TSTP Solution File: NUM925^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM925^3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 10:49:04 EDT 2023
% Result : Theorem 0.71s 1.30s
% Output : Proof 0.71s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.25 % Problem : NUM925^3 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.26 % Command : do_cvc5 %s %d
% 0.27/0.46 % Computer : n014.cluster.edu
% 0.27/0.46 % Model : x86_64 x86_64
% 0.27/0.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.46 % Memory : 8042.1875MB
% 0.27/0.46 % OS : Linux 3.10.0-693.el7.x86_64
% 0.27/0.46 % CPULimit : 300
% 0.27/0.46 % WCLimit : 300
% 0.27/0.46 % DateTime : Fri Aug 25 13:34:18 EDT 2023
% 0.27/0.46 % CPUTime :
% 0.32/0.72 %----Proving TH0
% 0.32/0.72 %------------------------------------------------------------------------------
% 0.32/0.72 % File : NUM925^3 : TPTP v8.1.2. Released v5.3.0.
% 0.32/0.72 % Domain : Number Theory
% 0.32/0.72 % Problem : Sum of two squares line 192, 1000 axioms selected
% 0.32/0.72 % Version : Especial.
% 0.32/0.72 % English :
% 0.32/0.72
% 0.32/0.72 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.32/0.72 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.32/0.72 % Source : [Bla11]
% 0.32/0.72 % Names : s2s_1000_thf_l192 [Bla11]
% 0.32/0.72
% 0.32/0.72 % Status : Theorem
% 0.32/0.72 % Rating : 0.23 v8.1.0, 0.18 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.57 v6.0.0, 0.71 v5.5.0, 0.50 v5.4.0, 0.80 v5.3.0
% 0.32/0.72 % Syntax : Number of formulae : 1266 ( 471 unt; 61 typ; 0 def)
% 0.32/0.72 % Number of atoms : 2562 ( 890 equ; 0 cnn)
% 0.32/0.72 % Maximal formula atoms : 7 ( 2 avg)
% 0.32/0.72 % Number of connectives : 10361 ( 219 ~; 66 |; 148 &;8742 @)
% 0.32/0.72 % ( 335 <=>; 851 =>; 0 <=; 0 <~>)
% 0.32/0.72 % Maximal formula depth : 18 ( 6 avg)
% 0.32/0.72 % Number of types : 4 ( 3 usr)
% 0.32/0.72 % Number of type conns : 87 ( 87 >; 0 *; 0 +; 0 <<)
% 0.32/0.72 % Number of symbols : 61 ( 58 usr; 19 con; 0-3 aty)
% 0.32/0.72 % Number of variables : 2501 ( 0 ^;2482 !; 19 ?;2501 :)
% 0.32/0.72 % SPC : TH0_THM_EQU_NAR
% 0.32/0.72
% 0.32/0.72 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.32/0.72 % 2011-08-09 19:49:12
% 0.32/0.72 %------------------------------------------------------------------------------
% 0.32/0.72 %----Should-be-implicit typings (3)
% 0.32/0.72 thf(ty_ty_tc__Int__Oint,type,
% 0.32/0.72 int: $tType ).
% 0.32/0.72
% 0.32/0.72 thf(ty_ty_tc__Nat__Onat,type,
% 0.32/0.72 nat: $tType ).
% 0.32/0.72
% 0.32/0.72 thf(ty_ty_tc__RealDef__Oreal,type,
% 0.32/0.72 real: $tType ).
% 0.32/0.72
% 0.32/0.72 %----Explicit typings (58)
% 0.32/0.72 thf(sy_c_All,type,
% 0.32/0.72 all: ( nat > $o ) > $o ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Ex,type,
% 0.32/0.72 ex: ( nat > $o ) > $o ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Groups_Oabs__class_Oabs_000tc__Int__Oint,type,
% 0.32/0.72 abs_abs_int: int > int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Groups_Oabs__class_Oabs_000tc__RealDef__Oreal,type,
% 0.32/0.72 abs_abs_real: real > real ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint,type,
% 0.32/0.72 minus_minus_int: int > int > int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat,type,
% 0.32/0.72 minus_minus_nat: nat > nat > nat ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Groups_Ominus__class_Ominus_000tc__RealDef__Oreal,type,
% 0.32/0.72 minus_minus_real: real > real > real ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Groups_Oone__class_Oone_000tc__Int__Oint,type,
% 0.32/0.72 one_one_int: int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat,type,
% 0.32/0.72 one_one_nat: nat ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Groups_Oone__class_Oone_000tc__RealDef__Oreal,type,
% 0.32/0.72 one_one_real: real ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint,type,
% 0.32/0.72 plus_plus_int: int > int > int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat,type,
% 0.32/0.72 plus_plus_nat: nat > nat > nat ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Groups_Oplus__class_Oplus_000tc__RealDef__Oreal,type,
% 0.32/0.72 plus_plus_real: real > real > real ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint,type,
% 0.32/0.72 times_times_int: int > int > int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Groups_Otimes__class_Otimes_000tc__Nat__Onat,type,
% 0.32/0.72 times_times_nat: nat > nat > nat ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Groups_Otimes__class_Otimes_000tc__RealDef__Oreal,type,
% 0.32/0.72 times_times_real: real > real > real ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint,type,
% 0.32/0.72 zero_zero_int: int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat,type,
% 0.32/0.72 zero_zero_nat: nat ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Groups_Ozero__class_Ozero_000tc__RealDef__Oreal,type,
% 0.32/0.72 zero_zero_real: real ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_If_000tc__Int__Oint,type,
% 0.32/0.72 if_int: $o > int > int > int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_If_000tc__Nat__Onat,type,
% 0.32/0.72 if_nat: $o > nat > nat > nat ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_IntPrimes_Ozcong,type,
% 0.32/0.72 zcong: int > int > int > $o ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_IntPrimes_Ozprime,type,
% 0.32/0.72 zprime: int > $o ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Int_OBit0,type,
% 0.32/0.72 bit0: int > int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Int_OBit1,type,
% 0.32/0.72 bit1: int > int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Int_OMin,type,
% 0.32/0.72 min: int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Int_OPls,type,
% 0.32/0.72 pls: int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Int_Onat,type,
% 0.32/0.72 nat_1: int > nat ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint,type,
% 0.32/0.72 number_number_of_int: int > int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Int_Onumber__class_Onumber__of_000tc__Nat__Onat,type,
% 0.32/0.72 number_number_of_nat: int > nat ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Int_Onumber__class_Onumber__of_000tc__RealDef__Oreal,type,
% 0.32/0.72 number267125858f_real: int > real ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Int_Osucc,type,
% 0.32/0.72 succ: int > int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_000tc__Int__Oint,type,
% 0.32/0.72 semiri1621563631at_int: nat > int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_000tc__Nat__Onat,type,
% 0.32/0.72 semiri984289939at_nat: nat > nat ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_000tc__RealDef__Oreal,type,
% 0.32/0.72 semiri132038758t_real: nat > real ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Orderings_Oord__class_Oless_000tc__Int__Oint,type,
% 0.32/0.72 ord_less_int: int > int > $o ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,
% 0.32/0.72 ord_less_nat: nat > nat > $o ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Orderings_Oord__class_Oless_000tc__RealDef__Oreal,type,
% 0.32/0.72 ord_less_real: real > real > $o ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__Int__Oint,type,
% 0.32/0.72 ord_less_eq_int: int > int > $o ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat,type,
% 0.32/0.72 ord_less_eq_nat: nat > nat > $o ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__RealDef__Oreal,type,
% 0.32/0.72 ord_less_eq_real: real > real > $o ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Power_Opower__class_Opower_000tc__Int__Oint,type,
% 0.32/0.72 power_power_int: int > nat > int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Power_Opower__class_Opower_000tc__Nat__Onat,type,
% 0.32/0.72 power_power_nat: nat > nat > nat ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Power_Opower__class_Opower_000tc__RealDef__Oreal,type,
% 0.32/0.72 power_power_real: real > nat > real ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Residues_OLegendre,type,
% 0.32/0.72 legendre: int > int > int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Residues_OQuadRes,type,
% 0.32/0.72 quadRes: int > int > $o ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Rings_Odvd__class_Odvd_000tc__Int__Oint,type,
% 0.32/0.72 dvd_dvd_int: int > int > $o ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_Rings_Odvd__class_Odvd_000tc__Nat__Onat,type,
% 0.32/0.72 dvd_dvd_nat: nat > nat > $o ).
% 0.32/0.72
% 0.32/0.72 thf(sy_c_TwoSquares__Mirabelle__dzzvbppuls_Ois__sum2sq,type,
% 0.32/0.72 twoSqu919416604sum2sq: int > $o ).
% 0.32/0.72
% 0.32/0.72 thf(sy_v_m,type,
% 0.32/0.72 m: int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_v_m1____,type,
% 0.32/0.72 m1: int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_v_n____,type,
% 0.32/0.72 n: nat ).
% 0.32/0.72
% 0.32/0.72 thf(sy_v_s1____,type,
% 0.32/0.72 s1: int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_v_s____,type,
% 0.32/0.72 s: int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_v_t____,type,
% 0.32/0.72 t: int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_v_tn____,type,
% 0.32/0.72 tn: nat ).
% 0.32/0.72
% 0.32/0.72 thf(sy_v_x____,type,
% 0.32/0.72 x: int ).
% 0.32/0.72
% 0.32/0.72 thf(sy_v_y____,type,
% 0.32/0.72 y: int ).
% 0.32/0.72
% 0.32/0.72 %----Relevant facts (1198)
% 0.32/0.72 thf(fact_0_n1pos,axiom,
% 0.32/0.72 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_1_t1,axiom,
% 0.32/0.72 ord_less_int @ one_one_int @ t ).
% 0.32/0.72
% 0.32/0.72 thf(fact_2_sum__power2__eq__zero__iff,axiom,
% 0.32/0.72 ! [X: int,Y: int] :
% 0.32/0.72 ( ( ( 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 ) ) ) ) )
% 0.32/0.72 = zero_zero_int )
% 0.32/0.72 <=> ( ( X = zero_zero_int )
% 0.32/0.72 & ( Y = zero_zero_int ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_3_sum__power2__eq__zero__iff,axiom,
% 0.32/0.72 ! [X: real,Y: real] :
% 0.32/0.72 ( ( ( 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 ) ) ) ) )
% 0.32/0.72 = zero_zero_real )
% 0.32/0.72 <=> ( ( X = zero_zero_real )
% 0.32/0.72 & ( Y = zero_zero_real ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_4_one__power2,axiom,
% 0.32/0.72 ( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.72 = one_one_int ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_5_one__power2,axiom,
% 0.32/0.72 ( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.72 = one_one_nat ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_6_one__power2,axiom,
% 0.32/0.72 ( ( power_power_real @ one_one_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.72 = one_one_real ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_7_zero__power2,axiom,
% 0.32/0.72 ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.72 = zero_zero_int ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_8_zero__power2,axiom,
% 0.32/0.72 ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.72 = zero_zero_nat ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_9_zero__power2,axiom,
% 0.32/0.72 ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.72 = zero_zero_real ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_10_zero__eq__power2,axiom,
% 0.32/0.72 ! [A_136: int] :
% 0.32/0.72 ( ( ( power_power_int @ A_136 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.72 = zero_zero_int )
% 0.32/0.72 <=> ( A_136 = zero_zero_int ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_11_zero__eq__power2,axiom,
% 0.32/0.72 ! [A_136: real] :
% 0.32/0.72 ( ( ( power_power_real @ A_136 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.72 = zero_zero_real )
% 0.32/0.72 <=> ( A_136 = zero_zero_real ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_12_add__special_I2_J,axiom,
% 0.32/0.72 ! [W_16: int] :
% 0.32/0.72 ( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_16 ) )
% 0.32/0.72 = ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ W_16 ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_13_add__special_I2_J,axiom,
% 0.32/0.72 ! [W_16: int] :
% 0.32/0.72 ( ( plus_plus_real @ one_one_real @ ( number267125858f_real @ W_16 ) )
% 0.32/0.72 = ( number267125858f_real @ ( plus_plus_int @ ( bit1 @ pls ) @ W_16 ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_14_add__special_I3_J,axiom,
% 0.32/0.72 ! [V_16: int] :
% 0.32/0.72 ( ( plus_plus_int @ ( number_number_of_int @ V_16 ) @ one_one_int )
% 0.32/0.72 = ( number_number_of_int @ ( plus_plus_int @ V_16 @ ( bit1 @ pls ) ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_15_add__special_I3_J,axiom,
% 0.32/0.72 ! [V_16: int] :
% 0.32/0.72 ( ( plus_plus_real @ ( number267125858f_real @ V_16 ) @ one_one_real )
% 0.32/0.72 = ( number267125858f_real @ ( plus_plus_int @ V_16 @ ( bit1 @ pls ) ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_16_one__add__one__is__two,axiom,
% 0.32/0.72 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 0.32/0.72 = ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_17_one__add__one__is__two,axiom,
% 0.32/0.72 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 0.32/0.72 = ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_18_semiring__one__add__one__is__two,axiom,
% 0.32/0.72 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 0.32/0.72 = ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_19_semiring__one__add__one__is__two,axiom,
% 0.32/0.72 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.32/0.72 = ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_20_semiring__one__add__one__is__two,axiom,
% 0.32/0.72 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 0.32/0.72 = ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_21_quartic__square__square,axiom,
% 0.32/0.72 ! [X: int] :
% 0.32/0.72 ( ( power_power_int @ ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.72 = ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_22_power__0__left__number__of,axiom,
% 0.32/0.72 ! [W_15: int] :
% 0.32/0.72 ( ( ( ( number_number_of_nat @ W_15 )
% 0.32/0.72 = zero_zero_nat )
% 0.32/0.72 => ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_15 ) )
% 0.32/0.72 = one_one_int ) )
% 0.32/0.72 & ( ( ( number_number_of_nat @ W_15 )
% 0.32/0.72 != zero_zero_nat )
% 0.32/0.72 => ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_15 ) )
% 0.32/0.72 = zero_zero_int ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_23_power__0__left__number__of,axiom,
% 0.32/0.72 ! [W_15: int] :
% 0.32/0.72 ( ( ( ( number_number_of_nat @ W_15 )
% 0.32/0.72 = zero_zero_nat )
% 0.32/0.72 => ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_15 ) )
% 0.32/0.72 = one_one_nat ) )
% 0.32/0.72 & ( ( ( number_number_of_nat @ W_15 )
% 0.32/0.72 != zero_zero_nat )
% 0.32/0.72 => ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_15 ) )
% 0.32/0.72 = zero_zero_nat ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_24_power__0__left__number__of,axiom,
% 0.32/0.72 ! [W_15: int] :
% 0.32/0.72 ( ( ( ( number_number_of_nat @ W_15 )
% 0.32/0.72 = zero_zero_nat )
% 0.32/0.72 => ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ W_15 ) )
% 0.32/0.72 = one_one_real ) )
% 0.32/0.72 & ( ( ( number_number_of_nat @ W_15 )
% 0.32/0.72 != zero_zero_nat )
% 0.32/0.72 => ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ W_15 ) )
% 0.32/0.72 = zero_zero_real ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_25_semiring__norm_I110_J,axiom,
% 0.32/0.72 ( one_one_int
% 0.32/0.72 = ( number_number_of_int @ ( bit1 @ pls ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_26_semiring__norm_I110_J,axiom,
% 0.32/0.72 ( one_one_real
% 0.32/0.72 = ( number267125858f_real @ ( bit1 @ pls ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_27_numeral__1__eq__1,axiom,
% 0.32/0.72 ( ( number_number_of_int @ ( bit1 @ pls ) )
% 0.32/0.72 = one_one_int ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_28_numeral__1__eq__1,axiom,
% 0.32/0.72 ( ( number267125858f_real @ ( bit1 @ pls ) )
% 0.32/0.72 = one_one_real ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_29_n0,axiom,
% 0.32/0.72 ord_less_nat @ zero_zero_nat @ n ).
% 0.32/0.72
% 0.32/0.72 thf(fact_30_zless__linear,axiom,
% 0.32/0.72 ! [X: int,Y: int] :
% 0.32/0.72 ( ( ord_less_int @ X @ Y )
% 0.32/0.72 | ( X = Y )
% 0.32/0.72 | ( ord_less_int @ Y @ X ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_31_less__number__of__int__code,axiom,
% 0.32/0.72 ! [K: int,L: int] :
% 0.32/0.72 ( ( ord_less_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
% 0.32/0.72 <=> ( ord_less_int @ K @ L ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_32_plus__numeral__code_I9_J,axiom,
% 0.32/0.72 ! [V_1: int,W: int] :
% 0.32/0.72 ( ( plus_plus_int @ ( number_number_of_int @ V_1 ) @ ( number_number_of_int @ W ) )
% 0.32/0.72 = ( number_number_of_int @ ( plus_plus_int @ V_1 @ W ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_33_less__number__of,axiom,
% 0.32/0.72 ! [X_30: int,Y_23: int] :
% 0.32/0.72 ( ( ord_less_int @ ( number_number_of_int @ X_30 ) @ ( number_number_of_int @ Y_23 ) )
% 0.32/0.72 <=> ( ord_less_int @ X_30 @ Y_23 ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_34_less__number__of,axiom,
% 0.32/0.72 ! [X_30: int,Y_23: int] :
% 0.32/0.72 ( ( ord_less_real @ ( number267125858f_real @ X_30 ) @ ( number267125858f_real @ Y_23 ) )
% 0.32/0.72 <=> ( ord_less_int @ X_30 @ Y_23 ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_35_zero__is__num__zero,axiom,
% 0.32/0.72 ( zero_zero_int
% 0.32/0.72 = ( number_number_of_int @ pls ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_36_zpower__int,axiom,
% 0.32/0.72 ! [M: nat,N: nat] :
% 0.32/0.72 ( ( power_power_int @ ( semiri1621563631at_int @ M ) @ N )
% 0.32/0.72 = ( semiri1621563631at_int @ ( power_power_nat @ M @ N ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_37_int__power,axiom,
% 0.32/0.72 ! [M: nat,N: nat] :
% 0.32/0.72 ( ( semiri1621563631at_int @ ( power_power_nat @ M @ N ) )
% 0.32/0.72 = ( power_power_int @ ( semiri1621563631at_int @ M ) @ N ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_38_zadd__int__left,axiom,
% 0.32/0.72 ! [M: nat,N: nat,Z: int] :
% 0.32/0.72 ( ( plus_plus_int @ ( semiri1621563631at_int @ M ) @ ( plus_plus_int @ ( semiri1621563631at_int @ N ) @ Z ) )
% 0.32/0.72 = ( plus_plus_int @ ( semiri1621563631at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_39_zadd__int,axiom,
% 0.32/0.72 ! [M: nat,N: nat] :
% 0.32/0.72 ( ( plus_plus_int @ ( semiri1621563631at_int @ M ) @ ( semiri1621563631at_int @ N ) )
% 0.32/0.72 = ( semiri1621563631at_int @ ( plus_plus_nat @ M @ N ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_40_int__1,axiom,
% 0.32/0.72 ( ( semiri1621563631at_int @ one_one_nat )
% 0.32/0.72 = one_one_int ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_41_nat__number__of__Pls,axiom,
% 0.32/0.72 ( ( number_number_of_nat @ pls )
% 0.32/0.72 = zero_zero_nat ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_42_semiring__norm_I113_J,axiom,
% 0.32/0.72 ( zero_zero_nat
% 0.32/0.72 = ( number_number_of_nat @ pls ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_43_int__eq__0__conv,axiom,
% 0.32/0.72 ! [N: nat] :
% 0.32/0.72 ( ( ( semiri1621563631at_int @ N )
% 0.32/0.72 = zero_zero_int )
% 0.32/0.72 <=> ( N = zero_zero_nat ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_44_int__0,axiom,
% 0.32/0.72 ( ( semiri1621563631at_int @ zero_zero_nat )
% 0.32/0.72 = zero_zero_int ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_45_nat__1__add__1,axiom,
% 0.32/0.72 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.32/0.72 = ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_46_less__int__code_I16_J,axiom,
% 0.32/0.72 ! [K1: int,K2: int] :
% 0.32/0.72 ( ( ord_less_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
% 0.32/0.72 <=> ( ord_less_int @ K1 @ K2 ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_47_rel__simps_I17_J,axiom,
% 0.32/0.72 ! [K: int,L: int] :
% 0.32/0.72 ( ( ord_less_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
% 0.32/0.72 <=> ( ord_less_int @ K @ L ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_48_rel__simps_I2_J,axiom,
% 0.32/0.72 ~ ( ord_less_int @ pls @ pls ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_49_less__int__code_I13_J,axiom,
% 0.32/0.72 ! [K1: int,K2: int] :
% 0.32/0.72 ( ( ord_less_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
% 0.32/0.72 <=> ( ord_less_int @ K1 @ K2 ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_50_rel__simps_I14_J,axiom,
% 0.32/0.72 ! [K: int,L: int] :
% 0.32/0.72 ( ( ord_less_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
% 0.32/0.72 <=> ( ord_less_int @ K @ L ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_51_zadd__strict__right__mono,axiom,
% 0.32/0.72 ! [K: int,I_1: int,J: int] :
% 0.32/0.72 ( ( ord_less_int @ I_1 @ J )
% 0.32/0.72 => ( ord_less_int @ ( plus_plus_int @ I_1 @ K ) @ ( plus_plus_int @ J @ K ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_52_add__nat__number__of,axiom,
% 0.32/0.72 ! [V_2: int,V_1: int] :
% 0.32/0.72 ( ( ( ord_less_int @ V_1 @ pls )
% 0.32/0.72 => ( ( plus_plus_nat @ ( number_number_of_nat @ V_1 ) @ ( number_number_of_nat @ V_2 ) )
% 0.32/0.72 = ( number_number_of_nat @ V_2 ) ) )
% 0.32/0.72 & ( ~ ( ord_less_int @ V_1 @ pls )
% 0.32/0.72 => ( ( ( ord_less_int @ V_2 @ pls )
% 0.32/0.72 => ( ( plus_plus_nat @ ( number_number_of_nat @ V_1 ) @ ( number_number_of_nat @ V_2 ) )
% 0.32/0.72 = ( number_number_of_nat @ V_1 ) ) )
% 0.32/0.72 & ( ~ ( ord_less_int @ V_2 @ pls )
% 0.32/0.72 => ( ( plus_plus_nat @ ( number_number_of_nat @ V_1 ) @ ( number_number_of_nat @ V_2 ) )
% 0.32/0.72 = ( number_number_of_nat @ ( plus_plus_int @ V_1 @ V_2 ) ) ) ) ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_53_one__is__num__one,axiom,
% 0.32/0.72 ( one_one_int
% 0.32/0.72 = ( number_number_of_int @ ( bit1 @ pls ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_54_nat__numeral__1__eq__1,axiom,
% 0.32/0.72 ( ( number_number_of_nat @ ( bit1 @ pls ) )
% 0.32/0.72 = one_one_nat ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_55_Numeral1__eq1__nat,axiom,
% 0.32/0.72 ( one_one_nat
% 0.32/0.72 = ( number_number_of_nat @ ( bit1 @ pls ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_56_eq__number__of,axiom,
% 0.32/0.72 ! [X_29: int,Y_22: int] :
% 0.32/0.72 ( ( ( number_number_of_int @ X_29 )
% 0.32/0.72 = ( number_number_of_int @ Y_22 ) )
% 0.32/0.72 <=> ( X_29 = Y_22 ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_57_eq__number__of,axiom,
% 0.32/0.72 ! [X_29: int,Y_22: int] :
% 0.32/0.72 ( ( ( number267125858f_real @ X_29 )
% 0.32/0.72 = ( number267125858f_real @ Y_22 ) )
% 0.32/0.72 <=> ( X_29 = Y_22 ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_58_number__of__reorient,axiom,
% 0.32/0.72 ! [W_14: int,X_28: nat] :
% 0.32/0.72 ( ( ( number_number_of_nat @ W_14 )
% 0.32/0.72 = X_28 )
% 0.32/0.72 <=> ( X_28
% 0.32/0.72 = ( number_number_of_nat @ W_14 ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_59_number__of__reorient,axiom,
% 0.32/0.72 ! [W_14: int,X_28: int] :
% 0.32/0.72 ( ( ( number_number_of_int @ W_14 )
% 0.32/0.72 = X_28 )
% 0.32/0.72 <=> ( X_28
% 0.32/0.72 = ( number_number_of_int @ W_14 ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_60_number__of__reorient,axiom,
% 0.32/0.72 ! [W_14: int,X_28: real] :
% 0.32/0.72 ( ( ( number267125858f_real @ W_14 )
% 0.32/0.72 = X_28 )
% 0.32/0.72 <=> ( X_28
% 0.32/0.72 = ( number267125858f_real @ W_14 ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_61_rel__simps_I51_J,axiom,
% 0.32/0.72 ! [K: int,L: int] :
% 0.32/0.72 ( ( ( bit1 @ K )
% 0.32/0.72 = ( bit1 @ L ) )
% 0.32/0.72 <=> ( K = L ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_62_rel__simps_I48_J,axiom,
% 0.32/0.72 ! [K: int,L: int] :
% 0.32/0.72 ( ( ( bit0 @ K )
% 0.32/0.72 = ( bit0 @ L ) )
% 0.32/0.72 <=> ( K = L ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_63_even__less__0__iff,axiom,
% 0.32/0.72 ! [A_135: int] :
% 0.32/0.72 ( ( ord_less_int @ ( plus_plus_int @ A_135 @ A_135 ) @ zero_zero_int )
% 0.32/0.72 <=> ( ord_less_int @ A_135 @ zero_zero_int ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_64_even__less__0__iff,axiom,
% 0.32/0.72 ! [A_135: real] :
% 0.32/0.72 ( ( ord_less_real @ ( plus_plus_real @ A_135 @ A_135 ) @ zero_zero_real )
% 0.32/0.72 <=> ( ord_less_real @ A_135 @ zero_zero_real ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_65_zadd__assoc,axiom,
% 0.32/0.72 ! [Z1: int,Z2: int,Z3: int] :
% 0.32/0.72 ( ( plus_plus_int @ ( plus_plus_int @ Z1 @ Z2 ) @ Z3 )
% 0.32/0.72 = ( plus_plus_int @ Z1 @ ( plus_plus_int @ Z2 @ Z3 ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_66_zadd__left__commute,axiom,
% 0.32/0.72 ! [X: int,Y: int,Z: int] :
% 0.32/0.72 ( ( plus_plus_int @ X @ ( plus_plus_int @ Y @ Z ) )
% 0.32/0.72 = ( plus_plus_int @ Y @ ( plus_plus_int @ X @ Z ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_67_zadd__commute,axiom,
% 0.32/0.72 ! [Z: int,W: int] :
% 0.32/0.72 ( ( plus_plus_int @ Z @ W )
% 0.32/0.72 = ( plus_plus_int @ W @ Z ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_68_int__int__eq,axiom,
% 0.32/0.72 ! [M: nat,N: nat] :
% 0.32/0.72 ( ( ( semiri1621563631at_int @ M )
% 0.32/0.72 = ( semiri1621563631at_int @ N ) )
% 0.32/0.72 <=> ( M = N ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_69_less__special_I3_J,axiom,
% 0.32/0.72 ! [X_27: int] :
% 0.32/0.72 ( ( ord_less_int @ ( number_number_of_int @ X_27 ) @ zero_zero_int )
% 0.32/0.72 <=> ( ord_less_int @ X_27 @ pls ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_70_less__special_I3_J,axiom,
% 0.32/0.72 ! [X_27: int] :
% 0.32/0.72 ( ( ord_less_real @ ( number267125858f_real @ X_27 ) @ zero_zero_real )
% 0.32/0.72 <=> ( ord_less_int @ X_27 @ pls ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_71_less__special_I1_J,axiom,
% 0.32/0.72 ! [Y_21: int] :
% 0.32/0.72 ( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ Y_21 ) )
% 0.32/0.72 <=> ( ord_less_int @ pls @ Y_21 ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_72_less__special_I1_J,axiom,
% 0.32/0.72 ! [Y_21: int] :
% 0.32/0.72 ( ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ Y_21 ) )
% 0.32/0.72 <=> ( ord_less_int @ pls @ Y_21 ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_73_rel__simps_I12_J,axiom,
% 0.32/0.72 ! [K: int] :
% 0.32/0.72 ( ( ord_less_int @ ( bit1 @ K ) @ pls )
% 0.32/0.72 <=> ( ord_less_int @ K @ pls ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_74_less__int__code_I15_J,axiom,
% 0.32/0.72 ! [K1: int,K2: int] :
% 0.32/0.72 ( ( ord_less_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
% 0.32/0.72 <=> ( ord_less_int @ K1 @ K2 ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_75_rel__simps_I16_J,axiom,
% 0.32/0.72 ! [K: int,L: int] :
% 0.32/0.72 ( ( ord_less_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
% 0.32/0.72 <=> ( ord_less_int @ K @ L ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_76_rel__simps_I10_J,axiom,
% 0.32/0.72 ! [K: int] :
% 0.32/0.72 ( ( ord_less_int @ ( bit0 @ K ) @ pls )
% 0.32/0.72 <=> ( ord_less_int @ K @ pls ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_77_rel__simps_I4_J,axiom,
% 0.32/0.72 ! [K: int] :
% 0.32/0.72 ( ( ord_less_int @ pls @ ( bit0 @ K ) )
% 0.32/0.72 <=> ( ord_less_int @ pls @ K ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_78_bin__less__0__simps_I4_J,axiom,
% 0.32/0.72 ! [W: int] :
% 0.32/0.72 ( ( ord_less_int @ ( bit1 @ W ) @ zero_zero_int )
% 0.32/0.72 <=> ( ord_less_int @ W @ zero_zero_int ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_79_bin__less__0__simps_I1_J,axiom,
% 0.32/0.72 ~ ( ord_less_int @ pls @ zero_zero_int ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_80_bin__less__0__simps_I3_J,axiom,
% 0.32/0.72 ! [W: int] :
% 0.32/0.72 ( ( ord_less_int @ ( bit0 @ W ) @ zero_zero_int )
% 0.32/0.72 <=> ( ord_less_int @ W @ zero_zero_int ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_81_int__0__less__1,axiom,
% 0.32/0.72 ord_less_int @ zero_zero_int @ one_one_int ).
% 0.32/0.72
% 0.32/0.72 thf(fact_82_zless__add1__eq,axiom,
% 0.32/0.72 ! [W: int,Z: int] :
% 0.32/0.72 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.32/0.72 <=> ( ( ord_less_int @ W @ Z )
% 0.32/0.72 | ( W = Z ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_83_int__less__0__conv,axiom,
% 0.32/0.72 ! [K: nat] :
% 0.32/0.72 ~ ( ord_less_int @ ( semiri1621563631at_int @ K ) @ zero_zero_int ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_84_less__special_I4_J,axiom,
% 0.32/0.72 ! [X_26: int] :
% 0.32/0.72 ( ( ord_less_int @ ( number_number_of_int @ X_26 ) @ one_one_int )
% 0.32/0.72 <=> ( ord_less_int @ X_26 @ ( bit1 @ pls ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_85_less__special_I4_J,axiom,
% 0.32/0.72 ! [X_26: int] :
% 0.32/0.72 ( ( ord_less_real @ ( number267125858f_real @ X_26 ) @ one_one_real )
% 0.32/0.72 <=> ( ord_less_int @ X_26 @ ( bit1 @ pls ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_86_less__special_I2_J,axiom,
% 0.32/0.72 ! [Y_20: int] :
% 0.32/0.72 ( ( ord_less_int @ one_one_int @ ( number_number_of_int @ Y_20 ) )
% 0.32/0.72 <=> ( ord_less_int @ ( bit1 @ pls ) @ Y_20 ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_87_less__special_I2_J,axiom,
% 0.32/0.72 ! [Y_20: int] :
% 0.32/0.72 ( ( ord_less_real @ one_one_real @ ( number267125858f_real @ Y_20 ) )
% 0.32/0.72 <=> ( ord_less_int @ ( bit1 @ pls ) @ Y_20 ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_88_odd__less__0,axiom,
% 0.32/0.72 ! [Z: int] :
% 0.32/0.72 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 0.32/0.72 <=> ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_89_double__eq__0__iff,axiom,
% 0.32/0.72 ! [A_134: int] :
% 0.32/0.72 ( ( ( plus_plus_int @ A_134 @ A_134 )
% 0.32/0.72 = zero_zero_int )
% 0.32/0.72 <=> ( A_134 = zero_zero_int ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_90_double__eq__0__iff,axiom,
% 0.32/0.72 ! [A_134: real] :
% 0.32/0.72 ( ( ( plus_plus_real @ A_134 @ A_134 )
% 0.32/0.72 = zero_zero_real )
% 0.32/0.72 <=> ( A_134 = zero_zero_real ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_91_rel__simps_I46_J,axiom,
% 0.32/0.72 ! [K: int] :
% 0.32/0.72 ( ( bit1 @ K )
% 0.32/0.72 != pls ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_92_rel__simps_I39_J,axiom,
% 0.32/0.72 ! [L: int] :
% 0.32/0.72 ( pls
% 0.32/0.72 != ( bit1 @ L ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_93_rel__simps_I50_J,axiom,
% 0.32/0.72 ! [K: int,L: int] :
% 0.32/0.72 ( ( bit1 @ K )
% 0.32/0.72 != ( bit0 @ L ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_94_rel__simps_I49_J,axiom,
% 0.32/0.72 ! [K: int,L: int] :
% 0.32/0.72 ( ( bit0 @ K )
% 0.32/0.72 != ( bit1 @ L ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_95_rel__simps_I44_J,axiom,
% 0.32/0.72 ! [K: int] :
% 0.32/0.72 ( ( ( bit0 @ K )
% 0.32/0.72 = pls )
% 0.32/0.72 <=> ( K = pls ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_96_rel__simps_I38_J,axiom,
% 0.32/0.72 ! [L: int] :
% 0.32/0.72 ( ( pls
% 0.32/0.72 = ( bit0 @ L ) )
% 0.32/0.72 <=> ( pls = L ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_97_Bit0__Pls,axiom,
% 0.32/0.72 ( ( bit0 @ pls )
% 0.32/0.72 = pls ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_98_Pls__def,axiom,
% 0.32/0.72 pls = zero_zero_int ).
% 0.32/0.72
% 0.32/0.72 thf(fact_99_int__0__neq__1,axiom,
% 0.32/0.72 zero_zero_int != one_one_int ).
% 0.32/0.72
% 0.32/0.72 thf(fact_100_add__Pls__right,axiom,
% 0.32/0.72 ! [K: int] :
% 0.32/0.72 ( ( plus_plus_int @ K @ pls )
% 0.32/0.72 = K ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_101_add__Pls,axiom,
% 0.32/0.72 ! [K: int] :
% 0.32/0.72 ( ( plus_plus_int @ pls @ K )
% 0.32/0.72 = K ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_102_add__Bit0__Bit0,axiom,
% 0.32/0.72 ! [K: int,L: int] :
% 0.32/0.72 ( ( plus_plus_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
% 0.32/0.72 = ( bit0 @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_103_Bit0__def,axiom,
% 0.32/0.72 ! [K: int] :
% 0.32/0.72 ( ( bit0 @ K )
% 0.32/0.72 = ( plus_plus_int @ K @ K ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_104_zadd__0__right,axiom,
% 0.32/0.72 ! [Z: int] :
% 0.32/0.72 ( ( plus_plus_int @ Z @ zero_zero_int )
% 0.32/0.72 = Z ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_105_zadd__0,axiom,
% 0.32/0.72 ! [Z: int] :
% 0.32/0.72 ( ( plus_plus_int @ zero_zero_int @ Z )
% 0.32/0.72 = Z ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_106_semiring__numeral__0__eq__0,axiom,
% 0.32/0.72 ( ( number_number_of_int @ pls )
% 0.32/0.72 = zero_zero_int ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_107_semiring__numeral__0__eq__0,axiom,
% 0.32/0.72 ( ( number_number_of_nat @ pls )
% 0.32/0.72 = zero_zero_nat ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_108_semiring__numeral__0__eq__0,axiom,
% 0.32/0.72 ( ( number267125858f_real @ pls )
% 0.32/0.72 = zero_zero_real ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_109_number__of__Pls,axiom,
% 0.32/0.72 ( ( number_number_of_int @ pls )
% 0.32/0.72 = zero_zero_int ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_110_number__of__Pls,axiom,
% 0.32/0.72 ( ( number267125858f_real @ pls )
% 0.32/0.72 = zero_zero_real ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_111_semiring__norm_I112_J,axiom,
% 0.32/0.72 ( zero_zero_int
% 0.32/0.72 = ( number_number_of_int @ pls ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_112_semiring__norm_I112_J,axiom,
% 0.32/0.72 ( zero_zero_real
% 0.32/0.72 = ( number267125858f_real @ pls ) ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_113_add__numeral__0,axiom,
% 0.32/0.72 ! [A_133: int] :
% 0.32/0.72 ( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A_133 )
% 0.32/0.72 = A_133 ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_114_add__numeral__0,axiom,
% 0.32/0.72 ! [A_133: real] :
% 0.32/0.72 ( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A_133 )
% 0.32/0.72 = A_133 ) ).
% 0.32/0.72
% 0.32/0.72 thf(fact_115_add__numeral__0__right,axiom,
% 0.32/0.73 ! [A_132: int] :
% 0.32/0.73 ( ( plus_plus_int @ A_132 @ ( number_number_of_int @ pls ) )
% 0.32/0.73 = A_132 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_116_add__numeral__0__right,axiom,
% 0.32/0.73 ! [A_132: real] :
% 0.32/0.73 ( ( plus_plus_real @ A_132 @ ( number267125858f_real @ pls ) )
% 0.32/0.73 = A_132 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_117_power__eq__0__iff__number__of,axiom,
% 0.32/0.73 ! [A_131: int,W_13: int] :
% 0.32/0.73 ( ( ( power_power_int @ A_131 @ ( number_number_of_nat @ W_13 ) )
% 0.32/0.73 = zero_zero_int )
% 0.32/0.73 <=> ( ( A_131 = zero_zero_int )
% 0.32/0.73 & ( ( number_number_of_nat @ W_13 )
% 0.32/0.73 != zero_zero_nat ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_118_power__eq__0__iff__number__of,axiom,
% 0.32/0.73 ! [A_131: nat,W_13: int] :
% 0.32/0.73 ( ( ( power_power_nat @ A_131 @ ( number_number_of_nat @ W_13 ) )
% 0.32/0.73 = zero_zero_nat )
% 0.32/0.73 <=> ( ( A_131 = zero_zero_nat )
% 0.32/0.73 & ( ( number_number_of_nat @ W_13 )
% 0.32/0.73 != zero_zero_nat ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_119_power__eq__0__iff__number__of,axiom,
% 0.32/0.73 ! [A_131: real,W_13: int] :
% 0.32/0.73 ( ( ( power_power_real @ A_131 @ ( number_number_of_nat @ W_13 ) )
% 0.32/0.73 = zero_zero_real )
% 0.32/0.73 <=> ( ( A_131 = zero_zero_real )
% 0.32/0.73 & ( ( number_number_of_nat @ W_13 )
% 0.32/0.73 != zero_zero_nat ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_120_add__number__of__left,axiom,
% 0.32/0.73 ! [V_15: int,W_12: int,Z_5: int] :
% 0.32/0.73 ( ( plus_plus_int @ ( number_number_of_int @ V_15 ) @ ( plus_plus_int @ ( number_number_of_int @ W_12 ) @ Z_5 ) )
% 0.32/0.73 = ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ V_15 @ W_12 ) ) @ Z_5 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_121_add__number__of__left,axiom,
% 0.32/0.73 ! [V_15: int,W_12: int,Z_5: real] :
% 0.32/0.73 ( ( plus_plus_real @ ( number267125858f_real @ V_15 ) @ ( plus_plus_real @ ( number267125858f_real @ W_12 ) @ Z_5 ) )
% 0.32/0.73 = ( plus_plus_real @ ( number267125858f_real @ ( plus_plus_int @ V_15 @ W_12 ) ) @ Z_5 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_122_add__number__of__eq,axiom,
% 0.32/0.73 ! [V_14: int,W_11: int] :
% 0.32/0.73 ( ( plus_plus_int @ ( number_number_of_int @ V_14 ) @ ( number_number_of_int @ W_11 ) )
% 0.32/0.73 = ( number_number_of_int @ ( plus_plus_int @ V_14 @ W_11 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_123_add__number__of__eq,axiom,
% 0.32/0.73 ! [V_14: int,W_11: int] :
% 0.32/0.73 ( ( plus_plus_real @ ( number267125858f_real @ V_14 ) @ ( number267125858f_real @ W_11 ) )
% 0.32/0.73 = ( number267125858f_real @ ( plus_plus_int @ V_14 @ W_11 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_124_number__of__add,axiom,
% 0.32/0.73 ! [V_13: int,W_10: int] :
% 0.32/0.73 ( ( number_number_of_int @ ( plus_plus_int @ V_13 @ W_10 ) )
% 0.32/0.73 = ( plus_plus_int @ ( number_number_of_int @ V_13 ) @ ( number_number_of_int @ W_10 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_125_number__of__add,axiom,
% 0.32/0.73 ! [V_13: int,W_10: int] :
% 0.32/0.73 ( ( number267125858f_real @ ( plus_plus_int @ V_13 @ W_10 ) )
% 0.32/0.73 = ( plus_plus_real @ ( number267125858f_real @ V_13 ) @ ( number267125858f_real @ W_10 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_126_add__Bit1__Bit0,axiom,
% 0.32/0.73 ! [K: int,L: int] :
% 0.32/0.73 ( ( plus_plus_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
% 0.32/0.73 = ( bit1 @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_127_add__Bit0__Bit1,axiom,
% 0.32/0.73 ! [K: int,L: int] :
% 0.32/0.73 ( ( plus_plus_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
% 0.32/0.73 = ( bit1 @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_128_Bit1__def,axiom,
% 0.32/0.73 ! [K: int] :
% 0.32/0.73 ( ( bit1 @ K )
% 0.32/0.73 = ( plus_plus_int @ ( plus_plus_int @ one_one_int @ K ) @ K ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_129_odd__nonzero,axiom,
% 0.32/0.73 ! [Z: int] :
% 0.32/0.73 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 0.32/0.73 != zero_zero_int ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_130_number__of__int,axiom,
% 0.32/0.73 ! [N_32: nat] :
% 0.32/0.73 ( ( number_number_of_nat @ ( semiri1621563631at_int @ N_32 ) )
% 0.32/0.73 = ( semiri984289939at_nat @ N_32 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_131_number__of__int,axiom,
% 0.32/0.73 ! [N_32: nat] :
% 0.32/0.73 ( ( number_number_of_int @ ( semiri1621563631at_int @ N_32 ) )
% 0.32/0.73 = ( semiri1621563631at_int @ N_32 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_132_number__of__int,axiom,
% 0.32/0.73 ! [N_32: nat] :
% 0.32/0.73 ( ( number267125858f_real @ ( semiri1621563631at_int @ N_32 ) )
% 0.32/0.73 = ( semiri132038758t_real @ N_32 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_133_zero__less__power2,axiom,
% 0.32/0.73 ! [A_130: int] :
% 0.32/0.73 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_130 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.32/0.73 <=> ( A_130 != zero_zero_int ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_134_zero__less__power2,axiom,
% 0.32/0.73 ! [A_130: real] :
% 0.32/0.73 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A_130 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.32/0.73 <=> ( A_130 != zero_zero_real ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_135_power2__less__0,axiom,
% 0.32/0.73 ! [A_129: int] :
% 0.32/0.73 ~ ( ord_less_int @ ( power_power_int @ A_129 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_136_power2__less__0,axiom,
% 0.32/0.73 ! [A_129: real] :
% 0.32/0.73 ~ ( ord_less_real @ ( power_power_real @ A_129 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_real ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_137_sum__power2__gt__zero__iff,axiom,
% 0.32/0.73 ! [X_25: int,Y_19: int] :
% 0.32/0.73 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_25 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_19 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
% 0.32/0.73 <=> ( ( X_25 != zero_zero_int )
% 0.32/0.73 | ( Y_19 != zero_zero_int ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_138_sum__power2__gt__zero__iff,axiom,
% 0.32/0.73 ! [X_25: real,Y_19: real] :
% 0.32/0.73 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X_25 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_19 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
% 0.32/0.73 <=> ( ( X_25 != zero_zero_real )
% 0.32/0.73 | ( Y_19 != zero_zero_real ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_139_not__sum__power2__lt__zero,axiom,
% 0.32/0.73 ! [X_24: int,Y_18: int] :
% 0.32/0.73 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X_24 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_140_not__sum__power2__lt__zero,axiom,
% 0.32/0.73 ! [X_24: real,Y_18: real] :
% 0.32/0.73 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X_24 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_141_number__of__Bit0,axiom,
% 0.32/0.73 ! [W_9: int] :
% 0.32/0.73 ( ( number_number_of_int @ ( bit0 @ W_9 ) )
% 0.32/0.73 = ( plus_plus_int @ ( plus_plus_int @ zero_zero_int @ ( number_number_of_int @ W_9 ) ) @ ( number_number_of_int @ W_9 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_142_number__of__Bit0,axiom,
% 0.32/0.73 ! [W_9: int] :
% 0.32/0.73 ( ( number267125858f_real @ ( bit0 @ W_9 ) )
% 0.32/0.73 = ( plus_plus_real @ ( plus_plus_real @ zero_zero_real @ ( number267125858f_real @ W_9 ) ) @ ( number267125858f_real @ W_9 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_143_number__of__Bit1,axiom,
% 0.32/0.73 ! [W_8: int] :
% 0.32/0.73 ( ( number_number_of_int @ ( bit1 @ W_8 ) )
% 0.32/0.73 = ( plus_plus_int @ ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_8 ) ) @ ( number_number_of_int @ W_8 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_144_number__of__Bit1,axiom,
% 0.32/0.73 ! [W_8: int] :
% 0.32/0.73 ( ( number267125858f_real @ ( bit1 @ W_8 ) )
% 0.32/0.73 = ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( number267125858f_real @ W_8 ) ) @ ( number267125858f_real @ W_8 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_145_semiring__numeral__1__eq__1,axiom,
% 0.32/0.73 ( ( number_number_of_int @ ( bit1 @ pls ) )
% 0.32/0.73 = one_one_int ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_146_semiring__numeral__1__eq__1,axiom,
% 0.32/0.73 ( ( number_number_of_nat @ ( bit1 @ pls ) )
% 0.32/0.73 = one_one_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_147_semiring__numeral__1__eq__1,axiom,
% 0.32/0.73 ( ( number267125858f_real @ ( bit1 @ pls ) )
% 0.32/0.73 = one_one_real ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_148_mn,axiom,
% 0.32/0.73 ord_less_int @ m1 @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_149_of__nat__less__two__power,axiom,
% 0.32/0.73 ! [N_31: nat] : ( ord_less_int @ ( semiri1621563631at_int @ N_31 ) @ ( power_power_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_31 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_150_of__nat__less__two__power,axiom,
% 0.32/0.73 ! [N_31: nat] : ( ord_less_real @ ( semiri132038758t_real @ N_31 ) @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_31 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_151_transfer__int__nat__numerals_I3_J,axiom,
% 0.32/0.73 ( ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) )
% 0.32/0.73 = ( semiri1621563631at_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_152_transfer__int__nat__numerals_I4_J,axiom,
% 0.32/0.73 ( ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) )
% 0.32/0.73 = ( semiri1621563631at_int @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_153_realpow__two__sum__zero__iff,axiom,
% 0.32/0.73 ! [X: real,Y: real] :
% 0.32/0.73 ( ( ( 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 ) ) ) ) )
% 0.32/0.73 = zero_zero_real )
% 0.32/0.73 <=> ( ( X = zero_zero_real )
% 0.32/0.73 & ( Y = zero_zero_real ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_154_of__nat__0__less__iff,axiom,
% 0.32/0.73 ! [N_30: nat] :
% 0.32/0.73 ( ( ord_less_int @ zero_zero_int @ ( semiri1621563631at_int @ N_30 ) )
% 0.32/0.73 <=> ( ord_less_nat @ zero_zero_nat @ N_30 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_155_of__nat__0__less__iff,axiom,
% 0.32/0.73 ! [N_30: nat] :
% 0.32/0.73 ( ( ord_less_nat @ zero_zero_nat @ ( semiri984289939at_nat @ N_30 ) )
% 0.32/0.73 <=> ( ord_less_nat @ zero_zero_nat @ N_30 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_156_of__nat__0__less__iff,axiom,
% 0.32/0.73 ! [N_30: nat] :
% 0.32/0.73 ( ( ord_less_real @ zero_zero_real @ ( semiri132038758t_real @ N_30 ) )
% 0.32/0.73 <=> ( ord_less_nat @ zero_zero_nat @ N_30 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_157_one__less__power,axiom,
% 0.32/0.73 ! [N_29: nat,A_128: int] :
% 0.32/0.73 ( ( ord_less_int @ one_one_int @ A_128 )
% 0.32/0.73 => ( ( ord_less_nat @ zero_zero_nat @ N_29 )
% 0.32/0.73 => ( ord_less_int @ one_one_int @ ( power_power_int @ A_128 @ N_29 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_158_one__less__power,axiom,
% 0.32/0.73 ! [N_29: nat,A_128: nat] :
% 0.32/0.73 ( ( ord_less_nat @ one_one_nat @ A_128 )
% 0.32/0.73 => ( ( ord_less_nat @ zero_zero_nat @ N_29 )
% 0.32/0.73 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A_128 @ N_29 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_159_one__less__power,axiom,
% 0.32/0.73 ! [N_29: nat,A_128: real] :
% 0.32/0.73 ( ( ord_less_real @ one_one_real @ A_128 )
% 0.32/0.73 => ( ( ord_less_nat @ zero_zero_nat @ N_29 )
% 0.32/0.73 => ( ord_less_real @ one_one_real @ ( power_power_real @ A_128 @ N_29 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_160_power__0__left,axiom,
% 0.32/0.73 ! [N_28: nat] :
% 0.32/0.73 ( ( ( N_28 = zero_zero_nat )
% 0.32/0.73 => ( ( power_power_int @ zero_zero_int @ N_28 )
% 0.32/0.73 = one_one_int ) )
% 0.32/0.73 & ( ( N_28 != zero_zero_nat )
% 0.32/0.73 => ( ( power_power_int @ zero_zero_int @ N_28 )
% 0.32/0.73 = zero_zero_int ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_161_power__0__left,axiom,
% 0.32/0.73 ! [N_28: nat] :
% 0.32/0.73 ( ( ( N_28 = zero_zero_nat )
% 0.32/0.73 => ( ( power_power_nat @ zero_zero_nat @ N_28 )
% 0.32/0.73 = one_one_nat ) )
% 0.32/0.73 & ( ( N_28 != zero_zero_nat )
% 0.32/0.73 => ( ( power_power_nat @ zero_zero_nat @ N_28 )
% 0.32/0.73 = zero_zero_nat ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_162_power__0__left,axiom,
% 0.32/0.73 ! [N_28: nat] :
% 0.32/0.73 ( ( ( N_28 = zero_zero_nat )
% 0.32/0.73 => ( ( power_power_real @ zero_zero_real @ N_28 )
% 0.32/0.73 = one_one_real ) )
% 0.32/0.73 & ( ( N_28 != zero_zero_nat )
% 0.32/0.73 => ( ( power_power_real @ zero_zero_real @ N_28 )
% 0.32/0.73 = zero_zero_real ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_163_power__strict__decreasing,axiom,
% 0.32/0.73 ! [A_127: int,N_27: nat,N_26: nat] :
% 0.32/0.73 ( ( ord_less_nat @ N_27 @ N_26 )
% 0.32/0.73 => ( ( ord_less_int @ zero_zero_int @ A_127 )
% 0.32/0.73 => ( ( ord_less_int @ A_127 @ one_one_int )
% 0.32/0.73 => ( ord_less_int @ ( power_power_int @ A_127 @ N_26 ) @ ( power_power_int @ A_127 @ N_27 ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_164_power__strict__decreasing,axiom,
% 0.32/0.73 ! [A_127: nat,N_27: nat,N_26: nat] :
% 0.32/0.73 ( ( ord_less_nat @ N_27 @ N_26 )
% 0.32/0.73 => ( ( ord_less_nat @ zero_zero_nat @ A_127 )
% 0.32/0.73 => ( ( ord_less_nat @ A_127 @ one_one_nat )
% 0.32/0.73 => ( ord_less_nat @ ( power_power_nat @ A_127 @ N_26 ) @ ( power_power_nat @ A_127 @ N_27 ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_165_power__strict__decreasing,axiom,
% 0.32/0.73 ! [A_127: real,N_27: nat,N_26: nat] :
% 0.32/0.73 ( ( ord_less_nat @ N_27 @ N_26 )
% 0.32/0.73 => ( ( ord_less_real @ zero_zero_real @ A_127 )
% 0.32/0.73 => ( ( ord_less_real @ A_127 @ one_one_real )
% 0.32/0.73 => ( ord_less_real @ ( power_power_real @ A_127 @ N_26 ) @ ( power_power_real @ A_127 @ N_27 ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_166_zero__less__two,axiom,
% 0.32/0.73 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_167_zero__less__two,axiom,
% 0.32/0.73 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_168_zero__less__two,axiom,
% 0.32/0.73 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_169_int__gr__induct,axiom,
% 0.32/0.73 ! [P: int > $o,K: int,I_1: int] :
% 0.32/0.73 ( ( ord_less_int @ K @ I_1 )
% 0.32/0.73 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 0.32/0.73 => ( ! [I: int] :
% 0.32/0.73 ( ( ord_less_int @ K @ I )
% 0.32/0.73 => ( ( P @ I )
% 0.32/0.73 => ( P @ ( plus_plus_int @ I @ one_one_int ) ) ) )
% 0.32/0.73 => ( P @ I_1 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_170_transfer__int__nat__numerals_I1_J,axiom,
% 0.32/0.73 ( zero_zero_int
% 0.32/0.73 = ( semiri1621563631at_int @ zero_zero_nat ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_171_tn0,axiom,
% 0.32/0.73 ord_less_nat @ zero_zero_nat @ tn ).
% 0.32/0.73
% 0.32/0.73 thf(fact_172_less__zeroE,axiom,
% 0.32/0.73 ! [N: nat] :
% 0.32/0.73 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_173_real__zero__not__eq__one,axiom,
% 0.32/0.73 zero_zero_real != one_one_real ).
% 0.32/0.73
% 0.32/0.73 thf(fact_174_less__not__refl,axiom,
% 0.32/0.73 ! [N: nat] :
% 0.32/0.73 ~ ( ord_less_nat @ N @ N ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_175_not__add__less1,axiom,
% 0.32/0.73 ! [I_1: nat,J: nat] :
% 0.32/0.73 ~ ( ord_less_nat @ ( plus_plus_nat @ I_1 @ J ) @ I_1 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_176_not__add__less2,axiom,
% 0.32/0.73 ! [J: nat,I_1: nat] :
% 0.32/0.73 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I_1 ) @ I_1 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_177_number__of__is__id,axiom,
% 0.32/0.73 ! [K: int] :
% 0.32/0.73 ( ( number_number_of_int @ K )
% 0.32/0.73 = K ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_178_nat__neq__iff,axiom,
% 0.32/0.73 ! [M: nat,N: nat] :
% 0.32/0.73 ( ( M != N )
% 0.32/0.73 <=> ( ( ord_less_nat @ M @ N )
% 0.32/0.73 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_179_nat__add__commute,axiom,
% 0.32/0.73 ! [M: nat,N: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ M @ N )
% 0.32/0.73 = ( plus_plus_nat @ N @ M ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_180_nat__add__left__commute,axiom,
% 0.32/0.73 ! [X: nat,Y: nat,Z: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ X @ ( plus_plus_nat @ Y @ Z ) )
% 0.32/0.73 = ( plus_plus_nat @ Y @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_181_nat__add__assoc,axiom,
% 0.32/0.73 ! [M: nat,N: nat,K: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 0.32/0.73 = ( plus_plus_nat @ M @ ( plus_plus_nat @ N @ K ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_182_nat__add__left__cancel,axiom,
% 0.32/0.73 ! [K: nat,M: nat,N: nat] :
% 0.32/0.73 ( ( ( plus_plus_nat @ K @ M )
% 0.32/0.73 = ( plus_plus_nat @ K @ N ) )
% 0.32/0.73 <=> ( M = N ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_183_nat__add__right__cancel,axiom,
% 0.32/0.73 ! [M: nat,K: nat,N: nat] :
% 0.32/0.73 ( ( ( plus_plus_nat @ M @ K )
% 0.32/0.73 = ( plus_plus_nat @ N @ K ) )
% 0.32/0.73 <=> ( M = N ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_184_nat__add__left__cancel__less,axiom,
% 0.32/0.73 ! [K: nat,M: nat,N: nat] :
% 0.32/0.73 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.32/0.73 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_185_linorder__neqE__nat,axiom,
% 0.32/0.73 ! [X: nat,Y: nat] :
% 0.32/0.73 ( ( X != Y )
% 0.32/0.73 => ( ~ ( ord_less_nat @ X @ Y )
% 0.32/0.73 => ( ord_less_nat @ Y @ X ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_186_less__irrefl__nat,axiom,
% 0.32/0.73 ! [N: nat] :
% 0.32/0.73 ~ ( ord_less_nat @ N @ N ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_187_less__not__refl2,axiom,
% 0.32/0.73 ! [N: nat,M: nat] :
% 0.32/0.73 ( ( ord_less_nat @ N @ M )
% 0.32/0.73 => ( M != N ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_188_less__not__refl3,axiom,
% 0.32/0.73 ! [S_1: nat,T: nat] :
% 0.32/0.73 ( ( ord_less_nat @ S_1 @ T )
% 0.32/0.73 => ( S_1 != T ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_189_trans__less__add1,axiom,
% 0.32/0.73 ! [M: nat,I_1: nat,J: nat] :
% 0.32/0.73 ( ( ord_less_nat @ I_1 @ J )
% 0.32/0.73 => ( ord_less_nat @ I_1 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_190_trans__less__add2,axiom,
% 0.32/0.73 ! [M: nat,I_1: nat,J: nat] :
% 0.32/0.73 ( ( ord_less_nat @ I_1 @ J )
% 0.32/0.73 => ( ord_less_nat @ I_1 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_191_add__less__mono1,axiom,
% 0.32/0.73 ! [K: nat,I_1: nat,J: nat] :
% 0.32/0.73 ( ( ord_less_nat @ I_1 @ J )
% 0.32/0.73 => ( ord_less_nat @ ( plus_plus_nat @ I_1 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_192_add__less__mono,axiom,
% 0.32/0.73 ! [K: nat,L: nat,I_1: nat,J: nat] :
% 0.32/0.73 ( ( ord_less_nat @ I_1 @ J )
% 0.32/0.73 => ( ( ord_less_nat @ K @ L )
% 0.32/0.73 => ( ord_less_nat @ ( plus_plus_nat @ I_1 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_193_less__add__eq__less,axiom,
% 0.32/0.73 ! [M: nat,N: nat,K: nat,L: nat] :
% 0.32/0.73 ( ( ord_less_nat @ K @ L )
% 0.32/0.73 => ( ( ( plus_plus_nat @ M @ L )
% 0.32/0.73 = ( plus_plus_nat @ K @ N ) )
% 0.32/0.73 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_194_add__lessD1,axiom,
% 0.32/0.73 ! [I_1: nat,J: nat,K: nat] :
% 0.32/0.73 ( ( ord_less_nat @ ( plus_plus_nat @ I_1 @ J ) @ K )
% 0.32/0.73 => ( ord_less_nat @ I_1 @ K ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_195_nat__less__cases,axiom,
% 0.32/0.73 ! [P: nat > nat > $o,M: nat,N: nat] :
% 0.32/0.73 ( ( ( ord_less_nat @ M @ N )
% 0.32/0.73 => ( P @ N @ M ) )
% 0.32/0.73 => ( ( ( M = N )
% 0.32/0.73 => ( P @ N @ M ) )
% 0.32/0.73 => ( ( ( ord_less_nat @ N @ M )
% 0.32/0.73 => ( P @ N @ M ) )
% 0.32/0.73 => ( P @ N @ M ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_196_gr0I,axiom,
% 0.32/0.73 ! [N: nat] :
% 0.32/0.73 ( ( N != zero_zero_nat )
% 0.32/0.73 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_197_gr__implies__not0,axiom,
% 0.32/0.73 ! [M: nat,N: nat] :
% 0.32/0.73 ( ( ord_less_nat @ M @ N )
% 0.32/0.73 => ( N != zero_zero_nat ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_198_nat__power__less__imp__less,axiom,
% 0.32/0.73 ! [M: nat,N: nat,I_1: nat] :
% 0.32/0.73 ( ( ord_less_nat @ zero_zero_nat @ I_1 )
% 0.32/0.73 => ( ( ord_less_nat @ ( power_power_nat @ I_1 @ M ) @ ( power_power_nat @ I_1 @ N ) )
% 0.32/0.73 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_199_less__nat__zero__code,axiom,
% 0.32/0.73 ! [N: nat] :
% 0.32/0.73 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_200_nat__zero__less__power__iff,axiom,
% 0.32/0.73 ! [X: nat,N: nat] :
% 0.32/0.73 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 0.32/0.73 <=> ( ( ord_less_nat @ zero_zero_nat @ X )
% 0.32/0.73 | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_201_add__gr__0,axiom,
% 0.32/0.73 ! [M: nat,N: nat] :
% 0.32/0.73 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.73 <=> ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.73 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_202_neq0__conv,axiom,
% 0.32/0.73 ! [N: nat] :
% 0.32/0.73 ( ( N != zero_zero_nat )
% 0.32/0.73 <=> ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_203_not__less0,axiom,
% 0.32/0.73 ! [N: nat] :
% 0.32/0.73 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_204_zero__less__power__nat__eq,axiom,
% 0.32/0.73 ! [X: nat,N: nat] :
% 0.32/0.73 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 0.32/0.73 <=> ( ( N = zero_zero_nat )
% 0.32/0.73 | ( ord_less_nat @ zero_zero_nat @ X ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_205_Nat__Transfer_Otransfer__int__nat__relations_I2_J,axiom,
% 0.32/0.73 ! [X: nat,Y: nat] :
% 0.32/0.73 ( ( ord_less_int @ ( semiri1621563631at_int @ X ) @ ( semiri1621563631at_int @ Y ) )
% 0.32/0.73 <=> ( ord_less_nat @ X @ Y ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_206_zero__less__power__nat__eq__number__of,axiom,
% 0.32/0.73 ! [X: nat,W: int] :
% 0.32/0.73 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ ( number_number_of_nat @ W ) ) )
% 0.32/0.73 <=> ( ( ( number_number_of_nat @ W )
% 0.32/0.73 = zero_zero_nat )
% 0.32/0.73 | ( ord_less_nat @ zero_zero_nat @ X ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_207_zless__int,axiom,
% 0.32/0.73 ! [M: nat,N: nat] :
% 0.32/0.73 ( ( ord_less_int @ ( semiri1621563631at_int @ M ) @ ( semiri1621563631at_int @ N ) )
% 0.32/0.73 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_208_less__nat__number__of,axiom,
% 0.32/0.73 ! [V_1: int,V_2: int] :
% 0.32/0.73 ( ( ord_less_nat @ ( number_number_of_nat @ V_1 ) @ ( number_number_of_nat @ V_2 ) )
% 0.32/0.73 <=> ( ( ( ord_less_int @ V_1 @ V_2 )
% 0.32/0.73 => ( ord_less_int @ pls @ V_2 ) )
% 0.32/0.73 & ( ord_less_int @ V_1 @ V_2 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_209_linorder__neqE__linordered__idom,axiom,
% 0.32/0.73 ! [X_23: int,Y_17: int] :
% 0.32/0.73 ( ( X_23 != Y_17 )
% 0.32/0.73 => ( ~ ( ord_less_int @ X_23 @ Y_17 )
% 0.32/0.73 => ( ord_less_int @ Y_17 @ X_23 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_210_linorder__neqE__linordered__idom,axiom,
% 0.32/0.73 ! [X_23: real,Y_17: real] :
% 0.32/0.73 ( ( X_23 != Y_17 )
% 0.32/0.73 => ( ~ ( ord_less_real @ X_23 @ Y_17 )
% 0.32/0.73 => ( ord_less_real @ Y_17 @ X_23 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_211_add__eq__self__zero,axiom,
% 0.32/0.73 ! [M: nat,N: nat] :
% 0.32/0.73 ( ( ( plus_plus_nat @ M @ N )
% 0.32/0.73 = M )
% 0.32/0.73 => ( N = zero_zero_nat ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_212_add__is__0,axiom,
% 0.32/0.73 ! [M: nat,N: nat] :
% 0.32/0.73 ( ( ( plus_plus_nat @ M @ N )
% 0.32/0.73 = zero_zero_nat )
% 0.32/0.73 <=> ( ( M = zero_zero_nat )
% 0.32/0.73 & ( N = zero_zero_nat ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_213_Nat_Oadd__0__right,axiom,
% 0.32/0.73 ! [M: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.32/0.73 = M ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_214_plus__nat_Oadd__0,axiom,
% 0.32/0.73 ! [N: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 0.32/0.73 = N ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_215_power__one__right,axiom,
% 0.32/0.73 ! [A_126: int] :
% 0.32/0.73 ( ( power_power_int @ A_126 @ one_one_nat )
% 0.32/0.73 = A_126 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_216_power__one__right,axiom,
% 0.32/0.73 ! [A_126: nat] :
% 0.32/0.73 ( ( power_power_nat @ A_126 @ one_one_nat )
% 0.32/0.73 = A_126 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_217_power__one__right,axiom,
% 0.32/0.73 ! [A_126: real] :
% 0.32/0.73 ( ( power_power_real @ A_126 @ one_one_nat )
% 0.32/0.73 = A_126 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_218_of__nat__eq__iff,axiom,
% 0.32/0.73 ! [M_14: nat,N_25: nat] :
% 0.32/0.73 ( ( ( semiri132038758t_real @ M_14 )
% 0.32/0.73 = ( semiri132038758t_real @ N_25 ) )
% 0.32/0.73 <=> ( M_14 = N_25 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_219_of__nat__eq__iff,axiom,
% 0.32/0.73 ! [M_14: nat,N_25: nat] :
% 0.32/0.73 ( ( ( semiri984289939at_nat @ M_14 )
% 0.32/0.73 = ( semiri984289939at_nat @ N_25 ) )
% 0.32/0.73 <=> ( M_14 = N_25 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_220_of__nat__eq__iff,axiom,
% 0.32/0.73 ! [M_14: nat,N_25: nat] :
% 0.32/0.73 ( ( ( semiri1621563631at_int @ M_14 )
% 0.32/0.73 = ( semiri1621563631at_int @ N_25 ) )
% 0.32/0.73 <=> ( M_14 = N_25 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_221_Nat__Transfer_Otransfer__int__nat__relations_I1_J,axiom,
% 0.32/0.73 ! [X: nat,Y: nat] :
% 0.32/0.73 ( ( ( semiri1621563631at_int @ X )
% 0.32/0.73 = ( semiri1621563631at_int @ Y ) )
% 0.32/0.73 <=> ( X = Y ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_222_int__if__cong,axiom,
% 0.32/0.73 ! [X: nat,Y: nat,P: $o] :
% 0.32/0.73 ( ( P
% 0.32/0.73 => ( ( semiri1621563631at_int @ X )
% 0.32/0.73 = ( semiri1621563631at_int @ ( if_nat @ P @ X @ Y ) ) ) )
% 0.32/0.73 & ( ~ P
% 0.32/0.73 => ( ( semiri1621563631at_int @ Y )
% 0.32/0.73 = ( semiri1621563631at_int @ ( if_nat @ P @ X @ Y ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_223_less__0__number__of,axiom,
% 0.32/0.73 ! [V_1: int] :
% 0.32/0.73 ( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ V_1 ) )
% 0.32/0.73 <=> ( ord_less_int @ pls @ V_1 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_224_zero__less__int__conv,axiom,
% 0.32/0.73 ! [N: nat] :
% 0.32/0.73 ( ( ord_less_int @ zero_zero_int @ ( semiri1621563631at_int @ N ) )
% 0.32/0.73 <=> ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_225_one__neq__zero,axiom,
% 0.32/0.73 one_one_int != zero_zero_int ).
% 0.32/0.73
% 0.32/0.73 thf(fact_226_one__neq__zero,axiom,
% 0.32/0.73 one_one_nat != zero_zero_nat ).
% 0.32/0.73
% 0.32/0.73 thf(fact_227_one__neq__zero,axiom,
% 0.32/0.73 one_one_real != zero_zero_real ).
% 0.32/0.73
% 0.32/0.73 thf(fact_228_zero__neq__one,axiom,
% 0.32/0.73 zero_zero_int != one_one_int ).
% 0.32/0.73
% 0.32/0.73 thf(fact_229_zero__neq__one,axiom,
% 0.32/0.73 zero_zero_nat != one_one_nat ).
% 0.32/0.73
% 0.32/0.73 thf(fact_230_zero__neq__one,axiom,
% 0.32/0.73 zero_zero_real != one_one_real ).
% 0.32/0.73
% 0.32/0.73 thf(fact_231_field__power__not__zero,axiom,
% 0.32/0.73 ! [N_24: nat,A_125: int] :
% 0.32/0.73 ( ( A_125 != zero_zero_int )
% 0.32/0.73 => ( ( power_power_int @ A_125 @ N_24 )
% 0.32/0.73 != zero_zero_int ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_232_field__power__not__zero,axiom,
% 0.32/0.73 ! [N_24: nat,A_125: real] :
% 0.32/0.73 ( ( A_125 != zero_zero_real )
% 0.32/0.73 => ( ( power_power_real @ A_125 @ N_24 )
% 0.32/0.73 != zero_zero_real ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_233_power__one,axiom,
% 0.32/0.73 ! [N_23: nat] :
% 0.32/0.73 ( ( power_power_int @ one_one_int @ N_23 )
% 0.32/0.73 = one_one_int ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_234_power__one,axiom,
% 0.32/0.73 ! [N_23: nat] :
% 0.32/0.73 ( ( power_power_nat @ one_one_nat @ N_23 )
% 0.32/0.73 = one_one_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_235_power__one,axiom,
% 0.32/0.73 ! [N_23: nat] :
% 0.32/0.73 ( ( power_power_real @ one_one_real @ N_23 )
% 0.32/0.73 = one_one_real ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_236_of__nat__less__iff,axiom,
% 0.32/0.73 ! [M_13: nat,N_22: nat] :
% 0.32/0.73 ( ( ord_less_int @ ( semiri1621563631at_int @ M_13 ) @ ( semiri1621563631at_int @ N_22 ) )
% 0.32/0.73 <=> ( ord_less_nat @ M_13 @ N_22 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_237_of__nat__less__iff,axiom,
% 0.32/0.73 ! [M_13: nat,N_22: nat] :
% 0.32/0.73 ( ( ord_less_nat @ ( semiri984289939at_nat @ M_13 ) @ ( semiri984289939at_nat @ N_22 ) )
% 0.32/0.73 <=> ( ord_less_nat @ M_13 @ N_22 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_238_of__nat__less__iff,axiom,
% 0.32/0.73 ! [M_13: nat,N_22: nat] :
% 0.32/0.73 ( ( ord_less_real @ ( semiri132038758t_real @ M_13 ) @ ( semiri132038758t_real @ N_22 ) )
% 0.32/0.73 <=> ( ord_less_nat @ M_13 @ N_22 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_239_less__imp__of__nat__less,axiom,
% 0.32/0.73 ! [M_12: nat,N_21: nat] :
% 0.32/0.73 ( ( ord_less_nat @ M_12 @ N_21 )
% 0.32/0.73 => ( ord_less_int @ ( semiri1621563631at_int @ M_12 ) @ ( semiri1621563631at_int @ N_21 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_240_less__imp__of__nat__less,axiom,
% 0.32/0.73 ! [M_12: nat,N_21: nat] :
% 0.32/0.73 ( ( ord_less_nat @ M_12 @ N_21 )
% 0.32/0.73 => ( ord_less_nat @ ( semiri984289939at_nat @ M_12 ) @ ( semiri984289939at_nat @ N_21 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_241_less__imp__of__nat__less,axiom,
% 0.32/0.73 ! [M_12: nat,N_21: nat] :
% 0.32/0.73 ( ( ord_less_nat @ M_12 @ N_21 )
% 0.32/0.73 => ( ord_less_real @ ( semiri132038758t_real @ M_12 ) @ ( semiri132038758t_real @ N_21 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_242_of__nat__less__imp__less,axiom,
% 0.32/0.73 ! [M_11: nat,N_20: nat] :
% 0.32/0.73 ( ( ord_less_int @ ( semiri1621563631at_int @ M_11 ) @ ( semiri1621563631at_int @ N_20 ) )
% 0.32/0.73 => ( ord_less_nat @ M_11 @ N_20 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_243_of__nat__less__imp__less,axiom,
% 0.32/0.73 ! [M_11: nat,N_20: nat] :
% 0.32/0.73 ( ( ord_less_nat @ ( semiri984289939at_nat @ M_11 ) @ ( semiri984289939at_nat @ N_20 ) )
% 0.32/0.73 => ( ord_less_nat @ M_11 @ N_20 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_244_of__nat__less__imp__less,axiom,
% 0.32/0.73 ! [M_11: nat,N_20: nat] :
% 0.32/0.73 ( ( ord_less_real @ ( semiri132038758t_real @ M_11 ) @ ( semiri132038758t_real @ N_20 ) )
% 0.32/0.73 => ( ord_less_nat @ M_11 @ N_20 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_245_of__nat__add,axiom,
% 0.32/0.73 ! [M_10: nat,N_19: nat] :
% 0.32/0.73 ( ( semiri1621563631at_int @ ( plus_plus_nat @ M_10 @ N_19 ) )
% 0.32/0.73 = ( plus_plus_int @ ( semiri1621563631at_int @ M_10 ) @ ( semiri1621563631at_int @ N_19 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_246_of__nat__add,axiom,
% 0.32/0.73 ! [M_10: nat,N_19: nat] :
% 0.32/0.73 ( ( semiri984289939at_nat @ ( plus_plus_nat @ M_10 @ N_19 ) )
% 0.32/0.73 = ( plus_plus_nat @ ( semiri984289939at_nat @ M_10 ) @ ( semiri984289939at_nat @ N_19 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_247_of__nat__add,axiom,
% 0.32/0.73 ! [M_10: nat,N_19: nat] :
% 0.32/0.73 ( ( semiri132038758t_real @ ( plus_plus_nat @ M_10 @ N_19 ) )
% 0.32/0.73 = ( plus_plus_real @ ( semiri132038758t_real @ M_10 ) @ ( semiri132038758t_real @ N_19 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_248_of__nat__1,axiom,
% 0.32/0.73 ( ( semiri1621563631at_int @ one_one_nat )
% 0.32/0.73 = one_one_int ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_249_of__nat__1,axiom,
% 0.32/0.73 ( ( semiri984289939at_nat @ one_one_nat )
% 0.32/0.73 = one_one_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_250_of__nat__1,axiom,
% 0.32/0.73 ( ( semiri132038758t_real @ one_one_nat )
% 0.32/0.73 = one_one_real ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_251_of__nat__power,axiom,
% 0.32/0.73 ! [M_9: nat,N_18: nat] :
% 0.32/0.73 ( ( semiri1621563631at_int @ ( power_power_nat @ M_9 @ N_18 ) )
% 0.32/0.73 = ( power_power_int @ ( semiri1621563631at_int @ M_9 ) @ N_18 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_252_of__nat__power,axiom,
% 0.32/0.73 ! [M_9: nat,N_18: nat] :
% 0.32/0.73 ( ( semiri984289939at_nat @ ( power_power_nat @ M_9 @ N_18 ) )
% 0.32/0.73 = ( power_power_nat @ ( semiri984289939at_nat @ M_9 ) @ N_18 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_253_of__nat__power,axiom,
% 0.32/0.73 ! [M_9: nat,N_18: nat] :
% 0.32/0.73 ( ( semiri132038758t_real @ ( power_power_nat @ M_9 @ N_18 ) )
% 0.32/0.73 = ( power_power_real @ ( semiri132038758t_real @ M_9 ) @ N_18 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_254_transfer__int__nat__numerals_I2_J,axiom,
% 0.32/0.73 ( one_one_int
% 0.32/0.73 = ( semiri1621563631at_int @ one_one_nat ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_255_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom,
% 0.32/0.73 ! [X: nat,Y: nat] :
% 0.32/0.73 ( ( plus_plus_int @ ( semiri1621563631at_int @ X ) @ ( semiri1621563631at_int @ Y ) )
% 0.32/0.73 = ( semiri1621563631at_int @ ( plus_plus_nat @ X @ Y ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_256_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom,
% 0.32/0.73 ! [X: nat,N: nat] :
% 0.32/0.73 ( ( power_power_int @ ( semiri1621563631at_int @ X ) @ N )
% 0.32/0.73 = ( semiri1621563631at_int @ ( power_power_nat @ X @ N ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_257_pos__add__strict,axiom,
% 0.32/0.73 ! [B_89: int,C_63: int,A_124: int] :
% 0.32/0.73 ( ( ord_less_int @ zero_zero_int @ A_124 )
% 0.32/0.73 => ( ( ord_less_int @ B_89 @ C_63 )
% 0.32/0.73 => ( ord_less_int @ B_89 @ ( plus_plus_int @ A_124 @ C_63 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_258_pos__add__strict,axiom,
% 0.32/0.73 ! [B_89: nat,C_63: nat,A_124: nat] :
% 0.32/0.73 ( ( ord_less_nat @ zero_zero_nat @ A_124 )
% 0.32/0.73 => ( ( ord_less_nat @ B_89 @ C_63 )
% 0.32/0.73 => ( ord_less_nat @ B_89 @ ( plus_plus_nat @ A_124 @ C_63 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_259_pos__add__strict,axiom,
% 0.32/0.73 ! [B_89: real,C_63: real,A_124: real] :
% 0.32/0.73 ( ( ord_less_real @ zero_zero_real @ A_124 )
% 0.32/0.73 => ( ( ord_less_real @ B_89 @ C_63 )
% 0.32/0.73 => ( ord_less_real @ B_89 @ ( plus_plus_real @ A_124 @ C_63 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_260_not__one__less__zero,axiom,
% 0.32/0.73 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_261_not__one__less__zero,axiom,
% 0.32/0.73 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_262_not__one__less__zero,axiom,
% 0.32/0.73 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_263_zero__less__one,axiom,
% 0.32/0.73 ord_less_int @ zero_zero_int @ one_one_int ).
% 0.32/0.73
% 0.32/0.73 thf(fact_264_zero__less__one,axiom,
% 0.32/0.73 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 0.32/0.73
% 0.32/0.73 thf(fact_265_zero__less__one,axiom,
% 0.32/0.73 ord_less_real @ zero_zero_real @ one_one_real ).
