%------------------------------------------------------------------------------ % File : cocATP---0.2.0 % Problem : NUM925^2 : TPTP v7.0.0. Released v5.3.0. % Transfm : none % Format : tptp:raw % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % Computer : n115.star.cs.uiowa.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz % Memory : 32218.625MB % OS : Linux 3.10.0-693.2.2.el7.x86_64 % CPULimit : 300s % DateTime : Mon Jan 8 13:12:04 EST 2018 % Result : Timeout 300.09s % Output : None % Verified : % SZS Type : None (Parsing solution fails) % Syntax : Number of formulae : 0 % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.03 % Problem : NUM925^2 : TPTP v7.0.0. Released v5.3.0. % 0.00/0.03 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p % 0.02/0.23 % Computer : n115.star.cs.uiowa.edu % 0.02/0.23 % Model : x86_64 x86_64 % 0.02/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz % 0.02/0.23 % Memory : 32218.625MB % 0.02/0.23 % OS : Linux 3.10.0-693.2.2.el7.x86_64 % 0.02/0.23 % CPULimit : 300 % 0.02/0.23 % DateTime : Fri Jan 5 15:53:49 CST 2018 % 0.02/0.23 % CPUTime : % 0.02/0.25 Python 2.7.13 % 0.09/0.50 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/'] % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2aa05c20>, <kernel.Type object at 0x2b3d2aa05830>) of role type named ty_ty_tc__Int__Oint % 0.09/0.50 Using role type % 0.09/0.50 Declaring int:Type % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2a6ac8c0>, <kernel.Type object at 0x2b3d2aa05878>) of role type named ty_ty_tc__Nat__Onat % 0.09/0.50 Using role type % 0.09/0.50 Declaring nat:Type % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2aa05b90>, <kernel.Type object at 0x2b3d2aa05a28>) of role type named ty_ty_tc__RealDef__Oreal % 0.09/0.50 Using role type % 0.09/0.50 Declaring real:Type % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2aa054d0>, <kernel.Constant object at 0x2b3d2aa05a70>) of role type named sy_c_Groups_Oone__class_Oone_000tc__Int__Oint % 0.09/0.50 Using role type % 0.09/0.50 Declaring one_one_int:int % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2aa05878>, <kernel.Constant object at 0x2b3d2aa05ea8>) of role type named sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat % 0.09/0.50 Using role type % 0.09/0.50 Declaring one_one_nat:nat % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2aa054d0>, <kernel.Constant object at 0x2b3d2a6a8ef0>) of role type named sy_c_Groups_Oone__class_Oone_000tc__RealDef__Oreal % 0.09/0.50 Using role type % 0.09/0.50 Declaring one_one_real:real % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2aa05ea8>, <kernel.DependentProduct object at 0x2b3d2b117368>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint % 0.09/0.50 Using role type % 0.09/0.50 Declaring plus_plus_int:(int->(int->int)) % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2b117368>, <kernel.DependentProduct object at 0x2b3d2a6a89e0>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat % 0.09/0.50 Using role type % 0.09/0.50 Declaring plus_plus_nat:(nat->(nat->nat)) % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2aa05ea8>, <kernel.DependentProduct object at 0x2b3d2a6a8ea8>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__RealDef__Oreal % 0.09/0.50 Using role type % 0.09/0.50 Declaring plus_plus_real:(real->(real->real)) % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2aa054d0>, <kernel.DependentProduct object at 0x2b3d2a6a5638>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint % 0.09/0.50 Using role type % 0.09/0.50 Declaring times_times_int:(int->(int->int)) % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2aa05a70>, <kernel.Constant object at 0x2b3d2a6a5680>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint % 0.09/0.50 Using role type % 0.09/0.50 Declaring zero_zero_int:int % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2aa05a70>, <kernel.Constant object at 0x2b3d2a6a8638>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat % 0.09/0.50 Using role type % 0.09/0.50 Declaring zero_zero_nat:nat % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2a6a5680>, <kernel.Constant object at 0x2b3d2a6a8ef0>) of role type named sy_c_Groups_Ozero__class_Ozero_000tc__RealDef__Oreal % 0.09/0.50 Using role type % 0.09/0.50 Declaring zero_zero_real:real % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2a6a5c20>, <kernel.DependentProduct object at 0x2b3d2a6a89e0>) of role type named sy_c_If_000tc__Nat__Onat % 0.09/0.50 Using role type % 0.09/0.50 Declaring if_nat:(Prop->(nat->(nat->nat))) % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2a6a5638>, <kernel.DependentProduct object at 0x2b3d2b123f80>) of role type named sy_c_Int_OBit0 % 0.09/0.50 Using role type % 0.09/0.50 Declaring bit0:(int->int) % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2a6a5638>, <kernel.DependentProduct object at 0x2b3d2b123b90>) of role type named sy_c_Int_OBit1 % 0.09/0.50 Using role type % 0.09/0.50 Declaring bit1:(int->int) % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2a6a8dd0>, <kernel.Constant object at 0x2b3d2a6a8638>) of role type named sy_c_Int_OPls % 0.09/0.50 Using role type % 0.09/0.50 Declaring pls:int % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2a6a85a8>, <kernel.DependentProduct object at 0x2b3d2b1236c8>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint % 0.09/0.50 Using role type % 0.09/0.50 Declaring number_number_of_int:(int->int) % 0.09/0.50 FOF formula (<kernel.Constant object at 0x2b3d2a6a8638>, <kernel.DependentProduct object at 0x2b3d2b123e60>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__Nat__Onat % 0.09/0.50 Using role type % 0.09/0.50 Declaring number_number_of_nat:(int->nat) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2a6a8ef0>, <kernel.DependentProduct object at 0x2b3d2b123fc8>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__RealDef__Oreal % 0.09/0.51 Using role type % 0.09/0.51 Declaring number267125858f_real:(int->real) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2a6a8638>, <kernel.DependentProduct object at 0x2b3d2b123ef0>) of role type named sy_c_Int_Osucc % 0.09/0.51 Using role type % 0.09/0.51 Declaring succ:(int->int) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2a6a8638>, <kernel.DependentProduct object at 0x2b3d2b123ea8>) of role type named sy_c_Nat_Osemiring__1__class_Oof__nat_000tc__Int__Oint % 0.09/0.51 Using role type % 0.09/0.51 Declaring semiri1621563631at_int:(nat->int) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2b123fc8>, <kernel.DependentProduct object at 0x2b3d2b123950>) of role type named sy_c_Nat_Osemiring__1__class_Oof__nat_000tc__Nat__Onat % 0.09/0.51 Using role type % 0.09/0.51 Declaring semiri984289939at_nat:(nat->nat) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2b123ef0>, <kernel.DependentProduct object at 0x2b3d2b123f38>) of role type named sy_c_Nat_Osemiring__1__class_Oof__nat_000tc__RealDef__Oreal % 0.09/0.51 Using role type % 0.09/0.51 Declaring semiri132038758t_real:(nat->real) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2b123ea8>, <kernel.DependentProduct object at 0x2b3d2b123b00>) of role type named sy_c_NthRoot_Osqrt % 0.09/0.51 Using role type % 0.09/0.51 Declaring sqrt:(real->real) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2b123950>, <kernel.DependentProduct object at 0x2b3d2b123fc8>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Int__Oint % 0.09/0.51 Using role type % 0.09/0.51 Declaring ord_less_int:(int->(int->Prop)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2b123f38>, <kernel.DependentProduct object at 0x2b3d2b1236c8>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat % 0.09/0.51 Using role type % 0.09/0.51 Declaring ord_less_nat:(nat->(nat->Prop)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2b123b00>, <kernel.DependentProduct object at 0x2b3d2b123ef0>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__RealDef__Oreal % 0.09/0.51 Using role type % 0.09/0.51 Declaring ord_less_real:(real->(real->Prop)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2b123fc8>, <kernel.DependentProduct object at 0x2b3d2b123ea8>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Int__Oint % 0.09/0.51 Using role type % 0.09/0.51 Declaring ord_less_eq_int:(int->(int->Prop)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2b1236c8>, <kernel.DependentProduct object at 0x2b3d2b123950>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat % 0.09/0.51 Using role type % 0.09/0.51 Declaring ord_less_eq_nat:(nat->(nat->Prop)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2b123ef0>, <kernel.DependentProduct object at 0x2b3d2b123f38>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__RealDef__Oreal % 0.09/0.51 Using role type % 0.09/0.51 Declaring ord_less_eq_real:(real->(real->Prop)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2b123ea8>, <kernel.DependentProduct object at 0x2b3d2b123b00>) of role type named sy_c_Power_Opower__class_Opower_000tc__Int__Oint % 0.09/0.51 Using role type % 0.09/0.51 Declaring power_power_int:(int->(nat->int)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2b123950>, <kernel.DependentProduct object at 0x2b3d2b123998>) of role type named sy_c_Power_Opower__class_Opower_000tc__Nat__Onat % 0.09/0.51 Using role type % 0.09/0.51 Declaring power_power_nat:(nat->(nat->nat)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2b123f38>, <kernel.DependentProduct object at 0x2b3d2b123a70>) of role type named sy_c_Power_Opower__class_Opower_000tc__RealDef__Oreal % 0.09/0.51 Using role type % 0.09/0.51 Declaring power_power_real:(real->(nat->real)) % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2b123b00>, <kernel.Constant object at 0x2b3d2b123a70>) of role type named sy_v_m1____ % 0.09/0.51 Using role type % 0.09/0.51 Declaring m1:int % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2b123950>, <kernel.Constant object at 0x2b3d2b123a70>) of role type named sy_v_n____ % 0.09/0.51 Using role type % 0.09/0.51 Declaring n:nat % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2b123f38>, <kernel.Constant object at 0x2b3d2b123a70>) of role type named sy_v_t____ % 0.09/0.51 Using role type % 0.09/0.51 Declaring t:int % 0.09/0.51 FOF formula (<kernel.Constant object at 0x2b3d2b123b00>, <kernel.Constant object at 0x2b3d2b123a70>) of role type named sy_v_tn____ % 0.35/0.52 Using role type % 0.35/0.52 Declaring tn:nat % 0.35/0.52 FOF formula ((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) (semiri1621563631at_int n))) of role axiom named fact_0_n1pos % 0.35/0.52 A new axiom: ((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) (semiri1621563631at_int n))) % 0.35/0.52 FOF formula ((ord_less_int one_one_int) t) of role axiom named fact_1_t1 % 0.35/0.52 A new axiom: ((ord_less_int one_one_int) t) % 0.35/0.52 FOF formula (forall (X:int) (Y:int), ((iff (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X) zero_zero_int)) (((eq int) Y) zero_zero_int)))) of role axiom named fact_2_sum__power2__eq__zero__iff % 0.35/0.52 A new axiom: (forall (X:int) (Y:int), ((iff (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X) zero_zero_int)) (((eq int) Y) zero_zero_int)))) % 0.35/0.52 FOF formula (forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real)))) of role axiom named fact_3_sum__power2__eq__zero__iff % 0.35/0.52 A new axiom: (forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real)))) % 0.35/0.52 FOF formula (((eq int) ((power_power_int one_one_int) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int) of role axiom named fact_4_one__power2 % 0.35/0.52 A new axiom: (((eq int) ((power_power_int one_one_int) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int) % 0.35/0.52 FOF formula (((eq nat) ((power_power_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls))))) one_one_nat) of role axiom named fact_5_one__power2 % 0.35/0.52 A new axiom: (((eq nat) ((power_power_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls))))) one_one_nat) % 0.35/0.52 FOF formula (((eq real) ((power_power_real one_one_real) (number_number_of_nat (bit0 (bit1 pls))))) one_one_real) of role axiom named fact_6_one__power2 % 0.35/0.52 A new axiom: (((eq real) ((power_power_real one_one_real) (number_number_of_nat (bit0 (bit1 pls))))) one_one_real) % 0.35/0.52 FOF formula (((eq int) ((power_power_int zero_zero_int) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int) of role axiom named fact_7_zero__power2 % 0.35/0.52 A new axiom: (((eq int) ((power_power_int zero_zero_int) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int) % 0.35/0.52 FOF formula (((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_nat) of role axiom named fact_8_zero__power2 % 0.35/0.52 A new axiom: (((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_nat) % 0.35/0.52 FOF formula (((eq real) ((power_power_real zero_zero_real) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real) of role axiom named fact_9_zero__power2 % 0.35/0.52 A new axiom: (((eq real) ((power_power_real zero_zero_real) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real) % 0.35/0.52 FOF formula (forall (A_86:int), ((iff (((eq int) ((power_power_int A_86) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)) (((eq int) A_86) zero_zero_int))) of role axiom named fact_10_zero__eq__power2 % 0.35/0.52 A new axiom: (forall (A_86:int), ((iff (((eq int) ((power_power_int A_86) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)) (((eq int) A_86) zero_zero_int))) % 0.35/0.52 FOF formula (forall (A_86:real), ((iff (((eq real) ((power_power_real A_86) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)) (((eq real) A_86) zero_zero_real))) of role axiom named fact_11_zero__eq__power2 % 0.35/0.52 A new axiom: (forall (A_86:real), ((iff (((eq real) ((power_power_real A_86) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)) (((eq real) A_86) zero_zero_real))) % 0.35/0.52 FOF formula (forall (W_11:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_11))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_11)))) of role axiom named fact_12_add__special_I2_J % 0.36/0.53 A new axiom: (forall (W_11:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_11))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_11)))) % 0.36/0.53 FOF formula (forall (W_11:int), (((eq real) ((plus_plus_real one_one_real) (number267125858f_real W_11))) (number267125858f_real ((plus_plus_int (bit1 pls)) W_11)))) of role axiom named fact_13_add__special_I2_J % 0.36/0.53 A new axiom: (forall (W_11:int), (((eq real) ((plus_plus_real one_one_real) (number267125858f_real W_11))) (number267125858f_real ((plus_plus_int (bit1 pls)) W_11)))) % 0.36/0.53 FOF formula (forall (V_11:int), (((eq int) ((plus_plus_int (number_number_of_int V_11)) one_one_int)) (number_number_of_int ((plus_plus_int V_11) (bit1 pls))))) of role axiom named fact_14_add__special_I3_J % 0.36/0.53 A new axiom: (forall (V_11:int), (((eq int) ((plus_plus_int (number_number_of_int V_11)) one_one_int)) (number_number_of_int ((plus_plus_int V_11) (bit1 pls))))) % 0.36/0.53 FOF formula (forall (V_11:int), (((eq real) ((plus_plus_real (number267125858f_real V_11)) one_one_real)) (number267125858f_real ((plus_plus_int V_11) (bit1 pls))))) of role axiom named fact_15_add__special_I3_J % 0.36/0.53 A new axiom: (forall (V_11:int), (((eq real) ((plus_plus_real (number267125858f_real V_11)) one_one_real)) (number267125858f_real ((plus_plus_int V_11) (bit1 pls))))) % 0.36/0.53 FOF formula (((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))) of role axiom named fact_16_one__add__one__is__two % 0.36/0.53 A new axiom: (((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))) % 0.36/0.53 FOF formula (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))) of role axiom named fact_17_one__add__one__is__two % 0.36/0.53 A new axiom: (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))) % 0.36/0.53 FOF formula (((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))) of role axiom named fact_18_semiring__one__add__one__is__two % 0.36/0.53 A new axiom: (((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))) % 0.36/0.53 FOF formula (((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))) of role axiom named fact_19_semiring__one__add__one__is__two % 0.36/0.53 A new axiom: (((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))) % 0.36/0.53 FOF formula (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))) of role axiom named fact_20_semiring__one__add__one__is__two % 0.36/0.53 A new axiom: (((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))) % 0.36/0.53 FOF formula (forall (X:int), (((eq int) ((power_power_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int X) (number_number_of_nat (bit0 (bit0 (bit1 pls))))))) of role axiom named fact_21_quartic__square__square % 0.36/0.53 A new axiom: (forall (X:int), (((eq int) ((power_power_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int X) (number_number_of_nat (bit0 (bit0 (bit1 pls))))))) % 0.36/0.53 FOF formula (forall (W_10:int), ((and ((((eq nat) (number_number_of_nat W_10)) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_10))) one_one_int))) ((not (((eq nat) (number_number_of_nat W_10)) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_10))) zero_zero_int)))) of role axiom named fact_22_power__0__left__number__of % 0.36/0.53 A new axiom: (forall (W_10:int), ((and ((((eq nat) (number_number_of_nat W_10)) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_10))) one_one_int))) ((not (((eq nat) (number_number_of_nat W_10)) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_10))) zero_zero_int)))) % 0.36/0.55 FOF formula (forall (W_10:int), ((and ((((eq nat) (number_number_of_nat W_10)) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_10))) one_one_nat))) ((not (((eq nat) (number_number_of_nat W_10)) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_10))) zero_zero_nat)))) of role axiom named fact_23_power__0__left__number__of % 0.36/0.55 A new axiom: (forall (W_10:int), ((and ((((eq nat) (number_number_of_nat W_10)) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_10))) one_one_nat))) ((not (((eq nat) (number_number_of_nat W_10)) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_10))) zero_zero_nat)))) % 0.36/0.55 FOF formula (forall (W_10:int), ((and ((((eq nat) (number_number_of_nat W_10)) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_10))) one_one_real))) ((not (((eq nat) (number_number_of_nat W_10)) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_10))) zero_zero_real)))) of role axiom named fact_24_power__0__left__number__of % 0.36/0.55 A new axiom: (forall (W_10:int), ((and ((((eq nat) (number_number_of_nat W_10)) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_10))) one_one_real))) ((not (((eq nat) (number_number_of_nat W_10)) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_10))) zero_zero_real)))) % 0.36/0.55 FOF formula (((eq int) one_one_int) (number_number_of_int (bit1 pls))) of role axiom named fact_25_semiring__norm_I110_J % 0.36/0.55 A new axiom: (((eq int) one_one_int) (number_number_of_int (bit1 pls))) % 0.36/0.55 FOF formula (((eq real) one_one_real) (number267125858f_real (bit1 pls))) of role axiom named fact_26_semiring__norm_I110_J % 0.36/0.55 A new axiom: (((eq real) one_one_real) (number267125858f_real (bit1 pls))) % 0.36/0.55 FOF formula (((eq int) (number_number_of_int (bit1 pls))) one_one_int) of role axiom named fact_27_numeral__1__eq__1 % 0.36/0.55 A new axiom: (((eq int) (number_number_of_int (bit1 pls))) one_one_int) % 0.36/0.55 FOF formula (((eq real) (number267125858f_real (bit1 pls))) one_one_real) of role axiom named fact_28_numeral__1__eq__1 % 0.36/0.55 A new axiom: (((eq real) (number267125858f_real (bit1 pls))) one_one_real) % 0.36/0.55 FOF formula ((ord_less_nat zero_zero_nat) n) of role axiom named fact_29_n0 % 0.36/0.55 A new axiom: ((ord_less_nat zero_zero_nat) n) % 0.36/0.55 FOF formula (forall (X:int) (Y:int), ((or ((or ((ord_less_int X) Y)) (((eq int) X) Y))) ((ord_less_int Y) X))) of role axiom named fact_30_zless__linear % 0.36/0.55 A new axiom: (forall (X:int) (Y:int), ((or ((or ((ord_less_int X) Y)) (((eq int) X) Y))) ((ord_less_int Y) X))) % 0.36/0.55 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_int K) L))) of role axiom named fact_31_less__number__of__int__code % 0.36/0.55 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))) % 0.36/0.55 FOF formula (forall (V_1:int) (W:int), (((eq int) ((plus_plus_int (number_number_of_int V_1)) (number_number_of_int W))) (number_number_of_int ((plus_plus_int V_1) W)))) of role axiom named fact_32_plus__numeral__code_I9_J % 0.36/0.55 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)))) % 0.36/0.55 FOF formula (forall (X_32:int) (Y_26:int), ((iff ((ord_less_int (number_number_of_int X_32)) (number_number_of_int Y_26))) ((ord_less_int X_32) Y_26))) of role axiom named fact_33_less__number__of % 0.36/0.55 A new axiom: (forall (X_32:int) (Y_26:int), ((iff ((ord_less_int (number_number_of_int X_32)) (number_number_of_int Y_26))) ((ord_less_int X_32) Y_26))) % 0.36/0.55 FOF formula (forall (X_32:int) (Y_26:int), ((iff ((ord_less_real (number267125858f_real X_32)) (number267125858f_real Y_26))) ((ord_less_int X_32) Y_26))) of role axiom named fact_34_less__number__of % 0.36/0.55 A new axiom: (forall (X_32:int) (Y_26:int), ((iff ((ord_less_real (number267125858f_real X_32)) (number267125858f_real Y_26))) ((ord_less_int X_32) Y_26))) % 0.36/0.56 FOF formula (((eq int) zero_zero_int) (number_number_of_int pls)) of role axiom named fact_35_zero__is__num__zero % 0.36/0.56 A new axiom: (((eq int) zero_zero_int) (number_number_of_int pls)) % 0.36/0.56 FOF formula (forall (M:nat) (N:nat), (((eq int) ((power_power_int (semiri1621563631at_int M)) N)) (semiri1621563631at_int ((power_power_nat M) N)))) of role axiom named fact_36_zpower__int % 0.36/0.56 A new axiom: (forall (M:nat) (N:nat), (((eq int) ((power_power_int (semiri1621563631at_int M)) N)) (semiri1621563631at_int ((power_power_nat M) N)))) % 0.36/0.56 FOF formula (forall (M:nat) (N:nat), (((eq int) (semiri1621563631at_int ((power_power_nat M) N))) ((power_power_int (semiri1621563631at_int M)) N))) of role axiom named fact_37_int__power % 0.36/0.56 A new axiom: (forall (M:nat) (N:nat), (((eq int) (semiri1621563631at_int ((power_power_nat M) N))) ((power_power_int (semiri1621563631at_int M)) N))) % 0.36/0.56 FOF formula (forall (M:nat) (N:nat) (Z_2:int), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) ((plus_plus_int (semiri1621563631at_int N)) Z_2))) ((plus_plus_int (semiri1621563631at_int ((plus_plus_nat M) N))) Z_2))) of role axiom named fact_38_zadd__int__left % 0.36/0.56 A new axiom: (forall (M:nat) (N:nat) (Z_2:int), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) ((plus_plus_int (semiri1621563631at_int N)) Z_2))) ((plus_plus_int (semiri1621563631at_int ((plus_plus_nat M) N))) Z_2))) % 0.36/0.56 FOF formula (forall (M:nat) (N:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((plus_plus_nat M) N)))) of role axiom named fact_39_zadd__int % 0.36/0.56 A new axiom: (forall (M:nat) (N:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((plus_plus_nat M) N)))) % 0.36/0.56 FOF formula (((eq int) (semiri1621563631at_int one_one_nat)) one_one_int) of role axiom named fact_40_int__1 % 0.36/0.56 A new axiom: (((eq int) (semiri1621563631at_int one_one_nat)) one_one_int) % 0.36/0.56 FOF formula (((eq nat) (number_number_of_nat pls)) zero_zero_nat) of role axiom named fact_41_nat__number__of__Pls % 0.36/0.56 A new axiom: (((eq nat) (number_number_of_nat pls)) zero_zero_nat) % 0.36/0.56 FOF formula (((eq nat) zero_zero_nat) (number_number_of_nat pls)) of role axiom named fact_42_semiring__norm_I113_J % 0.36/0.56 A new axiom: (((eq nat) zero_zero_nat) (number_number_of_nat pls)) % 0.36/0.56 FOF formula (forall (N:nat), ((iff (((eq int) (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat))) of role axiom named fact_43_int__eq__0__conv % 0.36/0.56 A new axiom: (forall (N:nat), ((iff (((eq int) (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat))) % 0.36/0.56 FOF formula (((eq int) (semiri1621563631at_int zero_zero_nat)) zero_zero_int) of role axiom named fact_44_int__0 % 0.36/0.56 A new axiom: (((eq int) (semiri1621563631at_int zero_zero_nat)) zero_zero_int) % 0.36/0.56 FOF formula (((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))) of role axiom named fact_45_nat__1__add__1 % 0.36/0.56 A new axiom: (((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))) % 0.36/0.56 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2))) of role axiom named fact_46_less__int__code_I16_J % 0.36/0.56 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2))) % 0.36/0.56 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L))) of role axiom named fact_47_rel__simps_I17_J % 0.36/0.56 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L))) % 0.36/0.56 FOF formula (((ord_less_int pls) pls)->False) of role axiom named fact_48_rel__simps_I2_J % 0.36/0.56 A new axiom: (((ord_less_int pls) pls)->False) % 0.36/0.56 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit0 K2))) ((ord_less_int K1) K2))) of role axiom named fact_49_less__int__code_I13_J % 0.36/0.56 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit0 K2))) ((ord_less_int K1) K2))) % 0.36/0.56 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit0 L))) ((ord_less_int K) L))) of role axiom named fact_50_rel__simps_I14_J % 0.36/0.56 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit0 L))) ((ord_less_int K) L))) % 0.36/0.58 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_51_zadd__strict__right__mono % 0.36/0.58 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)))) % 0.36/0.58 FOF formula (forall (V: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))) (number_number_of_nat V)))) ((((ord_less_int V_1) pls)->False)->((and (((ord_less_int V) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) (number_number_of_nat V))) (number_number_of_nat V_1)))) ((((ord_less_int V) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) (number_number_of_nat V))) (number_number_of_nat ((plus_plus_int V_1) V)))))))) of role axiom named fact_52_add__nat__number__of % 0.36/0.58 A new axiom: (forall (V: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))) (number_number_of_nat V)))) ((((ord_less_int V_1) pls)->False)->((and (((ord_less_int V) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) (number_number_of_nat V))) (number_number_of_nat V_1)))) ((((ord_less_int V) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) (number_number_of_nat V))) (number_number_of_nat ((plus_plus_int V_1) V)))))))) % 0.36/0.58 FOF formula (((eq int) one_one_int) (number_number_of_int (bit1 pls))) of role axiom named fact_53_one__is__num__one % 0.36/0.58 A new axiom: (((eq int) one_one_int) (number_number_of_int (bit1 pls))) % 0.36/0.58 FOF formula (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat) of role axiom named fact_54_nat__numeral__1__eq__1 % 0.36/0.58 A new axiom: (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat) % 0.36/0.58 FOF formula (((eq nat) one_one_nat) (number_number_of_nat (bit1 pls))) of role axiom named fact_55_Numeral1__eq1__nat % 0.36/0.58 A new axiom: (((eq nat) one_one_nat) (number_number_of_nat (bit1 pls))) % 0.36/0.58 FOF formula (forall (X_31:int) (Y_25:int), ((iff (((eq int) (number_number_of_int X_31)) (number_number_of_int Y_25))) (((eq int) X_31) Y_25))) of role axiom named fact_56_eq__number__of % 0.36/0.58 A new axiom: (forall (X_31:int) (Y_25:int), ((iff (((eq int) (number_number_of_int X_31)) (number_number_of_int Y_25))) (((eq int) X_31) Y_25))) % 0.36/0.58 FOF formula (forall (X_31:int) (Y_25:int), ((iff (((eq real) (number267125858f_real X_31)) (number267125858f_real Y_25))) (((eq int) X_31) Y_25))) of role axiom named fact_57_eq__number__of % 0.36/0.58 A new axiom: (forall (X_31:int) (Y_25:int), ((iff (((eq real) (number267125858f_real X_31)) (number267125858f_real Y_25))) (((eq int) X_31) Y_25))) % 0.36/0.58 FOF formula (forall (W_9:int) (X_30:nat), ((iff (((eq nat) (number_number_of_nat W_9)) X_30)) (((eq nat) X_30) (number_number_of_nat W_9)))) of role axiom named fact_58_number__of__reorient % 0.36/0.58 A new axiom: (forall (W_9:int) (X_30:nat), ((iff (((eq nat) (number_number_of_nat W_9)) X_30)) (((eq nat) X_30) (number_number_of_nat W_9)))) % 0.36/0.58 FOF formula (forall (W_9:int) (X_30:int), ((iff (((eq int) (number_number_of_int W_9)) X_30)) (((eq int) X_30) (number_number_of_int W_9)))) of role axiom named fact_59_number__of__reorient % 0.36/0.58 A new axiom: (forall (W_9:int) (X_30:int), ((iff (((eq int) (number_number_of_int W_9)) X_30)) (((eq int) X_30) (number_number_of_int W_9)))) % 0.36/0.58 FOF formula (forall (W_9:int) (X_30:real), ((iff (((eq real) (number267125858f_real W_9)) X_30)) (((eq real) X_30) (number267125858f_real W_9)))) of role axiom named fact_60_number__of__reorient % 0.36/0.58 A new axiom: (forall (W_9:int) (X_30:real), ((iff (((eq real) (number267125858f_real W_9)) X_30)) (((eq real) X_30) (number267125858f_real W_9)))) % 0.36/0.58 FOF formula (forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L))) of role axiom named fact_61_rel__simps_I51_J % 0.36/0.58 A new axiom: (forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L))) % 0.36/0.58 FOF formula (forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L))) of role axiom named fact_62_rel__simps_I48_J % 0.36/0.60 A new axiom: (forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L))) % 0.36/0.60 FOF formula (forall (A_85:int), ((iff ((ord_less_int ((plus_plus_int A_85) A_85)) zero_zero_int)) ((ord_less_int A_85) zero_zero_int))) of role axiom named fact_63_even__less__0__iff % 0.36/0.60 A new axiom: (forall (A_85:int), ((iff ((ord_less_int ((plus_plus_int A_85) A_85)) zero_zero_int)) ((ord_less_int A_85) zero_zero_int))) % 0.36/0.60 FOF formula (forall (A_85:real), ((iff ((ord_less_real ((plus_plus_real A_85) A_85)) zero_zero_real)) ((ord_less_real A_85) zero_zero_real))) of role axiom named fact_64_even__less__0__iff % 0.36/0.60 A new axiom: (forall (A_85:real), ((iff ((ord_less_real ((plus_plus_real A_85) A_85)) zero_zero_real)) ((ord_less_real A_85) zero_zero_real))) % 0.36/0.60 FOF formula (forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((plus_plus_int ((plus_plus_int Z1) Z2)) Z3)) ((plus_plus_int Z1) ((plus_plus_int Z2) Z3)))) of role axiom named fact_65_zadd__assoc % 0.36/0.60 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)))) % 0.36/0.60 FOF formula (forall (X:int) (Y:int) (Z_2:int), (((eq int) ((plus_plus_int X) ((plus_plus_int Y) Z_2))) ((plus_plus_int Y) ((plus_plus_int X) Z_2)))) of role axiom named fact_66_zadd__left__commute % 0.36/0.60 A new axiom: (forall (X:int) (Y:int) (Z_2:int), (((eq int) ((plus_plus_int X) ((plus_plus_int Y) Z_2))) ((plus_plus_int Y) ((plus_plus_int X) Z_2)))) % 0.36/0.60 FOF formula (forall (Z_2:int) (W:int), (((eq int) ((plus_plus_int Z_2) W)) ((plus_plus_int W) Z_2))) of role axiom named fact_67_zadd__commute % 0.36/0.60 A new axiom: (forall (Z_2:int) (W:int), (((eq int) ((plus_plus_int Z_2) W)) ((plus_plus_int W) Z_2))) % 0.36/0.60 FOF formula (forall (M:nat) (N:nat), ((iff (((eq int) (semiri1621563631at_int M)) (semiri1621563631at_int N))) (((eq nat) M) N))) of role axiom named fact_68_int__int__eq % 0.36/0.60 A new axiom: (forall (M:nat) (N:nat), ((iff (((eq int) (semiri1621563631at_int M)) (semiri1621563631at_int N))) (((eq nat) M) N))) % 0.36/0.60 FOF formula (forall (X_29:int), ((iff ((ord_less_int (number_number_of_int X_29)) zero_zero_int)) ((ord_less_int X_29) pls))) of role axiom named fact_69_less__special_I3_J % 0.36/0.60 A new axiom: (forall (X_29:int), ((iff ((ord_less_int (number_number_of_int X_29)) zero_zero_int)) ((ord_less_int X_29) pls))) % 0.36/0.60 FOF formula (forall (X_29:int), ((iff ((ord_less_real (number267125858f_real X_29)) zero_zero_real)) ((ord_less_int X_29) pls))) of role axiom named fact_70_less__special_I3_J % 0.36/0.60 A new axiom: (forall (X_29:int), ((iff ((ord_less_real (number267125858f_real X_29)) zero_zero_real)) ((ord_less_int X_29) pls))) % 0.36/0.60 FOF formula (forall (Y_24:int), ((iff ((ord_less_int zero_zero_int) (number_number_of_int Y_24))) ((ord_less_int pls) Y_24))) of role axiom named fact_71_less__special_I1_J % 0.36/0.60 A new axiom: (forall (Y_24:int), ((iff ((ord_less_int zero_zero_int) (number_number_of_int Y_24))) ((ord_less_int pls) Y_24))) % 0.36/0.60 FOF formula (forall (Y_24:int), ((iff ((ord_less_real zero_zero_real) (number267125858f_real Y_24))) ((ord_less_int pls) Y_24))) of role axiom named fact_72_less__special_I1_J % 0.36/0.60 A new axiom: (forall (Y_24:int), ((iff ((ord_less_real zero_zero_real) (number267125858f_real Y_24))) ((ord_less_int pls) Y_24))) % 0.36/0.60 FOF formula (forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_73_rel__simps_I12_J % 0.36/0.60 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls))) % 0.36/0.60 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2))) of role axiom named fact_74_less__int__code_I15_J % 0.36/0.60 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2))) % 0.36/0.60 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))) of role axiom named fact_75_rel__simps_I16_J % 0.36/0.60 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))) % 0.36/0.60 FOF formula (forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_76_rel__simps_I10_J % 0.45/0.61 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls))) % 0.45/0.61 FOF formula (forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K))) of role axiom named fact_77_rel__simps_I4_J % 0.45/0.61 A new axiom: (forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K))) % 0.45/0.61 FOF formula (forall (W:int), ((iff ((ord_less_int (bit1 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int))) of role axiom named fact_78_bin__less__0__simps_I4_J % 0.45/0.61 A new axiom: (forall (W:int), ((iff ((ord_less_int (bit1 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int))) % 0.45/0.61 FOF formula (((ord_less_int pls) zero_zero_int)->False) of role axiom named fact_79_bin__less__0__simps_I1_J % 0.45/0.61 A new axiom: (((ord_less_int pls) zero_zero_int)->False) % 0.45/0.61 FOF formula (forall (W:int), ((iff ((ord_less_int (bit0 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int))) of role axiom named fact_80_bin__less__0__simps_I3_J % 0.45/0.61 A new axiom: (forall (W:int), ((iff ((ord_less_int (bit0 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int))) % 0.45/0.61 FOF formula ((ord_less_int zero_zero_int) one_one_int) of role axiom named fact_81_int__0__less__1 % 0.45/0.61 A new axiom: ((ord_less_int zero_zero_int) one_one_int) % 0.45/0.61 FOF formula (forall (W:int) (Z_2:int), ((iff ((ord_less_int W) ((plus_plus_int Z_2) one_one_int))) ((or ((ord_less_int W) Z_2)) (((eq int) W) Z_2)))) of role axiom named fact_82_zless__add1__eq % 0.45/0.61 A new axiom: (forall (W:int) (Z_2:int), ((iff ((ord_less_int W) ((plus_plus_int Z_2) one_one_int))) ((or ((ord_less_int W) Z_2)) (((eq int) W) Z_2)))) % 0.45/0.61 FOF formula (forall (K:nat), (((ord_less_int (semiri1621563631at_int K)) zero_zero_int)->False)) of role axiom named fact_83_int__less__0__conv % 0.45/0.61 A new axiom: (forall (K:nat), (((ord_less_int (semiri1621563631at_int K)) zero_zero_int)->False)) % 0.45/0.61 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_84_less__special_I4_J % 0.45/0.61 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)))) % 0.45/0.61 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_85_less__special_I4_J % 0.45/0.61 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)))) % 0.45/0.61 FOF formula (forall (Y_23:int), ((iff ((ord_less_int one_one_int) (number_number_of_int Y_23))) ((ord_less_int (bit1 pls)) Y_23))) of role axiom named fact_86_less__special_I2_J % 0.45/0.61 A new axiom: (forall (Y_23:int), ((iff ((ord_less_int one_one_int) (number_number_of_int Y_23))) ((ord_less_int (bit1 pls)) Y_23))) % 0.45/0.61 FOF formula (forall (Y_23:int), ((iff ((ord_less_real one_one_real) (number267125858f_real Y_23))) ((ord_less_int (bit1 pls)) Y_23))) of role axiom named fact_87_less__special_I2_J % 0.45/0.61 A new axiom: (forall (Y_23:int), ((iff ((ord_less_real one_one_real) (number267125858f_real Y_23))) ((ord_less_int (bit1 pls)) Y_23))) % 0.45/0.61 FOF formula (forall (Z_2:int), ((iff ((ord_less_int ((plus_plus_int ((plus_plus_int one_one_int) Z_2)) Z_2)) zero_zero_int)) ((ord_less_int Z_2) zero_zero_int))) of role axiom named fact_88_odd__less__0 % 0.45/0.61 A new axiom: (forall (Z_2:int), ((iff ((ord_less_int ((plus_plus_int ((plus_plus_int one_one_int) Z_2)) Z_2)) zero_zero_int)) ((ord_less_int Z_2) zero_zero_int))) % 0.45/0.61 FOF formula (forall (A_84:int), ((iff (((eq int) ((plus_plus_int A_84) A_84)) zero_zero_int)) (((eq int) A_84) zero_zero_int))) of role axiom named fact_89_double__eq__0__iff % 0.45/0.61 A new axiom: (forall (A_84:int), ((iff (((eq int) ((plus_plus_int A_84) A_84)) zero_zero_int)) (((eq int) A_84) zero_zero_int))) % 0.45/0.61 FOF formula (forall (A_84:real), ((iff (((eq real) ((plus_plus_real A_84) A_84)) zero_zero_real)) (((eq real) A_84) zero_zero_real))) of role axiom named fact_90_double__eq__0__iff % 0.45/0.61 A new axiom: (forall (A_84:real), ((iff (((eq real) ((plus_plus_real A_84) A_84)) zero_zero_real)) (((eq real) A_84) zero_zero_real))) % 0.45/0.61 FOF formula (forall (K:int), (not (((eq int) (bit1 K)) pls))) of role axiom named fact_91_rel__simps_I46_J % 0.45/0.63 A new axiom: (forall (K:int), (not (((eq int) (bit1 K)) pls))) % 0.45/0.63 FOF formula (forall (L:int), (not (((eq int) pls) (bit1 L)))) of role axiom named fact_92_rel__simps_I39_J % 0.45/0.63 A new axiom: (forall (L:int), (not (((eq int) pls) (bit1 L)))) % 0.45/0.63 FOF formula (forall (K:int) (L:int), (not (((eq int) (bit1 K)) (bit0 L)))) of role axiom named fact_93_rel__simps_I50_J % 0.45/0.63 A new axiom: (forall (K:int) (L:int), (not (((eq int) (bit1 K)) (bit0 L)))) % 0.45/0.63 FOF formula (forall (K:int) (L:int), (not (((eq int) (bit0 K)) (bit1 L)))) of role axiom named fact_94_rel__simps_I49_J % 0.45/0.63 A new axiom: (forall (K:int) (L:int), (not (((eq int) (bit0 K)) (bit1 L)))) % 0.45/0.63 FOF formula (forall (K:int), ((iff (((eq int) (bit0 K)) pls)) (((eq int) K) pls))) of role axiom named fact_95_rel__simps_I44_J % 0.45/0.63 A new axiom: (forall (K:int), ((iff (((eq int) (bit0 K)) pls)) (((eq int) K) pls))) % 0.45/0.63 FOF formula (forall (L:int), ((iff (((eq int) pls) (bit0 L))) (((eq int) pls) L))) of role axiom named fact_96_rel__simps_I38_J % 0.45/0.63 A new axiom: (forall (L:int), ((iff (((eq int) pls) (bit0 L))) (((eq int) pls) L))) % 0.45/0.63 FOF formula (((eq int) (bit0 pls)) pls) of role axiom named fact_97_Bit0__Pls % 0.45/0.63 A new axiom: (((eq int) (bit0 pls)) pls) % 0.45/0.63 FOF formula (((eq int) pls) zero_zero_int) of role axiom named fact_98_Pls__def % 0.45/0.63 A new axiom: (((eq int) pls) zero_zero_int) % 0.45/0.63 FOF formula (not (((eq int) zero_zero_int) one_one_int)) of role axiom named fact_99_int__0__neq__1 % 0.45/0.63 A new axiom: (not (((eq int) zero_zero_int) one_one_int)) % 0.45/0.63 FOF formula (forall (K:int), (((eq int) ((plus_plus_int K) pls)) K)) of role axiom named fact_100_add__Pls__right % 0.45/0.63 A new axiom: (forall (K:int), (((eq int) ((plus_plus_int K) pls)) K)) % 0.45/0.63 FOF formula (forall (K:int), (((eq int) ((plus_plus_int pls) K)) K)) of role axiom named fact_101_add__Pls % 0.45/0.63 A new axiom: (forall (K:int), (((eq int) ((plus_plus_int pls) K)) K)) % 0.45/0.63 FOF formula (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit0 L))) (bit0 ((plus_plus_int K) L)))) of role axiom named fact_102_add__Bit0__Bit0 % 0.45/0.63 A new axiom: (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit0 L))) (bit0 ((plus_plus_int K) L)))) % 0.45/0.63 FOF formula (forall (K:int), (((eq int) (bit0 K)) ((plus_plus_int K) K))) of role axiom named fact_103_Bit0__def % 0.45/0.63 A new axiom: (forall (K:int), (((eq int) (bit0 K)) ((plus_plus_int K) K))) % 0.45/0.63 FOF formula (forall (Z_2:int), (((eq int) ((plus_plus_int Z_2) zero_zero_int)) Z_2)) of role axiom named fact_104_zadd__0__right % 0.45/0.63 A new axiom: (forall (Z_2:int), (((eq int) ((plus_plus_int Z_2) zero_zero_int)) Z_2)) % 0.45/0.63 FOF formula (forall (Z_2:int), (((eq int) ((plus_plus_int zero_zero_int) Z_2)) Z_2)) of role axiom named fact_105_zadd__0 % 0.45/0.63 A new axiom: (forall (Z_2:int), (((eq int) ((plus_plus_int zero_zero_int) Z_2)) Z_2)) % 0.45/0.63 FOF formula (((eq int) (number_number_of_int pls)) zero_zero_int) of role axiom named fact_106_semiring__numeral__0__eq__0 % 0.45/0.63 A new axiom: (((eq int) (number_number_of_int pls)) zero_zero_int) % 0.45/0.63 FOF formula (((eq nat) (number_number_of_nat pls)) zero_zero_nat) of role axiom named fact_107_semiring__numeral__0__eq__0 % 0.45/0.63 A new axiom: (((eq nat) (number_number_of_nat pls)) zero_zero_nat) % 0.45/0.63 FOF formula (((eq real) (number267125858f_real pls)) zero_zero_real) of role axiom named fact_108_semiring__numeral__0__eq__0 % 0.45/0.63 A new axiom: (((eq real) (number267125858f_real pls)) zero_zero_real) % 0.45/0.63 FOF formula (((eq int) (number_number_of_int pls)) zero_zero_int) of role axiom named fact_109_number__of__Pls % 0.45/0.63 A new axiom: (((eq int) (number_number_of_int pls)) zero_zero_int) % 0.45/0.63 FOF formula (((eq real) (number267125858f_real pls)) zero_zero_real) of role axiom named fact_110_number__of__Pls % 0.45/0.63 A new axiom: (((eq real) (number267125858f_real pls)) zero_zero_real) % 0.45/0.63 FOF formula (((eq int) zero_zero_int) (number_number_of_int pls)) of role axiom named fact_111_semiring__norm_I112_J % 0.45/0.63 A new axiom: (((eq int) zero_zero_int) (number_number_of_int pls)) % 0.45/0.63 FOF formula (((eq real) zero_zero_real) (number267125858f_real pls)) of role axiom named fact_112_semiring__norm_I112_J % 0.45/0.63 A new axiom: (((eq real) zero_zero_real) (number267125858f_real pls)) % 0.45/0.64 FOF formula (forall (A_83:int), (((eq int) ((plus_plus_int (number_number_of_int pls)) A_83)) A_83)) of role axiom named fact_113_add__numeral__0 % 0.45/0.64 A new axiom: (forall (A_83:int), (((eq int) ((plus_plus_int (number_number_of_int pls)) A_83)) A_83)) % 0.45/0.64 FOF formula (forall (A_83:real), (((eq real) ((plus_plus_real (number267125858f_real pls)) A_83)) A_83)) of role axiom named fact_114_add__numeral__0 % 0.45/0.64 A new axiom: (forall (A_83:real), (((eq real) ((plus_plus_real (number267125858f_real pls)) A_83)) A_83)) % 0.45/0.64 FOF formula (forall (A_82:int), (((eq int) ((plus_plus_int A_82) (number_number_of_int pls))) A_82)) of role axiom named fact_115_add__numeral__0__right % 0.45/0.64 A new axiom: (forall (A_82:int), (((eq int) ((plus_plus_int A_82) (number_number_of_int pls))) A_82)) % 0.45/0.64 FOF formula (forall (A_82:real), (((eq real) ((plus_plus_real A_82) (number267125858f_real pls))) A_82)) of role axiom named fact_116_add__numeral__0__right % 0.45/0.64 A new axiom: (forall (A_82:real), (((eq real) ((plus_plus_real A_82) (number267125858f_real pls))) A_82)) % 0.45/0.64 FOF formula (forall (A_81:int) (W_8:int), ((iff (((eq int) ((power_power_int A_81) (number_number_of_nat W_8))) zero_zero_int)) ((and (((eq int) A_81) zero_zero_int)) (not (((eq nat) (number_number_of_nat W_8)) zero_zero_nat))))) of role axiom named fact_117_power__eq__0__iff__number__of % 0.45/0.64 A new axiom: (forall (A_81:int) (W_8:int), ((iff (((eq int) ((power_power_int A_81) (number_number_of_nat W_8))) zero_zero_int)) ((and (((eq int) A_81) zero_zero_int)) (not (((eq nat) (number_number_of_nat W_8)) zero_zero_nat))))) % 0.45/0.64 FOF formula (forall (A_81:nat) (W_8:int), ((iff (((eq nat) ((power_power_nat A_81) (number_number_of_nat W_8))) zero_zero_nat)) ((and (((eq nat) A_81) zero_zero_nat)) (not (((eq nat) (number_number_of_nat W_8)) zero_zero_nat))))) of role axiom named fact_118_power__eq__0__iff__number__of % 0.45/0.64 A new axiom: (forall (A_81:nat) (W_8:int), ((iff (((eq nat) ((power_power_nat A_81) (number_number_of_nat W_8))) zero_zero_nat)) ((and (((eq nat) A_81) zero_zero_nat)) (not (((eq nat) (number_number_of_nat W_8)) zero_zero_nat))))) % 0.45/0.64 FOF formula (forall (A_81:real) (W_8:int), ((iff (((eq real) ((power_power_real A_81) (number_number_of_nat W_8))) zero_zero_real)) ((and (((eq real) A_81) zero_zero_real)) (not (((eq nat) (number_number_of_nat W_8)) zero_zero_nat))))) of role axiom named fact_119_power__eq__0__iff__number__of % 0.45/0.64 A new axiom: (forall (A_81:real) (W_8:int), ((iff (((eq real) ((power_power_real A_81) (number_number_of_nat W_8))) zero_zero_real)) ((and (((eq real) A_81) zero_zero_real)) (not (((eq nat) (number_number_of_nat W_8)) zero_zero_nat))))) % 0.45/0.64 FOF formula (forall (V_10:int) (W_7:int) (Z_4:int), (((eq int) ((plus_plus_int (number_number_of_int V_10)) ((plus_plus_int (number_number_of_int W_7)) Z_4))) ((plus_plus_int (number_number_of_int ((plus_plus_int V_10) W_7))) Z_4))) of role axiom named fact_120_add__number__of__left % 0.45/0.64 A new axiom: (forall (V_10:int) (W_7:int) (Z_4:int), (((eq int) ((plus_plus_int (number_number_of_int V_10)) ((plus_plus_int (number_number_of_int W_7)) Z_4))) ((plus_plus_int (number_number_of_int ((plus_plus_int V_10) W_7))) Z_4))) % 0.45/0.64 FOF formula (forall (V_10:int) (W_7:int) (Z_4:real), (((eq real) ((plus_plus_real (number267125858f_real V_10)) ((plus_plus_real (number267125858f_real W_7)) Z_4))) ((plus_plus_real (number267125858f_real ((plus_plus_int V_10) W_7))) Z_4))) of role axiom named fact_121_add__number__of__left % 0.45/0.64 A new axiom: (forall (V_10:int) (W_7:int) (Z_4:real), (((eq real) ((plus_plus_real (number267125858f_real V_10)) ((plus_plus_real (number267125858f_real W_7)) Z_4))) ((plus_plus_real (number267125858f_real ((plus_plus_int V_10) W_7))) Z_4))) % 0.45/0.64 FOF formula (forall (V_9:int) (W_6:int), (((eq int) ((plus_plus_int (number_number_of_int V_9)) (number_number_of_int W_6))) (number_number_of_int ((plus_plus_int V_9) W_6)))) of role axiom named fact_122_add__number__of__eq % 0.45/0.64 A new axiom: (forall (V_9:int) (W_6:int), (((eq int) ((plus_plus_int (number_number_of_int V_9)) (number_number_of_int W_6))) (number_number_of_int ((plus_plus_int V_9) W_6)))) % 0.45/0.64 FOF formula (forall (V_9:int) (W_6:int), (((eq real) ((plus_plus_real (number267125858f_real V_9)) (number267125858f_real W_6))) (number267125858f_real ((plus_plus_int V_9) W_6)))) of role axiom named fact_123_add__number__of__eq % 0.45/0.66 A new axiom: (forall (V_9:int) (W_6:int), (((eq real) ((plus_plus_real (number267125858f_real V_9)) (number267125858f_real W_6))) (number267125858f_real ((plus_plus_int V_9) W_6)))) % 0.45/0.66 FOF formula (forall (V_8:int) (W_5:int), (((eq int) (number_number_of_int ((plus_plus_int V_8) W_5))) ((plus_plus_int (number_number_of_int V_8)) (number_number_of_int W_5)))) of role axiom named fact_124_number__of__add % 0.45/0.66 A new axiom: (forall (V_8:int) (W_5:int), (((eq int) (number_number_of_int ((plus_plus_int V_8) W_5))) ((plus_plus_int (number_number_of_int V_8)) (number_number_of_int W_5)))) % 0.45/0.66 FOF formula (forall (V_8:int) (W_5:int), (((eq real) (number267125858f_real ((plus_plus_int V_8) W_5))) ((plus_plus_real (number267125858f_real V_8)) (number267125858f_real W_5)))) of role axiom named fact_125_number__of__add % 0.45/0.66 A new axiom: (forall (V_8:int) (W_5:int), (((eq real) (number267125858f_real ((plus_plus_int V_8) W_5))) ((plus_plus_real (number267125858f_real V_8)) (number267125858f_real W_5)))) % 0.45/0.66 FOF formula (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit0 L))) (bit1 ((plus_plus_int K) L)))) of role axiom named fact_126_add__Bit1__Bit0 % 0.45/0.66 A new axiom: (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit0 L))) (bit1 ((plus_plus_int K) L)))) % 0.45/0.66 FOF formula (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit1 L))) (bit1 ((plus_plus_int K) L)))) of role axiom named fact_127_add__Bit0__Bit1 % 0.45/0.66 A new axiom: (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit1 L))) (bit1 ((plus_plus_int K) L)))) % 0.45/0.66 FOF formula (forall (K:int), (((eq int) (bit1 K)) ((plus_plus_int ((plus_plus_int one_one_int) K)) K))) of role axiom named fact_128_Bit1__def % 0.45/0.66 A new axiom: (forall (K:int), (((eq int) (bit1 K)) ((plus_plus_int ((plus_plus_int one_one_int) K)) K))) % 0.45/0.66 FOF formula (forall (Z_2:int), (not (((eq int) ((plus_plus_int ((plus_plus_int one_one_int) Z_2)) Z_2)) zero_zero_int))) of role axiom named fact_129_odd__nonzero % 0.45/0.66 A new axiom: (forall (Z_2:int), (not (((eq int) ((plus_plus_int ((plus_plus_int one_one_int) Z_2)) Z_2)) zero_zero_int))) % 0.45/0.66 FOF formula (forall (N_35:nat), (((eq nat) (number_number_of_nat (semiri1621563631at_int N_35))) (semiri984289939at_nat N_35))) of role axiom named fact_130_number__of__int % 0.45/0.66 A new axiom: (forall (N_35:nat), (((eq nat) (number_number_of_nat (semiri1621563631at_int N_35))) (semiri984289939at_nat N_35))) % 0.45/0.66 FOF formula (forall (N_35:nat), (((eq int) (number_number_of_int (semiri1621563631at_int N_35))) (semiri1621563631at_int N_35))) of role axiom named fact_131_number__of__int % 0.45/0.66 A new axiom: (forall (N_35:nat), (((eq int) (number_number_of_int (semiri1621563631at_int N_35))) (semiri1621563631at_int N_35))) % 0.45/0.66 FOF formula (forall (N_35:nat), (((eq real) (number267125858f_real (semiri1621563631at_int N_35))) (semiri132038758t_real N_35))) of role axiom named fact_132_number__of__int % 0.45/0.66 A new axiom: (forall (N_35:nat), (((eq real) (number267125858f_real (semiri1621563631at_int N_35))) (semiri132038758t_real N_35))) % 0.45/0.66 FOF formula (forall (A_80:int), ((iff ((ord_less_int zero_zero_int) ((power_power_int A_80) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq int) A_80) zero_zero_int)))) of role axiom named fact_133_zero__less__power2 % 0.45/0.66 A new axiom: (forall (A_80:int), ((iff ((ord_less_int zero_zero_int) ((power_power_int A_80) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq int) A_80) zero_zero_int)))) % 0.45/0.66 FOF formula (forall (A_80:real), ((iff ((ord_less_real zero_zero_real) ((power_power_real A_80) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq real) A_80) zero_zero_real)))) of role axiom named fact_134_zero__less__power2 % 0.45/0.66 A new axiom: (forall (A_80:real), ((iff ((ord_less_real zero_zero_real) ((power_power_real A_80) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq real) A_80) zero_zero_real)))) % 0.45/0.66 FOF formula (forall (A_79:int), (((ord_less_int ((power_power_int A_79) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)->False)) of role axiom named fact_135_power2__less__0 % 0.45/0.67 A new axiom: (forall (A_79:int), (((ord_less_int ((power_power_int A_79) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)->False)) % 0.45/0.67 FOF formula (forall (A_79:real), (((ord_less_real ((power_power_real A_79) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)->False)) of role axiom named fact_136_power2__less__0 % 0.45/0.67 A new axiom: (forall (A_79:real), (((ord_less_real ((power_power_real A_79) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)->False)) % 0.45/0.67 FOF formula (forall (X_27:int) (Y_22:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((power_power_int X_27) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_22) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq int) X_27) zero_zero_int))) (not (((eq int) Y_22) zero_zero_int))))) of role axiom named fact_137_sum__power2__gt__zero__iff % 0.45/0.67 A new axiom: (forall (X_27:int) (Y_22:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((power_power_int X_27) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_22) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq int) X_27) zero_zero_int))) (not (((eq int) Y_22) zero_zero_int))))) % 0.45/0.67 FOF formula (forall (X_27:real) (Y_22:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((power_power_real X_27) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_22) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq real) X_27) zero_zero_real))) (not (((eq real) Y_22) zero_zero_real))))) of role axiom named fact_138_sum__power2__gt__zero__iff % 0.45/0.67 A new axiom: (forall (X_27:real) (Y_22:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((power_power_real X_27) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_22) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq real) X_27) zero_zero_real))) (not (((eq real) Y_22) zero_zero_real))))) % 0.45/0.67 FOF formula (forall (X_26:int) (Y_21:int), (((ord_less_int ((plus_plus_int ((power_power_int X_26) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_21) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)->False)) of role axiom named fact_139_not__sum__power2__lt__zero % 0.45/0.67 A new axiom: (forall (X_26:int) (Y_21:int), (((ord_less_int ((plus_plus_int ((power_power_int X_26) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_21) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)->False)) % 0.45/0.67 FOF formula (forall (X_26:real) (Y_21:real), (((ord_less_real ((plus_plus_real ((power_power_real X_26) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_21) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)->False)) of role axiom named fact_140_not__sum__power2__lt__zero % 0.45/0.67 A new axiom: (forall (X_26:real) (Y_21:real), (((ord_less_real ((plus_plus_real ((power_power_real X_26) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_21) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)->False)) % 0.45/0.67 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_141_number__of__Bit0 % 0.45/0.67 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)))) % 0.45/0.67 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_142_number__of__Bit0 % 0.45/0.67 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)))) % 0.45/0.67 FOF formula (forall (W_3:int), (((eq int) (number_number_of_int (bit1 W_3))) ((plus_plus_int ((plus_plus_int one_one_int) (number_number_of_int W_3))) (number_number_of_int W_3)))) of role axiom named fact_143_number__of__Bit1 % 0.45/0.67 A new axiom: (forall (W_3:int), (((eq int) (number_number_of_int (bit1 W_3))) ((plus_plus_int ((plus_plus_int one_one_int) (number_number_of_int W_3))) (number_number_of_int W_3)))) % 0.52/0.69 FOF formula (forall (W_3:int), (((eq real) (number267125858f_real (bit1 W_3))) ((plus_plus_real ((plus_plus_real one_one_real) (number267125858f_real W_3))) (number267125858f_real W_3)))) of role axiom named fact_144_number__of__Bit1 % 0.52/0.69 A new axiom: (forall (W_3:int), (((eq real) (number267125858f_real (bit1 W_3))) ((plus_plus_real ((plus_plus_real one_one_real) (number267125858f_real W_3))) (number267125858f_real W_3)))) % 0.52/0.69 FOF formula (((eq int) (number_number_of_int (bit1 pls))) one_one_int) of role axiom named fact_145_semiring__numeral__1__eq__1 % 0.52/0.69 A new axiom: (((eq int) (number_number_of_int (bit1 pls))) one_one_int) % 0.52/0.69 FOF formula (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat) of role axiom named fact_146_semiring__numeral__1__eq__1 % 0.52/0.69 A new axiom: (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat) % 0.52/0.69 FOF formula (((eq real) (number267125858f_real (bit1 pls))) one_one_real) of role axiom named fact_147_semiring__numeral__1__eq__1 % 0.52/0.69 A new axiom: (((eq real) (number267125858f_real (bit1 pls))) one_one_real) % 0.52/0.69 FOF formula ((ord_less_int m1) ((plus_plus_int one_one_int) (semiri1621563631at_int n))) of role axiom named fact_148_mn % 0.52/0.69 A new axiom: ((ord_less_int m1) ((plus_plus_int one_one_int) (semiri1621563631at_int n))) % 0.52/0.69 FOF formula (forall (N_34:nat), ((ord_less_int (semiri1621563631at_int N_34)) ((power_power_int (number_number_of_int (bit0 (bit1 pls)))) N_34))) of role axiom named fact_149_of__nat__less__two__power % 0.52/0.69 A new axiom: (forall (N_34:nat), ((ord_less_int (semiri1621563631at_int N_34)) ((power_power_int (number_number_of_int (bit0 (bit1 pls)))) N_34))) % 0.52/0.69 FOF formula (forall (N_34:nat), ((ord_less_real (semiri132038758t_real N_34)) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N_34))) of role axiom named fact_150_of__nat__less__two__power % 0.52/0.69 A new axiom: (forall (N_34:nat), ((ord_less_real (semiri132038758t_real N_34)) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N_34))) % 0.52/0.69 FOF formula (((eq int) (number_number_of_int (bit0 (bit1 pls)))) (semiri1621563631at_int (number_number_of_nat (bit0 (bit1 pls))))) of role axiom named fact_151_transfer__int__nat__numerals_I3_J % 0.52/0.69 A new axiom: (((eq int) (number_number_of_int (bit0 (bit1 pls)))) (semiri1621563631at_int (number_number_of_nat (bit0 (bit1 pls))))) % 0.52/0.69 FOF formula (((eq int) (number_number_of_int (bit1 (bit1 pls)))) (semiri1621563631at_int (number_number_of_nat (bit1 (bit1 pls))))) of role axiom named fact_152_transfer__int__nat__numerals_I4_J % 0.52/0.69 A new axiom: (((eq int) (number_number_of_int (bit1 (bit1 pls)))) (semiri1621563631at_int (number_number_of_nat (bit1 (bit1 pls))))) % 0.52/0.69 FOF formula (forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real)))) of role axiom named fact_153_realpow__two__sum__zero__iff % 0.52/0.69 A new axiom: (forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real)))) % 0.52/0.69 FOF formula (forall (N_33:nat), ((iff ((ord_less_int zero_zero_int) (semiri1621563631at_int N_33))) ((ord_less_nat zero_zero_nat) N_33))) of role axiom named fact_154_of__nat__0__less__iff % 0.52/0.69 A new axiom: (forall (N_33:nat), ((iff ((ord_less_int zero_zero_int) (semiri1621563631at_int N_33))) ((ord_less_nat zero_zero_nat) N_33))) % 0.52/0.69 FOF formula (forall (N_33:nat), ((iff ((ord_less_nat zero_zero_nat) (semiri984289939at_nat N_33))) ((ord_less_nat zero_zero_nat) N_33))) of role axiom named fact_155_of__nat__0__less__iff % 0.52/0.69 A new axiom: (forall (N_33:nat), ((iff ((ord_less_nat zero_zero_nat) (semiri984289939at_nat N_33))) ((ord_less_nat zero_zero_nat) N_33))) % 0.52/0.69 FOF formula (forall (N_33:nat), ((iff ((ord_less_real zero_zero_real) (semiri132038758t_real N_33))) ((ord_less_nat zero_zero_nat) N_33))) of role axiom named fact_156_of__nat__0__less__iff % 0.52/0.70 A new axiom: (forall (N_33:nat), ((iff ((ord_less_real zero_zero_real) (semiri132038758t_real N_33))) ((ord_less_nat zero_zero_nat) N_33))) % 0.52/0.70 FOF formula (forall (N_32:nat) (A_78:int), (((ord_less_int one_one_int) A_78)->(((ord_less_nat zero_zero_nat) N_32)->((ord_less_int one_one_int) ((power_power_int A_78) N_32))))) of role axiom named fact_157_one__less__power % 0.52/0.70 A new axiom: (forall (N_32:nat) (A_78:int), (((ord_less_int one_one_int) A_78)->(((ord_less_nat zero_zero_nat) N_32)->((ord_less_int one_one_int) ((power_power_int A_78) N_32))))) % 0.52/0.70 FOF formula (forall (N_32:nat) (A_78:nat), (((ord_less_nat one_one_nat) A_78)->(((ord_less_nat zero_zero_nat) N_32)->((ord_less_nat one_one_nat) ((power_power_nat A_78) N_32))))) of role axiom named fact_158_one__less__power % 0.52/0.70 A new axiom: (forall (N_32:nat) (A_78:nat), (((ord_less_nat one_one_nat) A_78)->(((ord_less_nat zero_zero_nat) N_32)->((ord_less_nat one_one_nat) ((power_power_nat A_78) N_32))))) % 0.52/0.70 FOF formula (forall (N_32:nat) (A_78:real), (((ord_less_real one_one_real) A_78)->(((ord_less_nat zero_zero_nat) N_32)->((ord_less_real one_one_real) ((power_power_real A_78) N_32))))) of role axiom named fact_159_one__less__power % 0.52/0.70 A new axiom: (forall (N_32:nat) (A_78:real), (((ord_less_real one_one_real) A_78)->(((ord_less_nat zero_zero_nat) N_32)->((ord_less_real one_one_real) ((power_power_real A_78) N_32))))) % 0.52/0.70 FOF formula (forall (N_31:nat), ((and ((((eq nat) N_31) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) N_31)) one_one_int))) ((not (((eq nat) N_31) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) N_31)) zero_zero_int)))) of role axiom named fact_160_power__0__left % 0.52/0.70 A new axiom: (forall (N_31:nat), ((and ((((eq nat) N_31) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) N_31)) one_one_int))) ((not (((eq nat) N_31) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) N_31)) zero_zero_int)))) % 0.52/0.70 FOF formula (forall (N_31:nat), ((and ((((eq nat) N_31) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) N_31)) one_one_nat))) ((not (((eq nat) N_31) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) N_31)) zero_zero_nat)))) of role axiom named fact_161_power__0__left % 0.52/0.70 A new axiom: (forall (N_31:nat), ((and ((((eq nat) N_31) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) N_31)) one_one_nat))) ((not (((eq nat) N_31) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) N_31)) zero_zero_nat)))) % 0.52/0.70 FOF formula (forall (N_31:nat), ((and ((((eq nat) N_31) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) N_31)) one_one_real))) ((not (((eq nat) N_31) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) N_31)) zero_zero_real)))) of role axiom named fact_162_power__0__left % 0.52/0.70 A new axiom: (forall (N_31:nat), ((and ((((eq nat) N_31) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) N_31)) one_one_real))) ((not (((eq nat) N_31) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) N_31)) zero_zero_real)))) % 0.52/0.70 FOF formula (forall (A_77:int) (N_30:nat) (N_29:nat), (((ord_less_nat N_30) N_29)->(((ord_less_int zero_zero_int) A_77)->(((ord_less_int A_77) one_one_int)->((ord_less_int ((power_power_int A_77) N_29)) ((power_power_int A_77) N_30)))))) of role axiom named fact_163_power__strict__decreasing % 0.52/0.70 A new axiom: (forall (A_77:int) (N_30:nat) (N_29:nat), (((ord_less_nat N_30) N_29)->(((ord_less_int zero_zero_int) A_77)->(((ord_less_int A_77) one_one_int)->((ord_less_int ((power_power_int A_77) N_29)) ((power_power_int A_77) N_30)))))) % 0.52/0.70 FOF formula (forall (A_77:nat) (N_30:nat) (N_29:nat), (((ord_less_nat N_30) N_29)->(((ord_less_nat zero_zero_nat) A_77)->(((ord_less_nat A_77) one_one_nat)->((ord_less_nat ((power_power_nat A_77) N_29)) ((power_power_nat A_77) N_30)))))) of role axiom named fact_164_power__strict__decreasing % 0.52/0.70 A new axiom: (forall (A_77:nat) (N_30:nat) (N_29:nat), (((ord_less_nat N_30) N_29)->(((ord_less_nat zero_zero_nat) A_77)->(((ord_less_nat A_77) one_one_nat)->((ord_less_nat ((power_power_nat A_77) N_29)) ((power_power_nat A_77) N_30)))))) % 0.52/0.72 FOF formula (forall (A_77:real) (N_30:nat) (N_29:nat), (((ord_less_nat N_30) N_29)->(((ord_less_real zero_zero_real) A_77)->(((ord_less_real A_77) one_one_real)->((ord_less_real ((power_power_real A_77) N_29)) ((power_power_real A_77) N_30)))))) of role axiom named fact_165_power__strict__decreasing % 0.52/0.72 A new axiom: (forall (A_77:real) (N_30:nat) (N_29:nat), (((ord_less_nat N_30) N_29)->(((ord_less_real zero_zero_real) A_77)->(((ord_less_real A_77) one_one_real)->((ord_less_real ((power_power_real A_77) N_29)) ((power_power_real A_77) N_30)))))) % 0.52/0.72 FOF formula ((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) one_one_int)) of role axiom named fact_166_zero__less__two % 0.52/0.72 A new axiom: ((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) one_one_int)) % 0.52/0.72 FOF formula ((ord_less_nat zero_zero_nat) ((plus_plus_nat one_one_nat) one_one_nat)) of role axiom named fact_167_zero__less__two % 0.52/0.72 A new axiom: ((ord_less_nat zero_zero_nat) ((plus_plus_nat one_one_nat) one_one_nat)) % 0.52/0.72 FOF formula ((ord_less_real zero_zero_real) ((plus_plus_real one_one_real) one_one_real)) of role axiom named fact_168_zero__less__two % 0.52/0.72 A new axiom: ((ord_less_real zero_zero_real) ((plus_plus_real one_one_real) one_one_real)) % 0.52/0.72 FOF formula (forall (P:(int->Prop)) (K:int) (_TPTP_I:int), (((ord_less_int K) _TPTP_I)->((P ((plus_plus_int K) one_one_int))->((forall (I_1:int), (((ord_less_int K) I_1)->((P I_1)->(P ((plus_plus_int I_1) one_one_int)))))->(P _TPTP_I))))) of role axiom named fact_169_int__gr__induct % 0.52/0.72 A new axiom: (forall (P:(int->Prop)) (K:int) (_TPTP_I:int), (((ord_less_int K) _TPTP_I)->((P ((plus_plus_int K) one_one_int))->((forall (I_1:int), (((ord_less_int K) I_1)->((P I_1)->(P ((plus_plus_int I_1) one_one_int)))))->(P _TPTP_I))))) % 0.52/0.72 FOF formula ((ord_less_nat zero_zero_nat) tn) of role axiom named fact_170_tn0 % 0.52/0.72 A new axiom: ((ord_less_nat zero_zero_nat) tn) % 0.52/0.72 FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_171_less__zeroE % 0.52/0.72 A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) % 0.52/0.72 FOF formula (not (((eq real) zero_zero_real) one_one_real)) of role axiom named fact_172_real__zero__not__eq__one % 0.52/0.72 A new axiom: (not (((eq real) zero_zero_real) one_one_real)) % 0.52/0.72 FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_173_less__not__refl % 0.52/0.72 A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False)) % 0.52/0.72 FOF formula (forall (_TPTP_I:nat) (J:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J)) _TPTP_I)->False)) of role axiom named fact_174_not__add__less1 % 0.52/0.72 A new axiom: (forall (_TPTP_I:nat) (J:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J)) _TPTP_I)->False)) % 0.52/0.72 FOF formula (forall (J:nat) (_TPTP_I:nat), (((ord_less_nat ((plus_plus_nat J) _TPTP_I)) _TPTP_I)->False)) of role axiom named fact_175_not__add__less2 % 0.52/0.72 A new axiom: (forall (J:nat) (_TPTP_I:nat), (((ord_less_nat ((plus_plus_nat J) _TPTP_I)) _TPTP_I)->False)) % 0.52/0.72 FOF formula (forall (K:int), (((eq int) (number_number_of_int K)) K)) of role axiom named fact_176_number__of__is__id % 0.52/0.72 A new axiom: (forall (K:int), (((eq int) (number_number_of_int K)) K)) % 0.52/0.72 FOF formula (forall (M:nat) (N:nat), ((iff (not (((eq nat) M) N))) ((or ((ord_less_nat M) N)) ((ord_less_nat N) M)))) of role axiom named fact_177_nat__neq__iff % 0.52/0.72 A new axiom: (forall (M:nat) (N:nat), ((iff (not (((eq nat) M) N))) ((or ((ord_less_nat M) N)) ((ord_less_nat N) M)))) % 0.52/0.72 FOF formula (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) N)) ((plus_plus_nat N) M))) of role axiom named fact_178_nat__add__commute % 0.52/0.72 A new axiom: (forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) N)) ((plus_plus_nat N) M))) % 0.52/0.72 FOF formula (forall (X:nat) (Y:nat) (Z_2:nat), (((eq nat) ((plus_plus_nat X) ((plus_plus_nat Y) Z_2))) ((plus_plus_nat Y) ((plus_plus_nat X) Z_2)))) of role axiom named fact_179_nat__add__left__commute % 0.52/0.72 A new axiom: (forall (X:nat) (Y:nat) (Z_2:nat), (((eq nat) ((plus_plus_nat X) ((plus_plus_nat Y) Z_2))) ((plus_plus_nat Y) ((plus_plus_nat X) Z_2)))) % 0.52/0.72 FOF formula (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M) N)) K)) ((plus_plus_nat M) ((plus_plus_nat N) K)))) of role axiom named fact_180_nat__add__assoc % 0.52/0.74 A new axiom: (forall (M:nat) (N:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M) N)) K)) ((plus_plus_nat M) ((plus_plus_nat N) K)))) % 0.52/0.74 FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) (((eq nat) M) N))) of role axiom named fact_181_nat__add__left__cancel % 0.52/0.74 A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) (((eq nat) M) N))) % 0.52/0.74 FOF formula (forall (M:nat) (K:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) K)) ((plus_plus_nat N) K))) (((eq nat) M) N))) of role axiom named fact_182_nat__add__right__cancel % 0.52/0.74 A new axiom: (forall (M:nat) (K:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) K)) ((plus_plus_nat N) K))) (((eq nat) M) N))) % 0.52/0.74 FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_nat M) N))) of role axiom named fact_183_nat__add__left__cancel__less % 0.52/0.74 A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_nat M) N))) % 0.52/0.74 FOF formula (forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X)))) of role axiom named fact_184_linorder__neqE__nat % 0.52/0.74 A new axiom: (forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X)))) % 0.52/0.74 FOF formula (forall (N:nat), (((ord_less_nat N) N)->False)) of role axiom named fact_185_less__irrefl__nat % 0.52/0.74 A new axiom: (forall (N:nat), (((ord_less_nat N) N)->False)) % 0.52/0.74 FOF formula (forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N)))) of role axiom named fact_186_less__not__refl2 % 0.52/0.74 A new axiom: (forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N)))) % 0.52/0.74 FOF formula (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))) of role axiom named fact_187_less__not__refl3 % 0.52/0.74 A new axiom: (forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))) % 0.52/0.74 FOF formula (forall (M:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat _TPTP_I) ((plus_plus_nat J) M)))) of role axiom named fact_188_trans__less__add1 % 0.52/0.74 A new axiom: (forall (M:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat _TPTP_I) ((plus_plus_nat J) M)))) % 0.52/0.74 FOF formula (forall (M:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat _TPTP_I) ((plus_plus_nat M) J)))) of role axiom named fact_189_trans__less__add2 % 0.52/0.74 A new axiom: (forall (M:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat _TPTP_I) ((plus_plus_nat M) J)))) % 0.52/0.74 FOF formula (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K)))) of role axiom named fact_190_add__less__mono1 % 0.52/0.74 A new axiom: (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K)))) % 0.52/0.74 FOF formula (forall (K:nat) (L:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L))))) of role axiom named fact_191_add__less__mono % 0.52/0.74 A new axiom: (forall (K:nat) (L:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L))))) % 0.52/0.74 FOF formula (forall (M:nat) (N:nat) (K:nat) (L:nat), (((ord_less_nat K) L)->((((eq nat) ((plus_plus_nat M) L)) ((plus_plus_nat K) N))->((ord_less_nat M) N)))) of role axiom named fact_192_less__add__eq__less % 0.52/0.74 A new axiom: (forall (M:nat) (N:nat) (K:nat) (L:nat), (((ord_less_nat K) L)->((((eq nat) ((plus_plus_nat M) L)) ((plus_plus_nat K) N))->((ord_less_nat M) N)))) % 0.52/0.74 FOF formula (forall (_TPTP_I:nat) (J:nat) (K:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J)) K)->((ord_less_nat _TPTP_I) K))) of role axiom named fact_193_add__lessD1 % 0.52/0.74 A new axiom: (forall (_TPTP_I:nat) (J:nat) (K:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J)) K)->((ord_less_nat _TPTP_I) K))) % 0.52/0.76 FOF formula (forall (P:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P N) M))->(((((eq nat) M) N)->((P N) M))->((((ord_less_nat N) M)->((P N) M))->((P N) M))))) of role axiom named fact_194_nat__less__cases % 0.52/0.76 A new axiom: (forall (P:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P N) M))->(((((eq nat) M) N)->((P N) M))->((((ord_less_nat N) M)->((P N) M))->((P N) M))))) % 0.52/0.76 FOF formula (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N))) of role axiom named fact_195_gr0I % 0.52/0.76 A new axiom: (forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N))) % 0.52/0.76 FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->(not (((eq nat) N) zero_zero_nat)))) of role axiom named fact_196_gr__implies__not0 % 0.52/0.76 A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->(not (((eq nat) N) zero_zero_nat)))) % 0.52/0.76 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_197_nat__power__less__imp__less % 0.52/0.76 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)))) % 0.52/0.76 FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_198_less__nat__zero__code % 0.52/0.76 A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) % 0.52/0.76 FOF formula (forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or ((ord_less_nat zero_zero_nat) X)) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_199_nat__zero__less__power__iff % 0.52/0.76 A new axiom: (forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or ((ord_less_nat zero_zero_nat) X)) (((eq nat) N) zero_zero_nat)))) % 0.52/0.76 FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M) N))) ((or ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N)))) of role axiom named fact_200_add__gr__0 % 0.52/0.76 A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M) N))) ((or ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N)))) % 0.52/0.76 FOF formula (forall (N:nat), ((iff (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N))) of role axiom named fact_201_neq0__conv % 0.52/0.76 A new axiom: (forall (N:nat), ((iff (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N))) % 0.52/0.76 FOF formula (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) of role axiom named fact_202_not__less0 % 0.52/0.76 A new axiom: (forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)) % 0.52/0.76 FOF formula (forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or (((eq nat) N) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X)))) of role axiom named fact_203_zero__less__power__nat__eq % 0.52/0.76 A new axiom: (forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or (((eq nat) N) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X)))) % 0.52/0.76 FOF formula (forall (X:nat) (Y:nat), ((iff ((ord_less_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_nat X) Y))) of role axiom named fact_204_Nat__Transfer_Otransfer__int__nat__relations_I2_J % 0.52/0.76 A new axiom: (forall (X:nat) (Y:nat), ((iff ((ord_less_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_nat X) Y))) % 0.52/0.76 FOF formula (forall (X:nat) (W:int), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) (number_number_of_nat W)))) ((or (((eq nat) (number_number_of_nat W)) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X)))) of role axiom named fact_205_zero__less__power__nat__eq__number__of % 0.52/0.76 A new axiom: (forall (X:nat) (W:int), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) (number_number_of_nat W)))) ((or (((eq nat) (number_number_of_nat W)) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X)))) % 0.60/0.77 FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_nat M) N))) of role axiom named fact_206_zless__int % 0.60/0.77 A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_nat M) N))) % 0.60/0.77 FOF formula (forall (V_1:int) (V:int), ((iff ((ord_less_nat (number_number_of_nat V_1)) (number_number_of_nat V))) ((and (((ord_less_int V_1) V)->((ord_less_int pls) V))) ((ord_less_int V_1) V)))) of role axiom named fact_207_less__nat__number__of % 0.60/0.77 A new axiom: (forall (V_1:int) (V:int), ((iff ((ord_less_nat (number_number_of_nat V_1)) (number_number_of_nat V))) ((and (((ord_less_int V_1) V)->((ord_less_int pls) V))) ((ord_less_int V_1) V)))) % 0.60/0.77 FOF formula (forall (X_25:real) (Y_20:real), ((not (((eq real) X_25) Y_20))->((((ord_less_real X_25) Y_20)->False)->((ord_less_real Y_20) X_25)))) of role axiom named fact_208_linorder__neqE__linordered__idom % 0.60/0.77 A new axiom: (forall (X_25:real) (Y_20:real), ((not (((eq real) X_25) Y_20))->((((ord_less_real X_25) Y_20)->False)->((ord_less_real Y_20) X_25)))) % 0.60/0.77 FOF formula (forall (X_25:int) (Y_20:int), ((not (((eq int) X_25) Y_20))->((((ord_less_int X_25) Y_20)->False)->((ord_less_int Y_20) X_25)))) of role axiom named fact_209_linorder__neqE__linordered__idom % 0.60/0.77 A new axiom: (forall (X_25:int) (Y_20:int), ((not (((eq int) X_25) Y_20))->((((ord_less_int X_25) Y_20)->False)->((ord_less_int Y_20) X_25)))) % 0.60/0.77 FOF formula (forall (M:nat) (N:nat), ((((eq nat) ((plus_plus_nat M) N)) M)->(((eq nat) N) zero_zero_nat))) of role axiom named fact_210_add__eq__self__zero % 0.60/0.77 A new axiom: (forall (M:nat) (N:nat), ((((eq nat) ((plus_plus_nat M) N)) M)->(((eq nat) N) zero_zero_nat))) % 0.60/0.77 FOF formula (forall (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) N)) zero_zero_nat)) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_211_add__is__0 % 0.60/0.77 A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) N)) zero_zero_nat)) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))) % 0.60/0.77 FOF formula (forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M)) of role axiom named fact_212_Nat_Oadd__0__right % 0.60/0.77 A new axiom: (forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M)) % 0.60/0.77 FOF formula (forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N)) of role axiom named fact_213_plus__nat_Oadd__0 % 0.60/0.77 A new axiom: (forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N)) % 0.60/0.77 FOF formula (forall (A_76:real), (((eq real) ((power_power_real A_76) one_one_nat)) A_76)) of role axiom named fact_214_power__one__right % 0.60/0.77 A new axiom: (forall (A_76:real), (((eq real) ((power_power_real A_76) one_one_nat)) A_76)) % 0.60/0.77 FOF formula (forall (A_76:nat), (((eq nat) ((power_power_nat A_76) one_one_nat)) A_76)) of role axiom named fact_215_power__one__right % 0.60/0.77 A new axiom: (forall (A_76:nat), (((eq nat) ((power_power_nat A_76) one_one_nat)) A_76)) % 0.60/0.77 FOF formula (forall (A_76:int), (((eq int) ((power_power_int A_76) one_one_nat)) A_76)) of role axiom named fact_216_power__one__right % 0.60/0.77 A new axiom: (forall (A_76:int), (((eq int) ((power_power_int A_76) one_one_nat)) A_76)) % 0.60/0.77 FOF formula (forall (M_13:nat) (N_28:nat), ((iff (((eq real) (semiri132038758t_real M_13)) (semiri132038758t_real N_28))) (((eq nat) M_13) N_28))) of role axiom named fact_217_of__nat__eq__iff % 0.60/0.77 A new axiom: (forall (M_13:nat) (N_28:nat), ((iff (((eq real) (semiri132038758t_real M_13)) (semiri132038758t_real N_28))) (((eq nat) M_13) N_28))) % 0.60/0.77 FOF formula (forall (M_13:nat) (N_28:nat), ((iff (((eq nat) (semiri984289939at_nat M_13)) (semiri984289939at_nat N_28))) (((eq nat) M_13) N_28))) of role axiom named fact_218_of__nat__eq__iff % 0.60/0.77 A new axiom: (forall (M_13:nat) (N_28:nat), ((iff (((eq nat) (semiri984289939at_nat M_13)) (semiri984289939at_nat N_28))) (((eq nat) M_13) N_28))) % 0.60/0.77 FOF formula (forall (M_13:nat) (N_28:nat), ((iff (((eq int) (semiri1621563631at_int M_13)) (semiri1621563631at_int N_28))) (((eq nat) M_13) N_28))) of role axiom named fact_219_of__nat__eq__iff % 0.60/0.77 A new axiom: (forall (M_13:nat) (N_28:nat), ((iff (((eq int) (semiri1621563631at_int M_13)) (semiri1621563631at_int N_28))) (((eq nat) M_13) N_28))) % 0.62/0.79 FOF formula (forall (X:nat) (Y:nat), ((iff (((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (((eq nat) X) Y))) of role axiom named fact_220_Nat__Transfer_Otransfer__int__nat__relations_I1_J % 0.62/0.79 A new axiom: (forall (X:nat) (Y:nat), ((iff (((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (((eq nat) X) Y))) % 0.62/0.79 FOF formula (forall (X:nat) (Y:nat) (P:Prop), ((and (P->(((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int (((if_nat P) X) Y))))) ((P->False)->(((eq int) (semiri1621563631at_int Y)) (semiri1621563631at_int (((if_nat P) X) Y)))))) of role axiom named fact_221_int__if__cong % 0.62/0.79 A new axiom: (forall (X:nat) (Y:nat) (P:Prop), ((and (P->(((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int (((if_nat P) X) Y))))) ((P->False)->(((eq int) (semiri1621563631at_int Y)) (semiri1621563631at_int (((if_nat P) X) Y)))))) % 0.62/0.79 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_222_less__0__number__of % 0.62/0.79 A new axiom: (forall (V_1:int), ((iff ((ord_less_nat zero_zero_nat) (number_number_of_nat V_1))) ((ord_less_int pls) V_1))) % 0.62/0.79 FOF formula (forall (N:nat), ((iff ((ord_less_int zero_zero_int) (semiri1621563631at_int N))) ((ord_less_nat zero_zero_nat) N))) of role axiom named fact_223_zero__less__int__conv % 0.62/0.79 A new axiom: (forall (N:nat), ((iff ((ord_less_int zero_zero_int) (semiri1621563631at_int N))) ((ord_less_nat zero_zero_nat) N))) % 0.62/0.79 FOF formula (not (((eq real) one_one_real) zero_zero_real)) of role axiom named fact_224_one__neq__zero % 0.62/0.79 A new axiom: (not (((eq real) one_one_real) zero_zero_real)) % 0.62/0.79 FOF formula (not (((eq nat) one_one_nat) zero_zero_nat)) of role axiom named fact_225_one__neq__zero % 0.62/0.79 A new axiom: (not (((eq nat) one_one_nat) zero_zero_nat)) % 0.62/0.79 FOF formula (not (((eq int) one_one_int) zero_zero_int)) of role axiom named fact_226_one__neq__zero % 0.62/0.79 A new axiom: (not (((eq int) one_one_int) zero_zero_int)) % 0.62/0.79 FOF formula (not (((eq real) zero_zero_real) one_one_real)) of role axiom named fact_227_zero__neq__one % 0.62/0.79 A new axiom: (not (((eq real) zero_zero_real) one_one_real)) % 0.62/0.79 FOF formula (not (((eq nat) zero_zero_nat) one_one_nat)) of role axiom named fact_228_zero__neq__one % 0.62/0.79 A new axiom: (not (((eq nat) zero_zero_nat) one_one_nat)) % 0.62/0.79 FOF formula (not (((eq int) zero_zero_int) one_one_int)) of role axiom named fact_229_zero__neq__one % 0.62/0.79 A new axiom: (not (((eq int) zero_zero_int) one_one_int)) % 0.62/0.79 FOF formula (forall (N_27:nat) (A_75:real), ((not (((eq real) A_75) zero_zero_real))->(not (((eq real) ((power_power_real A_75) N_27)) zero_zero_real)))) of role axiom named fact_230_field__power__not__zero % 0.62/0.79 A new axiom: (forall (N_27:nat) (A_75:real), ((not (((eq real) A_75) zero_zero_real))->(not (((eq real) ((power_power_real A_75) N_27)) zero_zero_real)))) % 0.62/0.79 FOF formula (forall (N_27:nat) (A_75:int), ((not (((eq int) A_75) zero_zero_int))->(not (((eq int) ((power_power_int A_75) N_27)) zero_zero_int)))) of role axiom named fact_231_field__power__not__zero % 0.62/0.79 A new axiom: (forall (N_27:nat) (A_75:int), ((not (((eq int) A_75) zero_zero_int))->(not (((eq int) ((power_power_int A_75) N_27)) zero_zero_int)))) % 0.62/0.79 FOF formula (forall (N_26:nat), (((eq real) ((power_power_real one_one_real) N_26)) one_one_real)) of role axiom named fact_232_power__one % 0.62/0.79 A new axiom: (forall (N_26:nat), (((eq real) ((power_power_real one_one_real) N_26)) one_one_real)) % 0.62/0.79 FOF formula (forall (N_26:nat), (((eq nat) ((power_power_nat one_one_nat) N_26)) one_one_nat)) of role axiom named fact_233_power__one % 0.62/0.79 A new axiom: (forall (N_26:nat), (((eq nat) ((power_power_nat one_one_nat) N_26)) one_one_nat)) % 0.62/0.79 FOF formula (forall (N_26:nat), (((eq int) ((power_power_int one_one_int) N_26)) one_one_int)) of role axiom named fact_234_power__one % 0.62/0.79 A new axiom: (forall (N_26:nat), (((eq int) ((power_power_int one_one_int) N_26)) one_one_int)) % 0.62/0.79 FOF formula (forall (M_12:nat) (N_25:nat), ((iff ((ord_less_real (semiri132038758t_real M_12)) (semiri132038758t_real N_25))) ((ord_less_nat M_12) N_25))) of role axiom named fact_235_of__nat__less__iff % 0.62/0.80 A new axiom: (forall (M_12:nat) (N_25:nat), ((iff ((ord_less_real (semiri132038758t_real M_12)) (semiri132038758t_real N_25))) ((ord_less_nat M_12) N_25))) % 0.62/0.80 FOF formula (forall (M_12:nat) (N_25:nat), ((iff ((ord_less_nat (semiri984289939at_nat M_12)) (semiri984289939at_nat N_25))) ((ord_less_nat M_12) N_25))) of role axiom named fact_236_of__nat__less__iff % 0.62/0.80 A new axiom: (forall (M_12:nat) (N_25:nat), ((iff ((ord_less_nat (semiri984289939at_nat M_12)) (semiri984289939at_nat N_25))) ((ord_less_nat M_12) N_25))) % 0.62/0.80 FOF formula (forall (M_12:nat) (N_25:nat), ((iff ((ord_less_int (semiri1621563631at_int M_12)) (semiri1621563631at_int N_25))) ((ord_less_nat M_12) N_25))) of role axiom named fact_237_of__nat__less__iff % 0.62/0.80 A new axiom: (forall (M_12:nat) (N_25:nat), ((iff ((ord_less_int (semiri1621563631at_int M_12)) (semiri1621563631at_int N_25))) ((ord_less_nat M_12) N_25))) % 0.62/0.80 FOF formula (forall (M_11:nat) (N_24:nat), (((ord_less_nat M_11) N_24)->((ord_less_real (semiri132038758t_real M_11)) (semiri132038758t_real N_24)))) of role axiom named fact_238_less__imp__of__nat__less % 0.62/0.80 A new axiom: (forall (M_11:nat) (N_24:nat), (((ord_less_nat M_11) N_24)->((ord_less_real (semiri132038758t_real M_11)) (semiri132038758t_real N_24)))) % 0.62/0.80 FOF formula (forall (M_11:nat) (N_24:nat), (((ord_less_nat M_11) N_24)->((ord_less_nat (semiri984289939at_nat M_11)) (semiri984289939at_nat N_24)))) of role axiom named fact_239_less__imp__of__nat__less % 0.62/0.80 A new axiom: (forall (M_11:nat) (N_24:nat), (((ord_less_nat M_11) N_24)->((ord_less_nat (semiri984289939at_nat M_11)) (semiri984289939at_nat N_24)))) % 0.62/0.80 FOF formula (forall (M_11:nat) (N_24:nat), (((ord_less_nat M_11) N_24)->((ord_less_int (semiri1621563631at_int M_11)) (semiri1621563631at_int N_24)))) of role axiom named fact_240_less__imp__of__nat__less % 0.62/0.80 A new axiom: (forall (M_11:nat) (N_24:nat), (((ord_less_nat M_11) N_24)->((ord_less_int (semiri1621563631at_int M_11)) (semiri1621563631at_int N_24)))) % 0.62/0.80 FOF formula (forall (M_10:nat) (N_23:nat), (((ord_less_real (semiri132038758t_real M_10)) (semiri132038758t_real N_23))->((ord_less_nat M_10) N_23))) of role axiom named fact_241_of__nat__less__imp__less % 0.62/0.80 A new axiom: (forall (M_10:nat) (N_23:nat), (((ord_less_real (semiri132038758t_real M_10)) (semiri132038758t_real N_23))->((ord_less_nat M_10) N_23))) % 0.62/0.80 FOF formula (forall (M_10:nat) (N_23:nat), (((ord_less_nat (semiri984289939at_nat M_10)) (semiri984289939at_nat N_23))->((ord_less_nat M_10) N_23))) of role axiom named fact_242_of__nat__less__imp__less % 0.62/0.80 A new axiom: (forall (M_10:nat) (N_23:nat), (((ord_less_nat (semiri984289939at_nat M_10)) (semiri984289939at_nat N_23))->((ord_less_nat M_10) N_23))) % 0.62/0.80 FOF formula (forall (M_10:nat) (N_23:nat), (((ord_less_int (semiri1621563631at_int M_10)) (semiri1621563631at_int N_23))->((ord_less_nat M_10) N_23))) of role axiom named fact_243_of__nat__less__imp__less % 0.62/0.80 A new axiom: (forall (M_10:nat) (N_23:nat), (((ord_less_int (semiri1621563631at_int M_10)) (semiri1621563631at_int N_23))->((ord_less_nat M_10) N_23))) % 0.62/0.80 FOF formula (forall (M_9:nat) (N_22:nat), (((eq real) (semiri132038758t_real ((plus_plus_nat M_9) N_22))) ((plus_plus_real (semiri132038758t_real M_9)) (semiri132038758t_real N_22)))) of role axiom named fact_244_of__nat__add % 0.62/0.80 A new axiom: (forall (M_9:nat) (N_22:nat), (((eq real) (semiri132038758t_real ((plus_plus_nat M_9) N_22))) ((plus_plus_real (semiri132038758t_real M_9)) (semiri132038758t_real N_22)))) % 0.62/0.80 FOF formula (forall (M_9:nat) (N_22:nat), (((eq nat) (semiri984289939at_nat ((plus_plus_nat M_9) N_22))) ((plus_plus_nat (semiri984289939at_nat M_9)) (semiri984289939at_nat N_22)))) of role axiom named fact_245_of__nat__add % 0.62/0.80 A new axiom: (forall (M_9:nat) (N_22:nat), (((eq nat) (semiri984289939at_nat ((plus_plus_nat M_9) N_22))) ((plus_plus_nat (semiri984289939at_nat M_9)) (semiri984289939at_nat N_22)))) % 0.62/0.80 FOF formula (forall (M_9:nat) (N_22:nat), (((eq int) (semiri1621563631at_int ((plus_plus_nat M_9) N_22))) ((plus_plus_int (semiri1621563631at_int M_9)) (semiri1621563631at_int N_22)))) of role axiom named fact_246_of__nat__add % 0.64/0.82 A new axiom: (forall (M_9:nat) (N_22:nat), (((eq int) (semiri1621563631at_int ((plus_plus_nat M_9) N_22))) ((plus_plus_int (semiri1621563631at_int M_9)) (semiri1621563631at_int N_22)))) % 0.64/0.82 FOF formula (((eq real) (semiri132038758t_real one_one_nat)) one_one_real) of role axiom named fact_247_of__nat__1 % 0.64/0.82 A new axiom: (((eq real) (semiri132038758t_real one_one_nat)) one_one_real) % 0.64/0.82 FOF formula (((eq nat) (semiri984289939at_nat one_one_nat)) one_one_nat) of role axiom named fact_248_of__nat__1 % 0.64/0.82 A new axiom: (((eq nat) (semiri984289939at_nat one_one_nat)) one_one_nat) % 0.64/0.82 FOF formula (((eq int) (semiri1621563631at_int one_one_nat)) one_one_int) of role axiom named fact_249_of__nat__1 % 0.64/0.82 A new axiom: (((eq int) (semiri1621563631at_int one_one_nat)) one_one_int) % 0.64/0.82 FOF formula (forall (M_8:nat) (N_21:nat), (((eq real) (semiri132038758t_real ((power_power_nat M_8) N_21))) ((power_power_real (semiri132038758t_real M_8)) N_21))) of role axiom named fact_250_of__nat__power % 0.64/0.82 A new axiom: (forall (M_8:nat) (N_21:nat), (((eq real) (semiri132038758t_real ((power_power_nat M_8) N_21))) ((power_power_real (semiri132038758t_real M_8)) N_21))) % 0.64/0.82 FOF formula (forall (M_8:nat) (N_21:nat), (((eq nat) (semiri984289939at_nat ((power_power_nat M_8) N_21))) ((power_power_nat (semiri984289939at_nat M_8)) N_21))) of role axiom named fact_251_of__nat__power % 0.64/0.82 A new axiom: (forall (M_8:nat) (N_21:nat), (((eq nat) (semiri984289939at_nat ((power_power_nat M_8) N_21))) ((power_power_nat (semiri984289939at_nat M_8)) N_21))) % 0.64/0.82 FOF formula (forall (M_8:nat) (N_21:nat), (((eq int) (semiri1621563631at_int ((power_power_nat M_8) N_21))) ((power_power_int (semiri1621563631at_int M_8)) N_21))) of role axiom named fact_252_of__nat__power % 0.64/0.82 A new axiom: (forall (M_8:nat) (N_21:nat), (((eq int) (semiri1621563631at_int ((power_power_nat M_8) N_21))) ((power_power_int (semiri1621563631at_int M_8)) N_21))) % 0.64/0.82 FOF formula (((eq int) one_one_int) (semiri1621563631at_int one_one_nat)) of role axiom named fact_253_transfer__int__nat__numerals_I2_J % 0.64/0.82 A new axiom: (((eq int) one_one_int) (semiri1621563631at_int one_one_nat)) % 0.64/0.82 FOF formula (forall (X:nat) (Y:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((plus_plus_nat X) Y)))) of role axiom named fact_254_Nat__Transfer_Otransfer__int__nat__functions_I1_J % 0.64/0.82 A new axiom: (forall (X:nat) (Y:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((plus_plus_nat X) Y)))) % 0.64/0.82 FOF formula (forall (X:nat) (N:nat), (((eq int) ((power_power_int (semiri1621563631at_int X)) N)) (semiri1621563631at_int ((power_power_nat X) N)))) of role axiom named fact_255_Nat__Transfer_Otransfer__int__nat__functions_I4_J % 0.64/0.82 A new axiom: (forall (X:nat) (N:nat), (((eq int) ((power_power_int (semiri1621563631at_int X)) N)) (semiri1621563631at_int ((power_power_nat X) N)))) % 0.64/0.82 FOF formula (forall (B_49:real) (C_36:real) (A_74:real), (((ord_less_real zero_zero_real) A_74)->(((ord_less_real B_49) C_36)->((ord_less_real B_49) ((plus_plus_real A_74) C_36))))) of role axiom named fact_256_pos__add__strict % 0.64/0.82 A new axiom: (forall (B_49:real) (C_36:real) (A_74:real), (((ord_less_real zero_zero_real) A_74)->(((ord_less_real B_49) C_36)->((ord_less_real B_49) ((plus_plus_real A_74) C_36))))) % 0.64/0.82 FOF formula (forall (B_49:nat) (C_36:nat) (A_74:nat), (((ord_less_nat zero_zero_nat) A_74)->(((ord_less_nat B_49) C_36)->((ord_less_nat B_49) ((plus_plus_nat A_74) C_36))))) of role axiom named fact_257_pos__add__strict % 0.64/0.82 A new axiom: (forall (B_49:nat) (C_36:nat) (A_74:nat), (((ord_less_nat zero_zero_nat) A_74)->(((ord_less_nat B_49) C_36)->((ord_less_nat B_49) ((plus_plus_nat A_74) C_36))))) % 0.64/0.82 FOF formula (forall (B_49:int) (C_36:int) (A_74:int), (((ord_less_int zero_zero_int) A_74)->(((ord_less_int B_49) C_36)->((ord_less_int B_49) ((plus_plus_int A_74) C_36))))) of role axiom named fact_258_pos__add__strict % 0.64/0.82 A new axiom: (forall (B_49:int) (C_36:int) (A_74:int), (((ord_less_int zero_zero_int) A_74)->(((ord_less_int B_49) C_36)->((ord_less_int B_49) ((plus_plus_int A_74) C_36))))) % 0.66/0.84 FOF formula (((ord_less_real one_one_real) zero_zero_real)->False) of role axiom named fact_259_not__one__less__zero % 0.66/0.84 A new axiom: (((ord_less_real one_one_real) zero_zero_real)->False) % 0.66/0.84 FOF formula (((ord_less_nat one_one_nat) zero_zero_nat)->False) of role axiom named fact_260_not__one__less__zero % 0.66/0.84 A new axiom: (((ord_less_nat one_one_nat) zero_zero_nat)->False) % 0.66/0.84 FOF formula (((ord_less_int one_one_int) zero_zero_int)->False) of role axiom named fact_261_not__one__less__zero % 0.66/0.84 A new axiom: (((ord_less_int one_one_int) zero_zero_int)->False) % 0.66/0.84 FOF formula ((ord_less_real zero_zero_real) one_one_real) of role axiom named fact_262_zero__less__one % 0.66/0.84 A new axiom: ((ord_less_real zero_zero_real) one_one_real) % 0.66/0.84 FOF formula ((ord_less_nat zero_zero_nat) one_one_nat) of role axiom named fact_263_zero__less__one % 0.66/0.84 A new axiom: ((ord_less_nat zero_zero_nat) one_one_nat) % 0.66/0.84 FOF formula ((ord_less_int zero_zero_int) one_one_int) of role axiom named fact_264_zero__less__one % 0.66/0.84 A new axiom: ((ord_less_int zero_zero_int) one_one_int) % 0.66/0.84 FOF formula (forall (N_20:nat) (A_73:real), (((ord_less_real zero_zero_real) A_73)->((ord_less_real zero_zero_real) ((power_power_real A_73) N_20)))) of role axiom named fact_265_zero__less__power % 0.66/0.84 A new axiom: (forall (N_20:nat) (A_73:real), (((ord_less_real zero_zero_real) A_73)->((ord_less_real zero_zero_real) ((power_power_real A_73) N_20)))) % 0.66/0.84 FOF formula (forall (N_20:nat) (A_73:nat), (((ord_less_nat zero_zero_nat) A_73)->((ord_less_nat zero_zero_nat) ((power_power_nat A_73) N_20)))) of role axiom named fact_266_zero__less__power % 0.66/0.84 A new axiom: (forall (N_20:nat) (A_73:nat), (((ord_less_nat zero_zero_nat) A_73)->((ord_less_nat zero_zero_nat) ((power_power_nat A_73) N_20)))) % 0.66/0.84 FOF formula (forall (N_20:nat) (A_73:int), (((ord_less_int zero_zero_int) A_73)->((ord_less_int zero_zero_int) ((power_power_int A_73) N_20)))) of role axiom named fact_267_zero__less__power % 0.66/0.84 A new axiom: (forall (N_20:nat) (A_73:int), (((ord_less_int zero_zero_int) A_73)->((ord_less_int zero_zero_int) ((power_power_int A_73) N_20)))) % 0.66/0.84 FOF formula (forall (A_72:real), ((ord_less_real A_72) ((plus_plus_real A_72) one_one_real))) of role axiom named fact_268_less__add__one % 0.66/0.84 A new axiom: (forall (A_72:real), ((ord_less_real A_72) ((plus_plus_real A_72) one_one_real))) % 0.66/0.84 FOF formula (forall (A_72:nat), ((ord_less_nat A_72) ((plus_plus_nat A_72) one_one_nat))) of