TSTP Solution File: NUM926^3 by cvc5---1.0.5
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%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : NUM926^3 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n023.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 10:49:09 EDT 2023
% Result : Theorem 1.17s 1.43s
% Output : Proof 1.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.27 % Problem : NUM926^3 : TPTP v8.1.2. Released v5.3.0.
% 0.13/0.28 % Command : do_cvc5 %s %d
% 0.28/0.49 % Computer : n023.cluster.edu
% 0.28/0.49 % Model : x86_64 x86_64
% 0.28/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.28/0.49 % Memory : 8042.1875MB
% 0.28/0.49 % OS : Linux 3.10.0-693.el7.x86_64
% 0.28/0.49 % CPULimit : 300
% 0.28/0.49 % WCLimit : 300
% 0.28/0.49 % DateTime : Fri Aug 25 09:23:42 EDT 2023
% 0.28/0.49 % CPUTime :
% 0.59/0.77 %----Proving TH0
% 0.59/0.77 %------------------------------------------------------------------------------
% 0.59/0.77 % File : NUM926^3 : TPTP v8.1.2. Released v5.3.0.
% 0.59/0.77 % Domain : Number Theory
% 0.59/0.77 % Problem : Sum of two squares line 258, 1000 axioms selected
% 0.59/0.77 % Version : Especial.
% 0.59/0.77 % English :
% 0.59/0.77
% 0.59/0.77 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day
% 0.59/0.77 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe
% 0.59/0.77 % Source : [Bla11]
% 0.59/0.77 % Names : s2s_1000_thf_l258 [Bla11]
% 0.59/0.77
% 0.59/0.77 % Status : Theorem
% 0.59/0.77 % Rating : 0.54 v8.1.0, 0.64 v7.5.0, 0.43 v7.4.0, 0.56 v7.2.0, 0.38 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.60 v6.2.0, 0.43 v6.1.0, 0.57 v5.5.0, 0.50 v5.4.0, 1.00 v5.3.0
% 0.59/0.77 % Syntax : Number of formulae : 1259 ( 455 unt; 60 typ; 0 def)
% 0.59/0.77 % Number of atoms : 2686 ( 842 equ; 1 cnn)
% 0.59/0.77 % Maximal formula atoms : 9 ( 2 avg)
% 0.59/0.77 % Number of connectives : 11416 ( 259 ~; 70 |; 166 &;9632 @)
% 0.59/0.77 % ( 254 <=>;1035 =>; 0 <=; 0 <~>)
% 0.59/0.77 % Maximal formula depth : 18 ( 7 avg)
% 0.59/0.77 % Number of types : 5 ( 4 usr)
% 0.59/0.77 % Number of type conns : 101 ( 101 >; 0 *; 0 +; 0 <<)
% 0.59/0.77 % Number of symbols : 58 ( 56 usr; 13 con; 0-3 aty)
% 0.59/0.77 % Number of variables : 2591 ( 1 ^;2567 !; 23 ?;2591 :)
% 0.59/0.77 % SPC : TH0_THM_EQU_NAR
% 0.59/0.77
% 0.59/0.77 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.59/0.77 % 2011-08-09 19:54:07
% 0.59/0.77 %------------------------------------------------------------------------------
% 0.59/0.77 %----Should-be-implicit typings (4)
% 0.59/0.77 thf(ty_ty_tc__Int__Oint,type,
% 0.59/0.77 int: $tType ).
% 0.59/0.77
% 0.59/0.77 thf(ty_ty_tc__Nat__Onat,type,
% 0.59/0.77 nat: $tType ).
% 0.59/0.77
% 0.59/0.77 thf(ty_ty_tc__RealDef__Oreal,type,
% 0.59/0.77 real: $tType ).
% 0.59/0.77
% 0.59/0.77 thf(ty_ty_tc__prod_Itc__Int__Oint_Mtc__Int__Oint_J,type,
% 0.59/0.77 product_prod_int_int: $tType ).
