TSTP Solution File: NUM926^1 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : NUM926^1 : TPTP v7.0.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n079.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 13:12:05 EST 2018
% Result : Timeout 300.01s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM926^1 : TPTP v7.0.0. Released v5.3.0.
% 0.00/0.04 % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.02/0.24 % Computer : n079.star.cs.uiowa.edu
% 0.02/0.24 % Model : x86_64 x86_64
% 0.02/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% 0.02/0.24 % Memory : 32218.625MB
% 0.02/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64
% 0.02/0.24 % CPULimit : 300
% 0.02/0.24 % DateTime : Fri Jan 5 16:07:19 CST 2018
% 0.02/0.24 % CPUTime :
% 0.02/0.25 Python 2.7.13
% 0.08/0.52 Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba5757d7128>, <kernel.Type object at 0x2ba5757d7950>) of role type named ty_ty_tc__Int__Oint
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring int:Type
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba5757abe18>, <kernel.Type object at 0x2ba5757d7a70>) of role type named ty_ty_tc__Nat__Onat
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring nat:Type
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba5757d7170>, <kernel.Constant object at 0x2ba5757d71b8>) of role type named sy_c_Groups_Oone__class_Oone_000tc__Int__Oint
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring one_one_int:int
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba5757d7950>, <kernel.Constant object at 0x2ba5757d71b8>) of role type named sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring one_one_nat:nat
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba5757d7128>, <kernel.DependentProduct object at 0x2ba5757d75a8>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring plus_plus_int:(int->(int->int))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba5757d7560>, <kernel.DependentProduct object at 0x2ba5757d7170>) of role type named sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring plus_plus_nat:(nat->(nat->nat))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba57511aea8>, <kernel.DependentProduct object at 0x2ba5757d7758>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring times_times_int:(int->(int->int))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba57511aea8>, <kernel.DependentProduct object at 0x2ba5757d7950>) of role type named sy_c_Groups_Otimes__class_Otimes_000tc__Nat__Onat
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring times_times_nat:(nat->(nat->nat))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba574d5e290>, <kernel.DependentProduct object at 0x2ba5757d75a8>) of role type named sy_c_IntPrimes_Ozprime
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring zprime:(int->Prop)
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba574d5e290>, <kernel.DependentProduct object at 0x2ba5757d79e0>) of role type named sy_c_Int_OBit0
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring bit0:(int->int)
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba5757d7170>, <kernel.DependentProduct object at 0x2ba5750b4200>) of role type named sy_c_Int_OBit1
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring bit1:(int->int)
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba5757d75a8>, <kernel.Constant object at 0x2ba5757d71b8>) of role type named sy_c_Int_OPls
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring pls:int
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba5757d79e0>, <kernel.DependentProduct object at 0x2ba5750b42d8>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring number_number_of_int:(int->int)
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba5757d7560>, <kernel.DependentProduct object at 0x2ba5750b4b00>) of role type named sy_c_Int_Onumber__class_Onumber__of_000tc__Nat__Onat
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring number_number_of_nat:(int->nat)
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba5757d75a8>, <kernel.DependentProduct object at 0x2ba5750b4b90>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Int__Oint
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring ord_less_int:(int->(int->Prop))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba5757d79e0>, <kernel.DependentProduct object at 0x2ba5750b4f80>) of role type named sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring ord_less_nat:(nat->(nat->Prop))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba5757d75a8>, <kernel.DependentProduct object at 0x2ba5750b4b48>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Int__Oint
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring ord_less_eq_int:(int->(int->Prop))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba5757d79e0>, <kernel.DependentProduct object at 0x2ba5750b4200>) of role type named sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat
% 0.08/0.52 Using role type
% 0.08/0.52 Declaring ord_less_eq_nat:(nat->(nat->Prop))
% 0.08/0.52 FOF formula (<kernel.Constant object at 0x2ba5757d7560>, <kernel.DependentProduct object at 0x2ba5750b4b00>) of role type named sy_c_Power_Opower__class_Opower_000tc__Int__Oint
% 0.08/0.53 Using role type
% 0.08/0.53 Declaring power_power_int:(int->(nat->int))
% 0.08/0.53 FOF formula (<kernel.Constant object at 0x2ba5757d7560>, <kernel.DependentProduct object at 0x2ba5750b45f0>) of role type named sy_c_Power_Opower__class_Opower_000tc__Nat__Onat
% 0.08/0.53 Using role type
% 0.08/0.53 Declaring power_power_nat:(nat->(nat->nat))
% 0.08/0.53 FOF formula (<kernel.Constant object at 0x2ba5750b4200>, <kernel.DependentProduct object at 0x2ba5750b4440>) of role type named sy_c_TwoSquares__Mirabelle__fqdbopfjxb_Ois__sum2sq
% 0.08/0.53 Using role type
% 0.08/0.53 Declaring twoSqu1013291560sum2sq:(int->Prop)
% 0.08/0.53 FOF formula (<kernel.Constant object at 0x2ba5750b4b00>, <kernel.Constant object at 0x2ba5750b4440>) of role type named sy_v_m
% 0.08/0.53 Using role type
% 0.08/0.53 Declaring m:int
% 0.08/0.53 FOF formula (<kernel.Constant object at 0x2ba5750b4e60>, <kernel.Constant object at 0x2ba5750b4440>) of role type named sy_v_s____
% 0.08/0.53 Using role type
% 0.08/0.53 Declaring s:int
% 0.08/0.53 FOF formula (<kernel.Constant object at 0x2ba5750b4200>, <kernel.Constant object at 0x2ba5750b4440>) of role type named sy_v_t____
% 0.08/0.53 Using role type
% 0.08/0.53 Declaring t:int
% 0.08/0.53 FOF formula ((ord_less_eq_int one_one_int) t) of role axiom named fact_0_tpos
% 0.08/0.53 A new axiom: ((ord_less_eq_int one_one_int) t)
% 0.08/0.53 FOF formula ((((eq int) t) one_one_int)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))) of role axiom named fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06
% 0.08/0.53 A new axiom: ((((eq int) t) one_one_int)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))))))
% 0.08/0.53 FOF formula (((ord_less_int one_one_int) t)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))) of role axiom named fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06
% 0.08/0.53 A new axiom: (((ord_less_int one_one_int) t)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))))))
% 0.08/0.53 FOF formula ((ord_less_int t) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) of role axiom named fact_3_t__l__p
% 0.08/0.53 A new axiom: ((ord_less_int t) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))
% 0.08/0.53 FOF formula (zprime ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) of role axiom named fact_4_p
% 0.08/0.53 A new axiom: (zprime ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))
% 0.08/0.53 FOF formula (((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)) of role axiom named fact_5_t
% 0.08/0.53 A new axiom: (((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t))
% 0.08/0.53 FOF formula (twoSqu1013291560sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)) of role axiom named fact_6_qf1pt
% 0.08/0.55 A new axiom: (twoSqu1013291560sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t))
% 0.08/0.55 FOF formula (forall (A_8:int) (B_4:int), (((eq int) ((power_power_int ((plus_plus_int A_8) B_4)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int A_8) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A_8)) B_4))) ((power_power_int B_4) (number_number_of_nat (bit0 (bit1 pls))))))) of role axiom named fact_7_zadd__power2
% 0.08/0.55 A new axiom: (forall (A_8:int) (B_4:int), (((eq int) ((power_power_int ((plus_plus_int A_8) B_4)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int A_8) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A_8)) B_4))) ((power_power_int B_4) (number_number_of_nat (bit0 (bit1 pls)))))))
% 0.08/0.55 FOF formula (forall (A_8:int) (B_4:int), (((eq int) ((power_power_int ((plus_plus_int A_8) B_4)) (number_number_of_nat (bit1 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((plus_plus_int ((power_power_int A_8) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) ((power_power_int A_8) (number_number_of_nat (bit0 (bit1 pls)))))) B_4))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) A_8)) ((power_power_int B_4) (number_number_of_nat (bit0 (bit1 pls))))))) ((power_power_int B_4) (number_number_of_nat (bit1 (bit1 pls))))))) of role axiom named fact_8_zadd__power3