role axiom named fact_269_less__add__one % 0.66/0.84 A new axiom: (forall (A_72:nat), ((ord_less_nat A_72) ((plus_plus_nat A_72) one_one_nat))) % 0.66/0.84 FOF formula (forall (A_72:int), ((ord_less_int A_72) ((plus_plus_int A_72) one_one_int))) of role axiom named fact_270_less__add__one % 0.66/0.84 A new axiom: (forall (A_72:int), ((ord_less_int A_72) ((plus_plus_int A_72) one_one_int))) % 0.66/0.84 FOF formula (forall (M_7:nat) (N_19:nat) (A_71:real), (((ord_less_real one_one_real) A_71)->((iff (((eq real) ((power_power_real A_71) M_7)) ((power_power_real A_71) N_19))) (((eq nat) M_7) N_19)))) of role axiom named fact_271_power__inject__exp % 0.66/0.84 A new axiom: (forall (M_7:nat) (N_19:nat) (A_71:real), (((ord_less_real one_one_real) A_71)->((iff (((eq real) ((power_power_real A_71) M_7)) ((power_power_real A_71) N_19))) (((eq nat) M_7) N_19)))) % 0.66/0.84 FOF formula (forall (M_7:nat) (N_19:nat) (A_71:nat), (((ord_less_nat one_one_nat) A_71)->((iff (((eq nat) ((power_power_nat A_71) M_7)) ((power_power_nat A_71) N_19))) (((eq nat) M_7) N_19)))) of role axiom named fact_272_power__inject__exp % 0.66/0.84 A new axiom: (forall (M_7:nat) (N_19:nat) (A_71:nat), (((ord_less_nat one_one_nat) A_71)->((iff (((eq nat) ((power_power_nat A_71) M_7)) ((power_power_nat A_71) N_19))) (((eq nat) M_7) N_19)))) % 0.66/0.84 FOF formula (forall (M_7:nat) (N_19:nat) (A_71:int), (((ord_less_int one_one_int) A_71)->((iff (((eq int) ((power_power_int A_71) M_7)) ((power_power_int A_71) N_19))) (((eq nat) M_7) N_19)))) of role axiom named fact_273_power__inject__exp % 0.66/0.84 A new axiom: (forall (M_7:nat) (N_19:nat) (A_71:int), (((ord_less_int one_one_int) A_71)->((iff (((eq int) ((power_power_int A_71) M_7)) ((power_power_int A_71) N_19))) (((eq nat) M_7) N_19)))) % 0.66/0.84 FOF formula (forall (X_24:nat) (Y_19:nat) (B_48:real), (((ord_less_real one_one_real) B_48)->((iff ((ord_less_real ((power_power_real B_48) X_24)) ((power_power_real B_48) Y_19))) ((ord_less_nat X_24) Y_19)))) of role axiom named fact_274_power__strict__increasing__iff % 0.66/0.85 A new axiom: (forall (X_24:nat) (Y_19:nat) (B_48:real), (((ord_less_real one_one_real) B_48)->((iff ((ord_less_real ((power_power_real B_48) X_24)) ((power_power_real B_48) Y_19))) ((ord_less_nat X_24) Y_19)))) % 0.66/0.85 FOF formula (forall (X_24:nat) (Y_19:nat) (B_48:nat), (((ord_less_nat one_one_nat) B_48)->((iff ((ord_less_nat ((power_power_nat B_48) X_24)) ((power_power_nat B_48) Y_19))) ((ord_less_nat X_24) Y_19)))) of role axiom named fact_275_power__strict__increasing__iff % 0.66/0.85 A new axiom: (forall (X_24:nat) (Y_19:nat) (B_48:nat), (((ord_less_nat one_one_nat) B_48)->((iff ((ord_less_nat ((power_power_nat B_48) X_24)) ((power_power_nat B_48) Y_19))) ((ord_less_nat X_24) Y_19)))) % 0.66/0.85 FOF formula (forall (X_24:nat) (Y_19:nat) (B_48:int), (((ord_less_int one_one_int) B_48)->((iff ((ord_less_int ((power_power_int B_48) X_24)) ((power_power_int B_48) Y_19))) ((ord_less_nat X_24) Y_19)))) of role axiom named fact_276_power__strict__increasing__iff % 0.66/0.85 A new axiom: (forall (X_24:nat) (Y_19:nat) (B_48:int), (((ord_less_int one_one_int) B_48)->((iff ((ord_less_int ((power_power_int B_48) X_24)) ((power_power_int B_48) Y_19))) ((ord_less_nat X_24) Y_19)))) % 0.66/0.85 FOF formula (forall (M_6:nat) (N_18:nat) (A_70:real), (((ord_less_real one_one_real) A_70)->(((ord_less_real ((power_power_real A_70) M_6)) ((power_power_real A_70) N_18))->((ord_less_nat M_6) N_18)))) of role axiom named fact_277_power__less__imp__less__exp % 0.66/0.85 A new axiom: (forall (M_6:nat) (N_18:nat) (A_70:real), (((ord_less_real one_one_real) A_70)->(((ord_less_real ((power_power_real A_70) M_6)) ((power_power_real A_70) N_18))->((ord_less_nat M_6) N_18)))) % 0.66/0.85 FOF formula (forall (M_6:nat) (N_18:nat) (A_70:nat), (((ord_less_nat one_one_nat) A_70)->(((ord_less_nat ((power_power_nat A_70) M_6)) ((power_power_nat A_70) N_18))->((ord_less_nat M_6) N_18)))) of role axiom named fact_278_power__less__imp__less__exp % 0.66/0.85 A new axiom: (forall (M_6:nat) (N_18:nat) (A_70:nat), (((ord_less_nat one_one_nat) A_70)->(((ord_less_nat ((power_power_nat A_70) M_6)) ((power_power_nat A_70) N_18))->((ord_less_nat M_6) N_18)))) % 0.66/0.85 FOF formula (forall (M_6:nat) (N_18:nat) (A_70:int), (((ord_less_int one_one_int) A_70)->(((ord_less_int ((power_power_int A_70) M_6)) ((power_power_int A_70) N_18))->((ord_less_nat M_6) N_18)))) of role axiom named fact_279_power__less__imp__less__exp % 0.66/0.85 A new axiom: (forall (M_6:nat) (N_18:nat) (A_70:int), (((ord_less_int one_one_int) A_70)->(((ord_less_int ((power_power_int A_70) M_6)) ((power_power_int A_70) N_18))->((ord_less_nat M_6) N_18)))) % 0.66/0.85 FOF formula (forall (A_69:real) (N_17:nat) (N_16:nat), (((ord_less_nat N_17) N_16)->(((ord_less_real one_one_real) A_69)->((ord_less_real ((power_power_real A_69) N_17)) ((power_power_real A_69) N_16))))) of role axiom named fact_280_power__strict__increasing % 0.66/0.85 A new axiom: (forall (A_69:real) (N_17:nat) (N_16:nat), (((ord_less_nat N_17) N_16)->(((ord_less_real one_one_real) A_69)->((ord_less_real ((power_power_real A_69) N_17)) ((power_power_real A_69) N_16))))) % 0.66/0.85 FOF formula (forall (A_69:nat) (N_17:nat) (N_16:nat), (((ord_less_nat N_17) N_16)->(((ord_less_nat one_one_nat) A_69)->((ord_less_nat ((power_power_nat A_69) N_17)) ((power_power_nat A_69) N_16))))) of role axiom named fact_281_power__strict__increasing % 0.66/0.85 A new axiom: (forall (A_69:nat) (N_17:nat) (N_16:nat), (((ord_less_nat N_17) N_16)->(((ord_less_nat one_one_nat) A_69)->((ord_less_nat ((power_power_nat A_69) N_17)) ((power_power_nat A_69) N_16))))) % 0.66/0.85 FOF formula (forall (A_69:int) (N_17:nat) (N_16:nat), (((ord_less_nat N_17) N_16)->(((ord_less_int one_one_int) A_69)->((ord_less_int ((power_power_int A_69) N_17)) ((power_power_int A_69) N_16))))) of role axiom named fact_282_power__strict__increasing % 0.66/0.85 A new axiom: (forall (A_69:int) (N_17:nat) (N_16:nat), (((ord_less_nat N_17) N_16)->(((ord_less_int one_one_int) A_69)->((ord_less_int ((power_power_int A_69) N_17)) ((power_power_int A_69) N_16))))) % 0.66/0.87 FOF formula (forall (A_68:real) (N_15:nat), ((iff (((eq real) ((power_power_real A_68) N_15)) zero_zero_real)) ((and (((eq real) A_68) zero_zero_real)) (not (((eq nat) N_15) zero_zero_nat))))) of role axiom named fact_283_power__eq__0__iff % 0.66/0.87 A new axiom: (forall (A_68:real) (N_15:nat), ((iff (((eq real) ((power_power_real A_68) N_15)) zero_zero_real)) ((and (((eq real) A_68) zero_zero_real)) (not (((eq nat) N_15) zero_zero_nat))))) % 0.66/0.87 FOF formula (forall (A_68:nat) (N_15:nat), ((iff (((eq nat) ((power_power_nat A_68) N_15)) zero_zero_nat)) ((and (((eq nat) A_68) zero_zero_nat)) (not (((eq nat) N_15) zero_zero_nat))))) of role axiom named fact_284_power__eq__0__iff % 0.66/0.87 A new axiom: (forall (A_68:nat) (N_15:nat), ((iff (((eq nat) ((power_power_nat A_68) N_15)) zero_zero_nat)) ((and (((eq nat) A_68) zero_zero_nat)) (not (((eq nat) N_15) zero_zero_nat))))) % 0.66/0.87 FOF formula (forall (A_68:int) (N_15:nat), ((iff (((eq int) ((power_power_int A_68) N_15)) zero_zero_int)) ((and (((eq int) A_68) zero_zero_int)) (not (((eq nat) N_15) zero_zero_nat))))) of role axiom named fact_285_power__eq__0__iff % 0.66/0.87 A new axiom: (forall (A_68:int) (N_15:nat), ((iff (((eq int) ((power_power_int A_68) N_15)) zero_zero_int)) ((and (((eq int) A_68) zero_zero_int)) (not (((eq nat) N_15) zero_zero_nat))))) % 0.66/0.87 FOF formula (forall (M_5:nat), (((ord_less_real (semiri132038758t_real M_5)) zero_zero_real)->False)) of role axiom named fact_286_of__nat__less__0__iff % 0.66/0.87 A new axiom: (forall (M_5:nat), (((ord_less_real (semiri132038758t_real M_5)) zero_zero_real)->False)) % 0.66/0.87 FOF formula (forall (M_5:nat), (((ord_less_nat (semiri984289939at_nat M_5)) zero_zero_nat)->False)) of role axiom named fact_287_of__nat__less__0__iff % 0.66/0.87 A new axiom: (forall (M_5:nat), (((ord_less_nat (semiri984289939at_nat M_5)) zero_zero_nat)->False)) % 0.66/0.87 FOF formula (forall (M_5:nat), (((ord_less_int (semiri1621563631at_int M_5)) zero_zero_int)->False)) of role axiom named fact_288_of__nat__less__0__iff % 0.66/0.87 A new axiom: (forall (M_5:nat), (((ord_less_int (semiri1621563631at_int M_5)) zero_zero_int)->False)) % 0.66/0.87 FOF formula (forall (A_67:real), (((eq real) ((power_power_real A_67) zero_zero_nat)) one_one_real)) of role axiom named fact_289_power__0 % 0.66/0.87 A new axiom: (forall (A_67:real), (((eq real) ((power_power_real A_67) zero_zero_nat)) one_one_real)) % 0.66/0.87 FOF formula (forall (A_67:nat), (((eq nat) ((power_power_nat A_67) zero_zero_nat)) one_one_nat)) of role axiom named fact_290_power__0 % 0.66/0.87 A new axiom: (forall (A_67:nat), (((eq nat) ((power_power_nat A_67) zero_zero_nat)) one_one_nat)) % 0.66/0.87 FOF formula (forall (A_67:int), (((eq int) ((power_power_int A_67) zero_zero_nat)) one_one_int)) of role axiom named fact_291_power__0 % 0.66/0.87 A new axiom: (forall (A_67:int), (((eq int) ((power_power_int A_67) zero_zero_nat)) one_one_int)) % 0.66/0.87 FOF formula (((eq real) (semiri132038758t_real zero_zero_nat)) zero_zero_real) of role axiom named fact_292_of__nat__0 % 0.66/0.87 A new axiom: (((eq real) (semiri132038758t_real zero_zero_nat)) zero_zero_real) % 0.66/0.87 FOF formula (((eq nat) (semiri984289939at_nat zero_zero_nat)) zero_zero_nat) of role axiom named fact_293_of__nat__0 % 0.66/0.87 A new axiom: (((eq nat) (semiri984289939at_nat zero_zero_nat)) zero_zero_nat) % 0.66/0.87 FOF formula (((eq int) (semiri1621563631at_int zero_zero_nat)) zero_zero_int) of role axiom named fact_294_of__nat__0 % 0.66/0.87 A new axiom: (((eq int) (semiri1621563631at_int zero_zero_nat)) zero_zero_int) % 0.66/0.87 FOF formula (((eq int) zero_zero_int) (semiri1621563631at_int zero_zero_nat)) of role axiom named fact_295_transfer__int__nat__numerals_I1_J % 0.66/0.87 A new axiom: (((eq int) zero_zero_int) (semiri1621563631at_int zero_zero_nat)) % 0.66/0.87 FOF formula ((ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls)))) of role axiom named fact_296_pos2 % 0.66/0.87 A new axiom: ((ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls)))) % 0.66/0.87 FOF formula (forall (K:int), (((ord_less_int zero_zero_int) K)->((ex nat) (fun (N_1:nat)=> ((and ((ord_less_nat zero_zero_nat) N_1)) (((eq int) K) (semiri1621563631at_int N_1))))))) of role axiom named fact_297_zero__less__imp__eq__int % 0.66/0.87 A new axiom: (forall (K:int), (((ord_less_int zero_zero_int) K)->((ex nat) (fun (N_1:nat)=> ((and ((ord_less_nat zero_zero_nat) N_1)) (((eq int) K) (semiri1621563631at_int N_1))))))) % 0.66/0.88 FOF formula (forall (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ex nat) (fun (K_1:nat)=> ((and ((ord_less_nat zero_zero_nat) K_1)) (((eq nat) ((plus_plus_nat _TPTP_I) K_1)) J)))))) of role axiom named fact_298_less__imp__add__positive % 0.66/0.88 A new axiom: (forall (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ex nat) (fun (K_1:nat)=> ((and ((ord_less_nat zero_zero_nat) K_1)) (((eq nat) ((plus_plus_nat _TPTP_I) K_1)) J)))))) % 0.66/0.88 FOF formula (forall (X:nat) (N:nat), ((iff (((eq nat) ((power_power_nat X) N)) one_one_nat)) ((or (((eq nat) X) one_one_nat)) (((eq nat) N) zero_zero_nat)))) of role axiom named fact_299_exp__eq__1 % 0.66/0.88 A new axiom: (forall (X:nat) (N:nat), ((iff (((eq nat) ((power_power_nat X) N)) one_one_nat)) ((or (((eq nat) X) one_one_nat)) (((eq nat) N) zero_zero_nat)))) % 0.66/0.88 FOF formula (forall (X_23:real), (((eq real) ((power_power_real X_23) zero_zero_nat)) one_one_real)) of role axiom named fact_300_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J % 0.66/0.88 A new axiom: (forall (X_23:real), (((eq real) ((power_power_real X_23) zero_zero_nat)) one_one_real)) % 0.66/0.88 FOF formula (forall (X_23:nat), (((eq nat) ((power_power_nat X_23) zero_zero_nat)) one_one_nat)) of role axiom named fact_301_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J % 0.66/0.88 A new axiom: (forall (X_23:nat), (((eq nat) ((power_power_nat X_23) zero_zero_nat)) one_one_nat)) % 0.66/0.88 FOF formula (forall (X_23:int), (((eq int) ((power_power_int X_23) zero_zero_nat)) one_one_int)) of role axiom named fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J % 0.66/0.88 A new axiom: (forall (X_23:int), (((eq int) ((power_power_int X_23) zero_zero_nat)) one_one_int)) % 0.66/0.88 FOF formula (forall (A_66:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real A_66) A_66))) ((ord_less_real zero_zero_real) A_66))) of role axiom named fact_303_zero__less__double__add__iff__zero__less__single__add % 0.66/0.88 A new axiom: (forall (A_66:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real A_66) A_66))) ((ord_less_real zero_zero_real) A_66))) % 0.66/0.88 FOF formula (forall (A_66:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int A_66) A_66))) ((ord_less_int zero_zero_int) A_66))) of role axiom named fact_304_zero__less__double__add__iff__zero__less__single__add % 0.66/0.88 A new axiom: (forall (A_66:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int A_66) A_66))) ((ord_less_int zero_zero_int) A_66))) % 0.66/0.88 FOF formula (forall (A_65:real), ((iff ((ord_less_real ((plus_plus_real A_65) A_65)) zero_zero_real)) ((ord_less_real A_65) zero_zero_real))) of role axiom named fact_305_double__add__less__zero__iff__single__add__less__zero % 0.66/0.88 A new axiom: (forall (A_65:real), ((iff ((ord_less_real ((plus_plus_real A_65) A_65)) zero_zero_real)) ((ord_less_real A_65) zero_zero_real))) % 0.66/0.88 FOF formula (forall (A_65:int), ((iff ((ord_less_int ((plus_plus_int A_65) A_65)) zero_zero_int)) ((ord_less_int A_65) zero_zero_int))) of role axiom named fact_306_double__add__less__zero__iff__single__add__less__zero % 0.66/0.88 A new axiom: (forall (A_65:int), ((iff ((ord_less_int ((plus_plus_int A_65) A_65)) zero_zero_int)) ((ord_less_int A_65) zero_zero_int))) % 0.66/0.88 FOF formula (forall (X_22:real), ((iff (((eq real) zero_zero_real) X_22)) (((eq real) X_22) zero_zero_real))) of role axiom named fact_307_zero__reorient % 0.66/0.88 A new axiom: (forall (X_22:real), ((iff (((eq real) zero_zero_real) X_22)) (((eq real) X_22) zero_zero_real))) % 0.66/0.88 FOF formula (forall (X_22:nat), ((iff (((eq nat) zero_zero_nat) X_22)) (((eq nat) X_22) zero_zero_nat))) of role axiom named fact_308_zero__reorient % 0.66/0.88 A new axiom: (forall (X_22:nat), ((iff (((eq nat) zero_zero_nat) X_22)) (((eq nat) X_22) zero_zero_nat))) % 0.66/0.88 FOF formula (forall (X_22:int), ((iff (((eq int) zero_zero_int) X_22)) (((eq int) X_22) zero_zero_int))) of role axiom named fact_309_zero__reorient % 0.66/0.88 A new axiom: (forall (X_22:int), ((iff (((eq int) zero_zero_int) X_22)) (((eq int) X_22) zero_zero_int))) % 0.66/0.88 FOF formula (forall (B_47:real) (A_64:real) (C_35:real), ((((eq real) ((plus_plus_real B_47) A_64)) ((plus_plus_real C_35) A_64))->(((eq real) B_47) C_35))) of role axiom named fact_310_add__right__imp__eq % 0.66/0.90 A new axiom: (forall (B_47:real) (A_64:real) (C_35:real), ((((eq real) ((plus_plus_real B_47) A_64)) ((plus_plus_real C_35) A_64))->(((eq real) B_47) C_35))) % 0.66/0.90 FOF formula (forall (B_47:nat) (A_64:nat) (C_35:nat), ((((eq nat) ((plus_plus_nat B_47) A_64)) ((plus_plus_nat C_35) A_64))->(((eq nat) B_47) C_35))) of role axiom named fact_311_add__right__imp__eq % 0.66/0.90 A new axiom: (forall (B_47:nat) (A_64:nat) (C_35:nat), ((((eq nat) ((plus_plus_nat B_47) A_64)) ((plus_plus_nat C_35) A_64))->(((eq nat) B_47) C_35))) % 0.66/0.90 FOF formula (forall (B_47:int) (A_64:int) (C_35:int), ((((eq int) ((plus_plus_int B_47) A_64)) ((plus_plus_int C_35) A_64))->(((eq int) B_47) C_35))) of role axiom named fact_312_add__right__imp__eq % 0.66/0.90 A new axiom: (forall (B_47:int) (A_64:int) (C_35:int), ((((eq int) ((plus_plus_int B_47) A_64)) ((plus_plus_int C_35) A_64))->(((eq int) B_47) C_35))) % 0.66/0.90 FOF formula (forall (A_63:real) (B_46:real) (C_34:real), ((((eq real) ((plus_plus_real A_63) B_46)) ((plus_plus_real A_63) C_34))->(((eq real) B_46) C_34))) of role axiom named fact_313_add__imp__eq % 0.66/0.90 A new axiom: (forall (A_63:real) (B_46:real) (C_34:real), ((((eq real) ((plus_plus_real A_63) B_46)) ((plus_plus_real A_63) C_34))->(((eq real) B_46) C_34))) % 0.66/0.90 FOF formula (forall (A_63:nat) (B_46:nat) (C_34:nat), ((((eq nat) ((plus_plus_nat A_63) B_46)) ((plus_plus_nat A_63) C_34))->(((eq nat) B_46) C_34))) of role axiom named fact_314_add__imp__eq % 0.66/0.90 A new axiom: (forall (A_63:nat) (B_46:nat) (C_34:nat), ((((eq nat) ((plus_plus_nat A_63) B_46)) ((plus_plus_nat A_63) C_34))->(((eq nat) B_46) C_34))) % 0.66/0.90 FOF formula (forall (A_63:int) (B_46:int) (C_34:int), ((((eq int) ((plus_plus_int A_63) B_46)) ((plus_plus_int A_63) C_34))->(((eq int) B_46) C_34))) of role axiom named fact_315_add__imp__eq % 0.66/0.90 A new axiom: (forall (A_63:int) (B_46:int) (C_34:int), ((((eq int) ((plus_plus_int A_63) B_46)) ((plus_plus_int A_63) C_34))->(((eq int) B_46) C_34))) % 0.66/0.90 FOF formula (forall (A_62:real) (B_45:real) (C_33:real), ((((eq real) ((plus_plus_real A_62) B_45)) ((plus_plus_real A_62) C_33))->(((eq real) B_45) C_33))) of role axiom named fact_316_add__left__imp__eq % 0.66/0.90 A new axiom: (forall (A_62:real) (B_45:real) (C_33:real), ((((eq real) ((plus_plus_real A_62) B_45)) ((plus_plus_real A_62) C_33))->(((eq real) B_45) C_33))) % 0.66/0.90 FOF formula (forall (A_62:nat) (B_45:nat) (C_33:nat), ((((eq nat) ((plus_plus_nat A_62) B_45)) ((plus_plus_nat A_62) C_33))->(((eq nat) B_45) C_33))) of role axiom named fact_317_add__left__imp__eq % 0.66/0.90 A new axiom: (forall (A_62:nat) (B_45:nat) (C_33:nat), ((((eq nat) ((plus_plus_nat A_62) B_45)) ((plus_plus_nat A_62) C_33))->(((eq nat) B_45) C_33))) % 0.66/0.90 FOF formula (forall (A_62:int) (B_45:int) (C_33:int), ((((eq int) ((plus_plus_int A_62) B_45)) ((plus_plus_int A_62) C_33))->(((eq int) B_45) C_33))) of role axiom named fact_318_add__left__imp__eq % 0.66/0.90 A new axiom: (forall (A_62:int) (B_45:int) (C_33:int), ((((eq int) ((plus_plus_int A_62) B_45)) ((plus_plus_int A_62) C_33))->(((eq int) B_45) C_33))) % 0.66/0.90 FOF formula (forall (A_61:real) (B_44:real) (C_32:real) (D_6:real), (((eq real) ((plus_plus_real ((plus_plus_real A_61) B_44)) ((plus_plus_real C_32) D_6))) ((plus_plus_real ((plus_plus_real A_61) C_32)) ((plus_plus_real B_44) D_6)))) of role axiom named fact_319_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J % 0.66/0.90 A new axiom: (forall (A_61:real) (B_44:real) (C_32:real) (D_6:real), (((eq real) ((plus_plus_real ((plus_plus_real A_61) B_44)) ((plus_plus_real C_32) D_6))) ((plus_plus_real ((plus_plus_real A_61) C_32)) ((plus_plus_real B_44) D_6)))) % 0.66/0.90 FOF formula (forall (A_61:nat) (B_44:nat) (C_32:nat) (D_6:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_61) B_44)) ((plus_plus_nat C_32) D_6))) ((plus_plus_nat ((plus_plus_nat A_61) C_32)) ((plus_plus_nat B_44) D_6)))) of role axiom named fact_320_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J % 0.66/0.90 A new axiom: (forall (A_61:nat) (B_44:nat) (C_32:nat) (D_6:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_61) B_44)) ((plus_plus_nat C_32) D_6))) ((plus_plus_nat ((plus_plus_nat A_61) C_32)) ((plus_plus_nat B_44) D_6)))) % 0.75/0.92 FOF formula (forall (A_61:int) (B_44:int) (C_32:int) (D_6:int), (((eq int) ((plus_plus_int ((plus_plus_int A_61) B_44)) ((plus_plus_int C_32) D_6))) ((plus_plus_int ((plus_plus_int A_61) C_32)) ((plus_plus_int B_44) D_6)))) of role axiom named fact_321_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J % 0.75/0.92 A new axiom: (forall (A_61:int) (B_44:int) (C_32:int) (D_6:int), (((eq int) ((plus_plus_int ((plus_plus_int A_61) B_44)) ((plus_plus_int C_32) D_6))) ((plus_plus_int ((plus_plus_int A_61) C_32)) ((plus_plus_int B_44) D_6)))) % 0.75/0.92 FOF formula (forall (B_43:real) (A_60:real) (C_31:real), ((iff (((eq real) ((plus_plus_real B_43) A_60)) ((plus_plus_real C_31) A_60))) (((eq real) B_43) C_31))) of role axiom named fact_322_add__right__cancel % 0.75/0.92 A new axiom: (forall (B_43:real) (A_60:real) (C_31:real), ((iff (((eq real) ((plus_plus_real B_43) A_60)) ((plus_plus_real C_31) A_60))) (((eq real) B_43) C_31))) % 0.75/0.92 FOF formula (forall (B_43:nat) (A_60:nat) (C_31:nat), ((iff (((eq nat) ((plus_plus_nat B_43) A_60)) ((plus_plus_nat C_31) A_60))) (((eq nat) B_43) C_31))) of role axiom named fact_323_add__right__cancel % 0.75/0.92 A new axiom: (forall (B_43:nat) (A_60:nat) (C_31:nat), ((iff (((eq nat) ((plus_plus_nat B_43) A_60)) ((plus_plus_nat C_31) A_60))) (((eq nat) B_43) C_31))) % 0.75/0.92 FOF formula (forall (B_43:int) (A_60:int) (C_31:int), ((iff (((eq int) ((plus_plus_int B_43) A_60)) ((plus_plus_int C_31) A_60))) (((eq int) B_43) C_31))) of role axiom named fact_324_add__right__cancel % 0.75/0.92 A new axiom: (forall (B_43:int) (A_60:int) (C_31:int), ((iff (((eq int) ((plus_plus_int B_43) A_60)) ((plus_plus_int C_31) A_60))) (((eq int) B_43) C_31))) % 0.75/0.92 FOF formula (forall (A_59:real) (B_42:real) (C_30:real), ((iff (((eq real) ((plus_plus_real A_59) B_42)) ((plus_plus_real A_59) C_30))) (((eq real) B_42) C_30))) of role axiom named fact_325_add__left__cancel % 0.75/0.92 A new axiom: (forall (A_59:real) (B_42:real) (C_30:real), ((iff (((eq real) ((plus_plus_real A_59) B_42)) ((plus_plus_real A_59) C_30))) (((eq real) B_42) C_30))) % 0.75/0.92 FOF formula (forall (A_59:nat) (B_42:nat) (C_30:nat), ((iff (((eq nat) ((plus_plus_nat A_59) B_42)) ((plus_plus_nat A_59) C_30))) (((eq nat) B_42) C_30))) of role axiom named fact_326_add__left__cancel % 0.75/0.92 A new axiom: (forall (A_59:nat) (B_42:nat) (C_30:nat), ((iff (((eq nat) ((plus_plus_nat A_59) B_42)) ((plus_plus_nat A_59) C_30))) (((eq nat) B_42) C_30))) % 0.75/0.92 FOF formula (forall (A_59:int) (B_42:int) (C_30:int), ((iff (((eq int) ((plus_plus_int A_59) B_42)) ((plus_plus_int A_59) C_30))) (((eq int) B_42) C_30))) of role axiom named fact_327_add__left__cancel % 0.75/0.92 A new axiom: (forall (A_59:int) (B_42:int) (C_30:int), ((iff (((eq int) ((plus_plus_int A_59) B_42)) ((plus_plus_int A_59) C_30))) (((eq int) B_42) C_30))) % 0.75/0.92 FOF formula (forall (A_58:real) (B_41:real) (C_29:real), (((eq real) ((plus_plus_real ((plus_plus_real A_58) B_41)) C_29)) ((plus_plus_real ((plus_plus_real A_58) C_29)) B_41))) of role axiom named fact_328_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J % 0.75/0.92 A new axiom: (forall (A_58:real) (B_41:real) (C_29:real), (((eq real) ((plus_plus_real ((plus_plus_real A_58) B_41)) C_29)) ((plus_plus_real ((plus_plus_real A_58) C_29)) B_41))) % 0.75/0.92 FOF formula (forall (A_58:nat) (B_41:nat) (C_29:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_58) B_41)) C_29)) ((plus_plus_nat ((plus_plus_nat A_58) C_29)) B_41))) of role axiom named fact_329_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J % 0.75/0.92 A new axiom: (forall (A_58:nat) (B_41:nat) (C_29:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_58) B_41)) C_29)) ((plus_plus_nat ((plus_plus_nat A_58) C_29)) B_41))) % 0.75/0.92 FOF formula (forall (A_58:int) (B_41:int) (C_29:int), (((eq int) ((plus_plus_int ((plus_plus_int A_58) B_41)) C_29)) ((plus_plus_int ((plus_plus_int A_58) C_29)) B_41))) of role axiom named fact_330_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J % 0.75/0.92 A new axiom: (forall (A_58:int) (B_41:int) (C_29:int), (((eq int) ((plus_plus_int ((plus_plus_int A_58) B_41)) C_29)) ((plus_plus_int ((plus_plus_int A_58) C_29)) B_41))) % 0.75/0.92 FOF formula (forall (A_57:real) (B_40:real) (C_28:real), (((eq real) ((plus_plus_real ((plus_plus_real A_57) B_40)) C_28)) ((plus_plus_real A_57) ((plus_plus_real B_40) C_28)))) of role axiom named fact_331_ab__semigroup__add__class_Oadd__ac_I1_J % 0.75/0.93 A new axiom: (forall (A_57:real) (B_40:real) (C_28:real), (((eq real) ((plus_plus_real ((plus_plus_real A_57) B_40)) C_28)) ((plus_plus_real A_57) ((plus_plus_real B_40) C_28)))) % 0.75/0.93 FOF formula (forall (A_57:nat) (B_40:nat) (C_28:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_57) B_40)) C_28)) ((plus_plus_nat A_57) ((plus_plus_nat B_40) C_28)))) of role axiom named fact_332_ab__semigroup__add__class_Oadd__ac_I1_J % 0.75/0.93 A new axiom: (forall (A_57:nat) (B_40:nat) (C_28:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_57) B_40)) C_28)) ((plus_plus_nat A_57) ((plus_plus_nat B_40) C_28)))) % 0.75/0.93 FOF formula (forall (A_57:int) (B_40:int) (C_28:int), (((eq int) ((plus_plus_int ((plus_plus_int A_57) B_40)) C_28)) ((plus_plus_int A_57) ((plus_plus_int B_40) C_28)))) of role axiom named fact_333_ab__semigroup__add__class_Oadd__ac_I1_J % 0.75/0.93 A new axiom: (forall (A_57:int) (B_40:int) (C_28:int), (((eq int) ((plus_plus_int ((plus_plus_int A_57) B_40)) C_28)) ((plus_plus_int A_57) ((plus_plus_int B_40) C_28)))) % 0.75/0.93 FOF formula (forall (A_56:real) (B_39:real) (C_27:real), (((eq real) ((plus_plus_real ((plus_plus_real A_56) B_39)) C_27)) ((plus_plus_real A_56) ((plus_plus_real B_39) C_27)))) of role axiom named fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J % 0.75/0.93 A new axiom: (forall (A_56:real) (B_39:real) (C_27:real), (((eq real) ((plus_plus_real ((plus_plus_real A_56) B_39)) C_27)) ((plus_plus_real A_56) ((plus_plus_real B_39) C_27)))) % 0.75/0.93 FOF formula (forall (A_56:nat) (B_39:nat) (C_27:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_56) B_39)) C_27)) ((plus_plus_nat A_56) ((plus_plus_nat B_39) C_27)))) of role axiom named fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J % 0.75/0.93 A new axiom: (forall (A_56:nat) (B_39:nat) (C_27:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_56) B_39)) C_27)) ((plus_plus_nat A_56) ((plus_plus_nat B_39) C_27)))) % 0.75/0.93 FOF formula (forall (A_56:int) (B_39:int) (C_27:int), (((eq int) ((plus_plus_int ((plus_plus_int A_56) B_39)) C_27)) ((plus_plus_int A_56) ((plus_plus_int B_39) C_27)))) of role axiom named fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J % 0.75/0.93 A new axiom: (forall (A_56:int) (B_39:int) (C_27:int), (((eq int) ((plus_plus_int ((plus_plus_int A_56) B_39)) C_27)) ((plus_plus_int A_56) ((plus_plus_int B_39) C_27)))) % 0.75/0.93 FOF formula (forall (A_55:real) (C_26:real) (D_5:real), (((eq real) ((plus_plus_real A_55) ((plus_plus_real C_26) D_5))) ((plus_plus_real ((plus_plus_real A_55) C_26)) D_5))) of role axiom named fact_337_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J % 0.75/0.93 A new axiom: (forall (A_55:real) (C_26:real) (D_5:real), (((eq real) ((plus_plus_real A_55) ((plus_plus_real C_26) D_5))) ((plus_plus_real ((plus_plus_real A_55) C_26)) D_5))) % 0.75/0.93 FOF formula (forall (A_55:nat) (C_26:nat) (D_5:nat), (((eq nat) ((plus_plus_nat A_55) ((plus_plus_nat C_26) D_5))) ((plus_plus_nat ((plus_plus_nat A_55) C_26)) D_5))) of role axiom named fact_338_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J % 0.75/0.93 A new axiom: (forall (A_55:nat) (C_26:nat) (D_5:nat), (((eq nat) ((plus_plus_nat A_55) ((plus_plus_nat C_26) D_5))) ((plus_plus_nat ((plus_plus_nat A_55) C_26)) D_5))) % 0.75/0.93 FOF formula (forall (A_55:int) (C_26:int) (D_5:int), (((eq int) ((plus_plus_int A_55) ((plus_plus_int C_26) D_5))) ((plus_plus_int ((plus_plus_int A_55) C_26)) D_5))) of role axiom named fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J % 0.75/0.93 A new axiom: (forall (A_55:int) (C_26:int) (D_5:int), (((eq int) ((plus_plus_int A_55) ((plus_plus_int C_26) D_5))) ((plus_plus_int ((plus_plus_int A_55) C_26)) D_5))) % 0.75/0.93 FOF formula (forall (A_54:real) (C_25:real) (D_4:real), (((eq real) ((plus_plus_real A_54) ((plus_plus_real C_25) D_4))) ((plus_plus_real C_25) ((plus_plus_real A_54) D_4)))) of role axiom named fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J % 0.75/0.95 A new axiom: (forall (A_54:real) (C_25:real) (D_4:real), (((eq real) ((plus_plus_real A_54) ((plus_plus_real C_25) D_4))) ((plus_plus_real C_25) ((plus_plus_real A_54) D_4)))) % 0.75/0.95 FOF formula (forall (A_54:nat) (C_25:nat) (D_4:nat), (((eq nat) ((plus_plus_nat A_54) ((plus_plus_nat C_25) D_4))) ((plus_plus_nat C_25) ((plus_plus_nat A_54) D_4)))) of role axiom named fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J % 0.75/0.95 A new axiom: (forall (A_54:nat) (C_25:nat) (D_4:nat), (((eq nat) ((plus_plus_nat A_54) ((plus_plus_nat C_25) D_4))) ((plus_plus_nat C_25) ((plus_plus_nat A_54) D_4)))) % 0.75/0.95 FOF formula (forall (A_54:int) (C_25:int) (D_4:int), (((eq int) ((plus_plus_int A_54) ((plus_plus_int C_25) D_4))) ((plus_plus_int C_25) ((plus_plus_int A_54) D_4)))) of role axiom named fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J % 0.75/0.95 A new axiom: (forall (A_54:int) (C_25:int) (D_4:int), (((eq int) ((plus_plus_int A_54) ((plus_plus_int C_25) D_4))) ((plus_plus_int C_25) ((plus_plus_int A_54) D_4)))) % 0.75/0.95 FOF formula (forall (A_53:real) (C_24:real), (((eq real) ((plus_plus_real A_53) C_24)) ((plus_plus_real C_24) A_53))) of role axiom named fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J % 0.75/0.95 A new axiom: (forall (A_53:real) (C_24:real), (((eq real) ((plus_plus_real A_53) C_24)) ((plus_plus_real C_24) A_53))) % 0.75/0.95 FOF formula (forall (A_53:nat) (C_24:nat), (((eq nat) ((plus_plus_nat A_53) C_24)) ((plus_plus_nat C_24) A_53))) of role axiom named fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J % 0.75/0.95 A new axiom: (forall (A_53:nat) (C_24:nat), (((eq nat) ((plus_plus_nat A_53) C_24)) ((plus_plus_nat C_24) A_53))) % 0.75/0.95 FOF formula (forall (A_53:int) (C_24:int), (((eq int) ((plus_plus_int A_53) C_24)) ((plus_plus_int C_24) A_53))) of role axiom named fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J % 0.75/0.95 A new axiom: (forall (A_53:int) (C_24:int), (((eq int) ((plus_plus_int A_53) C_24)) ((plus_plus_int C_24) A_53))) % 0.75/0.95 FOF formula (forall (X_21:real), ((iff (((eq real) one_one_real) X_21)) (((eq real) X_21) one_one_real))) of role axiom named fact_346_one__reorient % 0.75/0.95 A new axiom: (forall (X_21:real), ((iff (((eq real) one_one_real) X_21)) (((eq real) X_21) one_one_real))) % 0.75/0.95 FOF formula (forall (X_21:nat), ((iff (((eq nat) one_one_nat) X_21)) (((eq nat) X_21) one_one_nat))) of role axiom named fact_347_one__reorient % 0.75/0.95 A new axiom: (forall (X_21:nat), ((iff (((eq nat) one_one_nat) X_21)) (((eq nat) X_21) one_one_nat))) % 0.75/0.95 FOF formula (forall (X_21:int), ((iff (((eq int) one_one_int) X_21)) (((eq int) X_21) one_one_int))) of role axiom named fact_348_one__reorient % 0.75/0.95 A new axiom: (forall (X_21:int), ((iff (((eq int) one_one_int) X_21)) (((eq int) X_21) one_one_int))) % 0.75/0.95 FOF formula (forall (B_38:real) (A_52:real), ((iff (((eq real) B_38) ((plus_plus_real B_38) A_52))) (((eq real) A_52) zero_zero_real))) of role axiom named fact_349_add__0__iff % 0.75/0.95 A new axiom: (forall (B_38:real) (A_52:real), ((iff (((eq real) B_38) ((plus_plus_real B_38) A_52))) (((eq real) A_52) zero_zero_real))) % 0.75/0.95 FOF formula (forall (B_38:nat) (A_52:nat), ((iff (((eq nat) B_38) ((plus_plus_nat B_38) A_52))) (((eq nat) A_52) zero_zero_nat))) of role axiom named fact_350_add__0__iff % 0.75/0.95 A new axiom: (forall (B_38:nat) (A_52:nat), ((iff (((eq nat) B_38) ((plus_plus_nat B_38) A_52))) (((eq nat) A_52) zero_zero_nat))) % 0.75/0.95 FOF formula (forall (B_38:int) (A_52:int), ((iff (((eq int) B_38) ((plus_plus_int B_38) A_52))) (((eq int) A_52) zero_zero_int))) of role axiom named fact_351_add__0__iff % 0.75/0.95 A new axiom: (forall (B_38:int) (A_52:int), ((iff (((eq int) B_38) ((plus_plus_int B_38) A_52))) (((eq int) A_52) zero_zero_int))) % 0.75/0.95 FOF formula (forall (A_51:real), (((eq real) ((plus_plus_real A_51) zero_zero_real)) A_51)) of role axiom named fact_352_add_Ocomm__neutral % 0.75/0.95 A new axiom: (forall (A_51:real), (((eq real) ((plus_plus_real A_51) zero_zero_real)) A_51)) % 0.75/0.95 FOF formula (forall (A_51:nat), (((eq nat) ((plus_plus_nat A_51) zero_zero_nat)) A_51)) of role axiom named fact_353_add_Ocomm__neutral % 0.75/0.95 A new axiom: (forall (A_51:nat), (((eq nat) ((plus_plus_nat A_51) zero_zero_nat)) A_51)) % 0.75/0.96 FOF formula (forall (A_51:int), (((eq int) ((plus_plus_int A_51) zero_zero_int)) A_51)) of role axiom named fact_354_add_Ocomm__neutral % 0.75/0.96 A new axiom: (forall (A_51:int), (((eq int) ((plus_plus_int A_51) zero_zero_int)) A_51)) % 0.75/0.96 FOF formula (forall (A_50:real), (((eq real) ((plus_plus_real A_50) zero_zero_real)) A_50)) of role axiom named fact_355_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J % 0.75/0.96 A new axiom: (forall (A_50:real), (((eq real) ((plus_plus_real A_50) zero_zero_real)) A_50)) % 0.75/0.96 FOF formula (forall (A_50:nat), (((eq nat) ((plus_plus_nat A_50) zero_zero_nat)) A_50)) of role axiom named fact_356_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J % 0.75/0.96 A new axiom: (forall (A_50:nat), (((eq nat) ((plus_plus_nat A_50) zero_zero_nat)) A_50)) % 0.75/0.96 FOF formula (forall (A_50:int), (((eq int) ((plus_plus_int A_50) zero_zero_int)) A_50)) of role axiom named fact_357_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J % 0.75/0.96 A new axiom: (forall (A_50:int), (((eq int) ((plus_plus_int A_50) zero_zero_int)) A_50)) % 0.75/0.96 FOF formula (forall (A_49:real), (((eq real) ((plus_plus_real A_49) zero_zero_real)) A_49)) of role axiom named fact_358_add__0__right % 0.75/0.96 A new axiom: (forall (A_49:real), (((eq real) ((plus_plus_real A_49) zero_zero_real)) A_49)) % 0.75/0.96 FOF formula (forall (A_49:nat), (((eq nat) ((plus_plus_nat A_49) zero_zero_nat)) A_49)) of role axiom named fact_359_add__0__right % 0.75/0.96 A new axiom: (forall (A_49:nat), (((eq nat) ((plus_plus_nat A_49) zero_zero_nat)) A_49)) % 0.75/0.96 FOF formula (forall (A_49:int), (((eq int) ((plus_plus_int A_49) zero_zero_int)) A_49)) of role axiom named fact_360_add__0__right % 0.75/0.96 A new axiom: (forall (A_49:int), (((eq int) ((plus_plus_int A_49) zero_zero_int)) A_49)) % 0.75/0.96 FOF formula (forall (A_48:real), ((iff (((eq real) zero_zero_real) ((plus_plus_real A_48) A_48))) (((eq real) A_48) zero_zero_real))) of role axiom named fact_361_double__zero__sym % 0.75/0.96 A new axiom: (forall (A_48:real), ((iff (((eq real) zero_zero_real) ((plus_plus_real A_48) A_48))) (((eq real) A_48) zero_zero_real))) % 0.75/0.96 FOF formula (forall (A_48:int), ((iff (((eq int) zero_zero_int) ((plus_plus_int A_48) A_48))) (((eq int) A_48) zero_zero_int))) of role axiom named fact_362_double__zero__sym % 0.75/0.96 A new axiom: (forall (A_48:int), ((iff (((eq int) zero_zero_int) ((plus_plus_int A_48) A_48))) (((eq int) A_48) zero_zero_int))) % 0.75/0.96 FOF formula (forall (A_47:real), (((eq real) ((plus_plus_real zero_zero_real) A_47)) A_47)) of role axiom named fact_363_add__0 % 0.75/0.96 A new axiom: (forall (A_47:real), (((eq real) ((plus_plus_real zero_zero_real) A_47)) A_47)) % 0.75/0.96 FOF formula (forall (A_47:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_47)) A_47)) of role axiom named fact_364_add__0 % 0.75/0.96 A new axiom: (forall (A_47:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_47)) A_47)) % 0.75/0.96 FOF formula (forall (A_47:int), (((eq int) ((plus_plus_int zero_zero_int) A_47)) A_47)) of role axiom named fact_365_add__0 % 0.75/0.96 A new axiom: (forall (A_47:int), (((eq int) ((plus_plus_int zero_zero_int) A_47)) A_47)) % 0.75/0.96 FOF formula (forall (A_46:real), (((eq real) ((plus_plus_real zero_zero_real) A_46)) A_46)) of role axiom named fact_366_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J % 0.75/0.96 A new axiom: (forall (A_46:real), (((eq real) ((plus_plus_real zero_zero_real) A_46)) A_46)) % 0.75/0.96 FOF formula (forall (A_46:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_46)) A_46)) of role axiom named fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J % 0.75/0.96 A new axiom: (forall (A_46:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_46)) A_46)) % 0.75/0.96 FOF formula (forall (A_46:int), (((eq int) ((plus_plus_int zero_zero_int) A_46)) A_46)) of role axiom named fact_368_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J % 0.75/0.96 A new axiom: (forall (A_46:int), (((eq int) ((plus_plus_int zero_zero_int) A_46)) A_46)) % 0.75/0.96 FOF formula (forall (A_45:real), (((eq real) ((plus_plus_real zero_zero_real) A_45)) A_45)) of role axiom named fact_369_add__0__left % 0.75/0.96 A new axiom: (forall (A_45:real), (((eq real) ((plus_plus_real zero_zero_real) A_45)) A_45)) % 0.75/0.96 FOF formula (forall (A_45:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_45)) A_45)) of role axiom named fact_370_add__0__left % 0.75/0.98 A new axiom: (forall (A_45:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_45)) A_45)) % 0.75/0.98 FOF formula (forall (A_45:int), (((eq int) ((plus_plus_int zero_zero_int) A_45)) A_45)) of role axiom named fact_371_add__0__left % 0.75/0.98 A new axiom: (forall (A_45:int), (((eq int) ((plus_plus_int zero_zero_int) A_45)) A_45)) % 0.75/0.98 FOF formula (forall (C_23:real) (A_44:real) (B_37:real), (((ord_less_real ((plus_plus_real C_23) A_44)) ((plus_plus_real C_23) B_37))->((ord_less_real A_44) B_37))) of role axiom named fact_372_add__less__imp__less__left % 0.75/0.98 A new axiom: (forall (C_23:real) (A_44:real) (B_37:real), (((ord_less_real ((plus_plus_real C_23) A_44)) ((plus_plus_real C_23) B_37))->((ord_less_real A_44) B_37))) % 0.75/0.98 FOF formula (forall (C_23:nat) (A_44:nat) (B_37:nat), (((ord_less_nat ((plus_plus_nat C_23) A_44)) ((plus_plus_nat C_23) B_37))->((ord_less_nat A_44) B_37))) of role axiom named fact_373_add__less__imp__less__left % 0.75/0.98 A new axiom: (forall (C_23:nat) (A_44:nat) (B_37:nat), (((ord_less_nat ((plus_plus_nat C_23) A_44)) ((plus_plus_nat C_23) B_37))->((ord_less_nat A_44) B_37))) % 0.75/0.98 FOF formula (forall (C_23:int) (A_44:int) (B_37:int), (((ord_less_int ((plus_plus_int C_23) A_44)) ((plus_plus_int C_23) B_37))->((ord_less_int A_44) B_37))) of role axiom named fact_374_add__less__imp__less__left % 0.75/0.98 A new axiom: (forall (C_23:int) (A_44:int) (B_37:int), (((ord_less_int ((plus_plus_int C_23) A_44)) ((plus_plus_int C_23) B_37))->((ord_less_int A_44) B_37))) % 0.75/0.98 FOF formula (forall (A_43:real) (C_22:real) (B_36:real), (((ord_less_real ((plus_plus_real A_43) C_22)) ((plus_plus_real B_36) C_22))->((ord_less_real A_43) B_36))) of role axiom named fact_375_add__less__imp__less__right % 0.75/0.98 A new axiom: (forall (A_43:real) (C_22:real) (B_36:real), (((ord_less_real ((plus_plus_real A_43) C_22)) ((plus_plus_real B_36) C_22))->((ord_less_real A_43) B_36))) % 0.75/0.98 FOF formula (forall (A_43:nat) (C_22:nat) (B_36:nat), (((ord_less_nat ((plus_plus_nat A_43) C_22)) ((plus_plus_nat B_36) C_22))->((ord_less_nat A_43) B_36))) of role axiom named fact_376_add__less__imp__less__right % 0.75/0.98 A new axiom: (forall (A_43:nat) (C_22:nat) (B_36:nat), (((ord_less_nat ((plus_plus_nat A_43) C_22)) ((plus_plus_nat B_36) C_22))->((ord_less_nat A_43) B_36))) % 0.75/0.98 FOF formula (forall (A_43:int) (C_22:int) (B_36:int), (((ord_less_int ((plus_plus_int A_43) C_22)) ((plus_plus_int B_36) C_22))->((ord_less_int A_43) B_36))) of role axiom named fact_377_add__less__imp__less__right % 0.75/0.98 A new axiom: (forall (A_43:int) (C_22:int) (B_36:int), (((ord_less_int ((plus_plus_int A_43) C_22)) ((plus_plus_int B_36) C_22))->((ord_less_int A_43) B_36))) % 0.75/0.98 FOF formula (forall (C_21:real) (D_3:real) (A_42:real) (B_35:real), (((ord_less_real A_42) B_35)->(((ord_less_real C_21) D_3)->((ord_less_real ((plus_plus_real A_42) C_21)) ((plus_plus_real B_35) D_3))))) of role axiom named fact_378_add__strict__mono % 0.75/0.98 A new axiom: (forall (C_21:real) (D_3:real) (A_42:real) (B_35:real), (((ord_less_real A_42) B_35)->(((ord_less_real C_21) D_3)->((ord_less_real ((plus_plus_real A_42) C_21)) ((plus_plus_real B_35) D_3))))) % 0.75/0.98 FOF formula (forall (C_21:nat) (D_3:nat) (A_42:nat) (B_35:nat), (((ord_less_nat A_42) B_35)->(((ord_less_nat C_21) D_3)->((ord_less_nat ((plus_plus_nat A_42) C_21)) ((plus_plus_nat B_35) D_3))))) of role axiom named fact_379_add__strict__mono % 0.75/0.98 A new axiom: (forall (C_21:nat) (D_3:nat) (A_42:nat) (B_35:nat), (((ord_less_nat A_42) B_35)->(((ord_less_nat C_21) D_3)->((ord_less_nat ((plus_plus_nat A_42) C_21)) ((plus_plus_nat B_35) D_3))))) % 0.75/0.98 FOF formula (forall (C_21:int) (D_3:int) (A_42:int) (B_35:int), (((ord_less_int A_42) B_35)->(((ord_less_int C_21) D_3)->((ord_less_int ((plus_plus_int A_42) C_21)) ((plus_plus_int B_35) D_3))))) of role axiom named fact_380_add__strict__mono % 0.75/0.98 A new axiom: (forall (C_21:int) (D_3:int) (A_42:int) (B_35:int), (((ord_less_int A_42) B_35)->(((ord_less_int C_21) D_3)->((ord_less_int ((plus_plus_int A_42) C_21)) ((plus_plus_int B_35) D_3))))) % 0.75/0.98 FOF formula (forall (C_20:real) (A_41:real) (B_34:real), (((ord_less_real A_41) B_34)->((ord_less_real ((plus_plus_real C_20) A_41)) ((plus_plus_real C_20) B_34)))) of role axiom named fact_381_add__strict__left__mono % 0.82/1.00 A new axiom: (forall (C_20:real) (A_41:real) (B_34:real), (((ord_less_real A_41) B_34)->((ord_less_real ((plus_plus_real C_20) A_41)) ((plus_plus_real C_20) B_34)))) % 0.82/1.00 FOF formula (forall (C_20:nat) (A_41:nat) (B_34:nat), (((ord_less_nat A_41) B_34)->((ord_less_nat ((plus_plus_nat C_20) A_41)) ((plus_plus_nat C_20) B_34)))) of role axiom named fact_382_add__strict__left__mono % 0.82/1.00 A new axiom: (forall (C_20:nat) (A_41:nat) (B_34:nat), (((ord_less_nat A_41) B_34)->((ord_less_nat ((plus_plus_nat C_20) A_41)) ((plus_plus_nat C_20) B_34)))) % 0.82/1.00 FOF formula (forall (C_20:int) (A_41:int) (B_34:int), (((ord_less_int A_41) B_34)->((ord_less_int ((plus_plus_int C_20) A_41)) ((plus_plus_int C_20) B_34)))) of role axiom named fact_383_add__strict__left__mono % 0.82/1.00 A new axiom: (forall (C_20:int) (A_41:int) (B_34:int), (((ord_less_int A_41) B_34)->((ord_less_int ((plus_plus_int C_20) A_41)) ((plus_plus_int C_20) B_34)))) % 0.82/1.00 FOF formula (forall (C_19:real) (A_40:real) (B_33:real), (((ord_less_real A_40) B_33)->((ord_less_real ((plus_plus_real A_40) C_19)) ((plus_plus_real B_33) C_19)))) of role axiom named fact_384_add__strict__right__mono % 0.82/1.00 A new axiom: (forall (C_19:real) (A_40:real) (B_33:real), (((ord_less_real A_40) B_33)->((ord_less_real ((plus_plus_real A_40) C_19)) ((plus_plus_real B_33) C_19)))) % 0.82/1.00 FOF formula (forall (C_19:nat) (A_40:nat) (B_33:nat), (((ord_less_nat A_40) B_33)->((ord_less_nat ((plus_plus_nat A_40) C_19)) ((plus_plus_nat B_33) C_19)))) of role axiom named fact_385_add__strict__right__mono % 0.82/1.00 A new axiom: (forall (C_19:nat) (A_40:nat) (B_33:nat), (((ord_less_nat A_40) B_33)->((ord_less_nat ((plus_plus_nat A_40) C_19)) ((plus_plus_nat B_33) C_19)))) % 0.82/1.00 FOF formula (forall (C_19:int) (A_40:int) (B_33:int), (((ord_less_int A_40) B_33)->((ord_less_int ((plus_plus_int A_40) C_19)) ((plus_plus_int B_33) C_19)))) of role axiom named fact_386_add__strict__right__mono % 0.82/1.00 A new axiom: (forall (C_19:int) (A_40:int) (B_33:int), (((ord_less_int A_40) B_33)->((ord_less_int ((plus_plus_int A_40) C_19)) ((plus_plus_int B_33) C_19)))) % 0.82/1.00 FOF formula (forall (C_18:real) (A_39:real) (B_32:real), ((iff ((ord_less_real ((plus_plus_real C_18) A_39)) ((plus_plus_real C_18) B_32))) ((ord_less_real A_39) B_32))) of role axiom named fact_387_add__less__cancel__left % 0.82/1.00 A new axiom: (forall (C_18:real) (A_39:real) (B_32:real), ((iff ((ord_less_real ((plus_plus_real C_18) A_39)) ((plus_plus_real C_18) B_32))) ((ord_less_real A_39) B_32))) % 0.82/1.00 FOF formula (forall (C_18:nat) (A_39:nat) (B_32:nat), ((iff ((ord_less_nat ((plus_plus_nat C_18) A_39)) ((plus_plus_nat C_18) B_32))) ((ord_less_nat A_39) B_32))) of role axiom named fact_388_add__less__cancel__left % 0.82/1.00 A new axiom: (forall (C_18:nat) (A_39:nat) (B_32:nat), ((iff ((ord_less_nat ((plus_plus_nat C_18) A_39)) ((plus_plus_nat C_18) B_32))) ((ord_less_nat A_39) B_32))) % 0.82/1.00 FOF formula (forall (C_18:int) (A_39:int) (B_32:int), ((iff ((ord_less_int ((plus_plus_int C_18) A_39)) ((plus_plus_int C_18) B_32))) ((ord_less_int A_39) B_32))) of role axiom named fact_389_add__less__cancel__left % 0.82/1.00 A new axiom: (forall (C_18:int) (A_39:int) (B_32:int), ((iff ((ord_less_int ((plus_plus_int C_18) A_39)) ((plus_plus_int C_18) B_32))) ((ord_less_int A_39) B_32))) % 0.82/1.00 FOF formula (forall (A_38:real) (C_17:real) (B_31:real), ((iff ((ord_less_real ((plus_plus_real A_38) C_17)) ((plus_plus_real B_31) C_17))) ((ord_less_real A_38) B_31))) of role axiom named fact_390_add__less__cancel__right % 0.82/1.00 A new axiom: (forall (A_38:real) (C_17:real) (B_31:real), ((iff ((ord_less_real ((plus_plus_real A_38) C_17)) ((plus_plus_real B_31) C_17))) ((ord_less_real A_38) B_31))) % 0.82/1.00 FOF formula (forall (A_38:nat) (C_17:nat) (B_31:nat), ((iff ((ord_less_nat ((plus_plus_nat A_38) C_17)) ((plus_plus_nat B_31) C_17))) ((ord_less_nat A_38) B_31))) of role axiom named fact_391_add__less__cancel__right % 0.82/1.00 A new axiom: (forall (A_38:nat) (C_17:nat) (B_31:nat), ((iff ((ord_less_nat ((plus_plus_nat A_38) C_17)) ((plus_plus_nat B_31) C_17))) ((ord_less_nat A_38) B_31))) % 0.82/1.00 FOF formula (forall (A_38:int) (C_17:int) (B_31:int), ((iff ((ord_less_int ((plus_plus_int A_38) C_17)) ((plus_plus_int B_31) C_17))) ((ord_less_int A_38) B_31))) of role axiom named fact_392_add__less__cancel__right % 0.82/1.02 A new axiom: (forall (A_38:int) (C_17:int) (B_31:int), ((iff ((ord_less_int ((plus_plus_int A_38) C_17)) ((plus_plus_int B_31) C_17))) ((ord_less_int A_38) B_31))) % 0.82/1.02 FOF formula (forall (X_20:real), (((eq real) ((power_power_real X_20) one_one_nat)) X_20)) of role axiom named fact_393_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J % 0.82/1.02 A new axiom: (forall (X_20:real), (((eq real) ((power_power_real X_20) one_one_nat)) X_20)) % 0.82/1.02 FOF formula (forall (X_20:nat), (((eq nat) ((power_power_nat X_20) one_one_nat)) X_20)) of role axiom named fact_394_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J % 0.82/1.02 A new axiom: (forall (X_20:nat), (((eq nat) ((power_power_nat X_20) one_one_nat)) X_20)) % 0.82/1.02 FOF formula (forall (X_20:int), (((eq int) ((power_power_int X_20) one_one_nat)) X_20)) of role axiom named fact_395_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J % 0.82/1.02 A new axiom: (forall (X_20:int), (((eq int) ((power_power_int X_20) one_one_nat)) X_20)) % 0.82/1.02 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_396_nat__power__eq__0__iff % 0.82/1.02 A new axiom: (forall (M:nat) (N:nat), ((iff (((eq nat) ((power_power_nat M) N)) zero_zero_nat)) ((and (not (((eq nat) N) zero_zero_nat))) (((eq nat) M) zero_zero_nat)))) % 0.82/1.02 FOF formula (forall (B_30:real) (A_37:real), (((ord_less_real A_37) zero_zero_real)->(((ord_less_real B_30) zero_zero_real)->((ord_less_real ((plus_plus_real A_37) B_30)) zero_zero_real)))) of role axiom named fact_397_add__neg__neg % 0.82/1.02 A new axiom: (forall (B_30:real) (A_37:real), (((ord_less_real A_37) zero_zero_real)->(((ord_less_real B_30) zero_zero_real)->((ord_less_real ((plus_plus_real A_37) B_30)) zero_zero_real)))) % 0.82/1.02 FOF formula (forall (B_30:nat) (A_37:nat), (((ord_less_nat A_37) zero_zero_nat)->(((ord_less_nat B_30) zero_zero_nat)->((ord_less_nat ((plus_plus_nat A_37) B_30)) zero_zero_nat)))) of role axiom named fact_398_add__neg__neg % 0.82/1.02 A new axiom: (forall (B_30:nat) (A_37:nat), (((ord_less_nat A_37) zero_zero_nat)->(((ord_less_nat B_30) zero_zero_nat)->((ord_less_nat ((plus_plus_nat A_37) B_30)) zero_zero_nat)))) % 0.82/1.02 FOF formula (forall (B_30:int) (A_37:int), (((ord_less_int A_37) zero_zero_int)->(((ord_less_int B_30) zero_zero_int)->((ord_less_int ((plus_plus_int A_37) B_30)) zero_zero_int)))) of role axiom named fact_399_add__neg__neg % 0.82/1.02 A new axiom: (forall (B_30:int) (A_37:int), (((ord_less_int A_37) zero_zero_int)->(((ord_less_int B_30) zero_zero_int)->((ord_less_int ((plus_plus_int A_37) B_30)) zero_zero_int)))) % 0.82/1.02 FOF formula (forall (B_29:real) (A_36:real), (((ord_less_real zero_zero_real) A_36)->(((ord_less_real zero_zero_real) B_29)->((ord_less_real zero_zero_real) ((plus_plus_real A_36) B_29))))) of role axiom named fact_400_add__pos__pos % 0.82/1.02 A new axiom: (forall (B_29:real) (A_36:real), (((ord_less_real zero_zero_real) A_36)->(((ord_less_real zero_zero_real) B_29)->((ord_less_real zero_zero_real) ((plus_plus_real A_36) B_29))))) % 0.82/1.02 FOF formula (forall (B_29:nat) (A_36:nat), (((ord_less_nat zero_zero_nat) A_36)->(((ord_less_nat zero_zero_nat) B_29)->((ord_less_nat zero_zero_nat) ((plus_plus_nat A_36) B_29))))) of role axiom named fact_401_add__pos__pos % 0.82/1.02 A new axiom: (forall (B_29:nat) (A_36:nat), (((ord_less_nat zero_zero_nat) A_36)->(((ord_less_nat zero_zero_nat) B_29)->((ord_less_nat zero_zero_nat) ((plus_plus_nat A_36) B_29))))) % 0.82/1.02 FOF formula (forall (B_29:int) (A_36:int), (((ord_less_int zero_zero_int) A_36)->(((ord_less_int zero_zero_int) B_29)->((ord_less_int zero_zero_int) ((plus_plus_int A_36) B_29))))) of role axiom named fact_402_add__pos__pos % 0.82/1.02 A new axiom: (forall (B_29:int) (A_36:int), (((ord_less_int zero_zero_int) A_36)->(((ord_less_int zero_zero_int) B_29)->((ord_less_int zero_zero_int) ((plus_plus_int A_36) B_29))))) % 0.82/1.02 FOF formula (forall (A:real) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_real zero_zero_real) A)->((ex real) (fun (X_14:real)=> ((and ((and ((ord_less_real zero_zero_real) X_14)) (((eq real) ((power_power_real X_14) N)) A))) (forall (Y_18:real), (((and ((ord_less_real zero_zero_real) Y_18)) (((eq real) ((power_power_real Y_18) N)) A))->(((eq real) Y_18) X_14))))))))) of role axiom named fact_403_realpow__pos__nth__unique % 0.82/1.03 A new axiom: (forall (A:real) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_real zero_zero_real) A)->((ex real) (fun (X_14:real)=> ((and ((and ((ord_less_real zero_zero_real) X_14)) (((eq real) ((power_power_real X_14) N)) A))) (forall (Y_18:real), (((and ((ord_less_real zero_zero_real) Y_18)) (((eq real) ((power_power_real Y_18) N)) A))->(((eq real) Y_18) X_14))))))))) % 0.82/1.03 FOF formula (forall (A:real) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_real zero_zero_real) A)->((ex real) (fun (R:real)=> ((and ((ord_less_real zero_zero_real) R)) (((eq real) ((power_power_real R) N)) A))))))) of role axiom named fact_404_realpow__pos__nth % 0.82/1.03 A new axiom: (forall (A:real) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_real zero_zero_real) A)->((ex real) (fun (R:real)=> ((and ((ord_less_real zero_zero_real) R)) (((eq real) ((power_power_real R) N)) A))))))) % 0.82/1.03 FOF formula ((ord_less_eq_int one_one_int) t) of role axiom named fact_405_tpos % 0.82/1.03 A new axiom: ((ord_less_eq_int one_one_int) t) % 0.82/1.03 FOF formula (forall (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) one_one_nat)) one_one_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) one_one_nat)) (number_number_of_nat (succ V_1)))))) of role axiom named fact_406_nat__number__of__add__1 % 0.82/1.03 A new axiom: (forall (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) one_one_nat)) one_one_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) one_one_nat)) (number_number_of_nat (succ V_1)))))) % 0.82/1.03 FOF formula (forall (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V_1))) one_one_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V_1))) (number_number_of_nat (succ V_1)))))) of role axiom named fact_407_nat__1__add__number__of % 0.82/1.03 A new axiom: (forall (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V_1))) one_one_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V_1))) (number_number_of_nat (succ V_1)))))) % 0.82/1.03 FOF formula (forall (A_35:real) (C_16:real) (B_28:real), ((iff ((ord_less_eq_real ((plus_plus_real A_35) C_16)) ((plus_plus_real B_28) C_16))) ((ord_less_eq_real A_35) B_28))) of role axiom named fact_408_add__le__cancel__right % 0.82/1.03 A new axiom: (forall (A_35:real) (C_16:real) (B_28:real), ((iff ((ord_less_eq_real ((plus_plus_real A_35) C_16)) ((plus_plus_real B_28) C_16))) ((ord_less_eq_real A_35) B_28))) % 0.82/1.03 FOF formula (forall (A_35:nat) (C_16:nat) (B_28:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat A_35) C_16)) ((plus_plus_nat B_28) C_16))) ((ord_less_eq_nat A_35) B_28))) of role axiom named fact_409_add__le__cancel__right % 0.82/1.03 A new axiom: (forall (A_35:nat) (C_16:nat) (B_28:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat A_35) C_16)) ((plus_plus_nat B_28) C_16))) ((ord_less_eq_nat A_35) B_28))) % 0.82/1.03 FOF formula (forall (A_35:int) (C_16:int) (B_28:int), ((iff ((ord_less_eq_int ((plus_plus_int A_35) C_16)) ((plus_plus_int B_28) C_16))) ((ord_less_eq_int A_35) B_28))) of role axiom named fact_410_add__le__cancel__right % 0.82/1.03 A new axiom: (forall (A_35:int) (C_16:int) (B_28:int), ((iff ((ord_less_eq_int ((plus_plus_int A_35) C_16)) ((plus_plus_int B_28) C_16))) ((ord_less_eq_int A_35) B_28))) % 0.82/1.03 FOF formula (forall (C_15:real) (A_34:real) (B_27:real), ((iff ((ord_less_eq_real ((plus_plus_real C_15) A_34)) ((plus_plus_real C_15) B_27))) ((ord_less_eq_real A_34) B_27))) of role axiom named fact_411_add__le__cancel__left % 0.82/1.03 A new axiom: (forall (C_15:real) (A_34:real) (B_27:real), ((iff ((ord_less_eq_real ((plus_plus_real C_15) A_34)) ((plus_plus_real C_15) B_27))) ((ord_less_eq_real A_34) B_27))) % 0.82/1.05 FOF formula (forall (C_15:nat) (A_34:nat) (B_27:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat C_15) A_34)) ((plus_plus_nat C_15) B_27))) ((ord_less_eq_nat A_34) B_27))) of role axiom named fact_412_add__le__cancel__left % 0.82/1.05 A new axiom: (forall (C_15:nat) (A_34:nat) (B_27:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat C_15) A_34)) ((plus_plus_nat C_15) B_27))) ((ord_less_eq_nat A_34) B_27))) % 0.82/1.05 FOF formula (forall (C_15:int) (A_34:int) (B_27:int), ((iff ((ord_less_eq_int ((plus_plus_int C_15) A_34)) ((plus_plus_int C_15) B_27))) ((ord_less_eq_int A_34) B_27))) of role axiom named fact_413_add__le__cancel__left % 0.82/1.05 A new axiom: (forall (C_15:int) (A_34:int) (B_27:int), ((iff ((ord_less_eq_int ((plus_plus_int C_15) A_34)) ((plus_plus_int C_15) B_27))) ((ord_less_eq_int A_34) B_27))) % 0.82/1.05 FOF formula (forall (C_14:real) (A_33:real) (B_26:real), (((ord_less_eq_real A_33) B_26)->((ord_less_eq_real ((plus_plus_real A_33) C_14)) ((plus_plus_real B_26) C_14)))) of role axiom named fact_414_add__right__mono % 0.82/1.05 A new axiom: (forall (C_14:real) (A_33:real) (B_26:real), (((ord_less_eq_real A_33) B_26)->((ord_less_eq_real ((plus_plus_real A_33) C_14)) ((plus_plus_real B_26) C_14)))) % 0.82/1.05 FOF formula (forall (C_14:nat) (A_33:nat) (B_26:nat), (((ord_less_eq_nat A_33) B_26)->((ord_less_eq_nat ((plus_plus_nat A_33) C_14)) ((plus_plus_nat B_26) C_14)))) of role axiom named fact_415_add__right__mono % 0.82/1.05 A new axiom: (forall (C_14:nat) (A_33:nat) (B_26:nat), (((ord_less_eq_nat A_33) B_26)->((ord_less_eq_nat ((plus_plus_nat A_33) C_14)) ((plus_plus_nat B_26) C_14)))) % 0.82/1.05 FOF formula (forall (C_14:int) (A_33:int) (B_26:int), (((ord_less_eq_int A_33) B_26)->((ord_less_eq_int ((plus_plus_int A_33) C_14)) ((plus_plus_int B_26) C_14)))) of role axiom named fact_416_add__right__mono % 0.82/1.05 A new axiom: (forall (C_14:int) (A_33:int) (B_26:int), (((ord_less_eq_int A_33) B_26)->((ord_less_eq_int ((plus_plus_int A_33) C_14)) ((plus_plus_int B_26) C_14)))) % 0.82/1.05 FOF formula (forall (C_13:real) (A_32:real) (B_25:real), (((ord_less_eq_real A_32) B_25)->((ord_less_eq_real ((plus_plus_real C_13) A_32)) ((plus_plus_real C_13) B_25)))) of role axiom named fact_417_add__left__mono % 0.82/1.05 A new axiom: (forall (C_13:real) (A_32:real) (B_25:real), (((ord_less_eq_real A_32) B_25)->((ord_less_eq_real ((plus_plus_real C_13) A_32)) ((plus_plus_real C_13) B_25)))) % 0.82/1.05 FOF formula (forall (C_13:nat) (A_32:nat) (B_25:nat), (((ord_less_eq_nat A_32) B_25)->((ord_less_eq_nat ((plus_plus_nat C_13) A_32)) ((plus_plus_nat C_13) B_25)))) of role axiom named fact_418_add__left__mono % 0.82/1.05 A new axiom: (forall (C_13:nat) (A_32:nat) (B_25:nat), (((ord_less_eq_nat A_32) B_25)->((ord_less_eq_nat ((plus_plus_nat C_13) A_32)) ((plus_plus_nat C_13) B_25)))) % 0.82/1.05 FOF formula (forall (C_13:int) (A_32:int) (B_25:int), (((ord_less_eq_int A_32) B_25)->((ord_less_eq_int ((plus_plus_int C_13) A_32)) ((plus_plus_int C_13) B_25)))) of role axiom named fact_419_add__left__mono % 0.82/1.05 A new axiom: (forall (C_13:int) (A_32:int) (B_25:int), (((ord_less_eq_int A_32) B_25)->((ord_less_eq_int ((plus_plus_int C_13) A_32)) ((plus_plus_int C_13) B_25)))) % 0.82/1.05 FOF formula (forall (C_12:real) (D_2:real) (A_31:real) (B_24:real), (((ord_less_eq_real A_31) B_24)->(((ord_less_eq_real C_12) D_2)->((ord_less_eq_real ((plus_plus_real A_31) C_12)) ((plus_plus_real B_24) D_2))))) of role axiom named fact_420_add__mono % 0.82/1.05 A new axiom: (forall (C_12:real) (D_2:real) (A_31:real) (B_24:real), (((ord_less_eq_real A_31) B_24)->(((ord_less_eq_real C_12) D_2)->((ord_less_eq_real ((plus_plus_real A_31) C_12)) ((plus_plus_real B_24) D_2))))) % 0.82/1.05 FOF formula (forall (C_12:nat) (D_2:nat) (A_31:nat) (B_24:nat), (((ord_less_eq_nat A_31) B_24)->(((ord_less_eq_nat C_12) D_2)->((ord_less_eq_nat ((plus_plus_nat A_31) C_12)) ((plus_plus_nat B_24) D_2))))) of role axiom named fact_421_add__mono % 0.82/1.05 A new axiom: (forall (C_12:nat) (D_2:nat) (A_31:nat) (B_24:nat), (((ord_less_eq_nat A_31) B_24)->(((ord_less_eq_nat C_12) D_2)->((ord_less_eq_nat ((plus_plus_nat A_31) C_12)) ((plus_plus_nat B_24) D_2))))) % 0.90/1.07 FOF formula (forall (C_12:int) (D_2:int) (A_31:int) (B_24:int), (((ord_less_eq_int A_31) B_24)->(((ord_less_eq_int C_12) D_2)->((ord_less_eq_int ((plus_plus_int A_31) C_12)) ((plus_plus_int B_24) D_2))))) of role axiom named fact_422_add__mono % 0.90/1.07 A new axiom: (forall (C_12:int) (D_2:int) (A_31:int) (B_24:int), (((ord_less_eq_int A_31) B_24)->(((ord_less_eq_int C_12) D_2)->((ord_less_eq_int ((plus_plus_int A_31) C_12)) ((plus_plus_int B_24) D_2))))) % 0.90/1.07 FOF formula (forall (A_30:real) (C_11:real) (B_23:real), (((ord_less_eq_real ((plus_plus_real A_30) C_11)) ((plus_plus_real B_23) C_11))->((ord_less_eq_real A_30) B_23))) of role axiom named fact_423_add__le__imp__le__right % 0.90/1.07 A new axiom: (forall (A_30:real) (C_11:real) (B_23:real), (((ord_less_eq_real ((plus_plus_real A_30) C_11)) ((plus_plus_real B_23) C_11))->((ord_less_eq_real A_30) B_23))) % 0.90/1.07 FOF formula (forall (A_30:nat) (C_11:nat) (B_23:nat), (((ord_less_eq_nat ((plus_plus_nat A_30) C_11)) ((plus_plus_nat B_23) C_11))->((ord_less_eq_nat A_30) B_23))) of role axiom named fact_424_add__le__imp__le__right % 0.90/1.07 A new axiom: (forall (A_30:nat) (C_11:nat) (B_23:nat), (((ord_less_eq_nat ((plus_plus_nat A_30) C_11)) ((plus_plus_nat B_23) C_11))->((ord_less_eq_nat A_30) B_23))) % 0.90/1.07 FOF formula (forall (A_30:int) (C_11:int) (B_23:int), (((ord_less_eq_int ((plus_plus_int A_30) C_11)) ((plus_plus_int B_23) C_11))->((ord_less_eq_int A_30) B_23))) of role axiom named fact_425_add__le__imp__le__right % 0.90/1.07 A new axiom: (forall (A_30:int) (C_11:int) (B_23:int), (((ord_less_eq_int ((plus_plus_int A_30) C_11)) ((plus_plus_int B_23) C_11))->((ord_less_eq_int A_30) B_23))) % 0.90/1.07 FOF formula (forall (C_10:real) (A_29:real) (B_22:real), (((ord_less_eq_real ((plus_plus_real C_10) A_29)) ((plus_plus_real C_10) B_22))->((ord_less_eq_real A_29) B_22))) of role axiom named fact_426_add__le__imp__le__left % 0.90/1.07 A new axiom: (forall (C_10:real) (A_29:real) (B_22:real), (((ord_less_eq_real ((plus_plus_real C_10) A_29)) ((plus_plus_real C_10) B_22))->((ord_less_eq_real A_29) B_22))) % 0.90/1.07 FOF formula (forall (C_10:nat) (A_29:nat) (B_22:nat), (((ord_less_eq_nat ((plus_plus_nat C_10) A_29)) ((plus_plus_nat C_10) B_22))->((ord_less_eq_nat A_29) B_22))) of role axiom named fact_427_add__le__imp__le__left % 0.90/1.07 A new axiom: (forall (C_10:nat) (A_29:nat) (B_22:nat), (((ord_less_eq_nat ((plus_plus_nat C_10) A_29)) ((plus_plus_nat C_10) B_22))->((ord_less_eq_nat A_29) B_22))) % 0.90/1.07 FOF formula (forall (C_10:int) (A_29:int) (B_22:int), (((ord_less_eq_int ((plus_plus_int C_10) A_29)) ((plus_plus_int C_10) B_22))->((ord_less_eq_int A_29) B_22))) of role axiom named fact_428_add__le__imp__le__left % 0.90/1.07 A new axiom: (forall (C_10:int) (A_29:int) (B_22:int), (((ord_less_eq_int ((plus_plus_int C_10) A_29)) ((plus_plus_int C_10) B_22))->((ord_less_eq_int A_29) B_22))) % 0.90/1.07 FOF formula (forall (A_28:real) (N_14:nat) (N_13:nat), (((ord_less_eq_nat N_14) N_13)->(((ord_less_eq_real one_one_real) A_28)->((ord_less_eq_real ((power_power_real A_28) N_14)) ((power_power_real A_28) N_13))))) of role axiom named fact_429_power__increasing % 0.90/1.07 A new axiom: (forall (A_28:real) (N_14:nat) (N_13:nat), (((ord_less_eq_nat N_14) N_13)->(((ord_less_eq_real one_one_real) A_28)->((ord_less_eq_real ((power_power_real A_28) N_14)) ((power_power_real A_28) N_13))))) % 0.90/1.07 FOF formula (forall (A_28:nat) (N_14:nat) (N_13:nat), (((ord_less_eq_nat N_14) N_13)->(((ord_less_eq_nat one_one_nat) A_28)->((ord_less_eq_nat ((power_power_nat A_28) N_14)) ((power_power_nat A_28) N_13))))) of role axiom named fact_430_power__increasing % 0.90/1.07 A new axiom: (forall (A_28:nat) (N_14:nat) (N_13:nat), (((ord_less_eq_nat N_14) N_13)->(((ord_less_eq_nat one_one_nat) A_28)->((ord_less_eq_nat ((power_power_nat A_28) N_14)) ((power_power_nat A_28) N_13))))) % 0.90/1.07 FOF formula (forall (A_28:int) (N_14:nat) (N_13:nat), (((ord_less_eq_nat N_14) N_13)->(((ord_less_eq_int one_one_int) A_28)->((ord_less_eq_int ((power_power_int A_28) N_14)) ((power_power_int A_28) N_13))))) of role axiom named fact_431_power__increasing % 0.90/1.07 A new axiom: (forall (A_28:int) (N_14:nat) (N_13:nat), (((ord_less_eq_nat N_14) N_13)->(((ord_less_eq_int one_one_int) A_28)->((ord_less_eq_int ((power_power_int A_28) N_14)) ((power_power_int A_28) N_13))))) % 0.92/1.09 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_432_less__eq__int__code_I16_J % 0.92/1.09 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))) % 0.92/1.09 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_433_rel__simps_I34_J % 0.92/1.09 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit1 L))) ((ord_less_eq_int K) L))) % 0.92/1.09 FOF formula ((ord_less_eq_int pls) pls) of role axiom named fact_434_rel__simps_I19_J % 0.92/1.09 A new axiom: ((ord_less_eq_int pls) pls) % 0.92/1.09 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_435_less__eq__int__code_I13_J % 0.92/1.09 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit0 K2))) ((ord_less_eq_int K1) K2))) % 0.92/1.09 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_436_rel__simps_I31_J % 0.92/1.09 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit0 L))) ((ord_less_eq_int K) L))) % 0.92/1.09 FOF formula ((ord_less_eq_int zero_zero_int) zero_zero_int) of role axiom named fact_437_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J % 0.92/1.09 A new axiom: ((ord_less_eq_int zero_zero_int) zero_zero_int) % 0.92/1.09 FOF formula (forall (W:int), ((ord_less_eq_int W) W)) of role axiom named fact_438_zle__refl % 0.92/1.09 A new axiom: (forall (W:int), ((ord_less_eq_int W) W)) % 0.92/1.09 FOF formula (forall (Z_2:int) (W:int), ((or ((ord_less_eq_int Z_2) W)) ((ord_less_eq_int W) Z_2))) of role axiom named fact_439_zle__linear % 0.92/1.09 A new axiom: (forall (Z_2:int) (W:int), ((or ((ord_less_eq_int Z_2) W)) ((ord_less_eq_int W) Z_2))) % 0.92/1.09 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_440_zle__trans % 0.92/1.09 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)))) % 0.92/1.09 FOF formula (forall (Z_2:int) (W:int), (((ord_less_eq_int Z_2) W)->(((ord_less_eq_int W) Z_2)->(((eq int) Z_2) W)))) of role axiom named fact_441_zle__antisym % 0.92/1.09 A new axiom: (forall (Z_2:int) (W:int), (((ord_less_eq_int Z_2) W)->(((ord_less_eq_int W) Z_2)->(((eq int) Z_2) W)))) % 0.92/1.09 FOF formula (forall (X_19:int) (Y_17:int), ((iff ((ord_less_eq_real (number267125858f_real X_19)) (number267125858f_real Y_17))) ((ord_less_eq_int X_19) Y_17))) of role axiom named fact_442_le__number__of % 0.92/1.09 A new axiom: (forall (X_19:int) (Y_17:int), ((iff ((ord_less_eq_real (number267125858f_real X_19)) (number267125858f_real Y_17))) ((ord_less_eq_int X_19) Y_17))) % 0.92/1.09 FOF formula (forall (X_19:int) (Y_17:int), ((iff ((ord_less_eq_int (number_number_of_int X_19)) (number_number_of_int Y_17))) ((ord_less_eq_int X_19) Y_17))) of role axiom named fact_443_le__number__of % 0.92/1.09 A new axiom: (forall (X_19:int) (Y_17:int), ((iff ((ord_less_eq_int (number_number_of_int X_19)) (number_number_of_int Y_17))) ((ord_less_eq_int X_19) Y_17))) % 0.92/1.09 FOF formula (forall (M_4:nat) (N_12:nat), ((iff ((ord_less_eq_real (semiri132038758t_real M_4)) (semiri132038758t_real N_12))) ((ord_less_eq_nat M_4) N_12))) of role axiom named fact_444_of__nat__le__iff % 0.92/1.09 A new axiom: (forall (M_4:nat) (N_12:nat), ((iff ((ord_less_eq_real (semiri132038758t_real M_4)) (semiri132038758t_real N_12))) ((ord_less_eq_nat M_4) N_12))) % 0.92/1.09 FOF formula (forall (M_4:nat) (N_12:nat), ((iff ((ord_less_eq_nat (semiri984289939at_nat M_4)) (semiri984289939at_nat N_12))) ((ord_less_eq_nat M_4) N_12))) of role axiom named fact_445_of__nat__le__iff % 0.92/1.09 A new axiom: (forall (M_4:nat) (N_12:nat), ((iff ((ord_less_eq_nat (semiri984289939at_nat M_4)) (semiri984289939at_nat N_12))) ((ord_less_eq_nat M_4) N_12))) % 0.92/1.09 FOF formula (forall (M_4:nat) (N_12:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int M_4)) (semiri1621563631at_int N_12))) ((ord_less_eq_nat M_4) N_12))) of role axiom named fact_446_of__nat__le__iff % 0.92/1.10 A new axiom: (forall (M_4:nat) (N_12:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int M_4)) (semiri1621563631at_int N_12))) ((ord_less_eq_nat M_4) N_12))) % 0.92/1.10 FOF formula (forall (Z_2:int) (W:int), ((iff ((ord_less_int Z_2) W)) ((and ((ord_less_eq_int Z_2) W)) (not (((eq int) Z_2) W))))) of role axiom named fact_447_zless__le % 0.92/1.10 A new axiom: (forall (Z_2:int) (W:int), ((iff ((ord_less_int Z_2) W)) ((and ((ord_less_eq_int Z_2) W)) (not (((eq int) Z_2) W))))) % 0.92/1.10 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_448_zadd__left__mono % 0.92/1.10 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)))) % 0.92/1.10 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_449_less__eq__number__of__int__code % 0.92/1.10 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))) % 0.92/1.10 FOF formula (forall (Y_16:int), ((iff ((ord_less_eq_real zero_zero_real) (number267125858f_real Y_16))) ((ord_less_eq_int pls) Y_16))) of role axiom named fact_450_le__special_I1_J % 0.92/1.10 A new axiom: (forall (Y_16:int), ((iff ((ord_less_eq_real zero_zero_real) (number267125858f_real Y_16))) ((ord_less_eq_int pls) Y_16))) % 0.92/1.10 FOF formula (forall (Y_16:int), ((iff ((ord_less_eq_int zero_zero_int) (number_number_of_int Y_16))) ((ord_less_eq_int pls) Y_16))) of role axiom named fact_451_le__special_I1_J % 0.92/1.10 A new axiom: (forall (Y_16:int), ((iff ((ord_less_eq_int zero_zero_int) (number_number_of_int Y_16))) ((ord_less_eq_int pls) Y_16))) % 0.92/1.10 FOF formula (forall (X_18:int), ((iff ((ord_less_eq_real (number267125858f_real X_18)) zero_zero_real)) ((ord_less_eq_int X_18) pls))) of role axiom named fact_452_le__special_I3_J % 0.92/1.10 A new axiom: (forall (X_18:int), ((iff ((ord_less_eq_real (number267125858f_real X_18)) zero_zero_real)) ((ord_less_eq_int X_18) pls))) % 0.92/1.10 FOF formula (forall (X_18:int), ((iff ((ord_less_eq_int (number_number_of_int X_18)) zero_zero_int)) ((ord_less_eq_int X_18) pls))) of role axiom named fact_453_le__special_I3_J % 0.92/1.10 A new axiom: (forall (X_18:int), ((iff ((ord_less_eq_int (number_number_of_int X_18)) zero_zero_int)) ((ord_less_eq_int X_18) pls))) % 0.92/1.10 FOF formula (forall (A_27:real) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_real zero_zero_real) A_27)->(((ord_less_eq_real A_27) one_one_real)->((ord_less_eq_real ((power_power_real A_27) N_10)) ((power_power_real A_27) N_11)))))) of role axiom named fact_454_power__decreasing % 0.92/1.10 A new axiom: (forall (A_27:real) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_real zero_zero_real) A_27)->(((ord_less_eq_real A_27) one_one_real)->((ord_less_eq_real ((power_power_real A_27) N_10)) ((power_power_real A_27) N_11)))))) % 0.92/1.10 FOF formula (forall (A_27:nat) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_nat zero_zero_nat) A_27)->(((ord_less_eq_nat A_27) one_one_nat)->((ord_less_eq_nat ((power_power_nat A_27) N_10)) ((power_power_nat A_27) N_11)))))) of role axiom named fact_455_power__decreasing % 0.92/1.10 A new axiom: (forall (A_27:nat) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_nat zero_zero_nat) A_27)->(((ord_less_eq_nat A_27) one_one_nat)->((ord_less_eq_nat ((power_power_nat A_27) N_10)) ((power_power_nat A_27) N_11)))))) % 0.92/1.10 FOF formula (forall (A_27:int) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_int zero_zero_int) A_27)->(((ord_less_eq_int A_27) one_one_int)->((ord_less_eq_int ((power_power_int A_27) N_10)) ((power_power_int A_27) N_11)))))) of role axiom named fact_456_power__decreasing % 0.92/1.10 A new axiom: (forall (A_27:int) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_int zero_zero_int) A_27)->(((ord_less_eq_int A_27) one_one_int)->((ord_less_eq_int ((power_power_int A_27) N_10)) ((power_power_int A_27) N_11)))))) % 0.95/1.12 FOF formula (forall (X_17:nat) (Y_15:nat) (B_21:real), (((ord_less_real one_one_real) B_21)->((iff ((ord_less_eq_real ((power_power_real B_21) X_17)) ((power_power_real B_21) Y_15))) ((ord_less_eq_nat X_17) Y_15)))) of role axiom named fact_457_power__increasing__iff % 0.95/1.12 A new axiom: (forall (X_17:nat) (Y_15:nat) (B_21:real), (((ord_less_real one_one_real) B_21)->((iff ((ord_less_eq_real ((power_power_real B_21) X_17)) ((power_power_real B_21) Y_15))) ((ord_less_eq_nat X_17) Y_15)))) % 0.95/1.12 FOF formula (forall (X_17:nat) (Y_15:nat) (B_21:nat), (((ord_less_nat one_one_nat) B_21)->((iff ((ord_less_eq_nat ((power_power_nat B_21) X_17)) ((power_power_nat B_21) Y_15))) ((ord_less_eq_nat X_17) Y_15)))) of role axiom named fact_458_power__increasing__iff % 0.95/1.12 A new axiom: (forall (X_17:nat) (Y_15:nat) (B_21:nat), (((ord_less_nat one_one_nat) B_21)->((iff ((ord_less_eq_nat ((power_power_nat B_21) X_17)) ((power_power_nat B_21) Y_15))) ((ord_less_eq_nat X_17) Y_15)))) % 0.95/1.12 FOF formula (forall (X_17:nat) (Y_15:nat) (B_21:int), (((ord_less_int one_one_int) B_21)->((iff ((ord_less_eq_int ((power_power_int B_21) X_17)) ((power_power_int B_21) Y_15))) ((ord_less_eq_nat X_17) Y_15)))) of role axiom named fact_459_power__increasing__iff % 0.95/1.12 A new axiom: (forall (X_17:nat) (Y_15:nat) (B_21:int), (((ord_less_int one_one_int) B_21)->((iff ((ord_less_eq_int ((power_power_int B_21) X_17)) ((power_power_int B_21) Y_15))) ((ord_less_eq_nat X_17) Y_15)))) % 0.95/1.12 FOF formula (forall (M_3:nat) (N_9:nat) (A_26:real), (((ord_less_real one_one_real) A_26)->(((ord_less_eq_real ((power_power_real A_26) M_3)) ((power_power_real A_26) N_9))->((ord_less_eq_nat M_3) N_9)))) of role axiom named fact_460_power__le__imp__le__exp % 0.95/1.12 A new axiom: (forall (M_3:nat) (N_9:nat) (A_26:real), (((ord_less_real one_one_real) A_26)->(((ord_less_eq_real ((power_power_real A_26) M_3)) ((power_power_real A_26) N_9))->((ord_less_eq_nat M_3) N_9)))) % 0.95/1.12 FOF formula (forall (M_3:nat) (N_9:nat) (A_26:nat), (((ord_less_nat one_one_nat) A_26)->(((ord_less_eq_nat ((power_power_nat A_26) M_3)) ((power_power_nat A_26) N_9))->((ord_less_eq_nat M_3) N_9)))) of role axiom named fact_461_power__le__imp__le__exp % 0.95/1.12 A new axiom: (forall (M_3:nat) (N_9:nat) (A_26:nat), (((ord_less_nat one_one_nat) A_26)->(((ord_less_eq_nat ((power_power_nat A_26) M_3)) ((power_power_nat A_26) N_9))->((ord_less_eq_nat M_3) N_9)))) % 0.95/1.12 FOF formula (forall (M_3:nat) (N_9:nat) (A_26:int), (((ord_less_int one_one_int) A_26)->(((ord_less_eq_int ((power_power_int A_26) M_3)) ((power_power_int A_26) N_9))->((ord_less_eq_nat M_3) N_9)))) of role axiom named fact_462_power__le__imp__le__exp % 0.95/1.12 A new axiom: (forall (M_3:nat) (N_9:nat) (A_26:int), (((ord_less_int one_one_int) A_26)->(((ord_less_eq_int ((power_power_int A_26) M_3)) ((power_power_int A_26) N_9))->((ord_less_eq_nat M_3) N_9)))) % 0.95/1.12 FOF formula (forall (Y_14:int), ((iff ((ord_less_eq_real one_one_real) (number267125858f_real Y_14))) ((ord_less_eq_int (bit1 pls)) Y_14))) of role axiom named fact_463_le__special_I2_J % 0.95/1.12 A new axiom: (forall (Y_14:int), ((iff ((ord_less_eq_real one_one_real) (number267125858f_real Y_14))) ((ord_less_eq_int (bit1 pls)) Y_14))) % 0.95/1.12 FOF formula (forall (Y_14:int), ((iff ((ord_less_eq_int one_one_int) (number_number_of_int Y_14))) ((ord_less_eq_int (bit1 pls)) Y_14))) of role axiom named fact_464_le__special_I2_J % 0.95/1.12 A new axiom: (forall (Y_14:int), ((iff ((ord_less_eq_int one_one_int) (number_number_of_int Y_14))) ((ord_less_eq_int (bit1 pls)) Y_14))) % 0.95/1.12 FOF formula (forall (X_16:int), ((iff ((ord_less_eq_real (number267125858f_real X_16)) one_one_real)) ((ord_less_eq_int X_16) (bit1 pls)))) of role axiom named fact_465_le__special_I4_J % 0.95/1.12 A new axiom: (forall (X_16:int), ((iff ((ord_less_eq_real (number267125858f_real X_16)) one_one_real)) ((ord_less_eq_int X_16) (bit1 pls)))) % 0.95/1.12 FOF formula (forall (X_16:int), ((iff ((ord_less_eq_int (number_number_of_int X_16)) one_one_int)) ((ord_less_eq_int X_16) (bit1 pls)))) of role axiom named fact_466_le__special_I4_J % 0.95/1.12 A new axiom: (forall (X_16:int), ((iff ((ord_less_eq_int (number_number_of_int X_16)) one_one_int)) ((ord_less_eq_int X_16) (bit1 pls)))) % 0.97/1.14 FOF formula (forall (A_25:real), ((iff ((ord_less_eq_real zero_zero_real) ((plus_plus_real A_25) A_25))) ((ord_less_eq_real zero_zero_real) A_25))) of role axiom named fact_467_zero__le__double__add__iff__zero__le__single__add % 0.97/1.14 A new axiom: (forall (A_25:real), ((iff ((ord_less_eq_real zero_zero_real) ((plus_plus_real A_25) A_25))) ((ord_less_eq_real zero_zero_real) A_25))) % 0.97/1.14 FOF formula (forall (A_25:int), ((iff ((ord_less_eq_int zero_zero_int) ((plus_plus_int A_25) A_25))) ((ord_less_eq_int zero_zero_int) A_25))) of role axiom named fact_468_zero__le__double__add__iff__zero__le__single__add % 0.97/1.14 A new axiom: (forall (A_25:int), ((iff ((ord_less_eq_int zero_zero_int) ((plus_plus_int A_25) A_25))) ((ord_less_eq_int zero_zero_int) A_25))) % 0.97/1.14 FOF formula (forall (A_24:real), ((iff ((ord_less_eq_real ((plus_plus_real A_24) A_24)) zero_zero_real)) ((ord_less_eq_real A_24) zero_zero_real))) of role axiom named fact_469_double__add__le__zero__iff__single__add__le__zero % 0.97/1.14 A new axiom: (forall (A_24:real), ((iff ((ord_less_eq_real ((plus_plus_real A_24) A_24)) zero_zero_real)) ((ord_less_eq_real A_24) zero_zero_real))) % 0.97/1.14 FOF formula (forall (A_24:int), ((iff ((ord_less_eq_int ((plus_plus_int A_24) A_24)) zero_zero_int)) ((ord_less_eq_int A_24) zero_zero_int))) of role axiom named fact_470_double__add__le__zero__iff__single__add__le__zero % 0.97/1.14 A new axiom: (forall (A_24:int), ((iff ((ord_less_eq_int ((plus_plus_int A_24) A_24)) zero_zero_int)) ((ord_less_eq_int A_24) zero_zero_int))) % 0.97/1.14 FOF formula (forall (B_20:real) (A_23:real), (((ord_less_eq_real zero_zero_real) A_23)->(((ord_less_eq_real zero_zero_real) B_20)->((ord_less_eq_real zero_zero_real) ((plus_plus_real A_23) B_20))))) of role axiom named fact_471_add__nonneg__nonneg % 0.97/1.14 A new axiom: (forall (B_20:real) (A_23:real), (((ord_less_eq_real zero_zero_real) A_23)->(((ord_less_eq_real zero_zero_real) B_20)->((ord_less_eq_real zero_zero_real) ((plus_plus_real A_23) B_20))))) % 0.97/1.14 FOF formula (forall (B_20:nat) (A_23:nat), (((ord_less_eq_nat zero_zero_nat) A_23)->(((ord_less_eq_nat zero_zero_nat) B_20)->((ord_less_eq_nat zero_zero_nat) ((plus_plus_nat A_23) B_20))))) of role axiom named fact_472_add__nonneg__nonneg % 0.97/1.14 A new axiom: (forall (B_20:nat) (A_23:nat), (((ord_less_eq_nat zero_zero_nat) A_23)->(((ord_less_eq_nat zero_zero_nat) B_20)->((ord_less_eq_nat zero_zero_nat) ((plus_plus_nat A_23) B_20))))) % 0.97/1.14 FOF formula (forall (B_20:int) (A_23:int), (((ord_less_eq_int zero_zero_int) A_23)->(((ord_less_eq_int zero_zero_int) B_20)->((ord_less_eq_int zero_zero_int) ((plus_plus_int A_23) B_20))))) of role axiom named fact_473_add__nonneg__nonneg % 0.97/1.14 A new axiom: (forall (B_20:int) (A_23:int), (((ord_less_eq_int zero_zero_int) A_23)->(((ord_less_eq_int zero_zero_int) B_20)->((ord_less_eq_int zero_zero_int) ((plus_plus_int A_23) B_20))))) % 0.97/1.14 FOF formula (forall (Y_13:real) (X_15:real), (((ord_less_eq_real zero_zero_real) X_15)->(((ord_less_eq_real zero_zero_real) Y_13)->((iff (((eq real) ((plus_plus_real X_15) Y_13)) zero_zero_real)) ((and (((eq real) X_15) zero_zero_real)) (((eq real) Y_13) zero_zero_real)))))) of role axiom named fact_474_add__nonneg__eq__0__iff % 0.97/1.14 A new axiom: (forall (Y_13:real) (X_15:real), (((ord_less_eq_real zero_zero_real) X_15)->(((ord_less_eq_real zero_zero_real) Y_13)->((iff (((eq real) ((plus_plus_real X_15) Y_13)) zero_zero_real)) ((and (((eq real) X_15) zero_zero_real)) (((eq real) Y_13) zero_zero_real)))))) % 0.97/1.14 FOF formula (forall (Y_13:nat) (X_15:nat), (((ord_less_eq_nat zero_zero_nat) X_15)->(((ord_less_eq_nat zero_zero_nat) Y_13)->((iff (((eq nat) ((plus_plus_nat X_15) Y_13)) zero_zero_nat)) ((and (((eq nat) X_15) zero_zero_nat)) (((eq nat) Y_13) zero_zero_nat)))))) of role axiom named fact_475_add__nonneg__eq__0__iff % 0.97/1.14 A new axiom: (forall (Y_13:nat) (X_15:nat), (((ord_less_eq_nat zero_zero_nat) X_15)->(((ord_less_eq_nat zero_zero_nat) Y_13)->((iff (((eq nat) ((plus_plus_nat X_15) Y_13)) zero_zero_nat)) ((and (((eq nat) X_15) zero_zero_nat)) (((eq nat) Y_13) zero_zero_nat)))))) % 0.97/1.14 FOF formula (forall (Y_13:int) (X_15:int), (((ord_less_eq_int zero_zero_int) X_15)->(((ord_less_eq_int zero_zero_int) Y_13)->((iff (((eq int) ((plus_plus_int X_15) Y_13)) zero_zero_int)) ((and (((eq int) X_15) zero_zero_int)) (((eq int) Y_13) zero_zero_int)))))) of role axiom named fact_476_add__nonneg__eq__0__iff % 0.97/1.15 A new axiom: (forall (Y_13:int) (X_15:int), (((ord_less_eq_int zero_zero_int) X_15)->(((ord_less_eq_int zero_zero_int) Y_13)->((iff (((eq int) ((plus_plus_int X_15) Y_13)) zero_zero_int)) ((and (((eq int) X_15) zero_zero_int)) (((eq int) Y_13) zero_zero_int)))))) % 0.97/1.15 FOF formula (forall (B_19:real) (C_9:real) (A_22:real), (((ord_less_eq_real zero_zero_real) A_22)->(((ord_less_eq_real B_19) C_9)->((ord_less_eq_real B_19) ((plus_plus_real A_22) C_9))))) of role axiom named fact_477_add__increasing % 0.97/1.15 A new axiom: (forall (B_19:real) (C_9:real) (A_22:real), (((ord_less_eq_real zero_zero_real) A_22)->(((ord_less_eq_real B_19) C_9)->((ord_less_eq_real B_19) ((plus_plus_real A_22) C_9))))) % 0.97/1.15 FOF formula (forall (B_19:nat) (C_9:nat) (A_22:nat), (((ord_less_eq_nat zero_zero_nat) A_22)->(((ord_less_eq_nat B_19) C_9)->((ord_less_eq_nat B_19) ((plus_plus_nat A_22) C_9))))) of role axiom named fact_478_add__increasing % 0.97/1.15 A new axiom: (forall (B_19:nat) (C_9:nat) (A_22:nat), (((ord_less_eq_nat zero_zero_nat) A_22)->(((ord_less_eq_nat B_19) C_9)->((ord_less_eq_nat B_19) ((plus_plus_nat A_22) C_9))))) % 0.97/1.15 FOF formula (forall (B_19:int) (C_9:int) (A_22:int), (((ord_less_eq_int zero_zero_int) A_22)->(((ord_less_eq_int B_19) C_9)->((ord_less_eq_int B_19) ((plus_plus_int A_22) C_9))))) of role axiom named fact_479_add__increasing % 0.97/1.15 A new axiom: (forall (B_19:int) (C_9:int) (A_22:int), (((ord_less_eq_int zero_zero_int) A_22)->(((ord_less_eq_int B_19) C_9)->((ord_less_eq_int B_19) ((plus_plus_int A_22) C_9))))) % 0.97/1.15 FOF formula (forall (B_18:real) (A_21:real) (C_8:real), (((ord_less_eq_real zero_zero_real) C_8)->(((ord_less_eq_real B_18) A_21)->((ord_less_eq_real B_18) ((plus_plus_real A_21) C_8))))) of role axiom named fact_480_add__increasing2 % 0.97/1.15 A new axiom: (forall (B_18:real) (A_21:real) (C_8:real), (((ord_less_eq_real zero_zero_real) C_8)->(((ord_less_eq_real B_18) A_21)->((ord_less_eq_real B_18) ((plus_plus_real A_21) C_8))))) % 0.97/1.15 FOF formula (forall (B_18:nat) (A_21:nat) (C_8:nat), (((ord_less_eq_nat zero_zero_nat) C_8)->(((ord_less_eq_nat B_18) A_21)->((ord_less_eq_nat B_18) ((plus_plus_nat A_21) C_8))))) of role axiom named fact_481_add__increasing2 % 0.97/1.15 A new axiom: (forall (B_18:nat) (A_21:nat) (C_8:nat), (((ord_less_eq_nat zero_zero_nat) C_8)->(((ord_less_eq_nat B_18) A_21)->((ord_less_eq_nat B_18) ((plus_plus_nat A_21) C_8))))) % 0.97/1.15 FOF formula (forall (B_18:int) (A_21:int) (C_8:int), (((ord_less_eq_int zero_zero_int) C_8)->(((ord_less_eq_int B_18) A_21)->((ord_less_eq_int B_18) ((plus_plus_int A_21) C_8))))) of role axiom named fact_482_add__increasing2 % 0.97/1.15 A new axiom: (forall (B_18:int) (A_21:int) (C_8:int), (((ord_less_eq_int zero_zero_int) C_8)->(((ord_less_eq_int B_18) A_21)->((ord_less_eq_int B_18) ((plus_plus_int A_21) C_8))))) % 0.97/1.15 FOF formula (forall (B_17:real) (A_20:real), (((ord_less_eq_real A_20) zero_zero_real)->(((ord_less_eq_real B_17) zero_zero_real)->((ord_less_eq_real ((plus_plus_real A_20) B_17)) zero_zero_real)))) of role axiom named fact_483_add__nonpos__nonpos % 0.97/1.15 A new axiom: (forall (B_17:real) (A_20:real), (((ord_less_eq_real A_20) zero_zero_real)->(((ord_less_eq_real B_17) zero_zero_real)->((ord_less_eq_real ((plus_plus_real A_20) B_17)) zero_zero_real)))) % 0.97/1.15 FOF formula (forall (B_17:nat) (A_20:nat), (((ord_less_eq_nat A_20) zero_zero_nat)->(((ord_less_eq_nat B_17) zero_zero_nat)->((ord_less_eq_nat ((plus_plus_nat A_20) B_17)) zero_zero_nat)))) of role axiom named fact_484_add__nonpos__nonpos % 0.97/1.15 A new axiom: (forall (B_17:nat) (A_20:nat), (((ord_less_eq_nat A_20) zero_zero_nat)->(((ord_less_eq_nat B_17) zero_zero_nat)->((ord_less_eq_nat ((plus_plus_nat A_20) B_17)) zero_zero_nat)))) % 0.97/1.15 FOF formula (forall (B_17:int) (A_20:int), (((ord_less_eq_int A_20) zero_zero_int)->(((ord_less_eq_int B_17) zero_zero_int)->((ord_less_eq_int ((plus_plus_int A_20) B_17)) zero_zero_int)))) of role axiom named fact_485_add__nonpos__nonpos % 0.97/1.15 A new axiom: (forall (B_17:int) (A_20:int), (((ord_less_eq_int A_20) zero_zero_int)->(((ord_less_eq_int B_17) zero_zero_int)->((ord_less_eq_int ((plus_plus_int A_20) B_17)) zero_zero_int)))) % 0.97/1.17 FOF formula (forall (C_7:real) (D_1:real) (A_19:real) (B_16:real), (((ord_less_real A_19) B_16)->(((ord_less_eq_real C_7) D_1)->((ord_less_real ((plus_plus_real A_19) C_7)) ((plus_plus_real B_16) D_1))))) of role axiom named fact_486_add__less__le__mono % 0.97/1.17 A new axiom: (forall (C_7:real) (D_1:real) (A_19:real) (B_16:real), (((ord_less_real A_19) B_16)->(((ord_less_eq_real C_7) D_1)->((ord_less_real ((plus_plus_real A_19) C_7)) ((plus_plus_real B_16) D_1))))) % 0.97/1.17 FOF formula (forall (C_7:nat) (D_1:nat) (A_19:nat) (B_16:nat), (((ord_less_nat A_19) B_16)->(((ord_less_eq_nat C_7) D_1)->((ord_less_nat ((plus_plus_nat A_19) C_7)) ((plus_plus_nat B_16) D_1))))) of role axiom named fact_487_add__less__le__mono % 0.97/1.17 A new axiom: (forall (C_7:nat) (D_1:nat) (A_19:nat) (B_16:nat), (((ord_less_nat A_19) B_16)->(((ord_less_eq_nat C_7) D_1)->((ord_less_nat ((plus_plus_nat A_19) C_7)) ((plus_plus_nat B_16) D_1))))) % 0.97/1.17 FOF formula (forall (C_7:int) (D_1:int) (A_19:int) (B_16:int), (((ord_less_int A_19) B_16)->(((ord_less_eq_int C_7) D_1)->((ord_less_int ((plus_plus_int A_19) C_7)) ((plus_plus_int B_16) D_1))))) of role axiom named fact_488_add__less__le__mono % 0.97/1.17 A new axiom: (forall (C_7:int) (D_1:int) (A_19:int) (B_16:int), (((ord_less_int A_19) B_16)->(((ord_less_eq_int C_7) D_1)->((ord_less_int ((plus_plus_int A_19) C_7)) ((plus_plus_int B_16) D_1))))) % 0.97/1.17 FOF formula (forall (C_6:real) (D:real) (A_18:real) (B_15:real), (((ord_less_eq_real A_18) B_15)->(((ord_less_real C_6) D)->((ord_less_real ((plus_plus_real A_18) C_6)) ((plus_plus_real B_15) D))))) of role axiom named fact_489_add__le__less__mono % 0.97/1.17 A new axiom: (forall (C_6:real) (D:real) (A_18:real) (B_15:real), (((ord_less_eq_real A_18) B_15)->(((ord_less_real C_6) D)->((ord_less_real ((plus_plus_real A_18) C_6)) ((plus_plus_real B_15) D))))) % 0.97/1.17 FOF formula (forall (C_6:nat) (D:nat) (A_18:nat) (B_15:nat), (((ord_less_eq_nat A_18) B_15)->(((ord_less_nat C_6) D)->((ord_less_nat ((plus_plus_nat A_18) C_6)) ((plus_plus_nat B_15) D))))) of role axiom named fact_490_add__le__less__mono % 0.97/1.17 A new axiom: (forall (C_6:nat) (D:nat) (A_18:nat) (B_15:nat), (((ord_less_eq_nat A_18) B_15)->(((ord_less_nat C_6) D)->((ord_less_nat ((plus_plus_nat A_18) C_6)) ((plus_plus_nat B_15) D))))) % 0.97/1.17 FOF formula (forall (C_6:int) (D:int) (A_18:int) (B_15:int), (((ord_less_eq_int A_18) B_15)->(((ord_less_int C_6) D)->((ord_less_int ((plus_plus_int A_18) C_6)) ((plus_plus_int B_15) D))))) of role axiom named fact_491_add__le__less__mono % 0.97/1.17 A new axiom: (forall (C_6:int) (D:int) (A_18:int) (B_15:int), (((ord_less_eq_int A_18) B_15)->(((ord_less_int C_6) D)->((ord_less_int ((plus_plus_int A_18) C_6)) ((plus_plus_int B_15) D))))) % 0.97/1.17 FOF formula (((ord_less_eq_real one_one_real) zero_zero_real)->False) of role axiom named fact_492_not__one__le__zero % 0.97/1.17 A new axiom: (((ord_less_eq_real one_one_real) zero_zero_real)->False) % 0.97/1.17 FOF formula (((ord_less_eq_nat one_one_nat) zero_zero_nat)->False) of role axiom named fact_493_not__one__le__zero % 0.97/1.17 A new axiom: (((ord_less_eq_nat one_one_nat) zero_zero_nat)->False) % 0.97/1.17 FOF formula (((ord_less_eq_int one_one_int) zero_zero_int)->False) of role axiom named fact_494_not__one__le__zero % 0.97/1.17 A new axiom: (((ord_less_eq_int one_one_int) zero_zero_int)->False) % 0.97/1.17 FOF formula ((ord_less_eq_real zero_zero_real) one_one_real) of role axiom named fact_495_zero__le__one % 0.97/1.17 A new axiom: ((ord_less_eq_real zero_zero_real) one_one_real) % 0.97/1.17 FOF formula ((ord_less_eq_nat zero_zero_nat) one_one_nat) of role axiom named fact_496_zero__le__one % 0.97/1.17 A new axiom: ((ord_less_eq_nat zero_zero_nat) one_one_nat) % 0.97/1.17 FOF formula ((ord_less_eq_int zero_zero_int) one_one_int) of role axiom named fact_497_zero__le__one % 0.97/1.17 A new axiom: ((ord_less_eq_int zero_zero_int) one_one_int) % 0.97/1.17 FOF formula (forall (V_7:int) (W_2:int), ((iff ((ord_less_eq_real (number267125858f_real V_7)) (number267125858f_real W_2))) (((ord_less_real (number267125858f_real W_2)) (number267125858f_real V_7))->False))) of role axiom named fact_498_le__number__of__eq__not__less % 0.97/1.19 A new axiom: (forall (V_7:int) (W_2:int), ((iff ((ord_less_eq_real (number267125858f_real V_7)) (number267125858f_real W_2))) (((ord_less_real (number267125858f_real W_2)) (number267125858f_real V_7))->False))) % 0.97/1.19 FOF formula (forall (V_7:int) (W_2:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_7)) (number_number_of_nat W_2))) (((ord_less_nat (number_number_of_nat W_2)) (number_number_of_nat V_7))->False))) of role axiom named fact_499_le__number__of__eq__not__less % 0.97/1.19 A new axiom: (forall (V_7:int) (W_2:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_7)) (number_number_of_nat W_2))) (((ord_less_nat (number_number_of_nat W_2)) (number_number_of_nat V_7))->False))) % 0.97/1.19 FOF formula (forall (V_7:int) (W_2:int), ((iff ((ord_less_eq_int (number_number_of_int V_7)) (number_number_of_int W_2))) (((ord_less_int (number_number_of_int W_2)) (number_number_of_int V_7))->False))) of role axiom named fact_500_le__number__of__eq__not__less % 0.97/1.19 A new axiom: (forall (V_7:int) (W_2:int), ((iff ((ord_less_eq_int (number_number_of_int V_7)) (number_number_of_int W_2))) (((ord_less_int (number_number_of_int W_2)) (number_number_of_int V_7))->False))) % 0.97/1.19 FOF formula (forall (N_8:nat) (A_17:real), (((ord_less_eq_real zero_zero_real) A_17)->((ord_less_eq_real zero_zero_real) ((power_power_real A_17) N_8)))) of role axiom named fact_501_zero__le__power % 0.97/1.19 A new axiom: (forall (N_8:nat) (A_17:real), (((ord_less_eq_real zero_zero_real) A_17)->((ord_less_eq_real zero_zero_real) ((power_power_real A_17) N_8)))) % 0.97/1.19 FOF formula (forall (N_8:nat) (A_17:nat), (((ord_less_eq_nat zero_zero_nat) A_17)->((ord_less_eq_nat zero_zero_nat) ((power_power_nat A_17) N_8)))) of role axiom named fact_502_zero__le__power % 0.97/1.19 A new axiom: (forall (N_8:nat) (A_17:nat), (((ord_less_eq_nat zero_zero_nat) A_17)->((ord_less_eq_nat zero_zero_nat) ((power_power_nat A_17) N_8)))) % 0.97/1.19 FOF formula (forall (N_8:nat) (A_17:int), (((ord_less_eq_int zero_zero_int) A_17)->((ord_less_eq_int zero_zero_int) ((power_power_int A_17) N_8)))) of role axiom named fact_503_zero__le__power % 0.97/1.19 A new axiom: (forall (N_8:nat) (A_17:int), (((ord_less_eq_int zero_zero_int) A_17)->((ord_less_eq_int zero_zero_int) ((power_power_int A_17) N_8)))) % 0.97/1.19 FOF formula (forall (N_7:nat) (A_16:real) (B_14:real), (((ord_less_eq_real A_16) B_14)->(((ord_less_eq_real zero_zero_real) A_16)->((ord_less_eq_real ((power_power_real A_16) N_7)) ((power_power_real B_14) N_7))))) of role axiom named fact_504_power__mono % 0.97/1.19 A new axiom: (forall (N_7:nat) (A_16:real) (B_14:real), (((ord_less_eq_real A_16) B_14)->(((ord_less_eq_real zero_zero_real) A_16)->((ord_less_eq_real ((power_power_real A_16) N_7)) ((power_power_real B_14) N_7))))) % 0.97/1.19 FOF formula (forall (N_7:nat) (A_16:nat) (B_14:nat), (((ord_less_eq_nat A_16) B_14)->(((ord_less_eq_nat zero_zero_nat) A_16)->((ord_less_eq_nat ((power_power_nat A_16) N_7)) ((power_power_nat B_14) N_7))))) of role axiom named fact_505_power__mono % 0.97/1.19 A new axiom: (forall (N_7:nat) (A_16:nat) (B_14:nat), (((ord_less_eq_nat A_16) B_14)->(((ord_less_eq_nat zero_zero_nat) A_16)->((ord_less_eq_nat ((power_power_nat A_16) N_7)) ((power_power_nat B_14) N_7))))) % 0.97/1.19 FOF formula (forall (N_7:nat) (A_16:int) (B_14:int), (((ord_less_eq_int A_16) B_14)->(((ord_less_eq_int zero_zero_int) A_16)->((ord_less_eq_int ((power_power_int A_16) N_7)) ((power_power_int B_14) N_7))))) of role axiom named fact_506_power__mono % 0.97/1.19 A new axiom: (forall (N_7:nat) (A_16:int) (B_14:int), (((ord_less_eq_int A_16) B_14)->(((ord_less_eq_int zero_zero_int) A_16)->((ord_less_eq_int ((power_power_int A_16) N_7)) ((power_power_int B_14) N_7))))) % 0.97/1.19 FOF formula (forall (N_6:nat) (A_15:real), (((ord_less_eq_real one_one_real) A_15)->((ord_less_eq_real one_one_real) ((power_power_real A_15) N_6)))) of role axiom named fact_507_one__le__power % 0.97/1.19 A new axiom: (forall (N_6:nat) (A_15:real), (((ord_less_eq_real one_one_real) A_15)->((ord_less_eq_real one_one_real) ((power_power_real A_15) N_6)))) % 0.97/1.19 FOF formula (forall (N_6:nat) (A_15:nat), (((ord_less_eq_nat one_one_nat) A_15)->((ord_less_eq_nat one_one_nat) ((power_power_nat A_15) N_6)))) of role axiom named fact_508_one__le__power % 0.97/1.20 A new axiom: (forall (N_6:nat) (A_15:nat), (((ord_less_eq_nat one_one_nat) A_15)->((ord_less_eq_nat one_one_nat) ((power_power_nat A_15) N_6)))) % 0.97/1.20 FOF formula (forall (N_6:nat) (A_15:int), (((ord_less_eq_int one_one_int) A_15)->((ord_less_eq_int one_one_int) ((power_power_int A_15) N_6)))) of role axiom named fact_509_one__le__power % 0.97/1.20 A new axiom: (forall (N_6:nat) (A_15:int), (((ord_less_eq_int one_one_int) A_15)->((ord_less_eq_int one_one_int) ((power_power_int A_15) N_6)))) % 0.97/1.20 FOF formula (forall (M_2:nat), ((ord_less_eq_real zero_zero_real) (semiri132038758t_real M_2))) of role axiom named fact_510_zero__le__imp__of__nat % 0.97/1.20 A new axiom: (forall (M_2:nat), ((ord_less_eq_real zero_zero_real) (semiri132038758t_real M_2))) % 0.97/1.20 FOF formula (forall (M_2:nat), ((ord_less_eq_nat zero_zero_nat) (semiri984289939at_nat M_2))) of role axiom named fact_511_zero__le__imp__of__nat % 0.97/1.20 A new axiom: (forall (M_2:nat), ((ord_less_eq_nat zero_zero_nat) (semiri984289939at_nat M_2))) % 0.97/1.20 FOF formula (forall (M_2:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int M_2))) of role axiom named fact_512_zero__le__imp__of__nat % 0.97/1.20 A new axiom: (forall (M_2:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int M_2))) % 0.97/1.20 FOF formula (forall (N_5:nat), ((ord_less_eq_real zero_zero_real) (semiri132038758t_real N_5))) of role axiom named fact_513_of__nat__0__le__iff % 0.97/1.20 A new axiom: (forall (N_5:nat), ((ord_less_eq_real zero_zero_real) (semiri132038758t_real N_5))) % 0.97/1.20 FOF formula (forall (N_5:nat), ((ord_less_eq_nat zero_zero_nat) (semiri984289939at_nat N_5))) of role axiom named fact_514_of__nat__0__le__iff % 0.97/1.20 A new axiom: (forall (N_5:nat), ((ord_less_eq_nat zero_zero_nat) (semiri984289939at_nat N_5))) % 0.97/1.20 FOF formula (forall (N_5:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int N_5))) of role axiom named fact_515_of__nat__0__le__iff % 0.97/1.20 A new axiom: (forall (N_5:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int N_5))) % 0.97/1.20 FOF formula (forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_516_rel__simps_I22_J % 0.97/1.20 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) % 