% 0.59/0.77
% 0.59/0.77 %----Explicit typings (56)
% 0.59/0.77 thf(sy_c_Divides_Odiv__class_Omod_000tc__Int__Oint,type,
% 0.59/0.77 div_mod_int: int > int > int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Divides_Odiv__class_Omod_000tc__Nat__Onat,type,
% 0.59/0.77 div_mod_nat: nat > nat > nat ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Groups_Ominus__class_Ominus_000tc__Int__Oint,type,
% 0.59/0.77 minus_minus_int: int > int > int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Groups_Ominus__class_Ominus_000tc__Nat__Onat,type,
% 0.59/0.77 minus_minus_nat: nat > nat > nat ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Groups_Ominus__class_Ominus_000tc__RealDef__Oreal,type,
% 0.59/0.77 minus_minus_real: real > real > real ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Groups_Oone__class_Oone_000tc__Int__Oint,type,
% 0.59/0.77 one_one_int: int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Groups_Oone__class_Oone_000tc__Nat__Onat,type,
% 0.59/0.77 one_one_nat: nat ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Groups_Oone__class_Oone_000tc__RealDef__Oreal,type,
% 0.59/0.77 one_one_real: real ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Groups_Oplus__class_Oplus_000tc__Int__Oint,type,
% 0.59/0.77 plus_plus_int: int > int > int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Groups_Oplus__class_Oplus_000tc__Nat__Onat,type,
% 0.59/0.77 plus_plus_nat: nat > nat > nat ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Groups_Oplus__class_Oplus_000tc__RealDef__Oreal,type,
% 0.59/0.77 plus_plus_real: real > real > real ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Groups_Otimes__class_Otimes_000tc__Int__Oint,type,
% 0.59/0.77 times_times_int: int > int > int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Groups_Otimes__class_Otimes_000tc__Nat__Onat,type,
% 0.59/0.77 times_times_nat: nat > nat > nat ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Groups_Otimes__class_Otimes_000tc__RealDef__Oreal,type,
% 0.59/0.77 times_times_real: real > real > real ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Groups_Ozero__class_Ozero_000tc__Int__Oint,type,
% 0.59/0.77 zero_zero_int: int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Groups_Ozero__class_Ozero_000tc__Nat__Onat,type,
% 0.59/0.77 zero_zero_nat: nat ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Groups_Ozero__class_Ozero_000tc__RealDef__Oreal,type,
% 0.59/0.77 zero_zero_real: real ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Int2_OMultInv,type,
% 0.59/0.77 multInv: int > int > int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_IntFact_Od22set,type,
% 0.59/0.77 d22set: int > int > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_IntFact_Ozfact,type,
% 0.59/0.77 zfact: int > int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_IntPrimes_Ozcong,type,
% 0.59/0.77 zcong: int > int > int > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_IntPrimes_Ozprime,type,
% 0.59/0.77 zprime: int > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Int_OBit0,type,
% 0.59/0.77 bit0: int > int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Int_OBit1,type,
% 0.59/0.77 bit1: int > int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Int_OMin,type,
% 0.59/0.77 min: int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Int_OPls,type,
% 0.59/0.77 pls: int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Int_Onumber__class_Onumber__of_000tc__Int__Oint,type,
% 0.59/0.77 number_number_of_int: int > int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Int_Onumber__class_Onumber__of_000tc__Nat__Onat,type,
% 0.59/0.77 number_number_of_nat: int > nat ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Int_Onumber__class_Onumber__of_000tc__RealDef__Oreal,type,
% 0.59/0.77 number267125858f_real: int > real ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Orderings_Oord__class_Oless_000tc__Int__Oint,type,
% 0.59/0.77 ord_less_int: int > int > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Orderings_Oord__class_Oless_000tc__Nat__Onat,type,
% 0.59/0.77 ord_less_nat: nat > nat > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Orderings_Oord__class_Oless_000tc__RealDef__Oreal,type,
% 0.59/0.77 ord_less_real: real > real > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__Int__Oint,type,
% 0.59/0.77 ord_less_eq_int: int > int > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__Nat__Onat,type,
% 0.59/0.77 ord_less_eq_nat: nat > nat > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Orderings_Oord__class_Oless__eq_000tc__RealDef__Oreal,type,
% 0.59/0.77 ord_less_eq_real: real > real > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Power_Opower__class_Opower_000tc__Int__Oint,type,
% 0.59/0.77 power_power_int: int > nat > int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Power_Opower__class_Opower_000tc__Nat__Onat,type,
% 0.59/0.77 power_power_nat: nat > nat > nat ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Power_Opower__class_Opower_000tc__RealDef__Oreal,type,
% 0.59/0.77 power_power_real: real > nat > real ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Product__Type_OPair_000tc__Int__Oint_000tc__Int__Oint,type,
% 0.59/0.77 product_Pair_int_int: int > int > product_prod_int_int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Residues_OLegendre,type,
% 0.59/0.77 legendre: int > int > int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Residues_OQuadRes,type,
% 0.59/0.77 quadRes: int > int > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Residues_OSR,type,
% 0.59/0.77 sr: int > int > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Residues_OStandardRes,type,
% 0.59/0.77 standardRes: int > int > int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Rings_Odvd__class_Odvd_000tc__Int__Oint,type,
% 0.59/0.77 dvd_dvd_int: int > int > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Rings_Odvd__class_Odvd_000tc__Nat__Onat,type,
% 0.59/0.77 dvd_dvd_nat: nat > nat > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Rings_Odvd__class_Odvd_000tc__RealDef__Oreal,type,
% 0.59/0.77 dvd_dvd_real: real > real > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_Set_OCollect_000tc__Int__Oint,type,
% 0.59/0.77 collect_int: ( int > $o ) > int > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_TwoSquares__Mirabelle__dzzvbppuls_Ois__sum2sq,type,
% 0.59/0.77 twoSqu919416604sum2sq: int > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_TwoSquares__Mirabelle__dzzvbppuls_Osum2sq,type,
% 0.59/0.77 twoSqu2057625106sum2sq: product_prod_int_int > int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_WilsonRuss_Oinv,type,
% 0.59/0.77 inv: int > int > int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_WilsonRuss_Owset,type,
% 0.59/0.77 wset: int > int > int > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_c_member_000tc__Int__Oint,type,
% 0.59/0.77 member_int: int > ( int > $o ) > $o ).
% 0.59/0.77
% 0.59/0.77 thf(sy_v_m,type,
% 0.59/0.77 m: int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_v_s1____,type,
% 0.59/0.77 s1: int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_v_s____,type,
% 0.59/0.77 s: int ).
% 0.59/0.77
% 0.59/0.77 thf(sy_v_t____,type,
% 0.59/0.77 t: int ).
% 0.59/0.77
% 0.59/0.77 %----Relevant facts (1198)
% 0.59/0.77 thf(fact_0_tpos,axiom,
% 0.59/0.77 ord_less_eq_int @ one_one_int @ t ).