% 0.08/0.55 A new axiom: (forall (A_8:int) (B_4:int), (((eq int) ((power_power_int ((plus_plus_int A_8) B_4)) (number_number_of_nat (bit1 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((plus_plus_int ((power_power_int A_8) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) ((power_power_int A_8) (number_number_of_nat (bit0 (bit1 pls)))))) B_4))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) A_8)) ((power_power_int B_4) (number_number_of_nat (bit0 (bit1 pls))))))) ((power_power_int B_4) (number_number_of_nat (bit1 (bit1 pls)))))))
% 0.08/0.55 FOF formula (forall (X_11:nat) (Y_5:nat), (((eq nat) ((power_power_nat ((plus_plus_nat X_11) Y_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat ((plus_plus_nat ((power_power_nat X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) X_11)) Y_5)))) of role axiom named fact_9_power2__sum
% 0.08/0.55 A new axiom: (forall (X_11:nat) (Y_5:nat), (((eq nat) ((power_power_nat ((plus_plus_nat X_11) Y_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat ((plus_plus_nat ((power_power_nat X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) X_11)) Y_5))))
% 0.08/0.55 FOF formula (forall (X_11:int) (Y_5:int), (((eq int) ((power_power_int ((plus_plus_int X_11) Y_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) X_11)) Y_5)))) of role axiom named fact_10_power2__sum
% 0.08/0.55 A new axiom: (forall (X_11:int) (Y_5:int), (((eq int) ((power_power_int ((plus_plus_int X_11) Y_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) X_11)) Y_5))))
% 0.08/0.55 FOF formula (forall (W_5:int), (((eq int) ((power_power_int (number_number_of_int W_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int (number_number_of_int W_5)) (number_number_of_int W_5)))) of role axiom named fact_11_power2__eq__square__number__of
% 0.08/0.57 A new axiom: (forall (W_5:int), (((eq int) ((power_power_int (number_number_of_int W_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int (number_number_of_int W_5)) (number_number_of_int W_5))))
% 0.08/0.57 FOF formula (forall (W_5:int), (((eq nat) ((power_power_nat (number_number_of_nat W_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat (number_number_of_nat W_5)) (number_number_of_nat W_5)))) of role axiom named fact_12_power2__eq__square__number__of
% 0.08/0.57 A new axiom: (forall (W_5:int), (((eq nat) ((power_power_nat (number_number_of_nat W_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat (number_number_of_nat W_5)) (number_number_of_nat W_5))))
% 0.08/0.57 FOF formula (forall (A_8:int), (((eq int) ((times_times_int A_8) ((power_power_int A_8) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_int A_8) (number_number_of_nat (bit1 (bit1 pls)))))) of role axiom named fact_13_cube__square
% 0.08/0.57 A new axiom: (forall (A_8:int), (((eq int) ((times_times_int A_8) ((power_power_int A_8) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_int A_8) (number_number_of_nat (bit1 (bit1 pls))))))
% 0.08/0.57 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_14_one__power2
% 0.08/0.57 A new axiom: (((eq nat) ((power_power_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls))))) one_one_nat)
% 0.08/0.57 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_15_one__power2
% 0.08/0.57 A new axiom: (((eq int) ((power_power_int one_one_int) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)
% 0.08/0.57 FOF formula (forall (X_10:int), (((eq int) ((times_times_int X_10) X_10)) ((power_power_int X_10) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J
% 0.08/0.57 A new axiom: (forall (X_10:int), (((eq int) ((times_times_int X_10) X_10)) ((power_power_int X_10) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.08/0.57 FOF formula (forall (X_10:nat), (((eq nat) ((times_times_nat X_10) X_10)) ((power_power_nat X_10) (number_number_of_nat (bit0 (bit1 pls)))))) of role axiom named fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J
% 0.08/0.57 A new axiom: (forall (X_10:nat), (((eq nat) ((times_times_nat X_10) X_10)) ((power_power_nat X_10) (number_number_of_nat (bit0 (bit1 pls))))))
% 0.08/0.57 FOF formula (forall (A_7:int), (((eq int) ((power_power_int A_7) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int A_7) A_7))) of role axiom named fact_18_power2__eq__square
% 0.08/0.57 A new axiom: (forall (A_7:int), (((eq int) ((power_power_int A_7) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int A_7) A_7)))
% 0.08/0.57 FOF formula (forall (A_7:nat), (((eq nat) ((power_power_nat A_7) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat A_7) A_7))) of role axiom named fact_19_power2__eq__square
% 0.08/0.57 A new axiom: (forall (A_7:nat), (((eq nat) ((power_power_nat A_7) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat A_7) A_7)))
% 0.08/0.57 FOF formula (forall (X_9:int) (N:nat), (((eq int) ((power_power_int X_9) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N))) ((times_times_int ((power_power_int X_9) N)) ((power_power_int X_9) N)))) of role axiom named fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J
% 0.08/0.57 A new axiom: (forall (X_9:int) (N:nat), (((eq int) ((power_power_int X_9) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N))) ((times_times_int ((power_power_int X_9) N)) ((power_power_int X_9) N))))
% 0.08/0.57 FOF formula (forall (X_9:nat) (N:nat), (((eq nat) ((power_power_nat X_9) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N))) ((times_times_nat ((power_power_nat X_9) N)) ((power_power_nat X_9) N)))) of role axiom named fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J
% 0.08/0.57 A new axiom: (forall (X_9:nat) (N:nat), (((eq nat) ((power_power_nat X_9) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N))) ((times_times_nat ((power_power_nat X_9) N)) ((power_power_nat X_9) N))))
% 0.08/0.58 FOF formula (forall (W_4:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_4))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_4)))) of role axiom named fact_22_add__special_I2_J
% 0.08/0.58 A new axiom: (forall (W_4:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_4))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_4))))
% 0.08/0.58 FOF formula (forall (V_3:int), (((eq int) ((plus_plus_int (number_number_of_int V_3)) one_one_int)) (number_number_of_int ((plus_plus_int V_3) (bit1 pls))))) of role axiom named fact_23_add__special_I3_J
% 0.08/0.58 A new axiom: (forall (V_3:int), (((eq int) ((plus_plus_int (number_number_of_int V_3)) one_one_int)) (number_number_of_int ((plus_plus_int V_3) (bit1 pls)))))
% 0.08/0.58 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_24_one__add__one__is__two
% 0.08/0.58 A new axiom: (((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls))))
% 0.08/0.58 FOF formula ((forall (T:int), (not (((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) T))))->False) of role axiom named fact_25__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_
% 0.08/0.58 A new axiom: ((forall (T:int), (not (((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) T))))->False)
% 0.08/0.58 FOF formula (forall (W:int), ((ord_less_eq_int W) W)) of role axiom named fact_26_zle__refl
% 0.08/0.58 A new axiom: (forall (W:int), ((ord_less_eq_int W) W))
% 0.08/0.58 FOF formula (forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z))) of role axiom named fact_27_zle__linear
% 0.08/0.58 A new axiom: (forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z)))
% 0.08/0.58 FOF formula (forall (Z:int) (W:int), ((iff ((ord_less_int Z) W)) ((and ((ord_less_eq_int Z) W)) (not (((eq int) Z) W))))) of role axiom named fact_28_zless__le
% 0.08/0.58 A new axiom: (forall (Z:int) (W:int), ((iff ((ord_less_int Z) W)) ((and ((ord_less_eq_int Z) W)) (not (((eq int) Z) W)))))
% 0.08/0.58 FOF formula (forall (X_1:int) (Y_1:int), ((or ((or ((ord_less_int X_1) Y_1)) (((eq int) X_1) Y_1))) ((ord_less_int Y_1) X_1))) of role axiom named fact_29_zless__linear
% 0.08/0.58 A new axiom: (forall (X_1:int) (Y_1:int), ((or ((or ((ord_less_int X_1) Y_1)) (((eq int) X_1) Y_1))) ((ord_less_int Y_1) X_1)))
% 0.08/0.58 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_30_zle__trans
% 0.08/0.58 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))))
% 0.08/0.58 FOF formula (forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W)))) of role axiom named fact_31_zle__antisym
% 0.08/0.58 A new axiom: (forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W))))
% 0.08/0.58 FOF formula (forall (X_8:int) (P_1:nat) (Q_1:nat), (((eq int) ((power_power_int ((power_power_int X_8) P_1)) Q_1)) ((power_power_int X_8) ((times_times_nat P_1) Q_1)))) of role axiom named fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J
% 0.08/0.58 A new axiom: (forall (X_8:int) (P_1:nat) (Q_1:nat), (((eq int) ((power_power_int ((power_power_int X_8) P_1)) Q_1)) ((power_power_int X_8) ((times_times_nat P_1) Q_1))))
% 0.08/0.58 FOF formula (forall (X_8:nat) (P_1:nat) (Q_1:nat), (((eq nat) ((power_power_nat ((power_power_nat X_8) P_1)) Q_1)) ((power_power_nat X_8) ((times_times_nat P_1) Q_1)))) of role axiom named fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J
% 0.08/0.58 A new axiom: (forall (X_8:nat) (P_1:nat) (Q_1:nat), (((eq nat) ((power_power_nat ((power_power_nat X_8) P_1)) Q_1)) ((power_power_nat X_8) ((times_times_nat P_1) Q_1))))
% 0.08/0.60 FOF formula (forall (X_7:int), (((eq int) ((power_power_int X_7) one_one_nat)) X_7)) of role axiom named fact_34_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J
% 0.08/0.60 A new axiom: (forall (X_7:int), (((eq int) ((power_power_int X_7) one_one_nat)) X_7))
% 0.08/0.60 FOF formula (forall (X_7:nat), (((eq nat) ((power_power_nat X_7) one_one_nat)) X_7)) of role axiom named fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J
% 0.08/0.60 A new axiom: (forall (X_7:nat), (((eq nat) ((power_power_nat X_7) one_one_nat)) X_7))
