall (X_11:int) (Y_9:int), ((iff (((eq int) ((plus_plus_int ((power_power_int X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_9) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_11) zero_zero_int)) (((eq int) Y_9) zero_zero_int)))) % 1.03/1.25 FOF formula (forall (A_14:nat) (N_16:nat), (((eq nat) ((times_times_nat ((power_power_nat A_14) N_16)) A_14)) ((times_times_nat A_14) ((power_power_nat A_14) N_16)))) of role axiom named fact_455_power__commutes % 1.03/1.25 A new axiom: (forall (A_14:nat) (N_16:nat), (((eq nat) ((times_times_nat ((power_power_nat A_14) N_16)) A_14)) ((times_times_nat A_14) ((power_power_nat A_14) N_16)))) % 1.03/1.25 FOF formula (forall (A_14:real) (N_16:nat), (((eq real) ((times_times_real ((power_power_real A_14) N_16)) A_14)) ((times_times_real A_14) ((power_power_real A_14) N_16)))) of role axiom named fact_456_power__commutes % 1.03/1.25 A new axiom: (forall (A_14:real) (N_16:nat), (((eq real) ((times_times_real ((power_power_real A_14) N_16)) A_14)) ((times_times_real A_14) ((power_power_real A_14) N_16)))) % 1.03/1.25 FOF formula (forall (A_14:int) (N_16:nat), (((eq int) ((times_times_int ((power_power_int A_14) N_16)) A_14)) ((times_times_int A_14) ((power_power_int A_14) N_16)))) of role axiom named fact_457_power__commutes % 1.03/1.25 A new axiom: (forall (A_14:int) (N_16:nat), (((eq int) ((times_times_int ((power_power_int A_14) N_16)) A_14)) ((times_times_int A_14) ((power_power_int A_14) N_16)))) % 1.03/1.25 FOF formula (forall (A_13:nat) (B_3:nat) (N_15:nat), (((eq nat) ((power_power_nat ((times_times_nat A_13) B_3)) N_15)) ((times_times_nat ((power_power_nat A_13) N_15)) ((power_power_nat B_3) N_15)))) of role axiom named fact_458_power__mult__distrib % 1.03/1.25 A new axiom: (forall (A_13:nat) (B_3:nat) (N_15:nat), (((eq nat) ((power_power_nat ((times_times_nat A_13) B_3)) N_15)) ((times_times_nat ((power_power_nat A_13) N_15)) ((power_power_nat B_3) N_15)))) % 1.03/1.25 FOF formula (forall (A_13:real) (B_3:real) (N_15:nat), (((eq real) ((power_power_real ((times_times_real A_13) B_3)) N_15)) ((times_times_real ((power_power_real A_13) N_15)) ((power_power_real B_3) N_15)))) of role axiom named fact_459_power__mult__distrib % 1.03/1.25 A new axiom: (forall (A_13:real) (B_3:real) (N_15:nat), (((eq real) ((power_power_real ((times_times_real A_13) B_3)) N_15)) ((times_times_real ((power_power_real A_13) N_15)) ((power_power_real B_3) N_15)))) % 1.03/1.25 FOF formula (forall (A_13:int) (B_3:int) (N_15:nat), (((eq int) ((power_power_int ((times_times_int A_13) B_3)) N_15)) ((times_times_int ((power_power_int A_13) N_15)) ((power_power_int B_3) N_15)))) of role axiom named fact_460_power__mult__distrib % 1.03/1.25 A new axiom: (forall (A_13:int) (B_3:int) (N_15:nat), (((eq int) ((power_power_int ((times_times_int A_13) B_3)) N_15)) ((times_times_int ((power_power_int A_13) N_15)) ((power_power_int B_3) N_15)))) % 1.03/1.27 FOF formula (forall (A_12:nat) (M_5:nat) (N_14:nat), (((eq nat) ((power_power_nat A_12) ((plus_plus_nat M_5) N_14))) ((times_times_nat ((power_power_nat A_12) M_5)) ((power_power_nat A_12) N_14)))) of role axiom named fact_461_power__add % 1.03/1.27 A new axiom: (forall (A_12:nat) (M_5:nat) (N_14:nat), (((eq nat) ((power_power_nat A_12) ((plus_plus_nat M_5) N_14))) ((times_times_nat ((power_power_nat A_12) M_5)) ((power_power_nat A_12) N_14)))) % 1.03/1.27 FOF formula (forall (A_12:real) (M_5:nat) (N_14:nat), (((eq real) ((power_power_real A_12) ((plus_plus_nat M_5) N_14))) ((times_times_real ((power_power_real A_12) M_5)) ((power_power_real A_12) N_14)))) of role axiom named fact_462_power__add % 1.03/1.27 A new axiom: (forall (A_12:real) (M_5:nat) (N_14:nat), (((eq real) ((power_power_real A_12) ((plus_plus_nat M_5) N_14))) ((times_times_real ((power_power_real A_12) M_5)) ((power_power_real A_12) N_14)))) % 1.03/1.27 FOF formula (forall (A_12:int) (M_5:nat) (N_14:nat), (((eq int) ((power_power_int A_12) ((plus_plus_nat M_5) N_14))) ((times_times_int ((power_power_int A_12) M_5)) ((power_power_int A_12) N_14)))) of role axiom named fact_463_power__add % 1.03/1.27 A new axiom: (forall (A_12:int) (M_5:nat) (N_14:nat), (((eq int) ((power_power_int A_12) ((plus_plus_nat M_5) N_14))) ((times_times_int ((power_power_int A_12) M_5)) ((power_power_int A_12) N_14)))) % 1.03/1.27 FOF formula (forall (N_13:nat), (((eq real) ((power_power_real one_one_real) N_13)) one_one_real)) of role axiom named fact_464_power__one % 1.03/1.27 A new axiom: (forall (N_13:nat), (((eq real) ((power_power_real one_one_real) N_13)) one_one_real)) % 1.03/1.27 FOF formula (forall (N_13:nat), (((eq nat) ((power_power_nat one_one_nat) N_13)) one_one_nat)) of role axiom named fact_465_power__one % 1.03/1.27 A new axiom: (forall (N_13:nat), (((eq nat) ((power_power_nat one_one_nat) N_13)) one_one_nat)) % 1.03/1.27 FOF formula (forall (N_13:nat), (((eq int) ((power_power_int one_one_int) N_13)) one_one_int)) of role axiom named fact_466_power__one % 1.03/1.27 A new axiom: (forall (N_13:nat), (((eq int) ((power_power_int one_one_int) N_13)) one_one_int)) % 1.03/1.27 FOF formula (forall (A_11:nat) (M_4:nat) (N_12:nat), (((eq nat) ((power_power_nat A_11) ((times_times_nat M_4) N_12))) ((power_power_nat ((power_power_nat A_11) M_4)) N_12))) of role axiom named fact_467_power__mult % 1.03/1.27 A new axiom: (forall (A_11:nat) (M_4:nat) (N_12:nat), (((eq nat) ((power_power_nat A_11) ((times_times_nat M_4) N_12))) ((power_power_nat ((power_power_nat A_11) M_4)) N_12))) % 1.03/1.27 FOF formula (forall (A_11:real) (M_4:nat) (N_12:nat), (((eq real) ((power_power_real A_11) ((times_times_nat M_4) N_12))) ((power_power_real ((power_power_real A_11) M_4)) N_12))) of role axiom named fact_468_power__mult % 1.03/1.27 A new axiom: (forall (A_11:real) (M_4:nat) (N_12:nat), (((eq real) ((power_power_real A_11) ((times_times_nat M_4) N_12))) ((power_power_real ((power_power_real A_11) M_4)) N_12))) % 1.03/1.27 FOF formula (forall (A_11:int) (M_4:nat) (N_12:nat), (((eq int) ((power_power_int A_11) ((times_times_nat M_4) N_12))) ((power_power_int ((power_power_int A_11) M_4)) N_12))) of role axiom named fact_469_power__mult % 1.03/1.27 A new axiom: (forall (A_11:int) (M_4:nat) (N_12:nat), (((eq int) ((power_power_int A_11) ((times_times_nat M_4) N_12))) ((power_power_int ((power_power_int A_11) M_4)) N_12))) % 1.03/1.27 FOF formula (forall (X_10:real) (Y_8:real), (((ord_less_real ((power_power_real X_10) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_8) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_8)->((ord_less_real X_10) Y_8)))) of role axiom named fact_470_power2__less__imp__less % 1.03/1.27 A new axiom: (forall (X_10:real) (Y_8:real), (((ord_less_real ((power_power_real X_10) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_8) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_8)->((ord_less_real X_10) Y_8)))) % 1.03/1.27 FOF formula (forall (X_10:nat) (Y_8:nat), (((ord_less_nat ((power_power_nat X_10) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_8) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_8)->((ord_less_nat X_10) Y_8)))) of role axiom named fact_471_power2__less__imp__less % 1.11/1.29 A new axiom: (forall (X_10:nat) (Y_8:nat), (((ord_less_nat ((power_power_nat X_10) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_8) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_8)->((ord_less_nat X_10) Y_8)))) % 1.11/1.29 FOF formula (forall (X_10:int) (Y_8:int), (((ord_less_int ((power_power_int X_10) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_8) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_8)->((ord_less_int X_10) Y_8)))) of role axiom named fact_472_power2__less__imp__less % 1.11/1.29 A new axiom: (forall (X_10:int) (Y_8:int), (((ord_less_int ((power_power_int X_10) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_8) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_8)->((ord_less_int X_10) Y_8)))) % 1.11/1.29 FOF formula (forall (X_9:real) (Y_7:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((power_power_real X_9) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_7) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_473_sum__power2__ge__zero % 1.11/1.29 A new axiom: (forall (X_9:real) (Y_7:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((power_power_real X_9) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_7) (number_number_of_nat (bit0 (bit1 pls))))))) % 1.11/1.29 FOF formula (forall (X_9:int) (Y_7:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((power_power_int X_9) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_7) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_474_sum__power2__ge__zero % 1.11/1.29 A new axiom: (forall (X_9:int) (Y_7:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((power_power_int X_9) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_7) (number_number_of_nat (bit0 (bit1 pls))))))) % 1.11/1.29 FOF formula (forall (X_8:real) (Y_6:real), ((iff ((ord_less_eq_real ((plus_plus_real ((power_power_real X_8) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_6) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_8) zero_zero_real)) (((eq real) Y_6) zero_zero_real)))) of role axiom named fact_475_sum__power2__le__zero__iff % 1.11/1.29 A new axiom: (forall (X_8:real) (Y_6:real), ((iff ((ord_less_eq_real ((plus_plus_real ((power_power_real X_8) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_6) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_8) zero_zero_real)) (((eq real) Y_6) zero_zero_real)))) % 1.11/1.29 FOF formula (forall (X_8:int) (Y_6:int), ((iff ((ord_less_eq_int ((plus_plus_int ((power_power_int X_8) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_6) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_8) zero_zero_int)) (((eq int) Y_6) zero_zero_int)))) of role axiom named fact_476_sum__power2__le__zero__iff % 1.11/1.29 A new axiom: (forall (X_8:int) (Y_6:int), ((iff ((ord_less_eq_int ((plus_plus_int ((power_power_int X_8) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_6) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_8) zero_zero_int)) (((eq int) Y_6) zero_zero_int)))) % 1.11/1.29 FOF formula (forall (X_7:real) (Y_5:real), (((ord_less_real ((plus_plus_real ((power_power_real X_7) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)->False)) of role axiom named fact_477_not__sum__power2__lt__zero % 1.11/1.29 A new axiom: (forall (X_7:real) (Y_5:real), (((ord_less_real ((plus_plus_real ((power_power_real X_7) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)->False)) % 1.11/1.29 FOF formula (forall (X_7:int) (Y_5:int), (((ord_less_int ((plus_plus_int ((power_power_int X_7) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)->False)) of role axiom named fact_478_not__sum__power2__lt__zero % 1.11/1.30 A new axiom: (forall (X_7:int) (Y_5:int), (((ord_less_int ((plus_plus_int ((power_power_int X_7) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)->False)) % 1.11/1.30 FOF formula (forall (X_6:real) (Y_4:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((power_power_real X_6) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_4) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq real) X_6) zero_zero_real))) (not (((eq real) Y_4) zero_zero_real))))) of role axiom named fact_479_sum__power2__gt__zero__iff % 1.11/1.30 A new axiom: (forall (X_6:real) (Y_4:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((power_power_real X_6) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_4) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq real) X_6) zero_zero_real))) (not (((eq real) Y_4) zero_zero_real))))) % 1.11/1.30 FOF formula (forall (X_6:int) (Y_4:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((power_power_int X_6) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_4) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq int) X_6) zero_zero_int))) (not (((eq int) Y_4) zero_zero_int))))) of role axiom named fact_480_sum__power2__gt__zero__iff % 1.11/1.30 A new axiom: (forall (X_6:int) (Y_4:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((power_power_int X_6) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_4) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq int) X_6) zero_zero_int))) (not (((eq int) Y_4) zero_zero_int))))) % 1.11/1.30 FOF formula (forall (A_10:real) (N_11:nat), ((ord_less_eq_real zero_zero_real) ((power_power_real A_10) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_11)))) of role axiom named fact_481_zero__le__even__power_H % 1.11/1.30 A new axiom: (forall (A_10:real) (N_11:nat), ((ord_less_eq_real zero_zero_real) ((power_power_real A_10) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_11)))) % 1.11/1.30 FOF formula (forall (A_10:int) (N_11:nat), ((ord_less_eq_int zero_zero_int) ((power_power_int A_10) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_11)))) of role axiom named fact_482_zero__le__even__power_H % 1.11/1.30 A new axiom: (forall (A_10:int) (N_11:nat), ((ord_less_eq_int zero_zero_int) ((power_power_int A_10) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_11)))) % 1.11/1.30 FOF formula (forall (N_10:nat) (A_9:real), (((ord_less_eq_real one_one_real) A_9)->((ord_less_eq_real one_one_real) ((power_power_real A_9) N_10)))) of role axiom named fact_483_one__le__power % 1.11/1.30 A new axiom: (forall (N_10:nat) (A_9:real), (((ord_less_eq_real one_one_real) A_9)->((ord_less_eq_real one_one_real) ((power_power_real A_9) N_10)))) % 1.11/1.30 FOF formula (forall (N_10:nat) (A_9:nat), (((ord_less_eq_nat one_one_nat) A_9)->((ord_less_eq_nat one_one_nat) ((power_power_nat A_9) N_10)))) of role axiom named fact_484_one__le__power % 1.11/1.30 A new axiom: (forall (N_10:nat) (A_9:nat), (((ord_less_eq_nat one_one_nat) A_9)->((ord_less_eq_nat one_one_nat) ((power_power_nat A_9) N_10)))) % 1.11/1.30 FOF formula (forall (N_10:nat) (A_9:int), (((ord_less_eq_int one_one_int) A_9)->((ord_less_eq_int one_one_int) ((power_power_int A_9) N_10)))) of role axiom named fact_485_one__le__power % 1.11/1.30 A new axiom: (forall (N_10:nat) (A_9:int), (((ord_less_eq_int one_one_int) A_9)->((ord_less_eq_int one_one_int) ((power_power_int A_9) N_10)))) % 1.11/1.30 FOF formula (forall (A_8:real) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_real one_one_real) A_8)->((ord_less_eq_real ((power_power_real A_8) N_9)) ((power_power_real A_8) N_8))))) of role axiom named fact_486_power__increasing % 1.11/1.30 A new axiom: (forall (A_8:real) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_real one_one_real) A_8)->((ord_less_eq_real ((power_power_real A_8) N_9)) ((power_power_real A_8) N_8))))) % 1.11/1.30 FOF formula (forall (A_8:nat) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_nat one_one_nat) A_8)->((ord_less_eq_nat ((power_power_nat A_8) N_9)) ((power_power_nat A_8) N_8))))) of role axiom named fact_487_power__increasing % 1.11/1.32 A new axiom: (forall (A_8:nat) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_nat one_one_nat) A_8)->((ord_less_eq_nat ((power_power_nat A_8) N_9)) ((power_power_nat A_8) N_8))))) % 1.11/1.32 FOF formula (forall (A_8:int) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_int one_one_int) A_8)->((ord_less_eq_int ((power_power_int A_8) N_9)) ((power_power_int A_8) N_8))))) of role axiom named fact_488_power__increasing % 1.11/1.32 A new axiom: (forall (A_8:int) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_int one_one_int) A_8)->((ord_less_eq_int ((power_power_int A_8) N_9)) ((power_power_int A_8) N_8))))) % 1.11/1.32 FOF formula (forall (M_3:nat) (N_7:nat) (A_7:real), (((ord_less_real one_one_real) A_7)->((iff (((eq real) ((power_power_real A_7) M_3)) ((power_power_real A_7) N_7))) (((eq nat) M_3) N_7)))) of role axiom named fact_489_power__inject__exp % 1.11/1.32 A new axiom: (forall (M_3:nat) (N_7:nat) (A_7:real), (((ord_less_real one_one_real) A_7)->((iff (((eq real) ((power_power_real A_7) M_3)) ((power_power_real A_7) N_7))) (((eq nat) M_3) N_7)))) % 1.11/1.32 FOF formula (forall (M_3:nat) (N_7:nat) (A_7:nat), (((ord_less_nat one_one_nat) A_7)->((iff (((eq nat) ((power_power_nat A_7) M_3)) ((power_power_nat A_7) N_7))) (((eq nat) M_3) N_7)))) of role axiom named fact_490_power__inject__exp % 1.11/1.32 A new axiom: (forall (M_3:nat) (N_7:nat) (A_7:nat), (((ord_less_nat one_one_nat) A_7)->((iff (((eq nat) ((power_power_nat A_7) M_3)) ((power_power_nat A_7) N_7))) (((eq nat) M_3) N_7)))) % 1.11/1.32 FOF formula (forall (M_3:nat) (N_7:nat) (A_7:int), (((ord_less_int one_one_int) A_7)->((iff (((eq int) ((power_power_int A_7) M_3)) ((power_power_int A_7) N_7))) (((eq nat) M_3) N_7)))) of role axiom named fact_491_power__inject__exp % 1.11/1.32 A new axiom: (forall (M_3:nat) (N_7:nat) (A_7:int), (((ord_less_int one_one_int) A_7)->((iff (((eq int) ((power_power_int A_7) M_3)) ((power_power_int A_7) N_7))) (((eq nat) M_3) N_7)))) % 1.11/1.32 FOF formula (forall (X_5:nat) (Y_3:nat) (B_2:real), (((ord_less_real one_one_real) B_2)->((iff ((ord_less_real ((power_power_real B_2) X_5)) ((power_power_real B_2) Y_3))) ((ord_less_nat X_5) Y_3)))) of role axiom named fact_492_power__strict__increasing__iff % 1.11/1.32 A new axiom: (forall (X_5:nat) (Y_3:nat) (B_2:real), (((ord_less_real one_one_real) B_2)->((iff ((ord_less_real ((power_power_real B_2) X_5)) ((power_power_real B_2) Y_3))) ((ord_less_nat X_5) Y_3)))) % 1.11/1.32 FOF formula (forall (X_5:nat) (Y_3:nat) (B_2:nat), (((ord_less_nat one_one_nat) B_2)->((iff ((ord_less_nat ((power_power_nat B_2) X_5)) ((power_power_nat B_2) Y_3))) ((ord_less_nat X_5) Y_3)))) of role axiom named fact_493_power__strict__increasing__iff % 1.11/1.32 A new axiom: (forall (X_5:nat) (Y_3:nat) (B_2:nat), (((ord_less_nat one_one_nat) B_2)->((iff ((ord_less_nat ((power_power_nat B_2) X_5)) ((power_power_nat B_2) Y_3))) ((ord_less_nat X_5) Y_3)))) % 1.11/1.32 FOF formula (forall (X_5:nat) (Y_3:nat) (B_2:int), (((ord_less_int one_one_int) B_2)->((iff ((ord_less_int ((power_power_int B_2) X_5)) ((power_power_int B_2) Y_3))) ((ord_less_nat X_5) Y_3)))) of role axiom named fact_494_power__strict__increasing__iff % 1.11/1.32 A new axiom: (forall (X_5:nat) (Y_3:nat) (B_2:int), (((ord_less_int one_one_int) B_2)->((iff ((ord_less_int ((power_power_int B_2) X_5)) ((power_power_int B_2) Y_3))) ((ord_less_nat X_5) Y_3)))) % 1.11/1.32 FOF formula (forall (M_2:nat) (N_6:nat) (A_6:real), (((ord_less_real one_one_real) A_6)->(((ord_less_real ((power_power_real A_6) M_2)) ((power_power_real A_6) N_6))->((ord_less_nat M_2) N_6)))) of role axiom named fact_495_power__less__imp__less__exp % 1.11/1.32 A new axiom: (forall (M_2:nat) (N_6:nat) (A_6:real), (((ord_less_real one_one_real) A_6)->(((ord_less_real ((power_power_real A_6) M_2)) ((power_power_real A_6) N_6))->((ord_less_nat M_2) N_6)))) % 1.11/1.32 FOF formula (forall (M_2:nat) (N_6:nat) (A_6:nat), (((ord_less_nat one_one_nat) A_6)->(((ord_less_nat ((power_power_nat A_6) M_2)) ((power_power_nat A_6) N_6))->((ord_less_nat M_2) N_6)))) of role axiom named fact_496_power__less__imp__less__exp % 1.11/1.32 A new axiom: (forall (M_2:nat) (N_6:nat) (A_6:nat), (((ord_less_nat one_one_nat) A_6)->(((ord_less_nat ((power_power_nat A_6) M_2)) ((power_power_nat A_6) N_6))->((ord_less_nat M_2) N_6)))) % 1.11/1.34 FOF formula (forall (M_2:nat) (N_6:nat) (A_6:int), (((ord_less_int one_one_int) A_6)->(((ord_less_int ((power_power_int A_6) M_2)) ((power_power_int A_6) N_6))->((ord_less_nat M_2) N_6)))) of role axiom named fact_497_power__less__imp__less__exp % 1.11/1.34 A new axiom: (forall (M_2:nat) (N_6:nat) (A_6:int), (((ord_less_int one_one_int) A_6)->(((ord_less_int ((power_power_int A_6) M_2)) ((power_power_int A_6) N_6))->((ord_less_nat M_2) N_6)))) % 1.11/1.34 FOF formula (forall (A_5:real) (N_5:nat) (N_4:nat), (((ord_less_nat N_5) N_4)->(((ord_less_real one_one_real) A_5)->((ord_less_real ((power_power_real A_5) N_5)) ((power_power_real A_5) N_4))))) of role axiom named fact_498_power__strict__increasing % 1.11/1.34 A new axiom: (forall (A_5:real) (N_5:nat) (N_4:nat), (((ord_less_nat N_5) N_4)->(((ord_less_real one_one_real) A_5)->((ord_less_real ((power_power_real A_5) N_5)) ((power_power_real A_5) N_4))))) % 1.11/1.34 FOF formula (forall (A_5:nat) (N_5:nat) (N_4:nat), (((ord_less_nat N_5) N_4)->(((ord_less_nat one_one_nat) A_5)->((ord_less_nat ((power_power_nat A_5) N_5)) ((power_power_nat A_5) N_4))))) of role axiom named fact_499_power__strict__increasing % 1.11/1.34 A new axiom: (forall (A_5:nat) (N_5:nat) (N_4:nat), (((ord_less_nat N_5) N_4)->(((ord_less_nat one_one_nat) A_5)->((ord_less_nat ((power_power_nat A_5) N_5)) ((power_power_nat A_5) N_4))))) % 1.11/1.34 FOF formula (forall (A_5:int) (N_5:nat) (N_4:nat), (((ord_less_nat N_5) N_4)->(((ord_less_int one_one_int) A_5)->((ord_less_int ((power_power_int A_5) N_5)) ((power_power_int A_5) N_4))))) of role axiom named fact_500_power__strict__increasing % 1.11/1.34 A new axiom: (forall (A_5:int) (N_5:nat) (N_4:nat), (((ord_less_nat N_5) N_4)->(((ord_less_int one_one_int) A_5)->((ord_less_int ((power_power_int A_5) N_5)) ((power_power_int A_5) N_4))))) % 1.11/1.34 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_501_s % 1.11/1.34 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)) % 1.11/1.34 FOF formula (forall (Y_1:int) (X_1:int) (P:int), (((((zcong X_1) zero_zero_int) P)->False)->((((zcong ((power_power_int Y_1) (number_number_of_nat (bit0 (bit1 pls))))) X_1) P)->(((dvd_dvd_int P) Y_1)->False)))) of role axiom named fact_502_Euler_Oaux____1 % 1.11/1.34 A new axiom: (forall (Y_1:int) (X_1:int) (P:int), (((((zcong X_1) zero_zero_int) P)->False)->((((zcong ((power_power_int Y_1) (number_number_of_nat (bit0 (bit1 pls))))) X_1) P)->(((dvd_dvd_int P) Y_1)->False)))) % 1.11/1.34 FOF formula (forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_int X_1) (number_number_of_int (bit0 (bit1 pls))))->((or (((eq int) X_1) zero_zero_int)) (((eq int) X_1) one_one_int))))) of role axiom named fact_503_int__pos__lt__two__imp__zero__or__one % 1.11/1.34 A new axiom: (forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_int X_1) (number_number_of_int (bit0 (bit1 pls))))->((or (((eq int) X_1) zero_zero_int)) (((eq int) X_1) one_one_int))))) % 1.11/1.34 FOF formula (forall (A_4:real) (K_2:nat), (((ord_less_eq_real ((power_power_real A_4) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_2))) zero_zero_real)->(((eq real) A_4) zero_zero_real))) of role axiom named fact_504_even__power__le__0__imp__0 % 1.11/1.34 A new axiom: (forall (A_4:real) (K_2:nat), (((ord_less_eq_real ((power_power_real A_4) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_2))) zero_zero_real)->(((eq real) A_4) zero_zero_real))) % 1.11/1.34 FOF formula (forall (A_4:int) (K_2:nat), (((ord_less_eq_int ((power_power_int A_4) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_2))) zero_zero_int)->(((eq int) A_4) zero_zero_int))) of role axiom named fact_505_even__power__le__0__imp__0 % 1.11/1.34 A new axiom: (forall (A_4:int) (K_2:nat), (((ord_less_eq_int ((power_power_int A_4) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_2))) zero_zero_int)->(((eq int) A_4) zero_zero_int))) % 1.11/1.35 FOF formula (forall (P:int), ((iff (zprime P)) ((and ((ord_less_int one_one_int) P)) (forall (M_1:int), (((and ((ord_less_eq_int zero_zero_int) M_1)) ((dvd_dvd_int M_1) P))->((or (((eq int) M_1) one_one_int)) (((eq int) M_1) P))))))) of role axiom named fact_506_zprime__def % 1.11/1.35 A new axiom: (forall (P:int), ((iff (zprime P)) ((and ((ord_less_int one_one_int) P)) (forall (M_1:int), (((and ((ord_less_eq_int zero_zero_int) M_1)) ((dvd_dvd_int M_1) P))->((or (((eq int) M_1) one_one_int)) (((eq int) M_1) P))))))) % 1.11/1.35 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_507__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_ % 1.11/1.35 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) % 1.11/1.35 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_508__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096 % 1.11/1.35 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) % 1.11/1.35 FOF formula (forall (X_1:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) N))) ((or ((ord_less_nat zero_zero_nat) X_1)) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_509_nat__zero__less__power__iff % 1.11/1.35 A new axiom: (forall (X_1:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) N))) ((or ((ord_less_nat zero_zero_nat) X_1)) (((eq nat) N) zero_zero_nat)))) % 1.11/1.35 FOF formula (forall (X_1:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) N))) ((or (((eq nat) N) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X_1)))) of role axiom named fact_510_zero__less__power__nat__eq % 1.11/1.35 A new axiom: (forall (X_1:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) N))) ((or (((eq nat) N) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X_1)))) % 1.11/1.35 FOF formula (forall (X_1:nat) (W:int), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) (number_number_of_nat W)))) ((or (((eq nat) (number_number_of_nat W)) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X_1)))) of role axiom named fact_511_zero__less__power__nat__eq__number__of % 1.11/1.35 A new axiom: (forall (X_1:nat) (W:int), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) (number_number_of_nat W)))) ((or (((eq nat) (number_number_of_nat W)) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X_1)))) % 1.11/1.35 FOF formula (forall (M:nat) (N:nat) (_TPTP_I:nat), (((ord_less_nat zero_zero_nat) _TPTP_I)->(((ord_less_nat ((power_power_nat _TPTP_I) M)) ((power_power_nat _TPTP_I) N))->((ord_less_nat M) N)))) of role axiom named fact_512_nat__power__less__imp__less % 1.11/1.35 A new axiom: (forall (M:nat) (N:nat) (_TPTP_I:nat), (((ord_less_nat zero_zero_nat) _TPTP_I)->(((ord_less_nat ((power_power_nat _TPTP_I) M)) ((power_power_nat _TPTP_I) N))->((ord_less_nat M) N)))) % 1.11/1.35 FOF formula (forall (K:int), ((iff (((eq int) (bit1 K)) min)) (((eq int) K) min))) of role axiom named fact_513_rel__simps_I47_J % 1.11/1.35 A new axiom: (forall (K:int), ((iff (((eq int) (bit1 K)) min)) (((eq int) K) min))) % 1.11/1.35 FOF formula (forall (L:int), ((iff (((eq int) min) (bit1 L))) (((eq int) min) L))) of role axiom named fact_514_rel__simps_I43_J % 1.11/1.35 A new axiom: (forall (L:int), ((iff (((eq int) min) (bit1 L))) (((eq int) min) L))) % 1.11/1.35 FOF formula (((eq int) (bit1 min)) min) of role axiom named fact_515_Bit1__Min % 1.11/1.35 A new axiom: (((eq int) (bit1 min)) min) % 1.11/1.35 FOF formula (not (((eq int) pls) min)) of role axiom named fact_516_rel__simps_I37_J % 1.20/1.37 A new axiom: (not (((eq int) pls) min)) % 1.20/1.37 FOF formula (not (((eq int) min) pls)) of role axiom named fact_517_rel__simps_I40_J % 1.20/1.37 A new axiom: (not (((eq int) min) pls)) % 1.20/1.37 FOF formula (forall (K:int), (not (((eq int) (bit0 K)) min))) of role axiom named fact_518_rel__simps_I45_J % 1.20/1.37 A new axiom: (forall (K:int), (not (((eq int) (bit0 K)) min))) % 1.20/1.37 FOF formula (forall (L:int), (not (((eq int) min) (bit0 L)))) of role axiom named fact_519_rel__simps_I42_J % 1.20/1.37 A new axiom: (forall (L:int), (not (((eq int) min) (bit0 L)))) % 1.20/1.37 FOF formula (((ord_less_int min) min)->False) of role axiom named fact_520_rel__simps_I7_J % 1.20/1.37 A new axiom: (((ord_less_int min) min)->False) % 1.20/1.37 FOF formula ((ord_less_eq_int min) min) of role axiom named fact_521_rel__simps_I24_J % 1.20/1.37 A new axiom: ((ord_less_eq_int min) min) % 1.20/1.37 FOF formula (forall (X_1:real), ((iff (((ord_less_real zero_zero_real) ((times_times_real X_1) X_1))->False)) (((eq real) X_1) zero_zero_real))) of role axiom named fact_522_not__real__square__gt__zero % 1.20/1.37 A new axiom: (forall (X_1:real), ((iff (((ord_less_real zero_zero_real) ((times_times_real X_1) X_1))->False)) (((eq real) X_1) zero_zero_real))) % 1.20/1.37 FOF formula (forall (K:int), ((iff ((ord_less_int (bit1 K)) min)) ((ord_less_int K) min))) of role axiom named fact_523_rel__simps_I13_J % 1.20/1.37 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit1 K)) min)) ((ord_less_int K) min))) % 1.20/1.37 FOF formula (forall (K:int), ((iff ((ord_less_int min) (bit1 K))) ((ord_less_int min) K))) of role axiom named fact_524_rel__simps_I9_J % 1.20/1.37 A new axiom: (forall (K:int), ((iff ((ord_less_int min) (bit1 K))) ((ord_less_int min) K))) % 1.20/1.37 FOF formula (((ord_less_int pls) min)->False) of role axiom named fact_525_rel__simps_I3_J % 1.20/1.37 A new axiom: (((ord_less_int pls) min)->False) % 1.20/1.37 FOF formula ((ord_less_int min) pls) of role axiom named fact_526_rel__simps_I6_J % 1.20/1.37 A new axiom: ((ord_less_int min) pls) % 1.20/1.37 FOF formula (forall (K:int), ((iff ((ord_less_int min) (bit0 K))) ((ord_less_int min) K))) of role axiom named fact_527_rel__simps_I8_J % 1.20/1.37 A new axiom: (forall (K:int), ((iff ((ord_less_int min) (bit0 K))) ((ord_less_int min) K))) % 1.20/1.37 FOF formula ((ord_less_int min) zero_zero_int) of role axiom named fact_528_bin__less__0__simps_I2_J % 1.20/1.37 A new axiom: ((ord_less_int min) zero_zero_int) % 1.20/1.37 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) min)) ((ord_less_eq_int K) min))) of role axiom named fact_529_rel__simps_I30_J % 1.20/1.37 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) min)) ((ord_less_eq_int K) min))) % 1.20/1.37 FOF formula (forall (K:int), ((iff ((ord_less_eq_int min) (bit1 K))) ((ord_less_eq_int min) K))) of role axiom named fact_530_rel__simps_I26_J % 1.20/1.37 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int min) (bit1 K))) ((ord_less_eq_int min) K))) % 1.20/1.37 FOF formula (((ord_less_eq_int pls) min)->False) of role axiom named fact_531_rel__simps_I20_J % 1.20/1.37 A new axiom: (((ord_less_eq_int pls) min)->False) % 1.20/1.37 FOF formula ((ord_less_eq_int min) pls) of role axiom named fact_532_rel__simps_I23_J % 1.20/1.37 A new axiom: ((ord_less_eq_int min) pls) % 1.20/1.37 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) min)) ((ord_less_eq_int K) min))) of role axiom named fact_533_rel__simps_I28_J % 1.20/1.37 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) min)) ((ord_less_eq_int K) min))) % 1.20/1.37 FOF formula (not (((eq int) (number_number_of_int pls)) (number_number_of_int min))) of role axiom named fact_534_eq__number__of__Pls__Min % 1.20/1.37 A new axiom: (not (((eq int) (number_number_of_int pls)) (number_number_of_int min))) % 1.20/1.37 FOF formula (forall (_TPTP_I:nat) (M:nat) (N:nat), (((dvd_dvd_nat ((power_power_nat _TPTP_I) M)) ((power_power_nat _TPTP_I) N))->(((ord_less_nat one_one_nat) _TPTP_I)->((ord_less_eq_nat M) N)))) of role axiom named fact_535_power__dvd__imp__le % 1.20/1.37 A new axiom: (forall (_TPTP_I:nat) (M:nat) (N:nat), (((dvd_dvd_nat ((power_power_nat _TPTP_I) M)) ((power_power_nat _TPTP_I) N))->(((ord_less_nat one_one_nat) _TPTP_I)->((ord_less_eq_nat M) N)))) % 1.20/1.37 FOF formula (forall (X_4:real), (((eq real) ((power_power_real X_4) zero_zero_nat)) one_one_real)) of role axiom named fact_536_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J % 1.20/1.37 A new axiom: (forall (X_4:real), (((eq real) ((power_power_real X_4) zero_zero_nat)) one_one_real)) % 1.21/1.39 FOF formula (forall (X_4:nat), (((eq nat) ((power_power_nat X_4) zero_zero_nat)) one_one_nat)) of role axiom named fact_537_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J % 1.21/1.39 A new axiom: (forall (X_4:nat), (((eq nat) ((power_power_nat X_4) zero_zero_nat)) one_one_nat)) % 1.21/1.39 FOF formula (forall (X_4:int), (((eq int) ((power_power_int X_4) zero_zero_nat)) one_one_int)) of role axiom named fact_538_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J % 1.21/1.39 A new axiom: (forall (X_4:int), (((eq int) ((power_power_int X_4) zero_zero_nat)) one_one_int)) % 1.21/1.39 FOF formula (forall (A_3:real), (((eq real) ((power_power_real A_3) zero_zero_nat)) one_one_real)) of role axiom named fact_539_power__0 % 1.21/1.39 A new axiom: (forall (A_3:real), (((eq real) ((power_power_real A_3) zero_zero_nat)) one_one_real)) % 1.21/1.39 FOF formula (forall (A_3:nat), (((eq nat) ((power_power_nat A_3) zero_zero_nat)) one_one_nat)) of role axiom named fact_540_power__0 % 1.21/1.39 A new axiom: (forall (A_3:nat), (((eq nat) ((power_power_nat A_3) zero_zero_nat)) one_one_nat)) % 1.21/1.39 FOF formula (forall (A_3:int), (((eq int) ((power_power_int A_3) zero_zero_nat)) one_one_int)) of role axiom named fact_541_power__0 % 1.21/1.39 A new axiom: (forall (A_3:int), (((eq int) ((power_power_int A_3) zero_zero_nat)) one_one_int)) % 1.21/1.39 FOF formula (((eq nat) (number_number_of_nat pls)) zero_zero_nat) of role axiom named fact_542_nat__number__of__Pls % 1.21/1.39 A new axiom: (((eq nat) (number_number_of_nat pls)) zero_zero_nat) % 1.21/1.39 FOF formula (((eq nat) zero_zero_nat) (number_number_of_nat pls)) of role axiom named fact_543_semiring__norm_I113_J % 1.21/1.39 A new axiom: (((eq nat) zero_zero_nat) (number_number_of_nat pls)) % 1.21/1.39 FOF formula (forall (K:int), ((iff ((ord_less_eq_int min) (bit0 K))) ((ord_less_int min) K))) of role axiom named fact_544_rel__simps_I25_J % 1.21/1.39 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int min) (bit0 K))) ((ord_less_int min) K))) % 1.21/1.39 FOF formula (forall (K:int), ((iff ((ord_less_int (bit0 K)) min)) ((ord_less_eq_int K) min))) of role axiom named fact_545_rel__simps_I11_J % 1.21/1.39 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit0 K)) min)) ((ord_less_eq_int K) min))) % 1.21/1.39 FOF formula (forall (M:int) (N:int), ((((eq int) ((times_times_int M) N)) one_one_int)->((or (((eq int) M) one_one_int)) (((eq int) M) (number_number_of_int min))))) of role axiom named fact_546_pos__zmult__eq__1__iff__lemma % 1.21/1.39 A new axiom: (forall (M:int) (N:int), ((((eq int) ((times_times_int M) N)) one_one_int)->((or (((eq int) M) one_one_int)) (((eq int) M) (number_number_of_int min))))) % 1.21/1.39 FOF formula (forall (M:int) (N:int), ((iff (((eq int) ((times_times_int M) N)) one_one_int)) ((or ((and (((eq int) M) one_one_int)) (((eq int) N) one_one_int))) ((and (((eq int) M) (number_number_of_int min))) (((eq int) N) (number_number_of_int min)))))) of role axiom named fact_547_zmult__eq__1__iff % 1.21/1.39 A new axiom: (forall (M:int) (N:int), ((iff (((eq int) ((times_times_int M) N)) one_one_int)) ((or ((and (((eq int) M) one_one_int)) (((eq int) N) one_one_int))) ((and (((eq int) M) (number_number_of_int min))) (((eq int) N) (number_number_of_int min)))))) % 1.21/1.39 FOF formula (forall (N_3:nat) (A_2:real), (((ord_less_real one_one_real) A_2)->(((ord_less_nat zero_zero_nat) N_3)->((ord_less_real one_one_real) ((power_power_real A_2) N_3))))) of role axiom named fact_548_one__less__power % 1.21/1.39 A new axiom: (forall (N_3:nat) (A_2:real), (((ord_less_real one_one_real) A_2)->(((ord_less_nat zero_zero_nat) N_3)->((ord_less_real one_one_real) ((power_power_real A_2) N_3))))) % 1.21/1.39 FOF formula (forall (N_3:nat) (A_2:nat), (((ord_less_nat one_one_nat) A_2)->(((ord_less_nat zero_zero_nat) N_3)->((ord_less_nat one_one_nat) ((power_power_nat A_2) N_3))))) of role axiom named fact_549_one__less__power % 1.21/1.39 A new axiom: (forall (N_3:nat) (A_2:nat), (((ord_less_nat one_one_nat) A_2)->(((ord_less_nat zero_zero_nat) N_3)->((ord_less_nat one_one_nat) ((power_power_nat A_2) N_3))))) % 1.21/1.39 FOF formula (forall (N_3:nat) (A_2:int), (((ord_less_int one_one_int) A_2)->(((ord_less_nat zero_zero_nat) N_3)->((ord_less_int one_one_int) ((power_power_int A_2) N_3))))) of role axiom named fact_550_one__less__power % 1.21/1.41 A new axiom: (forall (N_3:nat) (A_2:int), (((ord_less_int one_one_int) A_2)->(((ord_less_nat zero_zero_nat) N_3)->((ord_less_int one_one_int) ((power_power_int A_2) N_3))))) % 1.21/1.41 FOF formula (forall (X_3:nat) (N_2:nat), (((or ((ord_less_nat zero_zero_nat) N_2)) (((eq nat) X_3) one_one_nat))->((dvd_dvd_nat X_3) ((power_power_nat X_3) N_2)))) of role axiom named fact_551_dvd__power % 1.21/1.41 A new axiom: (forall (X_3:nat) (N_2:nat), (((or ((ord_less_nat zero_zero_nat) N_2)) (((eq nat) X_3) one_one_nat))->((dvd_dvd_nat X_3) ((power_power_nat X_3) N_2)))) % 1.21/1.41 FOF formula (forall (X_3:int) (N_2:nat), (((or ((ord_less_nat zero_zero_nat) N_2)) (((eq int) X_3) one_one_int))->((dvd_dvd_int X_3) ((power_power_int X_3) N_2)))) of role axiom named fact_552_dvd__power % 1.21/1.41 A new axiom: (forall (X_3:int) (N_2:nat), (((or ((ord_less_nat zero_zero_nat) N_2)) (((eq int) X_3) one_one_int))->((dvd_dvd_int X_3) ((power_power_int X_3) N_2)))) % 1.21/1.41 FOF formula (forall (X_3:real) (N_2:nat), (((or ((ord_less_nat zero_zero_nat) N_2)) (((eq real) X_3) one_one_real))->((dvd_dvd_real X_3) ((power_power_real X_3) N_2)))) of role axiom named fact_553_dvd__power % 1.21/1.41 A new axiom: (forall (X_3:real) (N_2:nat), (((or ((ord_less_nat zero_zero_nat) N_2)) (((eq real) X_3) one_one_real))->((dvd_dvd_real X_3) ((power_power_real X_3) N_2)))) % 1.21/1.41 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_554_less__0__number__of % 1.21/1.41 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))) % 1.21/1.41 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_555_eq__number__of__0 % 1.21/1.41 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))) % 1.21/1.41 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_556_eq__0__number__of % 1.21/1.41 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))) % 1.21/1.41 FOF formula (forall (A:int) (B_1:int) (M:int), ((iff (((zcong A) B_1) M)) (((zcong B_1) A) M))) of role axiom named fact_557_zcong__sym % 1.21/1.41 A new axiom: (forall (A:int) (B_1:int) (M:int), ((iff (((zcong A) B_1) M)) (((zcong B_1) A) M))) % 1.21/1.41 FOF formula (forall (K:int) (M:int), (((zcong K) K) M)) of role axiom named fact_558_zcong__refl % 1.21/1.41 A new axiom: (forall (K:int) (M:int), (((zcong K) K) M)) % 1.21/1.41 FOF formula (forall (C:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((((zcong B_1) C) M)->(((zcong A) C) M)))) of role axiom named fact_559_zcong__trans % 1.21/1.41 A new axiom: (forall (C:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((((zcong B_1) C) M)->(((zcong A) C) M)))) % 1.21/1.41 FOF formula ((ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls)))) of role axiom named fact_560_pos2 % 1.21/1.41 A new axiom: ((ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls)))) % 1.21/1.41 FOF formula (forall (V_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_561_nat__number__of__mult__left % 1.21/1.41 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))))) % 1.21/1.41 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_562_mult__nat__number__of % 1.25/1.43 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)))))) % 1.25/1.43 FOF formula (forall (X_2:real) (Y_2:real), (((ord_less_eq_real X_2) Y_2)->((not (((eq real) X_2) Y_2))->((ord_less_real X_2) Y_2)))) of role axiom named fact_563_order__le__neq__implies__less % 1.25/1.43 A new axiom: (forall (X_2:real) (Y_2:real), (((ord_less_eq_real X_2) Y_2)->((not (((eq real) X_2) Y_2))->((ord_less_real X_2) Y_2)))) % 1.25/1.43 FOF formula (forall (X_2:nat) (Y_2:nat), (((ord_less_eq_nat X_2) Y_2)->((not (((eq nat) X_2) Y_2))->((ord_less_nat X_2) Y_2)))) of role axiom named fact_564_order__le__neq__implies__less % 1.25/1.43 A new axiom: (forall (X_2:nat) (Y_2:nat), (((ord_less_eq_nat X_2) Y_2)->((not (((eq nat) X_2) Y_2))->((ord_less_nat X_2) Y_2)))) % 1.25/1.43 FOF formula (forall (X_2:int) (Y_2:int), (((ord_less_eq_int X_2) Y_2)->((not (((eq int) X_2) Y_2))->((ord_less_int X_2) Y_2)))) of role axiom named fact_565_order__le__neq__implies__less % 1.25/1.43 A new axiom: (forall (X_2:int) (Y_2:int), (((ord_less_eq_int X_2) Y_2)->((not (((eq int) X_2) Y_2))->((ord_less_int X_2) Y_2)))) % 1.25/1.43 FOF formula (forall (B_1:int) (A:int) (C:int), (((ord_less_int A) C)->(((ord_less_int B_1) C)->((or ((ord_less_eq_int A) B_1)) ((ord_less_eq_int B_1) A))))) of role axiom named fact_566_Euler_Oaux2 % 1.25/1.43 A new axiom: (forall (B_1:int) (A:int) (C:int), (((ord_less_int A) C)->(((ord_less_int B_1) C)->((or ((ord_less_eq_int A) B_1)) ((ord_less_eq_int B_1) A))))) % 1.25/1.43 FOF formula (forall (A:int) (B_1:int), ((iff (((zcong A) B_1) zero_zero_int)) (((eq int) A) B_1))) of role axiom named fact_567_IntPrimes_Ozcong__zero % 1.25/1.43 A new axiom: (forall (A:int) (B_1:int), ((iff (((zcong A) B_1) zero_zero_int)) (((eq int) A) B_1))) % 1.25/1.43 FOF formula (forall (A:int) (B_1:int), (((zcong A) B_1) one_one_int)) of role axiom named fact_568_zcong__1 % 1.25/1.43 A new axiom: (forall (A:int) (B_1:int), (((zcong A) B_1) one_one_int)) % 1.25/1.43 FOF formula (forall (C:int) (D:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((((zcong C) D) M)->(((zcong ((times_times_int A) C)) ((times_times_int B_1) D)) M)))) of role axiom named fact_569_zcong__zmult % 1.25/1.43 A new axiom: (forall (C:int) (D:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((((zcong C) D) M)->(((zcong ((times_times_int A) C)) ((times_times_int B_1) D)) M)))) % 1.25/1.43 FOF formula (forall (K:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->(((zcong ((times_times_int K) A)) ((times_times_int K) B_1)) M))) of role axiom named fact_570_zcong__scalar2 % 1.25/1.43 A new axiom: (forall (K:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->(((zcong ((times_times_int K) A)) ((times_times_int K) B_1)) M))) % 1.25/1.43 FOF formula (forall (K:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->(((zcong ((times_times_int A) K)) ((times_times_int B_1) K)) M))) of role axiom named fact_571_zcong__scalar % 1.25/1.43 A new axiom: (forall (K:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->(((zcong ((times_times_int A) K)) ((times_times_int B_1) K)) M))) % 1.25/1.43 FOF formula (forall (A:int) (M:int) (B_1:int), (((zcong ((times_times_int A) M)) ((times_times_int B_1) M)) M)) of role axiom named fact_572_zcong__zmult__self % 1.25/1.43 A new axiom: (forall (A:int) (M:int) (B_1:int), (((zcong ((times_times_int A) M)) ((times_times_int B_1) M)) M)) % 1.25/1.43 FOF formula (forall (C:int) (D:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((((zcong C) D) M)->(((zcong ((plus_plus_int A) C)) ((plus_plus_int B_1) D)) M)))) of role axiom named fact_573_zcong__zadd % 1.25/1.43 A new axiom: (forall (C:int) (D:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((((zcong C) D) M)->(((zcong ((plus_plus_int A) C)) ((plus_plus_int B_1) D)) M)))) % 1.25/1.44 FOF formula (forall (N_1:nat), (((eq real) ((power_power_real (number267125858f_real min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_1))) one_one_real)) of role axiom named fact_574_power__m1__even % 1.25/1.44 A new axiom: (forall (N_1:nat), (((eq real) ((power_power_real (number267125858f_real min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_1))) one_one_real)) % 1.25/1.44 FOF formula (forall (N_1:nat), (((eq int) ((power_power_int (number_number_of_int min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_1))) one_one_int)) of role axiom named fact_575_power__m1__even % 1.25/1.44 A new axiom: (forall (N_1:nat), (((eq int) ((power_power_int (number_number_of_int min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_1))) one_one_int)) % 1.25/1.44 FOF formula (forall (A_1:real) (W_3:int), ((iff (((eq real) ((power_power_real A_1) (number_number_of_nat W_3))) zero_zero_real)) ((and (((eq real) A_1) zero_zero_real)) (not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))))) of role axiom named fact_576_power__eq__0__iff__number__of % 1.25/1.44 A new axiom: (forall (A_1:real) (W_3:int), ((iff (((eq real) ((power_power_real A_1) (number_number_of_nat W_3))) zero_zero_real)) ((and (((eq real) A_1) zero_zero_real)) (not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))))) % 1.25/1.44 FOF formula (forall (A_1:nat) (W_3:int), ((iff (((eq nat) ((power_power_nat A_1) (number_number_of_nat W_3))) zero_zero_nat)) ((and (((eq nat) A_1) zero_zero_nat)) (not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))))) of role axiom named fact_577_power__eq__0__iff__number__of % 1.25/1.44 A new axiom: (forall (A_1:nat) (W_3:int), ((iff (((eq nat) ((power_power_nat A_1) (number_number_of_nat W_3))) zero_zero_nat)) ((and (((eq nat) A_1) zero_zero_nat)) (not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))))) % 1.25/1.44 FOF formula (forall (A_1:int) (W_3:int), ((iff (((eq int) ((power_power_int A_1) (number_number_of_nat W_3))) zero_zero_int)) ((and (((eq int) A_1) zero_zero_int)) (not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))))) of role axiom named fact_578_power__eq__0__iff__number__of % 1.25/1.44 A new axiom: (forall (A_1:int) (W_3:int), ((iff (((eq int) ((power_power_int A_1) (number_number_of_nat W_3))) zero_zero_int)) ((and (((eq int) A_1) zero_zero_int)) (not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))))) % 1.25/1.44 FOF formula (forall (B_1:int) (M:int) (A:int), (((ord_less_int zero_zero_int) A)->(((ord_less_int A) M)->(((ord_less_int zero_zero_int) B_1)->(((ord_less_int B_1) A)->((((zcong A) B_1) M)->False)))))) of role axiom named fact_579_zcong__not % 1.25/1.44 A new axiom: (forall (B_1:int) (M:int) (A:int), (((ord_less_int zero_zero_int) A)->(((ord_less_int A) M)->(((ord_less_int zero_zero_int) B_1)->(((ord_less_int B_1) A)->((((zcong A) B_1) M)->False)))))) % 1.25/1.44 FOF formula (forall (A:int) (B_1:int) (M:int), ((iff (((zcong A) B_1) M)) ((ex int) (fun (K_1:int)=> (((eq int) B_1) ((plus_plus_int A) ((times_times_int M) K_1))))))) of role axiom named fact_580_zcong__iff__lin % 1.25/1.44 A new axiom: (forall (A:int) (B_1:int) (M:int), ((iff (((zcong A) B_1) M)) ((ex int) (fun (K_1:int)=> (((eq int) B_1) ((plus_plus_int A) ((times_times_int M) K_1))))))) % 1.25/1.44 FOF formula (forall (W_2:int), ((and ((((eq nat) (number_number_of_nat W_2)) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_2))) one_one_real))) ((not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_2))) zero_zero_real)))) of role axiom named fact_581_power__0__left__number__of % 1.25/1.44 A new axiom: (forall (W_2:int), ((and ((((eq nat) (number_number_of_nat W_2)) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_2))) one_one_real))) ((not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_2))) zero_zero_real)))) % 1.25/1.44 FOF formula (forall (W_2:int), ((and ((((eq nat) (number_number_of_nat W_2)) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_2))) one_one_nat))) ((not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_2))) zero_zero_nat)))) of role axiom named fact_582_power__0__left__number__of % 1.25/1.46 A new axiom: (forall (W_2:int), ((and ((((eq nat) (number_number_of_nat W_2)) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_2))) one_one_nat))) ((not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_2))) zero_zero_nat)))) % 1.25/1.46 FOF formula (forall (W_2:int), ((and ((((eq nat) (number_number_of_nat W_2)) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_2))) one_one_int))) ((not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_2))) zero_zero_int)))) of role axiom named fact_583_power__0__left__number__of % 1.25/1.46 A new axiom: (forall (W_2:int), ((and ((((eq nat) (number_number_of_nat W_2)) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_2))) one_one_int))) ((not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_2))) zero_zero_int)))) % 1.25/1.46 FOF formula (forall (B_1: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_1)->(((ord_less_int B_1) M)->((((zcong A) B_1) M)->(((eq int) A) B_1))))))) of role axiom named fact_584_zcong__zless__imp__eq % 1.25/1.46 A new axiom: (forall (B_1: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_1)->(((ord_less_int B_1) M)->((((zcong A) B_1) M)->(((eq int) A) B_1))))))) % 1.25/1.46 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_585_zcong__zless__0 % 1.25/1.46 A new axiom: (forall (M:int) (A:int), (((ord_less_eq_int zero_zero_int) A)->(((ord_less_int A) M)->((((zcong A) zero_zero_int) M)->(((eq int) A) zero_zero_int))))) % 1.25/1.46 FOF formula (forall (N:int) (P:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->((zprime P)->(((dvd_dvd_int P) ((times_times_int M) N))->((or ((dvd_dvd_int P) M)) ((dvd_dvd_int P) N)))))) of role axiom named fact_586_zprime__zdvd__zmult % 1.25/1.46 A new axiom: (forall (N:int) (P:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->((zprime P)->(((dvd_dvd_int P) ((times_times_int M) N))->((or ((dvd_dvd_int P) M)) ((dvd_dvd_int P) N)))))) % 1.25/1.46 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_587__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096 % 1.25/1.46 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)) % 1.25/1.46 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_588__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096 % 1.25/1.46 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))) % 1.25/1.46 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_589_neg__one__power__eq__mod__m % 1.25/1.46 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))))) % 1.25/1.48 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_590__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096 % 1.25/1.48 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)) % 1.25/1.48 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_591__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N % 1.25/1.48 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))) % 1.25/1.48 FOF formula (forall (C:int) (D:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((((zcong C) D) M)->(((zcong ((minus_minus_int A) C)) ((minus_minus_int B_1) D)) M)))) of role axiom named fact_592_zcong__zdiff % 1.25/1.48 A new axiom: (forall (C:int) (D:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((((zcong C) D) M)->(((zcong ((minus_minus_int A) C)) ((minus_minus_int B_1) D)) M)))) % 1.25/1.48 FOF formula (forall (K:int), (((eq int) ((minus_minus_int K) pls)) K)) of role axiom named fact_593_diff__bin__simps_I1_J % 1.25/1.48 A new axiom: (forall (K:int), (((eq int) ((minus_minus_int K) pls)) K)) % 1.25/1.48 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_594_diff__bin__simps_I7_J % 1.25/1.48 A new axiom: (forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit0 K)) (bit0 L))) (bit0 ((minus_minus_int K) L)))) % 1.25/1.48 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_595_zdiff__zmult__distrib % 1.25/1.48 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)))) % 1.25/1.48 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_596_zdiff__zmult__distrib2 % 1.25/1.48 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)))) % 1.25/1.48 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_597_zdvd__zdiffD % 1.25/1.48 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)))) % 1.25/1.48 FOF formula (forall (V:int) (W_1:int), (((eq int) (number_number_of_int ((minus_minus_int V) W_1))) ((minus_minus_int (number_number_of_int V)) (number_number_of_int W_1)))) of role axiom named fact_598_number__of__diff % 1.25/1.48 A new axiom: (forall (V:int) (W_1:int), (((eq int) (number_number_of_int ((minus_minus_int V) W_1))) ((minus_minus_int (number_number_of_int V)) (number_number_of_int W_1)))) % 1.25/1.48 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_599_diff__bin__simps_I9_J % 1.25/1.48 A new axiom: (forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit1 K)) (bit0 L))) (bit1 ((minus_minus_int K) L)))) % 1.25/1.50 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_600_diff__bin__simps_I10_J % 1.25/1.50 A new axiom: (forall (K:int) (L:int), (((eq int) ((minus_minus_int (bit1 K)) (bit1 L))) (bit0 ((minus_minus_int K) L)))) % 1.25/1.50 FOF formula (forall (L:int), (((eq int) ((minus_minus_int pls) (bit0 L))) (bit0 ((minus_minus_int pls) L)))) of role axiom named fact_601_diff__bin__simps_I3_J % 1.25/1.50 A new axiom: (forall (L:int), (((eq int) ((minus_minus_int pls) (bit0 L))) (bit0 ((minus_minus_int pls) L)))) % 1.25/1.50 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_602_less__bin__lemma % 1.25/1.50 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))) % 1.25/1.50 FOF formula (forall (A:int) (R_1:int) (B_1: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_1))) 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_1) M)) ((times_times_int D) N)))))) of role axiom named fact_603_xzgcda__linear__aux1 % 1.25/1.50 A new axiom: (forall (A:int) (R_1:int) (B_1: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_1))) 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_1) M)) ((times_times_int D) N)))))) % 1.25/1.50 FOF formula (forall (A:int) (B_1:int) (M:int), ((iff (((zcong A) B_1) M)) ((dvd_dvd_int M) ((minus_minus_int A) B_1)))) of role axiom named fact_604_zcong__def % 1.25/1.50 A new axiom: (forall (A:int) (B_1:int) (M:int), ((iff (((zcong A) B_1) M)) ((dvd_dvd_int M) ((minus_minus_int A) B_1)))) % 1.25/1.50 FOF formula (forall (A:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int X_1) A)->((not (((eq int) X_1) ((minus_minus_int A) one_one_int)))->((ord_less_int X_1) ((minus_minus_int A) one_one_int)))))) of role axiom named fact_605_Euler_Oaux1 % 1.25/1.50 A new axiom: (forall (A:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int X_1) A)->((not (((eq int) X_1) ((minus_minus_int A) one_one_int)))->((ord_less_int X_1) ((minus_minus_int A) one_one_int)))))) % 1.25/1.50 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_606_zle__diff1__eq % 1.25/1.50 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))) % 1.25/1.50 FOF formula (forall (L:int), (((eq int) ((minus_minus_int pls) (bit1 L))) (bit1 ((minus_minus_int min) L)))) of role axiom named fact_607_diff__bin__simps_I4_J % 1.25/1.50 A new axiom: (forall (L:int), (((eq int) ((minus_minus_int pls) (bit1 L))) (bit1 ((minus_minus_int min) L)))) % 1.25/1.50 FOF formula (forall (L:int), (((eq int) ((minus_minus_int min) (bit1 L))) (bit0 ((minus_minus_int min) L)))) of role axiom named fact_608_diff__bin__simps_I6_J % 1.25/1.50 A new axiom: (forall (L:int), (((eq int) ((minus_minus_int min) (bit1 L))) (bit0 ((minus_minus_int min) L)))) % 1.25/1.50 FOF formula (forall (L:int), (((eq int) ((minus_minus_int min) (bit0 L))) (bit1 ((minus_minus_int min) L)))) of role axiom named fact_609_diff__bin__simps_I5_J % 1.25/1.50 A new axiom: (forall (L:int), (((eq int) ((minus_minus_int min) (bit0 L))) (bit1 ((minus_minus_int min) L)))) % 1.25/1.50 FOF formula (forall (A:int) (P:int), ((iff (((zcong ((times_times_int A) ((minus_minus_int P) one_one_int))) one_one_int) P)) (((zcong A) ((minus_minus_int P) one_one_int)) P))) of role axiom named fact_610_inv__not__p__minus__1__aux % 1.25/1.50 A new axiom: (forall (A:int) (P:int), ((iff (((zcong ((times_times_int A) ((minus_minus_int P) one_one_int))) one_one_int) P)) (((zcong A) ((minus_minus_int P) one_one_int)) P))) % 1.25/1.50 FOF formula (forall (A:int) (B_1:int) (P:int) (Q:int), (((eq int) ((times_times_int (twoSqu1078207634sum2sq ((product_Pair_int_int A) B_1))) (twoSqu1078207634sum2sq ((product_Pair_int_int P) Q)))) (twoSqu1078207634sum2sq ((product_Pair_int_int ((plus_plus_int ((times_times_int A) P)) ((times_times_int B_1) Q))) ((minus_minus_int ((times_times_int A) Q)) ((times_times_int B_1) P)))))) of role axiom named fact_611_mult__sum2sq % 1.33/1.52 A new axiom: (forall (A:int) (B_1:int) (P:int) (Q:int), (((eq int) ((times_times_int (twoSqu1078207634sum2sq ((product_Pair_int_int A) B_1))) (twoSqu1078207634sum2sq ((product_Pair_int_int P) Q)))) (twoSqu1078207634sum2sq ((product_Pair_int_int ((plus_plus_int ((times_times_int A) P)) ((times_times_int B_1) Q))) ((minus_minus_int ((times_times_int A) Q)) ((times_times_int B_1) P)))))) % 1.33/1.52 FOF formula (forall (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) A)) one_one_int) P)->((or (((zcong A) one_one_int) P)) (((zcong A) ((minus_minus_int P) one_one_int)) P)))))) of role axiom named fact_612_zcong__square % 1.33/1.52 A new axiom: (forall (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) A)) one_one_int) P)->((or (((zcong A) one_one_int) P)) (((zcong A) ((minus_minus_int P) one_one_int)) P)))))) % 1.33/1.52 FOF formula (forall (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P)->((((zcong ((times_times_int A) A)) one_one_int) P)->((or (((eq int) A) one_one_int)) (((eq int) A) ((minus_minus_int P) one_one_int)))))))) of role axiom named fact_613_zcong__square__zless % 1.33/1.52 A new axiom: (forall (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P)->((((zcong ((times_times_int A) A)) one_one_int) P)->((or (((eq int) A) one_one_int)) (((eq int) A) ((minus_minus_int P) one_one_int)))))))) % 1.33/1.52 FOF formula (forall (A:int) (B_1:int), (((eq int) ((times_times_int ((plus_plus_int A) B_1)) ((minus_minus_int A) B_1))) ((minus_minus_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int B_1) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_614_zspecial__product % 1.33/1.52 A new axiom: (forall (A:int) (B_1:int), (((eq int) ((times_times_int ((plus_plus_int A) B_1)) ((minus_minus_int A) B_1))) ((minus_minus_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int B_1) (number_number_of_nat (bit0 (bit1 pls))))))) % 1.33/1.52 FOF formula (forall (A:int) (B_1:int), (((eq int) ((power_power_int ((minus_minus_int A) B_1)) (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_1))) ((power_power_int B_1) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_615_zdiff__power2 % 1.33/1.52 A new axiom: (forall (A:int) (B_1:int), (((eq int) ((power_power_int ((minus_minus_int A) B_1)) (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_1))) ((power_power_int B_1) (number_number_of_nat (bit0 (bit1 pls))))))) % 1.33/1.52 FOF formula (forall (A:int) (B_1:int), (((eq int) ((power_power_int ((minus_minus_int A) B_1)) (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_1))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) A)) ((power_power_int B_1) (number_number_of_nat (bit0 (bit1 pls))))))) ((power_power_int B_1) (number_number_of_nat (bit1 (bit1 pls))))))) of role axiom named fact_616_zdiff__power3 % 1.33/1.52 A new axiom: (forall (A:int) (B_1:int), (((eq int) ((power_power_int ((minus_minus_int A) B_1)) (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_1))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) A)) ((power_power_int B_1) (number_number_of_nat (bit0 (bit1 pls))))))) ((power_power_int B_1) (number_number_of_nat (bit1 (bit1 pls))))))) % 1.33/1.53 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_617_neg__one__power % 1.33/1.53 A new axiom: (forall (N:nat), ((or (((eq int) ((power_power_int (number_number_of_int min)) N)) one_one_int)) (((eq int) ((power_power_int (number_number_of_int min)) N)) (number_number_of_int min)))) % 1.33/1.53 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_618_Legendre__1mod4 % 1.33/1.53 A new axiom: (forall (M:int), ((zprime ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) M)) one_one_int))->(((eq int) ((legendre (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) M)) one_one_int))) one_one_int))) % 1.33/1.53 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_619_one__not__neg__one__mod__m % 1.33/1.53 A new axiom: (forall (M:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) M)->((((zcong one_one_int) (number_number_of_int min)) M)->False))) % 1.33/1.53 FOF formula (forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((((zcong X_1) (number_number_of_int min)) P)->((((zcong X_1) one_one_int) P)->False)))) of role axiom named fact_620_zcong__neg__1__impl__ne__1 % 1.33/1.53 A new axiom: (forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((((zcong X_1) (number_number_of_int min)) P)->((((zcong X_1) one_one_int) P)->False)))) % 1.33/1.53 FOF formula (forall (A:int) (P:int), ((and ((((zcong A) zero_zero_int) P)->(((eq int) ((legendre A) P)) zero_zero_int))) (((((zcong A) zero_zero_int) P)->False)->((and (((quadRes P) A)->(((eq int) ((legendre A) P)) one_one_int))) ((((quadRes P) A)->False)->(((eq int) ((legendre A) P)) (number_number_of_int min))))))) of role axiom named fact_621_Legendre__def % 1.33/1.53 A new axiom: (forall (A:int) (P:int), ((and ((((zcong A) zero_zero_int) P)->(((eq int) ((legendre A) P)) zero_zero_int))) (((((zcong A) zero_zero_int) P)->False)->((and (((quadRes P) A)->(((eq int) ((legendre A) P)) one_one_int))) ((((quadRes P) A)->False)->(((eq int) ((legendre A) P)) (number_number_of_int min))))))) % 1.33/1.53 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_622_divides__cases % 1.33/1.53 A new axiom: (forall (N:nat) (M:nat), (((dvd_dvd_nat N) M)->((or ((or (((eq nat) M) zero_zero_nat)) (((eq nat) M) N))) ((ord_less_eq_nat ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N)) M)))) % 1.33/1.53 FOF formula (forall (X_1:nat) (Y_1:nat), ((iff ((and ((dvd_dvd_nat X_1) Y_1)) ((dvd_dvd_nat Y_1) X_1))) (((eq nat) X_1) Y_1))) of role axiom named fact_623_divides__antisym % 1.33/1.53 A new axiom: (forall (X_1:nat) (Y_1:nat), ((iff ((and ((dvd_dvd_nat X_1) Y_1)) ((dvd_dvd_nat Y_1) X_1))) (((eq nat) X_1) Y_1))) % 1.33/1.53 FOF formula (forall (D:int) (C:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((((eq int) B_1) C)->((((zcong C) D) M)->(((zcong A) D) M))))) of role axiom named fact_624_zcong__eq__trans % 1.33/1.53 A new axiom: (forall (D:int) (C:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((((eq int) B_1) C)->((((zcong C) D) M)->(((zcong A) D) M))))) % 1.33/1.56 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_625_mult__eq__if % 1.33/1.56 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)))))) % 1.33/1.56 FOF formula (forall (P:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((power_power_nat P) M)) one_one_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((power_power_nat P) M)) ((times_times_nat P) ((power_power_nat P) ((minus_minus_nat M) one_one_nat))))))) of role axiom named fact_626_power__eq__if % 1.33/1.56 A new axiom: (forall (P:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((power_power_nat P) M)) one_one_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((power_power_nat P) M)) ((times_times_nat P) ((power_power_nat P) ((minus_minus_nat M) one_one_nat))))))) % 1.33/1.56 FOF formula (forall (X_1:nat) (Y_1:nat), (((eq nat) ((minus_minus_nat ((power_power_nat X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((plus_plus_nat X_1) Y_1)) ((minus_minus_nat X_1) Y_1)))) of role axiom named fact_627_diff__square % 1.33/1.56 A new axiom: (forall (X_1:nat) (Y_1:nat), (((eq nat) ((minus_minus_nat ((power_power_nat X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((plus_plus_nat X_1) Y_1)) ((minus_minus_nat X_1) Y_1)))) % 1.33/1.56 FOF formula (forall (B_1:nat) (D:nat) (A:nat), (((dvd_dvd_nat D) A)->(((dvd_dvd_nat D) ((plus_plus_nat A) B_1))->((dvd_dvd_nat D) B_1)))) of role axiom named fact_628_divides__add__revr % 1.33/1.56 A new axiom: (forall (B_1:nat) (D:nat) (A:nat), (((dvd_dvd_nat D) A)->(((dvd_dvd_nat D) ((plus_plus_nat A) B_1))->((dvd_dvd_nat D) B_1)))) % 1.33/1.56 FOF formula (forall (C:nat) (A:nat) (B_1:nat), (((dvd_dvd_nat A) B_1)->((dvd_dvd_nat ((times_times_nat C) A)) ((times_times_nat C) B_1)))) of role axiom named fact_629_divides__mul__l % 1.33/1.56 A new axiom: (forall (C:nat) (A:nat) (B_1:nat), (((dvd_dvd_nat A) B_1)->((dvd_dvd_nat ((times_times_nat C) A)) ((times_times_nat C) B_1)))) % 1.33/1.56 FOF formula (forall (C:nat) (A:nat) (B_1:nat), (((dvd_dvd_nat A) B_1)->((dvd_dvd_nat ((times_times_nat A) C)) ((times_times_nat B_1) C)))) of role axiom named fact_630_divides__mul__r % 1.33/1.56 A new axiom: (forall (C:nat) (A:nat) (B_1:nat), (((dvd_dvd_nat A) B_1)->((dvd_dvd_nat ((times_times_nat A) C)) ((times_times_nat B_1) C)))) % 1.33/1.56 FOF formula (forall (M:int), (((zcong M) zero_zero_int) M)) of role axiom named fact_631_zcong__id % 1.33/1.56 A new axiom: (forall (M:int), (((zcong M) zero_zero_int) M)) % 1.33/1.56 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_632_nat__mult__eq__one % 1.33/1.56 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)))) % 1.33/1.56 FOF formula (forall (A:int) (B_1:int) (C:int), ((((eq int) ((minus_minus_int A) B_1)) C)->(((eq int) A) ((plus_plus_int C) B_1)))) of role axiom named fact_633_Int2_Oaux1 % 1.33/1.56 A new axiom: (forall (A:int) (B_1:int) (C:int), ((((eq int) ((minus_minus_int A) B_1)) C)->(((eq int) A) ((plus_plus_int C) B_1)))) % 1.33/1.56 FOF formula (forall (C:int) (D:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((iff (((zcong C) ((times_times_int D) A)) M)) (((zcong C) ((times_times_int D) B_1)) M)))) of role axiom named fact_634_zcong__zmult__prop2 % 1.33/1.56 A new axiom: (forall (C:int) (D:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((iff (((zcong C) ((times_times_int D) A)) M)) (((zcong C) ((times_times_int D) B_1)) M)))) % 1.33/1.56 FOF formula (forall (C:int) (D:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((iff (((zcong C) ((times_times_int A) D)) M)) (((zcong C) ((times_times_int B_1) D)) M)))) of role axiom named fact_635_zcong__zmult__prop1 % 1.33/1.58 A new axiom: (forall (C:int) (D:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((iff (((zcong C) ((times_times_int A) D)) M)) (((zcong C) ((times_times_int B_1) D)) M)))) % 1.33/1.58 FOF formula (forall (C:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->(((zcong ((plus_plus_int A) C)) ((plus_plus_int B_1) C)) M))) of role axiom named fact_636_zcong__shift % 1.33/1.58 A new axiom: (forall (C:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->(((zcong ((plus_plus_int A) C)) ((plus_plus_int B_1) C)) M))) % 1.33/1.58 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_637_nat__power__eq__0__iff % 1.33/1.58 A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) ((power_power_nat M) N)) zero_zero_nat)) ((and (not (((eq nat) N) zero_zero_nat))) (((eq nat) M) zero_zero_nat)))) % 1.33/1.58 FOF formula (forall (N:nat) (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->((dvd_dvd_nat ((power_power_nat X_1) N)) ((power_power_nat Y_1) N)))) of role axiom named fact_638_divides__exp % 1.33/1.58 A new axiom: (forall (N:nat) (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->((dvd_dvd_nat ((power_power_nat X_1) N)) ((power_power_nat Y_1) N)))) % 1.33/1.58 FOF formula (forall (Z:nat) (X_1:int) (Y_1:int) (M:int), ((((zcong X_1) Y_1) M)->(((zcong ((power_power_int X_1) Z)) ((power_power_int Y_1) Z)) M))) of role axiom named fact_639_zcong__zpower % 1.33/1.58 A new axiom: (forall (Z:nat) (X_1:int) (Y_1:int) (M:int), ((((zcong X_1) Y_1) M)->(((zcong ((power_power_int X_1) Z)) ((power_power_int Y_1) Z)) M))) % 1.33/1.58 FOF formula (forall (A:nat) (B_1:nat), (((dvd_dvd_nat A) B_1)->((or (((eq nat) B_1) zero_zero_nat)) ((ord_less_eq_nat A) B_1)))) of role axiom named fact_640_divides__ge % 1.33/1.58 A new axiom: (forall (A:nat) (B_1:nat), (((dvd_dvd_nat A) B_1)->((or (((eq nat) B_1) zero_zero_nat)) ((ord_less_eq_nat A) B_1)))) % 1.33/1.58 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_641_nat__mult__dvd__cancel__disj_H % 1.33/1.58 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)))) % 1.33/1.58 FOF formula (forall (M:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int X_1) M)->((((zcong X_1) zero_zero_int) M)->False)))) of role axiom named fact_642_zcong__not__zero % 1.33/1.58 A new axiom: (forall (M:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int X_1) M)->((((zcong X_1) zero_zero_int) M)->False)))) % 1.33/1.58 FOF formula (forall (M:int) (Y_1:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int zero_zero_int) Y_1)->(((ord_less_int zero_zero_int) M)->((((zcong X_1) Y_1) M)->(((ord_less_int X_1) M)->(((ord_less_int Y_1) M)->(((eq int) X_1) Y_1)))))))) of role axiom named fact_643_zcong__less__eq % 1.33/1.58 A new axiom: (forall (M:int) (Y_1:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int zero_zero_int) Y_1)->(((ord_less_int zero_zero_int) M)->((((zcong X_1) Y_1) M)->(((ord_less_int X_1) M)->(((ord_less_int Y_1) M)->(((eq int) X_1) Y_1)))))))) % 1.33/1.58 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_644_zdvd__bounds % 1.33/1.58 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)))) % 1.33/1.58 FOF formula (forall (X_1:nat) (Y_1:nat) (N:nat), ((not (((eq nat) N) zero_zero_nat))->(((dvd_dvd_nat ((power_power_nat X_1) N)) Y_1)->((dvd_dvd_nat X_1) Y_1)))) of role axiom named fact_645_divides__exp2 % 1.33/1.58 A new axiom: (forall (X_1:nat) (Y_1:nat) (N:nat), ((not (((eq nat) N) zero_zero_nat))->(((dvd_dvd_nat ((power_power_nat X_1) N)) Y_1)->((dvd_dvd_nat X_1) Y_1)))) % 1.33/1.58 FOF formula (forall (A:nat) (N:nat) (B_1:nat), (((dvd_dvd_nat ((power_power_nat A) N)) ((power_power_nat B_1) N))->((not (((eq nat) N) zero_zero_nat))->((dvd_dvd_nat A) B_1)))) of role axiom named fact_646_divides__rev % 1.41/1.60 A new axiom: (forall (A:nat) (N:nat) (B_1:nat), (((dvd_dvd_nat ((power_power_nat A) N)) ((power_power_nat B_1) N))->((not (((eq nat) N) zero_zero_nat))->((dvd_dvd_nat A) B_1)))) % 1.41/1.60 FOF formula (forall (A:int) (M:int), ((iff (((zcong A) zero_zero_int) M)) ((dvd_dvd_int M) A))) of role axiom named fact_647_zcong__zero__equiv__div % 1.41/1.60 A new axiom: (forall (A:int) (M:int), ((iff (((zcong A) zero_zero_int) M)) ((dvd_dvd_int M) A))) % 1.41/1.60 FOF formula (forall (X_1:int) (P:int), ((iff (((zcong X_1) zero_zero_int) P)) ((dvd_dvd_int P) X_1))) of role axiom named fact_648_zcong__eq__zdvd__prop % 1.41/1.60 A new axiom: (forall (X_1:int) (P:int), ((iff (((zcong X_1) zero_zero_int) P)) ((dvd_dvd_int P) X_1))) % 1.41/1.60 FOF formula (forall (X_1:nat) (N:nat), ((iff (((eq nat) ((power_power_nat X_1) N)) one_one_nat)) ((or (((eq nat) X_1) one_one_nat)) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_649_exp__eq__1 % 1.41/1.60 A new axiom: (forall (X_1:nat) (N:nat), ((iff (((eq nat) ((power_power_nat X_1) N)) one_one_nat)) ((or (((eq nat) X_1) one_one_nat)) (((eq nat) N) zero_zero_nat)))) % 1.41/1.60 FOF formula (forall (M:int) (N:int) (P:int), ((zprime P)->(((dvd_dvd_int P) ((times_times_int M) N))->((or ((dvd_dvd_int P) M)) ((dvd_dvd_int P) N))))) of role axiom named fact_650_zprime__zdvd__zmult__better % 1.41/1.60 A new axiom: (forall (M:int) (N:int) (P:int), ((zprime P)->(((dvd_dvd_int P) ((times_times_int M) N))->((or ((dvd_dvd_int P) M)) ((dvd_dvd_int P) N))))) % 1.41/1.60 FOF formula (forall (M:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_int X_1) M)->((((zcong X_1) zero_zero_int) M)->(((eq int) X_1) zero_zero_int))))) of role axiom named fact_651_Int2_Ozcong__zero % 1.41/1.60 A new axiom: (forall (M:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_int X_1) M)->((((zcong X_1) zero_zero_int) M)->(((eq int) X_1) zero_zero_int))))) % 1.41/1.60 FOF formula (forall (P:int) (Y_1:int) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((dvd_dvd_int P) Y_1)->((dvd_dvd_int P) ((power_power_int Y_1) N))))) of role axiom named fact_652_zpower__zdvd__prop1 % 1.41/1.60 A new axiom: (forall (P:int) (Y_1:int) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((dvd_dvd_int P) Y_1)->((dvd_dvd_int P) ((power_power_int Y_1) N))))) % 1.41/1.60 FOF formula (forall (Y_1:int) (X_1:int) (P:int), ((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((((zcong Y_1) zero_zero_int) P)->False)->((((zcong ((times_times_int X_1) Y_1)) zero_zero_int) P)->False))))) of role axiom named fact_653_zcong__zmult__prop3 % 1.41/1.60 A new axiom: (forall (Y_1:int) (X_1:int) (P:int), ((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((((zcong Y_1) zero_zero_int) P)->False)->((((zcong ((times_times_int X_1) Y_1)) zero_zero_int) P)->False))))) % 1.41/1.60 FOF formula (forall (X_1:nat) (Q:nat) (N:nat) (R_1:nat), ((((eq nat) X_1) ((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_1)->False))))) of role axiom named fact_654_divides__div__not % 1.41/1.60 A new axiom: (forall (X_1:nat) (Q:nat) (N:nat) (R_1:nat), ((((eq nat) X_1) ((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_1)->False))))) % 1.41/1.60 FOF formula (forall (B_1:int) (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->(((and ((((zcong A) zero_zero_int) P)->False)) ((((zcong B_1) zero_zero_int) P)->False))->((((zcong ((times_times_int A) B_1)) zero_zero_int) P)->False))))) of role axiom named fact_655_zcong__zprime__prod__zero__contra % 1.41/1.60 A new axiom: (forall (B_1:int) (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->(((and ((((zcong A) zero_zero_int) P)->False)) ((((zcong B_1) zero_zero_int) P)->False))->((((zcong ((times_times_int A) B_1)) zero_zero_int) P)->False))))) % 1.41/1.60 FOF formula (forall (B_1:int) (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) B_1)) zero_zero_int) P)->((or (((zcong A) zero_zero_int) P)) (((zcong B_1) zero_zero_int) P)))))) of role axiom named fact_656_zcong__zprime__prod__zero % 1.41/1.61 A new axiom: (forall (B_1:int) (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) B_1)) zero_zero_int) P)->((or (((zcong A) zero_zero_int) P)) (((zcong B_1) zero_zero_int) P)))))) % 1.41/1.61 FOF formula (forall (Y_1:int) (N:nat) (P:int), ((zprime P)->(((dvd_dvd_int P) ((power_power_int Y_1) N))->(((ord_less_nat zero_zero_nat) N)->((dvd_dvd_int P) Y_1))))) of role axiom named fact_657_zpower__zdvd__prop2 % 1.41/1.61 A new axiom: (forall (Y_1:int) (N:nat) (P:int), ((zprime P)->(((dvd_dvd_int P) ((power_power_int Y_1) N))->(((ord_less_nat zero_zero_nat) N)->((dvd_dvd_int P) Y_1))))) % 1.41/1.61 FOF formula (forall (M:int) (X_1:int), ((iff ((quadRes M) X_1)) ((ex int) (fun (Y:int)=> (((zcong ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls))))) X_1) M))))) of role axiom named fact_658_QuadRes__def % 1.41/1.61 A new axiom: (forall (M:int) (X_1:int), ((iff ((quadRes M) X_1)) ((ex int) (fun (Y:int)=> (((zcong ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls))))) X_1) M))))) % 1.41/1.61 FOF formula (forall (X_1:real) (Y_1:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_1) zero_zero_real)) (((eq real) Y_1) zero_zero_real)))) of role axiom named fact_659_realpow__two__sum__zero__iff % 1.41/1.61 A new axiom: (forall (X_1:real) (Y_1:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_1) zero_zero_real)) (((eq real) Y_1) zero_zero_real)))) % 1.41/1.61 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_660_self__quotient__aux1 % 1.41/1.61 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))))) % 1.41/1.61 FOF formula (not (((eq real) zero_zero_real) one_one_real)) of role axiom named fact_661_real__zero__not__eq__one % 1.41/1.61 A new axiom: (not (((eq real) zero_zero_real) one_one_real)) % 1.41/1.61 FOF formula (forall (X_1:real) (Y_1:real), ((iff ((ord_less_eq_real X_1) Y_1)) ((ord_less_eq_real ((minus_minus_real X_1) Y_1)) zero_zero_real))) of role axiom named fact_662_real__le__eq__diff % 1.41/1.61 A new axiom: (forall (X_1:real) (Y_1:real), ((iff ((ord_less_eq_real X_1) Y_1)) ((ord_less_eq_real ((minus_minus_real X_1) Y_1)) zero_zero_real))) % 1.41/1.61 FOF formula (forall (X_1:real) (Y_1:real), ((iff ((ord_less_real X_1) Y_1)) ((and ((ord_less_eq_real X_1) Y_1)) (not (((eq real) X_1) Y_1))))) of role axiom named fact_663_real__less__def % 1.41/1.61 A new axiom: (forall (X_1:real) (Y_1:real), ((iff ((ord_less_real X_1) Y_1)) ((and ((ord_less_eq_real X_1) Y_1)) (not (((eq real) X_1) Y_1))))) % 1.41/1.61 FOF formula (forall (X_1:real) (Y_1:real), ((iff ((ord_less_eq_real X_1) Y_1)) ((or ((ord_less_real X_1) Y_1)) (((eq real) X_1) Y_1)))) of role axiom named fact_664_less__eq__real__def % 1.41/1.61 A new axiom: (forall (X_1:real) (Y_1:real), ((iff ((ord_less_eq_real X_1) Y_1)) ((or ((ord_less_real X_1) Y_1)) (((eq real) X_1) Y_1)))) % 1.41/1.61 FOF formula (forall (Z:real), (((eq real) ((times_times_real one_one_real) Z)) Z)) of role axiom named fact_665_real__mult__1 % 1.41/1.61 A new axiom: (forall (Z:real), (((eq real) ((times_times_real one_one_real) Z)) Z)) % 1.41/1.61 FOF formula (forall (Z:real) (W:real), (((eq real) ((times_times_real Z) W)) ((times_times_real W) Z))) of role axiom named fact_666_real__mult__commute % 1.41/1.61 A new axiom: (forall (Z:real) (W:real), (((eq real) ((times_times_real Z) W)) ((times_times_real W) Z))) % 1.41/1.61 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_667_real__mult__assoc % 1.41/1.61 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)))) % 1.41/1.63 FOF formula (forall (Z:real) (X_1:real) (Y_1:real), (((ord_less_eq_real X_1) Y_1)->((ord_less_eq_real ((plus_plus_real Z) X_1)) ((plus_plus_real Z) Y_1)))) of role axiom named fact_668_real__add__left__mono % 1.41/1.63 A new axiom: (forall (Z:real) (X_1:real) (Y_1:real), (((ord_less_eq_real X_1) Y_1)->((ord_less_eq_real ((plus_plus_real Z) X_1)) ((plus_plus_real Z) Y_1)))) % 1.41/1.63 FOF formula (forall (A:real) (B_1:real) (C:real), ((not (((eq real) C) zero_zero_real))->((iff (((eq real) ((times_times_real C) A)) ((times_times_real C) B_1))) (((eq real) A) B_1)))) of role axiom named fact_669_real__mult__left__cancel % 1.41/1.63 A new axiom: (forall (A:real) (B_1:real) (C:real), ((not (((eq real) C) zero_zero_real))->((iff (((eq real) ((times_times_real C) A)) ((times_times_real C) B_1))) (((eq real) A) B_1)))) % 1.41/1.63 FOF formula (forall (A:real) (B_1:real) (C:real), ((not (((eq real) C) zero_zero_real))->((iff (((eq real) ((times_times_real A) C)) ((times_times_real B_1) C))) (((eq real) A) B_1)))) of role axiom named fact_670_real__mult__right__cancel % 1.41/1.63 A new axiom: (forall (A:real) (B_1:real) (C:real), ((not (((eq real) C) zero_zero_real))->((iff (((eq real) ((times_times_real A) C)) ((times_times_real B_1) C))) (((eq real) A) B_1)))) % 1.41/1.63 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_671_real__add__mult__distrib % 1.41/1.63 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)))) % 1.41/1.63 FOF formula (forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->(((ord_less_real X_1) Y_1)->((ord_less_real ((times_times_real Z) X_1)) ((times_times_real Z) Y_1))))) of role axiom named fact_672_real__mult__less__mono2 % 1.41/1.63 A new axiom: (forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->(((ord_less_real X_1) Y_1)->((ord_less_real ((times_times_real Z) X_1)) ((times_times_real Z) Y_1))))) % 1.41/1.63 FOF formula (forall (Y_1:real) (X_1:real), (((ord_less_real zero_zero_real) X_1)->(((ord_less_real zero_zero_real) Y_1)->((ord_less_real zero_zero_real) ((times_times_real X_1) Y_1))))) of role axiom named fact_673_real__mult__order % 1.41/1.63 A new axiom: (forall (Y_1:real) (X_1:real), (((ord_less_real zero_zero_real) X_1)->(((ord_less_real zero_zero_real) Y_1)->((ord_less_real zero_zero_real) ((times_times_real X_1) Y_1))))) % 1.41/1.63 FOF formula (forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real Z) X_1)) ((times_times_real Z) Y_1))) ((ord_less_eq_real X_1) Y_1)))) of role axiom named fact_674_real__mult__le__cancel__iff2 % 1.41/1.63 A new axiom: (forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real Z) X_1)) ((times_times_real Z) Y_1))) ((ord_less_eq_real X_1) Y_1)))) % 1.41/1.63 FOF formula (forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real X_1) Z)) ((times_times_real Y_1) Z))) ((ord_less_eq_real X_1) Y_1)))) of role axiom named fact_675_real__mult__le__cancel__iff1 % 1.41/1.63 A new axiom: (forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real X_1) Z)) ((times_times_real Y_1) Z))) ((ord_less_eq_real X_1) Y_1)))) % 1.41/1.63 FOF formula (forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_real ((times_times_real X_1) Z)) ((times_times_real Y_1) Z))) ((ord_less_real X_1) Y_1)))) of role axiom named fact_676_real__mult__less__iff1 % 1.41/1.63 A new axiom: (forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_real ((times_times_real X_1) Z)) ((times_times_real Y_1) Z))) ((ord_less_real X_1) Y_1)))) % 1.41/1.63 FOF formula (forall (X_1:real) (Y_1:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X_1) X_1)) ((times_times_real Y_1) Y_1))) zero_zero_real)) ((and (((eq real) X_1) zero_zero_real)) (((eq real) Y_1) zero_zero_real)))) of role axiom named fact_677_real__two__squares__add__zero__iff % 1.41/1.66 A new axiom: (forall (X_1:real) (Y_1:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X_1) X_1)) ((times_times_real Y_1) Y_1))) zero_zero_real)) ((and (((eq real) X_1) zero_zero_real)) (((eq real) Y_1) zero_zero_real)))) % 1.41/1.66 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_678_two__realpow__ge__one % 1.41/1.66 A new axiom: (forall (N:nat), ((ord_less_eq_real one_one_real) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N))) % 1.41/1.66 FOF formula (forall (B:int) (Q_1:int) (R_2:int), (((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B) Q_1)) R_2))->(((ord_less_int R_2) B)->(((ord_less_int zero_zero_int) B)->((ord_less_eq_int zero_zero_int) Q_1))))) of role axiom named fact_679_q__pos__lemma % 1.41/1.66 A new axiom: (forall (B:int) (Q_1:int) (R_2:int), (((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B) Q_1)) R_2))->(((ord_less_int R_2) B)->(((ord_less_int zero_zero_int) B)->((ord_less_eq_int zero_zero_int) Q_1))))) % 1.41/1.66 FOF formula (forall (B:int) (Q_1:int) (R_2:int), (((ord_less_int ((plus_plus_int ((times_times_int B) Q_1)) R_2)) zero_zero_int)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B)->((ord_less_eq_int Q_1) zero_zero_int))))) of role axiom named fact_680_q__neg__lemma % 1.41/1.66 A new axiom: (forall (B:int) (Q_1:int) (R_2:int), (((ord_less_int ((plus_plus_int ((times_times_int B) Q_1)) R_2)) zero_zero_int)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B)->((ord_less_eq_int Q_1) zero_zero_int))))) % 1.41/1.66 FOF formula (forall (B_1:int) (Q_1:int) (R_2:int) (Q:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B_1) Q_1)) R_2)) ((plus_plus_int ((times_times_int B_1) Q)) R_1))->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int R_2) B_1)->(((ord_less_int R_1) B_1)->((ord_less_eq_int Q_1) Q)))))) of role axiom named fact_681_unique__quotient__lemma % 1.41/1.66 A new axiom: (forall (B_1:int) (Q_1:int) (R_2:int) (Q:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B_1) Q_1)) R_2)) ((plus_plus_int ((times_times_int B_1) Q)) R_1))->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int R_2) B_1)->(((ord_less_int R_1) B_1)->((ord_less_eq_int Q_1) Q)))))) % 1.41/1.66 FOF formula (forall (B_1:int) (Q:int) (R_1:int) (B:int) (Q_1:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B_1) Q)) R_1)) ((plus_plus_int ((times_times_int B) Q_1)) R_2))->(((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B) Q_1)) R_2))->(((ord_less_int R_2) B)->(((ord_less_eq_int zero_zero_int) R_1)->(((ord_less_int zero_zero_int) B)->(((ord_less_eq_int B) B_1)->((ord_less_eq_int Q) Q_1)))))))) of role axiom named fact_682_zdiv__mono2__lemma % 1.41/1.66 A new axiom: (forall (B_1:int) (Q:int) (R_1:int) (B:int) (Q_1:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B_1) Q)) R_1)) ((plus_plus_int ((times_times_int B) Q_1)) R_2))->(((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B) Q_1)) R_2))->(((ord_less_int R_2) B)->(((ord_less_eq_int zero_zero_int) R_1)->(((ord_less_int zero_zero_int) B)->(((ord_less_eq_int B) B_1)->((ord_less_eq_int