% 0.59/0.77
% 0.59/0.77 thf(fact_1__096t_A_061_A1_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
% 0.59/0.77 ( ( t = one_one_int )
% 0.59/0.77 => ? [X: int,Y: int] :
% 0.59/0.77 ( ( 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 ) ) ) ) )
% 0.59/0.77 = ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_2__0961_A_060_At_A_061_061_062_AEX_Ax_Ay_O_Ax_A_094_A2_A_L_Ay_A_094_A2_A_06,axiom,
% 0.59/0.77 ( ( ord_less_int @ one_one_int @ t )
% 0.59/0.77 => ? [X: int,Y: int] :
% 0.59/0.77 ( ( 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 ) ) ) ) )
% 0.59/0.77 = ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_3_t__l__p,axiom,
% 0.59/0.77 ord_less_int @ t @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_4_p,axiom,
% 0.59/0.77 zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_5_t,axiom,
% 0.59/0.77 ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
% 0.59/0.77 = ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_6_qf1pt,axiom,
% 0.59/0.77 twoSqu919416604sum2sq @ ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_7_zadd__power2,axiom,
% 0.59/0.77 ! [A: int,B: int] :
% 0.59/0.77 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.77 = ( 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 ) ) ) ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_8_zadd__power3,axiom,
% 0.59/0.77 ! [A: int,B: int] :
% 0.59/0.77 ( ( power_power_int @ ( plus_plus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
% 0.59/0.77 = ( 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 ) ) ) ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_9_power2__sum,axiom,
% 0.59/0.77 ! [X_44: int,Y_34: int] :
% 0.59/0.77 ( ( power_power_int @ ( plus_plus_int @ X_44 @ Y_34 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.77 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X_44 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_34 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_44 ) @ Y_34 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_10_power2__sum,axiom,
% 0.59/0.77 ! [X_44: nat,Y_34: nat] :
% 0.59/0.77 ( ( power_power_nat @ ( plus_plus_nat @ X_44 @ Y_34 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.77 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X_44 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y_34 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_44 ) @ Y_34 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_11_power2__sum,axiom,
% 0.59/0.77 ! [X_44: real,Y_34: real] :
% 0.59/0.77 ( ( power_power_real @ ( plus_plus_real @ X_44 @ Y_34 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.77 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X_44 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_34 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_44 ) @ Y_34 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_12_power2__eq__square__number__of,axiom,
% 0.59/0.77 ! [W_19: int] :
% 0.59/0.77 ( ( power_power_int @ ( number_number_of_int @ W_19 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.77 = ( times_times_int @ ( number_number_of_int @ W_19 ) @ ( number_number_of_int @ W_19 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_13_power2__eq__square__number__of,axiom,
% 0.59/0.77 ! [W_19: int] :
% 0.59/0.77 ( ( power_power_real @ ( number267125858f_real @ W_19 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.77 = ( times_times_real @ ( number267125858f_real @ W_19 ) @ ( number267125858f_real @ W_19 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_14_power2__eq__square__number__of,axiom,
% 0.59/0.77 ! [W_19: int] :
% 0.59/0.77 ( ( power_power_nat @ ( number_number_of_nat @ W_19 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.77 = ( times_times_nat @ ( number_number_of_nat @ W_19 ) @ ( number_number_of_nat @ W_19 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_15_cube__square,axiom,
% 0.59/0.77 ! [A: int] :
% 0.59/0.77 ( ( times_times_int @ A @ ( power_power_int @ A @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.77 = ( power_power_int @ A @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_16_one__power2,axiom,
% 0.59/0.77 ( ( power_power_int @ one_one_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.77 = one_one_int ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_17_one__power2,axiom,
% 0.59/0.77 ( ( power_power_nat @ one_one_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.77 = one_one_nat ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_18_one__power2,axiom,
% 0.59/0.77 ( ( power_power_real @ one_one_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.77 = one_one_real ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_19_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 0.59/0.77 ! [X_43: int] :
% 0.59/0.77 ( ( times_times_int @ X_43 @ X_43 )