% 0.08/0.60 FOF formula (forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int ((power_power_int X_1) Y_1)) Z)) ((power_power_int X_1) ((times_times_nat Y_1) Z)))) of role axiom named fact_36_zpower__zpower
% 0.08/0.60 A new axiom: (forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int ((power_power_int X_1) Y_1)) Z)) ((power_power_int X_1) ((times_times_nat Y_1) Z))))
% 0.08/0.60 FOF formula (forall (V_2:int) (W_3:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_2)) (number_number_of_nat W_3))) (((ord_less_nat (number_number_of_nat W_3)) (number_number_of_nat V_2))->False))) of role axiom named fact_37_le__number__of__eq__not__less
% 0.08/0.60 A new axiom: (forall (V_2:int) (W_3:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_2)) (number_number_of_nat W_3))) (((ord_less_nat (number_number_of_nat W_3)) (number_number_of_nat V_2))->False)))
% 0.08/0.60 FOF formula (forall (V_2:int) (W_3:int), ((iff ((ord_less_eq_int (number_number_of_int V_2)) (number_number_of_int W_3))) (((ord_less_int (number_number_of_int W_3)) (number_number_of_int V_2))->False))) of role axiom named fact_38_le__number__of__eq__not__less
% 0.08/0.60 A new axiom: (forall (V_2:int) (W_3:int), ((iff ((ord_less_eq_int (number_number_of_int V_2)) (number_number_of_int W_3))) (((ord_less_int (number_number_of_int W_3)) (number_number_of_int V_2))->False)))
% 0.08/0.60 FOF formula (forall (X_6:int) (Y_4:int), ((iff ((ord_less_int (number_number_of_int X_6)) (number_number_of_int Y_4))) ((ord_less_int X_6) Y_4))) of role axiom named fact_39_less__number__of
% 0.08/0.60 A new axiom: (forall (X_6:int) (Y_4:int), ((iff ((ord_less_int (number_number_of_int X_6)) (number_number_of_int Y_4))) ((ord_less_int X_6) Y_4)))
% 0.08/0.60 FOF formula (forall (X_5:int) (Y_3:int), ((iff ((ord_less_eq_int (number_number_of_int X_5)) (number_number_of_int Y_3))) ((ord_less_eq_int X_5) Y_3))) of role axiom named fact_40_le__number__of
% 0.08/0.60 A new axiom: (forall (X_5:int) (Y_3:int), ((iff ((ord_less_eq_int (number_number_of_int X_5)) (number_number_of_int Y_3))) ((ord_less_eq_int X_5) Y_3)))
% 0.08/0.60 FOF formula (forall (Z_1:int) (Z:int) (W_2:int) (W:int), (((ord_less_int W_2) W)->(((ord_less_eq_int Z_1) Z)->((ord_less_int ((plus_plus_int W_2) Z_1)) ((plus_plus_int W) Z))))) of role axiom named fact_41_zadd__zless__mono
% 0.08/0.60 A new axiom: (forall (Z_1:int) (Z:int) (W_2:int) (W:int), (((ord_less_int W_2) W)->(((ord_less_eq_int Z_1) Z)->((ord_less_int ((plus_plus_int W_2) Z_1)) ((plus_plus_int W) Z)))))
% 0.08/0.60 FOF formula (forall (X_4:int) (P:nat) (Q:nat), (((eq int) ((times_times_int ((power_power_int X_4) P)) ((power_power_int X_4) Q))) ((power_power_int X_4) ((plus_plus_nat P) Q)))) of role axiom named fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J
% 0.08/0.60 A new axiom: (forall (X_4:int) (P:nat) (Q:nat), (((eq int) ((times_times_int ((power_power_int X_4) P)) ((power_power_int X_4) Q))) ((power_power_int X_4) ((plus_plus_nat P) Q))))
% 0.08/0.60 FOF formula (forall (X_4:nat) (P:nat) (Q:nat), (((eq nat) ((times_times_nat ((power_power_nat X_4) P)) ((power_power_nat X_4) Q))) ((power_power_nat X_4) ((plus_plus_nat P) Q)))) of role axiom named fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J
% 0.08/0.60 A new axiom: (forall (X_4:nat) (P:nat) (Q:nat), (((eq nat) ((times_times_nat ((power_power_nat X_4) P)) ((power_power_nat X_4) Q))) ((power_power_nat X_4) ((plus_plus_nat P) Q))))
% 0.08/0.60 FOF formula (forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int X_1) ((plus_plus_nat Y_1) Z))) ((times_times_int ((power_power_int X_1) Y_1)) ((power_power_int X_1) Z)))) of role axiom named fact_44_zpower__zadd__distrib
% 0.42/0.62 A new axiom: (forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int X_1) ((plus_plus_nat Y_1) Z))) ((times_times_int ((power_power_int X_1) Y_1)) ((power_power_int X_1) Z))))
% 0.42/0.62 FOF formula (forall (Z:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z)) ((plus_plus_nat Z) Z))) of role axiom named fact_45_nat__mult__2
% 0.42/0.62 A new axiom: (forall (Z:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z)) ((plus_plus_nat Z) Z)))
% 0.42/0.62 FOF formula (forall (Z:nat), (((eq nat) ((times_times_nat Z) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z) Z))) of role axiom named fact_46_nat__mult__2__right
% 0.42/0.62 A new axiom: (forall (Z:nat), (((eq nat) ((times_times_nat Z) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z) Z)))
% 0.42/0.62 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_47_nat__1__add__1
% 0.42/0.62 A new axiom: (((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls))))
% 0.42/0.62 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_48_less__int__code_I16_J
% 0.42/0.62 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2)))
% 0.42/0.62 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_49_rel__simps_I17_J
% 0.42/0.62 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L)))
% 0.42/0.62 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_50_less__eq__int__code_I16_J
% 0.42/0.62 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2)))
% 0.42/0.62 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_51_rel__simps_I34_J
% 0.42/0.62 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit1 L))) ((ord_less_eq_int K) L)))
% 0.42/0.62 FOF formula (((ord_less_int pls) pls)->False) of role axiom named fact_52_rel__simps_I2_J
% 0.42/0.62 A new axiom: (((ord_less_int pls) pls)->False)
% 0.42/0.62 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_53_less__int__code_I13_J
% 0.42/0.62 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit0 K2))) ((ord_less_int K1) K2)))
% 0.42/0.62 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_54_rel__simps_I14_J
% 0.42/0.62 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit0 L))) ((ord_less_int K) L)))
% 0.42/0.62 FOF formula ((ord_less_eq_int pls) pls) of role axiom named fact_55_rel__simps_I19_J
% 0.42/0.62 A new axiom: ((ord_less_eq_int pls) pls)
% 0.42/0.62 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_56_less__eq__int__code_I13_J
% 0.42/0.62 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit0 K2))) ((ord_less_eq_int K1) K2)))
% 0.42/0.62 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_57_rel__simps_I31_J
% 0.42/0.62 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit0 L))) ((ord_less_eq_int K) L)))
% 0.42/0.62 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_58_less__number__of__int__code
% 0.42/0.62 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)))
% 0.42/0.62 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_59_less__eq__number__of__int__code
% 0.42/0.62 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)))
% 0.42/0.64 FOF formula (forall (K:int) (_TPTP_I:int) (J:int), (((ord_less_int _TPTP_I) J)->((ord_less_int ((plus_plus_int _TPTP_I) K)) ((plus_plus_int J) K)))) of role axiom named fact_60_zadd__strict__right__mono
% 0.42/0.64 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))))
% 0.42/0.64 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_61_zadd__left__mono
% 0.42/0.64 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))))
% 0.42/0.64 FOF formula (forall (V_1:int) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_1))) (number_number_of_nat V_1)))) ((((ord_less_int V) pls)->False)->((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_1))) (number_number_of_nat V)))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_1))) (number_number_of_nat ((plus_plus_int V) V_1)))))))) of role axiom named fact_62_add__nat__number__of
% 0.42/0.64 A new axiom: (forall (V_1:int) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_1))) (number_number_of_nat V_1)))) ((((ord_less_int V) pls)->False)->((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_1))) (number_number_of_nat V)))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_1))) (number_number_of_nat ((plus_plus_int V) V_1))))))))
% 0.42/0.64 FOF formula (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat) of role axiom named fact_63_nat__numeral__1__eq__1
% 0.42/0.64 A new axiom: (((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat)
% 0.42/0.64 FOF formula (((eq nat) one_one_nat) (number_number_of_nat (bit1 pls))) of role axiom named fact_64_Numeral1__eq1__nat
% 0.42/0.64 A new axiom: (((eq nat) one_one_nat) (number_number_of_nat (bit1 pls)))
% 0.42/0.64 FOF formula (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_65_rel__simps_I29_J
% 0.42/0.64 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls)))
% 0.42/0.64 FOF formula (forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_66_rel__simps_I5_J
% 0.42/0.64 A new axiom: (forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K)))
% 0.42/0.64 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_67_less__eq__int__code_I15_J
% 0.42/0.64 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2)))
% 0.42/0.64 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_68_rel__simps_I33_J
% 0.42/0.64 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit0 L))) ((ord_less_int K) L)))
% 0.42/0.64 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_69_less__int__code_I14_J
% 0.42/0.64 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2)))
% 0.42/0.64 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_70_rel__simps_I15_J
% 0.42/0.64 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L)))
% 0.42/0.64 FOF formula (forall (W:int) (Z:int), (((ord_less_int W) Z)->((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z))) of role axiom named fact_71_zless__imp__add1__zle