0.97/1.20 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_517_rel__simps_I32_J % 0.97/1.20 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))) % 0.97/1.20 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_518_less__eq__int__code_I14_J % 0.97/1.20 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))) % 0.97/1.20 FOF formula (forall (K:int), ((iff ((ord_less_eq_int pls) (bit0 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_519_rel__simps_I21_J % 0.97/1.20 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int pls) (bit0 K))) ((ord_less_eq_int pls) K))) % 0.97/1.20 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) pls)) ((ord_less_eq_int K) pls))) of role axiom named fact_520_rel__simps_I27_J % 0.97/1.20 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) pls)) ((ord_less_eq_int K) pls))) % 0.97/1.20 FOF formula ((ord_less_eq_int zero_zero_int) one_one_int) of role axiom named fact_521_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J % 0.97/1.20 A new axiom: ((ord_less_eq_int zero_zero_int) one_one_int) % 0.97/1.20 FOF formula (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X) Y))))) of role axiom named fact_522_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J % 0.97/1.20 A new axiom: (forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X) Y))))) % 0.97/1.20 FOF formula (forall (Z_3:int) (Z_2:int) (W_1:int) (W:int), (((ord_less_int W_1) W)->(((ord_less_eq_int Z_3) Z_2)->((ord_less_int ((plus_plus_int W_1) Z_3)) ((plus_plus_int W) Z_2))))) of role axiom named fact_523_zadd__zless__mono % 1.05/1.22 A new axiom: (forall (Z_3:int) (Z_2:int) (W_1:int) (W:int), (((ord_less_int W_1) W)->(((ord_less_eq_int Z_3) Z_2)->((ord_less_int ((plus_plus_int W_1) Z_3)) ((plus_plus_int W) Z_2))))) % 1.05/1.22 FOF formula (forall (Z_2:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int Z_2))) of role axiom named fact_524_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J % 1.05/1.22 A new axiom: (forall (Z_2:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int Z_2))) % 1.05/1.22 FOF formula (forall (P:(int->Prop)), ((iff ((ex int) (fun (X_14:int)=> ((and ((ord_less_eq_int zero_zero_int) X_14)) (P X_14))))) ((ex nat) (fun (X_14:nat)=> (P (semiri1621563631at_int X_14)))))) of role axiom named fact_525_transfer__int__nat__quantifiers_I2_J % 1.05/1.22 A new axiom: (forall (P:(int->Prop)), ((iff ((ex int) (fun (X_14:int)=> ((and ((ord_less_eq_int zero_zero_int) X_14)) (P X_14))))) ((ex nat) (fun (X_14:nat)=> (P (semiri1621563631at_int X_14)))))) % 1.05/1.22 FOF formula (forall (P:(int->Prop)), ((iff (forall (X_14:int), (((ord_less_eq_int zero_zero_int) X_14)->(P X_14)))) (forall (X_14:nat), (P (semiri1621563631at_int X_14))))) of role axiom named fact_526_transfer__int__nat__quantifiers_I1_J % 1.05/1.22 A new axiom: (forall (P:(int->Prop)), ((iff (forall (X_14:int), (((ord_less_eq_int zero_zero_int) X_14)->(P X_14)))) (forall (X_14:nat), (P (semiri1621563631at_int X_14))))) % 1.05/1.22 FOF formula (forall (N:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int N))) of role axiom named fact_527_zero__zle__int % 1.05/1.22 A new axiom: (forall (N:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int N))) % 1.05/1.22 FOF formula (forall (N:nat) (X:int), (((ord_less_eq_int zero_zero_int) X)->((ord_less_eq_int zero_zero_int) ((power_power_int X) N)))) of role axiom named fact_528_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J % 1.05/1.22 A new axiom: (forall (N:nat) (X:int), (((ord_less_eq_int zero_zero_int) X)->((ord_less_eq_int zero_zero_int) ((power_power_int X) N)))) % 1.05/1.22 FOF formula (forall (W:int) (Z_2:int), ((iff ((ord_less_eq_int W) Z_2)) ((ex nat) (fun (N_1:nat)=> (((eq int) Z_2) ((plus_plus_int W) (semiri1621563631at_int N_1))))))) of role axiom named fact_529_zle__iff__zadd % 1.05/1.22 A new axiom: (forall (W:int) (Z_2:int), ((iff ((ord_less_eq_int W) Z_2)) ((ex nat) (fun (N_1:nat)=> (((eq int) Z_2) ((plus_plus_int W) (semiri1621563631at_int N_1))))))) % 1.05/1.22 FOF formula (forall (V_6:int), (((ord_less_eq_int pls) V_6)->(((eq real) ((plus_plus_real one_one_real) (number267125858f_real V_6))) (number267125858f_real (succ V_6))))) of role axiom named fact_530_semiring__1__add__number__of % 1.05/1.22 A new axiom: (forall (V_6:int), (((ord_less_eq_int pls) V_6)->(((eq real) ((plus_plus_real one_one_real) (number267125858f_real V_6))) (number267125858f_real (succ V_6))))) % 1.05/1.22 FOF formula (forall (V_6:int), (((ord_less_eq_int pls) V_6)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V_6))) (number_number_of_nat (succ V_6))))) of role axiom named fact_531_semiring__1__add__number__of % 1.05/1.22 A new axiom: (forall (V_6:int), (((ord_less_eq_int pls) V_6)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V_6))) (number_number_of_nat (succ V_6))))) % 1.05/1.22 FOF formula (forall (V_6:int), (((ord_less_eq_int pls) V_6)->(((eq int) ((plus_plus_int one_one_int) (number_number_of_int V_6))) (number_number_of_int (succ V_6))))) of role axiom named fact_532_semiring__1__add__number__of % 1.05/1.22 A new axiom: (forall (V_6:int), (((ord_less_eq_int pls) V_6)->(((eq int) ((plus_plus_int one_one_int) (number_number_of_int V_6))) (number_number_of_int (succ V_6))))) % 1.05/1.22 FOF formula (forall (V_5:int), (((ord_less_eq_int pls) V_5)->(((eq real) ((plus_plus_real (number267125858f_real V_5)) one_one_real)) (number267125858f_real (succ V_5))))) of role axiom named fact_533_semiring__number__of__add__1 % 1.05/1.22 A new axiom: (forall (V_5:int), (((ord_less_eq_int pls) V_5)->(((eq real) ((plus_plus_real (number267125858f_real V_5)) one_one_real)) (number267125858f_real (succ V_5))))) % 1.05/1.22 FOF formula (forall (V_5:int), (((ord_less_eq_int pls) V_5)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_5)) one_one_nat)) (number_number_of_nat (succ V_5))))) of role axiom named fact_534_semiring__number__of__add__1 % 1.05/1.23 A new axiom: (forall (V_5:int), (((ord_less_eq_int pls) V_5)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_5)) one_one_nat)) (number_number_of_nat (succ V_5))))) % 1.05/1.23 FOF formula (forall (V_5:int), (((ord_less_eq_int pls) V_5)->(((eq int) ((plus_plus_int (number_number_of_int V_5)) one_one_int)) (number_number_of_int (succ V_5))))) of role axiom named fact_535_semiring__number__of__add__1 % 1.05/1.23 A new axiom: (forall (V_5:int), (((ord_less_eq_int pls) V_5)->(((eq int) ((plus_plus_int (number_number_of_int V_5)) one_one_int)) (number_number_of_int (succ V_5))))) % 1.05/1.23 FOF formula (forall (B_13:real) (A_14:real), (((ord_less_real zero_zero_real) A_14)->(((ord_less_eq_real zero_zero_real) B_13)->((ord_less_real zero_zero_real) ((plus_plus_real A_14) B_13))))) of role axiom named fact_536_add__pos__nonneg % 1.05/1.23 A new axiom: (forall (B_13:real) (A_14:real), (((ord_less_real zero_zero_real) A_14)->(((ord_less_eq_real zero_zero_real) B_13)->((ord_less_real zero_zero_real) ((plus_plus_real A_14) B_13))))) % 1.05/1.23 FOF formula (forall (B_13:nat) (A_14:nat), (((ord_less_nat zero_zero_nat) A_14)->(((ord_less_eq_nat zero_zero_nat) B_13)->((ord_less_nat zero_zero_nat) ((plus_plus_nat A_14) B_13))))) of role axiom named fact_537_add__pos__nonneg % 1.05/1.23 A new axiom: (forall (B_13:nat) (A_14:nat), (((ord_less_nat zero_zero_nat) A_14)->(((ord_less_eq_nat zero_zero_nat) B_13)->((ord_less_nat zero_zero_nat) ((plus_plus_nat A_14) B_13))))) % 1.05/1.23 FOF formula (forall (B_13:int) (A_14:int), (((ord_less_int zero_zero_int) A_14)->(((ord_less_eq_int zero_zero_int) B_13)->((ord_less_int zero_zero_int) ((plus_plus_int A_14) B_13))))) of role axiom named fact_538_add__pos__nonneg % 1.05/1.23 A new axiom: (forall (B_13:int) (A_14:int), (((ord_less_int zero_zero_int) A_14)->(((ord_less_eq_int zero_zero_int) B_13)->((ord_less_int zero_zero_int) ((plus_plus_int A_14) B_13))))) % 1.05/1.23 FOF formula (forall (B_12:real) (A_13:real), (((ord_less_eq_real zero_zero_real) A_13)->(((ord_less_real zero_zero_real) B_12)->((ord_less_real zero_zero_real) ((plus_plus_real A_13) B_12))))) of role axiom named fact_539_add__nonneg__pos % 1.05/1.23 A new axiom: (forall (B_12:real) (A_13:real), (((ord_less_eq_real zero_zero_real) A_13)->(((ord_less_real zero_zero_real) B_12)->((ord_less_real zero_zero_real) ((plus_plus_real A_13) B_12))))) % 1.05/1.23 FOF formula (forall (B_12:nat) (A_13:nat), (((ord_less_eq_nat zero_zero_nat) A_13)->(((ord_less_nat zero_zero_nat) B_12)->((ord_less_nat zero_zero_nat) ((plus_plus_nat A_13) B_12))))) of role axiom named fact_540_add__nonneg__pos % 1.05/1.23 A new axiom: (forall (B_12:nat) (A_13:nat), (((ord_less_eq_nat zero_zero_nat) A_13)->(((ord_less_nat zero_zero_nat) B_12)->((ord_less_nat zero_zero_nat) ((plus_plus_nat A_13) B_12))))) % 1.05/1.23 FOF formula (forall (B_12:int) (A_13:int), (((ord_less_eq_int zero_zero_int) A_13)->(((ord_less_int zero_zero_int) B_12)->((ord_less_int zero_zero_int) ((plus_plus_int A_13) B_12))))) of role axiom named fact_541_add__nonneg__pos % 1.05/1.23 A new axiom: (forall (B_12:int) (A_13:int), (((ord_less_eq_int zero_zero_int) A_13)->(((ord_less_int zero_zero_int) B_12)->((ord_less_int zero_zero_int) ((plus_plus_int A_13) B_12))))) % 1.05/1.23 FOF formula (forall (B_11:real) (C_5:real) (A_12:real), (((ord_less_real zero_zero_real) A_12)->(((ord_less_eq_real B_11) C_5)->((ord_less_real B_11) ((plus_plus_real A_12) C_5))))) of role axiom named fact_542_add__strict__increasing % 1.05/1.23 A new axiom: (forall (B_11:real) (C_5:real) (A_12:real), (((ord_less_real zero_zero_real) A_12)->(((ord_less_eq_real B_11) C_5)->((ord_less_real B_11) ((plus_plus_real A_12) C_5))))) % 1.05/1.23 FOF formula (forall (B_11:nat) (C_5:nat) (A_12:nat), (((ord_less_nat zero_zero_nat) A_12)->(((ord_less_eq_nat B_11) C_5)->((ord_less_nat B_11) ((plus_plus_nat A_12) C_5))))) of role axiom named fact_543_add__strict__increasing % 1.05/1.23 A new axiom: (forall (B_11:nat) (C_5:nat) (A_12:nat), (((ord_less_nat zero_zero_nat) A_12)->(((ord_less_eq_nat B_11) C_5)->((ord_less_nat B_11) ((plus_plus_nat A_12) C_5))))) % 1.05/1.23 FOF formula (forall (B_11:int) (C_5:int) (A_12:int), (((ord_less_int zero_zero_int) A_12)->(((ord_less_eq_int B_11) C_5)->((ord_less_int B_11) ((plus_plus_int A_12) C_5))))) of role axiom named fact_544_add__strict__increasing % 1.05/1.25 A new axiom: (forall (B_11:int) (C_5:int) (A_12:int), (((ord_less_int zero_zero_int) A_12)->(((ord_less_eq_int B_11) C_5)->((ord_less_int B_11) ((plus_plus_int A_12) C_5))))) % 1.05/1.25 FOF formula (forall (B_10:real) (C_4:real) (A_11:real), (((ord_less_eq_real zero_zero_real) A_11)->(((ord_less_real B_10) C_4)->((ord_less_real B_10) ((plus_plus_real A_11) C_4))))) of role axiom named fact_545_add__strict__increasing2 % 1.05/1.25 A new axiom: (forall (B_10:real) (C_4:real) (A_11:real), (((ord_less_eq_real zero_zero_real) A_11)->(((ord_less_real B_10) C_4)->((ord_less_real B_10) ((plus_plus_real A_11) C_4))))) % 1.05/1.25 FOF formula (forall (B_10:nat) (C_4:nat) (A_11:nat), (((ord_less_eq_nat zero_zero_nat) A_11)->(((ord_less_nat B_10) C_4)->((ord_less_nat B_10) ((plus_plus_nat A_11) C_4))))) of role axiom named fact_546_add__strict__increasing2 % 1.05/1.25 A new axiom: (forall (B_10:nat) (C_4:nat) (A_11:nat), (((ord_less_eq_nat zero_zero_nat) A_11)->(((ord_less_nat B_10) C_4)->((ord_less_nat B_10) ((plus_plus_nat A_11) C_4))))) % 1.05/1.25 FOF formula (forall (B_10:int) (C_4:int) (A_11:int), (((ord_less_eq_int zero_zero_int) A_11)->(((ord_less_int B_10) C_4)->((ord_less_int B_10) ((plus_plus_int A_11) C_4))))) of role axiom named fact_547_add__strict__increasing2 % 1.05/1.25 A new axiom: (forall (B_10:int) (C_4:int) (A_11:int), (((ord_less_eq_int zero_zero_int) A_11)->(((ord_less_int B_10) C_4)->((ord_less_int B_10) ((plus_plus_int A_11) C_4))))) % 1.05/1.25 FOF formula (forall (B_9:real) (A_10:real), (((ord_less_real A_10) zero_zero_real)->(((ord_less_eq_real B_9) zero_zero_real)->((ord_less_real ((plus_plus_real A_10) B_9)) zero_zero_real)))) of role axiom named fact_548_add__neg__nonpos % 1.05/1.25 A new axiom: (forall (B_9:real) (A_10:real), (((ord_less_real A_10) zero_zero_real)->(((ord_less_eq_real B_9) zero_zero_real)->((ord_less_real ((plus_plus_real A_10) B_9)) zero_zero_real)))) % 1.05/1.25 FOF formula (forall (B_9:nat) (A_10:nat), (((ord_less_nat A_10) zero_zero_nat)->(((ord_less_eq_nat B_9) zero_zero_nat)->((ord_less_nat ((plus_plus_nat A_10) B_9)) zero_zero_nat)))) of role axiom named fact_549_add__neg__nonpos % 1.05/1.25 A new axiom: (forall (B_9:nat) (A_10:nat), (((ord_less_nat A_10) zero_zero_nat)->(((ord_less_eq_nat B_9) zero_zero_nat)->((ord_less_nat ((plus_plus_nat A_10) B_9)) zero_zero_nat)))) % 1.05/1.25 FOF formula (forall (B_9:int) (A_10:int), (((ord_less_int A_10) zero_zero_int)->(((ord_less_eq_int B_9) zero_zero_int)->((ord_less_int ((plus_plus_int A_10) B_9)) zero_zero_int)))) of role axiom named fact_550_add__neg__nonpos % 1.05/1.25 A new axiom: (forall (B_9:int) (A_10:int), (((ord_less_int A_10) zero_zero_int)->(((ord_less_eq_int B_9) zero_zero_int)->((ord_less_int ((plus_plus_int A_10) B_9)) zero_zero_int)))) % 1.05/1.25 FOF formula (forall (B_8:real) (A_9:real), (((ord_less_eq_real A_9) zero_zero_real)->(((ord_less_real B_8) zero_zero_real)->((ord_less_real ((plus_plus_real A_9) B_8)) zero_zero_real)))) of role axiom named fact_551_add__nonpos__neg % 1.05/1.25 A new axiom: (forall (B_8:real) (A_9:real), (((ord_less_eq_real A_9) zero_zero_real)->(((ord_less_real B_8) zero_zero_real)->((ord_less_real ((plus_plus_real A_9) B_8)) zero_zero_real)))) % 1.05/1.25 FOF formula (forall (B_8:nat) (A_9:nat), (((ord_less_eq_nat A_9) zero_zero_nat)->(((ord_less_nat B_8) zero_zero_nat)->((ord_less_nat ((plus_plus_nat A_9) B_8)) zero_zero_nat)))) of role axiom named fact_552_add__nonpos__neg % 1.05/1.25 A new axiom: (forall (B_8:nat) (A_9:nat), (((ord_less_eq_nat A_9) zero_zero_nat)->(((ord_less_nat B_8) zero_zero_nat)->((ord_less_nat ((plus_plus_nat A_9) B_8)) zero_zero_nat)))) % 1.05/1.25 FOF formula (forall (B_8:int) (A_9:int), (((ord_less_eq_int A_9) zero_zero_int)->(((ord_less_int B_8) zero_zero_int)->((ord_less_int ((plus_plus_int A_9) B_8)) zero_zero_int)))) of role axiom named fact_553_add__nonpos__neg % 1.05/1.25 A new axiom: (forall (B_8:int) (A_9:int), (((ord_less_eq_int A_9) zero_zero_int)->(((ord_less_int B_8) zero_zero_int)->((ord_less_int ((plus_plus_int A_9) B_8)) zero_zero_int)))) % 1.05/1.25 FOF formula (forall (A_8:real) (N_4:nat) (B_7:real), (((ord_less_real ((power_power_real A_8) N_4)) ((power_power_real B_7) N_4))->(((ord_less_eq_real zero_zero_real) B_7)->((ord_less_real A_8) B_7)))) of role axiom named fact_554_power__less__imp__less__base % 1.05/1.27 A new axiom: (forall (A_8:real) (N_4:nat) (B_7:real), (((ord_less_real ((power_power_real A_8) N_4)) ((power_power_real B_7) N_4))->(((ord_less_eq_real zero_zero_real) B_7)->((ord_less_real A_8) B_7)))) % 1.05/1.27 FOF formula (forall (A_8:nat) (N_4:nat) (B_7:nat), (((ord_less_nat ((power_power_nat A_8) N_4)) ((power_power_nat B_7) N_4))->(((ord_less_eq_nat zero_zero_nat) B_7)->((ord_less_nat A_8) B_7)))) of role axiom named fact_555_power__less__imp__less__base % 1.05/1.27 A new axiom: (forall (A_8:nat) (N_4:nat) (B_7:nat), (((ord_less_nat ((power_power_nat A_8) N_4)) ((power_power_nat B_7) N_4))->(((ord_less_eq_nat zero_zero_nat) B_7)->((ord_less_nat A_8) B_7)))) % 1.05/1.27 FOF formula (forall (A_8:int) (N_4:nat) (B_7:int), (((ord_less_int ((power_power_int A_8) N_4)) ((power_power_int B_7) N_4))->(((ord_less_eq_int zero_zero_int) B_7)->((ord_less_int A_8) B_7)))) of role axiom named fact_556_power__less__imp__less__base % 1.05/1.27 A new axiom: (forall (A_8:int) (N_4:nat) (B_7:int), (((ord_less_int ((power_power_int A_8) N_4)) ((power_power_int B_7) N_4))->(((ord_less_eq_int zero_zero_int) B_7)->((ord_less_int A_8) B_7)))) % 1.05/1.27 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_557_eq__0__number__of % 1.05/1.27 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))) % 1.05/1.27 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_558_eq__number__of__0 % 1.05/1.27 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))) % 1.05/1.27 FOF formula (forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_559_rel__simps_I5_J % 1.05/1.27 A new axiom: (forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) % 1.05/1.27 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_560_rel__simps_I29_J % 1.05/1.27 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls))) % 1.05/1.27 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_561_rel__simps_I15_J % 1.05/1.27 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))) % 1.05/1.27 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_562_less__int__code_I14_J % 1.05/1.27 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))) % 1.05/1.27 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_563_rel__simps_I33_J % 1.05/1.27 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))) % 1.05/1.27 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_564_less__eq__int__code_I15_J % 1.05/1.27 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2))) % 1.05/1.27 FOF formula (forall (Z_2:int), ((iff ((ord_less_eq_int one_one_int) Z_2)) ((ord_less_int zero_zero_int) Z_2))) of role axiom named fact_565_int__one__le__iff__zero__less % 1.05/1.27 A new axiom: (forall (Z_2:int), ((iff ((ord_less_eq_int one_one_int) Z_2)) ((ord_less_int zero_zero_int) Z_2))) % 1.05/1.27 FOF formula (forall (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat))) of role axiom named fact_566_int__le__0__conv % 1.05/1.27 A new axiom: (forall (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat))) % 1.05/1.27 FOF formula (((eq int) (succ pls)) (bit1 pls)) of role axiom named fact_567_succ__Pls % 1.05/1.27 A new axiom: (((eq int) (succ pls)) (bit1 pls)) % 1.05/1.27 FOF formula (forall (K:int), (((eq int) (succ (bit0 K))) (bit1 K))) of role axiom named fact_568_succ__Bit0 % 1.11/1.29 A new axiom: (forall (K:int), (((eq int) (succ (bit0 K))) (bit1 K))) % 1.11/1.29 FOF formula (forall (K:int), (((eq int) (succ (bit1 K))) (bit0 (succ K)))) of role axiom named fact_569_succ__Bit1 % 1.11/1.29 A new axiom: (forall (K:int), (((eq int) (succ (bit1 K))) (bit0 (succ K)))) % 1.11/1.29 FOF formula (forall (W:int) (Z_2:int), ((iff ((ord_less_int W) ((plus_plus_int Z_2) one_one_int))) ((ord_less_eq_int W) Z_2))) of role axiom named fact_570_zle__add1__eq__le % 1.11/1.29 A new axiom: (forall (W:int) (Z_2:int), ((iff ((ord_less_int W) ((plus_plus_int Z_2) one_one_int))) ((ord_less_eq_int W) Z_2))) % 1.11/1.29 FOF formula (forall (W:int) (Z_2:int), ((iff ((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z_2)) ((ord_less_int W) Z_2))) of role axiom named fact_571_add1__zle__eq % 1.11/1.29 A new axiom: (forall (W:int) (Z_2:int), ((iff ((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z_2)) ((ord_less_int W) Z_2))) % 1.11/1.29 FOF formula (forall (W:int) (Z_2:int), (((ord_less_int W) Z_2)->((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z_2))) of role axiom named fact_572_zless__imp__add1__zle % 1.11/1.29 A new axiom: (forall (W:int) (Z_2:int), (((ord_less_int W) Z_2)->((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z_2))) % 1.11/1.29 FOF formula (forall (K:int), (((eq int) (succ K)) ((plus_plus_int K) one_one_int))) of role axiom named fact_573_succ__def % 1.11/1.29 A new axiom: (forall (K:int), (((eq int) (succ K)) ((plus_plus_int K) one_one_int))) % 1.11/1.29 FOF formula (forall (A_7:real) (N_3:nat) (B_6:real), ((((eq real) ((power_power_real A_7) N_3)) ((power_power_real B_6) N_3))->(((ord_less_eq_real zero_zero_real) A_7)->(((ord_less_eq_real zero_zero_real) B_6)->(((ord_less_nat zero_zero_nat) N_3)->(((eq real) A_7) B_6)))))) of role axiom named fact_574_power__eq__imp__eq__base % 1.11/1.29 A new axiom: (forall (A_7:real) (N_3:nat) (B_6:real), ((((eq real) ((power_power_real A_7) N_3)) ((power_power_real B_6) N_3))->(((ord_less_eq_real zero_zero_real) A_7)->(((ord_less_eq_real zero_zero_real) B_6)->(((ord_less_nat zero_zero_nat) N_3)->(((eq real) A_7) B_6)))))) % 1.11/1.29 FOF formula (forall (A_7:nat) (N_3:nat) (B_6:nat), ((((eq nat) ((power_power_nat A_7) N_3)) ((power_power_nat B_6) N_3))->(((ord_less_eq_nat zero_zero_nat) A_7)->(((ord_less_eq_nat zero_zero_nat) B_6)->(((ord_less_nat zero_zero_nat) N_3)->(((eq nat) A_7) B_6)))))) of role axiom named fact_575_power__eq__imp__eq__base % 1.11/1.29 A new axiom: (forall (A_7:nat) (N_3:nat) (B_6:nat), ((((eq nat) ((power_power_nat A_7) N_3)) ((power_power_nat B_6) N_3))->(((ord_less_eq_nat zero_zero_nat) A_7)->(((ord_less_eq_nat zero_zero_nat) B_6)->(((ord_less_nat zero_zero_nat) N_3)->(((eq nat) A_7) B_6)))))) % 1.11/1.29 FOF formula (forall (A_7:int) (N_3:nat) (B_6:int), ((((eq int) ((power_power_int A_7) N_3)) ((power_power_int B_6) N_3))->(((ord_less_eq_int zero_zero_int) A_7)->(((ord_less_eq_int zero_zero_int) B_6)->(((ord_less_nat zero_zero_nat) N_3)->(((eq int) A_7) B_6)))))) of role axiom named fact_576_power__eq__imp__eq__base % 1.11/1.29 A new axiom: (forall (A_7:int) (N_3:nat) (B_6:int), ((((eq int) ((power_power_int A_7) N_3)) ((power_power_int B_6) N_3))->(((ord_less_eq_int zero_zero_int) A_7)->(((ord_less_eq_int zero_zero_int) B_6)->(((ord_less_nat zero_zero_nat) N_3)->(((eq int) A_7) B_6)))))) % 1.11/1.29 FOF formula (forall (V_4:int) (V_3:int), (((ord_less_eq_int pls) V_3)->(((ord_less_eq_int pls) V_4)->(((eq real) ((plus_plus_real (number267125858f_real V_3)) (number267125858f_real V_4))) (number267125858f_real ((plus_plus_int V_3) V_4)))))) of role axiom named fact_577_semiring__add__number__of % 1.11/1.29 A new axiom: (forall (V_4:int) (V_3:int), (((ord_less_eq_int pls) V_3)->(((ord_less_eq_int pls) V_4)->(((eq real) ((plus_plus_real (number267125858f_real V_3)) (number267125858f_real V_4))) (number267125858f_real ((plus_plus_int V_3) V_4)))))) % 1.11/1.29 FOF formula (forall (V_4:int) (V_3:int), (((ord_less_eq_int pls) V_3)->(((ord_less_eq_int pls) V_4)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_3)) (number_number_of_nat V_4))) (number_number_of_nat ((plus_plus_int V_3) V_4)))))) of role axiom named fact_578_semiring__add__number__of % 1.11/1.29 A new axiom: (forall (V_4:int) (V_3:int), (((ord_less_eq_int pls) V_3)->(((ord_less_eq_int pls) V_4)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_3)) (number_number_of_nat V_4))) (number_number_of_nat ((plus_plus_int V_3) V_4)))))) % 1.11/1.31 FOF formula (forall (V_4:int) (V_3:int), (((ord_less_eq_int pls) V_3)->(((ord_less_eq_int pls) V_4)->(((eq int) ((plus_plus_int (number_number_of_int V_3)) (number_number_of_int V_4))) (number_number_of_int ((plus_plus_int V_3) V_4)))))) of role axiom named fact_579_semiring__add__number__of % 1.11/1.31 A new axiom: (forall (V_4:int) (V_3:int), (((ord_less_eq_int pls) V_3)->(((ord_less_eq_int pls) V_4)->(((eq int) ((plus_plus_int (number_number_of_int V_3)) (number_number_of_int V_4))) (number_number_of_int ((plus_plus_int V_3) V_4)))))) % 1.11/1.31 FOF formula ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 (bit1 pls)))) of role axiom named fact_580_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J % 1.11/1.31 A new axiom: ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 (bit1 pls)))) % 1.11/1.31 FOF formula (forall (Z_2:int), (((ord_less_eq_int zero_zero_int) Z_2)->((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) Z_2)))) of role axiom named fact_581_le__imp__0__less % 1.11/1.31 A new axiom: (forall (Z_2:int), (((ord_less_eq_int zero_zero_int) Z_2)->((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) Z_2)))) % 1.11/1.31 FOF formula (forall (K_2:int), (((eq real) (number267125858f_real (succ K_2))) ((plus_plus_real one_one_real) (number267125858f_real K_2)))) of role axiom named fact_582_number__of__succ % 1.11/1.31 A new axiom: (forall (K_2:int), (((eq real) (number267125858f_real (succ K_2))) ((plus_plus_real one_one_real) (number267125858f_real K_2)))) % 1.11/1.31 FOF formula (forall (K_2:int), (((eq int) (number_number_of_int (succ K_2))) ((plus_plus_int one_one_int) (number_number_of_int K_2)))) of role axiom named fact_583_number__of__succ % 1.11/1.31 A new axiom: (forall (K_2:int), (((eq int) (number_number_of_int (succ K_2))) ((plus_plus_int one_one_int) (number_number_of_int K_2)))) % 1.11/1.31 FOF formula (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit1 L))) (bit0 ((plus_plus_int K) (succ L))))) of role axiom named fact_584_add__Bit1__Bit1 % 1.11/1.31 A new axiom: (forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit1 L))) (bit0 ((plus_plus_int K) (succ L))))) % 1.11/1.31 FOF formula (forall (N_2:nat) (A_6:real) (B_5:real), (((ord_less_real A_6) B_5)->(((ord_less_eq_real zero_zero_real) A_6)->(((ord_less_nat zero_zero_nat) N_2)->((ord_less_real ((power_power_real A_6) N_2)) ((power_power_real B_5) N_2)))))) of role axiom named fact_585_power__strict__mono % 1.11/1.31 A new axiom: (forall (N_2:nat) (A_6:real) (B_5:real), (((ord_less_real A_6) B_5)->(((ord_less_eq_real zero_zero_real) A_6)->(((ord_less_nat zero_zero_nat) N_2)->((ord_less_real ((power_power_real A_6) N_2)) ((power_power_real B_5) N_2)))))) % 1.11/1.31 FOF formula (forall (N_2:nat) (A_6:nat) (B_5:nat), (((ord_less_nat A_6) B_5)->(((ord_less_eq_nat zero_zero_nat) A_6)->(((ord_less_nat zero_zero_nat) N_2)->((ord_less_nat ((power_power_nat A_6) N_2)) ((power_power_nat B_5) N_2)))))) of role axiom named fact_586_power__strict__mono % 1.11/1.31 A new axiom: (forall (N_2:nat) (A_6:nat) (B_5:nat), (((ord_less_nat A_6) B_5)->(((ord_less_eq_nat zero_zero_nat) A_6)->(((ord_less_nat zero_zero_nat) N_2)->((ord_less_nat ((power_power_nat A_6) N_2)) ((power_power_nat B_5) N_2)))))) % 1.11/1.31 FOF formula (forall (N_2:nat) (A_6:int) (B_5:int), (((ord_less_int A_6) B_5)->(((ord_less_eq_int zero_zero_int) A_6)->(((ord_less_nat zero_zero_nat) N_2)->((ord_less_int ((power_power_int A_6) N_2)) ((power_power_int B_5) N_2)))))) of role axiom named fact_587_power__strict__mono % 1.11/1.31 A new axiom: (forall (N_2:nat) (A_6:int) (B_5:int), (((ord_less_int A_6) B_5)->(((ord_less_eq_int zero_zero_int) A_6)->(((ord_less_nat zero_zero_nat) N_2)->((ord_less_int ((power_power_int A_6) N_2)) ((power_power_int B_5) N_2)))))) % 1.11/1.31 FOF formula ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 (bit1 pls)))) of role axiom named fact_588_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J % 1.11/1.31 A new axiom: ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 (bit1 pls)))) % 1.11/1.31 FOF formula (forall (X:int), ((ord_less_eq_int X) ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_589_power2__ge__self % 1.11/1.32 A new axiom: (forall (X:int), ((ord_less_eq_int X) ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls)))))) % 1.11/1.32 FOF formula (forall (A_5:real), ((ord_less_eq_real zero_zero_real) ((power_power_real A_5) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_590_zero__le__power2 % 1.11/1.32 A new axiom: (forall (A_5:real), ((ord_less_eq_real zero_zero_real) ((power_power_real A_5) (number_number_of_nat (bit0 (bit1 pls)))))) % 1.11/1.32 FOF formula (forall (A_5:int), ((ord_less_eq_int zero_zero_int) ((power_power_int A_5) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_591_zero__le__power2 % 1.11/1.32 A new axiom: (forall (A_5:int), ((ord_less_eq_int zero_zero_int) ((power_power_int A_5) (number_number_of_nat (bit0 (bit1 pls)))))) % 1.11/1.32 FOF formula (forall (X_13:real) (Y_12:real), (((ord_less_eq_real ((power_power_real X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_12)->((ord_less_eq_real X_13) Y_12)))) of role axiom named fact_592_power2__le__imp__le % 1.11/1.32 A new axiom: (forall (X_13:real) (Y_12:real), (((ord_less_eq_real ((power_power_real X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_12)->((ord_less_eq_real X_13) Y_12)))) % 1.11/1.32 FOF formula (forall (X_13:nat) (Y_12:nat), (((ord_less_eq_nat ((power_power_nat X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_12)->((ord_less_eq_nat X_13) Y_12)))) of role axiom named fact_593_power2__le__imp__le % 1.11/1.32 A new axiom: (forall (X_13:nat) (Y_12:nat), (((ord_less_eq_nat ((power_power_nat X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_12)->((ord_less_eq_nat X_13) Y_12)))) % 1.11/1.32 FOF formula (forall (X_13:int) (Y_12:int), (((ord_less_eq_int ((power_power_int X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_12)->((ord_less_eq_int X_13) Y_12)))) of role axiom named fact_594_power2__le__imp__le % 1.11/1.32 A new axiom: (forall (X_13:int) (Y_12:int), (((ord_less_eq_int ((power_power_int X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_12)->((ord_less_eq_int X_13) Y_12)))) % 1.11/1.32 FOF formula (forall (X_12:real) (Y_11:real), ((((eq real) ((power_power_real X_12) (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) X_12)->(((ord_less_eq_real zero_zero_real) Y_11)->(((eq real) X_12) Y_11))))) of role axiom named fact_595_power2__eq__imp__eq % 1.11/1.32 A new axiom: (forall (X_12:real) (Y_11:real), ((((eq real) ((power_power_real X_12) (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) X_12)->(((ord_less_eq_real zero_zero_real) Y_11)->(((eq real) X_12) Y_11))))) % 1.11/1.32 FOF formula (forall (X_12:nat) (Y_11:nat), ((((eq nat) ((power_power_nat X_12) (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) X_12)->(((ord_less_eq_nat zero_zero_nat) Y_11)->(((eq nat) X_12) Y_11))))) of role axiom named fact_596_power2__eq__imp__eq % 1.11/1.32 A new axiom: (forall (X_12:nat) (Y_11:nat), ((((eq nat) ((power_power_nat X_12) (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) X_12)->(((ord_less_eq_nat zero_zero_nat) Y_11)->(((eq nat) X_12) Y_11))))) % 1.11/1.32 FOF formula (forall (X_12:int) (Y_11:int), ((((eq int) ((power_power_int X_12) (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) X_12)->(((ord_less_eq_int zero_zero_int) Y_11)->(((eq int) X_12) Y_11))))) of role axiom named fact_597_power2__eq__imp__eq % 1.11/1.34 A new axiom: (forall (X_12:int) (Y_11:int), ((((eq int) ((power_power_int X_12) (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) X_12)->(((ord_less_eq_int zero_zero_int) Y_11)->(((eq int) X_12) Y_11))))) % 1.11/1.34 FOF formula (forall (V_2:int), ((and (((ord_less_eq_int zero_zero_int) (number_number_of_int V_2))->(((eq real) (semiri132038758t_real (number_number_of_nat V_2))) (number267125858f_real V_2)))) ((((ord_less_eq_int zero_zero_int) (number_number_of_int V_2))->False)->(((eq real) (semiri132038758t_real (number_number_of_nat V_2))) zero_zero_real)))) of role axiom named fact_598_of__nat__number__of__lemma % 1.11/1.34 A new axiom: (forall (V_2:int), ((and (((ord_less_eq_int zero_zero_int) (number_number_of_int V_2))->(((eq real) (semiri132038758t_real (number_number_of_nat V_2))) (number267125858f_real V_2)))) ((((ord_less_eq_int zero_zero_int) (number_number_of_int V_2))->False)->(((eq real) (semiri132038758t_real (number_number_of_nat V_2))) zero_zero_real)))) % 1.11/1.34 FOF formula (forall (V_2:int), ((and (((ord_less_eq_int zero_zero_int) (number_number_of_int V_2))->(((eq int) (semiri1621563631at_int (number_number_of_nat V_2))) (number_number_of_int V_2)))) ((((ord_less_eq_int zero_zero_int) (number_number_of_int V_2))->False)->(((eq int) (semiri1621563631at_int (number_number_of_nat V_2))) zero_zero_int)))) of role axiom named fact_599_of__nat__number__of__lemma % 1.11/1.34 A new axiom: (forall (V_2:int), ((and (((ord_less_eq_int zero_zero_int) (number_number_of_int V_2))->(((eq int) (semiri1621563631at_int (number_number_of_nat V_2))) (number_number_of_int V_2)))) ((((ord_less_eq_int zero_zero_int) (number_number_of_int V_2))->False)->(((eq int) (semiri1621563631at_int (number_number_of_nat V_2))) zero_zero_int)))) % 1.11/1.34 FOF formula (forall (X_11:real) (Y_10:real), (((ord_less_real ((power_power_real X_11) (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) Y_10)->((ord_less_real X_11) Y_10)))) of role axiom named fact_600_power2__less__imp__less % 1.11/1.34 A new axiom: (forall (X_11:real) (Y_10:real), (((ord_less_real ((power_power_real X_11) (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) Y_10)->((ord_less_real X_11) Y_10)))) % 1.11/1.34 FOF formula (forall (X_11:nat) (Y_10:nat), (((ord_less_nat ((power_power_nat X_11) (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) Y_10)->((ord_less_nat X_11) Y_10)))) of role axiom named fact_601_power2__less__imp__less % 1.11/1.34 A new axiom: (forall (X_11:nat) (Y_10:nat), (((ord_less_nat ((power_power_nat X_11) (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) Y_10)->((ord_less_nat X_11) Y_10)))) % 1.11/1.34 FOF formula (forall (X_11:int) (Y_10:int), (((ord_less_int ((power_power_int X_11) (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) Y_10)->((ord_less_int X_11) Y_10)))) of role axiom named fact_602_power2__less__imp__less % 1.11/1.34 A new axiom: (forall (X_11:int) (Y_10:int), (((ord_less_int ((power_power_int X_11) (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) Y_10)->((ord_less_int X_11) Y_10)))) % 1.11/1.34 FOF formula (forall (X_10:real) (Y_9:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((power_power_real X_10) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_9) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_603_sum__power2__ge__zero % 1.11/1.34 A new axiom: (forall (X_10:real) (Y_9:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((power_power_real X_10) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_9) (number_number_of_nat (bit0 (bit1 pls))))))) % 1.11/1.35 FOF formula (forall (X_10:int) (Y_9:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((power_power_int X_10) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_9) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_604_sum__power2__ge__zero % 1.11/1.35 A new axiom: (forall (X_10:int) (Y_9:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((power_power_int X_10) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_9) (number_number_of_nat (bit0 (bit1 pls))))))) % 1.11/1.35 FOF formula (forall (X_9:real) (Y_8:real), ((iff ((ord_less_eq_real ((plus_plus_real ((power_power_real X_9) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_8) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_9) zero_zero_real)) (((eq real) Y_8) zero_zero_real)))) of role axiom named fact_605_sum__power2__le__zero__iff % 1.11/1.35 A new axiom: (forall (X_9:real) (Y_8:real), ((iff ((ord_less_eq_real ((plus_plus_real ((power_power_real X_9) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_8) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_9) zero_zero_real)) (((eq real) Y_8) zero_zero_real)))) % 1.11/1.35 FOF formula (forall (X_9:int) (Y_8:int), ((iff ((ord_less_eq_int ((plus_plus_int ((power_power_int X_9) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_8) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_9) zero_zero_int)) (((eq int) Y_8) zero_zero_int)))) of role axiom named fact_606_sum__power2__le__zero__iff % 1.11/1.35 A new axiom: (forall (X_9:int) (Y_8:int), ((iff ((ord_less_eq_int ((plus_plus_int ((power_power_int X_9) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_8) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_9) zero_zero_int)) (((eq int) Y_8) zero_zero_int)))) % 1.11/1.35 FOF formula (forall (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_int X) (number_number_of_int (bit0 (bit1 pls))))->((or (((eq int) X) zero_zero_int)) (((eq int) X) one_one_int))))) of role axiom named fact_607_int__pos__lt__two__imp__zero__or__one % 1.11/1.35 A new axiom: (forall (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_int X) (number_number_of_int (bit0 (bit1 pls))))->((or (((eq int) X) zero_zero_int)) (((eq int) X) one_one_int))))) % 1.11/1.35 FOF formula (forall (N:int), (((ord_less_eq_int zero_zero_int) (number_number_of_int N))->((and ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 N)))) ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 N)))))) of role axiom named fact_608_number__of1 % 1.11/1.35 A new axiom: (forall (N:int), (((ord_less_eq_int zero_zero_int) (number_number_of_int N))->((and ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 N)))) ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 N)))))) % 1.11/1.35 FOF formula ((ord_less_eq_int zero_zero_int) (number_number_of_int pls)) of role axiom named fact_609_number__of2 % 1.11/1.35 A new axiom: ((ord_less_eq_int zero_zero_int) (number_number_of_int pls)) % 1.11/1.35 FOF formula (forall (K:int), (((ord_less_eq_int zero_zero_int) K)->((ex nat) (fun (N_1:nat)=> (((eq int) K) (semiri1621563631at_int N_1)))))) of role axiom named fact_610_zero__le__imp__eq__int % 1.11/1.35 A new axiom: (forall (K:int), (((ord_less_eq_int zero_zero_int) K)->((ex nat) (fun (N_1:nat)=> (((eq int) K) (semiri1621563631at_int N_1)))))) % 1.11/1.35 FOF formula (forall (K:int), (((ord_less_eq_int zero_zero_int) K)->((forall (N_1:nat), (not (((eq int) K) (semiri1621563631at_int N_1))))->False))) of role axiom named fact_611_nonneg__int__cases % 1.11/1.35 A new axiom: (forall (K:int), (((ord_less_eq_int zero_zero_int) K)->((forall (N_1:nat), (not (((eq int) K) (semiri1621563631at_int N_1))))->False))) % 1.11/1.35 FOF formula (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) of role axiom named fact_612_le0 % 1.11/1.35 A new axiom: (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) % 1.11/1.35 FOF formula (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) of role axiom named fact_613_less__eq__nat_Osimps_I1_J % 1.20/1.37 A new axiom: (forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)) % 1.20/1.37 FOF formula (forall (N:nat), ((iff ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat))) of role axiom named fact_614_le__0__eq % 1.20/1.37 A new axiom: (forall (N:nat), ((iff ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat))) % 1.20/1.37 FOF formula (forall (M:nat) (N:nat), (((or ((ord_less_nat M) N)) (((eq nat) M) N))->((ord_less_eq_nat M) N))) of role axiom named fact_615_less__or__eq__imp__le % 1.20/1.37 A new axiom: (forall (M:nat) (N:nat), (((or ((ord_less_nat M) N)) (((eq nat) M) N))->((ord_less_eq_nat M) N))) % 1.20/1.37 FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((not (((eq nat) M) N))->((ord_less_nat M) N)))) of role axiom named fact_616_le__neq__implies__less % 1.20/1.37 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((not (((eq nat) M) N))->((ord_less_nat M) N)))) % 1.20/1.37 FOF formula (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N))) of role axiom named fact_617_less__imp__le__nat % 1.20/1.37 A new axiom: (forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N))) % 1.20/1.37 FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((or ((ord_less_nat M) N)) (((eq nat) M) N)))) of role axiom named fact_618_le__eq__less__or__eq % 1.20/1.37 A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((or ((ord_less_nat M) N)) (((eq nat) M) N)))) % 1.20/1.37 FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) N)) ((and ((ord_less_eq_nat M) N)) (not (((eq nat) M) N))))) of role axiom named fact_619_nat__less__le % 1.20/1.37 A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_nat M) N)) ((and ((ord_less_eq_nat M) N)) (not (((eq nat) M) N))))) % 1.20/1.37 FOF formula (forall (N:nat), ((ord_less_eq_nat N) N)) of role axiom named fact_620_le__refl % 1.20/1.37 A new axiom: (forall (N:nat), ((ord_less_eq_nat N) N)) % 1.20/1.37 FOF formula (forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M))) of role axiom named fact_621_nat__le__linear % 1.20/1.37 A new axiom: (forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M))) % 1.20/1.37 FOF formula (forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N))) of role axiom named fact_622_eq__imp__le % 1.20/1.37 A new axiom: (forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N))) % 1.20/1.37 FOF formula (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat _TPTP_I) K)))) of role axiom named fact_623_le__trans % 1.20/1.37 A new axiom: (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat _TPTP_I) K)))) % 1.20/1.37 FOF formula (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N)))) of role axiom named fact_624_le__antisym % 1.20/1.37 A new axiom: (forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N)))) % 1.20/1.37 FOF formula (forall (X:real) (Y:real), ((iff ((ord_less_eq_real X) Y)) ((or ((ord_less_real X) Y)) (((eq real) X) Y)))) of role axiom named fact_625_less__eq__real__def % 1.20/1.37 A new axiom: (forall (X:real) (Y:real), ((iff ((ord_less_eq_real X) Y)) ((or ((ord_less_real X) Y)) (((eq real) X) Y)))) % 1.20/1.37 FOF formula (forall (X:real) (Y:real), ((iff ((ord_less_real X) Y)) ((and ((ord_less_eq_real X) Y)) (not (((eq real) X) Y))))) of role axiom named fact_626_real__less__def % 1.20/1.37 A new axiom: (forall (X:real) (Y:real), ((iff ((ord_less_real X) Y)) ((and ((ord_less_eq_real X) Y)) (not (((eq real) X) Y))))) % 1.20/1.37 FOF formula (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat M) N))) of role axiom named fact_627_le__add2 % 1.20/1.37 A new axiom: (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat M) N))) % 1.20/1.37 FOF formula (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M))) of role axiom named fact_628_le__add1 % 1.20/1.37 A new axiom: (forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M))) % 1.20/1.37 FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) ((plus_plus_nat M) K_1)))))) of role axiom named fact_629_le__iff__add % 1.22/1.39 A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) ((plus_plus_nat M) K_1)))))) % 1.22/1.39 FOF formula (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_eq_nat M) N))) of role axiom named fact_630_nat__add__left__cancel__le % 1.22/1.39 A new axiom: (forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_eq_nat M) N))) % 1.22/1.39 FOF formula (forall (M:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat J) M)))) of role axiom named fact_631_trans__le__add1 % 1.22/1.39 A new axiom: (forall (M:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat J) M)))) % 1.22/1.39 FOF formula (forall (M:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat M) J)))) of role axiom named fact_632_trans__le__add2 % 1.22/1.39 A new axiom: (forall (M:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat M) J)))) % 1.22/1.39 FOF formula (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K)))) of role axiom named fact_633_add__le__mono1 % 1.22/1.39 A new axiom: (forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K)))) % 1.22/1.39 FOF formula (forall (K:nat) (L:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L))))) of role axiom named fact_634_add__le__mono % 1.22/1.39 A new axiom: (forall (K:nat) (L:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L))))) % 1.22/1.39 FOF formula (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat K) N))) of role axiom named fact_635_add__leD2 % 1.22/1.39 A new axiom: (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat K) N))) % 1.22/1.39 FOF formula (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat M) N))) of role axiom named fact_636_add__leD1 % 1.22/1.39 A new axiom: (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat M) N))) % 1.22/1.39 FOF formula (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((((ord_less_eq_nat M) N)->(((ord_less_eq_nat K) N)->False))->False))) of role axiom named fact_637_add__leE % 1.22/1.39 A new axiom: (forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((((ord_less_eq_nat M) N)->(((ord_less_eq_nat K) N)->False))->False))) % 1.22/1.39 FOF formula (forall (Z_2:real) (X:real) (Y:real), (((ord_less_eq_real X) Y)->((ord_less_eq_real ((plus_plus_real Z_2) X)) ((plus_plus_real Z_2) Y)))) of role axiom named fact_638_real__add__left__mono % 1.22/1.39 A new axiom: (forall (Z_2:real) (X:real) (Y:real), (((ord_less_eq_real X) Y)->((ord_less_eq_real ((plus_plus_real Z_2) X)) ((plus_plus_real Z_2) Y)))) % 1.22/1.39 FOF formula (forall (X:nat) (Y:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_eq_nat X) Y))) of role axiom named fact_639_Nat__Transfer_Otransfer__int__nat__relations_I3_J % 1.22/1.39 A new axiom: (forall (X:nat) (Y:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_eq_nat X) Y))) % 1.22/1.39 FOF formula (forall (M:nat) (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_eq_nat M) N))) of role axiom named fact_640_zle__int % 1.22/1.39 A new axiom: (forall (M:nat) (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_eq_nat M) N))) % 1.22/1.39 FOF formula (forall (V_1:int) (V:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_1)) (number_number_of_nat V))) ((((ord_less_eq_int V_1) V)->False)->((ord_less_eq_int V_1) pls)))) of role axiom named fact_641_le__nat__number__of % 1.22/1.39 A new axiom: (forall (V_1:int) (V:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_1)) (number_number_of_nat V))) ((((ord_less_eq_int V_1) V)->False)->((ord_less_eq_int V_1) pls)))) % 1.25/1.41 FOF formula (forall (N:nat), ((ord_less_eq_real one_one_real) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N))) of role axiom named fact_642_two__realpow__ge__one % 1.25/1.41 A new axiom: (forall (N:nat), ((ord_less_eq_real one_one_real) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N))) % 1.25/1.41 FOF formula (forall (P_1:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_1))->((iff ((and ((ord_less_eq_int zero_zero_int) X)) P)) ((and ((ord_less_eq_int zero_zero_int) X)) P_1)))) of role axiom named fact_643_conj__le__cong % 1.25/1.41 A new axiom: (forall (P_1:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_1))->((iff ((and ((ord_less_eq_int zero_zero_int) X)) P)) ((and ((ord_less_eq_int zero_zero_int) X)) P_1)))) % 1.25/1.41 FOF formula (forall (P_1:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_1))->((iff (((ord_less_eq_int zero_zero_int) X)->P)) (((ord_less_eq_int zero_zero_int) X)->P_1)))) of role axiom named fact_644_imp__le__cong % 1.25/1.41 A new axiom: (forall (P_1:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_1))->((iff (((ord_less_eq_int zero_zero_int) X)->P)) (((ord_less_eq_int zero_zero_int) X)->P_1)))) % 1.25/1.41 FOF formula (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N)) (forall (I_1:nat), (((ord_less_eq_nat I_1) K_1)->((P I_1)->False))))) (P ((plus_plus_nat K_1) one_one_nat)))))))) of role axiom named fact_645_ex__least__nat__less % 1.25/1.41 A new axiom: (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N)) (forall (I_1:nat), (((ord_less_eq_nat I_1) K_1)->((P I_1)->False))))) (P ((plus_plus_nat K_1) one_one_nat)))))))) % 1.25/1.41 FOF formula (forall (Z_2:int), (((ord_less_eq_int zero_zero_int) Z_2)->((forall (M_1:nat), (not (((eq int) Z_2) (semiri1621563631at_int M_1))))->False))) of role axiom named fact_646_nonneg__eq__int % 1.25/1.41 A new axiom: (forall (Z_2:int), (((ord_less_eq_int zero_zero_int) Z_2)->((forall (M_1:nat), (not (((eq int) Z_2) (semiri1621563631at_int M_1))))->False))) % 1.25/1.41 