% 0.32/0.73
% 0.32/0.73 thf(fact_266_zero__less__power,axiom,
% 0.32/0.73 ! [N_17: nat,A_123: int] :
% 0.32/0.73 ( ( ord_less_int @ zero_zero_int @ A_123 )
% 0.32/0.73 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_123 @ N_17 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_267_zero__less__power,axiom,
% 0.32/0.73 ! [N_17: nat,A_123: nat] :
% 0.32/0.73 ( ( ord_less_nat @ zero_zero_nat @ A_123 )
% 0.32/0.73 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A_123 @ N_17 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_268_zero__less__power,axiom,
% 0.32/0.73 ! [N_17: nat,A_123: real] :
% 0.32/0.73 ( ( ord_less_real @ zero_zero_real @ A_123 )
% 0.32/0.73 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A_123 @ N_17 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_269_less__add__one,axiom,
% 0.32/0.73 ! [A_122: int] : ( ord_less_int @ A_122 @ ( plus_plus_int @ A_122 @ one_one_int ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_270_less__add__one,axiom,
% 0.32/0.73 ! [A_122: nat] : ( ord_less_nat @ A_122 @ ( plus_plus_nat @ A_122 @ one_one_nat ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_271_less__add__one,axiom,
% 0.32/0.73 ! [A_122: real] : ( ord_less_real @ A_122 @ ( plus_plus_real @ A_122 @ one_one_real ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_272_power__inject__exp,axiom,
% 0.32/0.73 ! [M_8: nat,N_16: nat,A_121: int] :
% 0.32/0.73 ( ( ord_less_int @ one_one_int @ A_121 )
% 0.32/0.73 => ( ( ( power_power_int @ A_121 @ M_8 )
% 0.32/0.73 = ( power_power_int @ A_121 @ N_16 ) )
% 0.32/0.73 <=> ( M_8 = N_16 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_273_power__inject__exp,axiom,
% 0.32/0.73 ! [M_8: nat,N_16: nat,A_121: nat] :
% 0.32/0.73 ( ( ord_less_nat @ one_one_nat @ A_121 )
% 0.32/0.73 => ( ( ( power_power_nat @ A_121 @ M_8 )
% 0.32/0.73 = ( power_power_nat @ A_121 @ N_16 ) )
% 0.32/0.73 <=> ( M_8 = N_16 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_274_power__inject__exp,axiom,
% 0.32/0.73 ! [M_8: nat,N_16: nat,A_121: real] :
% 0.32/0.73 ( ( ord_less_real @ one_one_real @ A_121 )
% 0.32/0.73 => ( ( ( power_power_real @ A_121 @ M_8 )
% 0.32/0.73 = ( power_power_real @ A_121 @ N_16 ) )
% 0.32/0.73 <=> ( M_8 = N_16 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_275_power__strict__increasing__iff,axiom,
% 0.32/0.73 ! [X_22: nat,Y_16: nat,B_88: int] :
% 0.32/0.73 ( ( ord_less_int @ one_one_int @ B_88 )
% 0.32/0.73 => ( ( ord_less_int @ ( power_power_int @ B_88 @ X_22 ) @ ( power_power_int @ B_88 @ Y_16 ) )
% 0.32/0.73 <=> ( ord_less_nat @ X_22 @ Y_16 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_276_power__strict__increasing__iff,axiom,
% 0.32/0.73 ! [X_22: nat,Y_16: nat,B_88: nat] :
% 0.32/0.73 ( ( ord_less_nat @ one_one_nat @ B_88 )
% 0.32/0.73 => ( ( ord_less_nat @ ( power_power_nat @ B_88 @ X_22 ) @ ( power_power_nat @ B_88 @ Y_16 ) )
% 0.32/0.73 <=> ( ord_less_nat @ X_22 @ Y_16 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_277_power__strict__increasing__iff,axiom,
% 0.32/0.73 ! [X_22: nat,Y_16: nat,B_88: real] :
% 0.32/0.73 ( ( ord_less_real @ one_one_real @ B_88 )
% 0.32/0.73 => ( ( ord_less_real @ ( power_power_real @ B_88 @ X_22 ) @ ( power_power_real @ B_88 @ Y_16 ) )
% 0.32/0.73 <=> ( ord_less_nat @ X_22 @ Y_16 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_278_power__less__imp__less__exp,axiom,
% 0.32/0.73 ! [M_7: nat,N_15: nat,A_120: int] :
% 0.32/0.73 ( ( ord_less_int @ one_one_int @ A_120 )
% 0.32/0.73 => ( ( ord_less_int @ ( power_power_int @ A_120 @ M_7 ) @ ( power_power_int @ A_120 @ N_15 ) )
% 0.32/0.73 => ( ord_less_nat @ M_7 @ N_15 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_279_power__less__imp__less__exp,axiom,
% 0.32/0.73 ! [M_7: nat,N_15: nat,A_120: nat] :
% 0.32/0.73 ( ( ord_less_nat @ one_one_nat @ A_120 )
% 0.32/0.73 => ( ( ord_less_nat @ ( power_power_nat @ A_120 @ M_7 ) @ ( power_power_nat @ A_120 @ N_15 ) )
% 0.32/0.73 => ( ord_less_nat @ M_7 @ N_15 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_280_power__less__imp__less__exp,axiom,
% 0.32/0.73 ! [M_7: nat,N_15: nat,A_120: real] :
% 0.32/0.73 ( ( ord_less_real @ one_one_real @ A_120 )
% 0.32/0.73 => ( ( ord_less_real @ ( power_power_real @ A_120 @ M_7 ) @ ( power_power_real @ A_120 @ N_15 ) )
% 0.32/0.73 => ( ord_less_nat @ M_7 @ N_15 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_281_power__strict__increasing,axiom,
% 0.32/0.73 ! [A_119: int,N_14: nat,N_13: nat] :
% 0.32/0.73 ( ( ord_less_nat @ N_14 @ N_13 )
% 0.32/0.73 => ( ( ord_less_int @ one_one_int @ A_119 )
% 0.32/0.73 => ( ord_less_int @ ( power_power_int @ A_119 @ N_14 ) @ ( power_power_int @ A_119 @ N_13 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_282_power__strict__increasing,axiom,
% 0.32/0.73 ! [A_119: nat,N_14: nat,N_13: nat] :
% 0.32/0.73 ( ( ord_less_nat @ N_14 @ N_13 )
% 0.32/0.73 => ( ( ord_less_nat @ one_one_nat @ A_119 )
% 0.32/0.73 => ( ord_less_nat @ ( power_power_nat @ A_119 @ N_14 ) @ ( power_power_nat @ A_119 @ N_13 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_283_power__strict__increasing,axiom,
% 0.32/0.73 ! [A_119: real,N_14: nat,N_13: nat] :
% 0.32/0.73 ( ( ord_less_nat @ N_14 @ N_13 )
% 0.32/0.73 => ( ( ord_less_real @ one_one_real @ A_119 )
% 0.32/0.73 => ( ord_less_real @ ( power_power_real @ A_119 @ N_14 ) @ ( power_power_real @ A_119 @ N_13 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_284_power__eq__0__iff,axiom,
% 0.32/0.73 ! [A_118: int,N_12: nat] :
% 0.32/0.73 ( ( ( power_power_int @ A_118 @ N_12 )
% 0.32/0.73 = zero_zero_int )
% 0.32/0.73 <=> ( ( A_118 = zero_zero_int )
% 0.32/0.73 & ( N_12 != zero_zero_nat ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_285_power__eq__0__iff,axiom,
% 0.32/0.73 ! [A_118: nat,N_12: nat] :
% 0.32/0.73 ( ( ( power_power_nat @ A_118 @ N_12 )
% 0.32/0.73 = zero_zero_nat )
% 0.32/0.73 <=> ( ( A_118 = zero_zero_nat )
% 0.32/0.73 & ( N_12 != zero_zero_nat ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_286_power__eq__0__iff,axiom,
% 0.32/0.73 ! [A_118: real,N_12: nat] :
% 0.32/0.73 ( ( ( power_power_real @ A_118 @ N_12 )
% 0.32/0.73 = zero_zero_real )
% 0.32/0.73 <=> ( ( A_118 = zero_zero_real )
% 0.32/0.73 & ( N_12 != zero_zero_nat ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_287_of__nat__less__0__iff,axiom,
% 0.32/0.73 ! [M_6: nat] :
% 0.32/0.73 ~ ( ord_less_int @ ( semiri1621563631at_int @ M_6 ) @ zero_zero_int ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_288_of__nat__less__0__iff,axiom,
% 0.32/0.73 ! [M_6: nat] :
% 0.32/0.73 ~ ( ord_less_nat @ ( semiri984289939at_nat @ M_6 ) @ zero_zero_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_289_of__nat__less__0__iff,axiom,
% 0.32/0.73 ! [M_6: nat] :
% 0.32/0.73 ~ ( ord_less_real @ ( semiri132038758t_real @ M_6 ) @ zero_zero_real ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_290_power__0,axiom,
% 0.32/0.73 ! [A_117: int] :
% 0.32/0.73 ( ( power_power_int @ A_117 @ zero_zero_nat )
% 0.32/0.73 = one_one_int ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_291_power__0,axiom,
% 0.32/0.73 ! [A_117: nat] :
% 0.32/0.73 ( ( power_power_nat @ A_117 @ zero_zero_nat )
% 0.32/0.73 = one_one_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_292_power__0,axiom,
% 0.32/0.73 ! [A_117: real] :
% 0.32/0.73 ( ( power_power_real @ A_117 @ zero_zero_nat )
% 0.32/0.73 = one_one_real ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_293_of__nat__0,axiom,
% 0.32/0.73 ( ( semiri1621563631at_int @ zero_zero_nat )
% 0.32/0.73 = zero_zero_int ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_294_of__nat__0,axiom,
% 0.32/0.73 ( ( semiri984289939at_nat @ zero_zero_nat )
% 0.32/0.73 = zero_zero_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_295_of__nat__0,axiom,
% 0.32/0.73 ( ( semiri132038758t_real @ zero_zero_nat )
% 0.32/0.73 = zero_zero_real ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_296_pos2,axiom,
% 0.32/0.73 ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_297_zero__less__imp__eq__int,axiom,
% 0.32/0.73 ! [K: int] :
% 0.32/0.73 ( ( ord_less_int @ zero_zero_int @ K )
% 0.32/0.73 => ? [N_1: nat] :
% 0.32/0.73 ( ( ord_less_nat @ zero_zero_nat @ N_1 )
% 0.32/0.73 & ( K
% 0.32/0.73 = ( semiri1621563631at_int @ N_1 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_298_less__imp__add__positive,axiom,
% 0.32/0.73 ! [I_1: nat,J: nat] :
% 0.32/0.73 ( ( ord_less_nat @ I_1 @ J )
% 0.32/0.73 => ? [K_1: nat] :
% 0.32/0.73 ( ( ord_less_nat @ zero_zero_nat @ K_1 )
% 0.32/0.73 & ( ( plus_plus_nat @ I_1 @ K_1 )
% 0.32/0.73 = J ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_299_exp__eq__1,axiom,
% 0.32/0.73 ! [X: nat,N: nat] :
% 0.32/0.73 ( ( ( power_power_nat @ X @ N )
% 0.32/0.73 = one_one_nat )
% 0.32/0.73 <=> ( ( X = one_one_nat )
% 0.32/0.73 | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_300_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 0.32/0.73 ! [X_21: int] :
% 0.32/0.73 ( ( power_power_int @ X_21 @ zero_zero_nat )
% 0.32/0.73 = one_one_int ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_301_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 0.32/0.73 ! [X_21: nat] :
% 0.32/0.73 ( ( power_power_nat @ X_21 @ zero_zero_nat )
% 0.32/0.73 = one_one_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_302_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 0.32/0.73 ! [X_21: real] :
% 0.32/0.73 ( ( power_power_real @ X_21 @ zero_zero_nat )
% 0.32/0.73 = one_one_real ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_303_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.32/0.73 ! [A_116: int] :
% 0.32/0.73 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A_116 @ A_116 ) )
% 0.32/0.73 <=> ( ord_less_int @ zero_zero_int @ A_116 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_304_zero__less__double__add__iff__zero__less__single__add,axiom,
% 0.32/0.73 ! [A_116: real] :
% 0.32/0.73 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A_116 @ A_116 ) )
% 0.32/0.73 <=> ( ord_less_real @ zero_zero_real @ A_116 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_305_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.32/0.73 ! [A_115: int] :
% 0.32/0.73 ( ( ord_less_int @ ( plus_plus_int @ A_115 @ A_115 ) @ zero_zero_int )
% 0.32/0.73 <=> ( ord_less_int @ A_115 @ zero_zero_int ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_306_double__add__less__zero__iff__single__add__less__zero,axiom,
% 0.32/0.73 ! [A_115: real] :
% 0.32/0.73 ( ( ord_less_real @ ( plus_plus_real @ A_115 @ A_115 ) @ zero_zero_real )
% 0.32/0.73 <=> ( ord_less_real @ A_115 @ zero_zero_real ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_307_add__pos__pos,axiom,
% 0.32/0.73 ! [B_87: int,A_114: int] :
% 0.32/0.73 ( ( ord_less_int @ zero_zero_int @ A_114 )
% 0.32/0.73 => ( ( ord_less_int @ zero_zero_int @ B_87 )
% 0.32/0.73 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A_114 @ B_87 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_308_add__pos__pos,axiom,
% 0.32/0.73 ! [B_87: nat,A_114: nat] :
% 0.32/0.73 ( ( ord_less_nat @ zero_zero_nat @ A_114 )
% 0.32/0.73 => ( ( ord_less_nat @ zero_zero_nat @ B_87 )
% 0.32/0.73 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A_114 @ B_87 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_309_add__pos__pos,axiom,
% 0.32/0.73 ! [B_87: real,A_114: real] :
% 0.32/0.73 ( ( ord_less_real @ zero_zero_real @ A_114 )
% 0.32/0.73 => ( ( ord_less_real @ zero_zero_real @ B_87 )
% 0.32/0.73 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A_114 @ B_87 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_310_add__neg__neg,axiom,
% 0.32/0.73 ! [B_86: int,A_113: int] :
% 0.32/0.73 ( ( ord_less_int @ A_113 @ zero_zero_int )
% 0.32/0.73 => ( ( ord_less_int @ B_86 @ zero_zero_int )
% 0.32/0.73 => ( ord_less_int @ ( plus_plus_int @ A_113 @ B_86 ) @ zero_zero_int ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_311_add__neg__neg,axiom,
% 0.32/0.73 ! [B_86: nat,A_113: nat] :
% 0.32/0.73 ( ( ord_less_nat @ A_113 @ zero_zero_nat )
% 0.32/0.73 => ( ( ord_less_nat @ B_86 @ zero_zero_nat )
% 0.32/0.73 => ( ord_less_nat @ ( plus_plus_nat @ A_113 @ B_86 ) @ zero_zero_nat ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_312_add__neg__neg,axiom,
% 0.32/0.73 ! [B_86: real,A_113: real] :
% 0.32/0.73 ( ( ord_less_real @ A_113 @ zero_zero_real )
% 0.32/0.73 => ( ( ord_less_real @ B_86 @ zero_zero_real )
% 0.32/0.73 => ( ord_less_real @ ( plus_plus_real @ A_113 @ B_86 ) @ zero_zero_real ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_313_zero__reorient,axiom,
% 0.32/0.73 ! [X_20: int] :
% 0.32/0.73 ( ( zero_zero_int = X_20 )
% 0.32/0.73 <=> ( X_20 = zero_zero_int ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_314_zero__reorient,axiom,
% 0.32/0.73 ! [X_20: nat] :
% 0.32/0.73 ( ( zero_zero_nat = X_20 )
% 0.32/0.73 <=> ( X_20 = zero_zero_nat ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_315_zero__reorient,axiom,
% 0.32/0.73 ! [X_20: real] :
% 0.32/0.73 ( ( zero_zero_real = X_20 )
% 0.32/0.73 <=> ( X_20 = zero_zero_real ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_316_add__right__imp__eq,axiom,
% 0.32/0.73 ! [B_85: int,A_112: int,C_62: int] :
% 0.32/0.73 ( ( ( plus_plus_int @ B_85 @ A_112 )
% 0.32/0.73 = ( plus_plus_int @ C_62 @ A_112 ) )
% 0.32/0.73 => ( B_85 = C_62 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_317_add__right__imp__eq,axiom,
% 0.32/0.73 ! [B_85: nat,A_112: nat,C_62: nat] :
% 0.32/0.73 ( ( ( plus_plus_nat @ B_85 @ A_112 )
% 0.32/0.73 = ( plus_plus_nat @ C_62 @ A_112 ) )
% 0.32/0.73 => ( B_85 = C_62 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_318_add__right__imp__eq,axiom,
% 0.32/0.73 ! [B_85: real,A_112: real,C_62: real] :
% 0.32/0.73 ( ( ( plus_plus_real @ B_85 @ A_112 )
% 0.32/0.73 = ( plus_plus_real @ C_62 @ A_112 ) )
% 0.32/0.73 => ( B_85 = C_62 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_319_add__imp__eq,axiom,
% 0.32/0.73 ! [A_111: int,B_84: int,C_61: int] :
% 0.32/0.73 ( ( ( plus_plus_int @ A_111 @ B_84 )
% 0.32/0.73 = ( plus_plus_int @ A_111 @ C_61 ) )
% 0.32/0.73 => ( B_84 = C_61 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_320_add__imp__eq,axiom,
% 0.32/0.73 ! [A_111: nat,B_84: nat,C_61: nat] :
% 0.32/0.73 ( ( ( plus_plus_nat @ A_111 @ B_84 )
% 0.32/0.73 = ( plus_plus_nat @ A_111 @ C_61 ) )
% 0.32/0.73 => ( B_84 = C_61 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_321_add__imp__eq,axiom,
% 0.32/0.73 ! [A_111: real,B_84: real,C_61: real] :
% 0.32/0.73 ( ( ( plus_plus_real @ A_111 @ B_84 )
% 0.32/0.73 = ( plus_plus_real @ A_111 @ C_61 ) )
% 0.32/0.73 => ( B_84 = C_61 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_322_add__left__imp__eq,axiom,
% 0.32/0.73 ! [A_110: int,B_83: int,C_60: int] :
% 0.32/0.73 ( ( ( plus_plus_int @ A_110 @ B_83 )
% 0.32/0.73 = ( plus_plus_int @ A_110 @ C_60 ) )
% 0.32/0.73 => ( B_83 = C_60 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_323_add__left__imp__eq,axiom,
% 0.32/0.73 ! [A_110: nat,B_83: nat,C_60: nat] :
% 0.32/0.73 ( ( ( plus_plus_nat @ A_110 @ B_83 )
% 0.32/0.73 = ( plus_plus_nat @ A_110 @ C_60 ) )
% 0.32/0.73 => ( B_83 = C_60 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_324_add__left__imp__eq,axiom,
% 0.32/0.73 ! [A_110: real,B_83: real,C_60: real] :
% 0.32/0.73 ( ( ( plus_plus_real @ A_110 @ B_83 )
% 0.32/0.73 = ( plus_plus_real @ A_110 @ C_60 ) )
% 0.32/0.73 => ( B_83 = C_60 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_325_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 0.32/0.73 ! [A_109: int,B_82: int,C_59: int,D_23: int] :
% 0.32/0.73 ( ( plus_plus_int @ ( plus_plus_int @ A_109 @ B_82 ) @ ( plus_plus_int @ C_59 @ D_23 ) )
% 0.32/0.73 = ( plus_plus_int @ ( plus_plus_int @ A_109 @ C_59 ) @ ( plus_plus_int @ B_82 @ D_23 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_326_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 0.32/0.73 ! [A_109: nat,B_82: nat,C_59: nat,D_23: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ ( plus_plus_nat @ A_109 @ B_82 ) @ ( plus_plus_nat @ C_59 @ D_23 ) )
% 0.32/0.73 = ( plus_plus_nat @ ( plus_plus_nat @ A_109 @ C_59 ) @ ( plus_plus_nat @ B_82 @ D_23 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_327_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 0.32/0.73 ! [A_109: real,B_82: real,C_59: real,D_23: real] :
% 0.32/0.73 ( ( plus_plus_real @ ( plus_plus_real @ A_109 @ B_82 ) @ ( plus_plus_real @ C_59 @ D_23 ) )
% 0.32/0.73 = ( plus_plus_real @ ( plus_plus_real @ A_109 @ C_59 ) @ ( plus_plus_real @ B_82 @ D_23 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_328_add__right__cancel,axiom,
% 0.32/0.73 ! [B_81: int,A_108: int,C_58: int] :
% 0.32/0.73 ( ( ( plus_plus_int @ B_81 @ A_108 )
% 0.32/0.73 = ( plus_plus_int @ C_58 @ A_108 ) )
% 0.32/0.73 <=> ( B_81 = C_58 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_329_add__right__cancel,axiom,
% 0.32/0.73 ! [B_81: nat,A_108: nat,C_58: nat] :
% 0.32/0.73 ( ( ( plus_plus_nat @ B_81 @ A_108 )
% 0.32/0.73 = ( plus_plus_nat @ C_58 @ A_108 ) )
% 0.32/0.73 <=> ( B_81 = C_58 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_330_add__right__cancel,axiom,
% 0.32/0.73 ! [B_81: real,A_108: real,C_58: real] :
% 0.32/0.73 ( ( ( plus_plus_real @ B_81 @ A_108 )
% 0.32/0.73 = ( plus_plus_real @ C_58 @ A_108 ) )
% 0.32/0.73 <=> ( B_81 = C_58 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_331_add__left__cancel,axiom,
% 0.32/0.73 ! [A_107: int,B_80: int,C_57: int] :
% 0.32/0.73 ( ( ( plus_plus_int @ A_107 @ B_80 )
% 0.32/0.73 = ( plus_plus_int @ A_107 @ C_57 ) )
% 0.32/0.73 <=> ( B_80 = C_57 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_332_add__left__cancel,axiom,
% 0.32/0.73 ! [A_107: nat,B_80: nat,C_57: nat] :
% 0.32/0.73 ( ( ( plus_plus_nat @ A_107 @ B_80 )
% 0.32/0.73 = ( plus_plus_nat @ A_107 @ C_57 ) )
% 0.32/0.73 <=> ( B_80 = C_57 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_333_add__left__cancel,axiom,
% 0.32/0.73 ! [A_107: real,B_80: real,C_57: real] :
% 0.32/0.73 ( ( ( plus_plus_real @ A_107 @ B_80 )
% 0.32/0.73 = ( plus_plus_real @ A_107 @ C_57 ) )
% 0.32/0.73 <=> ( B_80 = C_57 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_334_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 0.32/0.73 ! [A_106: int,B_79: int,C_56: int] :
% 0.32/0.73 ( ( plus_plus_int @ ( plus_plus_int @ A_106 @ B_79 ) @ C_56 )
% 0.32/0.73 = ( plus_plus_int @ ( plus_plus_int @ A_106 @ C_56 ) @ B_79 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_335_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 0.32/0.73 ! [A_106: nat,B_79: nat,C_56: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ ( plus_plus_nat @ A_106 @ B_79 ) @ C_56 )
% 0.32/0.73 = ( plus_plus_nat @ ( plus_plus_nat @ A_106 @ C_56 ) @ B_79 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_336_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 0.32/0.73 ! [A_106: real,B_79: real,C_56: real] :
% 0.32/0.73 ( ( plus_plus_real @ ( plus_plus_real @ A_106 @ B_79 ) @ C_56 )
% 0.32/0.73 = ( plus_plus_real @ ( plus_plus_real @ A_106 @ C_56 ) @ B_79 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_337_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.32/0.73 ! [A_105: int,B_78: int,C_55: int] :
% 0.32/0.73 ( ( plus_plus_int @ ( plus_plus_int @ A_105 @ B_78 ) @ C_55 )
% 0.32/0.73 = ( plus_plus_int @ A_105 @ ( plus_plus_int @ B_78 @ C_55 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_338_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.32/0.73 ! [A_105: nat,B_78: nat,C_55: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ ( plus_plus_nat @ A_105 @ B_78 ) @ C_55 )
% 0.32/0.73 = ( plus_plus_nat @ A_105 @ ( plus_plus_nat @ B_78 @ C_55 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_339_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.32/0.73 ! [A_105: real,B_78: real,C_55: real] :
% 0.32/0.73 ( ( plus_plus_real @ ( plus_plus_real @ A_105 @ B_78 ) @ C_55 )
% 0.32/0.73 = ( plus_plus_real @ A_105 @ ( plus_plus_real @ B_78 @ C_55 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_340_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 0.32/0.73 ! [A_104: int,B_77: int,C_54: int] :
% 0.32/0.73 ( ( plus_plus_int @ ( plus_plus_int @ A_104 @ B_77 ) @ C_54 )
% 0.32/0.73 = ( plus_plus_int @ A_104 @ ( plus_plus_int @ B_77 @ C_54 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 0.32/0.73 ! [A_104: nat,B_77: nat,C_54: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ ( plus_plus_nat @ A_104 @ B_77 ) @ C_54 )
% 0.32/0.73 = ( plus_plus_nat @ A_104 @ ( plus_plus_nat @ B_77 @ C_54 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 0.32/0.73 ! [A_104: real,B_77: real,C_54: real] :
% 0.32/0.73 ( ( plus_plus_real @ ( plus_plus_real @ A_104 @ B_77 ) @ C_54 )
% 0.32/0.73 = ( plus_plus_real @ A_104 @ ( plus_plus_real @ B_77 @ C_54 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 0.32/0.73 ! [A_103: int,C_53: int,D_22: int] :
% 0.32/0.73 ( ( plus_plus_int @ A_103 @ ( plus_plus_int @ C_53 @ D_22 ) )
% 0.32/0.73 = ( plus_plus_int @ ( plus_plus_int @ A_103 @ C_53 ) @ D_22 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 0.32/0.73 ! [A_103: nat,C_53: nat,D_22: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ A_103 @ ( plus_plus_nat @ C_53 @ D_22 ) )
% 0.32/0.73 = ( plus_plus_nat @ ( plus_plus_nat @ A_103 @ C_53 ) @ D_22 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 0.32/0.73 ! [A_103: real,C_53: real,D_22: real] :
% 0.32/0.73 ( ( plus_plus_real @ A_103 @ ( plus_plus_real @ C_53 @ D_22 ) )
% 0.32/0.73 = ( plus_plus_real @ ( plus_plus_real @ A_103 @ C_53 ) @ D_22 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 0.32/0.73 ! [A_102: int,C_52: int,D_21: int] :
% 0.32/0.73 ( ( plus_plus_int @ A_102 @ ( plus_plus_int @ C_52 @ D_21 ) )
% 0.32/0.73 = ( plus_plus_int @ C_52 @ ( plus_plus_int @ A_102 @ D_21 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 0.32/0.73 ! [A_102: nat,C_52: nat,D_21: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ A_102 @ ( plus_plus_nat @ C_52 @ D_21 ) )
% 0.32/0.73 = ( plus_plus_nat @ C_52 @ ( plus_plus_nat @ A_102 @ D_21 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 0.32/0.73 ! [A_102: real,C_52: real,D_21: real] :
% 0.32/0.73 ( ( plus_plus_real @ A_102 @ ( plus_plus_real @ C_52 @ D_21 ) )
% 0.32/0.73 = ( plus_plus_real @ C_52 @ ( plus_plus_real @ A_102 @ D_21 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 0.32/0.73 ! [A_101: int,C_51: int] :
% 0.32/0.73 ( ( plus_plus_int @ A_101 @ C_51 )
% 0.32/0.73 = ( plus_plus_int @ C_51 @ A_101 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 0.32/0.73 ! [A_101: nat,C_51: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ A_101 @ C_51 )
% 0.32/0.73 = ( plus_plus_nat @ C_51 @ A_101 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 0.32/0.73 ! [A_101: real,C_51: real] :
% 0.32/0.73 ( ( plus_plus_real @ A_101 @ C_51 )
% 0.32/0.73 = ( plus_plus_real @ C_51 @ A_101 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_352_one__reorient,axiom,
% 0.32/0.73 ! [X_19: int] :
% 0.32/0.73 ( ( one_one_int = X_19 )
% 0.32/0.73 <=> ( X_19 = one_one_int ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_353_one__reorient,axiom,
% 0.32/0.73 ! [X_19: nat] :
% 0.32/0.73 ( ( one_one_nat = X_19 )
% 0.32/0.73 <=> ( X_19 = one_one_nat ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_354_one__reorient,axiom,
% 0.32/0.73 ! [X_19: real] :
% 0.32/0.73 ( ( one_one_real = X_19 )
% 0.32/0.73 <=> ( X_19 = one_one_real ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_355_add__0__iff,axiom,
% 0.32/0.73 ! [B_76: int,A_100: int] :
% 0.32/0.73 ( ( B_76
% 0.32/0.73 = ( plus_plus_int @ B_76 @ A_100 ) )
% 0.32/0.73 <=> ( A_100 = zero_zero_int ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_356_add__0__iff,axiom,
% 0.32/0.73 ! [B_76: nat,A_100: nat] :
% 0.32/0.73 ( ( B_76
% 0.32/0.73 = ( plus_plus_nat @ B_76 @ A_100 ) )
% 0.32/0.73 <=> ( A_100 = zero_zero_nat ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_357_add__0__iff,axiom,
% 0.32/0.73 ! [B_76: real,A_100: real] :
% 0.32/0.73 ( ( B_76
% 0.32/0.73 = ( plus_plus_real @ B_76 @ A_100 ) )
% 0.32/0.73 <=> ( A_100 = zero_zero_real ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_358_add_Ocomm__neutral,axiom,
% 0.32/0.73 ! [A_99: int] :
% 0.32/0.73 ( ( plus_plus_int @ A_99 @ zero_zero_int )
% 0.32/0.73 = A_99 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_359_add_Ocomm__neutral,axiom,
% 0.32/0.73 ! [A_99: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ A_99 @ zero_zero_nat )
% 0.32/0.73 = A_99 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_360_add_Ocomm__neutral,axiom,
% 0.32/0.73 ! [A_99: real] :
% 0.32/0.73 ( ( plus_plus_real @ A_99 @ zero_zero_real )
% 0.32/0.73 = A_99 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_361_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 0.32/0.73 ! [A_98: int] :
% 0.32/0.73 ( ( plus_plus_int @ A_98 @ zero_zero_int )
% 0.32/0.73 = A_98 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_362_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 0.32/0.73 ! [A_98: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ A_98 @ zero_zero_nat )
% 0.32/0.73 = A_98 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_363_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 0.32/0.73 ! [A_98: real] :
% 0.32/0.73 ( ( plus_plus_real @ A_98 @ zero_zero_real )
% 0.32/0.73 = A_98 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_364_add__0__right,axiom,
% 0.32/0.73 ! [A_97: int] :
% 0.32/0.73 ( ( plus_plus_int @ A_97 @ zero_zero_int )
% 0.32/0.73 = A_97 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_365_add__0__right,axiom,
% 0.32/0.73 ! [A_97: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ A_97 @ zero_zero_nat )
% 0.32/0.73 = A_97 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_366_add__0__right,axiom,
% 0.32/0.73 ! [A_97: real] :
% 0.32/0.73 ( ( plus_plus_real @ A_97 @ zero_zero_real )
% 0.32/0.73 = A_97 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_367_double__zero__sym,axiom,
% 0.32/0.73 ! [A_96: int] :
% 0.32/0.73 ( ( zero_zero_int
% 0.32/0.73 = ( plus_plus_int @ A_96 @ A_96 ) )
% 0.32/0.73 <=> ( A_96 = zero_zero_int ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_368_double__zero__sym,axiom,
% 0.32/0.73 ! [A_96: real] :
% 0.32/0.73 ( ( zero_zero_real
% 0.32/0.73 = ( plus_plus_real @ A_96 @ A_96 ) )
% 0.32/0.73 <=> ( A_96 = zero_zero_real ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_369_add__0,axiom,
% 0.32/0.73 ! [A_95: int] :
% 0.32/0.73 ( ( plus_plus_int @ zero_zero_int @ A_95 )
% 0.32/0.73 = A_95 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_370_add__0,axiom,
% 0.32/0.73 ! [A_95: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ zero_zero_nat @ A_95 )
% 0.32/0.73 = A_95 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_371_add__0,axiom,
% 0.32/0.73 ! [A_95: real] :
% 0.32/0.73 ( ( plus_plus_real @ zero_zero_real @ A_95 )
% 0.32/0.73 = A_95 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_372_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 0.32/0.73 ! [A_94: int] :
% 0.32/0.73 ( ( plus_plus_int @ zero_zero_int @ A_94 )
% 0.32/0.73 = A_94 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_373_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 0.32/0.73 ! [A_94: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ zero_zero_nat @ A_94 )
% 0.32/0.73 = A_94 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_374_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 0.32/0.73 ! [A_94: real] :
% 0.32/0.73 ( ( plus_plus_real @ zero_zero_real @ A_94 )
% 0.32/0.73 = A_94 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_375_add__0__left,axiom,
% 0.32/0.73 ! [A_93: int] :
% 0.32/0.73 ( ( plus_plus_int @ zero_zero_int @ A_93 )
% 0.32/0.73 = A_93 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_376_add__0__left,axiom,
% 0.32/0.73 ! [A_93: nat] :
% 0.32/0.73 ( ( plus_plus_nat @ zero_zero_nat @ A_93 )
% 0.32/0.73 = A_93 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_377_add__0__left,axiom,
% 0.32/0.73 ! [A_93: real] :
% 0.32/0.73 ( ( plus_plus_real @ zero_zero_real @ A_93 )
% 0.32/0.73 = A_93 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_378_add__less__imp__less__left,axiom,
% 0.32/0.73 ! [C_50: int,A_92: int,B_75: int] :
% 0.32/0.73 ( ( ord_less_int @ ( plus_plus_int @ C_50 @ A_92 ) @ ( plus_plus_int @ C_50 @ B_75 ) )
% 0.32/0.73 => ( ord_less_int @ A_92 @ B_75 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_379_add__less__imp__less__left,axiom,
% 0.32/0.73 ! [C_50: nat,A_92: nat,B_75: nat] :
% 0.32/0.73 ( ( ord_less_nat @ ( plus_plus_nat @ C_50 @ A_92 ) @ ( plus_plus_nat @ C_50 @ B_75 ) )
% 0.32/0.73 => ( ord_less_nat @ A_92 @ B_75 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_380_add__less__imp__less__left,axiom,
% 0.32/0.73 ! [C_50: real,A_92: real,B_75: real] :
% 0.32/0.73 ( ( ord_less_real @ ( plus_plus_real @ C_50 @ A_92 ) @ ( plus_plus_real @ C_50 @ B_75 ) )
% 0.32/0.73 => ( ord_less_real @ A_92 @ B_75 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_381_add__less__imp__less__right,axiom,
% 0.32/0.73 ! [A_91: int,C_49: int,B_74: int] :
% 0.32/0.73 ( ( ord_less_int @ ( plus_plus_int @ A_91 @ C_49 ) @ ( plus_plus_int @ B_74 @ C_49 ) )
% 0.32/0.73 => ( ord_less_int @ A_91 @ B_74 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_382_add__less__imp__less__right,axiom,
% 0.32/0.73 ! [A_91: nat,C_49: nat,B_74: nat] :
% 0.32/0.73 ( ( ord_less_nat @ ( plus_plus_nat @ A_91 @ C_49 ) @ ( plus_plus_nat @ B_74 @ C_49 ) )
% 0.32/0.73 => ( ord_less_nat @ A_91 @ B_74 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_383_add__less__imp__less__right,axiom,
% 0.32/0.73 ! [A_91: real,C_49: real,B_74: real] :
% 0.32/0.73 ( ( ord_less_real @ ( plus_plus_real @ A_91 @ C_49 ) @ ( plus_plus_real @ B_74 @ C_49 ) )
% 0.32/0.73 => ( ord_less_real @ A_91 @ B_74 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_384_add__strict__mono,axiom,
% 0.32/0.73 ! [C_48: int,D_20: int,A_90: int,B_73: int] :
% 0.32/0.73 ( ( ord_less_int @ A_90 @ B_73 )
% 0.32/0.73 => ( ( ord_less_int @ C_48 @ D_20 )
% 0.32/0.73 => ( ord_less_int @ ( plus_plus_int @ A_90 @ C_48 ) @ ( plus_plus_int @ B_73 @ D_20 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_385_add__strict__mono,axiom,
% 0.32/0.73 ! [C_48: nat,D_20: nat,A_90: nat,B_73: nat] :
% 0.32/0.73 ( ( ord_less_nat @ A_90 @ B_73 )
% 0.32/0.73 => ( ( ord_less_nat @ C_48 @ D_20 )
% 0.32/0.73 => ( ord_less_nat @ ( plus_plus_nat @ A_90 @ C_48 ) @ ( plus_plus_nat @ B_73 @ D_20 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_386_add__strict__mono,axiom,
% 0.32/0.73 ! [C_48: real,D_20: real,A_90: real,B_73: real] :
% 0.32/0.73 ( ( ord_less_real @ A_90 @ B_73 )
% 0.32/0.73 => ( ( ord_less_real @ C_48 @ D_20 )
% 0.32/0.73 => ( ord_less_real @ ( plus_plus_real @ A_90 @ C_48 ) @ ( plus_plus_real @ B_73 @ D_20 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_387_add__strict__left__mono,axiom,
% 0.32/0.73 ! [C_47: int,A_89: int,B_72: int] :
% 0.32/0.73 ( ( ord_less_int @ A_89 @ B_72 )
% 0.32/0.73 => ( ord_less_int @ ( plus_plus_int @ C_47 @ A_89 ) @ ( plus_plus_int @ C_47 @ B_72 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_388_add__strict__left__mono,axiom,
% 0.32/0.73 ! [C_47: nat,A_89: nat,B_72: nat] :
% 0.32/0.73 ( ( ord_less_nat @ A_89 @ B_72 )
% 0.32/0.73 => ( ord_less_nat @ ( plus_plus_nat @ C_47 @ A_89 ) @ ( plus_plus_nat @ C_47 @ B_72 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_389_add__strict__left__mono,axiom,
% 0.32/0.73 ! [C_47: real,A_89: real,B_72: real] :
% 0.32/0.73 ( ( ord_less_real @ A_89 @ B_72 )
% 0.32/0.73 => ( ord_less_real @ ( plus_plus_real @ C_47 @ A_89 ) @ ( plus_plus_real @ C_47 @ B_72 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_390_add__strict__right__mono,axiom,
% 0.32/0.73 ! [C_46: int,A_88: int,B_71: int] :
% 0.32/0.73 ( ( ord_less_int @ A_88 @ B_71 )
% 0.32/0.73 => ( ord_less_int @ ( plus_plus_int @ A_88 @ C_46 ) @ ( plus_plus_int @ B_71 @ C_46 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_391_add__strict__right__mono,axiom,
% 0.32/0.73 ! [C_46: nat,A_88: nat,B_71: nat] :
% 0.32/0.73 ( ( ord_less_nat @ A_88 @ B_71 )
% 0.32/0.73 => ( ord_less_nat @ ( plus_plus_nat @ A_88 @ C_46 ) @ ( plus_plus_nat @ B_71 @ C_46 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_392_add__strict__right__mono,axiom,
% 0.32/0.73 ! [C_46: real,A_88: real,B_71: real] :
% 0.32/0.73 ( ( ord_less_real @ A_88 @ B_71 )
% 0.32/0.73 => ( ord_less_real @ ( plus_plus_real @ A_88 @ C_46 ) @ ( plus_plus_real @ B_71 @ C_46 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_393_add__less__cancel__left,axiom,
% 0.32/0.73 ! [C_45: int,A_87: int,B_70: int] :
% 0.32/0.73 ( ( ord_less_int @ ( plus_plus_int @ C_45 @ A_87 ) @ ( plus_plus_int @ C_45 @ B_70 ) )
% 0.32/0.73 <=> ( ord_less_int @ A_87 @ B_70 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_394_add__less__cancel__left,axiom,
% 0.32/0.73 ! [C_45: nat,A_87: nat,B_70: nat] :
% 0.32/0.73 ( ( ord_less_nat @ ( plus_plus_nat @ C_45 @ A_87 ) @ ( plus_plus_nat @ C_45 @ B_70 ) )
% 0.32/0.73 <=> ( ord_less_nat @ A_87 @ B_70 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_395_add__less__cancel__left,axiom,
% 0.32/0.73 ! [C_45: real,A_87: real,B_70: real] :
% 0.32/0.73 ( ( ord_less_real @ ( plus_plus_real @ C_45 @ A_87 ) @ ( plus_plus_real @ C_45 @ B_70 ) )
% 0.32/0.73 <=> ( ord_less_real @ A_87 @ B_70 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_396_add__less__cancel__right,axiom,
% 0.32/0.73 ! [A_86: int,C_44: int,B_69: int] :
% 0.32/0.73 ( ( ord_less_int @ ( plus_plus_int @ A_86 @ C_44 ) @ ( plus_plus_int @ B_69 @ C_44 ) )
% 0.32/0.73 <=> ( ord_less_int @ A_86 @ B_69 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_397_add__less__cancel__right,axiom,
% 0.32/0.73 ! [A_86: nat,C_44: nat,B_69: nat] :
% 0.32/0.73 ( ( ord_less_nat @ ( plus_plus_nat @ A_86 @ C_44 ) @ ( plus_plus_nat @ B_69 @ C_44 ) )
% 0.32/0.73 <=> ( ord_less_nat @ A_86 @ B_69 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_398_add__less__cancel__right,axiom,
% 0.32/0.73 ! [A_86: real,C_44: real,B_69: real] :
% 0.32/0.73 ( ( ord_less_real @ ( plus_plus_real @ A_86 @ C_44 ) @ ( plus_plus_real @ B_69 @ C_44 ) )
% 0.32/0.73 <=> ( ord_less_real @ A_86 @ B_69 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_399_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 0.32/0.73 ! [X_18: int] :
% 0.32/0.73 ( ( power_power_int @ X_18 @ one_one_nat )
% 0.32/0.73 = X_18 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_400_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 0.32/0.73 ! [X_18: nat] :
% 0.32/0.73 ( ( power_power_nat @ X_18 @ one_one_nat )
% 0.32/0.73 = X_18 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_401_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 0.32/0.73 ! [X_18: real] :
% 0.32/0.73 ( ( power_power_real @ X_18 @ one_one_nat )
% 0.32/0.73 = X_18 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_402_nat__power__eq__0__iff,axiom,
% 0.32/0.73 ! [M: nat,N: nat] :
% 0.32/0.73 ( ( ( power_power_nat @ M @ N )
% 0.32/0.73 = zero_zero_nat )
% 0.32/0.73 <=> ( ( N != zero_zero_nat )
% 0.32/0.73 & ( M = zero_zero_nat ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_403_realpow__pos__nth__unique,axiom,
% 0.32/0.73 ! [A: real,N: nat] :
% 0.32/0.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.73 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.73 => ? [X_1: real] :
% 0.32/0.73 ( ( ord_less_real @ zero_zero_real @ X_1 )
% 0.32/0.73 & ( ( power_power_real @ X_1 @ N )
% 0.32/0.73 = A )
% 0.32/0.73 & ! [Y_1: real] :
% 0.32/0.73 ( ( ( ord_less_real @ zero_zero_real @ Y_1 )
% 0.32/0.73 & ( ( power_power_real @ Y_1 @ N )
% 0.32/0.73 = A ) )
% 0.32/0.73 => ( Y_1 = X_1 ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_404_realpow__pos__nth,axiom,
% 0.32/0.73 ! [A: real,N: nat] :
% 0.32/0.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.73 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.32/0.73 => ? [R: real] :
% 0.32/0.73 ( ( ord_less_real @ zero_zero_real @ R )
% 0.32/0.73 & ( ( power_power_real @ R @ N )
% 0.32/0.73 = A ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_405_tpos,axiom,
% 0.32/0.73 ord_less_eq_int @ one_one_int @ t ).
% 0.32/0.73
% 0.32/0.73 thf(fact_406_nat__number__of__add__1,axiom,
% 0.32/0.73 ! [V_1: int] :
% 0.32/0.73 ( ( ( ord_less_int @ V_1 @ pls )
% 0.32/0.73 => ( ( plus_plus_nat @ ( number_number_of_nat @ V_1 ) @ one_one_nat )
% 0.32/0.73 = one_one_nat ) )
% 0.32/0.73 & ( ~ ( ord_less_int @ V_1 @ pls )
% 0.32/0.73 => ( ( plus_plus_nat @ ( number_number_of_nat @ V_1 ) @ one_one_nat )
% 0.32/0.73 = ( number_number_of_nat @ ( succ @ V_1 ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_407_nat__1__add__number__of,axiom,
% 0.32/0.73 ! [V_1: int] :
% 0.32/0.73 ( ( ( ord_less_int @ V_1 @ pls )
% 0.32/0.73 => ( ( plus_plus_nat @ one_one_nat @ ( number_number_of_nat @ V_1 ) )
% 0.32/0.73 = one_one_nat ) )
% 0.32/0.73 & ( ~ ( ord_less_int @ V_1 @ pls )
% 0.32/0.73 => ( ( plus_plus_nat @ one_one_nat @ ( number_number_of_nat @ V_1 ) )
% 0.32/0.73 = ( number_number_of_nat @ ( succ @ V_1 ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_408_zadd__power3,axiom,
% 0.32/0.73 ! [A: int,B: int] :
% 0.32/0.73 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
% 0.32/0.73 = ( plus_plus_int @ ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_409_zadd__power2,axiom,
% 0.32/0.73 ! [A: int,B: int] :
% 0.32/0.73 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.73 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_410_tn,axiom,
% 0.32/0.73 ( tn
% 0.32/0.73 = ( minus_minus_nat @ ( nat_1 @ t ) @ one_one_nat ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_411__096_B_Bthesis_O_A_I_B_Btn_O_A_091_124_Atn_A_061_Anat_At_A_N_A1_059_A0_,axiom,
% 0.32/0.73 ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ ( nat_1 @ t ) @ one_one_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_412_le__iff__diff__le__0,axiom,
% 0.32/0.73 ! [A_85: int,B_68: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ A_85 @ B_68 )
% 0.32/0.73 <=> ( ord_less_eq_int @ ( minus_minus_int @ A_85 @ B_68 ) @ zero_zero_int ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_413_le__iff__diff__le__0,axiom,
% 0.32/0.73 ! [A_85: real,B_68: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ A_85 @ B_68 )
% 0.32/0.73 <=> ( ord_less_eq_real @ ( minus_minus_real @ A_85 @ B_68 ) @ zero_zero_real ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_414_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 0.32/0.73 ! [A_84: int,B_67: int] :
% 0.32/0.73 ( ( times_times_int @ A_84 @ B_67 )
% 0.32/0.73 = ( times_times_int @ B_67 @ A_84 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_415_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 0.32/0.73 ! [A_84: nat,B_67: nat] :
% 0.32/0.73 ( ( times_times_nat @ A_84 @ B_67 )
% 0.32/0.73 = ( times_times_nat @ B_67 @ A_84 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_416_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 0.32/0.73 ! [A_84: real,B_67: real] :
% 0.32/0.73 ( ( times_times_real @ A_84 @ B_67 )
% 0.32/0.73 = ( times_times_real @ B_67 @ A_84 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_417_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 0.32/0.73 ! [Lx_6: int,Rx_6: int,Ry_4: int] :
% 0.32/0.73 ( ( times_times_int @ Lx_6 @ ( times_times_int @ Rx_6 @ Ry_4 ) )
% 0.32/0.73 = ( times_times_int @ Rx_6 @ ( times_times_int @ Lx_6 @ Ry_4 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_418_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 0.32/0.73 ! [Lx_6: nat,Rx_6: nat,Ry_4: nat] :
% 0.32/0.73 ( ( times_times_nat @ Lx_6 @ ( times_times_nat @ Rx_6 @ Ry_4 ) )
% 0.32/0.73 = ( times_times_nat @ Rx_6 @ ( times_times_nat @ Lx_6 @ Ry_4 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_419_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 0.32/0.73 ! [Lx_6: real,Rx_6: real,Ry_4: real] :
% 0.32/0.73 ( ( times_times_real @ Lx_6 @ ( times_times_real @ Rx_6 @ Ry_4 ) )
% 0.32/0.73 = ( times_times_real @ Rx_6 @ ( times_times_real @ Lx_6 @ Ry_4 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_420_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 0.32/0.73 ! [Lx_5: int,Rx_5: int,Ry_3: int] :
% 0.32/0.73 ( ( times_times_int @ Lx_5 @ ( times_times_int @ Rx_5 @ Ry_3 ) )
% 0.32/0.73 = ( times_times_int @ ( times_times_int @ Lx_5 @ Rx_5 ) @ Ry_3 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_421_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 0.32/0.73 ! [Lx_5: nat,Rx_5: nat,Ry_3: nat] :
% 0.32/0.73 ( ( times_times_nat @ Lx_5 @ ( times_times_nat @ Rx_5 @ Ry_3 ) )
% 0.32/0.73 = ( times_times_nat @ ( times_times_nat @ Lx_5 @ Rx_5 ) @ Ry_3 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_422_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 0.32/0.73 ! [Lx_5: real,Rx_5: real,Ry_3: real] :
% 0.32/0.73 ( ( times_times_real @ Lx_5 @ ( times_times_real @ Rx_5 @ Ry_3 ) )
% 0.32/0.73 = ( times_times_real @ ( times_times_real @ Lx_5 @ Rx_5 ) @ Ry_3 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_423_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.32/0.73 ! [A_83: int,B_66: int,C_43: int] :
% 0.32/0.73 ( ( times_times_int @ ( times_times_int @ A_83 @ B_66 ) @ C_43 )
% 0.32/0.73 = ( times_times_int @ A_83 @ ( times_times_int @ B_66 @ C_43 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_424_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.32/0.73 ! [A_83: nat,B_66: nat,C_43: nat] :
% 0.32/0.73 ( ( times_times_nat @ ( times_times_nat @ A_83 @ B_66 ) @ C_43 )
% 0.32/0.73 = ( times_times_nat @ A_83 @ ( times_times_nat @ B_66 @ C_43 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_425_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.32/0.73 ! [A_83: real,B_66: real,C_43: real] :
% 0.32/0.73 ( ( times_times_real @ ( times_times_real @ A_83 @ B_66 ) @ C_43 )
% 0.32/0.73 = ( times_times_real @ A_83 @ ( times_times_real @ B_66 @ C_43 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_426_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 0.32/0.73 ! [Lx_4: int,Ly_4: int,Rx_4: int] :
% 0.32/0.73 ( ( times_times_int @ ( times_times_int @ Lx_4 @ Ly_4 ) @ Rx_4 )
% 0.32/0.73 = ( times_times_int @ Lx_4 @ ( times_times_int @ Ly_4 @ Rx_4 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_427_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 0.32/0.73 ! [Lx_4: nat,Ly_4: nat,Rx_4: nat] :
% 0.32/0.73 ( ( times_times_nat @ ( times_times_nat @ Lx_4 @ Ly_4 ) @ Rx_4 )
% 0.32/0.73 = ( times_times_nat @ Lx_4 @ ( times_times_nat @ Ly_4 @ Rx_4 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_428_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 0.32/0.73 ! [Lx_4: real,Ly_4: real,Rx_4: real] :
% 0.32/0.73 ( ( times_times_real @ ( times_times_real @ Lx_4 @ Ly_4 ) @ Rx_4 )
% 0.32/0.73 = ( times_times_real @ Lx_4 @ ( times_times_real @ Ly_4 @ Rx_4 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_429_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 0.32/0.73 ! [Lx_3: int,Ly_3: int,Rx_3: int] :
% 0.32/0.73 ( ( times_times_int @ ( times_times_int @ Lx_3 @ Ly_3 ) @ Rx_3 )
% 0.32/0.73 = ( times_times_int @ ( times_times_int @ Lx_3 @ Rx_3 ) @ Ly_3 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_430_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 0.32/0.73 ! [Lx_3: nat,Ly_3: nat,Rx_3: nat] :
% 0.32/0.73 ( ( times_times_nat @ ( times_times_nat @ Lx_3 @ Ly_3 ) @ Rx_3 )
% 0.32/0.73 = ( times_times_nat @ ( times_times_nat @ Lx_3 @ Rx_3 ) @ Ly_3 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_431_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 0.32/0.73 ! [Lx_3: real,Ly_3: real,Rx_3: real] :
% 0.32/0.73 ( ( times_times_real @ ( times_times_real @ Lx_3 @ Ly_3 ) @ Rx_3 )
% 0.32/0.73 = ( times_times_real @ ( times_times_real @ Lx_3 @ Rx_3 ) @ Ly_3 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_432_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 0.32/0.73 ! [Lx_2: int,Ly_2: int,Rx_2: int,Ry_2: int] :
% 0.32/0.73 ( ( times_times_int @ ( times_times_int @ Lx_2 @ Ly_2 ) @ ( times_times_int @ Rx_2 @ Ry_2 ) )
% 0.32/0.73 = ( times_times_int @ Lx_2 @ ( times_times_int @ Ly_2 @ ( times_times_int @ Rx_2 @ Ry_2 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_433_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 0.32/0.73 ! [Lx_2: nat,Ly_2: nat,Rx_2: nat,Ry_2: nat] :
% 0.32/0.73 ( ( times_times_nat @ ( times_times_nat @ Lx_2 @ Ly_2 ) @ ( times_times_nat @ Rx_2 @ Ry_2 ) )
% 0.32/0.73 = ( times_times_nat @ Lx_2 @ ( times_times_nat @ Ly_2 @ ( times_times_nat @ Rx_2 @ Ry_2 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_434_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 0.32/0.73 ! [Lx_2: real,Ly_2: real,Rx_2: real,Ry_2: real] :
% 0.32/0.73 ( ( times_times_real @ ( times_times_real @ Lx_2 @ Ly_2 ) @ ( times_times_real @ Rx_2 @ Ry_2 ) )
% 0.32/0.73 = ( times_times_real @ Lx_2 @ ( times_times_real @ Ly_2 @ ( times_times_real @ Rx_2 @ Ry_2 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_435_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 0.32/0.73 ! [Lx_1: real,Ly_1: real,Rx_1: real,Ry_1: real] :
% 0.32/0.73 ( ( times_times_real @ ( times_times_real @ Lx_1 @ Ly_1 ) @ ( times_times_real @ Rx_1 @ Ry_1 ) )
% 0.32/0.73 = ( times_times_real @ Rx_1 @ ( times_times_real @ ( times_times_real @ Lx_1 @ Ly_1 ) @ Ry_1 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_436_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 0.32/0.73 ! [Lx_1: nat,Ly_1: nat,Rx_1: nat,Ry_1: nat] :
% 0.32/0.73 ( ( times_times_nat @ ( times_times_nat @ Lx_1 @ Ly_1 ) @ ( times_times_nat @ Rx_1 @ Ry_1 ) )
% 0.32/0.73 = ( times_times_nat @ Rx_1 @ ( times_times_nat @ ( times_times_nat @ Lx_1 @ Ly_1 ) @ Ry_1 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_437_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 0.32/0.73 ! [Lx_1: int,Ly_1: int,Rx_1: int,Ry_1: int] :
% 0.32/0.73 ( ( times_times_int @ ( times_times_int @ Lx_1 @ Ly_1 ) @ ( times_times_int @ Rx_1 @ Ry_1 ) )
% 0.32/0.73 = ( times_times_int @ Rx_1 @ ( times_times_int @ ( times_times_int @ Lx_1 @ Ly_1 ) @ Ry_1 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_438_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 0.32/0.73 ! [Lx: real,Ly: real,Rx: real,Ry: real] :
% 0.32/0.73 ( ( times_times_real @ ( times_times_real @ Lx @ Ly ) @ ( times_times_real @ Rx @ Ry ) )
% 0.32/0.73 = ( times_times_real @ ( times_times_real @ Lx @ Rx ) @ ( times_times_real @ Ly @ Ry ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_439_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 0.32/0.73 ! [Lx: nat,Ly: nat,Rx: nat,Ry: nat] :
% 0.32/0.73 ( ( times_times_nat @ ( times_times_nat @ Lx @ Ly ) @ ( times_times_nat @ Rx @ Ry ) )
% 0.32/0.73 = ( times_times_nat @ ( times_times_nat @ Lx @ Rx ) @ ( times_times_nat @ Ly @ Ry ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_440_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 0.32/0.73 ! [Lx: int,Ly: int,Rx: int,Ry: int] :
% 0.32/0.73 ( ( times_times_int @ ( times_times_int @ Lx @ Ly ) @ ( times_times_int @ Rx @ Ry ) )
% 0.32/0.73 = ( times_times_int @ ( times_times_int @ Lx @ Rx ) @ ( times_times_int @ Ly @ Ry ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_441_diff__eq__diff__eq,axiom,
% 0.32/0.73 ! [A_82: int,B_65: int,C_42: int,D_19: int] :
% 0.32/0.73 ( ( ( minus_minus_int @ A_82 @ B_65 )
% 0.32/0.73 = ( minus_minus_int @ C_42 @ D_19 ) )
% 0.32/0.73 => ( ( A_82 = B_65 )
% 0.32/0.73 <=> ( C_42 = D_19 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_442_diff__eq__diff__eq,axiom,
% 0.32/0.73 ! [A_82: real,B_65: real,C_42: real,D_19: real] :
% 0.32/0.73 ( ( ( minus_minus_real @ A_82 @ B_65 )
% 0.32/0.73 = ( minus_minus_real @ C_42 @ D_19 ) )
% 0.32/0.73 => ( ( A_82 = B_65 )
% 0.32/0.73 <=> ( C_42 = D_19 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_443_diff__eq__diff__less__eq,axiom,
% 0.32/0.73 ! [A_81: int,B_64: int,C_41: int,D_18: int] :
% 0.32/0.73 ( ( ( minus_minus_int @ A_81 @ B_64 )
% 0.32/0.73 = ( minus_minus_int @ C_41 @ D_18 ) )
% 0.32/0.73 => ( ( ord_less_eq_int @ A_81 @ B_64 )
% 0.32/0.73 <=> ( ord_less_eq_int @ C_41 @ D_18 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_444_diff__eq__diff__less__eq,axiom,
% 0.32/0.73 ! [A_81: real,B_64: real,C_41: real,D_18: real] :
% 0.32/0.73 ( ( ( minus_minus_real @ A_81 @ B_64 )
% 0.32/0.73 = ( minus_minus_real @ C_41 @ D_18 ) )
% 0.32/0.73 => ( ( ord_less_eq_real @ A_81 @ B_64 )
% 0.32/0.73 <=> ( ord_less_eq_real @ C_41 @ D_18 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_445_semiring__mult__number__of,axiom,
% 0.32/0.73 ! [V_12: int,V_11: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ pls @ V_11 )
% 0.32/0.73 => ( ( ord_less_eq_int @ pls @ V_12 )
% 0.32/0.73 => ( ( times_times_real @ ( number267125858f_real @ V_11 ) @ ( number267125858f_real @ V_12 ) )
% 0.32/0.73 = ( number267125858f_real @ ( times_times_int @ V_11 @ V_12 ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_446_semiring__mult__number__of,axiom,
% 0.32/0.73 ! [V_12: int,V_11: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ pls @ V_11 )
% 0.32/0.73 => ( ( ord_less_eq_int @ pls @ V_12 )
% 0.32/0.73 => ( ( times_times_nat @ ( number_number_of_nat @ V_11 ) @ ( number_number_of_nat @ V_12 ) )
% 0.32/0.73 = ( number_number_of_nat @ ( times_times_int @ V_11 @ V_12 ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_447_semiring__mult__number__of,axiom,
% 0.32/0.73 ! [V_12: int,V_11: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ pls @ V_11 )
% 0.32/0.73 => ( ( ord_less_eq_int @ pls @ V_12 )
% 0.32/0.73 => ( ( times_times_int @ ( number_number_of_int @ V_11 ) @ ( number_number_of_int @ V_12 ) )
% 0.32/0.73 = ( number_number_of_int @ ( times_times_int @ V_11 @ V_12 ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_448_zle__refl,axiom,
% 0.32/0.73 ! [W: int] : ( ord_less_eq_int @ W @ W ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_449_zmult__commute,axiom,
% 0.32/0.73 ! [Z: int,W: int] :
% 0.32/0.73 ( ( times_times_int @ Z @ W )
% 0.32/0.73 = ( times_times_int @ W @ Z ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_450_zle__linear,axiom,
% 0.32/0.73 ! [Z: int,W: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ Z @ W )
% 0.32/0.73 | ( ord_less_eq_int @ W @ Z ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_451_zmult__assoc,axiom,
% 0.32/0.73 ! [Z1: int,Z2: int,Z3: int] :
% 0.32/0.73 ( ( times_times_int @ ( times_times_int @ Z1 @ Z2 ) @ Z3 )
% 0.32/0.73 = ( times_times_int @ Z1 @ ( times_times_int @ Z2 @ Z3 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_452_zle__trans,axiom,
% 0.32/0.73 ! [K: int,I_1: int,J: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ I_1 @ J )
% 0.32/0.73 => ( ( ord_less_eq_int @ J @ K )
% 0.32/0.73 => ( ord_less_eq_int @ I_1 @ K ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_453_zle__antisym,axiom,
% 0.32/0.73 ! [Z: int,W: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ Z @ W )
% 0.32/0.73 => ( ( ord_less_eq_int @ W @ Z )
% 0.32/0.73 => ( Z = W ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_454_le__number__of,axiom,
% 0.32/0.73 ! [X_17: int,Y_15: int] :
% 0.32/0.73 ( ( ord_less_eq_real @ ( number267125858f_real @ X_17 ) @ ( number267125858f_real @ Y_15 ) )
% 0.32/0.73 <=> ( ord_less_eq_int @ X_17 @ Y_15 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_455_le__number__of,axiom,
% 0.32/0.73 ! [X_17: int,Y_15: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ ( number_number_of_int @ X_17 ) @ ( number_number_of_int @ Y_15 ) )
% 0.32/0.73 <=> ( ord_less_eq_int @ X_17 @ Y_15 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_456_number__of__mult,axiom,
% 0.32/0.73 ! [V_10: int,W_7: int] :
% 0.32/0.73 ( ( number267125858f_real @ ( times_times_int @ V_10 @ W_7 ) )
% 0.32/0.73 = ( times_times_real @ ( number267125858f_real @ V_10 ) @ ( number267125858f_real @ W_7 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_457_number__of__mult,axiom,
% 0.32/0.73 ! [V_10: int,W_7: int] :
% 0.32/0.73 ( ( number_number_of_int @ ( times_times_int @ V_10 @ W_7 ) )
% 0.32/0.73 = ( times_times_int @ ( number_number_of_int @ V_10 ) @ ( number_number_of_int @ W_7 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_458_arith__simps_I32_J,axiom,
% 0.32/0.73 ! [V_9: int,W_6: int] :
% 0.32/0.73 ( ( times_times_real @ ( number267125858f_real @ V_9 ) @ ( number267125858f_real @ W_6 ) )
% 0.32/0.73 = ( number267125858f_real @ ( times_times_int @ V_9 @ W_6 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_459_arith__simps_I32_J,axiom,
% 0.32/0.73 ! [V_9: int,W_6: int] :
% 0.32/0.73 ( ( times_times_int @ ( number_number_of_int @ V_9 ) @ ( number_number_of_int @ W_6 ) )
% 0.32/0.73 = ( number_number_of_int @ ( times_times_int @ V_9 @ W_6 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_460_mult__number__of__left,axiom,
% 0.32/0.73 ! [V_8: int,W_5: int,Z_4: real] :
% 0.32/0.73 ( ( times_times_real @ ( number267125858f_real @ V_8 ) @ ( times_times_real @ ( number267125858f_real @ W_5 ) @ Z_4 ) )
% 0.32/0.73 = ( times_times_real @ ( number267125858f_real @ ( times_times_int @ V_8 @ W_5 ) ) @ Z_4 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_461_mult__number__of__left,axiom,
% 0.32/0.73 ! [V_8: int,W_5: int,Z_4: int] :
% 0.32/0.73 ( ( times_times_int @ ( number_number_of_int @ V_8 ) @ ( times_times_int @ ( number_number_of_int @ W_5 ) @ Z_4 ) )
% 0.32/0.73 = ( times_times_int @ ( number_number_of_int @ ( times_times_int @ V_8 @ W_5 ) ) @ Z_4 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_462_eq__nat__nat__iff,axiom,
% 0.32/0.73 ! [Z_1: int,Z: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ Z_1 )
% 0.32/0.73 => ( ( ( nat_1 @ Z )
% 0.32/0.73 = ( nat_1 @ Z_1 ) )
% 0.32/0.73 <=> ( Z = Z_1 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_463_right__diff__distrib__number__of,axiom,
% 0.32/0.73 ! [V_7: int,B_63: int,C_40: int] :
% 0.32/0.73 ( ( times_times_int @ ( number_number_of_int @ V_7 ) @ ( minus_minus_int @ B_63 @ C_40 ) )
% 0.32/0.73 = ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ V_7 ) @ B_63 ) @ ( times_times_int @ ( number_number_of_int @ V_7 ) @ C_40 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_464_right__diff__distrib__number__of,axiom,
% 0.32/0.73 ! [V_7: int,B_63: real,C_40: real] :
% 0.32/0.73 ( ( times_times_real @ ( number267125858f_real @ V_7 ) @ ( minus_minus_real @ B_63 @ C_40 ) )
% 0.32/0.73 = ( minus_minus_real @ ( times_times_real @ ( number267125858f_real @ V_7 ) @ B_63 ) @ ( times_times_real @ ( number267125858f_real @ V_7 ) @ C_40 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_465_left__diff__distrib__number__of,axiom,
% 0.32/0.73 ! [A_80: int,B_62: int,V_6: int] :
% 0.32/0.73 ( ( times_times_int @ ( minus_minus_int @ A_80 @ B_62 ) @ ( number_number_of_int @ V_6 ) )
% 0.32/0.73 = ( minus_minus_int @ ( times_times_int @ A_80 @ ( number_number_of_int @ V_6 ) ) @ ( times_times_int @ B_62 @ ( number_number_of_int @ V_6 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_466_left__diff__distrib__number__of,axiom,
% 0.32/0.73 ! [A_80: real,B_62: real,V_6: int] :
% 0.32/0.73 ( ( times_times_real @ ( minus_minus_real @ A_80 @ B_62 ) @ ( number267125858f_real @ V_6 ) )
% 0.32/0.73 = ( minus_minus_real @ ( times_times_real @ A_80 @ ( number267125858f_real @ V_6 ) ) @ ( times_times_real @ B_62 @ ( number267125858f_real @ V_6 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_467_number__of__diff,axiom,
% 0.32/0.73 ! [V_5: int,W_4: int] :
% 0.32/0.73 ( ( number_number_of_int @ ( minus_minus_int @ V_5 @ W_4 ) )
% 0.32/0.73 = ( minus_minus_int @ ( number_number_of_int @ V_5 ) @ ( number_number_of_int @ W_4 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_468_number__of__diff,axiom,
% 0.32/0.73 ! [V_5: int,W_4: int] :
% 0.32/0.73 ( ( number267125858f_real @ ( minus_minus_int @ V_5 @ W_4 ) )
% 0.32/0.73 = ( minus_minus_real @ ( number267125858f_real @ V_5 ) @ ( number267125858f_real @ W_4 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_469_of__nat__mult,axiom,
% 0.32/0.73 ! [M_5: nat,N_11: nat] :
% 0.32/0.73 ( ( semiri132038758t_real @ ( times_times_nat @ M_5 @ N_11 ) )
% 0.32/0.73 = ( times_times_real @ ( semiri132038758t_real @ M_5 ) @ ( semiri132038758t_real @ N_11 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_470_of__nat__mult,axiom,
% 0.32/0.73 ! [M_5: nat,N_11: nat] :
% 0.32/0.73 ( ( semiri984289939at_nat @ ( times_times_nat @ M_5 @ N_11 ) )
% 0.32/0.73 = ( times_times_nat @ ( semiri984289939at_nat @ M_5 ) @ ( semiri984289939at_nat @ N_11 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_471_of__nat__mult,axiom,
% 0.32/0.73 ! [M_5: nat,N_11: nat] :
% 0.32/0.73 ( ( semiri1621563631at_int @ ( times_times_nat @ M_5 @ N_11 ) )
% 0.32/0.73 = ( times_times_int @ ( semiri1621563631at_int @ M_5 ) @ ( semiri1621563631at_int @ N_11 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_472_of__nat__le__iff,axiom,
% 0.32/0.73 ! [M_4: nat,N_10: nat] :
% 0.32/0.73 ( ( ord_less_eq_real @ ( semiri132038758t_real @ M_4 ) @ ( semiri132038758t_real @ N_10 ) )
% 0.32/0.73 <=> ( ord_less_eq_nat @ M_4 @ N_10 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_473_of__nat__le__iff,axiom,
% 0.32/0.73 ! [M_4: nat,N_10: nat] :
% 0.32/0.73 ( ( ord_less_eq_nat @ ( semiri984289939at_nat @ M_4 ) @ ( semiri984289939at_nat @ N_10 ) )
% 0.32/0.73 <=> ( ord_less_eq_nat @ M_4 @ N_10 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_474_of__nat__le__iff,axiom,
% 0.32/0.73 ! [M_4: nat,N_10: nat] :
% 0.32/0.73 ( ( ord_less_eq_int @ ( semiri1621563631at_int @ M_4 ) @ ( semiri1621563631at_int @ N_10 ) )
% 0.32/0.73 <=> ( ord_less_eq_nat @ M_4 @ N_10 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_475_diff__commute,axiom,
% 0.32/0.73 ! [I_1: nat,J: nat,K: nat] :
% 0.32/0.73 ( ( minus_minus_nat @ ( minus_minus_nat @ I_1 @ J ) @ K )
% 0.32/0.73 = ( minus_minus_nat @ ( minus_minus_nat @ I_1 @ K ) @ J ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_476_nat__if__cong,axiom,
% 0.32/0.73 ! [X: int,Y: int,P: $o] :
% 0.32/0.73 ( ( P
% 0.32/0.73 => ( ( nat_1 @ X )
% 0.32/0.73 = ( nat_1 @ ( if_int @ P @ X @ Y ) ) ) )
% 0.32/0.73 & ( ~ P
% 0.32/0.73 => ( ( nat_1 @ Y )
% 0.32/0.73 = ( nat_1 @ ( if_int @ P @ X @ Y ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_477_split__mult__neg__le,axiom,
% 0.32/0.73 ! [B_61: real,A_79: real] :
% 0.32/0.73 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A_79 )
% 0.32/0.73 & ( ord_less_eq_real @ B_61 @ zero_zero_real ) )
% 0.32/0.73 | ( ( ord_less_eq_real @ A_79 @ zero_zero_real )
% 0.32/0.73 & ( ord_less_eq_real @ zero_zero_real @ B_61 ) ) )
% 0.32/0.73 => ( ord_less_eq_real @ ( times_times_real @ A_79 @ B_61 ) @ zero_zero_real ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_478_split__mult__neg__le,axiom,
% 0.32/0.73 ! [B_61: nat,A_79: nat] :
% 0.32/0.73 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A_79 )
% 0.32/0.73 & ( ord_less_eq_nat @ B_61 @ zero_zero_nat ) )
% 0.32/0.73 | ( ( ord_less_eq_nat @ A_79 @ zero_zero_nat )
% 0.32/0.73 & ( ord_less_eq_nat @ zero_zero_nat @ B_61 ) ) )
% 0.32/0.73 => ( ord_less_eq_nat @ ( times_times_nat @ A_79 @ B_61 ) @ zero_zero_nat ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_479_split__mult__neg__le,axiom,
% 0.32/0.73 ! [B_61: int,A_79: int] :
% 0.32/0.73 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A_79 )
% 0.32/0.73 & ( ord_less_eq_int @ B_61 @ zero_zero_int ) )
% 0.32/0.73 | ( ( ord_less_eq_int @ A_79 @ zero_zero_int )
% 0.32/0.73 & ( ord_less_eq_int @ zero_zero_int @ B_61 ) ) )
% 0.32/0.73 => ( ord_less_eq_int @ ( times_times_int @ A_79 @ B_61 ) @ zero_zero_int ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_480_split__mult__pos__le,axiom,
% 0.32/0.73 ! [B_60: real,A_78: real] :
% 0.32/0.73 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A_78 )
% 0.32/0.73 & ( ord_less_eq_real @ zero_zero_real @ B_60 ) )
% 0.32/0.73 | ( ( ord_less_eq_real @ A_78 @ zero_zero_real )
% 0.32/0.73 & ( ord_less_eq_real @ B_60 @ zero_zero_real ) ) )
% 0.32/0.73 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A_78 @ B_60 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_481_split__mult__pos__le,axiom,
% 0.32/0.73 ! [B_60: int,A_78: int] :
% 0.32/0.73 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A_78 )
% 0.32/0.73 & ( ord_less_eq_int @ zero_zero_int @ B_60 ) )
% 0.32/0.73 | ( ( ord_less_eq_int @ A_78 @ zero_zero_int )
% 0.32/0.73 & ( ord_less_eq_int @ B_60 @ zero_zero_int ) ) )
% 0.32/0.73 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A_78 @ B_60 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_482_mult__mono,axiom,
% 0.32/0.73 ! [C_39: real,D_17: real,A_77: real,B_59: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ A_77 @ B_59 )
% 0.32/0.73 => ( ( ord_less_eq_real @ C_39 @ D_17 )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ B_59 )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ C_39 )
% 0.32/0.73 => ( ord_less_eq_real @ ( times_times_real @ A_77 @ C_39 ) @ ( times_times_real @ B_59 @ D_17 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_483_mult__mono,axiom,
% 0.32/0.73 ! [C_39: nat,D_17: nat,A_77: nat,B_59: nat] :
% 0.32/0.73 ( ( ord_less_eq_nat @ A_77 @ B_59 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ C_39 @ D_17 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ B_59 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C_39 )
% 0.32/0.73 => ( ord_less_eq_nat @ ( times_times_nat @ A_77 @ C_39 ) @ ( times_times_nat @ B_59 @ D_17 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_484_mult__mono,axiom,
% 0.32/0.73 ! [C_39: int,D_17: int,A_77: int,B_59: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ A_77 @ B_59 )
% 0.32/0.73 => ( ( ord_less_eq_int @ C_39 @ D_17 )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ B_59 )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ C_39 )
% 0.32/0.73 => ( ord_less_eq_int @ ( times_times_int @ A_77 @ C_39 ) @ ( times_times_int @ B_59 @ D_17 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_485_mult__mono_H,axiom,
% 0.32/0.73 ! [C_38: real,D_16: real,A_76: real,B_58: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ A_76 @ B_58 )
% 0.32/0.73 => ( ( ord_less_eq_real @ C_38 @ D_16 )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ A_76 )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ C_38 )
% 0.32/0.73 => ( ord_less_eq_real @ ( times_times_real @ A_76 @ C_38 ) @ ( times_times_real @ B_58 @ D_16 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_486_mult__mono_H,axiom,
% 0.32/0.73 ! [C_38: nat,D_16: nat,A_76: nat,B_58: nat] :
% 0.32/0.73 ( ( ord_less_eq_nat @ A_76 @ B_58 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ C_38 @ D_16 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ A_76 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C_38 )
% 0.32/0.73 => ( ord_less_eq_nat @ ( times_times_nat @ A_76 @ C_38 ) @ ( times_times_nat @ B_58 @ D_16 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_487_mult__mono_H,axiom,
% 0.32/0.73 ! [C_38: int,D_16: int,A_76: int,B_58: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ A_76 @ B_58 )
% 0.32/0.73 => ( ( ord_less_eq_int @ C_38 @ D_16 )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ A_76 )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ C_38 )
% 0.32/0.73 => ( ord_less_eq_int @ ( times_times_int @ A_76 @ C_38 ) @ ( times_times_int @ B_58 @ D_16 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_488_mult__left__mono__neg,axiom,
% 0.32/0.73 ! [C_37: real,B_57: real,A_75: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ B_57 @ A_75 )
% 0.32/0.73 => ( ( ord_less_eq_real @ C_37 @ zero_zero_real )
% 0.32/0.73 => ( ord_less_eq_real @ ( times_times_real @ C_37 @ A_75 ) @ ( times_times_real @ C_37 @ B_57 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_489_mult__left__mono__neg,axiom,
% 0.32/0.73 ! [C_37: int,B_57: int,A_75: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ B_57 @ A_75 )
% 0.32/0.73 => ( ( ord_less_eq_int @ C_37 @ zero_zero_int )
% 0.32/0.73 => ( ord_less_eq_int @ ( times_times_int @ C_37 @ A_75 ) @ ( times_times_int @ C_37 @ B_57 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_490_mult__right__mono__neg,axiom,
% 0.32/0.73 ! [C_36: real,B_56: real,A_74: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ B_56 @ A_74 )
% 0.32/0.73 => ( ( ord_less_eq_real @ C_36 @ zero_zero_real )
% 0.32/0.73 => ( ord_less_eq_real @ ( times_times_real @ A_74 @ C_36 ) @ ( times_times_real @ B_56 @ C_36 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_491_mult__right__mono__neg,axiom,
% 0.32/0.73 ! [C_36: int,B_56: int,A_74: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ B_56 @ A_74 )
% 0.32/0.73 => ( ( ord_less_eq_int @ C_36 @ zero_zero_int )
% 0.32/0.73 => ( ord_less_eq_int @ ( times_times_int @ A_74 @ C_36 ) @ ( times_times_int @ B_56 @ C_36 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_492_comm__mult__left__mono,axiom,
% 0.32/0.73 ! [C_35: real,A_73: real,B_55: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ A_73 @ B_55 )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ C_35 )
% 0.32/0.73 => ( ord_less_eq_real @ ( times_times_real @ C_35 @ A_73 ) @ ( times_times_real @ C_35 @ B_55 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_493_comm__mult__left__mono,axiom,
% 0.32/0.73 ! [C_35: nat,A_73: nat,B_55: nat] :
% 0.32/0.73 ( ( ord_less_eq_nat @ A_73 @ B_55 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C_35 )
% 0.32/0.73 => ( ord_less_eq_nat @ ( times_times_nat @ C_35 @ A_73 ) @ ( times_times_nat @ C_35 @ B_55 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_494_comm__mult__left__mono,axiom,
% 0.32/0.73 ! [C_35: int,A_73: int,B_55: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ A_73 @ B_55 )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ C_35 )
% 0.32/0.73 => ( ord_less_eq_int @ ( times_times_int @ C_35 @ A_73 ) @ ( times_times_int @ C_35 @ B_55 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_495_mult__left__mono,axiom,
% 0.32/0.73 ! [C_34: real,A_72: real,B_54: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ A_72 @ B_54 )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ C_34 )
% 0.32/0.73 => ( ord_less_eq_real @ ( times_times_real @ C_34 @ A_72 ) @ ( times_times_real @ C_34 @ B_54 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_496_mult__left__mono,axiom,
% 0.32/0.73 ! [C_34: nat,A_72: nat,B_54: nat] :
% 0.32/0.73 ( ( ord_less_eq_nat @ A_72 @ B_54 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C_34 )
% 0.32/0.73 => ( ord_less_eq_nat @ ( times_times_nat @ C_34 @ A_72 ) @ ( times_times_nat @ C_34 @ B_54 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_497_mult__left__mono,axiom,
% 0.32/0.73 ! [C_34: int,A_72: int,B_54: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ A_72 @ B_54 )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ C_34 )
% 0.32/0.73 => ( ord_less_eq_int @ ( times_times_int @ C_34 @ A_72 ) @ ( times_times_int @ C_34 @ B_54 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_498_mult__right__mono,axiom,
% 0.32/0.73 ! [C_33: real,A_71: real,B_53: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ A_71 @ B_53 )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ C_33 )
% 0.32/0.73 => ( ord_less_eq_real @ ( times_times_real @ A_71 @ C_33 ) @ ( times_times_real @ B_53 @ C_33 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_499_mult__right__mono,axiom,
% 0.32/0.73 ! [C_33: nat,A_71: nat,B_53: nat] :
% 0.32/0.73 ( ( ord_less_eq_nat @ A_71 @ B_53 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C_33 )
% 0.32/0.73 => ( ord_less_eq_nat @ ( times_times_nat @ A_71 @ C_33 ) @ ( times_times_nat @ B_53 @ C_33 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_500_mult__right__mono,axiom,
% 0.32/0.73 ! [C_33: int,A_71: int,B_53: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ A_71 @ B_53 )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ C_33 )
% 0.32/0.73 => ( ord_less_eq_int @ ( times_times_int @ A_71 @ C_33 ) @ ( times_times_int @ B_53 @ C_33 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_501_mult__nonpos__nonpos,axiom,
% 0.32/0.73 ! [B_52: real,A_70: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ A_70 @ zero_zero_real )
% 0.32/0.73 => ( ( ord_less_eq_real @ B_52 @ zero_zero_real )
% 0.32/0.73 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A_70 @ B_52 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_502_mult__nonpos__nonpos,axiom,
% 0.32/0.73 ! [B_52: int,A_70: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ A_70 @ zero_zero_int )
% 0.32/0.73 => ( ( ord_less_eq_int @ B_52 @ zero_zero_int )
% 0.32/0.73 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A_70 @ B_52 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_503_mult__nonpos__nonneg,axiom,
% 0.32/0.73 ! [B_51: real,A_69: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ A_69 @ zero_zero_real )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ B_51 )
% 0.32/0.73 => ( ord_less_eq_real @ ( times_times_real @ A_69 @ B_51 ) @ zero_zero_real ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_504_mult__nonpos__nonneg,axiom,
% 0.32/0.73 ! [B_51: nat,A_69: nat] :
% 0.32/0.73 ( ( ord_less_eq_nat @ A_69 @ zero_zero_nat )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ B_51 )
% 0.32/0.73 => ( ord_less_eq_nat @ ( times_times_nat @ A_69 @ B_51 ) @ zero_zero_nat ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_505_mult__nonpos__nonneg,axiom,
% 0.32/0.73 ! [B_51: int,A_69: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ A_69 @ zero_zero_int )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ B_51 )
% 0.32/0.73 => ( ord_less_eq_int @ ( times_times_int @ A_69 @ B_51 ) @ zero_zero_int ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_506_mult__nonneg__nonpos2,axiom,
% 0.32/0.73 ! [B_50: real,A_68: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ zero_zero_real @ A_68 )
% 0.32/0.73 => ( ( ord_less_eq_real @ B_50 @ zero_zero_real )
% 0.32/0.73 => ( ord_less_eq_real @ ( times_times_real @ B_50 @ A_68 ) @ zero_zero_real ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_507_mult__nonneg__nonpos2,axiom,
% 0.32/0.73 ! [B_50: nat,A_68: nat] :
% 0.32/0.73 ( ( ord_less_eq_nat @ zero_zero_nat @ A_68 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ B_50 @ zero_zero_nat )
% 0.32/0.73 => ( ord_less_eq_nat @ ( times_times_nat @ B_50 @ A_68 ) @ zero_zero_nat ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_508_mult__nonneg__nonpos2,axiom,
% 0.32/0.73 ! [B_50: int,A_68: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ zero_zero_int @ A_68 )
% 0.32/0.73 => ( ( ord_less_eq_int @ B_50 @ zero_zero_int )
% 0.32/0.73 => ( ord_less_eq_int @ ( times_times_int @ B_50 @ A_68 ) @ zero_zero_int ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_509_mult__nonneg__nonpos,axiom,
% 0.32/0.73 ! [B_49: real,A_67: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ zero_zero_real @ A_67 )
% 0.32/0.73 => ( ( ord_less_eq_real @ B_49 @ zero_zero_real )
% 0.32/0.73 => ( ord_less_eq_real @ ( times_times_real @ A_67 @ B_49 ) @ zero_zero_real ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_510_mult__nonneg__nonpos,axiom,
% 0.32/0.73 ! [B_49: nat,A_67: nat] :
% 0.32/0.73 ( ( ord_less_eq_nat @ zero_zero_nat @ A_67 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ B_49 @ zero_zero_nat )
% 0.32/0.73 => ( ord_less_eq_nat @ ( times_times_nat @ A_67 @ B_49 ) @ zero_zero_nat ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_511_mult__nonneg__nonpos,axiom,
% 0.32/0.73 ! [B_49: int,A_67: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ zero_zero_int @ A_67 )
% 0.32/0.73 => ( ( ord_less_eq_int @ B_49 @ zero_zero_int )
% 0.32/0.73 => ( ord_less_eq_int @ ( times_times_int @ A_67 @ B_49 ) @ zero_zero_int ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_512_transfer__nat__int__relations_I1_J,axiom,
% 0.32/0.73 ! [Y: int,X: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.73 => ( ( ( nat_1 @ X )
% 0.32/0.73 = ( nat_1 @ Y ) )
% 0.32/0.73 <=> ( X = Y ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_513_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 0.32/0.73 ! [Y: int,X: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.73 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ X @ Y ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_514_mult__nonneg__nonneg,axiom,
% 0.32/0.73 ! [B_48: real,A_66: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ zero_zero_real @ A_66 )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ B_48 )
% 0.32/0.73 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A_66 @ B_48 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_515_mult__nonneg__nonneg,axiom,
% 0.32/0.73 ! [B_48: nat,A_66: nat] :
% 0.32/0.73 ( ( ord_less_eq_nat @ zero_zero_nat @ A_66 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ B_48 )
% 0.32/0.73 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A_66 @ B_48 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_516_mult__nonneg__nonneg,axiom,
% 0.32/0.73 ! [B_48: int,A_66: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ zero_zero_int @ A_66 )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ B_48 )
% 0.32/0.73 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A_66 @ B_48 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_517_le__add__iff1,axiom,
% 0.32/0.73 ! [A_65: real,E_6: real,C_32: real,B_47: real,D_15: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A_65 @ E_6 ) @ C_32 ) @ ( plus_plus_real @ ( times_times_real @ B_47 @ E_6 ) @ D_15 ) )
% 0.32/0.73 <=> ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A_65 @ B_47 ) @ E_6 ) @ C_32 ) @ D_15 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_518_le__add__iff1,axiom,
% 0.32/0.73 ! [A_65: int,E_6: int,C_32: int,B_47: int,D_15: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A_65 @ E_6 ) @ C_32 ) @ ( plus_plus_int @ ( times_times_int @ B_47 @ E_6 ) @ D_15 ) )
% 0.32/0.73 <=> ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A_65 @ B_47 ) @ E_6 ) @ C_32 ) @ D_15 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_519_eq__add__iff1,axiom,
% 0.32/0.73 ! [A_64: real,E_5: real,C_31: real,B_46: real,D_14: real] :
% 0.32/0.73 ( ( ( plus_plus_real @ ( times_times_real @ A_64 @ E_5 ) @ C_31 )
% 0.32/0.73 = ( plus_plus_real @ ( times_times_real @ B_46 @ E_5 ) @ D_14 ) )
% 0.32/0.73 <=> ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A_64 @ B_46 ) @ E_5 ) @ C_31 )
% 0.32/0.73 = D_14 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_520_eq__add__iff1,axiom,
% 0.32/0.73 ! [A_64: int,E_5: int,C_31: int,B_46: int,D_14: int] :
% 0.32/0.73 ( ( ( plus_plus_int @ ( times_times_int @ A_64 @ E_5 ) @ C_31 )
% 0.32/0.73 = ( plus_plus_int @ ( times_times_int @ B_46 @ E_5 ) @ D_14 ) )
% 0.32/0.73 <=> ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A_64 @ B_46 ) @ E_5 ) @ C_31 )
% 0.32/0.73 = D_14 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_521_le__add__iff2,axiom,
% 0.32/0.73 ! [A_63: real,E_4: real,C_30: real,B_45: real,D_13: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A_63 @ E_4 ) @ C_30 ) @ ( plus_plus_real @ ( times_times_real @ B_45 @ E_4 ) @ D_13 ) )
% 0.32/0.73 <=> ( ord_less_eq_real @ C_30 @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B_45 @ A_63 ) @ E_4 ) @ D_13 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_522_le__add__iff2,axiom,
% 0.32/0.73 ! [A_63: int,E_4: int,C_30: int,B_45: int,D_13: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A_63 @ E_4 ) @ C_30 ) @ ( plus_plus_int @ ( times_times_int @ B_45 @ E_4 ) @ D_13 ) )
% 0.32/0.73 <=> ( ord_less_eq_int @ C_30 @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B_45 @ A_63 ) @ E_4 ) @ D_13 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_523_eq__add__iff2,axiom,
% 0.32/0.73 ! [A_62: real,E_3: real,C_29: real,B_44: real,D_12: real] :
% 0.32/0.73 ( ( ( plus_plus_real @ ( times_times_real @ A_62 @ E_3 ) @ C_29 )
% 0.32/0.73 = ( plus_plus_real @ ( times_times_real @ B_44 @ E_3 ) @ D_12 ) )
% 0.32/0.73 <=> ( C_29
% 0.32/0.73 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B_44 @ A_62 ) @ E_3 ) @ D_12 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_524_eq__add__iff2,axiom,
% 0.32/0.73 ! [A_62: int,E_3: int,C_29: int,B_44: int,D_12: int] :
% 0.32/0.73 ( ( ( plus_plus_int @ ( times_times_int @ A_62 @ E_3 ) @ C_29 )
% 0.32/0.73 = ( plus_plus_int @ ( times_times_int @ B_44 @ E_3 ) @ D_12 ) )
% 0.32/0.73 <=> ( C_29
% 0.32/0.73 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B_44 @ A_62 ) @ E_3 ) @ D_12 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_525_mult__diff__mult,axiom,
% 0.32/0.73 ! [X_16: real,Y_14: real,A_61: real,B_43: real] :
% 0.32/0.73 ( ( minus_minus_real @ ( times_times_real @ X_16 @ Y_14 ) @ ( times_times_real @ A_61 @ B_43 ) )
% 0.32/0.73 = ( plus_plus_real @ ( times_times_real @ X_16 @ ( minus_minus_real @ Y_14 @ B_43 ) ) @ ( times_times_real @ ( minus_minus_real @ X_16 @ A_61 ) @ B_43 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_526_mult__diff__mult,axiom,
% 0.32/0.73 ! [X_16: int,Y_14: int,A_61: int,B_43: int] :
% 0.32/0.73 ( ( minus_minus_int @ ( times_times_int @ X_16 @ Y_14 ) @ ( times_times_int @ A_61 @ B_43 ) )
% 0.32/0.73 = ( plus_plus_int @ ( times_times_int @ X_16 @ ( minus_minus_int @ Y_14 @ B_43 ) ) @ ( times_times_int @ ( minus_minus_int @ X_16 @ A_61 ) @ B_43 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_527_mult__le__0__iff,axiom,
% 0.32/0.73 ! [A_60: real,B_42: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ ( times_times_real @ A_60 @ B_42 ) @ zero_zero_real )
% 0.32/0.73 <=> ( ( ( ord_less_eq_real @ zero_zero_real @ A_60 )
% 0.32/0.73 & ( ord_less_eq_real @ B_42 @ zero_zero_real ) )
% 0.32/0.73 | ( ( ord_less_eq_real @ A_60 @ zero_zero_real )
% 0.32/0.73 & ( ord_less_eq_real @ zero_zero_real @ B_42 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_528_mult__le__0__iff,axiom,
% 0.32/0.73 ! [A_60: int,B_42: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ ( times_times_int @ A_60 @ B_42 ) @ zero_zero_int )
% 0.32/0.73 <=> ( ( ( ord_less_eq_int @ zero_zero_int @ A_60 )
% 0.32/0.73 & ( ord_less_eq_int @ B_42 @ zero_zero_int ) )
% 0.32/0.73 | ( ( ord_less_eq_int @ A_60 @ zero_zero_int )
% 0.32/0.73 & ( ord_less_eq_int @ zero_zero_int @ B_42 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_529_zero__le__mult__iff,axiom,
% 0.32/0.73 ! [A_59: real,B_41: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A_59 @ B_41 ) )
% 0.32/0.73 <=> ( ( ( ord_less_eq_real @ zero_zero_real @ A_59 )
% 0.32/0.73 & ( ord_less_eq_real @ zero_zero_real @ B_41 ) )
% 0.32/0.73 | ( ( ord_less_eq_real @ A_59 @ zero_zero_real )
% 0.32/0.73 & ( ord_less_eq_real @ B_41 @ zero_zero_real ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_530_zero__le__mult__iff,axiom,
% 0.32/0.73 ! [A_59: int,B_41: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A_59 @ B_41 ) )
% 0.32/0.73 <=> ( ( ( ord_less_eq_int @ zero_zero_int @ A_59 )
% 0.32/0.73 & ( ord_less_eq_int @ zero_zero_int @ B_41 ) )
% 0.32/0.73 | ( ( ord_less_eq_int @ A_59 @ zero_zero_int )
% 0.32/0.73 & ( ord_less_eq_int @ B_41 @ zero_zero_int ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_531_all__nat,axiom,
% 0.32/0.73 ! [P: nat > $o] :
% 0.32/0.73 ( ( all @ P )
% 0.32/0.73 <=> ! [X_1: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.32/0.73 => ( P @ ( nat_1 @ X_1 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_532_ex__nat,axiom,
% 0.32/0.73 ! [P: nat > $o] :
% 0.32/0.73 ( ( ex @ P )
% 0.32/0.73 <=> ? [X_1: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.32/0.73 & ( P @ ( nat_1 @ X_1 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_533_zero__le__square,axiom,
% 0.32/0.73 ! [A_58: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A_58 @ A_58 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_534_zero__le__square,axiom,
% 0.32/0.73 ! [A_58: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A_58 @ A_58 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_535_less__add__iff1,axiom,
% 0.32/0.73 ! [A_57: real,E_2: real,C_28: real,B_40: real,D_11: real] :
% 0.32/0.73 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A_57 @ E_2 ) @ C_28 ) @ ( plus_plus_real @ ( times_times_real @ B_40 @ E_2 ) @ D_11 ) )
% 0.32/0.73 <=> ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A_57 @ B_40 ) @ E_2 ) @ C_28 ) @ D_11 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_536_less__add__iff1,axiom,
% 0.32/0.73 ! [A_57: int,E_2: int,C_28: int,B_40: int,D_11: int] :
% 0.32/0.73 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A_57 @ E_2 ) @ C_28 ) @ ( plus_plus_int @ ( times_times_int @ B_40 @ E_2 ) @ D_11 ) )
% 0.32/0.73 <=> ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A_57 @ B_40 ) @ E_2 ) @ C_28 ) @ D_11 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_537_less__add__iff2,axiom,
% 0.32/0.73 ! [A_56: real,E_1: real,C_27: real,B_39: real,D_10: real] :
% 0.32/0.73 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A_56 @ E_1 ) @ C_27 ) @ ( plus_plus_real @ ( times_times_real @ B_39 @ E_1 ) @ D_10 ) )
% 0.32/0.73 <=> ( ord_less_real @ C_27 @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B_39 @ A_56 ) @ E_1 ) @ D_10 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_538_less__add__iff2,axiom,
% 0.32/0.73 ! [A_56: int,E_1: int,C_27: int,B_39: int,D_10: int] :
% 0.32/0.73 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A_56 @ E_1 ) @ C_27 ) @ ( plus_plus_int @ ( times_times_int @ B_39 @ E_1 ) @ D_10 ) )
% 0.32/0.73 <=> ( ord_less_int @ C_27 @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B_39 @ A_56 ) @ E_1 ) @ D_10 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_539_real__squared__diff__one__factored,axiom,
% 0.32/0.73 ! [X_15: real] :
% 0.32/0.73 ( ( minus_minus_real @ ( times_times_real @ X_15 @ X_15 ) @ one_one_real )
% 0.32/0.73 = ( times_times_real @ ( plus_plus_real @ X_15 @ one_one_real ) @ ( minus_minus_real @ X_15 @ one_one_real ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_540_real__squared__diff__one__factored,axiom,
% 0.32/0.73 ! [X_15: int] :
% 0.32/0.73 ( ( minus_minus_int @ ( times_times_int @ X_15 @ X_15 ) @ one_one_int )
% 0.32/0.73 = ( times_times_int @ ( plus_plus_int @ X_15 @ one_one_int ) @ ( minus_minus_int @ X_15 @ one_one_int ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_541_mult__left__le__imp__le,axiom,
% 0.32/0.73 ! [C_26: real,A_55: real,B_38: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ ( times_times_real @ C_26 @ A_55 ) @ ( times_times_real @ C_26 @ B_38 ) )
% 0.32/0.73 => ( ( ord_less_real @ zero_zero_real @ C_26 )
% 0.32/0.73 => ( ord_less_eq_real @ A_55 @ B_38 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_542_mult__left__le__imp__le,axiom,
% 0.32/0.73 ! [C_26: nat,A_55: nat,B_38: nat] :
% 0.32/0.73 ( ( ord_less_eq_nat @ ( times_times_nat @ C_26 @ A_55 ) @ ( times_times_nat @ C_26 @ B_38 ) )
% 0.32/0.73 => ( ( ord_less_nat @ zero_zero_nat @ C_26 )
% 0.32/0.73 => ( ord_less_eq_nat @ A_55 @ B_38 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_543_mult__left__le__imp__le,axiom,
% 0.32/0.73 ! [C_26: int,A_55: int,B_38: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ ( times_times_int @ C_26 @ A_55 ) @ ( times_times_int @ C_26 @ B_38 ) )
% 0.32/0.73 => ( ( ord_less_int @ zero_zero_int @ C_26 )
% 0.32/0.73 => ( ord_less_eq_int @ A_55 @ B_38 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_544_mult__right__le__imp__le,axiom,
% 0.32/0.73 ! [A_54: real,C_25: real,B_37: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ ( times_times_real @ A_54 @ C_25 ) @ ( times_times_real @ B_37 @ C_25 ) )
% 0.32/0.73 => ( ( ord_less_real @ zero_zero_real @ C_25 )
% 0.32/0.73 => ( ord_less_eq_real @ A_54 @ B_37 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_545_mult__right__le__imp__le,axiom,
% 0.32/0.73 ! [A_54: nat,C_25: nat,B_37: nat] :
% 0.32/0.73 ( ( ord_less_eq_nat @ ( times_times_nat @ A_54 @ C_25 ) @ ( times_times_nat @ B_37 @ C_25 ) )
% 0.32/0.73 => ( ( ord_less_nat @ zero_zero_nat @ C_25 )
% 0.32/0.73 => ( ord_less_eq_nat @ A_54 @ B_37 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_546_mult__right__le__imp__le,axiom,
% 0.32/0.73 ! [A_54: int,C_25: int,B_37: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ ( times_times_int @ A_54 @ C_25 ) @ ( times_times_int @ B_37 @ C_25 ) )
% 0.32/0.73 => ( ( ord_less_int @ zero_zero_int @ C_25 )
% 0.32/0.73 => ( ord_less_eq_int @ A_54 @ B_37 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_547_mult__less__imp__less__left,axiom,
% 0.32/0.73 ! [C_24: real,A_53: real,B_36: real] :
% 0.32/0.73 ( ( ord_less_real @ ( times_times_real @ C_24 @ A_53 ) @ ( times_times_real @ C_24 @ B_36 ) )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ C_24 )
% 0.32/0.73 => ( ord_less_real @ A_53 @ B_36 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_548_mult__less__imp__less__left,axiom,
% 0.32/0.73 ! [C_24: nat,A_53: nat,B_36: nat] :
% 0.32/0.73 ( ( ord_less_nat @ ( times_times_nat @ C_24 @ A_53 ) @ ( times_times_nat @ C_24 @ B_36 ) )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C_24 )
% 0.32/0.73 => ( ord_less_nat @ A_53 @ B_36 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_549_mult__less__imp__less__left,axiom,
% 0.32/0.73 ! [C_24: int,A_53: int,B_36: int] :
% 0.32/0.73 ( ( ord_less_int @ ( times_times_int @ C_24 @ A_53 ) @ ( times_times_int @ C_24 @ B_36 ) )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ C_24 )
% 0.32/0.73 => ( ord_less_int @ A_53 @ B_36 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_550_mult__left__less__imp__less,axiom,
% 0.32/0.73 ! [C_23: real,A_52: real,B_35: real] :
% 0.32/0.73 ( ( ord_less_real @ ( times_times_real @ C_23 @ A_52 ) @ ( times_times_real @ C_23 @ B_35 ) )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ C_23 )
% 0.32/0.73 => ( ord_less_real @ A_52 @ B_35 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_551_mult__left__less__imp__less,axiom,
% 0.32/0.73 ! [C_23: nat,A_52: nat,B_35: nat] :
% 0.32/0.73 ( ( ord_less_nat @ ( times_times_nat @ C_23 @ A_52 ) @ ( times_times_nat @ C_23 @ B_35 ) )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C_23 )
% 0.32/0.73 => ( ord_less_nat @ A_52 @ B_35 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_552_mult__left__less__imp__less,axiom,
% 0.32/0.73 ! [C_23: int,A_52: int,B_35: int] :
% 0.32/0.73 ( ( ord_less_int @ ( times_times_int @ C_23 @ A_52 ) @ ( times_times_int @ C_23 @ B_35 ) )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ C_23 )
% 0.32/0.73 => ( ord_less_int @ A_52 @ B_35 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_553_mult__less__imp__less__right,axiom,
% 0.32/0.73 ! [A_51: real,C_22: real,B_34: real] :
% 0.32/0.73 ( ( ord_less_real @ ( times_times_real @ A_51 @ C_22 ) @ ( times_times_real @ B_34 @ C_22 ) )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ C_22 )
% 0.32/0.73 => ( ord_less_real @ A_51 @ B_34 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_554_mult__less__imp__less__right,axiom,
% 0.32/0.73 ! [A_51: nat,C_22: nat,B_34: nat] :
% 0.32/0.73 ( ( ord_less_nat @ ( times_times_nat @ A_51 @ C_22 ) @ ( times_times_nat @ B_34 @ C_22 ) )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C_22 )
% 0.32/0.73 => ( ord_less_nat @ A_51 @ B_34 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_555_mult__less__imp__less__right,axiom,
% 0.32/0.73 ! [A_51: int,C_22: int,B_34: int] :
% 0.32/0.73 ( ( ord_less_int @ ( times_times_int @ A_51 @ C_22 ) @ ( times_times_int @ B_34 @ C_22 ) )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ C_22 )
% 0.32/0.73 => ( ord_less_int @ A_51 @ B_34 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_556_mult__right__less__imp__less,axiom,
% 0.32/0.73 ! [A_50: real,C_21: real,B_33: real] :
% 0.32/0.73 ( ( ord_less_real @ ( times_times_real @ A_50 @ C_21 ) @ ( times_times_real @ B_33 @ C_21 ) )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ C_21 )
% 0.32/0.73 => ( ord_less_real @ A_50 @ B_33 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_557_mult__right__less__imp__less,axiom,
% 0.32/0.73 ! [A_50: nat,C_21: nat,B_33: nat] :
% 0.32/0.73 ( ( ord_less_nat @ ( times_times_nat @ A_50 @ C_21 ) @ ( times_times_nat @ B_33 @ C_21 ) )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C_21 )
% 0.32/0.73 => ( ord_less_nat @ A_50 @ B_33 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_558_mult__right__less__imp__less,axiom,
% 0.32/0.73 ! [A_50: int,C_21: int,B_33: int] :
% 0.32/0.73 ( ( ord_less_int @ ( times_times_int @ A_50 @ C_21 ) @ ( times_times_int @ B_33 @ C_21 ) )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ C_21 )
% 0.32/0.73 => ( ord_less_int @ A_50 @ B_33 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_559_mult__le__less__imp__less,axiom,
% 0.32/0.73 ! [C_20: real,D_9: real,A_49: real,B_32: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ A_49 @ B_32 )
% 0.32/0.73 => ( ( ord_less_real @ C_20 @ D_9 )
% 0.32/0.73 => ( ( ord_less_real @ zero_zero_real @ A_49 )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ C_20 )
% 0.32/0.73 => ( ord_less_real @ ( times_times_real @ A_49 @ C_20 ) @ ( times_times_real @ B_32 @ D_9 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_560_mult__le__less__imp__less,axiom,
% 0.32/0.73 ! [C_20: nat,D_9: nat,A_49: nat,B_32: nat] :
% 0.32/0.73 ( ( ord_less_eq_nat @ A_49 @ B_32 )
% 0.32/0.73 => ( ( ord_less_nat @ C_20 @ D_9 )
% 0.32/0.73 => ( ( ord_less_nat @ zero_zero_nat @ A_49 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C_20 )
% 0.32/0.73 => ( ord_less_nat @ ( times_times_nat @ A_49 @ C_20 ) @ ( times_times_nat @ B_32 @ D_9 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_561_mult__le__less__imp__less,axiom,
% 0.32/0.73 ! [C_20: int,D_9: int,A_49: int,B_32: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ A_49 @ B_32 )
% 0.32/0.73 => ( ( ord_less_int @ C_20 @ D_9 )
% 0.32/0.73 => ( ( ord_less_int @ zero_zero_int @ A_49 )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ C_20 )
% 0.32/0.73 => ( ord_less_int @ ( times_times_int @ A_49 @ C_20 ) @ ( times_times_int @ B_32 @ D_9 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_562_mult__less__le__imp__less,axiom,
% 0.32/0.73 ! [C_19: real,D_8: real,A_48: real,B_31: real] :
% 0.32/0.73 ( ( ord_less_real @ A_48 @ B_31 )
% 0.32/0.73 => ( ( ord_less_eq_real @ C_19 @ D_8 )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ A_48 )
% 0.32/0.73 => ( ( ord_less_real @ zero_zero_real @ C_19 )
% 0.32/0.73 => ( ord_less_real @ ( times_times_real @ A_48 @ C_19 ) @ ( times_times_real @ B_31 @ D_8 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_563_mult__less__le__imp__less,axiom,
% 0.32/0.73 ! [C_19: nat,D_8: nat,A_48: nat,B_31: nat] :
% 0.32/0.73 ( ( ord_less_nat @ A_48 @ B_31 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ C_19 @ D_8 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ A_48 )
% 0.32/0.73 => ( ( ord_less_nat @ zero_zero_nat @ C_19 )
% 0.32/0.73 => ( ord_less_nat @ ( times_times_nat @ A_48 @ C_19 ) @ ( times_times_nat @ B_31 @ D_8 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_564_mult__less__le__imp__less,axiom,
% 0.32/0.73 ! [C_19: int,D_8: int,A_48: int,B_31: int] :
% 0.32/0.73 ( ( ord_less_int @ A_48 @ B_31 )
% 0.32/0.73 => ( ( ord_less_eq_int @ C_19 @ D_8 )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ A_48 )
% 0.32/0.73 => ( ( ord_less_int @ zero_zero_int @ C_19 )
% 0.32/0.73 => ( ord_less_int @ ( times_times_int @ A_48 @ C_19 ) @ ( times_times_int @ B_31 @ D_8 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_565_mult__strict__mono_H,axiom,
% 0.32/0.73 ! [C_18: real,D_7: real,A_47: real,B_30: real] :
% 0.32/0.73 ( ( ord_less_real @ A_47 @ B_30 )
% 0.32/0.73 => ( ( ord_less_real @ C_18 @ D_7 )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ A_47 )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ C_18 )
% 0.32/0.73 => ( ord_less_real @ ( times_times_real @ A_47 @ C_18 ) @ ( times_times_real @ B_30 @ D_7 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_566_mult__strict__mono_H,axiom,
% 0.32/0.73 ! [C_18: nat,D_7: nat,A_47: nat,B_30: nat] :
% 0.32/0.73 ( ( ord_less_nat @ A_47 @ B_30 )
% 0.32/0.73 => ( ( ord_less_nat @ C_18 @ D_7 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ A_47 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C_18 )
% 0.32/0.73 => ( ord_less_nat @ ( times_times_nat @ A_47 @ C_18 ) @ ( times_times_nat @ B_30 @ D_7 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_567_mult__strict__mono_H,axiom,
% 0.32/0.73 ! [C_18: int,D_7: int,A_47: int,B_30: int] :
% 0.32/0.73 ( ( ord_less_int @ A_47 @ B_30 )
% 0.32/0.73 => ( ( ord_less_int @ C_18 @ D_7 )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ A_47 )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ C_18 )
% 0.32/0.73 => ( ord_less_int @ ( times_times_int @ A_47 @ C_18 ) @ ( times_times_int @ B_30 @ D_7 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_568_mult__strict__mono,axiom,
% 0.32/0.73 ! [C_17: real,D_6: real,A_46: real,B_29: real] :
% 0.32/0.73 ( ( ord_less_real @ A_46 @ B_29 )
% 0.32/0.73 => ( ( ord_less_real @ C_17 @ D_6 )
% 0.32/0.73 => ( ( ord_less_real @ zero_zero_real @ B_29 )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ C_17 )
% 0.32/0.73 => ( ord_less_real @ ( times_times_real @ A_46 @ C_17 ) @ ( times_times_real @ B_29 @ D_6 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_569_mult__strict__mono,axiom,
% 0.32/0.73 ! [C_17: nat,D_6: nat,A_46: nat,B_29: nat] :
% 0.32/0.73 ( ( ord_less_nat @ A_46 @ B_29 )
% 0.32/0.73 => ( ( ord_less_nat @ C_17 @ D_6 )
% 0.32/0.73 => ( ( ord_less_nat @ zero_zero_nat @ B_29 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ zero_zero_nat @ C_17 )
% 0.32/0.73 => ( ord_less_nat @ ( times_times_nat @ A_46 @ C_17 ) @ ( times_times_nat @ B_29 @ D_6 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_570_mult__strict__mono,axiom,
% 0.32/0.73 ! [C_17: int,D_6: int,A_46: int,B_29: int] :
% 0.32/0.73 ( ( ord_less_int @ A_46 @ B_29 )
% 0.32/0.73 => ( ( ord_less_int @ C_17 @ D_6 )
% 0.32/0.73 => ( ( ord_less_int @ zero_zero_int @ B_29 )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ C_17 )
% 0.32/0.73 => ( ord_less_int @ ( times_times_int @ A_46 @ C_17 ) @ ( times_times_int @ B_29 @ D_6 ) ) ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_571_mult__le__cancel__left__neg,axiom,
% 0.32/0.73 ! [A_45: real,B_28: real,C_16: real] :
% 0.32/0.73 ( ( ord_less_real @ C_16 @ zero_zero_real )
% 0.32/0.73 => ( ( ord_less_eq_real @ ( times_times_real @ C_16 @ A_45 ) @ ( times_times_real @ C_16 @ B_28 ) )
% 0.32/0.73 <=> ( ord_less_eq_real @ B_28 @ A_45 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_572_mult__le__cancel__left__neg,axiom,
% 0.32/0.73 ! [A_45: int,B_28: int,C_16: int] :
% 0.32/0.73 ( ( ord_less_int @ C_16 @ zero_zero_int )
% 0.32/0.73 => ( ( ord_less_eq_int @ ( times_times_int @ C_16 @ A_45 ) @ ( times_times_int @ C_16 @ B_28 ) )
% 0.32/0.73 <=> ( ord_less_eq_int @ B_28 @ A_45 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_573_mult__le__cancel__left__pos,axiom,
% 0.32/0.73 ! [A_44: real,B_27: real,C_15: real] :
% 0.32/0.73 ( ( ord_less_real @ zero_zero_real @ C_15 )
% 0.32/0.73 => ( ( ord_less_eq_real @ ( times_times_real @ C_15 @ A_44 ) @ ( times_times_real @ C_15 @ B_27 ) )
% 0.32/0.73 <=> ( ord_less_eq_real @ A_44 @ B_27 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_574_mult__le__cancel__left__pos,axiom,
% 0.32/0.73 ! [A_44: int,B_27: int,C_15: int] :
% 0.32/0.73 ( ( ord_less_int @ zero_zero_int @ C_15 )
% 0.32/0.73 => ( ( ord_less_eq_int @ ( times_times_int @ C_15 @ A_44 ) @ ( times_times_int @ C_15 @ B_27 ) )
% 0.32/0.73 <=> ( ord_less_eq_int @ A_44 @ B_27 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_575_sum__squares__ge__zero,axiom,
% 0.32/0.73 ! [X_14: real,Y_13: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X_14 @ X_14 ) @ ( times_times_real @ Y_13 @ Y_13 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_576_sum__squares__ge__zero,axiom,
% 0.32/0.73 ! [X_14: int,Y_13: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_14 @ X_14 ) @ ( times_times_int @ Y_13 @ Y_13 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_577_sum__squares__le__zero__iff,axiom,
% 0.32/0.73 ! [X_13: real,Y_12: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X_13 @ X_13 ) @ ( times_times_real @ Y_12 @ Y_12 ) ) @ zero_zero_real )
% 0.32/0.73 <=> ( ( X_13 = zero_zero_real )
% 0.32/0.73 & ( Y_12 = zero_zero_real ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_578_sum__squares__le__zero__iff,axiom,
% 0.32/0.73 ! [X_13: int,Y_12: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_13 @ X_13 ) @ ( times_times_int @ Y_12 @ Y_12 ) ) @ zero_zero_int )
% 0.32/0.73 <=> ( ( X_13 = zero_zero_int )
% 0.32/0.73 & ( Y_12 = zero_zero_int ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_579_mult__right__le__one__le,axiom,
% 0.32/0.73 ! [Y_11: real,X_12: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ zero_zero_real @ X_12 )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ Y_11 )
% 0.32/0.73 => ( ( ord_less_eq_real @ Y_11 @ one_one_real )
% 0.32/0.73 => ( ord_less_eq_real @ ( times_times_real @ X_12 @ Y_11 ) @ X_12 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_580_mult__right__le__one__le,axiom,
% 0.32/0.73 ! [Y_11: int,X_12: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ zero_zero_int @ X_12 )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ Y_11 )
% 0.32/0.73 => ( ( ord_less_eq_int @ Y_11 @ one_one_int )
% 0.32/0.73 => ( ord_less_eq_int @ ( times_times_int @ X_12 @ Y_11 ) @ X_12 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_581_mult__left__le__one__le,axiom,
% 0.32/0.73 ! [Y_10: real,X_11: real] :
% 0.32/0.73 ( ( ord_less_eq_real @ zero_zero_real @ X_11 )
% 0.32/0.73 => ( ( ord_less_eq_real @ zero_zero_real @ Y_10 )
% 0.32/0.73 => ( ( ord_less_eq_real @ Y_10 @ one_one_real )
% 0.32/0.73 => ( ord_less_eq_real @ ( times_times_real @ Y_10 @ X_11 ) @ X_11 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_582_mult__left__le__one__le,axiom,
% 0.32/0.73 ! [Y_10: int,X_11: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ zero_zero_int @ X_11 )
% 0.32/0.73 => ( ( ord_less_eq_int @ zero_zero_int @ Y_10 )
% 0.32/0.73 => ( ( ord_less_eq_int @ Y_10 @ one_one_int )
% 0.32/0.73 => ( ord_less_eq_int @ ( times_times_int @ Y_10 @ X_11 ) @ X_11 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_583_nat__le__0,axiom,
% 0.32/0.73 ! [Z: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 0.32/0.73 => ( ( nat_1 @ Z )
% 0.32/0.73 = zero_zero_nat ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_584_nat__0__iff,axiom,
% 0.32/0.73 ! [I_1: int] :
% 0.32/0.73 ( ( ( nat_1 @ I_1 )
% 0.32/0.73 = zero_zero_nat )
% 0.32/0.73 <=> ( ord_less_eq_int @ I_1 @ zero_zero_int ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_585_power__increasing,axiom,
% 0.32/0.73 ! [A_43: real,N_9: nat,N_8: nat] :
% 0.32/0.73 ( ( ord_less_eq_nat @ N_9 @ N_8 )
% 0.32/0.73 => ( ( ord_less_eq_real @ one_one_real @ A_43 )
% 0.32/0.73 => ( ord_less_eq_real @ ( power_power_real @ A_43 @ N_9 ) @ ( power_power_real @ A_43 @ N_8 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_586_power__increasing,axiom,
% 0.32/0.73 ! [A_43: nat,N_9: nat,N_8: nat] :
% 0.32/0.73 ( ( ord_less_eq_nat @ N_9 @ N_8 )
% 0.32/0.73 => ( ( ord_less_eq_nat @ one_one_nat @ A_43 )
% 0.32/0.73 => ( ord_less_eq_nat @ ( power_power_nat @ A_43 @ N_9 ) @ ( power_power_nat @ A_43 @ N_8 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_587_power__increasing,axiom,
% 0.32/0.73 ! [A_43: int,N_9: nat,N_8: nat] :
% 0.32/0.73 ( ( ord_less_eq_nat @ N_9 @ N_8 )
% 0.32/0.73 => ( ( ord_less_eq_int @ one_one_int @ A_43 )
% 0.32/0.73 => ( ord_less_eq_int @ ( power_power_int @ A_43 @ N_9 ) @ ( power_power_int @ A_43 @ N_8 ) ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_588_int__nat__eq,axiom,
% 0.32/0.73 ! [Z: int] :
% 0.32/0.73 ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.73 => ( ( semiri1621563631at_int @ ( nat_1 @ Z ) )
% 0.32/0.73 = Z ) )
% 0.32/0.73 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.73 => ( ( semiri1621563631at_int @ ( nat_1 @ Z ) )
% 0.32/0.73 = zero_zero_int ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_589_int__eq__iff,axiom,
% 0.32/0.73 ! [M: nat,Z: int] :
% 0.32/0.73 ( ( ( semiri1621563631at_int @ M )
% 0.32/0.73 = Z )
% 0.32/0.73 <=> ( ( M
% 0.32/0.73 = ( nat_1 @ Z ) )
% 0.32/0.73 & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_590_nat__0__le,axiom,
% 0.32/0.73 ! [Z: int] :
% 0.32/0.73 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.73 => ( ( semiri1621563631at_int @ ( nat_1 @ Z ) )
% 0.32/0.73 = Z ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_591_right__minus__eq,axiom,
% 0.32/0.73 ! [A_42: real,B_26: real] :
% 0.32/0.73 ( ( ( minus_minus_real @ A_42 @ B_26 )
% 0.32/0.73 = zero_zero_real )
% 0.32/0.73 <=> ( A_42 = B_26 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_592_right__minus__eq,axiom,
% 0.32/0.73 ! [A_42: int,B_26: int] :
% 0.32/0.73 ( ( ( minus_minus_int @ A_42 @ B_26 )
% 0.32/0.73 = zero_zero_int )
% 0.32/0.73 <=> ( A_42 = B_26 ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_593_eq__iff__diff__eq__0,axiom,
% 0.32/0.73 ! [A_41: real,B_25: real] :
% 0.32/0.73 ( ( A_41 = B_25 )
% 0.32/0.73 <=> ( ( minus_minus_real @ A_41 @ B_25 )
% 0.32/0.73 = zero_zero_real ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_594_eq__iff__diff__eq__0,axiom,
% 0.32/0.73 ! [A_41: int,B_25: int] :
% 0.32/0.73 ( ( A_41 = B_25 )
% 0.32/0.73 <=> ( ( minus_minus_int @ A_41 @ B_25 )
% 0.32/0.73 = zero_zero_int ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_595_diff__self,axiom,
% 0.32/0.73 ! [A_40: real] :
% 0.32/0.73 ( ( minus_minus_real @ A_40 @ A_40 )
% 0.32/0.73 = zero_zero_real ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_596_diff__self,axiom,
% 0.32/0.73 ! [A_40: int] :
% 0.32/0.73 ( ( minus_minus_int @ A_40 @ A_40 )
% 0.32/0.73 = zero_zero_int ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_597_diff__0__right,axiom,
% 0.32/0.73 ! [A_39: real] :
% 0.32/0.73 ( ( minus_minus_real @ A_39 @ zero_zero_real )
% 0.32/0.73 = A_39 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_598_diff__0__right,axiom,
% 0.32/0.73 ! [A_39: int] :
% 0.32/0.73 ( ( minus_minus_int @ A_39 @ zero_zero_int )
% 0.32/0.73 = A_39 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_599_diff__eq__diff__less,axiom,
% 0.32/0.73 ! [A_38: int,B_24: int,C_14: int,D_5: int] :
% 0.32/0.73 ( ( ( minus_minus_int @ A_38 @ B_24 )
% 0.32/0.73 = ( minus_minus_int @ C_14 @ D_5 ) )
% 0.32/0.73 => ( ( ord_less_int @ A_38 @ B_24 )
% 0.32/0.73 <=> ( ord_less_int @ C_14 @ D_5 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_600_diff__eq__diff__less,axiom,
% 0.32/0.73 ! [A_38: real,B_24: real,C_14: real,D_5: real] :
% 0.32/0.73 ( ( ( minus_minus_real @ A_38 @ B_24 )
% 0.32/0.73 = ( minus_minus_real @ C_14 @ D_5 ) )
% 0.32/0.73 => ( ( ord_less_real @ A_38 @ B_24 )
% 0.32/0.73 <=> ( ord_less_real @ C_14 @ D_5 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_601_add__diff__add,axiom,
% 0.32/0.73 ! [A_37: real,C_13: real,B_23: real,D_4: real] :
% 0.32/0.73 ( ( minus_minus_real @ ( plus_plus_real @ A_37 @ C_13 ) @ ( plus_plus_real @ B_23 @ D_4 ) )
% 0.32/0.73 = ( plus_plus_real @ ( minus_minus_real @ A_37 @ B_23 ) @ ( minus_minus_real @ C_13 @ D_4 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_602_add__diff__add,axiom,
% 0.32/0.73 ! [A_37: int,C_13: int,B_23: int,D_4: int] :
% 0.32/0.73 ( ( minus_minus_int @ ( plus_plus_int @ A_37 @ C_13 ) @ ( plus_plus_int @ B_23 @ D_4 ) )
% 0.32/0.73 = ( plus_plus_int @ ( minus_minus_int @ A_37 @ B_23 ) @ ( minus_minus_int @ C_13 @ D_4 ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_603_add__diff__cancel,axiom,
% 0.32/0.73 ! [A_36: real,B_22: real] :
% 0.32/0.73 ( ( minus_minus_real @ ( plus_plus_real @ A_36 @ B_22 ) @ B_22 )
% 0.32/0.73 = A_36 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_604_add__diff__cancel,axiom,
% 0.32/0.73 ! [A_36: int,B_22: int] :
% 0.32/0.73 ( ( minus_minus_int @ ( plus_plus_int @ A_36 @ B_22 ) @ B_22 )
% 0.32/0.73 = A_36 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_605_diff__add__cancel,axiom,
% 0.32/0.73 ! [A_35: real,B_21: real] :
% 0.32/0.73 ( ( plus_plus_real @ ( minus_minus_real @ A_35 @ B_21 ) @ B_21 )
% 0.32/0.73 = A_35 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_606_diff__add__cancel,axiom,
% 0.32/0.73 ! [A_35: int,B_21: int] :
% 0.32/0.73 ( ( plus_plus_int @ ( minus_minus_int @ A_35 @ B_21 ) @ B_21 )
% 0.32/0.73 = A_35 ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_607_mult__zero__left,axiom,
% 0.32/0.73 ! [A_34: real] :
% 0.32/0.73 ( ( times_times_real @ zero_zero_real @ A_34 )
% 0.32/0.73 = zero_zero_real ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_608_mult__zero__left,axiom,
% 0.32/0.73 ! [A_34: nat] :
% 0.32/0.73 ( ( times_times_nat @ zero_zero_nat @ A_34 )
% 0.32/0.73 = zero_zero_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_609_mult__zero__left,axiom,
% 0.32/0.73 ! [A_34: int] :
% 0.32/0.73 ( ( times_times_int @ zero_zero_int @ A_34 )
% 0.32/0.73 = zero_zero_int ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_610_mult__zero__right,axiom,
% 0.32/0.73 ! [A_33: real] :
% 0.32/0.73 ( ( times_times_real @ A_33 @ zero_zero_real )
% 0.32/0.73 = zero_zero_real ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_611_mult__zero__right,axiom,
% 0.32/0.73 ! [A_33: nat] :
% 0.32/0.73 ( ( times_times_nat @ A_33 @ zero_zero_nat )
% 0.32/0.73 = zero_zero_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_612_mult__zero__right,axiom,
% 0.32/0.73 ! [A_33: int] :
% 0.32/0.73 ( ( times_times_int @ A_33 @ zero_zero_int )
% 0.32/0.73 = zero_zero_int ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_613_mult__eq__0__iff,axiom,
% 0.32/0.73 ! [A_32: real,B_20: real] :
% 0.32/0.73 ( ( ( times_times_real @ A_32 @ B_20 )
% 0.32/0.73 = zero_zero_real )
% 0.32/0.73 <=> ( ( A_32 = zero_zero_real )
% 0.32/0.73 | ( B_20 = zero_zero_real ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_614_mult__eq__0__iff,axiom,
% 0.32/0.73 ! [A_32: int,B_20: int] :
% 0.32/0.73 ( ( ( times_times_int @ A_32 @ B_20 )
% 0.32/0.73 = zero_zero_int )
% 0.32/0.73 <=> ( ( A_32 = zero_zero_int )
% 0.32/0.73 | ( B_20 = zero_zero_int ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_615_no__zero__divisors,axiom,
% 0.32/0.73 ! [B_19: real,A_31: real] :
% 0.32/0.73 ( ( A_31 != zero_zero_real )
% 0.32/0.73 => ( ( B_19 != zero_zero_real )
% 0.32/0.73 => ( ( times_times_real @ A_31 @ B_19 )
% 0.32/0.73 != zero_zero_real ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_616_no__zero__divisors,axiom,
% 0.32/0.73 ! [B_19: nat,A_31: nat] :
% 0.32/0.73 ( ( A_31 != zero_zero_nat )
% 0.32/0.73 => ( ( B_19 != zero_zero_nat )
% 0.32/0.73 => ( ( times_times_nat @ A_31 @ B_19 )
% 0.32/0.73 != zero_zero_nat ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_617_no__zero__divisors,axiom,
% 0.32/0.73 ! [B_19: int,A_31: int] :
% 0.32/0.73 ( ( A_31 != zero_zero_int )
% 0.32/0.73 => ( ( B_19 != zero_zero_int )
% 0.32/0.73 => ( ( times_times_int @ A_31 @ B_19 )
% 0.32/0.73 != zero_zero_int ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_618_divisors__zero,axiom,
% 0.32/0.73 ! [A_30: real,B_18: real] :
% 0.32/0.73 ( ( ( times_times_real @ A_30 @ B_18 )
% 0.32/0.73 = zero_zero_real )
% 0.32/0.73 => ( ( A_30 = zero_zero_real )
% 0.32/0.73 | ( B_18 = zero_zero_real ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_619_divisors__zero,axiom,
% 0.32/0.73 ! [A_30: nat,B_18: nat] :
% 0.32/0.73 ( ( ( times_times_nat @ A_30 @ B_18 )
% 0.32/0.73 = zero_zero_nat )
% 0.32/0.73 => ( ( A_30 = zero_zero_nat )
% 0.32/0.73 | ( B_18 = zero_zero_nat ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_620_divisors__zero,axiom,
% 0.32/0.73 ! [A_30: int,B_18: int] :
% 0.32/0.73 ( ( ( times_times_int @ A_30 @ B_18 )
% 0.32/0.73 = zero_zero_int )
% 0.32/0.73 => ( ( A_30 = zero_zero_int )
% 0.32/0.73 | ( B_18 = zero_zero_int ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_621_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 0.32/0.73 ! [A_29: real] :
% 0.32/0.73 ( ( times_times_real @ A_29 @ zero_zero_real )
% 0.32/0.73 = zero_zero_real ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_622_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 0.32/0.73 ! [A_29: nat] :
% 0.32/0.73 ( ( times_times_nat @ A_29 @ zero_zero_nat )
% 0.32/0.73 = zero_zero_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_623_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 0.32/0.73 ! [A_29: int] :
% 0.32/0.73 ( ( times_times_int @ A_29 @ zero_zero_int )
% 0.32/0.73 = zero_zero_int ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_624_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 0.32/0.73 ! [A_28: real] :
% 0.32/0.73 ( ( times_times_real @ zero_zero_real @ A_28 )
% 0.32/0.73 = zero_zero_real ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_625_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 0.32/0.73 ! [A_28: nat] :
% 0.32/0.73 ( ( times_times_nat @ zero_zero_nat @ A_28 )
% 0.32/0.73 = zero_zero_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_626_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 0.32/0.73 ! [A_28: int] :
% 0.32/0.73 ( ( times_times_int @ zero_zero_int @ A_28 )
% 0.32/0.73 = zero_zero_int ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_627_diffs0__imp__equal,axiom,
% 0.32/0.73 ! [M: nat,N: nat] :
% 0.32/0.73 ( ( ( minus_minus_nat @ M @ N )
% 0.32/0.73 = zero_zero_nat )
% 0.32/0.73 => ( ( ( minus_minus_nat @ N @ M )
% 0.32/0.73 = zero_zero_nat )
% 0.32/0.73 => ( M = N ) ) ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_628_diff__self__eq__0,axiom,
% 0.32/0.73 ! [M: nat] :
% 0.32/0.73 ( ( minus_minus_nat @ M @ M )
% 0.32/0.73 = zero_zero_nat ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_629_minus__nat_Odiff__0,axiom,
% 0.32/0.73 ! [M: nat] :
% 0.32/0.73 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.32/0.73 = M ) ).