% 0.59/0.77 = ( power_power_int @ X_43 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_20_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 0.59/0.77 ! [X_43: real] :
% 0.59/0.77 ( ( times_times_real @ X_43 @ X_43 )
% 0.59/0.77 = ( power_power_real @ X_43 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_21_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom,
% 0.59/0.77 ! [X_43: nat] :
% 0.59/0.77 ( ( times_times_nat @ X_43 @ X_43 )
% 0.59/0.77 = ( power_power_nat @ X_43 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_22_power2__eq__square,axiom,
% 0.59/0.77 ! [A_127: int] :
% 0.59/0.77 ( ( power_power_int @ A_127 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.77 = ( times_times_int @ A_127 @ A_127 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_23_power2__eq__square,axiom,
% 0.59/0.77 ! [A_127: real] :
% 0.59/0.77 ( ( power_power_real @ A_127 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.77 = ( times_times_real @ A_127 @ A_127 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_24_power2__eq__square,axiom,
% 0.59/0.77 ! [A_127: nat] :
% 0.59/0.77 ( ( power_power_nat @ A_127 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.77 = ( times_times_nat @ A_127 @ A_127 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_25_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 0.59/0.77 ! [X_42: int,N_41: nat] :
% 0.59/0.77 ( ( power_power_int @ X_42 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_41 ) )
% 0.59/0.77 = ( times_times_int @ ( power_power_int @ X_42 @ N_41 ) @ ( power_power_int @ X_42 @ N_41 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_26_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 0.59/0.77 ! [X_42: real,N_41: nat] :
% 0.59/0.77 ( ( power_power_real @ X_42 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_41 ) )
% 0.59/0.77 = ( times_times_real @ ( power_power_real @ X_42 @ N_41 ) @ ( power_power_real @ X_42 @ N_41 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_27_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom,
% 0.59/0.77 ! [X_42: nat,N_41: nat] :
% 0.59/0.77 ( ( power_power_nat @ X_42 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_41 ) )
% 0.59/0.77 = ( times_times_nat @ ( power_power_nat @ X_42 @ N_41 ) @ ( power_power_nat @ X_42 @ N_41 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_28_add__special_I2_J,axiom,
% 0.59/0.77 ! [W_18: int] :
% 0.59/0.77 ( ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_18 ) )
% 0.59/0.77 = ( number_number_of_int @ ( plus_plus_int @ ( bit1 @ pls ) @ W_18 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_29_add__special_I2_J,axiom,
% 0.59/0.77 ! [W_18: int] :
% 0.59/0.77 ( ( plus_plus_real @ one_one_real @ ( number267125858f_real @ W_18 ) )
% 0.59/0.77 = ( number267125858f_real @ ( plus_plus_int @ ( bit1 @ pls ) @ W_18 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_30_add__special_I3_J,axiom,
% 0.59/0.77 ! [V_20: int] :
% 0.59/0.77 ( ( plus_plus_int @ ( number_number_of_int @ V_20 ) @ one_one_int )
% 0.59/0.77 = ( number_number_of_int @ ( plus_plus_int @ V_20 @ ( bit1 @ pls ) ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_31_add__special_I3_J,axiom,
% 0.59/0.77 ! [V_20: int] :
% 0.59/0.77 ( ( plus_plus_real @ ( number267125858f_real @ V_20 ) @ one_one_real )
% 0.59/0.77 = ( number267125858f_real @ ( plus_plus_int @ V_20 @ ( bit1 @ pls ) ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_32_one__add__one__is__two,axiom,
% 0.59/0.77 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 0.59/0.77 = ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_33_one__add__one__is__two,axiom,
% 0.59/0.77 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 0.59/0.77 = ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_34__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_,axiom,
% 0.59/0.77 ~ ! [T_1: int] :
% 0.59/0.77 ( ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int )
% 0.59/0.77 != ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ T_1 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_35_zle__refl,axiom,
% 0.59/0.77 ! [W: int] : ( ord_less_eq_int @ W @ W ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_36_zle__linear,axiom,
% 0.59/0.77 ! [Z: int,W: int] :
% 0.59/0.77 ( ( ord_less_eq_int @ Z @ W )
% 0.59/0.77 | ( ord_less_eq_int @ W @ Z ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_37_zless__le,axiom,
% 0.59/0.77 ! [Z: int,W: int] :
% 0.59/0.77 ( ( ord_less_int @ Z @ W )
% 0.59/0.77 <=> ( ( ord_less_eq_int @ Z @ W )
% 0.59/0.77 & ( Z != W ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_38_zless__linear,axiom,
% 0.59/0.77 ! [X_1: int,Y_1: int] :
% 0.59/0.77 ( ( ord_less_int @ X_1 @ Y_1 )
% 0.59/0.77 | ( X_1 = Y_1 )
% 0.59/0.77 | ( ord_less_int @ Y_1 @ X_1 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_39_zle__trans,axiom,
% 0.59/0.77 ! [K: int,I_1: int,J_1: int] :
% 0.59/0.77 ( ( ord_less_eq_int @ I_1 @ J_1 )