Q) Q_1)))))))) % 1.41/1.66 FOF formula (forall (B_1:int) (Q_1:int) (R_2:int) (Q:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B_1) Q_1)) R_2)) ((plus_plus_int ((times_times_int B_1) Q)) R_1))->(((ord_less_eq_int R_1) zero_zero_int)->(((ord_less_int B_1) R_1)->(((ord_less_int B_1) R_2)->((ord_less_eq_int Q) Q_1)))))) of role axiom named fact_683_unique__quotient__lemma__neg % 1.41/1.66 A new axiom: (forall (B_1:int) (Q_1:int) (R_2:int) (Q:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B_1) Q_1)) R_2)) ((plus_plus_int ((times_times_int B_1) Q)) R_1))->(((ord_less_eq_int R_1) zero_zero_int)->(((ord_less_int B_1) R_1)->(((ord_less_int B_1) R_2)->((ord_less_eq_int Q) Q_1)))))) % 1.41/1.66 FOF formula (forall (B_1:int) (Q:int) (R_1:int) (B:int) (Q_1:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B_1) Q)) R_1)) ((plus_plus_int ((times_times_int B) Q_1)) R_2))->(((ord_less_int ((plus_plus_int ((times_times_int B) Q_1)) R_2)) zero_zero_int)->(((ord_less_int R_1) B_1)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B)->(((ord_less_eq_int B) B_1)->((ord_less_eq_int Q_1) Q)))))))) of role axiom named fact_684_zdiv__mono2__neg__lemma % 1.41/1.67 A new axiom: (forall (B_1:int) (Q:int) (R_1:int) (B:int) (Q_1:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B_1) Q)) R_1)) ((plus_plus_int ((times_times_int B) Q_1)) R_2))->(((ord_less_int ((plus_plus_int ((times_times_int B) Q_1)) R_2)) zero_zero_int)->(((ord_less_int R_1) B_1)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B)->(((ord_less_eq_int B) B_1)->((ord_less_eq_int Q_1) Q)))))))) % 1.41/1.67 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_685_self__quotient__aux2 % 1.41/1.67 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))))) % 1.41/1.67 FOF formula ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 (bit1 pls)))) of role axiom named fact_686_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J % 1.41/1.67 A new axiom: ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 (bit1 pls)))) % 1.41/1.67 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_687_real__le__antisym % 1.41/1.67 A new axiom: (forall (Z:real) (W:real), (((ord_less_eq_real Z) W)->(((ord_less_eq_real W) Z)->(((eq real) Z) W)))) % 1.41/1.67 FOF formula (forall (K:real) (_TPTP_I:real) (J:real), (((ord_less_eq_real _TPTP_I) J)->(((ord_less_eq_real J) K)->((ord_less_eq_real _TPTP_I) K)))) of role axiom named fact_688_real__le__trans % 1.41/1.67 A new axiom: (forall (K:real) (_TPTP_I:real) (J:real), (((ord_less_eq_real _TPTP_I) J)->(((ord_less_eq_real J) K)->((ord_less_eq_real _TPTP_I) K)))) % 1.41/1.67 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_689_real__le__linear % 1.41/1.67 A new axiom: (forall (Z:real) (W:real), ((or ((ord_less_eq_real Z) W)) ((ord_less_eq_real W) Z))) % 1.41/1.67 FOF formula (forall (W:real), ((ord_less_eq_real W) W)) of role axiom named fact_690_real__le__refl % 1.41/1.67 A new axiom: (forall (W:real), ((ord_less_eq_real W) W)) % 1.41/1.67 FOF formula ((ord_less_eq_int zero_zero_int) zero_zero_int) of role axiom named fact_691_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J % 1.41/1.67 A new axiom: ((ord_less_eq_int zero_zero_int) zero_zero_int) % 1.41/1.67 FOF formula ((ord_less_eq_int zero_zero_int) one_one_int) of role axiom named fact_692_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J % 1.41/1.67 A new axiom: ((ord_less_eq_int zero_zero_int) one_one_int) % 1.41/1.67 FOF formula (forall (Y_1:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_eq_int zero_zero_int) Y_1)->((ord_less_eq_int zero_zero_int) ((times_times_int X_1) Y_1))))) of role axiom named fact_693_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J % 1.41/1.67 A new axiom: (forall (Y_1:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_eq_int zero_zero_int) Y_1)->((ord_less_eq_int zero_zero_int) ((times_times_int X_1) Y_1))))) % 1.41/1.67 FOF formula (forall (Y_1:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_eq_int zero_zero_int) Y_1)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X_1) Y_1))))) of role axiom named fact_694_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J % 1.41/1.67 A new axiom: (forall (Y_1:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_eq_int zero_zero_int) Y_1)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X_1) Y_1))))) % 1.41/1.67 FOF formula (forall (N:nat) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->((ord_less_eq_int zero_zero_int) ((power_power_int X_1) N)))) of role axiom named fact_695_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J % 1.50/1.68 A new axiom: (forall (N:nat) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->((ord_less_eq_int zero_zero_int) ((power_power_int X_1) N)))) % 1.50/1.68 FOF formula ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 (bit1 pls)))) of role axiom named fact_696_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J % 1.50/1.68 A new axiom: ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 (bit1 pls)))) % 1.50/1.68 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_697_realpow__pos__nth % 1.50/1.68 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))))))) % 1.50/1.68 FOF formula ((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))))) of role conjecture named conj_0 % 1.50/1.68 Conjecture to prove = ((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))))):Prop % 1.50/1.68 Parameter product_prod_int_int_DUMMY:product_prod_int_int. % 1.50/1.68 We need to prove ['((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))'] % 1.50/1.68 Parameter int:Type. % 1.50/1.68 Parameter nat:Type. % 1.50/1.68 Parameter real:Type. % 1.50/1.68 Parameter product_prod_int_int:Type. % 1.50/1.68 Parameter minus_minus_int:(int->(int->int)). % 1.50/1.68 Parameter minus_minus_nat:(nat->(nat->nat)). % 1.50/1.68 Parameter minus_minus_real:(real->(real->real)). % 1.50/1.68 Parameter one_one_int:int. % 1.50/1.68 Parameter one_one_nat:nat. % 1.50/1.68 Parameter one_one_real:real. % 1.50/1.68 Parameter plus_plus_int:(int->(int->int)). % 1.50/1.68 Parameter plus_plus_nat:(nat->(nat->nat)). % 1.50/1.68 Parameter plus_plus_real:(real->(real->real)). % 1.50/1.68 Parameter times_times_int:(int->(int->int)). % 1.50/1.68 Parameter times_times_nat:(nat->(nat->nat)). % 1.50/1.68 Parameter times_times_real:(real->(real->real)). % 1.50/1.68 Parameter zero_zero_int:int. % 1.50/1.68 Parameter zero_zero_nat:nat. % 1.50/1.68 Parameter zero_zero_real:real. % 1.50/1.68 Parameter zcong:(int->(int->(int->Prop))). % 1.50/1.68 Parameter zprime:(int->Prop). % 1.50/1.68 Parameter bit0:(int->int). % 1.50/1.68 Parameter bit1:(int->int). % 1.50/1.68 Parameter min:int. % 1.50/1.68 Parameter pls:int. % 1.50/1.68 Parameter number_number_of_int:(int->int). % 1.50/1.68 Parameter number_number_of_nat:(int->nat). % 1.50/1.68 Parameter number267125858f_real:(int->real). % 1.50/1.68 Parameter ord_less_int:(int->(int->Prop)). % 1.50/1.68 Parameter ord_less_nat:(nat->(nat->Prop)). % 1.50/1.68 Parameter ord_less_real:(real->(real->Prop)). % 1.50/1.68 Parameter ord_less_eq_int:(int->(int->Prop)). % 1.50/1.68 Parameter ord_less_eq_nat:(nat->(nat->Prop)). % 1.50/1.68 Parameter ord_less_eq_real:(real->(real->Prop)). % 1.50/1.68 Parameter power_power_int:(int->(nat->int)). % 1.50/1.68 Parameter power_power_nat:(nat->(nat->nat)). % 1.50/1.68 Parameter power_power_real:(real->(nat->real)). % 1.50/1.68 Parameter product_Pair_int_int:(int->(int->product_prod_int_int)). % 1.50/1.68 Parameter legendre:(int->(int->int)). % 1.50/1.68 Parameter quadRes:(int->(int->Prop)). % 1.50/1.68 Parameter dvd_dvd_int:(int->(int->Prop)). % 1.50/1.68 Parameter dvd_dvd_nat:(nat->(nat->Prop)). % 1.50/1.68 Parameter dvd_dvd_real:(real->(real->Prop)). % 1.50/1.68 Parameter twoSqu362149276sum2sq:(int->Prop). % 1.50/1.68 Parameter twoSqu1078207634sum2sq:(product_prod_int_int->int). % 1.50/1.68 Parameter m:int. % 1.50/1.68 Parameter s1:int. % 1.50/1.68 Parameter s:int. % 1.50/1.68 Parameter t:int. % 1.50/1.68 Axiom fact_0_tpos:((ord_less_eq_int one_one_int) t). % 1.50/1.68 Axiom fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06:((((eq int) t) one_one_int)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))). % 1.50/1.69 Axiom fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06:(((ord_less_int one_one_int) t)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))). % 1.50/1.69 Axiom fact_3_t__l__p:((ord_less_int t) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)). % 1.50/1.69 Axiom fact_4_p:(zprime ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)). % 1.50/1.69 Axiom fact_5_t:(((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)). % 1.50/1.69 Axiom fact_6_qf1pt:(twoSqu362149276sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)). % 1.50/1.69 Axiom fact_7_zadd__power2:(forall (A:int) (B_1:int), (((eq int) ((power_power_int ((plus_plus_int A) B_1)) (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_1))) ((power_power_int B_1) (number_number_of_nat (bit0 (bit1 pls))))))). % 1.50/1.69 Axiom fact_8_zadd__power3:(forall (A:int) (B_1:int), (((eq int) ((power_power_int ((plus_plus_int A) B_1)) (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_1))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) A)) ((power_power_int B_1) (number_number_of_nat (bit0 (bit1 pls))))))) ((power_power_int B_1) (number_number_of_nat (bit1 (bit1 pls))))))). % 1.50/1.69 Axiom fact_9_power2__sum:(forall (X_38:real) (Y_30:real), (((eq real) ((power_power_real ((plus_plus_real X_38) Y_30)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X_38) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_30) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_38)) Y_30)))). % 1.50/1.69 Axiom fact_10_power2__sum:(forall (X_38:nat) (Y_30:nat), (((eq nat) ((power_power_nat ((plus_plus_nat X_38) Y_30)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat ((plus_plus_nat ((power_power_nat X_38) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_30) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) X_38)) Y_30)))). % 1.50/1.69 Axiom fact_11_power2__sum:(forall (X_38:int) (Y_30:int), (((eq int) ((power_power_int ((plus_plus_int X_38) Y_30)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int X_38) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_30) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) X_38)) Y_30)))). % 1.50/1.69 Axiom fact_12_power2__eq__square__number__of:(forall (W_18:int), (((eq nat) ((power_power_nat (number_number_of_nat W_18)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat (number_number_of_nat W_18)) (number_number_of_nat W_18)))). % 1.50/1.69 Axiom fact_13_power2__eq__square__number__of:(forall (W_18:int), (((eq real) ((power_power_real (number267125858f_real W_18)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real (number267125858f_real W_18)) (number267125858f_real W_18)))). % 1.50/1.69 Axiom fact_14_power2__eq__square__number__of:(forall (W_18:int), (((eq int) ((power_power_int (number_number_of_int W_18)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int (number_number_of_int W_18)) (number_number_of_int W_18)))). % 1.50/1.69 Axiom fact_15_cube__square:(forall (A:int), (((eq int) ((times_times_int A) ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_int A) (number_number_of_nat (bit1 (bit1 pls)))))). % 1.50/1.69 Axiom fact_16_one__power2:(((eq real) ((power_power_real one_one_real) (number_number_of_nat (bit0 (bit1 pls))))) one_one_real). % 1.50/1.69 Axiom fact_17_one__power2:(((eq nat) ((power_power_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls))))) one_one_nat). % 1.50/1.69 Axiom fact_18_one__power2:(((eq int) ((power_power_int one_one_int) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int). % 1.50/1.69 Axiom fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J:(forall (X_37:nat), (((eq nat) ((times_times_nat X_37) X_37)) ((power_power_nat X_37) (number_number_of_nat (bit0 (bit1 pls)))))). % 1.50/1.69 Axiom fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J:(forall (X_37:real), (((eq real) ((times_times_real X_37) X_37)) ((power_power_real X_37) (number_number_of_nat (bit0 (bit1 pls)))))). % 1.50/1.69 Axiom fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J:(forall (X_37:int), (((eq int) ((times_times_int X_37) X_37)) ((power_power_int X_37) (number_number_of_nat (bit0 (bit1 pls)))))). % 1.50/1.69 Axiom fact_22_power2__eq__square:(forall (A_65:nat), (((eq nat) ((power_power_nat A_65) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat A_65) A_65))). % 1.50/1.69 Axiom fact_23_power2__eq__square:(forall (A_65:real), (((eq real) ((power_power_real A_65) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_real A_65) A_65))). % 1.50/1.69 Axiom fact_24_power2__eq__square:(forall (A_65:int), (((eq int) ((power_power_int A_65) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int A_65) A_65))). % 1.50/1.69 Axiom fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J:(forall (X_36:nat) (N_39:nat), (((eq nat) ((power_power_nat X_36) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_39))) ((times_times_nat ((power_power_nat X_36) N_39)) ((power_power_nat X_36) N_39)))). % 1.50/1.69 Axiom fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J:(forall (X_36:real) (N_39:nat), (((eq real) ((power_power_real X_36) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_39))) ((times_times_real ((power_power_real X_36) N_39)) ((power_power_real X_36) N_39)))). % 1.50/1.69 Axiom fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J:(forall (X_36:int) (N_39:nat), (((eq int) ((power_power_int X_36) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_39))) ((times_times_int ((power_power_int X_36) N_39)) ((power_power_int X_36) N_39)))). % 1.50/1.69 Axiom fact_28_add__special_I2_J:(forall (W_17:int), (((eq real) ((plus_plus_real one_one_real) (number267125858f_real W_17))) (number267125858f_real ((plus_plus_int (bit1 pls)) W_17)))). % 1.50/1.69 Axiom fact_29_add__special_I2_J:(forall (W_17:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_17))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_17)))). % 1.50/1.69 Axiom fact_30_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))))). % 1.50/1.69 Axiom fact_31_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))))). % 1.50/1.69 Axiom fact_32_one__add__one__is__two:(((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))). % 1.50/1.69 Axiom fact_33_one__add__one__is__two:(((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))). % 1.50/1.69 Axiom fact_34__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_:((forall (T_1:int), (not (((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) T_1))))->False). % 1.50/1.69 Axiom fact_35_zle__refl:(forall (W:int), ((ord_less_eq_int W) W)). % 1.50/1.69 Axiom fact_36_zle__linear:(forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z))). % 1.50/1.69 Axiom fact_37_zless__le:(forall (Z:int) (W:int), ((iff ((ord_less_int Z) W)) ((and ((ord_less_eq_int Z) W)) (not (((eq int) Z) W))))). % 1.50/1.69 Axiom fact_38_zless__linear:(forall (X_1:int) (Y_1:int), ((or ((or ((ord_less_int X_1) Y_1)) (((eq int) X_1) Y_1))) ((ord_less_int Y_1) X_1))). % 1.50/1.69 Axiom fact_39_zle__trans:(forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_eq_int _TPTP_I) J)->(((ord_less_eq_int J) K)->((ord_less_eq_int _TPTP_I) K)))). % 1.50/1.69 Axiom fact_40_zle__antisym:(forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W)))). % 1.50/1.69 Axiom fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J:(forall (X_35:nat) (P_2:nat) (Q_4:nat), (((eq nat) ((power_power_nat ((power_power_nat X_35) P_2)) Q_4)) ((power_power_nat X_35) ((times_times_nat P_2) Q_4)))). % 1.50/1.69 Axiom fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J:(forall (X_35:real) (P_2:nat) (Q_4:nat), (((eq real) ((power_power_real ((power_power_real X_35) P_2)) Q_4)) ((power_power_real X_35) ((times_times_nat P_2) Q_4)))). % 1.50/1.69 Axiom fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J:(forall (X_35:int) (P_2:nat) (Q_4:nat), (((eq int) ((power_power_int ((power_power_int X_35) P_2)) Q_4)) ((power_power_int X_35) ((times_times_nat P_2) Q_4)))). % 1.50/1.69 Axiom fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J:(forall (X_34:nat), (((eq nat) ((power_power_nat X_34) one_one_nat)) X_34)). % 1.50/1.69 Axiom fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J:(forall (X_34:real), (((eq real) ((power_power_real X_34) one_one_nat)) X_34)). % 1.50/1.69 Axiom fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J:(forall (X_34:int), (((eq int) ((power_power_int X_34) one_one_nat)) X_34)). % 1.50/1.69 Axiom fact_47_zpower__zpower:(forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int ((power_power_int X_1) Y_1)) Z)) ((power_power_int X_1) ((times_times_nat Y_1) Z)))). % 1.50/1.69 Axiom fact_48_le__number__of__eq__not__less:(forall (V_15:int) (W_16:int), ((iff ((ord_less_eq_real (number267125858f_real V_15)) (number267125858f_real W_16))) (((ord_less_real (number267125858f_real W_16)) (number267125858f_real V_15))->False))). % 1.50/1.69 Axiom fact_49_le__number__of__eq__not__less:(forall (V_15:int) (W_16:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_15)) (number_number_of_nat W_16))) (((ord_less_nat (number_number_of_nat W_16)) (number_number_of_nat V_15))->False))). % 1.50/1.69 Axiom fact_50_le__number__of__eq__not__less:(forall (V_15:int) (W_16:int), ((iff ((ord_less_eq_int (number_number_of_int V_15)) (number_number_of_int W_16))) (((ord_less_int (number_number_of_int W_16)) (number_number_of_int V_15))->False))). % 1.50/1.69 Axiom fact_51_less__number__of:(forall (X_33:int) (Y_29:int), ((iff ((ord_less_real (number267125858f_real X_33)) (number267125858f_real Y_29))) ((ord_less_int X_33) Y_29))). % 1.50/1.69 Axiom fact_52_less__number__of:(forall (X_33:int) (Y_29:int), ((iff ((ord_less_int (number_number_of_int X_33)) (number_number_of_int Y_29))) ((ord_less_int X_33) Y_29))). % 1.50/1.69 Axiom fact_53_le__number__of:(forall (X_32:int) (Y_28:int), ((iff ((ord_less_eq_real (number267125858f_real X_32)) (number267125858f_real Y_28))) ((ord_less_eq_int X_32) Y_28))). % 1.50/1.69 Axiom fact_54_le__number__of:(forall (X_32:int) (Y_28:int), ((iff ((ord_less_eq_int (number_number_of_int X_32)) (number_number_of_int Y_28))) ((ord_less_eq_int X_32) Y_28))). % 1.50/1.69 Axiom fact_55_zadd__zless__mono:(forall (Z_9:int) (Z:int) (W_15:int) (W:int), (((ord_less_int W_15) W)->(((ord_less_eq_int Z_9) Z)->((ord_less_int ((plus_plus_int W_15) Z_9)) ((plus_plus_int W) Z))))). % 1.50/1.69 Axiom fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J:(forall (X_31:nat) (P_1:nat) (Q_3:nat), (((eq nat) ((times_times_nat ((power_power_nat X_31) P_1)) ((power_power_nat X_31) Q_3))) ((power_power_nat X_31) ((plus_plus_nat P_1) Q_3)))). % 1.50/1.69 Axiom fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J:(forall (X_31:real) (P_1:nat) (Q_3:nat), (((eq real) ((times_times_real ((power_power_real X_31) P_1)) ((power_power_real X_31) Q_3))) ((power_power_real X_31) ((plus_plus_nat P_1) Q_3)))). % 1.50/1.69 Axiom fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J:(forall (X_31:int) (P_1:nat) (Q_3:nat), (((eq int) ((times_times_int ((power_power_int X_31) P_1)) ((power_power_int X_31) Q_3))) ((power_power_int X_31) ((plus_plus_nat P_1) Q_3)))). % 1.50/1.69 Axiom fact_59_zpower__zadd__distrib:(forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int X_1) ((plus_plus_nat Y_1) Z))) ((times_times_int ((power_power_int X_1) Y_1)) ((power_power_int X_1) Z)))). % 1.50/1.69 Axiom fact_60_nat__mult__2:(forall (Z:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z)) ((plus_plus_nat Z) Z))). % 1.50/1.69 Axiom fact_61_nat__mult__2__right:(forall (Z:nat), (((eq nat) ((times_times_nat Z) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z) Z))). % 1.50/1.69 Axiom fact_62_nat__1__add__1:(((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))). % 1.50/1.69 Axiom fact_63_less__int__code_I16_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2))). % 1.50/1.69 Axiom fact_64_rel__simps_I17_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L))). % 1.50/1.69 Axiom fact_65_less__eq__int__code_I16_J:(forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))). % 1.50/1.69 Axiom fact_66_rel__simps_I34_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit1 L))) ((ord_less_eq_int K) L))). % 1.50/1.69 Axiom fact_67_rel__simps_I2_J:(((ord_less_int pls) pls)->False). % 1.50/1.69 Axiom fact_68_less__int__code_I13_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit0 K2))) ((ord_less_int K1) K2))). % 1.50/1.69 Axiom fact_69_rel__simps_I14_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit0 L))) ((ord_less_int K) L))). % 1.52/1.69 Axiom fact_70_rel__simps_I19_J:((ord_less_eq_int pls) pls). % 1.52/1.69 Axiom fact_71_less__eq__int__code_I13_J:(forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit0 K2))) ((ord_less_eq_int K1) K2))). % 1.52/1.69 Axiom fact_72_rel__simps_I31_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit0 L))) ((ord_less_eq_int K) L))). % 1.52/1.69 Axiom fact_73_less__number__of__int__code:(forall (K:int) (L:int), ((iff ((ord_less_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_int K) L))). % 1.52/1.69 Axiom fact_74_less__eq__number__of__int__code:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_eq_int K) L))). % 1.52/1.69 Axiom fact_75_zadd__strict__right__mono:(forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_int _TPTP_I) J)->((ord_less_int ((plus_plus_int _TPTP_I) K)) ((plus_plus_int J) K)))). % 1.52/1.69 Axiom fact_76_zadd__left__mono:(forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_eq_int _TPTP_I) J)->((ord_less_eq_int ((plus_plus_int K) _TPTP_I)) ((plus_plus_int K) J)))). % 1.52/1.69 Axiom fact_77_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)))))))). % 1.52/1.69 Axiom fact_78_nat__numeral__1__eq__1:(((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat). % 1.52/1.69 Axiom fact_79_Numeral1__eq1__nat:(((eq nat) one_one_nat) (number_number_of_nat (bit1 pls))). % 1.52/1.69 Axiom fact_80_rel__simps_I29_J:(forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls))). % 1.52/1.69 Axiom fact_81_rel__simps_I5_J:(forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K))). % 1.52/1.69 Axiom fact_82_less__eq__int__code_I15_J:(forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2))). % 1.52/1.69 Axiom fact_83_rel__simps_I33_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))). % 1.52/1.69 Axiom fact_84_less__int__code_I14_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))). % 1.52/1.69 Axiom fact_85_rel__simps_I15_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))). % 1.52/1.69 Axiom fact_86_zless__imp__add1__zle:(forall (W:int) (Z:int), (((ord_less_int W) Z)->((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z))). % 1.52/1.69 Axiom fact_87_add1__zle__eq:(forall (W:int) (Z:int), ((iff ((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z)) ((ord_less_int W) Z))). % 1.52/1.69 Axiom fact_88_zle__add1__eq__le:(forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((ord_less_eq_int W) Z))). % 1.52/1.69 Axiom fact_89_zprime__2:(zprime (number_number_of_int (bit0 (bit1 pls)))). % 1.52/1.69 Axiom fact_90_is__mult__sum2sq:(forall (Y_1:int) (X_1:int), ((twoSqu362149276sum2sq X_1)->((twoSqu362149276sum2sq Y_1)->(twoSqu362149276sum2sq ((times_times_int X_1) Y_1))))). % 1.52/1.69 Axiom fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J:(forall (Lx_6:real) (Ly_4:real) (Rx_6:real) (Ry_4:real), (((eq real) ((times_times_real ((times_times_real Lx_6) Ly_4)) ((times_times_real Rx_6) Ry_4))) ((times_times_real ((times_times_real Lx_6) Rx_6)) ((times_times_real Ly_4) Ry_4)))). % 1.52/1.69 Axiom fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J:(forall (Lx_6:nat) (Ly_4:nat) (Rx_6:nat) (Ry_4:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_6) Ly_4)) ((times_times_nat Rx_6) Ry_4))) ((times_times_nat ((times_times_nat Lx_6) Rx_6)) ((times_times_nat Ly_4) Ry_4)))). % 1.52/1.69 Axiom fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J:(forall (Lx_6:int) (Ly_4:int) (Rx_6:int) (Ry_4:int), (((eq int) ((times_times_int ((times_times_int Lx_6) Ly_4)) ((times_times_int Rx_6) Ry_4))) ((times_times_int ((times_times_int Lx_6) Rx_6)) ((times_times_int Ly_4) Ry_4)))). % 1.52/1.69 Axiom fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J:(forall (Lx_5:real) (Ly_3:real) (Rx_5:real) (Ry_3:real), (((eq real) ((times_times_real ((times_times_real Lx_5) Ly_3)) ((times_times_real Rx_5) Ry_3))) ((times_times_real Rx_5) ((times_times_real ((times_times_real Lx_5) Ly_3)) Ry_3)))). % 1.52/1.69 Axiom fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J:(forall (Lx_5:nat) (Ly_3:nat) (Rx_5:nat) (Ry_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) ((times_times_nat Rx_5) Ry_3))) ((times_times_nat Rx_5) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) Ry_3)))). % 1.52/1.69 Axiom fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J:(forall (Lx_5:int) (Ly_3:int) (Rx_5:int) (Ry_3:int), (((eq int) ((times_times_int ((times_times_int Lx_5) Ly_3)) ((times_times_int Rx_5) Ry_3))) ((times_times_int Rx_5) ((times_times_int ((times_times_int Lx_5) Ly_3)) Ry_3)))). % 1.52/1.69 Axiom fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J:(forall (Lx_4:real) (Ly_2:real) (Rx_4:real) (Ry_2:real), (((eq real) ((times_times_real ((times_times_real Lx_4) Ly_2)) ((times_times_real Rx_4) Ry_2))) ((times_times_real Lx_4) ((times_times_real Ly_2) ((times_times_real Rx_4) Ry_2))))). % 1.52/1.69 Axiom fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J:(forall (Lx_4:nat) (Ly_2:nat) (Rx_4:nat) (Ry_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_4) Ly_2)) ((times_times_nat Rx_4) Ry_2))) ((times_times_nat Lx_4) ((times_times_nat Ly_2) ((times_times_nat Rx_4) Ry_2))))). % 1.52/1.69 Axiom fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J:(forall (Lx_4:int) (Ly_2:int) (Rx_4:int) (Ry_2:int), (((eq int) ((times_times_int ((times_times_int Lx_4) Ly_2)) ((times_times_int Rx_4) Ry_2))) ((times_times_int Lx_4) ((times_times_int Ly_2) ((times_times_int Rx_4) Ry_2))))). % 1.52/1.69 Axiom fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J:(forall (Lx_3:real) (Ly_1:real) (Rx_3:real), (((eq real) ((times_times_real ((times_times_real Lx_3) Ly_1)) Rx_3)) ((times_times_real ((times_times_real Lx_3) Rx_3)) Ly_1))). % 1.52/1.69 Axiom fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J:(forall (Lx_3:nat) (Ly_1:nat) (Rx_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_3) Ly_1)) Rx_3)) ((times_times_nat ((times_times_nat Lx_3) Rx_3)) Ly_1))). % 1.52/1.69 Axiom fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J:(forall (Lx_3:int) (Ly_1:int) (Rx_3:int), (((eq int) ((times_times_int ((times_times_int Lx_3) Ly_1)) Rx_3)) ((times_times_int ((times_times_int Lx_3) Rx_3)) Ly_1))). % 1.52/1.69 Axiom fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J:(forall (Lx_2:real) (Ly:real) (Rx_2:real), (((eq real) ((times_times_real ((times_times_real Lx_2) Ly)) Rx_2)) ((times_times_real Lx_2) ((times_times_real Ly) Rx_2)))). % 1.52/1.69 Axiom fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J:(forall (Lx_2:nat) (Ly:nat) (Rx_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_2) Ly)) Rx_2)) ((times_times_nat Lx_2) ((times_times_nat Ly) Rx_2)))). % 1.52/1.69 Axiom fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J:(forall (Lx_2:int) (Ly:int) (Rx_2:int), (((eq int) ((times_times_int ((times_times_int Lx_2) Ly)) Rx_2)) ((times_times_int Lx_2) ((times_times_int Ly) Rx_2)))). % 1.52/1.69 Axiom fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J:(forall (Lx_1:real) (Rx_1:real) (Ry_1:real), (((eq