FOF formula (forall (M:nat) (K:nat) (F:(nat->nat)), ((forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_nat (F M_1)) (F N_1))))->((ord_less_eq_nat ((plus_plus_nat (F M)) K)) (F ((plus_plus_nat M) K))))) of role axiom named fact_647_mono__nat__linear__lb % 1.25/1.41 A new axiom: (forall (M:nat) (K:nat) (F:(nat->nat)), ((forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_nat (F M_1)) (F N_1))))->((ord_less_eq_nat ((plus_plus_nat (F M)) K)) (F ((plus_plus_nat M) K))))) % 1.25/1.41 FOF formula (forall (W:real), ((ord_less_eq_real W) W)) of role axiom named fact_648_real__le__refl % 1.25/1.41 A new axiom: (forall (W:real), ((ord_less_eq_real W) W)) % 1.25/1.41 FOF formula (forall (Z_2:real) (W:real), ((or ((ord_less_eq_real Z_2) W)) ((ord_less_eq_real W) Z_2))) of role axiom named fact_649_real__le__linear % 1.25/1.41 A new axiom: (forall (Z_2:real) (W:real), ((or ((ord_less_eq_real Z_2) W)) ((ord_less_eq_real W) Z_2))) % 1.25/1.41 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_650_real__le__trans % 1.25/1.41 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)))) % 1.25/1.41 FOF formula (forall (Z_2:real) (W:real), (((ord_less_eq_real Z_2) W)->(((ord_less_eq_real W) Z_2)->(((eq real) Z_2) W)))) of role axiom named fact_651_real__le__antisym % 1.25/1.41 A new axiom: (forall (Z_2:real) (W:real), (((ord_less_eq_real Z_2) W)->(((ord_less_eq_real W) Z_2)->(((eq real) Z_2) W)))) % 1.25/1.41 FOF formula (forall (P:(int->Prop)) (K:int) (_TPTP_I:int), (((ord_less_eq_int K) _TPTP_I)->((P K)->((forall (I_1:int), (((ord_less_eq_int K) I_1)->((P I_1)->(P ((plus_plus_int I_1) one_one_int)))))->(P _TPTP_I))))) of role axiom named fact_652_int__ge__induct % 1.27/1.43 A new axiom: (forall (P:(int->Prop)) (K:int) (_TPTP_I:int), (((ord_less_eq_int K) _TPTP_I)->((P K)->((forall (I_1:int), (((ord_less_eq_int K) I_1)->((P I_1)->(P ((plus_plus_int I_1) one_one_int)))))->(P _TPTP_I))))) % 1.27/1.43 FOF formula (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_eq_nat K_1) N)) (forall (I_1:nat), (((ord_less_nat I_1) K_1)->((P I_1)->False))))) (P K_1))))))) of role axiom named fact_653_ex__least__nat__le % 1.27/1.43 A new axiom: (forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_eq_nat K_1) N)) (forall (I_1:nat), (((ord_less_nat I_1) K_1)->((P I_1)->False))))) (P K_1))))))) % 1.27/1.43 FOF formula (forall (_TPTP_I:nat) (J:nat) (F:(nat->nat)), ((forall (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat (F I_1)) (F J_1))))->(((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat (F _TPTP_I)) (F J))))) of role axiom named fact_654_less__mono__imp__le__mono % 1.27/1.43 A new axiom: (forall (_TPTP_I:nat) (J:nat) (F:(nat->nat)), ((forall (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat (F I_1)) (F J_1))))->(((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat (F _TPTP_I)) (F J))))) % 1.27/1.43 FOF formula (forall (X_8:real), ((ord_less_eq_real X_8) X_8)) of role axiom named fact_655_order__refl % 1.27/1.43 A new axiom: (forall (X_8:real), ((ord_less_eq_real X_8) X_8)) % 1.27/1.43 FOF formula (forall (X_8:nat), ((ord_less_eq_nat X_8) X_8)) of role axiom named fact_656_order__refl % 1.27/1.43 A new axiom: (forall (X_8:nat), ((ord_less_eq_nat X_8) X_8)) % 1.27/1.43 FOF formula (forall (X_8:int), ((ord_less_eq_int X_8) X_8)) of role axiom named fact_657_order__refl % 1.27/1.43 A new axiom: (forall (X_8:int), ((ord_less_eq_int X_8) X_8)) % 1.27/1.43 FOF formula (forall (X_7:real) (Y_7:real), ((((ord_less_eq_real X_7) Y_7)->False)->((ord_less_eq_real Y_7) X_7))) of role axiom named fact_658_linorder__le__cases % 1.27/1.43 A new axiom: (forall (X_7:real) (Y_7:real), ((((ord_less_eq_real X_7) Y_7)->False)->((ord_less_eq_real Y_7) X_7))) % 1.27/1.43 FOF formula (forall (X_7:nat) (Y_7:nat), ((((ord_less_eq_nat X_7) Y_7)->False)->((ord_less_eq_nat Y_7) X_7))) of role axiom named fact_659_linorder__le__cases % 1.27/1.43 A new axiom: (forall (X_7:nat) (Y_7:nat), ((((ord_less_eq_nat X_7) Y_7)->False)->((ord_less_eq_nat Y_7) X_7))) % 1.27/1.43 FOF formula (forall (X_7:int) (Y_7:int), ((((ord_less_eq_int X_7) Y_7)->False)->((ord_less_eq_int Y_7) X_7))) of role axiom named fact_660_linorder__le__cases % 1.27/1.43 A new axiom: (forall (X_7:int) (Y_7:int), ((((ord_less_eq_int X_7) Y_7)->False)->((ord_less_eq_int Y_7) X_7))) % 1.27/1.43 FOF formula (forall (Z_1:real) (Y_6:real) (X_6:real), (((ord_less_eq_real Y_6) X_6)->(((ord_less_eq_real Z_1) Y_6)->((ord_less_eq_real Z_1) X_6)))) of role axiom named fact_661_xt1_I6_J % 1.27/1.43 A new axiom: (forall (Z_1:real) (Y_6:real) (X_6:real), (((ord_less_eq_real Y_6) X_6)->(((ord_less_eq_real Z_1) Y_6)->((ord_less_eq_real Z_1) X_6)))) % 1.27/1.43 FOF formula (forall (Z_1:nat) (Y_6:nat) (X_6:nat), (((ord_less_eq_nat Y_6) X_6)->(((ord_less_eq_nat Z_1) Y_6)->((ord_less_eq_nat Z_1) X_6)))) of role axiom named fact_662_xt1_I6_J % 1.27/1.43 A new axiom: (forall (Z_1:nat) (Y_6:nat) (X_6:nat), (((ord_less_eq_nat Y_6) X_6)->(((ord_less_eq_nat Z_1) Y_6)->((ord_less_eq_nat Z_1) X_6)))) % 1.27/1.43 FOF formula (forall (Z_1:int) (Y_6:int) (X_6:int), (((ord_less_eq_int Y_6) X_6)->(((ord_less_eq_int Z_1) Y_6)->((ord_less_eq_int Z_1) X_6)))) of role axiom named fact_663_xt1_I6_J % 1.27/1.43 A new axiom: (forall (Z_1:int) (Y_6:int) (X_6:int), (((ord_less_eq_int Y_6) X_6)->(((ord_less_eq_int Z_1) Y_6)->((ord_less_eq_int Z_1) X_6)))) % 1.27/1.43 FOF formula (forall (Y_5:real) (X_5:real), (((ord_less_eq_real Y_5) X_5)->(((ord_less_eq_real X_5) Y_5)->(((eq real) X_5) Y_5)))) of role axiom named fact_664_xt1_I5_J % 1.27/1.43 A new axiom: (forall (Y_5:real) (X_5:real), (((ord_less_eq_real Y_5) X_5)->(((ord_less_eq_real X_5) Y_5)->(((eq real) X_5) Y_5)))) % 1.27/1.43 FOF formula (forall (Y_5:nat) (X_5:nat), (((ord_less_eq_nat Y_5) X_5)->(((ord_less_eq_nat X_5) Y_5)->(((eq nat) X_5) Y_5)))) of role axiom named fact_665_xt1_I5_J % 1.27/1.43 A new axiom: (forall (Y_5:nat) (X_5:nat), (((ord_less_eq_nat Y_5) X_5)->(((ord_less_eq_nat X_5) Y_5)->(((eq nat) X_5) Y_5)))) % 1.27/1.46 FOF formula (forall (Y_5:int) (X_5:int), (((ord_less_eq_int Y_5) X_5)->(((ord_less_eq_int X_5) Y_5)->(((eq int) X_5) Y_5)))) of role axiom named fact_666_xt1_I5_J % 1.27/1.46 A new axiom: (forall (Y_5:int) (X_5:int), (((ord_less_eq_int Y_5) X_5)->(((ord_less_eq_int X_5) Y_5)->(((eq int) X_5) Y_5)))) % 1.27/1.46 FOF formula (forall (Z:real) (X_4:real) (Y_4:real), (((ord_less_eq_real X_4) Y_4)->(((ord_less_eq_real Y_4) Z)->((ord_less_eq_real X_4) Z)))) of role axiom named fact_667_order__trans % 1.27/1.46 A new axiom: (forall (Z:real) (X_4:real) (Y_4:real), (((ord_less_eq_real X_4) Y_4)->(((ord_less_eq_real Y_4) Z)->((ord_less_eq_real X_4) Z)))) % 1.27/1.46 FOF formula (forall (Z:nat) (X_4:nat) (Y_4:nat), (((ord_less_eq_nat X_4) Y_4)->(((ord_less_eq_nat Y_4) Z)->((ord_less_eq_nat X_4) Z)))) of role axiom named fact_668_order__trans % 1.27/1.46 A new axiom: (forall (Z:nat) (X_4:nat) (Y_4:nat), (((ord_less_eq_nat X_4) Y_4)->(((ord_less_eq_nat Y_4) Z)->((ord_less_eq_nat X_4) Z)))) % 1.27/1.46 FOF formula (forall (Z:int) (X_4:int) (Y_4:int), (((ord_less_eq_int X_4) Y_4)->(((ord_less_eq_int Y_4) Z)->((ord_less_eq_int X_4) Z)))) of role axiom named fact_669_order__trans % 1.27/1.46 A new axiom: (forall (Z:int) (X_4:int) (Y_4:int), (((ord_less_eq_int X_4) Y_4)->(((ord_less_eq_int Y_4) Z)->((ord_less_eq_int X_4) Z)))) % 1.27/1.46 FOF formula (forall (X_3:real) (Y_3:real), (((ord_less_eq_real X_3) Y_3)->(((ord_less_eq_real Y_3) X_3)->(((eq real) X_3) Y_3)))) of role axiom named fact_670_order__antisym % 1.27/1.46 A new axiom: (forall (X_3:real) (Y_3:real), (((ord_less_eq_real X_3) Y_3)->(((ord_less_eq_real Y_3) X_3)->(((eq real) X_3) Y_3)))) % 1.27/1.46 FOF formula (forall (X_3:nat) (Y_3:nat), (((ord_less_eq_nat X_3) Y_3)->(((ord_less_eq_nat Y_3) X_3)->(((eq nat) X_3) Y_3)))) of role axiom named fact_671_order__antisym % 1.27/1.46 A new axiom: (forall (X_3:nat) (Y_3:nat), (((ord_less_eq_nat X_3) Y_3)->(((ord_less_eq_nat Y_3) X_3)->(((eq nat) X_3) Y_3)))) % 1.27/1.46 FOF formula (forall (X_3:int) (Y_3:int), (((ord_less_eq_int X_3) Y_3)->(((ord_less_eq_int Y_3) X_3)->(((eq int) X_3) Y_3)))) of role axiom named fact_672_order__antisym % 1.27/1.46 A new axiom: (forall (X_3:int) (Y_3:int), (((ord_less_eq_int X_3) Y_3)->(((ord_less_eq_int Y_3) X_3)->(((eq int) X_3) Y_3)))) % 1.27/1.46 FOF formula (forall (C_3:real) (B_4:real) (A_4:real), (((ord_less_eq_real B_4) A_4)->((((eq real) B_4) C_3)->((ord_less_eq_real C_3) A_4)))) of role axiom named fact_673_xt1_I4_J % 1.27/1.46 A new axiom: (forall (C_3:real) (B_4:real) (A_4:real), (((ord_less_eq_real B_4) A_4)->((((eq real) B_4) C_3)->((ord_less_eq_real C_3) A_4)))) % 1.27/1.46 FOF formula (forall (C_3:nat) (B_4:nat) (A_4:nat), (((ord_less_eq_nat B_4) A_4)->((((eq nat) B_4) C_3)->((ord_less_eq_nat C_3) A_4)))) of role axiom named fact_674_xt1_I4_J % 1.27/1.46 A new axiom: (forall (C_3:nat) (B_4:nat) (A_4:nat), (((ord_less_eq_nat B_4) A_4)->((((eq nat) B_4) C_3)->((ord_less_eq_nat C_3) A_4)))) % 1.27/1.46 FOF formula (forall (C_3:int) (B_4:int) (A_4:int), (((ord_less_eq_int B_4) A_4)->((((eq int) B_4) C_3)->((ord_less_eq_int C_3) A_4)))) of role axiom named fact_675_xt1_I4_J % 1.27/1.46 A new axiom: (forall (C_3:int) (B_4:int) (A_4:int), (((ord_less_eq_int B_4) A_4)->((((eq int) B_4) C_3)->((ord_less_eq_int C_3) A_4)))) % 1.27/1.46 FOF formula (forall (C_2:real) (A_3:real) (B_3:real), (((ord_less_eq_real A_3) B_3)->((((eq real) B_3) C_2)->((ord_less_eq_real A_3) C_2)))) of role axiom named fact_676_ord__le__eq__trans % 1.27/1.46 A new axiom: (forall (C_2:real) (A_3:real) (B_3:real), (((ord_less_eq_real A_3) B_3)->((((eq real) B_3) C_2)->((ord_less_eq_real A_3) C_2)))) % 1.27/1.46 FOF formula (forall (C_2:nat) (A_3:nat) (B_3:nat), (((ord_less_eq_nat A_3) B_3)->((((eq nat) B_3) C_2)->((ord_less_eq_nat A_3) C_2)))) of role axiom named fact_677_ord__le__eq__trans % 1.27/1.46 A new axiom: (forall (C_2:nat) (A_3:nat) (B_3:nat), (((ord_less_eq_nat A_3) B_3)->((((eq nat) B_3) C_2)->((ord_less_eq_nat A_3) C_2)))) % 1.27/1.46 FOF formula (forall (C_2:int) (A_3:int) (B_3:int), (((ord_less_eq_int A_3) B_3)->((((eq int) B_3) C_2)->((ord_less_eq_int A_3) C_2)))) of role axiom named fact_678_ord__le__eq__trans % 1.27/1.46 A new axiom: (forall (C_2:int) (A_3:int) (B_3:int), (((ord_less_eq_int A_3) B_3)->((((eq int) B_3) C_2)->((ord_less_eq_int A_3) C_2)))) % 1.27/1.46 FOF formula (forall (C_1:real) (A_2:real) (B_2:real), ((((eq real) A_2) B_2)->(((ord_less_eq_real C_1) B_2)->((ord_less_eq_real C_1) A_2)))) of role axiom named fact_679_xt1_I3_J % 1.27/1.48 A new axiom: (forall (C_1:real) (A_2:real) (B_2:real), ((((eq real) A_2) B_2)->(((ord_less_eq_real C_1) B_2)->((ord_less_eq_real C_1) A_2)))) % 1.27/1.48 FOF formula (forall (C_1:nat) (A_2:nat) (B_2:nat), ((((eq nat) A_2) B_2)->(((ord_less_eq_nat C_1) B_2)->((ord_less_eq_nat C_1) A_2)))) of role axiom named fact_680_xt1_I3_J % 1.27/1.48 A new axiom: (forall (C_1:nat) (A_2:nat) (B_2:nat), ((((eq nat) A_2) B_2)->(((ord_less_eq_nat C_1) B_2)->((ord_less_eq_nat C_1) A_2)))) % 1.27/1.48 FOF formula (forall (C_1:int) (A_2:int) (B_2:int), ((((eq int) A_2) B_2)->(((ord_less_eq_int C_1) B_2)->((ord_less_eq_int C_1) A_2)))) of role axiom named fact_681_xt1_I3_J % 1.27/1.48 A new axiom: (forall (C_1:int) (A_2:int) (B_2:int), ((((eq int) A_2) B_2)->(((ord_less_eq_int C_1) B_2)->((ord_less_eq_int C_1) A_2)))) % 1.27/1.48 FOF formula (forall (C:real) (A_1:real) (B_1:real), ((((eq real) A_1) B_1)->(((ord_less_eq_real B_1) C)->((ord_less_eq_real A_1) C)))) of role axiom named fact_682_ord__eq__le__trans % 1.27/1.48 A new axiom: (forall (C:real) (A_1:real) (B_1:real), ((((eq real) A_1) B_1)->(((ord_less_eq_real B_1) C)->((ord_less_eq_real A_1) C)))) % 1.27/1.48 FOF formula (forall (C:nat) (A_1:nat) (B_1:nat), ((((eq nat) A_1) B_1)->(((ord_less_eq_nat B_1) C)->((ord_less_eq_nat A_1) C)))) of role axiom named fact_683_ord__eq__le__trans % 1.27/1.48 A new axiom: (forall (C:nat) (A_1:nat) (B_1:nat), ((((eq nat) A_1) B_1)->(((ord_less_eq_nat B_1) C)->((ord_less_eq_nat A_1) C)))) % 1.27/1.48 FOF formula (forall (C:int) (A_1:int) (B_1:int), ((((eq int) A_1) B_1)->(((ord_less_eq_int B_1) C)->((ord_less_eq_int A_1) C)))) of role axiom named fact_684_ord__eq__le__trans % 1.27/1.48 A new axiom: (forall (C:int) (A_1:int) (B_1:int), ((((eq int) A_1) B_1)->(((ord_less_eq_int B_1) C)->((ord_less_eq_int A_1) C)))) % 1.27/1.48 FOF formula (forall (Y_2:real) (X_2:real), (((ord_less_eq_real Y_2) X_2)->((iff ((ord_less_eq_real X_2) Y_2)) (((eq real) X_2) Y_2)))) of role axiom named fact_685_order__antisym__conv % 1.27/1.48 A new axiom: (forall (Y_2:real) (X_2:real), (((ord_less_eq_real Y_2) X_2)->((iff ((ord_less_eq_real X_2) Y_2)) (((eq real) X_2) Y_2)))) % 1.27/1.48 FOF formula (forall (Y_2:nat) (X_2:nat), (((ord_less_eq_nat Y_2) X_2)->((iff ((ord_less_eq_nat X_2) Y_2)) (((eq nat) X_2) Y_2)))) of role axiom named fact_686_order__antisym__conv % 1.27/1.48 A new axiom: (forall (Y_2:nat) (X_2:nat), (((ord_less_eq_nat Y_2) X_2)->((iff ((ord_less_eq_nat X_2) Y_2)) (((eq nat) X_2) Y_2)))) % 1.27/1.48 FOF formula (forall (Y_2:int) (X_2:int), (((ord_less_eq_int Y_2) X_2)->((iff ((ord_less_eq_int X_2) Y_2)) (((eq int) X_2) Y_2)))) of role axiom named fact_687_order__antisym__conv % 1.27/1.48 A new axiom: (forall (Y_2:int) (X_2:int), (((ord_less_eq_int Y_2) X_2)->((iff ((ord_less_eq_int X_2) Y_2)) (((eq int) X_2) Y_2)))) % 1.27/1.48 FOF formula (forall (X_1:int) (Y_1:int), ((((eq int) X_1) Y_1)->((ord_less_eq_int X_1) Y_1))) of role axiom named fact_688_order__eq__refl % 1.27/1.48 A new axiom: (forall (X_1:int) (Y_1:int), ((((eq int) X_1) Y_1)->((ord_less_eq_int X_1) Y_1))) % 1.27/1.48 FOF formula (forall (D2:real) (D1:real), (((ord_less_real zero_zero_real) D1)->(((ord_less_real zero_zero_real) D2)->((ex real) (fun (E:real)=> ((and ((and ((ord_less_real zero_zero_real) E)) ((ord_less_real E) D1))) ((ord_less_real E) D2))))))) of role axiom named fact_689_real__lbound__gt__zero % 1.27/1.48 A new axiom: (forall (D2:real) (D1:real), (((ord_less_real zero_zero_real) D1)->(((ord_less_real zero_zero_real) D2)->((ex real) (fun (E:real)=> ((and ((and ((ord_less_real zero_zero_real) E)) ((ord_less_real E) D1))) ((ord_less_real E) D2))))))) % 1.27/1.48 FOF formula (forall (X:real) (Y:real), ((ord_less_eq_real zero_zero_real) (sqrt ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))))) of role axiom named fact_690_real__sqrt__sum__squares__ge__zero % 1.27/1.48 A new axiom: (forall (X:real) (Y:real), ((ord_less_eq_real zero_zero_real) (sqrt ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))))) % 1.27/1.48 FOF formula (forall (A:int) (B:int), (((eq int) ((power_power_int ((plus_plus_int A) B)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A)) B))) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_691_zadd__power2 % 1.27/1.50 A new axiom: (forall (A:int) (B:int), (((eq int) ((power_power_int ((plus_plus_int A) B)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int A) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A)) B))) ((power_power_int B) (number_number_of_nat (bit0 (bit1 pls))))))) % 1.27/1.50 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_692_mult__Bit1 % 1.27/1.50 A new axiom: (forall (K:int) (L:int), (((eq int) ((times_times_int (bit1 K)) L)) ((plus_plus_int (bit0 ((times_times_int K) L))) L))) % 1.27/1.50 FOF formula (forall (X:real), (((ord_less_real zero_zero_real) X)->((ord_less_real zero_zero_real) (sqrt X)))) of role axiom named fact_693_real__sqrt__gt__zero % 1.27/1.50 A new axiom: (forall (X:real), (((ord_less_real zero_zero_real) X)->((ord_less_real zero_zero_real) (sqrt X)))) % 1.27/1.50 FOF formula (forall (X:real), (((ord_less_real zero_zero_real) X)->(not (((eq real) (sqrt X)) zero_zero_real)))) of role axiom named fact_694_real__sqrt__not__eq__zero % 1.27/1.50 A new axiom: (forall (X:real), (((ord_less_real zero_zero_real) X)->(not (((eq real) (sqrt X)) zero_zero_real)))) % 1.27/1.50 FOF formula (forall (X:real), ((iff ((ord_less_real (sqrt X)) zero_zero_real)) ((ord_less_real X) zero_zero_real))) of role axiom named fact_695_real__sqrt__lt__0__iff % 1.27/1.50 A new axiom: (forall (X:real), ((iff ((ord_less_real (sqrt X)) zero_zero_real)) ((ord_less_real X) zero_zero_real))) % 1.27/1.50 FOF formula (forall (Y:real), ((iff ((ord_less_real zero_zero_real) (sqrt Y))) ((ord_less_real zero_zero_real) Y))) of role axiom named fact_696_real__sqrt__gt__0__iff % 1.27/1.50 A new axiom: (forall (Y:real), ((iff ((ord_less_real zero_zero_real) (sqrt Y))) ((ord_less_real zero_zero_real) Y))) % 1.27/1.50 FOF formula (forall (X:real), ((iff ((ord_less_real (sqrt X)) one_one_real)) ((ord_less_real X) one_one_real))) of role axiom named fact_697_real__sqrt__lt__1__iff % 1.27/1.50 A new axiom: (forall (X:real), ((iff ((ord_less_real (sqrt X)) one_one_real)) ((ord_less_real X) one_one_real))) % 1.27/1.50 FOF formula (forall (Y:real), ((iff ((ord_less_real one_one_real) (sqrt Y))) ((ord_less_real one_one_real) Y))) of role axiom named fact_698_real__sqrt__gt__1__iff % 1.27/1.50 A new axiom: (forall (Y:real), ((iff ((ord_less_real one_one_real) (sqrt Y))) ((ord_less_real one_one_real) Y))) % 1.27/1.50 FOF formula (forall (X:nat) (Y:nat), (((eq nat) (((if_nat True) X) Y)) X)) of role axiom named help_If_1_1_If_000tc__Nat__Onat_T % 1.27/1.50 A new axiom: (forall (X:nat) (Y:nat), (((eq nat) (((if_nat True) X) Y)) X)) % 1.27/1.50 FOF formula (forall (X:nat) (Y:nat), (((eq nat) (((if_nat False) X) Y)) Y)) of role axiom named help_If_2_1_If_000tc__Nat__Onat_T % 1.27/1.50 A new axiom: (forall (X:nat) (Y:nat), (((eq nat) (((if_nat False) X) Y)) Y)) % 1.27/1.50 FOF formula (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))) of role axiom named help_If_3_1_If_000tc__Nat__Onat_T % 1.27/1.50 A new axiom: (forall (P:Prop), ((or (((eq Prop) P) True)) (((eq Prop) P) False))) % 1.27/1.50 FOF formula (not (((eq int) ((power_power_int ((plus_plus_int one_one_int) (semiri1621563631at_int n))) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)) of role conjecture named conj_0 % 1.27/1.50 Conjecture to prove = (not (((eq int) ((power_power_int ((plus_plus_int one_one_int) (semiri1621563631at_int n))) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)):Prop % 1.27/1.50 We need to prove ['(not (((eq int) ((power_power_int ((plus_plus_int one_one_int) (semiri1621563631at_int n))) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int))'] % 1.27/1.50 Parameter int:Type. % 1.27/1.50 Parameter nat:Type. % 1.27/1.50 Parameter real:Type. % 1.27/1.50 Parameter one_one_int:int. % 1.27/1.50 Parameter one_one_nat:nat. % 1.27/1.50 Parameter one_one_real:real. % 1.27/1.50 Parameter plus_plus_int:(int->(int->int)). % 1.27/1.50 Parameter plus_plus_nat:(nat->(nat->nat)). % 1.27/1.50 Parameter plus_plus_real:(real->(real->real)). % 1.27/1.50 Parameter times_times_int:(int->(int->int)). % 1.27/1.50 Parameter zero_zero_int:int. % 1.27/1.50 Parameter zero_zero_nat:nat. % 1.27/1.50 Parameter zero_zero_real:real. % 1.27/1.50 Parameter if_nat:(Prop->(nat->(nat->nat))). % 1.27/1.50 Parameter bit0:(int->int). % 1.27/1.50 Parameter bit1:(int->int). % 1.27/1.50 Parameter pls:int. % 1.27/1.50 Parameter number_number_of_int:(int->int). % 1.27/1.50 Parameter number_number_of_nat:(int->nat). % 1.27/1.50 Parameter number267125858f_real:(int->real). % 1.27/1.50 Parameter succ:(int->int). % 1.27/1.50 Parameter semiri1621563631at_int:(nat->int). % 1.27/1.50 Parameter semiri984289939at_nat:(nat->nat). % 1.27/1.50 Parameter semiri132038758t_real:(nat->real). % 1.27/1.50 Parameter sqrt:(real->real). % 1.27/1.50 Parameter ord_less_int:(int->(int->Prop)). % 1.27/1.50 Parameter ord_less_nat:(nat->(nat->Prop)). % 1.27/1.50 Parameter ord_less_real:(real->(real->Prop)). % 1.27/1.50 Parameter ord_less_eq_int:(int->(int->Prop)). % 1.27/1.50 Parameter ord_less_eq_nat:(nat->(nat->Prop)). % 1.27/1.50 Parameter ord_less_eq_real:(real->(real->Prop)). % 1.27/1.50 Parameter power_power_int:(int->(nat->int)). % 1.27/1.50 Parameter power_power_nat:(nat->(nat->nat)). % 1.27/1.50 Parameter power_power_real:(real->(nat->real)). % 1.27/1.50 Parameter m1:int. % 1.27/1.50 Parameter n:nat. % 1.27/1.50 Parameter t:int. % 1.27/1.50 Parameter tn:nat. % 1.27/1.50 Axiom fact_0_n1pos:((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) (semiri1621563631at_int n))). % 1.27/1.50 Axiom fact_1_t1:((ord_less_int one_one_int) t). % 1.27/1.50 Axiom fact_2_sum__power2__eq__zero__iff:(forall (X:int) (Y:int), ((iff (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X) zero_zero_int)) (((eq int) Y) zero_zero_int)))). % 1.27/1.50 Axiom fact_3_sum__power2__eq__zero__iff:(forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real)))). % 1.27/1.50 Axiom fact_4_one__power2:(((eq int) ((power_power_int one_one_int) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int). % 1.27/1.50 Axiom fact_5_one__power2:(((eq nat) ((power_power_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls))))) one_one_nat). % 1.27/1.50 Axiom fact_6_one__power2:(((eq real) ((power_power_real one_one_real) (number_number_of_nat (bit0 (bit1 pls))))) one_one_real). % 1.27/1.50 Axiom fact_7_zero__power2:(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int). % 1.27/1.50 Axiom fact_8_zero__power2:(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_nat). % 1.27/1.50 Axiom fact_9_zero__power2:(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real). % 1.27/1.50 Axiom fact_10_zero__eq__power2:(forall (A_86:int), ((iff (((eq int) ((power_power_int A_86) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)) (((eq int) A_86) zero_zero_int))). % 1.27/1.50 Axiom fact_11_zero__eq__power2:(forall (A_86:real), ((iff (((eq real) ((power_power_real A_86) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)) (((eq real) A_86) zero_zero_real))). % 1.27/1.50 Axiom fact_12_add__special_I2_J:(forall (W_11:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_11))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_11)))). % 1.27/1.50 Axiom fact_13_add__special_I2_J:(forall (W_11:int), (((eq real) ((plus_plus_real one_one_real) (number267125858f_real W_11))) (number267125858f_real ((plus_plus_int (bit1 pls)) W_11)))). % 1.27/1.50 Axiom fact_14_add__special_I3_J:(forall (V_11:int), (((eq int) ((plus_plus_int (number_number_of_int V_11)) one_one_int)) (number_number_of_int ((plus_plus_int V_11) (bit1 pls))))). % 1.27/1.50 Axiom fact_15_add__special_I3_J:(forall (V_11:int), (((eq real) ((plus_plus_real (number267125858f_real V_11)) one_one_real)) (number267125858f_real ((plus_plus_int V_11) (bit1 pls))))). % 1.27/1.50 Axiom fact_16_one__add__one__is__two:(((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))). % 1.27/1.50 Axiom fact_17_one__add__one__is__two:(((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))). % 1.27/1.50 Axiom fact_18_semiring__one__add__one__is__two:(((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))). % 1.27/1.50 Axiom fact_19_semiring__one__add__one__is__two:(((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))). % 1.27/1.50 Axiom fact_20_semiring__one__add__one__is__two:(((eq real) ((plus_plus_real one_one_real) one_one_real)) (number267125858f_real (bit0 (bit1 pls)))). % 1.27/1.50 Axiom fact_21_quartic__square__square:(forall (X:int), (((eq int) ((power_power_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int X) (number_number_of_nat (bit0 (bit0 (bit1 pls))))))). % 1.27/1.50 Axiom fact_22_power__0__left__number__of:(forall (W_10:int), ((and ((((eq nat) (number_number_of_nat W_10)) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_10))) one_one_int))) ((not (((eq nat) (number_number_of_nat W_10)) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) (number_number_of_nat W_10))) zero_zero_int)))). % 1.27/1.50 Axiom fact_23_power__0__left__number__of:(forall (W_10:int), ((and ((((eq nat) (number_number_of_nat W_10)) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_10))) one_one_nat))) ((not (((eq nat) (number_number_of_nat W_10)) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) (number_number_of_nat W_10))) zero_zero_nat)))). % 1.27/1.50 Axiom fact_24_power__0__left__number__of:(forall (W_10:int), ((and ((((eq nat) (number_number_of_nat W_10)) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_10))) one_one_real))) ((not (((eq nat) (number_number_of_nat W_10)) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) (number_number_of_nat W_10))) zero_zero_real)))). % 1.27/1.50 Axiom fact_25_semiring__norm_I110_J:(((eq int) one_one_int) (number_number_of_int (bit1 pls))). % 1.27/1.50 Axiom fact_26_semiring__norm_I110_J:(((eq real) one_one_real) (number267125858f_real (bit1 pls))). % 1.27/1.50 Axiom fact_27_numeral__1__eq__1:(((eq int) (number_number_of_int (bit1 pls))) one_one_int). % 1.27/1.50 Axiom fact_28_numeral__1__eq__1:(((eq real) (number267125858f_real (bit1 pls))) one_one_real). % 1.27/1.50 Axiom fact_29_n0:((ord_less_nat zero_zero_nat) n). % 1.27/1.50 Axiom fact_30_zless__linear:(forall (X:int) (Y:int), ((or ((or ((ord_less_int X) Y)) (((eq int) X) Y))) ((ord_less_int Y) X))). % 1.27/1.50 Axiom fact_31_less__number__of__int__code:(forall (K:int) (L:int), ((iff ((ord_less_int (number_number_of_int K)) (number_number_of_int L))) ((ord_less_int K) L))). % 1.27/1.50 Axiom fact_32_plus__numeral__code_I9_J:(forall (V_1:int) (W:int), (((eq int) ((plus_plus_int (number_number_of_int V_1)) (number_number_of_int W))) (number_number_of_int ((plus_plus_int V_1) W)))). % 1.27/1.50 Axiom fact_33_less__number__of:(forall (X_32:int) (Y_26:int), ((iff ((ord_less_int (number_number_of_int X_32)) (number_number_of_int Y_26))) ((ord_less_int X_32) Y_26))). % 1.27/1.50 Axiom fact_34_less__number__of:(forall (X_32:int) (Y_26:int), ((iff ((ord_less_real (number267125858f_real X_32)) (number267125858f_real Y_26))) ((ord_less_int X_32) Y_26))). % 1.27/1.50 Axiom fact_35_zero__is__num__zero:(((eq int) zero_zero_int) (number_number_of_int pls)). % 1.27/1.50 Axiom fact_36_zpower__int:(forall (M:nat) (N:nat), (((eq int) ((power_power_int (semiri1621563631at_int M)) N)) (semiri1621563631at_int ((power_power_nat M) N)))). % 1.27/1.50 Axiom fact_37_int__power:(forall (M:nat) (N:nat), (((eq int) (semiri1621563631at_int ((power_power_nat M) N))) ((power_power_int (semiri1621563631at_int M)) N))). % 1.27/1.50 Axiom fact_38_zadd__int__left:(forall (M:nat) (N:nat) (Z_2:int), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) ((plus_plus_int (semiri1621563631at_int N)) Z_2))) ((plus_plus_int (semiri1621563631at_int ((plus_plus_nat M) N))) Z_2))). % 1.27/1.50 Axiom fact_39_zadd__int:(forall (M:nat) (N:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) (semiri1621563631at_int ((plus_plus_nat M) N)))). % 1.27/1.50 Axiom fact_40_int__1:(((eq int) (semiri1621563631at_int one_one_nat)) one_one_int). % 1.27/1.50 Axiom fact_41_nat__number__of__Pls:(((eq nat) (number_number_of_nat pls)) zero_zero_nat). % 1.27/1.50 Axiom fact_42_semiring__norm_I113_J:(((eq nat) zero_zero_nat) (number_number_of_nat pls)). % 1.27/1.50 Axiom fact_43_int__eq__0__conv:(forall (N:nat), ((iff (((eq int) (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat))). % 1.27/1.50 Axiom fact_44_int__0:(((eq int) (semiri1621563631at_int zero_zero_nat)) zero_zero_int). % 1.27/1.50 Axiom fact_45_nat__1__add__1:(((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))). % 1.27/1.50 Axiom fact_46_less__int__code_I16_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2))). % 1.27/1.50 Axiom fact_47_rel__simps_I17_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L))). % 1.27/1.50 Axiom fact_48_rel__simps_I2_J:(((ord_less_int pls) pls)->False). % 1.27/1.50 Axiom fact_49_less__int__code_I13_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit0 K2))) ((ord_less_int K1) K2))). % 1.27/1.50 Axiom fact_50_rel__simps_I14_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit0 L))) ((ord_less_int K) L))). % 1.27/1.50 Axiom fact_51_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)))). % 1.27/1.50 Axiom fact_52_add__nat__number__of:(forall (V: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))) (number_number_of_nat V)))) ((((ord_less_int V_1) pls)->False)->((and (((ord_less_int V) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) (number_number_of_nat V))) (number_number_of_nat V_1)))) ((((ord_less_int V) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) (number_number_of_nat V))) (number_number_of_nat ((plus_plus_int V_1) V)))))))). % 1.27/1.50 Axiom fact_53_one__is__num__one:(((eq int) one_one_int) (number_number_of_int (bit1 pls))). % 1.27/1.50 Axiom fact_54_nat__numeral__1__eq__1:(((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat). % 1.27/1.50 Axiom fact_55_Numeral1__eq1__nat:(((eq nat) one_one_nat) (number_number_of_nat (bit1 pls))). % 1.27/1.50 Axiom fact_56_eq__number__of:(forall (X_31:int) (Y_25:int), ((iff (((eq int) (number_number_of_int X_31)) (number_number_of_int Y_25))) (((eq int) X_31) Y_25))). % 1.27/1.50 Axiom fact_57_eq__number__of:(forall (X_31:int) (Y_25:int), ((iff (((eq real) (number267125858f_real X_31)) (number267125858f_real Y_25))) (((eq int) X_31) Y_25))). % 1.27/1.50 Axiom fact_58_number__of__reorient:(forall (W_9:int) (X_30:nat), ((iff (((eq nat) (number_number_of_nat W_9)) X_30)) (((eq nat) X_30) (number_number_of_nat W_9)))). % 1.27/1.50 Axiom fact_59_number__of__reorient:(forall (W_9:int) (X_30:int), ((iff (((eq int) (number_number_of_int W_9)) X_30)) (((eq int) X_30) (number_number_of_int W_9)))). % 1.27/1.50 Axiom fact_60_number__of__reorient:(forall (W_9:int) (X_30:real), ((iff (((eq real) (number267125858f_real W_9)) X_30)) (((eq real) X_30) (number267125858f_real W_9)))). % 1.27/1.50 Axiom fact_61_rel__simps_I51_J:(forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L))). % 1.27/1.50 Axiom fact_62_rel__simps_I48_J:(forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L))). % 1.27/1.50 Axiom fact_63_even__less__0__iff:(forall (A_85:int), ((iff ((ord_less_int ((plus_plus_int A_85) A_85)) zero_zero_int)) ((ord_less_int A_85) zero_zero_int))). % 1.27/1.50 Axiom fact_64_even__less__0__iff:(forall (A_85:real), ((iff ((ord_less_real ((plus_plus_real A_85) A_85)) zero_zero_real)) ((ord_less_real A_85) zero_zero_real))). % 1.27/1.50 Axiom fact_65_zadd__assoc:(forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((plus_plus_int ((plus_plus_int Z1) Z2)) Z3)) ((plus_plus_int Z1) ((plus_plus_int Z2) Z3)))). % 1.27/1.50 Axiom fact_66_zadd__left__commute:(forall (X:int) (Y:int) (Z_2:int), (((eq int) ((plus_plus_int X) ((plus_plus_int Y) Z_2))) ((plus_plus_int Y) ((plus_plus_int X) Z_2)))). % 1.27/1.50 Axiom fact_67_zadd__commute:(forall (Z_2:int) (W:int), (((eq int) ((plus_plus_int Z_2) W)) ((plus_plus_int W) Z_2))). % 1.27/1.50 Axiom fact_68_int__int__eq:(forall (M:nat) (N:nat), ((iff (((eq int) (semiri1621563631at_int M)) (semiri1621563631at_int N))) (((eq nat) M) N))). % 1.27/1.50 Axiom fact_69_less__special_I3_J:(forall (X_29:int), ((iff ((ord_less_int (number_number_of_int X_29)) zero_zero_int)) ((ord_less_int X_29) pls))). % 1.27/1.50 Axiom fact_70_less__special_I3_J:(forall (X_29:int), ((iff ((ord_less_real (number267125858f_real X_29)) zero_zero_real)) ((ord_less_int X_29) pls))). % 1.27/1.50 Axiom fact_71_less__special_I1_J:(forall (Y_24:int), ((iff ((ord_less_int zero_zero_int) (number_number_of_int Y_24))) ((ord_less_int pls) Y_24))). % 1.27/1.50 Axiom fact_72_less__special_I1_J:(forall (Y_24:int), ((iff ((ord_less_real zero_zero_real) (number267125858f_real Y_24))) ((ord_less_int pls) Y_24))). % 1.27/1.50 Axiom fact_73_rel__simps_I12_J:(forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls))). % 1.27/1.50 Axiom fact_74_less__int__code_I15_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2))). % 1.27/1.50 Axiom fact_75_rel__simps_I16_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))). % 1.27/1.50 Axiom fact_76_rel__simps_I10_J:(forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls))). % 1.27/1.50 Axiom fact_77_rel__simps_I4_J:(forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K))). % 1.27/1.50 Axiom fact_78_bin__less__0__simps_I4_J:(forall (W:int), ((iff ((ord_less_int (bit1 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int))). % 1.27/1.50 Axiom fact_79_bin__less__0__simps_I1_J:(((ord_less_int pls) zero_zero_int)->False). % 1.27/1.50 Axiom fact_80_bin__less__0__simps_I3_J:(forall (W:int), ((iff ((ord_less_int (bit0 W)) zero_zero_int)) ((ord_less_int W) zero_zero_int))). % 1.27/1.50 Axiom fact_81_int__0__less__1:((ord_less_int zero_zero_int) one_one_int). % 1.27/1.50 Axiom fact_82_zless__add1__eq:(forall (W:int) (Z_2:int), ((iff ((ord_less_int W) ((plus_plus_int Z_2) one_one_int))) ((or ((ord_less_int W) Z_2)) (((eq int) W) Z_2)))). % 1.27/1.50 Axiom fact_83_int__less__0__conv:(forall (K:nat), (((ord_less_int (semiri1621563631at_int K)) zero_zero_int)->False)). % 1.27/1.50 Axiom fact_84_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)))). % 1.27/1.50 Axiom fact_85_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)))). % 1.27/1.50 Axiom fact_86_less__special_I2_J:(forall (Y_23:int), ((iff ((ord_less_int one_one_int) (number_number_of_int Y_23))) ((ord_less_int (bit1 pls)) Y_23))). % 1.27/1.50 Axiom fact_87_less__special_I2_J:(forall (Y_23:int), ((iff ((ord_less_real one_one_real) (number267125858f_real Y_23))) ((ord_less_int (bit1 pls)) Y_23))). % 1.27/1.50 Axiom fact_88_odd__less__0:(forall (Z_2:int), ((iff ((ord_less_int ((plus_plus_int ((plus_plus_int one_one_int) Z_2)) Z_2)) zero_zero_int)) ((ord_less_int Z_2) zero_zero_int))). % 1.27/1.50 Axiom fact_89_double__eq__0__iff:(forall (A_84:int), ((iff (((eq int) ((plus_plus_int A_84) A_84)) zero_zero_int)) (((eq int) A_84) zero_zero_int))). % 1.27/1.50 Axiom fact_90_double__eq__0__iff:(forall (A_84:real), ((iff (((eq real) ((plus_plus_real A_84) A_84)) zero_zero_real)) (((eq real) A_84) zero_zero_real))). % 1.27/1.50 Axiom fact_91_rel__simps_I46_J:(forall (K:int), (not (((eq int) (bit1 K)) pls))). % 1.27/1.50 Axiom fact_92_rel__simps_I39_J:(forall (L:int), (not (((eq int) pls) (bit1 L)))). % 1.27/1.50 Axiom fact_93_rel__simps_I50_J:(forall (K:int) (L:int), (not (((eq int) (bit1 K)) (bit0 L)))). % 1.27/1.50 Axiom fact_94_rel__simps_I49_J:(forall (K:int) (L:int), (not (((eq int) (bit0 K)) (bit1 L)))). % 1.27/1.50 Axiom fact_95_rel__simps_I44_J:(forall (K:int), ((iff (((eq int) (bit0 K)) pls)) (((eq int) K) pls))). % 1.27/1.50 Axiom fact_96_rel__simps_I38_J:(forall (L:int), ((iff (((eq int) pls) (bit0 L))) (((eq int) pls) L))). % 1.27/1.50 Axiom fact_97_Bit0__Pls:(((eq int) (bit0 pls)) pls). % 1.27/1.50 Axiom fact_98_Pls__def:(((eq int) pls) zero_zero_int). % 1.27/1.50 Axiom fact_99_int__0__neq__1:(not (((eq int) zero_zero_int) one_one_int)). % 1.27/1.50 Axiom fact_100_add__Pls__right:(forall (K:int), (((eq int) ((plus_plus_int K) pls)) K)). % 1.27/1.50 Axiom fact_101_add__Pls:(forall (K:int), (((eq int) ((plus_plus_int pls) K)) K)). % 1.27/1.50 Axiom fact_102_add__Bit0__Bit0:(forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit0 L))) (bit0 ((plus_plus_int K) L)))). % 1.27/1.50 Axiom fact_103_Bit0__def:(forall (K:int), (((eq int) (bit0 K)) ((plus_plus_int K) K))). % 1.27/1.50 Axiom fact_104_zadd__0__right:(forall (Z_2:int), (((eq int) ((plus_plus_int Z_2) zero_zero_int)) Z_2)). % 1.27/1.50 Axiom fact_105_zadd__0:(forall (Z_2:int), (((eq int) ((plus_plus_int zero_zero_int) Z_2)) Z_2)). % 1.27/1.50 Axiom fact_106_semiring__numeral__0__eq__0:(((eq int) (number_number_of_int pls)) zero_zero_int). % 1.27/1.50 Axiom fact_107_semiring__numeral__0__eq__0:(((eq nat) (number_number_of_nat pls)) zero_zero_nat). % 1.27/1.50 Axiom fact_108_semiring__numeral__0__eq__0:(((eq real) (number267125858f_real pls)) zero_zero_real). % 1.27/1.50 Axiom fact_109_number__of__Pls:(((eq int) (number_number_of_int pls)) zero_zero_int). % 1.27/1.50 Axiom fact_110_number__of__Pls:(((eq real) (number267125858f_real pls)) zero_zero_real). % 1.27/1.50 Axiom fact_111_semiring__norm_I112_J:(((eq int) zero_zero_int) (number_number_of_int pls)). % 1.27/1.50 Axiom fact_112_semiring__norm_I112_J:(((eq real) zero_zero_real) (number267125858f_real pls)). % 1.27/1.50 Axiom fact_113_add__numeral__0:(forall (A_83:int), (((eq int) ((plus_plus_int (number_number_of_int pls)) A_83)) A_83)). % 1.27/1.50 Axiom fact_114_add__numeral__0:(forall (A_83:real), (((eq real) ((plus_plus_real (number267125858f_real pls)) A_83)) A_83)). % 1.27/1.50 Axiom fact_115_add__numeral__0__right:(forall (A_82:int), (((eq int) ((plus_plus_int A_82) (number_number_of_int pls))) A_82)). % 1.27/1.50 Axiom fact_116_add__numeral__0__right:(forall (A_82:real), (((eq real) ((plus_plus_real A_82) (number267125858f_real pls))) A_82)). % 1.27/1.50 Axiom fact_117_power__eq__0__iff__number__of:(forall (A_81:int) (W_8:int), ((iff (((eq int) ((power_power_int A_81) (number_number_of_nat W_8))) zero_zero_int)) ((and (((eq int) A_81) zero_zero_int)) (not (((eq nat) (number_number_of_nat W_8)) zero_zero_nat))))). % 1.27/1.50 Axiom fact_118_power__eq__0__iff__number__of:(forall (A_81:nat) (W_8:int), ((iff (((eq nat) ((power_power_nat A_81) (number_number_of_nat W_8))) zero_zero_nat)) ((and (((eq nat) A_81) zero_zero_nat)) (not (((eq nat) (number_number_of_nat W_8)) zero_zero_nat))))). % 1.27/1.50 Axiom fact_119_power__eq__0__iff__number__of:(forall (A_81:real) (W_8:int), ((iff (((eq real) ((power_power_real A_81) (number_number_of_nat W_8))) zero_zero_real)) ((and (((eq real) A_81) zero_zero_real)) (not (((eq nat) (number_number_of_nat W_8)) zero_zero_nat))))). % 1.27/1.50 Axiom fact_120_add__number__of__left:(forall (V_10:int) (W_7:int) (Z_4:int), (((eq int) ((plus_plus_int (number_number_of_int V_10)) ((plus_plus_int (number_number_of_int W_7)) Z_4))) ((plus_plus_int (number_number_of_int ((plus_plus_int V_10) W_7))) Z_4))). % 1.27/1.50 Axiom fact_121_add__number__of__left:(forall (V_10:int) (W_7:int) (Z_4:real), (((eq real) ((plus_plus_real (number267125858f_real V_10)) ((plus_plus_real (number267125858f_real W_7)) Z_4))) ((plus_plus_real (number267125858f_real ((plus_plus_int V_10) W_7))) Z_4))). % 1.27/1.50 Axiom fact_122_add__number__of__eq:(forall (V_9:int) (W_6:int), (((eq int) ((plus_plus_int (number_number_of_int V_9)) (number_number_of_int W_6))) (number_number_of_int ((plus_plus_int V_9) W_6)))). % 1.27/1.50 Axiom fact_123_add__number__of__eq:(forall (V_9:int) (W_6:int), (((eq real) ((plus_plus_real (number267125858f_real V_9)) (number267125858f_real W_6))) (number267125858f_real ((plus_plus_int V_9) W_6)))). % 1.27/1.50 Axiom fact_124_number__of__add:(forall (V_8:int) (W_5:int), (((eq int) (number_number_of_int ((plus_plus_int V_8) W_5))) ((plus_plus_int (number_number_of_int V_8)) (number_number_of_int W_5)))). % 1.27/1.50 Axiom fact_125_number__of__add:(forall (V_8:int) (W_5:int), (((eq real) (number267125858f_real ((plus_plus_int V_8) W_5))) ((plus_plus_real (number267125858f_real V_8)) (number267125858f_real W_5)))). % 1.27/1.50 Axiom fact_126_add__Bit1__Bit0:(forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit0 L))) (bit1 ((plus_plus_int K) L)))). % 1.27/1.50 Axiom fact_127_add__Bit0__Bit1:(forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit0 K)) (bit1 L))) (bit1 ((plus_plus_int K) L)))). % 1.27/1.50 Axiom fact_128_Bit1__def:(forall (K:int), (((eq int) (bit1 K)) ((plus_plus_int ((plus_plus_int one_one_int) K)) K))). % 1.27/1.50 Axiom fact_129_odd__nonzero:(forall (Z_2:int), (not (((eq int) ((plus_plus_int ((plus_plus_int one_one_int) Z_2)) Z_2)) zero_zero_int))). % 1.27/1.50 Axiom fact_130_number__of__int:(forall (N_35:nat), (((eq nat) (number_number_of_nat (semiri1621563631at_int N_35))) (semiri984289939at_nat N_35))). % 1.27/1.51 Axiom fact_131_number__of__int:(forall (N_35:nat), (((eq int) (number_number_of_int (semiri1621563631at_int N_35))) (semiri1621563631at_int N_35))). % 1.27/1.51 Axiom fact_132_number__of__int:(forall (N_35:nat), (((eq real) (number267125858f_real (semiri1621563631at_int N_35))) (semiri132038758t_real N_35))). % 1.27/1.51 Axiom fact_133_zero__less__power2:(forall (A_80:int), ((iff ((ord_less_int zero_zero_int) ((power_power_int A_80) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq int) A_80) zero_zero_int)))). % 1.27/1.51 Axiom fact_134_zero__less__power2:(forall (A_80:real), ((iff ((ord_less_real zero_zero_real) ((power_power_real A_80) (number_number_of_nat (bit0 (bit1 pls)))))) (not (((eq real) A_80) zero_zero_real)))). % 1.27/1.51 Axiom fact_135_power2__less__0:(forall (A_79:int), (((ord_less_int ((power_power_int A_79) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_int)->False)). % 1.27/1.51 Axiom fact_136_power2__less__0:(forall (A_79:real), (((ord_less_real ((power_power_real A_79) (number_number_of_nat (bit0 (bit1 pls))))) zero_zero_real)->False)). % 1.27/1.51 Axiom fact_137_sum__power2__gt__zero__iff:(forall (X_27:int) (Y_22:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int ((power_power_int X_27) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_22) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq int) X_27) zero_zero_int))) (not (((eq int) Y_22) zero_zero_int))))). % 1.27/1.51 Axiom fact_138_sum__power2__gt__zero__iff:(forall (X_27:real) (Y_22:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real ((power_power_real X_27) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_22) (number_number_of_nat (bit0 (bit1 pls))))))) ((or (not (((eq real) X_27) zero_zero_real))) (not (((eq real) Y_22) zero_zero_real))))). % 1.27/1.51 Axiom fact_139_not__sum__power2__lt__zero:(forall (X_26:int) (Y_21:int), (((ord_less_int ((plus_plus_int ((power_power_int X_26) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_21) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)->False)). % 1.27/1.51 Axiom fact_140_not__sum__power2__lt__zero:(forall (X_26:real) (Y_21:real), (((ord_less_real ((plus_plus_real ((power_power_real X_26) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_21) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)->False)). % 1.27/1.51 Axiom fact_141_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)))). % 1.27/1.51 Axiom fact_142_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)))). % 1.27/1.51 Axiom fact_143_number__of__Bit1:(forall (W_3:int), (((eq int) (number_number_of_int (bit1 W_3))) ((plus_plus_int ((plus_plus_int one_one_int) (number_number_of_int W_3))) (number_number_of_int W_3)))). % 1.27/1.51 Axiom fact_144_number__of__Bit1:(forall (W_3:int), (((eq real) (number267125858f_real (bit1 W_3))) ((plus_plus_real ((plus_plus_real one_one_real) (number267125858f_real W_3))) (number267125858f_real W_3)))). % 1.27/1.51 Axiom fact_145_semiring__numeral__1__eq__1:(((eq int) (number_number_of_int (bit1 pls))) one_one_int). % 1.27/1.51 Axiom fact_146_semiring__numeral__1__eq__1:(((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat). % 1.27/1.51 Axiom fact_147_semiring__numeral__1__eq__1:(((eq real) (number267125858f_real (bit1 pls))) one_one_real). % 1.27/1.51 Axiom fact_148_mn:((ord_less_int m1) ((plus_plus_int one_one_int) (semiri1621563631at_int n))). % 1.27/1.51 Axiom fact_149_of__nat__less__two__power:(forall (N_34:nat), ((ord_less_int (semiri1621563631at_int N_34)) ((power_power_int (number_number_of_int (bit0 (bit1 pls)))) N_34))). % 1.27/1.51 Axiom fact_150_of__nat__less__two__power:(forall (N_34:nat), ((ord_less_real (semiri132038758t_real N_34)) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N_34))). % 1.27/1.51 Axiom fact_151_transfer__int__nat__numerals_I3_J:(((eq int) (number_number_of_int (bit0 (bit1 pls)))) (semiri1621563631at_int (number_number_of_nat (bit0 (bit1 pls))))). % 1.27/1.51 Axiom fact_152_transfer__int__nat__numerals_I4_J:(((eq int) (number_number_of_int (bit1 (bit1 pls)))) (semiri1621563631at_int (number_number_of_nat (bit1 (bit1 pls))))). % 1.27/1.51 Axiom fact_153_realpow__two__sum__zero__iff:(forall (X:real) (Y:real), ((iff (((eq real) ((plus_plus_real ((power_power_real X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X) zero_zero_real)) (((eq real) Y) zero_zero_real)))). % 1.27/1.51 Axiom fact_154_of__nat__0__less__iff:(forall (N_33:nat), ((iff ((ord_less_int zero_zero_int) (semiri1621563631at_int N_33))) ((ord_less_nat zero_zero_nat) N_33))). % 1.27/1.51 Axiom fact_155_of__nat__0__less__iff:(forall (N_33:nat), ((iff ((ord_less_nat zero_zero_nat) (semiri984289939at_nat N_33))) ((ord_less_nat zero_zero_nat) N_33))). % 1.27/1.51 Axiom fact_156_of__nat__0__less__iff:(forall (N_33:nat), ((iff ((ord_less_real zero_zero_real) (semiri132038758t_real N_33))) ((ord_less_nat zero_zero_nat) N_33))). % 1.27/1.51 Axiom fact_157_one__less__power:(forall (N_32:nat) (A_78:int), (((ord_less_int one_one_int) A_78)->(((ord_less_nat zero_zero_nat) N_32)->((ord_less_int one_one_int) ((power_power_int A_78) N_32))))). % 1.27/1.51 Axiom fact_158_one__less__power:(forall (N_32:nat) (A_78:nat), (((ord_less_nat one_one_nat) A_78)->(((ord_less_nat zero_zero_nat) N_32)->((ord_less_nat one_one_nat) ((power_power_nat A_78) N_32))))). % 1.27/1.51 Axiom fact_159_one__less__power:(forall (N_32:nat) (A_78:real), (((ord_less_real one_one_real) A_78)->(((ord_less_nat zero_zero_nat) N_32)->((ord_less_real one_one_real) ((power_power_real A_78) N_32))))). % 1.27/1.51 Axiom fact_160_power__0__left:(forall (N_31:nat), ((and ((((eq nat) N_31) zero_zero_nat)->(((eq int) ((power_power_int zero_zero_int) N_31)) one_one_int))) ((not (((eq nat) N_31) zero_zero_nat))->(((eq int) ((power_power_int zero_zero_int) N_31)) zero_zero_int)))). % 1.27/1.51 Axiom fact_161_power__0__left:(forall (N_31:nat), ((and ((((eq nat) N_31) zero_zero_nat)->(((eq nat) ((power_power_nat zero_zero_nat) N_31)) one_one_nat))) ((not (((eq nat) N_31) zero_zero_nat))->(((eq nat) ((power_power_nat zero_zero_nat) N_31)) zero_zero_nat)))). % 1.27/1.51 Axiom fact_162_power__0__left:(forall (N_31:nat), ((and ((((eq nat) N_31) zero_zero_nat)->(((eq real) ((power_power_real zero_zero_real) N_31)) one_one_real))) ((not (((eq nat) N_31) zero_zero_nat))->(((eq real) ((power_power_real zero_zero_real) N_31)) zero_zero_real)))). % 1.27/1.51 Axiom fact_163_power__strict__decreasing:(forall (A_77:int) (N_30:nat) (N_29:nat), (((ord_less_nat N_30) N_29)->(((ord_less_int zero_zero_int) A_77)->(((ord_less_int A_77) one_one_int)->((ord_less_int ((power_power_int A_77) N_29)) ((power_power_int A_77) N_30)))))). % 1.27/1.51 Axiom fact_164_power__strict__decreasing:(forall (A_77:nat) (N_30:nat) (N_29:nat), (((ord_less_nat N_30) N_29)->(((ord_less_nat zero_zero_nat) A_77)->(((ord_less_nat A_77) one_one_nat)->((ord_less_nat ((power_power_nat A_77) N_29)) ((power_power_nat A_77) N_30)))))). % 1.27/1.51 Axiom fact_165_power__strict__decreasing:(forall (A_77:real) (N_30:nat) (N_29:nat), (((ord_less_nat N_30) N_29)->(((ord_less_real zero_zero_real) A_77)->(((ord_less_real A_77) one_one_real)->((ord_less_real ((power_power_real A_77) N_29)) ((power_power_real A_77) N_30)))))). % 1.27/1.51 Axiom fact_166_zero__less__two:((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) one_one_int)). % 