% 0.42/0.64 A new axiom: (forall (W:int) (Z:int), (((ord_less_int W) Z)->((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z)))
% 0.42/0.64 FOF formula (forall (W:int) (Z:int), ((iff ((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z)) ((ord_less_int W) Z))) of role axiom named fact_72_add1__zle__eq
% 0.42/0.66 A new axiom: (forall (W:int) (Z:int), ((iff ((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z)) ((ord_less_int W) Z)))
% 0.42/0.66 FOF formula (forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((ord_less_eq_int W) Z))) of role axiom named fact_73_zle__add1__eq__le
% 0.42/0.66 A new axiom: (forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((ord_less_eq_int W) Z)))
% 0.42/0.66 FOF formula (zprime (number_number_of_int (bit0 (bit1 pls)))) of role axiom named fact_74_zprime__2
% 0.42/0.66 A new axiom: (zprime (number_number_of_int (bit0 (bit1 pls))))
% 0.42/0.66 FOF formula (forall (Y_1:int) (X_1:int), ((twoSqu1013291560sum2sq X_1)->((twoSqu1013291560sum2sq Y_1)->(twoSqu1013291560sum2sq ((times_times_int X_1) Y_1))))) of role axiom named fact_75_is__mult__sum2sq
% 0.42/0.66 A new axiom: (forall (Y_1:int) (X_1:int), ((twoSqu1013291560sum2sq X_1)->((twoSqu1013291560sum2sq Y_1)->(twoSqu1013291560sum2sq ((times_times_int X_1) Y_1)))))
% 0.42/0.66 FOF formula (forall (Lx_6:int) (Ly_4:int) (Rx_6:int) (Ry_4:int), (((eq int) ((times_times_int ((times_times_int Lx_6) Ly_4)) ((times_times_int Rx_6) Ry_4))) ((times_times_int ((times_times_int Lx_6) Rx_6)) ((times_times_int Ly_4) Ry_4)))) of role axiom named fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J
% 0.42/0.66 A new axiom: (forall (Lx_6:int) (Ly_4:int) (Rx_6:int) (Ry_4:int), (((eq int) ((times_times_int ((times_times_int Lx_6) Ly_4)) ((times_times_int Rx_6) Ry_4))) ((times_times_int ((times_times_int Lx_6) Rx_6)) ((times_times_int Ly_4) Ry_4))))
% 0.42/0.66 FOF formula (forall (Lx_6:nat) (Ly_4:nat) (Rx_6:nat) (Ry_4:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_6) Ly_4)) ((times_times_nat Rx_6) Ry_4))) ((times_times_nat ((times_times_nat Lx_6) Rx_6)) ((times_times_nat Ly_4) Ry_4)))) of role axiom named fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J
% 0.42/0.66 A new axiom: (forall (Lx_6:nat) (Ly_4:nat) (Rx_6:nat) (Ry_4:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_6) Ly_4)) ((times_times_nat Rx_6) Ry_4))) ((times_times_nat ((times_times_nat Lx_6) Rx_6)) ((times_times_nat Ly_4) Ry_4))))
% 0.42/0.66 FOF formula (forall (Lx_5:int) (Ly_3:int) (Rx_5:int) (Ry_3:int), (((eq int) ((times_times_int ((times_times_int Lx_5) Ly_3)) ((times_times_int Rx_5) Ry_3))) ((times_times_int Rx_5) ((times_times_int ((times_times_int Lx_5) Ly_3)) Ry_3)))) of role axiom named fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J
% 0.42/0.66 A new axiom: (forall (Lx_5:int) (Ly_3:int) (Rx_5:int) (Ry_3:int), (((eq int) ((times_times_int ((times_times_int Lx_5) Ly_3)) ((times_times_int Rx_5) Ry_3))) ((times_times_int Rx_5) ((times_times_int ((times_times_int Lx_5) Ly_3)) Ry_3))))
% 0.42/0.66 FOF formula (forall (Lx_5:nat) (Ly_3:nat) (Rx_5:nat) (Ry_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) ((times_times_nat Rx_5) Ry_3))) ((times_times_nat Rx_5) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) Ry_3)))) of role axiom named fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J
% 0.42/0.66 A new axiom: (forall (Lx_5:nat) (Ly_3:nat) (Rx_5:nat) (Ry_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) ((times_times_nat Rx_5) Ry_3))) ((times_times_nat Rx_5) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) Ry_3))))
% 0.42/0.66 FOF formula (forall (Lx_4:int) (Ly_2:int) (Rx_4:int) (Ry_2:int), (((eq int) ((times_times_int ((times_times_int Lx_4) Ly_2)) ((times_times_int Rx_4) Ry_2))) ((times_times_int Lx_4) ((times_times_int Ly_2) ((times_times_int Rx_4) Ry_2))))) of role axiom named fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J
% 0.42/0.66 A new axiom: (forall (Lx_4:int) (Ly_2:int) (Rx_4:int) (Ry_2:int), (((eq int) ((times_times_int ((times_times_int Lx_4) Ly_2)) ((times_times_int Rx_4) Ry_2))) ((times_times_int Lx_4) ((times_times_int Ly_2) ((times_times_int Rx_4) Ry_2)))))
% 0.42/0.66 FOF formula (forall (Lx_4:nat) (Ly_2:nat) (Rx_4:nat) (Ry_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_4) Ly_2)) ((times_times_nat Rx_4) Ry_2))) ((times_times_nat Lx_4) ((times_times_nat Ly_2) ((times_times_nat Rx_4) Ry_2))))) of role axiom named fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J
% 0.42/0.67 A new axiom: (forall (Lx_4:nat) (Ly_2:nat) (Rx_4:nat) (Ry_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_4) Ly_2)) ((times_times_nat Rx_4) Ry_2))) ((times_times_nat Lx_4) ((times_times_nat Ly_2) ((times_times_nat Rx_4) Ry_2)))))
% 0.42/0.67 FOF formula (forall (Lx_3:int) (Ly_1:int) (Rx_3:int), (((eq int) ((times_times_int ((times_times_int Lx_3) Ly_1)) Rx_3)) ((times_times_int ((times_times_int Lx_3) Rx_3)) Ly_1))) of role axiom named fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J
% 0.42/0.67 A new axiom: (forall (Lx_3:int) (Ly_1:int) (Rx_3:int), (((eq int) ((times_times_int ((times_times_int Lx_3) Ly_1)) Rx_3)) ((times_times_int ((times_times_int Lx_3) Rx_3)) Ly_1)))
% 0.42/0.67 FOF formula (forall (Lx_3:nat) (Ly_1:nat) (Rx_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_3) Ly_1)) Rx_3)) ((times_times_nat ((times_times_nat Lx_3) Rx_3)) Ly_1))) of role axiom named fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J
% 0.42/0.67 A new axiom: (forall (Lx_3:nat) (Ly_1:nat) (Rx_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_3) Ly_1)) Rx_3)) ((times_times_nat ((times_times_nat Lx_3) Rx_3)) Ly_1)))
% 0.42/0.67 FOF formula (forall (Lx_2:int) (Ly:int) (Rx_2:int), (((eq int) ((times_times_int ((times_times_int Lx_2) Ly)) Rx_2)) ((times_times_int Lx_2) ((times_times_int Ly) Rx_2)))) of role axiom named fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J
% 0.42/0.67 A new axiom: (forall (Lx_2:int) (Ly:int) (Rx_2:int), (((eq int) ((times_times_int ((times_times_int Lx_2) Ly)) Rx_2)) ((times_times_int Lx_2) ((times_times_int Ly) Rx_2))))
% 0.42/0.67 FOF formula (forall (Lx_2:nat) (Ly:nat) (Rx_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_2) Ly)) Rx_2)) ((times_times_nat Lx_2) ((times_times_nat Ly) Rx_2)))) of role axiom named fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J
% 0.42/0.67 A new axiom: (forall (Lx_2:nat) (Ly:nat) (Rx_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_2) Ly)) Rx_2)) ((times_times_nat Lx_2) ((times_times_nat Ly) Rx_2))))
% 0.42/0.67 FOF formula (forall (Lx_1:int) (Rx_1:int) (Ry_1:int), (((eq int) ((times_times_int Lx_1) ((times_times_int Rx_1) Ry_1))) ((times_times_int ((times_times_int Lx_1) Rx_1)) Ry_1))) of role axiom named fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J
% 0.42/0.67 A new axiom: (forall (Lx_1:int) (Rx_1:int) (Ry_1:int), (((eq int) ((times_times_int Lx_1) ((times_times_int Rx_1) Ry_1))) ((times_times_int ((times_times_int Lx_1) Rx_1)) Ry_1)))
% 0.42/0.67 FOF formula (forall (Lx_1:nat) (Rx_1:nat) (Ry_1:nat), (((eq nat) ((times_times_nat Lx_1) ((times_times_nat Rx_1) Ry_1))) ((times_times_nat ((times_times_nat Lx_1) Rx_1)) Ry_1))) of role axiom named fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J
% 0.42/0.67 A new axiom: (forall (Lx_1:nat) (Rx_1:nat) (Ry_1:nat), (((eq nat) ((times_times_nat Lx_1) ((times_times_nat Rx_1) Ry_1))) ((times_times_nat ((times_times_nat Lx_1) Rx_1)) Ry_1)))
% 0.42/0.67 FOF formula (forall (Lx:int) (Rx:int) (Ry:int), (((eq int) ((times_times_int Lx) ((times_times_int Rx) Ry))) ((times_times_int Rx) ((times_times_int Lx) Ry)))) of role axiom named fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J
% 0.42/0.67 A new axiom: (forall (Lx:int) (Rx:int) (Ry:int), (((eq int) ((times_times_int Lx) ((times_times_int Rx) Ry))) ((times_times_int Rx) ((times_times_int Lx) Ry))))
% 0.42/0.67 FOF formula (forall (Lx:nat) (Rx:nat) (Ry:nat), (((eq nat) ((times_times_nat Lx) ((times_times_nat Rx) Ry))) ((times_times_nat Rx) ((times_times_nat Lx) Ry)))) of role axiom named fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J
% 0.42/0.67 A new axiom: (forall (Lx:nat) (Rx:nat) (Ry:nat), (((eq nat) ((times_times_nat Lx) ((times_times_nat Rx) Ry))) ((times_times_nat Rx) ((times_times_nat Lx) Ry))))
% 0.42/0.67 FOF formula (forall (A_6:int) (B_3:int), (((eq int) ((times_times_int A_6) B_3)) ((times_times_int B_3) A_6))) of role axiom named fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J
% 0.42/0.67 A new axiom: (forall (A_6:int) (B_3:int), (((eq int) ((times_times_int A_6) B_3)) ((times_times_int B_3) A_6)))
% 0.42/0.69 FOF formula (forall (A_6:nat) (B_3:nat), (((eq nat) ((times_times_nat A_6) B_3)) ((times_times_nat B_3) A_6))) of role axiom named fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J
% 0.42/0.69 A new axiom: (forall (A_6:nat) (B_3:nat), (((eq nat) ((times_times_nat A_6) B_3)) ((times_times_nat B_3) A_6)))
% 0.42/0.69 FOF formula (forall (A_5:int) (B_2:int) (C_5:int) (D_2:int), (((eq int) ((plus_plus_int ((plus_plus_int A_5) B_2)) ((plus_plus_int C_5) D_2))) ((plus_plus_int ((plus_plus_int A_5) C_5)) ((plus_plus_int B_2) D_2)))) of role axiom named fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J
% 0.42/0.69 A new axiom: (forall (A_5:int) (B_2:int) (C_5:int) (D_2:int), (((eq int) ((plus_plus_int ((plus_plus_int A_5) B_2)) ((plus_plus_int C_5) D_2))) ((plus_plus_int ((plus_plus_int A_5) C_5)) ((plus_plus_int B_2) D_2))))