real) ((times_times_real Lx_1) ((times_times_real Rx_1) Ry_1))) ((times_times_real ((times_times_real Lx_1) Rx_1)) Ry_1))). % 1.52/1.69 Axiom fact_107_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J:(forall (Lx_1:nat) (Rx_1:nat) (Ry_1:nat), (((eq nat) ((times_times_nat Lx_1) ((times_times_nat Rx_1) Ry_1))) ((times_times_nat ((times_times_nat Lx_1) Rx_1)) Ry_1))). % 1.52/1.69 Axiom fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J:(forall (Lx_1:int) (Rx_1:int) (Ry_1:int), (((eq int) ((times_times_int Lx_1) ((times_times_int Rx_1) Ry_1))) ((times_times_int ((times_times_int Lx_1) Rx_1)) Ry_1))). % 1.52/1.69 Axiom fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J:(forall (Lx:real) (Rx:real) (Ry:real), (((eq real) ((times_times_real Lx) ((times_times_real Rx) Ry))) ((times_times_real Rx) ((times_times_real Lx) Ry)))). % 1.52/1.69 Axiom fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J:(forall (Lx:nat) (Rx:nat) (Ry:nat), (((eq nat) ((times_times_nat Lx) ((times_times_nat Rx) Ry))) ((times_times_nat Rx) ((times_times_nat Lx) Ry)))). % 1.52/1.69 Axiom fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J:(forall (Lx:int) (Rx:int) (Ry:int), (((eq int) ((times_times_int Lx) ((times_times_int Rx) Ry))) ((times_times_int Rx) ((times_times_int Lx) Ry)))). % 1.52/1.69 Axiom fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J:(forall (A_64:real) (B_20:real), (((eq real) ((times_times_real A_64) B_20)) ((times_times_real B_20) A_64))). % 1.52/1.69 Axiom fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J:(forall (A_64:nat) (B_20:nat), (((eq nat) ((times_times_nat A_64) B_20)) ((times_times_nat B_20) A_64))). % 1.52/1.69 Axiom fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J:(forall (A_64:int) (B_20:int), (((eq int) ((times_times_int A_64) B_20)) ((times_times_int B_20) A_64))). % 1.52/1.69 Axiom fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_63:real) (B_19:real) (C_10:real) (D_5:real), (((eq real) ((plus_plus_real ((plus_plus_real A_63) B_19)) ((plus_plus_real C_10) D_5))) ((plus_plus_real ((plus_plus_real A_63) C_10)) ((plus_plus_real B_19) D_5)))). % 1.52/1.69 Axiom fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_63:nat) (B_19:nat) (C_10:nat) (D_5:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_63) B_19)) ((plus_plus_nat C_10) D_5))) ((plus_plus_nat ((plus_plus_nat A_63) C_10)) ((plus_plus_nat B_19) D_5)))). % 1.52/1.69 Axiom fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_63:int) (B_19:int) (C_10:int) (D_5:int), (((eq int) ((plus_plus_int ((plus_plus_int A_63) B_19)) ((plus_plus_int C_10) D_5))) ((plus_plus_int ((plus_plus_int A_63) C_10)) ((plus_plus_int B_19) D_5)))). % 1.52/1.70 Axiom fact_118_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_62:real) (B_18:real) (C_9:real), (((eq real) ((plus_plus_real ((plus_plus_real A_62) B_18)) C_9)) ((plus_plus_real ((plus_plus_real A_62) C_9)) B_18))). % 1.52/1.70 Axiom fact_119_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_62:nat) (B_18:nat) (C_9:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_62) B_18)) C_9)) ((plus_plus_nat ((plus_plus_nat A_62) C_9)) B_18))). % 1.52/1.70 Axiom fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_62:int) (B_18:int) (C_9:int), (((eq int) ((plus_plus_int ((plus_plus_int A_62) B_18)) C_9)) ((plus_plus_int ((plus_plus_int A_62) C_9)) B_18))). % 1.52/1.70 Axiom fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_61:real) (B_17:real) (C_8:real), (((eq real) ((plus_plus_real ((plus_plus_real A_61) B_17)) C_8)) ((plus_plus_real A_61) ((plus_plus_real B_17) C_8)))). % 1.52/1.70 Axiom fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_61:nat) (B_17:nat) (C_8:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_61) B_17)) C_8)) ((plus_plus_nat A_61) ((plus_plus_nat B_17) C_8)))). % 1.52/1.70 Axiom fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_61:int) (B_17:int) (C_8:int), (((eq int) ((plus_plus_int ((plus_plus_int A_61) B_17)) C_8)) ((plus_plus_int A_61) ((plus_plus_int B_17) C_8)))). % 1.52/1.70 Axiom fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_60:real) (C_7:real) (D_4:real), (((eq real) ((plus_plus_real A_60) ((plus_plus_real C_7) D_4))) ((plus_plus_real ((plus_plus_real A_60) C_7)) D_4))). % 1.52/1.70 Axiom fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_60:nat) (C_7:nat) (D_4:nat), (((eq nat) ((plus_plus_nat A_60) ((plus_plus_nat C_7) D_4))) ((plus_plus_nat ((plus_plus_nat A_60) C_7)) D_4))). % 1.52/1.70 Axiom fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_60:int) (C_7:int) (D_4:int), (((eq int) ((plus_plus_int A_60) ((plus_plus_int C_7) D_4))) ((plus_plus_int ((plus_plus_int A_60) C_7)) D_4))). % 1.52/1.70 Axiom fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_59:real) (C_6:real) (D_3:real), (((eq real) ((plus_plus_real A_59) ((plus_plus_real C_6) D_3))) ((plus_plus_real C_6) ((plus_plus_real A_59) D_3)))). % 1.52/1.70 Axiom fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_59:nat) (C_6:nat) (D_3:nat), (((eq nat) ((plus_plus_nat A_59) ((plus_plus_nat C_6) D_3))) ((plus_plus_nat C_6) ((plus_plus_nat A_59) D_3)))). % 1.52/1.70 Axiom fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_59:int) (C_6:int) (D_3:int), (((eq int) ((plus_plus_int A_59) ((plus_plus_int C_6) D_3))) ((plus_plus_int C_6) ((plus_plus_int A_59) D_3)))). % 1.52/1.70 Axiom fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A_58:real) (C_5:real), (((eq real) ((plus_plus_real A_58) C_5)) ((plus_plus_real C_5) A_58))). % 1.52/1.70 Axiom fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A_58:nat) (C_5:nat), (((eq nat) ((plus_plus_nat A_58) C_5)) ((plus_plus_nat C_5) A_58))). % 1.52/1.70 Axiom fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A_58:int) (C_5:int), (((eq int) ((plus_plus_int A_58) C_5)) ((plus_plus_int C_5) A_58))). % 1.52/1.70 Axiom fact_133_eq__number__of:(forall (X_30:int) (Y_27:int), ((iff (((eq real) (number267125858f_real X_30)) (number267125858f_real Y_27))) (((eq int) X_30) Y_27))). % 1.52/1.70 Axiom fact_134_eq__number__of:(forall (X_30:int) (Y_27:int), ((iff (((eq int) (number_number_of_int X_30)) (number_number_of_int Y_27))) (((eq int) X_30) Y_27))). % 1.52/1.70 Axiom fact_135_number__of__reorient:(forall (W_14:int) (X_29:real), ((iff (((eq real) (number267125858f_real W_14)) X_29)) (((eq real) X_29) (number267125858f_real W_14)))). % 1.52/1.70 Axiom fact_136_number__of__reorient:(forall (W_14:int) (X_29:int), ((iff (((eq int) (number_number_of_int W_14)) X_29)) (((eq int) X_29) (number_number_of_int W_14)))). % 1.52/1.70 Axiom fact_137_number__of__reorient:(forall (W_14:int) (X_29:nat), ((iff (((eq nat) (number_number_of_nat W_14)) X_29)) (((eq nat) X_29) (number_number_of_nat W_14)))). % 1.52/1.70 Axiom fact_138_rel__simps_I51_J:(forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L))). % 1.52/1.70 Axiom fact_139_rel__simps_I48_J:(forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L))). % 1.52/1.70 Axiom fact_140_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)))). % 1.52/1.70 Axiom fact_141_zmult__commute:(forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z))). % 1.52/1.70 Axiom fact_142_number__of__is__id:(forall (K:int), (((eq int) (number_number_of_int K)) K)). % 1.52/1.70 Axiom fact_143_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)))). % 1.52/1.70 Axiom fact_144_zadd__left__commute:(forall (X_1:int) (Y_1:int) (Z:int), (((eq int) ((plus_plus_int X_1) ((plus_plus_int Y_1) Z))) ((plus_plus_int Y_1) ((plus_plus_int X_1) Z)))). % 1.52/1.70 Axiom fact_145_zadd__commute:(forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z))). % 1.52/1.70 Axiom fact_146_rel__simps_I12_J:(forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls))). % 1.52/1.70 Axiom fact_147_less__int__code_I15_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2))). % 1.52/1.70 Axiom fact_148_rel__simps_I16_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))). % 1.52/1.70 Axiom fact_149_rel__simps_I10_J:(forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls))). % 1.52/1.70 Axiom fact_150_rel__simps_I4_J:(forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K))). % 1.52/1.70 Axiom fact_151_rel__simps_I22_J:(forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K))). % 1.52/1.70 Axiom fact_152_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))). % 1.52/1.70 Axiom fact_153_rel__simps_I32_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))). % 1.52/1.70 Axiom fact_154_rel__simps_I27_J:(forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) pls)) ((ord_less_eq_int K) pls))). % 1.52/1.70 Axiom fact_155_rel__simps_I21_J:(forall (K:int), ((iff ((ord_less_eq_int pls) (bit0 K))) ((ord_less_eq_int pls) K))). % 1.52/1.70 Axiom fact_156_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)))). % 1.52/1.70 Axiom fact_157_power__even__eq:(forall (A_57:nat) (N_38:nat), (((eq nat) ((power_power_nat A_57) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_38))) ((power_power_nat ((power_power_nat A_57) N_38)) (number_number_of_nat (bit0 (bit1 pls)))))). % 1.52/1.70 Axiom fact_158_power__even__eq:(forall (A_57:real) (N_38:nat), (((eq real) ((power_power_real A_57) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_38))) ((power_power_real ((power_power_real A_57) N_38)) (number_number_of_nat (bit0 (bit1 pls)))))). % 1.52/1.70 Axiom fact_159_power__even__eq:(forall (A_57:int) (N_38:nat), (((eq int) ((power_power_int A_57) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_38))) ((power_power_int ((power_power_int A_57) N_38)) (number_number_of_nat (bit0 (bit1 pls)))))). % 1.52/1.70 Axiom fact_160_less__special_I4_J:(forall (X_28:int), ((iff ((ord_less_real (number267125858f_real X_28)) one_one_real)) ((ord_less_int X_28) (bit1 pls)))). % 1.52/1.70 Axiom fact_161_less__special_I4_J:(forall (X_28:int), ((iff ((ord_less_int (number_number_of_int X_28)) one_one_int)) ((ord_less_int X_28) (bit1 pls)))). % 1.52/1.70 Axiom fact_162_less__special_I2_J:(forall (Y_26:int), ((iff ((ord_less_real one_one_real) (number267125858f_real Y_26))) ((ord_less_int (bit1 pls)) Y_26))). % 1.52/1.70 Axiom fact_163_less__special_I2_J:(forall (Y_26:int), ((iff ((ord_less_int one_one_int) (number_number_of_int Y_26))) ((ord_less_int (bit1 pls)) Y_26))). % 1.52/1.70 Axiom fact_164_le__special_I4_J:(forall (X_27:int), ((iff ((ord_less_eq_real (number267125858f_real X_27)) one_one_real)) ((ord_less_eq_int X_27) (bit1 pls)))). % 1.52/1.70 Axiom fact_165_le__special_I4_J:(forall (X_27:int), ((iff ((ord_less_eq_int (number_number_of_int X_27)) one_one_int)) ((ord_less_eq_int X_27) (bit1 pls)))). % 1.52/1.70 Axiom fact_166_le__special_I2_J:(forall (Y_25:int), ((iff ((ord_less_eq_real one_one_real) (number267125858f_real Y_25))) ((ord_less_eq_int (bit1 pls)) Y_25))). % 1.52/1.70 Axiom fact_167_le__special_I2_J:(forall (Y_25:int), ((iff ((ord_less_eq_int one_one_int) (number_number_of_int Y_25))) ((ord_less_eq_int (bit1 pls)) Y_25))). % 1.52/1.70 Axiom fact_168_crossproduct__eq:(forall (W_13:real) (Y_24:real) (X_26:real) (Z_8:real), ((iff (((eq real) ((plus_plus_real ((times_times_real W_13) Y_24)) ((times_times_real X_26) Z_8))) ((plus_plus_real ((times_times_real W_13) Z_8)) ((times_times_real X_26) Y_24)))) ((or (((eq real) W_13) X_26)) (((eq real) Y_24) Z_8)))). % 1.52/1.70 Axiom fact_169_crossproduct__eq:(forall (W_13:nat) (Y_24:nat) (X_26:nat) (Z_8:nat), ((iff (((eq nat) ((plus_plus_nat ((times_times_nat W_13) Y_24)) ((times_times_nat X_26) Z_8))) ((plus_plus_nat ((times_times_nat W_13) Z_8)) ((times_times_nat X_26) Y_24)))) ((or (((eq nat) W_13) X_26)) (((eq nat) Y_24) Z_8)))). % 1.52/1.70 Axiom fact_170_crossproduct__eq:(forall (W_13:int) (Y_24:int) (X_26:int) (Z_8:int), ((iff (((eq int) ((plus_plus_int ((times_times_int W_13) Y_24)) ((times_times_int X_26) Z_8))) ((plus_plus_int ((times_times_int W_13) Z_8)) ((times_times_int X_26) Y_24)))) ((or (((eq int) W_13) X_26)) (((eq int) Y_24) Z_8)))). % 1.52/1.70 Axiom fact_171_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J:(forall (A_56:real) (M_13:real) (B_16:real), (((eq real) ((plus_plus_real ((times_times_real A_56) M_13)) ((times_times_real B_16) M_13))) ((times_times_real ((plus_plus_real A_56) B_16)) M_13))). % 1.52/1.70 Axiom fact_172_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J:(forall (A_56:nat) (M_13:nat) (B_16:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_56) M_13)) ((times_times_nat B_16) M_13))) ((times_times_nat ((plus_plus_nat A_56) B_16)) M_13))). % 1.52/1.70 Axiom fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J:(forall (A_56:int) (M_13:int) (B_16:int), (((eq int) ((plus_plus_int ((times_times_int A_56) M_13)) ((times_times_int B_16) M_13))) ((times_times_int ((plus_plus_int A_56) B_16)) M_13))). % 1.52/1.70 Axiom fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J:(forall (A_55:real) (B_15:real) (C_4:real), (((eq real) ((times_times_real ((plus_plus_real A_55) B_15)) C_4)) ((plus_plus_real ((times_times_real A_55) C_4)) ((times_times_real B_15) C_4)))). % 1.52/1.70 Axiom fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J:(forall (A_55:nat) (B_15:nat) (C_4:nat), (((eq nat) ((times_times_nat ((plus_plus_nat A_55) B_15)) C_4)) ((plus_plus_nat ((times_times_nat A_55) C_4)) ((times_times_nat B_15) C_4)))). % 1.52/1.70 Axiom fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J:(forall (A_55:int) (B_15:int) (C_4:int), (((eq int) ((times_times_int ((plus_plus_int A_55) B_15)) C_4)) ((plus_plus_int ((times_times_int A_55) C_4)) ((times_times_int B_15) C_4)))). % 1.52/1.70 Axiom fact_177_crossproduct__noteq:(forall (C_3:real) (D_2:real) (A_54:real) (B_14:real), ((iff ((and (not (((eq real) A_54) B_14))) (not (((eq real) C_3) D_2)))) (not (((eq real) ((plus_plus_real ((times_times_real A_54) C_3)) ((times_times_real B_14) D_2))) ((plus_plus_real ((times_times_real A_54) D_2)) ((times_times_real B_14) C_3)))))). % 1.52/1.70 Axiom fact_178_crossproduct__noteq:(forall (C_3:nat) (D_2:nat) (A_54:nat) (B_14:nat), ((iff ((and (not (((eq nat) A_54) B_14))) (not (((eq nat) C_3) D_2)))) (not (((eq nat) ((plus_plus_nat ((times_times_nat A_54) C_3)) ((times_times_nat B_14) D_2))) ((plus_plus_nat ((times_times_nat A_54) D_2)) ((times_times_nat B_14) C_3)))))). % 1.52/1.70 Axiom fact_179_crossproduct__noteq:(forall (C_3:int) (D_2:int) (A_54:int) (B_14:int), ((iff ((and (not (((eq int) A_54) B_14))) (not (((eq int) C_3) D_2)))) (not (((eq int) ((plus_plus_int ((times_times_int A_54) C_3)) ((times_times_int B_14) D_2))) ((plus_plus_int ((times_times_int A_54) D_2)) ((times_times_int B_14) C_3)))))). % 1.52/1.70 Axiom fact_180_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J:(forall (X_25:real) (Y_23:real) (Z_7:real), (((eq real) ((times_times_real X_25) ((plus_plus_real Y_23) Z_7))) ((plus_plus_real ((times_times_real X_25) Y_23)) ((times_times_real X_25) Z_7)))). % 1.52/1.70 Axiom fact_181_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J:(forall (X_25:nat) (Y_23:nat) (Z_7:nat), (((eq nat) ((times_times_nat X_25) ((plus_plus_nat Y_23) Z_7))) ((plus_plus_nat ((times_times_nat X_25) Y_23)) ((times_times_nat X_25) Z_7)))). % 1.52/1.70 Axiom fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J:(forall (X_25:int) (Y_23:int) (Z_7:int), (((eq int) ((times_times_int X_25) ((plus_plus_int Y_23) Z_7))) ((plus_plus_int ((times_times_int X_25) Y_23)) ((times_times_int X_25) Z_7)))). % 1.52/1.70 Axiom fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J:(forall (A_53:real), (((eq real) ((times_times_real A_53) one_one_real)) A_53)). % 1.52/1.70 Axiom fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J:(forall (A_53:nat), (((eq nat) ((times_times_nat A_53) one_one_nat)) A_53)). % 1.52/1.70 Axiom fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J:(forall (A_53:int), (((eq int) ((times_times_int A_53) one_one_int)) A_53)). % 1.52/1.70 Axiom fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J:(forall (A_52:real), (((eq real) ((times_times_real one_one_real) A_52)) A_52)). % 1.52/1.70 Axiom fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J:(forall (A_52:nat), (((eq nat) ((times_times_nat one_one_nat) A_52)) A_52)). % 1.52/1.70 Axiom fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J:(forall (A_52:int), (((eq int) ((times_times_int one_one_int) A_52)) A_52)). % 1.52/1.70 Axiom fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J:(forall (X_24:nat) (Y_22:nat) (Q_2:nat), (((eq nat) ((power_power_nat ((times_times_nat X_24) Y_22)) Q_2)) ((times_times_nat ((power_power_nat X_24) Q_2)) ((power_power_nat Y_22) Q_2)))). % 1.52/1.70 Axiom fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J:(forall (X_24:real) (Y_22:real) (Q_2:nat), (((eq real) ((power_power_real ((times_times_real X_24) Y_22)) Q_2)) ((times_times_real ((power_power_real X_24) Q_2)) ((power_power_real Y_22) Q_2)))). % 1.52/1.70 Axiom fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J:(forall (X_24:int) (Y_22:int) (Q_2:nat), (((eq int) ((power_power_int ((times_times_int X_24) Y_22)) Q_2)) ((times_times_int ((power_power_int X_24) Q_2)) ((power_power_int Y_22) Q_2)))). % 1.52/1.70 Axiom fact_192_rel__simps_I46_J:(forall (K:int), (not (((eq int) (bit1 K)) pls))). % 1.52/1.70 Axiom fact_193_rel__simps_I39_J:(forall (L:int), (not (((eq int) pls) (bit1 L)))). % 1.52/1.70 Axiom fact_194_rel__simps_I50_J:(forall (K:int) (L:int), (not (((eq int) (bit1 K)) (bit0 L)))). % 1.52/1.70 Axiom fact_195_rel__simps_I49_J:(forall (K:int) (L:int), (not (((eq int) (bit0 K)) (bit1 L)))). % 1.52/1.70 Axiom fact_196_rel__simps_I44_J:(forall (K:int), ((iff (((eq int) (bit0 K)) pls)) (((eq int) K) pls))). % 1.52/1.70 Axiom fact_197_rel__simps_I38_J:(forall (L:int), ((iff (((eq int) pls) (bit0 L))) (((eq int) pls) L))). % 1.52/1.70 Axiom fact_198_Bit0__Pls:(((eq int) (bit0 pls)) pls). % 1.52/1.70 Axiom fact_199_mult__Pls:(forall (W:int), (((eq int) ((times_times_int pls) W)) pls)). % 1.52/1.70 Axiom fact_200_mult__Bit0:(forall (K:int) (L:int), (((eq int) ((times_times_int (bit0 K)) L)) (bit0 ((times_times_int K) L)))). % 1.52/1.70 Axiom fact_201_add__Pls__right:(forall (K:int), (((eq int) ((plus_plus_int K) pls)) K)). % 1.52/1.70 Axiom fact_202_add__Pls:(forall (K:int), (((eq int) ((plus_plus_int pls) K)) K)). % 1.52/1.70 Axiom fact_203_add__Bit0__Bit0:(forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit0 L))) (bit0 ((plus_plus_int K) L)))). % 1.52/1.70 Axiom fact_204_Bit0__def:(forall (K:int), (((eq int) (bit0 K)) ((plus_plus_int K) K))). % 1.52/1.70 Axiom fact_205_zmult__1__right:(forall (Z:int), (((eq int) ((times_times_int Z) one_one_int)) Z)). % 1.52/1.70 Axiom fact_206_zmult__1:(forall (Z:int), (((eq int) ((times_times_int one_one_int) Z)) Z)). % 1.52/1.70 Axiom fact_207_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)))). % 1.52/1.70 Axiom fact_208_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)))). % 1.52/1.70 Axiom fact_209_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)))). % 1.52/1.70 Axiom fact_210_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)))). % 1.52/1.70 Axiom fact_211_semiring__mult__number__of:(forall (V_14:int) (V_13:int), (((ord_less_eq_int pls) V_13)->(((ord_less_eq_int pls) V_14)->(((eq real) ((times_times_real (number267125858f_real V_13)) (number267125858f_real V_14))) (number267125858f_real ((times_times_int V_13) V_14)))))). % 1.52/1.70 Axiom fact_212_semiring__mult__number__of:(forall (V_14:int) (V_13:int), (((ord_less_eq_int pls) V_13)->(((ord_less_eq_int pls) V_14)->(((eq nat) ((times_times_nat (number_number_of_nat V_13)) (number_number_of_nat V_14))) (number_number_of_nat ((times_times_int V_13) V_14)))))). % 1.52/1.70 Axiom fact_213_semiring__mult__number__of:(forall (V_14:int) (V_13:int), (((ord_less_eq_int pls) V_13)->(((ord_less_eq_int pls) V_14)->(((eq int) ((times_times_int (number_number_of_int V_13)) (number_number_of_int V_14))) (number_number_of_int ((times_times_int V_13) V_14)))))). % 1.52/1.70 Axiom fact_214_semiring__add__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) ((plus_plus_real (number267125858f_real V_11)) (number267125858f_real V_12))) (number267125858f_real ((plus_plus_int V_11) V_12)))))). % 1.52/1.70 Axiom fact_215_semiring__add__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) ((plus_plus_nat (number_number_of_nat V_11)) (number_number_of_nat V_12))) (number_number_of_nat ((plus_plus_int V_11) V_12)))))). % 1.52/1.70 Axiom fact_216_semiring__add__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) ((plus_plus_int (number_number_of_int V_11)) (number_number_of_int V_12))) (number_number_of_int ((plus_plus_int V_11) V_12)))))). % 1.52/1.70 Axiom fact_217_power2__ge__self:(forall (X_1:int), ((ord_less_eq_int X_1) ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls)))))). % 1.52/1.70 Axiom fact_218_left__distrib__number__of:(forall (A_51:real) (B_13:real) (V_10:int), (((eq real) ((times_times_real ((plus_plus_real A_51) B_13)) (number267125858f_real V_10))) ((plus_plus_real ((times_times_real A_51) (number267125858f_real V_10))) ((times_times_real B_13) (number267125858f_real V_10))))). % 1.52/1.70 Axiom fact_219_left__distrib__number__of:(forall (A_51:nat) (B_13:nat) (V_10:int), (((eq nat) ((times_times_nat ((plus_plus_nat A_51) B_13)) (number_number_of_nat V_10))) ((plus_plus_nat ((times_times_nat A_51) (number_number_of_nat V_10))) ((times_times_nat B_13) (number_number_of_nat V_10))))). % 1.52/1.70 Axiom fact_220_left__distrib__number__of:(forall (A_51:int) (B_13:int) (V_10:int), (((eq int) ((times_times_int ((plus_plus_int A_51) B_13)) (number_number_of_int V_10))) ((plus_plus_int ((times_times_int A_51) (number_number_of_int V_10))) ((times_times_int B_13) (number_number_of_int V_10))))). % 1.52/1.70 Axiom fact_221_right__distrib__number__of:(forall (V_9:int) (B_12:real) (C_2:real), (((eq real) ((times_times_real (number267125858f_real V_9)) ((plus_plus_real B_12) C_2))) ((plus_plus_real ((times_times_real (number267125858f_real V_9)) B_12)) ((times_times_real (number267125858f_real V_9)) C_2)))). % 1.52/1.70 Axiom fact_222_right__distrib__number__of:(forall (V_9:int) (B_12:nat) (C_2:nat), (((eq nat) ((times_times_nat (number_number_of_nat V_9)) ((plus_plus_nat B_12) C_2))) ((plus_plus_nat ((times_times_nat (number_number_of_nat V_9)) B_12)) ((times_times_nat (number_number_of_nat V_9)) C_2)))). % 1.52/1.70 Axiom fact_223_right__distrib__number__of:(forall (V_9:int) (B_12:int) (C_2:int), (((eq int) ((times_times_int (number_number_of_int V_9)) ((plus_plus_int B_12) C_2))) ((plus_plus_int ((times_times_int (number_number_of_int V_9)) B_12)) ((times_times_int (number_number_of_int V_9)) C_2)))). % 1.52/1.70 Axiom fact_224_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J:(forall (A_50:real) (M_12:real), (((eq real) ((plus_plus_real ((times_times_real A_50) M_12)) M_12)) ((times_times_real ((plus_plus_real A_50) one_one_real)) M_12))). % 1.52/1.70 Axiom fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J:(forall (A_50:nat) (M_12:nat), (((eq nat) ((plus_plus_nat ((times_times_nat A_50) M_12)) M_12)) ((times_times_nat ((plus_plus_nat A_50) one_one_nat)) M_12))). % 1.52/1.70 Axiom fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J:(forall (A_50:int) (M_12:int), (((eq int) ((plus_plus_int ((times_times_int A_50) M_12)) M_12)) ((times_times_int ((plus_plus_int A_50) one_one_int)) M_12))). % 1.52/1.70 Axiom fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J:(forall (M_11:real) (A_49:real), (((eq real) ((plus_plus_real M_11) ((times_times_real A_49) M_11))) ((times_times_real ((plus_plus_real A_49) one_one_real)) M_11))). % 1.52/1.70 Axiom fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J:(forall (M_11:nat) (A_49:nat), (((eq nat) ((plus_plus_nat M_11) ((times_times_nat A_49) M_11))) ((times_times_nat ((plus_plus_nat A_49) one_one_nat)) M_11))). % 1.52/1.70 Axiom fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J:(forall (M_11:int) (A_49:int), (((eq int) ((plus_plus_int M_11) ((times_times_int A_49) M_11))) ((times_times_int ((plus_plus_int A_49) one_one_int)) M_11))). % 1.52/1.70 Axiom fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J:(forall (M_10:real), (((eq real) ((plus_plus_real M_10) M_10)) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) M_10))). % 1.52/1.70 Axiom fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J:(forall (M_10:nat), (((eq nat) ((plus_plus_nat M_10) M_10)) ((times_times_nat ((plus_plus_nat one_one_nat) one_one_nat)) M_10))). % 1.52/1.70 Axiom fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J:(forall (M_10:int), (((eq int) ((plus_plus_int M_10) M_10)) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) M_10))). % 1.52/1.70 Axiom fact_233_add__numeral__0:(forall (A_48:real), (((eq real) ((plus_plus_real (number267125858f_real pls)) A_48)) A_48)). % 1.52/1.70 Axiom fact_234_add__numeral__0:(forall (A_48:int), (((eq int) ((plus_plus_int (number_number_of_int pls)) A_48)) A_48)). % 1.52/1.70 Axiom fact_235_add__numeral__0__right:(forall (A_47:real), (((eq real) ((plus_plus_real A_47) (number267125858f_real pls))) A_47)). % 1.52/1.70 Axiom fact_236_add__numeral__0__right:(forall (A_47:int), (((eq int) ((plus_plus_int A_47) (number_number_of_int pls))) A_47)). % 1.52/1.70 Axiom fact_237_mult__number__of__left:(forall (V_8:int) (W_12:int) (Z_6:real), (((eq real) ((times_times_real (number267125858f_real V_8)) ((times_times_real (number267125858f_real W_12)) Z_6))) ((times_times_real (number267125858f_real ((times_times_int V_8) W_12))) Z_6))). % 1.52/1.70 Axiom fact_238_mult__number__of__left:(forall (V_8:int) (W_12:int) (Z_6:int), (((eq int) ((times_times_int (number_number_of_int V_8)) ((times_times_int (number_number_of_int W_12)) Z_6))) ((times_times_int (number_number_of_int ((times_times_int V_8) W_12))) Z_6))). % 1.52/1.70 Axiom fact_239_arith__simps_I32_J:(forall (V_7:int) (W_11:int), (((eq real) ((times_times_real (number267125858f_real V_7)) (number267125858f_real W_11))) (number267125858f_real ((times_times_int V_7) W_11)))). % 1.52/1.70 Axiom fact_240_arith__simps_I32_J:(forall (V_7:int) (W_11:int), (((eq int) ((times_times_int (number_number_of_int V_7)) (number_number_of_int W_11))) (number_number_of_int ((times_times_int V_7) W_11)))). % 1.52/1.70 Axiom fact_241_number__of__mult:(forall (V_6:int) (W_10:int), (((eq real) (number267125858f_real ((times_times_int V_6) W_10))) ((times_times_real (number267125858f_real V_6)) (number267125858f_real W_10)))). % 1.52/1.70 Axiom fact_242_number__of__mult:(forall (V_6:int) (W_10:int), (((eq int) (number_number_of_int ((times_times_int V_6) W_10))) ((times_times_int (number_number_of_int V_6)) (number_number_of_int W_10)))). % 1.52/1.71 Axiom fact_243_add__number__of__left:(forall (V_5:int) (W_9:int) (Z_5:real), (((eq real) ((plus_plus_real (number267125858f_real V_5)) ((plus_plus_real (number267125858f_real W_9)) Z_5))) ((plus_plus_real (number267125858f_real ((plus_plus_int V_5) W_9))) Z_5))). % 1.52/1.71 Axiom fact_244_add__number__of__left:(forall (V_5:int) (W_9:int) (Z_5:int), (((eq int) ((plus_plus_int (number_number_of_int V_5)) ((plus_plus_int (number_number_of_int W_9)) Z_5))) ((plus_plus_int (number_number_of_int ((plus_plus_int V_5) W_9))) Z_5))). % 1.52/1.71 Axiom fact_245_add__number__of__eq:(forall (V_4:int) (W_8:int), (((eq real) ((plus_plus_real (number267125858f_real V_4)) (number267125858f_real W_8))) (number267125858f_real ((plus_plus_int V_4) W_8)))). % 1.52/1.71 Axiom fact_246_add__number__of__eq:(forall (V_4:int) (W_8:int), (((eq int) ((plus_plus_int (number_number_of_int V_4)) (number_number_of_int W_8))) (number_number_of_int ((plus_plus_int V_4) W_8)))). % 1.52/1.71 Axiom fact_247_number__of__add:(forall (V_3:int) (W_7:int), (((eq real) (number267125858f_real ((plus_plus_int V_3) W_7))) ((plus_plus_real (number267125858f_real V_3)) (number267125858f_real W_7)))). % 1.52/1.71 Axiom fact_248_number__of__add:(forall (V_3:int) (W_7:int), (((eq int) (number_number_of_int ((plus_plus_int V_3) W_7))) ((plus_plus_int (number_number_of_int V_3)) (number_number_of_int W_7)))). % 1.52/1.71 Axiom fact_249_add__Bit1__Bit0:(forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit0 L))) (bit1 ((plus_plus_int K) L)))). % 1.52/1.71 Axiom fact_250_add__Bit0__Bit1:(forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit1 L))) (bit1 ((plus_plus_int K) L)))). % 1.52/1.71 Axiom fact_251_Bit1__def:(forall (K:int), (((eq int) (bit1 K)) ((plus_plus_int ((plus_plus_int one_one_int) K)) K))). % 1.52/1.71 Axiom fact_252_number__of__Bit1:(forall (W_6:int), (((eq real) (number267125858f_real (bit1 W_6))) ((plus_plus_real ((plus_plus_real one_one_real) (number267125858f_real W_6))) (number267125858f_real W_6)))). % 1.52/1.71 Axiom fact_253_number__of__Bit1:(forall (W_6:int), (((eq int) (number_number_of_int (bit1 W_6))) ((plus_plus_int ((plus_plus_int one_one_int) (number_number_of_int W_6))) (number_number_of_int W_6)))). % 1.52/1.71 Axiom fact_254_mult__numeral__1:(forall (A_46:real), (((eq real) ((times_times_real (number267125858f_real (bit1 pls))) A_46)) A_46)). % 1.52/1.71 Axiom fact_255_mult__numeral__1:(forall (A_46:int), (((eq int) ((times_times_int (number_number_of_int (bit1 pls))) A_46)) A_46)). % 1.52/1.71 Axiom fact_256_mult__numeral__1__right:(forall (A_45:real), (((eq real) ((times_times_real A_45) (number267125858f_real (bit1 pls)))) A_45)). % 1.52/1.71 Axiom fact_257_mult__numeral__1__right:(forall (A_45:int), (((eq int) ((times_times_int A_45) (number_number_of_int (bit1 pls)))) A_45)). % 1.52/1.71 Axiom fact_258_semiring__numeral__1__eq__1:(((eq real) (number267125858f_real (bit1 pls))) one_one_real). % 1.52/1.71 Axiom fact_259_semiring__numeral__1__eq__1:(((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat). % 1.52/1.71 Axiom fact_260_semiring__numeral__1__eq__1:(((eq int) (number_number_of_int (bit1 pls))) one_one_int). % 1.52/1.71 Axiom fact_261_numeral__1__eq__1:(((eq real) (number267125858f_real (bit1 pls))) one_one_real). % 1.52/1.71 Axiom fact_262_numeral__1__eq__1:(((eq int) (number_number_of_int (bit1 pls))) one_one_int). % 1.52/1.71 Axiom fact_263_semiring__norm_I110_J:(((eq real) one_one_real) (number267125858f_real (bit1 pls))). % 1.52/1.71 Axiom fact_264_semiring__norm_I110_J:(((eq int) one_one_int) (number_number_of_int (bit1 pls))). % 1.52/1.71 Axiom fact_265_one__is__num__one:(((eq int) one_one_int) (number_number_of_int (bit1 pls))). % 1.52/1.71 Axiom fact_266_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))). % 1.52/1.71 Axiom fact_267_double__number__of__Bit0:(forall (W_5:int), (((eq real) ((times_times_real ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real W_5))) (number267125858f_real (bit0 W_5)))). % 1.52/1.71 Axiom fact_268_double__number__of__Bit0:(forall (W_5:int), (((eq int) ((times_times_int ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int W_5))) (number_number_of_int (bit0 W_5)))). % 1.52/1.71 Axiom fact_269_power3__eq__cube:(forall (A_44:nat), (((eq nat) ((power_power_nat A_44) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_nat ((times_times_nat A_44) A_44)) A_44))). % 1.52/1.71 Axiom fact_270_power3__eq__cube:(forall (A_44:real), (((eq real) ((power_power_real A_44) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_real ((times_times_real A_44) A_44)) A_44))). % 1.52/1.71 Axiom fact_271_power3__eq__cube:(forall (A_44:int), (((eq int) ((power_power_int A_44) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int A_44) A_44)) A_44))). % 1.52/1.71 Axiom fact_272_quartic__square__square:(forall (X_1:int), (((eq int) ((power_power_int ((power_power_int X_1) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int X_1) (number_number_of_nat (bit0 (bit0 (bit1 pls))))))). % 1.52/1.71 Axiom fact_273_semiring__mult__2:(forall (Z_4:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_4)) ((plus_plus_real Z_4) Z_4))). % 1.52/1.71 Axiom fact_274_semiring__mult__2:(forall (Z_4:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z_4)) ((plus_plus_nat Z_4) Z_4))). % 1.52/1.71 Axiom fact_275_semiring__mult__2:(forall (Z_4:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_4)) ((plus_plus_int Z_4) Z_4))). % 1.52/1.71 Axiom fact_276_mult__2:(forall (Z_3:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) Z_3)) ((plus_plus_real Z_3) Z_3))). % 1.52/1.71 Axiom fact_277_mult__2:(forall (Z_3:int), (((eq int) ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) Z_3)) ((plus_plus_int Z_3) Z_3))). % 1.52/1.71 Axiom fact_278_semiring__mult__2__right:(forall (Z_2:real), (((eq real) ((times_times_real Z_2) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_2) Z_2))). % 1.52/1.71 Axiom fact_279_semiring__mult__2__right:(forall (Z_2:nat), (((eq nat) ((times_times_nat Z_2) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z_2) Z_2))). % 1.52/1.71 Axiom fact_280_semiring__mult__2__right:(forall (Z_2:int), (((eq int) ((times_times_int Z_2) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_2) Z_2))). % 1.52/1.71 Axiom fact_281_mult__2__right:(forall (Z_1:real), (((eq real) ((times_times_real Z_1) (number267125858f_real (bit0 (bit1 pls))))) ((plus_plus_real Z_1) Z_1))). % 1.52/1.71 Axiom fact_282_mult__2__right:(forall (Z_1:int), (((eq int) ((times_times_int Z_1) (number_number_of_int (bit0 (bit1 pls))))) ((plus_plus_int Z_1) Z_1))). % 1.52/1.71 Axiom fact_283_semiring__one__add__one__is__two:(((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))). % 1.52/1.71 Axiom fact_284_semiring__one__add__one__is__two:(((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))). % 1.52/1.71 Axiom fact_285_semiring__one__add__one__is__two:(((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))). % 1.52/1.71 Axiom fact_286_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)). % 1.52/1.71 Axiom fact_287__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)). % 1.52/1.71 Axiom fact_288_prime__g__5:(forall (P:int), ((zprime P)->((not (((eq int) P) (number_number_of_int (bit0 (bit1 pls)))))->((not (((eq int) P) (number_number_of_int (bit1 (bit1 pls)))))->((ord_less_eq_int (number_number_of_int (bit1 (bit0 (bit1 pls))))) P))))). % 1.52/1.71 Axiom fact_289__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096:(((eq int) (twoSqu1078207634sum2sq ((product_Pair_int_int s) one_one_int))) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)). % 1.52/1.71 Axiom fact_290_real__sum__squared__expand:(forall (X_1:real) (Y_1:real), (((eq real) ((power_power_real ((plus_plus_real X_1) Y_1)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_real ((plus_plus_real ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_1)) Y_1)))). % 1.52/1.71 Axiom fact_291_four__x__squared:(forall (X_1:real), (((eq real) ((times_times_real (number267125858f_real (bit0 (bit0 (bit1 pls))))) ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_real ((times_times_real (number267125858f_real (bit0 (bit1 pls)))) X_1)) (number_number_of_nat (bit0 (bit1 pls)))))). % 1.52/1.71 Axiom fact_292_power__less__power__Suc:(forall (N_37:nat) (A_43:real), (((ord_less_real one_one_real) A_43)->((ord_less_real ((power_power_real A_43) N_37)) ((times_times_real A_43) ((power_power_real A_43) N_37))))). % 1.52/1.71 Axiom fact_293_power__less__power__Suc:(forall (N_37:nat) (A_43:nat), (((ord_less_nat one_one_nat) A_43)->((ord_less_nat ((power_power_nat A_43) N_37)) ((times_times_nat A_43) ((power_power_nat A_43) N_37))))). % 1.52/1.71 Axiom fact_294_power__less__power__Suc:(forall (N_37:nat) (A_43:int), (((ord_less_int one_one_int) A_43)->((ord_less_int ((power_power_int A_43) N_37)) ((times_times_int A_43) ((power_power_int A_43) N_37))))). % 1.52/1.71 Axiom fact_295_power__gt1__lemma:(forall (N_36:nat) (A_42:real), (((ord_less_real one_one_real) A_42)->((ord_less_real one_one_real) ((times_times_real A_42) ((power_power_real A_42) N_36))))). % 1.52/1.71 Axiom fact_296_power__gt1__lemma:(forall (N_36:nat) (A_42:nat), (((ord_less_nat one_one_nat) A_42)->((ord_less_nat one_one_nat) ((times_times_nat A_42) ((power_power_nat A_42) N_36))))). % 1.52/1.71 Axiom fact_297_power__gt1__lemma:(forall (N_36:nat) (A_42:int), (((ord_less_int one_one_int) A_42)->((ord_less_int one_one_int) ((times_times_int A_42) ((power_power_int A_42) N_36))))). % 1.52/1.71 Axiom fact_298_power__le__imp__le__exp:(forall (M_9:nat) (N_35:nat) (A_41:real), (((ord_less_real one_one_real) A_41)->(((ord_less_eq_real ((power_power_real A_41) M_9)) ((power_power_real A_41) N_35))->((ord_less_eq_nat M_9) N_35)))). % 1.52/1.71 Axiom fact_299_power__le__imp__le__exp:(forall (M_9:nat) (N_35:nat) (A_41:nat), (((ord_less_nat one_one_nat) A_41)->(((ord_less_eq_nat ((power_power_nat A_41) M_9)) ((power_power_nat A_41) N_35))->((ord_less_eq_nat M_9) N_35)))). % 1.52/1.71 Axiom fact_300_power__le__imp__le__exp:(forall (M_9:nat) (N_35:nat) (A_41:int), (((ord_less_int one_one_int) A_41)->(((ord_less_eq_int ((power_power_int A_41) M_9)) ((power_power_int A_41) N_35))->((ord_less_eq_nat M_9) N_35)))). % 1.52/1.71 Axiom fact_301_power__increasing__iff:(forall (X_23:nat) (Y_21:nat) (B_11:real), (((ord_less_real one_one_real) B_11)->((iff ((ord_less_eq_real ((power_power_real B_11) X_23)) ((power_power_real B_11) Y_21))) ((ord_less_eq_nat X_23) Y_21)))). % 1.52/1.71 Axiom fact_302_power__increasing__iff:(forall (X_23:nat) (Y_21:nat) (B_11:nat), (((ord_less_nat one_one_nat) B_11)->((iff ((ord_less_eq_nat ((power_power_nat B_11) X_23)) ((power_power_nat B_11) Y_21))) ((ord_less_eq_nat X_23) Y_21)))). % 1.52/1.71 Axiom fact_303_power__increasing__iff:(forall (X_23:nat) (Y_21:nat) (B_11:int), (((ord_less_int one_one_int) B_11)->((iff ((ord_less_eq_int ((power_power_int B_11) X_23)) ((power_power_int B_11) Y_21))) ((ord_less_eq_nat X_23) Y_21)))). % 1.52/1.71 Axiom fact_304__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096:(((zcong ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int s1) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)). % 1.52/1.71 Axiom fact_305_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))). % 1.52/1.71 Axiom fact_306__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1:((ex int) (fun (X:int)=> ((and ((and ((and ((ord_less_eq_int zero_zero_int) X)) ((ord_less_int X) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) X) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (forall (Y:int), (((and ((and ((ord_less_eq_int zero_zero_int) Y)) ((ord_less_int Y) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))) (((zcong s1) Y) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))->(((eq int) Y) X)))))). % 1.52/1.71 Axiom fact_307__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). % 1.52/1.71 Axiom fact_308_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)). % 1.52/1.71 Axiom fact_309_power__eq__0__iff:(forall (A_40:real) (N_34:nat), ((iff (((eq real) ((power_power_real A_40) N_34)) zero_zero_real)) ((and (((eq real) A_40) zero_zero_real)) (not (((eq nat) N_34) zero_zero_nat))))). % 1.52/1.71 Axiom fact_310_power__eq__0__iff:(forall (A_40:nat) (N_34:nat), ((iff (((eq nat) ((power_power_nat A_40) N_34)) zero_zero_nat)) ((and (((eq nat) A_40) zero_zero_nat)) (not (((eq nat) N_34) zero_zero_nat))))). % 1.52/1.71 Axiom fact_311_power__eq__0__iff:(forall (A_40:int) (N_34:nat), ((iff (((eq int) ((power_power_int A_40) N_34)) zero_zero_int)) ((and (((eq int) A_40) zero_zero_int)) (not (((eq nat) N_34) zero_zero_nat))))). % 1.52/1.71 Axiom fact_312_le__imp__power__dvd:(forall (A_39:nat) (M_8:nat) (N_33:nat), (((ord_less_eq_nat M_8) N_33)->((dvd_dvd_nat ((power_power_nat A_39) M_8)) ((power_power_nat A_39) N_33)))). % 1.52/1.71 Axiom fact_313_le__imp__power__dvd:(forall (A_39:int) (M_8:nat) (N_33:nat), (((ord_less_eq_nat M_8) N_33)->((dvd_dvd_int ((power_power_int A_39) M_8)) ((power_power_int A_39) N_33)))). % 1.52/1.71 Axiom fact_314_le__imp__power__dvd:(forall (A_39:real) (M_8:nat) (N_33:nat), (((ord_less_eq_nat M_8) N_33)->((dvd_dvd_real ((power_power_real A_39) M_8)) ((power_power_real A_39) N_33)))). % 1.52/1.71 Axiom fact_315_dvd__power__le:(forall (N_32:nat) (M_7:nat) (X_22:nat) (Y_20:nat), (((dvd_dvd_nat X_22) Y_20)->(((ord_less_eq_nat N_32) M_7)->((dvd_dvd_nat ((power_power_nat X_22) N_32)) ((power_power_nat Y_20) M_7))))). % 1.52/1.71 Axiom fact_316_dvd__power__le:(forall (N_32:nat) (M_7:nat) (X_22:int) (Y_20:int), (((dvd_dvd_int X_22) Y_20)->(((ord_less_eq_nat N_32) M_7)->((dvd_dvd_int ((power_power_int X_22) N_32)) ((power_power_int Y_20) M_7))))). % 1.52/1.71 Axiom fact_317_dvd__power__le:(forall (N_32:nat) (M_7:nat) (X_22:real) (Y_20:real), (((dvd_dvd_real X_22) Y_20)->(((ord_less_eq_nat N_32) M_7)->((dvd_dvd_real ((power_power_real X_22) N_32)) ((power_power_real Y_20) M_7))))). % 1.52/1.71 Axiom fact_318_power__le__dvd:(forall (M_6:nat) (A_38:nat) (N_31:nat) (B_10:nat), (((dvd_dvd_nat ((power_power_nat A_38) N_31)) B_10)->(((ord_less_eq_nat M_6) N_31)->((dvd_dvd_nat ((power_power_nat A_38) M_6)) B_10)))). % 1.52/1.71 Axiom fact_319_power__le__dvd:(forall (M_6:nat) (A_38:int) (N_31:nat) (B_10:int), (((dvd_dvd_int ((power_power_int A_38) N_31)) B_10)->(((ord_less_eq_nat M_6) N_31)->((dvd_dvd_int ((power_power_int A_38) M_6)) B_10)))). % 1.52/1.71 Axiom fact_320_power__le__dvd:(forall (M_6:nat) (A_38:real) (N_31:nat) (B_10:real), (((dvd_dvd_real ((power_power_real A_38) N_31)) B_10)->(((ord_less_eq_nat M_6) N_31)->((dvd_dvd_real ((power_power_real A_38) M_6)) B_10)))). % 1.52/1.71 Axiom fact_321_power__eq__imp__eq__base:(forall (A_37:real) (N_30:nat) (B_9:real), ((((eq real) ((power_power_real A_37) N_30)) ((power_power_real B_9) N_30))->(((ord_less_eq_real zero_zero_real) A_37)->(((ord_less_eq_real zero_zero_real) B_9)->(((ord_less_nat zero_zero_nat) N_30)->(((eq real) A_37) B_9)))))). % 1.52/1.71 Axiom fact_322_power__eq__imp__eq__base:(forall (A_37:nat) (N_30:nat) (B_9:nat), ((((eq nat) ((power_power_nat A_37) N_30)) ((power_power_nat B_9) N_30))->(((ord_less_eq_nat zero_zero_nat) A_37)->(((ord_less_eq_nat zero_zero_nat) B_9)->(((ord_less_nat zero_zero_nat) N_30)->(((eq nat) A_37) B_9)))))). % 1.52/1.71 Axiom fact_323_power__eq__imp__eq__base:(forall (A_37:int) (N_30:nat) (B_9:int), ((((eq int) ((power_power_int A_37) N_30)) ((power_power_int B_9) N_30))->(((ord_less_eq_int zero_zero_int) A_37)->(((ord_less_eq_int zero_zero_int) B_9)->(((ord_less_nat zero_zero_nat) N_30)->(((eq int) A_37) B_9)))))). % 1.52/1.71 Axiom fact_324_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)))). % 1.52/1.71 Axiom fact_325_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)))))). % 1.52/1.71 Axiom fact_326_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)))). % 1.52/1.71 Axiom fact_327_dvd__power__same:(forall (N_29:nat) (X_21:nat) (Y_19:nat), (((dvd_dvd_nat X_21) Y_19)->((dvd_dvd_nat ((power_power_nat X_21) N_29)) ((power_power_nat Y_19) N_29)))). % 1.52/1.71 Axiom fact_328_dvd__power__same:(forall (N_29:nat) (X_21:int) (Y_19:int), (((dvd_dvd_int X_21) Y_19)->((dvd_dvd_int ((power_power_int X_21) N_29)) ((power_power_int Y_19) N_29)))). % 1.52/1.71 Axiom fact_329_dvd__power__same:(forall (N_29:nat) (X_21:real) (Y_19:real), (((dvd_dvd_real X_21) Y_19)->((dvd_dvd_real ((power_power_real X_21) N_29)) ((power_power_real Y_19) N_29)))). % 1.52/1.71 Axiom fact_330_field__power__not__zero:(forall (N_28:nat) (A_36:real), ((not (((eq real) A_36) zero_zero_real))->(not (((eq real) ((power_power_real A_36) N_28)) zero_zero_real)))). % 1.52/1.71 Axiom fact_331_field__power__not__zero:(forall (N_28:nat) (A_36:int), ((not (((eq int) A_36) zero_zero_int))->(not (((eq int) ((power_power_int A_36) N_28)) zero_zero_int)))). % 1.52/1.71 Axiom fact_332_power__0__left:(forall (N_27:nat), ((and ((((eq nat) N_27) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) N_27)) one_one_real))) ((not (((eq nat) N_27) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) N_27)) zero_zero_real)))). % 1.52/1.71 Axiom fact_333_power__0__left:(forall (N_27:nat), ((and ((((eq nat) N_27) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) N_27)) one_one_nat))) ((not (((eq nat) N_27) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) N_27)) zero_zero_nat)))). % 1.52/1.71 Axiom fact_334_power__0__left:(forall (N_27:nat), ((and ((((eq nat) N_27) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) N_27)) one_one_int))) ((not (((eq nat) N_27) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) N_27)) zero_zero_int)))). % 1.52/1.71 Axiom fact_335_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)))). % 1.52/1.71 Axiom fact_336_power__strict__mono:(forall (N_26:nat) (A_35:real) (B_8:real), (((ord_less_real A_35) B_8)->(((ord_less_eq_real zero_zero_real) A_35)->(((ord_less_nat zero_zero_nat) N_26)->((ord_less_real ((power_power_real A_35) N_26)) ((power_power_real B_8) N_26)))))). % 1.52/1.71 Axiom fact_337_power__strict__mono:(forall (N_26:nat) (A_35:nat) (B_8:nat), (((ord_less_nat A_35) B_8)->(((ord_less_eq_nat zero_zero_nat) A_35)->(((ord_less_nat zero_zero_nat) N_26)->((ord_less_nat ((power_power_nat A_35) N_26)) ((power_power_nat B_8) N_26)))))). % 1.52/1.71 Axiom fact_338_power__strict__mono:(forall (N_26:nat) (A_35:int) (B_8:int), (((ord_less_int A_35) B_8)->(((ord_less_eq_int zero_zero_int) A_35)->(((ord_less_nat zero_zero_nat) N_26)->((ord_less_int ((power_power_int A_35) N_26)) ((power_power_int B_8) N_26)))))). % 1.52/1.71 Axiom fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J:(forall (A_34:real), (((eq real) ((times_times_real zero_zero_real) A_34)) zero_zero_real)). % 1.52/1.71 Axiom fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J:(forall (A_34:nat), (((eq nat) ((times_times_nat zero_zero_nat) A_34)) zero_zero_nat)). % 1.52/1.71 Axiom fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J:(forall (A_34:int), (((eq int) ((times_times_int zero_zero_int) A_34)) zero_zero_int)). % 1.52/1.71 Axiom fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J:(forall (A_33:real), (((eq real) ((times_times_real A_33) zero_zero_real)) zero_zero_real)). % 1.52/1.71 Axiom fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J:(forall (A_33:nat), (((eq nat) ((times_times_nat A_33) zero_zero_nat)) zero_zero_nat)). % 1.52/1.71 Axiom fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J:(forall (A_33:int), (((eq int) ((times_times_int A_33) zero_zero_int)) zero_zero_int)). % 1.52/1.71 Axiom fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J:(forall (A_32:real), (((eq real) ((plus_plus_real zero_zero_real) A_32)) A_32)). % 1.52/1.71 Axiom fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J:(forall (A_32:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_32)) A_32)). % 1.52/1.71 Axiom fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J:(forall (A_32:int), (((eq int) ((plus_plus_int zero_zero_int) A_32)) A_32)). % 1.52/1.71 Axiom fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J:(forall (A_31:real), (((eq real) ((plus_plus_real A_31) zero_zero_real)) A_31)). % 1.52/1.71 Axiom fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J:(forall (A_31:nat), (((eq nat) ((plus_plus_nat A_31) zero_zero_nat)) A_31)). % 1.52/1.71 Axiom fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J:(forall (A_31:int), (((eq int) ((plus_plus_int A_31) zero_zero_int)) A_31)). % 1.52/1.71 Axiom fact_351_add__0__iff:(forall (B_7:real) (A_30:real), ((iff (((eq real) B_7) ((plus_plus_real B_7) A_30))) (((eq real) A_30) zero_zero_real))). % 1.52/1.71 Axiom fact_352_add__0__iff:(forall (B_7:nat) (A_30:nat), ((iff (((eq nat) B_7) ((plus_plus_nat B_7) A_30))) (((eq nat) A_30) zero_zero_nat))). % 1.52/1.71 Axiom fact_353_add__0__iff:(forall (B_7:int) (A_30:int), ((iff (((eq int) B_7) ((plus_plus_int B_7) A_30))) (((eq int) A_30) zero_zero_int))). % 1.52/1.71 Axiom fact_354_double__eq__0__iff:(forall (A_29:real), ((iff (((eq real) ((plus_plus_real A_29) A_29)) zero_zero_real)) (((eq real) A_29) zero_zero_real))). % 1.52/1.71 Axiom fact_355_double__eq__0__iff:(forall (A_29:int), ((iff (((eq int) ((plus_plus_int A_29) A_29)) zero_zero_int)) (((eq int) A_29) zero_zero_int))). % 1.52/1.71 Axiom fact_356_Pls__def:(((eq int) pls) zero_zero_int). % 1.52/1.71 Axiom fact_357_int__0__neq__1:(not (((eq int) zero_zero_int) one_one_int)). % 1.52/1.71 Axiom fact_358_zadd__0:(forall (Z:int), (((eq int) ((plus_plus_int zero_zero_int) Z)) Z)). % 1.52/1.71 Axiom fact_359_zadd__0__right:(forall (Z:int), (((eq int) ((plus_plus_int Z) zero_zero_int)) Z)). % 1.52/1.71 Axiom fact_360_zero__le__power:(forall (N_25:nat) (A_28:real), (((ord_less_eq_real zero_zero_real) A_28)->((ord_less_eq_real zero_zero_real) ((power_power_real A_28) N_25)))). % 1.52/1.71 Axiom fact_361_zero__le__power:(forall (N_25:nat) (A_28:nat), (((ord_less_eq_nat zero_zero_nat) A_28)->((ord_less_eq_nat zero_zero_nat) ((power_power_nat A_28) N_25)))). % 1.52/1.71 Axiom fact_362_zero__le__power:(forall (N_25:nat) (A_28:int), (((ord_less_eq_int zero_zero_int) A_28)->((ord_less_eq_int zero_zero_int) ((power_power_int A_28) N_25)))). % 1.52/1.71 Axiom fact_363_power__mono:(forall (N_24:nat) (A_27:real) (B_6:real), (((ord_less_eq_real A_27) B_6)->(((ord_less_eq_real zero_zero_real) A_27)->((ord_less_eq_real ((power_power_real A_27) N_24)) ((power_power_real B_6) N_24))))). % 1.52/1.71 Axiom fact_364_power__mono:(forall (N_24:nat) (A_27:nat) (B_6:nat), (((ord_less_eq_nat A_27) B_6)->(((ord_less_eq_nat zero_zero_nat) A_27)->((ord_less_eq_nat ((power_power_nat A_27) N_24)) ((power_power_nat B_6) N_24))))). % 1.52/1.71 Axiom fact_365_power__mono:(forall (N_24:nat) (A_27:int) (B_6:int), (((ord_less_eq_int A_27) B_6)->(((ord_less_eq_int zero_zero_int) A_27)->((ord_less_eq_int ((power_power_int A_27) N_24)) ((power_power_int B_6) N_24))))). % 1.52/1.71 Axiom fact_366_zero__less__power:(forall (N_23:nat) (A_26:real), (((ord_less_real zero_zero_real) A_26)->((ord_less_real zero_zero_real) ((power_power_real A_26) N_23)))). % 1.52/1.71 Axiom fact_367_zero__less__power:(forall (N_23:nat) (A_26:nat), (((ord_less_nat zero_zero_nat) A_26)->((ord_less_nat zero_zero_nat) ((power_power_nat A_26) N_23)))). % 1.52/1.71 Axiom fact_368_zero__less__power:(forall (N_23:nat) (A_26:int), (((ord_less_int zero_zero_int) A_26)->((ord_less_int zero_zero_int) ((power_power_int A_26) N_23)))). % 1.52/1.72 Axiom fact_369_zcong__zpower__zmult:(forall (Z:nat) (X_1:int) (Y_1:nat) (P:int), ((((zcong ((power_power_int X_1) Y_1)) one_one_int) P)->(((zcong ((power_power_int X_1) ((times_times_nat Y_1) Z))) one_one_int) P))). % 1.52/1.72 Axiom fact_370_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))). % 1.52/1.72 Axiom fact_371_zdvd__period:(forall (C:int) (X_1:int) (T:int) (A:int) (D:int), (((dvd_dvd_int A) D)->((iff ((dvd_dvd_int A) ((plus_plus_int X_1) T))) ((dvd_dvd_int A) ((plus_plus_int ((plus_plus_int X_1) ((times_times_int C) D))) T))))). % 1.52/1.72 Axiom fact_372_power__less__imp__less__base:(forall (A_25:real) (N_22:nat) (B_5:real), (((ord_less_real ((power_power_real A_25) N_22)) ((power_power_real B_5) N_22))->(((ord_less_eq_real zero_zero_real) B_5)->((ord_less_real A_25) B_5)))). % 1.52/1.72 Axiom fact_373_power__less__imp__less__base:(forall (A_25:nat) (N_22:nat) (B_5:nat), (((ord_less_nat ((power_power_nat A_25) N_22)) ((power_power_nat B_5) N_22))->(((ord_less_eq_nat zero_zero_nat) B_5)->((ord_less_nat A_25) B_5)))). % 1.52/1.72 Axiom fact_374_power__less__imp__less__base:(forall (A_25:int) (N_22:nat) (B_5:int), (((ord_less_int ((power_power_int A_25) N_22)) ((power_power_int B_5) N_22))->(((ord_less_eq_int zero_zero_int) B_5)->((ord_less_int A_25) B_5)))). % 1.52/1.72 Axiom fact_375_power__decreasing:(forall (A_24:real) (N_21:nat) (N_20:nat), (((ord_less_eq_nat N_21) N_20)->(((ord_less_eq_real zero_zero_real) A_24)->(((ord_less_eq_real A_24) one_one_real)->((ord_less_eq_real ((power_power_real A_24) N_20)) ((power_power_real A_24) N_21)))))). % 1.52/1.72 Axiom fact_376_power__decreasing:(forall (A_24:nat) (N_21:nat) (N_20:nat), (((ord_less_eq_nat N_21) N_20)->(((ord_less_eq_nat zero_zero_nat) A_24)->(((ord_less_eq_nat A_24) one_one_nat)->((ord_less_eq_nat ((power_power_nat A_24) N_20)) ((power_power_nat A_24) N_21)))))). % 1.52/1.72 Axiom fact_377_power__decreasing:(forall (A_24:int) (N_21:nat) (N_20:nat), (((ord_less_eq_nat N_21) N_20)->(((ord_less_eq_int zero_zero_int) A_24)->(((ord_less_eq_int A_24) one_one_int)->((ord_less_eq_int ((power_power_int A_24) N_20)) ((power_power_int A_24) N_21)))))). % 1.52/1.72 Axiom fact_378_power__strict__decreasing:(forall (A_23:real) (N_19:nat) (N_18:nat), (((ord_less_nat N_19) N_18)->(((ord_less_real zero_zero_real) A_23)->(((ord_less_real A_23) one_one_real)->((ord_less_real ((power_power_real A_23) N_18)) ((power_power_real A_23) N_19)))))). % 1.52/1.72 Axiom fact_379_power__strict__decreasing:(forall (A_23:nat) (N_19:nat) (N_18:nat), (((ord_less_nat N_19) N_18)->(((ord_less_nat zero_zero_nat) A_23)->(((ord_less_nat A_23) one_one_nat)->((ord_less_nat ((power_power_nat A_23) N_18)) ((power_power_nat A_23) N_19)))))). % 1.52/1.72 Axiom fact_380_power__strict__decreasing:(forall (A_23:int) (N_19:nat) (N_18:nat), (((ord_less_nat N_19) N_18)->(((ord_less_int zero_zero_int) A_23)->(((ord_less_int A_23) one_one_int)->((ord_less_int ((power_power_int A_23) N_18)) ((power_power_int A_23) N_19)))))). % 1.52/1.72 Axiom fact_381_even__less__0__iff:(forall (A_22:real), ((iff ((ord_less_real ((plus_plus_real A_22) A_22)) zero_zero_real)) ((ord_less_real A_22) zero_zero_real))). % 1.52/1.72 Axiom fact_382_even__less__0__iff:(forall (A_22:int), ((iff ((ord_less_int ((plus_plus_int A_22) A_22)) zero_zero_int)) ((ord_less_int A_22) zero_zero_int))). % 1.52/1.72 Axiom fact_383_sum__squares__eq__zero__iff:(forall (X_20:real) (Y_18:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X_20) X_20)) ((times_times_real Y_18) Y_18))) zero_zero_real)) ((and (((eq real) X_20) zero_zero_real)) (((eq real) Y_18) zero_zero_real)))). % 1.52/1.72 Axiom fact_384_sum__squares__eq__zero__iff:(forall (X_20:int) (Y_18:int), ((iff (((eq int) ((plus_plus_int ((times_times_int X_20) X_20)) ((times_times_int Y_18) Y_18))) zero_zero_int)) ((and (((eq int) X_20) zero_zero_int)) (((eq int) Y_18) zero_zero_int)))). % 1.52/1.72 Axiom fact_385_add__scale__eq__noteq:(forall (C_1:real) (D_1:real) (A_21:real) (B_4:real) (R_3:real), ((not (((eq real) R_3) zero_zero_real))->(((and (((eq real) A_21) B_4)) (not (((eq real) C_1) D_1)))->(not (((eq real) ((plus_plus_real A_21) ((times_times_real R_3) C_1))) ((plus_plus_real B_4) ((times_times_real R_3) D_1))))))). % 1.52/1.72 Axiom fact_386_add__scale__eq__noteq:(forall (C_1:nat) (D_1:nat) (A_21:nat) (B_4:nat) (R_3:nat), ((not (((eq nat) R_3) zero_zero_nat))->(((and (((eq nat) A_21) B_4)) (not (((eq nat) C_1) D_1)))->(not (((eq nat) ((plus_plus_nat A_21) ((times_times_nat R_3) C_1))) ((plus_plus_nat B_4) ((times_times_nat R_3) D_1))))))). % 1.52/1.72 Axiom fact_387_add__scale__eq__noteq:(forall (C_1:int) (D_1:int) (A_21:int) (B_4:int) (R_3:int), ((not (((eq int) R_3) zero_zero_int))->(((and (((eq int) A_21) B_4)) (not (((eq int) C_1) D_1)))->(not (((eq int) ((plus_plus_int A_21) ((times_times_int R_3) C_1))) ((plus_plus_int B_4) ((times_times_int R_3) D_1))))))). % 1.52/1.72 Axiom fact_388_zprime__zdvd__power:(forall (A:int) (N:nat) (P:int), ((zprime P)->(((dvd_dvd_int P) ((power_power_int A) N))->((dvd_dvd_int P) A)))). % 1.52/1.72 Axiom fact_389_semiring__norm_I112_J:(((eq real) zero_zero_real) (number267125858f_real pls)). % 1.52/1.72 Axiom fact_390_semiring__norm_I112_J:(((eq