% 0.32/0.73
% 0.32/0.73 thf(fact_630_diff__0__eq__0,axiom,
% 0.32/0.74 ! [N: nat] :
% 0.32/0.74 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 0.32/0.74 = zero_zero_nat ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_631_comm__semiring__class_Odistrib,axiom,
% 0.32/0.74 ! [A_27: real,B_17: real,C_12: real] :
% 0.32/0.74 ( ( times_times_real @ ( plus_plus_real @ A_27 @ B_17 ) @ C_12 )
% 0.32/0.74 = ( plus_plus_real @ ( times_times_real @ A_27 @ C_12 ) @ ( times_times_real @ B_17 @ C_12 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_632_comm__semiring__class_Odistrib,axiom,
% 0.32/0.74 ! [A_27: nat,B_17: nat,C_12: nat] :
% 0.32/0.74 ( ( times_times_nat @ ( plus_plus_nat @ A_27 @ B_17 ) @ C_12 )
% 0.32/0.74 = ( plus_plus_nat @ ( times_times_nat @ A_27 @ C_12 ) @ ( times_times_nat @ B_17 @ C_12 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_633_comm__semiring__class_Odistrib,axiom,
% 0.32/0.74 ! [A_27: int,B_17: int,C_12: int] :
% 0.32/0.74 ( ( times_times_int @ ( plus_plus_int @ A_27 @ B_17 ) @ C_12 )
% 0.32/0.74 = ( plus_plus_int @ ( times_times_int @ A_27 @ C_12 ) @ ( times_times_int @ B_17 @ C_12 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_634_combine__common__factor,axiom,
% 0.32/0.74 ! [A_26: real,E: real,B_16: real,C_11: real] :
% 0.32/0.74 ( ( plus_plus_real @ ( times_times_real @ A_26 @ E ) @ ( plus_plus_real @ ( times_times_real @ B_16 @ E ) @ C_11 ) )
% 0.32/0.74 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A_26 @ B_16 ) @ E ) @ C_11 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_635_combine__common__factor,axiom,
% 0.32/0.74 ! [A_26: nat,E: nat,B_16: nat,C_11: nat] :
% 0.32/0.74 ( ( plus_plus_nat @ ( times_times_nat @ A_26 @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B_16 @ E ) @ C_11 ) )
% 0.32/0.74 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A_26 @ B_16 ) @ E ) @ C_11 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_636_combine__common__factor,axiom,
% 0.32/0.74 ! [A_26: int,E: int,B_16: int,C_11: int] :
% 0.32/0.74 ( ( plus_plus_int @ ( times_times_int @ A_26 @ E ) @ ( plus_plus_int @ ( times_times_int @ B_16 @ E ) @ C_11 ) )
% 0.32/0.74 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A_26 @ B_16 ) @ E ) @ C_11 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_637_crossproduct__eq,axiom,
% 0.32/0.74 ! [W_3: real,Y_9: real,X_10: real,Z_3: real] :
% 0.32/0.74 ( ( ( plus_plus_real @ ( times_times_real @ W_3 @ Y_9 ) @ ( times_times_real @ X_10 @ Z_3 ) )
% 0.32/0.74 = ( plus_plus_real @ ( times_times_real @ W_3 @ Z_3 ) @ ( times_times_real @ X_10 @ Y_9 ) ) )
% 0.32/0.74 <=> ( ( W_3 = X_10 )
% 0.32/0.74 | ( Y_9 = Z_3 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_638_crossproduct__eq,axiom,
% 0.32/0.74 ! [W_3: nat,Y_9: nat,X_10: nat,Z_3: nat] :
% 0.32/0.74 ( ( ( plus_plus_nat @ ( times_times_nat @ W_3 @ Y_9 ) @ ( times_times_nat @ X_10 @ Z_3 ) )
% 0.32/0.74 = ( plus_plus_nat @ ( times_times_nat @ W_3 @ Z_3 ) @ ( times_times_nat @ X_10 @ Y_9 ) ) )
% 0.32/0.74 <=> ( ( W_3 = X_10 )
% 0.32/0.74 | ( Y_9 = Z_3 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_639_crossproduct__eq,axiom,
% 0.32/0.74 ! [W_3: int,Y_9: int,X_10: int,Z_3: int] :
% 0.32/0.74 ( ( ( plus_plus_int @ ( times_times_int @ W_3 @ Y_9 ) @ ( times_times_int @ X_10 @ Z_3 ) )
% 0.32/0.74 = ( plus_plus_int @ ( times_times_int @ W_3 @ Z_3 ) @ ( times_times_int @ X_10 @ Y_9 ) ) )
% 0.32/0.74 <=> ( ( W_3 = X_10 )
% 0.32/0.74 | ( Y_9 = Z_3 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_640_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 0.32/0.74 ! [A_25: real,M_3: real,B_15: real] :
% 0.32/0.74 ( ( plus_plus_real @ ( times_times_real @ A_25 @ M_3 ) @ ( times_times_real @ B_15 @ M_3 ) )
% 0.32/0.74 = ( times_times_real @ ( plus_plus_real @ A_25 @ B_15 ) @ M_3 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_641_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 0.32/0.74 ! [A_25: nat,M_3: nat,B_15: nat] :
% 0.32/0.74 ( ( plus_plus_nat @ ( times_times_nat @ A_25 @ M_3 ) @ ( times_times_nat @ B_15 @ M_3 ) )
% 0.32/0.74 = ( times_times_nat @ ( plus_plus_nat @ A_25 @ B_15 ) @ M_3 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_642_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 0.32/0.74 ! [A_25: int,M_3: int,B_15: int] :
% 0.32/0.74 ( ( plus_plus_int @ ( times_times_int @ A_25 @ M_3 ) @ ( times_times_int @ B_15 @ M_3 ) )
% 0.32/0.74 = ( times_times_int @ ( plus_plus_int @ A_25 @ B_15 ) @ M_3 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_643_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 0.32/0.74 ! [A_24: real,B_14: real,C_10: real] :
% 0.32/0.74 ( ( times_times_real @ ( plus_plus_real @ A_24 @ B_14 ) @ C_10 )
% 0.32/0.74 = ( plus_plus_real @ ( times_times_real @ A_24 @ C_10 ) @ ( times_times_real @ B_14 @ C_10 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_644_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 0.32/0.74 ! [A_24: nat,B_14: nat,C_10: nat] :
% 0.32/0.74 ( ( times_times_nat @ ( plus_plus_nat @ A_24 @ B_14 ) @ C_10 )
% 0.32/0.74 = ( plus_plus_nat @ ( times_times_nat @ A_24 @ C_10 ) @ ( times_times_nat @ B_14 @ C_10 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_645_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 0.32/0.74 ! [A_24: int,B_14: int,C_10: int] :
% 0.32/0.74 ( ( times_times_int @ ( plus_plus_int @ A_24 @ B_14 ) @ C_10 )
% 0.32/0.74 = ( plus_plus_int @ ( times_times_int @ A_24 @ C_10 ) @ ( times_times_int @ B_14 @ C_10 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_646_crossproduct__noteq,axiom,
% 0.32/0.74 ! [C_9: real,D_3: real,A_23: real,B_13: real] :
% 0.32/0.74 ( ( ( A_23 != B_13 )
% 0.32/0.74 & ( C_9 != D_3 ) )
% 0.32/0.74 <=> ( ( plus_plus_real @ ( times_times_real @ A_23 @ C_9 ) @ ( times_times_real @ B_13 @ D_3 ) )
% 0.32/0.74 != ( plus_plus_real @ ( times_times_real @ A_23 @ D_3 ) @ ( times_times_real @ B_13 @ C_9 ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_647_crossproduct__noteq,axiom,
% 0.32/0.74 ! [C_9: nat,D_3: nat,A_23: nat,B_13: nat] :
% 0.32/0.74 ( ( ( A_23 != B_13 )
% 0.32/0.74 & ( C_9 != D_3 ) )
% 0.32/0.74 <=> ( ( plus_plus_nat @ ( times_times_nat @ A_23 @ C_9 ) @ ( times_times_nat @ B_13 @ D_3 ) )
% 0.32/0.74 != ( plus_plus_nat @ ( times_times_nat @ A_23 @ D_3 ) @ ( times_times_nat @ B_13 @ C_9 ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_648_crossproduct__noteq,axiom,
% 0.32/0.74 ! [C_9: int,D_3: int,A_23: int,B_13: int] :
% 0.32/0.74 ( ( ( A_23 != B_13 )
% 0.32/0.74 & ( C_9 != D_3 ) )
% 0.32/0.74 <=> ( ( plus_plus_int @ ( times_times_int @ A_23 @ C_9 ) @ ( times_times_int @ B_13 @ D_3 ) )
% 0.32/0.74 != ( plus_plus_int @ ( times_times_int @ A_23 @ D_3 ) @ ( times_times_int @ B_13 @ C_9 ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_649_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 0.32/0.74 ! [X_9: real,Y_8: real,Z_2: real] :
% 0.32/0.74 ( ( times_times_real @ X_9 @ ( plus_plus_real @ Y_8 @ Z_2 ) )
% 0.32/0.74 = ( plus_plus_real @ ( times_times_real @ X_9 @ Y_8 ) @ ( times_times_real @ X_9 @ Z_2 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_650_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 0.32/0.74 ! [X_9: nat,Y_8: nat,Z_2: nat] :
% 0.32/0.74 ( ( times_times_nat @ X_9 @ ( plus_plus_nat @ Y_8 @ Z_2 ) )
% 0.32/0.74 = ( plus_plus_nat @ ( times_times_nat @ X_9 @ Y_8 ) @ ( times_times_nat @ X_9 @ Z_2 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_651_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 0.32/0.74 ! [X_9: int,Y_8: int,Z_2: int] :
% 0.32/0.74 ( ( times_times_int @ X_9 @ ( plus_plus_int @ Y_8 @ Z_2 ) )
% 0.32/0.74 = ( plus_plus_int @ ( times_times_int @ X_9 @ Y_8 ) @ ( times_times_int @ X_9 @ Z_2 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_652_nat__int,axiom,
% 0.32/0.74 ! [N: nat] :
% 0.32/0.74 ( ( nat_1 @ ( semiri1621563631at_int @ N ) )
% 0.32/0.74 = N ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_653_mult_Ocomm__neutral,axiom,
% 0.32/0.74 ! [A_22: real] :
% 0.32/0.74 ( ( times_times_real @ A_22 @ one_one_real )
% 0.32/0.74 = A_22 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_654_mult_Ocomm__neutral,axiom,
% 0.32/0.74 ! [A_22: nat] :
% 0.32/0.74 ( ( times_times_nat @ A_22 @ one_one_nat )
% 0.32/0.74 = A_22 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_655_mult_Ocomm__neutral,axiom,
% 0.32/0.74 ! [A_22: int] :
% 0.32/0.74 ( ( times_times_int @ A_22 @ one_one_int )
% 0.32/0.74 = A_22 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_656_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 0.32/0.74 ! [A_21: real] :
% 0.32/0.74 ( ( times_times_real @ A_21 @ one_one_real )
% 0.32/0.74 = A_21 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_657_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 0.32/0.74 ! [A_21: nat] :
% 0.32/0.74 ( ( times_times_nat @ A_21 @ one_one_nat )
% 0.32/0.74 = A_21 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_658_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 0.32/0.74 ! [A_21: int] :
% 0.32/0.74 ( ( times_times_int @ A_21 @ one_one_int )
% 0.32/0.74 = A_21 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_659_mult__1__right,axiom,
% 0.32/0.74 ! [A_20: real] :
% 0.32/0.74 ( ( times_times_real @ A_20 @ one_one_real )
% 0.32/0.74 = A_20 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_660_mult__1__right,axiom,
% 0.32/0.74 ! [A_20: nat] :
% 0.32/0.74 ( ( times_times_nat @ A_20 @ one_one_nat )
% 0.32/0.74 = A_20 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_661_mult__1__right,axiom,
% 0.32/0.74 ! [A_20: int] :
% 0.32/0.74 ( ( times_times_int @ A_20 @ one_one_int )
% 0.32/0.74 = A_20 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_662_mult__1,axiom,
% 0.32/0.74 ! [A_19: real] :
% 0.32/0.74 ( ( times_times_real @ one_one_real @ A_19 )
% 0.32/0.74 = A_19 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_663_mult__1,axiom,
% 0.32/0.74 ! [A_19: nat] :
% 0.32/0.74 ( ( times_times_nat @ one_one_nat @ A_19 )
% 0.32/0.74 = A_19 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_664_mult__1,axiom,
% 0.32/0.74 ! [A_19: int] :
% 0.32/0.74 ( ( times_times_int @ one_one_int @ A_19 )
% 0.32/0.74 = A_19 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_665_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 0.32/0.74 ! [A_18: real] :
% 0.32/0.74 ( ( times_times_real @ one_one_real @ A_18 )
% 0.32/0.74 = A_18 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_666_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 0.32/0.74 ! [A_18: nat] :
% 0.32/0.74 ( ( times_times_nat @ one_one_nat @ A_18 )
% 0.32/0.74 = A_18 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_667_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 0.32/0.74 ! [A_18: int] :
% 0.32/0.74 ( ( times_times_int @ one_one_int @ A_18 )
% 0.32/0.74 = A_18 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_668_mult__1__left,axiom,
% 0.32/0.74 ! [A_17: real] :
% 0.32/0.74 ( ( times_times_real @ one_one_real @ A_17 )
% 0.32/0.74 = A_17 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_669_mult__1__left,axiom,
% 0.32/0.74 ! [A_17: nat] :
% 0.32/0.74 ( ( times_times_nat @ one_one_nat @ A_17 )
% 0.32/0.74 = A_17 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_670_mult__1__left,axiom,
% 0.32/0.74 ! [A_17: int] :
% 0.32/0.74 ( ( times_times_int @ one_one_int @ A_17 )
% 0.32/0.74 = A_17 ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_671_add__le__imp__le__left,axiom,
% 0.32/0.74 ! [C_8: real,A_16: real,B_12: real] :
% 0.32/0.74 ( ( ord_less_eq_real @ ( plus_plus_real @ C_8 @ A_16 ) @ ( plus_plus_real @ C_8 @ B_12 ) )
% 0.32/0.74 => ( ord_less_eq_real @ A_16 @ B_12 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_672_add__le__imp__le__left,axiom,
% 0.32/0.74 ! [C_8: nat,A_16: nat,B_12: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C_8 @ A_16 ) @ ( plus_plus_nat @ C_8 @ B_12 ) )
% 0.32/0.74 => ( ord_less_eq_nat @ A_16 @ B_12 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_673_add__le__imp__le__left,axiom,
% 0.32/0.74 ! [C_8: int,A_16: int,B_12: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( plus_plus_int @ C_8 @ A_16 ) @ ( plus_plus_int @ C_8 @ B_12 ) )
% 0.32/0.74 => ( ord_less_eq_int @ A_16 @ B_12 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_674_add__le__imp__le__right,axiom,
% 0.32/0.74 ! [A_15: real,C_7: real,B_11: real] :
% 0.32/0.74 ( ( ord_less_eq_real @ ( plus_plus_real @ A_15 @ C_7 ) @ ( plus_plus_real @ B_11 @ C_7 ) )
% 0.32/0.74 => ( ord_less_eq_real @ A_15 @ B_11 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_675_add__le__imp__le__right,axiom,
% 0.32/0.74 ! [A_15: nat,C_7: nat,B_11: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A_15 @ C_7 ) @ ( plus_plus_nat @ B_11 @ C_7 ) )
% 0.32/0.74 => ( ord_less_eq_nat @ A_15 @ B_11 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_676_add__le__imp__le__right,axiom,
% 0.32/0.74 ! [A_15: int,C_7: int,B_11: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( plus_plus_int @ A_15 @ C_7 ) @ ( plus_plus_int @ B_11 @ C_7 ) )
% 0.32/0.74 => ( ord_less_eq_int @ A_15 @ B_11 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_677_add__mono,axiom,
% 0.32/0.74 ! [C_6: real,D_2: real,A_14: real,B_10: real] :
% 0.32/0.74 ( ( ord_less_eq_real @ A_14 @ B_10 )
% 0.32/0.74 => ( ( ord_less_eq_real @ C_6 @ D_2 )
% 0.32/0.74 => ( ord_less_eq_real @ ( plus_plus_real @ A_14 @ C_6 ) @ ( plus_plus_real @ B_10 @ D_2 ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_678_add__mono,axiom,
% 0.32/0.74 ! [C_6: nat,D_2: nat,A_14: nat,B_10: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ A_14 @ B_10 )
% 0.32/0.74 => ( ( ord_less_eq_nat @ C_6 @ D_2 )
% 0.32/0.74 => ( ord_less_eq_nat @ ( plus_plus_nat @ A_14 @ C_6 ) @ ( plus_plus_nat @ B_10 @ D_2 ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_679_add__mono,axiom,
% 0.32/0.74 ! [C_6: int,D_2: int,A_14: int,B_10: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ A_14 @ B_10 )
% 0.32/0.74 => ( ( ord_less_eq_int @ C_6 @ D_2 )
% 0.32/0.74 => ( ord_less_eq_int @ ( plus_plus_int @ A_14 @ C_6 ) @ ( plus_plus_int @ B_10 @ D_2 ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_680_add__left__mono,axiom,
% 0.32/0.74 ! [C_5: real,A_13: real,B_9: real] :
% 0.32/0.74 ( ( ord_less_eq_real @ A_13 @ B_9 )
% 0.32/0.74 => ( ord_less_eq_real @ ( plus_plus_real @ C_5 @ A_13 ) @ ( plus_plus_real @ C_5 @ B_9 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_681_add__left__mono,axiom,
% 0.32/0.74 ! [C_5: nat,A_13: nat,B_9: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ A_13 @ B_9 )
% 0.32/0.74 => ( ord_less_eq_nat @ ( plus_plus_nat @ C_5 @ A_13 ) @ ( plus_plus_nat @ C_5 @ B_9 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_682_add__left__mono,axiom,
% 0.32/0.74 ! [C_5: int,A_13: int,B_9: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ A_13 @ B_9 )
% 0.32/0.74 => ( ord_less_eq_int @ ( plus_plus_int @ C_5 @ A_13 ) @ ( plus_plus_int @ C_5 @ B_9 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_683_add__right__mono,axiom,
% 0.32/0.74 ! [C_4: real,A_12: real,B_8: real] :
% 0.32/0.74 ( ( ord_less_eq_real @ A_12 @ B_8 )
% 0.32/0.74 => ( ord_less_eq_real @ ( plus_plus_real @ A_12 @ C_4 ) @ ( plus_plus_real @ B_8 @ C_4 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_684_add__right__mono,axiom,
% 0.32/0.74 ! [C_4: nat,A_12: nat,B_8: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ A_12 @ B_8 )
% 0.32/0.74 => ( ord_less_eq_nat @ ( plus_plus_nat @ A_12 @ C_4 ) @ ( plus_plus_nat @ B_8 @ C_4 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_685_add__right__mono,axiom,
% 0.32/0.74 ! [C_4: int,A_12: int,B_8: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ A_12 @ B_8 )
% 0.32/0.74 => ( ord_less_eq_int @ ( plus_plus_int @ A_12 @ C_4 ) @ ( plus_plus_int @ B_8 @ C_4 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_686_add__le__cancel__left,axiom,
% 0.32/0.74 ! [C_3: real,A_11: real,B_7: real] :
% 0.32/0.74 ( ( ord_less_eq_real @ ( plus_plus_real @ C_3 @ A_11 ) @ ( plus_plus_real @ C_3 @ B_7 ) )
% 0.32/0.74 <=> ( ord_less_eq_real @ A_11 @ B_7 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_687_add__le__cancel__left,axiom,
% 0.32/0.74 ! [C_3: nat,A_11: nat,B_7: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C_3 @ A_11 ) @ ( plus_plus_nat @ C_3 @ B_7 ) )
% 0.32/0.74 <=> ( ord_less_eq_nat @ A_11 @ B_7 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_688_add__le__cancel__left,axiom,
% 0.32/0.74 ! [C_3: int,A_11: int,B_7: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( plus_plus_int @ C_3 @ A_11 ) @ ( plus_plus_int @ C_3 @ B_7 ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ A_11 @ B_7 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_689_add__le__cancel__right,axiom,
% 0.32/0.74 ! [A_10: real,C_2: real,B_6: real] :
% 0.32/0.74 ( ( ord_less_eq_real @ ( plus_plus_real @ A_10 @ C_2 ) @ ( plus_plus_real @ B_6 @ C_2 ) )
% 0.32/0.74 <=> ( ord_less_eq_real @ A_10 @ B_6 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_690_add__le__cancel__right,axiom,
% 0.32/0.74 ! [A_10: nat,C_2: nat,B_6: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A_10 @ C_2 ) @ ( plus_plus_nat @ B_6 @ C_2 ) )
% 0.32/0.74 <=> ( ord_less_eq_nat @ A_10 @ B_6 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_691_add__le__cancel__right,axiom,
% 0.32/0.74 ! [A_10: int,C_2: int,B_6: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( plus_plus_int @ A_10 @ C_2 ) @ ( plus_plus_int @ B_6 @ C_2 ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ A_10 @ B_6 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_692_less__imp__diff__less,axiom,
% 0.32/0.74 ! [N: nat,J: nat,K: nat] :
% 0.32/0.74 ( ( ord_less_nat @ J @ K )
% 0.32/0.74 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_693_diff__less__mono2,axiom,
% 0.32/0.74 ! [L: nat,M: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_nat @ M @ N )
% 0.32/0.74 => ( ( ord_less_nat @ M @ L )
% 0.32/0.74 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_694_power__commutes,axiom,
% 0.32/0.74 ! [A_9: real,N_7: nat] :
% 0.32/0.74 ( ( times_times_real @ ( power_power_real @ A_9 @ N_7 ) @ A_9 )
% 0.32/0.74 = ( times_times_real @ A_9 @ ( power_power_real @ A_9 @ N_7 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_695_power__commutes,axiom,
% 0.32/0.74 ! [A_9: nat,N_7: nat] :
% 0.32/0.74 ( ( times_times_nat @ ( power_power_nat @ A_9 @ N_7 ) @ A_9 )
% 0.32/0.74 = ( times_times_nat @ A_9 @ ( power_power_nat @ A_9 @ N_7 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_696_power__commutes,axiom,
% 0.32/0.74 ! [A_9: int,N_7: nat] :
% 0.32/0.74 ( ( times_times_int @ ( power_power_int @ A_9 @ N_7 ) @ A_9 )
% 0.32/0.74 = ( times_times_int @ A_9 @ ( power_power_int @ A_9 @ N_7 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_697_power__mult__distrib,axiom,
% 0.32/0.74 ! [A_8: real,B_5: real,N_6: nat] :
% 0.32/0.74 ( ( power_power_real @ ( times_times_real @ A_8 @ B_5 ) @ N_6 )
% 0.32/0.74 = ( times_times_real @ ( power_power_real @ A_8 @ N_6 ) @ ( power_power_real @ B_5 @ N_6 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_698_power__mult__distrib,axiom,
% 0.32/0.74 ! [A_8: nat,B_5: nat,N_6: nat] :
% 0.32/0.74 ( ( power_power_nat @ ( times_times_nat @ A_8 @ B_5 ) @ N_6 )
% 0.32/0.74 = ( times_times_nat @ ( power_power_nat @ A_8 @ N_6 ) @ ( power_power_nat @ B_5 @ N_6 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_699_power__mult__distrib,axiom,
% 0.32/0.74 ! [A_8: int,B_5: int,N_6: nat] :
% 0.32/0.74 ( ( power_power_int @ ( times_times_int @ A_8 @ B_5 ) @ N_6 )
% 0.32/0.74 = ( times_times_int @ ( power_power_int @ A_8 @ N_6 ) @ ( power_power_int @ B_5 @ N_6 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_700_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 0.32/0.74 ! [X_8: real,Y_7: real,Q_2: nat] :
% 0.32/0.74 ( ( power_power_real @ ( times_times_real @ X_8 @ Y_7 ) @ Q_2 )
% 0.32/0.74 = ( times_times_real @ ( power_power_real @ X_8 @ Q_2 ) @ ( power_power_real @ Y_7 @ Q_2 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_701_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 0.32/0.74 ! [X_8: nat,Y_7: nat,Q_2: nat] :
% 0.32/0.74 ( ( power_power_nat @ ( times_times_nat @ X_8 @ Y_7 ) @ Q_2 )
% 0.32/0.74 = ( times_times_nat @ ( power_power_nat @ X_8 @ Q_2 ) @ ( power_power_nat @ Y_7 @ Q_2 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_702_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 0.32/0.74 ! [X_8: int,Y_7: int,Q_2: nat] :
% 0.32/0.74 ( ( power_power_int @ ( times_times_int @ X_8 @ Y_7 ) @ Q_2 )
% 0.32/0.74 = ( times_times_int @ ( power_power_int @ X_8 @ Q_2 ) @ ( power_power_int @ Y_7 @ Q_2 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_703_diff__add__inverse2,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 0.32/0.74 = M ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_704_diff__add__inverse,axiom,
% 0.32/0.74 ! [N: nat,M: nat] :
% 0.32/0.74 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 0.32/0.74 = M ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_705_diff__diff__left,axiom,
% 0.32/0.74 ! [I_1: nat,J: nat,K: nat] :
% 0.32/0.74 ( ( minus_minus_nat @ ( minus_minus_nat @ I_1 @ J ) @ K )
% 0.32/0.74 = ( minus_minus_nat @ I_1 @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_706_Nat_Odiff__cancel,axiom,
% 0.32/0.74 ! [K: nat,M: nat,N: nat] :
% 0.32/0.74 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.32/0.74 = ( minus_minus_nat @ M @ N ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_707_diff__cancel2,axiom,
% 0.32/0.74 ! [M: nat,K: nat,N: nat] :
% 0.32/0.74 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 0.32/0.74 = ( minus_minus_nat @ M @ N ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_708_mult__Pls,axiom,
% 0.32/0.74 ! [W: int] :
% 0.32/0.74 ( ( times_times_int @ pls @ W )
% 0.32/0.74 = pls ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_709_mult__Bit0,axiom,
% 0.32/0.74 ! [K: int,L: int] :
% 0.32/0.74 ( ( times_times_int @ ( bit0 @ K ) @ L )
% 0.32/0.74 = ( bit0 @ ( times_times_int @ K @ L ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_710_rel__simps_I34_J,axiom,
% 0.32/0.74 ! [K: int,L: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ K @ L ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_711_less__eq__int__code_I16_J,axiom,
% 0.32/0.74 ! [K1: int,K2: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ K1 @ K2 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_712_rel__simps_I19_J,axiom,
% 0.32/0.74 ord_less_eq_int @ pls @ pls ).
% 0.32/0.74
% 0.32/0.74 thf(fact_713_rel__simps_I31_J,axiom,
% 0.32/0.74 ! [K: int,L: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ K @ L ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_714_less__eq__int__code_I13_J,axiom,
% 0.32/0.74 ! [K1: int,K2: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ K1 @ K2 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_715_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 0.32/0.74 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.32/0.74
% 0.32/0.74 thf(fact_716_zmult__1,axiom,
% 0.32/0.74 ! [Z: int] :
% 0.32/0.74 ( ( times_times_int @ one_one_int @ Z )
% 0.32/0.74 = Z ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_717_zmult__1__right,axiom,
% 0.32/0.74 ! [Z: int] :
% 0.32/0.74 ( ( times_times_int @ Z @ one_one_int )
% 0.32/0.74 = Z ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_718_zless__le,axiom,
% 0.32/0.74 ! [Z: int,W: int] :
% 0.32/0.74 ( ( ord_less_int @ Z @ W )
% 0.32/0.74 <=> ( ( ord_less_eq_int @ Z @ W )
% 0.32/0.74 & ( Z != W ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_719_zadd__zmult__distrib2,axiom,
% 0.32/0.74 ! [W: int,Z1: int,Z2: int] :
% 0.32/0.74 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z2 ) )
% 0.32/0.74 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z2 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_720_zadd__zmult__distrib,axiom,
% 0.32/0.74 ! [Z1: int,Z2: int,W: int] :
% 0.32/0.74 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z2 ) @ W )
% 0.32/0.74 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z2 @ W ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_721_zadd__left__mono,axiom,
% 0.32/0.74 ! [K: int,I_1: int,J: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ I_1 @ J )
% 0.32/0.74 => ( ord_less_eq_int @ ( plus_plus_int @ K @ I_1 ) @ ( plus_plus_int @ K @ J ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_722_times__numeral__code_I5_J,axiom,
% 0.32/0.74 ! [V_1: int,W: int] :
% 0.32/0.74 ( ( times_times_int @ ( number_number_of_int @ V_1 ) @ ( number_number_of_int @ W ) )
% 0.32/0.74 = ( number_number_of_int @ ( times_times_int @ V_1 @ W ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_723_less__eq__number__of__int__code,axiom,
% 0.32/0.74 ! [K: int,L: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ K @ L ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_724_convex__bound__le,axiom,
% 0.32/0.74 ! [V_4: real,U_2: real,Y_6: real,X_7: real,A_7: real] :
% 0.32/0.74 ( ( ord_less_eq_real @ X_7 @ A_7 )
% 0.32/0.74 => ( ( ord_less_eq_real @ Y_6 @ A_7 )
% 0.32/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ U_2 )
% 0.32/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ V_4 )
% 0.32/0.74 => ( ( ( plus_plus_real @ U_2 @ V_4 )
% 0.32/0.74 = one_one_real )
% 0.32/0.74 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U_2 @ X_7 ) @ ( times_times_real @ V_4 @ Y_6 ) ) @ A_7 ) ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_725_convex__bound__le,axiom,
% 0.32/0.74 ! [V_4: int,U_2: int,Y_6: int,X_7: int,A_7: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ X_7 @ A_7 )
% 0.32/0.74 => ( ( ord_less_eq_int @ Y_6 @ A_7 )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ U_2 )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ V_4 )
% 0.32/0.74 => ( ( ( plus_plus_int @ U_2 @ V_4 )
% 0.32/0.74 = one_one_int )
% 0.32/0.74 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U_2 @ X_7 ) @ ( times_times_int @ V_4 @ Y_6 ) ) @ A_7 ) ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_726_transfer__nat__int__relations_I2_J,axiom,
% 0.32/0.74 ! [Y: int,X: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.74 => ( ( ord_less_nat @ ( nat_1 @ X ) @ ( nat_1 @ Y ) )
% 0.32/0.74 <=> ( ord_less_int @ X @ Y ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_727_nat__less__eq__zless,axiom,
% 0.32/0.74 ! [Z: int,W: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.32/0.74 => ( ( ord_less_nat @ ( nat_1 @ W ) @ ( nat_1 @ Z ) )
% 0.32/0.74 <=> ( ord_less_int @ W @ Z ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_728_le__special_I1_J,axiom,
% 0.32/0.74 ! [Y_5: int] :
% 0.32/0.74 ( ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ Y_5 ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ pls @ Y_5 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_729_le__special_I1_J,axiom,
% 0.32/0.74 ! [Y_5: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ Y_5 ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ pls @ Y_5 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_730_le__special_I3_J,axiom,
% 0.32/0.74 ! [X_6: int] :
% 0.32/0.74 ( ( ord_less_eq_real @ ( number267125858f_real @ X_6 ) @ zero_zero_real )
% 0.32/0.74 <=> ( ord_less_eq_int @ X_6 @ pls ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_731_le__special_I3_J,axiom,
% 0.32/0.74 ! [X_6: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( number_number_of_int @ X_6 ) @ zero_zero_int )
% 0.32/0.74 <=> ( ord_less_eq_int @ X_6 @ pls ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_732_power__decreasing,axiom,
% 0.32/0.74 ! [A_6: real,N_5: nat,N_4: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ N_5 @ N_4 )
% 0.32/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ A_6 )
% 0.32/0.74 => ( ( ord_less_eq_real @ A_6 @ one_one_real )
% 0.32/0.74 => ( ord_less_eq_real @ ( power_power_real @ A_6 @ N_4 ) @ ( power_power_real @ A_6 @ N_5 ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_733_power__decreasing,axiom,
% 0.32/0.74 ! [A_6: nat,N_5: nat,N_4: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ N_5 @ N_4 )
% 0.32/0.74 => ( ( ord_less_eq_nat @ zero_zero_nat @ A_6 )
% 0.32/0.74 => ( ( ord_less_eq_nat @ A_6 @ one_one_nat )
% 0.32/0.74 => ( ord_less_eq_nat @ ( power_power_nat @ A_6 @ N_4 ) @ ( power_power_nat @ A_6 @ N_5 ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_734_power__decreasing,axiom,
% 0.32/0.74 ! [A_6: int,N_5: nat,N_4: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ N_5 @ N_4 )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ A_6 )
% 0.32/0.74 => ( ( ord_less_eq_int @ A_6 @ one_one_int )
% 0.32/0.74 => ( ord_less_eq_int @ ( power_power_int @ A_6 @ N_4 ) @ ( power_power_int @ A_6 @ N_5 ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_735_power__increasing__iff,axiom,
% 0.32/0.74 ! [X_5: nat,Y_4: nat,B_4: real] :
% 0.32/0.74 ( ( ord_less_real @ one_one_real @ B_4 )
% 0.32/0.74 => ( ( ord_less_eq_real @ ( power_power_real @ B_4 @ X_5 ) @ ( power_power_real @ B_4 @ Y_4 ) )
% 0.32/0.74 <=> ( ord_less_eq_nat @ X_5 @ Y_4 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_736_power__increasing__iff,axiom,
% 0.32/0.74 ! [X_5: nat,Y_4: nat,B_4: nat] :
% 0.32/0.74 ( ( ord_less_nat @ one_one_nat @ B_4 )
% 0.32/0.74 => ( ( ord_less_eq_nat @ ( power_power_nat @ B_4 @ X_5 ) @ ( power_power_nat @ B_4 @ Y_4 ) )
% 0.32/0.74 <=> ( ord_less_eq_nat @ X_5 @ Y_4 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_737_power__increasing__iff,axiom,
% 0.32/0.74 ! [X_5: nat,Y_4: nat,B_4: int] :
% 0.32/0.74 ( ( ord_less_int @ one_one_int @ B_4 )
% 0.32/0.74 => ( ( ord_less_eq_int @ ( power_power_int @ B_4 @ X_5 ) @ ( power_power_int @ B_4 @ Y_4 ) )
% 0.32/0.74 <=> ( ord_less_eq_nat @ X_5 @ Y_4 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_738_power__le__imp__le__exp,axiom,
% 0.32/0.74 ! [M_2: nat,N_3: nat,A_5: real] :
% 0.32/0.74 ( ( ord_less_real @ one_one_real @ A_5 )
% 0.32/0.74 => ( ( ord_less_eq_real @ ( power_power_real @ A_5 @ M_2 ) @ ( power_power_real @ A_5 @ N_3 ) )
% 0.32/0.74 => ( ord_less_eq_nat @ M_2 @ N_3 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_739_power__le__imp__le__exp,axiom,
% 0.32/0.74 ! [M_2: nat,N_3: nat,A_5: nat] :
% 0.32/0.74 ( ( ord_less_nat @ one_one_nat @ A_5 )
% 0.32/0.74 => ( ( ord_less_eq_nat @ ( power_power_nat @ A_5 @ M_2 ) @ ( power_power_nat @ A_5 @ N_3 ) )
% 0.32/0.74 => ( ord_less_eq_nat @ M_2 @ N_3 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_740_power__le__imp__le__exp,axiom,
% 0.32/0.74 ! [M_2: nat,N_3: nat,A_5: int] :
% 0.32/0.74 ( ( ord_less_int @ one_one_int @ A_5 )
% 0.32/0.74 => ( ( ord_less_eq_int @ ( power_power_int @ A_5 @ M_2 ) @ ( power_power_int @ A_5 @ N_3 ) )
% 0.32/0.74 => ( ord_less_eq_nat @ M_2 @ N_3 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_741_nat__eq__iff2,axiom,
% 0.32/0.74 ! [M: nat,W: int] :
% 0.32/0.74 ( ( M
% 0.32/0.74 = ( nat_1 @ W ) )
% 0.32/0.74 <=> ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.32/0.74 => ( W
% 0.32/0.74 = ( semiri1621563631at_int @ M ) ) )
% 0.32/0.74 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 0.32/0.74 => ( M = zero_zero_nat ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_742_nat__eq__iff,axiom,
% 0.32/0.74 ! [W: int,M: nat] :
% 0.32/0.74 ( ( ( nat_1 @ W )
% 0.32/0.74 = M )
% 0.32/0.74 <=> ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.32/0.74 => ( W
% 0.32/0.74 = ( semiri1621563631at_int @ M ) ) )
% 0.32/0.74 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 0.32/0.74 => ( M = zero_zero_nat ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_743_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom,
% 0.32/0.74 ! [Y: int,X: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.74 => ( ( plus_plus_nat @ ( nat_1 @ X ) @ ( nat_1 @ Y ) )
% 0.32/0.74 = ( nat_1 @ ( plus_plus_int @ X @ Y ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_744_nat__add__distrib,axiom,
% 0.32/0.74 ! [Z_1: int,Z: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ Z_1 )
% 0.32/0.74 => ( ( nat_1 @ ( plus_plus_int @ Z @ Z_1 ) )
% 0.32/0.74 = ( plus_plus_nat @ ( nat_1 @ Z ) @ ( nat_1 @ Z_1 ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_745_int__eq__iff__number__of,axiom,
% 0.32/0.74 ! [M: nat,V_1: int] :
% 0.32/0.74 ( ( ( semiri1621563631at_int @ M )
% 0.32/0.74 = ( number_number_of_int @ V_1 ) )
% 0.32/0.74 <=> ( ( M
% 0.32/0.74 = ( nat_1 @ ( number_number_of_int @ V_1 ) ) )
% 0.32/0.74 & ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ V_1 ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_746_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom,
% 0.32/0.74 ! [N: nat,X: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.74 => ( ( power_power_nat @ ( nat_1 @ X ) @ N )
% 0.32/0.74 = ( nat_1 @ ( power_power_int @ X @ N ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_747_nat__power__eq,axiom,
% 0.32/0.74 ! [N: nat,Z: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.74 => ( ( nat_1 @ ( power_power_int @ Z @ N ) )
% 0.32/0.74 = ( power_power_nat @ ( nat_1 @ Z ) @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_748_convex__bound__lt,axiom,
% 0.32/0.74 ! [V_3: real,U_1: real,Y_3: real,X_4: real,A_4: real] :
% 0.32/0.74 ( ( ord_less_real @ X_4 @ A_4 )
% 0.32/0.74 => ( ( ord_less_real @ Y_3 @ A_4 )
% 0.32/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ U_1 )
% 0.32/0.74 => ( ( ord_less_eq_real @ zero_zero_real @ V_3 )
% 0.32/0.74 => ( ( ( plus_plus_real @ U_1 @ V_3 )
% 0.32/0.74 = one_one_real )
% 0.32/0.74 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U_1 @ X_4 ) @ ( times_times_real @ V_3 @ Y_3 ) ) @ A_4 ) ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_749_convex__bound__lt,axiom,
% 0.32/0.74 ! [V_3: int,U_1: int,Y_3: int,X_4: int,A_4: int] :
% 0.32/0.74 ( ( ord_less_int @ X_4 @ A_4 )
% 0.32/0.74 => ( ( ord_less_int @ Y_3 @ A_4 )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ U_1 )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ V_3 )
% 0.32/0.74 => ( ( ( plus_plus_int @ U_1 @ V_3 )
% 0.32/0.74 = one_one_int )
% 0.32/0.74 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U_1 @ X_4 ) @ ( times_times_int @ V_3 @ Y_3 ) ) @ A_4 ) ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_750_nat__less__iff,axiom,
% 0.32/0.74 ! [M: nat,W: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 0.32/0.74 => ( ( ord_less_nat @ ( nat_1 @ W ) @ M )
% 0.32/0.74 <=> ( ord_less_int @ W @ ( semiri1621563631at_int @ M ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_751_le__special_I2_J,axiom,
% 0.32/0.74 ! [Y_2: int] :
% 0.32/0.74 ( ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ Y_2 ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_2 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_752_le__special_I2_J,axiom,
% 0.32/0.74 ! [Y_2: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ Y_2 ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_2 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_753_le__special_I4_J,axiom,
% 0.32/0.74 ! [X_3: int] :
% 0.32/0.74 ( ( ord_less_eq_real @ ( number267125858f_real @ X_3 ) @ one_one_real )
% 0.32/0.74 <=> ( ord_less_eq_int @ X_3 @ ( bit1 @ pls ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_754_le__special_I4_J,axiom,
% 0.32/0.74 ! [X_3: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( number_number_of_int @ X_3 ) @ one_one_int )
% 0.32/0.74 <=> ( ord_less_eq_int @ X_3 @ ( bit1 @ pls ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_755_realpow__minus__mult,axiom,
% 0.32/0.74 ! [X_2: real,N_2: nat] :
% 0.32/0.74 ( ( ord_less_nat @ zero_zero_nat @ N_2 )
% 0.32/0.74 => ( ( times_times_real @ ( power_power_real @ X_2 @ ( minus_minus_nat @ N_2 @ one_one_nat ) ) @ X_2 )
% 0.32/0.74 = ( power_power_real @ X_2 @ N_2 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_756_realpow__minus__mult,axiom,
% 0.32/0.74 ! [X_2: nat,N_2: nat] :
% 0.32/0.74 ( ( ord_less_nat @ zero_zero_nat @ N_2 )
% 0.32/0.74 => ( ( times_times_nat @ ( power_power_nat @ X_2 @ ( minus_minus_nat @ N_2 @ one_one_nat ) ) @ X_2 )
% 0.32/0.74 = ( power_power_nat @ X_2 @ N_2 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_757_realpow__minus__mult,axiom,
% 0.32/0.74 ! [X_2: int,N_2: nat] :
% 0.32/0.74 ( ( ord_less_nat @ zero_zero_nat @ N_2 )
% 0.32/0.74 => ( ( times_times_int @ ( power_power_int @ X_2 @ ( minus_minus_nat @ N_2 @ one_one_nat ) ) @ X_2 )
% 0.32/0.74 = ( power_power_int @ X_2 @ N_2 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_758_less__iff__diff__less__0,axiom,
% 0.32/0.74 ! [A_3: real,B_3: real] :
% 0.32/0.74 ( ( ord_less_real @ A_3 @ B_3 )
% 0.32/0.74 <=> ( ord_less_real @ ( minus_minus_real @ A_3 @ B_3 ) @ zero_zero_real ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_759_less__iff__diff__less__0,axiom,
% 0.32/0.74 ! [A_3: int,B_3: int] :
% 0.32/0.74 ( ( ord_less_int @ A_3 @ B_3 )
% 0.32/0.74 <=> ( ord_less_int @ ( minus_minus_int @ A_3 @ B_3 ) @ zero_zero_int ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_760_transfer__nat__int__numerals_I1_J,axiom,
% 0.32/0.74 ( zero_zero_nat
% 0.32/0.74 = ( nat_1 @ zero_zero_int ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_761_nat__0,axiom,
% 0.32/0.74 ( ( nat_1 @ zero_zero_int )
% 0.32/0.74 = zero_zero_nat ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_762_not__square__less__zero,axiom,
% 0.32/0.74 ! [A_2: real] :
% 0.32/0.74 ~ ( ord_less_real @ ( times_times_real @ A_2 @ A_2 ) @ zero_zero_real ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_763_not__square__less__zero,axiom,
% 0.32/0.74 ! [A_2: int] :
% 0.32/0.74 ~ ( ord_less_int @ ( times_times_int @ A_2 @ A_2 ) @ zero_zero_int ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_764_mult__less__cancel__right__disj,axiom,
% 0.32/0.74 ! [A_1: real,C_1: real,B_2: real] :
% 0.32/0.74 ( ( ord_less_real @ ( times_times_real @ A_1 @ C_1 ) @ ( times_times_real @ B_2 @ C_1 ) )
% 0.32/0.74 <=> ( ( ( ord_less_real @ zero_zero_real @ C_1 )
% 0.32/0.74 & ( ord_less_real @ A_1 @ B_2 ) )
% 0.32/0.74 | ( ( ord_less_real @ C_1 @ zero_zero_real )
% 0.32/0.74 & ( ord_less_real @ B_2 @ A_1 ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_765_mult__less__cancel__right__disj,axiom,
% 0.32/0.74 ! [A_1: int,C_1: int,B_2: int] :
% 0.32/0.74 ( ( ord_less_int @ ( times_times_int @ A_1 @ C_1 ) @ ( times_times_int @ B_2 @ C_1 ) )
% 0.32/0.74 <=> ( ( ( ord_less_int @ zero_zero_int @ C_1 )
% 0.32/0.74 & ( ord_less_int @ A_1 @ B_2 ) )
% 0.32/0.74 | ( ( ord_less_int @ C_1 @ zero_zero_int )
% 0.32/0.74 & ( ord_less_int @ B_2 @ A_1 ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_766_nat__number__of,axiom,
% 0.32/0.74 ! [W: int] :
% 0.32/0.74 ( ( nat_1 @ ( number_number_of_int @ W ) )
% 0.32/0.74 = ( number_number_of_nat @ W ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_767_nat__number__of__def,axiom,
% 0.32/0.74 ! [V_1: int] :
% 0.32/0.74 ( ( number_number_of_nat @ V_1 )
% 0.32/0.74 = ( nat_1 @ ( number_number_of_int @ V_1 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_768_transfer__nat__int__numerals_I2_J,axiom,
% 0.32/0.74 ( one_one_nat
% 0.32/0.74 = ( nat_1 @ one_one_int ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_769_zero__less__diff,axiom,
% 0.32/0.74 ! [N: nat,M: nat] :
% 0.32/0.74 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 0.32/0.74 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_770_diff__less,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.74 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.74 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_771_diff__add__0,axiom,
% 0.32/0.74 ! [N: nat,M: nat] :
% 0.32/0.74 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 0.32/0.74 = zero_zero_nat ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_772_less__diff__conv,axiom,
% 0.32/0.74 ! [I_1: nat,J: nat,K: nat] :
% 0.32/0.74 ( ( ord_less_nat @ I_1 @ ( minus_minus_nat @ J @ K ) )
% 0.32/0.74 <=> ( ord_less_nat @ ( plus_plus_nat @ I_1 @ K ) @ J ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_773_add__diff__inverse,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ~ ( ord_less_nat @ M @ N )
% 0.32/0.74 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.74 = M ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_774_rel__simps_I22_J,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ pls @ ( bit1 @ K ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ pls @ K ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_775_rel__simps_I32_J,axiom,
% 0.32/0.74 ! [K: int,L: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ K @ L ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_776_less__eq__int__code_I14_J,axiom,
% 0.32/0.74 ! [K1: int,K2: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ K1 @ K2 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_777_rel__simps_I21_J,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ pls @ ( bit0 @ K ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ pls @ K ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_778_rel__simps_I27_J,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( bit0 @ K ) @ pls )
% 0.32/0.74 <=> ( ord_less_eq_int @ K @ pls ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_779_pos__zmult__pos,axiom,
% 0.32/0.74 ! [B: int,A: int] :
% 0.32/0.74 ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.74 => ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.32/0.74 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_780_zmult__zless__mono2,axiom,
% 0.32/0.74 ! [K: int,I_1: int,J: int] :
% 0.32/0.74 ( ( ord_less_int @ I_1 @ J )
% 0.32/0.74 => ( ( ord_less_int @ zero_zero_int @ K )
% 0.32/0.74 => ( ord_less_int @ ( times_times_int @ K @ I_1 ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_781_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 0.32/0.74 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.32/0.74
% 0.32/0.74 thf(fact_782_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 0.32/0.74 ! [Y: int,X: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.74 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ X @ Y ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_783_zadd__zless__mono,axiom,
% 0.32/0.74 ! [Z_1: int,Z: int,W_2: int,W: int] :
% 0.32/0.74 ( ( ord_less_int @ W_2 @ W )
% 0.32/0.74 => ( ( ord_less_eq_int @ Z_1 @ Z )
% 0.32/0.74 => ( ord_less_int @ ( plus_plus_int @ W_2 @ Z_1 ) @ ( plus_plus_int @ W @ Z ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_784_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom,
% 0.32/0.74 ! [Z: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1621563631at_int @ Z ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_785_transfer__int__nat__quantifiers_I2_J,axiom,
% 0.32/0.74 ! [P: int > $o] :
% 0.32/0.74 ( ? [X_1: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.32/0.74 & ( P @ X_1 ) )
% 0.32/0.74 <=> ? [X_1: nat] : ( P @ ( semiri1621563631at_int @ X_1 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_786_transfer__int__nat__quantifiers_I1_J,axiom,
% 0.32/0.74 ! [P: int > $o] :
% 0.32/0.74 ( ! [X_1: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.32/0.74 => ( P @ X_1 ) )
% 0.32/0.74 <=> ! [X_1: nat] : ( P @ ( semiri1621563631at_int @ X_1 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_787_zero__zle__int,axiom,
% 0.32/0.74 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1621563631at_int @ N ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_788_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 0.32/0.74 ! [N: nat,X: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.74 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ X @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_789_zle__iff__zadd,axiom,
% 0.32/0.74 ! [W: int,Z: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ W @ Z )
% 0.32/0.74 <=> ? [N_1: nat] :
% 0.32/0.74 ( Z
% 0.32/0.74 = ( plus_plus_int @ W @ ( semiri1621563631at_int @ N_1 ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_790_zpower__zadd__distrib,axiom,
% 0.32/0.74 ! [X: int,Y: nat,Z: nat] :
% 0.32/0.74 ( ( power_power_int @ X @ ( plus_plus_nat @ Y @ Z ) )
% 0.32/0.74 = ( times_times_int @ ( power_power_int @ X @ Y ) @ ( power_power_int @ X @ Z ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_791_nat__mono__iff,axiom,
% 0.32/0.74 ! [W: int,Z: int] :
% 0.32/0.74 ( ( ord_less_int @ zero_zero_int @ Z )
% 0.32/0.74 => ( ( ord_less_nat @ ( nat_1 @ W ) @ ( nat_1 @ Z ) )
% 0.32/0.74 <=> ( ord_less_int @ W @ Z ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_792_zless__nat__conj,axiom,
% 0.32/0.74 ! [W: int,Z: int] :
% 0.32/0.74 ( ( ord_less_nat @ ( nat_1 @ W ) @ ( nat_1 @ Z ) )
% 0.32/0.74 <=> ( ( ord_less_int @ zero_zero_int @ Z )
% 0.32/0.74 & ( ord_less_int @ W @ Z ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_793_zless__nat__eq__int__zless,axiom,
% 0.32/0.74 ! [M: nat,Z: int] :
% 0.32/0.74 ( ( ord_less_nat @ M @ ( nat_1 @ Z ) )
% 0.32/0.74 <=> ( ord_less_int @ ( semiri1621563631at_int @ M ) @ Z ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_794_nat__diff__split__asm,axiom,
% 0.32/0.74 ! [P: nat > $o,A: nat,B: nat] :
% 0.32/0.74 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 0.32/0.74 <=> ~ ( ( ( ord_less_nat @ A @ B )
% 0.32/0.74 & ~ ( P @ zero_zero_nat ) )
% 0.32/0.74 | ? [D_1: nat] :
% 0.32/0.74 ( ( A
% 0.32/0.74 = ( plus_plus_nat @ B @ D_1 ) )
% 0.32/0.74 & ~ ( P @ D_1 ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_795_nat__diff__split,axiom,
% 0.32/0.74 ! [P: nat > $o,A: nat,B: nat] :
% 0.32/0.74 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 0.32/0.74 <=> ( ( ( ord_less_nat @ A @ B )
% 0.32/0.74 => ( P @ zero_zero_nat ) )
% 0.32/0.74 & ! [D_1: nat] :
% 0.32/0.74 ( ( A
% 0.32/0.74 = ( plus_plus_nat @ B @ D_1 ) )
% 0.32/0.74 => ( P @ D_1 ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_796_eq__0__number__of,axiom,
% 0.32/0.74 ! [V_1: int] :
% 0.32/0.74 ( ( zero_zero_nat
% 0.32/0.74 = ( number_number_of_nat @ V_1 ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ V_1 @ pls ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_797_eq__number__of__0,axiom,
% 0.32/0.74 ! [V_1: int] :
% 0.32/0.74 ( ( ( number_number_of_nat @ V_1 )
% 0.32/0.74 = zero_zero_nat )
% 0.32/0.74 <=> ( ord_less_eq_int @ V_1 @ pls ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_798_rel__simps_I5_J,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( ord_less_int @ pls @ ( bit1 @ K ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ pls @ K ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_799_rel__simps_I29_J,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( bit1 @ K ) @ pls )
% 0.32/0.74 <=> ( ord_less_int @ K @ pls ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_800_rel__simps_I15_J,axiom,
% 0.32/0.74 ! [K: int,L: int] :
% 0.32/0.74 ( ( ord_less_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ K @ L ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_801_less__int__code_I14_J,axiom,
% 0.32/0.74 ! [K1: int,K2: int] :
% 0.32/0.74 ( ( ord_less_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ K1 @ K2 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_802_rel__simps_I33_J,axiom,
% 0.32/0.74 ! [K: int,L: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
% 0.32/0.74 <=> ( ord_less_int @ K @ L ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_803_less__eq__int__code_I15_J,axiom,
% 0.32/0.74 ! [K1: int,K2: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
% 0.32/0.74 <=> ( ord_less_int @ K1 @ K2 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_804_mult__Bit1,axiom,
% 0.32/0.74 ! [K: int,L: int] :
% 0.32/0.74 ( ( times_times_int @ ( bit1 @ K ) @ L )
% 0.32/0.74 = ( plus_plus_int @ ( bit0 @ ( times_times_int @ K @ L ) ) @ L ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_805_pos__zmult__eq__1__iff,axiom,
% 0.32/0.74 ! [N: int,M: int] :
% 0.32/0.74 ( ( ord_less_int @ zero_zero_int @ M )
% 0.32/0.74 => ( ( ( times_times_int @ M @ N )
% 0.32/0.74 = one_one_int )
% 0.32/0.74 <=> ( ( M = one_one_int )
% 0.32/0.74 & ( N = one_one_int ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_806_int__one__le__iff__zero__less,axiom,
% 0.32/0.74 ! [Z: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ one_one_int @ Z )
% 0.32/0.74 <=> ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_807_int__le__0__conv,axiom,
% 0.32/0.74 ! [N: nat] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( semiri1621563631at_int @ N ) @ zero_zero_int )
% 0.32/0.74 <=> ( N = zero_zero_nat ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_808_succ__Pls,axiom,
% 0.32/0.74 ( ( succ @ pls )
% 0.32/0.74 = ( bit1 @ pls ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_809_succ__Bit0,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( succ @ ( bit0 @ K ) )
% 0.32/0.74 = ( bit1 @ K ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_810_succ__Bit1,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( succ @ ( bit1 @ K ) )
% 0.32/0.74 = ( bit0 @ ( succ @ K ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_811_zle__add1__eq__le,axiom,
% 0.32/0.74 ! [W: int,Z: int] :
% 0.32/0.74 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ W @ Z ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_812_add1__zle__eq,axiom,
% 0.32/0.74 ! [W: int,Z: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 0.32/0.74 <=> ( ord_less_int @ W @ Z ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_813_zless__imp__add1__zle,axiom,
% 0.32/0.74 ! [W: int,Z: int] :
% 0.32/0.74 ( ( ord_less_int @ W @ Z )
% 0.32/0.74 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_814_succ__def,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( succ @ K )
% 0.32/0.74 = ( plus_plus_int @ K @ one_one_int ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_815_zero__less__nat__eq,axiom,
% 0.32/0.74 ! [Z: int] :
% 0.32/0.74 ( ( ord_less_nat @ zero_zero_nat @ ( nat_1 @ Z ) )
% 0.32/0.74 <=> ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_816_transfer__nat__int__numerals_I4_J,axiom,
% 0.32/0.74 ( ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) )
% 0.32/0.74 = ( nat_1 @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_817_split__nat,axiom,
% 0.32/0.74 ! [P: nat > $o,I_1: int] :
% 0.32/0.74 ( ( P @ ( nat_1 @ I_1 ) )
% 0.32/0.74 <=> ( ! [N_1: nat] :
% 0.32/0.74 ( ( I_1
% 0.32/0.74 = ( semiri1621563631at_int @ N_1 ) )
% 0.32/0.74 => ( P @ N_1 ) )
% 0.32/0.74 & ( ( ord_less_int @ I_1 @ zero_zero_int )
% 0.32/0.74 => ( P @ zero_zero_nat ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_818_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 0.32/0.74 ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_819_le__imp__0__less,axiom,
% 0.32/0.74 ! [Z: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.74 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_820_zmult__zless__mono2__lemma,axiom,
% 0.32/0.74 ! [K: nat,I_1: int,J: int] :
% 0.32/0.74 ( ( ord_less_int @ I_1 @ J )
% 0.32/0.74 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.74 => ( ord_less_int @ ( times_times_int @ ( semiri1621563631at_int @ K ) @ I_1 ) @ ( times_times_int @ ( semiri1621563631at_int @ K ) @ J ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_821_add__Bit1__Bit1,axiom,
% 0.32/0.74 ! [K: int,L: int] :
% 0.32/0.74 ( ( plus_plus_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
% 0.32/0.74 = ( bit0 @ ( plus_plus_int @ K @ ( succ @ L ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_822_transfer__nat__int__numerals_I3_J,axiom,
% 0.32/0.74 ( ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) )
% 0.32/0.74 = ( nat_1 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_823_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 0.32/0.74 ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_824_cube__square,axiom,
% 0.32/0.74 ! [A: int] :
% 0.32/0.74 ( ( times_times_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.32/0.74 = ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_825_power2__ge__self,axiom,
% 0.32/0.74 ! [X: int] : ( ord_less_eq_int @ X @ ( power_power_int @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_826_int__pos__lt__two__imp__zero__or__one,axiom,
% 0.32/0.74 ! [X: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.74 => ( ( ord_less_int @ X @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.74 => ( ( X = zero_zero_int )
% 0.32/0.74 | ( X = one_one_int ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_827_Euler_Oaux__1,axiom,
% 0.32/0.74 ! [A: int,P_1: int] :
% 0.32/0.74 ( ( ord_less_int @ zero_zero_int @ P_1 )
% 0.32/0.74 => ( ( power_power_int @ A @ ( nat_1 @ P_1 ) )
% 0.32/0.74 = ( times_times_int @ A @ ( power_power_int @ A @ ( minus_minus_nat @ ( nat_1 @ P_1 ) @ one_one_nat ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_828_self__quotient__aux2,axiom,
% 0.32/0.74 ! [R_1: int,Q: int,A: int] :
% 0.32/0.74 ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.74 => ( ( A
% 0.32/0.74 = ( plus_plus_int @ R_1 @ ( times_times_int @ A @ Q ) ) )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ R_1 )
% 0.32/0.74 => ( ord_less_eq_int @ Q @ one_one_int ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_829_self__quotient__aux1,axiom,
% 0.32/0.74 ! [R_1: int,Q: int,A: int] :
% 0.32/0.74 ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.74 => ( ( A
% 0.32/0.74 = ( plus_plus_int @ R_1 @ ( times_times_int @ A @ Q ) ) )
% 0.32/0.74 => ( ( ord_less_int @ R_1 @ A )
% 0.32/0.74 => ( ord_less_eq_int @ one_one_int @ Q ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_830_smaller_I2_J,axiom,
% 0.32/0.74 ~ ( ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
% 0.32/0.74 => ~ ( twoSqu919416604sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_831_q__pos__lemma,axiom,
% 0.32/0.74 ! [B_1: int,Q_1: int,R_2: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B_1 @ Q_1 ) @ R_2 ) )
% 0.32/0.74 => ( ( ord_less_int @ R_2 @ B_1 )
% 0.32/0.74 => ( ( ord_less_int @ zero_zero_int @ B_1 )
% 0.32/0.74 => ( ord_less_eq_int @ zero_zero_int @ Q_1 ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_832_q__neg__lemma,axiom,
% 0.32/0.74 ! [B_1: int,Q_1: int,R_2: int] :
% 0.32/0.74 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B_1 @ Q_1 ) @ R_2 ) @ zero_zero_int )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ R_2 )
% 0.32/0.74 => ( ( ord_less_int @ zero_zero_int @ B_1 )
% 0.32/0.74 => ( ord_less_eq_int @ Q_1 @ zero_zero_int ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_833_nQ1,axiom,
% 0.32/0.74 ~ ( twoSqu919416604sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ zero_zero_nat ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_834_le0,axiom,
% 0.32/0.74 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_835_p0,axiom,
% 0.32/0.74 ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_836_t__l__p,axiom,
% 0.32/0.74 ord_less_int @ t @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_837_qf1pt,axiom,
% 0.32/0.74 twoSqu919416604sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_838_IH,axiom,
% 0.32/0.74 ( ( ord_less_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
% 0.32/0.74 & ( twoSqu919416604sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_839__096_B_Bthesis_O_A_I_B_Bx_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_061_A_I4_A,axiom,
% 0.32/0.74 ~ ! [X_1: int,Y_1: int] :
% 0.32/0.74 ( ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.32/0.74 != ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_840_t,axiom,
% 0.32/0.74 ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
% 0.32/0.74 = ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_841_p,axiom,
% 0.32/0.74 zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_842__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_,axiom,
% 0.32/0.74 ( ( t = one_one_int )
% 0.32/0.74 => ? [X_1: int,Y_1: int] :
% 0.32/0.74 ( ( plus_plus_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.32/0.74 = ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_843_le__refl,axiom,
% 0.32/0.74 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_844_le__square,axiom,
% 0.32/0.74 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_845_le__cube,axiom,
% 0.32/0.74 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_846_nat__mult__commute,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( times_times_nat @ M @ N )
% 0.32/0.74 = ( times_times_nat @ N @ M ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_847_nat__le__linear,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.74 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_848_nat__mult__assoc,axiom,
% 0.32/0.74 ! [M: nat,N: nat,K: nat] :
% 0.32/0.74 ( ( times_times_nat @ ( times_times_nat @ M @ N ) @ K )
% 0.32/0.74 = ( times_times_nat @ M @ ( times_times_nat @ N @ K ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_849_eq__imp__le,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( M = N )
% 0.32/0.74 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_850_mult__le__mono1,axiom,
% 0.32/0.74 ! [K: nat,I_1: nat,J: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.32/0.74 => ( ord_less_eq_nat @ ( times_times_nat @ I_1 @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_851_mult__le__mono2,axiom,
% 0.32/0.74 ! [K: nat,I_1: nat,J: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.32/0.74 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I_1 ) @ ( times_times_nat @ K @ J ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_852_le__trans,axiom,
% 0.32/0.74 ! [K: nat,I_1: nat,J: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.32/0.74 => ( ( ord_less_eq_nat @ J @ K )
% 0.32/0.74 => ( ord_less_eq_nat @ I_1 @ K ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_853_le__antisym,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.74 => ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.74 => ( M = N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_854_mult__le__mono,axiom,
% 0.32/0.74 ! [K: nat,L: nat,I_1: nat,J: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.32/0.74 => ( ( ord_less_eq_nat @ K @ L )
% 0.32/0.74 => ( ord_less_eq_nat @ ( times_times_nat @ I_1 @ K ) @ ( times_times_nat @ J @ L ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_855_real__le__eq__diff,axiom,
% 0.32/0.74 ! [X: real,Y: real] :
% 0.32/0.74 ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.74 <=> ( ord_less_eq_real @ ( minus_minus_real @ X @ Y ) @ zero_zero_real ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_856_mult__le__cancel2,axiom,
% 0.32/0.74 ! [M: nat,K: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.32/0.74 <=> ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.74 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_857_mult__le__cancel1,axiom,
% 0.32/0.74 ! [K: nat,M: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.32/0.74 <=> ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.74 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_858_real__mult__le__cancel__iff1,axiom,
% 0.32/0.74 ! [X: real,Y: real,Z: real] :
% 0.32/0.74 ( ( ord_less_real @ zero_zero_real @ Z )
% 0.32/0.74 => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 0.32/0.74 <=> ( ord_less_eq_real @ X @ Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_859_real__mult__le__cancel__iff2,axiom,
% 0.32/0.74 ! [X: real,Y: real,Z: real] :
% 0.32/0.74 ( ( ord_less_real @ zero_zero_real @ Z )
% 0.32/0.74 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) )
% 0.32/0.74 <=> ( ord_less_eq_real @ X @ Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_860_zdiff__int,axiom,
% 0.32/0.74 ! [N: nat,M: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.74 => ( ( minus_minus_int @ ( semiri1621563631at_int @ M ) @ ( semiri1621563631at_int @ N ) )
% 0.32/0.74 = ( semiri1621563631at_int @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_861_diff__bin__simps_I1_J,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( minus_minus_int @ K @ pls )
% 0.32/0.74 = K ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_862_diff__bin__simps_I7_J,axiom,
% 0.32/0.74 ! [K: int,L: int] :
% 0.32/0.74 ( ( minus_minus_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
% 0.32/0.74 = ( bit0 @ ( minus_minus_int @ K @ L ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_863_zdiff__zmult__distrib,axiom,
% 0.32/0.74 ! [Z1: int,Z2: int,W: int] :
% 0.32/0.74 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z2 ) @ W )
% 0.32/0.74 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z2 @ W ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_864_zdiff__zmult__distrib2,axiom,
% 0.32/0.74 ! [W: int,Z1: int,Z2: int] :
% 0.32/0.74 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z2 ) )
% 0.32/0.74 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z2 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_865_mult__0,axiom,
% 0.32/0.74 ! [N: nat] :
% 0.32/0.74 ( ( times_times_nat @ zero_zero_nat @ N )
% 0.32/0.74 = zero_zero_nat ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_866_mult__0__right,axiom,
% 0.32/0.74 ! [M: nat] :
% 0.32/0.74 ( ( times_times_nat @ M @ zero_zero_nat )
% 0.32/0.74 = zero_zero_nat ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_867_mult__is__0,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( ( times_times_nat @ M @ N )
% 0.32/0.74 = zero_zero_nat )
% 0.32/0.74 <=> ( ( M = zero_zero_nat )
% 0.32/0.74 | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_868_mult__cancel1,axiom,
% 0.32/0.74 ! [K: nat,M: nat,N: nat] :
% 0.32/0.74 ( ( ( times_times_nat @ K @ M )
% 0.32/0.74 = ( times_times_nat @ K @ N ) )
% 0.32/0.74 <=> ( ( M = N )
% 0.32/0.74 | ( K = zero_zero_nat ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_869_mult__cancel2,axiom,
% 0.32/0.74 ! [M: nat,K: nat,N: nat] :
% 0.32/0.74 ( ( ( times_times_nat @ M @ K )
% 0.32/0.74 = ( times_times_nat @ N @ K ) )
% 0.32/0.74 <=> ( ( M = N )
% 0.32/0.74 | ( K = zero_zero_nat ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_870_less__eq__nat_Osimps_I1_J,axiom,
% 0.32/0.74 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_871_le__0__eq,axiom,
% 0.32/0.74 ! [N: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.32/0.74 <=> ( N = zero_zero_nat ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_872_real__mult__left__cancel,axiom,
% 0.32/0.74 ! [A: real,B: real,C: real] :
% 0.32/0.74 ( ( C != zero_zero_real )
% 0.32/0.74 => ( ( ( times_times_real @ C @ A )
% 0.32/0.74 = ( times_times_real @ C @ B ) )
% 0.32/0.74 <=> ( A = B ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_873_real__mult__right__cancel,axiom,
% 0.32/0.74 ! [A: real,B: real,C: real] :
% 0.32/0.74 ( ( C != zero_zero_real )
% 0.32/0.74 => ( ( ( times_times_real @ A @ C )
% 0.32/0.74 = ( times_times_real @ B @ C ) )
% 0.32/0.74 <=> ( A = B ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_874_less__or__eq__imp__le,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( ( ord_less_nat @ M @ N )
% 0.32/0.74 | ( M = N ) )
% 0.32/0.74 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_875_le__neq__implies__less,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.74 => ( ( M != N )
% 0.32/0.74 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_876_less__imp__le__nat,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_nat @ M @ N )
% 0.32/0.74 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_877_le__eq__less__or__eq,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.74 <=> ( ( ord_less_nat @ M @ N )
% 0.32/0.74 | ( M = N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_878_nat__less__le,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_nat @ M @ N )
% 0.32/0.74 <=> ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.74 & ( M != N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_879_real__less__def,axiom,
% 0.32/0.74 ! [X: real,Y: real] :
% 0.32/0.74 ( ( ord_less_real @ X @ Y )
% 0.32/0.74 <=> ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.74 & ( X != Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_880_less__eq__real__def,axiom,
% 0.32/0.74 ! [X: real,Y: real] :
% 0.32/0.74 ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.74 <=> ( ( ord_less_real @ X @ Y )
% 0.32/0.74 | ( X = Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_881_add__mult__distrib,axiom,
% 0.32/0.74 ! [M: nat,N: nat,K: nat] :
% 0.32/0.74 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 0.32/0.74 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_882_add__mult__distrib2,axiom,
% 0.32/0.74 ! [K: nat,M: nat,N: nat] :
% 0.32/0.74 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 0.32/0.74 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_883_add__leE,axiom,
% 0.32/0.74 ! [M: nat,K: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.32/0.74 => ~ ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.74 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_884_add__leD1,axiom,
% 0.32/0.74 ! [M: nat,K: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.32/0.74 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_885_add__leD2,axiom,
% 0.32/0.74 ! [M: nat,K: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.32/0.74 => ( ord_less_eq_nat @ K @ N ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_886_add__le__mono,axiom,
% 0.32/0.74 ! [K: nat,L: nat,I_1: nat,J: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.32/0.74 => ( ( ord_less_eq_nat @ K @ L )
% 0.32/0.74 => ( ord_less_eq_nat @ ( plus_plus_nat @ I_1 @ K ) @ ( plus_plus_nat @ J @ L ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_887_add__le__mono1,axiom,
% 0.32/0.74 ! [K: nat,I_1: nat,J: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.32/0.74 => ( ord_less_eq_nat @ ( plus_plus_nat @ I_1 @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_888_trans__le__add2,axiom,
% 0.32/0.74 ! [M: nat,I_1: nat,J: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.32/0.74 => ( ord_less_eq_nat @ I_1 @ ( plus_plus_nat @ M @ J ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_889_trans__le__add1,axiom,
% 0.32/0.74 ! [M: nat,I_1: nat,J: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.32/0.74 => ( ord_less_eq_nat @ I_1 @ ( plus_plus_nat @ J @ M ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_890_nat__add__left__cancel__le,axiom,
% 0.32/0.74 ! [K: nat,M: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.32/0.74 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_891_le__iff__add,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.74 <=> ? [K_1: nat] :
% 0.32/0.74 ( N
% 0.32/0.74 = ( plus_plus_nat @ M @ K_1 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_892_le__add1,axiom,
% 0.32/0.74 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_893_le__add2,axiom,
% 0.32/0.74 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_894_nat__mult__eq__one,axiom,
% 0.32/0.74 ! [N: nat,M: nat] :
% 0.32/0.74 ( ( ( times_times_nat @ N @ M )
% 0.32/0.74 = one_one_nat )
% 0.32/0.74 <=> ( ( N = one_one_nat )
% 0.32/0.74 & ( M = one_one_nat ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_895_nat__mult__eq__1__iff,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( ( times_times_nat @ M @ N )
% 0.32/0.74 = one_one_nat )
% 0.32/0.74 <=> ( ( M = one_one_nat )
% 0.32/0.74 & ( N = one_one_nat ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_896_nat__mult__1__right,axiom,
% 0.32/0.74 ! [N: nat] :
% 0.32/0.74 ( ( times_times_nat @ N @ one_one_nat )
% 0.32/0.74 = N ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_897_nat__1__eq__mult__iff,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( one_one_nat
% 0.32/0.74 = ( times_times_nat @ M @ N ) )
% 0.32/0.74 <=> ( ( M = one_one_nat )
% 0.32/0.74 & ( N = one_one_nat ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_898_nat__mult__1,axiom,
% 0.32/0.74 ! [N: nat] :
% 0.32/0.74 ( ( times_times_nat @ one_one_nat @ N )
% 0.32/0.74 = N ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_899_diff__mult__distrib,axiom,
% 0.32/0.74 ! [M: nat,N: nat,K: nat] :
% 0.32/0.74 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 0.32/0.74 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_900_diff__mult__distrib2,axiom,
% 0.32/0.74 ! [K: nat,M: nat,N: nat] :
% 0.32/0.74 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.74 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_901_real__mult__1,axiom,
% 0.32/0.74 ! [Z: real] :
% 0.32/0.74 ( ( times_times_real @ one_one_real @ Z )
% 0.32/0.74 = Z ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_902_le__diff__iff,axiom,
% 0.32/0.74 ! [N: nat,K: nat,M: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ K @ M )
% 0.32/0.74 => ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.74 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.32/0.74 <=> ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_903_Nat_Odiff__diff__eq,axiom,
% 0.32/0.74 ! [N: nat,K: nat,M: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ K @ M )
% 0.32/0.74 => ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.74 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.32/0.74 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_904_eq__diff__iff,axiom,
% 0.32/0.74 ! [N: nat,K: nat,M: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ K @ M )
% 0.32/0.74 => ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.74 => ( ( ( minus_minus_nat @ M @ K )
% 0.32/0.74 = ( minus_minus_nat @ N @ K ) )
% 0.32/0.74 <=> ( M = N ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_905_diff__diff__cancel,axiom,
% 0.32/0.74 ! [I_1: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ I_1 @ N )
% 0.32/0.74 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I_1 ) )
% 0.32/0.74 = I_1 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_906_diff__le__mono,axiom,
% 0.32/0.74 ! [L: nat,M: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.74 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_907_diff__le__mono2,axiom,
% 0.32/0.74 ! [L: nat,M: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.74 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_908_Nat_Odiff__le__self,axiom,
% 0.32/0.74 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_909_real__add__mult__distrib,axiom,
% 0.32/0.74 ! [Z1: real,Z2: real,W: real] :
% 0.32/0.74 ( ( times_times_real @ ( plus_plus_real @ Z1 @ Z2 ) @ W )
% 0.32/0.74 = ( plus_plus_real @ ( times_times_real @ Z1 @ W ) @ ( times_times_real @ Z2 @ W ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_910_zpower__zpower,axiom,
% 0.32/0.74 ! [X: int,Y: nat,Z: nat] :
% 0.32/0.74 ( ( power_power_int @ ( power_power_int @ X @ Y ) @ Z )
% 0.32/0.74 = ( power_power_int @ X @ ( times_times_nat @ Y @ Z ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_911_real__add__left__mono,axiom,
% 0.32/0.74 ! [Z: real,X: real,Y: real] :
% 0.32/0.74 ( ( ord_less_eq_real @ X @ Y )
% 0.32/0.74 => ( ord_less_eq_real @ ( plus_plus_real @ Z @ X ) @ ( plus_plus_real @ Z @ Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_912_diff__bin__simps_I10_J,axiom,
% 0.32/0.74 ! [K: int,L: int] :
% 0.32/0.74 ( ( minus_minus_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
% 0.32/0.74 = ( bit0 @ ( minus_minus_int @ K @ L ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_913_diff__bin__simps_I9_J,axiom,
% 0.32/0.74 ! [K: int,L: int] :
% 0.32/0.74 ( ( minus_minus_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
% 0.32/0.74 = ( bit1 @ ( minus_minus_int @ K @ L ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_914_diff__bin__simps_I3_J,axiom,
% 0.32/0.74 ! [L: int] :
% 0.32/0.74 ( ( minus_minus_int @ pls @ ( bit0 @ L ) )
% 0.32/0.74 = ( bit0 @ ( minus_minus_int @ pls @ L ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_915_Euler_Oaux1,axiom,
% 0.32/0.74 ! [A: int,X: int] :
% 0.32/0.74 ( ( ord_less_int @ zero_zero_int @ X )
% 0.32/0.74 => ( ( ord_less_int @ X @ A )
% 0.32/0.74 => ( ( X
% 0.32/0.74 != ( minus_minus_int @ A @ one_one_int ) )
% 0.32/0.74 => ( ord_less_int @ X @ ( minus_minus_int @ A @ one_one_int ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_916_less__bin__lemma,axiom,
% 0.32/0.74 ! [K: int,L: int] :
% 0.32/0.74 ( ( ord_less_int @ K @ L )
% 0.32/0.74 <=> ( ord_less_int @ ( minus_minus_int @ K @ L ) @ zero_zero_int ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_917_mult__less__mono2,axiom,
% 0.32/0.74 ! [K: nat,I_1: nat,J: nat] :
% 0.32/0.74 ( ( ord_less_nat @ I_1 @ J )
% 0.32/0.74 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.74 => ( ord_less_nat @ ( times_times_nat @ K @ I_1 ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_918_mult__less__mono1,axiom,
% 0.32/0.74 ! [K: nat,I_1: nat,J: nat] :
% 0.32/0.74 ( ( ord_less_nat @ I_1 @ J )
% 0.32/0.74 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.74 => ( ord_less_nat @ ( times_times_nat @ I_1 @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_919_mult__less__cancel2,axiom,
% 0.32/0.74 ! [M: nat,K: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.32/0.74 <=> ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.74 & ( ord_less_nat @ M @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_920_mult__less__cancel1,axiom,
% 0.32/0.74 ! [K: nat,M: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.32/0.74 <=> ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.74 & ( ord_less_nat @ M @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_921_nat__0__less__mult__iff,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 0.32/0.74 <=> ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.74 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_922_not__real__square__gt__zero,axiom,
% 0.32/0.74 ! [X: real] :
% 0.32/0.74 ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) )
% 0.32/0.74 <=> ( X = zero_zero_real ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_923_real__mult__less__mono2,axiom,
% 0.32/0.74 ! [X: real,Y: real,Z: real] :
% 0.32/0.74 ( ( ord_less_real @ zero_zero_real @ Z )
% 0.32/0.74 => ( ( ord_less_real @ X @ Y )
% 0.32/0.74 => ( ord_less_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_924_real__mult__order,axiom,
% 0.32/0.74 ! [Y: real,X: real] :
% 0.32/0.74 ( ( ord_less_real @ zero_zero_real @ X )
% 0.32/0.74 => ( ( ord_less_real @ zero_zero_real @ Y )
% 0.32/0.74 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ Y ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_925_real__mult__less__iff1,axiom,
% 0.32/0.74 ! [X: real,Y: real,Z: real] :
% 0.32/0.74 ( ( ord_less_real @ zero_zero_real @ Z )
% 0.32/0.74 => ( ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 0.32/0.74 <=> ( ord_less_real @ X @ Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_926_mult__eq__self__implies__10,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( M
% 0.32/0.74 = ( times_times_nat @ M @ N ) )
% 0.32/0.74 => ( ( N = one_one_nat )
% 0.32/0.74 | ( M = zero_zero_nat ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_927_diff__is__0__eq,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( ( minus_minus_nat @ M @ N )
% 0.32/0.74 = zero_zero_nat )
% 0.32/0.74 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_928_diff__is__0__eq_H,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ M @ N )
% 0.32/0.74 => ( ( minus_minus_nat @ M @ N )
% 0.32/0.74 = zero_zero_nat ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_929_real__two__squares__add__zero__iff,axiom,
% 0.32/0.74 ! [X: real,Y: real] :
% 0.32/0.74 ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 0.32/0.74 = zero_zero_real )
% 0.32/0.74 <=> ( ( X = zero_zero_real )
% 0.32/0.74 & ( Y = zero_zero_real ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_930_diff__less__mono,axiom,
% 0.32/0.74 ! [C: nat,A: nat,B: nat] :
% 0.32/0.74 ( ( ord_less_nat @ A @ B )
% 0.32/0.74 => ( ( ord_less_eq_nat @ C @ A )
% 0.32/0.74 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_931_less__diff__iff,axiom,
% 0.32/0.74 ! [N: nat,K: nat,M: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ K @ M )
% 0.32/0.74 => ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.74 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.32/0.74 <=> ( ord_less_nat @ M @ N ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_932_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( times_times_int @ ( semiri1621563631at_int @ X ) @ ( semiri1621563631at_int @ Y ) )
% 0.32/0.74 = ( semiri1621563631at_int @ ( times_times_nat @ X @ Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_933_zmult__int,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( times_times_int @ ( semiri1621563631at_int @ M ) @ ( semiri1621563631at_int @ N ) )
% 0.32/0.74 = ( semiri1621563631at_int @ ( times_times_nat @ M @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_934_int__mult,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( semiri1621563631at_int @ ( times_times_nat @ M @ N ) )
% 0.32/0.74 = ( times_times_int @ ( semiri1621563631at_int @ M ) @ ( semiri1621563631at_int @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_935_diff__diff__right,axiom,
% 0.32/0.74 ! [I_1: nat,K: nat,J: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ K @ J )
% 0.32/0.74 => ( ( minus_minus_nat @ I_1 @ ( minus_minus_nat @ J @ K ) )
% 0.32/0.74 = ( minus_minus_nat @ ( plus_plus_nat @ I_1 @ K ) @ J ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_936_le__diff__conv,axiom,
% 0.32/0.74 ! [J: nat,K: nat,I_1: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I_1 )
% 0.32/0.74 <=> ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I_1 @ K ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_937_le__add__diff,axiom,
% 0.32/0.74 ! [M: nat,K: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ K @ N )
% 0.32/0.74 => ( ord_less_eq_nat @ M @ ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ K ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_938_le__add__diff__inverse,axiom,
% 0.32/0.74 ! [N: nat,M: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.74 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.74 = M ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_939_add__diff__assoc,axiom,
% 0.32/0.74 ! [I_1: nat,K: nat,J: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ K @ J )
% 0.32/0.74 => ( ( plus_plus_nat @ I_1 @ ( minus_minus_nat @ J @ K ) )
% 0.32/0.74 = ( minus_minus_nat @ ( plus_plus_nat @ I_1 @ J ) @ K ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_940_le__diff__conv2,axiom,
% 0.32/0.74 ! [I_1: nat,K: nat,J: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ K @ J )
% 0.32/0.74 => ( ( ord_less_eq_nat @ I_1 @ ( minus_minus_nat @ J @ K ) )
% 0.32/0.74 <=> ( ord_less_eq_nat @ ( plus_plus_nat @ I_1 @ K ) @ J ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_941_le__add__diff__inverse2,axiom,
% 0.32/0.74 ! [N: nat,M: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.74 => ( ( plus_plus_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 0.32/0.74 = M ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_942_le__imp__diff__is__add,axiom,
% 0.32/0.74 ! [K: nat,I_1: nat,J: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.32/0.74 => ( ( ( minus_minus_nat @ J @ I_1 )
% 0.32/0.74 = K )
% 0.32/0.74 <=> ( J
% 0.32/0.74 = ( plus_plus_nat @ K @ I_1 ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_943_diff__add__assoc,axiom,
% 0.32/0.74 ! [I_1: nat,K: nat,J: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ K @ J )
% 0.32/0.74 => ( ( minus_minus_nat @ ( plus_plus_nat @ I_1 @ J ) @ K )
% 0.32/0.74 = ( plus_plus_nat @ I_1 @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_944_add__diff__assoc2,axiom,
% 0.32/0.74 ! [I_1: nat,K: nat,J: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ K @ J )
% 0.32/0.74 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I_1 )
% 0.32/0.74 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I_1 ) @ K ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_945_diff__add__assoc2,axiom,
% 0.32/0.74 ! [I_1: nat,K: nat,J: nat] :
% 0.32/0.74 ( ( ord_less_eq_nat @ K @ J )
% 0.32/0.74 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I_1 ) @ K )
% 0.32/0.74 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I_1 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_946_Nat__Transfer_Otransfer__int__nat__relations_I3_J,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( semiri1621563631at_int @ X ) @ ( semiri1621563631at_int @ Y ) )
% 0.32/0.74 <=> ( ord_less_eq_nat @ X @ Y ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_947_zle__int,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( semiri1621563631at_int @ M ) @ ( semiri1621563631at_int @ N ) )
% 0.32/0.74 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_948_is__mult__sum2sq,axiom,
% 0.32/0.74 ! [Y: int,X: int] :
% 0.32/0.74 ( ( twoSqu919416604sum2sq @ X )
% 0.32/0.74 => ( ( twoSqu919416604sum2sq @ Y )
% 0.32/0.74 => ( twoSqu919416604sum2sq @ ( times_times_int @ X @ Y ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_949_zle__diff1__eq,axiom,
% 0.32/0.74 ! [W: int,Z: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 0.32/0.74 <=> ( ord_less_int @ W @ Z ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_950_le__nat__number__of,axiom,
% 0.32/0.74 ! [V_1: int,V_2: int] :
% 0.32/0.74 ( ( ord_less_eq_nat @ ( number_number_of_nat @ V_1 ) @ ( number_number_of_nat @ V_2 ) )
% 0.32/0.74 <=> ( ~ ( ord_less_eq_int @ V_1 @ V_2 )
% 0.32/0.74 => ( ord_less_eq_int @ V_1 @ pls ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_951_transfer__nat__int__relations_I3_J,axiom,
% 0.32/0.74 ! [Y: int,X: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.74 => ( ( ord_less_eq_nat @ ( nat_1 @ X ) @ ( nat_1 @ Y ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ X @ Y ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_952_nat__diff__distrib,axiom,
% 0.32/0.74 ! [Z: int,Z_1: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ Z_1 )
% 0.32/0.74 => ( ( ord_less_eq_int @ Z_1 @ Z )
% 0.32/0.74 => ( ( nat_1 @ ( minus_minus_int @ Z @ Z_1 ) )
% 0.32/0.74 = ( minus_minus_nat @ ( nat_1 @ Z ) @ ( nat_1 @ Z_1 ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_953_nat__mult__distrib,axiom,
% 0.32/0.74 ! [Z_1: int,Z: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.74 => ( ( nat_1 @ ( times_times_int @ Z @ Z_1 ) )
% 0.32/0.74 = ( times_times_nat @ ( nat_1 @ Z ) @ ( nat_1 @ Z_1 ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_954_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom,
% 0.32/0.74 ! [Y: int,X: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.74 => ( ( times_times_nat @ ( nat_1 @ X ) @ ( nat_1 @ Y ) )
% 0.32/0.74 = ( nat_1 @ ( times_times_int @ X @ Y ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_955_mult__eq__if,axiom,
% 0.32/0.74 ! [N: nat,M: nat] :
% 0.32/0.74 ( ( ( M = zero_zero_nat )
% 0.32/0.74 => ( ( times_times_nat @ M @ N )
% 0.32/0.74 = zero_zero_nat ) )
% 0.32/0.74 & ( ( M != zero_zero_nat )
% 0.32/0.74 => ( ( times_times_nat @ M @ N )
% 0.32/0.74 = ( plus_plus_nat @ N @ ( times_times_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_956_nat__le__eq__zle,axiom,
% 0.32/0.74 ! [Z: int,W: int] :
% 0.32/0.74 ( ( ( ord_less_int @ zero_zero_int @ W )
% 0.32/0.74 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 0.32/0.74 => ( ( ord_less_eq_nat @ ( nat_1 @ W ) @ ( nat_1 @ Z ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ W @ Z ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_957_power__eq__if,axiom,
% 0.32/0.74 ! [P_1: nat,M: nat] :
% 0.32/0.74 ( ( ( M = zero_zero_nat )
% 0.32/0.74 => ( ( power_power_nat @ P_1 @ M )
% 0.32/0.74 = one_one_nat ) )
% 0.32/0.74 & ( ( M != zero_zero_nat )
% 0.32/0.74 => ( ( power_power_nat @ P_1 @ M )
% 0.32/0.74 = ( times_times_nat @ P_1 @ ( power_power_nat @ P_1 @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_958_nat__mult__2,axiom,
% 0.32/0.74 ! [Z: nat] :
% 0.32/0.74 ( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z )
% 0.32/0.74 = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_959_nat__mult__2__right,axiom,
% 0.32/0.74 ! [Z: nat] :
% 0.32/0.74 ( ( times_times_nat @ Z @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.74 = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_960_nat__number__of__mult__left,axiom,
% 0.32/0.74 ! [V_2: int,K: nat,V_1: int] :
% 0.32/0.74 ( ( ( ord_less_int @ V_1 @ pls )
% 0.32/0.74 => ( ( times_times_nat @ ( number_number_of_nat @ V_1 ) @ ( times_times_nat @ ( number_number_of_nat @ V_2 ) @ K ) )
% 0.32/0.74 = zero_zero_nat ) )
% 0.32/0.74 & ( ~ ( ord_less_int @ V_1 @ pls )
% 0.32/0.74 => ( ( times_times_nat @ ( number_number_of_nat @ V_1 ) @ ( times_times_nat @ ( number_number_of_nat @ V_2 ) @ K ) )
% 0.32/0.74 = ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ V_1 @ V_2 ) ) @ K ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_961_mult__nat__number__of,axiom,
% 0.32/0.74 ! [V_2: int,V_1: int] :
% 0.32/0.74 ( ( ( ord_less_int @ V_1 @ pls )
% 0.32/0.74 => ( ( times_times_nat @ ( number_number_of_nat @ V_1 ) @ ( number_number_of_nat @ V_2 ) )
% 0.32/0.74 = zero_zero_nat ) )
% 0.32/0.74 & ( ~ ( ord_less_int @ V_1 @ pls )
% 0.32/0.74 => ( ( times_times_nat @ ( number_number_of_nat @ V_1 ) @ ( number_number_of_nat @ V_2 ) )
% 0.32/0.74 = ( number_number_of_nat @ ( times_times_int @ V_1 @ V_2 ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_962_four__x__squared,axiom,
% 0.32/0.74 ! [X: real] :
% 0.32/0.74 ( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.32/0.74 = ( power_power_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_963_two__realpow__ge__one,axiom,
% 0.32/0.74 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_964_Euler_Oaux2,axiom,
% 0.32/0.74 ! [B: int,A: int,C: int] :
% 0.32/0.74 ( ( ord_less_int @ A @ C )
% 0.32/0.74 => ( ( ord_less_int @ B @ C )
% 0.32/0.74 => ( ( ord_less_eq_int @ A @ B )
% 0.32/0.74 | ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_965_zspecial__product,axiom,
% 0.32/0.74 ! [A: int,B: int] :
% 0.32/0.74 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( minus_minus_int @ A @ B ) )
% 0.32/0.74 = ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_966_diff__square,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( minus_minus_nat @ ( power_power_nat @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.32/0.74 = ( times_times_nat @ ( plus_plus_nat @ X @ Y ) @ ( minus_minus_nat @ X @ Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_967_zdiff__power3,axiom,
% 0.32/0.74 ! [A: int,B: int] :
% 0.32/0.74 ( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
% 0.32/0.74 = ( minus_minus_int @ ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ B ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) @ A ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_968_zdiff__power2,axiom,
% 0.32/0.74 ! [A: int,B: int] :
% 0.32/0.74 ( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.74 = ( plus_plus_int @ ( minus_minus_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) @ B ) ) @ ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_969_zdiv__mono2__neg__lemma,axiom,
% 0.32/0.74 ! [B: int,Q: int,R_1: int,B_1: int,Q_1: int,R_2: int] :
% 0.32/0.74 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R_1 )
% 0.32/0.74 = ( plus_plus_int @ ( times_times_int @ B_1 @ Q_1 ) @ R_2 ) )
% 0.32/0.74 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B_1 @ Q_1 ) @ R_2 ) @ zero_zero_int )
% 0.32/0.74 => ( ( ord_less_int @ R_1 @ B )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ R_2 )
% 0.32/0.74 => ( ( ord_less_int @ zero_zero_int @ B_1 )
% 0.32/0.74 => ( ( ord_less_eq_int @ B_1 @ B )
% 0.32/0.74 => ( ord_less_eq_int @ Q_1 @ Q ) ) ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_970_unique__quotient__lemma__neg,axiom,
% 0.32/0.74 ! [B: int,Q_1: int,R_2: int,Q: int,R_1: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q_1 ) @ R_2 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R_1 ) )
% 0.32/0.74 => ( ( ord_less_eq_int @ R_1 @ zero_zero_int )
% 0.32/0.74 => ( ( ord_less_int @ B @ R_1 )
% 0.32/0.74 => ( ( ord_less_int @ B @ R_2 )
% 0.32/0.74 => ( ord_less_eq_int @ Q @ Q_1 ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_971_zdiv__mono2__lemma,axiom,
% 0.32/0.74 ! [B: int,Q: int,R_1: int,B_1: int,Q_1: int,R_2: int] :
% 0.32/0.74 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R_1 )
% 0.32/0.74 = ( plus_plus_int @ ( times_times_int @ B_1 @ Q_1 ) @ R_2 ) )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B_1 @ Q_1 ) @ R_2 ) )
% 0.32/0.74 => ( ( ord_less_int @ R_2 @ B_1 )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ R_1 )
% 0.32/0.74 => ( ( ord_less_int @ zero_zero_int @ B_1 )
% 0.32/0.74 => ( ( ord_less_eq_int @ B_1 @ B )
% 0.32/0.74 => ( ord_less_eq_int @ Q @ Q_1 ) ) ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_972_unique__quotient__lemma,axiom,
% 0.32/0.74 ! [B: int,Q_1: int,R_2: int,Q: int,R_1: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q_1 ) @ R_2 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R_1 ) )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ R_2 )
% 0.32/0.74 => ( ( ord_less_int @ R_2 @ B )
% 0.32/0.74 => ( ( ord_less_int @ R_1 @ B )
% 0.32/0.74 => ( ord_less_eq_int @ Q_1 @ Q ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_973_xy,axiom,
% 0.32/0.74 ( ( 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 ) ) ) ) )
% 0.32/0.74 = ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_974_Int2_Oaux__1,axiom,
% 0.32/0.74 ! [P_1: int] :
% 0.32/0.74 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P_1 )
% 0.32/0.74 => ( ( minus_minus_nat @ ( nat_1 @ P_1 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.74 = ( nat_1 @ ( minus_minus_int @ P_1 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_975_Int2_Oaux__2,axiom,
% 0.32/0.74 ! [P_1: int] :
% 0.32/0.74 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P_1 )
% 0.32/0.74 => ( ord_less_nat @ zero_zero_nat @ ( nat_1 @ ( minus_minus_int @ P_1 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_976__096_B_Bthesis_O_A_I_B_Bt_O_As_____A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_,axiom,
% 0.32/0.74 ~ ! [T_1: int] :
% 0.32/0.74 ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
% 0.32/0.74 != ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ T_1 ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_977_real__le__refl,axiom,
% 0.32/0.74 ! [W: real] : ( ord_less_eq_real @ W @ W ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_978_real__mult__commute,axiom,
% 0.32/0.74 ! [Z: real,W: real] :
% 0.32/0.74 ( ( times_times_real @ Z @ W )
% 0.32/0.74 = ( times_times_real @ W @ Z ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_979_real__le__linear,axiom,
% 0.32/0.74 ! [Z: real,W: real] :
% 0.32/0.74 ( ( ord_less_eq_real @ Z @ W )
% 0.32/0.74 | ( ord_less_eq_real @ W @ Z ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_980_real__mult__assoc,axiom,
% 0.32/0.74 ! [Z1: real,Z2: real,Z3: real] :
% 0.32/0.74 ( ( times_times_real @ ( times_times_real @ Z1 @ Z2 ) @ Z3 )
% 0.32/0.74 = ( times_times_real @ Z1 @ ( times_times_real @ Z2 @ Z3 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_981_real__le__trans,axiom,
% 0.32/0.74 ! [K: real,I_1: real,J: real] :
% 0.32/0.74 ( ( ord_less_eq_real @ I_1 @ J )
% 0.32/0.74 => ( ( ord_less_eq_real @ J @ K )
% 0.32/0.74 => ( ord_less_eq_real @ I_1 @ K ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_982_real__le__antisym,axiom,
% 0.32/0.74 ! [Z: real,W: real] :
% 0.32/0.74 ( ( ord_less_eq_real @ Z @ W )
% 0.32/0.74 => ( ( ord_less_eq_real @ W @ Z )
% 0.32/0.74 => ( Z = W ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_983_zprime__2,axiom,
% 0.32/0.74 zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_984_Int2_Oaux1,axiom,
% 0.32/0.74 ! [A: int,B: int,C: int] :
% 0.32/0.74 ( ( ( minus_minus_int @ A @ B )
% 0.32/0.74 = C )
% 0.32/0.74 => ( A
% 0.32/0.74 = ( plus_plus_int @ C @ B ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_985__0964_A_K_Am_A_L_A1_Advd_As_____A_094_A2_A_L_A1_096,axiom,
% 0.32/0.74 dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_986_real__sum__squared__expand,axiom,
% 0.32/0.74 ! [X: real,Y: real] :
% 0.32/0.74 ( ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.74 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X ) @ Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_987__096s_____A_094_A2_A_N_A_N1_A_061_As_____A_094_A2_A_L_A1_096,axiom,
% 0.32/0.74 ( ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) )
% 0.32/0.74 = ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_988__0964_A_K_Am_A_L_A1_Advd_As_____A_094_A2_A_N_A_N1_096,axiom,
% 0.32/0.74 dvd_dvd_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_989__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096,axiom,
% 0.32/0.74 ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
% 0.32/0.74 = one_one_int ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_990_zdvd__zdiffD,axiom,
% 0.32/0.74 ! [K: int,M: int,N: int] :
% 0.32/0.74 ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
% 0.32/0.74 => ( ( dvd_dvd_int @ K @ N )
% 0.32/0.74 => ( dvd_dvd_int @ K @ M ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_991_zprime__zdvd__zmult__better,axiom,
% 0.32/0.74 ! [M: int,N: int,P_1: int] :
% 0.32/0.74 ( ( zprime @ P_1 )
% 0.32/0.74 => ( ( dvd_dvd_int @ P_1 @ ( times_times_int @ M @ N ) )
% 0.32/0.74 => ( ( dvd_dvd_int @ P_1 @ M )
% 0.32/0.74 | ( dvd_dvd_int @ P_1 @ N ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_992_rel__simps_I24_J,axiom,
% 0.32/0.74 ord_less_eq_int @ min @ min ).