% 0.42/0.69 FOF formula (forall (A_5:nat) (B_2:nat) (C_5:nat) (D_2:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_5) B_2)) ((plus_plus_nat C_5) D_2))) ((plus_plus_nat ((plus_plus_nat A_5) C_5)) ((plus_plus_nat B_2) D_2)))) of role axiom named fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J
% 0.42/0.69 A new axiom: (forall (A_5:nat) (B_2:nat) (C_5:nat) (D_2:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_5) B_2)) ((plus_plus_nat C_5) D_2))) ((plus_plus_nat ((plus_plus_nat A_5) C_5)) ((plus_plus_nat B_2) D_2))))
% 0.42/0.69 FOF formula (forall (A_4:int) (B_1:int) (C_4:int), (((eq int) ((plus_plus_int ((plus_plus_int A_4) B_1)) C_4)) ((plus_plus_int ((plus_plus_int A_4) C_4)) B_1))) of role axiom named fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J
% 0.42/0.69 A new axiom: (forall (A_4:int) (B_1:int) (C_4:int), (((eq int) ((plus_plus_int ((plus_plus_int A_4) B_1)) C_4)) ((plus_plus_int ((plus_plus_int A_4) C_4)) B_1)))
% 0.42/0.69 FOF formula (forall (A_4:nat) (B_1:nat) (C_4:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_4) B_1)) C_4)) ((plus_plus_nat ((plus_plus_nat A_4) C_4)) B_1))) of role axiom named fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J
% 0.42/0.69 A new axiom: (forall (A_4:nat) (B_1:nat) (C_4:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_4) B_1)) C_4)) ((plus_plus_nat ((plus_plus_nat A_4) C_4)) B_1)))
% 0.42/0.69 FOF formula (forall (A_3:int) (B:int) (C_3:int), (((eq int) ((plus_plus_int ((plus_plus_int A_3) B)) C_3)) ((plus_plus_int A_3) ((plus_plus_int B) C_3)))) of role axiom named fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J
% 0.42/0.69 A new axiom: (forall (A_3:int) (B:int) (C_3:int), (((eq int) ((plus_plus_int ((plus_plus_int A_3) B)) C_3)) ((plus_plus_int A_3) ((plus_plus_int B) C_3))))
% 0.42/0.69 FOF formula (forall (A_3:nat) (B:nat) (C_3:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_3) B)) C_3)) ((plus_plus_nat A_3) ((plus_plus_nat B) C_3)))) of role axiom named fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J
% 0.42/0.69 A new axiom: (forall (A_3:nat) (B:nat) (C_3:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_3) B)) C_3)) ((plus_plus_nat A_3) ((plus_plus_nat B) C_3))))
% 0.42/0.69 FOF formula (forall (A_2:int) (C_2:int) (D_1:int), (((eq int) ((plus_plus_int A_2) ((plus_plus_int C_2) D_1))) ((plus_plus_int ((plus_plus_int A_2) C_2)) D_1))) of role axiom named fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J
% 0.42/0.69 A new axiom: (forall (A_2:int) (C_2:int) (D_1:int), (((eq int) ((plus_plus_int A_2) ((plus_plus_int C_2) D_1))) ((plus_plus_int ((plus_plus_int A_2) C_2)) D_1)))
% 0.42/0.69 FOF formula (forall (A_2:nat) (C_2:nat) (D_1:nat), (((eq nat) ((plus_plus_nat A_2) ((plus_plus_nat C_2) D_1))) ((plus_plus_nat ((plus_plus_nat A_2) C_2)) D_1))) of role axiom named fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J
% 0.42/0.69 A new axiom: (forall (A_2:nat) (C_2:nat) (D_1:nat), (((eq nat) ((plus_plus_nat A_2) ((plus_plus_nat C_2) D_1))) ((plus_plus_nat ((plus_plus_nat A_2) C_2)) D_1)))
% 0.42/0.69 FOF formula (forall (A_1:int) (C_1:int) (D:int), (((eq int) ((plus_plus_int A_1) ((plus_plus_int C_1) D))) ((plus_plus_int C_1) ((plus_plus_int A_1) D)))) of role axiom named fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J
% 0.42/0.71 A new axiom: (forall (A_1:int) (C_1:int) (D:int), (((eq int) ((plus_plus_int A_1) ((plus_plus_int C_1) D))) ((plus_plus_int C_1) ((plus_plus_int A_1) D))))
% 0.42/0.71 FOF formula (forall (A_1:nat) (C_1:nat) (D:nat), (((eq nat) ((plus_plus_nat A_1) ((plus_plus_nat C_1) D))) ((plus_plus_nat C_1) ((plus_plus_nat A_1) D)))) of role axiom named fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J
% 0.42/0.71 A new axiom: (forall (A_1:nat) (C_1:nat) (D:nat), (((eq nat) ((plus_plus_nat A_1) ((plus_plus_nat C_1) D))) ((plus_plus_nat C_1) ((plus_plus_nat A_1) D))))
% 0.42/0.71 FOF formula (forall (A:int) (C:int), (((eq int) ((plus_plus_int A) C)) ((plus_plus_int C) A))) of role axiom named fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J
% 0.42/0.71 A new axiom: (forall (A:int) (C:int), (((eq int) ((plus_plus_int A) C)) ((plus_plus_int C) A)))
% 0.42/0.71 FOF formula (forall (A:nat) (C:nat), (((eq nat) ((plus_plus_nat A) C)) ((plus_plus_nat C) A))) of role axiom named fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J
% 0.42/0.71 A new axiom: (forall (A:nat) (C:nat), (((eq nat) ((plus_plus_nat A) C)) ((plus_plus_nat C) A)))
% 0.42/0.71 FOF formula (forall (X_3:int) (Y_2:int), ((iff (((eq int) (number_number_of_int X_3)) (number_number_of_int Y_2))) (((eq int) X_3) Y_2))) of role axiom named fact_104_eq__number__of
% 0.42/0.71 A new axiom: (forall (X_3:int) (Y_2:int), ((iff (((eq int) (number_number_of_int X_3)) (number_number_of_int Y_2))) (((eq int) X_3) Y_2)))
% 0.42/0.71 FOF formula (forall (W_1:int) (X_2:nat), ((iff (((eq nat) (number_number_of_nat W_1)) X_2)) (((eq nat) X_2) (number_number_of_nat W_1)))) of role axiom named fact_105_number__of__reorient
% 0.42/0.71 A new axiom: (forall (W_1:int) (X_2:nat), ((iff (((eq nat) (number_number_of_nat W_1)) X_2)) (((eq nat) X_2) (number_number_of_nat W_1))))
% 0.42/0.71 FOF formula (forall (W_1:int) (X_2:int), ((iff (((eq int) (number_number_of_int W_1)) X_2)) (((eq int) X_2) (number_number_of_int W_1)))) of role axiom named fact_106_number__of__reorient
% 0.42/0.71 A new axiom: (forall (W_1:int) (X_2:int), ((iff (((eq int) (number_number_of_int W_1)) X_2)) (((eq int) X_2) (number_number_of_int W_1))))
% 0.42/0.71 FOF formula (forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L))) of role axiom named fact_107_rel__simps_I51_J
% 0.42/0.71 A new axiom: (forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L)))
% 0.42/0.71 FOF formula (forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L))) of role axiom named fact_108_rel__simps_I48_J
% 0.42/0.71 A new axiom: (forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L)))
% 0.42/0.71 FOF formula (forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((times_times_int ((times_times_int Z1) Z2)) Z3)) ((times_times_int Z1) ((times_times_int Z2) Z3)))) of role axiom named fact_109_zmult__assoc
% 0.42/0.71 A new axiom: (forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((times_times_int ((times_times_int Z1) Z2)) Z3)) ((times_times_int Z1) ((times_times_int Z2) Z3))))
% 0.42/0.71 FOF formula (forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z))) of role axiom named fact_110_zmult__commute
% 0.42/0.71 A new axiom: (forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z)))
% 0.42/0.71 FOF formula (forall (K:int), (((eq int) (number_number_of_int K)) K)) of role axiom named fact_111_number__of__is__id
% 0.42/0.71 A new axiom: (forall (K:int), (((eq int) (number_number_of_int K)) K))
% 0.42/0.71 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_112_zadd__assoc
% 0.42/0.71 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))))
% 0.42/0.71 FOF formula (forall (X_1:int) (Y_1:int) (Z:int), (((eq int) ((plus_plus_int X_1) ((plus_plus_int Y_1) Z))) ((plus_plus_int Y_1) ((plus_plus_int X_1) Z)))) of role axiom named fact_113_zadd__left__commute
% 0.42/0.71 A new axiom: (forall (X_1:int) (Y_1:int) (Z:int), (((eq int) ((plus_plus_int X_1) ((plus_plus_int Y_1) Z))) ((plus_plus_int Y_1) ((plus_plus_int X_1) Z))))
% 0.42/0.71 FOF formula (forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z))) of role axiom named fact_114_zadd__commute
% 0.52/0.72 A new axiom: (forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z)))
% 0.52/0.72 FOF formula (forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_115_rel__simps_I12_J
% 0.52/0.72 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls)))
% 0.52/0.72 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_116_less__int__code_I15_J
% 0.52/0.72 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2)))
% 0.52/0.72 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_117_rel__simps_I16_J
% 0.52/0.72 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit0 L))) ((ord_less_int K) L)))
% 0.52/0.72 FOF formula (forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls))) of role axiom named fact_118_rel__simps_I10_J
% 0.52/0.72 A new axiom: (forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls)))
% 0.52/0.72 FOF formula (forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K))) of role axiom named fact_119_rel__simps_I4_J
% 0.52/0.72 A new axiom: (forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K)))
% 0.52/0.72 FOF formula (forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K))) of role axiom named fact_120_rel__simps_I22_J
% 0.52/0.72 A new axiom: (forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K)))
% 0.52/0.72 FOF formula (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))) of role axiom named fact_121_less__eq__int__code_I14_J
% 0.52/0.72 A new axiom: (forall (K1:int) (K2:int), ((iff ((ord_less_eq_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2)))
% 0.52/0.72 FOF formula (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))) of role axiom named fact_122_rel__simps_I32_J
% 0.52/0.72 A new axiom: (forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L)))
% 0.52/0.72 FOF formula ((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))))) of role conjecture named conj_0
% 0.52/0.72 Conjecture to prove = ((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)))))):Prop
% 0.52/0.72 We need to prove ['((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))']
% 0.52/0.72 Parameter int:Type.
% 0.52/0.72 Parameter nat:Type.
% 0.52/0.72 Parameter one_one_int:int.