% 0.59/0.77 => ( ( ord_less_eq_int @ J_1 @ K )
% 0.59/0.77 => ( ord_less_eq_int @ I_1 @ K ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_40_zle__antisym,axiom,
% 0.59/0.77 ! [Z: int,W: int] :
% 0.59/0.77 ( ( ord_less_eq_int @ Z @ W )
% 0.59/0.77 => ( ( ord_less_eq_int @ W @ Z )
% 0.59/0.77 => ( Z = W ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_41_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 0.59/0.77 ! [X_41: int,P_6: nat,Q_6: nat] :
% 0.59/0.77 ( ( power_power_int @ ( power_power_int @ X_41 @ P_6 ) @ Q_6 )
% 0.59/0.77 = ( power_power_int @ X_41 @ ( times_times_nat @ P_6 @ Q_6 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_42_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 0.59/0.77 ! [X_41: real,P_6: nat,Q_6: nat] :
% 0.59/0.77 ( ( power_power_real @ ( power_power_real @ X_41 @ P_6 ) @ Q_6 )
% 0.59/0.77 = ( power_power_real @ X_41 @ ( times_times_nat @ P_6 @ Q_6 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_43_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom,
% 0.59/0.77 ! [X_41: nat,P_6: nat,Q_6: nat] :
% 0.59/0.77 ( ( power_power_nat @ ( power_power_nat @ X_41 @ P_6 ) @ Q_6 )
% 0.59/0.77 = ( power_power_nat @ X_41 @ ( times_times_nat @ P_6 @ Q_6 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_44_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 0.59/0.77 ! [X_40: int] :
% 0.59/0.77 ( ( power_power_int @ X_40 @ one_one_nat )
% 0.59/0.77 = X_40 ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_45_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 0.59/0.77 ! [X_40: real] :
% 0.59/0.77 ( ( power_power_real @ X_40 @ one_one_nat )
% 0.59/0.77 = X_40 ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_46_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom,
% 0.59/0.77 ! [X_40: nat] :
% 0.59/0.77 ( ( power_power_nat @ X_40 @ one_one_nat )
% 0.59/0.77 = X_40 ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_47_zpower__zpower,axiom,
% 0.59/0.77 ! [X_1: int,Y_1: nat,Z: nat] :
% 0.59/0.77 ( ( power_power_int @ ( power_power_int @ X_1 @ Y_1 ) @ Z )
% 0.59/0.77 = ( power_power_int @ X_1 @ ( times_times_nat @ Y_1 @ Z ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_48_le__number__of__eq__not__less,axiom,
% 0.59/0.77 ! [V_19: int,W_17: int] :
% 0.59/0.77 ( ( ord_less_eq_int @ ( number_number_of_int @ V_19 ) @ ( number_number_of_int @ W_17 ) )
% 0.59/0.77 <=> ~ ( ord_less_int @ ( number_number_of_int @ W_17 ) @ ( number_number_of_int @ V_19 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_49_le__number__of__eq__not__less,axiom,
% 0.59/0.77 ! [V_19: int,W_17: int] :
% 0.59/0.77 ( ( ord_less_eq_nat @ ( number_number_of_nat @ V_19 ) @ ( number_number_of_nat @ W_17 ) )
% 0.59/0.77 <=> ~ ( ord_less_nat @ ( number_number_of_nat @ W_17 ) @ ( number_number_of_nat @ V_19 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_50_le__number__of__eq__not__less,axiom,
% 0.59/0.77 ! [V_19: int,W_17: int] :
% 0.59/0.77 ( ( ord_less_eq_real @ ( number267125858f_real @ V_19 ) @ ( number267125858f_real @ W_17 ) )
% 0.59/0.77 <=> ~ ( ord_less_real @ ( number267125858f_real @ W_17 ) @ ( number267125858f_real @ V_19 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_51_less__number__of,axiom,
% 0.59/0.77 ! [X_39: int,Y_33: int] :
% 0.59/0.77 ( ( ord_less_int @ ( number_number_of_int @ X_39 ) @ ( number_number_of_int @ Y_33 ) )
% 0.59/0.77 <=> ( ord_less_int @ X_39 @ Y_33 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_52_less__number__of,axiom,
% 0.59/0.77 ! [X_39: int,Y_33: int] :
% 0.59/0.77 ( ( ord_less_real @ ( number267125858f_real @ X_39 ) @ ( number267125858f_real @ Y_33 ) )
% 0.59/0.77 <=> ( ord_less_int @ X_39 @ Y_33 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_53_le__number__of,axiom,
% 0.59/0.77 ! [X_38: int,Y_32: int] :
% 0.59/0.77 ( ( ord_less_eq_int @ ( number_number_of_int @ X_38 ) @ ( number_number_of_int @ Y_32 ) )
% 0.59/0.77 <=> ( ord_less_eq_int @ X_38 @ Y_32 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_54_le__number__of,axiom,
% 0.59/0.77 ! [X_38: int,Y_32: int] :
% 0.59/0.77 ( ( ord_less_eq_real @ ( number267125858f_real @ X_38 ) @ ( number267125858f_real @ Y_32 ) )
% 0.59/0.77 <=> ( ord_less_eq_int @ X_38 @ Y_32 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_55_zadd__zless__mono,axiom,
% 0.59/0.77 ! [Z_10: int,Z: int,W_16: int,W: int] :
% 0.59/0.77 ( ( ord_less_int @ W_16 @ W )
% 0.59/0.77 => ( ( ord_less_eq_int @ Z_10 @ Z )
% 0.59/0.77 => ( ord_less_int @ ( plus_plus_int @ W_16 @ Z_10 ) @ ( plus_plus_int @ W @ Z ) ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_56_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 0.59/0.77 ! [X_37: int,P_5: nat,Q_5: nat] :
% 0.59/0.77 ( ( times_times_int @ ( power_power_int @ X_37 @ P_5 ) @ ( power_power_int @ X_37 @ Q_5 ) )