% 0.32/0.74
% 0.32/0.74 thf(fact_993_zdvd__bounds,axiom,
% 0.32/0.74 ! [N: int,M: int] :
% 0.32/0.74 ( ( dvd_dvd_int @ N @ M )
% 0.32/0.74 => ( ( ord_less_eq_int @ M @ zero_zero_int )
% 0.32/0.74 | ( ord_less_eq_int @ N @ M ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_994_zprime__zdvd__power,axiom,
% 0.32/0.74 ! [A: int,N: nat,P_1: int] :
% 0.32/0.74 ( ( zprime @ P_1 )
% 0.32/0.74 => ( ( dvd_dvd_int @ P_1 @ ( power_power_int @ A @ N ) )
% 0.32/0.74 => ( dvd_dvd_int @ P_1 @ A ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_995_zdvd__not__zless,axiom,
% 0.32/0.74 ! [N: int,M: int] :
% 0.32/0.74 ( ( ord_less_int @ zero_zero_int @ M )
% 0.32/0.74 => ( ( ord_less_int @ M @ N )
% 0.32/0.74 => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_996_zdvd__mult__cancel,axiom,
% 0.32/0.74 ! [K: int,M: int,N: int] :
% 0.32/0.74 ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 0.32/0.74 => ( ( K != zero_zero_int )
% 0.32/0.74 => ( dvd_dvd_int @ M @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_997_zdvd__antisym__nonneg,axiom,
% 0.32/0.74 ! [N: int,M: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 0.32/0.74 => ( ( dvd_dvd_int @ M @ N )
% 0.32/0.74 => ( ( dvd_dvd_int @ N @ M )
% 0.32/0.74 => ( M = N ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_998_zdvd__reduce,axiom,
% 0.32/0.74 ! [K: int,N: int,M: int] :
% 0.32/0.74 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 0.32/0.74 <=> ( dvd_dvd_int @ K @ N ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_999_zdvd__period,axiom,
% 0.32/0.74 ! [C: int,X: int,T: int,A: int,D: int] :
% 0.32/0.74 ( ( dvd_dvd_int @ A @ D )
% 0.32/0.74 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
% 0.32/0.74 <=> ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1000_rel__simps_I9_J,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( ord_less_int @ min @ ( bit1 @ K ) )
% 0.32/0.74 <=> ( ord_less_int @ min @ K ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1001_rel__simps_I13_J,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( ord_less_int @ ( bit1 @ K ) @ min )
% 0.32/0.74 <=> ( ord_less_int @ K @ min ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1002_rel__simps_I6_J,axiom,
% 0.32/0.74 ord_less_int @ min @ pls ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1003_rel__simps_I3_J,axiom,
% 0.32/0.74 ~ ( ord_less_int @ pls @ min ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1004_rel__simps_I8_J,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( ord_less_int @ min @ ( bit0 @ K ) )
% 0.32/0.74 <=> ( ord_less_int @ min @ K ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1005_rel__simps_I26_J,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ min @ ( bit1 @ K ) )
% 0.32/0.74 <=> ( ord_less_eq_int @ min @ K ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1006_rel__simps_I30_J,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( bit1 @ K ) @ min )
% 0.32/0.74 <=> ( ord_less_eq_int @ K @ min ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1007_bin__less__0__simps_I2_J,axiom,
% 0.32/0.74 ord_less_int @ min @ zero_zero_int ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1008_rel__simps_I23_J,axiom,
% 0.32/0.74 ord_less_eq_int @ min @ pls ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1009_rel__simps_I20_J,axiom,
% 0.32/0.74 ~ ( ord_less_eq_int @ pls @ min ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1010_rel__simps_I28_J,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ ( bit0 @ K ) @ min )
% 0.32/0.74 <=> ( ord_less_eq_int @ K @ min ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1011_eq__number__of__Pls__Min,axiom,
% 0.32/0.74 ( ( number_number_of_int @ pls )
% 0.32/0.74 != ( number_number_of_int @ min ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1012_rel__simps_I7_J,axiom,
% 0.32/0.74 ~ ( ord_less_int @ min @ min ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1013_rel__simps_I42_J,axiom,
% 0.32/0.74 ! [L: int] :
% 0.32/0.74 ( min
% 0.32/0.74 != ( bit0 @ L ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1014_rel__simps_I45_J,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( bit0 @ K )
% 0.32/0.74 != min ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1015_rel__simps_I40_J,axiom,
% 0.32/0.74 min != pls ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1016_rel__simps_I37_J,axiom,
% 0.32/0.74 pls != min ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1017_Bit1__Min,axiom,
% 0.32/0.74 ( ( bit1 @ min )
% 0.32/0.74 = min ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1018_rel__simps_I43_J,axiom,
% 0.32/0.74 ! [L: int] :
% 0.32/0.74 ( ( min
% 0.32/0.74 = ( bit1 @ L ) )
% 0.32/0.74 <=> ( min = L ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1019_rel__simps_I47_J,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( ( bit1 @ K )
% 0.32/0.74 = min )
% 0.32/0.74 <=> ( K = min ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1020_succ__Min,axiom,
% 0.32/0.74 ( ( succ @ min )
% 0.32/0.74 = pls ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1021_diff__bin__simps_I2_J,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( minus_minus_int @ K @ min )
% 0.32/0.74 = ( succ @ K ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1022_zdvd__imp__le,axiom,
% 0.32/0.74 ! [Z: int,N: int] :
% 0.32/0.74 ( ( dvd_dvd_int @ Z @ N )
% 0.32/0.74 => ( ( ord_less_int @ zero_zero_int @ N )
% 0.32/0.74 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1023_zpower__zdvd__prop1,axiom,
% 0.32/0.74 ! [P_1: int,Y: int,N: nat] :
% 0.32/0.74 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.74 => ( ( dvd_dvd_int @ P_1 @ Y )
% 0.32/0.74 => ( dvd_dvd_int @ P_1 @ ( power_power_int @ Y @ N ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1024_rel__simps_I25_J,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ min @ ( bit0 @ K ) )
% 0.32/0.74 <=> ( ord_less_int @ min @ K ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1025_rel__simps_I11_J,axiom,
% 0.32/0.74 ! [K: int] :
% 0.32/0.74 ( ( ord_less_int @ ( bit0 @ K ) @ min )
% 0.32/0.74 <=> ( ord_less_eq_int @ K @ min ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1026_diff__bin__simps_I4_J,axiom,
% 0.32/0.74 ! [L: int] :
% 0.32/0.74 ( ( minus_minus_int @ pls @ ( bit1 @ L ) )
% 0.32/0.74 = ( bit1 @ ( minus_minus_int @ min @ L ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1027_diff__bin__simps_I6_J,axiom,
% 0.32/0.74 ! [L: int] :
% 0.32/0.74 ( ( minus_minus_int @ min @ ( bit1 @ L ) )
% 0.32/0.74 = ( bit0 @ ( minus_minus_int @ min @ L ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1028_diff__bin__simps_I5_J,axiom,
% 0.32/0.74 ! [L: int] :
% 0.32/0.74 ( ( minus_minus_int @ min @ ( bit0 @ L ) )
% 0.32/0.74 = ( bit1 @ ( minus_minus_int @ min @ L ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1029_zmult__eq__1__iff,axiom,
% 0.32/0.74 ! [M: int,N: int] :
% 0.32/0.74 ( ( ( times_times_int @ M @ N )
% 0.32/0.74 = one_one_int )
% 0.32/0.74 <=> ( ( ( M = one_one_int )
% 0.32/0.74 & ( N = one_one_int ) )
% 0.32/0.74 | ( ( M
% 0.32/0.74 = ( number_number_of_int @ min ) )
% 0.32/0.74 & ( N
% 0.32/0.74 = ( number_number_of_int @ min ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1030_pos__zmult__eq__1__iff__lemma,axiom,
% 0.32/0.74 ! [M: int,N: int] :
% 0.32/0.74 ( ( ( times_times_int @ M @ N )
% 0.32/0.74 = one_one_int )
% 0.32/0.74 => ( ( M = one_one_int )
% 0.32/0.74 | ( M
% 0.32/0.74 = ( number_number_of_int @ min ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1031_zprime__power__zdvd__cancel__right,axiom,
% 0.32/0.74 ! [N: nat,A: int,B: int,P_1: int] :
% 0.32/0.74 ( ( zprime @ P_1 )
% 0.32/0.74 => ( ~ ( dvd_dvd_int @ P_1 @ B )
% 0.32/0.74 => ( ( dvd_dvd_int @ ( power_power_int @ P_1 @ N ) @ ( times_times_int @ A @ B ) )
% 0.32/0.74 => ( dvd_dvd_int @ ( power_power_int @ P_1 @ N ) @ A ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1032_zprime__power__zdvd__cancel__left,axiom,
% 0.32/0.74 ! [N: nat,B: int,A: int,P_1: int] :
% 0.32/0.74 ( ( zprime @ P_1 )
% 0.32/0.74 => ( ~ ( dvd_dvd_int @ P_1 @ A )
% 0.32/0.74 => ( ( dvd_dvd_int @ ( power_power_int @ P_1 @ N ) @ ( times_times_int @ A @ B ) )
% 0.32/0.74 => ( dvd_dvd_int @ ( power_power_int @ P_1 @ N ) @ B ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1033_zpower__zdvd__prop2,axiom,
% 0.32/0.74 ! [Y: int,N: nat,P_1: int] :
% 0.32/0.74 ( ( zprime @ P_1 )
% 0.32/0.74 => ( ( dvd_dvd_int @ P_1 @ ( power_power_int @ Y @ N ) )
% 0.32/0.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.74 => ( dvd_dvd_int @ P_1 @ Y ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1034__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096,axiom,
% 0.32/0.74 quadRes @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( number_number_of_int @ min ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1035_s,axiom,
% 0.32/0.74 zcong @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1036__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_,axiom,
% 0.32/0.74 ( ~ ( quadRes @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( number_number_of_int @ min ) )
% 0.32/0.74 => ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
% 0.32/0.74 != one_one_int ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1037_s1,axiom,
% 0.32/0.74 zcong @ ( power_power_int @ s1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1038_s0p,axiom,
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ s )
% 0.32/0.74 & ( ord_less_int @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
% 0.32/0.74 & ( zcong @ s1 @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1039__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4,axiom,
% 0.32/0.74 ~ ! [S1: int] :
% 0.32/0.74 ~ ( zcong @ ( power_power_int @ S1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1040_divides__mul__r,axiom,
% 0.32/0.74 ! [C: nat,A: nat,B: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.74 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1041_divides__mul__l,axiom,
% 0.32/0.74 ! [C: nat,A: nat,B: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.74 => ( dvd_dvd_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1042_dvd__diff__nat,axiom,
% 0.32/0.74 ! [N: nat,K: nat,M: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ K @ M )
% 0.32/0.74 => ( ( dvd_dvd_nat @ K @ N )
% 0.32/0.74 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1043_zcong__eq__zdvd__prop,axiom,
% 0.32/0.74 ! [X: int,P_1: int] :
% 0.32/0.74 ( ( zcong @ X @ zero_zero_int @ P_1 )
% 0.32/0.74 <=> ( dvd_dvd_int @ P_1 @ X ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1044_zcong__zero__equiv__div,axiom,
% 0.32/0.74 ! [A: int,M: int] :
% 0.32/0.74 ( ( zcong @ A @ zero_zero_int @ M )
% 0.32/0.74 <=> ( dvd_dvd_int @ M @ A ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1045_nat__dvd__not__less,axiom,
% 0.32/0.74 ! [N: nat,M: nat] :
% 0.32/0.74 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.74 => ( ( ord_less_nat @ M @ N )
% 0.32/0.74 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1046_divides__ge,axiom,
% 0.32/0.74 ! [A: nat,B: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.74 => ( ( B = zero_zero_nat )
% 0.32/0.74 | ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1047_nat__mult__dvd__cancel__disj_H,axiom,
% 0.32/0.74 ! [M: nat,K: nat,N: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.32/0.74 <=> ( ( K = zero_zero_nat )
% 0.32/0.74 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1048_dvd__diffD,axiom,
% 0.32/0.74 ! [K: nat,M: nat,N: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.74 => ( ( dvd_dvd_nat @ K @ N )
% 0.32/0.74 => ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.74 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1049_dvd__diffD1,axiom,
% 0.32/0.74 ! [K: nat,M: nat,N: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.32/0.74 => ( ( dvd_dvd_nat @ K @ M )
% 0.32/0.74 => ( ( ord_less_eq_nat @ N @ M )
% 0.32/0.74 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1050_divides__rev,axiom,
% 0.32/0.74 ! [A: nat,N: nat,B: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.32/0.74 => ( ( N != zero_zero_nat )
% 0.32/0.74 => ( dvd_dvd_nat @ A @ B ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1051_divides__exp2,axiom,
% 0.32/0.74 ! [X: nat,Y: nat,N: nat] :
% 0.32/0.74 ( ( N != zero_zero_nat )
% 0.32/0.74 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ Y )
% 0.32/0.74 => ( dvd_dvd_nat @ X @ Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1052_Nat__Transfer_Otransfer__int__nat__relations_I4_J,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( dvd_dvd_int @ ( semiri1621563631at_int @ X ) @ ( semiri1621563631at_int @ Y ) )
% 0.32/0.74 <=> ( dvd_dvd_nat @ X @ Y ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1053_zdvd__int,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 <=> ( dvd_dvd_int @ ( semiri1621563631at_int @ X ) @ ( semiri1621563631at_int @ Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1054_divides__exp,axiom,
% 0.32/0.74 ! [N: nat,X: nat,Y: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1055_nat__dvd__1__iff__1,axiom,
% 0.32/0.74 ! [M: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 0.32/0.74 <=> ( M = one_one_nat ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1056_dvd__reduce,axiom,
% 0.32/0.74 ! [K: nat,N: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ K @ ( plus_plus_nat @ N @ K ) )
% 0.32/0.74 <=> ( dvd_dvd_nat @ K @ N ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1057_divides__add__revr,axiom,
% 0.32/0.74 ! [B: nat,D: nat,A: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ D @ A )
% 0.32/0.74 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 0.32/0.74 => ( dvd_dvd_nat @ D @ B ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1058_zcong__id,axiom,
% 0.32/0.74 ! [M: int] : ( zcong @ M @ zero_zero_int @ M ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1059_zcong__shift,axiom,
% 0.32/0.74 ! [C: int,A: int,B: int,M: int] :
% 0.32/0.74 ( ( zcong @ A @ B @ M )
% 0.32/0.74 => ( zcong @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) @ M ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1060_zcong__eq__trans,axiom,
% 0.32/0.74 ! [D: int,C: int,A: int,B: int,M: int] :
% 0.32/0.74 ( ( zcong @ A @ B @ M )
% 0.32/0.74 => ( ( B = C )
% 0.32/0.74 => ( ( zcong @ C @ D @ M )
% 0.32/0.74 => ( zcong @ A @ D @ M ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1061_zcong__zpower,axiom,
% 0.32/0.74 ! [Z: nat,X: int,Y: int,M: int] :
% 0.32/0.74 ( ( zcong @ X @ Y @ M )
% 0.32/0.74 => ( zcong @ ( power_power_int @ X @ Z ) @ ( power_power_int @ Y @ Z ) @ M ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1062_zcong__less__eq,axiom,
% 0.32/0.74 ! [M: int,Y: int,X: int] :
% 0.32/0.74 ( ( ord_less_int @ zero_zero_int @ X )
% 0.32/0.74 => ( ( ord_less_int @ zero_zero_int @ Y )
% 0.32/0.74 => ( ( ord_less_int @ zero_zero_int @ M )
% 0.32/0.74 => ( ( zcong @ X @ Y @ M )
% 0.32/0.74 => ( ( ord_less_int @ X @ M )
% 0.32/0.74 => ( ( ord_less_int @ Y @ M )
% 0.32/0.74 => ( X = Y ) ) ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1063_zcong__not__zero,axiom,
% 0.32/0.74 ! [M: int,X: int] :
% 0.32/0.74 ( ( ord_less_int @ zero_zero_int @ X )
% 0.32/0.74 => ( ( ord_less_int @ X @ M )
% 0.32/0.74 => ~ ( zcong @ X @ zero_zero_int @ M ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1064_zcong__zmult__prop1,axiom,
% 0.32/0.74 ! [C: int,D: int,A: int,B: int,M: int] :
% 0.32/0.74 ( ( zcong @ A @ B @ M )
% 0.32/0.74 => ( ( zcong @ C @ ( times_times_int @ A @ D ) @ M )
% 0.32/0.74 <=> ( zcong @ C @ ( times_times_int @ B @ D ) @ M ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1065_zcong__zmult__prop2,axiom,
% 0.32/0.74 ! [C: int,D: int,A: int,B: int,M: int] :
% 0.32/0.74 ( ( zcong @ A @ B @ M )
% 0.32/0.74 => ( ( zcong @ C @ ( times_times_int @ D @ A ) @ M )
% 0.32/0.74 <=> ( zcong @ C @ ( times_times_int @ D @ B ) @ M ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1066_Int2_Ozcong__zero,axiom,
% 0.32/0.74 ! [M: int,X: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.74 => ( ( ord_less_int @ X @ M )
% 0.32/0.74 => ( ( zcong @ X @ zero_zero_int @ M )
% 0.32/0.74 => ( X = zero_zero_int ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1067_zcong__zmult__prop3,axiom,
% 0.32/0.74 ! [Y: int,X: int,P_1: int] :
% 0.32/0.74 ( ( zprime @ P_1 )
% 0.32/0.74 => ( ~ ( zcong @ X @ zero_zero_int @ P_1 )
% 0.32/0.74 => ( ~ ( zcong @ Y @ zero_zero_int @ P_1 )
% 0.32/0.74 => ~ ( zcong @ ( times_times_int @ X @ Y ) @ zero_zero_int @ P_1 ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1068_dvd__imp__le,axiom,
% 0.32/0.74 ! [K: nat,N: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ K @ N )
% 0.32/0.74 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.32/0.74 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1069_dvd__mult__cancel,axiom,
% 0.32/0.74 ! [K: nat,M: nat,N: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.32/0.74 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.74 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1070_zcong__zprime__prod__zero,axiom,
% 0.32/0.74 ! [B: int,A: int,P_1: int] :
% 0.32/0.74 ( ( zprime @ P_1 )
% 0.32/0.74 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.74 => ( ( zcong @ ( times_times_int @ A @ B ) @ zero_zero_int @ P_1 )
% 0.32/0.74 => ( ( zcong @ A @ zero_zero_int @ P_1 )
% 0.32/0.74 | ( zcong @ B @ zero_zero_int @ P_1 ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1071_zcong__zprime__prod__zero__contra,axiom,
% 0.32/0.74 ! [B: int,A: int,P_1: int] :
% 0.32/0.74 ( ( zprime @ P_1 )
% 0.32/0.74 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.74 => ( ( ~ ( zcong @ A @ zero_zero_int @ P_1 )
% 0.32/0.74 & ~ ( zcong @ B @ zero_zero_int @ P_1 ) )
% 0.32/0.74 => ~ ( zcong @ ( times_times_int @ A @ B ) @ zero_zero_int @ P_1 ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1072_divides__div__not,axiom,
% 0.32/0.74 ! [X: nat,Q: nat,N: nat,R_1: nat] :
% 0.32/0.74 ( ( X
% 0.32/0.74 = ( plus_plus_nat @ ( times_times_nat @ Q @ N ) @ R_1 ) )
% 0.32/0.74 => ( ( ord_less_nat @ zero_zero_nat @ R_1 )
% 0.32/0.74 => ( ( ord_less_nat @ R_1 @ N )
% 0.32/0.74 => ~ ( dvd_dvd_nat @ N @ X ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1073_dvd__mult__cancel1,axiom,
% 0.32/0.74 ! [N: nat,M: nat] :
% 0.32/0.74 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.74 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 0.32/0.74 <=> ( N = one_one_nat ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1074_dvd__mult__cancel2,axiom,
% 0.32/0.74 ! [N: nat,M: nat] :
% 0.32/0.74 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.32/0.74 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 0.32/0.74 <=> ( N = one_one_nat ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1075_transfer__nat__int__relations_I4_J,axiom,
% 0.32/0.74 ! [Y: int,X: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.74 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.32/0.74 => ( ( dvd_dvd_nat @ ( nat_1 @ X ) @ ( nat_1 @ Y ) )
% 0.32/0.74 <=> ( dvd_dvd_int @ X @ Y ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1076_power__dvd__imp__le,axiom,
% 0.32/0.74 ! [I_1: nat,M: nat,N: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ ( power_power_nat @ I_1 @ M ) @ ( power_power_nat @ I_1 @ N ) )
% 0.32/0.74 => ( ( ord_less_nat @ one_one_nat @ I_1 )
% 0.32/0.74 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1077_nat__dvd__iff,axiom,
% 0.32/0.74 ! [Z: int,M: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ ( nat_1 @ Z ) @ M )
% 0.32/0.74 <=> ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.74 => ( dvd_dvd_int @ Z @ ( semiri1621563631at_int @ M ) ) )
% 0.32/0.74 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.32/0.74 => ( M = zero_zero_nat ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1078_zcong__neg__1__impl__ne__1,axiom,
% 0.32/0.74 ! [X: int,P_1: int] :
% 0.32/0.74 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P_1 )
% 0.32/0.74 => ( ( zcong @ X @ ( number_number_of_int @ min ) @ P_1 )
% 0.32/0.74 => ~ ( zcong @ X @ one_one_int @ P_1 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1079_Euler_Oaux____1,axiom,
% 0.32/0.74 ! [Y: int,X: int,P_1: int] :
% 0.32/0.74 ( ~ ( zcong @ X @ zero_zero_int @ P_1 )
% 0.32/0.74 => ( ( zcong @ ( power_power_int @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X @ P_1 )
% 0.32/0.74 => ~ ( dvd_dvd_int @ P_1 @ Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1080_divides__cases,axiom,
% 0.32/0.74 ! [N: nat,M: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ N @ M )
% 0.32/0.74 => ( ( M = zero_zero_nat )
% 0.32/0.74 | ( M = N )
% 0.32/0.74 | ( ord_less_eq_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) @ M ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1081_Legendre__1mod4,axiom,
% 0.32/0.74 ! [M: int] :
% 0.32/0.74 ( ( zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ M ) @ one_one_int ) )
% 0.32/0.74 => ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ M ) @ one_one_int ) )
% 0.32/0.74 = one_one_int ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1082__096_091s_____A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_,axiom,
% 0.32/0.74 zcong @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ s1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1083__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s,axiom,
% 0.32/0.74 ? [X_1: int] :
% 0.32/0.74 ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.32/0.74 & ( ord_less_int @ X_1 @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
% 0.32/0.74 & ( zcong @ s1 @ X_1 @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
% 0.32/0.74 & ! [Y_1: int] :
% 0.32/0.74 ( ( ( ord_less_eq_int @ zero_zero_int @ Y_1 )
% 0.32/0.74 & ( ord_less_int @ Y_1 @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
% 0.32/0.74 & ( zcong @ s1 @ Y_1 @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
% 0.32/0.74 => ( Y_1 = X_1 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1084_dvd_Oorder__refl,axiom,
% 0.32/0.74 ! [X: nat] : ( dvd_dvd_nat @ X @ X ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1085__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L,axiom,
% 0.32/0.74 ~ ! [S: int] :
% 0.32/0.74 ~ ( ( ord_less_eq_int @ zero_zero_int @ S )
% 0.32/0.74 & ( ord_less_int @ S @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
% 0.32/0.74 & ( zcong @ s1 @ S @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1086_dvd_Oless__asym,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Y @ X ) )
% 0.32/0.74 => ~ ( ( dvd_dvd_nat @ Y @ X )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ X @ Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1087_dvd_Oless__trans,axiom,
% 0.32/0.74 ! [Z: nat,X: nat,Y: nat] :
% 0.32/0.74 ( ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Y @ X ) )
% 0.32/0.74 => ( ( ( dvd_dvd_nat @ Y @ Z )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Z @ Y ) )
% 0.32/0.74 => ( ( dvd_dvd_nat @ X @ Z )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Z @ X ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1088_dvd_Oless__asym_H,axiom,
% 0.32/0.74 ! [A: nat,B: nat] :
% 0.32/0.74 ( ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ B @ A ) )
% 0.32/0.74 => ~ ( ( dvd_dvd_nat @ B @ A )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ A @ B ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1089_dvd_Oless__le__trans,axiom,
% 0.32/0.74 ! [Z: nat,X: nat,Y: nat] :
% 0.32/0.74 ( ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Y @ X ) )
% 0.32/0.74 => ( ( dvd_dvd_nat @ Y @ Z )
% 0.32/0.74 => ( ( dvd_dvd_nat @ X @ Z )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Z @ X ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1090_dvd_Oord__less__eq__trans,axiom,
% 0.32/0.74 ! [C: nat,A: nat,B: nat] :
% 0.32/0.74 ( ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ B @ A ) )
% 0.32/0.74 => ( ( B = C )
% 0.32/0.74 => ( ( dvd_dvd_nat @ A @ C )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ C @ A ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1091_dvd_Oless__imp__triv,axiom,
% 0.32/0.74 ! [P: $o,X: nat,Y: nat] :
% 0.32/0.74 ( ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Y @ X ) )
% 0.32/0.74 => ( ( ( dvd_dvd_nat @ Y @ X )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ X @ Y ) )
% 0.32/0.74 => P ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1092_dvd_Oless__imp__not__eq2,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Y @ X ) )
% 0.32/0.74 => ( Y != X ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1093_dvd_Oless__imp__not__eq,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Y @ X ) )
% 0.32/0.74 => ( X != Y ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1094_dvd_Oless__imp__not__less,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Y @ X ) )
% 0.32/0.74 => ~ ( ( dvd_dvd_nat @ Y @ X )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ X @ Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1095_dvd_Oless__imp__le,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Y @ X ) )
% 0.32/0.74 => ( dvd_dvd_nat @ X @ Y ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1096_dvd_Oless__not__sym,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Y @ X ) )
% 0.32/0.74 => ~ ( ( dvd_dvd_nat @ Y @ X )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ X @ Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1097_dvd_Oless__imp__neq,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Y @ X ) )
% 0.32/0.74 => ( X != Y ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1098_dvd_Ole__less__trans,axiom,
% 0.32/0.74 ! [Z: nat,X: nat,Y: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 => ( ( ( dvd_dvd_nat @ Y @ Z )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Z @ Y ) )
% 0.32/0.74 => ( ( dvd_dvd_nat @ X @ Z )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Z @ X ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1099_dvd_Oord__eq__less__trans,axiom,
% 0.32/0.74 ! [C: nat,A: nat,B: nat] :
% 0.32/0.74 ( ( A = B )
% 0.32/0.74 => ( ( ( dvd_dvd_nat @ B @ C )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ C @ B ) )
% 0.32/0.74 => ( ( dvd_dvd_nat @ A @ C )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ C @ A ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1100_dvd_Oorder__trans,axiom,
% 0.32/0.74 ! [Z: nat,X: nat,Y: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 => ( ( dvd_dvd_nat @ Y @ Z )
% 0.32/0.74 => ( dvd_dvd_nat @ X @ Z ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1101_dvd_Oantisym,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 => ( ( dvd_dvd_nat @ Y @ X )
% 0.32/0.74 => ( X = Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1102_dvd__antisym,axiom,
% 0.32/0.74 ! [M: nat,N: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ M @ N )
% 0.32/0.74 => ( ( dvd_dvd_nat @ N @ M )
% 0.32/0.74 => ( M = N ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1103_dvd_Oord__le__eq__trans,axiom,
% 0.32/0.74 ! [C: nat,A: nat,B: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.74 => ( ( B = C )
% 0.32/0.74 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1104_dvd_Oord__eq__le__trans,axiom,
% 0.32/0.74 ! [C: nat,A: nat,B: nat] :
% 0.32/0.74 ( ( A = B )
% 0.32/0.74 => ( ( dvd_dvd_nat @ B @ C )
% 0.32/0.74 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1105_dvd_Ole__neq__trans,axiom,
% 0.32/0.74 ! [A: nat,B: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.74 => ( ( A != B )
% 0.32/0.74 => ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1106_dvd_Ole__imp__less__or__eq,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 => ( ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Y @ X ) )
% 0.32/0.74 | ( X = Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1107_dvd_Oantisym__conv,axiom,
% 0.32/0.74 ! [Y: nat,X: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ Y @ X )
% 0.32/0.74 => ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 <=> ( X = Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1108_dvd_Oeq__refl,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( X = Y )
% 0.32/0.74 => ( dvd_dvd_nat @ X @ Y ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1109_dvd_Oneq__le__trans,axiom,
% 0.32/0.74 ! [A: nat,B: nat] :
% 0.32/0.74 ( ( A != B )
% 0.32/0.74 => ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.74 => ( ( dvd_dvd_nat @ A @ B )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1110_dvd_Oless__le__not__le,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Y @ X ) )
% 0.32/0.74 <=> ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Y @ X ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1111_dvd_Oless__le,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Y @ X ) )
% 0.32/0.74 <=> ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ( X != Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1112_dvd_Ole__less,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 <=> ( ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ Y @ X ) )
% 0.32/0.74 | ( X = Y ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1113_dvd_Oeq__iff,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( X = Y )
% 0.32/0.74 <=> ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ( dvd_dvd_nat @ Y @ X ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1114_dvd_Oless__irrefl,axiom,
% 0.32/0.74 ! [X: nat] :
% 0.32/0.74 ~ ( ( dvd_dvd_nat @ X @ X )
% 0.32/0.74 & ~ ( dvd_dvd_nat @ X @ X ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1115_divides__antisym,axiom,
% 0.32/0.74 ! [X: nat,Y: nat] :
% 0.32/0.74 ( ( ( dvd_dvd_nat @ X @ Y )
% 0.32/0.74 & ( dvd_dvd_nat @ Y @ X ) )
% 0.32/0.74 <=> ( X = Y ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1116_neg__one__power__eq__mod__m,axiom,
% 0.32/0.74 ! [J: nat,K: nat,M: int] :
% 0.32/0.74 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ M )
% 0.32/0.74 => ( ( zcong @ ( power_power_int @ ( number_number_of_int @ min ) @ J ) @ ( power_power_int @ ( number_number_of_int @ min ) @ K ) @ M )
% 0.32/0.74 => ( ( power_power_int @ ( number_number_of_int @ min ) @ J )
% 0.32/0.74 = ( power_power_int @ ( number_number_of_int @ min ) @ K ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1117_one__not__neg__one__mod__m,axiom,
% 0.32/0.74 ! [M: int] :
% 0.32/0.74 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ M )
% 0.32/0.74 => ~ ( zcong @ one_one_int @ ( number_number_of_int @ min ) @ M ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1118_neg__one__power,axiom,
% 0.32/0.74 ! [N: nat] :
% 0.32/0.74 ( ( ( power_power_int @ ( number_number_of_int @ min ) @ N )
% 0.32/0.74 = one_one_int )
% 0.32/0.74 | ( ( power_power_int @ ( number_number_of_int @ min ) @ N )
% 0.32/0.74 = ( number_number_of_int @ min ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1119_Legendre__def,axiom,
% 0.32/0.74 ! [A: int,P_1: int] :
% 0.32/0.74 ( ( ( zcong @ A @ zero_zero_int @ P_1 )
% 0.32/0.74 => ( ( legendre @ A @ P_1 )
% 0.32/0.74 = zero_zero_int ) )
% 0.32/0.74 & ( ~ ( zcong @ A @ zero_zero_int @ P_1 )
% 0.32/0.74 => ( ( ( quadRes @ P_1 @ A )
% 0.32/0.74 => ( ( legendre @ A @ P_1 )
% 0.32/0.74 = one_one_int ) )
% 0.32/0.74 & ( ~ ( quadRes @ P_1 @ A )
% 0.32/0.74 => ( ( legendre @ A @ P_1 )
% 0.32/0.74 = ( number_number_of_int @ min ) ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1120_QuadRes__def,axiom,
% 0.32/0.74 ! [M: int,X: int] :
% 0.32/0.74 ( ( quadRes @ M @ X )
% 0.32/0.74 <=> ? [Y_1: int] : ( zcong @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X @ M ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1121_Little__Fermat,axiom,
% 0.32/0.74 ! [X: int,P_1: int] :
% 0.32/0.74 ( ( zprime @ P_1 )
% 0.32/0.74 => ( ~ ( dvd_dvd_int @ P_1 @ X )
% 0.32/0.74 => ( zcong @ ( power_power_int @ X @ ( nat_1 @ ( minus_minus_int @ P_1 @ one_one_int ) ) ) @ one_one_int @ P_1 ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1122_zcong__square__zless,axiom,
% 0.32/0.74 ! [A: int,P_1: int] :
% 0.32/0.74 ( ( zprime @ P_1 )
% 0.32/0.74 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.74 => ( ( ord_less_int @ A @ P_1 )
% 0.32/0.74 => ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ P_1 )
% 0.32/0.74 => ( ( A = one_one_int )
% 0.32/0.74 | ( A
% 0.32/0.74 = ( minus_minus_int @ P_1 @ one_one_int ) ) ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1123_zcong__trans,axiom,
% 0.32/0.74 ! [C: int,A: int,B: int,M: int] :
% 0.32/0.74 ( ( zcong @ A @ B @ M )
% 0.32/0.74 => ( ( zcong @ B @ C @ M )
% 0.32/0.74 => ( zcong @ A @ C @ M ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1124_zcong__refl,axiom,
% 0.32/0.74 ! [K: int,M: int] : ( zcong @ K @ K @ M ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1125_zcong__sym,axiom,
% 0.32/0.74 ! [A: int,B: int,M: int] :
% 0.32/0.74 ( ( zcong @ A @ B @ M )
% 0.32/0.74 <=> ( zcong @ B @ A @ M ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1126_IntPrimes_Ozcong__zero,axiom,
% 0.32/0.74 ! [A: int,B: int] :
% 0.32/0.74 ( ( zcong @ A @ B @ zero_zero_int )
% 0.32/0.74 <=> ( A = B ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1127_zcong__1,axiom,
% 0.32/0.74 ! [A: int,B: int] : ( zcong @ A @ B @ one_one_int ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1128_zcong__zmult__self,axiom,
% 0.32/0.74 ! [A: int,M: int,B: int] : ( zcong @ ( times_times_int @ A @ M ) @ ( times_times_int @ B @ M ) @ M ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1129_zcong__scalar,axiom,
% 0.32/0.74 ! [K: int,A: int,B: int,M: int] :
% 0.32/0.74 ( ( zcong @ A @ B @ M )
% 0.32/0.74 => ( zcong @ ( times_times_int @ A @ K ) @ ( times_times_int @ B @ K ) @ M ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1130_zcong__scalar2,axiom,
% 0.32/0.74 ! [K: int,A: int,B: int,M: int] :
% 0.32/0.74 ( ( zcong @ A @ B @ M )
% 0.32/0.74 => ( zcong @ ( times_times_int @ K @ A ) @ ( times_times_int @ K @ B ) @ M ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1131_zcong__zmult,axiom,
% 0.32/0.74 ! [C: int,D: int,A: int,B: int,M: int] :
% 0.32/0.74 ( ( zcong @ A @ B @ M )
% 0.32/0.74 => ( ( zcong @ C @ D @ M )
% 0.32/0.74 => ( zcong @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) @ M ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1132_zcong__zadd,axiom,
% 0.32/0.74 ! [C: int,D: int,A: int,B: int,M: int] :
% 0.32/0.74 ( ( zcong @ A @ B @ M )
% 0.32/0.74 => ( ( zcong @ C @ D @ M )
% 0.32/0.74 => ( zcong @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) @ M ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1133_zcong__zdiff,axiom,
% 0.32/0.74 ! [C: int,D: int,A: int,B: int,M: int] :
% 0.32/0.74 ( ( zcong @ A @ B @ M )
% 0.32/0.74 => ( ( zcong @ C @ D @ M )
% 0.32/0.74 => ( zcong @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) @ M ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1134_zcong__not,axiom,
% 0.32/0.74 ! [B: int,M: int,A: int] :
% 0.32/0.74 ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.74 => ( ( ord_less_int @ A @ M )
% 0.32/0.74 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.32/0.74 => ( ( ord_less_int @ B @ A )
% 0.32/0.74 => ~ ( zcong @ A @ B @ M ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1135_xzgcda__linear__aux1,axiom,
% 0.32/0.74 ! [A: int,R_1: int,B: int,M: int,C: int,D: int,N: int] :
% 0.32/0.74 ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ ( times_times_int @ R_1 @ B ) ) @ M ) @ ( times_times_int @ ( minus_minus_int @ C @ ( times_times_int @ R_1 @ D ) ) @ N ) )
% 0.32/0.74 = ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ A @ M ) @ ( times_times_int @ C @ N ) ) @ ( times_times_int @ R_1 @ ( plus_plus_int @ ( times_times_int @ B @ M ) @ ( times_times_int @ D @ N ) ) ) ) ) ).
% 0.32/0.74
% 0.32/0.74 thf(fact_1136_zcong__iff__lin,axiom,
% 0.32/0.74 ! [A: int,B: int,M: int] :
% 0.32/0.74 ( ( zcong @ A @ B @ M )
% 0.32/0.74 <=> ? [K_1: int] :
% 0.32/0.74 ( B
% 0.32/0.74 = ( plus_plus_int @ A @ ( times_times_int @ M @ K_1 ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1137_zcong__def,axiom,
% 0.32/0.75 ! [A: int,B: int,M: int] :
% 0.32/0.75 ( ( zcong @ A @ B @ M )
% 0.32/0.75 <=> ( dvd_dvd_int @ M @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1138_norR__mem__unique__aux,axiom,
% 0.32/0.75 ! [A: int,B: int] :
% 0.32/0.75 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
% 0.32/0.75 => ( ord_less_int @ A @ B ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1139_zcong__zless__0,axiom,
% 0.32/0.75 ! [M: int,A: int] :
% 0.32/0.75 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.75 => ( ( ord_less_int @ A @ M )
% 0.32/0.75 => ( ( zcong @ A @ zero_zero_int @ M )
% 0.32/0.75 => ( A = zero_zero_int ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1140_zcong__zless__imp__eq,axiom,
% 0.32/0.75 ! [B: int,M: int,A: int] :
% 0.32/0.75 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.32/0.75 => ( ( ord_less_int @ A @ M )
% 0.32/0.75 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.32/0.75 => ( ( ord_less_int @ B @ M )
% 0.32/0.75 => ( ( zcong @ A @ B @ M )
% 0.32/0.75 => ( A = B ) ) ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1141_zprime__zdvd__zmult,axiom,
% 0.32/0.75 ! [N: int,P_1: int,M: int] :
% 0.32/0.75 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 0.32/0.75 => ( ( zprime @ P_1 )
% 0.32/0.75 => ( ( dvd_dvd_int @ P_1 @ ( times_times_int @ M @ N ) )
% 0.32/0.75 => ( ( dvd_dvd_int @ P_1 @ M )
% 0.32/0.75 | ( dvd_dvd_int @ P_1 @ N ) ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1142_zprime__def,axiom,
% 0.32/0.75 ! [P_1: int] :
% 0.32/0.75 ( ( zprime @ P_1 )
% 0.32/0.75 <=> ( ( ord_less_int @ one_one_int @ P_1 )
% 0.32/0.75 & ! [M_1: int] :
% 0.32/0.75 ( ( ( ord_less_eq_int @ zero_zero_int @ M_1 )
% 0.32/0.75 & ( dvd_dvd_int @ M_1 @ P_1 ) )
% 0.32/0.75 => ( ( M_1 = one_one_int )
% 0.32/0.75 | ( M_1 = P_1 ) ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1143_zcong__square,axiom,
% 0.32/0.75 ! [A: int,P_1: int] :
% 0.32/0.75 ( ( zprime @ P_1 )
% 0.32/0.75 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.32/0.75 => ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ P_1 )
% 0.32/0.75 => ( ( zcong @ A @ one_one_int @ P_1 )
% 0.32/0.75 | ( zcong @ A @ ( minus_minus_int @ P_1 @ one_one_int ) @ P_1 ) ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1144_zdiff__int__split,axiom,
% 0.32/0.75 ! [P: int > $o,X: nat,Y: nat] :
% 0.32/0.75 ( ( P @ ( semiri1621563631at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 0.32/0.75 <=> ( ( ( ord_less_eq_nat @ Y @ X )
% 0.32/0.75 => ( P @ ( minus_minus_int @ ( semiri1621563631at_int @ X ) @ ( semiri1621563631at_int @ Y ) ) ) )
% 0.32/0.75 & ( ( ord_less_nat @ X @ Y )
% 0.32/0.75 => ( P @ zero_zero_int ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1145_prime__g__5,axiom,
% 0.32/0.75 ! [P_1: int] :
% 0.32/0.75 ( ( zprime @ P_1 )
% 0.32/0.75 => ( ( P_1
% 0.32/0.75 != ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.75 => ( ( P_1
% 0.32/0.75 != ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
% 0.32/0.75 => ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ P_1 ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1146_conj__le__cong,axiom,
% 0.32/0.75 ! [P_2: $o,P: $o,X: int] :
% 0.32/0.75 ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.75 => ( P
% 0.32/0.75 <=> P_2 ) )
% 0.32/0.75 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.75 & P )
% 0.32/0.75 <=> ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.75 & P_2 ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1147_imp__le__cong,axiom,
% 0.32/0.75 ! [P_2: $o,P: $o,X: int] :
% 0.32/0.75 ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.75 => ( P
% 0.32/0.75 <=> P_2 ) )
% 0.32/0.75 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.75 => P )
% 0.32/0.75 <=> ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.32/0.75 => P_2 ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1148_zdvd__mono,axiom,
% 0.32/0.75 ! [M: int,T: int,K: int] :
% 0.32/0.75 ( ( K != zero_zero_int )
% 0.32/0.75 => ( ( dvd_dvd_int @ M @ T )
% 0.32/0.75 <=> ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1149_number__of2,axiom,
% 0.32/0.75 ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ pls ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1150_inv__not__p__minus__1__aux,axiom,
% 0.32/0.75 ! [A: int,P_1: int] :
% 0.32/0.75 ( ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ P_1 @ one_one_int ) ) @ one_one_int @ P_1 )
% 0.32/0.75 <=> ( zcong @ A @ ( minus_minus_int @ P_1 @ one_one_int ) @ P_1 ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1151_zcong__zpower__zmult,axiom,
% 0.32/0.75 ! [Z: nat,X: int,Y: nat,P_1: int] :
% 0.32/0.75 ( ( zcong @ ( power_power_int @ X @ Y ) @ one_one_int @ P_1 )
% 0.32/0.75 => ( zcong @ ( power_power_int @ X @ ( times_times_nat @ Y @ Z ) ) @ one_one_int @ P_1 ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1152_number__of1,axiom,
% 0.32/0.75 ! [N: int] :
% 0.32/0.75 ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ N ) )
% 0.32/0.75 => ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ N ) ) )
% 0.32/0.75 & ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ N ) ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1153__096_B_Bthesis_O_A_I_B_Bs_Aw_O_Aw_A_061_Ay_A_N_As_A_K_A_I1_A_L_Aint_An,axiom,
% 0.32/0.75 ~ ! [S: int,W_1: int] :
% 0.32/0.75 ~ ( ( W_1
% 0.32/0.75 = ( minus_minus_int @ y @ ( times_times_int @ S @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) )
% 0.32/0.75 & ( ord_less_eq_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs_int @ W_1 ) ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1154__096_B_Bthesis_O_A_I_B_Br_Av_O_Av_A_061_Ax_A_N_Ar_A_K_A_I1_A_L_Aint_An,axiom,
% 0.32/0.75 ~ ! [R: int,V: int] :
% 0.32/0.75 ~ ( ( V
% 0.32/0.75 = ( minus_minus_int @ x @ ( times_times_int @ R @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) )
% 0.32/0.75 & ( ord_less_eq_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs_int @ V ) ) @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1155_dvd__imp__le__int,axiom,
% 0.32/0.75 ! [D: int,I_1: int] :
% 0.32/0.75 ( ( I_1 != zero_zero_int )
% 0.32/0.75 => ( ( dvd_dvd_int @ D @ I_1 )
% 0.32/0.75 => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I_1 ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1156_nat__abs__mult__distrib,axiom,
% 0.32/0.75 ! [W: int,Z: int] :
% 0.32/0.75 ( ( nat_1 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 0.32/0.75 = ( times_times_nat @ ( nat_1 @ ( abs_abs_int @ W ) ) @ ( nat_1 @ ( abs_abs_int @ Z ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1157_zdvd__antisym__abs,axiom,
% 0.32/0.75 ! [A: int,B: int] :
% 0.32/0.75 ( ( dvd_dvd_int @ A @ B )
% 0.32/0.75 => ( ( dvd_dvd_int @ B @ A )
% 0.32/0.75 => ( ( abs_abs_int @ A )
% 0.32/0.75 = ( abs_abs_int @ B ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1158_zdvd1__eq,axiom,
% 0.32/0.75 ! [X: int] :
% 0.32/0.75 ( ( dvd_dvd_int @ X @ one_one_int )
% 0.32/0.75 <=> ( ( abs_abs_int @ X )
% 0.32/0.75 = one_one_int ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1159_abs__int__eq,axiom,
% 0.32/0.75 ! [M: nat] :
% 0.32/0.75 ( ( abs_abs_int @ ( semiri1621563631at_int @ M ) )
% 0.32/0.75 = ( semiri1621563631at_int @ M ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1160_abs__zmult__eq__1,axiom,
% 0.32/0.75 ! [M: int,N: int] :
% 0.32/0.75 ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 0.32/0.75 = one_one_int )
% 0.32/0.75 => ( ( abs_abs_int @ M )
% 0.32/0.75 = one_one_int ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1161_zero__le__zpower__abs,axiom,
% 0.32/0.75 ! [X: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ X ) @ N ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1162_zabs__less__one__iff,axiom,
% 0.32/0.75 ! [Z: int] :
% 0.32/0.75 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 0.32/0.75 <=> ( Z = zero_zero_int ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1163_abs__eq__1__iff,axiom,
% 0.32/0.75 ! [Z: int] :
% 0.32/0.75 ( ( ( abs_abs_int @ Z )
% 0.32/0.75 = one_one_int )
% 0.32/0.75 <=> ( ( Z = one_one_int )
% 0.32/0.75 | ( Z
% 0.32/0.75 = ( number_number_of_int @ min ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1164_abs__power3__distrib,axiom,
% 0.32/0.75 ! [X: int] :
% 0.32/0.75 ( ( abs_abs_int @ ( power_power_int @ X @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) )
% 0.32/0.75 = ( power_power_int @ ( abs_abs_int @ X ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1165_zero__less__zpower__abs__iff,axiom,
% 0.32/0.75 ! [X: int,N: nat] :
% 0.32/0.75 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ X ) @ N ) )
% 0.32/0.75 <=> ( ( X != zero_zero_int )
% 0.32/0.75 | ( N = zero_zero_nat ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1166_zdvd__mult__cancel1,axiom,
% 0.32/0.75 ! [N: int,M: int] :
% 0.32/0.75 ( ( M != zero_zero_int )
% 0.32/0.75 => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 0.32/0.75 <=> ( ( abs_abs_int @ N )
% 0.32/0.75 = one_one_int ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1167_int__dvd__iff,axiom,
% 0.32/0.75 ! [M: nat,Z: int] :
% 0.32/0.75 ( ( dvd_dvd_int @ ( semiri1621563631at_int @ M ) @ Z )
% 0.32/0.75 <=> ( dvd_dvd_nat @ M @ ( nat_1 @ ( abs_abs_int @ Z ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1168_dvd__int__iff,axiom,
% 0.32/0.75 ! [Z: int,M: nat] :
% 0.32/0.75 ( ( dvd_dvd_int @ Z @ ( semiri1621563631at_int @ M ) )
% 0.32/0.75 <=> ( dvd_dvd_nat @ ( nat_1 @ ( abs_abs_int @ Z ) ) @ M ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1169_abs__power2__distrib,axiom,
% 0.32/0.75 ! [A: int] :
% 0.32/0.75 ( ( abs_abs_int @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.32/0.75 = ( power_power_int @ ( abs_abs_int @ A ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1170_power2__eq__iff__abs__eq,axiom,
% 0.32/0.75 ! [A: int,B: int] :
% 0.32/0.75 ( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.75 = ( power_power_int @ B @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.32/0.75 <=> ( ( abs_abs_int @ A )
% 0.32/0.75 = ( abs_abs_int @ B ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1171_power2__eq1__iff,axiom,
% 0.32/0.75 ! [A: int] :
% 0.32/0.75 ( ( ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.32/0.75 = one_one_int )
% 0.32/0.75 => ( ( abs_abs_int @ A )
% 0.32/0.75 = one_one_int ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1172_incr__lemma,axiom,
% 0.32/0.75 ! [Z: int,X: int,D: int] :
% 0.32/0.75 ( ( ord_less_int @ zero_zero_int @ D )
% 0.32/0.75 => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1173_decr__lemma,axiom,
% 0.32/0.75 ! [X: int,Z: int,D: int] :
% 0.32/0.75 ( ( ord_less_int @ zero_zero_int @ D )
% 0.32/0.75 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1174_best__division__abs,axiom,
% 0.32/0.75 ! [Y: int,X: int] :
% 0.32/0.75 ( ( ord_less_int @ zero_zero_int @ X )
% 0.32/0.75 => ? [N_1: int] : ( ord_less_eq_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ Y @ ( times_times_int @ N_1 @ X ) ) ) ) @ X ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1175_decr__mult__lemma,axiom,
% 0.32/0.75 ! [K: int,P: int > $o,D: int] :
% 0.32/0.75 ( ( ord_less_int @ zero_zero_int @ D )
% 0.32/0.75 => ( ! [X_1: int] :
% 0.32/0.75 ( ( P @ X_1 )
% 0.32/0.75 => ( P @ ( minus_minus_int @ X_1 @ D ) ) )
% 0.32/0.75 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.75 => ! [X_1: int] :
% 0.32/0.75 ( ( P @ X_1 )
% 0.32/0.75 => ( P @ ( minus_minus_int @ X_1 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1176_abs__add__one__not__less__self,axiom,
% 0.32/0.75 ! [X: real] :
% 0.32/0.75 ~ ( ord_less_real @ ( plus_plus_real @ ( abs_abs_real @ X ) @ one_one_real ) @ X ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1177_abs__add__one__gt__zero,axiom,
% 0.32/0.75 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1178_less__one__imp__sqr__less__one,axiom,
% 0.32/0.75 ! [X: real] :
% 0.32/0.75 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 0.32/0.75 => ( ord_less_real @ ( power_power_real @ X @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_real ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1179_ex__least__nat__less,axiom,
% 0.32/0.75 ! [N: nat,P: nat > $o] :
% 0.32/0.75 ( ~ ( P @ zero_zero_nat )
% 0.32/0.75 => ( ( P @ N )
% 0.32/0.75 => ? [K_1: nat] :
% 0.32/0.75 ( ( ord_less_nat @ K_1 @ N )
% 0.32/0.75 & ! [I: nat] :
% 0.32/0.75 ( ( ord_less_eq_nat @ I @ K_1 )
% 0.32/0.75 => ~ ( P @ I ) )
% 0.32/0.75 & ( P @ ( plus_plus_nat @ K_1 @ one_one_nat ) ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1180_incr__mult__lemma,axiom,
% 0.32/0.75 ! [K: int,P: int > $o,D: int] :
% 0.32/0.75 ( ( ord_less_int @ zero_zero_int @ D )
% 0.32/0.75 => ( ! [X_1: int] :
% 0.32/0.75 ( ( P @ X_1 )
% 0.32/0.75 => ( P @ ( plus_plus_int @ X_1 @ D ) ) )
% 0.32/0.75 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.32/0.75 => ! [X_1: int] :
% 0.32/0.75 ( ( P @ X_1 )
% 0.32/0.75 => ( P @ ( plus_plus_int @ X_1 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1181_nat__less__add__iff1,axiom,
% 0.32/0.75 ! [U: nat,M: nat,N: nat,J: nat,I_1: nat] :
% 0.32/0.75 ( ( ord_less_eq_nat @ J @ I_1 )
% 0.32/0.75 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.32/0.75 <=> ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I_1 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1182_nat__less__add__iff2,axiom,
% 0.32/0.75 ! [U: nat,M: nat,N: nat,I_1: nat,J: nat] :
% 0.32/0.75 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.32/0.75 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.32/0.75 <=> ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I_1 ) @ U ) @ N ) ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1183_nat__mult__eq__cancel__disj,axiom,
% 0.32/0.75 ! [K: nat,M: nat,N: nat] :
% 0.32/0.75 ( ( ( times_times_nat @ K @ M )
% 0.32/0.75 = ( times_times_nat @ K @ N ) )
% 0.32/0.75 <=> ( ( K = zero_zero_nat )
% 0.32/0.75 | ( M = N ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1184_left__add__mult__distrib,axiom,
% 0.32/0.75 ! [I_1: nat,U: nat,J: nat,K: nat] :
% 0.32/0.75 ( ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 0.32/0.75 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I_1 @ J ) @ U ) @ K ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1185_nat__mult__less__cancel1,axiom,
% 0.32/0.75 ! [M: nat,N: nat,K: nat] :
% 0.32/0.75 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.75 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.32/0.75 <=> ( ord_less_nat @ M @ N ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1186_nat__mult__eq__cancel1,axiom,
% 0.32/0.75 ! [M: nat,N: nat,K: nat] :
% 0.32/0.75 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.75 => ( ( ( times_times_nat @ K @ M )
% 0.32/0.75 = ( times_times_nat @ K @ N ) )
% 0.32/0.75 <=> ( M = N ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1187_nat__mult__dvd__cancel__disj,axiom,
% 0.32/0.75 ! [K: nat,M: nat,N: nat] :
% 0.32/0.75 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.32/0.75 <=> ( ( K = zero_zero_nat )
% 0.32/0.75 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1188_nat__mult__dvd__cancel1,axiom,
% 0.32/0.75 ! [M: nat,N: nat,K: nat] :
% 0.32/0.75 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.75 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.32/0.75 <=> ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1189_nat__mult__le__cancel1,axiom,
% 0.32/0.75 ! [M: nat,N: nat,K: nat] :
% 0.32/0.75 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.32/0.75 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.32/0.75 <=> ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1190_nat__le__add__iff1,axiom,
% 0.32/0.75 ! [U: nat,M: nat,N: nat,J: nat,I_1: nat] :
% 0.32/0.75 ( ( ord_less_eq_nat @ J @ I_1 )
% 0.32/0.75 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.32/0.75 <=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I_1 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1191_nat__diff__add__eq1,axiom,
% 0.32/0.75 ! [U: nat,M: nat,N: nat,J: nat,I_1: nat] :
% 0.32/0.75 ( ( ord_less_eq_nat @ J @ I_1 )
% 0.32/0.75 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.32/0.75 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I_1 @ J ) @ U ) @ M ) @ N ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1192_nat__eq__add__iff1,axiom,
% 0.32/0.75 ! [U: nat,M: nat,N: nat,J: nat,I_1: nat] :
% 0.32/0.75 ( ( ord_less_eq_nat @ J @ I_1 )
% 0.32/0.75 => ( ( ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M )
% 0.32/0.75 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.32/0.75 <=> ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I_1 @ J ) @ U ) @ M )
% 0.32/0.75 = N ) ) ) ).
% 0.32/0.75
% 0.32/0.75 thf(fact_1193_nat__le__add__iff2,axiom,
% 0.32/0.75 ! [U: nat,M: nat,N: nat,I_1: nat,J: nat] :
% 0.63/0.88 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.63/0.88 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.63/0.88 <=> ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I_1 ) @ U ) @ N ) ) ) ) ).
% 0.63/0.88
% 0.63/0.88 thf(fact_1194_nat__diff__add__eq2,axiom,
% 0.63/0.88 ! [U: nat,M: nat,N: nat,I_1: nat,J: nat] :
% 0.63/0.88 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.63/0.88 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.63/0.88 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I_1 ) @ U ) @ N ) ) ) ) ).
% 0.63/0.88
% 0.63/0.88 thf(fact_1195_nat__eq__add__iff2,axiom,
% 0.63/0.88 ! [U: nat,M: nat,N: nat,I_1: nat,J: nat] :
% 0.63/0.88 ( ( ord_less_eq_nat @ I_1 @ J )
% 0.63/0.88 => ( ( ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M )
% 0.63/0.88 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 0.63/0.88 <=> ( M
% 0.63/0.88 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I_1 ) @ U ) @ N ) ) ) ) ).
% 0.63/0.88
% 0.63/0.88 thf(fact_1196_nat0__intermed__int__val,axiom,
% 0.63/0.88 ! [K: int,F: nat > int,N: nat] :
% 0.63/0.88 ( ! [I: nat] :
% 0.63/0.88 ( ( ord_less_nat @ I @ N )
% 0.63/0.88 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I @ one_one_nat ) ) @ ( F @ I ) ) ) @ one_one_int ) )
% 0.63/0.88 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.63/0.88 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.63/0.88 => ? [I: nat] :
% 0.63/0.88 ( ( ord_less_eq_nat @ I @ N )
% 0.63/0.88 & ( ( F @ I )
% 0.63/0.88 = K ) ) ) ) ) ).
% 0.63/0.88
% 0.63/0.88 thf(fact_1197_int__val__lemma,axiom,
% 0.63/0.88 ! [K: int,F: nat > int,N: nat] :
% 0.63/0.88 ( ! [I: nat] :
% 0.63/0.88 ( ( ord_less_nat @ I @ N )
% 0.63/0.88 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I @ one_one_nat ) ) @ ( F @ I ) ) ) @ one_one_int ) )
% 0.63/0.88 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 0.63/0.88 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 0.63/0.88 => ? [I: nat] :
% 0.63/0.88 ( ( ord_less_eq_nat @ I @ N )
% 0.63/0.88 & ( ( F @ I )
% 0.63/0.88 = K ) ) ) ) ) ).
% 0.63/0.88
% 0.63/0.88 %----Helper facts (6)
% 0.63/0.88 thf(help_If_1_1_If_000tc__Int__Oint_T,axiom,
% 0.63/0.88 ! [X: int,Y: int] :
% 0.63/0.88 ( ( if_int @ $true @ X @ Y )
% 0.63/0.88 = X ) ).
% 0.63/0.88
% 0.63/0.88 thf(help_If_2_1_If_000tc__Int__Oint_T,axiom,
% 0.63/0.88 ! [X: int,Y: int] :
% 0.63/0.88 ( ( if_int @ $false @ X @ Y )
% 0.63/0.88 = Y ) ).
% 0.63/0.88
% 0.63/0.88 thf(help_If_3_1_If_000tc__Int__Oint_T,axiom,
% 0.63/0.88 ! [P: $o] :
% 0.63/0.88 ( ( P = $true )
% 0.63/0.88 | ( P = $false ) ) ).
% 0.63/0.88
% 0.63/0.88 thf(help_If_1_1_If_000tc__Nat__Onat_T,axiom,
% 0.63/0.88 ! [X: nat,Y: nat] :
% 0.63/0.88 ( ( if_nat @ $true @ X @ Y )
% 0.63/0.88 = X ) ).
% 0.63/0.88
% 0.63/0.88 thf(help_If_2_1_If_000tc__Nat__Onat_T,axiom,
% 0.63/0.88 ! [X: nat,Y: nat] :
% 0.63/0.88 ( ( if_nat @ $false @ X @ Y )
% 0.63/0.88 = Y ) ).
% 0.63/0.88
% 0.63/0.88 thf(help_If_3_1_If_000tc__Nat__Onat_T,axiom,
% 0.63/0.88 ! [P: $o] :
% 0.63/0.88 ( ( P = $true )
% 0.63/0.88 | ( P = $false ) ) ).
% 0.63/0.88
% 0.63/0.88 %----Conjectures (1)
% 0.63/0.88 thf(conj_0,conjecture,
% 0.63/0.88 ( ( power_power_int @ ( plus_plus_int @ one_one_int @ ( semiri1621563631at_int @ n ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.63/0.88 != zero_zero_int ) ).
% 0.63/0.88
% 0.63/0.88 %------------------------------------------------------------------------------
% 0.63/0.88 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.XYKb8qzj26/cvc5---1.0.5_24761.p...