1.27/1.51 Axiom fact_167_zero__less__two:((ord_less_nat zero_zero_nat) ((plus_plus_nat one_one_nat) one_one_nat)). % 1.27/1.51 Axiom fact_168_zero__less__two:((ord_less_real zero_zero_real) ((plus_plus_real one_one_real) one_one_real)). % 1.27/1.51 Axiom fact_169_int__gr__induct:(forall (P:(int->Prop)) (K:int) (_TPTP_I:int), (((ord_less_int K) _TPTP_I)->((P ((plus_plus_int K) one_one_int))->((forall (I_1:int), (((ord_less_int K) I_1)->((P I_1)->(P ((plus_plus_int I_1) one_one_int)))))->(P _TPTP_I))))). % 1.27/1.51 Axiom fact_170_tn0:((ord_less_nat zero_zero_nat) tn). % 1.27/1.51 Axiom fact_171_less__zeroE:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)). % 1.27/1.51 Axiom fact_172_real__zero__not__eq__one:(not (((eq real) zero_zero_real) one_one_real)). % 1.27/1.51 Axiom fact_173_less__not__refl:(forall (N:nat), (((ord_less_nat N) N)->False)). % 1.27/1.51 Axiom fact_174_not__add__less1:(forall (_TPTP_I:nat) (J:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J)) _TPTP_I)->False)). % 1.27/1.51 Axiom fact_175_not__add__less2:(forall (J:nat) (_TPTP_I:nat), (((ord_less_nat ((plus_plus_nat J) _TPTP_I)) _TPTP_I)->False)). % 1.27/1.51 Axiom fact_176_number__of__is__id:(forall (K:int), (((eq int) (number_number_of_int K)) K)). % 1.27/1.51 Axiom fact_177_nat__neq__iff:(forall (M:nat) (N:nat), ((iff (not (((eq nat) M) N))) ((or ((ord_less_nat M) N)) ((ord_less_nat N) M)))). % 1.27/1.51 Axiom fact_178_nat__add__commute:(forall (M:nat) (N:nat), (((eq nat) ((plus_plus_nat M) N)) ((plus_plus_nat N) M))). % 1.27/1.51 Axiom fact_179_nat__add__left__commute:(forall (X:nat) (Y:nat) (Z_2:nat), (((eq nat) ((plus_plus_nat X) ((plus_plus_nat Y) Z_2))) ((plus_plus_nat Y) ((plus_plus_nat X) Z_2)))). % 1.27/1.51 Axiom fact_180_nat__add__assoc:(forall (M:nat) (N:nat) (K:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat M) N)) K)) ((plus_plus_nat M) ((plus_plus_nat N) K)))). % 1.27/1.51 Axiom fact_181_nat__add__left__cancel:(forall (K:nat) (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) (((eq nat) M) N))). % 1.27/1.51 Axiom fact_182_nat__add__right__cancel:(forall (M:nat) (K:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) K)) ((plus_plus_nat N) K))) (((eq nat) M) N))). % 1.27/1.51 Axiom fact_183_nat__add__left__cancel__less:(forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_nat M) N))). % 1.27/1.51 Axiom fact_184_linorder__neqE__nat:(forall (X:nat) (Y:nat), ((not (((eq nat) X) Y))->((((ord_less_nat X) Y)->False)->((ord_less_nat Y) X)))). % 1.27/1.51 Axiom fact_185_less__irrefl__nat:(forall (N:nat), (((ord_less_nat N) N)->False)). % 1.27/1.51 Axiom fact_186_less__not__refl2:(forall (N:nat) (M:nat), (((ord_less_nat N) M)->(not (((eq nat) M) N)))). % 1.27/1.51 Axiom fact_187_less__not__refl3:(forall (S:nat) (T:nat), (((ord_less_nat S) T)->(not (((eq nat) S) T)))). % 1.27/1.51 Axiom fact_188_trans__less__add1:(forall (M:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat _TPTP_I) ((plus_plus_nat J) M)))). % 1.27/1.51 Axiom fact_189_trans__less__add2:(forall (M:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat _TPTP_I) ((plus_plus_nat M) J)))). % 1.27/1.51 Axiom fact_190_add__less__mono1:(forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K)))). % 1.27/1.51 Axiom fact_191_add__less__mono:(forall (K:nat) (L:nat) (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->(((ord_less_nat K) L)->((ord_less_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L))))). % 1.27/1.51 Axiom fact_192_less__add__eq__less:(forall (M:nat) (N:nat) (K:nat) (L:nat), (((ord_less_nat K) L)->((((eq nat) ((plus_plus_nat M) L)) ((plus_plus_nat K) N))->((ord_less_nat M) N)))). % 1.27/1.51 Axiom fact_193_add__lessD1:(forall (_TPTP_I:nat) (J:nat) (K:nat), (((ord_less_nat ((plus_plus_nat _TPTP_I) J)) K)->((ord_less_nat _TPTP_I) K))). % 1.27/1.51 Axiom fact_194_nat__less__cases:(forall (P:(nat->(nat->Prop))) (M:nat) (N:nat), ((((ord_less_nat M) N)->((P N) M))->(((((eq nat) M) N)->((P N) M))->((((ord_less_nat N) M)->((P N) M))->((P N) M))))). % 1.27/1.51 Axiom fact_195_gr0I:(forall (N:nat), ((not (((eq nat) N) zero_zero_nat))->((ord_less_nat zero_zero_nat) N))). % 1.27/1.51 Axiom fact_196_gr__implies__not0:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->(not (((eq nat) N) zero_zero_nat)))). % 1.27/1.51 Axiom fact_197_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)))). % 1.27/1.51 Axiom fact_198_less__nat__zero__code:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)). % 1.27/1.51 Axiom fact_199_nat__zero__less__power__iff:(forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or ((ord_less_nat zero_zero_nat) X)) (((eq nat) N) zero_zero_nat)))). % 1.27/1.51 Axiom fact_200_add__gr__0:(forall (M:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((plus_plus_nat M) N))) ((or ((ord_less_nat zero_zero_nat) M)) ((ord_less_nat zero_zero_nat) N)))). % 1.27/1.51 Axiom fact_201_neq0__conv:(forall (N:nat), ((iff (not (((eq nat) N) zero_zero_nat))) ((ord_less_nat zero_zero_nat) N))). % 1.27/1.51 Axiom fact_202_not__less0:(forall (N:nat), (((ord_less_nat N) zero_zero_nat)->False)). % 1.27/1.51 Axiom fact_203_zero__less__power__nat__eq:(forall (X:nat) (N:nat), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) N))) ((or (((eq nat) N) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X)))). % 1.27/1.51 Axiom fact_204_Nat__Transfer_Otransfer__int__nat__relations_I2_J:(forall (X:nat) (Y:nat), ((iff ((ord_less_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_nat X) Y))). % 1.27/1.51 Axiom fact_205_zero__less__power__nat__eq__number__of:(forall (X:nat) (W:int), ((iff ((ord_less_nat zero_zero_nat) ((power_power_nat X) (number_number_of_nat W)))) ((or (((eq nat) (number_number_of_nat W)) zero_zero_nat)) ((ord_less_nat zero_zero_nat) X)))). % 1.27/1.51 Axiom fact_206_zless__int:(forall (M:nat) (N:nat), ((iff ((ord_less_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_nat M) N))). % 1.27/1.51 Axiom fact_207_less__nat__number__of:(forall (V_1:int) (V:int), ((iff ((ord_less_nat (number_number_of_nat V_1)) (number_number_of_nat V))) ((and (((ord_less_int V_1) V)->((ord_less_int pls) V))) ((ord_less_int V_1) V)))). % 1.27/1.51 Axiom fact_208_linorder__neqE__linordered__idom:(forall (X_25:real) (Y_20:real), ((not (((eq real) X_25) Y_20))->((((ord_less_real X_25) Y_20)->False)->((ord_less_real Y_20) X_25)))). % 1.27/1.51 Axiom fact_209_linorder__neqE__linordered__idom:(forall (X_25:int) (Y_20:int), ((not (((eq int) X_25) Y_20))->((((ord_less_int X_25) Y_20)->False)->((ord_less_int Y_20) X_25)))). % 1.27/1.51 Axiom fact_210_add__eq__self__zero:(forall (M:nat) (N:nat), ((((eq nat) ((plus_plus_nat M) N)) M)->(((eq nat) N) zero_zero_nat))). % 1.27/1.51 Axiom fact_211_add__is__0:(forall (M:nat) (N:nat), ((iff (((eq nat) ((plus_plus_nat M) N)) zero_zero_nat)) ((and (((eq nat) M) zero_zero_nat)) (((eq nat) N) zero_zero_nat)))). % 1.27/1.51 Axiom fact_212_Nat_Oadd__0__right:(forall (M:nat), (((eq nat) ((plus_plus_nat M) zero_zero_nat)) M)). % 1.27/1.51 Axiom fact_213_plus__nat_Oadd__0:(forall (N:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) N)) N)). % 1.27/1.51 Axiom fact_214_power__one__right:(forall (A_76:real), (((eq real) ((power_power_real A_76) one_one_nat)) A_76)). % 1.27/1.51 Axiom fact_215_power__one__right:(forall (A_76:nat), (((eq nat) ((power_power_nat A_76) one_one_nat)) A_76)). % 1.27/1.51 Axiom fact_216_power__one__right:(forall (A_76:int), (((eq int) ((power_power_int A_76) one_one_nat)) A_76)). % 1.27/1.51 Axiom fact_217_of__nat__eq__iff:(forall (M_13:nat) (N_28:nat), ((iff (((eq real) (semiri132038758t_real M_13)) (semiri132038758t_real N_28))) (((eq nat) M_13) N_28))). % 1.27/1.51 Axiom fact_218_of__nat__eq__iff:(forall (M_13:nat) (N_28:nat), ((iff (((eq nat) (semiri984289939at_nat M_13)) (semiri984289939at_nat N_28))) (((eq nat) M_13) N_28))). % 1.27/1.51 Axiom fact_219_of__nat__eq__iff:(forall (M_13:nat) (N_28:nat), ((iff (((eq int) (semiri1621563631at_int M_13)) (semiri1621563631at_int N_28))) (((eq nat) M_13) N_28))). % 1.27/1.51 Axiom fact_220_Nat__Transfer_Otransfer__int__nat__relations_I1_J:(forall (X:nat) (Y:nat), ((iff (((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (((eq nat) X) Y))). % 1.27/1.51 Axiom fact_221_int__if__cong:(forall (X:nat) (Y:nat) (P:Prop), ((and (P->(((eq int) (semiri1621563631at_int X)) (semiri1621563631at_int (((if_nat P) X) Y))))) ((P->False)->(((eq int) (semiri1621563631at_int Y)) (semiri1621563631at_int (((if_nat P) X) Y)))))). % 1.27/1.51 Axiom fact_222_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))). % 1.27/1.51 Axiom fact_223_zero__less__int__conv:(forall (N:nat), ((iff ((ord_less_int zero_zero_int) (semiri1621563631at_int N))) ((ord_less_nat zero_zero_nat) N))). % 1.27/1.51 Axiom fact_224_one__neq__zero:(not (((eq real) one_one_real) zero_zero_real)). % 1.27/1.51 Axiom fact_225_one__neq__zero:(not (((eq nat) one_one_nat) zero_zero_nat)). % 1.27/1.51 Axiom fact_226_one__neq__zero:(not (((eq int) one_one_int) zero_zero_int)). % 1.27/1.51 Axiom fact_227_zero__neq__one:(not (((eq real) zero_zero_real) one_one_real)). % 1.27/1.51 Axiom fact_228_zero__neq__one:(not (((eq nat) zero_zero_nat) one_one_nat)). % 1.27/1.51 Axiom fact_229_zero__neq__one:(not (((eq int) zero_zero_int) one_one_int)). % 1.27/1.51 Axiom fact_230_field__power__not__zero:(forall (N_27:nat) (A_75:real), ((not (((eq real) A_75) zero_zero_real))->(not (((eq real) ((power_power_real A_75) N_27)) zero_zero_real)))). % 1.35/1.51 Axiom fact_231_field__power__not__zero:(forall (N_27:nat) (A_75:int), ((not (((eq int) A_75) zero_zero_int))->(not (((eq int) ((power_power_int A_75) N_27)) zero_zero_int)))). % 1.35/1.51 Axiom fact_232_power__one:(forall (N_26:nat), (((eq real) ((power_power_real one_one_real) N_26)) one_one_real)). % 1.35/1.51 Axiom fact_233_power__one:(forall (N_26:nat), (((eq nat) ((power_power_nat one_one_nat) N_26)) one_one_nat)). % 1.35/1.51 Axiom fact_234_power__one:(forall (N_26:nat), (((eq int) ((power_power_int one_one_int) N_26)) one_one_int)). % 1.35/1.51 Axiom fact_235_of__nat__less__iff:(forall (M_12:nat) (N_25:nat), ((iff ((ord_less_real (semiri132038758t_real M_12)) (semiri132038758t_real N_25))) ((ord_less_nat M_12) N_25))). % 1.35/1.51 Axiom fact_236_of__nat__less__iff:(forall (M_12:nat) (N_25:nat), ((iff ((ord_less_nat (semiri984289939at_nat M_12)) (semiri984289939at_nat N_25))) ((ord_less_nat M_12) N_25))). % 1.35/1.51 Axiom fact_237_of__nat__less__iff:(forall (M_12:nat) (N_25:nat), ((iff ((ord_less_int (semiri1621563631at_int M_12)) (semiri1621563631at_int N_25))) ((ord_less_nat M_12) N_25))). % 1.35/1.51 Axiom fact_238_less__imp__of__nat__less:(forall (M_11:nat) (N_24:nat), (((ord_less_nat M_11) N_24)->((ord_less_real (semiri132038758t_real M_11)) (semiri132038758t_real N_24)))). % 1.35/1.51 Axiom fact_239_less__imp__of__nat__less:(forall (M_11:nat) (N_24:nat), (((ord_less_nat M_11) N_24)->((ord_less_nat (semiri984289939at_nat M_11)) (semiri984289939at_nat N_24)))). % 1.35/1.51 Axiom fact_240_less__imp__of__nat__less:(forall (M_11:nat) (N_24:nat), (((ord_less_nat M_11) N_24)->((ord_less_int (semiri1621563631at_int M_11)) (semiri1621563631at_int N_24)))). % 1.35/1.51 Axiom fact_241_of__nat__less__imp__less:(forall (M_10:nat) (N_23:nat), (((ord_less_real (semiri132038758t_real M_10)) (semiri132038758t_real N_23))->((ord_less_nat M_10) N_23))). % 1.35/1.51 Axiom fact_242_of__nat__less__imp__less:(forall (M_10:nat) (N_23:nat), (((ord_less_nat (semiri984289939at_nat M_10)) (semiri984289939at_nat N_23))->((ord_less_nat M_10) N_23))). % 1.35/1.51 Axiom fact_243_of__nat__less__imp__less:(forall (M_10:nat) (N_23:nat), (((ord_less_int (semiri1621563631at_int M_10)) (semiri1621563631at_int N_23))->((ord_less_nat M_10) N_23))). % 1.35/1.51 Axiom fact_244_of__nat__add:(forall (M_9:nat) (N_22:nat), (((eq real) (semiri132038758t_real ((plus_plus_nat M_9) N_22))) ((plus_plus_real (semiri132038758t_real M_9)) (semiri132038758t_real N_22)))). % 1.35/1.51 Axiom fact_245_of__nat__add:(forall (M_9:nat) (N_22:nat), (((eq nat) (semiri984289939at_nat ((plus_plus_nat M_9) N_22))) ((plus_plus_nat (semiri984289939at_nat M_9)) (semiri984289939at_nat N_22)))). % 1.35/1.51 Axiom fact_246_of__nat__add:(forall (M_9:nat) (N_22:nat), (((eq int) (semiri1621563631at_int ((plus_plus_nat M_9) N_22))) ((plus_plus_int (semiri1621563631at_int M_9)) (semiri1621563631at_int N_22)))). % 1.35/1.51 Axiom fact_247_of__nat__1:(((eq real) (semiri132038758t_real one_one_nat)) one_one_real). % 1.35/1.51 Axiom fact_248_of__nat__1:(((eq nat) (semiri984289939at_nat one_one_nat)) one_one_nat). % 1.35/1.51 Axiom fact_249_of__nat__1:(((eq int) (semiri1621563631at_int one_one_nat)) one_one_int). % 1.35/1.51 Axiom fact_250_of__nat__power:(forall (M_8:nat) (N_21:nat), (((eq real) (semiri132038758t_real ((power_power_nat M_8) N_21))) ((power_power_real (semiri132038758t_real M_8)) N_21))). % 1.35/1.51 Axiom fact_251_of__nat__power:(forall (M_8:nat) (N_21:nat), (((eq nat) (semiri984289939at_nat ((power_power_nat M_8) N_21))) ((power_power_nat (semiri984289939at_nat M_8)) N_21))). % 1.35/1.51 Axiom fact_252_of__nat__power:(forall (M_8:nat) (N_21:nat), (((eq int) (semiri1621563631at_int ((power_power_nat M_8) N_21))) ((power_power_int (semiri1621563631at_int M_8)) N_21))). % 1.35/1.51 Axiom fact_253_transfer__int__nat__numerals_I2_J:(((eq int) one_one_int) (semiri1621563631at_int one_one_nat)). % 1.35/1.51 Axiom fact_254_Nat__Transfer_Otransfer__int__nat__functions_I1_J:(forall (X:nat) (Y:nat), (((eq int) ((plus_plus_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) (semiri1621563631at_int ((plus_plus_nat X) Y)))). % 1.35/1.51 Axiom fact_255_Nat__Transfer_Otransfer__int__nat__functions_I4_J:(forall (X:nat) (N:nat), (((eq int) ((power_power_int (semiri1621563631at_int X)) N)) (semiri1621563631at_int ((power_power_nat X) N)))). % 1.35/1.51 Axiom fact_256_pos__add__strict:(forall (B_49:real) (C_36:real) (A_74:real), (((ord_less_real zero_zero_real) A_74)->(((ord_less_real B_49) C_36)->((ord_less_real B_49) ((plus_plus_real A_74) C_36))))). % 1.35/1.51 Axiom fact_257_pos__add__strict:(forall (B_49:nat) (C_36:nat) (A_74:nat), (((ord_less_nat zero_zero_nat) A_74)->(((ord_less_nat B_49) C_36)->((ord_less_nat B_49) ((plus_plus_nat A_74) C_36))))). % 1.35/1.51 Axiom fact_258_pos__add__strict:(forall (B_49:int) (C_36:int) (A_74:int), (((ord_less_int zero_zero_int) A_74)->(((ord_less_int B_49) C_36)->((ord_less_int B_49) ((plus_plus_int A_74) C_36))))). % 1.35/1.51 Axiom fact_259_not__one__less__zero:(((ord_less_real one_one_real) zero_zero_real)->False). % 1.35/1.51 Axiom fact_260_not__one__less__zero:(((ord_less_nat one_one_nat) zero_zero_nat)->False). % 1.35/1.51 Axiom fact_261_not__one__less__zero:(((ord_less_int one_one_int) zero_zero_int)->False). % 1.35/1.51 Axiom fact_262_zero__less__one:((ord_less_real zero_zero_real) one_one_real). % 1.35/1.51 Axiom fact_263_zero__less__one:((ord_less_nat zero_zero_nat) one_one_nat). % 1.35/1.51 Axiom fact_264_zero__less__one:((ord_less_int zero_zero_int) one_one_int). % 1.35/1.51 Axiom fact_265_zero__less__power:(forall (N_20:nat) (A_73:real), (((ord_less_real zero_zero_real) A_73)->((ord_less_real zero_zero_real) ((power_power_real A_73) N_20)))). % 1.35/1.51 Axiom fact_266_zero__less__power:(forall (N_20:nat) (A_73:nat), (((ord_less_nat zero_zero_nat) A_73)->((ord_less_nat zero_zero_nat) ((power_power_nat A_73) N_20)))). % 1.35/1.51 Axiom fact_267_zero__less__power:(forall (N_20:nat) (A_73:int), (((ord_less_int zero_zero_int) A_73)->((ord_less_int zero_zero_int) ((power_power_int A_73) N_20)))). % 1.35/1.51 Axiom fact_268_less__add__one:(forall (A_72:real), ((ord_less_real A_72) ((plus_plus_real A_72) one_one_real))). % 1.35/1.51 Axiom fact_269_less__add__one:(forall (A_72:nat), ((ord_less_nat A_72) ((plus_plus_nat A_72) one_one_nat))). % 1.35/1.51 Axiom fact_270_less__add__one:(forall (A_72:int), ((ord_less_int A_72) ((plus_plus_int A_72) one_one_int))). % 1.35/1.51 Axiom fact_271_power__inject__exp:(forall (M_7:nat) (N_19:nat) (A_71:real), (((ord_less_real one_one_real) A_71)->((iff (((eq real) ((power_power_real A_71) M_7)) ((power_power_real A_71) N_19))) (((eq nat) M_7) N_19)))). % 1.35/1.51 Axiom fact_272_power__inject__exp:(forall (M_7:nat) (N_19:nat) (A_71:nat), (((ord_less_nat one_one_nat) A_71)->((iff (((eq nat) ((power_power_nat A_71) M_7)) ((power_power_nat A_71) N_19))) (((eq nat) M_7) N_19)))). % 1.35/1.51 Axiom fact_273_power__inject__exp:(forall (M_7:nat) (N_19:nat) (A_71:int), (((ord_less_int one_one_int) A_71)->((iff (((eq int) ((power_power_int A_71) M_7)) ((power_power_int A_71) N_19))) (((eq nat) M_7) N_19)))). % 1.35/1.51 Axiom fact_274_power__strict__increasing__iff:(forall (X_24:nat) (Y_19:nat) (B_48:real), (((ord_less_real one_one_real) B_48)->((iff ((ord_less_real ((power_power_real B_48) X_24)) ((power_power_real B_48) Y_19))) ((ord_less_nat X_24) Y_19)))). % 1.35/1.51 Axiom fact_275_power__strict__increasing__iff:(forall (X_24:nat) (Y_19:nat) (B_48:nat), (((ord_less_nat one_one_nat) B_48)->((iff ((ord_less_nat ((power_power_nat B_48) X_24)) ((power_power_nat B_48) Y_19))) ((ord_less_nat X_24) Y_19)))). % 1.35/1.51 Axiom fact_276_power__strict__increasing__iff:(forall (X_24:nat) (Y_19:nat) (B_48:int), (((ord_less_int one_one_int) B_48)->((iff ((ord_less_int ((power_power_int B_48) X_24)) ((power_power_int B_48) Y_19))) ((ord_less_nat X_24) Y_19)))). % 1.35/1.51 Axiom fact_277_power__less__imp__less__exp:(forall (M_6:nat) (N_18:nat) (A_70:real), (((ord_less_real one_one_real) A_70)->(((ord_less_real ((power_power_real A_70) M_6)) ((power_power_real A_70) N_18))->((ord_less_nat M_6) N_18)))). % 1.35/1.51 Axiom fact_278_power__less__imp__less__exp:(forall (M_6:nat) (N_18:nat) (A_70:nat), (((ord_less_nat one_one_nat) A_70)->(((ord_less_nat ((power_power_nat A_70) M_6)) ((power_power_nat A_70) N_18))->((ord_less_nat M_6) N_18)))). % 1.35/1.51 Axiom fact_279_power__less__imp__less__exp:(forall (M_6:nat) (N_18:nat) (A_70:int), (((ord_less_int one_one_int) A_70)->(((ord_less_int ((power_power_int A_70) M_6)) ((power_power_int A_70) N_18))->((ord_less_nat M_6) N_18)))). % 1.35/1.52 Axiom fact_280_power__strict__increasing:(forall (A_69:real) (N_17:nat) (N_16:nat), (((ord_less_nat N_17) N_16)->(((ord_less_real one_one_real) A_69)->((ord_less_real ((power_power_real A_69) N_17)) ((power_power_real A_69) N_16))))). % 1.35/1.52 Axiom fact_281_power__strict__increasing:(forall (A_69:nat) (N_17:nat) (N_16:nat), (((ord_less_nat N_17) N_16)->(((ord_less_nat one_one_nat) A_69)->((ord_less_nat ((power_power_nat A_69) N_17)) ((power_power_nat A_69) N_16))))). % 1.35/1.52 Axiom fact_282_power__strict__increasing:(forall (A_69:int) (N_17:nat) (N_16:nat), (((ord_less_nat N_17) N_16)->(((ord_less_int one_one_int) A_69)->((ord_less_int ((power_power_int A_69) N_17)) ((power_power_int A_69) N_16))))). % 1.35/1.52 Axiom fact_283_power__eq__0__iff:(forall (A_68:real) (N_15:nat), ((iff (((eq real) ((power_power_real A_68) N_15)) zero_zero_real)) ((and (((eq real) A_68) zero_zero_real)) (not (((eq nat) N_15) zero_zero_nat))))). % 1.35/1.52 Axiom fact_284_power__eq__0__iff:(forall (A_68:nat) (N_15:nat), ((iff (((eq nat) ((power_power_nat A_68) N_15)) zero_zero_nat)) ((and (((eq nat) A_68) zero_zero_nat)) (not (((eq nat) N_15) zero_zero_nat))))). % 1.35/1.52 Axiom fact_285_power__eq__0__iff:(forall (A_68:int) (N_15:nat), ((iff (((eq int) ((power_power_int A_68) N_15)) zero_zero_int)) ((and (((eq int) A_68) zero_zero_int)) (not (((eq nat) N_15) zero_zero_nat))))). % 1.35/1.52 Axiom fact_286_of__nat__less__0__iff:(forall (M_5:nat), (((ord_less_real (semiri132038758t_real M_5)) zero_zero_real)->False)). % 1.35/1.52 Axiom fact_287_of__nat__less__0__iff:(forall (M_5:nat), (((ord_less_nat (semiri984289939at_nat M_5)) zero_zero_nat)->False)). % 1.35/1.52 Axiom fact_288_of__nat__less__0__iff:(forall (M_5:nat), (((ord_less_int (semiri1621563631at_int M_5)) zero_zero_int)->False)). % 1.35/1.52 Axiom fact_289_power__0:(forall (A_67:real), (((eq real) ((power_power_real A_67) zero_zero_nat)) one_one_real)). % 1.35/1.52 Axiom fact_290_power__0:(forall (A_67:nat), (((eq nat) ((power_power_nat A_67) zero_zero_nat)) one_one_nat)). % 1.35/1.52 Axiom fact_291_power__0:(forall (A_67:int), (((eq int) ((power_power_int A_67) zero_zero_nat)) one_one_int)). % 1.35/1.52 Axiom fact_292_of__nat__0:(((eq real) (semiri132038758t_real zero_zero_nat)) zero_zero_real). % 1.35/1.52 Axiom fact_293_of__nat__0:(((eq nat) (semiri984289939at_nat zero_zero_nat)) zero_zero_nat). % 1.35/1.52 Axiom fact_294_of__nat__0:(((eq int) (semiri1621563631at_int zero_zero_nat)) zero_zero_int). % 1.35/1.52 Axiom fact_295_transfer__int__nat__numerals_I1_J:(((eq int) zero_zero_int) (semiri1621563631at_int zero_zero_nat)). % 1.35/1.52 Axiom fact_296_pos2:((ord_less_nat zero_zero_nat) (number_number_of_nat (bit0 (bit1 pls)))). % 1.35/1.52 Axiom fact_297_zero__less__imp__eq__int:(forall (K:int), (((ord_less_int zero_zero_int) K)->((ex nat) (fun (N_1:nat)=> ((and ((ord_less_nat zero_zero_nat) N_1)) (((eq int) K) (semiri1621563631at_int N_1))))))). % 1.35/1.52 Axiom fact_298_less__imp__add__positive:(forall (_TPTP_I:nat) (J:nat), (((ord_less_nat _TPTP_I) J)->((ex nat) (fun (K_1:nat)=> ((and ((ord_less_nat zero_zero_nat) K_1)) (((eq nat) ((plus_plus_nat _TPTP_I) K_1)) J)))))). % 1.35/1.52 Axiom fact_299_exp__eq__1:(forall (X:nat) (N:nat), ((iff (((eq nat) ((power_power_nat X) N)) one_one_nat)) ((or (((eq nat) X) one_one_nat)) (((eq nat) N) zero_zero_nat)))). % 1.35/1.52 Axiom fact_300_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J:(forall (X_23:real), (((eq real) ((power_power_real X_23) zero_zero_nat)) one_one_real)). % 1.35/1.52 Axiom fact_301_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J:(forall (X_23:nat), (((eq nat) ((power_power_nat X_23) zero_zero_nat)) one_one_nat)). % 1.35/1.52 Axiom fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J:(forall (X_23:int), (((eq int) ((power_power_int X_23) zero_zero_nat)) one_one_int)). % 1.35/1.52 Axiom fact_303_zero__less__double__add__iff__zero__less__single__add:(forall (A_66:real), ((iff ((ord_less_real zero_zero_real) ((plus_plus_real A_66) A_66))) ((ord_less_real zero_zero_real) A_66))). % 1.35/1.52 Axiom fact_304_zero__less__double__add__iff__zero__less__single__add:(forall (A_66:int), ((iff ((ord_less_int zero_zero_int) ((plus_plus_int A_66) A_66))) ((ord_less_int zero_zero_int) A_66))). % 1.35/1.52 Axiom fact_305_double__add__less__zero__iff__single__add__less__zero:(forall (A_65:real), ((iff ((ord_less_real ((plus_plus_real A_65) A_65)) zero_zero_real)) ((ord_less_real A_65) zero_zero_real))). % 1.35/1.52 Axiom fact_306_double__add__less__zero__iff__single__add__less__zero:(forall (A_65:int), ((iff ((ord_less_int ((plus_plus_int A_65) A_65)) zero_zero_int)) ((ord_less_int A_65) zero_zero_int))). % 1.35/1.52 Axiom fact_307_zero__reorient:(forall (X_22:real), ((iff (((eq real) zero_zero_real) X_22)) (((eq real) X_22) zero_zero_real))). % 1.35/1.52 Axiom fact_308_zero__reorient:(forall (X_22:nat), ((iff (((eq nat) zero_zero_nat) X_22)) (((eq nat) X_22) zero_zero_nat))). % 1.35/1.52 Axiom fact_309_zero__reorient:(forall (X_22:int), ((iff (((eq int) zero_zero_int) X_22)) (((eq int) X_22) zero_zero_int))). % 1.35/1.52 Axiom fact_310_add__right__imp__eq:(forall (B_47:real) (A_64:real) (C_35:real), ((((eq real) ((plus_plus_real B_47) A_64)) ((plus_plus_real C_35) A_64))->(((eq real) B_47) C_35))). % 1.35/1.52 Axiom fact_311_add__right__imp__eq:(forall (B_47:nat) (A_64:nat) (C_35:nat), ((((eq nat) ((plus_plus_nat B_47) A_64)) ((plus_plus_nat C_35) A_64))->(((eq nat) B_47) C_35))). % 1.35/1.52 Axiom fact_312_add__right__imp__eq:(forall (B_47:int) (A_64:int) (C_35:int), ((((eq int) ((plus_plus_int B_47) A_64)) ((plus_plus_int C_35) A_64))->(((eq int) B_47) C_35))). % 1.35/1.52 Axiom fact_313_add__imp__eq:(forall (A_63:real) (B_46:real) (C_34:real), ((((eq real) ((plus_plus_real A_63) B_46)) ((plus_plus_real A_63) C_34))->(((eq real) B_46) C_34))). % 1.35/1.52 Axiom fact_314_add__imp__eq:(forall (A_63:nat) (B_46:nat) (C_34:nat), ((((eq nat) ((plus_plus_nat A_63) B_46)) ((plus_plus_nat A_63) C_34))->(((eq nat) B_46) C_34))). % 1.35/1.52 Axiom fact_315_add__imp__eq:(forall (A_63:int) (B_46:int) (C_34:int), ((((eq int) ((plus_plus_int A_63) B_46)) ((plus_plus_int A_63) C_34))->(((eq int) B_46) C_34))). % 1.35/1.52 Axiom fact_316_add__left__imp__eq:(forall (A_62:real) (B_45:real) (C_33:real), ((((eq real) ((plus_plus_real A_62) B_45)) ((plus_plus_real A_62) C_33))->(((eq real) B_45) C_33))). % 1.35/1.52 Axiom fact_317_add__left__imp__eq:(forall (A_62:nat) (B_45:nat) (C_33:nat), ((((eq nat) ((plus_plus_nat A_62) B_45)) ((plus_plus_nat A_62) C_33))->(((eq nat) B_45) C_33))). % 1.35/1.52 Axiom fact_318_add__left__imp__eq:(forall (A_62:int) (B_45:int) (C_33:int), ((((eq int) ((plus_plus_int A_62) B_45)) ((plus_plus_int A_62) C_33))->(((eq int) B_45) C_33))). % 1.35/1.52 Axiom fact_319_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_61:real) (B_44:real) (C_32:real) (D_6:real), (((eq real) ((plus_plus_real ((plus_plus_real A_61) B_44)) ((plus_plus_real C_32) D_6))) ((plus_plus_real ((plus_plus_real A_61) C_32)) ((plus_plus_real B_44) D_6)))). % 1.35/1.52 Axiom fact_320_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_61:nat) (B_44:nat) (C_32:nat) (D_6:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_61) B_44)) ((plus_plus_nat C_32) D_6))) ((plus_plus_nat ((plus_plus_nat A_61) C_32)) ((plus_plus_nat B_44) D_6)))). % 1.35/1.52 Axiom fact_321_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_61:int) (B_44:int) (C_32:int) (D_6:int), (((eq int) ((plus_plus_int ((plus_plus_int A_61) B_44)) ((plus_plus_int C_32) D_6))) ((plus_plus_int ((plus_plus_int A_61) C_32)) ((plus_plus_int B_44) D_6)))). % 1.35/1.52 Axiom fact_322_add__right__cancel:(forall (B_43:real) (A_60:real) (C_31:real), ((iff (((eq real) ((plus_plus_real B_43) A_60)) ((plus_plus_real C_31) A_60))) (((eq real) B_43) C_31))). % 1.35/1.52 Axiom fact_323_add__right__cancel:(forall (B_43:nat) (A_60:nat) (C_31:nat), ((iff (((eq nat) ((plus_plus_nat B_43) A_60)) ((plus_plus_nat C_31) A_60))) (((eq nat) B_43) C_31))). % 1.35/1.52 Axiom fact_324_add__right__cancel:(forall (B_43:int) (A_60:int) (C_31:int), ((iff (((eq int) ((plus_plus_int B_43) A_60)) ((plus_plus_int C_31) A_60))) (((eq int) B_43) C_31))). % 1.35/1.52 Axiom fact_325_add__left__cancel:(forall (A_59:real) (B_42:real) (C_30:real), ((iff (((eq real) ((plus_plus_real A_59) B_42)) ((plus_plus_real A_59) C_30))) (((eq real) B_42) C_30))). % 1.35/1.52 Axiom fact_326_add__left__cancel:(forall (A_59:nat) (B_42:nat) (C_30:nat), ((iff (((eq nat) ((plus_plus_nat A_59) B_42)) ((plus_plus_nat A_59) C_30))) (((eq nat) B_42) C_30))). % 1.35/1.52 Axiom fact_327_add__left__cancel:(forall (A_59:int) (B_42:int) (C_30:int), ((iff (((eq int) ((plus_plus_int A_59) B_42)) ((plus_plus_int A_59) C_30))) (((eq int) B_42) C_30))). % 1.35/1.52 Axiom fact_328_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_58:real) (B_41:real) (C_29:real), (((eq real) ((plus_plus_real ((plus_plus_real A_58) B_41)) C_29)) ((plus_plus_real ((plus_plus_real A_58) C_29)) B_41))). % 1.35/1.52 Axiom fact_329_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_58:nat) (B_41:nat) (C_29:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_58) B_41)) C_29)) ((plus_plus_nat ((plus_plus_nat A_58) C_29)) B_41))). % 1.35/1.52 Axiom fact_330_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_58:int) (B_41:int) (C_29:int), (((eq int) ((plus_plus_int ((plus_plus_int A_58) B_41)) C_29)) ((plus_plus_int ((plus_plus_int A_58) C_29)) B_41))). % 1.35/1.52 Axiom fact_331_ab__semigroup__add__class_Oadd__ac_I1_J:(forall (A_57:real) (B_40:real) (C_28:real), (((eq real) ((plus_plus_real ((plus_plus_real A_57) B_40)) C_28)) ((plus_plus_real A_57) ((plus_plus_real B_40) C_28)))). % 1.35/1.52 Axiom fact_332_ab__semigroup__add__class_Oadd__ac_I1_J:(forall (A_57:nat) (B_40:nat) (C_28:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_57) B_40)) C_28)) ((plus_plus_nat A_57) ((plus_plus_nat B_40) C_28)))). % 1.35/1.52 Axiom fact_333_ab__semigroup__add__class_Oadd__ac_I1_J:(forall (A_57:int) (B_40:int) (C_28:int), (((eq int) ((plus_plus_int ((plus_plus_int A_57) B_40)) C_28)) ((plus_plus_int A_57) ((plus_plus_int B_40) C_28)))). % 1.35/1.52 Axiom fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_56:real) (B_39:real) (C_27:real), (((eq real) ((plus_plus_real ((plus_plus_real A_56) B_39)) C_27)) ((plus_plus_real A_56) ((plus_plus_real B_39) C_27)))). % 1.35/1.52 Axiom fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_56:nat) (B_39:nat) (C_27:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_56) B_39)) C_27)) ((plus_plus_nat A_56) ((plus_plus_nat B_39) C_27)))). % 1.35/1.52 Axiom fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_56:int) (B_39:int) (C_27:int), (((eq int) ((plus_plus_int ((plus_plus_int A_56) B_39)) C_27)) ((plus_plus_int A_56) ((plus_plus_int B_39) C_27)))). % 1.35/1.52 Axiom fact_337_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_55:real) (C_26:real) (D_5:real), (((eq real) ((plus_plus_real A_55) ((plus_plus_real C_26) D_5))) ((plus_plus_real ((plus_plus_real A_55) C_26)) D_5))). % 1.35/1.52 Axiom fact_338_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_55:nat) (C_26:nat) (D_5:nat), (((eq nat) ((plus_plus_nat A_55) ((plus_plus_nat C_26) D_5))) ((plus_plus_nat ((plus_plus_nat A_55) C_26)) D_5))). % 1.35/1.52 Axiom fact_339_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_55:int) (C_26:int) (D_5:int), (((eq int) ((plus_plus_int A_55) ((plus_plus_int C_26) D_5))) ((plus_plus_int ((plus_plus_int A_55) C_26)) D_5))). % 1.35/1.52 Axiom fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_54:real) (C_25:real) (D_4:real), (((eq real) ((plus_plus_real A_54) ((plus_plus_real C_25) D_4))) ((plus_plus_real C_25) ((plus_plus_real A_54) D_4)))). % 1.35/1.52 Axiom fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_54:nat) (C_25:nat) (D_4:nat), (((eq nat) ((plus_plus_nat A_54) ((plus_plus_nat C_25) D_4))) ((plus_plus_nat C_25) ((plus_plus_nat A_54) D_4)))). % 1.35/1.52 Axiom fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_54:int) (C_25:int) (D_4:int), (((eq int) ((plus_plus_int A_54) ((plus_plus_int C_25) D_4))) ((plus_plus_int C_25) ((plus_plus_int A_54) D_4)))). % 1.35/1.52 Axiom fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A_53:real) (C_24:real), (((eq real) ((plus_plus_real A_53) C_24)) ((plus_plus_real C_24) A_53))). % 1.35/1.52 Axiom fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A_53:nat) (C_24:nat), (((eq nat) ((plus_plus_nat A_53) C_24)) ((plus_plus_nat C_24) A_53))). % 1.35/1.52 Axiom fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A_53:int) (C_24:int), (((eq int) ((plus_plus_int A_53) C_24)) ((plus_plus_int C_24) A_53))). % 1.35/1.52 Axiom fact_346_one__reorient:(forall (X_21:real), ((iff (((eq real) one_one_real) X_21)) (((eq real) X_21) one_one_real))). % 1.35/1.52 Axiom fact_347_one__reorient:(forall (X_21:nat), ((iff (((eq nat) one_one_nat) X_21)) (((eq nat) X_21) one_one_nat))). % 1.35/1.52 Axiom fact_348_one__reorient:(forall (X_21:int), ((iff (((eq int) one_one_int) X_21)) (((eq int) X_21) one_one_int))). % 1.35/1.52 Axiom fact_349_add__0__iff:(forall (B_38:real) (A_52:real), ((iff (((eq real) B_38) ((plus_plus_real B_38) A_52))) (((eq real) A_52) zero_zero_real))). % 1.35/1.52 Axiom fact_350_add__0__iff:(forall (B_38:nat) (A_52:nat), ((iff (((eq nat) B_38) ((plus_plus_nat B_38) A_52))) (((eq nat) A_52) zero_zero_nat))). % 1.35/1.52 Axiom fact_351_add__0__iff:(forall (B_38:int) (A_52:int), ((iff (((eq int) B_38) ((plus_plus_int B_38) A_52))) (((eq int) A_52) zero_zero_int))). % 1.35/1.52 Axiom fact_352_add_Ocomm__neutral:(forall (A_51:real), (((eq real) ((plus_plus_real A_51) zero_zero_real)) A_51)). % 1.35/1.52 Axiom fact_353_add_Ocomm__neutral:(forall (A_51:nat), (((eq nat) ((plus_plus_nat A_51) zero_zero_nat)) A_51)). % 1.35/1.52 Axiom fact_354_add_Ocomm__neutral:(forall (A_51:int), (((eq int) ((plus_plus_int A_51) zero_zero_int)) A_51)). % 1.35/1.52 Axiom fact_355_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J:(forall (A_50:real), (((eq real) ((plus_plus_real A_50) zero_zero_real)) A_50)). % 1.35/1.52 Axiom fact_356_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J:(forall (A_50:nat), (((eq nat) ((plus_plus_nat A_50) zero_zero_nat)) A_50)). % 1.35/1.52 Axiom fact_357_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J:(forall (A_50:int), (((eq int) ((plus_plus_int A_50) zero_zero_int)) A_50)). % 1.35/1.52 Axiom fact_358_add__0__right:(forall (A_49:real), (((eq real) ((plus_plus_real A_49) zero_zero_real)) A_49)). % 1.35/1.52 Axiom fact_359_add__0__right:(forall (A_49:nat), (((eq nat) ((plus_plus_nat A_49) zero_zero_nat)) A_49)). % 1.35/1.52 Axiom fact_360_add__0__right:(forall (A_49:int), (((eq int) ((plus_plus_int A_49) zero_zero_int)) A_49)). % 1.35/1.52 Axiom fact_361_double__zero__sym:(forall (A_48:real), ((iff (((eq real) zero_zero_real) ((plus_plus_real A_48) A_48))) (((eq real) A_48) zero_zero_real))). % 1.35/1.52 Axiom fact_362_double__zero__sym:(forall (A_48:int), ((iff (((eq int) zero_zero_int) ((plus_plus_int A_48) A_48))) (((eq int) A_48) zero_zero_int))). % 1.35/1.52 Axiom fact_363_add__0:(forall (A_47:real), (((eq real) ((plus_plus_real zero_zero_real) A_47)) A_47)). % 1.35/1.52 Axiom fact_364_add__0:(forall (A_47:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_47)) A_47)). % 1.35/1.52 Axiom fact_365_add__0:(forall (A_47:int), (((eq int) ((plus_plus_int zero_zero_int) A_47)) A_47)). % 1.35/1.52 Axiom fact_366_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J:(forall (A_46:real), (((eq real) ((plus_plus_real zero_zero_real) A_46)) A_46)). % 1.35/1.52 Axiom fact_367_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J:(forall (A_46:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_46)) A_46)). % 1.35/1.52 Axiom fact_368_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J:(forall (A_46:int), (((eq int) ((plus_plus_int zero_zero_int) A_46)) A_46)). % 1.35/1.52 Axiom fact_369_add__0__left:(forall (A_45:real), (((eq real) ((plus_plus_real zero_zero_real) A_45)) A_45)). % 1.35/1.52 Axiom fact_370_add__0__left:(forall (A_45:nat), (((eq nat) ((plus_plus_nat zero_zero_nat) A_45)) A_45)). % 1.35/1.52 Axiom fact_371_add__0__left:(forall (A_45:int), (((eq int) ((plus_plus_int zero_zero_int) A_45)) A_45)). % 1.35/1.52 Axiom fact_372_add__less__imp__less__left:(forall (C_23:real) (A_44:real) (B_37:real), (((ord_less_real ((plus_plus_real C_23) A_44)) ((plus_plus_real C_23) B_37))->((ord_less_real A_44) B_37))). % 1.35/1.52 Axiom fact_373_add__less__imp__less__left:(forall (C_23:nat) (A_44:nat) (B_37:nat), (((ord_less_nat ((plus_plus_nat C_23) A_44)) ((plus_plus_nat C_23) B_37))->((ord_less_nat A_44) B_37))). % 1.35/1.52 Axiom fact_374_add__less__imp__less__left:(forall (C_23:int) (A_44:int) (B_37:int), (((ord_less_int ((plus_plus_int C_23) A_44)) ((plus_plus_int C_23) B_37))->((ord_less_int A_44) B_37))). % 1.35/1.52 Axiom fact_375_add__less__imp__less__right:(forall (A_43:real) (C_22:real) (B_36:real), (((ord_less_real ((plus_plus_real A_43) C_22)) ((plus_plus_real B_36) C_22))->((ord_less_real A_43) B_36))). % 1.35/1.52 Axiom fact_376_add__less__imp__less__right:(forall (A_43:nat) (C_22:nat) (B_36:nat), (((ord_less_nat ((plus_plus_nat A_43) C_22)) ((plus_plus_nat B_36) C_22))->((ord_less_nat A_43) B_36))). % 1.35/1.52 Axiom fact_377_add__less__imp__less__right:(forall (A_43:int) (C_22:int) (B_36:int), (((ord_less_int ((plus_plus_int A_43) C_22)) ((plus_plus_int B_36) C_22))->((ord_less_int A_43) B_36))). % 1.35/1.52 Axiom fact_378_add__strict__mono:(forall (C_21:real) (D_3:real) (A_42:real) (B_35:real), (((ord_less_real A_42) B_35)->(((ord_less_real C_21) D_3)->((ord_less_real ((plus_plus_real A_42) C_21)) ((plus_plus_real B_35) D_3))))). % 1.35/1.52 Axiom fact_379_add__strict__mono:(forall (C_21:nat) (D_3:nat) (A_42:nat) (B_35:nat), (((ord_less_nat A_42) B_35)->(((ord_less_nat C_21) D_3)->((ord_less_nat ((plus_plus_nat A_42) C_21)) ((plus_plus_nat B_35) D_3))))). % 1.35/1.52 Axiom fact_380_add__strict__mono:(forall (C_21:int) (D_3:int) (A_42:int) (B_35:int), (((ord_less_int A_42) B_35)->(((ord_less_int C_21) D_3)->((ord_less_int ((plus_plus_int A_42) C_21)) ((plus_plus_int B_35) D_3))))). % 1.35/1.52 Axiom fact_381_add__strict__left__mono:(forall (C_20:real) (A_41:real) (B_34:real), (((ord_less_real A_41) B_34)->((ord_less_real ((plus_plus_real C_20) A_41)) ((plus_plus_real C_20) B_34)))). % 1.35/1.52 Axiom fact_382_add__strict__left__mono:(forall (C_20:nat) (A_41:nat) (B_34:nat), (((ord_less_nat A_41) B_34)->((ord_less_nat ((plus_plus_nat C_20) A_41)) ((plus_plus_nat C_20) B_34)))). % 1.35/1.52 Axiom fact_383_add__strict__left__mono:(forall (C_20:int) (A_41:int) (B_34:int), (((ord_less_int A_41) B_34)->((ord_less_int ((plus_plus_int C_20) A_41)) ((plus_plus_int C_20) B_34)))). % 1.35/1.52 Axiom fact_384_add__strict__right__mono:(forall (C_19:real) (A_40:real) (B_33:real), (((ord_less_real A_40) B_33)->((ord_less_real ((plus_plus_real A_40) C_19)) ((plus_plus_real B_33) C_19)))). % 1.35/1.52 Axiom fact_385_add__strict__right__mono:(forall (C_19:nat) (A_40:nat) (B_33:nat), (((ord_less_nat A_40) B_33)->((ord_less_nat ((plus_plus_nat A_40) C_19)) ((plus_plus_nat B_33) C_19)))). % 1.35/1.52 Axiom fact_386_add__strict__right__mono:(forall (C_19:int) (A_40:int) (B_33:int), (((ord_less_int A_40) B_33)->((ord_less_int ((plus_plus_int A_40) C_19)) ((plus_plus_int B_33) C_19)))). % 1.35/1.52 Axiom fact_387_add__less__cancel__left:(forall (C_18:real) (A_39:real) (B_32:real), ((iff ((ord_less_real ((plus_plus_real C_18) A_39)) ((plus_plus_real C_18) B_32))) ((ord_less_real A_39) B_32))). % 1.35/1.52 Axiom fact_388_add__less__cancel__left:(forall (C_18:nat) (A_39:nat) (B_32:nat), ((iff ((ord_less_nat ((plus_plus_nat C_18) A_39)) ((plus_plus_nat C_18) B_32))) ((ord_less_nat A_39) B_32))). % 1.35/1.52 Axiom fact_389_add__less__cancel__left:(forall (C_18:int) (A_39:int) (B_32:int), ((iff ((ord_less_int ((plus_plus_int C_18) A_39)) ((plus_plus_int C_18) B_32))) ((ord_less_int A_39) B_32))). % 1.35/1.52 Axiom fact_390_add__less__cancel__right:(forall (A_38:real) (C_17:real) (B_31:real), ((iff ((ord_less_real ((plus_plus_real A_38) C_17)) ((plus_plus_real B_31) C_17))) ((ord_less_real A_38) B_31))). % 1.35/1.52 Axiom fact_391_add__less__cancel__right:(forall (A_38:nat) (C_17:nat) (B_31:nat), ((iff ((ord_less_nat ((plus_plus_nat A_38) C_17)) ((plus_plus_nat B_31) C_17))) ((ord_less_nat A_38) B_31))). % 1.35/1.52 Axiom fact_392_add__less__cancel__right:(forall (A_38:int) (C_17:int) (B_31:int), ((iff ((ord_less_int ((plus_plus_int A_38) C_17)) ((plus_plus_int B_31) C_17))) ((ord_less_int A_38) B_31))). % 1.35/1.52 Axiom fact_393_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J:(forall (X_20:real), (((eq real) ((power_power_real X_20) one_one_nat)) X_20)). % 1.35/1.52 Axiom fact_394_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J:(forall (X_20:nat), (((eq nat) ((power_power_nat X_20) one_one_nat)) X_20)). % 1.35/1.52 Axiom fact_395_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J:(forall (X_20:int), (((eq int) ((power_power_int X_20) one_one_nat)) X_20)). % 1.35/1.52 Axiom fact_396_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)))). % 1.35/1.52 Axiom fact_397_add__neg__neg:(forall (B_30:real) (A_37:real), (((ord_less_real A_37) zero_zero_real)->(((ord_less_real B_30) zero_zero_real)->((ord_less_real ((plus_plus_real A_37) B_30)) zero_zero_real)))). % 1.35/1.53 Axiom fact_398_add__neg__neg:(forall (B_30:nat) (A_37:nat), (((ord_less_nat A_37) zero_zero_nat)->(((ord_less_nat B_30) zero_zero_nat)->((ord_less_nat ((plus_plus_nat A_37) B_30)) zero_zero_nat)))). % 1.35/1.53 Axiom fact_399_add__neg__neg:(forall (B_30:int) (A_37:int), (((ord_less_int A_37) zero_zero_int)->(((ord_less_int B_30) zero_zero_int)->((ord_less_int ((plus_plus_int A_37) B_30)) zero_zero_int)))). % 1.35/1.53 Axiom fact_400_add__pos__pos:(forall (B_29:real) (A_36:real), (((ord_less_real zero_zero_real) A_36)->(((ord_less_real zero_zero_real) B_29)->((ord_less_real zero_zero_real) ((plus_plus_real A_36) B_29))))). % 1.35/1.53 Axiom fact_401_add__pos__pos:(forall (B_29:nat) (A_36:nat), (((ord_less_nat zero_zero_nat) A_36)->(((ord_less_nat zero_zero_nat) B_29)->((ord_less_nat zero_zero_nat) ((plus_plus_nat A_36) B_29))))). % 1.35/1.53 Axiom fact_402_add__pos__pos:(forall (B_29:int) (A_36:int), (((ord_less_int zero_zero_int) A_36)->(((ord_less_int zero_zero_int) B_29)->((ord_less_int zero_zero_int) ((plus_plus_int A_36) B_29))))). % 1.35/1.53 Axiom fact_403_realpow__pos__nth__unique:(forall (A:real) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_real zero_zero_real) A)->((ex real) (fun (X_14:real)=> ((and ((and ((ord_less_real zero_zero_real) X_14)) (((eq real) ((power_power_real X_14) N)) A))) (forall (Y_18:real), (((and ((ord_less_real zero_zero_real) Y_18)) (((eq real) ((power_power_real Y_18) N)) A))->(((eq real) Y_18) X_14))))))))). % 1.35/1.53 Axiom fact_404_realpow__pos__nth:(forall (A:real) (N:nat), (((ord_less_nat zero_zero_nat) N)->(((ord_less_real zero_zero_real) A)->((ex real) (fun (R:real)=> ((and ((ord_less_real zero_zero_real) R)) (((eq real) ((power_power_real R) N)) A))))))). % 1.35/1.53 Axiom fact_405_tpos:((ord_less_eq_int one_one_int) t). % 1.35/1.53 Axiom fact_406_nat__number__of__add__1:(forall (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) one_one_nat)) one_one_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_1)) one_one_nat)) (number_number_of_nat (succ V_1)))))). % 1.35/1.53 Axiom fact_407_nat__1__add__number__of:(forall (V_1:int), ((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V_1))) one_one_nat))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V_1))) (number_number_of_nat (succ V_1)))))). % 1.35/1.53 Axiom fact_408_add__le__cancel__right:(forall (A_35:real) (C_16:real) (B_28:real), ((iff ((ord_less_eq_real ((plus_plus_real A_35) C_16)) ((plus_plus_real B_28) C_16))) ((ord_less_eq_real A_35) B_28))). % 1.35/1.53 Axiom fact_409_add__le__cancel__right:(forall (A_35:nat) (C_16:nat) (B_28:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat A_35) C_16)) ((plus_plus_nat B_28) C_16))) ((ord_less_eq_nat A_35) B_28))). % 1.35/1.53 Axiom fact_410_add__le__cancel__right:(forall (A_35:int) (C_16:int) (B_28:int), ((iff ((ord_less_eq_int ((plus_plus_int A_35) C_16)) ((plus_plus_int B_28) C_16))) ((ord_less_eq_int A_35) B_28))). % 1.35/1.53 Axiom fact_411_add__le__cancel__left:(forall (C_15:real) (A_34:real) (B_27:real), ((iff ((ord_less_eq_real ((plus_plus_real C_15) A_34)) ((plus_plus_real C_15) B_27))) ((ord_less_eq_real A_34) B_27))). % 1.35/1.53 Axiom fact_412_add__le__cancel__left:(forall (C_15:nat) (A_34:nat) (B_27:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat C_15) A_34)) ((plus_plus_nat C_15) B_27))) ((ord_less_eq_nat A_34) B_27))). % 1.35/1.53 Axiom fact_413_add__le__cancel__left:(forall (C_15:int) (A_34:int) (B_27:int), ((iff ((ord_less_eq_int ((plus_plus_int C_15) A_34)) ((plus_plus_int C_15) B_27))) ((ord_less_eq_int A_34) B_27))). % 1.35/1.53 Axiom fact_414_add__right__mono:(forall (C_14:real) (A_33:real) (B_26:real), (((ord_less_eq_real A_33) B_26)->((ord_less_eq_real ((plus_plus_real A_33) C_14)) ((plus_plus_real B_26) C_14)))). % 1.35/1.53 Axiom fact_415_add__right__mono:(forall (C_14:nat) (A_33:nat) (B_26:nat), (((ord_less_eq_nat A_33) B_26)->((ord_less_eq_nat ((plus_plus_nat A_33) C_14)) ((plus_plus_nat B_26) C_14)))). % 1.35/1.53 Axiom fact_416_add__right__mono:(forall (C_14:int) (A_33:int) (B_26:int), (((ord_less_eq_int A_33) B_26)->((ord_less_eq_int ((plus_plus_int A_33) C_14)) ((plus_plus_int B_26) C_14)))). % 1.35/1.53 Axiom fact_417_add__left__mono:(forall (C_13:real) (A_32:real) (B_25:real), (((ord_less_eq_real A_32) B_25)->((ord_less_eq_real ((plus_plus_real C_13) A_32)) ((plus_plus_real C_13) B_25)))). % 1.35/1.53 Axiom fact_418_add__left__mono:(forall (C_13:nat) (A_32:nat) (B_25:nat), (((ord_less_eq_nat A_32) B_25)->((ord_less_eq_nat ((plus_plus_nat C_13) A_32)) ((plus_plus_nat C_13) B_25)))). % 1.35/1.53 Axiom fact_419_add__left__mono:(forall (C_13:int) (A_32:int) (B_25:int), (((ord_less_eq_int A_32) B_25)->((ord_less_eq_int ((plus_plus_int C_13) A_32)) ((plus_plus_int C_13) B_25)))). % 1.35/1.53 Axiom fact_420_add__mono:(forall (C_12:real) (D_2:real) (A_31:real) (B_24:real), (((ord_less_eq_real A_31) B_24)->(((ord_less_eq_real C_12) D_2)->((ord_less_eq_real ((plus_plus_real A_31) C_12)) ((plus_plus_real B_24) D_2))))). % 1.35/1.53 Axiom fact_421_add__mono:(forall (C_12:nat) (D_2:nat) (A_31:nat) (B_24:nat), (((ord_less_eq_nat A_31) B_24)->(((ord_less_eq_nat C_12) D_2)->((ord_less_eq_nat ((plus_plus_nat A_31) C_12)) ((plus_plus_nat B_24) D_2))))). % 1.35/1.53 Axiom fact_422_add__mono:(forall (C_12:int) (D_2:int) (A_31:int) (B_24:int), (((ord_less_eq_int A_31) B_24)->(((ord_less_eq_int C_12) D_2)->((ord_less_eq_int ((plus_plus_int A_31) C_12)) ((plus_plus_int B_24) D_2))))). % 1.35/1.53 Axiom fact_423_add__le__imp__le__right:(forall (A_30:real) (C_11:real) (B_23:real), (((ord_less_eq_real ((plus_plus_real A_30) C_11)) ((plus_plus_real B_23) C_11))->((ord_less_eq_real A_30) B_23))). % 1.35/1.53 Axiom fact_424_add__le__imp__le__right:(forall (A_30:nat) (C_11:nat) (B_23:nat), (((ord_less_eq_nat ((plus_plus_nat A_30) C_11)) ((plus_plus_nat B_23) C_11))->((ord_less_eq_nat A_30) B_23))). % 1.35/1.53 Axiom fact_425_add__le__imp__le__right:(forall (A_30:int) (C_11:int) (B_23:int), (((ord_less_eq_int ((plus_plus_int A_30) C_11)) ((plus_plus_int B_23) C_11))->((ord_less_eq_int A_30) B_23))). % 1.35/1.53 Axiom fact_426_add__le__imp__le__left:(forall (C_10:real) (A_29:real) (B_22:real), (((ord_less_eq_real ((plus_plus_real C_10) A_29)) ((plus_plus_real C_10) B_22))->((ord_less_eq_real A_29) B_22))). % 1.35/1.53 Axiom fact_427_add__le__imp__le__left:(forall (C_10:nat) (A_29:nat) (B_22:nat), (((ord_less_eq_nat ((plus_plus_nat C_10) A_29)) ((plus_plus_nat C_10) B_22))->((ord_less_eq_nat A_29) B_22))). % 1.35/1.53 Axiom fact_428_add__le__imp__le__left:(forall (C_10:int) (A_29:int) (B_22:int), (((ord_less_eq_int ((plus_plus_int C_10) A_29)) ((plus_plus_int C_10) B_22))->((ord_less_eq_int A_29) B_22))). % 1.35/1.53 Axiom fact_429_power__increasing:(forall (A_28:real) (N_14:nat) (N_13:nat), (((ord_less_eq_nat N_14) N_13)->(((ord_less_eq_real one_one_real) A_28)->((ord_less_eq_real ((power_power_real A_28) N_14)) ((power_power_real A_28) N_13))))). % 1.35/1.53 Axiom fact_430_power__increasing:(forall (A_28:nat) (N_14:nat) (N_13:nat), (((ord_less_eq_nat N_14) N_13)->(((ord_less_eq_nat one_one_nat) A_28)->((ord_less_eq_nat ((power_power_nat A_28) N_14)) ((power_power_nat A_28) N_13))))). % 1.35/1.53 Axiom fact_431_power__increasing:(forall (A_28:int) (N_14:nat) (N_13:nat), (((ord_less_eq_nat N_14) N_13)->(((ord_less_eq_int