% 0.59/0.77 = ( power_power_int @ X_37 @ ( plus_plus_nat @ P_5 @ Q_5 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_57_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 0.59/0.77 ! [X_37: real,P_5: nat,Q_5: nat] :
% 0.59/0.77 ( ( times_times_real @ ( power_power_real @ X_37 @ P_5 ) @ ( power_power_real @ X_37 @ Q_5 ) )
% 0.59/0.77 = ( power_power_real @ X_37 @ ( plus_plus_nat @ P_5 @ Q_5 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_58_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom,
% 0.59/0.77 ! [X_37: nat,P_5: nat,Q_5: nat] :
% 0.59/0.77 ( ( times_times_nat @ ( power_power_nat @ X_37 @ P_5 ) @ ( power_power_nat @ X_37 @ Q_5 ) )
% 0.59/0.77 = ( power_power_nat @ X_37 @ ( plus_plus_nat @ P_5 @ Q_5 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_59_zpower__zadd__distrib,axiom,
% 0.59/0.77 ! [X_1: int,Y_1: nat,Z: nat] :
% 0.59/0.77 ( ( power_power_int @ X_1 @ ( plus_plus_nat @ Y_1 @ Z ) )
% 0.59/0.77 = ( times_times_int @ ( power_power_int @ X_1 @ Y_1 ) @ ( power_power_int @ X_1 @ Z ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_60_nat__mult__2,axiom,
% 0.59/0.77 ! [Z: nat] :
% 0.59/0.77 ( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z )
% 0.59/0.77 = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_61_nat__mult__2__right,axiom,
% 0.59/0.77 ! [Z: nat] :
% 0.59/0.77 ( ( times_times_nat @ Z @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.77 = ( plus_plus_nat @ Z @ Z ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_62_nat__1__add__1,axiom,
% 0.59/0.77 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.59/0.77 = ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_63_less__int__code_I16_J,axiom,
% 0.59/0.77 ! [K1: int,K2: int] :
% 0.59/0.77 ( ( ord_less_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
% 0.59/0.77 <=> ( ord_less_int @ K1 @ K2 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_64_rel__simps_I17_J,axiom,
% 0.59/0.77 ! [K: int,L: int] :
% 0.59/0.77 ( ( ord_less_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
% 0.59/0.77 <=> ( ord_less_int @ K @ L ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_65_less__eq__int__code_I16_J,axiom,
% 0.59/0.77 ! [K1: int,K2: int] :
% 0.59/0.77 ( ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit1 @ K2 ) )
% 0.59/0.77 <=> ( ord_less_eq_int @ K1 @ K2 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_66_rel__simps_I34_J,axiom,
% 0.59/0.77 ! [K: int,L: int] :
% 0.59/0.77 ( ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
% 0.59/0.77 <=> ( ord_less_eq_int @ K @ L ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_67_rel__simps_I2_J,axiom,
% 0.59/0.77 ~ ( ord_less_int @ pls @ pls ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_68_less__int__code_I13_J,axiom,
% 0.59/0.77 ! [K1: int,K2: int] :
% 0.59/0.77 ( ( ord_less_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
% 0.59/0.77 <=> ( ord_less_int @ K1 @ K2 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_69_rel__simps_I14_J,axiom,
% 0.59/0.77 ! [K: int,L: int] :
% 0.59/0.77 ( ( ord_less_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
% 0.59/0.77 <=> ( ord_less_int @ K @ L ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_70_rel__simps_I19_J,axiom,
% 0.59/0.77 ord_less_eq_int @ pls @ pls ).
% 0.59/0.77
% 0.59/0.77 thf(fact_71_less__eq__int__code_I13_J,axiom,
% 0.59/0.77 ! [K1: int,K2: int] :
% 0.59/0.77 ( ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit0 @ K2 ) )
% 0.59/0.77 <=> ( ord_less_eq_int @ K1 @ K2 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_72_rel__simps_I31_J,axiom,
% 0.59/0.77 ! [K: int,L: int] :
% 0.59/0.77 ( ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
% 0.59/0.77 <=> ( ord_less_eq_int @ K @ L ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_73_less__number__of__int__code,axiom,
% 0.59/0.77 ! [K: int,L: int] :
% 0.59/0.77 ( ( ord_less_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
% 0.59/0.77 <=> ( ord_less_int @ K @ L ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_74_less__eq__number__of__int__code,axiom,
% 0.59/0.77 ! [K: int,L: int] :
% 0.59/0.77 ( ( ord_less_eq_int @ ( number_number_of_int @ K ) @ ( number_number_of_int @ L ) )
% 0.59/0.77 <=> ( ord_less_eq_int @ K @ L ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_75_zadd__strict__right__mono,axiom,
% 0.59/0.77 ! [K: int,I_1: int,J_1: int] :
% 0.59/0.77 ( ( ord_less_int @ I_1 @ J_1 )
% 0.59/0.77 => ( ord_less_int @ ( plus_plus_int @ I_1 @ K ) @ ( plus_plus_int @ J_1 @ K ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_76_zadd__left__mono,axiom,
% 0.59/0.77 ! [K: int,I_1: int,J_1: int] :
% 0.59/0.77 ( ( ord_less_eq_int @ I_1 @ J_1 )
% 0.59/0.77 => ( ord_less_eq_int @ ( plus_plus_int @ K @ I_1 ) @ ( plus_plus_int @ K @ J_1 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_77_add__nat__number__of,axiom,
% 0.59/0.77 ! [V_6: int,V: int] :
% 0.59/0.77 ( ( ( ord_less_int @ V @ pls )
% 0.59/0.77 => ( ( plus_plus_nat @ ( number_number_of_nat @ V ) @ ( number_number_of_nat @ V_6 ) )