% 0.63/0.88 (declare-sort $$unsorted 0)
% 0.63/0.88 (declare-sort tptp.int 0)
% 0.63/0.88 (declare-sort tptp.nat 0)
% 0.63/0.88 (declare-sort tptp.real 0)
% 0.63/0.88 (declare-fun tptp.all ((-> tptp.nat Bool)) Bool)
% 0.63/0.88 (declare-fun tptp.ex ((-> tptp.nat Bool)) Bool)
% 0.63/0.88 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 0.63/0.88 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 0.63/0.88 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 0.63/0.88 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.63/0.88 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 0.63/0.88 (declare-fun tptp.one_one_int () tptp.int)
% 0.63/0.88 (declare-fun tptp.one_one_nat () tptp.nat)
% 0.63/0.88 (declare-fun tptp.one_one_real () tptp.real)
% 0.63/0.88 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 0.63/0.88 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.63/0.88 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 0.63/0.88 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 0.63/0.88 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 0.63/0.88 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 0.63/0.88 (declare-fun tptp.zero_zero_int () tptp.int)
% 0.63/0.88 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.63/0.88 (declare-fun tptp.zero_zero_real () tptp.real)
% 0.63/0.88 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 0.63/0.88 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 0.63/0.88 (declare-fun tptp.zcong (tptp.int tptp.int tptp.int) Bool)
% 0.63/0.88 (declare-fun tptp.zprime (tptp.int) Bool)
% 0.63/0.88 (declare-fun tptp.bit0 (tptp.int) tptp.int)
% 0.63/0.88 (declare-fun tptp.bit1 (tptp.int) tptp.int)
% 0.63/0.88 (declare-fun tptp.min () tptp.int)
% 0.63/0.88 (declare-fun tptp.pls () tptp.int)
% 0.63/0.88 (declare-fun tptp.nat_1 (tptp.int) tptp.nat)
% 0.63/0.88 (declare-fun tptp.number_number_of_int (tptp.int) tptp.int)
% 0.63/0.88 (declare-fun tptp.number_number_of_nat (tptp.int) tptp.nat)
% 0.63/0.88 (declare-fun tptp.number267125858f_real (tptp.int) tptp.real)
% 0.63/0.88 (declare-fun tptp.succ (tptp.int) tptp.int)
% 0.63/0.88 (declare-fun tptp.semiri1621563631at_int (tptp.nat) tptp.int)
% 0.63/0.88 (declare-fun tptp.semiri984289939at_nat (tptp.nat) tptp.nat)
% 0.63/0.88 (declare-fun tptp.semiri132038758t_real (tptp.nat) tptp.real)
% 0.63/0.88 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 0.63/0.88 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.63/0.88 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 0.63/0.88 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 0.63/0.88 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.63/0.88 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 0.63/0.88 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 0.63/0.88 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 0.63/0.88 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 0.63/0.88 (declare-fun tptp.legendre (tptp.int tptp.int) tptp.int)
% 0.63/0.88 (declare-fun tptp.quadRes (tptp.int tptp.int) Bool)
% 0.63/0.88 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 0.63/0.88 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 0.63/0.88 (declare-fun tptp.twoSqu919416604sum2sq (tptp.int) Bool)
% 0.63/0.88 (declare-fun tptp.m () tptp.int)
% 0.63/0.88 (declare-fun tptp.m1 () tptp.int)
% 0.63/0.88 (declare-fun tptp.n () tptp.nat)
% 0.63/0.88 (declare-fun tptp.s1 () tptp.int)
% 0.63/0.88 (declare-fun tptp.s () tptp.int)
% 0.63/0.88 (declare-fun tptp.t () tptp.int)
% 0.63/0.88 (declare-fun tptp.tn () tptp.nat)
% 0.63/0.88 (declare-fun tptp.x () tptp.int)
% 0.63/0.88 (declare-fun tptp.y () tptp.int)
% 0.63/0.88 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1621563631at_int tptp.n))))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.t))
% 0.63/0.88 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 0.63/0.88 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 0.63/0.88 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.one_one_int))
% 0.63/0.88 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.one_one_nat))
% 0.63/0.88 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.one_one_real))
% 0.63/0.88 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_int))
% 0.63/0.88 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_nat))
% 0.63/0.88 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_real))
% 0.63/0.88 (assert (forall ((A_136 tptp.int)) (= (= (@ (@ tptp.power_power_int A_136) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_int) (= A_136 tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((A_136 tptp.real)) (= (= (@ (@ tptp.power_power_real A_136) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_real) (= A_136 tptp.zero_zero_real))))
% 0.63/0.88 (assert (forall ((W_16 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.number_number_of_int W_16)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int (@ tptp.bit1 tptp.pls)) W_16)))))
% 0.63/0.88 (assert (forall ((W_16 tptp.int)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.number267125858f_real W_16)) (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int (@ tptp.bit1 tptp.pls)) W_16)))))
% 0.63/0.88 (assert (forall ((V_16 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_16)) tptp.one_one_int) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_16) (@ tptp.bit1 tptp.pls))))))
% 0.63/0.88 (assert (forall ((V_16 tptp.int)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_16)) tptp.one_one_real) (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_16) (@ tptp.bit1 tptp.pls))))))
% 0.63/0.88 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.63/0.88 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.number267125858f_real (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.63/0.88 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.63/0.88 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.63/0.88 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.number267125858f_real (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.63/0.88 (assert (forall ((X tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.power_power_int X))) (let ((_let_3 (@ tptp.number_number_of_nat _let_1))) (= (@ (@ tptp.power_power_int (@ _let_2 _let_3)) _let_3) (@ _let_2 (@ tptp.number_number_of_nat (@ tptp.bit0 _let_1)))))))))
% 0.63/0.88 (assert (forall ((W_15 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_15))) (let ((_let_2 (@ (@ tptp.power_power_int tptp.zero_zero_int) _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 tptp.zero_zero_int))))))))
% 0.63/0.88 (assert (forall ((W_15 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_15))) (let ((_let_2 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 tptp.zero_zero_nat))))))))
% 0.63/0.88 (assert (forall ((W_15 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_15))) (let ((_let_2 (@ (@ tptp.power_power_real tptp.zero_zero_real) _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 tptp.zero_zero_real))))))))
% 0.63/0.88 (assert (= tptp.one_one_int (@ tptp.number_number_of_int (@ tptp.bit1 tptp.pls))))
% 0.63/0.88 (assert (= tptp.one_one_real (@ tptp.number267125858f_real (@ tptp.bit1 tptp.pls))))
% 0.63/0.88 (assert (= (@ tptp.number_number_of_int (@ tptp.bit1 tptp.pls)) tptp.one_one_int))
% 0.63/0.88 (assert (= (@ tptp.number267125858f_real (@ tptp.bit1 tptp.pls)) tptp.one_one_real))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.n))
% 0.63/0.88 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int K)) (@ tptp.number_number_of_int L)) (@ (@ tptp.ord_less_int K) L))))
% 0.63/0.88 (assert (forall ((V_1 tptp.int) (W tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_1)) (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_1) W)))))
% 0.63/0.88 (assert (forall ((X_30 tptp.int) (Y_23 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int X_30)) (@ tptp.number_number_of_int Y_23)) (@ (@ tptp.ord_less_int X_30) Y_23))))
% 0.63/0.88 (assert (forall ((X_30 tptp.int) (Y_23 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.number267125858f_real X_30)) (@ tptp.number267125858f_real Y_23)) (@ (@ tptp.ord_less_int X_30) Y_23))))
% 0.63/0.88 (assert (= tptp.zero_zero_int (@ tptp.number_number_of_int tptp.pls)))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.semiri1621563631at_int M)) N) (@ tptp.semiri1621563631at_int (@ (@ tptp.power_power_nat M) N)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1621563631at_int (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_int (@ tptp.semiri1621563631at_int M)) N))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int N)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int (@ (@ tptp.plus_plus_nat M) N))) Z))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ tptp.semiri1621563631at_int (@ (@ tptp.plus_plus_nat M) N)))))
% 0.63/0.88 (assert (= (@ tptp.semiri1621563631at_int tptp.one_one_nat) tptp.one_one_int))
% 0.63/0.88 (assert (= (@ tptp.number_number_of_nat tptp.pls) tptp.zero_zero_nat))
% 0.63/0.88 (assert (= tptp.zero_zero_nat (@ tptp.number_number_of_nat tptp.pls)))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1621563631at_int N) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 0.63/0.88 (assert (= (@ tptp.semiri1621563631at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 0.63/0.88 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.63/0.88 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_int K1) K2))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_int K) L))))
% 0.63/0.88 (assert (not (@ (@ tptp.ord_less_int tptp.pls) tptp.pls)))
% 0.63/0.88 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K1)) (@ tptp.bit0 K2)) (@ (@ tptp.ord_less_int K1) K2))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K)) (@ tptp.bit0 L)) (@ (@ tptp.ord_less_int K) L))))
% 0.63/0.88 (assert (forall ((K tptp.int) (I_1 tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_int I_1) J) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I_1) K)) (@ (@ tptp.plus_plus_int J) K)))))
% 0.63/0.88 (assert (forall ((V_2 tptp.int) (V_1 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V_2))) (let ((_let_2 (@ tptp.number_number_of_nat V_1))) (let ((_let_3 (@ (@ tptp.plus_plus_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_int V_2) tptp.pls))) (let ((_let_5 (@ (@ tptp.ord_less_int V_1) tptp.pls))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ tptp.number_number_of_nat (@ (@ tptp.plus_plus_int V_1) V_2))))))))))))))
% 0.63/0.88 (assert (= tptp.one_one_int (@ tptp.number_number_of_int (@ tptp.bit1 tptp.pls))))
% 0.63/0.88 (assert (= (@ tptp.number_number_of_nat (@ tptp.bit1 tptp.pls)) tptp.one_one_nat))
% 0.63/0.88 (assert (= tptp.one_one_nat (@ tptp.number_number_of_nat (@ tptp.bit1 tptp.pls))))
% 0.63/0.88 (assert (forall ((X_29 tptp.int) (Y_22 tptp.int)) (= (= (@ tptp.number_number_of_int X_29) (@ tptp.number_number_of_int Y_22)) (= X_29 Y_22))))
% 0.63/0.88 (assert (forall ((X_29 tptp.int) (Y_22 tptp.int)) (= (= (@ tptp.number267125858f_real X_29) (@ tptp.number267125858f_real Y_22)) (= X_29 Y_22))))
% 0.63/0.88 (assert (forall ((W_14 tptp.int) (X_28 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat W_14))) (= (= _let_1 X_28) (= X_28 _let_1)))))
% 0.63/0.88 (assert (forall ((W_14 tptp.int) (X_28 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W_14))) (= (= _let_1 X_28) (= X_28 _let_1)))))
% 0.63/0.88 (assert (forall ((W_14 tptp.int) (X_28 tptp.real)) (let ((_let_1 (@ tptp.number267125858f_real W_14))) (= (= _let_1 X_28) (= X_28 _let_1)))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (= (@ tptp.bit1 K) (@ tptp.bit1 L)) (= K L))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (= (@ tptp.bit0 K) (@ tptp.bit0 L)) (= K L))))
% 0.63/0.88 (assert (forall ((A_135 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_135) A_135)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A_135) tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((A_135 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A_135) A_135)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A_135) tptp.zero_zero_real))))
% 0.63/0.88 (assert (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int Z1))) (= (@ (@ tptp.plus_plus_int (@ _let_1 Z2)) Z3) (@ _let_1 (@ (@ tptp.plus_plus_int Z2) Z3))))))
% 0.63/0.88 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.plus_plus_int Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.63/0.88 (assert (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.plus_plus_int Z) W) (@ (@ tptp.plus_plus_int W) Z))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1621563631at_int M) (@ tptp.semiri1621563631at_int N)) (= M N))))
% 0.63/0.88 (assert (forall ((X_27 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int X_27)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int X_27) tptp.pls))))
% 0.63/0.88 (assert (forall ((X_27 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.number267125858f_real X_27)) tptp.zero_zero_real) (@ (@ tptp.ord_less_int X_27) tptp.pls))))
% 0.63/0.88 (assert (forall ((Y_21 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.number_number_of_int Y_21)) (@ (@ tptp.ord_less_int tptp.pls) Y_21))))
% 0.63/0.88 (assert (forall ((Y_21 tptp.int)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.number267125858f_real Y_21)) (@ (@ tptp.ord_less_int tptp.pls) Y_21))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K)) tptp.pls) (@ (@ tptp.ord_less_int K) tptp.pls))))
% 0.63/0.88 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K1)) (@ tptp.bit0 K2)) (@ (@ tptp.ord_less_int K1) K2))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K)) (@ tptp.bit0 L)) (@ (@ tptp.ord_less_int K) L))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K)) tptp.pls) (@ (@ tptp.ord_less_int K) tptp.pls))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.pls))) (= (@ _let_1 (@ tptp.bit0 K)) (@ _let_1 K)))))
% 0.63/0.88 (assert (forall ((W tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 W)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int W) tptp.zero_zero_int))))
% 0.63/0.88 (assert (not (@ (@ tptp.ord_less_int tptp.pls) tptp.zero_zero_int)))
% 0.63/0.88 (assert (forall ((W tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 W)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int W) tptp.zero_zero_int))))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 0.63/0.88 (assert (forall ((W tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (or (@ _let_1 Z) (= W Z))))))
% 0.63/0.88 (assert (forall ((K tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int K)) tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((X_26 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int X_26)) tptp.one_one_int) (@ (@ tptp.ord_less_int X_26) (@ tptp.bit1 tptp.pls)))))
% 0.63/0.88 (assert (forall ((X_26 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.number267125858f_real X_26)) tptp.one_one_real) (@ (@ tptp.ord_less_int X_26) (@ tptp.bit1 tptp.pls)))))
% 0.63/0.88 (assert (forall ((Y_20 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.number_number_of_int Y_20)) (@ (@ tptp.ord_less_int (@ tptp.bit1 tptp.pls)) Y_20))))
% 0.63/0.88 (assert (forall ((Y_20 tptp.int)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.number267125858f_real Y_20)) (@ (@ tptp.ord_less_int (@ tptp.bit1 tptp.pls)) Y_20))))
% 0.63/0.88 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((A_134 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A_134) A_134) tptp.zero_zero_int) (= A_134 tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((A_134 tptp.real)) (= (= (@ (@ tptp.plus_plus_real A_134) A_134) tptp.zero_zero_real) (= A_134 tptp.zero_zero_real))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (not (= (@ tptp.bit1 K) tptp.pls))))
% 0.63/0.88 (assert (forall ((L tptp.int)) (not (= tptp.pls (@ tptp.bit1 L)))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (not (= (@ tptp.bit1 K) (@ tptp.bit0 L)))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (not (= (@ tptp.bit0 K) (@ tptp.bit1 L)))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (= (@ tptp.bit0 K) tptp.pls) (= K tptp.pls))))
% 0.63/0.88 (assert (forall ((L tptp.int)) (= (= tptp.pls (@ tptp.bit0 L)) (= tptp.pls L))))
% 0.63/0.88 (assert (= (@ tptp.bit0 tptp.pls) tptp.pls))
% 0.63/0.88 (assert (= tptp.pls tptp.zero_zero_int))
% 0.63/0.88 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.pls) K)))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.pls) K) K)))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.bit0 K)) (@ tptp.bit0 L)) (@ tptp.bit0 (@ (@ tptp.plus_plus_int K) L)))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ tptp.bit0 K) (@ (@ tptp.plus_plus_int K) K))))
% 0.63/0.88 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.plus_plus_int Z) tptp.zero_zero_int) Z)))
% 0.63/0.88 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) Z) Z)))
% 0.63/0.88 (assert (= (@ tptp.number_number_of_int tptp.pls) tptp.zero_zero_int))
% 0.63/0.88 (assert (= (@ tptp.number_number_of_nat tptp.pls) tptp.zero_zero_nat))
% 0.63/0.88 (assert (= (@ tptp.number267125858f_real tptp.pls) tptp.zero_zero_real))
% 0.63/0.88 (assert (= (@ tptp.number_number_of_int tptp.pls) tptp.zero_zero_int))
% 0.63/0.88 (assert (= (@ tptp.number267125858f_real tptp.pls) tptp.zero_zero_real))
% 0.63/0.88 (assert (= tptp.zero_zero_int (@ tptp.number_number_of_int tptp.pls)))
% 0.63/0.88 (assert (= tptp.zero_zero_real (@ tptp.number267125858f_real tptp.pls)))
% 0.63/0.88 (assert (forall ((A_133 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int tptp.pls)) A_133) A_133)))
% 0.63/0.88 (assert (forall ((A_133 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real tptp.pls)) A_133) A_133)))
% 0.63/0.88 (assert (forall ((A_132 tptp.int)) (= (@ (@ tptp.plus_plus_int A_132) (@ tptp.number_number_of_int tptp.pls)) A_132)))
% 0.63/0.88 (assert (forall ((A_132 tptp.real)) (= (@ (@ tptp.plus_plus_real A_132) (@ tptp.number267125858f_real tptp.pls)) A_132)))
% 0.63/0.88 (assert (forall ((A_131 tptp.int) (W_13 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_13))) (= (= (@ (@ tptp.power_power_int A_131) _let_1) tptp.zero_zero_int) (and (= A_131 tptp.zero_zero_int) (not (= _let_1 tptp.zero_zero_nat)))))))
% 0.63/0.88 (assert (forall ((A_131 tptp.nat) (W_13 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_13))) (= (= (@ (@ tptp.power_power_nat A_131) _let_1) tptp.zero_zero_nat) (and (= A_131 tptp.zero_zero_nat) (not (= _let_1 tptp.zero_zero_nat)))))))
% 0.63/0.88 (assert (forall ((A_131 tptp.real) (W_13 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_13))) (= (= (@ (@ tptp.power_power_real A_131) _let_1) tptp.zero_zero_real) (and (= A_131 tptp.zero_zero_real) (not (= _let_1 tptp.zero_zero_nat)))))))
% 0.63/0.88 (assert (forall ((V_15 tptp.int) (W_12 tptp.int) (Z_5 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_15)) (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int W_12)) Z_5)) (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_15) W_12))) Z_5))))
% 0.63/0.88 (assert (forall ((V_15 tptp.int) (W_12 tptp.int) (Z_5 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_15)) (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real W_12)) Z_5)) (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_15) W_12))) Z_5))))
% 0.63/0.88 (assert (forall ((V_14 tptp.int) (W_11 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_14)) (@ tptp.number_number_of_int W_11)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_14) W_11)))))
% 0.63/0.88 (assert (forall ((V_14 tptp.int) (W_11 tptp.int)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_14)) (@ tptp.number267125858f_real W_11)) (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_14) W_11)))))
% 0.63/0.88 (assert (forall ((V_13 tptp.int) (W_10 tptp.int)) (= (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_13) W_10)) (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_13)) (@ tptp.number_number_of_int W_10)))))
% 0.63/0.88 (assert (forall ((V_13 tptp.int) (W_10 tptp.int)) (= (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_13) W_10)) (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_13)) (@ tptp.number267125858f_real W_10)))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.bit1 K)) (@ tptp.bit0 L)) (@ tptp.bit1 (@ (@ tptp.plus_plus_int K) L)))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.bit0 K)) (@ tptp.bit1 L)) (@ tptp.bit1 (@ (@ tptp.plus_plus_int K) L)))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ tptp.bit1 K) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) K)) K))))
% 0.63/0.88 (assert (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((N_32 tptp.nat)) (= (@ tptp.number_number_of_nat (@ tptp.semiri1621563631at_int N_32)) (@ tptp.semiri984289939at_nat N_32))))
% 0.63/0.88 (assert (forall ((N_32 tptp.nat)) (let ((_let_1 (@ tptp.semiri1621563631at_int N_32))) (= (@ tptp.number_number_of_int _let_1) _let_1))))
% 0.63/0.88 (assert (forall ((N_32 tptp.nat)) (= (@ tptp.number267125858f_real (@ tptp.semiri1621563631at_int N_32)) (@ tptp.semiri132038758t_real N_32))))
% 0.63/0.88 (assert (forall ((A_130 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A_130) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (not (= A_130 tptp.zero_zero_int)))))
% 0.63/0.88 (assert (forall ((A_130 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A_130) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (not (= A_130 tptp.zero_zero_real)))))
% 0.63/0.88 (assert (forall ((A_129 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A_129) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((A_129 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A_129) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.zero_zero_real))))
% 0.63/0.88 (assert (forall ((X_25 tptp.int) (Y_19 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_25) _let_1)) (@ (@ tptp.power_power_int Y_19) _let_1))) (or (not (= X_25 tptp.zero_zero_int)) (not (= Y_19 tptp.zero_zero_int)))))))
% 0.63/0.88 (assert (forall ((X_25 tptp.real) (Y_19 tptp.real)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X_25) _let_1)) (@ (@ tptp.power_power_real Y_19) _let_1))) (or (not (= X_25 tptp.zero_zero_real)) (not (= Y_19 tptp.zero_zero_real)))))))
% 0.63/0.88 (assert (forall ((X_24 tptp.int) (Y_18 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_24) _let_1)) (@ (@ tptp.power_power_int Y_18) _let_1))) tptp.zero_zero_int)))))
% 0.63/0.88 (assert (forall ((X_24 tptp.real) (Y_18 tptp.real)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X_24) _let_1)) (@ (@ tptp.power_power_real Y_18) _let_1))) tptp.zero_zero_real)))))
% 0.63/0.88 (assert (forall ((W_9 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W_9))) (= (@ tptp.number_number_of_int (@ tptp.bit0 W_9)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.zero_zero_int) _let_1)) _let_1)))))
% 0.63/0.88 (assert (forall ((W_9 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real W_9))) (= (@ tptp.number267125858f_real (@ tptp.bit0 W_9)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.zero_zero_real) _let_1)) _let_1)))))
% 0.63/0.88 (assert (forall ((W_8 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W_8))) (= (@ tptp.number_number_of_int (@ tptp.bit1 W_8)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1)) _let_1)))))
% 0.63/0.88 (assert (forall ((W_8 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real W_8))) (= (@ tptp.number267125858f_real (@ tptp.bit1 W_8)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1)) _let_1)))))
% 0.63/0.88 (assert (= (@ tptp.number_number_of_int (@ tptp.bit1 tptp.pls)) tptp.one_one_int))
% 0.63/0.88 (assert (= (@ tptp.number_number_of_nat (@ tptp.bit1 tptp.pls)) tptp.one_one_nat))
% 0.63/0.88 (assert (= (@ tptp.number267125858f_real (@ tptp.bit1 tptp.pls)) tptp.one_one_real))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_int tptp.m1) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1621563631at_int tptp.n))))
% 0.63/0.88 (assert (forall ((N_31 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int N_31)) (@ (@ tptp.power_power_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_31))))
% 0.63/0.88 (assert (forall ((N_31 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri132038758t_real N_31)) (@ (@ tptp.power_power_real (@ tptp.number267125858f_real (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_31))))
% 0.63/0.88 (assert (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (= (@ tptp.number_number_of_int _let_1) (@ tptp.semiri1621563631at_int (@ tptp.number_number_of_nat _let_1)))))
% 0.63/0.88 (assert (let ((_let_1 (@ tptp.bit1 (@ tptp.bit1 tptp.pls)))) (= (@ tptp.number_number_of_int _let_1) (@ tptp.semiri1621563631at_int (@ tptp.number_number_of_nat _let_1)))))
% 0.63/0.88 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 0.63/0.88 (assert (forall ((N_30 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1621563631at_int N_30)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_30))))
% 0.63/0.88 (assert (forall ((N_30 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri984289939at_nat N_30)) (@ _let_1 N_30)))))
% 0.63/0.88 (assert (forall ((N_30 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri132038758t_real N_30)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_30))))
% 0.63/0.88 (assert (forall ((N_29 tptp.nat) (A_128 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A_128) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_29) (@ _let_1 (@ (@ tptp.power_power_int A_128) N_29)))))))
% 0.63/0.88 (assert (forall ((N_29 tptp.nat) (A_128 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A_128) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_29) (@ _let_1 (@ (@ tptp.power_power_nat A_128) N_29)))))))
% 0.63/0.88 (assert (forall ((N_29 tptp.nat) (A_128 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A_128) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_29) (@ _let_1 (@ (@ tptp.power_power_real A_128) N_29)))))))
% 0.63/0.88 (assert (forall ((N_28 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N_28))) (let ((_let_2 (= N_28 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 0.63/0.88 (assert (forall ((N_28 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N_28))) (let ((_let_2 (= N_28 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 0.63/0.88 (assert (forall ((N_28 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real tptp.zero_zero_real) N_28))) (let ((_let_2 (= N_28 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 0.63/0.88 (assert (forall ((A_127 tptp.int) (N_27 tptp.nat) (N_26 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_127))) (=> (@ (@ tptp.ord_less_nat N_27) N_26) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_127) (=> (@ (@ tptp.ord_less_int A_127) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N_26)) (@ _let_1 N_27))))))))
% 0.63/0.88 (assert (forall ((A_127 tptp.nat) (N_27 tptp.nat) (N_26 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_127))) (=> (@ (@ tptp.ord_less_nat N_27) N_26) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_127) (=> (@ (@ tptp.ord_less_nat A_127) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N_26)) (@ _let_1 N_27))))))))
% 0.63/0.88 (assert (forall ((A_127 tptp.real) (N_27 tptp.nat) (N_26 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_127))) (=> (@ (@ tptp.ord_less_nat N_27) N_26) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A_127) (=> (@ (@ tptp.ord_less_real A_127) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N_26)) (@ _let_1 N_27))))))))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 0.63/0.88 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int) (I_1 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I_1) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_int K) I) (=> (@ P I) (@ P (@ (@ tptp.plus_plus_int I) tptp.one_one_int))))) (@ P I_1))))))
% 0.63/0.88 (assert (= tptp.zero_zero_int (@ tptp.semiri1621563631at_int tptp.zero_zero_nat)))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.tn))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.63/0.88 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.63/0.88 (assert (forall ((I_1 tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) J)) I_1))))
% 0.63/0.88 (assert (forall ((J tptp.nat) (I_1 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I_1)) I_1))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ tptp.number_number_of_int K) K)))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) N) (@ (@ tptp.plus_plus_nat N) M))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (let ((_let_2 (@ tptp.plus_plus_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 N)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) K))))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) K) (@ (@ tptp.plus_plus_nat N) K)) (= M N))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 0.63/0.88 (assert (forall ((S_1 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S_1) T) (not (= S_1 T)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I_1))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I_1))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.63/0.88 (assert (forall ((I_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) J)) K) (@ (@ tptp.ord_less_nat I_1) K))))
% 0.63/0.88 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ P N) M))) (=> (=> (@ (@ tptp.ord_less_nat M) N) _let_1) (=> (=> (= M N) _let_1) (=> (=> (@ (@ tptp.ord_less_nat N) M) _let_1) _let_1))))))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat) (I_1 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I_1) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N)) (or (@ _let_1 X) (= N tptp.zero_zero_nat))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (@ _let_1 M) (@ _let_1 N))))))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N)) (or (= N tptp.zero_zero_nat) (@ _let_1 X))))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ (@ tptp.ord_less_nat X) Y))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (W tptp.int)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.number_number_of_nat W))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (@ _let_1 X)))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ (@ tptp.ord_less_nat M) N))))
% 0.63/0.88 (assert (forall ((V_1 tptp.int) (V_2 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_int V_1) V_2))) (= (@ (@ tptp.ord_less_nat (@ tptp.number_number_of_nat V_1)) (@ tptp.number_number_of_nat V_2)) (and (=> _let_1 (@ (@ tptp.ord_less_int tptp.pls) V_2)) _let_1)))))
% 0.63/0.88 (assert (forall ((X_23 tptp.int) (Y_17 tptp.int)) (=> (not (= X_23 Y_17)) (=> (not (@ (@ tptp.ord_less_int X_23) Y_17)) (@ (@ tptp.ord_less_int Y_17) X_23)))))
% 0.63/0.88 (assert (forall ((X_23 tptp.real) (Y_17 tptp.real)) (=> (not (= X_23 Y_17)) (=> (not (@ (@ tptp.ord_less_real X_23) Y_17)) (@ (@ tptp.ord_less_real Y_17) X_23)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 0.63/0.88 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 0.63/0.88 (assert (forall ((A_126 tptp.int)) (= (@ (@ tptp.power_power_int A_126) tptp.one_one_nat) A_126)))
% 0.63/0.88 (assert (forall ((A_126 tptp.nat)) (= (@ (@ tptp.power_power_nat A_126) tptp.one_one_nat) A_126)))
% 0.63/0.88 (assert (forall ((A_126 tptp.real)) (= (@ (@ tptp.power_power_real A_126) tptp.one_one_nat) A_126)))
% 0.63/0.88 (assert (forall ((M_14 tptp.nat) (N_25 tptp.nat)) (= (= (@ tptp.semiri132038758t_real M_14) (@ tptp.semiri132038758t_real N_25)) (= M_14 N_25))))
% 0.63/0.88 (assert (forall ((M_14 tptp.nat) (N_25 tptp.nat)) (= (= (@ tptp.semiri984289939at_nat M_14) (@ tptp.semiri984289939at_nat N_25)) (= M_14 N_25))))
% 0.63/0.88 (assert (forall ((M_14 tptp.nat) (N_25 tptp.nat)) (= (= (@ tptp.semiri1621563631at_int M_14) (@ tptp.semiri1621563631at_int N_25)) (= M_14 N_25))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.semiri1621563631at_int X) (@ tptp.semiri1621563631at_int Y)) (= X Y))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (let ((_let_1 (@ tptp.semiri1621563631at_int (@ (@ (@ tptp.if_nat P) X) Y)))) (and (=> P (= (@ tptp.semiri1621563631at_int X) _let_1)) (=> (not P) (= (@ tptp.semiri1621563631at_int Y) _let_1))))))
% 0.63/0.88 (assert (forall ((V_1 tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.number_number_of_nat V_1)) (@ (@ tptp.ord_less_int tptp.pls) V_1))))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1621563631at_int N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.63/0.88 (assert (not (= tptp.one_one_int tptp.zero_zero_int)))
% 0.63/0.88 (assert (not (= tptp.one_one_nat tptp.zero_zero_nat)))
% 0.63/0.88 (assert (not (= tptp.one_one_real tptp.zero_zero_real)))
% 0.63/0.88 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 0.63/0.88 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 0.63/0.88 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 0.63/0.88 (assert (forall ((N_24 tptp.nat) (A_125 tptp.int)) (=> (not (= A_125 tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A_125) N_24) tptp.zero_zero_int)))))
% 0.63/0.88 (assert (forall ((N_24 tptp.nat) (A_125 tptp.real)) (=> (not (= A_125 tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A_125) N_24) tptp.zero_zero_real)))))
% 0.63/0.88 (assert (forall ((N_23 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N_23) tptp.one_one_int)))
% 0.63/0.88 (assert (forall ((N_23 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N_23) tptp.one_one_nat)))
% 0.63/0.88 (assert (forall ((N_23 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N_23) tptp.one_one_real)))
% 0.63/0.88 (assert (forall ((M_13 tptp.nat) (N_22 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int M_13)) (@ tptp.semiri1621563631at_int N_22)) (@ (@ tptp.ord_less_nat M_13) N_22))))
% 0.63/0.88 (assert (forall ((M_13 tptp.nat) (N_22 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri984289939at_nat M_13)) (@ tptp.semiri984289939at_nat N_22)) (@ (@ tptp.ord_less_nat M_13) N_22))))
% 0.63/0.88 (assert (forall ((M_13 tptp.nat) (N_22 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri132038758t_real M_13)) (@ tptp.semiri132038758t_real N_22)) (@ (@ tptp.ord_less_nat M_13) N_22))))
% 0.63/0.88 (assert (forall ((M_12 tptp.nat) (N_21 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M_12) N_21) (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int M_12)) (@ tptp.semiri1621563631at_int N_21)))))
% 0.63/0.88 (assert (forall ((M_12 tptp.nat) (N_21 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M_12) N_21) (@ (@ tptp.ord_less_nat (@ tptp.semiri984289939at_nat M_12)) (@ tptp.semiri984289939at_nat N_21)))))
% 0.63/0.88 (assert (forall ((M_12 tptp.nat) (N_21 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M_12) N_21) (@ (@ tptp.ord_less_real (@ tptp.semiri132038758t_real M_12)) (@ tptp.semiri132038758t_real N_21)))))
% 0.63/0.88 (assert (forall ((M_11 tptp.nat) (N_20 tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int M_11)) (@ tptp.semiri1621563631at_int N_20)) (@ (@ tptp.ord_less_nat M_11) N_20))))
% 0.63/0.88 (assert (forall ((M_11 tptp.nat) (N_20 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri984289939at_nat M_11)) (@ tptp.semiri984289939at_nat N_20)) (@ (@ tptp.ord_less_nat M_11) N_20))))
% 0.63/0.88 (assert (forall ((M_11 tptp.nat) (N_20 tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri132038758t_real M_11)) (@ tptp.semiri132038758t_real N_20)) (@ (@ tptp.ord_less_nat M_11) N_20))))
% 0.63/0.88 (assert (forall ((M_10 tptp.nat) (N_19 tptp.nat)) (= (@ tptp.semiri1621563631at_int (@ (@ tptp.plus_plus_nat M_10) N_19)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int M_10)) (@ tptp.semiri1621563631at_int N_19)))))
% 0.63/0.88 (assert (forall ((M_10 tptp.nat) (N_19 tptp.nat)) (= (@ tptp.semiri984289939at_nat (@ (@ tptp.plus_plus_nat M_10) N_19)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri984289939at_nat M_10)) (@ tptp.semiri984289939at_nat N_19)))))
% 0.63/0.88 (assert (forall ((M_10 tptp.nat) (N_19 tptp.nat)) (= (@ tptp.semiri132038758t_real (@ (@ tptp.plus_plus_nat M_10) N_19)) (@ (@ tptp.plus_plus_real (@ tptp.semiri132038758t_real M_10)) (@ tptp.semiri132038758t_real N_19)))))
% 0.63/0.88 (assert (= (@ tptp.semiri1621563631at_int tptp.one_one_nat) tptp.one_one_int))
% 0.63/0.88 (assert (= (@ tptp.semiri984289939at_nat tptp.one_one_nat) tptp.one_one_nat))
% 0.63/0.88 (assert (= (@ tptp.semiri132038758t_real tptp.one_one_nat) tptp.one_one_real))
% 0.63/0.88 (assert (forall ((M_9 tptp.nat) (N_18 tptp.nat)) (= (@ tptp.semiri1621563631at_int (@ (@ tptp.power_power_nat M_9) N_18)) (@ (@ tptp.power_power_int (@ tptp.semiri1621563631at_int M_9)) N_18))))
% 0.63/0.88 (assert (forall ((M_9 tptp.nat) (N_18 tptp.nat)) (= (@ tptp.semiri984289939at_nat (@ (@ tptp.power_power_nat M_9) N_18)) (@ (@ tptp.power_power_nat (@ tptp.semiri984289939at_nat M_9)) N_18))))
% 0.63/0.88 (assert (forall ((M_9 tptp.nat) (N_18 tptp.nat)) (= (@ tptp.semiri132038758t_real (@ (@ tptp.power_power_nat M_9) N_18)) (@ (@ tptp.power_power_real (@ tptp.semiri132038758t_real M_9)) N_18))))
% 0.63/0.88 (assert (= tptp.one_one_int (@ tptp.semiri1621563631at_int tptp.one_one_nat)))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ tptp.semiri1621563631at_int (@ (@ tptp.plus_plus_nat X) Y)))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.semiri1621563631at_int X)) N) (@ tptp.semiri1621563631at_int (@ (@ tptp.power_power_nat X) N)))))
% 0.63/0.88 (assert (forall ((B_89 tptp.int) (C_63 tptp.int) (A_124 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B_89))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_124) (=> (@ _let_1 C_63) (@ _let_1 (@ (@ tptp.plus_plus_int A_124) C_63)))))))
% 0.63/0.88 (assert (forall ((B_89 tptp.nat) (C_63 tptp.nat) (A_124 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B_89))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_124) (=> (@ _let_1 C_63) (@ _let_1 (@ (@ tptp.plus_plus_nat A_124) C_63)))))))
% 0.63/0.88 (assert (forall ((B_89 tptp.real) (C_63 tptp.real) (A_124 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B_89))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A_124) (=> (@ _let_1 C_63) (@ _let_1 (@ (@ tptp.plus_plus_real A_124) C_63)))))))
% 0.63/0.88 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 0.63/0.88 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 0.63/0.88 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 0.63/0.88 (assert (forall ((N_17 tptp.nat) (A_123 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A_123) (@ _let_1 (@ (@ tptp.power_power_int A_123) N_17))))))
% 0.63/0.88 (assert (forall ((N_17 tptp.nat) (A_123 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A_123) (@ _let_1 (@ (@ tptp.power_power_nat A_123) N_17))))))
% 0.63/0.88 (assert (forall ((N_17 tptp.nat) (A_123 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A_123) (@ _let_1 (@ (@ tptp.power_power_real A_123) N_17))))))
% 0.63/0.88 (assert (forall ((A_122 tptp.int)) (@ (@ tptp.ord_less_int A_122) (@ (@ tptp.plus_plus_int A_122) tptp.one_one_int))))
% 0.63/0.88 (assert (forall ((A_122 tptp.nat)) (@ (@ tptp.ord_less_nat A_122) (@ (@ tptp.plus_plus_nat A_122) tptp.one_one_nat))))
% 0.63/0.88 (assert (forall ((A_122 tptp.real)) (@ (@ tptp.ord_less_real A_122) (@ (@ tptp.plus_plus_real A_122) tptp.one_one_real))))
% 0.63/0.88 (assert (forall ((M_8 tptp.nat) (N_16 tptp.nat) (A_121 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A_121))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_121) (= (= (@ _let_1 M_8) (@ _let_1 N_16)) (= M_8 N_16))))))
% 0.63/0.88 (assert (forall ((M_8 tptp.nat) (N_16 tptp.nat) (A_121 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_121))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_121) (= (= (@ _let_1 M_8) (@ _let_1 N_16)) (= M_8 N_16))))))
% 0.63/0.88 (assert (forall ((M_8 tptp.nat) (N_16 tptp.nat) (A_121 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A_121))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_121) (= (= (@ _let_1 M_8) (@ _let_1 N_16)) (= M_8 N_16))))))
% 0.63/0.88 (assert (forall ((X_22 tptp.nat) (Y_16 tptp.nat) (B_88 tptp.int)) (let ((_let_1 (@ tptp.power_power_int B_88))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B_88) (= (@ (@ tptp.ord_less_int (@ _let_1 X_22)) (@ _let_1 Y_16)) (@ (@ tptp.ord_less_nat X_22) Y_16))))))
% 0.63/0.88 (assert (forall ((X_22 tptp.nat) (Y_16 tptp.nat) (B_88 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B_88))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B_88) (= (@ (@ tptp.ord_less_nat (@ _let_1 X_22)) (@ _let_1 Y_16)) (@ (@ tptp.ord_less_nat X_22) Y_16))))))
% 0.63/0.88 (assert (forall ((X_22 tptp.nat) (Y_16 tptp.nat) (B_88 tptp.real)) (let ((_let_1 (@ tptp.power_power_real B_88))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B_88) (= (@ (@ tptp.ord_less_real (@ _let_1 X_22)) (@ _let_1 Y_16)) (@ (@ tptp.ord_less_nat X_22) Y_16))))))
% 0.63/0.88 (assert (forall ((M_7 tptp.nat) (N_15 tptp.nat) (A_120 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A_120))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_120) (=> (@ (@ tptp.ord_less_int (@ _let_1 M_7)) (@ _let_1 N_15)) (@ (@ tptp.ord_less_nat M_7) N_15))))))
% 0.63/0.88 (assert (forall ((M_7 tptp.nat) (N_15 tptp.nat) (A_120 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_120))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_120) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M_7)) (@ _let_1 N_15)) (@ (@ tptp.ord_less_nat M_7) N_15))))))
% 0.63/0.88 (assert (forall ((M_7 tptp.nat) (N_15 tptp.nat) (A_120 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A_120))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_120) (=> (@ (@ tptp.ord_less_real (@ _let_1 M_7)) (@ _let_1 N_15)) (@ (@ tptp.ord_less_nat M_7) N_15))))))
% 0.63/0.88 (assert (forall ((A_119 tptp.int) (N_14 tptp.nat) (N_13 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_119))) (=> (@ (@ tptp.ord_less_nat N_14) N_13) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_119) (@ (@ tptp.ord_less_int (@ _let_1 N_14)) (@ _let_1 N_13)))))))
% 0.63/0.88 (assert (forall ((A_119 tptp.nat) (N_14 tptp.nat) (N_13 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_119))) (=> (@ (@ tptp.ord_less_nat N_14) N_13) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_119) (@ (@ tptp.ord_less_nat (@ _let_1 N_14)) (@ _let_1 N_13)))))))
% 0.63/0.88 (assert (forall ((A_119 tptp.real) (N_14 tptp.nat) (N_13 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_119))) (=> (@ (@ tptp.ord_less_nat N_14) N_13) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_119) (@ (@ tptp.ord_less_real (@ _let_1 N_14)) (@ _let_1 N_13)))))))
% 0.63/0.88 (assert (forall ((A_118 tptp.int) (N_12 tptp.nat)) (= (= (@ (@ tptp.power_power_int A_118) N_12) tptp.zero_zero_int) (and (= A_118 tptp.zero_zero_int) (not (= N_12 tptp.zero_zero_nat))))))
% 0.63/0.88 (assert (forall ((A_118 tptp.nat) (N_12 tptp.nat)) (= (= (@ (@ tptp.power_power_nat A_118) N_12) tptp.zero_zero_nat) (and (= A_118 tptp.zero_zero_nat) (not (= N_12 tptp.zero_zero_nat))))))
% 0.63/0.88 (assert (forall ((A_118 tptp.real) (N_12 tptp.nat)) (= (= (@ (@ tptp.power_power_real A_118) N_12) tptp.zero_zero_real) (and (= A_118 tptp.zero_zero_real) (not (= N_12 tptp.zero_zero_nat))))))
% 0.63/0.88 (assert (forall ((M_6 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int M_6)) tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((M_6 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri984289939at_nat M_6)) tptp.zero_zero_nat))))
% 0.63/0.88 (assert (forall ((M_6 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri132038758t_real M_6)) tptp.zero_zero_real))))
% 0.63/0.88 (assert (forall ((A_117 tptp.int)) (= (@ (@ tptp.power_power_int A_117) tptp.zero_zero_nat) tptp.one_one_int)))
% 0.63/0.88 (assert (forall ((A_117 tptp.nat)) (= (@ (@ tptp.power_power_nat A_117) tptp.zero_zero_nat) tptp.one_one_nat)))
% 0.63/0.88 (assert (forall ((A_117 tptp.real)) (= (@ (@ tptp.power_power_real A_117) tptp.zero_zero_nat) tptp.one_one_real)))
% 0.63/0.88 (assert (= (@ tptp.semiri1621563631at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 0.63/0.88 (assert (= (@ tptp.semiri984289939at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 0.63/0.88 (assert (= (@ tptp.semiri132038758t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N_1 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_1) (= K (@ tptp.semiri1621563631at_int N_1)))))))
% 0.63/0.88 (assert (forall ((I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (exists ((K_1 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K_1) (= (@ (@ tptp.plus_plus_nat I_1) K_1) J))))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat X) N) tptp.one_one_nat) (or (= X tptp.one_one_nat) (= N tptp.zero_zero_nat)))))
% 0.63/0.88 (assert (forall ((X_21 tptp.int)) (= (@ (@ tptp.power_power_int X_21) tptp.zero_zero_nat) tptp.one_one_int)))
% 0.63/0.88 (assert (forall ((X_21 tptp.nat)) (= (@ (@ tptp.power_power_nat X_21) tptp.zero_zero_nat) tptp.one_one_nat)))
% 0.63/0.88 (assert (forall ((X_21 tptp.real)) (= (@ (@ tptp.power_power_real X_21) tptp.zero_zero_nat) tptp.one_one_real)))
% 0.63/0.88 (assert (forall ((A_116 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A_116) A_116)) (@ _let_1 A_116)))))
% 0.63/0.88 (assert (forall ((A_116 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A_116) A_116)) (@ _let_1 A_116)))))
% 0.63/0.88 (assert (forall ((A_115 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_115) A_115)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A_115) tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((A_115 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A_115) A_115)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A_115) tptp.zero_zero_real))))
% 0.63/0.88 (assert (forall ((B_87 tptp.int) (A_114 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A_114) (=> (@ _let_1 B_87) (@ _let_1 (@ (@ tptp.plus_plus_int A_114) B_87)))))))
% 0.63/0.88 (assert (forall ((B_87 tptp.nat) (A_114 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A_114) (=> (@ _let_1 B_87) (@ _let_1 (@ (@ tptp.plus_plus_nat A_114) B_87)))))))
% 0.63/0.88 (assert (forall ((B_87 tptp.real) (A_114 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A_114) (=> (@ _let_1 B_87) (@ _let_1 (@ (@ tptp.plus_plus_real A_114) B_87)))))))
% 0.63/0.88 (assert (forall ((B_86 tptp.int) (A_113 tptp.int)) (=> (@ (@ tptp.ord_less_int A_113) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B_86) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_113) B_86)) tptp.zero_zero_int)))))
% 0.63/0.88 (assert (forall ((B_86 tptp.nat) (A_113 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_113) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B_86) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_113) B_86)) tptp.zero_zero_nat)))))
% 0.63/0.88 (assert (forall ((B_86 tptp.real) (A_113 tptp.real)) (=> (@ (@ tptp.ord_less_real A_113) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B_86) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A_113) B_86)) tptp.zero_zero_real)))))
% 0.63/0.88 (assert (forall ((X_20 tptp.int)) (= (= tptp.zero_zero_int X_20) (= X_20 tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((X_20 tptp.nat)) (= (= tptp.zero_zero_nat X_20) (= X_20 tptp.zero_zero_nat))))
% 0.63/0.88 (assert (forall ((X_20 tptp.real)) (= (= tptp.zero_zero_real X_20) (= X_20 tptp.zero_zero_real))))
% 0.63/0.88 (assert (forall ((B_85 tptp.int) (A_112 tptp.int) (C_62 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B_85) A_112) (@ (@ tptp.plus_plus_int C_62) A_112)) (= B_85 C_62))))
% 0.63/0.88 (assert (forall ((B_85 tptp.nat) (A_112 tptp.nat) (C_62 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B_85) A_112) (@ (@ tptp.plus_plus_nat C_62) A_112)) (= B_85 C_62))))
% 0.63/0.88 (assert (forall ((B_85 tptp.real) (A_112 tptp.real) (C_62 tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B_85) A_112) (@ (@ tptp.plus_plus_real C_62) A_112)) (= B_85 C_62))))
% 0.63/0.88 (assert (forall ((A_111 tptp.int) (B_84 tptp.int) (C_61 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_111))) (=> (= (@ _let_1 B_84) (@ _let_1 C_61)) (= B_84 C_61)))))
% 0.63/0.88 (assert (forall ((A_111 tptp.nat) (B_84 tptp.nat) (C_61 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_111))) (=> (= (@ _let_1 B_84) (@ _let_1 C_61)) (= B_84 C_61)))))
% 0.63/0.88 (assert (forall ((A_111 tptp.real) (B_84 tptp.real) (C_61 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_111))) (=> (= (@ _let_1 B_84) (@ _let_1 C_61)) (= B_84 C_61)))))
% 0.63/0.88 (assert (forall ((A_110 tptp.int) (B_83 tptp.int) (C_60 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_110))) (=> (= (@ _let_1 B_83) (@ _let_1 C_60)) (= B_83 C_60)))))
% 0.63/0.88 (assert (forall ((A_110 tptp.nat) (B_83 tptp.nat) (C_60 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_110))) (=> (= (@ _let_1 B_83) (@ _let_1 C_60)) (= B_83 C_60)))))
% 0.63/0.88 (assert (forall ((A_110 tptp.real) (B_83 tptp.real) (C_60 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_110))) (=> (= (@ _let_1 B_83) (@ _let_1 C_60)) (= B_83 C_60)))))
% 0.63/0.88 (assert (forall ((A_109 tptp.int) (B_82 tptp.int) (C_59 tptp.int) (D_23 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_109))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_82)) (@ (@ tptp.plus_plus_int C_59) D_23)) (@ (@ tptp.plus_plus_int (@ _let_1 C_59)) (@ (@ tptp.plus_plus_int B_82) D_23))))))
% 0.63/0.88 (assert (forall ((A_109 tptp.nat) (B_82 tptp.nat) (C_59 tptp.nat) (D_23 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_109))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_82)) (@ (@ tptp.plus_plus_nat C_59) D_23)) (@ (@ tptp.plus_plus_nat (@ _let_1 C_59)) (@ (@ tptp.plus_plus_nat B_82) D_23))))))
% 0.63/0.88 (assert (forall ((A_109 tptp.real) (B_82 tptp.real) (C_59 tptp.real) (D_23 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_109))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B_82)) (@ (@ tptp.plus_plus_real C_59) D_23)) (@ (@ tptp.plus_plus_real (@ _let_1 C_59)) (@ (@ tptp.plus_plus_real B_82) D_23))))))
% 0.63/0.88 (assert (forall ((B_81 tptp.int) (A_108 tptp.int) (C_58 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B_81) A_108) (@ (@ tptp.plus_plus_int C_58) A_108)) (= B_81 C_58))))
% 0.63/0.88 (assert (forall ((B_81 tptp.nat) (A_108 tptp.nat) (C_58 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B_81) A_108) (@ (@ tptp.plus_plus_nat C_58) A_108)) (= B_81 C_58))))
% 0.63/0.88 (assert (forall ((B_81 tptp.real) (A_108 tptp.real) (C_58 tptp.real)) (= (= (@ (@ tptp.plus_plus_real B_81) A_108) (@ (@ tptp.plus_plus_real C_58) A_108)) (= B_81 C_58))))
% 0.63/0.88 (assert (forall ((A_107 tptp.int) (B_80 tptp.int) (C_57 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_107))) (= (= (@ _let_1 B_80) (@ _let_1 C_57)) (= B_80 C_57)))))
% 0.63/0.88 (assert (forall ((A_107 tptp.nat) (B_80 tptp.nat) (C_57 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_107))) (= (= (@ _let_1 B_80) (@ _let_1 C_57)) (= B_80 C_57)))))
% 0.63/0.88 (assert (forall ((A_107 tptp.real) (B_80 tptp.real) (C_57 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_107))) (= (= (@ _let_1 B_80) (@ _let_1 C_57)) (= B_80 C_57)))))
% 0.63/0.88 (assert (forall ((A_106 tptp.int) (B_79 tptp.int) (C_56 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_106))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_79)) C_56) (@ (@ tptp.plus_plus_int (@ _let_1 C_56)) B_79)))))
% 0.63/0.88 (assert (forall ((A_106 tptp.nat) (B_79 tptp.nat) (C_56 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_106))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_79)) C_56) (@ (@ tptp.plus_plus_nat (@ _let_1 C_56)) B_79)))))
% 0.63/0.88 (assert (forall ((A_106 tptp.real) (B_79 tptp.real) (C_56 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_106))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B_79)) C_56) (@ (@ tptp.plus_plus_real (@ _let_1 C_56)) B_79)))))
% 0.63/0.88 (assert (forall ((A_105 tptp.int) (B_78 tptp.int) (C_55 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_105))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_78)) C_55) (@ _let_1 (@ (@ tptp.plus_plus_int B_78) C_55))))))
% 0.63/0.88 (assert (forall ((A_105 tptp.nat) (B_78 tptp.nat) (C_55 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_105))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_78)) C_55) (@ _let_1 (@ (@ tptp.plus_plus_nat B_78) C_55))))))
% 0.63/0.88 (assert (forall ((A_105 tptp.real) (B_78 tptp.real) (C_55 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_105))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B_78)) C_55) (@ _let_1 (@ (@ tptp.plus_plus_real B_78) C_55))))))
% 0.63/0.88 (assert (forall ((A_104 tptp.int) (B_77 tptp.int) (C_54 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_104))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_77)) C_54) (@ _let_1 (@ (@ tptp.plus_plus_int B_77) C_54))))))
% 0.63/0.88 (assert (forall ((A_104 tptp.nat) (B_77 tptp.nat) (C_54 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_104))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_77)) C_54) (@ _let_1 (@ (@ tptp.plus_plus_nat B_77) C_54))))))
% 0.63/0.88 (assert (forall ((A_104 tptp.real) (B_77 tptp.real) (C_54 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_104))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B_77)) C_54) (@ _let_1 (@ (@ tptp.plus_plus_real B_77) C_54))))))
% 0.63/0.88 (assert (forall ((A_103 tptp.int) (C_53 tptp.int) (D_22 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_103))) (= (@ _let_1 (@ (@ tptp.plus_plus_int C_53) D_22)) (@ (@ tptp.plus_plus_int (@ _let_1 C_53)) D_22)))))
% 0.63/0.88 (assert (forall ((A_103 tptp.nat) (C_53 tptp.nat) (D_22 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_103))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat C_53) D_22)) (@ (@ tptp.plus_plus_nat (@ _let_1 C_53)) D_22)))))
% 0.63/0.88 (assert (forall ((A_103 tptp.real) (C_53 tptp.real) (D_22 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_103))) (= (@ _let_1 (@ (@ tptp.plus_plus_real C_53) D_22)) (@ (@ tptp.plus_plus_real (@ _let_1 C_53)) D_22)))))
% 0.63/0.88 (assert (forall ((A_102 tptp.int) (C_52 tptp.int) (D_21 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_102))) (let ((_let_2 (@ tptp.plus_plus_int C_52))) (= (@ _let_1 (@ _let_2 D_21)) (@ _let_2 (@ _let_1 D_21)))))))
% 0.63/0.88 (assert (forall ((A_102 tptp.nat) (C_52 tptp.nat) (D_21 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_102))) (let ((_let_2 (@ tptp.plus_plus_nat C_52))) (= (@ _let_1 (@ _let_2 D_21)) (@ _let_2 (@ _let_1 D_21)))))))
% 0.63/0.88 (assert (forall ((A_102 tptp.real) (C_52 tptp.real) (D_21 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_102))) (let ((_let_2 (@ tptp.plus_plus_real C_52))) (= (@ _let_1 (@ _let_2 D_21)) (@ _let_2 (@ _let_1 D_21)))))))
% 0.63/0.88 (assert (forall ((A_101 tptp.int) (C_51 tptp.int)) (= (@ (@ tptp.plus_plus_int A_101) C_51) (@ (@ tptp.plus_plus_int C_51) A_101))))
% 0.63/0.88 (assert (forall ((A_101 tptp.nat) (C_51 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_101) C_51) (@ (@ tptp.plus_plus_nat C_51) A_101))))
% 0.63/0.88 (assert (forall ((A_101 tptp.real) (C_51 tptp.real)) (= (@ (@ tptp.plus_plus_real A_101) C_51) (@ (@ tptp.plus_plus_real C_51) A_101))))
% 0.63/0.88 (assert (forall ((X_19 tptp.int)) (= (= tptp.one_one_int X_19) (= X_19 tptp.one_one_int))))
% 0.63/0.88 (assert (forall ((X_19 tptp.nat)) (= (= tptp.one_one_nat X_19) (= X_19 tptp.one_one_nat))))
% 0.63/0.88 (assert (forall ((X_19 tptp.real)) (= (= tptp.one_one_real X_19) (= X_19 tptp.one_one_real))))
% 0.63/0.88 (assert (forall ((B_76 tptp.int) (A_100 tptp.int)) (= (= B_76 (@ (@ tptp.plus_plus_int B_76) A_100)) (= A_100 tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((B_76 tptp.nat) (A_100 tptp.nat)) (= (= B_76 (@ (@ tptp.plus_plus_nat B_76) A_100)) (= A_100 tptp.zero_zero_nat))))
% 0.63/0.88 (assert (forall ((B_76 tptp.real) (A_100 tptp.real)) (= (= B_76 (@ (@ tptp.plus_plus_real B_76) A_100)) (= A_100 tptp.zero_zero_real))))
% 0.63/0.88 (assert (forall ((A_99 tptp.int)) (= (@ (@ tptp.plus_plus_int A_99) tptp.zero_zero_int) A_99)))
% 0.63/0.88 (assert (forall ((A_99 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_99) tptp.zero_zero_nat) A_99)))
% 0.63/0.88 (assert (forall ((A_99 tptp.real)) (= (@ (@ tptp.plus_plus_real A_99) tptp.zero_zero_real) A_99)))
% 0.63/0.88 (assert (forall ((A_98 tptp.int)) (= (@ (@ tptp.plus_plus_int A_98) tptp.zero_zero_int) A_98)))
% 0.63/0.88 (assert (forall ((A_98 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_98) tptp.zero_zero_nat) A_98)))
% 0.63/0.88 (assert (forall ((A_98 tptp.real)) (= (@ (@ tptp.plus_plus_real A_98) tptp.zero_zero_real) A_98)))
% 0.63/0.88 (assert (forall ((A_97 tptp.int)) (= (@ (@ tptp.plus_plus_int A_97) tptp.zero_zero_int) A_97)))
% 0.63/0.88 (assert (forall ((A_97 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_97) tptp.zero_zero_nat) A_97)))
% 0.63/0.88 (assert (forall ((A_97 tptp.real)) (= (@ (@ tptp.plus_plus_real A_97) tptp.zero_zero_real) A_97)))
% 0.63/0.88 (assert (forall ((A_96 tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A_96) A_96)) (= A_96 tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((A_96 tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A_96) A_96)) (= A_96 tptp.zero_zero_real))))
% 0.63/0.88 (assert (forall ((A_95 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A_95) A_95)))
% 0.63/0.88 (assert (forall ((A_95 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A_95) A_95)))
% 0.63/0.88 (assert (forall ((A_95 tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A_95) A_95)))
% 0.63/0.88 (assert (forall ((A_94 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A_94) A_94)))
% 0.63/0.88 (assert (forall ((A_94 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A_94) A_94)))
% 0.63/0.88 (assert (forall ((A_94 tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A_94) A_94)))
% 0.63/0.88 (assert (forall ((A_93 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A_93) A_93)))
% 0.63/0.88 (assert (forall ((A_93 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A_93) A_93)))
% 0.63/0.88 (assert (forall ((A_93 tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A_93) A_93)))
% 0.63/0.88 (assert (forall ((C_50 tptp.int) (A_92 tptp.int) (B_75 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_50))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A_92)) (@ _let_1 B_75)) (@ (@ tptp.ord_less_int A_92) B_75)))))
% 0.63/0.88 (assert (forall ((C_50 tptp.nat) (A_92 tptp.nat) (B_75 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_50))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A_92)) (@ _let_1 B_75)) (@ (@ tptp.ord_less_nat A_92) B_75)))))
% 0.63/0.88 (assert (forall ((C_50 tptp.real) (A_92 tptp.real) (B_75 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C_50))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A_92)) (@ _let_1 B_75)) (@ (@ tptp.ord_less_real A_92) B_75)))))
% 0.63/0.88 (assert (forall ((A_91 tptp.int) (C_49 tptp.int) (B_74 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_91) C_49)) (@ (@ tptp.plus_plus_int B_74) C_49)) (@ (@ tptp.ord_less_int A_91) B_74))))
% 0.63/0.88 (assert (forall ((A_91 tptp.nat) (C_49 tptp.nat) (B_74 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_91) C_49)) (@ (@ tptp.plus_plus_nat B_74) C_49)) (@ (@ tptp.ord_less_nat A_91) B_74))))
% 0.63/0.88 (assert (forall ((A_91 tptp.real) (C_49 tptp.real) (B_74 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A_91) C_49)) (@ (@ tptp.plus_plus_real B_74) C_49)) (@ (@ tptp.ord_less_real A_91) B_74))))
% 0.63/0.88 (assert (forall ((C_48 tptp.int) (D_20 tptp.int) (A_90 tptp.int) (B_73 tptp.int)) (=> (@ (@ tptp.ord_less_int A_90) B_73) (=> (@ (@ tptp.ord_less_int C_48) D_20) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_90) C_48)) (@ (@ tptp.plus_plus_int B_73) D_20))))))
% 0.63/0.88 (assert (forall ((C_48 tptp.nat) (D_20 tptp.nat) (A_90 tptp.nat) (B_73 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_90) B_73) (=> (@ (@ tptp.ord_less_nat C_48) D_20) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_90) C_48)) (@ (@ tptp.plus_plus_nat B_73) D_20))))))
% 0.63/0.88 (assert (forall ((C_48 tptp.real) (D_20 tptp.real) (A_90 tptp.real) (B_73 tptp.real)) (=> (@ (@ tptp.ord_less_real A_90) B_73) (=> (@ (@ tptp.ord_less_real C_48) D_20) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A_90) C_48)) (@ (@ tptp.plus_plus_real B_73) D_20))))))
% 0.63/0.88 (assert (forall ((C_47 tptp.int) (A_89 tptp.int) (B_72 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_47))) (=> (@ (@ tptp.ord_less_int A_89) B_72) (@ (@ tptp.ord_less_int (@ _let_1 A_89)) (@ _let_1 B_72))))))
% 0.63/0.88 (assert (forall ((C_47 tptp.nat) (A_89 tptp.nat) (B_72 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_47))) (=> (@ (@ tptp.ord_less_nat A_89) B_72) (@ (@ tptp.ord_less_nat (@ _let_1 A_89)) (@ _let_1 B_72))))))
% 0.63/0.88 (assert (forall ((C_47 tptp.real) (A_89 tptp.real) (B_72 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C_47))) (=> (@ (@ tptp.ord_less_real A_89) B_72) (@ (@ tptp.ord_less_real (@ _let_1 A_89)) (@ _let_1 B_72))))))
% 0.63/0.88 (assert (forall ((C_46 tptp.int) (A_88 tptp.int) (B_71 tptp.int)) (=> (@ (@ tptp.ord_less_int A_88) B_71) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_88) C_46)) (@ (@ tptp.plus_plus_int B_71) C_46)))))
% 0.63/0.88 (assert (forall ((C_46 tptp.nat) (A_88 tptp.nat) (B_71 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_88) B_71) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_88) C_46)) (@ (@ tptp.plus_plus_nat B_71) C_46)))))
% 0.63/0.88 (assert (forall ((C_46 tptp.real) (A_88 tptp.real) (B_71 tptp.real)) (=> (@ (@ tptp.ord_less_real A_88) B_71) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A_88) C_46)) (@ (@ tptp.plus_plus_real B_71) C_46)))))
% 0.63/0.88 (assert (forall ((C_45 tptp.int) (A_87 tptp.int) (B_70 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_45))) (= (@ (@ tptp.ord_less_int (@ _let_1 A_87)) (@ _let_1 B_70)) (@ (@ tptp.ord_less_int A_87) B_70)))))
% 0.63/0.88 (assert (forall ((C_45 tptp.nat) (A_87 tptp.nat) (B_70 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_45))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A_87)) (@ _let_1 B_70)) (@ (@ tptp.ord_less_nat A_87) B_70)))))
% 0.63/0.88 (assert (forall ((C_45 tptp.real) (A_87 tptp.real) (B_70 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C_45))) (= (@ (@ tptp.ord_less_real (@ _let_1 A_87)) (@ _let_1 B_70)) (@ (@ tptp.ord_less_real A_87) B_70)))))
% 0.63/0.88 (assert (forall ((A_86 tptp.int) (C_44 tptp.int) (B_69 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_86) C_44)) (@ (@ tptp.plus_plus_int B_69) C_44)) (@ (@ tptp.ord_less_int A_86) B_69))))
% 0.63/0.88 (assert (forall ((A_86 tptp.nat) (C_44 tptp.nat) (B_69 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_86) C_44)) (@ (@ tptp.plus_plus_nat B_69) C_44)) (@ (@ tptp.ord_less_nat A_86) B_69))))
% 0.63/0.88 (assert (forall ((A_86 tptp.real) (C_44 tptp.real) (B_69 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A_86) C_44)) (@ (@ tptp.plus_plus_real B_69) C_44)) (@ (@ tptp.ord_less_real A_86) B_69))))
% 0.63/0.88 (assert (forall ((X_18 tptp.int)) (= (@ (@ tptp.power_power_int X_18) tptp.one_one_nat) X_18)))
% 0.63/0.88 (assert (forall ((X_18 tptp.nat)) (= (@ (@ tptp.power_power_nat X_18) tptp.one_one_nat) X_18)))
% 0.63/0.88 (assert (forall ((X_18 tptp.real)) (= (@ (@ tptp.power_power_real X_18) tptp.one_one_nat) X_18)))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat M) N) tptp.zero_zero_nat) (and (not (= N tptp.zero_zero_nat)) (= M tptp.zero_zero_nat)))))
% 0.63/0.88 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X_1 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X_1) (= (@ (@ tptp.power_power_real X_1) N) A) (forall ((Y_1 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y_1) (= (@ (@ tptp.power_power_real Y_1) N) A)) (= Y_1 X_1)))))))))
% 0.63/0.88 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (= (@ (@ tptp.power_power_real R) N) A)))))))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.t))
% 0.63/0.88 (assert (forall ((V_1 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat V_1)) tptp.one_one_nat))) (let ((_let_2 (@ (@ tptp.ord_less_int V_1) tptp.pls))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (@ tptp.number_number_of_nat (@ tptp.succ V_1)))))))))
% 0.63/0.88 (assert (forall ((V_1 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.number_number_of_nat V_1)))) (let ((_let_2 (@ (@ tptp.ord_less_int V_1) tptp.pls))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (@ tptp.number_number_of_nat (@ tptp.succ V_1)))))))))
% 0.63/0.88 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit1 tptp.pls))) (let ((_let_2 (@ tptp.bit1 _let_1))) (let ((_let_3 (@ tptp.number_number_of_nat _let_2))) (let ((_let_4 (@ tptp.power_power_int B))) (let ((_let_5 (@ tptp.number_number_of_nat (@ tptp.bit0 _let_1)))) (let ((_let_6 (@ tptp.times_times_int (@ tptp.number_number_of_int _let_2)))) (let ((_let_7 (@ tptp.power_power_int A))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B)) _let_3) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ _let_7 _let_3)) (@ (@ tptp.times_times_int (@ _let_6 (@ _let_7 _let_5))) B))) (@ (@ tptp.times_times_int (@ _let_6 A)) (@ _let_4 _let_5)))) (@ _let_4 _let_3))))))))))))
% 0.63/0.88 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.number_number_of_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int A) _let_2)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int _let_1)) A)) B))) (@ (@ tptp.power_power_int B) _let_2)))))))
% 0.63/0.88 (assert (= tptp.tn (@ (@ tptp.minus_minus_nat (@ tptp.nat_1 tptp.t)) tptp.one_one_nat)))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ tptp.nat_1 tptp.t)) tptp.one_one_nat)))
% 0.63/0.88 (assert (forall ((A_85 tptp.int) (B_68 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A_85) B_68) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A_85) B_68)) tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((A_85 tptp.real) (B_68 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A_85) B_68) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A_85) B_68)) tptp.zero_zero_real))))
% 0.63/0.88 (assert (forall ((A_84 tptp.int) (B_67 tptp.int)) (= (@ (@ tptp.times_times_int A_84) B_67) (@ (@ tptp.times_times_int B_67) A_84))))
% 0.63/0.88 (assert (forall ((A_84 tptp.nat) (B_67 tptp.nat)) (= (@ (@ tptp.times_times_nat A_84) B_67) (@ (@ tptp.times_times_nat B_67) A_84))))
% 0.63/0.88 (assert (forall ((A_84 tptp.real) (B_67 tptp.real)) (= (@ (@ tptp.times_times_real A_84) B_67) (@ (@ tptp.times_times_real B_67) A_84))))
% 0.63/0.88 (assert (forall ((Lx_6 tptp.int) (Rx_6 tptp.int) (Ry_4 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_6))) (let ((_let_2 (@ tptp.times_times_int Rx_6))) (= (@ _let_1 (@ _let_2 Ry_4)) (@ _let_2 (@ _let_1 Ry_4)))))))
% 0.63/0.88 (assert (forall ((Lx_6 tptp.nat) (Rx_6 tptp.nat) (Ry_4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx_6))) (let ((_let_2 (@ tptp.times_times_nat Rx_6))) (= (@ _let_1 (@ _let_2 Ry_4)) (@ _let_2 (@ _let_1 Ry_4)))))))
% 0.63/0.88 (assert (forall ((Lx_6 tptp.real) (Rx_6 tptp.real) (Ry_4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx_6))) (let ((_let_2 (@ tptp.times_times_real Rx_6))) (= (@ _let_1 (@ _let_2 Ry_4)) (@ _let_2 (@ _let_1 Ry_4)))))))
% 0.63/0.88 (assert (forall ((Lx_5 tptp.int) (Rx_5 tptp.int) (Ry_3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_5))) (= (@ _let_1 (@ (@ tptp.times_times_int Rx_5) Ry_3)) (@ (@ tptp.times_times_int (@ _let_1 Rx_5)) Ry_3)))))
% 0.63/0.88 (assert (forall ((Lx_5 tptp.nat) (Rx_5 tptp.nat) (Ry_3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx_5))) (= (@ _let_1 (@ (@ tptp.times_times_nat Rx_5) Ry_3)) (@ (@ tptp.times_times_nat (@ _let_1 Rx_5)) Ry_3)))))
% 0.63/0.88 (assert (forall ((Lx_5 tptp.real) (Rx_5 tptp.real) (Ry_3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx_5))) (= (@ _let_1 (@ (@ tptp.times_times_real Rx_5) Ry_3)) (@ (@ tptp.times_times_real (@ _let_1 Rx_5)) Ry_3)))))
% 0.63/0.88 (assert (forall ((A_83 tptp.int) (B_66 tptp.int) (C_43 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A_83))) (= (@ (@ tptp.times_times_int (@ _let_1 B_66)) C_43) (@ _let_1 (@ (@ tptp.times_times_int B_66) C_43))))))
% 0.63/0.88 (assert (forall ((A_83 tptp.nat) (B_66 tptp.nat) (C_43 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A_83))) (= (@ (@ tptp.times_times_nat (@ _let_1 B_66)) C_43) (@ _let_1 (@ (@ tptp.times_times_nat B_66) C_43))))))
% 0.63/0.88 (assert (forall ((A_83 tptp.real) (B_66 tptp.real) (C_43 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A_83))) (= (@ (@ tptp.times_times_real (@ _let_1 B_66)) C_43) (@ _let_1 (@ (@ tptp.times_times_real B_66) C_43))))))
% 0.63/0.88 (assert (forall ((Lx_4 tptp.int) (Ly_4 tptp.int) (Rx_4 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_4))) (= (@ (@ tptp.times_times_int (@ _let_1 Ly_4)) Rx_4) (@ _let_1 (@ (@ tptp.times_times_int Ly_4) Rx_4))))))
% 0.63/0.88 (assert (forall ((Lx_4 tptp.nat) (Ly_4 tptp.nat) (Rx_4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx_4))) (= (@ (@ tptp.times_times_nat (@ _let_1 Ly_4)) Rx_4) (@ _let_1 (@ (@ tptp.times_times_nat Ly_4) Rx_4))))))
% 0.63/0.88 (assert (forall ((Lx_4 tptp.real) (Ly_4 tptp.real) (Rx_4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx_4))) (= (@ (@ tptp.times_times_real (@ _let_1 Ly_4)) Rx_4) (@ _let_1 (@ (@ tptp.times_times_real Ly_4) Rx_4))))))
% 0.63/0.88 (assert (forall ((Lx_3 tptp.int) (Ly_3 tptp.int) (Rx_3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_3))) (= (@ (@ tptp.times_times_int (@ _let_1 Ly_3)) Rx_3) (@ (@ tptp.times_times_int (@ _let_1 Rx_3)) Ly_3)))))
% 0.63/0.88 (assert (forall ((Lx_3 tptp.nat) (Ly_3 tptp.nat) (Rx_3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx_3))) (= (@ (@ tptp.times_times_nat (@ _let_1 Ly_3)) Rx_3) (@ (@ tptp.times_times_nat (@ _let_1 Rx_3)) Ly_3)))))
% 0.63/0.88 (assert (forall ((Lx_3 tptp.real) (Ly_3 tptp.real) (Rx_3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx_3))) (= (@ (@ tptp.times_times_real (@ _let_1 Ly_3)) Rx_3) (@ (@ tptp.times_times_real (@ _let_1 Rx_3)) Ly_3)))))
% 0.63/0.88 (assert (forall ((Lx_2 tptp.int) (Ly_2 tptp.int) (Rx_2 tptp.int) (Ry_2 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int Rx_2) Ry_2))) (let ((_let_2 (@ tptp.times_times_int Lx_2))) (= (@ (@ tptp.times_times_int (@ _let_2 Ly_2)) _let_1) (@ _let_2 (@ (@ tptp.times_times_int Ly_2) _let_1)))))))
% 0.63/0.88 (assert (forall ((Lx_2 tptp.nat) (Ly_2 tptp.nat) (Rx_2 tptp.nat) (Ry_2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat Rx_2) Ry_2))) (let ((_let_2 (@ tptp.times_times_nat Lx_2))) (= (@ (@ tptp.times_times_nat (@ _let_2 Ly_2)) _let_1) (@ _let_2 (@ (@ tptp.times_times_nat Ly_2) _let_1)))))))
% 0.63/0.88 (assert (forall ((Lx_2 tptp.real) (Ly_2 tptp.real) (Rx_2 tptp.real) (Ry_2 tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real Rx_2) Ry_2))) (let ((_let_2 (@ tptp.times_times_real Lx_2))) (= (@ (@ tptp.times_times_real (@ _let_2 Ly_2)) _let_1) (@ _let_2 (@ (@ tptp.times_times_real Ly_2) _let_1)))))))
% 0.63/0.88 (assert (forall ((Lx_1 tptp.real) (Ly_1 tptp.real) (Rx_1 tptp.real) (Ry_1 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.times_times_real Lx_1) Ly_1)))) (let ((_let_2 (@ tptp.times_times_real Rx_1))) (= (@ _let_1 (@ _let_2 Ry_1)) (@ _let_2 (@ _let_1 Ry_1)))))))
% 0.63/0.88 (assert (forall ((Lx_1 tptp.nat) (Ly_1 tptp.nat) (Rx_1 tptp.nat) (Ry_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ (@ tptp.times_times_nat Lx_1) Ly_1)))) (let ((_let_2 (@ tptp.times_times_nat Rx_1))) (= (@ _let_1 (@ _let_2 Ry_1)) (@ _let_2 (@ _let_1 Ry_1)))))))
% 0.63/0.88 (assert (forall ((Lx_1 tptp.int) (Ly_1 tptp.int) (Rx_1 tptp.int) (Ry_1 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.times_times_int Lx_1) Ly_1)))) (let ((_let_2 (@ tptp.times_times_int Rx_1))) (= (@ _let_1 (@ _let_2 Ry_1)) (@ _let_2 (@ _let_1 Ry_1)))))))
% 0.63/0.88 (assert (forall ((Lx tptp.real) (Ly tptp.real) (Rx tptp.real) (Ry tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx))) (= (@ (@ tptp.times_times_real (@ _let_1 Ly)) (@ (@ tptp.times_times_real Rx) Ry)) (@ (@ tptp.times_times_real (@ _let_1 Rx)) (@ (@ tptp.times_times_real Ly) Ry))))))
% 0.63/0.88 (assert (forall ((Lx tptp.nat) (Ly tptp.nat) (Rx tptp.nat) (Ry tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx))) (= (@ (@ tptp.times_times_nat (@ _let_1 Ly)) (@ (@ tptp.times_times_nat Rx) Ry)) (@ (@ tptp.times_times_nat (@ _let_1 Rx)) (@ (@ tptp.times_times_nat Ly) Ry))))))
% 0.63/0.88 (assert (forall ((Lx tptp.int) (Ly tptp.int) (Rx tptp.int) (Ry tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx))) (= (@ (@ tptp.times_times_int (@ _let_1 Ly)) (@ (@ tptp.times_times_int Rx) Ry)) (@ (@ tptp.times_times_int (@ _let_1 Rx)) (@ (@ tptp.times_times_int Ly) Ry))))))
% 0.63/0.88 (assert (forall ((A_82 tptp.int) (B_65 tptp.int) (C_42 tptp.int) (D_19 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A_82) B_65) (@ (@ tptp.minus_minus_int C_42) D_19)) (= (= A_82 B_65) (= C_42 D_19)))))
% 0.63/0.88 (assert (forall ((A_82 tptp.real) (B_65 tptp.real) (C_42 tptp.real) (D_19 tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A_82) B_65) (@ (@ tptp.minus_minus_real C_42) D_19)) (= (= A_82 B_65) (= C_42 D_19)))))
% 0.63/0.88 (assert (forall ((A_81 tptp.int) (B_64 tptp.int) (C_41 tptp.int) (D_18 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A_81) B_64) (@ (@ tptp.minus_minus_int C_41) D_18)) (= (@ (@ tptp.ord_less_eq_int A_81) B_64) (@ (@ tptp.ord_less_eq_int C_41) D_18)))))
% 0.63/0.88 (assert (forall ((A_81 tptp.real) (B_64 tptp.real) (C_41 tptp.real) (D_18 tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A_81) B_64) (@ (@ tptp.minus_minus_real C_41) D_18)) (= (@ (@ tptp.ord_less_eq_real A_81) B_64) (@ (@ tptp.ord_less_eq_real C_41) D_18)))))
% 0.63/0.88 (assert (forall ((V_12 tptp.int) (V_11 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_11) (=> (@ _let_1 V_12) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real V_11)) (@ tptp.number267125858f_real V_12)) (@ tptp.number267125858f_real (@ (@ tptp.times_times_int V_11) V_12))))))))
% 0.63/0.88 (assert (forall ((V_12 tptp.int) (V_11 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_11) (=> (@ _let_1 V_12) (= (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V_11)) (@ tptp.number_number_of_nat V_12)) (@ tptp.number_number_of_nat (@ (@ tptp.times_times_int V_11) V_12))))))))
% 0.63/0.88 (assert (forall ((V_12 tptp.int) (V_11 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_11) (=> (@ _let_1 V_12) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_11)) (@ tptp.number_number_of_int V_12)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_11) V_12))))))))
% 0.63/0.88 (assert (forall ((W tptp.int)) (@ (@ tptp.ord_less_eq_int W) W)))
% 0.63/0.88 (assert (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int Z) W) (@ (@ tptp.times_times_int W) Z))))
% 0.63/0.88 (assert (forall ((Z tptp.int) (W tptp.int)) (or (@ (@ tptp.ord_less_eq_int Z) W) (@ (@ tptp.ord_less_eq_int W) Z))))
% 0.63/0.88 (assert (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z1))) (= (@ (@ tptp.times_times_int (@ _let_1 Z2)) Z3) (@ _let_1 (@ (@ tptp.times_times_int Z2) Z3))))))
% 0.63/0.88 (assert (forall ((K tptp.int) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int I_1))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_int J) K) (@ _let_1 K))))))
% 0.63/0.88 (assert (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) W) (=> (@ (@ tptp.ord_less_eq_int W) Z) (= Z W)))))
% 0.63/0.88 (assert (forall ((X_17 tptp.int) (Y_15 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.number267125858f_real X_17)) (@ tptp.number267125858f_real Y_15)) (@ (@ tptp.ord_less_eq_int X_17) Y_15))))
% 0.63/0.88 (assert (forall ((X_17 tptp.int) (Y_15 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_17)) (@ tptp.number_number_of_int Y_15)) (@ (@ tptp.ord_less_eq_int X_17) Y_15))))
% 0.63/0.88 (assert (forall ((V_10 tptp.int) (W_7 tptp.int)) (= (@ tptp.number267125858f_real (@ (@ tptp.times_times_int V_10) W_7)) (@ (@ tptp.times_times_real (@ tptp.number267125858f_real V_10)) (@ tptp.number267125858f_real W_7)))))
% 0.63/0.88 (assert (forall ((V_10 tptp.int) (W_7 tptp.int)) (= (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_10) W_7)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_10)) (@ tptp.number_number_of_int W_7)))))
% 0.63/0.88 (assert (forall ((V_9 tptp.int) (W_6 tptp.int)) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real V_9)) (@ tptp.number267125858f_real W_6)) (@ tptp.number267125858f_real (@ (@ tptp.times_times_int V_9) W_6)))))
% 0.63/0.88 (assert (forall ((V_9 tptp.int) (W_6 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_9)) (@ tptp.number_number_of_int W_6)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_9) W_6)))))
% 0.63/0.88 (assert (forall ((V_8 tptp.int) (W_5 tptp.int) (Z_4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real V_8)) (@ (@ tptp.times_times_real (@ tptp.number267125858f_real W_5)) Z_4)) (@ (@ tptp.times_times_real (@ tptp.number267125858f_real (@ (@ tptp.times_times_int V_8) W_5))) Z_4))))
% 0.63/0.88 (assert (forall ((V_8 tptp.int) (W_5 tptp.int) (Z_4 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_8)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int W_5)) Z_4)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_8) W_5))) Z_4))))
% 0.63/0.88 (assert (forall ((Z_1 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z_1) (= (= (@ tptp.nat_1 Z) (@ tptp.nat_1 Z_1)) (= Z Z_1)))))))
% 0.63/0.88 (assert (forall ((V_7 tptp.int) (B_63 tptp.int) (C_40 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.number_number_of_int V_7)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B_63) C_40)) (@ (@ tptp.minus_minus_int (@ _let_1 B_63)) (@ _let_1 C_40))))))
% 0.63/0.88 (assert (forall ((V_7 tptp.int) (B_63 tptp.real) (C_40 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.number267125858f_real V_7)))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B_63) C_40)) (@ (@ tptp.minus_minus_real (@ _let_1 B_63)) (@ _let_1 C_40))))))
% 0.63/0.88 (assert (forall ((A_80 tptp.int) (B_62 tptp.int) (V_6 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V_6))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A_80) B_62)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A_80) _let_1)) (@ (@ tptp.times_times_int B_62) _let_1))))))
% 0.63/0.88 (assert (forall ((A_80 tptp.real) (B_62 tptp.real) (V_6 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real V_6))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A_80) B_62)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A_80) _let_1)) (@ (@ tptp.times_times_real B_62) _let_1))))))
% 0.63/0.88 (assert (forall ((V_5 tptp.int) (W_4 tptp.int)) (= (@ tptp.number_number_of_int (@ (@ tptp.minus_minus_int V_5) W_4)) (@ (@ tptp.minus_minus_int (@ tptp.number_number_of_int V_5)) (@ tptp.number_number_of_int W_4)))))
% 0.63/0.88 (assert (forall ((V_5 tptp.int) (W_4 tptp.int)) (= (@ tptp.number267125858f_real (@ (@ tptp.minus_minus_int V_5) W_4)) (@ (@ tptp.minus_minus_real (@ tptp.number267125858f_real V_5)) (@ tptp.number267125858f_real W_4)))))
% 0.63/0.88 (assert (forall ((M_5 tptp.nat) (N_11 tptp.nat)) (= (@ tptp.semiri132038758t_real (@ (@ tptp.times_times_nat M_5) N_11)) (@ (@ tptp.times_times_real (@ tptp.semiri132038758t_real M_5)) (@ tptp.semiri132038758t_real N_11)))))
% 0.63/0.88 (assert (forall ((M_5 tptp.nat) (N_11 tptp.nat)) (= (@ tptp.semiri984289939at_nat (@ (@ tptp.times_times_nat M_5) N_11)) (@ (@ tptp.times_times_nat (@ tptp.semiri984289939at_nat M_5)) (@ tptp.semiri984289939at_nat N_11)))))
% 0.63/0.88 (assert (forall ((M_5 tptp.nat) (N_11 tptp.nat)) (= (@ tptp.semiri1621563631at_int (@ (@ tptp.times_times_nat M_5) N_11)) (@ (@ tptp.times_times_int (@ tptp.semiri1621563631at_int M_5)) (@ tptp.semiri1621563631at_int N_11)))))
% 0.63/0.88 (assert (forall ((M_4 tptp.nat) (N_10 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri132038758t_real M_4)) (@ tptp.semiri132038758t_real N_10)) (@ (@ tptp.ord_less_eq_nat M_4) N_10))))
% 0.63/0.88 (assert (forall ((M_4 tptp.nat) (N_10 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri984289939at_nat M_4)) (@ tptp.semiri984289939at_nat N_10)) (@ (@ tptp.ord_less_eq_nat M_4) N_10))))
% 0.63/0.88 (assert (forall ((M_4 tptp.nat) (N_10 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1621563631at_int M_4)) (@ tptp.semiri1621563631at_int N_10)) (@ (@ tptp.ord_less_eq_nat M_4) N_10))))
% 0.63/0.88 (assert (forall ((I_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I_1))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))))
% 0.63/0.88 (assert (forall ((X tptp.int) (Y tptp.int) (P Bool)) (let ((_let_1 (@ tptp.nat_1 (@ (@ (@ tptp.if_int P) X) Y)))) (and (=> P (= (@ tptp.nat_1 X) _let_1)) (=> (not P) (= (@ tptp.nat_1 Y) _let_1))))))
% 0.63/0.88 (assert (forall ((B_61 tptp.real) (A_79 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A_79) (@ (@ tptp.ord_less_eq_real B_61) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A_79) tptp.zero_zero_real) (@ _let_1 B_61))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_79) B_61)) tptp.zero_zero_real)))))
% 0.63/0.88 (assert (forall ((B_61 tptp.nat) (A_79 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A_79) (@ (@ tptp.ord_less_eq_nat B_61) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A_79) tptp.zero_zero_nat) (@ _let_1 B_61))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_79) B_61)) tptp.zero_zero_nat)))))
% 0.63/0.88 (assert (forall ((B_61 tptp.int) (A_79 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A_79) (@ (@ tptp.ord_less_eq_int B_61) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A_79) tptp.zero_zero_int) (@ _let_1 B_61))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_79) B_61)) tptp.zero_zero_int)))))
% 0.63/0.88 (assert (forall ((B_60 tptp.real) (A_78 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A_78) (@ _let_1 B_60)) (and (@ (@ tptp.ord_less_eq_real A_78) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B_60) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.times_times_real A_78) B_60))))))
% 0.63/0.88 (assert (forall ((B_60 tptp.int) (A_78 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A_78) (@ _let_1 B_60)) (and (@ (@ tptp.ord_less_eq_int A_78) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B_60) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A_78) B_60))))))
% 0.63/0.88 (assert (forall ((C_39 tptp.real) (D_17 tptp.real) (A_77 tptp.real) (B_59 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A_77) B_59) (=> (@ (@ tptp.ord_less_eq_real C_39) D_17) (=> (@ _let_1 B_59) (=> (@ _let_1 C_39) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_77) C_39)) (@ (@ tptp.times_times_real B_59) D_17)))))))))
% 0.63/0.88 (assert (forall ((C_39 tptp.nat) (D_17 tptp.nat) (A_77 tptp.nat) (B_59 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A_77) B_59) (=> (@ (@ tptp.ord_less_eq_nat C_39) D_17) (=> (@ _let_1 B_59) (=> (@ _let_1 C_39) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_77) C_39)) (@ (@ tptp.times_times_nat B_59) D_17)))))))))
% 0.63/0.88 (assert (forall ((C_39 tptp.int) (D_17 tptp.int) (A_77 tptp.int) (B_59 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A_77) B_59) (=> (@ (@ tptp.ord_less_eq_int C_39) D_17) (=> (@ _let_1 B_59) (=> (@ _let_1 C_39) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_77) C_39)) (@ (@ tptp.times_times_int B_59) D_17)))))))))
% 0.63/0.88 (assert (forall ((C_38 tptp.real) (D_16 tptp.real) (A_76 tptp.real) (B_58 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A_76) B_58) (=> (@ (@ tptp.ord_less_eq_real C_38) D_16) (=> (@ _let_1 A_76) (=> (@ _let_1 C_38) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_76) C_38)) (@ (@ tptp.times_times_real B_58) D_16)))))))))
% 0.63/0.88 (assert (forall ((C_38 tptp.nat) (D_16 tptp.nat) (A_76 tptp.nat) (B_58 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A_76) B_58) (=> (@ (@ tptp.ord_less_eq_nat C_38) D_16) (=> (@ _let_1 A_76) (=> (@ _let_1 C_38) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_76) C_38)) (@ (@ tptp.times_times_nat B_58) D_16)))))))))
% 0.63/0.88 (assert (forall ((C_38 tptp.int) (D_16 tptp.int) (A_76 tptp.int) (B_58 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A_76) B_58) (=> (@ (@ tptp.ord_less_eq_int C_38) D_16) (=> (@ _let_1 A_76) (=> (@ _let_1 C_38) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_76) C_38)) (@ (@ tptp.times_times_int B_58) D_16)))))))))
% 0.63/0.88 (assert (forall ((C_37 tptp.real) (B_57 tptp.real) (A_75 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_37))) (=> (@ (@ tptp.ord_less_eq_real B_57) A_75) (=> (@ (@ tptp.ord_less_eq_real C_37) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A_75)) (@ _let_1 B_57)))))))
% 0.63/0.88 (assert (forall ((C_37 tptp.int) (B_57 tptp.int) (A_75 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_37))) (=> (@ (@ tptp.ord_less_eq_int B_57) A_75) (=> (@ (@ tptp.ord_less_eq_int C_37) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A_75)) (@ _let_1 B_57)))))))
% 0.63/0.88 (assert (forall ((C_36 tptp.real) (B_56 tptp.real) (A_74 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B_56) A_74) (=> (@ (@ tptp.ord_less_eq_real C_36) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_74) C_36)) (@ (@ tptp.times_times_real B_56) C_36))))))
% 0.63/0.88 (assert (forall ((C_36 tptp.int) (B_56 tptp.int) (A_74 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B_56) A_74) (=> (@ (@ tptp.ord_less_eq_int C_36) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_74) C_36)) (@ (@ tptp.times_times_int B_56) C_36))))))
% 0.63/0.88 (assert (forall ((C_35 tptp.real) (A_73 tptp.real) (B_55 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_35))) (=> (@ (@ tptp.ord_less_eq_real A_73) B_55) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_35) (@ (@ tptp.ord_less_eq_real (@ _let_1 A_73)) (@ _let_1 B_55)))))))
% 0.63/0.88 (assert (forall ((C_35 tptp.nat) (A_73 tptp.nat) (B_55 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_35))) (=> (@ (@ tptp.ord_less_eq_nat A_73) B_55) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_35) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_73)) (@ _let_1 B_55)))))))
% 0.63/0.88 (assert (forall ((C_35 tptp.int) (A_73 tptp.int) (B_55 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_35))) (=> (@ (@ tptp.ord_less_eq_int A_73) B_55) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_35) (@ (@ tptp.ord_less_eq_int (@ _let_1 A_73)) (@ _let_1 B_55)))))))
% 0.63/0.88 (assert (forall ((C_34 tptp.real) (A_72 tptp.real) (B_54 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_34))) (=> (@ (@ tptp.ord_less_eq_real A_72) B_54) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_34) (@ (@ tptp.ord_less_eq_real (@ _let_1 A_72)) (@ _let_1 B_54)))))))
% 0.63/0.88 (assert (forall ((C_34 tptp.nat) (A_72 tptp.nat) (B_54 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_34))) (=> (@ (@ tptp.ord_less_eq_nat A_72) B_54) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_34) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_72)) (@ _let_1 B_54)))))))
% 0.63/0.88 (assert (forall ((C_34 tptp.int) (A_72 tptp.int) (B_54 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_34))) (=> (@ (@ tptp.ord_less_eq_int A_72) B_54) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_34) (@ (@ tptp.ord_less_eq_int (@ _let_1 A_72)) (@ _let_1 B_54)))))))
% 0.63/0.88 (assert (forall ((C_33 tptp.real) (A_71 tptp.real) (B_53 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_71) B_53) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_33) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_71) C_33)) (@ (@ tptp.times_times_real B_53) C_33))))))
% 0.63/0.88 (assert (forall ((C_33 tptp.nat) (A_71 tptp.nat) (B_53 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_71) B_53) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_33) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_71) C_33)) (@ (@ tptp.times_times_nat B_53) C_33))))))
% 0.63/0.88 (assert (forall ((C_33 tptp.int) (A_71 tptp.int) (B_53 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_71) B_53) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_33) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_71) C_33)) (@ (@ tptp.times_times_int B_53) C_33))))))
% 0.63/0.88 (assert (forall ((B_52 tptp.real) (A_70 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_70) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B_52) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A_70) B_52))))))
% 0.63/0.88 (assert (forall ((B_52 tptp.int) (A_70 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_70) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B_52) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A_70) B_52))))))
% 0.63/0.88 (assert (forall ((B_51 tptp.real) (A_69 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_69) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B_51) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_69) B_51)) tptp.zero_zero_real)))))
% 0.63/0.88 (assert (forall ((B_51 tptp.nat) (A_69 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_69) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B_51) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_69) B_51)) tptp.zero_zero_nat)))))
% 0.63/0.88 (assert (forall ((B_51 tptp.int) (A_69 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_69) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B_51) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_69) B_51)) tptp.zero_zero_int)))))
% 0.63/0.88 (assert (forall ((B_50 tptp.real) (A_68 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_68) (=> (@ (@ tptp.ord_less_eq_real B_50) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real B_50) A_68)) tptp.zero_zero_real)))))
% 0.63/0.88 (assert (forall ((B_50 tptp.nat) (A_68 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_68) (=> (@ (@ tptp.ord_less_eq_nat B_50) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B_50) A_68)) tptp.zero_zero_nat)))))
% 0.63/0.88 (assert (forall ((B_50 tptp.int) (A_68 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_68) (=> (@ (@ tptp.ord_less_eq_int B_50) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B_50) A_68)) tptp.zero_zero_int)))))
% 0.63/0.88 (assert (forall ((B_49 tptp.real) (A_67 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_67) (=> (@ (@ tptp.ord_less_eq_real B_49) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_67) B_49)) tptp.zero_zero_real)))))
% 0.63/0.88 (assert (forall ((B_49 tptp.nat) (A_67 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_67) (=> (@ (@ tptp.ord_less_eq_nat B_49) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_67) B_49)) tptp.zero_zero_nat)))))
% 0.63/0.88 (assert (forall ((B_49 tptp.int) (A_67 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_67) (=> (@ (@ tptp.ord_less_eq_int B_49) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_67) B_49)) tptp.zero_zero_int)))))
% 0.63/0.88 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ tptp.nat_1 X) (@ tptp.nat_1 Y)) (= X Y)))))))
% 0.63/0.88 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.times_times_int X) Y)))))))
% 0.63/0.88 (assert (forall ((B_48 tptp.real) (A_66 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A_66) (=> (@ _let_1 B_48) (@ _let_1 (@ (@ tptp.times_times_real A_66) B_48)))))))
% 0.63/0.88 (assert (forall ((B_48 tptp.nat) (A_66 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A_66) (=> (@ _let_1 B_48) (@ _let_1 (@ (@ tptp.times_times_nat A_66) B_48)))))))
% 0.63/0.88 (assert (forall ((B_48 tptp.int) (A_66 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A_66) (=> (@ _let_1 B_48) (@ _let_1 (@ (@ tptp.times_times_int A_66) B_48)))))))
% 0.63/0.88 (assert (forall ((A_65 tptp.real) (E_6 tptp.real) (C_32 tptp.real) (B_47 tptp.real) (D_15 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_65) E_6)) C_32)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B_47) E_6)) D_15)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A_65) B_47)) E_6)) C_32)) D_15))))
% 0.63/0.88 (assert (forall ((A_65 tptp.int) (E_6 tptp.int) (C_32 tptp.int) (B_47 tptp.int) (D_15 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_65) E_6)) C_32)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_47) E_6)) D_15)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A_65) B_47)) E_6)) C_32)) D_15))))
% 0.63/0.88 (assert (forall ((A_64 tptp.real) (E_5 tptp.real) (C_31 tptp.real) (B_46 tptp.real) (D_14 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_64) E_5)) C_31) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B_46) E_5)) D_14)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A_64) B_46)) E_5)) C_31) D_14))))
% 0.63/0.88 (assert (forall ((A_64 tptp.int) (E_5 tptp.int) (C_31 tptp.int) (B_46 tptp.int) (D_14 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_64) E_5)) C_31) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_46) E_5)) D_14)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A_64) B_46)) E_5)) C_31) D_14))))
% 0.63/0.88 (assert (forall ((A_63 tptp.real) (E_4 tptp.real) (C_30 tptp.real) (B_45 tptp.real) (D_13 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_63) E_4)) C_30)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B_45) E_4)) D_13)) (@ (@ tptp.ord_less_eq_real C_30) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B_45) A_63)) E_4)) D_13)))))
% 0.63/0.88 (assert (forall ((A_63 tptp.int) (E_4 tptp.int) (C_30 tptp.int) (B_45 tptp.int) (D_13 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_63) E_4)) C_30)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_45) E_4)) D_13)) (@ (@ tptp.ord_less_eq_int C_30) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B_45) A_63)) E_4)) D_13)))))
% 0.63/0.88 (assert (forall ((A_62 tptp.real) (E_3 tptp.real) (C_29 tptp.real) (B_44 tptp.real) (D_12 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_62) E_3)) C_29) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B_44) E_3)) D_12)) (= C_29 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B_44) A_62)) E_3)) D_12)))))
% 0.63/0.88 (assert (forall ((A_62 tptp.int) (E_3 tptp.int) (C_29 tptp.int) (B_44 tptp.int) (D_12 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_62) E_3)) C_29) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_44) E_3)) D_12)) (= C_29 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B_44) A_62)) E_3)) D_12)))))
% 0.63/0.88 (assert (forall ((X_16 tptp.real) (Y_14 tptp.real) (A_61 tptp.real) (B_43 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X_16))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y_14)) (@ (@ tptp.times_times_real A_61) B_43)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y_14) B_43))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X_16) A_61)) B_43))))))
% 0.63/0.88 (assert (forall ((X_16 tptp.int) (Y_14 tptp.int) (A_61 tptp.int) (B_43 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X_16))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y_14)) (@ (@ tptp.times_times_int A_61) B_43)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y_14) B_43))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X_16) A_61)) B_43))))))
% 0.63/0.88 (assert (forall ((A_60 tptp.real) (B_42 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_60) B_42)) tptp.zero_zero_real) (or (and (@ _let_1 A_60) (@ (@ tptp.ord_less_eq_real B_42) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A_60) tptp.zero_zero_real) (@ _let_1 B_42)))))))
% 0.63/0.88 (assert (forall ((A_60 tptp.int) (B_42 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_60) B_42)) tptp.zero_zero_int) (or (and (@ _let_1 A_60) (@ (@ tptp.ord_less_eq_int B_42) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A_60) tptp.zero_zero_int) (@ _let_1 B_42)))))))
% 0.63/0.88 (assert (forall ((A_59 tptp.real) (B_41 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A_59) B_41)) (or (and (@ _let_1 A_59) (@ _let_1 B_41)) (and (@ (@ tptp.ord_less_eq_real A_59) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B_41) tptp.zero_zero_real)))))))
% 0.63/0.88 (assert (forall ((A_59 tptp.int) (B_41 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A_59) B_41)) (or (and (@ _let_1 A_59) (@ _let_1 B_41)) (and (@ (@ tptp.ord_less_eq_int A_59) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B_41) tptp.zero_zero_int)))))))
% 0.63/0.88 (assert (forall ((P (-> tptp.nat Bool))) (= (@ tptp.all P) (forall ((X_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P (@ tptp.nat_1 X_1)))))))
% 0.63/0.88 (assert (forall ((P (-> tptp.nat Bool))) (= (@ tptp.ex P) (exists ((X_1 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P (@ tptp.nat_1 X_1)))))))
% 0.63/0.88 (assert (forall ((A_58 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A_58) A_58))))
% 0.63/0.88 (assert (forall ((A_58 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A_58) A_58))))
% 0.63/0.88 (assert (forall ((A_57 tptp.real) (E_2 tptp.real) (C_28 tptp.real) (B_40 tptp.real) (D_11 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_57) E_2)) C_28)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B_40) E_2)) D_11)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A_57) B_40)) E_2)) C_28)) D_11))))
% 0.63/0.88 (assert (forall ((A_57 tptp.int) (E_2 tptp.int) (C_28 tptp.int) (B_40 tptp.int) (D_11 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_57) E_2)) C_28)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_40) E_2)) D_11)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A_57) B_40)) E_2)) C_28)) D_11))))
% 0.63/0.88 (assert (forall ((A_56 tptp.real) (E_1 tptp.real) (C_27 tptp.real) (B_39 tptp.real) (D_10 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_56) E_1)) C_27)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B_39) E_1)) D_10)) (@ (@ tptp.ord_less_real C_27) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B_39) A_56)) E_1)) D_10)))))
% 0.63/0.88 (assert (forall ((A_56 tptp.int) (E_1 tptp.int) (C_27 tptp.int) (B_39 tptp.int) (D_10 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_56) E_1)) C_27)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_39) E_1)) D_10)) (@ (@ tptp.ord_less_int C_27) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B_39) A_56)) E_1)) D_10)))))
% 0.63/0.88 (assert (forall ((X_15 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X_15) X_15)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X_15) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X_15) tptp.one_one_real)))))
% 0.63/0.88 (assert (forall ((X_15 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X_15) X_15)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X_15) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X_15) tptp.one_one_int)))))
% 0.63/0.88 (assert (forall ((C_26 tptp.real) (A_55 tptp.real) (B_38 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_26))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A_55)) (@ _let_1 B_38)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_26) (@ (@ tptp.ord_less_eq_real A_55) B_38))))))
% 0.63/0.88 (assert (forall ((C_26 tptp.nat) (A_55 tptp.nat) (B_38 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_26))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_55)) (@ _let_1 B_38)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C_26) (@ (@ tptp.ord_less_eq_nat A_55) B_38))))))
% 0.63/0.88 (assert (forall ((C_26 tptp.int) (A_55 tptp.int) (B_38 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_26))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A_55)) (@ _let_1 B_38)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_26) (@ (@ tptp.ord_less_eq_int A_55) B_38))))))
% 0.63/0.88 (assert (forall ((A_54 tptp.real) (C_25 tptp.real) (B_37 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_54) C_25)) (@ (@ tptp.times_times_real B_37) C_25)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_25) (@ (@ tptp.ord_less_eq_real A_54) B_37)))))
% 0.63/0.88 (assert (forall ((A_54 tptp.nat) (C_25 tptp.nat) (B_37 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_54) C_25)) (@ (@ tptp.times_times_nat B_37) C_25)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C_25) (@ (@ tptp.ord_less_eq_nat A_54) B_37)))))
% 0.63/0.88 (assert (forall ((A_54 tptp.int) (C_25 tptp.int) (B_37 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_54) C_25)) (@ (@ tptp.times_times_int B_37) C_25)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_25) (@ (@ tptp.ord_less_eq_int A_54) B_37)))))
% 0.63/0.88 (assert (forall ((C_24 tptp.real) (A_53 tptp.real) (B_36 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_24))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A_53)) (@ _let_1 B_36)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_24) (@ (@ tptp.ord_less_real A_53) B_36))))))
% 0.63/0.88 (assert (forall ((C_24 tptp.nat) (A_53 tptp.nat) (B_36 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_24))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A_53)) (@ _let_1 B_36)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_24) (@ (@ tptp.ord_less_nat A_53) B_36))))))
% 0.63/0.88 (assert (forall ((C_24 tptp.int) (A_53 tptp.int) (B_36 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_24))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A_53)) (@ _let_1 B_36)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_24) (@ (@ tptp.ord_less_int A_53) B_36))))))
% 0.63/0.88 (assert (forall ((C_23 tptp.real) (A_52 tptp.real) (B_35 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_23))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A_52)) (@ _let_1 B_35)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_23) (@ (@ tptp.ord_less_real A_52) B_35))))))
% 0.63/0.88 (assert (forall ((C_23 tptp.nat) (A_52 tptp.nat) (B_35 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_23))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A_52)) (@ _let_1 B_35)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_23) (@ (@ tptp.ord_less_nat A_52) B_35))))))
% 0.63/0.88 (assert (forall ((C_23 tptp.int) (A_52 tptp.int) (B_35 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_23))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A_52)) (@ _let_1 B_35)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_23) (@ (@ tptp.ord_less_int A_52) B_35))))))
% 0.63/0.88 (assert (forall ((A_51 tptp.real) (C_22 tptp.real) (B_34 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_51) C_22)) (@ (@ tptp.times_times_real B_34) C_22)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_22) (@ (@ tptp.ord_less_real A_51) B_34)))))
% 0.63/0.88 (assert (forall ((A_51 tptp.nat) (C_22 tptp.nat) (B_34 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_51) C_22)) (@ (@ tptp.times_times_nat B_34) C_22)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_22) (@ (@ tptp.ord_less_nat A_51) B_34)))))
% 0.63/0.88 (assert (forall ((A_51 tptp.int) (C_22 tptp.int) (B_34 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_51) C_22)) (@ (@ tptp.times_times_int B_34) C_22)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_22) (@ (@ tptp.ord_less_int A_51) B_34)))))
% 0.63/0.88 (assert (forall ((A_50 tptp.real) (C_21 tptp.real) (B_33 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_50) C_21)) (@ (@ tptp.times_times_real B_33) C_21)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_21) (@ (@ tptp.ord_less_real A_50) B_33)))))
% 0.63/0.88 (assert (forall ((A_50 tptp.nat) (C_21 tptp.nat) (B_33 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_50) C_21)) (@ (@ tptp.times_times_nat B_33) C_21)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_21) (@ (@ tptp.ord_less_nat A_50) B_33)))))
% 0.63/0.88 (assert (forall ((A_50 tptp.int) (C_21 tptp.int) (B_33 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_50) C_21)) (@ (@ tptp.times_times_int B_33) C_21)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_21) (@ (@ tptp.ord_less_int A_50) B_33)))))