one_one_int) A_28)->((ord_less_eq_int ((power_power_int A_28) N_14)) ((power_power_int A_28) N_13))))). % 1.35/1.53 Axiom fact_432_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))). % 1.35/1.53 Axiom fact_433_rel__simps_I34_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit1 L))) ((ord_less_eq_int K) L))). % 1.35/1.53 Axiom fact_434_rel__simps_I19_J:((ord_less_eq_int pls) pls). % 1.35/1.53 Axiom fact_435_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))). % 1.35/1.53 Axiom fact_436_rel__simps_I31_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit0 L))) ((ord_less_eq_int K) L))). % 1.35/1.53 Axiom fact_437_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J:((ord_less_eq_int zero_zero_int) zero_zero_int). % 1.35/1.53 Axiom fact_438_zle__refl:(forall (W:int), ((ord_less_eq_int W) W)). % 1.35/1.53 Axiom fact_439_zle__linear:(forall (Z_2:int) (W:int), ((or ((ord_less_eq_int Z_2) W)) ((ord_less_eq_int W) Z_2))). % 1.35/1.53 Axiom fact_440_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)))). % 1.35/1.53 Axiom fact_441_zle__antisym:(forall (Z_2:int) (W:int), (((ord_less_eq_int Z_2) W)->(((ord_less_eq_int W) Z_2)->(((eq int) Z_2) W)))). % 1.35/1.53 Axiom fact_442_le__number__of:(forall (X_19:int) (Y_17:int), ((iff ((ord_less_eq_real (number267125858f_real X_19)) (number267125858f_real Y_17))) ((ord_less_eq_int X_19) Y_17))). % 1.35/1.53 Axiom fact_443_le__number__of:(forall (X_19:int) (Y_17:int), ((iff ((ord_less_eq_int (number_number_of_int X_19)) (number_number_of_int Y_17))) ((ord_less_eq_int X_19) Y_17))). % 1.35/1.53 Axiom fact_444_of__nat__le__iff:(forall (M_4:nat) (N_12:nat), ((iff ((ord_less_eq_real (semiri132038758t_real M_4)) (semiri132038758t_real N_12))) ((ord_less_eq_nat M_4) N_12))). % 1.35/1.53 Axiom fact_445_of__nat__le__iff:(forall (M_4:nat) (N_12:nat), ((iff ((ord_less_eq_nat (semiri984289939at_nat M_4)) (semiri984289939at_nat N_12))) ((ord_less_eq_nat M_4) N_12))). % 1.35/1.53 Axiom fact_446_of__nat__le__iff:(forall (M_4:nat) (N_12:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int M_4)) (semiri1621563631at_int N_12))) ((ord_less_eq_nat M_4) N_12))). % 1.35/1.53 Axiom fact_447_zless__le:(forall (Z_2:int) (W:int), ((iff ((ord_less_int Z_2) W)) ((and ((ord_less_eq_int Z_2) W)) (not (((eq int) Z_2) W))))). % 1.35/1.53 Axiom fact_448_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)))). % 1.35/1.53 Axiom fact_449_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))). % 1.35/1.53 Axiom fact_450_le__special_I1_J:(forall (Y_16:int), ((iff ((ord_less_eq_real zero_zero_real) (number267125858f_real Y_16))) ((ord_less_eq_int pls) Y_16))). % 1.35/1.53 Axiom fact_451_le__special_I1_J:(forall (Y_16:int), ((iff ((ord_less_eq_int zero_zero_int) (number_number_of_int Y_16))) ((ord_less_eq_int pls) Y_16))). % 1.35/1.53 Axiom fact_452_le__special_I3_J:(forall (X_18:int), ((iff ((ord_less_eq_real (number267125858f_real X_18)) zero_zero_real)) ((ord_less_eq_int X_18) pls))). % 1.35/1.53 Axiom fact_453_le__special_I3_J:(forall (X_18:int), ((iff ((ord_less_eq_int (number_number_of_int X_18)) zero_zero_int)) ((ord_less_eq_int X_18) pls))). % 1.35/1.53 Axiom fact_454_power__decreasing:(forall (A_27:real) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_real zero_zero_real) A_27)->(((ord_less_eq_real A_27) one_one_real)->((ord_less_eq_real ((power_power_real A_27) N_10)) ((power_power_real A_27) N_11)))))). % 1.35/1.53 Axiom fact_455_power__decreasing:(forall (A_27:nat) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_nat zero_zero_nat) A_27)->(((ord_less_eq_nat A_27) one_one_nat)->((ord_less_eq_nat ((power_power_nat A_27) N_10)) ((power_power_nat A_27) N_11)))))). % 1.35/1.53 Axiom fact_456_power__decreasing:(forall (A_27:int) (N_11:nat) (N_10:nat), (((ord_less_eq_nat N_11) N_10)->(((ord_less_eq_int zero_zero_int) A_27)->(((ord_less_eq_int A_27) one_one_int)->((ord_less_eq_int ((power_power_int A_27) N_10)) ((power_power_int A_27) N_11)))))). % 1.35/1.53 Axiom fact_457_power__increasing__iff:(forall (X_17:nat) (Y_15:nat) (B_21:real), (((ord_less_real one_one_real) B_21)->((iff ((ord_less_eq_real ((power_power_real B_21) X_17)) ((power_power_real B_21) Y_15))) ((ord_less_eq_nat X_17) Y_15)))). % 1.35/1.53 Axiom fact_458_power__increasing__iff:(forall (X_17:nat) (Y_15:nat) (B_21:nat), (((ord_less_nat one_one_nat) B_21)->((iff ((ord_less_eq_nat ((power_power_nat B_21) X_17)) ((power_power_nat B_21) Y_15))) ((ord_less_eq_nat X_17) Y_15)))). % 1.35/1.53 Axiom fact_459_power__increasing__iff:(forall (X_17:nat) (Y_15:nat) (B_21:int), (((ord_less_int one_one_int) B_21)->((iff ((ord_less_eq_int ((power_power_int B_21) X_17)) ((power_power_int B_21) Y_15))) ((ord_less_eq_nat X_17) Y_15)))). % 1.35/1.53 Axiom fact_460_power__le__imp__le__exp:(forall (M_3:nat) (N_9:nat) (A_26:real), (((ord_less_real one_one_real) A_26)->(((ord_less_eq_real ((power_power_real A_26) M_3)) ((power_power_real A_26) N_9))->((ord_less_eq_nat M_3) N_9)))). % 1.35/1.53 Axiom fact_461_power__le__imp__le__exp:(forall (M_3:nat) (N_9:nat) (A_26:nat), (((ord_less_nat one_one_nat) A_26)->(((ord_less_eq_nat ((power_power_nat A_26) M_3)) ((power_power_nat A_26) N_9))->((ord_less_eq_nat M_3) N_9)))). % 1.35/1.53 Axiom fact_462_power__le__imp__le__exp:(forall (M_3:nat) (N_9:nat) (A_26:int), (((ord_less_int one_one_int) A_26)->(((ord_less_eq_int ((power_power_int A_26) M_3)) ((power_power_int A_26) N_9))->((ord_less_eq_nat M_3) N_9)))). % 1.35/1.53 Axiom fact_463_le__special_I2_J:(forall (Y_14:int), ((iff ((ord_less_eq_real one_one_real) (number267125858f_real Y_14))) ((ord_less_eq_int (bit1 pls)) Y_14))). % 1.35/1.53 Axiom fact_464_le__special_I2_J:(forall (Y_14:int), ((iff ((ord_less_eq_int one_one_int) (number_number_of_int Y_14))) ((ord_less_eq_int (bit1 pls)) Y_14))). % 1.35/1.53 Axiom fact_465_le__special_I4_J:(forall (X_16:int), ((iff ((ord_less_eq_real (number267125858f_real X_16)) one_one_real)) ((ord_less_eq_int X_16) (bit1 pls)))). % 1.35/1.53 Axiom fact_466_le__special_I4_J:(forall (X_16:int), ((iff ((ord_less_eq_int (number_number_of_int X_16)) one_one_int)) ((ord_less_eq_int X_16) (bit1 pls)))). % 1.35/1.53 Axiom fact_467_zero__le__double__add__iff__zero__le__single__add:(forall (A_25:real), ((iff ((ord_less_eq_real zero_zero_real) ((plus_plus_real A_25) A_25))) ((ord_less_eq_real zero_zero_real) A_25))). % 1.35/1.53 Axiom fact_468_zero__le__double__add__iff__zero__le__single__add:(forall (A_25:int), ((iff ((ord_less_eq_int zero_zero_int) ((plus_plus_int A_25) A_25))) ((ord_less_eq_int zero_zero_int) A_25))). % 1.35/1.53 Axiom fact_469_double__add__le__zero__iff__single__add__le__zero:(forall (A_24:real), ((iff ((ord_less_eq_real ((plus_plus_real A_24) A_24)) zero_zero_real)) ((ord_less_eq_real A_24) zero_zero_real))). % 1.35/1.53 Axiom fact_470_double__add__le__zero__iff__single__add__le__zero:(forall (A_24:int), ((iff ((ord_less_eq_int ((plus_plus_int A_24) A_24)) zero_zero_int)) ((ord_less_eq_int A_24) zero_zero_int))). % 1.35/1.53 Axiom fact_471_add__nonneg__nonneg:(forall (B_20:real) (A_23:real), (((ord_less_eq_real zero_zero_real) A_23)->(((ord_less_eq_real zero_zero_real) B_20)->((ord_less_eq_real zero_zero_real) ((plus_plus_real A_23) B_20))))). % 1.35/1.53 Axiom fact_472_add__nonneg__nonneg:(forall (B_20:nat) (A_23:nat), (((ord_less_eq_nat zero_zero_nat) A_23)->(((ord_less_eq_nat zero_zero_nat) B_20)->((ord_less_eq_nat zero_zero_nat) ((plus_plus_nat A_23) B_20))))). % 1.35/1.53 Axiom fact_473_add__nonneg__nonneg:(forall (B_20:int) (A_23:int), (((ord_less_eq_int zero_zero_int) A_23)->(((ord_less_eq_int zero_zero_int) B_20)->((ord_less_eq_int zero_zero_int) ((plus_plus_int A_23) B_20))))). % 1.35/1.53 Axiom fact_474_add__nonneg__eq__0__iff:(forall (Y_13:real) (X_15:real), (((ord_less_eq_real zero_zero_real) X_15)->(((ord_less_eq_real zero_zero_real) Y_13)->((iff (((eq real) ((plus_plus_real X_15) Y_13)) zero_zero_real)) ((and (((eq real) X_15) zero_zero_real)) (((eq real) Y_13) zero_zero_real)))))). % 1.35/1.53 Axiom fact_475_add__nonneg__eq__0__iff:(forall (Y_13:nat) (X_15:nat), (((ord_less_eq_nat zero_zero_nat) X_15)->(((ord_less_eq_nat zero_zero_nat) Y_13)->((iff (((eq nat) ((plus_plus_nat X_15) Y_13)) zero_zero_nat)) ((and (((eq nat) X_15) zero_zero_nat)) (((eq nat) Y_13) zero_zero_nat)))))). % 1.35/1.53 Axiom fact_476_add__nonneg__eq__0__iff:(forall (Y_13:int) (X_15:int), (((ord_less_eq_int zero_zero_int) X_15)->(((ord_less_eq_int zero_zero_int) Y_13)->((iff (((eq int) ((plus_plus_int X_15) Y_13)) zero_zero_int)) ((and (((eq int) X_15) zero_zero_int)) (((eq int) Y_13) zero_zero_int)))))). % 1.35/1.53 Axiom fact_477_add__increasing:(forall (B_19:real) (C_9:real) (A_22:real), (((ord_less_eq_real zero_zero_real) A_22)->(((ord_less_eq_real B_19) C_9)->((ord_less_eq_real B_19) ((plus_plus_real A_22) C_9))))). % 1.35/1.53 Axiom fact_478_add__increasing:(forall (B_19:nat) (C_9:nat) (A_22:nat), (((ord_less_eq_nat zero_zero_nat) A_22)->(((ord_less_eq_nat B_19) C_9)->((ord_less_eq_nat B_19) ((plus_plus_nat A_22) C_9))))). % 1.35/1.53 Axiom fact_479_add__increasing:(forall (B_19:int) (C_9:int) (A_22:int), (((ord_less_eq_int zero_zero_int) A_22)->(((ord_less_eq_int B_19) C_9)->((ord_less_eq_int B_19) ((plus_plus_int A_22) C_9))))). % 1.35/1.53 Axiom fact_480_add__increasing2:(forall (B_18:real) (A_21:real) (C_8:real), (((ord_less_eq_real zero_zero_real) C_8)->(((ord_less_eq_real B_18) A_21)->((ord_less_eq_real B_18) ((plus_plus_real A_21) C_8))))). % 1.35/1.53 Axiom fact_481_add__increasing2:(forall (B_18:nat) (A_21:nat) (C_8:nat), (((ord_less_eq_nat zero_zero_nat) C_8)->(((ord_less_eq_nat B_18) A_21)->((ord_less_eq_nat B_18) ((plus_plus_nat A_21) C_8))))). % 1.35/1.53 Axiom fact_482_add__increasing2:(forall (B_18:int) (A_21:int) (C_8:int), (((ord_less_eq_int zero_zero_int) C_8)->(((ord_less_eq_int B_18) A_21)->((ord_less_eq_int B_18) ((plus_plus_int A_21) C_8))))). % 1.35/1.53 Axiom fact_483_add__nonpos__nonpos:(forall (B_17:real) (A_20:real), (((ord_less_eq_real A_20) zero_zero_real)->(((ord_less_eq_real B_17) zero_zero_real)->((ord_less_eq_real ((plus_plus_real A_20) B_17)) zero_zero_real)))). % 1.35/1.53 Axiom fact_484_add__nonpos__nonpos:(forall (B_17:nat) (A_20:nat), (((ord_less_eq_nat A_20) zero_zero_nat)->(((ord_less_eq_nat B_17) zero_zero_nat)->((ord_less_eq_nat ((plus_plus_nat A_20) B_17)) zero_zero_nat)))). % 1.35/1.53 Axiom fact_485_add__nonpos__nonpos:(forall (B_17:int) (A_20:int), (((ord_less_eq_int A_20) zero_zero_int)->(((ord_less_eq_int B_17) zero_zero_int)->((ord_less_eq_int ((plus_plus_int A_20) B_17)) zero_zero_int)))). % 1.35/1.53 Axiom fact_486_add__less__le__mono:(forall (C_7:real) (D_1:real) (A_19:real) (B_16:real), (((ord_less_real A_19) B_16)->(((ord_less_eq_real C_7) D_1)->((ord_less_real ((plus_plus_real A_19) C_7)) ((plus_plus_real B_16) D_1))))). % 1.35/1.53 Axiom fact_487_add__less__le__mono:(forall (C_7:nat) (D_1:nat) (A_19:nat) (B_16:nat), (((ord_less_nat A_19) B_16)->(((ord_less_eq_nat C_7) D_1)->((ord_less_nat ((plus_plus_nat A_19) C_7)) ((plus_plus_nat B_16) D_1))))). % 1.35/1.53 Axiom fact_488_add__less__le__mono:(forall (C_7:int) (D_1:int) (A_19:int) (B_16:int), (((ord_less_int A_19) B_16)->(((ord_less_eq_int C_7) D_1)->((ord_less_int ((plus_plus_int A_19) C_7)) ((plus_plus_int B_16) D_1))))). % 1.35/1.53 Axiom fact_489_add__le__less__mono:(forall (C_6:real) (D:real) (A_18:real) (B_15:real), (((ord_less_eq_real A_18) B_15)->(((ord_less_real C_6) D)->((ord_less_real ((plus_plus_real A_18) C_6)) ((plus_plus_real B_15) D))))). % 1.35/1.53 Axiom fact_490_add__le__less__mono:(forall (C_6:nat) (D:nat) (A_18:nat) (B_15:nat), (((ord_less_eq_nat A_18) B_15)->(((ord_less_nat C_6) D)->((ord_less_nat ((plus_plus_nat A_18) C_6)) ((plus_plus_nat B_15) D))))). % 1.35/1.53 Axiom fact_491_add__le__less__mono:(forall (C_6:int) (D:int) (A_18:int) (B_15:int), (((ord_less_eq_int A_18) B_15)->(((ord_less_int C_6) D)->((ord_less_int ((plus_plus_int A_18) C_6)) ((plus_plus_int B_15) D))))). % 1.35/1.53 Axiom fact_492_not__one__le__zero:(((ord_less_eq_real one_one_real) zero_zero_real)->False). % 1.35/1.53 Axiom fact_493_not__one__le__zero:(((ord_less_eq_nat one_one_nat) zero_zero_nat)->False). % 1.35/1.53 Axiom fact_494_not__one__le__zero:(((ord_less_eq_int one_one_int) zero_zero_int)->False). % 1.35/1.53 Axiom fact_495_zero__le__one:((ord_less_eq_real zero_zero_real) one_one_real). % 1.35/1.53 Axiom fact_496_zero__le__one:((ord_less_eq_nat zero_zero_nat) one_one_nat). % 1.35/1.53 Axiom fact_497_zero__le__one:((ord_less_eq_int zero_zero_int) one_one_int). % 1.35/1.53 Axiom fact_498_le__number__of__eq__not__less:(forall (V_7:int) (W_2:int), ((iff ((ord_less_eq_real (number267125858f_real V_7)) (number267125858f_real W_2))) (((ord_less_real (number267125858f_real W_2)) (number267125858f_real V_7))->False))). % 1.35/1.53 Axiom fact_499_le__number__of__eq__not__less:(forall (V_7:int) (W_2:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_7)) (number_number_of_nat W_2))) (((ord_less_nat (number_number_of_nat W_2)) (number_number_of_nat V_7))->False))). % 1.35/1.53 Axiom fact_500_le__number__of__eq__not__less:(forall (V_7:int) (W_2:int), ((iff ((ord_less_eq_int (number_number_of_int V_7)) (number_number_of_int W_2))) (((ord_less_int (number_number_of_int W_2)) (number_number_of_int V_7))->False))). % 1.35/1.53 Axiom fact_501_zero__le__power:(forall (N_8:nat) (A_17:real), (((ord_less_eq_real zero_zero_real) A_17)->((ord_less_eq_real zero_zero_real) ((power_power_real A_17) N_8)))). % 1.35/1.53 Axiom fact_502_zero__le__power:(forall (N_8:nat) (A_17:nat), (((ord_less_eq_nat zero_zero_nat) A_17)->((ord_less_eq_nat zero_zero_nat) ((power_power_nat A_17) N_8)))). % 1.35/1.53 Axiom fact_503_zero__le__power:(forall (N_8:nat) (A_17:int), (((ord_less_eq_int zero_zero_int) A_17)->((ord_less_eq_int zero_zero_int) ((power_power_int A_17) N_8)))). % 1.35/1.53 Axiom fact_504_power__mono:(forall (N_7:nat) (A_16:real) (B_14:real), (((ord_less_eq_real A_16) B_14)->(((ord_less_eq_real zero_zero_real) A_16)->((ord_less_eq_real ((power_power_real A_16) N_7)) ((power_power_real B_14) N_7))))). % 1.35/1.53 Axiom fact_505_power__mono:(forall (N_7:nat) (A_16:nat) (B_14:nat), (((ord_less_eq_nat A_16) B_14)->(((ord_less_eq_nat zero_zero_nat) A_16)->((ord_less_eq_nat ((power_power_nat A_16) N_7)) ((power_power_nat B_14) N_7))))). % 1.35/1.53 Axiom fact_506_power__mono:(forall (N_7:nat) (A_16:int) (B_14:int), (((ord_less_eq_int A_16) B_14)->(((ord_less_eq_int zero_zero_int) A_16)->((ord_less_eq_int ((power_power_int A_16) N_7)) ((power_power_int B_14) N_7))))). % 1.35/1.53 Axiom fact_507_one__le__power:(forall (N_6:nat) (A_15:real), (((ord_less_eq_real one_one_real) A_15)->((ord_less_eq_real one_one_real) ((power_power_real A_15) N_6)))). % 1.35/1.53 Axiom fact_508_one__le__power:(forall (N_6:nat) (A_15:nat), (((ord_less_eq_nat one_one_nat) A_15)->((ord_less_eq_nat one_one_nat) ((power_power_nat A_15) N_6)))). % 1.35/1.53 Axiom fact_509_one__le__power:(forall (N_6:nat) (A_15:int), (((ord_less_eq_int one_one_int) A_15)->((ord_less_eq_int one_one_int) ((power_power_int A_15) N_6)))). % 1.35/1.53 Axiom fact_510_zero__le__imp__of__nat:(forall (M_2:nat), ((ord_less_eq_real zero_zero_real) (semiri132038758t_real M_2))). % 1.35/1.53 Axiom fact_511_zero__le__imp__of__nat:(forall (M_2:nat), ((ord_less_eq_nat zero_zero_nat) (semiri984289939at_nat M_2))). % 1.35/1.53 Axiom fact_512_zero__le__imp__of__nat:(forall (M_2:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int M_2))). % 1.35/1.53 Axiom fact_513_of__nat__0__le__iff:(forall (N_5:nat), ((ord_less_eq_real zero_zero_real) (semiri132038758t_real N_5))). % 1.35/1.53 Axiom fact_514_of__nat__0__le__iff:(forall (N_5:nat), ((ord_less_eq_nat zero_zero_nat) (semiri984289939at_nat N_5))). % 1.35/1.53 Axiom fact_515_of__nat__0__le__iff:(forall (N_5:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int N_5))). % 1.35/1.53 Axiom fact_516_rel__simps_I22_J:(forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K))). % 1.35/1.53 Axiom fact_517_rel__simps_I32_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))). % 1.35/1.53 Axiom fact_518_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))). % 1.35/1.53 Axiom fact_519_rel__simps_I21_J:(forall (K:int), ((iff ((ord_less_eq_int pls) (bit0 K))) ((ord_less_eq_int pls) K))). % 1.35/1.53 Axiom fact_520_rel__simps_I27_J:(forall (K:int), ((iff ((ord_less_eq_int (bit0 K)) pls)) ((ord_less_eq_int K) pls))). % 1.35/1.53 Axiom fact_521_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J:((ord_less_eq_int zero_zero_int) one_one_int). % 1.35/1.53 Axiom fact_522_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J:(forall (Y:int) (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_eq_int zero_zero_int) Y)->((ord_less_eq_int zero_zero_int) ((plus_plus_int X) Y))))). % 1.35/1.53 Axiom fact_523_zadd__zless__mono:(forall (Z_3:int) (Z_2:int) (W_1:int) (W:int), (((ord_less_int W_1) W)->(((ord_less_eq_int Z_3) Z_2)->((ord_less_int ((plus_plus_int W_1) Z_3)) ((plus_plus_int W) Z_2))))). % 1.35/1.53 Axiom fact_524_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J:(forall (Z_2:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int Z_2))). % 1.35/1.53 Axiom fact_525_transfer__int__nat__quantifiers_I2_J:(forall (P:(int->Prop)), ((iff ((ex int) (fun (X_14:int)=> ((and ((ord_less_eq_int zero_zero_int) X_14)) (P X_14))))) ((ex nat) (fun (X_14:nat)=> (P (semiri1621563631at_int X_14)))))). % 1.35/1.53 Axiom fact_526_transfer__int__nat__quantifiers_I1_J:(forall (P:(int->Prop)), ((iff (forall (X_14:int), (((ord_less_eq_int zero_zero_int) X_14)->(P X_14)))) (forall (X_14:nat), (P (semiri1621563631at_int X_14))))). % 1.35/1.53 Axiom fact_527_zero__zle__int:(forall (N:nat), ((ord_less_eq_int zero_zero_int) (semiri1621563631at_int N))). % 1.35/1.53 Axiom fact_528_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J:(forall (N:nat) (X:int), (((ord_less_eq_int zero_zero_int) X)->((ord_less_eq_int zero_zero_int) ((power_power_int X) N)))). % 1.35/1.54 Axiom fact_529_zle__iff__zadd:(forall (W:int) (Z_2:int), ((iff ((ord_less_eq_int W) Z_2)) ((ex nat) (fun (N_1:nat)=> (((eq int) Z_2) ((plus_plus_int W) (semiri1621563631at_int N_1))))))). % 1.35/1.54 Axiom fact_530_semiring__1__add__number__of:(forall (V_6:int), (((ord_less_eq_int pls) V_6)->(((eq real) ((plus_plus_real one_one_real) (number267125858f_real V_6))) (number267125858f_real (succ V_6))))). % 1.35/1.54 Axiom fact_531_semiring__1__add__number__of:(forall (V_6:int), (((ord_less_eq_int pls) V_6)->(((eq nat) ((plus_plus_nat one_one_nat) (number_number_of_nat V_6))) (number_number_of_nat (succ V_6))))). % 1.35/1.54 Axiom fact_532_semiring__1__add__number__of:(forall (V_6:int), (((ord_less_eq_int pls) V_6)->(((eq int) ((plus_plus_int one_one_int) (number_number_of_int V_6))) (number_number_of_int (succ V_6))))). % 1.35/1.54 Axiom fact_533_semiring__number__of__add__1:(forall (V_5:int), (((ord_less_eq_int pls) V_5)->(((eq real) ((plus_plus_real (number267125858f_real V_5)) one_one_real)) (number267125858f_real (succ V_5))))). % 1.35/1.54 Axiom fact_534_semiring__number__of__add__1:(forall (V_5:int), (((ord_less_eq_int pls) V_5)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_5)) one_one_nat)) (number_number_of_nat (succ V_5))))). % 1.35/1.54 Axiom fact_535_semiring__number__of__add__1:(forall (V_5:int), (((ord_less_eq_int pls) V_5)->(((eq int) ((plus_plus_int (number_number_of_int V_5)) one_one_int)) (number_number_of_int (succ V_5))))). % 1.35/1.54 Axiom fact_536_add__pos__nonneg:(forall (B_13:real) (A_14:real), (((ord_less_real zero_zero_real) A_14)->(((ord_less_eq_real zero_zero_real) B_13)->((ord_less_real zero_zero_real) ((plus_plus_real A_14) B_13))))). % 1.35/1.54 Axiom fact_537_add__pos__nonneg:(forall (B_13:nat) (A_14:nat), (((ord_less_nat zero_zero_nat) A_14)->(((ord_less_eq_nat zero_zero_nat) B_13)->((ord_less_nat zero_zero_nat) ((plus_plus_nat A_14) B_13))))). % 1.35/1.54 Axiom fact_538_add__pos__nonneg:(forall (B_13:int) (A_14:int), (((ord_less_int zero_zero_int) A_14)->(((ord_less_eq_int zero_zero_int) B_13)->((ord_less_int zero_zero_int) ((plus_plus_int A_14) B_13))))). % 1.35/1.54 Axiom fact_539_add__nonneg__pos:(forall (B_12:real) (A_13:real), (((ord_less_eq_real zero_zero_real) A_13)->(((ord_less_real zero_zero_real) B_12)->((ord_less_real zero_zero_real) ((plus_plus_real A_13) B_12))))). % 1.35/1.54 Axiom fact_540_add__nonneg__pos:(forall (B_12:nat) (A_13:nat), (((ord_less_eq_nat zero_zero_nat) A_13)->(((ord_less_nat zero_zero_nat) B_12)->((ord_less_nat zero_zero_nat) ((plus_plus_nat A_13) B_12))))). % 1.35/1.54 Axiom fact_541_add__nonneg__pos:(forall (B_12:int) (A_13:int), (((ord_less_eq_int zero_zero_int) A_13)->(((ord_less_int zero_zero_int) B_12)->((ord_less_int zero_zero_int) ((plus_plus_int A_13) B_12))))). % 1.35/1.54 Axiom fact_542_add__strict__increasing:(forall (B_11:real) (C_5:real) (A_12:real), (((ord_less_real zero_zero_real) A_12)->(((ord_less_eq_real B_11) C_5)->((ord_less_real B_11) ((plus_plus_real A_12) C_5))))). % 1.35/1.54 Axiom fact_543_add__strict__increasing:(forall (B_11:nat) (C_5:nat) (A_12:nat), (((ord_less_nat zero_zero_nat) A_12)->(((ord_less_eq_nat B_11) C_5)->((ord_less_nat B_11) ((plus_plus_nat A_12) C_5))))). % 1.35/1.54 Axiom fact_544_add__strict__increasing:(forall (B_11:int) (C_5:int) (A_12:int), (((ord_less_int zero_zero_int) A_12)->(((ord_less_eq_int B_11) C_5)->((ord_less_int B_11) ((plus_plus_int A_12) C_5))))). % 1.35/1.54 Axiom fact_545_add__strict__increasing2:(forall (B_10:real) (C_4:real) (A_11:real), (((ord_less_eq_real zero_zero_real) A_11)->(((ord_less_real B_10) C_4)->((ord_less_real B_10) ((plus_plus_real A_11) C_4))))). % 1.35/1.54 Axiom fact_546_add__strict__increasing2:(forall (B_10:nat) (C_4:nat) (A_11:nat), (((ord_less_eq_nat zero_zero_nat) A_11)->(((ord_less_nat B_10) C_4)->((ord_less_nat B_10) ((plus_plus_nat A_11) C_4))))). % 1.35/1.54 Axiom fact_547_add__strict__increasing2:(forall (B_10:int) (C_4:int) (A_11:int), (((ord_less_eq_int zero_zero_int) A_11)->(((ord_less_int B_10) C_4)->((ord_less_int B_10) ((plus_plus_int A_11) C_4))))). % 1.35/1.54 Axiom fact_548_add__neg__nonpos:(forall (B_9:real) (A_10:real), (((ord_less_real A_10) zero_zero_real)->(((ord_less_eq_real B_9) zero_zero_real)->((ord_less_real ((plus_plus_real A_10) B_9)) zero_zero_real)))). % 1.35/1.54 Axiom fact_549_add__neg__nonpos:(forall (B_9:nat) (A_10:nat), (((ord_less_nat A_10) zero_zero_nat)->(((ord_less_eq_nat B_9) zero_zero_nat)->((ord_less_nat ((plus_plus_nat A_10) B_9)) zero_zero_nat)))). % 1.35/1.54 Axiom fact_550_add__neg__nonpos:(forall (B_9:int) (A_10:int), (((ord_less_int A_10) zero_zero_int)->(((ord_less_eq_int B_9) zero_zero_int)->((ord_less_int ((plus_plus_int A_10) B_9)) zero_zero_int)))). % 1.35/1.54 Axiom fact_551_add__nonpos__neg:(forall (B_8:real) (A_9:real), (((ord_less_eq_real A_9) zero_zero_real)->(((ord_less_real B_8) zero_zero_real)->((ord_less_real ((plus_plus_real A_9) B_8)) zero_zero_real)))). % 1.35/1.54 Axiom fact_552_add__nonpos__neg:(forall (B_8:nat) (A_9:nat), (((ord_less_eq_nat A_9) zero_zero_nat)->(((ord_less_nat B_8) zero_zero_nat)->((ord_less_nat ((plus_plus_nat A_9) B_8)) zero_zero_nat)))). % 1.35/1.54 Axiom fact_553_add__nonpos__neg:(forall (B_8:int) (A_9:int), (((ord_less_eq_int A_9) zero_zero_int)->(((ord_less_int B_8) zero_zero_int)->((ord_less_int ((plus_plus_int A_9) B_8)) zero_zero_int)))). % 1.35/1.54 Axiom fact_554_power__less__imp__less__base:(forall (A_8:real) (N_4:nat) (B_7:real), (((ord_less_real ((power_power_real A_8) N_4)) ((power_power_real B_7) N_4))->(((ord_less_eq_real zero_zero_real) B_7)->((ord_less_real A_8) B_7)))). % 1.35/1.54 Axiom fact_555_power__less__imp__less__base:(forall (A_8:nat) (N_4:nat) (B_7:nat), (((ord_less_nat ((power_power_nat A_8) N_4)) ((power_power_nat B_7) N_4))->(((ord_less_eq_nat zero_zero_nat) B_7)->((ord_less_nat A_8) B_7)))). % 1.35/1.54 Axiom fact_556_power__less__imp__less__base:(forall (A_8:int) (N_4:nat) (B_7:int), (((ord_less_int ((power_power_int A_8) N_4)) ((power_power_int B_7) N_4))->(((ord_less_eq_int zero_zero_int) B_7)->((ord_less_int A_8) B_7)))). % 1.35/1.54 Axiom fact_557_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))). % 1.35/1.54 Axiom fact_558_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))). % 1.35/1.54 Axiom fact_559_rel__simps_I5_J:(forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K))). % 1.35/1.54 Axiom fact_560_rel__simps_I29_J:(forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls))). % 1.35/1.54 Axiom fact_561_rel__simps_I15_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))). % 1.35/1.54 Axiom fact_562_less__int__code_I14_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))). % 1.35/1.54 Axiom fact_563_rel__simps_I33_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))). % 1.35/1.54 Axiom fact_564_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))). % 1.35/1.54 Axiom fact_565_int__one__le__iff__zero__less:(forall (Z_2:int), ((iff ((ord_less_eq_int one_one_int) Z_2)) ((ord_less_int zero_zero_int) Z_2))). % 1.35/1.54 Axiom fact_566_int__le__0__conv:(forall (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int N)) zero_zero_int)) (((eq nat) N) zero_zero_nat))). % 1.35/1.54 Axiom fact_567_succ__Pls:(((eq int) (succ pls)) (bit1 pls)). % 1.35/1.54 Axiom fact_568_succ__Bit0:(forall (K:int), (((eq int) (succ (bit0 K))) (bit1 K))). % 1.35/1.54 Axiom fact_569_succ__Bit1:(forall (K:int), (((eq int) (succ (bit1 K))) (bit0 (succ K)))). % 1.35/1.54 Axiom fact_570_zle__add1__eq__le:(forall (W:int) (Z_2:int), ((iff ((ord_less_int W) ((plus_plus_int Z_2) one_one_int))) ((ord_less_eq_int W) Z_2))). % 1.35/1.54 Axiom fact_571_add1__zle__eq:(forall (W:int) (Z_2:int), ((iff ((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z_2)) ((ord_less_int W) Z_2))). % 1.35/1.54 Axiom fact_572_zless__imp__add1__zle:(forall (W:int) (Z_2:int), (((ord_less_int W) Z_2)->((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z_2))). % 1.35/1.54 Axiom fact_573_succ__def:(forall (K:int), (((eq int) (succ K)) ((plus_plus_int K) one_one_int))). % 1.35/1.54 Axiom fact_574_power__eq__imp__eq__base:(forall (A_7:real) (N_3:nat) (B_6:real), ((((eq real) ((power_power_real A_7) N_3)) ((power_power_real B_6) N_3))->(((ord_less_eq_real zero_zero_real) A_7)->(((ord_less_eq_real zero_zero_real) B_6)->(((ord_less_nat zero_zero_nat) N_3)->(((eq real) A_7) B_6)))))). % 1.35/1.54 Axiom fact_575_power__eq__imp__eq__base:(forall (A_7:nat) (N_3:nat) (B_6:nat), ((((eq nat) ((power_power_nat A_7) N_3)) ((power_power_nat B_6) N_3))->(((ord_less_eq_nat zero_zero_nat) A_7)->(((ord_less_eq_nat zero_zero_nat) B_6)->(((ord_less_nat zero_zero_nat) N_3)->(((eq nat) A_7) B_6)))))). % 1.35/1.54 Axiom fact_576_power__eq__imp__eq__base:(forall (A_7:int) (N_3:nat) (B_6:int), ((((eq int) ((power_power_int A_7) N_3)) ((power_power_int B_6) N_3))->(((ord_less_eq_int zero_zero_int) A_7)->(((ord_less_eq_int zero_zero_int) B_6)->(((ord_less_nat zero_zero_nat) N_3)->(((eq int) A_7) B_6)))))). % 1.35/1.54 Axiom fact_577_semiring__add__number__of:(forall (V_4:int) (V_3:int), (((ord_less_eq_int pls) V_3)->(((ord_less_eq_int pls) V_4)->(((eq real) ((plus_plus_real (number267125858f_real V_3)) (number267125858f_real V_4))) (number267125858f_real ((plus_plus_int V_3) V_4)))))). % 1.35/1.54 Axiom fact_578_semiring__add__number__of:(forall (V_4:int) (V_3:int), (((ord_less_eq_int pls) V_3)->(((ord_less_eq_int pls) V_4)->(((eq nat) ((plus_plus_nat (number_number_of_nat V_3)) (number_number_of_nat V_4))) (number_number_of_nat ((plus_plus_int V_3) V_4)))))). % 1.35/1.54 Axiom fact_579_semiring__add__number__of:(forall (V_4:int) (V_3:int), (((ord_less_eq_int pls) V_3)->(((ord_less_eq_int pls) V_4)->(((eq int) ((plus_plus_int (number_number_of_int V_3)) (number_number_of_int V_4))) (number_number_of_int ((plus_plus_int V_3) V_4)))))). % 1.35/1.54 Axiom fact_580_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J:((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 (bit1 pls)))). % 1.35/1.54 Axiom fact_581_le__imp__0__less:(forall (Z_2:int), (((ord_less_eq_int zero_zero_int) Z_2)->((ord_less_int zero_zero_int) ((plus_plus_int one_one_int) Z_2)))). % 1.35/1.54 Axiom fact_582_number__of__succ:(forall (K_2:int), (((eq real) (number267125858f_real (succ K_2))) ((plus_plus_real one_one_real) (number267125858f_real K_2)))). % 1.35/1.54 Axiom fact_583_number__of__succ:(forall (K_2:int), (((eq int) (number_number_of_int (succ K_2))) ((plus_plus_int one_one_int) (number_number_of_int K_2)))). % 1.35/1.54 Axiom fact_584_add__Bit1__Bit1:(forall (K:int) (L:int), (((eq int) ((plus_plus_int (bit1 K)) (bit1 L))) (bit0 ((plus_plus_int K) (succ L))))). % 1.35/1.54 Axiom fact_585_power__strict__mono:(forall (N_2:nat) (A_6:real) (B_5:real), (((ord_less_real A_6) B_5)->(((ord_less_eq_real zero_zero_real) A_6)->(((ord_less_nat zero_zero_nat) N_2)->((ord_less_real ((power_power_real A_6) N_2)) ((power_power_real B_5) N_2)))))). % 1.35/1.54 Axiom fact_586_power__strict__mono:(forall (N_2:nat) (A_6:nat) (B_5:nat), (((ord_less_nat A_6) B_5)->(((ord_less_eq_nat zero_zero_nat) A_6)->(((ord_less_nat zero_zero_nat) N_2)->((ord_less_nat ((power_power_nat A_6) N_2)) ((power_power_nat B_5) N_2)))))). % 1.35/1.54 Axiom fact_587_power__strict__mono:(forall (N_2:nat) (A_6:int) (B_5:int), (((ord_less_int A_6) B_5)->(((ord_less_eq_int zero_zero_int) A_6)->(((ord_less_nat zero_zero_nat) N_2)->((ord_less_int ((power_power_int A_6) N_2)) ((power_power_int B_5) N_2)))))). % 1.35/1.54 Axiom fact_588_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J:((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 (bit1 pls)))). % 1.35/1.54 Axiom fact_589_power2__ge__self:(forall (X:int), ((ord_less_eq_int X) ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls)))))). % 1.35/1.54 Axiom fact_590_zero__le__power2:(forall (A_5:real), ((ord_less_eq_real zero_zero_real) ((power_power_real A_5) (number_number_of_nat (bit0 (bit1 pls)))))). % 1.35/1.54 Axiom fact_591_zero__le__power2:(forall (A_5:int), ((ord_less_eq_int zero_zero_int) ((power_power_int A_5) (number_number_of_nat (bit0 (bit1 pls)))))). % 1.35/1.54 Axiom fact_592_power2__le__imp__le:(forall (X_13:real) (Y_12:real), (((ord_less_eq_real ((power_power_real X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_real zero_zero_real) Y_12)->((ord_less_eq_real X_13) Y_12)))). % 1.35/1.54 Axiom fact_593_power2__le__imp__le:(forall (X_13:nat) (Y_12:nat), (((ord_less_eq_nat ((power_power_nat X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_nat zero_zero_nat) Y_12)->((ord_less_eq_nat X_13) Y_12)))). % 1.35/1.54 Axiom fact_594_power2__le__imp__le:(forall (X_13:int) (Y_12:int), (((ord_less_eq_int ((power_power_int X_13) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_12) (number_number_of_nat (bit0 (bit1 pls)))))->(((ord_less_eq_int zero_zero_int) Y_12)->((ord_less_eq_int X_13) Y_12)))). % 1.35/1.54 Axiom fact_595_power2__eq__imp__eq:(forall (X_12:real) (Y_11:real), ((((eq real) ((power_power_real X_12) (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) X_12)->(((ord_less_eq_real zero_zero_real) Y_11)->(((eq real) X_12) Y_11))))). % 1.35/1.54 Axiom fact_596_power2__eq__imp__eq:(forall (X_12:nat) (Y_11:nat), ((((eq nat) ((power_power_nat X_12) (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) X_12)->(((ord_less_eq_nat zero_zero_nat) Y_11)->(((eq nat) X_12) Y_11))))). % 1.35/1.54 Axiom fact_597_power2__eq__imp__eq:(forall (X_12:int) (Y_11:int), ((((eq int) ((power_power_int X_12) (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) X_12)->(((ord_less_eq_int zero_zero_int) Y_11)->(((eq int) X_12) Y_11))))). % 1.35/1.54 Axiom fact_598_of__nat__number__of__lemma:(forall (V_2:int), ((and (((ord_less_eq_int zero_zero_int) (number_number_of_int V_2))->(((eq real) (semiri132038758t_real (number_number_of_nat V_2))) (number267125858f_real V_2)))) ((((ord_less_eq_int zero_zero_int) (number_number_of_int V_2))->False)->(((eq real) (semiri132038758t_real (number_number_of_nat V_2))) zero_zero_real)))). % 1.35/1.54 Axiom fact_599_of__nat__number__of__lemma:(forall (V_2:int), ((and (((ord_less_eq_int zero_zero_int) (number_number_of_int V_2))->(((eq int) (semiri1621563631at_int (number_number_of_nat V_2))) (number_number_of_int V_2)))) ((((ord_less_eq_int zero_zero_int) (number_number_of_int V_2))->False)->(((eq int) (semiri1621563631at_int (number_number_of_nat V_2))) zero_zero_int)))). % 1.35/1.54 Axiom fact_600_power2__less__imp__less:(forall (X_11:real) (Y_10:real), (((ord_less_real ((power_power_real X_11) (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) Y_10)->((ord_less_real X_11) Y_10)))). % 1.35/1.54 Axiom fact_601_power2__less__imp__less:(forall (X_11:nat) (Y_10:nat), (((ord_less_nat ((power_power_nat X_11) (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) Y_10)->((ord_less_nat X_11) Y_10)))). % 1.35/1.54 Axiom fact_602_power2__less__imp__less:(forall (X_11:int) (Y_10:int), (((ord_less_int ((power_power_int X_11) (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) Y_10)->((ord_less_int X_11) Y_10)))). % 1.35/1.54 Axiom fact_603_sum__power2__ge__zero:(forall (X_10:real) (Y_9:real), ((ord_less_eq_real zero_zero_real) ((plus_plus_real ((power_power_real X_10) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_9) (number_number_of_nat (bit0 (bit1 pls))))))). % 1.35/1.54 Axiom fact_604_sum__power2__ge__zero:(forall (X_10:int) (Y_9:int), ((ord_less_eq_int zero_zero_int) ((plus_plus_int ((power_power_int X_10) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_9) (number_number_of_nat (bit0 (bit1 pls))))))). % 1.35/1.54 Axiom fact_605_sum__power2__le__zero__iff:(forall (X_9:real) (Y_8:real), ((iff ((ord_less_eq_real ((plus_plus_real ((power_power_real X_9) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_real Y_8) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_real)) ((and (((eq real) X_9) zero_zero_real)) (((eq real) Y_8) zero_zero_real)))). % 1.35/1.54 Axiom fact_606_sum__power2__le__zero__iff:(forall (X_9:int) (Y_8:int), ((iff ((ord_less_eq_int ((plus_plus_int ((power_power_int X_9) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_8) (number_number_of_nat (bit0 (bit1 pls)))))) zero_zero_int)) ((and (((eq int) X_9) zero_zero_int)) (((eq int) Y_8) zero_zero_int)))). % 1.35/1.54 Axiom fact_607_int__pos__lt__two__imp__zero__or__one:(forall (X:int), (((ord_less_eq_int zero_zero_int) X)->(((ord_less_int X) (number_number_of_int (bit0 (bit1 pls))))->((or (((eq int) X) zero_zero_int)) (((eq int) X) one_one_int))))). % 1.35/1.54 Axiom fact_608_number__of1:(forall (N:int), (((ord_less_eq_int zero_zero_int) (number_number_of_int N))->((and ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit0 N)))) ((ord_less_eq_int zero_zero_int) (number_number_of_int (bit1 N)))))). % 1.35/1.54 Axiom fact_609_number__of2:((ord_less_eq_int zero_zero_int) (number_number_of_int pls)). % 1.35/1.54 Axiom fact_610_zero__le__imp__eq__int:(forall (K:int), (((ord_less_eq_int zero_zero_int) K)->((ex nat) (fun (N_1:nat)=> (((eq int) K) (semiri1621563631at_int N_1)))))). % 1.35/1.54 Axiom fact_611_nonneg__int__cases:(forall (K:int), (((ord_less_eq_int zero_zero_int) K)->((forall (N_1:nat), (not (((eq int) K) (semiri1621563631at_int N_1))))->False))). % 1.35/1.54 Axiom fact_612_le0:(forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)). % 1.35/1.54 Axiom fact_613_less__eq__nat_Osimps_I1_J:(forall (N:nat), ((ord_less_eq_nat zero_zero_nat) N)). % 1.35/1.54 Axiom fact_614_le__0__eq:(forall (N:nat), ((iff ((ord_less_eq_nat N) zero_zero_nat)) (((eq nat) N) zero_zero_nat))). % 1.35/1.54 Axiom fact_615_less__or__eq__imp__le:(forall (M:nat) (N:nat), (((or ((ord_less_nat M) N)) (((eq nat) M) N))->((ord_less_eq_nat M) N))). % 1.35/1.54 Axiom fact_616_le__neq__implies__less:(forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->((not (((eq nat) M) N))->((ord_less_nat M) N)))). % 1.35/1.54 Axiom fact_617_less__imp__le__nat:(forall (M:nat) (N:nat), (((ord_less_nat M) N)->((ord_less_eq_nat M) N))). % 1.35/1.54 Axiom fact_618_le__eq__less__or__eq:(forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((or ((ord_less_nat M) N)) (((eq nat) M) N)))). % 1.35/1.54 Axiom fact_619_nat__less__le:(forall (M:nat) (N:nat), ((iff ((ord_less_nat M) N)) ((and ((ord_less_eq_nat M) N)) (not (((eq nat) M) N))))). % 1.35/1.54 Axiom fact_620_le__refl:(forall (N:nat), ((ord_less_eq_nat N) N)). % 1.35/1.54 Axiom fact_621_nat__le__linear:(forall (M:nat) (N:nat), ((or ((ord_less_eq_nat M) N)) ((ord_less_eq_nat N) M))). % 1.35/1.54 Axiom fact_622_eq__imp__le:(forall (M:nat) (N:nat), ((((eq nat) M) N)->((ord_less_eq_nat M) N))). % 1.35/1.54 Axiom fact_623_le__trans:(forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat J) K)->((ord_less_eq_nat _TPTP_I) K)))). % 1.35/1.54 Axiom fact_624_le__antisym:(forall (M:nat) (N:nat), (((ord_less_eq_nat M) N)->(((ord_less_eq_nat N) M)->(((eq nat) M) N)))). % 1.35/1.54 Axiom fact_625_less__eq__real__def:(forall (X:real) (Y:real), ((iff ((ord_less_eq_real X) Y)) ((or ((ord_less_real X) Y)) (((eq real) X) Y)))). % 1.35/1.54 Axiom fact_626_real__less__def:(forall (X:real) (Y:real), ((iff ((ord_less_real X) Y)) ((and ((ord_less_eq_real X) Y)) (not (((eq real) X) Y))))). % 1.35/1.54 Axiom fact_627_le__add2:(forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat M) N))). % 1.35/1.54 Axiom fact_628_le__add1:(forall (N:nat) (M:nat), ((ord_less_eq_nat N) ((plus_plus_nat N) M))). % 1.35/1.54 Axiom fact_629_le__iff__add:(forall (M:nat) (N:nat), ((iff ((ord_less_eq_nat M) N)) ((ex nat) (fun (K_1:nat)=> (((eq nat) N) ((plus_plus_nat M) K_1)))))). % 1.35/1.54 Axiom fact_630_nat__add__left__cancel__le:(forall (K:nat) (M:nat) (N:nat), ((iff ((ord_less_eq_nat ((plus_plus_nat K) M)) ((plus_plus_nat K) N))) ((ord_less_eq_nat M) N))). % 1.35/1.54 Axiom fact_631_trans__le__add1:(forall (M:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat J) M)))). % 1.35/1.54 Axiom fact_632_trans__le__add2:(forall (M:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat _TPTP_I) ((plus_plus_nat M) J)))). % 1.35/1.54 Axiom fact_633_add__le__mono1:(forall (K:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) K)))). % 1.35/1.54 Axiom fact_634_add__le__mono:(forall (K:nat) (L:nat) (_TPTP_I:nat) (J:nat), (((ord_less_eq_nat _TPTP_I) J)->(((ord_less_eq_nat K) L)->((ord_less_eq_nat ((plus_plus_nat _TPTP_I) K)) ((plus_plus_nat J) L))))). % 1.35/1.55 Axiom fact_635_add__leD2:(forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat K) N))). % 1.35/1.55 Axiom fact_636_add__leD1:(forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((ord_less_eq_nat M) N))). % 1.35/1.55 Axiom fact_637_add__leE:(forall (M:nat) (K:nat) (N:nat), (((ord_less_eq_nat ((plus_plus_nat M) K)) N)->((((ord_less_eq_nat M) N)->(((ord_less_eq_nat K) N)->False))->False))). % 1.35/1.55 Axiom fact_638_real__add__left__mono:(forall (Z_2:real) (X:real) (Y:real), (((ord_less_eq_real X) Y)->((ord_less_eq_real ((plus_plus_real Z_2) X)) ((plus_plus_real Z_2) Y)))). % 1.35/1.55 Axiom fact_639_Nat__Transfer_Otransfer__int__nat__relations_I3_J:(forall (X:nat) (Y:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int X)) (semiri1621563631at_int Y))) ((ord_less_eq_nat X) Y))). % 1.35/1.55 Axiom fact_640_zle__int:(forall (M:nat) (N:nat), ((iff ((ord_less_eq_int (semiri1621563631at_int M)) (semiri1621563631at_int N))) ((ord_less_eq_nat M) N))). % 1.35/1.55 Axiom fact_641_le__nat__number__of:(forall (V_1:int) (V:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_1)) (number_number_of_nat V))) ((((ord_less_eq_int V_1) V)->False)->((ord_less_eq_int V_1) pls)))). % 1.35/1.55 Axiom fact_642_two__realpow__ge__one:(forall (N:nat), ((ord_less_eq_real one_one_real) ((power_power_real (number267125858f_real (bit0 (bit1 pls)))) N))). % 1.35/1.55 Axiom fact_643_conj__le__cong:(forall (P_1:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_1))->((iff ((and ((ord_less_eq_int zero_zero_int) X)) P)) ((and ((ord_less_eq_int zero_zero_int) X)) P_1)))). % 1.35/1.55 Axiom fact_644_imp__le__cong:(forall (P_1:Prop) (P:Prop) (X:int), ((((ord_less_eq_int zero_zero_int) X)->((iff P) P_1))->((iff (((ord_less_eq_int zero_zero_int) X)->P)) (((ord_less_eq_int zero_zero_int) X)->P_1)))). % 1.35/1.55 Axiom fact_645_ex__least__nat__less:(forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_nat K_1) N)) (forall (I_1:nat), (((ord_less_eq_nat I_1) K_1)->((P I_1)->False))))) (P ((plus_plus_nat K_1) one_one_nat)))))))). % 1.35/1.55 Axiom fact_646_nonneg__eq__int:(forall (Z_2:int), (((ord_less_eq_int zero_zero_int) Z_2)->((forall (M_1:nat), (not (((eq int) Z_2) (semiri1621563631at_int M_1))))->False))). % 1.35/1.55 Axiom fact_647_mono__nat__linear__lb:(forall (M:nat) (K:nat) (F:(nat->nat)), ((forall (M_1:nat) (N_1:nat), (((ord_less_nat M_1) N_1)->((ord_less_nat (F M_1)) (F N_1))))->((ord_less_eq_nat ((plus_plus_nat (F M)) K)) (F ((plus_plus_nat M) K))))). % 1.35/1.55 Axiom fact_648_real__le__refl:(forall (W:real), ((ord_less_eq_real W) W)). % 1.35/1.55 Axiom fact_649_real__le__linear:(forall (Z_2:real) (W:real), ((or ((ord_less_eq_real Z_2) W)) ((ord_less_eq_real W) Z_2))). % 1.35/1.55 Axiom fact_650_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)))). % 1.35/1.55 Axiom fact_651_real__le__antisym:(forall (Z_2:real) (W:real), (((ord_less_eq_real Z_2) W)->(((ord_less_eq_real W) Z_2)->(((eq real) Z_2) W)))). % 1.35/1.55 Axiom fact_652_int__ge__induct:(forall (P:(int->Prop)) (K:int) (_TPTP_I:int), (((ord_less_eq_int K) _TPTP_I)->((P K)->((forall (I_1:int), (((ord_less_eq_int K) I_1)->((P I_1)->(P ((plus_plus_int I_1) one_one_int)))))->(P _TPTP_I))))). % 1.35/1.55 Axiom fact_653_ex__least__nat__le:(forall (N:nat) (P:(nat->Prop)), (((P zero_zero_nat)->False)->((P N)->((ex nat) (fun (K_1:nat)=> ((and ((and ((ord_less_eq_nat K_1) N)) (forall (I_1:nat), (((ord_less_nat I_1) K_1)->((P I_1)->False))))) (P K_1))))))). % 1.35/1.55 Axiom fact_654_less__mono__imp__le__mono:(forall (_TPTP_I:nat) (J:nat) (F:(nat->nat)), ((forall (I_1:nat) (J_1:nat), (((ord_less_nat I_1) J_1)->((ord_less_nat (F I_1)) (F J_1))))->(((ord_less_eq_nat _TPTP_I) J)->((ord_less_eq_nat (F _TPTP_I)) (F J))))). % 1.35/1.55 Axiom fact_655_order__refl:(forall (X_8:real), ((ord_less_eq_real X_8) X_8)). % 1.35/1.55 Axiom fact_656_order__refl:(forall (X_8:nat), ((ord_less_eq_nat X_8) X_8)). % 1.35/1.55 Axiom fact_657_order__refl:(forall (X_8:int), ((ord_less_eq_int X_8) X_8)). % 1.35/1.55 Axiom fact_658_linorder__le__cases:(forall (X_7:real) (Y_7:real), ((((ord_less_eq_real X_7) Y_7)->False)->((ord_less_eq_real Y_7) X_7))). % 1.35/1.55 Axiom fact_659_linorder__le__cases:(forall (X_7:nat) (Y_7:nat), ((((ord_less_eq_nat X_7) Y_7)->False)->((ord_less_eq_nat Y_7) X_7))). % 1.35/1.55 Axiom fact_660_linorder__le__cases:(forall (X_7:int) (Y_7:int), ((((ord_less_eq_int X_7) Y_7)->False)->((ord_less_eq_int Y_7) X_7))). % 1.35/1.55 Axiom fact_661_xt1_I6_J:(forall (Z_1:real) (Y_6:real) (X_6:real), (((ord_less_eq_real Y_6) X_6)->(((ord_less_eq_real Z_1) Y_6)->((ord_less_eq_real Z_1) X_6)))). % 1.35/1.55 Axiom fact_662_xt1_I6_J:(forall (Z_1:nat) (Y_6:nat) (X_6:nat), (((ord_less_eq_nat Y_6) X_6)->(((ord_less_eq_nat Z_1) Y_6)->((ord_less_eq_nat Z_1) X_6)))). % 1.35/1.55 Axiom fact_663_xt1_I6_J:(forall (Z_1:int) (Y_6:int) (X_6:int), (((ord_less_eq_int Y_6) X_6)->(((ord_less_eq_int Z_1) Y_6)->((ord_less_eq_int Z_1) X_6)))). % 1.35/1.55 Axiom fact_664_xt1_I5_J:(forall (Y_5:real) (X_5:real), (((ord_less_eq_real Y_5) X_5)->(((ord_less_eq_real X_5) Y_5)->(((eq real) X_5) Y_5)))). % 1.35/1.55 Axiom fact_665_xt1_I5_J:(forall (Y_5:nat) (X_5:nat), (((ord_less_eq_nat Y_5) X_5)->(((ord_less_eq_nat X_5) Y_5)->(((eq nat) X_5) Y_5)))). % 1.35/1.55 Axiom fact_666_xt1_I5_J:(forall (Y_5:int) (X_5:int), (((ord_less_eq_int Y_5) X_5)->(((ord_less_eq_int X_5) Y_5)->(((eq int) X_5) Y_5)))). % 1.35/1.55 Axiom fact_667_order__trans:(forall (Z:real) (X_4:real) (Y_4:real), (((ord_less_eq_real X_4) Y_4)->(((ord_less_eq_real Y_4) Z)->((ord_less_eq_real X_4) Z)))). % 1.35/1.55 Axiom fact_668_order__trans:(forall (Z:nat) (X_4:nat) (Y_4:nat), (((ord_less_eq_nat X_4) Y_4)->(((ord_less_eq_nat Y_4) Z)->((ord_less_eq_nat X_4) Z)))). % 1.35/1.55 Axiom fact_669_order__trans:(forall (Z:int) (X_4:int) (Y_4:int), (((ord_less_eq_int X_4) Y_4)->(((ord_less_eq_int Y_4) Z)->((ord_less_eq_int X_4) Z)))). % 1.35/1.55 Axiom fact_670_order__antisym:(forall (X_3:real) (Y_3:real), (((ord_less_eq_real X_3) Y_3)->(((ord_less_eq_real Y_3) X_3)->(((eq real) X_3) Y_3)))). % 1.35/1.55 Axiom fact_671_order__antisym:(forall (X_3:nat) (Y_3:nat), (((ord_less_eq_nat X_3) Y_3)->(((ord_less_eq_nat Y_3) X_3)->(((eq nat) X_3) Y_3)))). % 1.35/1.55 Axiom fact_672_order__antisym:(forall (X_3:int) (Y_3:int), (((ord_less_eq_int X_3) Y_3)->(((ord_less_eq_int Y_3) X_3)->(((eq int) X_3) Y_3)))). % 1.35/1.55 Axiom fact_673_xt1_I4_J:(forall (C_3:real) (B_4:real) (A_4:real), (((ord_less_eq_real B_4) A_4)->((((eq real) B_4) C_3)->((ord_less_eq_real C_3) A_4)))). % 1.35/1.55 Axiom fact_674_xt1_I4_J:(forall (C_3:nat) (B_4:nat) (A_4:nat), (((ord_less_eq_nat B_4) A_4)->((((eq nat) B_4) C_3)->((ord_less_eq_nat C_3) A_4)))). % 1.35/1.55 Axiom fact_675_xt1_I4_J:(forall (C_3:int) (B_4:int) (A_4:int), (((ord_less_eq_int B_4) A_4)->((((eq int) B_4) C_3)->((ord_less_eq_int C_3) A_4)))). % 1.35/1.55 Axiom fact_676_ord__le__eq__trans:(forall (C_2:real) (A_3:real) (B_3:real), (((ord_less_eq_real A_3) B_3)->((((eq real) B_3) C_2)->((ord_less_eq_real A_3) C_2)))). % 1.35/1.55 Axiom fact_677_ord__le__eq__trans:(forall (C_2:nat) (A_3:nat) (B_3:nat), (((ord_less_eq_nat A_3) B_3)->((((eq nat) B_3) C_2)->((ord_less_eq_nat A_3) C_2)))). % 1.35/1.55 Axiom fact_678_ord__le__eq__trans:(forall (C_2:int) (A_3:int) (B_3:int), (((ord_less_eq_int A_3) B_3)->((((eq int) B_3) C_2)->((ord_less_eq_int A_3) C_2)))). % 1.35/1.55 Axiom fact_679_xt1_I3_J:(forall (C_1:real) (A_2:real) (B_2:real), ((((eq real) A_2) B_2)->(((ord_less_eq_real C_1) B_2)->((ord_less_eq_real C_1) A_2)))). % 1.35/1.55 Axiom fact_680_xt1_I3_J:(forall (C_1:nat) (A_2:nat) (B_2:nat), ((((eq nat) A_2) B_2)->(((ord_less_eq_nat C_1) B_2)->((ord_less_eq_nat C_1) A_2)))). % 1.35/1.55 Axiom fact_681_xt1_I3_J:(forall (C_1:int) (A_2:int) (B_2:int), ((((eq int) A_2) B_2)->(((ord_less_eq_int C_1) B_2)->((ord_less_eq_int C_1) A_2)))). % 1.35/1.55 Axiom fact_682_ord__eq__le__trans:(forall (C:real) (A_1:real) (B_1:real), ((((eq real) A_1) B_1)->(((ord_less_eq_real B_1) C)->((ord_less_eq_real A_1) C)))). % 1.35/1.55 Axiom fact_683_ord__eq__le__trans:(forall (C:nat) (A_1:nat) (B_1:nat), ((((eq nat) A_1) B_1)->(((ord_less_eq_nat B_1) C)->((ord_less_eq_nat A_1) C)))). % 1.35/1.55 Axiom fact_684_ord__eq__le__trans:(forall (C:int) (A_1:int) (B_1:int), ((((eq int) A_1) B_1)->(((ord_less_eq_int B_1) C)->((ord_less_eq_int A_1) C)))). % 1.35/1.55 Axiom fact_685_order__antisym__conv:(forall (Y_2:real) (X_2:real), (((ord_less_eq_real Y_2) X_2)->((iff ((ord_less_eq_real X_2) Y_2)) (((eq real) X_2) Y_2)))). %------------------------------------------------------------------------------