% 0.52/0.72 Parameter one_one_nat:nat.
% 0.52/0.72 Parameter plus_plus_int:(int->(int->int)).
% 0.52/0.72 Parameter plus_plus_nat:(nat->(nat->nat)).
% 0.52/0.72 Parameter times_times_int:(int->(int->int)).
% 0.52/0.72 Parameter times_times_nat:(nat->(nat->nat)).
% 0.52/0.72 Parameter zprime:(int->Prop).
% 0.52/0.72 Parameter bit0:(int->int).
% 0.52/0.72 Parameter bit1:(int->int).
% 0.52/0.72 Parameter pls:int.
% 0.52/0.72 Parameter number_number_of_int:(int->int).
% 0.52/0.72 Parameter number_number_of_nat:(int->nat).
% 0.52/0.72 Parameter ord_less_int:(int->(int->Prop)).
% 0.52/0.72 Parameter ord_less_nat:(nat->(nat->Prop)).
% 0.52/0.72 Parameter ord_less_eq_int:(int->(int->Prop)).
% 0.52/0.72 Parameter ord_less_eq_nat:(nat->(nat->Prop)).
% 0.52/0.72 Parameter power_power_int:(int->(nat->int)).
% 0.52/0.72 Parameter power_power_nat:(nat->(nat->nat)).
% 0.52/0.72 Parameter twoSqu1013291560sum2sq:(int->Prop).
% 0.52/0.72 Parameter m:int.
% 0.52/0.72 Parameter s:int.
% 0.52/0.72 Parameter t:int.
% 0.52/0.72 Axiom fact_0_tpos:((ord_less_eq_int one_one_int) t).
% 0.52/0.73 Axiom fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06:((((eq int) t) one_one_int)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))).
% 0.52/0.73 Axiom fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06:(((ord_less_int one_one_int) t)->((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))).
% 0.52/0.73 Axiom fact_3_t__l__p:((ord_less_int t) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)).
% 0.52/0.73 Axiom fact_4_p:(zprime ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)).
% 0.52/0.73 Axiom fact_5_t:(((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)).
% 0.52/0.73 Axiom fact_6_qf1pt:(twoSqu1013291560sum2sq ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) t)).
% 0.52/0.73 Axiom fact_7_zadd__power2:(forall (A_8:int) (B_4:int), (((eq int) ((power_power_int ((plus_plus_int A_8) B_4)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int A_8) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) A_8)) B_4))) ((power_power_int B_4) (number_number_of_nat (bit0 (bit1 pls))))))).
% 0.52/0.73 Axiom fact_8_zadd__power3:(forall (A_8:int) (B_4:int), (((eq int) ((power_power_int ((plus_plus_int A_8) B_4)) (number_number_of_nat (bit1 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((plus_plus_int ((power_power_int A_8) (number_number_of_nat (bit1 (bit1 pls))))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) ((power_power_int A_8) (number_number_of_nat (bit0 (bit1 pls)))))) B_4))) ((times_times_int ((times_times_int (number_number_of_int (bit1 (bit1 pls)))) A_8)) ((power_power_int B_4) (number_number_of_nat (bit0 (bit1 pls))))))) ((power_power_int B_4) (number_number_of_nat (bit1 (bit1 pls))))))).
% 0.52/0.73 Axiom fact_9_power2__sum:(forall (X_11:nat) (Y_5:nat), (((eq nat) ((power_power_nat ((plus_plus_nat X_11) Y_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat ((plus_plus_nat ((power_power_nat X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_nat Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_nat ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) X_11)) Y_5)))).
% 0.52/0.73 Axiom fact_10_power2__sum:(forall (X_11:int) (Y_5:int), (((eq int) ((power_power_int ((plus_plus_int X_11) Y_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_int ((plus_plus_int ((power_power_int X_11) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y_5) (number_number_of_nat (bit0 (bit1 pls)))))) ((times_times_int ((times_times_int (number_number_of_int (bit0 (bit1 pls)))) X_11)) Y_5)))).
% 0.52/0.73 Axiom fact_11_power2__eq__square__number__of:(forall (W_5:int), (((eq int) ((power_power_int (number_number_of_int W_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int (number_number_of_int W_5)) (number_number_of_int W_5)))).
% 0.52/0.73 Axiom fact_12_power2__eq__square__number__of:(forall (W_5:int), (((eq nat) ((power_power_nat (number_number_of_nat W_5)) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat (number_number_of_nat W_5)) (number_number_of_nat W_5)))).
% 0.52/0.73 Axiom fact_13_cube__square:(forall (A_8:int), (((eq int) ((times_times_int A_8) ((power_power_int A_8) (number_number_of_nat (bit0 (bit1 pls)))))) ((power_power_int A_8) (number_number_of_nat (bit1 (bit1 pls)))))).
% 0.52/0.73 Axiom fact_14_one__power2:(((eq nat) ((power_power_nat one_one_nat) (number_number_of_nat (bit0 (bit1 pls))))) one_one_nat).
% 0.52/0.73 Axiom fact_15_one__power2:(((eq int) ((power_power_int one_one_int) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int).
% 0.52/0.73 Axiom fact_16_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J:(forall (X_10:int), (((eq int) ((times_times_int X_10) X_10)) ((power_power_int X_10) (number_number_of_nat (bit0 (bit1 pls)))))).
% 0.52/0.73 Axiom fact_17_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J:(forall (X_10:nat), (((eq nat) ((times_times_nat X_10) X_10)) ((power_power_nat X_10) (number_number_of_nat (bit0 (bit1 pls)))))).
% 0.52/0.73 Axiom fact_18_power2__eq__square:(forall (A_7:int), (((eq int) ((power_power_int A_7) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_int A_7) A_7))).
% 0.52/0.73 Axiom fact_19_power2__eq__square:(forall (A_7:nat), (((eq nat) ((power_power_nat A_7) (number_number_of_nat (bit0 (bit1 pls))))) ((times_times_nat A_7) A_7))).
% 0.52/0.73 Axiom fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J:(forall (X_9:int) (N:nat), (((eq int) ((power_power_int X_9) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N))) ((times_times_int ((power_power_int X_9) N)) ((power_power_int X_9) N)))).
% 0.52/0.73 Axiom fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J:(forall (X_9:nat) (N:nat), (((eq nat) ((power_power_nat X_9) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) N))) ((times_times_nat ((power_power_nat X_9) N)) ((power_power_nat X_9) N)))).
% 0.52/0.73 Axiom fact_22_add__special_I2_J:(forall (W_4:int), (((eq int) ((plus_plus_int one_one_int) (number_number_of_int W_4))) (number_number_of_int ((plus_plus_int (bit1 pls)) W_4)))).
% 0.52/0.73 Axiom fact_23_add__special_I3_J:(forall (V_3:int), (((eq int) ((plus_plus_int (number_number_of_int V_3)) one_one_int)) (number_number_of_int ((plus_plus_int V_3) (bit1 pls))))).
% 0.52/0.73 Axiom fact_24_one__add__one__is__two:(((eq int) ((plus_plus_int one_one_int) one_one_int)) (number_number_of_int (bit0 (bit1 pls)))).
% 0.52/0.73 Axiom fact_25__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_:((forall (T:int), (not (((eq int) ((plus_plus_int ((power_power_int s) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)) ((times_times_int ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int)) T))))->False).
% 0.52/0.73 Axiom fact_26_zle__refl:(forall (W:int), ((ord_less_eq_int W) W)).
% 0.52/0.73 Axiom fact_27_zle__linear:(forall (Z:int) (W:int), ((or ((ord_less_eq_int Z) W)) ((ord_less_eq_int W) Z))).
% 0.52/0.73 Axiom fact_28_zless__le:(forall (Z:int) (W:int), ((iff ((ord_less_int Z) W)) ((and ((ord_less_eq_int Z) W)) (not (((eq int) Z) W))))).
% 0.52/0.73 Axiom fact_29_zless__linear:(forall (X_1:int) (Y_1:int), ((or ((or ((ord_less_int X_1) Y_1)) (((eq int) X_1) Y_1))) ((ord_less_int Y_1) X_1))).
% 0.52/0.73 Axiom fact_30_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)))).
% 0.52/0.73 Axiom fact_31_zle__antisym:(forall (Z:int) (W:int), (((ord_less_eq_int Z) W)->(((ord_less_eq_int W) Z)->(((eq int) Z) W)))).
% 0.52/0.73 Axiom fact_32_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J:(forall (X_8:int) (P_1:nat) (Q_1:nat), (((eq int) ((power_power_int ((power_power_int X_8) P_1)) Q_1)) ((power_power_int X_8) ((times_times_nat P_1) Q_1)))).
% 0.52/0.73 Axiom fact_33_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J:(forall (X_8:nat) (P_1:nat) (Q_1:nat), (((eq nat) ((power_power_nat ((power_power_nat X_8) P_1)) Q_1)) ((power_power_nat X_8) ((times_times_nat P_1) Q_1)))).
% 0.52/0.73 Axiom fact_34_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J:(forall (X_7:int), (((eq int) ((power_power_int X_7) one_one_nat)) X_7)).
% 0.52/0.73 Axiom fact_35_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J:(forall (X_7:nat), (((eq nat) ((power_power_nat X_7) one_one_nat)) X_7)).
% 0.52/0.73 Axiom fact_36_zpower__zpower:(forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int ((power_power_int X_1) Y_1)) Z)) ((power_power_int X_1) ((times_times_nat Y_1) Z)))).
% 0.52/0.73 Axiom fact_37_le__number__of__eq__not__less:(forall (V_2:int) (W_3:int), ((iff ((ord_less_eq_nat (number_number_of_nat V_2)) (number_number_of_nat W_3))) (((ord_less_nat (number_number_of_nat W_3)) (number_number_of_nat V_2))->False))).
% 0.52/0.73 Axiom fact_38_le__number__of__eq__not__less:(forall (V_2:int) (W_3:int), ((iff ((ord_less_eq_int (number_number_of_int V_2)) (number_number_of_int W_3))) (((ord_less_int (number_number_of_int W_3)) (number_number_of_int V_2))->False))).