int) zero_zero_int) (number_number_of_int pls)). % 1.52/1.72 Axiom fact_391_number__of__Pls:(((eq real) (number267125858f_real pls)) zero_zero_real). % 1.52/1.72 Axiom fact_392_number__of__Pls:(((eq int) (number_number_of_int pls)) zero_zero_int). % 1.52/1.72 Axiom fact_393_semiring__numeral__0__eq__0:(((eq real) (number267125858f_real pls)) zero_zero_real). % 1.52/1.72 Axiom fact_394_semiring__numeral__0__eq__0:(((eq nat) (number_number_of_nat pls)) zero_zero_nat). % 1.52/1.72 Axiom fact_395_semiring__numeral__0__eq__0:(((eq int) (number_number_of_int pls)) zero_zero_int). % 1.52/1.72 Axiom fact_396_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))). % 1.52/1.72 Axiom fact_397_bin__less__0__simps_I1_J:(((ord_less_int pls) zero_zero_int)->False). % 1.52/1.72 Axiom fact_398_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))). % 1.52/1.72 Axiom fact_399_zero__is__num__zero:(((eq int) zero_zero_int) (number_number_of_int pls)). % 1.52/1.72 Axiom fact_400_int__0__less__1:((ord_less_int zero_zero_int) one_one_int). % 1.52/1.72 Axiom fact_401_pos__zmult__pos:(forall (B_1:int) (A:int), (((ord_less_int zero_zero_int) A)->(((ord_less_int zero_zero_int) ((times_times_int A) B_1))->((ord_less_int zero_zero_int) B_1)))). % 1.52/1.72 Axiom fact_402_zmult__zless__mono2:(forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_int _TPTP_I) J)->(((ord_less_int zero_zero_int) K)->((ord_less_int ((times_times_int K) _TPTP_I)) ((times_times_int K) J))))). % 1.52/1.72 Axiom fact_403_odd__nonzero:(forall (Z:int), (not (((eq int) ((plus_plus_int ((plus_plus_int one_one_int) Z)) Z)) zero_zero_int))). % 1.52/1.72 Axiom fact_404_power__Suc__less:(forall (N_17:nat) (A_20:real), (((ord_less_real zero_zero_real) A_20)->(((ord_less_real A_20) one_one_real)->((ord_less_real ((times_times_real A_20) ((power_power_real A_20) N_17))) ((power_power_real A_20) N_17))))). % 1.52/1.72 Axiom fact_405_power__Suc__less:(forall (N_17:nat) (A_20:nat), (((ord_less_nat zero_zero_nat) A_20)->(((ord_less_nat A_20) one_one_nat)->((ord_less_nat ((times_times_nat A_20) ((power_power_nat A_20) N_17))) ((power_power_nat A_20) N_17))))). % 1.52/1.72 Axiom fact_406_power__Suc__less:(forall (N_17:nat) (A_20:int), (((ord_less_int zero_zero_int) A_20)->(((ord_less_int A_20) one_one_int)->((ord_less_int ((times_times_int A_20) ((power_power_int A_20) N_17))) ((power_power_int A_20) N_17))))). % 1.52/1.72 Axiom fact_407_zprime__power__zdvd__cancel__left:(forall (N:nat) (B_1:int) (A:int) (P:int), ((zprime P)->((((dvd_dvd_int P) A)->False)->(((dvd_dvd_int ((power_power_int P) N)) ((times_times_int A) B_1))->((dvd_dvd_int ((power_power_int P) N)) B_1))))). % 1.52/1.72 Axiom fact_408_zprime__power__zdvd__cancel__right:(forall (N:nat) (A:int) (B_1:int) (P:int), ((zprime P)->((((dvd_dvd_int P) B_1)->False)->(((dvd_dvd_int ((power_power_int P) N)) ((times_times_int A) B_1))->((dvd_dvd_int ((power_power_int P) N)) A))))). % 1.52/1.72 Axiom fact_409_sum__squares__ge__zero:(forall (X_19:real) (Y_17:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((times_times_real X_19) X_19)) ((times_times_real Y_17) Y_17)))). % 1.52/1.72 Axiom fact_410_sum__squares__ge__zero:(forall (X_19:int) (Y_17:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int X_19) X_19)) ((times_times_int Y_17) Y_17)))). % 1.55/1.72 Axiom fact_411_sum__squares__le__zero__iff:(forall (X_18:real) (Y_16:real), ((iff ((ord_less_eq_real ((plus_plus_real ((times_times_real X_18) X_18)) ((times_times_real Y_16) Y_16))) zero_zero_real)) ((and (((eq real) X_18) zero_zero_real)) (((eq real) Y_16) zero_zero_real)))). % 1.55/1.72 Axiom fact_412_sum__squares__le__zero__iff:(forall (X_18:int) (Y_16:int), ((iff ((ord_less_eq_int ((plus_plus_int ((times_times_int X_18) X_18)) ((times_times_int Y_16) Y_16))) zero_zero_int)) ((and (((eq int) X_18) zero_zero_int)) (((eq int) Y_16) zero_zero_int)))). % 1.55/1.72 Axiom fact_413_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)))). % 1.55/1.72 Axiom fact_414_not__sum__squares__lt__zero:(forall (X_17:real) (Y_15:real), (((ord_less_real ((plus_plus_real ((times_times_real X_17) X_17)) ((times_times_real Y_15) Y_15))) zero_zero_real)->False)). % 1.55/1.72 Axiom fact_415_not__sum__squares__lt__zero:(forall (X_17:int) (Y_15:int), (((ord_less_int ((plus_plus_int ((times_times_int X_17) X_17)) ((times_times_int Y_15) Y_15))) zero_zero_int)->False)). % 1.55/1.72 Axiom fact_416_sum__squares__gt__zero__iff:(forall (X_16:real) (Y_14:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((times_times_real X_16) X_16)) ((times_times_real Y_14) Y_14)))) ((or (not (((eq real) X_16) zero_zero_real))) (not (((eq real) Y_14) zero_zero_real))))). % 1.55/1.72 Axiom fact_417_sum__squares__gt__zero__iff:(forall (X_16:int) (Y_14:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((times_times_int X_16) X_16)) ((times_times_int Y_14) Y_14)))) ((or (not (((eq int) X_16) zero_zero_int))) (not (((eq int) Y_14) zero_zero_int))))). % 1.55/1.72 Axiom fact_418_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)))). % 1.55/1.72 Axiom fact_419_number__of__Bit0:(forall (W_4:int), (((eq real) (number267125858f_real (bit0 W_4))) ((plus_plus_real ((plus_plus_real zero_zero_real) (number267125858f_real W_4))) (number267125858f_real W_4)))). % 1.55/1.72 Axiom fact_420_number__of__Bit0:(forall (W_4:int), (((eq int) (number_number_of_int (bit0 W_4))) ((plus_plus_int ((plus_plus_int zero_zero_int) (number_number_of_int W_4))) (number_number_of_int W_4)))). % 1.55/1.72 Axiom fact_421_power__one__right:(forall (A_19:nat), (((eq nat) ((power_power_nat A_19) one_one_nat)) A_19)). % 1.55/1.72 Axiom fact_422_power__one__right:(forall (A_19:real), (((eq real) ((power_power_real A_19) one_one_nat)) A_19)). % 1.55/1.72 Axiom fact_423_power__one__right:(forall (A_19:int), (((eq int) ((power_power_int A_19) one_one_nat)) A_19)). % 1.55/1.72 Axiom fact_424_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))). % 1.55/1.72 Axiom fact_425_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))))). % 1.55/1.72 Axiom fact_426_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))). % 1.55/1.72 Axiom fact_427_less__special_I1_J:(forall (Y_13:int), ((iff ((ord_less_real zero_zero_real) (number267125858f_real Y_13))) ((ord_less_int pls) Y_13))). % 1.55/1.72 Axiom fact_428_less__special_I1_J:(forall (Y_13:int), ((iff ((ord_less_int zero_zero_int) (number_number_of_int Y_13))) ((ord_less_int pls) Y_13))). % 1.55/1.72 Axiom fact_429_less__special_I3_J:(forall (X_15:int), ((iff ((ord_less_real (number267125858f_real X_15)) zero_zero_real)) ((ord_less_int X_15) pls))). % 1.55/1.72 Axiom fact_430_less__special_I3_J:(forall (X_15:int), ((iff ((ord_less_int (number_number_of_int X_15)) zero_zero_int)) ((ord_less_int X_15) pls))). % 1.55/1.72 Axiom fact_431_le__special_I1_J:(forall (Y_12:int), ((iff ((ord_less_eq_real zero_zero_real) (number267125858f_real Y_12))) ((ord_less_eq_int pls) Y_12))). % 1.55/1.72 Axiom fact_432_le__special_I1_J:(forall (Y_12:int), ((iff ((ord_less_eq_int zero_zero_int) (number_number_of_int Y_12))) ((ord_less_eq_int pls) Y_12))). % 1.55/1.72 Axiom fact_433_le__special_I3_J:(forall (X_14:int), ((iff ((ord_less_eq_real (number267125858f_real X_14)) zero_zero_real)) ((ord_less_eq_int X_14) pls))). % 1.55/1.72 Axiom fact_434_le__special_I3_J:(forall (X_14:int), ((iff ((ord_less_eq_int (number_number_of_int X_14)) zero_zero_int)) ((ord_less_eq_int X_14) pls))). % 1.55/1.72 Axiom fact_435_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)))). % 1.55/1.72 Axiom fact_436_zero__power2:(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real). % 1.55/1.72 Axiom fact_437_zero__power2:(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_nat). % 1.55/1.72 Axiom fact_438_zero__power2:(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int). % 1.55/1.72 Axiom fact_439_zero__eq__power2:(forall (A_18:real), ((iff (((eq real) ((power_power_real A_18) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)) (((eq real) A_18) zero_zero_real))). % 1.55/1.72 Axiom fact_440_zero__eq__power2:(forall (A_18:int), ((iff (((eq int) ((power_power_int A_18) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)) (((eq int) A_18) zero_zero_int))). % 1.55/1.72 Axiom fact_441_zero__le__power2:(forall (A_17:real), ((ord_less_eq_real zero_zero_real) ((power_power_real A_17) (number_number_of_nat (bit0 (bit1 pls)))))). % 1.55/1.72 Axiom fact_442_zero__le__power2:(forall (A_17:int), ((ord_less_eq_int zero_zero_int) ((power_power_int A_17) (number_number_of_nat (bit0 (bit1 pls)))))). % 1.55/1.72 Axiom fact_443_power2__le__imp__le:(forall (X_13:real) (Y_11:real), (((ord_less_eq_real ((power_power_real X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_11) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_11)->((ord_less_eq_real X_13) Y_11)))). % 1.55/1.72 Axiom fact_444_power2__le__imp__le:(forall (X_13:nat) (Y_11:nat), (((ord_less_eq_nat ((power_power_nat X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_11) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_11)->((ord_less_eq_nat X_13) Y_11)))). % 1.55/1.72 Axiom fact_445_power2__le__imp__le:(forall (X_13:int) (Y_11:int), (((ord_less_eq_int ((power_power_int X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_11) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_11)->((ord_less_eq_int X_13) Y_11)))). % 1.55/1.72 Axiom fact_446_power2__eq__imp__eq:(forall (X_12:real) (Y_10:real), ((((eq real) ((power_power_real X_12) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_10) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) X_12)->(((ord_less_eq_real zero_zero_real) Y_10)->(((eq real) X_12) Y_10))))). % 1.55/1.72 Axiom fact_447_power2__eq__imp__eq:(forall (X_12:nat) (Y_10:nat), ((((eq nat) ((power_power_nat X_12) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_10) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) X_12)->(((ord_less_eq_nat zero_zero_nat) Y_10)->(((eq nat) X_12) Y_10))))). % 1.55/1.72 Axiom fact_448_power2__eq__imp__eq:(forall (X_12:int) (Y_10:int), ((((eq int) ((power_power_int X_12) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_10) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) X_12)->(((ord_less_eq_int zero_zero_int) Y_10)->(((eq int) X_12) Y_10))))). % 1.55/1.72 Axiom fact_449_power2__less__0:(forall (A_16:real), (((ord_less_real ((power_power_real A_16) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)->False)). % 1.55/1.72 Axiom fact_450_power2__less__0:(forall (A_16:int), (((ord_less_int ((power_power_int A_16) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)->False)). % 1.55/1.72 Axiom fact_451_zero__less__power2:(forall (A_15:real), ((iff ((ord_less_real zero_zero_real) ((power_power_real A_15) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq real) A_15) zero_zero_real)))). % 1.55/1.72 Axiom fact_452_zero__less__power2:(forall (A_15:int), ((iff ((ord_less_int zero_zero_int) ((power_power_int A_15) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq int) A_15) zero_zero_int)))). % 1.55/1.72 Axiom fact_453_sum__power2__eq__zero__iff:(forall (X_11:real) (Y_9:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_9) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_11) zero_zero_real)) (((eq real) Y_9) zero_zero_real)))). % 1.55/1.72 Axiom fact_454_sum__power2__eq__zero__iff:(forall (X_11:int) (Y_9:int), ((iff (((eq int) ((plus_plus_int ((power_power_int X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_9) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_11) zero_zero_int)) (((eq int) Y_9) zero_zero_int)))). % 1.55/1.72 Axiom fact_455_power__commutes:(forall (A_14:nat) (N_16:nat), (((eq nat) ((times_times_nat ((power_power_nat A_14) N_16)) A_14)) ((times_times_nat A_14) ((power_power_nat A_14) N_16)))). % 1.55/1.72 Axiom fact_456_power__commutes:(forall (A_14:real) (N_16:nat), (((eq real) ((times_times_real ((power_power_real A_14) N_16)) A_14)) ((times_times_real A_14) ((power_power_real A_14) N_16)))). % 1.55/1.72 Axiom fact_457_power__commutes:(forall (A_14:int) (N_16:nat), (((eq int) ((times_times_int ((power_power_int A_14) N_16)) A_14)) ((times_times_int A_14) ((power_power_int A_14) N_16)))). % 1.55/1.72 Axiom fact_458_power__mult__distrib:(forall (A_13:nat) (B_3:nat) (N_15:nat), (((eq nat) ((power_power_nat ((times_times_nat A_13) B_3)) N_15)) ((times_times_nat ((power_power_nat A_13) N_15)) ((power_power_nat B_3) N_15)))). % 1.55/1.72 Axiom fact_459_power__mult__distrib:(forall (A_13:real) (B_3:real) (N_15:nat), (((eq real) ((power_power_real ((times_times_real A_13) B_3)) N_15)) ((times_times_real ((power_power_real A_13) N_15)) ((power_power_real B_3) N_15)))). % 1.55/1.72 Axiom fact_460_power__mult__distrib:(forall (A_13:int) (B_3:int) (N_15:nat), (((eq int) ((power_power_int ((times_times_int A_13) B_3)) N_15)) ((times_times_int ((power_power_int A_13) N_15)) ((power_power_int B_3) N_15)))). % 1.55/1.72 Axiom fact_461_power__add:(forall (A_12:nat) (M_5:nat) (N_14:nat), (((eq nat) ((power_power_nat A_12) ((plus_plus_nat M_5) N_14))) ((times_times_nat ((power_power_nat A_12) M_5)) ((power_power_nat A_12) N_14)))). % 1.55/1.72 Axiom fact_462_power__add:(forall (A_12:real) (M_5:nat) (N_14:nat), (((eq real) ((power_power_real A_12) ((plus_plus_nat M_5) N_14))) ((times_times_real ((power_power_real A_12) M_5)) ((power_power_real A_12) N_14)))). % 1.55/1.72 Axiom fact_463_power__add:(forall (A_12:int) (M_5:nat) (N_14:nat), (((eq int) ((power_power_int A_12) ((plus_plus_nat M_5) N_14))) ((times_times_int ((power_power_int A_12) M_5)) ((power_power_int A_12) N_14)))). % 1.55/1.72 Axiom fact_464_power__one:(forall (N_13:nat), (((eq real) ((power_power_real one_one_real) N_13)) one_one_real)). % 1.55/1.72 Axiom fact_465_power__one:(forall (N_13:nat), (((eq nat) ((power_power_nat one_one_nat) N_13)) one_one_nat)). % 1.55/1.72 Axiom fact_466_power__one:(forall (N_13:nat), (((eq int) ((power_power_int one_one_int) N_13)) one_one_int)). % 1.55/1.72 Axiom fact_467_power__mult:(forall (A_11:nat) (M_4:nat) (N_12:nat), (((eq nat) ((power_power_nat A_11) ((times_times_nat M_4) N_12))) ((power_power_nat ((power_power_nat A_11) M_4)) N_12))). % 1.55/1.72 Axiom fact_468_power__mult:(forall (A_11:real) (M_4:nat) (N_12:nat), (((eq real) ((power_power_real A_11) ((times_times_nat M_4) N_12))) ((power_power_real ((power_power_real A_11) M_4)) N_12))). % 1.55/1.72 Axiom fact_469_power__mult:(forall (A_11:int) (M_4:nat) (N_12:nat), (((eq int) ((power_power_int A_11) ((times_times_nat M_4) N_12))) ((power_power_int ((power_power_int A_11) M_4)) N_12))). % 1.55/1.72 Axiom fact_470_power2__less__imp__less:(forall (X_10:real) (Y_8:real), (((ord_less_real ((power_power_real X_10) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_8) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_8)->((ord_less_real X_10) Y_8)))). % 1.55/1.72 Axiom fact_471_power2__less__imp__less:(forall (X_10:nat) (Y_8:nat), (((ord_less_nat ((power_power_nat X_10) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_8) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_8)->((ord_less_nat X_10) Y_8)))). % 1.55/1.73 Axiom fact_472_power2__less__imp__less:(forall (X_10:int) (Y_8:int), (((ord_less_int ((power_power_int X_10) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_8) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_8)->((ord_less_int X_10) Y_8)))). % 1.55/1.73 Axiom fact_473_sum__power2__ge__zero:(forall (X_9:real) (Y_7:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((power_power_real X_9) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_7) (number_number_of_nat (bit0 (bit1 pls))))))). % 1.55/1.73 Axiom fact_474_sum__power2__ge__zero:(forall (X_9:int) (Y_7:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((power_power_int X_9) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_7) (number_number_of_nat (bit0 (bit1 pls))))))). % 1.55/1.73 Axiom fact_475_sum__power2__le__zero__iff:(forall (X_8:real) (Y_6:real), ((iff ((ord_less_eq_real ((plus_plus_real ((power_power_real X_8) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_6) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_8) zero_zero_real)) (((eq real) Y_6) zero_zero_real)))). % 1.55/1.73 Axiom fact_476_sum__power2__le__zero__iff:(forall (X_8:int) (Y_6:int), ((iff ((ord_less_eq_int ((plus_plus_int ((power_power_int X_8) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_6) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_8) zero_zero_int)) (((eq int) Y_6) zero_zero_int)))). % 1.55/1.73 Axiom fact_477_not__sum__power2__lt__zero:(forall (X_7:real) (Y_5:real), (((ord_less_real ((plus_plus_real ((power_power_real X_7) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)->False)). % 1.55/1.73 Axiom fact_478_not__sum__power2__lt__zero:(forall (X_7:int) (Y_5:int), (((ord_less_int ((plus_plus_int ((power_power_int X_7) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)->False)). % 1.55/1.73 Axiom fact_479_sum__power2__gt__zero__iff:(forall (X_6:real) (Y_4:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((power_power_real X_6) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_4) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq real) X_6) zero_zero_real))) (not (((eq real) Y_4) zero_zero_real))))). % 1.55/1.73 Axiom fact_480_sum__power2__gt__zero__iff:(forall (X_6:int) (Y_4:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((power_power_int X_6) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_4) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq int) X_6) zero_zero_int))) (not (((eq int) Y_4) zero_zero_int))))). % 1.55/1.73 Axiom fact_481_zero__le__even__power_H:(forall (A_10:real) (N_11:nat), ((ord_less_eq_real zero_zero_real) ((power_power_real A_10) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_11)))). % 1.55/1.73 Axiom fact_482_zero__le__even__power_H:(forall (A_10:int) (N_11:nat), ((ord_less_eq_int zero_zero_int) ((power_power_int A_10) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_11)))). % 1.55/1.73 Axiom fact_483_one__le__power:(forall (N_10:nat) (A_9:real), (((ord_less_eq_real one_one_real) A_9)->((ord_less_eq_real one_one_real) ((power_power_real A_9) N_10)))). % 1.55/1.73 Axiom fact_484_one__le__power:(forall (N_10:nat) (A_9:nat), (((ord_less_eq_nat one_one_nat) A_9)->((ord_less_eq_nat one_one_nat) ((power_power_nat A_9) N_10)))). % 1.55/1.73 Axiom fact_485_one__le__power:(forall (N_10:nat) (A_9:int), (((ord_less_eq_int one_one_int) A_9)->((ord_less_eq_int one_one_int) ((power_power_int A_9) N_10)))). % 1.55/1.73 Axiom fact_486_power__increasing:(forall (A_8:real) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_real one_one_real) A_8)->((ord_less_eq_real ((power_power_real A_8) N_9)) ((power_power_real A_8) N_8))))). % 1.55/1.73 Axiom fact_487_power__increasing:(forall (A_8:nat) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_nat one_one_nat) A_8)->((ord_less_eq_nat ((power_power_nat A_8) N_9)) ((power_power_nat A_8) N_8))))). % 1.55/1.73 Axiom fact_488_power__increasing:(forall (A_8:int) (N_9:nat) (N_8:nat), (((ord_less_eq_nat N_9) N_8)->(((ord_less_eq_int one_one_int) A_8)->((ord_less_eq_int ((power_power_int A_8) N_9)) ((power_power_int A_8) N_8))))). % 1.55/1.73 Axiom fact_489_power__inject__exp:(forall (M_3:nat) (N_7:nat) (A_7:real), (((ord_less_real one_one_real) A_7)->((iff (((eq real) ((power_power_real A_7) M_3)) ((power_power_real A_7) N_7))) (((eq nat) M_3) N_7)))). % 1.55/1.73 Axiom fact_490_power__inject__exp:(forall (M_3:nat) (N_7:nat) (A_7:nat), (((ord_less_nat one_one_nat) A_7)->((iff (((eq nat) ((power_power_nat A_7) M_3)) ((power_power_nat A_7) N_7))) (((eq nat) M_3) N_7)))). % 1.55/1.73 Axiom fact_491_power__inject__exp:(forall (M_3:nat) (N_7:nat) (A_7:int), (((ord_less_int one_one_int) A_7)->((iff (((eq int) ((power_power_int A_7) M_3)) ((power_power_int A_7) N_7))) (((eq nat) M_3) N_7)))). % 1.55/1.73 Axiom fact_492_power__strict__increasing__iff:(forall (X_5:nat) (Y_3:nat) (B_2:real), (((ord_less_real one_one_real) B_2)->((iff ((ord_less_real ((power_power_real B_2) X_5)) ((power_power_real B_2) Y_3))) ((ord_less_nat X_5) Y_3)))). % 1.55/1.73 Axiom fact_493_power__strict__increasing__iff:(forall (X_5:nat) (Y_3:nat) (B_2:nat), (((ord_less_nat one_one_nat) B_2)->((iff ((ord_less_nat ((power_power_nat B_2) X_5)) ((power_power_nat B_2) Y_3))) ((ord_less_nat X_5) Y_3)))). % 1.55/1.73 Axiom fact_494_power__strict__increasing__iff:(forall (X_5:nat) (Y_3:nat) (B_2:int), (((ord_less_int one_one_int) B_2)->((iff ((ord_less_int ((power_power_int B_2) X_5)) ((power_power_int B_2) Y_3))) ((ord_less_nat X_5) Y_3)))). % 1.55/1.73 Axiom fact_495_power__less__imp__less__exp:(forall (M_2:nat) (N_6:nat) (A_6:real), (((ord_less_real one_one_real) A_6)->(((ord_less_real ((power_power_real A_6) M_2)) ((power_power_real A_6) N_6))->((ord_less_nat M_2) N_6)))). % 1.55/1.73 Axiom fact_496_power__less__imp__less__exp:(forall (M_2:nat) (N_6:nat) (A_6:nat), (((ord_less_nat one_one_nat) A_6)->(((ord_less_nat ((power_power_nat A_6) M_2)) ((power_power_nat A_6) N_6))->((ord_less_nat M_2) N_6)))). % 1.55/1.73 Axiom fact_497_power__less__imp__less__exp:(forall (M_2:nat) (N_6:nat) (A_6:int), (((ord_less_int one_one_int) A_6)->(((ord_less_int ((power_power_int A_6) M_2)) ((power_power_int A_6) N_6))->((ord_less_nat M_2) N_6)))). % 1.55/1.73 Axiom fact_498_power__strict__increasing:(forall (A_5:real) (N_5:nat) (N_4:nat), (((ord_less_nat N_5) N_4)->(((ord_less_real one_one_real) A_5)->((ord_less_real ((power_power_real A_5) N_5)) ((power_power_real A_5) N_4))))). % 1.55/1.73 Axiom fact_499_power__strict__increasing:(forall (A_5:nat) (N_5:nat) (N_4:nat), (((ord_less_nat N_5) N_4)->(((ord_less_nat one_one_nat) A_5)->((ord_less_nat ((power_power_nat A_5) N_5)) ((power_power_nat A_5) N_4))))). % 1.55/1.73 Axiom fact_500_power__strict__increasing:(forall (A_5:int) (N_5:nat) (N_4:nat), (((ord_less_nat N_5) N_4)->(((ord_less_int one_one_int) A_5)->((ord_less_int ((power_power_int A_5) N_5)) ((power_power_int A_5) N_4))))). % 1.55/1.73 Axiom fact_501_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)). % 1.55/1.73 Axiom fact_502_Euler_Oaux____1:(forall (Y_1:int) (X_1:int) (P:int), (((((zcong X_1) zero_zero_int) P)->False)->((((zcong ((power_power_int Y_1) (number_number_of_nat (bit0 (bit1 pls))))) X_1) P)->(((dvd_dvd_int P) Y_1)->False)))). % 1.55/1.73 Axiom fact_503_int__pos__lt__two__imp__zero__or__one:(forall (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_int X_1) (number_number_of_int (bit0 (bit1 pls))))->((or (((eq int) X_1) zero_zero_int)) (((eq int) X_1) one_one_int))))). % 1.55/1.73 Axiom fact_504_even__power__le__0__imp__0:(forall (A_4:real) (K_2:nat), (((ord_less_eq_real ((power_power_real A_4) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_2))) zero_zero_real)->(((eq real) A_4) zero_zero_real))). % 1.55/1.73 Axiom fact_505_even__power__le__0__imp__0:(forall (A_4:int) (K_2:nat), (((ord_less_eq_int ((power_power_int A_4) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) K_2))) zero_zero_int)->(((eq int) A_4) zero_zero_int))). % 1.55/1.73 Axiom fact_506_zprime__def:(forall (P:int), ((iff (zprime P)) ((and ((ord_less_int one_one_int) P)) (forall (M_1:int), (((and ((ord_less_eq_int zero_zero_int) M_1)) ((dvd_dvd_int M_1) P))->((or (((eq int) M_1) one_one_int)) (((eq int) M_1) P))))))). % 1.55/1.73 Axiom fact_507__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). % 1.55/1.73 Axiom fact_508__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). % 1.55/1.73 Axiom fact_509_nat__zero__less__power__iff:(forall (X_1:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) N))) ((or ((ord_less_nat zero_zero_nat) X_1)) (((eq nat) N) zero_zero_nat)))). % 1.55/1.73 Axiom fact_510_zero__less__power__nat__eq:(forall (X_1:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) N))) ((or (((eq nat) N) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X_1)))). % 1.55/1.73 Axiom fact_511_zero__less__power__nat__eq__number__of:(forall (X_1:nat) (W:int), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X_1) (number_number_of_nat W)))) ((or (((eq nat) (number_number_of_nat W)) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X_1)))). % 1.55/1.73 Axiom fact_512_nat__power__less__imp__less:(forall (M:nat) (N:nat) (_TPTP_I:nat), (((ord_less_nat zero_zero_nat) _TPTP_I)->(((ord_less_nat ((power_power_nat _TPTP_I) M)) ((power_power_nat _TPTP_I) N))->((ord_less_nat M) N)))). % 1.55/1.73 Axiom fact_513_rel__simps_I47_J:(forall (K:int), ((iff (((eq int) (bit1 K)) min)) (((eq int) K) min))). % 1.55/1.73 Axiom fact_514_rel__simps_I43_J:(forall (L:int), ((iff (((eq int) min) (bit1 L))) (((eq int) min) L))). % 1.55/1.73 Axiom fact_515_Bit1__Min:(((eq int) (bit1 min)) min). % 1.55/1.73 Axiom fact_516_rel__simps_I37_J:(not (((eq int) pls) min)). % 1.55/1.73 Axiom fact_517_rel__simps_I40_J:(not (((eq int) min) pls)). % 1.55/1.73 Axiom fact_518_rel__simps_I45_J:(forall (K:int), (not (((eq int) (bit0 K)) min))). % 1.55/1.73 Axiom fact_519_rel__simps_I42_J:(forall (L:int), (not (((eq int) min) (bit0 L)))). % 1.55/1.73 Axiom fact_520_rel__simps_I7_J:(((ord_less_int min) min)->False). % 1.55/1.73 Axiom fact_521_rel__simps_I24_J:((ord_less_eq_int min) min). % 1.55/1.73 Axiom fact_522_not__real__square__gt__zero:(forall (X_1:real), ((iff (((ord_less_real zero_zero_real) ((times_times_real X_1) X_1))->False)) (((eq real) X_1) zero_zero_real))). % 1.55/1.73 Axiom fact_523_rel__simps_I13_J:(forall (K:int), ((iff ((ord_less_int (bit1 K)) min)) ((ord_less_int K) min))). % 1.55/1.73 Axiom fact_524_rel__simps_I9_J:(forall (K:int), ((iff ((ord_less_int min) (bit1 K))) ((ord_less_int min) K))). % 1.55/1.73 Axiom fact_525_rel__simps_I3_J:(((ord_less_int pls) min)->False). % 1.55/1.73 Axiom fact_526_rel__simps_I6_J:((ord_less_int min) pls). % 1.55/1.73 Axiom fact_527_rel__simps_I8_J:(forall (K:int), ((iff ((ord_less_int min) (bit0 K))) ((ord_less_int min) K))). % 1.55/1.73 Axiom fact_528_bin__less__0__simps_I2_J:((ord_less_int min) zero_zero_int). % 1.55/1.73 Axiom fact_529_rel__simps_I30_J:(forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) min)) ((ord_less_eq_int K) min))). % 1.55/1.73 Axiom fact_530_rel__simps_I26_J:(forall (K:int), ((iff ((ord_less_eq_int min) (bit1 K))) ((ord_less_eq_int min) K))). % 1.55/1.73 Axiom fact_531_rel__simps_I20_J:(((ord_less_eq_int pls) min)->False). % 1.55/1.73 Axiom fact_532_rel__simps_I23_J:((ord_less_eq_int min) pls). % 1.55/1.73 Axiom fact_533_rel__simps_I28_J:(forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) min)) ((ord_less_eq_int K) min))). % 1.55/1.73 Axiom fact_534_eq__number__of__Pls__Min:(not (((eq int) (number_number_of_int pls)) (number_number_of_int min))). % 1.55/1.73 Axiom fact_535_power__dvd__imp__le:(forall (_TPTP_I:nat) (M:nat) (N:nat), (((dvd_dvd_nat ((power_power_nat _TPTP_I) M)) ((power_power_nat _TPTP_I) N))->(((ord_less_nat one_one_nat) _TPTP_I)->((ord_less_eq_nat M) N)))). % 1.55/1.73 Axiom fact_536_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J:(forall (X_4:real), (((eq real) ((power_power_real X_4) zero_zero_nat)) one_one_real)). % 1.55/1.73 Axiom fact_537_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J:(forall (X_4:nat), (((eq nat) ((power_power_nat X_4) zero_zero_nat)) one_one_nat)). % 1.55/1.73 Axiom fact_538_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J:(forall (X_4:int), (((eq int) ((power_power_int X_4) zero_zero_nat)) one_one_int)). % 1.55/1.73 Axiom fact_539_power__0:(forall (A_3:real), (((eq real) ((power_power_real A_3) zero_zero_nat)) one_one_real)). % 1.55/1.73 Axiom fact_540_power__0:(forall (A_3:nat), (((eq nat) ((power_power_nat A_3) zero_zero_nat)) one_one_nat)). % 1.55/1.73 Axiom