% 0.59/0.77 = ( number_number_of_nat @ V_6 ) ) )
% 0.59/0.77 & ( ~ ( ord_less_int @ V @ pls )
% 0.59/0.77 => ( ( ( ord_less_int @ V_6 @ pls )
% 0.59/0.77 => ( ( plus_plus_nat @ ( number_number_of_nat @ V ) @ ( number_number_of_nat @ V_6 ) )
% 0.59/0.77 = ( number_number_of_nat @ V ) ) )
% 0.59/0.77 & ( ~ ( ord_less_int @ V_6 @ pls )
% 0.59/0.77 => ( ( plus_plus_nat @ ( number_number_of_nat @ V ) @ ( number_number_of_nat @ V_6 ) )
% 0.59/0.77 = ( number_number_of_nat @ ( plus_plus_int @ V @ V_6 ) ) ) ) ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_78_nat__numeral__1__eq__1,axiom,
% 0.59/0.77 ( ( number_number_of_nat @ ( bit1 @ pls ) )
% 0.59/0.77 = one_one_nat ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_79_Numeral1__eq1__nat,axiom,
% 0.59/0.77 ( one_one_nat
% 0.59/0.77 = ( number_number_of_nat @ ( bit1 @ pls ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_80_rel__simps_I29_J,axiom,
% 0.59/0.77 ! [K: int] :
% 0.59/0.77 ( ( ord_less_eq_int @ ( bit1 @ K ) @ pls )
% 0.59/0.77 <=> ( ord_less_int @ K @ pls ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_81_rel__simps_I5_J,axiom,
% 0.59/0.77 ! [K: int] :
% 0.59/0.77 ( ( ord_less_int @ pls @ ( bit1 @ K ) )
% 0.59/0.77 <=> ( ord_less_eq_int @ pls @ K ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_82_less__eq__int__code_I15_J,axiom,
% 0.59/0.77 ! [K1: int,K2: int] :
% 0.59/0.77 ( ( ord_less_eq_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
% 0.59/0.77 <=> ( ord_less_int @ K1 @ K2 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_83_rel__simps_I33_J,axiom,
% 0.59/0.77 ! [K: int,L: int] :
% 0.59/0.77 ( ( ord_less_eq_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
% 0.59/0.77 <=> ( ord_less_int @ K @ L ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_84_less__int__code_I14_J,axiom,
% 0.59/0.77 ! [K1: int,K2: int] :
% 0.59/0.77 ( ( ord_less_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
% 0.59/0.77 <=> ( ord_less_eq_int @ K1 @ K2 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_85_rel__simps_I15_J,axiom,
% 0.59/0.77 ! [K: int,L: int] :
% 0.59/0.77 ( ( ord_less_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
% 0.59/0.77 <=> ( ord_less_eq_int @ K @ L ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_86_zless__imp__add1__zle,axiom,
% 0.59/0.77 ! [W: int,Z: int] :
% 0.59/0.77 ( ( ord_less_int @ W @ Z )
% 0.59/0.77 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_87_add1__zle__eq,axiom,
% 0.59/0.77 ! [W: int,Z: int] :
% 0.59/0.77 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 0.59/0.77 <=> ( ord_less_int @ W @ Z ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_88_zle__add1__eq__le,axiom,
% 0.59/0.77 ! [W: int,Z: int] :
% 0.59/0.77 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.59/0.77 <=> ( ord_less_eq_int @ W @ Z ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_89_zprime__2,axiom,
% 0.59/0.77 zprime @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_90_is__mult__sum2sq,axiom,
% 0.59/0.77 ! [Y_1: int,X_1: int] :
% 0.59/0.77 ( ( twoSqu919416604sum2sq @ X_1 )
% 0.59/0.77 => ( ( twoSqu919416604sum2sq @ Y_1 )
% 0.59/0.77 => ( twoSqu919416604sum2sq @ ( times_times_int @ X_1 @ Y_1 ) ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_91_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 0.59/0.77 ! [Lx_6: int,Ly_4: int,Rx_6: int,Ry_4: int] :
% 0.59/0.77 ( ( times_times_int @ ( times_times_int @ Lx_6 @ Ly_4 ) @ ( times_times_int @ Rx_6 @ Ry_4 ) )
% 0.59/0.77 = ( times_times_int @ ( times_times_int @ Lx_6 @ Rx_6 ) @ ( times_times_int @ Ly_4 @ Ry_4 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_92_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 0.59/0.77 ! [Lx_6: nat,Ly_4: nat,Rx_6: nat,Ry_4: nat] :
% 0.59/0.77 ( ( times_times_nat @ ( times_times_nat @ Lx_6 @ Ly_4 ) @ ( times_times_nat @ Rx_6 @ Ry_4 ) )
% 0.59/0.77 = ( times_times_nat @ ( times_times_nat @ Lx_6 @ Rx_6 ) @ ( times_times_nat @ Ly_4 @ Ry_4 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_93_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom,
% 0.59/0.77 ! [Lx_6: real,Ly_4: real,Rx_6: real,Ry_4: real] :
% 0.59/0.77 ( ( times_times_real @ ( times_times_real @ Lx_6 @ Ly_4 ) @ ( times_times_real @ Rx_6 @ Ry_4 ) )
% 0.59/0.77 = ( times_times_real @ ( times_times_real @ Lx_6 @ Rx_6 ) @ ( times_times_real @ Ly_4 @ Ry_4 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_94_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 0.59/0.77 ! [Lx_5: int,Ly_3: int,Rx_5: int,Ry_3: int] :
% 0.59/0.77 ( ( times_times_int @ ( times_times_int @ Lx_5 @ Ly_3 ) @ ( times_times_int @ Rx_5 @ Ry_3 ) )
% 0.59/0.77 = ( times_times_int @ Rx_5 @ ( times_times_int @ ( times_times_int @ Lx_5 @ Ly_3 ) @ Ry_3 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_95_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 0.59/0.77 ! [Lx_5: nat,Ly_3: nat,Rx_5: nat,Ry_3: nat] :