% 0.63/0.88 (assert (forall ((C_20 tptp.real) (D_9 tptp.real) (A_49 tptp.real) (B_32 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_49) B_32) (=> (@ (@ tptp.ord_less_real C_20) D_9) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A_49) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_20) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_49) C_20)) (@ (@ tptp.times_times_real B_32) D_9))))))))
% 0.63/0.88 (assert (forall ((C_20 tptp.nat) (D_9 tptp.nat) (A_49 tptp.nat) (B_32 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_49) B_32) (=> (@ (@ tptp.ord_less_nat C_20) D_9) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_49) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_20) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_49) C_20)) (@ (@ tptp.times_times_nat B_32) D_9))))))))
% 0.63/0.88 (assert (forall ((C_20 tptp.int) (D_9 tptp.int) (A_49 tptp.int) (B_32 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_49) B_32) (=> (@ (@ tptp.ord_less_int C_20) D_9) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_49) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_20) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_49) C_20)) (@ (@ tptp.times_times_int B_32) D_9))))))))
% 0.63/0.88 (assert (forall ((C_19 tptp.real) (D_8 tptp.real) (A_48 tptp.real) (B_31 tptp.real)) (=> (@ (@ tptp.ord_less_real A_48) B_31) (=> (@ (@ tptp.ord_less_eq_real C_19) D_8) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_48) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_19) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_48) C_19)) (@ (@ tptp.times_times_real B_31) D_8))))))))
% 0.63/0.88 (assert (forall ((C_19 tptp.nat) (D_8 tptp.nat) (A_48 tptp.nat) (B_31 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_48) B_31) (=> (@ (@ tptp.ord_less_eq_nat C_19) D_8) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_48) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C_19) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_48) C_19)) (@ (@ tptp.times_times_nat B_31) D_8))))))))
% 0.63/0.88 (assert (forall ((C_19 tptp.int) (D_8 tptp.int) (A_48 tptp.int) (B_31 tptp.int)) (=> (@ (@ tptp.ord_less_int A_48) B_31) (=> (@ (@ tptp.ord_less_eq_int C_19) D_8) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_48) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_19) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_48) C_19)) (@ (@ tptp.times_times_int B_31) D_8))))))))
% 0.63/0.88 (assert (forall ((C_18 tptp.real) (D_7 tptp.real) (A_47 tptp.real) (B_30 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real A_47) B_30) (=> (@ (@ tptp.ord_less_real C_18) D_7) (=> (@ _let_1 A_47) (=> (@ _let_1 C_18) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_47) C_18)) (@ (@ tptp.times_times_real B_30) D_7)))))))))
% 0.63/0.88 (assert (forall ((C_18 tptp.nat) (D_7 tptp.nat) (A_47 tptp.nat) (B_30 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A_47) B_30) (=> (@ (@ tptp.ord_less_nat C_18) D_7) (=> (@ _let_1 A_47) (=> (@ _let_1 C_18) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_47) C_18)) (@ (@ tptp.times_times_nat B_30) D_7)))))))))
% 0.63/0.88 (assert (forall ((C_18 tptp.int) (D_7 tptp.int) (A_47 tptp.int) (B_30 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A_47) B_30) (=> (@ (@ tptp.ord_less_int C_18) D_7) (=> (@ _let_1 A_47) (=> (@ _let_1 C_18) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_47) C_18)) (@ (@ tptp.times_times_int B_30) D_7)))))))))
% 0.63/0.88 (assert (forall ((C_17 tptp.real) (D_6 tptp.real) (A_46 tptp.real) (B_29 tptp.real)) (=> (@ (@ tptp.ord_less_real A_46) B_29) (=> (@ (@ tptp.ord_less_real C_17) D_6) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B_29) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_17) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_46) C_17)) (@ (@ tptp.times_times_real B_29) D_6))))))))
% 0.63/0.88 (assert (forall ((C_17 tptp.nat) (D_6 tptp.nat) (A_46 tptp.nat) (B_29 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_46) B_29) (=> (@ (@ tptp.ord_less_nat C_17) D_6) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B_29) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_17) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_46) C_17)) (@ (@ tptp.times_times_nat B_29) D_6))))))))
% 0.63/0.88 (assert (forall ((C_17 tptp.int) (D_6 tptp.int) (A_46 tptp.int) (B_29 tptp.int)) (=> (@ (@ tptp.ord_less_int A_46) B_29) (=> (@ (@ tptp.ord_less_int C_17) D_6) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_29) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_17) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_46) C_17)) (@ (@ tptp.times_times_int B_29) D_6))))))))
% 0.63/0.88 (assert (forall ((A_45 tptp.real) (B_28 tptp.real) (C_16 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_16))) (=> (@ (@ tptp.ord_less_real C_16) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A_45)) (@ _let_1 B_28)) (@ (@ tptp.ord_less_eq_real B_28) A_45))))))
% 0.63/0.88 (assert (forall ((A_45 tptp.int) (B_28 tptp.int) (C_16 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_16))) (=> (@ (@ tptp.ord_less_int C_16) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A_45)) (@ _let_1 B_28)) (@ (@ tptp.ord_less_eq_int B_28) A_45))))))
% 0.63/0.88 (assert (forall ((A_44 tptp.real) (B_27 tptp.real) (C_15 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_15))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_15) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A_44)) (@ _let_1 B_27)) (@ (@ tptp.ord_less_eq_real A_44) B_27))))))
% 0.63/0.88 (assert (forall ((A_44 tptp.int) (B_27 tptp.int) (C_15 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_15))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_15) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A_44)) (@ _let_1 B_27)) (@ (@ tptp.ord_less_eq_int A_44) B_27))))))
% 0.63/0.88 (assert (forall ((X_14 tptp.real) (Y_13 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X_14) X_14)) (@ (@ tptp.times_times_real Y_13) Y_13)))))
% 0.63/0.88 (assert (forall ((X_14 tptp.int) (Y_13 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_14) X_14)) (@ (@ tptp.times_times_int Y_13) Y_13)))))
% 0.63/0.88 (assert (forall ((X_13 tptp.real) (Y_12 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X_13) X_13)) (@ (@ tptp.times_times_real Y_12) Y_12))) tptp.zero_zero_real) (and (= X_13 tptp.zero_zero_real) (= Y_12 tptp.zero_zero_real)))))
% 0.63/0.88 (assert (forall ((X_13 tptp.int) (Y_12 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_13) X_13)) (@ (@ tptp.times_times_int Y_12) Y_12))) tptp.zero_zero_int) (and (= X_13 tptp.zero_zero_int) (= Y_12 tptp.zero_zero_int)))))
% 0.63/0.88 (assert (forall ((Y_11 tptp.real) (X_12 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X_12) (=> (@ _let_1 Y_11) (=> (@ (@ tptp.ord_less_eq_real Y_11) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X_12) Y_11)) X_12)))))))
% 0.63/0.88 (assert (forall ((Y_11 tptp.int) (X_12 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X_12) (=> (@ _let_1 Y_11) (=> (@ (@ tptp.ord_less_eq_int Y_11) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X_12) Y_11)) X_12)))))))
% 0.63/0.88 (assert (forall ((Y_10 tptp.real) (X_11 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X_11) (=> (@ _let_1 Y_10) (=> (@ (@ tptp.ord_less_eq_real Y_10) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y_10) X_11)) X_11)))))))
% 0.63/0.88 (assert (forall ((Y_10 tptp.int) (X_11 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X_11) (=> (@ _let_1 Y_10) (=> (@ (@ tptp.ord_less_eq_int Y_10) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y_10) X_11)) X_11)))))))
% 0.63/0.88 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat_1 Z) tptp.zero_zero_nat))))
% 0.63/0.88 (assert (forall ((I_1 tptp.int)) (= (= (@ tptp.nat_1 I_1) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I_1) tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((A_43 tptp.real) (N_9 tptp.nat) (N_8 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_43))) (=> (@ (@ tptp.ord_less_eq_nat N_9) N_8) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A_43) (@ (@ tptp.ord_less_eq_real (@ _let_1 N_9)) (@ _let_1 N_8)))))))
% 0.63/0.88 (assert (forall ((A_43 tptp.nat) (N_9 tptp.nat) (N_8 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_43))) (=> (@ (@ tptp.ord_less_eq_nat N_9) N_8) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A_43) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N_9)) (@ _let_1 N_8)))))))
% 0.63/0.88 (assert (forall ((A_43 tptp.int) (N_9 tptp.nat) (N_8 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_43))) (=> (@ (@ tptp.ord_less_eq_nat N_9) N_8) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A_43) (@ (@ tptp.ord_less_eq_int (@ _let_1 N_9)) (@ _let_1 N_8)))))))
% 0.63/0.88 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.semiri1621563631at_int (@ tptp.nat_1 Z)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (and (=> _let_2 (= _let_1 Z)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (= (@ tptp.semiri1621563631at_int M) Z) (and (= M (@ tptp.nat_1 Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)))))
% 0.63/0.88 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1621563631at_int (@ tptp.nat_1 Z)) Z))))
% 0.63/0.88 (assert (forall ((A_42 tptp.real) (B_26 tptp.real)) (= (= (@ (@ tptp.minus_minus_real A_42) B_26) tptp.zero_zero_real) (= A_42 B_26))))
% 0.63/0.88 (assert (forall ((A_42 tptp.int) (B_26 tptp.int)) (= (= (@ (@ tptp.minus_minus_int A_42) B_26) tptp.zero_zero_int) (= A_42 B_26))))
% 0.63/0.88 (assert (forall ((A_41 tptp.real) (B_25 tptp.real)) (= (= A_41 B_25) (= (@ (@ tptp.minus_minus_real A_41) B_25) tptp.zero_zero_real))))
% 0.63/0.88 (assert (forall ((A_41 tptp.int) (B_25 tptp.int)) (= (= A_41 B_25) (= (@ (@ tptp.minus_minus_int A_41) B_25) tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((A_40 tptp.real)) (= (@ (@ tptp.minus_minus_real A_40) A_40) tptp.zero_zero_real)))
% 0.63/0.88 (assert (forall ((A_40 tptp.int)) (= (@ (@ tptp.minus_minus_int A_40) A_40) tptp.zero_zero_int)))
% 0.63/0.88 (assert (forall ((A_39 tptp.real)) (= (@ (@ tptp.minus_minus_real A_39) tptp.zero_zero_real) A_39)))
% 0.63/0.88 (assert (forall ((A_39 tptp.int)) (= (@ (@ tptp.minus_minus_int A_39) tptp.zero_zero_int) A_39)))
% 0.63/0.88 (assert (forall ((A_38 tptp.int) (B_24 tptp.int) (C_14 tptp.int) (D_5 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A_38) B_24) (@ (@ tptp.minus_minus_int C_14) D_5)) (= (@ (@ tptp.ord_less_int A_38) B_24) (@ (@ tptp.ord_less_int C_14) D_5)))))
% 0.63/0.88 (assert (forall ((A_38 tptp.real) (B_24 tptp.real) (C_14 tptp.real) (D_5 tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A_38) B_24) (@ (@ tptp.minus_minus_real C_14) D_5)) (= (@ (@ tptp.ord_less_real A_38) B_24) (@ (@ tptp.ord_less_real C_14) D_5)))))
% 0.63/0.88 (assert (forall ((A_37 tptp.real) (C_13 tptp.real) (B_23 tptp.real) (D_4 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A_37) C_13)) (@ (@ tptp.plus_plus_real B_23) D_4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A_37) B_23)) (@ (@ tptp.minus_minus_real C_13) D_4)))))
% 0.63/0.88 (assert (forall ((A_37 tptp.int) (C_13 tptp.int) (B_23 tptp.int) (D_4 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A_37) C_13)) (@ (@ tptp.plus_plus_int B_23) D_4)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A_37) B_23)) (@ (@ tptp.minus_minus_int C_13) D_4)))))
% 0.63/0.88 (assert (forall ((A_36 tptp.real) (B_22 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A_36) B_22)) B_22) A_36)))
% 0.63/0.88 (assert (forall ((A_36 tptp.int) (B_22 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A_36) B_22)) B_22) A_36)))
% 0.63/0.88 (assert (forall ((A_35 tptp.real) (B_21 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A_35) B_21)) B_21) A_35)))
% 0.63/0.88 (assert (forall ((A_35 tptp.int) (B_21 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A_35) B_21)) B_21) A_35)))
% 0.63/0.88 (assert (forall ((A_34 tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A_34) tptp.zero_zero_real)))
% 0.63/0.88 (assert (forall ((A_34 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A_34) tptp.zero_zero_nat)))
% 0.63/0.88 (assert (forall ((A_34 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A_34) tptp.zero_zero_int)))
% 0.63/0.88 (assert (forall ((A_33 tptp.real)) (= (@ (@ tptp.times_times_real A_33) tptp.zero_zero_real) tptp.zero_zero_real)))
% 0.63/0.88 (assert (forall ((A_33 tptp.nat)) (= (@ (@ tptp.times_times_nat A_33) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 0.63/0.88 (assert (forall ((A_33 tptp.int)) (= (@ (@ tptp.times_times_int A_33) tptp.zero_zero_int) tptp.zero_zero_int)))
% 0.63/0.88 (assert (forall ((A_32 tptp.real) (B_20 tptp.real)) (= (= (@ (@ tptp.times_times_real A_32) B_20) tptp.zero_zero_real) (or (= A_32 tptp.zero_zero_real) (= B_20 tptp.zero_zero_real)))))
% 0.63/0.88 (assert (forall ((A_32 tptp.int) (B_20 tptp.int)) (= (= (@ (@ tptp.times_times_int A_32) B_20) tptp.zero_zero_int) (or (= A_32 tptp.zero_zero_int) (= B_20 tptp.zero_zero_int)))))
% 0.63/0.88 (assert (forall ((B_19 tptp.real) (A_31 tptp.real)) (=> (not (= A_31 tptp.zero_zero_real)) (=> (not (= B_19 tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A_31) B_19) tptp.zero_zero_real))))))
% 0.63/0.88 (assert (forall ((B_19 tptp.nat) (A_31 tptp.nat)) (=> (not (= A_31 tptp.zero_zero_nat)) (=> (not (= B_19 tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A_31) B_19) tptp.zero_zero_nat))))))
% 0.63/0.88 (assert (forall ((B_19 tptp.int) (A_31 tptp.int)) (=> (not (= A_31 tptp.zero_zero_int)) (=> (not (= B_19 tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A_31) B_19) tptp.zero_zero_int))))))
% 0.63/0.88 (assert (forall ((A_30 tptp.real) (B_18 tptp.real)) (=> (= (@ (@ tptp.times_times_real A_30) B_18) tptp.zero_zero_real) (or (= A_30 tptp.zero_zero_real) (= B_18 tptp.zero_zero_real)))))
% 0.63/0.88 (assert (forall ((A_30 tptp.nat) (B_18 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A_30) B_18) tptp.zero_zero_nat) (or (= A_30 tptp.zero_zero_nat) (= B_18 tptp.zero_zero_nat)))))
% 0.63/0.88 (assert (forall ((A_30 tptp.int) (B_18 tptp.int)) (=> (= (@ (@ tptp.times_times_int A_30) B_18) tptp.zero_zero_int) (or (= A_30 tptp.zero_zero_int) (= B_18 tptp.zero_zero_int)))))
% 0.63/0.88 (assert (forall ((A_29 tptp.real)) (= (@ (@ tptp.times_times_real A_29) tptp.zero_zero_real) tptp.zero_zero_real)))
% 0.63/0.88 (assert (forall ((A_29 tptp.nat)) (= (@ (@ tptp.times_times_nat A_29) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 0.63/0.88 (assert (forall ((A_29 tptp.int)) (= (@ (@ tptp.times_times_int A_29) tptp.zero_zero_int) tptp.zero_zero_int)))
% 0.63/0.88 (assert (forall ((A_28 tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A_28) tptp.zero_zero_real)))
% 0.63/0.88 (assert (forall ((A_28 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A_28) tptp.zero_zero_nat)))
% 0.63/0.88 (assert (forall ((A_28 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A_28) tptp.zero_zero_int)))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))))
% 0.63/0.88 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 0.63/0.88 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 0.63/0.88 (assert (forall ((A_27 tptp.real) (B_17 tptp.real) (C_12 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_27) B_17)) C_12) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_27) C_12)) (@ (@ tptp.times_times_real B_17) C_12)))))
% 0.63/0.88 (assert (forall ((A_27 tptp.nat) (B_17 tptp.nat) (C_12 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_27) B_17)) C_12) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_27) C_12)) (@ (@ tptp.times_times_nat B_17) C_12)))))
% 0.63/0.88 (assert (forall ((A_27 tptp.int) (B_17 tptp.int) (C_12 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_27) B_17)) C_12) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_27) C_12)) (@ (@ tptp.times_times_int B_17) C_12)))))
% 0.63/0.88 (assert (forall ((A_26 tptp.real) (E tptp.real) (B_16 tptp.real) (C_11 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_26) E)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B_16) E)) C_11)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_26) B_16)) E)) C_11))))
% 0.63/0.88 (assert (forall ((A_26 tptp.nat) (E tptp.nat) (B_16 tptp.nat) (C_11 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_26) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B_16) E)) C_11)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_26) B_16)) E)) C_11))))
% 0.63/0.88 (assert (forall ((A_26 tptp.int) (E tptp.int) (B_16 tptp.int) (C_11 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_26) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_16) E)) C_11)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_26) B_16)) E)) C_11))))
% 0.63/0.88 (assert (forall ((W_3 tptp.real) (Y_9 tptp.real) (X_10 tptp.real) (Z_3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X_10))) (let ((_let_2 (@ tptp.times_times_real W_3))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y_9)) (@ _let_1 Z_3)) (@ (@ tptp.plus_plus_real (@ _let_2 Z_3)) (@ _let_1 Y_9))) (or (= W_3 X_10) (= Y_9 Z_3)))))))
% 0.63/0.88 (assert (forall ((W_3 tptp.nat) (Y_9 tptp.nat) (X_10 tptp.nat) (Z_3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X_10))) (let ((_let_2 (@ tptp.times_times_nat W_3))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y_9)) (@ _let_1 Z_3)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z_3)) (@ _let_1 Y_9))) (or (= W_3 X_10) (= Y_9 Z_3)))))))
% 0.63/0.88 (assert (forall ((W_3 tptp.int) (Y_9 tptp.int) (X_10 tptp.int) (Z_3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X_10))) (let ((_let_2 (@ tptp.times_times_int W_3))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y_9)) (@ _let_1 Z_3)) (@ (@ tptp.plus_plus_int (@ _let_2 Z_3)) (@ _let_1 Y_9))) (or (= W_3 X_10) (= Y_9 Z_3)))))))
% 0.63/0.88 (assert (forall ((A_25 tptp.real) (M_3 tptp.real) (B_15 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_25) M_3)) (@ (@ tptp.times_times_real B_15) M_3)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_25) B_15)) M_3))))
% 0.63/0.88 (assert (forall ((A_25 tptp.nat) (M_3 tptp.nat) (B_15 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_25) M_3)) (@ (@ tptp.times_times_nat B_15) M_3)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_25) B_15)) M_3))))
% 0.63/0.88 (assert (forall ((A_25 tptp.int) (M_3 tptp.int) (B_15 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_25) M_3)) (@ (@ tptp.times_times_int B_15) M_3)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_25) B_15)) M_3))))
% 0.63/0.88 (assert (forall ((A_24 tptp.real) (B_14 tptp.real) (C_10 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_24) B_14)) C_10) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_24) C_10)) (@ (@ tptp.times_times_real B_14) C_10)))))
% 0.63/0.88 (assert (forall ((A_24 tptp.nat) (B_14 tptp.nat) (C_10 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_24) B_14)) C_10) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_24) C_10)) (@ (@ tptp.times_times_nat B_14) C_10)))))
% 0.63/0.88 (assert (forall ((A_24 tptp.int) (B_14 tptp.int) (C_10 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_24) B_14)) C_10) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_24) C_10)) (@ (@ tptp.times_times_int B_14) C_10)))))
% 0.63/0.88 (assert (forall ((C_9 tptp.real) (D_3 tptp.real) (A_23 tptp.real) (B_13 tptp.real)) (let ((_let_1 (@ tptp.times_times_real B_13))) (let ((_let_2 (@ tptp.times_times_real A_23))) (= (and (not (= A_23 B_13)) (not (= C_9 D_3))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C_9)) (@ _let_1 D_3)) (@ (@ tptp.plus_plus_real (@ _let_2 D_3)) (@ _let_1 C_9)))))))))
% 0.63/0.88 (assert (forall ((C_9 tptp.nat) (D_3 tptp.nat) (A_23 tptp.nat) (B_13 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B_13))) (let ((_let_2 (@ tptp.times_times_nat A_23))) (= (and (not (= A_23 B_13)) (not (= C_9 D_3))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C_9)) (@ _let_1 D_3)) (@ (@ tptp.plus_plus_nat (@ _let_2 D_3)) (@ _let_1 C_9)))))))))
% 0.63/0.88 (assert (forall ((C_9 tptp.int) (D_3 tptp.int) (A_23 tptp.int) (B_13 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B_13))) (let ((_let_2 (@ tptp.times_times_int A_23))) (= (and (not (= A_23 B_13)) (not (= C_9 D_3))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C_9)) (@ _let_1 D_3)) (@ (@ tptp.plus_plus_int (@ _let_2 D_3)) (@ _let_1 C_9)))))))))
% 0.63/0.88 (assert (forall ((X_9 tptp.real) (Y_8 tptp.real) (Z_2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X_9))) (= (@ _let_1 (@ (@ tptp.plus_plus_real Y_8) Z_2)) (@ (@ tptp.plus_plus_real (@ _let_1 Y_8)) (@ _let_1 Z_2))))))
% 0.63/0.88 (assert (forall ((X_9 tptp.nat) (Y_8 tptp.nat) (Z_2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X_9))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat Y_8) Z_2)) (@ (@ tptp.plus_plus_nat (@ _let_1 Y_8)) (@ _let_1 Z_2))))))
% 0.63/0.88 (assert (forall ((X_9 tptp.int) (Y_8 tptp.int) (Z_2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X_9))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Y_8) Z_2)) (@ (@ tptp.plus_plus_int (@ _let_1 Y_8)) (@ _let_1 Z_2))))))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (= (@ tptp.nat_1 (@ tptp.semiri1621563631at_int N)) N)))
% 0.63/0.88 (assert (forall ((A_22 tptp.real)) (= (@ (@ tptp.times_times_real A_22) tptp.one_one_real) A_22)))
% 0.63/0.88 (assert (forall ((A_22 tptp.nat)) (= (@ (@ tptp.times_times_nat A_22) tptp.one_one_nat) A_22)))
% 0.63/0.88 (assert (forall ((A_22 tptp.int)) (= (@ (@ tptp.times_times_int A_22) tptp.one_one_int) A_22)))
% 0.63/0.88 (assert (forall ((A_21 tptp.real)) (= (@ (@ tptp.times_times_real A_21) tptp.one_one_real) A_21)))
% 0.63/0.88 (assert (forall ((A_21 tptp.nat)) (= (@ (@ tptp.times_times_nat A_21) tptp.one_one_nat) A_21)))
% 0.63/0.88 (assert (forall ((A_21 tptp.int)) (= (@ (@ tptp.times_times_int A_21) tptp.one_one_int) A_21)))
% 0.63/0.88 (assert (forall ((A_20 tptp.real)) (= (@ (@ tptp.times_times_real A_20) tptp.one_one_real) A_20)))
% 0.63/0.88 (assert (forall ((A_20 tptp.nat)) (= (@ (@ tptp.times_times_nat A_20) tptp.one_one_nat) A_20)))
% 0.63/0.88 (assert (forall ((A_20 tptp.int)) (= (@ (@ tptp.times_times_int A_20) tptp.one_one_int) A_20)))
% 0.63/0.88 (assert (forall ((A_19 tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A_19) A_19)))
% 0.63/0.88 (assert (forall ((A_19 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A_19) A_19)))
% 0.63/0.88 (assert (forall ((A_19 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A_19) A_19)))
% 0.63/0.88 (assert (forall ((A_18 tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A_18) A_18)))
% 0.63/0.88 (assert (forall ((A_18 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A_18) A_18)))
% 0.63/0.88 (assert (forall ((A_18 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A_18) A_18)))
% 0.63/0.88 (assert (forall ((A_17 tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A_17) A_17)))
% 0.63/0.88 (assert (forall ((A_17 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A_17) A_17)))
% 0.63/0.88 (assert (forall ((A_17 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A_17) A_17)))
% 0.63/0.88 (assert (forall ((C_8 tptp.real) (A_16 tptp.real) (B_12 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C_8))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A_16)) (@ _let_1 B_12)) (@ (@ tptp.ord_less_eq_real A_16) B_12)))))
% 0.63/0.88 (assert (forall ((C_8 tptp.nat) (A_16 tptp.nat) (B_12 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_8))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_16)) (@ _let_1 B_12)) (@ (@ tptp.ord_less_eq_nat A_16) B_12)))))
% 0.63/0.88 (assert (forall ((C_8 tptp.int) (A_16 tptp.int) (B_12 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_8))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A_16)) (@ _let_1 B_12)) (@ (@ tptp.ord_less_eq_int A_16) B_12)))))
% 0.63/0.88 (assert (forall ((A_15 tptp.real) (C_7 tptp.real) (B_11 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A_15) C_7)) (@ (@ tptp.plus_plus_real B_11) C_7)) (@ (@ tptp.ord_less_eq_real A_15) B_11))))
% 0.63/0.88 (assert (forall ((A_15 tptp.nat) (C_7 tptp.nat) (B_11 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A_15) C_7)) (@ (@ tptp.plus_plus_nat B_11) C_7)) (@ (@ tptp.ord_less_eq_nat A_15) B_11))))
% 0.63/0.88 (assert (forall ((A_15 tptp.int) (C_7 tptp.int) (B_11 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_15) C_7)) (@ (@ tptp.plus_plus_int B_11) C_7)) (@ (@ tptp.ord_less_eq_int A_15) B_11))))
% 0.63/0.88 (assert (forall ((C_6 tptp.real) (D_2 tptp.real) (A_14 tptp.real) (B_10 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_14) B_10) (=> (@ (@ tptp.ord_less_eq_real C_6) D_2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A_14) C_6)) (@ (@ tptp.plus_plus_real B_10) D_2))))))
% 0.63/0.88 (assert (forall ((C_6 tptp.nat) (D_2 tptp.nat) (A_14 tptp.nat) (B_10 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_14) B_10) (=> (@ (@ tptp.ord_less_eq_nat C_6) D_2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A_14) C_6)) (@ (@ tptp.plus_plus_nat B_10) D_2))))))
% 0.63/0.88 (assert (forall ((C_6 tptp.int) (D_2 tptp.int) (A_14 tptp.int) (B_10 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_14) B_10) (=> (@ (@ tptp.ord_less_eq_int C_6) D_2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_14) C_6)) (@ (@ tptp.plus_plus_int B_10) D_2))))))
% 0.63/0.88 (assert (forall ((C_5 tptp.real) (A_13 tptp.real) (B_9 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C_5))) (=> (@ (@ tptp.ord_less_eq_real A_13) B_9) (@ (@ tptp.ord_less_eq_real (@ _let_1 A_13)) (@ _let_1 B_9))))))
% 0.63/0.88 (assert (forall ((C_5 tptp.nat) (A_13 tptp.nat) (B_9 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_5))) (=> (@ (@ tptp.ord_less_eq_nat A_13) B_9) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_13)) (@ _let_1 B_9))))))
% 0.63/0.88 (assert (forall ((C_5 tptp.int) (A_13 tptp.int) (B_9 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_5))) (=> (@ (@ tptp.ord_less_eq_int A_13) B_9) (@ (@ tptp.ord_less_eq_int (@ _let_1 A_13)) (@ _let_1 B_9))))))
% 0.63/0.88 (assert (forall ((C_4 tptp.real) (A_12 tptp.real) (B_8 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_12) B_8) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A_12) C_4)) (@ (@ tptp.plus_plus_real B_8) C_4)))))
% 0.63/0.88 (assert (forall ((C_4 tptp.nat) (A_12 tptp.nat) (B_8 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_12) B_8) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A_12) C_4)) (@ (@ tptp.plus_plus_nat B_8) C_4)))))
% 0.63/0.88 (assert (forall ((C_4 tptp.int) (A_12 tptp.int) (B_8 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_12) B_8) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_12) C_4)) (@ (@ tptp.plus_plus_int B_8) C_4)))))
% 0.63/0.88 (assert (forall ((C_3 tptp.real) (A_11 tptp.real) (B_7 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C_3))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A_11)) (@ _let_1 B_7)) (@ (@ tptp.ord_less_eq_real A_11) B_7)))))
% 0.63/0.88 (assert (forall ((C_3 tptp.nat) (A_11 tptp.nat) (B_7 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_3))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_11)) (@ _let_1 B_7)) (@ (@ tptp.ord_less_eq_nat A_11) B_7)))))
% 0.63/0.88 (assert (forall ((C_3 tptp.int) (A_11 tptp.int) (B_7 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_3))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A_11)) (@ _let_1 B_7)) (@ (@ tptp.ord_less_eq_int A_11) B_7)))))
% 0.63/0.88 (assert (forall ((A_10 tptp.real) (C_2 tptp.real) (B_6 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A_10) C_2)) (@ (@ tptp.plus_plus_real B_6) C_2)) (@ (@ tptp.ord_less_eq_real A_10) B_6))))
% 0.63/0.88 (assert (forall ((A_10 tptp.nat) (C_2 tptp.nat) (B_6 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A_10) C_2)) (@ (@ tptp.plus_plus_nat B_6) C_2)) (@ (@ tptp.ord_less_eq_nat A_10) B_6))))
% 0.63/0.88 (assert (forall ((A_10 tptp.int) (C_2 tptp.int) (B_6 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_10) C_2)) (@ (@ tptp.plus_plus_int B_6) C_2)) (@ (@ tptp.ord_less_eq_int A_10) B_6))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N)) K))))
% 0.63/0.88 (assert (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))))
% 0.63/0.88 (assert (forall ((A_9 tptp.real) (N_7 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A_9) N_7))) (= (@ (@ tptp.times_times_real _let_1) A_9) (@ (@ tptp.times_times_real A_9) _let_1)))))
% 0.63/0.88 (assert (forall ((A_9 tptp.nat) (N_7 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A_9) N_7))) (= (@ (@ tptp.times_times_nat _let_1) A_9) (@ (@ tptp.times_times_nat A_9) _let_1)))))
% 0.63/0.88 (assert (forall ((A_9 tptp.int) (N_7 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A_9) N_7))) (= (@ (@ tptp.times_times_int _let_1) A_9) (@ (@ tptp.times_times_int A_9) _let_1)))))
% 0.63/0.88 (assert (forall ((A_8 tptp.real) (B_5 tptp.real) (N_6 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A_8) B_5)) N_6) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A_8) N_6)) (@ (@ tptp.power_power_real B_5) N_6)))))
% 0.63/0.88 (assert (forall ((A_8 tptp.nat) (B_5 tptp.nat) (N_6 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A_8) B_5)) N_6) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A_8) N_6)) (@ (@ tptp.power_power_nat B_5) N_6)))))
% 0.63/0.88 (assert (forall ((A_8 tptp.int) (B_5 tptp.int) (N_6 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A_8) B_5)) N_6) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A_8) N_6)) (@ (@ tptp.power_power_int B_5) N_6)))))
% 0.63/0.88 (assert (forall ((X_8 tptp.real) (Y_7 tptp.real) (Q_2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real X_8) Y_7)) Q_2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X_8) Q_2)) (@ (@ tptp.power_power_real Y_7) Q_2)))))
% 0.63/0.88 (assert (forall ((X_8 tptp.nat) (Y_7 tptp.nat) (Q_2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat X_8) Y_7)) Q_2) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X_8) Q_2)) (@ (@ tptp.power_power_nat Y_7) Q_2)))))
% 0.63/0.88 (assert (forall ((X_8 tptp.int) (Y_7 tptp.int) (Q_2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int X_8) Y_7)) Q_2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X_8) Q_2)) (@ (@ tptp.power_power_int Y_7) Q_2)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 0.63/0.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 0.63/0.88 (assert (forall ((I_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I_1))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.minus_minus_nat M) N)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K)) (@ (@ tptp.minus_minus_nat M) N))))
% 0.63/0.88 (assert (forall ((W tptp.int)) (= (@ (@ tptp.times_times_int tptp.pls) W) tptp.pls)))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.bit0 K)) L) (@ tptp.bit0 (@ (@ tptp.times_times_int K) L)))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_eq_int K) L))))
% 0.63/0.88 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_eq_int tptp.pls) tptp.pls))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) (@ tptp.bit0 L)) (@ (@ tptp.ord_less_eq_int K) L))))
% 0.63/0.88 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K1)) (@ tptp.bit0 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 0.63/0.88 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) Z) Z)))
% 0.63/0.88 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) tptp.one_one_int) Z)))
% 0.63/0.88 (assert (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.ord_less_int Z) W) (and (@ (@ tptp.ord_less_eq_int Z) W) (not (= Z W))))))
% 0.63/0.88 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z2)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z2))))))
% 0.63/0.88 (assert (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z2)) W) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z2) W)))))
% 0.63/0.88 (assert (forall ((K tptp.int) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (@ (@ tptp.ord_less_eq_int I_1) J) (@ (@ tptp.ord_less_eq_int (@ _let_1 I_1)) (@ _let_1 J))))))
% 0.63/0.88 (assert (forall ((V_1 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_1)) (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_1) W)))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int K)) (@ tptp.number_number_of_int L)) (@ (@ tptp.ord_less_eq_int K) L))))
% 0.63/0.88 (assert (forall ((V_4 tptp.real) (U_2 tptp.real) (Y_6 tptp.real) (X_7 tptp.real) (A_7 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real X_7) A_7) (=> (@ (@ tptp.ord_less_eq_real Y_6) A_7) (=> (@ _let_1 U_2) (=> (@ _let_1 V_4) (=> (= (@ (@ tptp.plus_plus_real U_2) V_4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U_2) X_7)) (@ (@ tptp.times_times_real V_4) Y_6))) A_7)))))))))
% 0.63/0.88 (assert (forall ((V_4 tptp.int) (U_2 tptp.int) (Y_6 tptp.int) (X_7 tptp.int) (A_7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X_7) A_7) (=> (@ (@ tptp.ord_less_eq_int Y_6) A_7) (=> (@ _let_1 U_2) (=> (@ _let_1 V_4) (=> (= (@ (@ tptp.plus_plus_int U_2) V_4) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U_2) X_7)) (@ (@ tptp.times_times_int V_4) Y_6))) A_7)))))))))
% 0.63/0.88 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_nat (@ tptp.nat_1 X)) (@ tptp.nat_1 Y)) (@ (@ tptp.ord_less_int X) Y)))))))
% 0.63/0.88 (assert (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat_1 W)) (@ tptp.nat_1 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 0.63/0.88 (assert (forall ((Y_5 tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.number267125858f_real Y_5)) (@ (@ tptp.ord_less_eq_int tptp.pls) Y_5))))
% 0.63/0.88 (assert (forall ((Y_5 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.number_number_of_int Y_5)) (@ (@ tptp.ord_less_eq_int tptp.pls) Y_5))))
% 0.63/0.88 (assert (forall ((X_6 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.number267125858f_real X_6)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_int X_6) tptp.pls))))
% 0.63/0.88 (assert (forall ((X_6 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_6)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int X_6) tptp.pls))))
% 0.63/0.88 (assert (forall ((A_6 tptp.real) (N_5 tptp.nat) (N_4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_6))) (=> (@ (@ tptp.ord_less_eq_nat N_5) N_4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_6) (=> (@ (@ tptp.ord_less_eq_real A_6) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N_4)) (@ _let_1 N_5))))))))
% 0.63/0.88 (assert (forall ((A_6 tptp.nat) (N_5 tptp.nat) (N_4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_6))) (=> (@ (@ tptp.ord_less_eq_nat N_5) N_4) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_6) (=> (@ (@ tptp.ord_less_eq_nat A_6) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N_4)) (@ _let_1 N_5))))))))
% 0.63/0.88 (assert (forall ((A_6 tptp.int) (N_5 tptp.nat) (N_4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_6))) (=> (@ (@ tptp.ord_less_eq_nat N_5) N_4) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_6) (=> (@ (@ tptp.ord_less_eq_int A_6) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N_4)) (@ _let_1 N_5))))))))
% 0.63/0.88 (assert (forall ((X_5 tptp.nat) (Y_4 tptp.nat) (B_4 tptp.real)) (let ((_let_1 (@ tptp.power_power_real B_4))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B_4) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X_5)) (@ _let_1 Y_4)) (@ (@ tptp.ord_less_eq_nat X_5) Y_4))))))
% 0.63/0.88 (assert (forall ((X_5 tptp.nat) (Y_4 tptp.nat) (B_4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B_4))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B_4) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X_5)) (@ _let_1 Y_4)) (@ (@ tptp.ord_less_eq_nat X_5) Y_4))))))
% 0.63/0.88 (assert (forall ((X_5 tptp.nat) (Y_4 tptp.nat) (B_4 tptp.int)) (let ((_let_1 (@ tptp.power_power_int B_4))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B_4) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X_5)) (@ _let_1 Y_4)) (@ (@ tptp.ord_less_eq_nat X_5) Y_4))))))
% 0.63/0.88 (assert (forall ((M_2 tptp.nat) (N_3 tptp.nat) (A_5 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A_5))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_5) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 M_2)) (@ _let_1 N_3)) (@ (@ tptp.ord_less_eq_nat M_2) N_3))))))
% 0.63/0.88 (assert (forall ((M_2 tptp.nat) (N_3 tptp.nat) (A_5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_5))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_5) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M_2)) (@ _let_1 N_3)) (@ (@ tptp.ord_less_eq_nat M_2) N_3))))))
% 0.63/0.88 (assert (forall ((M_2 tptp.nat) (N_3 tptp.nat) (A_5 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A_5))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_5) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M_2)) (@ _let_1 N_3)) (@ (@ tptp.ord_less_eq_nat M_2) N_3))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (W tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= M (@ tptp.nat_1 W)) (and (=> _let_1 (= W (@ tptp.semiri1621563631at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 0.63/0.88 (assert (forall ((W tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= (@ tptp.nat_1 W) M) (and (=> _let_1 (= W (@ tptp.semiri1621563631at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 0.63/0.88 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.plus_plus_nat (@ tptp.nat_1 X)) (@ tptp.nat_1 Y)) (@ tptp.nat_1 (@ (@ tptp.plus_plus_int X) Y))))))))
% 0.63/0.88 (assert (forall ((Z_1 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z_1) (= (@ tptp.nat_1 (@ (@ tptp.plus_plus_int Z) Z_1)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_1 Z)) (@ tptp.nat_1 Z_1))))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (V_1 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V_1))) (= (= (@ tptp.semiri1621563631at_int M) _let_1) (and (= M (@ tptp.nat_1 _let_1)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1))))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ (@ tptp.power_power_nat (@ tptp.nat_1 X)) N) (@ tptp.nat_1 (@ (@ tptp.power_power_int X) N))))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat_1 (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_nat (@ tptp.nat_1 Z)) N)))))
% 0.63/0.88 (assert (forall ((V_3 tptp.real) (U_1 tptp.real) (Y_3 tptp.real) (X_4 tptp.real) (A_4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X_4) A_4) (=> (@ (@ tptp.ord_less_real Y_3) A_4) (=> (@ _let_1 U_1) (=> (@ _let_1 V_3) (=> (= (@ (@ tptp.plus_plus_real U_1) V_3) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U_1) X_4)) (@ (@ tptp.times_times_real V_3) Y_3))) A_4)))))))))
% 0.63/0.88 (assert (forall ((V_3 tptp.int) (U_1 tptp.int) (Y_3 tptp.int) (X_4 tptp.int) (A_4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X_4) A_4) (=> (@ (@ tptp.ord_less_int Y_3) A_4) (=> (@ _let_1 U_1) (=> (@ _let_1 V_3) (=> (= (@ (@ tptp.plus_plus_int U_1) V_3) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U_1) X_4)) (@ (@ tptp.times_times_int V_3) Y_3))) A_4)))))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (W tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat_1 W)) M) (@ (@ tptp.ord_less_int W) (@ tptp.semiri1621563631at_int M))))))
% 0.63/0.88 (assert (forall ((Y_2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.number267125858f_real Y_2)) (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 tptp.pls)) Y_2))))
% 0.63/0.88 (assert (forall ((Y_2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.number_number_of_int Y_2)) (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 tptp.pls)) Y_2))))
% 0.63/0.88 (assert (forall ((X_3 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.number267125858f_real X_3)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_int X_3) (@ tptp.bit1 tptp.pls)))))
% 0.63/0.88 (assert (forall ((X_3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_3)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int X_3) (@ tptp.bit1 tptp.pls)))))
% 0.63/0.88 (assert (forall ((X_2 tptp.real) (N_2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X_2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_2) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N_2) tptp.one_one_nat))) X_2) (@ _let_1 N_2))))))
% 0.63/0.88 (assert (forall ((X_2 tptp.nat) (N_2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X_2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_2) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N_2) tptp.one_one_nat))) X_2) (@ _let_1 N_2))))))
% 0.63/0.88 (assert (forall ((X_2 tptp.int) (N_2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X_2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_2) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N_2) tptp.one_one_nat))) X_2) (@ _let_1 N_2))))))
% 0.63/0.88 (assert (forall ((A_3 tptp.real) (B_3 tptp.real)) (= (@ (@ tptp.ord_less_real A_3) B_3) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A_3) B_3)) tptp.zero_zero_real))))
% 0.63/0.88 (assert (forall ((A_3 tptp.int) (B_3 tptp.int)) (= (@ (@ tptp.ord_less_int A_3) B_3) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A_3) B_3)) tptp.zero_zero_int))))
% 0.63/0.88 (assert (= tptp.zero_zero_nat (@ tptp.nat_1 tptp.zero_zero_int)))
% 0.63/0.88 (assert (= (@ tptp.nat_1 tptp.zero_zero_int) tptp.zero_zero_nat))
% 0.63/0.88 (assert (forall ((A_2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_2) A_2)) tptp.zero_zero_real))))
% 0.63/0.88 (assert (forall ((A_2 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_2) A_2)) tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((A_1 tptp.real) (C_1 tptp.real) (B_2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_1) C_1)) (@ (@ tptp.times_times_real B_2) C_1)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_1) (@ (@ tptp.ord_less_real A_1) B_2)) (and (@ (@ tptp.ord_less_real C_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B_2) A_1))))))
% 0.63/0.88 (assert (forall ((A_1 tptp.int) (C_1 tptp.int) (B_2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_1) C_1)) (@ (@ tptp.times_times_int B_2) C_1)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_1) (@ (@ tptp.ord_less_int A_1) B_2)) (and (@ (@ tptp.ord_less_int C_1) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B_2) A_1))))))
% 0.63/0.88 (assert (forall ((W tptp.int)) (= (@ tptp.nat_1 (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_nat W))))
% 0.63/0.88 (assert (forall ((V_1 tptp.int)) (= (@ tptp.number_number_of_nat V_1) (@ tptp.nat_1 (@ tptp.number_number_of_int V_1)))))
% 0.63/0.88 (assert (= tptp.one_one_nat (@ tptp.nat_1 tptp.one_one_int)))
% 0.63/0.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.ord_less_nat M) N))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) M))))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 0.63/0.88 (assert (forall ((I_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I_1) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K)) J))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (= (@ _let_1 (@ tptp.bit1 K)) (@ _let_1 K)))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_eq_int K) L))))
% 0.63/0.88 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (= (@ _let_1 (@ tptp.bit0 K)) (@ _let_1 K)))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) tptp.pls) (@ (@ tptp.ord_less_eq_int K) tptp.pls))))
% 0.63/0.88 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (@ _let_1 B))))))
% 0.63/0.88 (assert (forall ((K tptp.int) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I_1) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I_1)) (@ _let_1 J)))))))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 0.63/0.88 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.plus_plus_int X) Y)))))))
% 0.63/0.88 (assert (forall ((Z_1 tptp.int) (Z tptp.int) (W_2 tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int W_2) W) (=> (@ (@ tptp.ord_less_eq_int Z_1) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int W_2) Z_1)) (@ (@ tptp.plus_plus_int W) Z))))))
% 0.63/0.88 (assert (forall ((Z tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1621563631at_int Z))))
% 0.63/0.88 (assert (forall ((P (-> tptp.int Bool))) (= (exists ((X_1 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P X_1))) (exists ((X_1 tptp.nat)) (@ P (@ tptp.semiri1621563631at_int X_1))))))
% 0.63/0.88 (assert (forall ((P (-> tptp.int Bool))) (= (forall ((X_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P X_1))) (forall ((X_1 tptp.nat)) (@ P (@ tptp.semiri1621563631at_int X_1))))))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1621563631at_int N))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.power_power_int X) N))))))
% 0.63/0.88 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) Z) (exists ((N_1 tptp.nat)) (= Z (@ (@ tptp.plus_plus_int W) (@ tptp.semiri1621563631at_int N_1)))))))
% 0.63/0.88 (assert (forall ((X tptp.int) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z)) (@ (@ tptp.times_times_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 0.63/0.88 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_nat (@ tptp.nat_1 W)) (@ tptp.nat_1 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 0.63/0.88 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat_1 W)) (@ tptp.nat_1 Z)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int W) Z)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.nat_1 Z)) (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int M)) Z))))
% 0.63/0.88 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (not (or (and (@ (@ tptp.ord_less_nat A) B) (not (@ P tptp.zero_zero_nat))) (exists ((D_1 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D_1)) (not (@ P D_1)))))))))
% 0.63/0.88 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (and (=> (@ (@ tptp.ord_less_nat A) B) (@ P tptp.zero_zero_nat)) (forall ((D_1 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D_1)) (@ P D_1)))))))
% 0.63/0.88 (assert (forall ((V_1 tptp.int)) (= (= tptp.zero_zero_nat (@ tptp.number_number_of_nat V_1)) (@ (@ tptp.ord_less_eq_int V_1) tptp.pls))))
% 0.63/0.88 (assert (forall ((V_1 tptp.int)) (= (= (@ tptp.number_number_of_nat V_1) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int V_1) tptp.pls))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int tptp.pls) (@ tptp.bit1 K)) (@ (@ tptp.ord_less_eq_int tptp.pls) K))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) tptp.pls) (@ (@ tptp.ord_less_int K) tptp.pls))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_eq_int K) L))))
% 0.63/0.88 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) (@ tptp.bit0 L)) (@ (@ tptp.ord_less_int K) L))))
% 0.63/0.88 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K1)) (@ tptp.bit0 K2)) (@ (@ tptp.ord_less_int K1) K2))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.bit1 K)) L) (@ (@ tptp.plus_plus_int (@ tptp.bit0 (@ (@ tptp.times_times_int K) L))) L))))
% 0.63/0.88 (assert (forall ((N tptp.int) (M tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (and (= M tptp.one_one_int) (= N tptp.one_one_int))))))
% 0.63/0.88 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1621563631at_int N)) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 0.63/0.88 (assert (= (@ tptp.succ tptp.pls) (@ tptp.bit1 tptp.pls)))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ tptp.succ (@ tptp.bit0 K)) (@ tptp.bit1 K))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ tptp.succ (@ tptp.bit1 K)) (@ tptp.bit0 (@ tptp.succ K)))))
% 0.63/0.88 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 0.63/0.88 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z) (@ (@ tptp.ord_less_int W) Z))))
% 0.63/0.88 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int W) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ tptp.succ K) (@ (@ tptp.plus_plus_int K) tptp.one_one_int))))
% 0.63/0.88 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat_1 Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 0.63/0.88 (assert (let ((_let_1 (@ tptp.bit1 (@ tptp.bit1 tptp.pls)))) (= (@ tptp.number_number_of_nat _let_1) (@ tptp.nat_1 (@ tptp.number_number_of_int _let_1)))))
% 0.63/0.88 (assert (forall ((P (-> tptp.nat Bool)) (I_1 tptp.int)) (= (@ P (@ tptp.nat_1 I_1)) (and (forall ((N_1 tptp.nat)) (=> (= I_1 (@ tptp.semiri1621563631at_int N_1)) (@ P N_1))) (=> (@ (@ tptp.ord_less_int I_1) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.number_number_of_int (@ tptp.bit1 (@ tptp.bit1 tptp.pls)))))
% 0.63/0.88 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1621563631at_int K)))) (=> (@ (@ tptp.ord_less_int I_1) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I_1)) (@ _let_1 J)))))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.bit1 K)) (@ tptp.bit1 L)) (@ tptp.bit0 (@ (@ tptp.plus_plus_int K) (@ tptp.succ L))))))
% 0.63/0.88 (assert (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (= (@ tptp.number_number_of_nat _let_1) (@ tptp.nat_1 (@ tptp.number_number_of_int _let_1)))))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.63/0.88 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.bit1 tptp.pls))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int A) (@ _let_2 (@ tptp.number_number_of_nat (@ tptp.bit0 _let_1)))) (@ _let_2 (@ tptp.number_number_of_nat (@ tptp.bit1 _let_1))))))))
% 0.63/0.88 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int X) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))))
% 0.63/0.88 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (or (= X tptp.zero_zero_int) (= X tptp.one_one_int))))))
% 0.63/0.88 (assert (forall ((A tptp.int) (P_1 tptp.int)) (let ((_let_1 (@ tptp.nat_1 P_1))) (let ((_let_2 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) P_1) (= (@ _let_2 _let_1) (@ (@ tptp.times_times_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat)))))))))
% 0.63/0.88 (assert (forall ((R_1 tptp.int) (Q tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (= A (@ (@ tptp.plus_plus_int R_1) (@ (@ tptp.times_times_int A) Q))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R_1) (@ (@ tptp.ord_less_eq_int Q) tptp.one_one_int))))))
% 0.63/0.88 (assert (forall ((R_1 tptp.int) (Q tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (= A (@ (@ tptp.plus_plus_int R_1) (@ (@ tptp.times_times_int A) Q))) (=> (@ (@ tptp.ord_less_int R_1) A) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Q))))))
% 0.63/0.88 (assert (let ((_let_1 (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1621563631at_int tptp.n)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (not (=> (@ (@ tptp.ord_less_int _let_1) _let_2) (not (@ tptp.twoSqu919416604sum2sq (@ (@ tptp.times_times_int _let_2) _let_1))))))))
% 0.63/0.88 (assert (forall ((B_1 tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q_1)) R_2)) (=> (@ (@ tptp.ord_less_int R_2) B_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1) (@ _let_1 Q_1)))))))
% 0.63/0.88 (assert (forall ((B_1 tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q_1)) R_2)) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R_2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1) (@ (@ tptp.ord_less_eq_int Q_1) tptp.zero_zero_int))))))
% 0.63/0.88 (assert (not (@ tptp.twoSqu919416604sum2sq (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1621563631at_int tptp.zero_zero_nat))))))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int)))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_int tptp.t) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int)))
% 0.63/0.88 (assert (@ tptp.twoSqu919416604sum2sq (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int)) tptp.t)))
% 0.63/0.88 (assert (let ((_let_1 (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1621563631at_int tptp.n)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (and (@ (@ tptp.ord_less_int _let_1) _let_2) (@ tptp.twoSqu919416604sum2sq (@ (@ tptp.times_times_int _let_2) _let_1))))))
% 0.63/0.88 (assert (not (forall ((X_1 tptp.int) (Y_1 tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.number_number_of_nat _let_1))) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_1) _let_2)) (@ (@ tptp.power_power_int Y_1) _let_2)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1621563631at_int tptp.n))))))))))
% 0.63/0.88 (assert (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int tptp.s) (@ tptp.number_number_of_nat _let_1))) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)) tptp.t))))
% 0.63/0.88 (assert (@ tptp.zprime (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int)))
% 0.63/0.88 (assert (=> (= tptp.t tptp.one_one_int) (exists ((X_1 tptp.int) (Y_1 tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.number_number_of_nat _let_1))) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_1) _let_2)) (@ (@ tptp.power_power_int Y_1) _let_2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)))))))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 0.63/0.88 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 0.63/0.88 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat M) N) (@ (@ tptp.times_times_nat N) M))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ (@ tptp.times_times_nat (@ _let_1 N)) K) (@ _let_1 (@ (@ tptp.times_times_nat N) K))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I_1) K)) (@ (@ tptp.times_times_nat J) K)))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I_1)) (@ _let_1 J))))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I_1) K)) (@ (@ tptp.times_times_nat J) L))))))
% 0.63/0.88 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) Y)) tptp.zero_zero_real))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 0.63/0.88 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_eq_real X) Y)))))
% 0.63/0.88 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ tptp.semiri1621563631at_int (@ (@ tptp.minus_minus_nat M) N))))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.pls) K)))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.bit0 K)) (@ tptp.bit0 L)) (@ tptp.bit0 (@ (@ tptp.minus_minus_int K) L)))))
% 0.63/0.88 (assert (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z2)) W) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z2) W)))))
% 0.63/0.88 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z2)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z2))))))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 0.63/0.88 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= M N) (= K tptp.zero_zero_nat))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N) K)) (or (= M N) (= K tptp.zero_zero_nat)))))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 0.63/0.88 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 0.63/0.88 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B) C)) (= A B)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat M) N) (or (@ (@ tptp.ord_less_nat M) N) (= M N)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (not (= M N))))))
% 0.63/0.88 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real X) Y) (and (@ (@ tptp.ord_less_eq_real X) Y) (not (= X Y))))))
% 0.63/0.88 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real X) Y) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J) L))))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J) K)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat M) N) (exists ((K_1 tptp.nat)) (= N (@ (@ tptp.plus_plus_nat M) K_1))))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.times_times_nat N) M) tptp.one_one_nat) (and (= N tptp.one_one_nat) (= M tptp.one_one_nat)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N)) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N))))))
% 0.63/0.88 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) Z) Z)))
% 0.63/0.88 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N) K)) (= M N)))))))
% 0.63/0.88 (assert (forall ((I_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I_1) N) (= (@ _let_1 (@ _let_1 I_1)) I_1)))))
% 0.63/0.88 (assert (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N) L)))))
% 0.63/0.88 (assert (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 0.63/0.88 (assert (forall ((Z1 tptp.real) (Z2 tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z1) Z2)) W) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real Z1) W)) (@ (@ tptp.times_times_real Z2) W)))))
% 0.63/0.88 (assert (forall ((X tptp.int) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.power_power_int (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.times_times_nat Y) Z))))))
% 0.63/0.88 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real Z))) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y))))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.bit1 K)) (@ tptp.bit1 L)) (@ tptp.bit0 (@ (@ tptp.minus_minus_int K) L)))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.bit1 K)) (@ tptp.bit0 L)) (@ tptp.bit1 (@ (@ tptp.minus_minus_int K) L)))))
% 0.63/0.88 (assert (forall ((L tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int tptp.pls))) (= (@ _let_1 (@ tptp.bit0 L)) (@ tptp.bit0 (@ _let_1 L))))))
% 0.63/0.88 (assert (forall ((A tptp.int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int A) tptp.one_one_int))) (let ((_let_2 (@ tptp.ord_less_int X))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (=> (@ _let_2 A) (=> (not (= X _let_1)) (@ _let_2 _let_1))))))))
% 0.63/0.88 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int K) L) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int K) L)) tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I_1) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I_1)) (@ _let_1 J)))))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I_1) K)) (@ (@ tptp.times_times_nat J) K))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N)))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 0.63/0.88 (assert (forall ((X tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X) X))) (= X tptp.zero_zero_real))))
% 0.63/0.88 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 0.63/0.88 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.times_times_real X) Y)))))))
% 0.63/0.88 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_real X) Y)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N)) (or (= N tptp.one_one_nat) (= M tptp.zero_zero_nat)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat))))
% 0.63/0.88 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 0.63/0.88 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B) C))))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_nat M) N)))))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.times_times_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ tptp.semiri1621563631at_int (@ (@ tptp.times_times_nat X) Y)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ tptp.semiri1621563631at_int (@ (@ tptp.times_times_nat M) N)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1621563631at_int (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)))))
% 0.63/0.88 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I_1) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I_1) K)) J)))))
% 0.63/0.88 (assert (forall ((J tptp.nat) (K tptp.nat) (I_1 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I_1) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I_1) K)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) K)))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))))
% 0.63/0.88 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I_1))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))))
% 0.63/0.88 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I_1) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) J)))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M) N)) N) M))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (= (@ (@ tptp.minus_minus_nat J) I_1) K) (= J (@ (@ tptp.plus_plus_nat K) I_1))))))
% 0.63/0.88 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I_1))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))))
% 0.63/0.88 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I_1)) K)))))
% 0.63/0.88 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I_1)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I_1)))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.63/0.88 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ tptp.twoSqu919416604sum2sq X) (=> (@ tptp.twoSqu919416604sum2sq Y) (@ tptp.twoSqu919416604sum2sq (@ (@ tptp.times_times_int X) Y))))))
% 0.63/0.88 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) (@ (@ tptp.minus_minus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_int W) Z))))
% 0.63/0.88 (assert (forall ((V_1 tptp.int) (V_2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int V_1))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.number_number_of_nat V_1)) (@ tptp.number_number_of_nat V_2)) (=> (not (@ _let_1 V_2)) (@ _let_1 tptp.pls))))))
% 0.63/0.88 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat_1 X)) (@ tptp.nat_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y)))))))
% 0.63/0.88 (assert (forall ((Z tptp.int) (Z_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z_1) (=> (@ (@ tptp.ord_less_eq_int Z_1) Z) (= (@ tptp.nat_1 (@ (@ tptp.minus_minus_int Z) Z_1)) (@ (@ tptp.minus_minus_nat (@ tptp.nat_1 Z)) (@ tptp.nat_1 Z_1)))))))
% 0.63/0.88 (assert (forall ((Z_1 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat_1 (@ (@ tptp.times_times_int Z) Z_1)) (@ (@ tptp.times_times_nat (@ tptp.nat_1 Z)) (@ tptp.nat_1 Z_1))))))
% 0.63/0.88 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.times_times_nat (@ tptp.nat_1 X)) (@ tptp.nat_1 Y)) (@ tptp.nat_1 (@ (@ tptp.times_times_int X) Y))))))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat M) N))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) N)))))))))
% 0.63/0.88 (assert (forall ((Z tptp.int) (W tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat_1 W)) (@ tptp.nat_1 Z)) (@ (@ tptp.ord_less_eq_int W) Z)))))
% 0.63/0.88 (assert (forall ((P_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat P_1))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.times_times_nat P_1) (@ _let_1 (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))))))))
% 0.63/0.88 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 0.63/0.88 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 0.63/0.88 (assert (forall ((V_2 tptp.int) (K tptp.nat) (V_1 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V_1)) (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V_2)) K)))) (let ((_let_2 (@ (@ tptp.ord_less_int V_1) tptp.pls))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ (@ tptp.times_times_int V_1) V_2))) K))))))))
% 0.63/0.88 (assert (forall ((V_2 tptp.int) (V_1 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V_1)) (@ tptp.number_number_of_nat V_2)))) (let ((_let_2 (@ (@ tptp.ord_less_int V_1) tptp.pls))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (@ tptp.number_number_of_nat (@ (@ tptp.times_times_int V_1) V_2)))))))))
% 0.63/0.88 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.number_number_of_nat _let_1))) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real (@ tptp.bit0 _let_1))) (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.number267125858f_real _let_1)) X)) _let_2))))))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.number267125858f_real (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N))))
% 0.63/0.88 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) C) (=> (@ (@ tptp.ord_less_int B) C) (or (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int B) A))))))
% 0.63/0.88 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B) _let_1))))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat X) Y)) (@ (@ tptp.minus_minus_nat X) Y))))))
% 0.63/0.88 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit1 tptp.pls))) (let ((_let_2 (@ tptp.bit1 _let_1))) (let ((_let_3 (@ tptp.number_number_of_nat _let_2))) (let ((_let_4 (@ tptp.power_power_int B))) (let ((_let_5 (@ tptp.number_number_of_nat (@ tptp.bit0 _let_1)))) (let ((_let_6 (@ tptp.times_times_int (@ tptp.number_number_of_int _let_2)))) (let ((_let_7 (@ tptp.power_power_int A))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int A) B)) _let_3) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int (@ _let_7 _let_3)) (@ (@ tptp.times_times_int (@ _let_6 (@ _let_7 _let_5))) B))) (@ (@ tptp.times_times_int (@ _let_6 A)) (@ _let_4 _let_5)))) (@ _let_4 _let_3))))))))))))
% 0.63/0.88 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.number_number_of_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int A) B)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int A) _let_2)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int _let_1)) A)) B))) (@ (@ tptp.power_power_int B) _let_2)))))))
% 0.63/0.88 (assert (forall ((B tptp.int) (Q tptp.int) (R_1 tptp.int) (B_1 tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q_1)) R_2))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q)) R_1) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R_1) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R_2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1) (=> (@ (@ tptp.ord_less_eq_int B_1) B) (@ (@ tptp.ord_less_eq_int Q_1) Q))))))))))
% 0.63/0.88 (assert (forall ((B tptp.int) (Q_1 tptp.int) (R_2 tptp.int) (Q tptp.int) (R_1 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_2 Q_1)) R_2)) (@ (@ tptp.plus_plus_int (@ _let_2 Q)) R_1)) (=> (@ (@ tptp.ord_less_eq_int R_1) tptp.zero_zero_int) (=> (@ _let_1 R_1) (=> (@ _let_1 R_2) (@ (@ tptp.ord_less_eq_int Q) Q_1)))))))))
% 0.63/0.88 (assert (forall ((B tptp.int) (Q tptp.int) (R_1 tptp.int) (B_1 tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q_1)) R_2))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q)) R_1) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R_2) B_1) (=> (@ _let_1 R_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1) (=> (@ (@ tptp.ord_less_eq_int B_1) B) (@ (@ tptp.ord_less_eq_int Q) Q_1)))))))))))
% 0.63/0.88 (assert (forall ((B tptp.int) (Q_1 tptp.int) (R_2 tptp.int) (Q tptp.int) (R_1 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q_1)) R_2)) (@ (@ tptp.plus_plus_int (@ _let_1 Q)) R_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R_2) (=> (@ (@ tptp.ord_less_int R_2) B) (=> (@ (@ tptp.ord_less_int R_1) B) (@ (@ tptp.ord_less_eq_int Q_1) Q))))))))
% 0.63/0.88 (assert (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.number_number_of_nat _let_1))) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int tptp.x) _let_2)) (@ (@ tptp.power_power_int tptp.y) _let_2)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1621563631at_int tptp.n)))))))
% 0.63/0.88 (assert (forall ((P_1 tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.number_number_of_int _let_1))) (=> (@ (@ tptp.ord_less_int _let_2) P_1) (= (@ (@ tptp.minus_minus_nat (@ tptp.nat_1 P_1)) (@ tptp.number_number_of_nat _let_1)) (@ tptp.nat_1 (@ (@ tptp.minus_minus_int P_1) _let_2))))))))
% 0.63/0.88 (assert (forall ((P_1 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (@ (@ tptp.ord_less_int _let_1) P_1) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat_1 (@ (@ tptp.minus_minus_int P_1) _let_1)))))))
% 0.63/0.88 (assert (not (forall ((T_1 tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int tptp.s) (@ tptp.number_number_of_nat _let_1))) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)) T_1)))))))
% 0.63/0.88 (assert (forall ((W tptp.real)) (@ (@ tptp.ord_less_eq_real W) W)))
% 0.63/0.88 (assert (forall ((Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real Z) W) (@ (@ tptp.times_times_real W) Z))))
% 0.63/0.88 (assert (forall ((Z tptp.real) (W tptp.real)) (or (@ (@ tptp.ord_less_eq_real Z) W) (@ (@ tptp.ord_less_eq_real W) Z))))
% 0.63/0.88 (assert (forall ((Z1 tptp.real) (Z2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z1))) (= (@ (@ tptp.times_times_real (@ _let_1 Z2)) Z3) (@ _let_1 (@ (@ tptp.times_times_real Z2) Z3))))))
% 0.63/0.88 (assert (forall ((K tptp.real) (I_1 tptp.real) (J tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real I_1))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_real J) K) (@ _let_1 K))))))
% 0.63/0.88 (assert (forall ((Z tptp.real) (W tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Z) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (= Z W)))))
% 0.63/0.88 (assert (@ tptp.zprime (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.63/0.88 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) C) (= A (@ (@ tptp.plus_plus_int C) B)))))
% 0.63/0.88 (assert (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int tptp.s) (@ tptp.number_number_of_nat _let_1))) tptp.one_one_int))))
% 0.63/0.88 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.number_number_of_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.number267125858f_real _let_1)) X)) Y)))))))
% 0.63/0.88 (assert (let ((_let_1 (@ (@ tptp.power_power_int tptp.s) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (= (@ (@ tptp.minus_minus_int _let_1) (@ tptp.number_number_of_int tptp.min)) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))
% 0.63/0.88 (assert (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int tptp.s) (@ tptp.number_number_of_nat _let_1))) (@ tptp.number_number_of_int tptp.min)))))
% 0.63/0.88 (assert (= (@ (@ tptp.legendre (@ tptp.number_number_of_int tptp.min)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int)) tptp.one_one_int))
% 0.63/0.88 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_int M) N)) (=> (@ _let_1 N) (@ _let_1 M))))))
% 0.63/0.88 (assert (forall ((M tptp.int) (N tptp.int) (P_1 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int P_1))) (=> (@ tptp.zprime P_1) (=> (@ _let_1 (@ (@ tptp.times_times_int M) N)) (or (@ _let_1 M) (@ _let_1 N)))))))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_eq_int tptp.min) tptp.min))
% 0.63/0.88 (assert (forall ((N tptp.int) (M tptp.int)) (=> (@ (@ tptp.dvd_dvd_int N) M) (or (@ (@ tptp.ord_less_eq_int M) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int N) M)))))
% 0.63/0.88 (assert (forall ((A tptp.int) (N tptp.nat) (P_1 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int P_1))) (=> (@ tptp.zprime P_1) (=> (@ _let_1 (@ (@ tptp.power_power_int A) N)) (@ _let_1 A))))))
% 0.63/0.88 (assert (forall ((N tptp.int) (M tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_int M) N) (not (@ (@ tptp.dvd_dvd_int N) M))))))
% 0.63/0.88 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (=> (not (= K tptp.zero_zero_int)) (@ (@ tptp.dvd_dvd_int M) N))))))
% 0.63/0.88 (assert (forall ((N tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 M) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_int M) N) (=> (@ (@ tptp.dvd_dvd_int N) M) (= M N))))))))
% 0.63/0.88 (assert (forall ((K tptp.int) (N tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (= (@ _let_1 (@ (@ tptp.plus_plus_int N) (@ (@ tptp.times_times_int K) M))) (@ _let_1 N)))))
% 0.63/0.88 (assert (forall ((C tptp.int) (X tptp.int) (T tptp.int) (A tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.dvd_dvd_int A))) (=> (@ _let_2 D) (= (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.times_times_int C) D))) T))))))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.min))) (= (@ _let_1 (@ tptp.bit1 K)) (@ _let_1 K)))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K)) tptp.min) (@ (@ tptp.ord_less_int K) tptp.min))))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_int tptp.min) tptp.pls))
% 0.63/0.88 (assert (not (@ (@ tptp.ord_less_int tptp.pls) tptp.min)))
% 0.63/0.88 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.min))) (= (@ _let_1 (@ tptp.bit0 K)) (@ _let_1 K)))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.min))) (= (@ _let_1 (@ tptp.bit1 K)) (@ _let_1 K)))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) tptp.min) (@ (@ tptp.ord_less_eq_int K) tptp.min))))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_int tptp.min) tptp.zero_zero_int))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_eq_int tptp.min) tptp.pls))
% 0.63/0.88 (assert (not (@ (@ tptp.ord_less_eq_int tptp.pls) tptp.min)))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) tptp.min) (@ (@ tptp.ord_less_eq_int K) tptp.min))))
% 0.63/0.88 (assert (not (= (@ tptp.number_number_of_int tptp.pls) (@ tptp.number_number_of_int tptp.min))))
% 0.63/0.88 (assert (not (@ (@ tptp.ord_less_int tptp.min) tptp.min)))
% 0.63/0.88 (assert (forall ((L tptp.int)) (not (= tptp.min (@ tptp.bit0 L)))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (not (= (@ tptp.bit0 K) tptp.min))))
% 0.63/0.88 (assert (not (= tptp.min tptp.pls)))
% 0.63/0.88 (assert (not (= tptp.pls tptp.min)))
% 0.63/0.88 (assert (= (@ tptp.bit1 tptp.min) tptp.min))
% 0.63/0.88 (assert (forall ((L tptp.int)) (= (= tptp.min (@ tptp.bit1 L)) (= tptp.min L))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (= (@ tptp.bit1 K) tptp.min) (= K tptp.min))))
% 0.63/0.88 (assert (= (@ tptp.succ tptp.min) tptp.pls))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.min) (@ tptp.succ K))))
% 0.63/0.88 (assert (forall ((Z tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z) N) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int Z) N)))))
% 0.63/0.88 (assert (forall ((P_1 tptp.int) (Y tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int P_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.power_power_int Y) N)))))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.min) (@ tptp.bit0 K)) (@ (@ tptp.ord_less_int tptp.min) K))))
% 0.63/0.88 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K)) tptp.min) (@ (@ tptp.ord_less_eq_int K) tptp.min))))
% 0.63/0.88 (assert (forall ((L tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.pls) (@ tptp.bit1 L)) (@ tptp.bit1 (@ (@ tptp.minus_minus_int tptp.min) L)))))
% 0.63/0.88 (assert (forall ((L tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int tptp.min))) (= (@ _let_1 (@ tptp.bit1 L)) (@ tptp.bit0 (@ _let_1 L))))))
% 0.63/0.88 (assert (forall ((L tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int tptp.min))) (= (@ _let_1 (@ tptp.bit0 L)) (@ tptp.bit1 (@ _let_1 L))))))
% 0.63/0.88 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int tptp.min))) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (or (and (= M tptp.one_one_int) (= N tptp.one_one_int)) (and (= M _let_1) (= N _let_1)))))))
% 0.63/0.88 (assert (forall ((M tptp.int) (N tptp.int)) (=> (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (or (= M tptp.one_one_int) (= M (@ tptp.number_number_of_int tptp.min))))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int) (P_1 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int P_1) N)))) (=> (@ tptp.zprime P_1) (=> (not (@ (@ tptp.dvd_dvd_int P_1) B)) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (@ _let_1 A)))))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (B tptp.int) (A tptp.int) (P_1 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int P_1) N)))) (=> (@ tptp.zprime P_1) (=> (not (@ (@ tptp.dvd_dvd_int P_1) A)) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (@ _let_1 B)))))))
% 0.63/0.88 (assert (forall ((Y tptp.int) (N tptp.nat) (P_1 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int P_1))) (=> (@ tptp.zprime P_1) (=> (@ _let_1 (@ (@ tptp.power_power_int Y) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 Y)))))))
% 0.63/0.88 (assert (@ (@ tptp.quadRes (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int)) (@ tptp.number_number_of_int tptp.min)))
% 0.63/0.88 (assert (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int tptp.s) (@ tptp.number_number_of_nat _let_1))) (@ tptp.number_number_of_int tptp.min)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int))))
% 0.63/0.88 (assert (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (let ((_let_2 (@ tptp.number_number_of_int tptp.min))) (=> (not (@ (@ tptp.quadRes _let_1) _let_2)) (not (= (@ (@ tptp.legendre _let_2) _let_1) tptp.one_one_int))))))
% 0.63/0.88 (assert (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int tptp.s1) (@ tptp.number_number_of_nat _let_1))) (@ tptp.number_number_of_int tptp.min)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int))))
% 0.63/0.88 (assert (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.s) (@ (@ tptp.ord_less_int tptp.s) _let_1) (@ (@ (@ tptp.zcong tptp.s1) tptp.s) _let_1))))
% 0.63/0.88 (assert (not (forall ((S1 tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (not (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int S1) (@ tptp.number_number_of_nat _let_1))) (@ tptp.number_number_of_int tptp.min)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)))))))
% 0.63/0.88 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 0.63/0.88 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.dvd_dvd_nat A) B) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A)) (@ _let_1 B))))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))))))
% 0.63/0.88 (assert (forall ((X tptp.int) (P_1 tptp.int)) (= (@ (@ (@ tptp.zcong X) tptp.zero_zero_int) P_1) (@ (@ tptp.dvd_dvd_int P_1) X))))
% 0.63/0.88 (assert (forall ((A tptp.int) (M tptp.int)) (= (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) M) (@ (@ tptp.dvd_dvd_int M) A))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (not (@ (@ tptp.dvd_dvd_nat N) M))))))
% 0.63/0.88 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (or (= B tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M) N)))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 M)))))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 M) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 N)))))))
% 0.63/0.88 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.dvd_dvd_nat A) B)))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N)) Y) (@ (@ tptp.dvd_dvd_nat X) Y)))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ (@ tptp.dvd_dvd_nat X) Y))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat X) Y) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y) N)))))
% 0.63/0.88 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 N)))))
% 0.63/0.88 (assert (forall ((B tptp.nat) (D tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D))) (=> (@ _let_1 A) (=> (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (@ _let_1 B))))))
% 0.63/0.88 (assert (forall ((M tptp.int)) (@ (@ (@ tptp.zcong M) tptp.zero_zero_int) M)))
% 0.63/0.88 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (@ (@ (@ tptp.zcong A) B) M) (@ (@ (@ tptp.zcong (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) M))))
% 0.63/0.88 (assert (forall ((D tptp.int) (C tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.zcong A))) (=> (@ (@ _let_1 B) M) (=> (= B C) (=> (@ (@ (@ tptp.zcong C) D) M) (@ (@ _let_1 D) M)))))))
% 0.63/0.88 (assert (forall ((Z tptp.nat) (X tptp.int) (Y tptp.int) (M tptp.int)) (=> (@ (@ (@ tptp.zcong X) Y) M) (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int X) Z)) (@ (@ tptp.power_power_int Y) Z)) M))))
% 0.63/0.88 (assert (forall ((M tptp.int) (Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ _let_1 M) (=> (@ (@ (@ tptp.zcong X) Y) M) (=> (@ (@ tptp.ord_less_int X) M) (=> (@ (@ tptp.ord_less_int Y) M) (= X Y))))))))))
% 0.63/0.88 (assert (forall ((M tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) M) (not (@ (@ (@ tptp.zcong X) tptp.zero_zero_int) M))))))
% 0.63/0.88 (assert (forall ((C tptp.int) (D tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.zcong C))) (=> (@ (@ (@ tptp.zcong A) B) M) (= (@ (@ _let_1 (@ (@ tptp.times_times_int A) D)) M) (@ (@ _let_1 (@ (@ tptp.times_times_int B) D)) M))))))
% 0.63/0.88 (assert (forall ((C tptp.int) (D tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.times_times_int D))) (let ((_let_2 (@ tptp.zcong C))) (=> (@ (@ (@ tptp.zcong A) B) M) (= (@ (@ _let_2 (@ _let_1 A)) M) (@ (@ _let_2 (@ _let_1 B)) M)))))))
% 0.63/0.88 (assert (forall ((M tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) M) (=> (@ (@ (@ tptp.zcong X) tptp.zero_zero_int) M) (= X tptp.zero_zero_int))))))
% 0.63/0.88 (assert (forall ((Y tptp.int) (X tptp.int) (P_1 tptp.int)) (=> (@ tptp.zprime P_1) (=> (not (@ (@ (@ tptp.zcong X) tptp.zero_zero_int) P_1)) (=> (not (@ (@ (@ tptp.zcong Y) tptp.zero_zero_int) P_1)) (not (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int X) Y)) tptp.zero_zero_int) P_1)))))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat K) N)))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 0.63/0.88 (assert (forall ((B tptp.int) (A tptp.int) (P_1 tptp.int)) (=> (@ tptp.zprime P_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) P_1) (or (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) P_1) (@ (@ (@ tptp.zcong B) tptp.zero_zero_int) P_1)))))))
% 0.63/0.88 (assert (forall ((B tptp.int) (A tptp.int) (P_1 tptp.int)) (=> (@ tptp.zprime P_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (and (not (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) P_1)) (not (@ (@ (@ tptp.zcong B) tptp.zero_zero_int) P_1))) (not (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) P_1)))))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Q tptp.nat) (N tptp.nat) (R_1 tptp.nat)) (=> (= X (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Q) N)) R_1)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) R_1) (=> (@ (@ tptp.ord_less_nat R_1) N) (not (@ (@ tptp.dvd_dvd_nat N) X)))))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) N)) M) (= N tptp.one_one_nat)))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N) M)) M) (= N tptp.one_one_nat)))))
% 0.63/0.88 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat_1 X)) (@ tptp.nat_1 Y)) (@ (@ tptp.dvd_dvd_int X) Y)))))))
% 0.63/0.88 (assert (forall ((I_1 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I_1))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I_1) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 0.63/0.88 (assert (forall ((Z tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat_1 Z)) M) (and (=> _let_1 (@ (@ tptp.dvd_dvd_int Z) (@ tptp.semiri1621563631at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 0.63/0.88 (assert (forall ((X tptp.int) (P_1 tptp.int)) (let ((_let_1 (@ tptp.zcong X))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P_1) (=> (@ (@ _let_1 (@ tptp.number_number_of_int tptp.min)) P_1) (not (@ (@ _let_1 tptp.one_one_int) P_1)))))))
% 0.63/0.88 (assert (forall ((Y tptp.int) (X tptp.int) (P_1 tptp.int)) (=> (not (@ (@ (@ tptp.zcong X) tptp.zero_zero_int) P_1)) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int Y) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) X) P_1) (not (@ (@ tptp.dvd_dvd_int P_1) Y))))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat N) M) (or (= M tptp.zero_zero_nat) (= M N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N)) M)))))
% 0.63/0.88 (assert (forall ((M tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) M)) tptp.one_one_int))) (=> (@ tptp.zprime _let_1) (= (@ (@ tptp.legendre (@ tptp.number_number_of_int tptp.min)) _let_1) tptp.one_one_int)))))
% 0.63/0.88 (assert (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.number_number_of_nat _let_1))) (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int tptp.s) _let_2)) (@ (@ tptp.power_power_int tptp.s1) _let_2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)))))
% 0.63/0.88 (assert (exists ((X_1 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ (@ tptp.ord_less_int X_1) _let_1) (@ (@ (@ tptp.zcong tptp.s1) X_1) _let_1) (forall ((Y_1 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y_1) (@ (@ tptp.ord_less_int Y_1) _let_1) (@ (@ (@ tptp.zcong tptp.s1) Y_1) _let_1)) (= Y_1 X_1))))))))
% 0.63/0.88 (assert (forall ((X tptp.nat)) (@ (@ tptp.dvd_dvd_nat X) X)))
% 0.63/0.88 (assert (not (forall ((S tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (not (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) S) (@ (@ tptp.ord_less_int S) _let_1) (@ (@ (@ tptp.zcong tptp.s1) S) _let_1)))))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) Y))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat Y) X))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))))
% 0.63/0.88 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat Z))) (let ((_let_2 (@ tptp.dvd_dvd_nat X))) (let ((_let_3 (@ tptp.dvd_dvd_nat Y))) (=> (and (@ _let_2 Y) (not (@ _let_3 X))) (=> (and (@ _let_3 Z) (not (@ _let_1 Y))) (and (@ _let_2 Z) (not (@ _let_1 X))))))))))
% 0.63/0.88 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat A) B))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat B) A))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))))
% 0.63/0.88 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat X))) (let ((_let_2 (@ tptp.dvd_dvd_nat Y))) (=> (and (@ _let_1 Y) (not (@ _let_2 X))) (=> (@ _let_2 Z) (and (@ _let_1 Z) (not (@ (@ tptp.dvd_dvd_nat Z) X)))))))))
% 0.63/0.88 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (and (@ _let_1 B) (not (@ (@ tptp.dvd_dvd_nat B) A))) (=> (= B C) (and (@ _let_1 C) (not (@ (@ tptp.dvd_dvd_nat C) A))))))))
% 0.63/0.88 (assert (forall ((P Bool) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) Y))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat Y) X))) (=> (and _let_1 (not _let_2)) (=> (and _let_2 (not _let_1)) P))))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (and (@ (@ tptp.dvd_dvd_nat X) Y) (not (@ (@ tptp.dvd_dvd_nat Y) X))) (not (= Y X)))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (and (@ (@ tptp.dvd_dvd_nat X) Y) (not (@ (@ tptp.dvd_dvd_nat Y) X))) (not (= X Y)))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) Y))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat Y) X))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) Y))) (=> (and _let_1 (not (@ (@ tptp.dvd_dvd_nat Y) X))) _let_1))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) Y))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat Y) X))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (and (@ (@ tptp.dvd_dvd_nat X) Y) (not (@ (@ tptp.dvd_dvd_nat Y) X))) (not (= X Y)))))
% 0.63/0.88 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat Z))) (let ((_let_2 (@ tptp.dvd_dvd_nat X))) (=> (@ _let_2 Y) (=> (and (@ (@ tptp.dvd_dvd_nat Y) Z) (not (@ _let_1 Y))) (and (@ _let_2 Z) (not (@ _let_1 X)))))))))
% 0.63/0.88 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (= A B) (=> (and (@ (@ tptp.dvd_dvd_nat B) C) (not (@ _let_1 B))) (and (@ (@ tptp.dvd_dvd_nat A) C) (not (@ _let_1 A))))))))
% 0.63/0.88 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.dvd_dvd_nat Y) Z) (@ _let_1 Z))))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (=> (@ (@ tptp.dvd_dvd_nat Y) X) (= X Y)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))))
% 0.63/0.88 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 0.63/0.88 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (= A B) (=> (@ (@ tptp.dvd_dvd_nat B) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 0.63/0.88 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat A) B))) (=> _let_1 (=> (not (= A B)) (and _let_1 (not (@ (@ tptp.dvd_dvd_nat B) A))))))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) Y))) (=> _let_1 (or (and _let_1 (not (@ (@ tptp.dvd_dvd_nat Y) X))) (= X Y))))))
% 0.63/0.88 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat Y) X) (= (@ (@ tptp.dvd_dvd_nat X) Y) (= X Y)))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.dvd_dvd_nat X) Y))))
% 0.63/0.88 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat A) B))) (=> (not (= A B)) (=> _let_1 (and _let_1 (not (@ (@ tptp.dvd_dvd_nat B) A))))))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (and (@ (@ tptp.dvd_dvd_nat X) Y) (not (@ (@ tptp.dvd_dvd_nat Y) X))))) (= _let_1 _let_1))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) Y))) (= (and _let_1 (not (@ (@ tptp.dvd_dvd_nat Y) X))) (and _let_1 (not (= X Y)))))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) Y))) (= _let_1 (or (and _let_1 (not (@ (@ tptp.dvd_dvd_nat Y) X))) (= X Y))))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= X Y) (and (@ (@ tptp.dvd_dvd_nat X) Y) (@ (@ tptp.dvd_dvd_nat Y) X)))))
% 0.63/0.88 (assert (forall ((X tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) X))) (not (and _let_1 (not _let_1))))))
% 0.63/0.88 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (and (@ (@ tptp.dvd_dvd_nat X) Y) (@ (@ tptp.dvd_dvd_nat Y) X)) (= X Y))))
% 0.63/0.88 (assert (forall ((J tptp.nat) (K tptp.nat) (M tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.number_number_of_int tptp.min)))) (let ((_let_2 (@ _let_1 K))) (let ((_let_3 (@ _let_1 J))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) M) (=> (@ (@ (@ tptp.zcong _let_3) _let_2) M) (= _let_3 _let_2))))))))
% 0.63/0.88 (assert (forall ((M tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) M) (not (@ (@ (@ tptp.zcong tptp.one_one_int) (@ tptp.number_number_of_int tptp.min)) M)))))
% 0.63/0.88 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_int tptp.min))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (or (= _let_2 tptp.one_one_int) (= _let_2 _let_1))))))
% 0.63/0.88 (assert (forall ((A tptp.int) (P_1 tptp.int)) (let ((_let_1 (@ (@ tptp.legendre A) P_1))) (let ((_let_2 (@ (@ tptp.quadRes P_1) A))) (let ((_let_3 (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) P_1))) (and (=> _let_3 (= _let_1 tptp.zero_zero_int)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (@ tptp.number_number_of_int tptp.min)))))))))))
% 0.63/0.88 (assert (forall ((M tptp.int) (X tptp.int)) (= (@ (@ tptp.quadRes M) X) (exists ((Y_1 tptp.int)) (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int Y_1) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) X) M)))))
% 0.63/0.88 (assert (forall ((X tptp.int) (P_1 tptp.int)) (=> (@ tptp.zprime P_1) (=> (not (@ (@ tptp.dvd_dvd_int P_1) X)) (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int X) (@ tptp.nat_1 (@ (@ tptp.minus_minus_int P_1) tptp.one_one_int)))) tptp.one_one_int) P_1)))))
% 0.63/0.88 (assert (forall ((A tptp.int) (P_1 tptp.int)) (=> (@ tptp.zprime P_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) P_1) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) A)) tptp.one_one_int) P_1) (or (= A tptp.one_one_int) (= A (@ (@ tptp.minus_minus_int P_1) tptp.one_one_int)))))))))
% 0.63/0.88 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.zcong A))) (=> (@ (@ _let_1 B) M) (=> (@ (@ (@ tptp.zcong B) C) M) (@ (@ _let_1 C) M))))))
% 0.63/0.88 (assert (forall ((K tptp.int) (M tptp.int)) (@ (@ (@ tptp.zcong K) K) M)))
% 0.63/0.88 (assert (forall ((A tptp.int) (B tptp.int) (M tptp.int)) (= (@ (@ (@ tptp.zcong A) B) M) (@ (@ (@ tptp.zcong B) A) M))))
% 0.63/0.88 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ (@ tptp.zcong A) B) tptp.zero_zero_int) (= A B))))
% 0.63/0.88 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ (@ tptp.zcong A) B) tptp.one_one_int)))
% 0.63/0.88 (assert (forall ((A tptp.int) (M tptp.int) (B tptp.int)) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) M)) (@ (@ tptp.times_times_int B) M)) M)))
% 0.63/0.88 (assert (forall ((K tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (@ (@ (@ tptp.zcong A) B) M) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) K)) (@ (@ tptp.times_times_int B) K)) M))))
% 0.63/0.88 (assert (forall ((K tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ (@ tptp.zcong A) B) M) (@ (@ (@ tptp.zcong (@ _let_1 A)) (@ _let_1 B)) M)))))
% 0.63/0.88 (assert (forall ((C tptp.int) (D tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (@ (@ (@ tptp.zcong A) B) M) (=> (@ (@ (@ tptp.zcong C) D) M) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)) M)))))
% 0.63/0.88 (assert (forall ((C tptp.int) (D tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (@ (@ (@ tptp.zcong A) B) M) (=> (@ (@ (@ tptp.zcong C) D) M) (@ (@ (@ tptp.zcong (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D)) M)))))
% 0.63/0.88 (assert (forall ((C tptp.int) (D tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (@ (@ (@ tptp.zcong A) B) M) (=> (@ (@ (@ tptp.zcong C) D) M) (@ (@ (@ tptp.zcong (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D)) M)))))
% 0.63/0.88 (assert (forall ((B tptp.int) (M tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_int A) M) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ (@ tptp.zcong A) B) M)))))))))
% 0.63/0.88 (assert (forall ((A tptp.int) (R_1 tptp.int) (B tptp.int) (M tptp.int) (C tptp.int) (D tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int R_1))) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) (@ _let_1 B))) M)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int C) (@ _let_1 D))) N)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) M)) (@ (@ tptp.times_times_int C) N))) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) M)) (@ (@ tptp.times_times_int D) N))))))))
% 0.63/0.88 (assert (forall ((A tptp.int) (B tptp.int) (M tptp.int)) (= (@ (@ (@ tptp.zcong A) B) M) (exists ((K_1 tptp.int)) (= B (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int M) K_1)))))))
% 0.63/0.88 (assert (forall ((A tptp.int) (B tptp.int) (M tptp.int)) (= (@ (@ (@ tptp.zcong A) B) M) (@ (@ tptp.dvd_dvd_int M) (@ (@ tptp.minus_minus_int A) B)))))
% 0.63/0.88 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.minus_minus_int B) tptp.one_one_int)) (@ (@ tptp.ord_less_int A) B))))
% 0.63/0.88 (assert (forall ((M tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) M) (=> (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) M) (= A tptp.zero_zero_int))))))
% 0.63/0.88 (assert (forall ((B tptp.int) (M tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_int A) M) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) M) (=> (@ (@ (@ tptp.zcong A) B) M) (= A B)))))))))
% 0.63/0.88 (assert (forall ((N tptp.int) (P_1 tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int P_1))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M) (=> (@ tptp.zprime P_1) (=> (@ _let_1 (@ (@ tptp.times_times_int M) N)) (or (@ _let_1 M) (@ _let_1 N))))))))
% 0.63/0.88 (assert (forall ((P_1 tptp.int)) (= (@ tptp.zprime P_1) (and (@ (@ tptp.ord_less_int tptp.one_one_int) P_1) (forall ((M_1 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M_1) (@ (@ tptp.dvd_dvd_int M_1) P_1)) (or (= M_1 tptp.one_one_int) (= M_1 P_1))))))))
% 0.63/0.88 (assert (forall ((A tptp.int) (P_1 tptp.int)) (let ((_let_1 (@ tptp.zcong A))) (=> (@ tptp.zprime P_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) A)) tptp.one_one_int) P_1) (or (@ (@ _let_1 tptp.one_one_int) P_1) (@ (@ _let_1 (@ (@ tptp.minus_minus_int P_1) tptp.one_one_int)) P_1))))))))
% 0.63/0.88 (assert (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1621563631at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P tptp.zero_zero_int))))))
% 0.63/0.88 (assert (forall ((P_1 tptp.int)) (let ((_let_1 (@ tptp.bit1 tptp.pls))) (let ((_let_2 (@ tptp.bit0 _let_1))) (=> (@ tptp.zprime P_1) (=> (not (= P_1 (@ tptp.number_number_of_int _let_2))) (=> (not (= P_1 (@ tptp.number_number_of_int (@ tptp.bit1 _let_1)))) (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int (@ tptp.bit1 _let_2))) P_1))))))))
% 0.63/0.88 (assert (forall ((P_2 Bool) (P Bool) (X tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X))) (=> (=> _let_1 (= P P_2)) (= (and _let_1 P) (and _let_1 P_2))))))
% 0.63/0.88 (assert (forall ((P_2 Bool) (P Bool) (X tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X))) (=> (=> _let_1 (= P P_2)) (= (=> _let_1 P) (=> _let_1 P_2))))))
% 0.63/0.88 (assert (forall ((M tptp.int) (T tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (not (= K tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int M) T) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 T)))))))
% 0.63/0.88 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.number_number_of_int tptp.pls)))
% 0.63/0.88 (assert (forall ((A tptp.int) (P_1 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int P_1) tptp.one_one_int))) (= (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) _let_1)) tptp.one_one_int) P_1) (@ (@ (@ tptp.zcong A) _let_1) P_1)))))
% 0.63/0.88 (assert (forall ((Z tptp.nat) (X tptp.int) (Y tptp.nat) (P_1 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (@ (@ (@ tptp.zcong (@ _let_1 Y)) tptp.one_one_int) P_1) (@ (@ (@ tptp.zcong (@ _let_1 (@ (@ tptp.times_times_nat Y) Z))) tptp.one_one_int) P_1)))))
% 0.63/0.88 (assert (forall ((N tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ tptp.number_number_of_int N)) (and (@ _let_1 (@ tptp.number_number_of_int (@ tptp.bit0 N))) (@ _let_1 (@ tptp.number_number_of_int (@ tptp.bit1 N))))))))
% 0.63/0.88 (assert (not (forall ((S tptp.int) (W_1 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1621563631at_int tptp.n)))) (not (and (= W_1 (@ (@ tptp.minus_minus_int tptp.y) (@ (@ tptp.times_times_int S) _let_1))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ tptp.abs_abs_int W_1))) _let_1)))))))
% 0.63/0.88 (assert (not (forall ((R tptp.int) (V tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1621563631at_int tptp.n)))) (not (and (= V (@ (@ tptp.minus_minus_int tptp.x) (@ (@ tptp.times_times_int R) _let_1))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ tptp.abs_abs_int V))) _let_1)))))))
% 0.63/0.88 (assert (forall ((D tptp.int) (I_1 tptp.int)) (=> (not (= I_1 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int D) I_1) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int D)) (@ tptp.abs_abs_int I_1))))))
% 0.63/0.88 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.nat_1 (@ tptp.abs_abs_int (@ (@ tptp.times_times_int W) Z))) (@ (@ tptp.times_times_nat (@ tptp.nat_1 (@ tptp.abs_abs_int W))) (@ tptp.nat_1 (@ tptp.abs_abs_int Z))))))
% 0.63/0.88 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ tptp.abs_abs_int A) (@ tptp.abs_abs_int B))))))
% 0.63/0.88 (assert (forall ((X tptp.int)) (= (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))))
% 0.63/0.88 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.semiri1621563631at_int M))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 0.63/0.88 (assert (forall ((M tptp.int) (N tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M) N)) tptp.one_one_int) (= (@ tptp.abs_abs_int M) tptp.one_one_int))))
% 0.63/0.88 (assert (forall ((X tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int X)) N))))
% 0.63/0.88 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 0.63/0.88 (assert (forall ((Z tptp.int)) (= (= (@ tptp.abs_abs_int Z) tptp.one_one_int) (or (= Z tptp.one_one_int) (= Z (@ tptp.number_number_of_int tptp.min))))))
% 0.63/0.88 (assert (forall ((X tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit1 (@ tptp.bit1 tptp.pls))))) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int X)) _let_1)))))
% 0.63/0.88 (assert (forall ((X tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int X)) N)) (or (not (= X tptp.zero_zero_int)) (= N tptp.zero_zero_nat)))))
% 0.63/0.88 (assert (forall ((N tptp.int) (M tptp.int)) (=> (not (= M tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int M) N)) M) (= (@ tptp.abs_abs_int N) tptp.one_one_int)))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1621563631at_int M)) Z) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.nat_1 (@ tptp.abs_abs_int Z))))))
% 0.63/0.88 (assert (forall ((Z tptp.int) (M tptp.nat)) (= (@ (@ tptp.dvd_dvd_int Z) (@ tptp.semiri1621563631at_int M)) (@ (@ tptp.dvd_dvd_nat (@ tptp.nat_1 (@ tptp.abs_abs_int Z))) M))))
% 0.63/0.88 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) _let_1)))))
% 0.63/0.88 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (= (@ (@ tptp.power_power_int A) _let_1) (@ (@ tptp.power_power_int B) _let_1)) (= (@ tptp.abs_abs_int A) (@ tptp.abs_abs_int B))))))
% 0.63/0.88 (assert (forall ((A tptp.int)) (=> (= (@ (@ tptp.power_power_int A) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.one_one_int) (= (@ tptp.abs_abs_int A) tptp.one_one_int))))
% 0.63/0.88 (assert (forall ((Z tptp.int) (X tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Z))) tptp.one_one_int)) D))))))
% 0.63/0.88 (assert (forall ((X tptp.int) (Z tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D))) Z)))))
% 0.63/0.88 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (exists ((N_1 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int Y) (@ (@ tptp.times_times_int N_1) X))))) X)))))
% 0.63/0.88 (assert (forall ((K tptp.int) (P (-> tptp.int Bool)) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X_1 tptp.int)) (=> (@ P X_1) (@ P (@ (@ tptp.minus_minus_int X_1) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X_1 tptp.int)) (=> (@ P X_1) (@ P (@ (@ tptp.minus_minus_int X_1) (@ (@ tptp.times_times_int K) D))))))))))
% 0.63/0.88 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X)) tptp.one_one_real)) X))))
% 0.63/0.88 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X)))))
% 0.63/0.88 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.one_one_real))))
% 0.63/0.88 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (@ P N) (exists ((K_1 tptp.nat)) (and (@ (@ tptp.ord_less_nat K_1) N) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) K_1) (not (@ P I)))) (@ P (@ (@ tptp.plus_plus_nat K_1) tptp.one_one_nat))))))))
% 0.63/0.88 (assert (forall ((K tptp.int) (P (-> tptp.int Bool)) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X_1 tptp.int)) (=> (@ P X_1) (@ P (@ (@ tptp.plus_plus_int X_1) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X_1 tptp.int)) (=> (@ P X_1) (@ P (@ (@ tptp.plus_plus_int X_1) (@ (@ tptp.times_times_int K) D))))))))))
% 0.63/0.88 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I_1) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J)) U)) M)) N)))))
% 0.63/0.88 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I_1)) U)) N))))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (= M N))))))
% 0.63/0.88 (assert (forall ((I_1 tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I_1) J)) U)) K))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 0.63/0.88 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 0.63/0.88 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 0.63/0.88 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I_1) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J)) U)) M)) N)))))
% 0.63/0.88 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I_1) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J)) U)) M)) N)))))
% 0.63/0.88 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I_1) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J)) U)) M) N)))))
% 0.63/0.88 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I_1)) U)) N))))))
% 0.71/1.30 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I_1)) U)) N))))))
% 0.71/1.30 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I_1)) U)) N))))))
% 0.71/1.30 (assert (forall ((K tptp.int) (F (-> tptp.nat tptp.int)) (N tptp.nat)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat))) (@ F I)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I) N) (= (@ F I) K))))))))
% 0.71/1.30 (assert (forall ((K tptp.int) (F (-> tptp.nat tptp.int)) (N tptp.nat)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat))) (@ F I)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I) N) (= (@ F I) K))))))))
% 0.71/1.30 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)))
% 0.71/1.30 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)))
% 0.71/1.30 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 0.71/1.30 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)))
% 0.71/1.30 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)))
% 0.71/1.30 (assert (forall ((P Bool)) (or (= P true) (= P false))))
% 0.71/1.30 (assert (not (not (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1621563631at_int tptp.n))) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_int))))
% 0.71/1.30 (set-info :filename cvc5---1.0.5_24761)
% 0.71/1.30 (check-sat-assuming ( true ))
% 0.71/1.30 ------- get file name : TPTP file name is NUM925^3
% 0.71/1.30 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_24761.smt2...
% 0.71/1.30 --- Run --ho-elim --full-saturate-quant at 10...