fact_541_power__0:(forall (A_3:int), (((eq int) ((power_power_int A_3) zero_zero_nat)) one_one_int)). % 1.55/1.73 Axiom fact_542_nat__number__of__Pls:(((eq nat) (number_number_of_nat pls)) zero_zero_nat). % 1.55/1.73 Axiom fact_543_semiring__norm_I113_J:(((eq nat) zero_zero_nat) (number_number_of_nat pls)). % 1.55/1.73 Axiom fact_544_rel__simps_I25_J:(forall (K:int), ((iff ((ord_less_eq_int min) (bit0 K))) ((ord_less_int min) K))). % 1.55/1.73 Axiom fact_545_rel__simps_I11_J:(forall (K:int), ((iff ((ord_less_int (bit0 K)) min)) ((ord_less_eq_int K) min))). % 1.55/1.73 Axiom fact_546_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))))). % 1.55/1.73 Axiom fact_547_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)))))). % 1.55/1.73 Axiom fact_548_one__less__power:(forall (N_3:nat) (A_2:real), (((ord_less_real one_one_real) A_2)->(((ord_less_nat zero_zero_nat) N_3)->((ord_less_real one_one_real) ((power_power_real A_2) N_3))))). % 1.55/1.73 Axiom fact_549_one__less__power:(forall (N_3:nat) (A_2:nat), (((ord_less_nat one_one_nat) A_2)->(((ord_less_nat zero_zero_nat) N_3)->((ord_less_nat one_one_nat) ((power_power_nat A_2) N_3))))). % 1.55/1.73 Axiom fact_550_one__less__power:(forall (N_3:nat) (A_2:int), (((ord_less_int one_one_int) A_2)->(((ord_less_nat zero_zero_nat) N_3)->((ord_less_int one_one_int) ((power_power_int A_2) N_3))))). % 1.55/1.73 Axiom fact_551_dvd__power:(forall (X_3:nat) (N_2:nat), (((or ((ord_less_nat zero_zero_nat) N_2)) (((eq nat) X_3) one_one_nat))->((dvd_dvd_nat X_3) ((power_power_nat X_3) N_2)))). % 1.55/1.73 Axiom fact_552_dvd__power:(forall (X_3:int) (N_2:nat), (((or ((ord_less_nat zero_zero_nat) N_2)) (((eq int) X_3) one_one_int))->((dvd_dvd_int X_3) ((power_power_int X_3) N_2)))). % 1.55/1.73 Axiom fact_553_dvd__power:(forall (X_3:real) (N_2:nat), (((or ((ord_less_nat zero_zero_nat) N_2)) (((eq real) X_3) one_one_real))->((dvd_dvd_real X_3) ((power_power_real X_3) N_2)))). % 1.55/1.73 Axiom fact_554_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))). % 1.55/1.73 Axiom fact_555_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))). % 1.55/1.73 Axiom fact_556_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))). % 1.55/1.73 Axiom fact_557_zcong__sym:(forall (A:int) (B_1:int) (M:int), ((iff (((zcong A) B_1) M)) (((zcong B_1) A) M))). % 1.55/1.73 Axiom fact_558_zcong__refl:(forall (K:int) (M:int), (((zcong K) K) M)). % 1.55/1.73 Axiom fact_559_zcong__trans:(forall (C:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((((zcong B_1) C) M)->(((zcong A) C) M)))). % 1.55/1.73 Axiom fact_560_pos2:((ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls)))). % 1.55/1.73 Axiom fact_561_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))))). % 1.55/1.73 Axiom fact_562_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)))))). % 1.55/1.73 Axiom fact_563_order__le__neq__implies__less:(forall (X_2:real) (Y_2:real), (((ord_less_eq_real X_2) Y_2)->((not (((eq real) X_2) Y_2))->((ord_less_real X_2) Y_2)))). % 1.55/1.73 Axiom fact_564_order__le__neq__implies__less:(forall (X_2:nat) (Y_2:nat), (((ord_less_eq_nat X_2) Y_2)->((not (((eq nat) X_2) Y_2))->((ord_less_nat X_2) Y_2)))). % 1.55/1.73 Axiom fact_565_order__le__neq__implies__less:(forall (X_2:int) (Y_2:int), (((ord_less_eq_int X_2) Y_2)->((not (((eq int) X_2) Y_2))->((ord_less_int X_2) Y_2)))). % 1.55/1.73 Axiom fact_566_Euler_Oaux2:(forall (B_1:int) (A:int) (C:int), (((ord_less_int A) C)->(((ord_less_int B_1) C)->((or ((ord_less_eq_int A) B_1)) ((ord_less_eq_int B_1) A))))). % 1.55/1.73 Axiom fact_567_IntPrimes_Ozcong__zero:(forall (A:int) (B_1:int), ((iff (((zcong A) B_1) zero_zero_int)) (((eq int) A) B_1))). % 1.55/1.73 Axiom fact_568_zcong__1:(forall (A:int) (B_1:int), (((zcong A) B_1) one_one_int)). % 1.55/1.73 Axiom fact_569_zcong__zmult:(forall (C:int) (D:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((((zcong C) D) M)->(((zcong ((times_times_int A) C)) ((times_times_int B_1) D)) M)))). % 1.55/1.73 Axiom fact_570_zcong__scalar2:(forall (K:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->(((zcong ((times_times_int K) A)) ((times_times_int K) B_1)) M))). % 1.55/1.73 Axiom fact_571_zcong__scalar:(forall (K:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->(((zcong ((times_times_int A) K)) ((times_times_int B_1) K)) M))). % 1.55/1.73 Axiom fact_572_zcong__zmult__self:(forall (A:int) (M:int) (B_1:int), (((zcong ((times_times_int A) M)) ((times_times_int B_1) M)) M)). % 1.55/1.73 Axiom fact_573_zcong__zadd:(forall (C:int) (D:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((((zcong C) D) M)->(((zcong ((plus_plus_int A) C)) ((plus_plus_int B_1) D)) M)))). % 1.55/1.73 Axiom fact_574_power__m1__even:(forall (N_1:nat), (((eq real) ((power_power_real (number267125858f_real min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_1))) one_one_real)). % 1.55/1.73 Axiom fact_575_power__m1__even:(forall (N_1:nat), (((eq int) ((power_power_int (number_number_of_int min)) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N_1))) one_one_int)). % 1.55/1.73 Axiom fact_576_power__eq__0__iff__number__of:(forall (A_1:real) (W_3:int), ((iff (((eq real) ((power_power_real A_1) (number_number_of_nat W_3))) zero_zero_real)) ((and (((eq real) A_1) zero_zero_real)) (not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))))). % 1.55/1.73 Axiom fact_577_power__eq__0__iff__number__of:(forall (A_1:nat) (W_3:int), ((iff (((eq nat) ((power_power_nat A_1) (number_number_of_nat W_3))) zero_zero_nat)) ((and (((eq nat) A_1) zero_zero_nat)) (not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))))). % 1.55/1.73 Axiom fact_578_power__eq__0__iff__number__of:(forall (A_1:int) (W_3:int), ((iff (((eq int) ((power_power_int A_1) (number_number_of_nat W_3))) zero_zero_int)) ((and (((eq int) A_1) zero_zero_int)) (not (((eq nat) (number_number_of_nat W_3)) zero_zero_nat))))). % 1.55/1.73 Axiom fact_579_zcong__not:(forall (B_1:int) (M:int) (A:int), (((ord_less_int zero_zero_int) A)->(((ord_less_int A) M)->(((ord_less_int zero_zero_int) B_1)->(((ord_less_int B_1) A)->((((zcong A) B_1) M)->False)))))). % 1.55/1.73 Axiom fact_580_zcong__iff__lin:(forall (A:int) (B_1:int) (M:int), ((iff (((zcong A) B_1) M)) ((ex int) (fun (K_1:int)=> (((eq int) B_1) ((plus_plus_int A) ((times_times_int M) K_1))))))). % 1.55/1.73 Axiom fact_581_power__0__left__number__of:(forall (W_2:int), ((and ((((eq nat) (number_number_of_nat W_2)) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_2))) one_one_real))) ((not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_2))) zero_zero_real)))). % 1.55/1.73 Axiom fact_582_power__0__left__number__of:(forall (W_2:int), ((and ((((eq nat) (number_number_of_nat W_2)) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_2))) one_one_nat))) ((not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_2))) zero_zero_nat)))). % 1.55/1.73 Axiom fact_583_power__0__left__number__of:(forall (W_2:int), ((and ((((eq nat) (number_number_of_nat W_2)) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_2))) one_one_int))) ((not (((eq nat) (number_number_of_nat W_2)) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_2))) zero_zero_int)))). % 1.55/1.73 Axiom fact_584_zcong__zless__imp__eq:(forall (B_1: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_1)->(((ord_less_int B_1) M)->((((zcong A) B_1) M)->(((eq int) A) B_1))))))). % 1.55/1.73 Axiom fact_585_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))))). % 1.55/1.73 Axiom fact_586_zprime__zdvd__zmult:(forall (N:int) (P:int) (M:int), (((ord_less_eq_int zero_zero_int) M)->((zprime P)->(((dvd_dvd_int P) ((times_times_int M) N))->((or ((dvd_dvd_int P) M)) ((dvd_dvd_int P) N)))))). % 1.55/1.73 Axiom fact_587__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)). % 1.55/1.73 Axiom fact_588__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))). % 1.55/1.73 Axiom fact_589_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))))). % 1.55/1.73 Axiom fact_590__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)). % 1.55/1.73 Axiom fact_591__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N:((((quadRes ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) (number_number_of_int min))->False)->(not (((eq int) ((legendre (number_number_of_int min)) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))) one_one_int))). % 1.55/1.73 Axiom fact_592_zcong__zdiff:(forall (C:int) (D:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((((zcong C) D) M)->(((zcong ((minus_minus_int A) C)) ((minus_minus_int B_1) D)) M)))). % 1.55/1.73 Axiom fact_593_diff__bin__simps_I1_J:(forall (K:int), (((eq int) ((minus_minus_int K) pls)) K)). % 1.55/1.73 Axiom fact_594_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)))). % 1.55/1.73 Axiom fact_595_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)))). % 1.55/1.73 Axiom fact_596_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)))). % 1.55/1.73 Axiom fact_597_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)))). % 1.55/1.73 Axiom fact_598_number__of__diff:(forall (V:int) (W_1:int), (((eq int) (number_number_of_int ((minus_minus_int V) W_1))) ((minus_minus_int (number_number_of_int V)) (number_number_of_int W_1)))). % 1.55/1.73 Axiom fact_599_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)))). % 1.55/1.73 Axiom fact_600_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)))). % 1.55/1.74 Axiom fact_601_diff__bin__simps_I3_J:(forall (L:int), (((eq int) ((minus_minus_int pls) (bit0 L))) (bit0 ((minus_minus_int pls) L)))). % 1.55/1.74 Axiom fact_602_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))). % 1.55/1.74 Axiom fact_603_xzgcda__linear__aux1:(forall (A:int) (R_1:int) (B_1: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_1))) 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_1) M)) ((times_times_int D) N)))))). % 1.55/1.74 Axiom fact_604_zcong__def:(forall (A:int) (B_1:int) (M:int), ((iff (((zcong A) B_1) M)) ((dvd_dvd_int M) ((minus_minus_int A) B_1)))). % 1.55/1.74 Axiom fact_605_Euler_Oaux1:(forall (A:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int X_1) A)->((not (((eq int) X_1) ((minus_minus_int A) one_one_int)))->((ord_less_int X_1) ((minus_minus_int A) one_one_int)))))). % 1.55/1.74 Axiom fact_606_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))). % 1.55/1.74 Axiom fact_607_diff__bin__simps_I4_J:(forall (L:int), (((eq int) ((minus_minus_int pls) (bit1 L))) (bit1 ((minus_minus_int min) L)))). % 1.55/1.74 Axiom fact_608_diff__bin__simps_I6_J:(forall (L:int), (((eq int) ((minus_minus_int min) (bit1 L))) (bit0 ((minus_minus_int min) L)))). % 1.55/1.74 Axiom fact_609_diff__bin__simps_I5_J:(forall (L:int), (((eq int) ((minus_minus_int min) (bit0 L))) (bit1 ((minus_minus_int min) L)))). % 1.55/1.74 Axiom fact_610_inv__not__p__minus__1__aux:(forall (A:int) (P:int), ((iff (((zcong ((times_times_int A) ((minus_minus_int P) one_one_int))) one_one_int) P)) (((zcong A) ((minus_minus_int P) one_one_int)) P))). % 1.55/1.74 Axiom fact_611_mult__sum2sq:(forall (A:int) (B_1:int) (P:int) (Q:int), (((eq int) ((times_times_int (twoSqu1078207634sum2sq ((product_Pair_int_int A) B_1))) (twoSqu1078207634sum2sq ((product_Pair_int_int P) Q)))) (twoSqu1078207634sum2sq ((product_Pair_int_int ((plus_plus_int ((times_times_int A) P)) ((times_times_int B_1) Q))) ((minus_minus_int ((times_times_int A) Q)) ((times_times_int B_1) P)))))). % 1.55/1.74 Axiom fact_612_zcong__square:(forall (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) A)) one_one_int) P)->((or (((zcong A) one_one_int) P)) (((zcong A) ((minus_minus_int P) one_one_int)) P)))))). % 1.55/1.74 Axiom fact_613_zcong__square__zless:(forall (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->(((ord_less_int A) P)->((((zcong ((times_times_int A) A)) one_one_int) P)->((or (((eq int) A) one_one_int)) (((eq int) A) ((minus_minus_int P) one_one_int)))))))). % 1.55/1.74 Axiom fact_614_zspecial__product:(forall (A:int) (B_1:int), (((eq int) ((times_times_int ((plus_plus_int A) B_1)) ((minus_minus_int A) B_1))) ((minus_minus_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int B_1) (number_number_of_nat (bit0 (bit1 pls))))))). % 1.55/1.74 Axiom fact_615_zdiff__power2:(forall (A:int) (B_1:int), (((eq int) ((power_power_int ((minus_minus_int A) B_1)) (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_1))) ((power_power_int B_1) (number_number_of_nat (bit0 (bit1 pls))))))). % 1.55/1.74 Axiom fact_616_zdiff__power3:(forall (A:int) (B_1:int), (((eq int) ((power_power_int ((minus_minus_int A) B_1)) (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_1))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) A)) ((power_power_int B_1) (number_number_of_nat (bit0 (bit1 pls))))))) ((power_power_int B_1) (number_number_of_nat (bit1 (bit1 pls))))))). % 1.55/1.74 Axiom fact_617_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)))). % 1.55/1.74 Axiom fact_618_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))). % 1.55/1.74 Axiom fact_619_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))). % 1.55/1.74 Axiom fact_620_zcong__neg__1__impl__ne__1:(forall (X_1:int) (P:int), (((ord_less_int (number_number_of_int (bit0 (bit1 pls)))) P)->((((zcong X_1) (number_number_of_int min)) P)->((((zcong X_1) one_one_int) P)->False)))). % 1.55/1.74 Axiom fact_621_Legendre__def:(forall (A:int) (P:int), ((and ((((zcong A) zero_zero_int) P)->(((eq int) ((legendre A) P)) zero_zero_int))) (((((zcong A) zero_zero_int) P)->False)->((and (((quadRes P) A)->(((eq int) ((legendre A) P)) one_one_int))) ((((quadRes P) A)->False)->(((eq int) ((legendre A) P)) (number_number_of_int min))))))). % 1.55/1.74 Axiom fact_622_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)))). % 1.55/1.74 Axiom fact_623_divides__antisym:(forall (X_1:nat) (Y_1:nat), ((iff ((and ((dvd_dvd_nat X_1) Y_1)) ((dvd_dvd_nat Y_1) X_1))) (((eq nat) X_1) Y_1))). % 1.55/1.74 Axiom fact_624_zcong__eq__trans:(forall (D:int) (C:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((((eq int) B_1) C)->((((zcong C) D) M)->(((zcong A) D) M))))). % 1.55/1.74 Axiom fact_625_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)))))). % 1.55/1.74 Axiom fact_626_power__eq__if:(forall (P:nat) (M:nat), ((and ((((eq nat) M) zero_zero_nat)->(((eq nat) ((power_power_nat P) M)) one_one_nat))) ((not (((eq nat) M) zero_zero_nat))->(((eq nat) ((power_power_nat P) M)) ((times_times_nat P) ((power_power_nat P) ((minus_minus_nat M) one_one_nat))))))). % 1.55/1.74 Axiom fact_627_diff__square:(forall (X_1:nat) (Y_1:nat), (((eq nat) ((minus_minus_nat ((power_power_nat X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((plus_plus_nat X_1) Y_1)) ((minus_minus_nat X_1) Y_1)))). % 1.55/1.74 Axiom fact_628_divides__add__revr:(forall (B_1:nat) (D:nat) (A:nat), (((dvd_dvd_nat D) A)->(((dvd_dvd_nat D) ((plus_plus_nat A) B_1))->((dvd_dvd_nat D) B_1)))). % 1.55/1.74 Axiom fact_629_divides__mul__l:(forall (C:nat) (A:nat) (B_1:nat), (((dvd_dvd_nat A) B_1)->((dvd_dvd_nat ((times_times_nat C) A)) ((times_times_nat C) B_1)))). % 1.55/1.74 Axiom fact_630_divides__mul__r:(forall (C:nat) (A:nat) (B_1:nat), (((dvd_dvd_nat A) B_1)->((dvd_dvd_nat ((times_times_nat A) C)) ((times_times_nat B_1) C)))). % 1.55/1.74 Axiom fact_631_zcong__id:(forall (M:int), (((zcong M) zero_zero_int) M)). % 1.55/1.74 Axiom fact_632_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)))). % 1.55/1.74 Axiom fact_633_Int2_Oaux1:(forall (A:int) (B_1:int) (C:int), ((((eq int) ((minus_minus_int A) B_1)) C)->(((eq int) A) ((plus_plus_int C) B_1)))). % 1.55/1.74 Axiom fact_634_zcong__zmult__prop2:(forall (C:int) (D:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((iff (((zcong C) ((times_times_int D) A)) M)) (((zcong C) ((times_times_int D) B_1)) M)))). % 1.55/1.74 Axiom fact_635_zcong__zmult__prop1:(forall (C:int) (D:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->((iff (((zcong C) ((times_times_int A) D)) M)) (((zcong C) ((times_times_int B_1) D)) M)))). % 1.55/1.74 Axiom fact_636_zcong__shift:(forall (C:int) (A:int) (B_1:int) (M:int), ((((zcong A) B_1) M)->(((zcong ((plus_plus_int A) C)) ((plus_plus_int B_1) C)) M))). % 1.55/1.74 Axiom fact_637_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)))). % 1.55/1.74 Axiom fact_638_divides__exp:(forall (N:nat) (X_1:nat) (Y_1:nat), (((dvd_dvd_nat X_1) Y_1)->((dvd_dvd_nat ((power_power_nat X_1) N)) ((power_power_nat Y_1) N)))). % 1.55/1.74 Axiom fact_639_zcong__zpower:(forall (Z:nat) (X_1:int) (Y_1:int) (M:int), ((((zcong X_1) Y_1) M)->(((zcong ((power_power_int X_1) Z)) ((power_power_int Y_1) Z)) M))). % 1.55/1.74 Axiom fact_640_divides__ge:(forall (A:nat) (B_1:nat), (((dvd_dvd_nat A) B_1)->((or (((eq nat) B_1) zero_zero_nat)) ((ord_less_eq_nat A) B_1)))). % 1.55/1.74 Axiom fact_641_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)))). % 1.55/1.74 Axiom fact_642_zcong__not__zero:(forall (M:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int X_1) M)->((((zcong X_1) zero_zero_int) M)->False)))). % 1.55/1.74 Axiom fact_643_zcong__less__eq:(forall (M:int) (Y_1:int) (X_1:int), (((ord_less_int zero_zero_int) X_1)->(((ord_less_int zero_zero_int) Y_1)->(((ord_less_int zero_zero_int) M)->((((zcong X_1) Y_1) M)->(((ord_less_int X_1) M)->(((ord_less_int Y_1) M)->(((eq int) X_1) Y_1)))))))). % 1.55/1.74 Axiom fact_644_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)))). % 1.55/1.74 Axiom fact_645_divides__exp2:(forall (X_1:nat) (Y_1:nat) (N:nat), ((not (((eq nat) N) zero_zero_nat))->(((dvd_dvd_nat ((power_power_nat X_1) N)) Y_1)->((dvd_dvd_nat X_1) Y_1)))). % 1.55/1.74 Axiom fact_646_divides__rev:(forall (A:nat) (N:nat) (B_1:nat), (((dvd_dvd_nat ((power_power_nat A) N)) ((power_power_nat B_1) N))->((not (((eq nat) N) zero_zero_nat))->((dvd_dvd_nat A) B_1)))). % 1.55/1.74 Axiom fact_647_zcong__zero__equiv__div:(forall (A:int) (M:int), ((iff (((zcong A) zero_zero_int) M)) ((dvd_dvd_int M) A))). % 1.55/1.74 Axiom fact_648_zcong__eq__zdvd__prop:(forall (X_1:int) (P:int), ((iff (((zcong X_1) zero_zero_int) P)) ((dvd_dvd_int P) X_1))). % 1.55/1.74 Axiom fact_649_exp__eq__1:(forall (X_1:nat) (N:nat), ((iff (((eq nat) ((power_power_nat X_1) N)) one_one_nat)) ((or (((eq nat) X_1) one_one_nat)) (((eq nat) N) zero_zero_nat)))). % 1.55/1.74 Axiom fact_650_zprime__zdvd__zmult__better:(forall (M:int) (N:int) (P:int), ((zprime P)->(((dvd_dvd_int P) ((times_times_int M) N))->((or ((dvd_dvd_int P) M)) ((dvd_dvd_int P) N))))). % 1.55/1.74 Axiom fact_651_Int2_Ozcong__zero:(forall (M:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_int X_1) M)->((((zcong X_1) zero_zero_int) M)->(((eq int) X_1) zero_zero_int))))). % 1.55/1.74 Axiom fact_652_zpower__zdvd__prop1:(forall (P:int) (Y_1:int) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((dvd_dvd_int P) Y_1)->((dvd_dvd_int P) ((power_power_int Y_1) N))))). % 1.55/1.74 Axiom fact_653_zcong__zmult__prop3:(forall (Y_1:int) (X_1:int) (P:int), ((zprime P)->(((((zcong X_1) zero_zero_int) P)->False)->(((((zcong Y_1) zero_zero_int) P)->False)->((((zcong ((times_times_int X_1) Y_1)) zero_zero_int) P)->False))))). % 1.55/1.74 Axiom fact_654_divides__div__not:(forall (X_1:nat) (Q:nat) (N:nat) (R_1:nat), ((((eq nat) X_1) ((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_1)->False))))). % 1.55/1.74 Axiom fact_655_zcong__zprime__prod__zero__contra:(forall (B_1:int) (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->(((and ((((zcong A) zero_zero_int) P)->False)) ((((zcong B_1) zero_zero_int) P)->False))->((((zcong ((times_times_int A) B_1)) zero_zero_int) P)->False))))). % 1.55/1.74 Axiom fact_656_zcong__zprime__prod__zero:(forall (B_1:int) (A:int) (P:int), ((zprime P)->(((ord_less_int zero_zero_int) A)->((((zcong ((times_times_int A) B_1)) zero_zero_int) P)->((or (((zcong A) zero_zero_int) P)) (((zcong B_1) zero_zero_int) P)))))). % 1.55/1.74 Axiom fact_657_zpower__zdvd__prop2:(forall (Y_1:int) (N:nat) (P:int), ((zprime P)->(((dvd_dvd_int P) ((power_power_int Y_1) N))->(((ord_less_nat zero_zero_nat) N)->((dvd_dvd_int P) Y_1))))). % 1.55/1.74 Axiom fact_658_QuadRes__def:(forall (M:int) (X_1:int), ((iff ((quadRes M) X_1)) ((ex int) (fun (Y:int)=> (((zcong ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls))))) X_1) M))))). % 1.55/1.74 Axiom fact_659_realpow__two__sum__zero__iff:(forall (X_1:real) (Y_1:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X_1) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_1) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_1) zero_zero_real)) (((eq real) Y_1) zero_zero_real)))). % 1.55/1.74 Axiom fact_660_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))))). % 1.55/1.74 Axiom fact_661_real__zero__not__eq__one:(not (((eq real) zero_zero_real) one_one_real)). % 1.55/1.74 Axiom fact_662_real__le__eq__diff:(forall (X_1:real) (Y_1:real), ((iff ((ord_less_eq_real X_1) Y_1)) ((ord_less_eq_real ((minus_minus_real X_1) Y_1)) zero_zero_real))). % 1.55/1.74 Axiom fact_663_real__less__def:(forall (X_1:real) (Y_1:real), ((iff ((ord_less_real X_1) Y_1)) ((and ((ord_less_eq_real X_1) Y_1)) (not (((eq real) X_1) Y_1))))). % 1.55/1.74 Axiom fact_664_less__eq__real__def:(forall (X_1:real) (Y_1:real), ((iff ((ord_less_eq_real X_1) Y_1)) ((or ((ord_less_real X_1) Y_1)) (((eq real) X_1) Y_1)))). % 1.55/1.74 Axiom fact_665_real__mult__1:(forall (Z:real), (((eq real) ((times_times_real one_one_real) Z)) Z)). % 1.55/1.74 Axiom fact_666_real__mult__commute:(forall (Z:real) (W:real), (((eq real) ((times_times_real Z) W)) ((times_times_real W) Z))). % 1.55/1.74 Axiom fact_667_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)))). % 1.55/1.74 Axiom fact_668_real__add__left__mono:(forall (Z:real) (X_1:real) (Y_1:real), (((ord_less_eq_real X_1) Y_1)->((ord_less_eq_real ((plus_plus_real Z) X_1)) ((plus_plus_real Z) Y_1)))). % 1.55/1.74 Axiom fact_669_real__mult__left__cancel:(forall (A:real) (B_1:real) (C:real), ((not (((eq real) C) zero_zero_real))->((iff (((eq real) ((times_times_real C) A)) ((times_times_real C) B_1))) (((eq real) A) B_1)))). % 1.55/1.74 Axiom fact_670_real__mult__right__cancel:(forall (A:real) (B_1:real) (C:real), ((not (((eq real) C) zero_zero_real))->((iff (((eq real) ((times_times_real A) C)) ((times_times_real B_1) C))) (((eq real) A) B_1)))). % 1.55/1.74 Axiom fact_671_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)))). % 1.55/1.74 Axiom fact_672_real__mult__less__mono2:(forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->(((ord_less_real X_1) Y_1)->((ord_less_real ((times_times_real Z) X_1)) ((times_times_real Z) Y_1))))). % 1.55/1.74 Axiom fact_673_real__mult__order:(forall (Y_1:real) (X_1:real), (((ord_less_real zero_zero_real) X_1)->(((ord_less_real zero_zero_real) Y_1)->((ord_less_real zero_zero_real) ((times_times_real X_1) Y_1))))). % 1.55/1.74 Axiom fact_674_real__mult__le__cancel__iff2:(forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real Z) X_1)) ((times_times_real Z) Y_1))) ((ord_less_eq_real X_1) Y_1)))). % 1.55/1.74 Axiom fact_675_real__mult__le__cancel__iff1:(forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_eq_real ((times_times_real X_1) Z)) ((times_times_real Y_1) Z))) ((ord_less_eq_real X_1) Y_1)))). % 1.55/1.74 Axiom fact_676_real__mult__less__iff1:(forall (X_1:real) (Y_1:real) (Z:real), (((ord_less_real zero_zero_real) Z)->((iff ((ord_less_real ((times_times_real X_1) Z)) ((times_times_real Y_1) Z))) ((ord_less_real X_1) Y_1)))). % 1.55/1.74 Axiom fact_677_real__two__squares__add__zero__iff:(forall (X_1:real) (Y_1:real), ((iff (((eq real) ((plus_plus_real ((times_times_real X_1) X_1)) ((times_times_real Y_1) Y_1))) zero_zero_real)) ((and (((eq real) X_1) zero_zero_real)) (((eq real) Y_1) zero_zero_real)))). % 1.55/1.75 Axiom fact_678_two__realpow__ge__one:(forall (N:nat), ((ord_less_eq_real one_one_real) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N))). % 1.55/1.75 Axiom fact_679_q__pos__lemma:(forall (B:int) (Q_1:int) (R_2:int), (((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B) Q_1)) R_2))->(((ord_less_int R_2) B)->(((ord_less_int zero_zero_int) B)->((ord_less_eq_int zero_zero_int) Q_1))))). % 1.55/1.75 Axiom fact_680_q__neg__lemma:(forall (B:int) (Q_1:int) (R_2:int), (((ord_less_int ((plus_plus_int ((times_times_int B) Q_1)) R_2)) zero_zero_int)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B)->((ord_less_eq_int Q_1) zero_zero_int))))). % 1.55/1.75 Axiom fact_681_unique__quotient__lemma:(forall (B_1:int) (Q_1:int) (R_2:int) (Q:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B_1) Q_1)) R_2)) ((plus_plus_int ((times_times_int B_1) Q)) R_1))->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int R_2) B_1)->(((ord_less_int R_1) B_1)->((ord_less_eq_int Q_1) Q)))))). % 1.55/1.75 Axiom fact_682_zdiv__mono2__lemma:(forall (B_1:int) (Q:int) (R_1:int) (B:int) (Q_1:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B_1) Q)) R_1)) ((plus_plus_int ((times_times_int B) Q_1)) R_2))->(((ord_less_eq_int zero_zero_int) ((plus_plus_int ((times_times_int B) Q_1)) R_2))->(((ord_less_int R_2) B)->(((ord_less_eq_int zero_zero_int) R_1)->(((ord_less_int zero_zero_int) B)->(((ord_less_eq_int B) B_1)->((ord_less_eq_int Q) Q_1)))))))). % 1.55/1.75 Axiom fact_683_unique__quotient__lemma__neg:(forall (B_1:int) (Q_1:int) (R_2:int) (Q:int) (R_1:int), (((ord_less_eq_int ((plus_plus_int ((times_times_int B_1) Q_1)) R_2)) ((plus_plus_int ((times_times_int B_1) Q)) R_1))->(((ord_less_eq_int R_1) zero_zero_int)->(((ord_less_int B_1) R_1)->(((ord_less_int B_1) R_2)->((ord_less_eq_int Q) Q_1)))))). % 1.55/1.75 Axiom fact_684_zdiv__mono2__neg__lemma:(forall (B_1:int) (Q:int) (R_1:int) (B:int) (Q_1:int) (R_2:int), ((((eq int) ((plus_plus_int ((times_times_int B_1) Q)) R_1)) ((plus_plus_int ((times_times_int B) Q_1)) R_2))->(((ord_less_int ((plus_plus_int ((times_times_int B) Q_1)) R_2)) zero_zero_int)->(((ord_less_int R_1) B_1)->(((ord_less_eq_int zero_zero_int) R_2)->(((ord_less_int zero_zero_int) B)->(((ord_less_eq_int B) B_1)->((ord_less_eq_int Q_1) Q)))))))). % 1.55/1.75 Axiom fact_685_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))))). % 1.55/1.75 Axiom fact_686_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J:((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 (bit1 pls)))). % 1.55/1.75 Axiom fact_687_real__le__antisym:(forall (Z:real) (W:real), (((ord_less_eq_real Z) W)->(((ord_less_eq_real W) Z)->(((eq real) Z) W)))). % 1.55/1.75 Axiom fact_688_real__le__trans:(forall (K:real) (_TPTP_I:real) (J:real), (((ord_less_eq_real _TPTP_I) J)->(((ord_less_eq_real J) K)->((ord_less_eq_real _TPTP_I) K)))). % 1.55/1.75 Axiom fact_689_real__le__linear:(forall (Z:real) (W:real), ((or ((ord_less_eq_real Z) W)) ((ord_less_eq_real W) Z))). % 1.55/1.75 Axiom fact_690_real__le__refl:(forall (W:real), ((ord_less_eq_real W) W)). % 1.55/1.75 Axiom fact_691_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J:((ord_less_eq_int zero_zero_int) zero_zero_int). % 1.55/1.75 Axiom fact_692_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J:((ord_less_eq_int zero_zero_int) one_one_int). % 1.55/1.75 Axiom fact_693_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J:(forall (Y_1:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_eq_int zero_zero_int) Y_1)->((ord_less_eq_int zero_zero_int) ((times_times_int X_1) Y_1))))). % 1.55/1.75 Axiom fact_694_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J:(forall (Y_1:int) (X_1:int), (((ord_less_eq_int zero_zero_int) X_1)->(((ord_less_eq_int zero_zero_int) Y_1)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X_1) Y_1))))). % 1.55/1.75 Axiom fact_695_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J:(forall (N:nat) (X_1:int), ((( %------------------------------------------------------------------------------