% 0.52/0.73 Axiom fact_39_less__number__of:(forall (X_6:int) (Y_4:int), ((iff ((ord_less_int (number_number_of_int X_6)) (number_number_of_int Y_4))) ((ord_less_int X_6) Y_4))).
% 0.52/0.73 Axiom fact_40_le__number__of:(forall (X_5:int) (Y_3:int), ((iff ((ord_less_eq_int (number_number_of_int X_5)) (number_number_of_int Y_3))) ((ord_less_eq_int X_5) Y_3))).
% 0.52/0.73 Axiom fact_41_zadd__zless__mono:(forall (Z_1:int) (Z:int) (W_2:int) (W:int), (((ord_less_int W_2) W)->(((ord_less_eq_int Z_1) Z)->((ord_less_int ((plus_plus_int W_2) Z_1)) ((plus_plus_int W) Z))))).
% 0.52/0.73 Axiom fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J:(forall (X_4:int) (P:nat) (Q:nat), (((eq int) ((times_times_int ((power_power_int X_4) P)) ((power_power_int X_4) Q))) ((power_power_int X_4) ((plus_plus_nat P) Q)))).
% 0.52/0.73 Axiom fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J:(forall (X_4:nat) (P:nat) (Q:nat), (((eq nat) ((times_times_nat ((power_power_nat X_4) P)) ((power_power_nat X_4) Q))) ((power_power_nat X_4) ((plus_plus_nat P) Q)))).
% 0.52/0.73 Axiom fact_44_zpower__zadd__distrib:(forall (X_1:int) (Y_1:nat) (Z:nat), (((eq int) ((power_power_int X_1) ((plus_plus_nat Y_1) Z))) ((times_times_int ((power_power_int X_1) Y_1)) ((power_power_int X_1) Z)))).
% 0.52/0.73 Axiom fact_45_nat__mult__2:(forall (Z:nat), (((eq nat) ((times_times_nat (number_number_of_nat (bit0 (bit1 pls)))) Z)) ((plus_plus_nat Z) Z))).
% 0.52/0.73 Axiom fact_46_nat__mult__2__right:(forall (Z:nat), (((eq nat) ((times_times_nat Z) (number_number_of_nat (bit0 (bit1 pls))))) ((plus_plus_nat Z) Z))).
% 0.52/0.73 Axiom fact_47_nat__1__add__1:(((eq nat) ((plus_plus_nat one_one_nat) one_one_nat)) (number_number_of_nat (bit0 (bit1 pls)))).
% 0.52/0.73 Axiom fact_48_less__int__code_I16_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit1 K2))) ((ord_less_int K1) K2))).
% 0.52/0.73 Axiom fact_49_rel__simps_I17_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit1 L))) ((ord_less_int K) L))).
% 0.52/0.73 Axiom fact_50_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))).
% 0.52/0.73 Axiom fact_51_rel__simps_I34_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit1 L))) ((ord_less_eq_int K) L))).
% 0.52/0.73 Axiom fact_52_rel__simps_I2_J:(((ord_less_int pls) pls)->False).
% 0.52/0.73 Axiom fact_53_less__int__code_I13_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit0 K2))) ((ord_less_int K1) K2))).
% 0.52/0.73 Axiom fact_54_rel__simps_I14_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit0 L))) ((ord_less_int K) L))).
% 0.52/0.73 Axiom fact_55_rel__simps_I19_J:((ord_less_eq_int pls) pls).
% 0.52/0.73 Axiom fact_56_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))).
% 0.52/0.73 Axiom fact_57_rel__simps_I31_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit0 L))) ((ord_less_eq_int K) L))).
% 0.52/0.73 Axiom fact_58_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))).
% 0.52/0.73 Axiom fact_59_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))).
% 0.52/0.73 Axiom fact_60_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)))).
% 0.52/0.73 Axiom fact_61_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)))).
% 0.52/0.73 Axiom fact_62_add__nat__number__of:(forall (V_1:int) (V:int), ((and (((ord_less_int V) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_1))) (number_number_of_nat V_1)))) ((((ord_less_int V) pls)->False)->((and (((ord_less_int V_1) pls)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_1))) (number_number_of_nat V)))) ((((ord_less_int V_1) pls)->False)->(((eq nat) ((plus_plus_nat (number_number_of_nat V)) (number_number_of_nat V_1))) (number_number_of_nat ((plus_plus_int V) V_1)))))))).
% 0.52/0.73 Axiom fact_63_nat__numeral__1__eq__1:(((eq nat) (number_number_of_nat (bit1 pls))) one_one_nat).
% 0.52/0.73 Axiom fact_64_Numeral1__eq1__nat:(((eq nat) one_one_nat) (number_number_of_nat (bit1 pls))).
% 0.52/0.73 Axiom fact_65_rel__simps_I29_J:(forall (K:int), ((iff ((ord_less_eq_int (bit1 K)) pls)) ((ord_less_int K) pls))).
% 0.52/0.73 Axiom fact_66_rel__simps_I5_J:(forall (K:int), ((iff ((ord_less_int pls) (bit1 K))) ((ord_less_eq_int pls) K))).
% 0.52/0.73 Axiom fact_67_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))).
% 0.52/0.73 Axiom fact_68_rel__simps_I33_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))).
% 0.52/0.73 Axiom fact_69_less__int__code_I14_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit0 K1)) (bit1 K2))) ((ord_less_eq_int K1) K2))).
% 0.52/0.73 Axiom fact_70_rel__simps_I15_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))).
% 0.52/0.73 Axiom fact_71_zless__imp__add1__zle:(forall (W:int) (Z:int), (((ord_less_int W) Z)->((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z))).
% 0.52/0.73 Axiom fact_72_add1__zle__eq:(forall (W:int) (Z:int), ((iff ((ord_less_eq_int ((plus_plus_int W) one_one_int)) Z)) ((ord_less_int W) Z))).
% 0.52/0.73 Axiom fact_73_zle__add1__eq__le:(forall (W:int) (Z:int), ((iff ((ord_less_int W) ((plus_plus_int Z) one_one_int))) ((ord_less_eq_int W) Z))).
% 0.52/0.73 Axiom fact_74_zprime__2:(zprime (number_number_of_int (bit0 (bit1 pls)))).
% 0.52/0.73 Axiom fact_75_is__mult__sum2sq:(forall (Y_1:int) (X_1:int), ((twoSqu1013291560sum2sq X_1)->((twoSqu1013291560sum2sq Y_1)->(twoSqu1013291560sum2sq ((times_times_int X_1) Y_1))))).
% 0.52/0.73 Axiom fact_76_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J:(forall (Lx_6:int) (Ly_4:int) (Rx_6:int) (Ry_4:int), (((eq int) ((times_times_int ((times_times_int Lx_6) Ly_4)) ((times_times_int Rx_6) Ry_4))) ((times_times_int ((times_times_int Lx_6) Rx_6)) ((times_times_int Ly_4) Ry_4)))).
% 0.52/0.73 Axiom fact_77_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J:(forall (Lx_6:nat) (Ly_4:nat) (Rx_6:nat) (Ry_4:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_6) Ly_4)) ((times_times_nat Rx_6) Ry_4))) ((times_times_nat ((times_times_nat Lx_6) Rx_6)) ((times_times_nat Ly_4) Ry_4)))).
% 0.52/0.73 Axiom fact_78_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J:(forall (Lx_5:int) (Ly_3:int) (Rx_5:int) (Ry_3:int), (((eq int) ((times_times_int ((times_times_int Lx_5) Ly_3)) ((times_times_int Rx_5) Ry_3))) ((times_times_int Rx_5) ((times_times_int ((times_times_int Lx_5) Ly_3)) Ry_3)))).
% 0.52/0.73 Axiom fact_79_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J:(forall (Lx_5:nat) (Ly_3:nat) (Rx_5:nat) (Ry_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) ((times_times_nat Rx_5) Ry_3))) ((times_times_nat Rx_5) ((times_times_nat ((times_times_nat Lx_5) Ly_3)) Ry_3)))).
% 0.52/0.73 Axiom fact_80_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J:(forall (Lx_4:int) (Ly_2:int) (Rx_4:int) (Ry_2:int), (((eq int) ((times_times_int ((times_times_int Lx_4) Ly_2)) ((times_times_int Rx_4) Ry_2))) ((times_times_int Lx_4) ((times_times_int Ly_2) ((times_times_int Rx_4) Ry_2))))).
% 0.52/0.73 Axiom fact_81_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J:(forall (Lx_4:nat) (Ly_2:nat) (Rx_4:nat) (Ry_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_4) Ly_2)) ((times_times_nat Rx_4) Ry_2))) ((times_times_nat Lx_4) ((times_times_nat Ly_2) ((times_times_nat Rx_4) Ry_2))))).
% 0.52/0.73 Axiom fact_82_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J:(forall (Lx_3:int) (Ly_1:int) (Rx_3:int), (((eq int) ((times_times_int ((times_times_int Lx_3) Ly_1)) Rx_3)) ((times_times_int ((times_times_int Lx_3) Rx_3)) Ly_1))).
% 0.52/0.73 Axiom fact_83_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J:(forall (Lx_3:nat) (Ly_1:nat) (Rx_3:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_3) Ly_1)) Rx_3)) ((times_times_nat ((times_times_nat Lx_3) Rx_3)) Ly_1))).
% 0.52/0.73 Axiom fact_84_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J:(forall (Lx_2:int) (Ly:int) (Rx_2:int), (((eq int) ((times_times_int ((times_times_int Lx_2) Ly)) Rx_2)) ((times_times_int Lx_2) ((times_times_int Ly) Rx_2)))).
% 0.52/0.73 Axiom fact_85_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J:(forall (Lx_2:nat) (Ly:nat) (Rx_2:nat), (((eq nat) ((times_times_nat ((times_times_nat Lx_2) Ly)) Rx_2)) ((times_times_nat Lx_2) ((times_times_nat Ly) Rx_2)))).