% 0.71/1.30 % SZS status Theorem for NUM925^3
% 0.71/1.30 % SZS output start Proof for NUM925^3
% 0.71/1.30 (
% 0.71/1.30 (let ((_let_1 (@ tptp.bit1 tptp.pls))) (let ((_let_2 (@ tptp.bit0 _let_1))) (let ((_let_3 (@ tptp.number_number_of_nat _let_2))) (let ((_let_4 (@ tptp.semiri1621563631at_int tptp.n))) (let ((_let_5 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_6 (@ _let_5 _let_4))) (let ((_let_7 (@ (@ tptp.power_power_int _let_6) _let_3))) (let ((_let_8 (not (not (= _let_7 tptp.zero_zero_int))))) (let ((_let_9 (@ tptp.number_number_of_int tptp.pls))) (let ((_let_10 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_11 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_2))) tptp.m)) tptp.one_one_int))) (let ((_let_12 (@ (@ tptp.power_power_int tptp.s1) _let_3))) (let ((_let_13 (@ (@ tptp.power_power_int tptp.s) _let_3))) (let ((_let_14 (@ tptp.zcong _let_13))) (let ((_let_15 (@ tptp.number_number_of_int tptp.min))) (let ((_let_16 (= (@ (@ tptp.legendre _let_15) _let_11) tptp.one_one_int))) (let ((_let_17 (@ (@ tptp.quadRes _let_11) _let_15))) (let ((_let_18 (@ tptp.succ tptp.min))) (let ((_let_19 (= _let_18 tptp.pls))) (let ((_let_20 (@ tptp.ord_less_int tptp.min))) (let ((_let_21 (@ tptp.ord_less_eq_int tptp.pls))) (let ((_let_22 (@ tptp.ord_less_eq_int tptp.min))) (let ((_let_23 (@ tptp.ord_less_int tptp.pls))) (let ((_let_24 (@ (@ tptp.minus_minus_int _let_13) _let_15))) (let ((_let_25 (@ tptp.dvd_dvd_int _let_11))) (let ((_let_26 (@ (@ tptp.plus_plus_int _let_13) tptp.one_one_int))) (let ((_let_27 (@ tptp.number_number_of_int _let_2))) (let ((_let_28 (@ tptp.times_times_int _let_11))) (let ((_let_29 (@ _let_28 _let_6))) (let ((_let_30 (@ _let_28 tptp.t))) (let ((_let_31 (@ tptp.twoSqu919416604sum2sq _let_29))) (let ((_let_32 (@ (@ tptp.ord_less_int _let_6) _let_11))) (let ((_let_33 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_34 (@ tptp.semiri1621563631at_int tptp.zero_zero_nat))) (let ((_let_35 (@ tptp.bit1 _let_1))) (let ((_let_36 (@ tptp.number_number_of_int _let_35))) (let ((_let_37 (@ tptp.number_number_of_nat _let_35))) (let ((_let_38 (@ tptp.nat_1 tptp.zero_zero_int))) (let ((_let_39 (@ (@ tptp.minus_minus_nat (@ tptp.nat_1 tptp.t)) tptp.one_one_nat))) (let ((_let_40 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_41 (= tptp.tn _let_39))) (let ((_let_42 (= _let_34 tptp.zero_zero_int))) (let ((_let_43 (forall ((N_17 tptp.nat) (A_123 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A_123) (@ _let_1 (@ (@ tptp.power_power_int A_123) N_17))))))) (let ((_let_44 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_45 (@ _let_33 tptp.one_one_int))) (let ((_let_46 (@ tptp.ord_less_int tptp.one_one_int))) (let ((_let_47 (@ tptp.semiri1621563631at_int tptp.one_one_nat))) (let ((_let_48 (= _let_47 tptp.one_one_int))) (let ((_let_49 (not (= tptp.zero_zero_real tptp.one_one_real)))) (let ((_let_50 (not (= tptp.zero_zero_int tptp.one_one_int)))) (let ((_let_51 (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) (let ((_let_52 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat))) (let ((_let_53 (@ _let_5 tptp.one_one_int))) (let ((_let_54 (@ tptp.number267125858f_real _let_1))) (let ((_let_55 (= _let_54 tptp.one_one_real))) (let ((_let_56 (@ tptp.number_number_of_nat _let_1))) (let ((_let_57 (= _let_56 tptp.one_one_nat))) (let ((_let_58 (@ tptp.number_number_of_int _let_1))) (let ((_let_59 (= _let_58 tptp.one_one_int))) (let ((_let_60 (@ tptp.number267125858f_real tptp.pls))) (let ((_let_61 (= tptp.zero_zero_real _let_60))) (let ((_let_62 (= tptp.zero_zero_int _let_9))) (let ((_let_63 (= _let_60 tptp.zero_zero_real))) (let ((_let_64 (= _let_9 tptp.zero_zero_int))) (let ((_let_65 (@ tptp.number_number_of_nat tptp.pls))) (let ((_let_66 (= _let_65 tptp.zero_zero_nat))) (let ((_let_67 (= tptp.pls tptp.zero_zero_int))) (let ((_let_68 (not (@ _let_23 tptp.zero_zero_int)))) (let ((_let_69 (= tptp.one_one_nat _let_56))) (let ((_let_70 (= tptp.one_one_int _let_58))) (let ((_let_71 (= _let_52 _let_3))) (let ((_let_72 (= tptp.zero_zero_nat _let_65))) (let ((_let_73 (= tptp.one_one_real _let_54))) (let ((_let_74 (= _let_51 (@ tptp.number267125858f_real _let_2)))) (let ((_let_75 (= _let_53 _let_27))) (let ((_let_76 (@ _let_33 _let_6))) (let ((_let_77 (ho_5 k_4 tptp.min))) (let ((_let_78 (ho_5 k_7 _let_77))) (let ((_let_79 (ho_12 (ho_11 k_10 _let_77) _let_78))) (let ((_let_80 (= _let_77 _let_78))) (let ((_let_81 (ho_5 k_6 _let_77))) (let ((_let_82 (ho_15 k_14 (ho_5 k_13 _let_81)))) (let ((_let_83 (ho_5 (ho_9 k_8 (ho_5 k_7 _let_81)) (ho_3 k_2 tptp.n)))) (let ((_let_84 (ho_3 (ho_17 k_16 _let_83) _let_82))) (let ((_let_85 (= _let_78 _let_84))) (let ((_let_86 (ho_11 k_10 _let_78))) (let ((_let_87 (ho_12 _let_86 _let_84))) (let ((_let_88 (not _let_79))) (let ((_let_89 (@ tptp.number_number_of_int _let_18))) (let ((_let_90 (ASSUME :args (_let_70)))) (let ((_let_91 (ASSUME :args (_let_73)))) (let ((_let_92 (ASSUME :args (_let_62)))) (let ((_let_93 (ASSUME :args (_let_72)))) (let ((_let_94 (ASSUME :args (_let_69)))) (let ((_let_95 (ASSUME :args (_let_61)))) (let ((_let_96 (AND_INTRO (SYMM (ASSUME :args (_let_19))) (EQ_RESOLVE (ASSUME :args (_let_41)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_95 _let_94 _let_93 _let_92 _let_91 _let_90) :args (_let_41 SB_DEFAULT SBA_FIXPOINT))) _let_95 _let_94 _let_93 _let_92 _let_91 _let_90))) (let ((_let_97 (EQ_RESOLVE (ASSUME :args (_let_68)) (TRANS (MACRO_SR_EQ_INTRO _let_96 :args (_let_68 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (not (@ (@ tptp.ord_less_int _let_18) _let_89)) _let_88))))))) (let ((_let_98 (EQ_RESOLVE (ASSUME :args (_let_67)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_67 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_96 :args ((= tptp.zero_zero_int tptp.pls) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (= _let_18 _let_89) _let_80))))))) (let ((_let_99 (@ tptp.bit1 _let_18))) (let ((_let_100 (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int _let_99)) _let_4))) (let ((_let_101 (EQ_RESOLVE (ASSUME :args (_let_8)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_96 :args ((= tptp.zero_zero_int _let_7) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (= _let_89 (@ (@ tptp.power_power_int _let_100) (@ tptp.number_number_of_nat (@ tptp.bit0 _let_99)))) _let_85))))))) (let ((_let_102 (ho_12 _let_86 _let_83))) (let ((_let_103 (not _let_102))) (let ((_let_104 (or _let_103 _let_87))) (let ((_let_105 (forall ((N_17 tptp.nat) (A_123 tptp.int)) (let ((_let_1 (ho_11 k_10 (ho_5 k_7 (ho_5 k_4 tptp.min))))) (or (not (ho_12 _let_1 A_123)) (ho_12 _let_1 (ho_3 (ho_17 k_16 A_123) N_17))))))) (let ((_let_106 (EQ_RESOLVE (ASSUME :args (_let_43)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_43 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_96 :args ((forall ((N_17 tptp.nat) (A_123 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (or (not (@ _let_1 A_123)) (@ _let_1 (@ (@ tptp.power_power_int A_123) N_17))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((N_17 tptp.nat) (A_123 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.succ tptp.min))))) (or (not (@ _let_1 A_123)) (@ _let_1 (@ (@ tptp.power_power_int A_123) N_17))))) _let_105))))))) (let ((_let_107 (forall ((u |u_(-> tptp.real tptp.nat tptp.real)|) (e |u_(-> tptp.nat tptp.real)|) (i tptp.real)) (not (forall ((v |u_(-> tptp.real tptp.nat tptp.real)|)) (not (forall ((ii tptp.real)) (= (ho_21 v ii) (ite (= i ii) e (ho_21 u ii)))))))))) (let ((_let_108 (forall ((x |u_(-> tptp.real tptp.nat tptp.real)|) (y |u_(-> tptp.real tptp.nat tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_21 x z) (ho_21 y z)))) (= x y))))) (let ((_let_109 (forall ((u |u_(-> tptp.nat tptp.real)|) (e tptp.real) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.real)|)) (not (forall ((ii tptp.nat)) (= (ho_22 v ii) (ite (= i ii) e (ho_22 u ii)))))))))) (let ((_let_110 (forall ((x |u_(-> tptp.nat tptp.real)|) (y |u_(-> tptp.nat tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_22 x z) (ho_22 y z)))) (= x y))))) (let ((_let_111 (forall ((u |u_(-> tptp.real Bool)|) (e Bool) (i tptp.real)) (not (forall ((v |u_(-> tptp.real Bool)|)) (not (forall ((ii tptp.real)) (= (ho_35 v ii) (ite (= i ii) e (ho_35 u ii)))))))))) (let ((_let_112 (forall ((x |u_(-> tptp.real Bool)|) (y |u_(-> tptp.real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_35 x z) (ho_35 y z)))) (= x y))))) (let ((_let_113 (forall ((u |u_(-> tptp.int tptp.real)|) (e tptp.real) (i tptp.int)) (not (forall ((v |u_(-> tptp.int tptp.real)|)) (not (forall ((ii tptp.int)) (= (ho_19 v ii) (ite (= i ii) e (ho_19 u ii)))))))))) (let ((_let_114 (forall ((x |u_(-> tptp.int tptp.real)|) (y |u_(-> tptp.int tptp.real)|)) (or (not (forall ((z tptp.int)) (= (ho_19 x z) (ho_19 y z)))) (= x y))))) (let ((_let_115 (forall ((u |u_(-> tptp.real tptp.real tptp.real)|) (e |u_(-> tptp.real tptp.real)|) (i tptp.real)) (not (forall ((v |u_(-> tptp.real tptp.real tptp.real)|)) (not (forall ((ii tptp.real)) (= (ho_24 v ii) (ite (= i ii) e (ho_24 u ii)))))))))) (let ((_let_116 (forall ((x |u_(-> tptp.real tptp.real tptp.real)|) (y |u_(-> tptp.real tptp.real tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_24 x z) (ho_24 y z)))) (= x y))))) (let ((_let_117 (forall ((u |u_(-> tptp.int tptp.nat)|) (e tptp.nat) (i tptp.int)) (not (forall ((v |u_(-> tptp.int tptp.nat)|)) (not (forall ((ii tptp.int)) (= (ho_15 v ii) (ite (= i ii) e (ho_15 u ii)))))))))) (let ((_let_118 (forall ((x |u_(-> tptp.int tptp.nat)|) (y |u_(-> tptp.int tptp.nat)|)) (or (not (forall ((z tptp.int)) (= (ho_15 x z) (ho_15 y z)))) (= x y))))) (let ((_let_119 (forall ((u |u_(-> tptp.int tptp.int Bool)|) (e |u_(-> tptp.int Bool)|) (i tptp.int)) (not (forall ((v |u_(-> tptp.int tptp.int Bool)|)) (not (forall ((ii tptp.int)) (= (ho_11 v ii) (ite (= i ii) e (ho_11 u ii)))))))))) (let ((_let_120 (forall ((x |u_(-> tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_11 x z) (ho_11 y z)))) (= x y))))) (let ((_let_121 (forall ((u |u_(-> tptp.nat tptp.nat)|) (e tptp.nat) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_28 v ii) (ite (= i ii) e (ho_28 u ii)))))))))) (let ((_let_122 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_28 x z) (ho_28 y z)))) (= x y))))) (let ((_let_123 (forall ((u |u_(-> tptp.int tptp.nat tptp.int)|) (e |u_(-> tptp.nat tptp.int)|) (i tptp.int)) (not (forall ((v |u_(-> tptp.int tptp.nat tptp.int)|)) (not (forall ((ii tptp.int)) (= (ho_17 v ii) (ite (= i ii) e (ho_17 u ii)))))))))) (let ((_let_124 (forall ((x |u_(-> tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_17 x z) (ho_17 y z)))) (= x y))))) (let ((_let_125 (forall ((u |u_(-> tptp.int tptp.int tptp.int)|) (e |u_(-> tptp.int tptp.int)|) (i tptp.int)) (not (forall ((v |u_(-> tptp.int tptp.int tptp.int)|)) (not (forall ((ii tptp.int)) (= (ho_9 v ii) (ite (= i ii) e (ho_9 u ii)))))))))) (let ((_let_126 (forall ((x |u_(-> tptp.int tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_9 x z) (ho_9 y z)))) (= x y))))) (let ((_let_127 (forall ((u |u_(-> tptp.int tptp.int)|) (e tptp.int) (i tptp.int)) (not (forall ((v |u_(-> tptp.int tptp.int)|)) (not (forall ((ii tptp.int)) (= (ho_5 v ii) (ite (= i ii) e (ho_5 u ii)))))))))) (let ((_let_128 (forall ((x |u_(-> tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_5 x z) (ho_5 y z)))) (= x y))))) (let ((_let_129 (forall ((u |u_(-> tptp.real tptp.real)|) (e tptp.real) (i tptp.real)) (not (forall ((v |u_(-> tptp.real tptp.real)|)) (not (forall ((ii tptp.real)) (= (ho_25 v ii) (ite (= i ii) e (ho_25 u ii)))))))))) (let ((_let_130 (forall ((x |u_(-> tptp.real tptp.real)|) (y |u_(-> tptp.real tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_25 x z) (ho_25 y z)))) (= x y))))) (let ((_let_131 (forall ((u |u_(-> tptp.int Bool)|) (e Bool) (i tptp.int)) (not (forall ((v |u_(-> tptp.int Bool)|)) (not (forall ((ii tptp.int)) (= (ho_12 v ii) (ite (= i ii) e (ho_12 u ii)))))))))) (let ((_let_132 (forall ((x |u_(-> tptp.int Bool)|) (y |u_(-> tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_12 x z) (ho_12 y z)))) (= x y))))) (let ((_let_133 (forall ((u |u_(-> tptp.nat tptp.int)|) (e tptp.int) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.int)|)) (not (forall ((ii tptp.nat)) (= (ho_3 v ii) (ite (= i ii) e (ho_3 u ii)))))))))) (let ((_let_134 (forall ((x |u_(-> tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_3 x z) (ho_3 y z)))) (= x y))))) (let ((_let_135 (forall ((u |u_(-> tptp.nat tptp.nat tptp.nat)|) (e |u_(-> tptp.nat tptp.nat)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat tptp.nat)|)) (not (forall ((ii tptp.nat)) (= (ho_27 v ii) (ite (= i ii) e (ho_27 u ii)))))))))) (let ((_let_136 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_27 x z) (ho_27 y z)))) (= x y))))) (let ((_let_137 (forall ((u |u_(-> tptp.nat Bool)|) (e Bool) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_32 v ii) (ite (= i ii) e (ho_32 u ii)))))))))) (let ((_let_138 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_32 x z) (ho_32 y z)))) (= x y))))) (let ((_let_139 (forall ((u |u_(-> tptp.nat tptp.nat Bool)|) (e |u_(-> tptp.nat Bool)|) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_31 v ii) (ite (= i ii) e (ho_31 u ii)))))))))) (let ((_let_140 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_31 x z) (ho_31 y z)))) (= x y))))) (let ((_let_141 (forall ((u |u_(-> tptp.real tptp.real Bool)|) (e |u_(-> tptp.real Bool)|) (i tptp.real)) (not (forall ((v |u_(-> tptp.real tptp.real Bool)|)) (not (forall ((ii tptp.real)) (= (ho_34 v ii) (ite (= i ii) e (ho_34 u ii)))))))))) (let ((_let_142 (forall ((x |u_(-> tptp.real tptp.real Bool)|) (y |u_(-> tptp.real tptp.real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_34 x z) (ho_34 y z)))) (= x y))))) (let ((_let_143 (forall ((u |u_(-> Bool tptp.int tptp.int tptp.int)|) (e |u_(-> tptp.int tptp.int tptp.int)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.int tptp.int tptp.int)|)) (not (forall ((ii Bool)) (= (ho_51 v ii) (ite (= i ii) e (ho_51 u ii)))))))))) (let ((_let_144 (forall ((x |u_(-> Bool tptp.int tptp.int tptp.int)|) (y |u_(-> Bool tptp.int tptp.int tptp.int)|)) (or (not (forall ((z Bool)) (= (ho_51 x z) (ho_51 y z)))) (= x y))))) (let ((_let_145 (forall ((u |u_(-> Bool tptp.nat tptp.nat tptp.nat)|) (e |u_(-> tptp.nat tptp.nat tptp.nat)|) (i Bool)) (not (forall ((v |u_(-> Bool tptp.nat tptp.nat tptp.nat)|)) (not (forall ((ii Bool)) (= (ho_41 v ii) (ite (= i ii) e (ho_41 u ii)))))))))) (let ((_let_146 (forall ((x |u_(-> Bool tptp.nat tptp.nat tptp.nat)|) (y |u_(-> Bool tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z Bool)) (= (ho_41 x z) (ho_41 y z)))) (= x y))))) (let ((_let_147 (forall ((u |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.nat Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.nat Bool)|)) (= (ho_53 v ii) (ite (= i ii) e (ho_53 u ii)))))))))) (let ((_let_148 (forall ((x |u_(-> _u_(-> tptp.nat Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.nat Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.nat Bool)|)) (= (ho_53 x z) (ho_53 y z)))) (= x y))))) (let ((_let_149 (forall ((u |u_(-> tptp.int tptp.int tptp.int Bool)|) (e |u_(-> tptp.int tptp.int Bool)|) (i tptp.int)) (not (forall ((v |u_(-> tptp.int tptp.int tptp.int Bool)|)) (not (forall ((ii tptp.int)) (= (ho_61 v ii) (ite (= i ii) e (ho_61 u ii)))))))))) (let ((_let_150 (forall ((x |u_(-> tptp.int tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_61 x z) (ho_61 y z)))) (= x y))))) (let ((_let_151 (ASSUME :args (_let_87)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (EQ_RESOLVE (NOT_AND (MACRO_SR_PRED_TRANSFORM (SCOPE (AND_INTRO _let_151 _let_98 _let_101 _let_97) :args (_let_88 _let_80 _let_85 _let_87)) (SCOPE (MACRO_SR_PRED_ELIM (TRANS (SYMM (FALSE_INTRO _let_97)) (CONG (CONG (REFL :args (k_10)) (SYMM (SYMM _let_98)) :args (APPLY_UF ho_11)) (SYMM (SYMM _let_101)) :args (APPLY_UF ho_12)) (TRUE_INTRO _let_151))) :args (_let_87 _let_80 _let_85 _let_88)) :args ((not (and _let_88 _let_80 _let_85 _let_87)) SB_LITERAL))) (CONG (MACRO_SR_PRED_INTRO :args ((= (not _let_88) _let_79))) (REFL :args ((not _let_80))) (REFL :args ((not _let_85))) (REFL :args ((not _let_87))) :args (or))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_104)) :args ((or _let_103 _let_87 (not _let_104)))) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_76)) (TRANS (MACRO_SR_EQ_INTRO _let_96 :args (_let_76 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (@ (@ tptp.ord_less_int _let_89) _let_100) _let_102))))) (PREPROCESS :args ((and _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107)))) :args ((and _let_102 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107))) :args (0)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_106 :args (_let_82 _let_83 QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_105))) _let_106 :args (_let_104 false _let_105)) :args (_let_87 false _let_102 false _let_104)) _let_101 _let_98 _let_97 :args (false false _let_87 false _let_85 false _let_80 true _let_79)) :args (_let_76 (@ _let_46 tptp.t) (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))) (= (@ (@ tptp.power_power_int tptp.one_one_int) _let_3) tptp.one_one_int) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) _let_3) tptp.one_one_nat) (= (@ (@ tptp.power_power_real tptp.one_one_real) _let_3) tptp.one_one_real) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) _let_3) tptp.zero_zero_int) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) _let_3) tptp.zero_zero_nat) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) _let_3) tptp.zero_zero_real) (forall ((A_136 tptp.int)) (= (= (@ (@ tptp.power_power_int A_136) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_int) (= A_136 tptp.zero_zero_int))) (forall ((A_136 tptp.real)) (= (= (@ (@ tptp.power_power_real A_136) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_real) (= A_136 tptp.zero_zero_real))) (forall ((W_16 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.number_number_of_int W_16)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int (@ tptp.bit1 tptp.pls)) W_16)))) (forall ((W_16 tptp.int)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.number267125858f_real W_16)) (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int (@ tptp.bit1 tptp.pls)) W_16)))) (forall ((V_16 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_16)) tptp.one_one_int) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_16) (@ tptp.bit1 tptp.pls))))) (forall ((V_16 tptp.int)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_16)) tptp.one_one_real) (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_16) (@ tptp.bit1 tptp.pls))))) _let_75 _let_74 _let_75 _let_71 _let_74 (forall ((X tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.power_power_int X))) (let ((_let_3 (@ tptp.number_number_of_nat _let_1))) (= (@ (@ tptp.power_power_int (@ _let_2 _let_3)) _let_3) (@ _let_2 (@ tptp.number_number_of_nat (@ tptp.bit0 _let_1)))))))) (forall ((W_15 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_15))) (let ((_let_2 (@ (@ tptp.power_power_int tptp.zero_zero_int) _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 tptp.zero_zero_int))))))) (forall ((W_15 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_15))) (let ((_let_2 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 tptp.zero_zero_nat))))))) (forall ((W_15 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_15))) (let ((_let_2 (@ (@ tptp.power_power_real tptp.zero_zero_real) _let_1))) (let ((_let_3 (= _let_1 tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 tptp.zero_zero_real))))))) _let_70 _let_73 _let_59 _let_55 (@ _let_40 tptp.n) (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int K)) (@ tptp.number_number_of_int L)) (@ (@ tptp.ord_less_int K) L))) (forall ((V_1 tptp.int) (W tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_1)) (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_1) W)))) (forall ((X_30 tptp.int) (Y_23 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int X_30)) (@ tptp.number_number_of_int Y_23)) (@ (@ tptp.ord_less_int X_30) Y_23))) (forall ((X_30 tptp.int) (Y_23 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.number267125858f_real X_30)) (@ tptp.number267125858f_real Y_23)) (@ (@ tptp.ord_less_int X_30) Y_23))) _let_62 (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.semiri1621563631at_int M)) N) (@ tptp.semiri1621563631at_int (@ (@ tptp.power_power_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1621563631at_int (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_int (@ tptp.semiri1621563631at_int M)) N))) (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int N)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int (@ (@ tptp.plus_plus_nat M) N))) Z))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ tptp.semiri1621563631at_int (@ (@ tptp.plus_plus_nat M) N)))) _let_48 _let_66 _let_72 (forall ((N tptp.nat)) (= (= (@ tptp.semiri1621563631at_int N) tptp.zero_zero_int) (= N tptp.zero_zero_nat))) _let_42 _let_71 (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_int K1) K2))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_int K) L))) (not (@ _let_23 tptp.pls)) (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K1)) (@ tptp.bit0 K2)) (@ (@ tptp.ord_less_int K1) K2))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K)) (@ tptp.bit0 L)) (@ (@ tptp.ord_less_int K) L))) (forall ((K tptp.int) (I_1 tptp.int) (J tptp.int)) (=> (@ (@ tptp.ord_less_int I_1) J) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I_1) K)) (@ (@ tptp.plus_plus_int J) K)))) (forall ((V_2 tptp.int) (V_1 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V_2))) (let ((_let_2 (@ tptp.number_number_of_nat V_1))) (let ((_let_3 (@ (@ tptp.plus_plus_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_int V_2) tptp.pls))) (let ((_let_5 (@ (@ tptp.ord_less_int V_1) tptp.pls))) (and (=> _let_5 (= _let_3 _let_1)) (=> (not _let_5) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ tptp.number_number_of_nat (@ (@ tptp.plus_plus_int V_1) V_2))))))))))))) _let_70 _let_57 _let_69 (forall ((X_29 tptp.int) (Y_22 tptp.int)) (= (= (@ tptp.number_number_of_int X_29) (@ tptp.number_number_of_int Y_22)) (= X_29 Y_22))) (forall ((X_29 tptp.int) (Y_22 tptp.int)) (= (= (@ tptp.number267125858f_real X_29) (@ tptp.number267125858f_real Y_22)) (= X_29 Y_22))) (forall ((W_14 tptp.int) (X_28 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat W_14))) (= (= _let_1 X_28) (= X_28 _let_1)))) (forall ((W_14 tptp.int) (X_28 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W_14))) (= (= _let_1 X_28) (= X_28 _let_1)))) (forall ((W_14 tptp.int) (X_28 tptp.real)) (let ((_let_1 (@ tptp.number267125858f_real W_14))) (= (= _let_1 X_28) (= X_28 _let_1)))) (forall ((K tptp.int) (L tptp.int)) (= (= (@ tptp.bit1 K) (@ tptp.bit1 L)) (= K L))) (forall ((K tptp.int) (L tptp.int)) (= (= (@ tptp.bit0 K) (@ tptp.bit0 L)) (= K L))) (forall ((A_135 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_135) A_135)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A_135) tptp.zero_zero_int))) (forall ((A_135 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A_135) A_135)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A_135) tptp.zero_zero_real))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int Z1))) (= (@ (@ tptp.plus_plus_int (@ _let_1 Z2)) Z3) (@ _let_1 (@ (@ tptp.plus_plus_int Z2) Z3))))) (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.plus_plus_int Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.plus_plus_int Z) W) (@ (@ tptp.plus_plus_int W) Z))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1621563631at_int M) (@ tptp.semiri1621563631at_int N)) (= M N))) (forall ((X_27 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int X_27)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int X_27) tptp.pls))) (forall ((X_27 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.number267125858f_real X_27)) tptp.zero_zero_real) (@ (@ tptp.ord_less_int X_27) tptp.pls))) (forall ((Y_21 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.number_number_of_int Y_21)) (@ (@ tptp.ord_less_int tptp.pls) Y_21))) (forall ((Y_21 tptp.int)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.number267125858f_real Y_21)) (@ (@ tptp.ord_less_int tptp.pls) Y_21))) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K)) tptp.pls) (@ (@ tptp.ord_less_int K) tptp.pls))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K1)) (@ tptp.bit0 K2)) (@ (@ tptp.ord_less_int K1) K2))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K)) (@ tptp.bit0 L)) (@ (@ tptp.ord_less_int K) L))) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K)) tptp.pls) (@ (@ tptp.ord_less_int K) tptp.pls))) (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.pls))) (= (@ _let_1 (@ tptp.bit0 K)) (@ _let_1 K)))) (forall ((W tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 W)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int W) tptp.zero_zero_int))) _let_68 (forall ((W tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 W)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int W) tptp.zero_zero_int))) _let_45 (forall ((W tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (or (@ _let_1 Z) (= W Z))))) (forall ((K tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int K)) tptp.zero_zero_int))) (forall ((X_26 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int X_26)) tptp.one_one_int) (@ (@ tptp.ord_less_int X_26) (@ tptp.bit1 tptp.pls)))) (forall ((X_26 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.number267125858f_real X_26)) tptp.one_one_real) (@ (@ tptp.ord_less_int X_26) (@ tptp.bit1 tptp.pls)))) (forall ((Y_20 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.number_number_of_int Y_20)) (@ (@ tptp.ord_less_int (@ tptp.bit1 tptp.pls)) Y_20))) (forall ((Y_20 tptp.int)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.number267125858f_real Y_20)) (@ (@ tptp.ord_less_int (@ tptp.bit1 tptp.pls)) Y_20))) (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))) (forall ((A_134 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A_134) A_134) tptp.zero_zero_int) (= A_134 tptp.zero_zero_int))) (forall ((A_134 tptp.real)) (= (= (@ (@ tptp.plus_plus_real A_134) A_134) tptp.zero_zero_real) (= A_134 tptp.zero_zero_real))) (forall ((K tptp.int)) (not (= (@ tptp.bit1 K) tptp.pls))) (forall ((L tptp.int)) (not (= tptp.pls (@ tptp.bit1 L)))) (forall ((K tptp.int) (L tptp.int)) (not (= (@ tptp.bit1 K) (@ tptp.bit0 L)))) (forall ((K tptp.int) (L tptp.int)) (not (= (@ tptp.bit0 K) (@ tptp.bit1 L)))) (forall ((K tptp.int)) (= (= (@ tptp.bit0 K) tptp.pls) (= K tptp.pls))) (forall ((L tptp.int)) (= (= tptp.pls (@ tptp.bit0 L)) (= tptp.pls L))) (= (@ tptp.bit0 tptp.pls) tptp.pls) _let_67 _let_50 (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.pls) K)) (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.pls) K) K)) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.bit0 K)) (@ tptp.bit0 L)) (@ tptp.bit0 (@ (@ tptp.plus_plus_int K) L)))) (forall ((K tptp.int)) (= (@ tptp.bit0 K) (@ (@ tptp.plus_plus_int K) K))) (forall ((Z tptp.int)) (= (@ (@ tptp.plus_plus_int Z) tptp.zero_zero_int) Z)) (forall ((Z tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) Z) Z)) _let_64 _let_66 _let_63 _let_64 _let_63 _let_62 _let_61 (forall ((A_133 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int tptp.pls)) A_133) A_133)) (forall ((A_133 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real tptp.pls)) A_133) A_133)) (forall ((A_132 tptp.int)) (= (@ (@ tptp.plus_plus_int A_132) (@ tptp.number_number_of_int tptp.pls)) A_132)) (forall ((A_132 tptp.real)) (= (@ (@ tptp.plus_plus_real A_132) (@ tptp.number267125858f_real tptp.pls)) A_132)) (forall ((A_131 tptp.int) (W_13 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_13))) (= (= (@ (@ tptp.power_power_int A_131) _let_1) tptp.zero_zero_int) (and (= A_131 tptp.zero_zero_int) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A_131 tptp.nat) (W_13 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_13))) (= (= (@ (@ tptp.power_power_nat A_131) _let_1) tptp.zero_zero_nat) (and (= A_131 tptp.zero_zero_nat) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A_131 tptp.real) (W_13 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_13))) (= (= (@ (@ tptp.power_power_real A_131) _let_1) tptp.zero_zero_real) (and (= A_131 tptp.zero_zero_real) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((V_15 tptp.int) (W_12 tptp.int) (Z_5 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_15)) (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int W_12)) Z_5)) (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_15) W_12))) Z_5))) (forall ((V_15 tptp.int) (W_12 tptp.int) (Z_5 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_15)) (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real W_12)) Z_5)) (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_15) W_12))) Z_5))) (forall ((V_14 tptp.int) (W_11 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_14)) (@ tptp.number_number_of_int W_11)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_14) W_11)))) (forall ((V_14 tptp.int) (W_11 tptp.int)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_14)) (@ tptp.number267125858f_real W_11)) (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_14) W_11)))) (forall ((V_13 tptp.int) (W_10 tptp.int)) (= (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_13) W_10)) (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_13)) (@ tptp.number_number_of_int W_10)))) (forall ((V_13 tptp.int) (W_10 tptp.int)) (= (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_13) W_10)) (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_13)) (@ tptp.number267125858f_real W_10)))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.bit1 K)) (@ tptp.bit0 L)) (@ tptp.bit1 (@ (@ tptp.plus_plus_int K) L)))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.bit0 K)) (@ tptp.bit1 L)) (@ tptp.bit1 (@ (@ tptp.plus_plus_int K) L)))) (forall ((K tptp.int)) (= (@ tptp.bit1 K) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) K)) K))) (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))) (forall ((N_32 tptp.nat)) (= (@ tptp.number_number_of_nat (@ tptp.semiri1621563631at_int N_32)) (@ tptp.semiri984289939at_nat N_32))) (forall ((N_32 tptp.nat)) (let ((_let_1 (@ tptp.semiri1621563631at_int N_32))) (= (@ tptp.number_number_of_int _let_1) _let_1))) (forall ((N_32 tptp.nat)) (= (@ tptp.number267125858f_real (@ tptp.semiri1621563631at_int N_32)) (@ tptp.semiri132038758t_real N_32))) (forall ((A_130 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A_130) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (not (= A_130 tptp.zero_zero_int)))) (forall ((A_130 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A_130) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (not (= A_130 tptp.zero_zero_real)))) (forall ((A_129 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A_129) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.zero_zero_int))) (forall ((A_129 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A_129) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.zero_zero_real))) (forall ((X_25 tptp.int) (Y_19 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_25) _let_1)) (@ (@ tptp.power_power_int Y_19) _let_1))) (or (not (= X_25 tptp.zero_zero_int)) (not (= Y_19 tptp.zero_zero_int)))))) (forall ((X_25 tptp.real) (Y_19 tptp.real)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X_25) _let_1)) (@ (@ tptp.power_power_real Y_19) _let_1))) (or (not (= X_25 tptp.zero_zero_real)) (not (= Y_19 tptp.zero_zero_real)))))) (forall ((X_24 tptp.int) (Y_18 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_24) _let_1)) (@ (@ tptp.power_power_int Y_18) _let_1))) tptp.zero_zero_int)))) (forall ((X_24 tptp.real) (Y_18 tptp.real)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X_24) _let_1)) (@ (@ tptp.power_power_real Y_18) _let_1))) tptp.zero_zero_real)))) (forall ((W_9 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W_9))) (= (@ tptp.number_number_of_int (@ tptp.bit0 W_9)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.zero_zero_int) _let_1)) _let_1)))) (forall ((W_9 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real W_9))) (= (@ tptp.number267125858f_real (@ tptp.bit0 W_9)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.zero_zero_real) _let_1)) _let_1)))) (forall ((W_8 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W_8))) (= (@ tptp.number_number_of_int (@ tptp.bit1 W_8)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1)) _let_1)))) (forall ((W_8 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real W_8))) (= (@ tptp.number267125858f_real (@ tptp.bit1 W_8)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1)) _let_1)))) _let_59 _let_57 _let_55 (@ (@ tptp.ord_less_int tptp.m1) _let_6) (forall ((N_31 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int N_31)) (@ (@ tptp.power_power_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_31))) (forall ((N_31 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri132038758t_real N_31)) (@ (@ tptp.power_power_real (@ tptp.number267125858f_real (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_31))) (= _let_27 (@ tptp.semiri1621563631at_int _let_3)) (= _let_36 (@ tptp.semiri1621563631at_int _let_37)) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))) (forall ((N_30 tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1621563631at_int N_30)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_30))) (forall ((N_30 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri984289939at_nat N_30)) (@ _let_1 N_30)))) (forall ((N_30 tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri132038758t_real N_30)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_30))) (forall ((N_29 tptp.nat) (A_128 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A_128) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_29) (@ _let_1 (@ (@ tptp.power_power_int A_128) N_29)))))) (forall ((N_29 tptp.nat) (A_128 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A_128) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_29) (@ _let_1 (@ (@ tptp.power_power_nat A_128) N_29)))))) (forall ((N_29 tptp.nat) (A_128 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A_128) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_29) (@ _let_1 (@ (@ tptp.power_power_real A_128) N_29)))))) (forall ((N_28 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N_28))) (let ((_let_2 (= N_28 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((N_28 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N_28))) (let ((_let_2 (= N_28 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N_28 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real tptp.zero_zero_real) N_28))) (let ((_let_2 (= N_28 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (forall ((A_127 tptp.int) (N_27 tptp.nat) (N_26 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_127))) (=> (@ (@ tptp.ord_less_nat N_27) N_26) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_127) (=> (@ (@ tptp.ord_less_int A_127) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N_26)) (@ _let_1 N_27))))))) (forall ((A_127 tptp.nat) (N_27 tptp.nat) (N_26 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_127))) (=> (@ (@ tptp.ord_less_nat N_27) N_26) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_127) (=> (@ (@ tptp.ord_less_nat A_127) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N_26)) (@ _let_1 N_27))))))) (forall ((A_127 tptp.real) (N_27 tptp.nat) (N_26 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_127))) (=> (@ (@ tptp.ord_less_nat N_27) N_26) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A_127) (=> (@ (@ tptp.ord_less_real A_127) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N_26)) (@ _let_1 N_27))))))) (@ _let_33 _let_53) (@ _let_40 _let_52) (@ _let_44 _let_51) (forall ((P (-> tptp.int Bool)) (K tptp.int) (I_1 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I_1) (=> (@ P (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_int K) I) (=> (@ P I) (@ P (@ (@ tptp.plus_plus_int I) tptp.one_one_int))))) (@ P I_1))))) (= tptp.zero_zero_int _let_34) (@ _let_40 tptp.tn) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) _let_49 (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((I_1 tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) J)) I_1))) (forall ((J tptp.nat) (I_1 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I_1)) I_1))) (forall ((K tptp.int)) (= (@ tptp.number_number_of_int K) K)) (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) N) (@ (@ tptp.plus_plus_nat N) M))) (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (let ((_let_2 (@ tptp.plus_plus_nat Y))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 N)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) K))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) K) (@ (@ tptp.plus_plus_nat N) K)) (= M N))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))) (forall ((S_1 tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S_1) T) (not (= S_1 T)))) (forall ((M tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I_1))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))) (forall ((M tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I_1))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J) K)))) (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J) L))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat) (L tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L) (=> (= (@ (@ tptp.plus_plus_nat M) L) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((I_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) J)) K) (@ (@ tptp.ord_less_nat I_1) K))) (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ P N) M))) (=> (=> (@ (@ tptp.ord_less_nat M) N) _let_1) (=> (=> (= M N) _let_1) (=> (=> (@ (@ tptp.ord_less_nat N) M) _let_1) _let_1))))) (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N tptp.nat) (I_1 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I_1) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N)) (or (@ _let_1 X) (= N tptp.zero_zero_nat))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (@ _let_1 M) (@ _let_1 N))))) (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N)) (or (= N tptp.zero_zero_nat) (@ _let_1 X))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ (@ tptp.ord_less_nat X) Y))) (forall ((X tptp.nat) (W tptp.int)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.number_number_of_nat W))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (@ _let_1 X)))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ (@ tptp.ord_less_nat M) N))) (forall ((V_1 tptp.int) (V_2 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_int V_1) V_2))) (= (@ (@ tptp.ord_less_nat (@ tptp.number_number_of_nat V_1)) (@ tptp.number_number_of_nat V_2)) (and (=> _let_1 (@ (@ tptp.ord_less_int tptp.pls) V_2)) _let_1)))) (forall ((X_23 tptp.int) (Y_17 tptp.int)) (=> (not (= X_23 Y_17)) (=> (not (@ (@ tptp.ord_less_int X_23) Y_17)) (@ (@ tptp.ord_less_int Y_17) X_23)))) (forall ((X_23 tptp.real) (Y_17 tptp.real)) (=> (not (= X_23 Y_17)) (=> (not (@ (@ tptp.ord_less_real X_23) Y_17)) (@ (@ tptp.ord_less_real Y_17) X_23)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)) (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)) (forall ((A_126 tptp.int)) (= (@ (@ tptp.power_power_int A_126) tptp.one_one_nat) A_126)) (forall ((A_126 tptp.nat)) (= (@ (@ tptp.power_power_nat A_126) tptp.one_one_nat) A_126)) (forall ((A_126 tptp.real)) (= (@ (@ tptp.power_power_real A_126) tptp.one_one_nat) A_126)) (forall ((M_14 tptp.nat) (N_25 tptp.nat)) (= (= (@ tptp.semiri132038758t_real M_14) (@ tptp.semiri132038758t_real N_25)) (= M_14 N_25))) (forall ((M_14 tptp.nat) (N_25 tptp.nat)) (= (= (@ tptp.semiri984289939at_nat M_14) (@ tptp.semiri984289939at_nat N_25)) (= M_14 N_25))) (forall ((M_14 tptp.nat) (N_25 tptp.nat)) (= (= (@ tptp.semiri1621563631at_int M_14) (@ tptp.semiri1621563631at_int N_25)) (= M_14 N_25))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.semiri1621563631at_int X) (@ tptp.semiri1621563631at_int Y)) (= X Y))) (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (let ((_let_1 (@ tptp.semiri1621563631at_int (@ (@ (@ tptp.if_nat P) X) Y)))) (and (=> P (= (@ tptp.semiri1621563631at_int X) _let_1)) (=> (not P) (= (@ tptp.semiri1621563631at_int Y) _let_1))))) (forall ((V_1 tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.number_number_of_nat V_1)) (@ (@ tptp.ord_less_int tptp.pls) V_1))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1621563631at_int N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (not (= tptp.one_one_int tptp.zero_zero_int)) (not (= tptp.one_one_nat tptp.zero_zero_nat)) (not (= tptp.one_one_real tptp.zero_zero_real)) _let_50 (not (= tptp.zero_zero_nat tptp.one_one_nat)) _let_49 (forall ((N_24 tptp.nat) (A_125 tptp.int)) (=> (not (= A_125 tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A_125) N_24) tptp.zero_zero_int)))) (forall ((N_24 tptp.nat) (A_125 tptp.real)) (=> (not (= A_125 tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A_125) N_24) tptp.zero_zero_real)))) (forall ((N_23 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N_23) tptp.one_one_int)) (forall ((N_23 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N_23) tptp.one_one_nat)) (forall ((N_23 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N_23) tptp.one_one_real)) (forall ((M_13 tptp.nat) (N_22 tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int M_13)) (@ tptp.semiri1621563631at_int N_22)) (@ (@ tptp.ord_less_nat M_13) N_22))) (forall ((M_13 tptp.nat) (N_22 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri984289939at_nat M_13)) (@ tptp.semiri984289939at_nat N_22)) (@ (@ tptp.ord_less_nat M_13) N_22))) (forall ((M_13 tptp.nat) (N_22 tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri132038758t_real M_13)) (@ tptp.semiri132038758t_real N_22)) (@ (@ tptp.ord_less_nat M_13) N_22))) (forall ((M_12 tptp.nat) (N_21 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M_12) N_21) (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int M_12)) (@ tptp.semiri1621563631at_int N_21)))) (forall ((M_12 tptp.nat) (N_21 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M_12) N_21) (@ (@ tptp.ord_less_nat (@ tptp.semiri984289939at_nat M_12)) (@ tptp.semiri984289939at_nat N_21)))) (forall ((M_12 tptp.nat) (N_21 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M_12) N_21) (@ (@ tptp.ord_less_real (@ tptp.semiri132038758t_real M_12)) (@ tptp.semiri132038758t_real N_21)))) (forall ((M_11 tptp.nat) (N_20 tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int M_11)) (@ tptp.semiri1621563631at_int N_20)) (@ (@ tptp.ord_less_nat M_11) N_20))) (forall ((M_11 tptp.nat) (N_20 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri984289939at_nat M_11)) (@ tptp.semiri984289939at_nat N_20)) (@ (@ tptp.ord_less_nat M_11) N_20))) (forall ((M_11 tptp.nat) (N_20 tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri132038758t_real M_11)) (@ tptp.semiri132038758t_real N_20)) (@ (@ tptp.ord_less_nat M_11) N_20))) (forall ((M_10 tptp.nat) (N_19 tptp.nat)) (= (@ tptp.semiri1621563631at_int (@ (@ tptp.plus_plus_nat M_10) N_19)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int M_10)) (@ tptp.semiri1621563631at_int N_19)))) (forall ((M_10 tptp.nat) (N_19 tptp.nat)) (= (@ tptp.semiri984289939at_nat (@ (@ tptp.plus_plus_nat M_10) N_19)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri984289939at_nat M_10)) (@ tptp.semiri984289939at_nat N_19)))) (forall ((M_10 tptp.nat) (N_19 tptp.nat)) (= (@ tptp.semiri132038758t_real (@ (@ tptp.plus_plus_nat M_10) N_19)) (@ (@ tptp.plus_plus_real (@ tptp.semiri132038758t_real M_10)) (@ tptp.semiri132038758t_real N_19)))) _let_48 (= (@ tptp.semiri984289939at_nat tptp.one_one_nat) tptp.one_one_nat) (= (@ tptp.semiri132038758t_real tptp.one_one_nat) tptp.one_one_real) (forall ((M_9 tptp.nat) (N_18 tptp.nat)) (= (@ tptp.semiri1621563631at_int (@ (@ tptp.power_power_nat M_9) N_18)) (@ (@ tptp.power_power_int (@ tptp.semiri1621563631at_int M_9)) N_18))) (forall ((M_9 tptp.nat) (N_18 tptp.nat)) (= (@ tptp.semiri984289939at_nat (@ (@ tptp.power_power_nat M_9) N_18)) (@ (@ tptp.power_power_nat (@ tptp.semiri984289939at_nat M_9)) N_18))) (forall ((M_9 tptp.nat) (N_18 tptp.nat)) (= (@ tptp.semiri132038758t_real (@ (@ tptp.power_power_nat M_9) N_18)) (@ (@ tptp.power_power_real (@ tptp.semiri132038758t_real M_9)) N_18))) (= tptp.one_one_int _let_47) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ tptp.semiri1621563631at_int (@ (@ tptp.plus_plus_nat X) Y)))) (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.semiri1621563631at_int X)) N) (@ tptp.semiri1621563631at_int (@ (@ tptp.power_power_nat X) N)))) (forall ((B_89 tptp.int) (C_63 tptp.int) (A_124 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B_89))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_124) (=> (@ _let_1 C_63) (@ _let_1 (@ (@ tptp.plus_plus_int A_124) C_63)))))) (forall ((B_89 tptp.nat) (C_63 tptp.nat) (A_124 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B_89))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_124) (=> (@ _let_1 C_63) (@ _let_1 (@ (@ tptp.plus_plus_nat A_124) C_63)))))) (forall ((B_89 tptp.real) (C_63 tptp.real) (A_124 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B_89))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A_124) (=> (@ _let_1 C_63) (@ _let_1 (@ (@ tptp.plus_plus_real A_124) C_63)))))) (not (@ _let_46 tptp.zero_zero_int)) (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)) _let_45 (@ _let_40 tptp.one_one_nat) (@ _let_44 tptp.one_one_real) _let_43 (forall ((N_17 tptp.nat) (A_123 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A_123) (@ _let_1 (@ (@ tptp.power_power_nat A_123) N_17))))) (forall ((N_17 tptp.nat) (A_123 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A_123) (@ _let_1 (@ (@ tptp.power_power_real A_123) N_17))))) (forall ((A_122 tptp.int)) (@ (@ tptp.ord_less_int A_122) (@ (@ tptp.plus_plus_int A_122) tptp.one_one_int))) (forall ((A_122 tptp.nat)) (@ (@ tptp.ord_less_nat A_122) (@ (@ tptp.plus_plus_nat A_122) tptp.one_one_nat))) (forall ((A_122 tptp.real)) (@ (@ tptp.ord_less_real A_122) (@ (@ tptp.plus_plus_real A_122) tptp.one_one_real))) (forall ((M_8 tptp.nat) (N_16 tptp.nat) (A_121 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A_121))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_121) (= (= (@ _let_1 M_8) (@ _let_1 N_16)) (= M_8 N_16))))) (forall ((M_8 tptp.nat) (N_16 tptp.nat) (A_121 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_121))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_121) (= (= (@ _let_1 M_8) (@ _let_1 N_16)) (= M_8 N_16))))) (forall ((M_8 tptp.nat) (N_16 tptp.nat) (A_121 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A_121))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_121) (= (= (@ _let_1 M_8) (@ _let_1 N_16)) (= M_8 N_16))))) (forall ((X_22 tptp.nat) (Y_16 tptp.nat) (B_88 tptp.int)) (let ((_let_1 (@ tptp.power_power_int B_88))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B_88) (= (@ (@ tptp.ord_less_int (@ _let_1 X_22)) (@ _let_1 Y_16)) (@ (@ tptp.ord_less_nat X_22) Y_16))))) (forall ((X_22 tptp.nat) (Y_16 tptp.nat) (B_88 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B_88))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B_88) (= (@ (@ tptp.ord_less_nat (@ _let_1 X_22)) (@ _let_1 Y_16)) (@ (@ tptp.ord_less_nat X_22) Y_16))))) (forall ((X_22 tptp.nat) (Y_16 tptp.nat) (B_88 tptp.real)) (let ((_let_1 (@ tptp.power_power_real B_88))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B_88) (= (@ (@ tptp.ord_less_real (@ _let_1 X_22)) (@ _let_1 Y_16)) (@ (@ tptp.ord_less_nat X_22) Y_16))))) (forall ((M_7 tptp.nat) (N_15 tptp.nat) (A_120 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A_120))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_120) (=> (@ (@ tptp.ord_less_int (@ _let_1 M_7)) (@ _let_1 N_15)) (@ (@ tptp.ord_less_nat M_7) N_15))))) (forall ((M_7 tptp.nat) (N_15 tptp.nat) (A_120 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_120))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_120) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M_7)) (@ _let_1 N_15)) (@ (@ tptp.ord_less_nat M_7) N_15))))) (forall ((M_7 tptp.nat) (N_15 tptp.nat) (A_120 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A_120))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_120) (=> (@ (@ tptp.ord_less_real (@ _let_1 M_7)) (@ _let_1 N_15)) (@ (@ tptp.ord_less_nat M_7) N_15))))) (forall ((A_119 tptp.int) (N_14 tptp.nat) (N_13 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_119))) (=> (@ (@ tptp.ord_less_nat N_14) N_13) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_119) (@ (@ tptp.ord_less_int (@ _let_1 N_14)) (@ _let_1 N_13)))))) (forall ((A_119 tptp.nat) (N_14 tptp.nat) (N_13 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_119))) (=> (@ (@ tptp.ord_less_nat N_14) N_13) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_119) (@ (@ tptp.ord_less_nat (@ _let_1 N_14)) (@ _let_1 N_13)))))) (forall ((A_119 tptp.real) (N_14 tptp.nat) (N_13 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_119))) (=> (@ (@ tptp.ord_less_nat N_14) N_13) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_119) (@ (@ tptp.ord_less_real (@ _let_1 N_14)) (@ _let_1 N_13)))))) (forall ((A_118 tptp.int) (N_12 tptp.nat)) (= (= (@ (@ tptp.power_power_int A_118) N_12) tptp.zero_zero_int) (and (= A_118 tptp.zero_zero_int) (not (= N_12 tptp.zero_zero_nat))))) (forall ((A_118 tptp.nat) (N_12 tptp.nat)) (= (= (@ (@ tptp.power_power_nat A_118) N_12) tptp.zero_zero_nat) (and (= A_118 tptp.zero_zero_nat) (not (= N_12 tptp.zero_zero_nat))))) (forall ((A_118 tptp.real) (N_12 tptp.nat)) (= (= (@ (@ tptp.power_power_real A_118) N_12) tptp.zero_zero_real) (and (= A_118 tptp.zero_zero_real) (not (= N_12 tptp.zero_zero_nat))))) (forall ((M_6 tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int M_6)) tptp.zero_zero_int))) (forall ((M_6 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri984289939at_nat M_6)) tptp.zero_zero_nat))) (forall ((M_6 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri132038758t_real M_6)) tptp.zero_zero_real))) (forall ((A_117 tptp.int)) (= (@ (@ tptp.power_power_int A_117) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((A_117 tptp.nat)) (= (@ (@ tptp.power_power_nat A_117) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A_117 tptp.real)) (= (@ (@ tptp.power_power_real A_117) tptp.zero_zero_nat) tptp.one_one_real)) _let_42 (= (@ tptp.semiri984289939at_nat tptp.zero_zero_nat) tptp.zero_zero_nat) (= (@ tptp.semiri132038758t_real tptp.zero_zero_nat) tptp.zero_zero_real) (@ _let_40 _let_3) (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N_1 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_1) (= K (@ tptp.semiri1621563631at_int N_1)))))) (forall ((I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (exists ((K_1 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K_1) (= (@ (@ tptp.plus_plus_nat I_1) K_1) J))))) (forall ((X tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat X) N) tptp.one_one_nat) (or (= X tptp.one_one_nat) (= N tptp.zero_zero_nat)))) (forall ((X_21 tptp.int)) (= (@ (@ tptp.power_power_int X_21) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((X_21 tptp.nat)) (= (@ (@ tptp.power_power_nat X_21) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((X_21 tptp.real)) (= (@ (@ tptp.power_power_real X_21) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A_116 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A_116) A_116)) (@ _let_1 A_116)))) (forall ((A_116 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A_116) A_116)) (@ _let_1 A_116)))) (forall ((A_115 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_115) A_115)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A_115) tptp.zero_zero_int))) (forall ((A_115 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A_115) A_115)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A_115) tptp.zero_zero_real))) (forall ((B_87 tptp.int) (A_114 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A_114) (=> (@ _let_1 B_87) (@ _let_1 (@ (@ tptp.plus_plus_int A_114) B_87)))))) (forall ((B_87 tptp.nat) (A_114 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A_114) (=> (@ _let_1 B_87) (@ _let_1 (@ (@ tptp.plus_plus_nat A_114) B_87)))))) (forall ((B_87 tptp.real) (A_114 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A_114) (=> (@ _let_1 B_87) (@ _let_1 (@ (@ tptp.plus_plus_real A_114) B_87)))))) (forall ((B_86 tptp.int) (A_113 tptp.int)) (=> (@ (@ tptp.ord_less_int A_113) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B_86) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_113) B_86)) tptp.zero_zero_int)))) (forall ((B_86 tptp.nat) (A_113 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_113) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B_86) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_113) B_86)) tptp.zero_zero_nat)))) (forall ((B_86 tptp.real) (A_113 tptp.real)) (=> (@ (@ tptp.ord_less_real A_113) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B_86) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A_113) B_86)) tptp.zero_zero_real)))) (forall ((X_20 tptp.int)) (= (= tptp.zero_zero_int X_20) (= X_20 tptp.zero_zero_int))) (forall ((X_20 tptp.nat)) (= (= tptp.zero_zero_nat X_20) (= X_20 tptp.zero_zero_nat))) (forall ((X_20 tptp.real)) (= (= tptp.zero_zero_real X_20) (= X_20 tptp.zero_zero_real))) (forall ((B_85 tptp.int) (A_112 tptp.int) (C_62 tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B_85) A_112) (@ (@ tptp.plus_plus_int C_62) A_112)) (= B_85 C_62))) (forall ((B_85 tptp.nat) (A_112 tptp.nat) (C_62 tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B_85) A_112) (@ (@ tptp.plus_plus_nat C_62) A_112)) (= B_85 C_62))) (forall ((B_85 tptp.real) (A_112 tptp.real) (C_62 tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B_85) A_112) (@ (@ tptp.plus_plus_real C_62) A_112)) (= B_85 C_62))) (forall ((A_111 tptp.int) (B_84 tptp.int) (C_61 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_111))) (=> (= (@ _let_1 B_84) (@ _let_1 C_61)) (= B_84 C_61)))) (forall ((A_111 tptp.nat) (B_84 tptp.nat) (C_61 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_111))) (=> (= (@ _let_1 B_84) (@ _let_1 C_61)) (= B_84 C_61)))) (forall ((A_111 tptp.real) (B_84 tptp.real) (C_61 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_111))) (=> (= (@ _let_1 B_84) (@ _let_1 C_61)) (= B_84 C_61)))) (forall ((A_110 tptp.int) (B_83 tptp.int) (C_60 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_110))) (=> (= (@ _let_1 B_83) (@ _let_1 C_60)) (= B_83 C_60)))) (forall ((A_110 tptp.nat) (B_83 tptp.nat) (C_60 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_110))) (=> (= (@ _let_1 B_83) (@ _let_1 C_60)) (= B_83 C_60)))) (forall ((A_110 tptp.real) (B_83 tptp.real) (C_60 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_110))) (=> (= (@ _let_1 B_83) (@ _let_1 C_60)) (= B_83 C_60)))) (forall ((A_109 tptp.int) (B_82 tptp.int) (C_59 tptp.int) (D_23 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_109))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_82)) (@ (@ tptp.plus_plus_int C_59) D_23)) (@ (@ tptp.plus_plus_int (@ _let_1 C_59)) (@ (@ tptp.plus_plus_int B_82) D_23))))) (forall ((A_109 tptp.nat) (B_82 tptp.nat) (C_59 tptp.nat) (D_23 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_109))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_82)) (@ (@ tptp.plus_plus_nat C_59) D_23)) (@ (@ tptp.plus_plus_nat (@ _let_1 C_59)) (@ (@ tptp.plus_plus_nat B_82) D_23))))) (forall ((A_109 tptp.real) (B_82 tptp.real) (C_59 tptp.real) (D_23 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_109))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B_82)) (@ (@ tptp.plus_plus_real C_59) D_23)) (@ (@ tptp.plus_plus_real (@ _let_1 C_59)) (@ (@ tptp.plus_plus_real B_82) D_23))))) (forall ((B_81 tptp.int) (A_108 tptp.int) (C_58 tptp.int)) (= (= (@ (@ tptp.plus_plus_int B_81) A_108) (@ (@ tptp.plus_plus_int C_58) A_108)) (= B_81 C_58))) (forall ((B_81 tptp.nat) (A_108 tptp.nat) (C_58 tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B_81) A_108) (@ (@ tptp.plus_plus_nat C_58) A_108)) (= B_81 C_58))) (forall ((B_81 tptp.real) (A_108 tptp.real) (C_58 tptp.real)) (= (= (@ (@ tptp.plus_plus_real B_81) A_108) (@ (@ tptp.plus_plus_real C_58) A_108)) (= B_81 C_58))) (forall ((A_107 tptp.int) (B_80 tptp.int) (C_57 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_107))) (= (= (@ _let_1 B_80) (@ _let_1 C_57)) (= B_80 C_57)))) (forall ((A_107 tptp.nat) (B_80 tptp.nat) (C_57 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_107))) (= (= (@ _let_1 B_80) (@ _let_1 C_57)) (= B_80 C_57)))) (forall ((A_107 tptp.real) (B_80 tptp.real) (C_57 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_107))) (= (= (@ _let_1 B_80) (@ _let_1 C_57)) (= B_80 C_57)))) (forall ((A_106 tptp.int) (B_79 tptp.int) (C_56 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_106))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_79)) C_56) (@ (@ tptp.plus_plus_int (@ _let_1 C_56)) B_79)))) (forall ((A_106 tptp.nat) (B_79 tptp.nat) (C_56 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_106))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_79)) C_56) (@ (@ tptp.plus_plus_nat (@ _let_1 C_56)) B_79)))) (forall ((A_106 tptp.real) (B_79 tptp.real) (C_56 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_106))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B_79)) C_56) (@ (@ tptp.plus_plus_real (@ _let_1 C_56)) B_79)))) (forall ((A_105 tptp.int) (B_78 tptp.int) (C_55 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_105))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_78)) C_55) (@ _let_1 (@ (@ tptp.plus_plus_int B_78) C_55))))) (forall ((A_105 tptp.nat) (B_78 tptp.nat) (C_55 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_105))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_78)) C_55) (@ _let_1 (@ (@ tptp.plus_plus_nat B_78) C_55))))) (forall ((A_105 tptp.real) (B_78 tptp.real) (C_55 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_105))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B_78)) C_55) (@ _let_1 (@ (@ tptp.plus_plus_real B_78) C_55))))) (forall ((A_104 tptp.int) (B_77 tptp.int) (C_54 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_104))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_77)) C_54) (@ _let_1 (@ (@ tptp.plus_plus_int B_77) C_54))))) (forall ((A_104 tptp.nat) (B_77 tptp.nat) (C_54 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_104))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_77)) C_54) (@ _let_1 (@ (@ tptp.plus_plus_nat B_77) C_54))))) (forall ((A_104 tptp.real) (B_77 tptp.real) (C_54 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_104))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B_77)) C_54) (@ _let_1 (@ (@ tptp.plus_plus_real B_77) C_54))))) (forall ((A_103 tptp.int) (C_53 tptp.int) (D_22 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_103))) (= (@ _let_1 (@ (@ tptp.plus_plus_int C_53) D_22)) (@ (@ tptp.plus_plus_int (@ _let_1 C_53)) D_22)))) (forall ((A_103 tptp.nat) (C_53 tptp.nat) (D_22 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_103))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat C_53) D_22)) (@ (@ tptp.plus_plus_nat (@ _let_1 C_53)) D_22)))) (forall ((A_103 tptp.real) (C_53 tptp.real) (D_22 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_103))) (= (@ _let_1 (@ (@ tptp.plus_plus_real C_53) D_22)) (@ (@ tptp.plus_plus_real (@ _let_1 C_53)) D_22)))) (forall ((A_102 tptp.int) (C_52 tptp.int) (D_21 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_102))) (let ((_let_2 (@ tptp.plus_plus_int C_52))) (= (@ _let_1 (@ _let_2 D_21)) (@ _let_2 (@ _let_1 D_21)))))) (forall ((A_102 tptp.nat) (C_52 tptp.nat) (D_21 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_102))) (let ((_let_2 (@ tptp.plus_plus_nat C_52))) (= (@ _let_1 (@ _let_2 D_21)) (@ _let_2 (@ _let_1 D_21)))))) (forall ((A_102 tptp.real) (C_52 tptp.real) (D_21 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_102))) (let ((_let_2 (@ tptp.plus_plus_real C_52))) (= (@ _let_1 (@ _let_2 D_21)) (@ _let_2 (@ _let_1 D_21)))))) (forall ((A_101 tptp.int) (C_51 tptp.int)) (= (@ (@ tptp.plus_plus_int A_101) C_51) (@ (@ tptp.plus_plus_int C_51) A_101))) (forall ((A_101 tptp.nat) (C_51 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_101) C_51) (@ (@ tptp.plus_plus_nat C_51) A_101))) (forall ((A_101 tptp.real) (C_51 tptp.real)) (= (@ (@ tptp.plus_plus_real A_101) C_51) (@ (@ tptp.plus_plus_real C_51) A_101))) (forall ((X_19 tptp.int)) (= (= tptp.one_one_int X_19) (= X_19 tptp.one_one_int))) (forall ((X_19 tptp.nat)) (= (= tptp.one_one_nat X_19) (= X_19 tptp.one_one_nat))) (forall ((X_19 tptp.real)) (= (= tptp.one_one_real X_19) (= X_19 tptp.one_one_real))) (forall ((B_76 tptp.int) (A_100 tptp.int)) (= (= B_76 (@ (@ tptp.plus_plus_int B_76) A_100)) (= A_100 tptp.zero_zero_int))) (forall ((B_76 tptp.nat) (A_100 tptp.nat)) (= (= B_76 (@ (@ tptp.plus_plus_nat B_76) A_100)) (= A_100 tptp.zero_zero_nat))) (forall ((B_76 tptp.real) (A_100 tptp.real)) (= (= B_76 (@ (@ tptp.plus_plus_real B_76) A_100)) (= A_100 tptp.zero_zero_real))) (forall ((A_99 tptp.int)) (= (@ (@ tptp.plus_plus_int A_99) tptp.zero_zero_int) A_99)) (forall ((A_99 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_99) tptp.zero_zero_nat) A_99)) (forall ((A_99 tptp.real)) (= (@ (@ tptp.plus_plus_real A_99) tptp.zero_zero_real) A_99)) (forall ((A_98 tptp.int)) (= (@ (@ tptp.plus_plus_int A_98) tptp.zero_zero_int) A_98)) (forall ((A_98 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_98) tptp.zero_zero_nat) A_98)) (forall ((A_98 tptp.real)) (= (@ (@ tptp.plus_plus_real A_98) tptp.zero_zero_real) A_98)) (forall ((A_97 tptp.int)) (= (@ (@ tptp.plus_plus_int A_97) tptp.zero_zero_int) A_97)) (forall ((A_97 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_97) tptp.zero_zero_nat) A_97)) (forall ((A_97 tptp.real)) (= (@ (@ tptp.plus_plus_real A_97) tptp.zero_zero_real) A_97)) (forall ((A_96 tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A_96) A_96)) (= A_96 tptp.zero_zero_int))) (forall ((A_96 tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A_96) A_96)) (= A_96 tptp.zero_zero_real))) (forall ((A_95 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A_95) A_95)) (forall ((A_95 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A_95) A_95)) (forall ((A_95 tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A_95) A_95)) (forall ((A_94 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A_94) A_94)) (forall ((A_94 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A_94) A_94)) (forall ((A_94 tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A_94) A_94)) (forall ((A_93 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A_93) A_93)) (forall ((A_93 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A_93) A_93)) (forall ((A_93 tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A_93) A_93)) (forall ((C_50 tptp.int) (A_92 tptp.int) (B_75 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_50))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A_92)) (@ _let_1 B_75)) (@ (@ tptp.ord_less_int A_92) B_75)))) (forall ((C_50 tptp.nat) (A_92 tptp.nat) (B_75 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_50))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A_92)) (@ _let_1 B_75)) (@ (@ tptp.ord_less_nat A_92) B_75)))) (forall ((C_50 tptp.real) (A_92 tptp.real) (B_75 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C_50))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A_92)) (@ _let_1 B_75)) (@ (@ tptp.ord_less_real A_92) B_75)))) (forall ((A_91 tptp.int) (C_49 tptp.int) (B_74 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_91) C_49)) (@ (@ tptp.plus_plus_int B_74) C_49)) (@ (@ tptp.ord_less_int A_91) B_74))) (forall ((A_91 tptp.nat) (C_49 tptp.nat) (B_74 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_91) C_49)) (@ (@ tptp.plus_plus_nat B_74) C_49)) (@ (@ tptp.ord_less_nat A_91) B_74))) (forall ((A_91 tptp.real) (C_49 tptp.real) (B_74 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A_91) C_49)) (@ (@ tptp.plus_plus_real B_74) C_49)) (@ (@ tptp.ord_less_real A_91) B_74))) (forall ((C_48 tptp.int) (D_20 tptp.int) (A_90 tptp.int) (B_73 tptp.int)) (=> (@ (@ tptp.ord_less_int A_90) B_73) (=> (@ (@ tptp.ord_less_int C_48) D_20) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_90) C_48)) (@ (@ tptp.plus_plus_int B_73) D_20))))) (forall ((C_48 tptp.nat) (D_20 tptp.nat) (A_90 tptp.nat) (B_73 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_90) B_73) (=> (@ (@ tptp.ord_less_nat C_48) D_20) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_90) C_48)) (@ (@ tptp.plus_plus_nat B_73) D_20))))) (forall ((C_48 tptp.real) (D_20 tptp.real) (A_90 tptp.real) (B_73 tptp.real)) (=> (@ (@ tptp.ord_less_real A_90) B_73) (=> (@ (@ tptp.ord_less_real C_48) D_20) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A_90) C_48)) (@ (@ tptp.plus_plus_real B_73) D_20))))) (forall ((C_47 tptp.int) (A_89 tptp.int) (B_72 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_47))) (=> (@ (@ tptp.ord_less_int A_89) B_72) (@ (@ tptp.ord_less_int (@ _let_1 A_89)) (@ _let_1 B_72))))) (forall ((C_47 tptp.nat) (A_89 tptp.nat) (B_72 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_47))) (=> (@ (@ tptp.ord_less_nat A_89) B_72) (@ (@ tptp.ord_less_nat (@ _let_1 A_89)) (@ _let_1 B_72))))) (forall ((C_47 tptp.real) (A_89 tptp.real) (B_72 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C_47))) (=> (@ (@ tptp.ord_less_real A_89) B_72) (@ (@ tptp.ord_less_real (@ _let_1 A_89)) (@ _let_1 B_72))))) (forall ((C_46 tptp.int) (A_88 tptp.int) (B_71 tptp.int)) (=> (@ (@ tptp.ord_less_int A_88) B_71) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_88) C_46)) (@ (@ tptp.plus_plus_int B_71) C_46)))) (forall ((C_46 tptp.nat) (A_88 tptp.nat) (B_71 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_88) B_71) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_88) C_46)) (@ (@ tptp.plus_plus_nat B_71) C_46)))) (forall ((C_46 tptp.real) (A_88 tptp.real) (B_71 tptp.real)) (=> (@ (@ tptp.ord_less_real A_88) B_71) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A_88) C_46)) (@ (@ tptp.plus_plus_real B_71) C_46)))) (forall ((C_45 tptp.int) (A_87 tptp.int) (B_70 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_45))) (= (@ (@ tptp.ord_less_int (@ _let_1 A_87)) (@ _let_1 B_70)) (@ (@ tptp.ord_less_int A_87) B_70)))) (forall ((C_45 tptp.nat) (A_87 tptp.nat) (B_70 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_45))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A_87)) (@ _let_1 B_70)) (@ (@ tptp.ord_less_nat A_87) B_70)))) (forall ((C_45 tptp.real) (A_87 tptp.real) (B_70 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C_45))) (= (@ (@ tptp.ord_less_real (@ _let_1 A_87)) (@ _let_1 B_70)) (@ (@ tptp.ord_less_real A_87) B_70)))) (forall ((A_86 tptp.int) (C_44 tptp.int) (B_69 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_86) C_44)) (@ (@ tptp.plus_plus_int B_69) C_44)) (@ (@ tptp.ord_less_int A_86) B_69))) (forall ((A_86 tptp.nat) (C_44 tptp.nat) (B_69 tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A_86) C_44)) (@ (@ tptp.plus_plus_nat B_69) C_44)) (@ (@ tptp.ord_less_nat A_86) B_69))) (forall ((A_86 tptp.real) (C_44 tptp.real) (B_69 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A_86) C_44)) (@ (@ tptp.plus_plus_real B_69) C_44)) (@ (@ tptp.ord_less_real A_86) B_69))) (forall ((X_18 tptp.int)) (= (@ (@ tptp.power_power_int X_18) tptp.one_one_nat) X_18)) (forall ((X_18 tptp.nat)) (= (@ (@ tptp.power_power_nat X_18) tptp.one_one_nat) X_18)) (forall ((X_18 tptp.real)) (= (@ (@ tptp.power_power_real X_18) tptp.one_one_nat) X_18)) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat M) N) tptp.zero_zero_nat) (and (not (= N tptp.zero_zero_nat)) (= M tptp.zero_zero_nat)))) (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X_1 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X_1) (= (@ (@ tptp.power_power_real X_1) N) A) (forall ((Y_1 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y_1) (= (@ (@ tptp.power_power_real Y_1) N) A)) (= Y_1 X_1)))))))) (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R) (= (@ (@ tptp.power_power_real R) N) A)))))) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.t) (forall ((V_1 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat V_1)) tptp.one_one_nat))) (let ((_let_2 (@ (@ tptp.ord_less_int V_1) tptp.pls))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (@ tptp.number_number_of_nat (@ tptp.succ V_1)))))))) (forall ((V_1 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.number_number_of_nat V_1)))) (let ((_let_2 (@ (@ tptp.ord_less_int V_1) tptp.pls))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 (@ tptp.number_number_of_nat (@ tptp.succ V_1)))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit1 tptp.pls))) (let ((_let_2 (@ tptp.bit1 _let_1))) (let ((_let_3 (@ tptp.number_number_of_nat _let_2))) (let ((_let_4 (@ tptp.power_power_int B))) (let ((_let_5 (@ tptp.number_number_of_nat (@ tptp.bit0 _let_1)))) (let ((_let_6 (@ tptp.times_times_int (@ tptp.number_number_of_int _let_2)))) (let ((_let_7 (@ tptp.power_power_int A))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B)) _let_3) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ _let_7 _let_3)) (@ (@ tptp.times_times_int (@ _let_6 (@ _let_7 _let_5))) B))) (@ (@ tptp.times_times_int (@ _let_6 A)) (@ _let_4 _let_5)))) (@ _let_4 _let_3))))))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.number_number_of_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int A) B)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int A) _let_2)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int _let_1)) A)) B))) (@ (@ tptp.power_power_int B) _let_2)))))) _let_41 (@ _let_40 _let_39) (forall ((A_85 tptp.int) (B_68 tptp.int)) (= (@ (@ tptp.ord_less_eq_int A_85) B_68) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A_85) B_68)) tptp.zero_zero_int))) (forall ((A_85 tptp.real) (B_68 tptp.real)) (= (@ (@ tptp.ord_less_eq_real A_85) B_68) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A_85) B_68)) tptp.zero_zero_real))) (forall ((A_84 tptp.int) (B_67 tptp.int)) (= (@ (@ tptp.times_times_int A_84) B_67) (@ (@ tptp.times_times_int B_67) A_84))) (forall ((A_84 tptp.nat) (B_67 tptp.nat)) (= (@ (@ tptp.times_times_nat A_84) B_67) (@ (@ tptp.times_times_nat B_67) A_84))) (forall ((A_84 tptp.real) (B_67 tptp.real)) (= (@ (@ tptp.times_times_real A_84) B_67) (@ (@ tptp.times_times_real B_67) A_84))) (forall ((Lx_6 tptp.int) (Rx_6 tptp.int) (Ry_4 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_6))) (let ((_let_2 (@ tptp.times_times_int Rx_6))) (= (@ _let_1 (@ _let_2 Ry_4)) (@ _let_2 (@ _let_1 Ry_4)))))) (forall ((Lx_6 tptp.nat) (Rx_6 tptp.nat) (Ry_4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx_6))) (let ((_let_2 (@ tptp.times_times_nat Rx_6))) (= (@ _let_1 (@ _let_2 Ry_4)) (@ _let_2 (@ _let_1 Ry_4)))))) (forall ((Lx_6 tptp.real) (Rx_6 tptp.real) (Ry_4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx_6))) (let ((_let_2 (@ tptp.times_times_real Rx_6))) (= (@ _let_1 (@ _let_2 Ry_4)) (@ _let_2 (@ _let_1 Ry_4)))))) (forall ((Lx_5 tptp.int) (Rx_5 tptp.int) (Ry_3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_5))) (= (@ _let_1 (@ (@ tptp.times_times_int Rx_5) Ry_3)) (@ (@ tptp.times_times_int (@ _let_1 Rx_5)) Ry_3)))) (forall ((Lx_5 tptp.nat) (Rx_5 tptp.nat) (Ry_3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx_5))) (= (@ _let_1 (@ (@ tptp.times_times_nat Rx_5) Ry_3)) (@ (@ tptp.times_times_nat (@ _let_1 Rx_5)) Ry_3)))) (forall ((Lx_5 tptp.real) (Rx_5 tptp.real) (Ry_3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx_5))) (= (@ _let_1 (@ (@ tptp.times_times_real Rx_5) Ry_3)) (@ (@ tptp.times_times_real (@ _let_1 Rx_5)) Ry_3)))) (forall ((A_83 tptp.int) (B_66 tptp.int) (C_43 tptp.int)) (let ((_let_1 (@ tptp.times_times_int A_83))) (= (@ (@ tptp.times_times_int (@ _let_1 B_66)) C_43) (@ _let_1 (@ (@ tptp.times_times_int B_66) C_43))))) (forall ((A_83 tptp.nat) (B_66 tptp.nat) (C_43 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A_83))) (= (@ (@ tptp.times_times_nat (@ _let_1 B_66)) C_43) (@ _let_1 (@ (@ tptp.times_times_nat B_66) C_43))))) (forall ((A_83 tptp.real) (B_66 tptp.real) (C_43 tptp.real)) (let ((_let_1 (@ tptp.times_times_real A_83))) (= (@ (@ tptp.times_times_real (@ _let_1 B_66)) C_43) (@ _let_1 (@ (@ tptp.times_times_real B_66) C_43))))) (forall ((Lx_4 tptp.int) (Ly_4 tptp.int) (Rx_4 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_4))) (= (@ (@ tptp.times_times_int (@ _let_1 Ly_4)) Rx_4) (@ _let_1 (@ (@ tptp.times_times_int Ly_4) Rx_4))))) (forall ((Lx_4 tptp.nat) (Ly_4 tptp.nat) (Rx_4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx_4))) (= (@ (@ tptp.times_times_nat (@ _let_1 Ly_4)) Rx_4) (@ _let_1 (@ (@ tptp.times_times_nat Ly_4) Rx_4))))) (forall ((Lx_4 tptp.real) (Ly_4 tptp.real) (Rx_4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx_4))) (= (@ (@ tptp.times_times_real (@ _let_1 Ly_4)) Rx_4) (@ _let_1 (@ (@ tptp.times_times_real Ly_4) Rx_4))))) (forall ((Lx_3 tptp.int) (Ly_3 tptp.int) (Rx_3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_3))) (= (@ (@ tptp.times_times_int (@ _let_1 Ly_3)) Rx_3) (@ (@ tptp.times_times_int (@ _let_1 Rx_3)) Ly_3)))) (forall ((Lx_3 tptp.nat) (Ly_3 tptp.nat) (Rx_3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx_3))) (= (@ (@ tptp.times_times_nat (@ _let_1 Ly_3)) Rx_3) (@ (@ tptp.times_times_nat (@ _let_1 Rx_3)) Ly_3)))) (forall ((Lx_3 tptp.real) (Ly_3 tptp.real) (Rx_3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx_3))) (= (@ (@ tptp.times_times_real (@ _let_1 Ly_3)) Rx_3) (@ (@ tptp.times_times_real (@ _let_1 Rx_3)) Ly_3)))) (forall ((Lx_2 tptp.int) (Ly_2 tptp.int) (Rx_2 tptp.int) (Ry_2 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int Rx_2) Ry_2))) (let ((_let_2 (@ tptp.times_times_int Lx_2))) (= (@ (@ tptp.times_times_int (@ _let_2 Ly_2)) _let_1) (@ _let_2 (@ (@ tptp.times_times_int Ly_2) _let_1)))))) (forall ((Lx_2 tptp.nat) (Ly_2 tptp.nat) (Rx_2 tptp.nat) (Ry_2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat Rx_2) Ry_2))) (let ((_let_2 (@ tptp.times_times_nat Lx_2))) (= (@ (@ tptp.times_times_nat (@ _let_2 Ly_2)) _let_1) (@ _let_2 (@ (@ tptp.times_times_nat Ly_2) _let_1)))))) (forall ((Lx_2 tptp.real) (Ly_2 tptp.real) (Rx_2 tptp.real) (Ry_2 tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real Rx_2) Ry_2))) (let ((_let_2 (@ tptp.times_times_real Lx_2))) (= (@ (@ tptp.times_times_real (@ _let_2 Ly_2)) _let_1) (@ _let_2 (@ (@ tptp.times_times_real Ly_2) _let_1)))))) (forall ((Lx_1 tptp.real) (Ly_1 tptp.real) (Rx_1 tptp.real) (Ry_1 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.times_times_real Lx_1) Ly_1)))) (let ((_let_2 (@ tptp.times_times_real Rx_1))) (= (@ _let_1 (@ _let_2 Ry_1)) (@ _let_2 (@ _let_1 Ry_1)))))) (forall ((Lx_1 tptp.nat) (Ly_1 tptp.nat) (Rx_1 tptp.nat) (Ry_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ (@ tptp.times_times_nat Lx_1) Ly_1)))) (let ((_let_2 (@ tptp.times_times_nat Rx_1))) (= (@ _let_1 (@ _let_2 Ry_1)) (@ _let_2 (@ _let_1 Ry_1)))))) (forall ((Lx_1 tptp.int) (Ly_1 tptp.int) (Rx_1 tptp.int) (Ry_1 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.times_times_int Lx_1) Ly_1)))) (let ((_let_2 (@ tptp.times_times_int Rx_1))) (= (@ _let_1 (@ _let_2 Ry_1)) (@ _let_2 (@ _let_1 Ry_1)))))) (forall ((Lx tptp.real) (Ly tptp.real) (Rx tptp.real) (Ry tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx))) (= (@ (@ tptp.times_times_real (@ _let_1 Ly)) (@ (@ tptp.times_times_real Rx) Ry)) (@ (@ tptp.times_times_real (@ _let_1 Rx)) (@ (@ tptp.times_times_real Ly) Ry))))) (forall ((Lx tptp.nat) (Ly tptp.nat) (Rx tptp.nat) (Ry tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx))) (= (@ (@ tptp.times_times_nat (@ _let_1 Ly)) (@ (@ tptp.times_times_nat Rx) Ry)) (@ (@ tptp.times_times_nat (@ _let_1 Rx)) (@ (@ tptp.times_times_nat Ly) Ry))))) (forall ((Lx tptp.int) (Ly tptp.int) (Rx tptp.int) (Ry tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx))) (= (@ (@ tptp.times_times_int (@ _let_1 Ly)) (@ (@ tptp.times_times_int Rx) Ry)) (@ (@ tptp.times_times_int (@ _let_1 Rx)) (@ (@ tptp.times_times_int Ly) Ry))))) (forall ((A_82 tptp.int) (B_65 tptp.int) (C_42 tptp.int) (D_19 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A_82) B_65) (@ (@ tptp.minus_minus_int C_42) D_19)) (= (= A_82 B_65) (= C_42 D_19)))) (forall ((A_82 tptp.real) (B_65 tptp.real) (C_42 tptp.real) (D_19 tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A_82) B_65) (@ (@ tptp.minus_minus_real C_42) D_19)) (= (= A_82 B_65) (= C_42 D_19)))) (forall ((A_81 tptp.int) (B_64 tptp.int) (C_41 tptp.int) (D_18 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A_81) B_64) (@ (@ tptp.minus_minus_int C_41) D_18)) (= (@ (@ tptp.ord_less_eq_int A_81) B_64) (@ (@ tptp.ord_less_eq_int C_41) D_18)))) (forall ((A_81 tptp.real) (B_64 tptp.real) (C_41 tptp.real) (D_18 tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A_81) B_64) (@ (@ tptp.minus_minus_real C_41) D_18)) (= (@ (@ tptp.ord_less_eq_real A_81) B_64) (@ (@ tptp.ord_less_eq_real C_41) D_18)))) (forall ((V_12 tptp.int) (V_11 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_11) (=> (@ _let_1 V_12) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real V_11)) (@ tptp.number267125858f_real V_12)) (@ tptp.number267125858f_real (@ (@ tptp.times_times_int V_11) V_12))))))) (forall ((V_12 tptp.int) (V_11 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_11) (=> (@ _let_1 V_12) (= (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V_11)) (@ tptp.number_number_of_nat V_12)) (@ tptp.number_number_of_nat (@ (@ tptp.times_times_int V_11) V_12))))))) (forall ((V_12 tptp.int) (V_11 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_11) (=> (@ _let_1 V_12) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_11)) (@ tptp.number_number_of_int V_12)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_11) V_12))))))) (forall ((W tptp.int)) (@ (@ tptp.ord_less_eq_int W) W)) (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int Z) W) (@ (@ tptp.times_times_int W) Z))) (forall ((Z tptp.int) (W tptp.int)) (or (@ (@ tptp.ord_less_eq_int Z) W) (@ (@ tptp.ord_less_eq_int W) Z))) (forall ((Z1 tptp.int) (Z2 tptp.int) (Z3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z1))) (= (@ (@ tptp.times_times_int (@ _let_1 Z2)) Z3) (@ _let_1 (@ (@ tptp.times_times_int Z2) Z3))))) (forall ((K tptp.int) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int I_1))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_int J) K) (@ _let_1 K))))) (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) W) (=> (@ (@ tptp.ord_less_eq_int W) Z) (= Z W)))) (forall ((X_17 tptp.int) (Y_15 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.number267125858f_real X_17)) (@ tptp.number267125858f_real Y_15)) (@ (@ tptp.ord_less_eq_int X_17) Y_15))) (forall ((X_17 tptp.int) (Y_15 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_17)) (@ tptp.number_number_of_int Y_15)) (@ (@ tptp.ord_less_eq_int X_17) Y_15))) (forall ((V_10 tptp.int) (W_7 tptp.int)) (= (@ tptp.number267125858f_real (@ (@ tptp.times_times_int V_10) W_7)) (@ (@ tptp.times_times_real (@ tptp.number267125858f_real V_10)) (@ tptp.number267125858f_real W_7)))) (forall ((V_10 tptp.int) (W_7 tptp.int)) (= (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_10) W_7)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_10)) (@ tptp.number_number_of_int W_7)))) (forall ((V_9 tptp.int) (W_6 tptp.int)) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real V_9)) (@ tptp.number267125858f_real W_6)) (@ tptp.number267125858f_real (@ (@ tptp.times_times_int V_9) W_6)))) (forall ((V_9 tptp.int) (W_6 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_9)) (@ tptp.number_number_of_int W_6)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_9) W_6)))) (forall ((V_8 tptp.int) (W_5 tptp.int) (Z_4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real V_8)) (@ (@ tptp.times_times_real (@ tptp.number267125858f_real W_5)) Z_4)) (@ (@ tptp.times_times_real (@ tptp.number267125858f_real (@ (@ tptp.times_times_int V_8) W_5))) Z_4))) (forall ((V_8 tptp.int) (W_5 tptp.int) (Z_4 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_8)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int W_5)) Z_4)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_8) W_5))) Z_4))) (forall ((Z_1 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z_1) (= (= (@ tptp.nat_1 Z) (@ tptp.nat_1 Z_1)) (= Z Z_1)))))) (forall ((V_7 tptp.int) (B_63 tptp.int) (C_40 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.number_number_of_int V_7)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B_63) C_40)) (@ (@ tptp.minus_minus_int (@ _let_1 B_63)) (@ _let_1 C_40))))) (forall ((V_7 tptp.int) (B_63 tptp.real) (C_40 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.number267125858f_real V_7)))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B_63) C_40)) (@ (@ tptp.minus_minus_real (@ _let_1 B_63)) (@ _let_1 C_40))))) (forall ((A_80 tptp.int) (B_62 tptp.int) (V_6 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V_6))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A_80) B_62)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A_80) _let_1)) (@ (@ tptp.times_times_int B_62) _let_1))))) (forall ((A_80 tptp.real) (B_62 tptp.real) (V_6 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real V_6))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A_80) B_62)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A_80) _let_1)) (@ (@ tptp.times_times_real B_62) _let_1))))) (forall ((V_5 tptp.int) (W_4 tptp.int)) (= (@ tptp.number_number_of_int (@ (@ tptp.minus_minus_int V_5) W_4)) (@ (@ tptp.minus_minus_int (@ tptp.number_number_of_int V_5)) (@ tptp.number_number_of_int W_4)))) (forall ((V_5 tptp.int) (W_4 tptp.int)) (= (@ tptp.number267125858f_real (@ (@ tptp.minus_minus_int V_5) W_4)) (@ (@ tptp.minus_minus_real (@ tptp.number267125858f_real V_5)) (@ tptp.number267125858f_real W_4)))) (forall ((M_5 tptp.nat) (N_11 tptp.nat)) (= (@ tptp.semiri132038758t_real (@ (@ tptp.times_times_nat M_5) N_11)) (@ (@ tptp.times_times_real (@ tptp.semiri132038758t_real M_5)) (@ tptp.semiri132038758t_real N_11)))) (forall ((M_5 tptp.nat) (N_11 tptp.nat)) (= (@ tptp.semiri984289939at_nat (@ (@ tptp.times_times_nat M_5) N_11)) (@ (@ tptp.times_times_nat (@ tptp.semiri984289939at_nat M_5)) (@ tptp.semiri984289939at_nat N_11)))) (forall ((M_5 tptp.nat) (N_11 tptp.nat)) (= (@ tptp.semiri1621563631at_int (@ (@ tptp.times_times_nat M_5) N_11)) (@ (@ tptp.times_times_int (@ tptp.semiri1621563631at_int M_5)) (@ tptp.semiri1621563631at_int N_11)))) (forall ((M_4 tptp.nat) (N_10 tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri132038758t_real M_4)) (@ tptp.semiri132038758t_real N_10)) (@ (@ tptp.ord_less_eq_nat M_4) N_10))) (forall ((M_4 tptp.nat) (N_10 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri984289939at_nat M_4)) (@ tptp.semiri984289939at_nat N_10)) (@ (@ tptp.ord_less_eq_nat M_4) N_10))) (forall ((M_4 tptp.nat) (N_10 tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1621563631at_int M_4)) (@ tptp.semiri1621563631at_int N_10)) (@ (@ tptp.ord_less_eq_nat M_4) N_10))) (forall ((I_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I_1))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J)))) (forall ((X tptp.int) (Y tptp.int) (P Bool)) (let ((_let_1 (@ tptp.nat_1 (@ (@ (@ tptp.if_int P) X) Y)))) (and (=> P (= (@ tptp.nat_1 X) _let_1)) (=> (not P) (= (@ tptp.nat_1 Y) _let_1))))) (forall ((B_61 tptp.real) (A_79 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A_79) (@ (@ tptp.ord_less_eq_real B_61) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A_79) tptp.zero_zero_real) (@ _let_1 B_61))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_79) B_61)) tptp.zero_zero_real)))) (forall ((B_61 tptp.nat) (A_79 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A_79) (@ (@ tptp.ord_less_eq_nat B_61) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A_79) tptp.zero_zero_nat) (@ _let_1 B_61))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_79) B_61)) tptp.zero_zero_nat)))) (forall ((B_61 tptp.int) (A_79 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A_79) (@ (@ tptp.ord_less_eq_int B_61) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A_79) tptp.zero_zero_int) (@ _let_1 B_61))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_79) B_61)) tptp.zero_zero_int)))) (forall ((B_60 tptp.real) (A_78 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A_78) (@ _let_1 B_60)) (and (@ (@ tptp.ord_less_eq_real A_78) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B_60) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.times_times_real A_78) B_60))))) (forall ((B_60 tptp.int) (A_78 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A_78) (@ _let_1 B_60)) (and (@ (@ tptp.ord_less_eq_int A_78) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B_60) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A_78) B_60))))) (forall ((C_39 tptp.real) (D_17 tptp.real) (A_77 tptp.real) (B_59 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A_77) B_59) (=> (@ (@ tptp.ord_less_eq_real C_39) D_17) (=> (@ _let_1 B_59) (=> (@ _let_1 C_39) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_77) C_39)) (@ (@ tptp.times_times_real B_59) D_17)))))))) (forall ((C_39 tptp.nat) (D_17 tptp.nat) (A_77 tptp.nat) (B_59 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A_77) B_59) (=> (@ (@ tptp.ord_less_eq_nat C_39) D_17) (=> (@ _let_1 B_59) (=> (@ _let_1 C_39) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_77) C_39)) (@ (@ tptp.times_times_nat B_59) D_17)))))))) (forall ((C_39 tptp.int) (D_17 tptp.int) (A_77 tptp.int) (B_59 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A_77) B_59) (=> (@ (@ tptp.ord_less_eq_int C_39) D_17) (=> (@ _let_1 B_59) (=> (@ _let_1 C_39) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_77) C_39)) (@ (@ tptp.times_times_int B_59) D_17)))))))) (forall ((C_38 tptp.real) (D_16 tptp.real) (A_76 tptp.real) (B_58 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A_76) B_58) (=> (@ (@ tptp.ord_less_eq_real C_38) D_16) (=> (@ _let_1 A_76) (=> (@ _let_1 C_38) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_76) C_38)) (@ (@ tptp.times_times_real B_58) D_16)))))))) (forall ((C_38 tptp.nat) (D_16 tptp.nat) (A_76 tptp.nat) (B_58 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A_76) B_58) (=> (@ (@ tptp.ord_less_eq_nat C_38) D_16) (=> (@ _let_1 A_76) (=> (@ _let_1 C_38) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_76) C_38)) (@ (@ tptp.times_times_nat B_58) D_16)))))))) (forall ((C_38 tptp.int) (D_16 tptp.int) (A_76 tptp.int) (B_58 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A_76) B_58) (=> (@ (@ tptp.ord_less_eq_int C_38) D_16) (=> (@ _let_1 A_76) (=> (@ _let_1 C_38) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_76) C_38)) (@ (@ tptp.times_times_int B_58) D_16)))))))) (forall ((C_37 tptp.real) (B_57 tptp.real) (A_75 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_37))) (=> (@ (@ tptp.ord_less_eq_real B_57) A_75) (=> (@ (@ tptp.ord_less_eq_real C_37) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A_75)) (@ _let_1 B_57)))))) (forall ((C_37 tptp.int) (B_57 tptp.int) (A_75 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_37))) (=> (@ (@ tptp.ord_less_eq_int B_57) A_75) (=> (@ (@ tptp.ord_less_eq_int C_37) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A_75)) (@ _let_1 B_57)))))) (forall ((C_36 tptp.real) (B_56 tptp.real) (A_74 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B_56) A_74) (=> (@ (@ tptp.ord_less_eq_real C_36) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_74) C_36)) (@ (@ tptp.times_times_real B_56) C_36))))) (forall ((C_36 tptp.int) (B_56 tptp.int) (A_74 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B_56) A_74) (=> (@ (@ tptp.ord_less_eq_int C_36) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_74) C_36)) (@ (@ tptp.times_times_int B_56) C_36))))) (forall ((C_35 tptp.real) (A_73 tptp.real) (B_55 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_35))) (=> (@ (@ tptp.ord_less_eq_real A_73) B_55) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_35) (@ (@ tptp.ord_less_eq_real (@ _let_1 A_73)) (@ _let_1 B_55)))))) (forall ((C_35 tptp.nat) (A_73 tptp.nat) (B_55 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_35))) (=> (@ (@ tptp.ord_less_eq_nat A_73) B_55) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_35) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_73)) (@ _let_1 B_55)))))) (forall ((C_35 tptp.int) (A_73 tptp.int) (B_55 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_35))) (=> (@ (@ tptp.ord_less_eq_int A_73) B_55) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_35) (@ (@ tptp.ord_less_eq_int (@ _let_1 A_73)) (@ _let_1 B_55)))))) (forall ((C_34 tptp.real) (A_72 tptp.real) (B_54 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_34))) (=> (@ (@ tptp.ord_less_eq_real A_72) B_54) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_34) (@ (@ tptp.ord_less_eq_real (@ _let_1 A_72)) (@ _let_1 B_54)))))) (forall ((C_34 tptp.nat) (A_72 tptp.nat) (B_54 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_34))) (=> (@ (@ tptp.ord_less_eq_nat A_72) B_54) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_34) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_72)) (@ _let_1 B_54)))))) (forall ((C_34 tptp.int) (A_72 tptp.int) (B_54 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_34))) (=> (@ (@ tptp.ord_less_eq_int A_72) B_54) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_34) (@ (@ tptp.ord_less_eq_int (@ _let_1 A_72)) (@ _let_1 B_54)))))) (forall ((C_33 tptp.real) (A_71 tptp.real) (B_53 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_71) B_53) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_33) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_71) C_33)) (@ (@ tptp.times_times_real B_53) C_33))))) (forall ((C_33 tptp.nat) (A_71 tptp.nat) (B_53 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_71) B_53) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_33) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_71) C_33)) (@ (@ tptp.times_times_nat B_53) C_33))))) (forall ((C_33 tptp.int) (A_71 tptp.int) (B_53 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_71) B_53) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_33) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_71) C_33)) (@ (@ tptp.times_times_int B_53) C_33))))) (forall ((B_52 tptp.real) (A_70 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_70) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B_52) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A_70) B_52))))) (forall ((B_52 tptp.int) (A_70 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_70) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B_52) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A_70) B_52))))) (forall ((B_51 tptp.real) (A_69 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_69) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B_51) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_69) B_51)) tptp.zero_zero_real)))) (forall ((B_51 tptp.nat) (A_69 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_69) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B_51) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_69) B_51)) tptp.zero_zero_nat)))) (forall ((B_51 tptp.int) (A_69 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_69) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B_51) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_69) B_51)) tptp.zero_zero_int)))) (forall ((B_50 tptp.real) (A_68 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_68) (=> (@ (@ tptp.ord_less_eq_real B_50) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real B_50) A_68)) tptp.zero_zero_real)))) (forall ((B_50 tptp.nat) (A_68 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_68) (=> (@ (@ tptp.ord_less_eq_nat B_50) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B_50) A_68)) tptp.zero_zero_nat)))) (forall ((B_50 tptp.int) (A_68 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_68) (=> (@ (@ tptp.ord_less_eq_int B_50) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B_50) A_68)) tptp.zero_zero_int)))) (forall ((B_49 tptp.real) (A_67 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_67) (=> (@ (@ tptp.ord_less_eq_real B_49) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_67) B_49)) tptp.zero_zero_real)))) (forall ((B_49 tptp.nat) (A_67 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_67) (=> (@ (@ tptp.ord_less_eq_nat B_49) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_67) B_49)) tptp.zero_zero_nat)))) (forall ((B_49 tptp.int) (A_67 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_67) (=> (@ (@ tptp.ord_less_eq_int B_49) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_67) B_49)) tptp.zero_zero_int)))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ tptp.nat_1 X) (@ tptp.nat_1 Y)) (= X Y)))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.times_times_int X) Y)))))) (forall ((B_48 tptp.real) (A_66 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A_66) (=> (@ _let_1 B_48) (@ _let_1 (@ (@ tptp.times_times_real A_66) B_48)))))) (forall ((B_48 tptp.nat) (A_66 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A_66) (=> (@ _let_1 B_48) (@ _let_1 (@ (@ tptp.times_times_nat A_66) B_48)))))) (forall ((B_48 tptp.int) (A_66 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A_66) (=> (@ _let_1 B_48) (@ _let_1 (@ (@ tptp.times_times_int A_66) B_48)))))) (forall ((A_65 tptp.real) (E_6 tptp.real) (C_32 tptp.real) (B_47 tptp.real) (D_15 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_65) E_6)) C_32)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B_47) E_6)) D_15)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A_65) B_47)) E_6)) C_32)) D_15))) (forall ((A_65 tptp.int) (E_6 tptp.int) (C_32 tptp.int) (B_47 tptp.int) (D_15 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_65) E_6)) C_32)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_47) E_6)) D_15)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A_65) B_47)) E_6)) C_32)) D_15))) (forall ((A_64 tptp.real) (E_5 tptp.real) (C_31 tptp.real) (B_46 tptp.real) (D_14 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_64) E_5)) C_31) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B_46) E_5)) D_14)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A_64) B_46)) E_5)) C_31) D_14))) (forall ((A_64 tptp.int) (E_5 tptp.int) (C_31 tptp.int) (B_46 tptp.int) (D_14 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_64) E_5)) C_31) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_46) E_5)) D_14)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A_64) B_46)) E_5)) C_31) D_14))) (forall ((A_63 tptp.real) (E_4 tptp.real) (C_30 tptp.real) (B_45 tptp.real) (D_13 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_63) E_4)) C_30)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B_45) E_4)) D_13)) (@ (@ tptp.ord_less_eq_real C_30) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B_45) A_63)) E_4)) D_13)))) (forall ((A_63 tptp.int) (E_4 tptp.int) (C_30 tptp.int) (B_45 tptp.int) (D_13 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_63) E_4)) C_30)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_45) E_4)) D_13)) (@ (@ tptp.ord_less_eq_int C_30) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B_45) A_63)) E_4)) D_13)))) (forall ((A_62 tptp.real) (E_3 tptp.real) (C_29 tptp.real) (B_44 tptp.real) (D_12 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_62) E_3)) C_29) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B_44) E_3)) D_12)) (= C_29 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B_44) A_62)) E_3)) D_12)))) (forall ((A_62 tptp.int) (E_3 tptp.int) (C_29 tptp.int) (B_44 tptp.int) (D_12 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_62) E_3)) C_29) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_44) E_3)) D_12)) (= C_29 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B_44) A_62)) E_3)) D_12)))) (forall ((X_16 tptp.real) (Y_14 tptp.real) (A_61 tptp.real) (B_43 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X_16))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y_14)) (@ (@ tptp.times_times_real A_61) B_43)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y_14) B_43))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X_16) A_61)) B_43))))) (forall ((X_16 tptp.int) (Y_14 tptp.int) (A_61 tptp.int) (B_43 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X_16))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y_14)) (@ (@ tptp.times_times_int A_61) B_43)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y_14) B_43))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X_16) A_61)) B_43))))) (forall ((A_60 tptp.real) (B_42 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_60) B_42)) tptp.zero_zero_real) (or (and (@ _let_1 A_60) (@ (@ tptp.ord_less_eq_real B_42) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A_60) tptp.zero_zero_real) (@ _let_1 B_42)))))) (forall ((A_60 tptp.int) (B_42 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_60) B_42)) tptp.zero_zero_int) (or (and (@ _let_1 A_60) (@ (@ tptp.ord_less_eq_int B_42) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A_60) tptp.zero_zero_int) (@ _let_1 B_42)))))) (forall ((A_59 tptp.real) (B_41 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A_59) B_41)) (or (and (@ _let_1 A_59) (@ _let_1 B_41)) (and (@ (@ tptp.ord_less_eq_real A_59) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B_41) tptp.zero_zero_real)))))) (forall ((A_59 tptp.int) (B_41 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A_59) B_41)) (or (and (@ _let_1 A_59) (@ _let_1 B_41)) (and (@ (@ tptp.ord_less_eq_int A_59) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B_41) tptp.zero_zero_int)))))) (forall ((P (-> tptp.nat Bool))) (= (@ tptp.all P) (forall ((X_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P (@ tptp.nat_1 X_1)))))) (forall ((P (-> tptp.nat Bool))) (= (@ tptp.ex P) (exists ((X_1 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P (@ tptp.nat_1 X_1)))))) (forall ((A_58 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A_58) A_58))) (forall ((A_58 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A_58) A_58))) (forall ((A_57 tptp.real) (E_2 tptp.real) (C_28 tptp.real) (B_40 tptp.real) (D_11 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_57) E_2)) C_28)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B_40) E_2)) D_11)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A_57) B_40)) E_2)) C_28)) D_11))) (forall ((A_57 tptp.int) (E_2 tptp.int) (C_28 tptp.int) (B_40 tptp.int) (D_11 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_57) E_2)) C_28)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_40) E_2)) D_11)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A_57) B_40)) E_2)) C_28)) D_11))) (forall ((A_56 tptp.real) (E_1 tptp.real) (C_27 tptp.real) (B_39 tptp.real) (D_10 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_56) E_1)) C_27)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B_39) E_1)) D_10)) (@ (@ tptp.ord_less_real C_27) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B_39) A_56)) E_1)) D_10)))) (forall ((A_56 tptp.int) (E_1 tptp.int) (C_27 tptp.int) (B_39 tptp.int) (D_10 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_56) E_1)) C_27)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_39) E_1)) D_10)) (@ (@ tptp.ord_less_int C_27) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B_39) A_56)) E_1)) D_10)))) (forall ((X_15 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X_15) X_15)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X_15) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X_15) tptp.one_one_real)))) (forall ((X_15 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X_15) X_15)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X_15) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X_15) tptp.one_one_int)))) (forall ((C_26 tptp.real) (A_55 tptp.real) (B_38 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_26))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A_55)) (@ _let_1 B_38)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_26) (@ (@ tptp.ord_less_eq_real A_55) B_38))))) (forall ((C_26 tptp.nat) (A_55 tptp.nat) (B_38 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_26))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_55)) (@ _let_1 B_38)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C_26) (@ (@ tptp.ord_less_eq_nat A_55) B_38))))) (forall ((C_26 tptp.int) (A_55 tptp.int) (B_38 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_26))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A_55)) (@ _let_1 B_38)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_26) (@ (@ tptp.ord_less_eq_int A_55) B_38))))) (forall ((A_54 tptp.real) (C_25 tptp.real) (B_37 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_54) C_25)) (@ (@ tptp.times_times_real B_37) C_25)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_25) (@ (@ tptp.ord_less_eq_real A_54) B_37)))) (forall ((A_54 tptp.nat) (C_25 tptp.nat) (B_37 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_54) C_25)) (@ (@ tptp.times_times_nat B_37) C_25)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C_25) (@ (@ tptp.ord_less_eq_nat A_54) B_37)))) (forall ((A_54 tptp.int) (C_25 tptp.int) (B_37 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_54) C_25)) (@ (@ tptp.times_times_int B_37) C_25)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_25) (@ (@ tptp.ord_less_eq_int A_54) B_37)))) (forall ((C_24 tptp.real) (A_53 tptp.real) (B_36 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_24))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A_53)) (@ _let_1 B_36)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_24) (@ (@ tptp.ord_less_real A_53) B_36))))) (forall ((C_24 tptp.nat) (A_53 tptp.nat) (B_36 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_24))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A_53)) (@ _let_1 B_36)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_24) (@ (@ tptp.ord_less_nat A_53) B_36))))) (forall ((C_24 tptp.int) (A_53 tptp.int) (B_36 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_24))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A_53)) (@ _let_1 B_36)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_24) (@ (@ tptp.ord_less_int A_53) B_36))))) (forall ((C_23 tptp.real) (A_52 tptp.real) (B_35 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_23))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A_52)) (@ _let_1 B_35)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_23) (@ (@ tptp.ord_less_real A_52) B_35))))) (forall ((C_23 tptp.nat) (A_52 tptp.nat) (B_35 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_23))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A_52)) (@ _let_1 B_35)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_23) (@ (@ tptp.ord_less_nat A_52) B_35))))) (forall ((C_23 tptp.int) (A_52 tptp.int) (B_35 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_23))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A_52)) (@ _let_1 B_35)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_23) (@ (@ tptp.ord_less_int A_52) B_35))))) (forall ((A_51 tptp.real) (C_22 tptp.real) (B_34 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_51) C_22)) (@ (@ tptp.times_times_real B_34) C_22)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_22) (@ (@ tptp.ord_less_real A_51) B_34)))) (forall ((A_51 tptp.nat) (C_22 tptp.nat) (B_34 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_51) C_22)) (@ (@ tptp.times_times_nat B_34) C_22)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_22) (@ (@ tptp.ord_less_nat A_51) B_34)))) (forall ((A_51 tptp.int) (C_22 tptp.int) (B_34 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_51) C_22)) (@ (@ tptp.times_times_int B_34) C_22)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_22) (@ (@ tptp.ord_less_int A_51) B_34)))) (forall ((A_50 tptp.real) (C_21 tptp.real) (B_33 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_50) C_21)) (@ (@ tptp.times_times_real B_33) C_21)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_21) (@ (@ tptp.ord_less_real A_50) B_33)))) (forall ((A_50 tptp.nat) (C_21 tptp.nat) (B_33 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_50) C_21)) (@ (@ tptp.times_times_nat B_33) C_21)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_21) (@ (@ tptp.ord_less_nat A_50) B_33)))) (forall ((A_50 tptp.int) (C_21 tptp.int) (B_33 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_50) C_21)) (@ (@ tptp.times_times_int B_33) C_21)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_21) (@ (@ tptp.ord_less_int A_50) B_33)))) (forall ((C_20 tptp.real) (D_9 tptp.real) (A_49 tptp.real) (B_32 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_49) B_32) (=> (@ (@ tptp.ord_less_real C_20) D_9) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A_49) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_20) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_49) C_20)) (@ (@ tptp.times_times_real B_32) D_9))))))) (forall ((C_20 tptp.nat) (D_9 tptp.nat) (A_49 tptp.nat) (B_32 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_49) B_32) (=> (@ (@ tptp.ord_less_nat C_20) D_9) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_49) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_20) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_49) C_20)) (@ (@ tptp.times_times_nat B_32) D_9))))))) (forall ((C_20 tptp.int) (D_9 tptp.int) (A_49 tptp.int) (B_32 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_49) B_32) (=> (@ (@ tptp.ord_less_int C_20) D_9) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_49) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_20) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_49) C_20)) (@ (@ tptp.times_times_int B_32) D_9))))))) (forall ((C_19 tptp.real) (D_8 tptp.real) (A_48 tptp.real) (B_31 tptp.real)) (=> (@ (@ tptp.ord_less_real A_48) B_31) (=> (@ (@ tptp.ord_less_eq_real C_19) D_8) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_48) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_19) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_48) C_19)) (@ (@ tptp.times_times_real B_31) D_8))))))) (forall ((C_19 tptp.nat) (D_8 tptp.nat) (A_48 tptp.nat) (B_31 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_48) B_31) (=> (@ (@ tptp.ord_less_eq_nat C_19) D_8) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_48) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C_19) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_48) C_19)) (@ (@ tptp.times_times_nat B_31) D_8))))))) (forall ((C_19 tptp.int) (D_8 tptp.int) (A_48 tptp.int) (B_31 tptp.int)) (=> (@ (@ tptp.ord_less_int A_48) B_31) (=> (@ (@ tptp.ord_less_eq_int C_19) D_8) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_48) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_19) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_48) C_19)) (@ (@ tptp.times_times_int B_31) D_8))))))) (forall ((C_18 tptp.real) (D_7 tptp.real) (A_47 tptp.real) (B_30 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real A_47) B_30) (=> (@ (@ tptp.ord_less_real C_18) D_7) (=> (@ _let_1 A_47) (=> (@ _let_1 C_18) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_47) C_18)) (@ (@ tptp.times_times_real B_30) D_7)))))))) (forall ((C_18 tptp.nat) (D_7 tptp.nat) (A_47 tptp.nat) (B_30 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A_47) B_30) (=> (@ (@ tptp.ord_less_nat C_18) D_7) (=> (@ _let_1 A_47) (=> (@ _let_1 C_18) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_47) C_18)) (@ (@ tptp.times_times_nat B_30) D_7)))))))) (forall ((C_18 tptp.int) (D_7 tptp.int) (A_47 tptp.int) (B_30 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A_47) B_30) (=> (@ (@ tptp.ord_less_int C_18) D_7) (=> (@ _let_1 A_47) (=> (@ _let_1 C_18) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_47) C_18)) (@ (@ tptp.times_times_int B_30) D_7)))))))) (forall ((C_17 tptp.real) (D_6 tptp.real) (A_46 tptp.real) (B_29 tptp.real)) (=> (@ (@ tptp.ord_less_real A_46) B_29) (=> (@ (@ tptp.ord_less_real C_17) D_6) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B_29) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_17) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_46) C_17)) (@ (@ tptp.times_times_real B_29) D_6))))))) (forall ((C_17 tptp.nat) (D_6 tptp.nat) (A_46 tptp.nat) (B_29 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_46) B_29) (=> (@ (@ tptp.ord_less_nat C_17) D_6) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B_29) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_17) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_46) C_17)) (@ (@ tptp.times_times_nat B_29) D_6))))))) (forall ((C_17 tptp.int) (D_6 tptp.int) (A_46 tptp.int) (B_29 tptp.int)) (=> (@ (@ tptp.ord_less_int A_46) B_29) (=> (@ (@ tptp.ord_less_int C_17) D_6) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_29) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_17) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_46) C_17)) (@ (@ tptp.times_times_int B_29) D_6))))))) (forall ((A_45 tptp.real) (B_28 tptp.real) (C_16 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_16))) (=> (@ (@ tptp.ord_less_real C_16) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A_45)) (@ _let_1 B_28)) (@ (@ tptp.ord_less_eq_real B_28) A_45))))) (forall ((A_45 tptp.int) (B_28 tptp.int) (C_16 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_16))) (=> (@ (@ tptp.ord_less_int C_16) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A_45)) (@ _let_1 B_28)) (@ (@ tptp.ord_less_eq_int B_28) A_45))))) (forall ((A_44 tptp.real) (B_27 tptp.real) (C_15 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_15))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_15) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A_44)) (@ _let_1 B_27)) (@ (@ tptp.ord_less_eq_real A_44) B_27))))) (forall ((A_44 tptp.int) (B_27 tptp.int) (C_15 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_15))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_15) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A_44)) (@ _let_1 B_27)) (@ (@ tptp.ord_less_eq_int A_44) B_27))))) (forall ((X_14 tptp.real) (Y_13 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X_14) X_14)) (@ (@ tptp.times_times_real Y_13) Y_13)))) (forall ((X_14 tptp.int) (Y_13 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_14) X_14)) (@ (@ tptp.times_times_int Y_13) Y_13)))) (forall ((X_13 tptp.real) (Y_12 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X_13) X_13)) (@ (@ tptp.times_times_real Y_12) Y_12))) tptp.zero_zero_real) (and (= X_13 tptp.zero_zero_real) (= Y_12 tptp.zero_zero_real)))) (forall ((X_13 tptp.int) (Y_12 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_13) X_13)) (@ (@ tptp.times_times_int Y_12) Y_12))) tptp.zero_zero_int) (and (= X_13 tptp.zero_zero_int) (= Y_12 tptp.zero_zero_int)))) (forall ((Y_11 tptp.real) (X_12 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X_12) (=> (@ _let_1 Y_11) (=> (@ (@ tptp.ord_less_eq_real Y_11) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X_12) Y_11)) X_12)))))) (forall ((Y_11 tptp.int) (X_12 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X_12) (=> (@ _let_1 Y_11) (=> (@ (@ tptp.ord_less_eq_int Y_11) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X_12) Y_11)) X_12)))))) (forall ((Y_10 tptp.real) (X_11 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X_11) (=> (@ _let_1 Y_10) (=> (@ (@ tptp.ord_less_eq_real Y_10) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y_10) X_11)) X_11)))))) (forall ((Y_10 tptp.int) (X_11 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X_11) (=> (@ _let_1 Y_10) (=> (@ (@ tptp.ord_less_eq_int Y_10) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y_10) X_11)) X_11)))))) (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat_1 Z) tptp.zero_zero_nat))) (forall ((I_1 tptp.int)) (= (= (@ tptp.nat_1 I_1) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I_1) tptp.zero_zero_int))) (forall ((A_43 tptp.real) (N_9 tptp.nat) (N_8 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_43))) (=> (@ (@ tptp.ord_less_eq_nat N_9) N_8) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A_43) (@ (@ tptp.ord_less_eq_real (@ _let_1 N_9)) (@ _let_1 N_8)))))) (forall ((A_43 tptp.nat) (N_9 tptp.nat) (N_8 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_43))) (=> (@ (@ tptp.ord_less_eq_nat N_9) N_8) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A_43) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N_9)) (@ _let_1 N_8)))))) (forall ((A_43 tptp.int) (N_9 tptp.nat) (N_8 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_43))) (=> (@ (@ tptp.ord_less_eq_nat N_9) N_8) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A_43) (@ (@ tptp.ord_less_eq_int (@ _let_1 N_9)) (@ _let_1 N_8)))))) (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.semiri1621563631at_int (@ tptp.nat_1 Z)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (and (=> _let_2 (= _let_1 Z)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((M tptp.nat) (Z tptp.int)) (= (= (@ tptp.semiri1621563631at_int M) Z) (and (= M (@ tptp.nat_1 Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)))) (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1621563631at_int (@ tptp.nat_1 Z)) Z))) (forall ((A_42 tptp.real) (B_26 tptp.real)) (= (= (@ (@ tptp.minus_minus_real A_42) B_26) tptp.zero_zero_real) (= A_42 B_26))) (forall ((A_42 tptp.int) (B_26 tptp.int)) (= (= (@ (@ tptp.minus_minus_int A_42) B_26) tptp.zero_zero_int) (= A_42 B_26))) (forall ((A_41 tptp.real) (B_25 tptp.real)) (= (= A_41 B_25) (= (@ (@ tptp.minus_minus_real A_41) B_25) tptp.zero_zero_real))) (forall ((A_41 tptp.int) (B_25 tptp.int)) (= (= A_41 B_25) (= (@ (@ tptp.minus_minus_int A_41) B_25) tptp.zero_zero_int))) (forall ((A_40 tptp.real)) (= (@ (@ tptp.minus_minus_real A_40) A_40) tptp.zero_zero_real)) (forall ((A_40 tptp.int)) (= (@ (@ tptp.minus_minus_int A_40) A_40) tptp.zero_zero_int)) (forall ((A_39 tptp.real)) (= (@ (@ tptp.minus_minus_real A_39) tptp.zero_zero_real) A_39)) (forall ((A_39 tptp.int)) (= (@ (@ tptp.minus_minus_int A_39) tptp.zero_zero_int) A_39)) (forall ((A_38 tptp.int) (B_24 tptp.int) (C_14 tptp.int) (D_5 tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A_38) B_24) (@ (@ tptp.minus_minus_int C_14) D_5)) (= (@ (@ tptp.ord_less_int A_38) B_24) (@ (@ tptp.ord_less_int C_14) D_5)))) (forall ((A_38 tptp.real) (B_24 tptp.real) (C_14 tptp.real) (D_5 tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A_38) B_24) (@ (@ tptp.minus_minus_real C_14) D_5)) (= (@ (@ tptp.ord_less_real A_38) B_24) (@ (@ tptp.ord_less_real C_14) D_5)))) (forall ((A_37 tptp.real) (C_13 tptp.real) (B_23 tptp.real) (D_4 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A_37) C_13)) (@ (@ tptp.plus_plus_real B_23) D_4)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A_37) B_23)) (@ (@ tptp.minus_minus_real C_13) D_4)))) (forall ((A_37 tptp.int) (C_13 tptp.int) (B_23 tptp.int) (D_4 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A_37) C_13)) (@ (@ tptp.plus_plus_int B_23) D_4)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A_37) B_23)) (@ (@ tptp.minus_minus_int C_13) D_4)))) (forall ((A_36 tptp.real) (B_22 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A_36) B_22)) B_22) A_36)) (forall ((A_36 tptp.int) (B_22 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A_36) B_22)) B_22) A_36)) (forall ((A_35 tptp.real) (B_21 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A_35) B_21)) B_21) A_35)) (forall ((A_35 tptp.int) (B_21 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A_35) B_21)) B_21) A_35)) (forall ((A_34 tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A_34) tptp.zero_zero_real)) (forall ((A_34 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A_34) tptp.zero_zero_nat)) (forall ((A_34 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A_34) tptp.zero_zero_int)) (forall ((A_33 tptp.real)) (= (@ (@ tptp.times_times_real A_33) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A_33 tptp.nat)) (= (@ (@ tptp.times_times_nat A_33) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A_33 tptp.int)) (= (@ (@ tptp.times_times_int A_33) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A_32 tptp.real) (B_20 tptp.real)) (= (= (@ (@ tptp.times_times_real A_32) B_20) tptp.zero_zero_real) (or (= A_32 tptp.zero_zero_real) (= B_20 tptp.zero_zero_real)))) (forall ((A_32 tptp.int) (B_20 tptp.int)) (= (= (@ (@ tptp.times_times_int A_32) B_20) tptp.zero_zero_int) (or (= A_32 tptp.zero_zero_int) (= B_20 tptp.zero_zero_int)))) (forall ((B_19 tptp.real) (A_31 tptp.real)) (=> (not (= A_31 tptp.zero_zero_real)) (=> (not (= B_19 tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A_31) B_19) tptp.zero_zero_real))))) (forall ((B_19 tptp.nat) (A_31 tptp.nat)) (=> (not (= A_31 tptp.zero_zero_nat)) (=> (not (= B_19 tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A_31) B_19) tptp.zero_zero_nat))))) (forall ((B_19 tptp.int) (A_31 tptp.int)) (=> (not (= A_31 tptp.zero_zero_int)) (=> (not (= B_19 tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A_31) B_19) tptp.zero_zero_int))))) (forall ((A_30 tptp.real) (B_18 tptp.real)) (=> (= (@ (@ tptp.times_times_real A_30) B_18) tptp.zero_zero_real) (or (= A_30 tptp.zero_zero_real) (= B_18 tptp.zero_zero_real)))) (forall ((A_30 tptp.nat) (B_18 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A_30) B_18) tptp.zero_zero_nat) (or (= A_30 tptp.zero_zero_nat) (= B_18 tptp.zero_zero_nat)))) (forall ((A_30 tptp.int) (B_18 tptp.int)) (=> (= (@ (@ tptp.times_times_int A_30) B_18) tptp.zero_zero_int) (or (= A_30 tptp.zero_zero_int) (= B_18 tptp.zero_zero_int)))) (forall ((A_29 tptp.real)) (= (@ (@ tptp.times_times_real A_29) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A_29 tptp.nat)) (= (@ (@ tptp.times_times_nat A_29) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A_29 tptp.int)) (= (@ (@ tptp.times_times_int A_29) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A_28 tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A_28) tptp.zero_zero_real)) (forall ((A_28 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A_28) tptp.zero_zero_nat)) (forall ((A_28 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A_28) tptp.zero_zero_int)) (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)) (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((A_27 tptp.real) (B_17 tptp.real) (C_12 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_27) B_17)) C_12) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_27) C_12)) (@ (@ tptp.times_times_real B_17) C_12)))) (forall ((A_27 tptp.nat) (B_17 tptp.nat) (C_12 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_27) B_17)) C_12) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_27) C_12)) (@ (@ tptp.times_times_nat B_17) C_12)))) (forall ((A_27 tptp.int) (B_17 tptp.int) (C_12 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_27) B_17)) C_12) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_27) C_12)) (@ (@ tptp.times_times_int B_17) C_12)))) (forall ((A_26 tptp.real) (E tptp.real) (B_16 tptp.real) (C_11 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_26) E)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B_16) E)) C_11)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_26) B_16)) E)) C_11))) (forall ((A_26 tptp.nat) (E tptp.nat) (B_16 tptp.nat) (C_11 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_26) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B_16) E)) C_11)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_26) B_16)) E)) C_11))) (forall ((A_26 tptp.int) (E tptp.int) (B_16 tptp.int) (C_11 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_26) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_16) E)) C_11)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_26) B_16)) E)) C_11))) (forall ((W_3 tptp.real) (Y_9 tptp.real) (X_10 tptp.real) (Z_3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X_10))) (let ((_let_2 (@ tptp.times_times_real W_3))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y_9)) (@ _let_1 Z_3)) (@ (@ tptp.plus_plus_real (@ _let_2 Z_3)) (@ _let_1 Y_9))) (or (= W_3 X_10) (= Y_9 Z_3)))))) (forall ((W_3 tptp.nat) (Y_9 tptp.nat) (X_10 tptp.nat) (Z_3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X_10))) (let ((_let_2 (@ tptp.times_times_nat W_3))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y_9)) (@ _let_1 Z_3)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z_3)) (@ _let_1 Y_9))) (or (= W_3 X_10) (= Y_9 Z_3)))))) (forall ((W_3 tptp.int) (Y_9 tptp.int) (X_10 tptp.int) (Z_3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X_10))) (let ((_let_2 (@ tptp.times_times_int W_3))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y_9)) (@ _let_1 Z_3)) (@ (@ tptp.plus_plus_int (@ _let_2 Z_3)) (@ _let_1 Y_9))) (or (= W_3 X_10) (= Y_9 Z_3)))))) (forall ((A_25 tptp.real) (M_3 tptp.real) (B_15 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_25) M_3)) (@ (@ tptp.times_times_real B_15) M_3)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_25) B_15)) M_3))) (forall ((A_25 tptp.nat) (M_3 tptp.nat) (B_15 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_25) M_3)) (@ (@ tptp.times_times_nat B_15) M_3)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_25) B_15)) M_3))) (forall ((A_25 tptp.int) (M_3 tptp.int) (B_15 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_25) M_3)) (@ (@ tptp.times_times_int B_15) M_3)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_25) B_15)) M_3))) (forall ((A_24 tptp.real) (B_14 tptp.real) (C_10 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_24) B_14)) C_10) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_24) C_10)) (@ (@ tptp.times_times_real B_14) C_10)))) (forall ((A_24 tptp.nat) (B_14 tptp.nat) (C_10 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_24) B_14)) C_10) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_24) C_10)) (@ (@ tptp.times_times_nat B_14) C_10)))) (forall ((A_24 tptp.int) (B_14 tptp.int) (C_10 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_24) B_14)) C_10) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_24) C_10)) (@ (@ tptp.times_times_int B_14) C_10)))) (forall ((C_9 tptp.real) (D_3 tptp.real) (A_23 tptp.real) (B_13 tptp.real)) (let ((_let_1 (@ tptp.times_times_real B_13))) (let ((_let_2 (@ tptp.times_times_real A_23))) (= (and (not (= A_23 B_13)) (not (= C_9 D_3))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C_9)) (@ _let_1 D_3)) (@ (@ tptp.plus_plus_real (@ _let_2 D_3)) (@ _let_1 C_9)))))))) (forall ((C_9 tptp.nat) (D_3 tptp.nat) (A_23 tptp.nat) (B_13 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B_13))) (let ((_let_2 (@ tptp.times_times_nat A_23))) (= (and (not (= A_23 B_13)) (not (= C_9 D_3))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C_9)) (@ _let_1 D_3)) (@ (@ tptp.plus_plus_nat (@ _let_2 D_3)) (@ _let_1 C_9)))))))) (forall ((C_9 tptp.int) (D_3 tptp.int) (A_23 tptp.int) (B_13 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B_13))) (let ((_let_2 (@ tptp.times_times_int A_23))) (= (and (not (= A_23 B_13)) (not (= C_9 D_3))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C_9)) (@ _let_1 D_3)) (@ (@ tptp.plus_plus_int (@ _let_2 D_3)) (@ _let_1 C_9)))))))) (forall ((X_9 tptp.real) (Y_8 tptp.real) (Z_2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X_9))) (= (@ _let_1 (@ (@ tptp.plus_plus_real Y_8) Z_2)) (@ (@ tptp.plus_plus_real (@ _let_1 Y_8)) (@ _let_1 Z_2))))) (forall ((X_9 tptp.nat) (Y_8 tptp.nat) (Z_2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X_9))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat Y_8) Z_2)) (@ (@ tptp.plus_plus_nat (@ _let_1 Y_8)) (@ _let_1 Z_2))))) (forall ((X_9 tptp.int) (Y_8 tptp.int) (Z_2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X_9))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Y_8) Z_2)) (@ (@ tptp.plus_plus_int (@ _let_1 Y_8)) (@ _let_1 Z_2))))) (forall ((N tptp.nat)) (= (@ tptp.nat_1 (@ tptp.semiri1621563631at_int N)) N)) (forall ((A_22 tptp.real)) (= (@ (@ tptp.times_times_real A_22) tptp.one_one_real) A_22)) (forall ((A_22 tptp.nat)) (= (@ (@ tptp.times_times_nat A_22) tptp.one_one_nat) A_22)) (forall ((A_22 tptp.int)) (= (@ (@ tptp.times_times_int A_22) tptp.one_one_int) A_22)) (forall ((A_21 tptp.real)) (= (@ (@ tptp.times_times_real A_21) tptp.one_one_real) A_21)) (forall ((A_21 tptp.nat)) (= (@ (@ tptp.times_times_nat A_21) tptp.one_one_nat) A_21)) (forall ((A_21 tptp.int)) (= (@ (@ tptp.times_times_int A_21) tptp.one_one_int) A_21)) (forall ((A_20 tptp.real)) (= (@ (@ tptp.times_times_real A_20) tptp.one_one_real) A_20)) (forall ((A_20 tptp.nat)) (= (@ (@ tptp.times_times_nat A_20) tptp.one_one_nat) A_20)) (forall ((A_20 tptp.int)) (= (@ (@ tptp.times_times_int A_20) tptp.one_one_int) A_20)) (forall ((A_19 tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A_19) A_19)) (forall ((A_19 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A_19) A_19)) (forall ((A_19 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A_19) A_19)) (forall ((A_18 tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A_18) A_18)) (forall ((A_18 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A_18) A_18)) (forall ((A_18 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A_18) A_18)) (forall ((A_17 tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A_17) A_17)) (forall ((A_17 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A_17) A_17)) (forall ((A_17 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A_17) A_17)) (forall ((C_8 tptp.real) (A_16 tptp.real) (B_12 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C_8))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A_16)) (@ _let_1 B_12)) (@ (@ tptp.ord_less_eq_real A_16) B_12)))) (forall ((C_8 tptp.nat) (A_16 tptp.nat) (B_12 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_8))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_16)) (@ _let_1 B_12)) (@ (@ tptp.ord_less_eq_nat A_16) B_12)))) (forall ((C_8 tptp.int) (A_16 tptp.int) (B_12 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_8))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A_16)) (@ _let_1 B_12)) (@ (@ tptp.ord_less_eq_int A_16) B_12)))) (forall ((A_15 tptp.real) (C_7 tptp.real) (B_11 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A_15) C_7)) (@ (@ tptp.plus_plus_real B_11) C_7)) (@ (@ tptp.ord_less_eq_real A_15) B_11))) (forall ((A_15 tptp.nat) (C_7 tptp.nat) (B_11 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A_15) C_7)) (@ (@ tptp.plus_plus_nat B_11) C_7)) (@ (@ tptp.ord_less_eq_nat A_15) B_11))) (forall ((A_15 tptp.int) (C_7 tptp.int) (B_11 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_15) C_7)) (@ (@ tptp.plus_plus_int B_11) C_7)) (@ (@ tptp.ord_less_eq_int A_15) B_11))) (forall ((C_6 tptp.real) (D_2 tptp.real) (A_14 tptp.real) (B_10 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_14) B_10) (=> (@ (@ tptp.ord_less_eq_real C_6) D_2) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A_14) C_6)) (@ (@ tptp.plus_plus_real B_10) D_2))))) (forall ((C_6 tptp.nat) (D_2 tptp.nat) (A_14 tptp.nat) (B_10 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_14) B_10) (=> (@ (@ tptp.ord_less_eq_nat C_6) D_2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A_14) C_6)) (@ (@ tptp.plus_plus_nat B_10) D_2))))) (forall ((C_6 tptp.int) (D_2 tptp.int) (A_14 tptp.int) (B_10 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_14) B_10) (=> (@ (@ tptp.ord_less_eq_int C_6) D_2) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_14) C_6)) (@ (@ tptp.plus_plus_int B_10) D_2))))) (forall ((C_5 tptp.real) (A_13 tptp.real) (B_9 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C_5))) (=> (@ (@ tptp.ord_less_eq_real A_13) B_9) (@ (@ tptp.ord_less_eq_real (@ _let_1 A_13)) (@ _let_1 B_9))))) (forall ((C_5 tptp.nat) (A_13 tptp.nat) (B_9 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_5))) (=> (@ (@ tptp.ord_less_eq_nat A_13) B_9) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_13)) (@ _let_1 B_9))))) (forall ((C_5 tptp.int) (A_13 tptp.int) (B_9 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_5))) (=> (@ (@ tptp.ord_less_eq_int A_13) B_9) (@ (@ tptp.ord_less_eq_int (@ _let_1 A_13)) (@ _let_1 B_9))))) (forall ((C_4 tptp.real) (A_12 tptp.real) (B_8 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_12) B_8) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A_12) C_4)) (@ (@ tptp.plus_plus_real B_8) C_4)))) (forall ((C_4 tptp.nat) (A_12 tptp.nat) (B_8 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_12) B_8) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A_12) C_4)) (@ (@ tptp.plus_plus_nat B_8) C_4)))) (forall ((C_4 tptp.int) (A_12 tptp.int) (B_8 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_12) B_8) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_12) C_4)) (@ (@ tptp.plus_plus_int B_8) C_4)))) (forall ((C_3 tptp.real) (A_11 tptp.real) (B_7 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C_3))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A_11)) (@ _let_1 B_7)) (@ (@ tptp.ord_less_eq_real A_11) B_7)))) (forall ((C_3 tptp.nat) (A_11 tptp.nat) (B_7 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C_3))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_11)) (@ _let_1 B_7)) (@ (@ tptp.ord_less_eq_nat A_11) B_7)))) (forall ((C_3 tptp.int) (A_11 tptp.int) (B_7 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C_3))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A_11)) (@ _let_1 B_7)) (@ (@ tptp.ord_less_eq_int A_11) B_7)))) (forall ((A_10 tptp.real) (C_2 tptp.real) (B_6 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A_10) C_2)) (@ (@ tptp.plus_plus_real B_6) C_2)) (@ (@ tptp.ord_less_eq_real A_10) B_6))) (forall ((A_10 tptp.nat) (C_2 tptp.nat) (B_6 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A_10) C_2)) (@ (@ tptp.plus_plus_nat B_6) C_2)) (@ (@ tptp.ord_less_eq_nat A_10) B_6))) (forall ((A_10 tptp.int) (C_2 tptp.int) (B_6 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A_10) C_2)) (@ (@ tptp.plus_plus_int B_6) C_2)) (@ (@ tptp.ord_less_eq_int A_10) B_6))) (forall ((N tptp.nat) (J tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N)) K))) (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))) (forall ((A_9 tptp.real) (N_7 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A_9) N_7))) (= (@ (@ tptp.times_times_real _let_1) A_9) (@ (@ tptp.times_times_real A_9) _let_1)))) (forall ((A_9 tptp.nat) (N_7 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A_9) N_7))) (= (@ (@ tptp.times_times_nat _let_1) A_9) (@ (@ tptp.times_times_nat A_9) _let_1)))) (forall ((A_9 tptp.int) (N_7 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A_9) N_7))) (= (@ (@ tptp.times_times_int _let_1) A_9) (@ (@ tptp.times_times_int A_9) _let_1)))) (forall ((A_8 tptp.real) (B_5 tptp.real) (N_6 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A_8) B_5)) N_6) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A_8) N_6)) (@ (@ tptp.power_power_real B_5) N_6)))) (forall ((A_8 tptp.nat) (B_5 tptp.nat) (N_6 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A_8) B_5)) N_6) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A_8) N_6)) (@ (@ tptp.power_power_nat B_5) N_6)))) (forall ((A_8 tptp.int) (B_5 tptp.int) (N_6 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A_8) B_5)) N_6) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A_8) N_6)) (@ (@ tptp.power_power_int B_5) N_6)))) (forall ((X_8 tptp.real) (Y_7 tptp.real) (Q_2 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real X_8) Y_7)) Q_2) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X_8) Q_2)) (@ (@ tptp.power_power_real Y_7) Q_2)))) (forall ((X_8 tptp.nat) (Y_7 tptp.nat) (Q_2 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat X_8) Y_7)) Q_2) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X_8) Q_2)) (@ (@ tptp.power_power_nat Y_7) Q_2)))) (forall ((X_8 tptp.int) (Y_7 tptp.int) (Q_2 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int X_8) Y_7)) Q_2) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X_8) Q_2)) (@ (@ tptp.power_power_int Y_7) Q_2)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)) (forall ((I_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I_1))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J) K))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.minus_minus_nat M) N)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K)) (@ (@ tptp.minus_minus_nat M) N))) (forall ((W tptp.int)) (= (@ (@ tptp.times_times_int tptp.pls) W) tptp.pls)) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.bit0 K)) L) (@ tptp.bit0 (@ (@ tptp.times_times_int K) L)))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_eq_int K) L))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))) (@ _let_21 tptp.pls) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) (@ tptp.bit0 L)) (@ (@ tptp.ord_less_eq_int K) L))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K1)) (@ tptp.bit0 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))) (@ _let_10 tptp.zero_zero_int) (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) Z) Z)) (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) tptp.one_one_int) Z)) (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.ord_less_int Z) W) (and (@ (@ tptp.ord_less_eq_int Z) W) (not (= Z W))))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z2)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z2))))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z2)) W) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z2) W)))) (forall ((K tptp.int) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (@ (@ tptp.ord_less_eq_int I_1) J) (@ (@ tptp.ord_less_eq_int (@ _let_1 I_1)) (@ _let_1 J))))) (forall ((V_1 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_1)) (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_1) W)))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int K)) (@ tptp.number_number_of_int L)) (@ (@ tptp.ord_less_eq_int K) L))) (forall ((V_4 tptp.real) (U_2 tptp.real) (Y_6 tptp.real) (X_7 tptp.real) (A_7 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real X_7) A_7) (=> (@ (@ tptp.ord_less_eq_real Y_6) A_7) (=> (@ _let_1 U_2) (=> (@ _let_1 V_4) (=> (= (@ (@ tptp.plus_plus_real U_2) V_4) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U_2) X_7)) (@ (@ tptp.times_times_real V_4) Y_6))) A_7)))))))) (forall ((V_4 tptp.int) (U_2 tptp.int) (Y_6 tptp.int) (X_7 tptp.int) (A_7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X_7) A_7) (=> (@ (@ tptp.ord_less_eq_int Y_6) A_7) (=> (@ _let_1 U_2) (=> (@ _let_1 V_4) (=> (= (@ (@ tptp.plus_plus_int U_2) V_4) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U_2) X_7)) (@ (@ tptp.times_times_int V_4) Y_6))) A_7)))))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_nat (@ tptp.nat_1 X)) (@ tptp.nat_1 Y)) (@ (@ tptp.ord_less_int X) Y)))))) (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat_1 W)) (@ tptp.nat_1 Z)) (@ (@ tptp.ord_less_int W) Z)))) (forall ((Y_5 tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.number267125858f_real Y_5)) (@ (@ tptp.ord_less_eq_int tptp.pls) Y_5))) (forall ((Y_5 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.number_number_of_int Y_5)) (@ (@ tptp.ord_less_eq_int tptp.pls) Y_5))) (forall ((X_6 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.number267125858f_real X_6)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_int X_6) tptp.pls))) (forall ((X_6 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_6)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int X_6) tptp.pls))) (forall ((A_6 tptp.real) (N_5 tptp.nat) (N_4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_6))) (=> (@ (@ tptp.ord_less_eq_nat N_5) N_4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_6) (=> (@ (@ tptp.ord_less_eq_real A_6) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N_4)) (@ _let_1 N_5))))))) (forall ((A_6 tptp.nat) (N_5 tptp.nat) (N_4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_6))) (=> (@ (@ tptp.ord_less_eq_nat N_5) N_4) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_6) (=> (@ (@ tptp.ord_less_eq_nat A_6) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N_4)) (@ _let_1 N_5))))))) (forall ((A_6 tptp.int) (N_5 tptp.nat) (N_4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_6))) (=> (@ (@ tptp.ord_less_eq_nat N_5) N_4) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_6) (=> (@ (@ tptp.ord_less_eq_int A_6) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N_4)) (@ _let_1 N_5))))))) (forall ((X_5 tptp.nat) (Y_4 tptp.nat) (B_4 tptp.real)) (let ((_let_1 (@ tptp.power_power_real B_4))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B_4) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X_5)) (@ _let_1 Y_4)) (@ (@ tptp.ord_less_eq_nat X_5) Y_4))))) (forall ((X_5 tptp.nat) (Y_4 tptp.nat) (B_4 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B_4))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B_4) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X_5)) (@ _let_1 Y_4)) (@ (@ tptp.ord_less_eq_nat X_5) Y_4))))) (forall ((X_5 tptp.nat) (Y_4 tptp.nat) (B_4 tptp.int)) (let ((_let_1 (@ tptp.power_power_int B_4))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B_4) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X_5)) (@ _let_1 Y_4)) (@ (@ tptp.ord_less_eq_nat X_5) Y_4))))) (forall ((M_2 tptp.nat) (N_3 tptp.nat) (A_5 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A_5))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_5) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 M_2)) (@ _let_1 N_3)) (@ (@ tptp.ord_less_eq_nat M_2) N_3))))) (forall ((M_2 tptp.nat) (N_3 tptp.nat) (A_5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_5))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_5) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M_2)) (@ _let_1 N_3)) (@ (@ tptp.ord_less_eq_nat M_2) N_3))))) (forall ((M_2 tptp.nat) (N_3 tptp.nat) (A_5 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A_5))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_5) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M_2)) (@ _let_1 N_3)) (@ (@ tptp.ord_less_eq_nat M_2) N_3))))) (forall ((M tptp.nat) (W tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= M (@ tptp.nat_1 W)) (and (=> _let_1 (= W (@ tptp.semiri1621563631at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))) (forall ((W tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= (@ tptp.nat_1 W) M) (and (=> _let_1 (= W (@ tptp.semiri1621563631at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.plus_plus_nat (@ tptp.nat_1 X)) (@ tptp.nat_1 Y)) (@ tptp.nat_1 (@ (@ tptp.plus_plus_int X) Y))))))) (forall ((Z_1 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z_1) (= (@ tptp.nat_1 (@ (@ tptp.plus_plus_int Z) Z_1)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_1 Z)) (@ tptp.nat_1 Z_1))))))) (forall ((M tptp.nat) (V_1 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V_1))) (= (= (@ tptp.semiri1621563631at_int M) _let_1) (and (= M (@ tptp.nat_1 _let_1)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1))))) (forall ((N tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ (@ tptp.power_power_nat (@ tptp.nat_1 X)) N) (@ tptp.nat_1 (@ (@ tptp.power_power_int X) N))))) (forall ((N tptp.nat) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat_1 (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_nat (@ tptp.nat_1 Z)) N)))) (forall ((V_3 tptp.real) (U_1 tptp.real) (Y_3 tptp.real) (X_4 tptp.real) (A_4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X_4) A_4) (=> (@ (@ tptp.ord_less_real Y_3) A_4) (=> (@ _let_1 U_1) (=> (@ _let_1 V_3) (=> (= (@ (@ tptp.plus_plus_real U_1) V_3) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U_1) X_4)) (@ (@ tptp.times_times_real V_3) Y_3))) A_4)))))))) (forall ((V_3 tptp.int) (U_1 tptp.int) (Y_3 tptp.int) (X_4 tptp.int) (A_4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X_4) A_4) (=> (@ (@ tptp.ord_less_int Y_3) A_4) (=> (@ _let_1 U_1) (=> (@ _let_1 V_3) (=> (= (@ (@ tptp.plus_plus_int U_1) V_3) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U_1) X_4)) (@ (@ tptp.times_times_int V_3) Y_3))) A_4)))))))) (forall ((M tptp.nat) (W tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat_1 W)) M) (@ (@ tptp.ord_less_int W) (@ tptp.semiri1621563631at_int M))))) (forall ((Y_2 tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.number267125858f_real Y_2)) (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 tptp.pls)) Y_2))) (forall ((Y_2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.number_number_of_int Y_2)) (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 tptp.pls)) Y_2))) (forall ((X_3 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.number267125858f_real X_3)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_int X_3) (@ tptp.bit1 tptp.pls)))) (forall ((X_3 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_3)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int X_3) (@ tptp.bit1 tptp.pls)))) (forall ((X_2 tptp.real) (N_2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X_2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_2) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N_2) tptp.one_one_nat))) X_2) (@ _let_1 N_2))))) (forall ((X_2 tptp.nat) (N_2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X_2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_2) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N_2) tptp.one_one_nat))) X_2) (@ _let_1 N_2))))) (forall ((X_2 tptp.int) (N_2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X_2))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_2) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N_2) tptp.one_one_nat))) X_2) (@ _let_1 N_2))))) (forall ((A_3 tptp.real) (B_3 tptp.real)) (= (@ (@ tptp.ord_less_real A_3) B_3) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A_3) B_3)) tptp.zero_zero_real))) (forall ((A_3 tptp.int) (B_3 tptp.int)) (= (@ (@ tptp.ord_less_int A_3) B_3) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A_3) B_3)) tptp.zero_zero_int))) (= tptp.zero_zero_nat _let_38) (= _let_38 tptp.zero_zero_nat) (forall ((A_2 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_2) A_2)) tptp.zero_zero_real))) (forall ((A_2 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_2) A_2)) tptp.zero_zero_int))) (forall ((A_1 tptp.real) (C_1 tptp.real) (B_2 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_1) C_1)) (@ (@ tptp.times_times_real B_2) C_1)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_1) (@ (@ tptp.ord_less_real A_1) B_2)) (and (@ (@ tptp.ord_less_real C_1) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B_2) A_1))))) (forall ((A_1 tptp.int) (C_1 tptp.int) (B_2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_1) C_1)) (@ (@ tptp.times_times_int B_2) C_1)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_1) (@ (@ tptp.ord_less_int A_1) B_2)) (and (@ (@ tptp.ord_less_int C_1) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B_2) A_1))))) (forall ((W tptp.int)) (= (@ tptp.nat_1 (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_nat W))) (forall ((V_1 tptp.int)) (= (@ tptp.number_number_of_nat V_1) (@ tptp.nat_1 (@ tptp.number_number_of_int V_1)))) (= tptp.one_one_nat (@ tptp.nat_1 tptp.one_one_int)) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.ord_less_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) M))))) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)) (forall ((I_1 tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I_1) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K)) J))) (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))) (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (= (@ _let_1 (@ tptp.bit1 K)) (@ _let_1 K)))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_eq_int K) L))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))) (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (= (@ _let_1 (@ tptp.bit0 K)) (@ _let_1 K)))) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) tptp.pls) (@ (@ tptp.ord_less_eq_int K) tptp.pls))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (@ _let_1 B))))) (forall ((K tptp.int) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I_1) J) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I_1)) (@ _let_1 J)))))) (@ _let_10 tptp.one_one_int) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.plus_plus_int X) Y)))))) (forall ((Z_1 tptp.int) (Z tptp.int) (W_2 tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int W_2) W) (=> (@ (@ tptp.ord_less_eq_int Z_1) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int W_2) Z_1)) (@ (@ tptp.plus_plus_int W) Z))))) (forall ((Z tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1621563631at_int Z))) (forall ((P (-> tptp.int Bool))) (= (exists ((X_1 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P X_1))) (exists ((X_1 tptp.nat)) (@ P (@ tptp.semiri1621563631at_int X_1))))) (forall ((P (-> tptp.int Bool))) (= (forall ((X_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ P X_1))) (forall ((X_1 tptp.nat)) (@ P (@ tptp.semiri1621563631at_int X_1))))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1621563631at_int N))) (forall ((N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.power_power_int X) N))))) (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) Z) (exists ((N_1 tptp.nat)) (= Z (@ (@ tptp.plus_plus_int W) (@ tptp.semiri1621563631at_int N_1)))))) (forall ((X tptp.int) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat Y) Z)) (@ (@ tptp.times_times_int (@ _let_1 Y)) (@ _let_1 Z))))) (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_nat (@ tptp.nat_1 W)) (@ tptp.nat_1 Z)) (@ (@ tptp.ord_less_int W) Z)))) (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat_1 W)) (@ tptp.nat_1 Z)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int W) Z)))) (forall ((M tptp.nat) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.nat_1 Z)) (@ (@ tptp.ord_less_int (@ tptp.semiri1621563631at_int M)) Z))) (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (not (or (and (@ (@ tptp.ord_less_nat A) B) (not (@ P tptp.zero_zero_nat))) (exists ((D_1 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D_1)) (not (@ P D_1)))))))) (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (and (=> (@ (@ tptp.ord_less_nat A) B) (@ P tptp.zero_zero_nat)) (forall ((D_1 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D_1)) (@ P D_1)))))) (forall ((V_1 tptp.int)) (= (= tptp.zero_zero_nat (@ tptp.number_number_of_nat V_1)) (@ (@ tptp.ord_less_eq_int V_1) tptp.pls))) (forall ((V_1 tptp.int)) (= (= (@ tptp.number_number_of_nat V_1) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int V_1) tptp.pls))) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int tptp.pls) (@ tptp.bit1 K)) (@ (@ tptp.ord_less_eq_int tptp.pls) K))) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) tptp.pls) (@ (@ tptp.ord_less_int K) tptp.pls))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_eq_int K) L))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) (@ tptp.bit0 L)) (@ (@ tptp.ord_less_int K) L))) (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K1)) (@ tptp.bit0 K2)) (@ (@ tptp.ord_less_int K1) K2))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.bit1 K)) L) (@ (@ tptp.plus_plus_int (@ tptp.bit0 (@ (@ tptp.times_times_int K) L))) L))) (forall ((N tptp.int) (M tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (and (= M tptp.one_one_int) (= N tptp.one_one_int))))) (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1621563631at_int N)) tptp.zero_zero_int) (= N tptp.zero_zero_nat))) (= (@ tptp.succ tptp.pls) _let_1) (forall ((K tptp.int)) (= (@ tptp.succ (@ tptp.bit0 K)) (@ tptp.bit1 K))) (forall ((K tptp.int)) (= (@ tptp.succ (@ tptp.bit1 K)) (@ tptp.bit0 (@ tptp.succ K)))) (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W) Z))) (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z) (@ (@ tptp.ord_less_int W) Z))) (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int W) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z))) (forall ((K tptp.int)) (= (@ tptp.succ K) (@ (@ tptp.plus_plus_int K) tptp.one_one_int))) (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat_1 Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))) (= _let_37 (@ tptp.nat_1 _let_36)) (forall ((P (-> tptp.nat Bool)) (I_1 tptp.int)) (= (@ P (@ tptp.nat_1 I_1)) (and (forall ((N_1 tptp.nat)) (=> (= I_1 (@ tptp.semiri1621563631at_int N_1)) (@ P N_1))) (=> (@ (@ tptp.ord_less_int I_1) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))) (@ _let_10 _let_36) (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)))) (forall ((K tptp.nat) (I_1 tptp.int) (J tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.semiri1621563631at_int K)))) (=> (@ (@ tptp.ord_less_int I_1) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_int (@ _let_1 I_1)) (@ _let_1 J)))))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.bit1 K)) (@ tptp.bit1 L)) (@ tptp.bit0 (@ (@ tptp.plus_plus_int K) (@ tptp.succ L))))) (= _let_3 (@ tptp.nat_1 _let_27)) (@ _let_10 _let_27) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.bit1 tptp.pls))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int A) (@ _let_2 (@ tptp.number_number_of_nat (@ tptp.bit0 _let_1)))) (@ _let_2 (@ tptp.number_number_of_nat (@ tptp.bit1 _let_1))))))) (forall ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int X) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (or (= X tptp.zero_zero_int) (= X tptp.one_one_int))))) (forall ((A tptp.int) (P_1 tptp.int)) (let ((_let_1 (@ tptp.nat_1 P_1))) (let ((_let_2 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) P_1) (= (@ _let_2 _let_1) (@ (@ tptp.times_times_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat _let_1) tptp.one_one_nat)))))))) (forall ((R_1 tptp.int) (Q tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (= A (@ (@ tptp.plus_plus_int R_1) (@ (@ tptp.times_times_int A) Q))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R_1) (@ (@ tptp.ord_less_eq_int Q) tptp.one_one_int))))) (forall ((R_1 tptp.int) (Q tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (= A (@ (@ tptp.plus_plus_int R_1) (@ (@ tptp.times_times_int A) Q))) (=> (@ (@ tptp.ord_less_int R_1) A) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Q))))) (not (=> _let_32 (not _let_31))) (forall ((B_1 tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q_1)) R_2)) (=> (@ (@ tptp.ord_less_int R_2) B_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1) (@ _let_1 Q_1)))))) (forall ((B_1 tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q_1)) R_2)) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R_2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1) (@ (@ tptp.ord_less_eq_int Q_1) tptp.zero_zero_int))))) (not (@ tptp.twoSqu919416604sum2sq (@ _let_28 (@ _let_5 _let_34)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (@ _let_33 _let_11) (@ (@ tptp.ord_less_int tptp.t) _let_11) (@ tptp.twoSqu919416604sum2sq _let_30) (and _let_32 _let_31) (not (forall ((X_1 tptp.int) (Y_1 tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.number_number_of_nat _let_1))) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_1) _let_2)) (@ (@ tptp.power_power_int Y_1) _let_2)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1621563631at_int tptp.n))))))))) (= _let_26 _let_30) (@ tptp.zprime _let_11) (=> (= tptp.t tptp.one_one_int) (exists ((X_1 tptp.int) (Y_1 tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.number_number_of_nat _let_1))) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_1) _let_2)) (@ (@ tptp.power_power_int Y_1) _let_2)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)))))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)) (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))) (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat M) N) (@ (@ tptp.times_times_nat N) M))) (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ (@ tptp.times_times_nat (@ _let_1 N)) K) (@ _let_1 (@ (@ tptp.times_times_nat N) K))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I_1) K)) (@ (@ tptp.times_times_nat J) K)))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I_1)) (@ _let_1 J))))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_nat J) K) (@ _let_1 K))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))) (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I_1) K)) (@ (@ tptp.times_times_nat J) L))))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) Y)) tptp.zero_zero_real))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_eq_real X) Y)))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ tptp.semiri1621563631at_int (@ (@ tptp.minus_minus_nat M) N))))) (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.pls) K)) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.bit0 K)) (@ tptp.bit0 L)) (@ tptp.bit0 (@ (@ tptp.minus_minus_int K) L)))) (forall ((Z1 tptp.int) (Z2 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z2)) W) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z2) W)))) (forall ((W tptp.int) (Z1 tptp.int) (Z2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z2)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z2))))) (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= M N) (= K tptp.zero_zero_nat))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N) K)) (or (= M N) (= K tptp.zero_zero_nat)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))) (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B) C)) (= A B)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat M) N) (or (@ (@ tptp.ord_less_nat M) N) (= M N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (not (= M N))))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real X) Y) (and (@ (@ tptp.ord_less_eq_real X) Y) (not (= X Y))))) (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real X) Y) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))) (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J) L))))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J) K)))) (forall ((M tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))) (forall ((M tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat M) N) (exists ((K_1 tptp.nat)) (= N (@ (@ tptp.plus_plus_nat M) K_1))))) (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))) (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))) (forall ((N tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.times_times_nat N) M) tptp.one_one_nat) (and (= N tptp.one_one_nat) (= M tptp.one_one_nat)))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)) (forall ((M tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N)) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))) (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N))))) (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) Z) Z)) (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M) N)))))) (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))) (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N) K)) (= M N)))))) (forall ((I_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I_1) N) (= (@ _let_1 (@ _let_1 I_1)) I_1)))) (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L)) (@ (@ tptp.minus_minus_nat N) L)))) (forall ((L tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)) (forall ((Z1 tptp.real) (Z2 tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real Z1) Z2)) W) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real Z1) W)) (@ (@ tptp.times_times_real Z2) W)))) (forall ((X tptp.int) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.power_power_int (@ _let_1 Y)) Z) (@ _let_1 (@ (@ tptp.times_times_nat Y) Z))))) (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real Z))) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y))))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.bit1 K)) (@ tptp.bit1 L)) (@ tptp.bit0 (@ (@ tptp.minus_minus_int K) L)))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.bit1 K)) (@ tptp.bit0 L)) (@ tptp.bit1 (@ (@ tptp.minus_minus_int K) L)))) (forall ((L tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int tptp.pls))) (= (@ _let_1 (@ tptp.bit0 L)) (@ tptp.bit0 (@ _let_1 L))))) (forall ((A tptp.int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int A) tptp.one_one_int))) (let ((_let_2 (@ tptp.ord_less_int X))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (=> (@ _let_2 A) (=> (not (= X _let_1)) (@ _let_2 _let_1))))))) (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int K) L) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int K) L)) tptp.zero_zero_int))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I_1) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I_1)) (@ _let_1 J)))))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat I_1) K)) (@ (@ tptp.times_times_nat J) K))))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))) (forall ((X tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X) X))) (= X tptp.zero_zero_real))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)))))) (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.times_times_real X) Y)))))) (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_real X) Y)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N)) (or (= N tptp.one_one_nat) (= M tptp.zero_zero_nat)))) (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat))) (forall ((X tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B) C))))) (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_nat M) N)))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.times_times_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ tptp.semiri1621563631at_int (@ (@ tptp.times_times_nat X) Y)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ tptp.semiri1621563631at_int (@ (@ tptp.times_times_nat M) N)))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1621563631at_int (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)))) (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat I_1) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I_1) K)) J)))) (forall ((J tptp.nat) (K tptp.nat) (I_1 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J) K)) I_1) (@ (@ tptp.ord_less_eq_nat J) (@ (@ tptp.plus_plus_nat I_1) K)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) K)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))) (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I_1))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K))))) (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.ord_less_eq_nat I_1) (@ (@ tptp.minus_minus_nat J) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) J)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M) N)) N) M))) (forall ((K tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (= (@ (@ tptp.minus_minus_nat J) I_1) K) (= J (@ (@ tptp.plus_plus_nat K) I_1))))) (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I_1))) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J) K)))))) (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I_1)) K)))) (forall ((I_1 tptp.nat) (K tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J) I_1)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J) K)) I_1)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ (@ tptp.ord_less_eq_nat X) Y))) (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1621563631at_int M)) (@ tptp.semiri1621563631at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ tptp.twoSqu919416604sum2sq X) (=> (@ tptp.twoSqu919416604sum2sq Y) (@ tptp.twoSqu919416604sum2sq (@ (@ tptp.times_times_int X) Y))))) (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) (@ (@ tptp.minus_minus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_int W) Z))) (forall ((V_1 tptp.int) (V_2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int V_1))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.number_number_of_nat V_1)) (@ tptp.number_number_of_nat V_2)) (=> (not (@ _let_1 V_2)) (@ _let_1 tptp.pls))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat_1 X)) (@ tptp.nat_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y)))))) (forall ((Z tptp.int) (Z_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z_1) (=> (@ (@ tptp.ord_less_eq_int Z_1) Z) (= (@ tptp.nat_1 (@ (@ tptp.minus_minus_int Z) Z_1)) (@ (@ tptp.minus_minus_nat (@ tptp.nat_1 Z)) (@ tptp.nat_1 Z_1)))))) (forall ((Z_1 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat_1 (@ (@ tptp.times_times_int Z) Z_1)) (@ (@ tptp.times_times_nat (@ tptp.nat_1 Z)) (@ tptp.nat_1 Z_1))))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.times_times_nat (@ tptp.nat_1 X)) (@ tptp.nat_1 Y)) (@ tptp.nat_1 (@ (@ tptp.times_times_int X) Y))))))) (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat M) N))) (let ((_let_2 (= M tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)) N)))))))) (forall ((Z tptp.int) (W tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat_1 W)) (@ tptp.nat_1 Z)) (@ (@ tptp.ord_less_eq_int W) Z)))) (forall ((P_1 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat P_1))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (= M tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.one_one_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.times_times_nat P_1) (@ _let_1 (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) Z) (@ (@ tptp.plus_plus_nat Z) Z))) (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.plus_plus_nat Z) Z))) (forall ((V_2 tptp.int) (K tptp.nat) (V_1 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V_1)) (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V_2)) K)))) (let ((_let_2 (@ (@ tptp.ord_less_int V_1) tptp.pls))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ (@ tptp.times_times_int V_1) V_2))) K))))))) (forall ((V_2 tptp.int) (V_1 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V_1)) (@ tptp.number_number_of_nat V_2)))) (let ((_let_2 (@ (@ tptp.ord_less_int V_1) tptp.pls))) (and (=> _let_2 (= _let_1 tptp.zero_zero_nat)) (=> (not _let_2) (= _let_1 (@ tptp.number_number_of_nat (@ (@ tptp.times_times_int V_1) V_2)))))))) (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.number_number_of_nat _let_1))) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real (@ tptp.bit0 _let_1))) (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.number267125858f_real _let_1)) X)) _let_2))))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.number267125858f_real (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N))) (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) C) (=> (@ (@ tptp.ord_less_int B) C) (or (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int B) A))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B) _let_1))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat X) Y)) (@ (@ tptp.minus_minus_nat X) Y))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit1 tptp.pls))) (let ((_let_2 (@ tptp.bit1 _let_1))) (let ((_let_3 (@ tptp.number_number_of_nat _let_2))) (let ((_let_4 (@ tptp.power_power_int B))) (let ((_let_5 (@ tptp.number_number_of_nat (@ tptp.bit0 _let_1)))) (let ((_let_6 (@ tptp.times_times_int (@ tptp.number_number_of_int _let_2)))) (let ((_let_7 (@ tptp.power_power_int A))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int A) B)) _let_3) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int (@ _let_7 _let_3)) (@ (@ tptp.times_times_int (@ _let_6 (@ _let_7 _let_5))) B))) (@ (@ tptp.times_times_int (@ _let_6 A)) (@ _let_4 _let_5)))) (@ _let_4 _let_3))))))))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.number_number_of_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int A) B)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int A) _let_2)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int _let_1)) A)) B))) (@ (@ tptp.power_power_int B) _let_2)))))) (forall ((B tptp.int) (Q tptp.int) (R_1 tptp.int) (B_1 tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q_1)) R_2))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q)) R_1) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R_1) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R_2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1) (=> (@ (@ tptp.ord_less_eq_int B_1) B) (@ (@ tptp.ord_less_eq_int Q_1) Q))))))))) (forall ((B tptp.int) (Q_1 tptp.int) (R_2 tptp.int) (Q tptp.int) (R_1 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_2 Q_1)) R_2)) (@ (@ tptp.plus_plus_int (@ _let_2 Q)) R_1)) (=> (@ (@ tptp.ord_less_eq_int R_1) tptp.zero_zero_int) (=> (@ _let_1 R_1) (=> (@ _let_1 R_2) (@ (@ tptp.ord_less_eq_int Q) Q_1)))))))) (forall ((B tptp.int) (Q tptp.int) (R_1 tptp.int) (B_1 tptp.int) (Q_1 tptp.int) (R_2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q_1)) R_2))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q)) R_1) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R_2) B_1) (=> (@ _let_1 R_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1) (=> (@ (@ tptp.ord_less_eq_int B_1) B) (@ (@ tptp.ord_less_eq_int Q) Q_1)))))))))) (forall ((B tptp.int) (Q_1 tptp.int) (R_2 tptp.int) (Q tptp.int) (R_1 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q_1)) R_2)) (@ (@ tptp.plus_plus_int (@ _let_1 Q)) R_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R_2) (=> (@ (@ tptp.ord_less_int R_2) B) (=> (@ (@ tptp.ord_less_int R_1) B) (@ (@ tptp.ord_less_eq_int Q_1) Q))))))) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int tptp.x) _let_3)) (@ (@ tptp.power_power_int tptp.y) _let_3)) _let_29) (forall ((P_1 tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.number_number_of_int _let_1))) (=> (@ (@ tptp.ord_less_int _let_2) P_1) (= (@ (@ tptp.minus_minus_nat (@ tptp.nat_1 P_1)) (@ tptp.number_number_of_nat _let_1)) (@ tptp.nat_1 (@ (@ tptp.minus_minus_int P_1) _let_2))))))) (forall ((P_1 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (@ (@ tptp.ord_less_int _let_1) P_1) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat_1 (@ (@ tptp.minus_minus_int P_1) _let_1)))))) (not (forall ((T_1 tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int tptp.s) (@ tptp.number_number_of_nat _let_1))) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)) T_1)))))) (forall ((W tptp.real)) (@ (@ tptp.ord_less_eq_real W) W)) (forall ((Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real Z) W) (@ (@ tptp.times_times_real W) Z))) (forall ((Z tptp.real) (W tptp.real)) (or (@ (@ tptp.ord_less_eq_real Z) W) (@ (@ tptp.ord_less_eq_real W) Z))) (forall ((Z1 tptp.real) (Z2 tptp.real) (Z3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z1))) (= (@ (@ tptp.times_times_real (@ _let_1 Z2)) Z3) (@ _let_1 (@ (@ tptp.times_times_real Z2) Z3))))) (forall ((K tptp.real) (I_1 tptp.real) (J tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real I_1))) (=> (@ _let_1 J) (=> (@ (@ tptp.ord_less_eq_real J) K) (@ _let_1 K))))) (forall ((Z tptp.real) (W tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Z) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (= Z W)))) (@ tptp.zprime _let_27) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) C) (= A (@ (@ tptp.plus_plus_int C) B)))) (@ _let_25 _let_26) (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.number_number_of_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.number267125858f_real _let_1)) X)) Y)))))) (= _let_24 _let_26) (@ _let_25 _let_24) _let_16 (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_int M) N)) (=> (@ _let_1 N) (@ _let_1 M))))) (forall ((M tptp.int) (N tptp.int) (P_1 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int P_1))) (=> (@ tptp.zprime P_1) (=> (@ _let_1 (@ (@ tptp.times_times_int M) N)) (or (@ _let_1 M) (@ _let_1 N)))))) (@ _let_22 tptp.min) (forall ((N tptp.int) (M tptp.int)) (=> (@ (@ tptp.dvd_dvd_int N) M) (or (@ (@ tptp.ord_less_eq_int M) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int N) M)))) (forall ((A tptp.int) (N tptp.nat) (P_1 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int P_1))) (=> (@ tptp.zprime P_1) (=> (@ _let_1 (@ (@ tptp.power_power_int A) N)) (@ _let_1 A))))) (forall ((N tptp.int) (M tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_int M) N) (not (@ (@ tptp.dvd_dvd_int N) M))))) (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (=> (not (= K tptp.zero_zero_int)) (@ (@ tptp.dvd_dvd_int M) N))))) (forall ((N tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 M) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_int M) N) (=> (@ (@ tptp.dvd_dvd_int N) M) (= M N))))))) (forall ((K tptp.int) (N tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (= (@ _let_1 (@ (@ tptp.plus_plus_int N) (@ (@ tptp.times_times_int K) M))) (@ _let_1 N)))) (forall ((C tptp.int) (X tptp.int) (T tptp.int) (A tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (let ((_let_2 (@ tptp.dvd_dvd_int A))) (=> (@ _let_2 D) (= (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.times_times_int C) D))) T))))))) (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.min))) (= (@ _let_1 (@ tptp.bit1 K)) (@ _let_1 K)))) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K)) tptp.min) (@ (@ tptp.ord_less_int K) tptp.min))) (@ _let_20 tptp.pls) (not (@ _let_23 tptp.min)) (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.min))) (= (@ _let_1 (@ tptp.bit0 K)) (@ _let_1 K)))) (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.min))) (= (@ _let_1 (@ tptp.bit1 K)) (@ _let_1 K)))) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) tptp.min) (@ (@ tptp.ord_less_eq_int K) tptp.min))) (@ _let_20 tptp.zero_zero_int) (@ _let_22 tptp.pls) (not (@ _let_21 tptp.min)) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) tptp.min) (@ (@ tptp.ord_less_eq_int K) tptp.min))) (not (= _let_9 _let_15)) (not (@ _let_20 tptp.min)) (forall ((L tptp.int)) (not (= tptp.min (@ tptp.bit0 L)))) (forall ((K tptp.int)) (not (= (@ tptp.bit0 K) tptp.min))) (not (= tptp.min tptp.pls)) (not (= tptp.pls tptp.min)) (= (@ tptp.bit1 tptp.min) tptp.min) (forall ((L tptp.int)) (= (= tptp.min (@ tptp.bit1 L)) (= tptp.min L))) (forall ((K tptp.int)) (= (= (@ tptp.bit1 K) tptp.min) (= K tptp.min))) _let_19 (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.min) (@ tptp.succ K))) (forall ((Z tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z) N) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int Z) N)))) (forall ((P_1 tptp.int) (Y tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int P_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.power_power_int Y) N)))))) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.min) (@ tptp.bit0 K)) (@ (@ tptp.ord_less_int tptp.min) K))) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K)) tptp.min) (@ (@ tptp.ord_less_eq_int K) tptp.min))) (forall ((L tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.pls) (@ tptp.bit1 L)) (@ tptp.bit1 (@ (@ tptp.minus_minus_int tptp.min) L)))) (forall ((L tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int tptp.min))) (= (@ _let_1 (@ tptp.bit1 L)) (@ tptp.bit0 (@ _let_1 L))))) (forall ((L tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int tptp.min))) (= (@ _let_1 (@ tptp.bit0 L)) (@ tptp.bit1 (@ _let_1 L))))) (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int tptp.min))) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (or (and (= M tptp.one_one_int) (= N tptp.one_one_int)) (and (= M _let_1) (= N _let_1)))))) (forall ((M tptp.int) (N tptp.int)) (=> (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (or (= M tptp.one_one_int) (= M (@ tptp.number_number_of_int tptp.min))))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int) (P_1 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int P_1) N)))) (=> (@ tptp.zprime P_1) (=> (not (@ (@ tptp.dvd_dvd_int P_1) B)) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (@ _let_1 A)))))) (forall ((N tptp.nat) (B tptp.int) (A tptp.int) (P_1 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int P_1) N)))) (=> (@ tptp.zprime P_1) (=> (not (@ (@ tptp.dvd_dvd_int P_1) A)) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (@ _let_1 B)))))) (forall ((Y tptp.int) (N tptp.nat) (P_1 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int P_1))) (=> (@ tptp.zprime P_1) (=> (@ _let_1 (@ (@ tptp.power_power_int Y) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 Y)))))) _let_17 (@ (@ _let_14 _let_15) _let_11) (=> (not _let_17) (not _let_16)) (@ (@ (@ tptp.zcong _let_12) _let_15) _let_11) (and (@ _let_10 tptp.s) (@ (@ tptp.ord_less_int tptp.s) _let_11) (@ (@ (@ tptp.zcong tptp.s1) tptp.s) _let_11)) (not (forall ((S1 tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (not (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int S1) (@ tptp.number_number_of_nat _let_1))) (@ tptp.number_number_of_int tptp.min)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_1))) tptp.m)) tptp.one_one_int)))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.dvd_dvd_nat A) B) (@ (@ tptp.dvd_dvd_nat (@ _let_1 A)) (@ _let_1 B))))) (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))))) (forall ((X tptp.int) (P_1 tptp.int)) (= (@ (@ (@ tptp.zcong X) tptp.zero_zero_int) P_1) (@ (@ tptp.dvd_dvd_int P_1) X))) (forall ((A tptp.int) (M tptp.int)) (= (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) M) (@ (@ tptp.dvd_dvd_int M) A))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (not (@ (@ tptp.dvd_dvd_nat N) M))))) (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (or (= B tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat A) B)))) (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M) N)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 M)))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 M) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 N)))))) (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.dvd_dvd_nat A) B)))) (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N)) Y) (@ (@ tptp.dvd_dvd_nat X) Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)) (@ (@ tptp.dvd_dvd_nat X) Y))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat X) Y) (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)))) (forall ((N tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y) N)))) (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))) (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 N)))) (forall ((B tptp.nat) (D tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D))) (=> (@ _let_1 A) (=> (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (@ _let_1 B))))) (forall ((M tptp.int)) (@ (@ (@ tptp.zcong M) tptp.zero_zero_int) M)) (forall ((C tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (@ (@ (@ tptp.zcong A) B) M) (@ (@ (@ tptp.zcong (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) M))) (forall ((D tptp.int) (C tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.zcong A))) (=> (@ (@ _let_1 B) M) (=> (= B C) (=> (@ (@ (@ tptp.zcong C) D) M) (@ (@ _let_1 D) M)))))) (forall ((Z tptp.nat) (X tptp.int) (Y tptp.int) (M tptp.int)) (=> (@ (@ (@ tptp.zcong X) Y) M) (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int X) Z)) (@ (@ tptp.power_power_int Y) Z)) M))) (forall ((M tptp.int) (Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ _let_1 M) (=> (@ (@ (@ tptp.zcong X) Y) M) (=> (@ (@ tptp.ord_less_int X) M) (=> (@ (@ tptp.ord_less_int Y) M) (= X Y))))))))) (forall ((M tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) M) (not (@ (@ (@ tptp.zcong X) tptp.zero_zero_int) M))))) (forall ((C tptp.int) (D tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.zcong C))) (=> (@ (@ (@ tptp.zcong A) B) M) (= (@ (@ _let_1 (@ (@ tptp.times_times_int A) D)) M) (@ (@ _let_1 (@ (@ tptp.times_times_int B) D)) M))))) (forall ((C tptp.int) (D tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.times_times_int D))) (let ((_let_2 (@ tptp.zcong C))) (=> (@ (@ (@ tptp.zcong A) B) M) (= (@ (@ _let_2 (@ _let_1 A)) M) (@ (@ _let_2 (@ _let_1 B)) M)))))) (forall ((M tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) M) (=> (@ (@ (@ tptp.zcong X) tptp.zero_zero_int) M) (= X tptp.zero_zero_int))))) (forall ((Y tptp.int) (X tptp.int) (P_1 tptp.int)) (=> (@ tptp.zprime P_1) (=> (not (@ (@ (@ tptp.zcong X) tptp.zero_zero_int) P_1)) (=> (not (@ (@ (@ tptp.zcong Y) tptp.zero_zero_int) P_1)) (not (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int X) Y)) tptp.zero_zero_int) P_1)))))) (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat K) N)))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M) N))))) (forall ((B tptp.int) (A tptp.int) (P_1 tptp.int)) (=> (@ tptp.zprime P_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) P_1) (or (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) P_1) (@ (@ (@ tptp.zcong B) tptp.zero_zero_int) P_1)))))) (forall ((B tptp.int) (A tptp.int) (P_1 tptp.int)) (=> (@ tptp.zprime P_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (and (not (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) P_1)) (not (@ (@ (@ tptp.zcong B) tptp.zero_zero_int) P_1))) (not (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) P_1)))))) (forall ((X tptp.nat) (Q tptp.nat) (N tptp.nat) (R_1 tptp.nat)) (=> (= X (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Q) N)) R_1)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) R_1) (=> (@ (@ tptp.ord_less_nat R_1) N) (not (@ (@ tptp.dvd_dvd_nat N) X)))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) N)) M) (= N tptp.one_one_nat)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N) M)) M) (= N tptp.one_one_nat)))) (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat_1 X)) (@ tptp.nat_1 Y)) (@ (@ tptp.dvd_dvd_int X) Y)))))) (forall ((I_1 tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I_1))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I_1) (@ (@ tptp.ord_less_eq_nat M) N))))) (forall ((Z tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat_1 Z)) M) (and (=> _let_1 (@ (@ tptp.dvd_dvd_int Z) (@ tptp.semiri1621563631at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))) (forall ((X tptp.int) (P_1 tptp.int)) (let ((_let_1 (@ tptp.zcong X))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P_1) (=> (@ (@ _let_1 (@ tptp.number_number_of_int tptp.min)) P_1) (not (@ (@ _let_1 tptp.one_one_int) P_1)))))) (forall ((Y tptp.int) (X tptp.int) (P_1 tptp.int)) (=> (not (@ (@ (@ tptp.zcong X) tptp.zero_zero_int) P_1)) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int Y) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) X) P_1) (not (@ (@ tptp.dvd_dvd_int P_1) Y))))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat N) M) (or (= M tptp.zero_zero_nat) (= M N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N)) M)))) (forall ((M tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) M)) tptp.one_one_int))) (=> (@ tptp.zprime _let_1) (= (@ (@ tptp.legendre (@ tptp.number_number_of_int tptp.min)) _let_1) tptp.one_one_int)))) (@ (@ _let_14 _let_12) _let_11) (exists ((X_1 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (@ (@ tptp.ord_less_int X_1) _let_1) (@ (@ (@ tptp.zcong tptp.s1) X_1) _let_1) (forall ((Y_1 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y_1) (@ (@ tptp.ord_less_int Y_1) _let_1) (@ (@ (@ tptp.zcong tptp.s1) Y_1) _let_1)) (= Y_1 X_1))))))) (forall ((X tptp.nat)) (@ (@ tptp.dvd_dvd_nat X) X)) (not (forall ((S tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.m)) tptp.one_one_int))) (not (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) S) (@ (@ tptp.ord_less_int S) _let_1) (@ (@ (@ tptp.zcong tptp.s1) S) _let_1)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) Y))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat Y) X))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat Z))) (let ((_let_2 (@ tptp.dvd_dvd_nat X))) (let ((_let_3 (@ tptp.dvd_dvd_nat Y))) (=> (and (@ _let_2 Y) (not (@ _let_3 X))) (=> (and (@ _let_3 Z) (not (@ _let_1 Y))) (and (@ _let_2 Z) (not (@ _let_1 X))))))))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat A) B))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat B) A))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat X))) (let ((_let_2 (@ tptp.dvd_dvd_nat Y))) (=> (and (@ _let_1 Y) (not (@ _let_2 X))) (=> (@ _let_2 Z) (and (@ _let_1 Z) (not (@ (@ tptp.dvd_dvd_nat Z) X)))))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (and (@ _let_1 B) (not (@ (@ tptp.dvd_dvd_nat B) A))) (=> (= B C) (and (@ _let_1 C) (not (@ (@ tptp.dvd_dvd_nat C) A))))))) (forall ((P Bool) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) Y))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat Y) X))) (=> (and _let_1 (not _let_2)) (=> (and _let_2 (not _let_1)) P))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (and (@ (@ tptp.dvd_dvd_nat X) Y) (not (@ (@ tptp.dvd_dvd_nat Y) X))) (not (= Y X)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (and (@ (@ tptp.dvd_dvd_nat X) Y) (not (@ (@ tptp.dvd_dvd_nat Y) X))) (not (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) Y))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat Y) X))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) Y))) (=> (and _let_1 (not (@ (@ tptp.dvd_dvd_nat Y) X))) _let_1))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) Y))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat Y) X))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (and (@ (@ tptp.dvd_dvd_nat X) Y) (not (@ (@ tptp.dvd_dvd_nat Y) X))) (not (= X Y)))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat Z))) (let ((_let_2 (@ tptp.dvd_dvd_nat X))) (=> (@ _let_2 Y) (=> (and (@ (@ tptp.dvd_dvd_nat Y) Z) (not (@ _let_1 Y))) (and (@ _let_2 Z) (not (@ _let_1 X)))))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (= A B) (=> (and (@ (@ tptp.dvd_dvd_nat B) C) (not (@ _let_1 B))) (and (@ (@ tptp.dvd_dvd_nat A) C) (not (@ _let_1 A))))))) (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.dvd_dvd_nat Y) Z) (@ _let_1 Z))))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (=> (@ (@ tptp.dvd_dvd_nat Y) X) (= X Y)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))) (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (= A B) (=> (@ (@ tptp.dvd_dvd_nat B) C) (@ (@ tptp.dvd_dvd_nat A) C)))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat A) B))) (=> _let_1 (=> (not (= A B)) (and _let_1 (not (@ (@ tptp.dvd_dvd_nat B) A))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) Y))) (=> _let_1 (or (and _let_1 (not (@ (@ tptp.dvd_dvd_nat Y) X))) (= X Y))))) (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat Y) X) (= (@ (@ tptp.dvd_dvd_nat X) Y) (= X Y)))) (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.dvd_dvd_nat X) Y))) (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat A) B))) (=> (not (= A B)) (=> _let_1 (and _let_1 (not (@ (@ tptp.dvd_dvd_nat B) A))))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (and (@ (@ tptp.dvd_dvd_nat X) Y) (not (@ (@ tptp.dvd_dvd_nat Y) X))))) (= _let_1 _let_1))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) Y))) (= (and _let_1 (not (@ (@ tptp.dvd_dvd_nat Y) X))) (and _let_1 (not (= X Y)))))) (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) Y))) (= _let_1 (or (and _let_1 (not (@ (@ tptp.dvd_dvd_nat Y) X))) (= X Y))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (= X Y) (and (@ (@ tptp.dvd_dvd_nat X) Y) (@ (@ tptp.dvd_dvd_nat Y) X)))) (forall ((X tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X) X))) (not (and _let_1 (not _let_1))))) (forall ((X tptp.nat) (Y tptp.nat)) (= (and (@ (@ tptp.dvd_dvd_nat X) Y) (@ (@ tptp.dvd_dvd_nat Y) X)) (= X Y))) (forall ((J tptp.nat) (K tptp.nat) (M tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.number_number_of_int tptp.min)))) (let ((_let_2 (@ _let_1 K))) (let ((_let_3 (@ _let_1 J))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) M) (=> (@ (@ (@ tptp.zcong _let_3) _let_2) M) (= _let_3 _let_2))))))) (forall ((M tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) M) (not (@ (@ (@ tptp.zcong tptp.one_one_int) (@ tptp.number_number_of_int tptp.min)) M)))) (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_int tptp.min))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (or (= _let_2 tptp.one_one_int) (= _let_2 _let_1))))) (forall ((A tptp.int) (P_1 tptp.int)) (let ((_let_1 (@ (@ tptp.legendre A) P_1))) (let ((_let_2 (@ (@ tptp.quadRes P_1) A))) (let ((_let_3 (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) P_1))) (and (=> _let_3 (= _let_1 tptp.zero_zero_int)) (=> (not _let_3) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (@ tptp.number_number_of_int tptp.min)))))))))) (forall ((M tptp.int) (X tptp.int)) (= (@ (@ tptp.quadRes M) X) (exists ((Y_1 tptp.int)) (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int Y_1) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) X) M)))) (forall ((X tptp.int) (P_1 tptp.int)) (=> (@ tptp.zprime P_1) (=> (not (@ (@ tptp.dvd_dvd_int P_1) X)) (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int X) (@ tptp.nat_1 (@ (@ tptp.minus_minus_int P_1) tptp.one_one_int)))) tptp.one_one_int) P_1)))) (forall ((A tptp.int) (P_1 tptp.int)) (=> (@ tptp.zprime P_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) P_1) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) A)) tptp.one_one_int) P_1) (or (= A tptp.one_one_int) (= A (@ (@ tptp.minus_minus_int P_1) tptp.one_one_int)))))))) (forall ((C tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.zcong A))) (=> (@ (@ _let_1 B) M) (=> (@ (@ (@ tptp.zcong B) C) M) (@ (@ _let_1 C) M))))) (forall ((K tptp.int) (M tptp.int)) (@ (@ (@ tptp.zcong K) K) M)) (forall ((A tptp.int) (B tptp.int) (M tptp.int)) (= (@ (@ (@ tptp.zcong A) B) M) (@ (@ (@ tptp.zcong B) A) M))) (forall ((A tptp.int) (B tptp.int)) (= (@ (@ (@ tptp.zcong A) B) tptp.zero_zero_int) (= A B))) (forall ((A tptp.int) (B tptp.int)) (@ (@ (@ tptp.zcong A) B) tptp.one_one_int)) (forall ((A tptp.int) (M tptp.int) (B tptp.int)) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) M)) (@ (@ tptp.times_times_int B) M)) M)) (forall ((K tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (@ (@ (@ tptp.zcong A) B) M) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) K)) (@ (@ tptp.times_times_int B) K)) M))) (forall ((K tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ (@ tptp.zcong A) B) M) (@ (@ (@ tptp.zcong (@ _let_1 A)) (@ _let_1 B)) M)))) (forall ((C tptp.int) (D tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (@ (@ (@ tptp.zcong A) B) M) (=> (@ (@ (@ tptp.zcong C) D) M) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)) M)))) (forall ((C tptp.int) (D tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (@ (@ (@ tptp.zcong A) B) M) (=> (@ (@ (@ tptp.zcong C) D) M) (@ (@ (@ tptp.zcong (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D)) M)))) (forall ((C tptp.int) (D tptp.int) (A tptp.int) (B tptp.int) (M tptp.int)) (=> (@ (@ (@ tptp.zcong A) B) M) (=> (@ (@ (@ tptp.zcong C) D) M) (@ (@ (@ tptp.zcong (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D)) M)))) (forall ((B tptp.int) (M tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_int A) M) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ (@ tptp.zcong A) B) M)))))))) (forall ((A tptp.int) (R_1 tptp.int) (B tptp.int) (M tptp.int) (C tptp.int) (D tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int R_1))) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) (@ _let_1 B))) M)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int C) (@ _let_1 D))) N)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) M)) (@ (@ tptp.times_times_int C) N))) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) M)) (@ (@ tptp.times_times_int D) N))))))) (forall ((A tptp.int) (B tptp.int) (M tptp.int)) (= (@ (@ (@ tptp.zcong A) B) M) (exists ((K_1 tptp.int)) (= B (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int M) K_1)))))) (forall ((A tptp.int) (B tptp.int) (M tptp.int)) (= (@ (@ (@ tptp.zcong A) B) M) (@ (@ tptp.dvd_dvd_int M) (@ (@ tptp.minus_minus_int A) B)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.minus_minus_int B) tptp.one_one_int)) (@ (@ tptp.ord_less_int A) B))) (forall ((M tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) M) (=> (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) M) (= A tptp.zero_zero_int))))) (forall ((B tptp.int) (M tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_int A) M) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) M) (=> (@ (@ (@ tptp.zcong A) B) M) (= A B)))))))) (forall ((N tptp.int) (P_1 tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int P_1))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M) (=> (@ tptp.zprime P_1) (=> (@ _let_1 (@ (@ tptp.times_times_int M) N)) (or (@ _let_1 M) (@ _let_1 N))))))) (forall ((P_1 tptp.int)) (= (@ tptp.zprime P_1) (and (@ (@ tptp.ord_less_int tptp.one_one_int) P_1) (forall ((M_1 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M_1) (@ (@ tptp.dvd_dvd_int M_1) P_1)) (or (= M_1 tptp.one_one_int) (= M_1 P_1))))))) (forall ((A tptp.int) (P_1 tptp.int)) (let ((_let_1 (@ tptp.zcong A))) (=> (@ tptp.zprime P_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) A)) tptp.one_one_int) P_1) (or (@ (@ _let_1 tptp.one_one_int) P_1) (@ (@ _let_1 (@ (@ tptp.minus_minus_int P_1) tptp.one_one_int)) P_1))))))) (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1621563631at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1621563631at_int X)) (@ tptp.semiri1621563631at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P tptp.zero_zero_int))))) (forall ((P_1 tptp.int)) (let ((_let_1 (@ tptp.bit1 tptp.pls))) (let ((_let_2 (@ tptp.bit0 _let_1))) (=> (@ tptp.zprime P_1) (=> (not (= P_1 (@ tptp.number_number_of_int _let_2))) (=> (not (= P_1 (@ tptp.number_number_of_int (@ tptp.bit1 _let_1)))) (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int (@ tptp.bit1 _let_2))) P_1))))))) (forall ((P_2 Bool) (P Bool) (X tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X))) (=> (=> _let_1 (= P P_2)) (= (and _let_1 P) (and _let_1 P_2))))) (forall ((P_2 Bool) (P Bool) (X tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X))) (=> (=> _let_1 (= P P_2)) (= (=> _let_1 P) (=> _let_1 P_2))))) (forall ((M tptp.int) (T tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (not (= K tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int M) T) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 T)))))) (@ _let_10 _let_9) (forall ((A tptp.int) (P_1 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int P_1) tptp.one_one_int))) (= (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) _let_1)) tptp.one_one_int) P_1) (@ (@ (@ tptp.zcong A) _let_1) P_1)))) (forall ((Z tptp.nat) (X tptp.int) (Y tptp.nat) (P_1 tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (@ (@ (@ tptp.zcong (@ _let_1 Y)) tptp.one_one_int) P_1) (@ (@ (@ tptp.zcong (@ _let_1 (@ (@ tptp.times_times_nat Y) Z))) tptp.one_one_int) P_1)))) (forall ((N tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ tptp.number_number_of_int N)) (and (@ _let_1 (@ tptp.number_number_of_int (@ tptp.bit0 N))) (@ _let_1 (@ tptp.number_number_of_int (@ tptp.bit1 N))))))) (not (forall ((S tptp.int) (W_1 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1621563631at_int tptp.n)))) (not (and (= W_1 (@ (@ tptp.minus_minus_int tptp.y) (@ (@ tptp.times_times_int S) _let_1))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ tptp.abs_abs_int W_1))) _let_1)))))) (not (forall ((R tptp.int) (V tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1621563631at_int tptp.n)))) (not (and (= V (@ (@ tptp.minus_minus_int tptp.x) (@ (@ tptp.times_times_int R) _let_1))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ tptp.abs_abs_int V))) _let_1)))))) (forall ((D tptp.int) (I_1 tptp.int)) (=> (not (= I_1 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int D) I_1) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int D)) (@ tptp.abs_abs_int I_1))))) (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.nat_1 (@ tptp.abs_abs_int (@ (@ tptp.times_times_int W) Z))) (@ (@ tptp.times_times_nat (@ tptp.nat_1 (@ tptp.abs_abs_int W))) (@ tptp.nat_1 (@ tptp.abs_abs_int Z))))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ tptp.abs_abs_int A) (@ tptp.abs_abs_int B))))) (forall ((X tptp.int)) (= (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))) (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.semiri1621563631at_int M))) (= (@ tptp.abs_abs_int _let_1) _let_1))) (forall ((M tptp.int) (N tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M) N)) tptp.one_one_int) (= (@ tptp.abs_abs_int M) tptp.one_one_int))) (forall ((X tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int X)) N))) (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))) (forall ((Z tptp.int)) (= (= (@ tptp.abs_abs_int Z) tptp.one_one_int) (or (= Z tptp.one_one_int) (= Z (@ tptp.number_number_of_int tptp.min))))) (forall ((X tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit1 (@ tptp.bit1 tptp.pls))))) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int X)) _let_1)))) (forall ((X tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int X)) N)) (or (not (= X tptp.zero_zero_int)) (= N tptp.zero_zero_nat)))) (forall ((N tptp.int) (M tptp.int)) (=> (not (= M tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int M) N)) M) (= (@ tptp.abs_abs_int N) tptp.one_one_int)))) (forall ((M tptp.nat) (Z tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1621563631at_int M)) Z) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.nat_1 (@ tptp.abs_abs_int Z))))) (forall ((Z tptp.int) (M tptp.nat)) (= (@ (@ tptp.dvd_dvd_int Z) (@ tptp.semiri1621563631at_int M)) (@ (@ tptp.dvd_dvd_nat (@ tptp.nat_1 (@ tptp.abs_abs_int Z))) M))) (forall ((A tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) _let_1)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (= (@ (@ tptp.power_power_int A) _let_1) (@ (@ tptp.power_power_int B) _let_1)) (= (@ tptp.abs_abs_int A) (@ tptp.abs_abs_int B))))) (forall ((A tptp.int)) (=> (= (@ (@ tptp.power_power_int A) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.one_one_int) (= (@ tptp.abs_abs_int A) tptp.one_one_int))) (forall ((Z tptp.int) (X tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Z))) tptp.one_one_int)) D))))) (forall ((X tptp.int) (Z tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D))) Z)))) (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (exists ((N_1 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int Y) (@ (@ tptp.times_times_int N_1) X))))) X)))) (forall ((K tptp.int) (P (-> tptp.int Bool)) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X_1 tptp.int)) (=> (@ P X_1) (@ P (@ (@ tptp.minus_minus_int X_1) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X_1 tptp.int)) (=> (@ P X_1) (@ P (@ (@ tptp.minus_minus_int X_1) (@ (@ tptp.times_times_int K) D))))))))) (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X)) tptp.one_one_real)) X))) (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X)))) (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.one_one_real))) (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (@ P N) (exists ((K_1 tptp.nat)) (and (@ (@ tptp.ord_less_nat K_1) N) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) K_1) (not (@ P I)))) (@ P (@ (@ tptp.plus_plus_nat K_1) tptp.one_one_nat))))))) (forall ((K tptp.int) (P (-> tptp.int Bool)) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X_1 tptp.int)) (=> (@ P X_1) (@ P (@ (@ tptp.plus_plus_int X_1) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X_1 tptp.int)) (=> (@ P X_1) (@ P (@ (@ tptp.plus_plus_int X_1) (@ (@ tptp.times_times_int K) D))))))))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I_1) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J)) U)) M)) N)))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I_1)) U)) N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (= M N))))) (forall ((I_1 tptp.nat) (U tptp.nat) (J tptp.nat) (K tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I_1) J)) U)) K))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))) (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.dvd_dvd_nat M) N))))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I_1) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J)) U)) M)) N)))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I_1) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J)) U)) M)) N)))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I_1) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J)) U)) M) N)))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I_1)) U)) N))))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I_1)) U)) N))))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I_1)) U)) N))))) (forall ((K tptp.int) (F (-> tptp.nat tptp.int)) (N tptp.nat)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat))) (@ F I)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I) N) (= (@ F I) K))))))) (forall ((K tptp.int) (F (-> tptp.nat tptp.int)) (N tptp.nat)) (=> (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I) tptp.one_one_nat))) (@ F I)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I) N) (= (@ F I) K))))))) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)) (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)) (forall ((P Bool)) (or (= P true) (= P false))) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)) (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)) (forall ((P Bool)) (or (= P true) (= P false))) _let_8 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.71/1.31 )
% 0.71/1.31 % SZS output end Proof for NUM925^3
% 0.71/1.31 % cvc5---1.0.5 exiting
% 0.71/1.31 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------