% 0.52/0.73 Axiom fact_86_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J:(forall (Lx_1:int) (Rx_1:int) (Ry_1:int), (((eq int) ((times_times_int Lx_1) ((times_times_int Rx_1) Ry_1))) ((times_times_int ((times_times_int Lx_1) Rx_1)) Ry_1))).
% 0.52/0.73 Axiom fact_87_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J:(forall (Lx_1:nat) (Rx_1:nat) (Ry_1:nat), (((eq nat) ((times_times_nat Lx_1) ((times_times_nat Rx_1) Ry_1))) ((times_times_nat ((times_times_nat Lx_1) Rx_1)) Ry_1))).
% 0.52/0.73 Axiom fact_88_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J:(forall (Lx:int) (Rx:int) (Ry:int), (((eq int) ((times_times_int Lx) ((times_times_int Rx) Ry))) ((times_times_int Rx) ((times_times_int Lx) Ry)))).
% 0.52/0.73 Axiom fact_89_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J:(forall (Lx:nat) (Rx:nat) (Ry:nat), (((eq nat) ((times_times_nat Lx) ((times_times_nat Rx) Ry))) ((times_times_nat Rx) ((times_times_nat Lx) Ry)))).
% 0.52/0.73 Axiom fact_90_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J:(forall (A_6:int) (B_3:int), (((eq int) ((times_times_int A_6) B_3)) ((times_times_int B_3) A_6))).
% 0.52/0.73 Axiom fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J:(forall (A_6:nat) (B_3:nat), (((eq nat) ((times_times_nat A_6) B_3)) ((times_times_nat B_3) A_6))).
% 0.52/0.73 Axiom fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_5:int) (B_2:int) (C_5:int) (D_2:int), (((eq int) ((plus_plus_int ((plus_plus_int A_5) B_2)) ((plus_plus_int C_5) D_2))) ((plus_plus_int ((plus_plus_int A_5) C_5)) ((plus_plus_int B_2) D_2)))).
% 0.52/0.73 Axiom fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J:(forall (A_5:nat) (B_2:nat) (C_5:nat) (D_2:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_5) B_2)) ((plus_plus_nat C_5) D_2))) ((plus_plus_nat ((plus_plus_nat A_5) C_5)) ((plus_plus_nat B_2) D_2)))).
% 0.52/0.73 Axiom fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_4:int) (B_1:int) (C_4:int), (((eq int) ((plus_plus_int ((plus_plus_int A_4) B_1)) C_4)) ((plus_plus_int ((plus_plus_int A_4) C_4)) B_1))).
% 0.52/0.73 Axiom fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J:(forall (A_4:nat) (B_1:nat) (C_4:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_4) B_1)) C_4)) ((plus_plus_nat ((plus_plus_nat A_4) C_4)) B_1))).
% 0.52/0.73 Axiom fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_3:int) (B:int) (C_3:int), (((eq int) ((plus_plus_int ((plus_plus_int A_3) B)) C_3)) ((plus_plus_int A_3) ((plus_plus_int B) C_3)))).
% 0.52/0.73 Axiom fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J:(forall (A_3:nat) (B:nat) (C_3:nat), (((eq nat) ((plus_plus_nat ((plus_plus_nat A_3) B)) C_3)) ((plus_plus_nat A_3) ((plus_plus_nat B) C_3)))).
% 0.52/0.73 Axiom fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_2:int) (C_2:int) (D_1:int), (((eq int) ((plus_plus_int A_2) ((plus_plus_int C_2) D_1))) ((plus_plus_int ((plus_plus_int A_2) C_2)) D_1))).
% 0.52/0.73 Axiom fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J:(forall (A_2:nat) (C_2:nat) (D_1:nat), (((eq nat) ((plus_plus_nat A_2) ((plus_plus_nat C_2) D_1))) ((plus_plus_nat ((plus_plus_nat A_2) C_2)) D_1))).
% 0.52/0.73 Axiom fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_1:int) (C_1:int) (D:int), (((eq int) ((plus_plus_int A_1) ((plus_plus_int C_1) D))) ((plus_plus_int C_1) ((plus_plus_int A_1) D)))).
% 78.17/78.40 Axiom fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J:(forall (A_1:nat) (C_1:nat) (D:nat), (((eq nat) ((plus_plus_nat A_1) ((plus_plus_nat C_1) D))) ((plus_plus_nat C_1) ((plus_plus_nat A_1) D)))).
% 78.17/78.40 Axiom fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A:int) (C:int), (((eq int) ((plus_plus_int A) C)) ((plus_plus_int C) A))).
% 78.17/78.40 Axiom fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J:(forall (A:nat) (C:nat), (((eq nat) ((plus_plus_nat A) C)) ((plus_plus_nat C) A))).
% 78.17/78.40 Axiom fact_104_eq__number__of:(forall (X_3:int) (Y_2:int), ((iff (((eq int) (number_number_of_int X_3)) (number_number_of_int Y_2))) (((eq int) X_3) Y_2))).
% 78.17/78.40 Axiom fact_105_number__of__reorient:(forall (W_1:int) (X_2:nat), ((iff (((eq nat) (number_number_of_nat W_1)) X_2)) (((eq nat) X_2) (number_number_of_nat W_1)))).
% 78.17/78.40 Axiom fact_106_number__of__reorient:(forall (W_1:int) (X_2:int), ((iff (((eq int) (number_number_of_int W_1)) X_2)) (((eq int) X_2) (number_number_of_int W_1)))).
% 78.17/78.40 Axiom fact_107_rel__simps_I51_J:(forall (K:int) (L:int), ((iff (((eq int) (bit1 K)) (bit1 L))) (((eq int) K) L))).
% 78.17/78.40 Axiom fact_108_rel__simps_I48_J:(forall (K:int) (L:int), ((iff (((eq int) (bit0 K)) (bit0 L))) (((eq int) K) L))).
% 78.17/78.40 Axiom fact_109_zmult__assoc:(forall (Z1:int) (Z2:int) (Z3:int), (((eq int) ((times_times_int ((times_times_int Z1) Z2)) Z3)) ((times_times_int Z1) ((times_times_int Z2) Z3)))).
% 78.17/78.40 Axiom fact_110_zmult__commute:(forall (Z:int) (W:int), (((eq int) ((times_times_int Z) W)) ((times_times_int W) Z))).
% 78.17/78.40 Axiom fact_111_number__of__is__id:(forall (K:int), (((eq int) (number_number_of_int K)) K)).
% 78.17/78.40 Axiom fact_112_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)))).
% 78.17/78.40 Axiom fact_113_zadd__left__commute:(forall (X_1:int) (Y_1:int) (Z:int), (((eq int) ((plus_plus_int X_1) ((plus_plus_int Y_1) Z))) ((plus_plus_int Y_1) ((plus_plus_int X_1) Z)))).
% 78.17/78.40 Axiom fact_114_zadd__commute:(forall (Z:int) (W:int), (((eq int) ((plus_plus_int Z) W)) ((plus_plus_int W) Z))).
% 78.17/78.40 Axiom fact_115_rel__simps_I12_J:(forall (K:int), ((iff ((ord_less_int (bit1 K)) pls)) ((ord_less_int K) pls))).
% 78.17/78.40 Axiom fact_116_less__int__code_I15_J:(forall (K1:int) (K2:int), ((iff ((ord_less_int (bit1 K1)) (bit0 K2))) ((ord_less_int K1) K2))).
% 78.17/78.40 Axiom fact_117_rel__simps_I16_J:(forall (K:int) (L:int), ((iff ((ord_less_int (bit1 K)) (bit0 L))) ((ord_less_int K) L))).
% 78.17/78.40 Axiom fact_118_rel__simps_I10_J:(forall (K:int), ((iff ((ord_less_int (bit0 K)) pls)) ((ord_less_int K) pls))).
% 78.17/78.40 Axiom fact_119_rel__simps_I4_J:(forall (K:int), ((iff ((ord_less_int pls) (bit0 K))) ((ord_less_int pls) K))).
% 78.17/78.40 Axiom fact_120_rel__simps_I22_J:(forall (K:int), ((iff ((ord_less_eq_int pls) (bit1 K))) ((ord_less_eq_int pls) K))).
% 78.17/78.40 Axiom fact_121_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))).
% 78.17/78.40 Axiom fact_122_rel__simps_I32_J:(forall (K:int) (L:int), ((iff ((ord_less_eq_int (bit0 K)) (bit1 L))) ((ord_less_eq_int K) L))).
% 78.17/78.40 Trying to prove ((ex int) (fun (X:int)=> ((ex int) (fun (Y:int)=> (((eq int) ((plus_plus_int ((power_power_int X) (number_number_of_nat (bit0 (bit1 pls))))) ((power_power_int Y) (number_number_of_nat (bit0 (bit1 pls)))))) ((plus_plus_int ((times_times_int (number_number_of_int (bit0 (bit0 (bit1 pls))))) m)) one_one_int))))))
% 78.17/78.40 Found fact_0_tpos:((ord_less_eq_int one_one_int) t)
% 78.17/78.40 Found fact_0_tpos as proof of ((ord_less_eq_int one_one_int) t)
% 78.17/78.40 Found fact_15_one__power20:=(fact_15_one__power2 (fun (x:int)=> (P t))):((P t)->(P t))
% 78.17/78.40 Found (fact_15_one__power2 (fun (x:int)=> (P t))) as proof of (P0 t)
% 78.17/78.40 Found (fact_15_one__power2 (fun (x:int)=> (P t))) as proof of (P0 t)
% 78.17/78.40 Found fact_15_one__power2:(((eq int) ((power_power_int one_one_int) (number_number_of_nat (bit0 (bit1 pls))))) one_one_int)
% 78.17/78.40 Instantiate: b:=((power_power_int one_one_int) (number_number_of_nat (bit0 (bit1 pls)))):int
% 78.17/78.40 Found fact_15_one__power2 as proof of (((eq int) b) one_one_int)
% 78.17/78.40 Found eq_ref00:=(eq_ref
%------------------------------------------------------------------------------