% 0.59/0.77 ( ( times_times_nat @ ( times_times_nat @ Lx_5 @ Ly_3 ) @ ( times_times_nat @ Rx_5 @ Ry_3 ) )
% 0.59/0.77 = ( times_times_nat @ Rx_5 @ ( times_times_nat @ ( times_times_nat @ Lx_5 @ Ly_3 ) @ Ry_3 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_96_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom,
% 0.59/0.77 ! [Lx_5: real,Ly_3: real,Rx_5: real,Ry_3: real] :
% 0.59/0.77 ( ( times_times_real @ ( times_times_real @ Lx_5 @ Ly_3 ) @ ( times_times_real @ Rx_5 @ Ry_3 ) )
% 0.59/0.77 = ( times_times_real @ Rx_5 @ ( times_times_real @ ( times_times_real @ Lx_5 @ Ly_3 ) @ Ry_3 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_97_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 0.59/0.77 ! [Lx_4: int,Ly_2: int,Rx_4: int,Ry_2: int] :
% 0.59/0.77 ( ( times_times_int @ ( times_times_int @ Lx_4 @ Ly_2 ) @ ( times_times_int @ Rx_4 @ Ry_2 ) )
% 0.59/0.77 = ( times_times_int @ Lx_4 @ ( times_times_int @ Ly_2 @ ( times_times_int @ Rx_4 @ Ry_2 ) ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_98_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 0.59/0.77 ! [Lx_4: nat,Ly_2: nat,Rx_4: nat,Ry_2: nat] :
% 0.59/0.77 ( ( times_times_nat @ ( times_times_nat @ Lx_4 @ Ly_2 ) @ ( times_times_nat @ Rx_4 @ Ry_2 ) )
% 0.59/0.77 = ( times_times_nat @ Lx_4 @ ( times_times_nat @ Ly_2 @ ( times_times_nat @ Rx_4 @ Ry_2 ) ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_99_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom,
% 0.59/0.77 ! [Lx_4: real,Ly_2: real,Rx_4: real,Ry_2: real] :
% 0.59/0.77 ( ( times_times_real @ ( times_times_real @ Lx_4 @ Ly_2 ) @ ( times_times_real @ Rx_4 @ Ry_2 ) )
% 0.59/0.77 = ( times_times_real @ Lx_4 @ ( times_times_real @ Ly_2 @ ( times_times_real @ Rx_4 @ Ry_2 ) ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_100_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 0.59/0.77 ! [Lx_3: int,Ly_1: int,Rx_3: int] :
% 0.59/0.77 ( ( times_times_int @ ( times_times_int @ Lx_3 @ Ly_1 ) @ Rx_3 )
% 0.59/0.77 = ( times_times_int @ ( times_times_int @ Lx_3 @ Rx_3 ) @ Ly_1 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_101_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 0.59/0.77 ! [Lx_3: nat,Ly_1: nat,Rx_3: nat] :
% 0.59/0.77 ( ( times_times_nat @ ( times_times_nat @ Lx_3 @ Ly_1 ) @ Rx_3 )
% 0.59/0.77 = ( times_times_nat @ ( times_times_nat @ Lx_3 @ Rx_3 ) @ Ly_1 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_102_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom,
% 0.59/0.77 ! [Lx_3: real,Ly_1: real,Rx_3: real] :
% 0.59/0.77 ( ( times_times_real @ ( times_times_real @ Lx_3 @ Ly_1 ) @ Rx_3 )
% 0.59/0.77 = ( times_times_real @ ( times_times_real @ Lx_3 @ Rx_3 ) @ Ly_1 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_103_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 0.59/0.77 ! [Lx_2: int,Ly: int,Rx_2: int] :
% 0.59/0.77 ( ( times_times_int @ ( times_times_int @ Lx_2 @ Ly ) @ Rx_2 )
% 0.59/0.77 = ( times_times_int @ Lx_2 @ ( times_times_int @ Ly @ Rx_2 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_104_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 0.59/0.77 ! [Lx_2: nat,Ly: nat,Rx_2: nat] :
% 0.59/0.77 ( ( times_times_nat @ ( times_times_nat @ Lx_2 @ Ly ) @ Rx_2 )
% 0.59/0.77 = ( times_times_nat @ Lx_2 @ ( times_times_nat @ Ly @ Rx_2 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_105_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom,
% 0.59/0.77 ! [Lx_2: real,Ly: real,Rx_2: real] :
% 0.59/0.77 ( ( times_times_real @ ( times_times_real @ Lx_2 @ Ly ) @ Rx_2 )
% 0.59/0.77 = ( times_times_real @ Lx_2 @ ( times_times_real @ Ly @ Rx_2 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_106_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 0.59/0.77 ! [Lx_1: int,Rx_1: int,Ry_1: int] :
% 0.59/0.77 ( ( times_times_int @ Lx_1 @ ( times_times_int @ Rx_1 @ Ry_1 ) )
% 0.59/0.77 = ( times_times_int @ ( times_times_int @ Lx_1 @ Rx_1 ) @ Ry_1 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_107_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 0.59/0.77 ! [Lx_1: nat,Rx_1: nat,Ry_1: nat] :
% 0.59/0.77 ( ( times_times_nat @ Lx_1 @ ( times_times_nat @ Rx_1 @ Ry_1 ) )
% 0.59/0.77 = ( times_times_nat @ ( times_times_nat @ Lx_1 @ Rx_1 ) @ Ry_1 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_108_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom,
% 0.59/0.77 ! [Lx_1: real,Rx_1: real,Ry_1: real] :
% 0.59/0.77 ( ( times_times_real @ Lx_1 @ ( times_times_real @ Rx_1 @ Ry_1 ) )
% 0.59/0.77 = ( times_times_real @ ( times_times_real @ Lx_1 @ Rx_1 ) @ Ry_1 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_109_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 0.59/0.77 ! [Lx: int,Rx: int,Ry: int] :
% 0.59/0.77 ( ( times_times_int @ Lx @ ( times_times_int @ Rx @ Ry ) )
% 0.59/0.77 = ( times_times_int @ Rx @ ( times_times_int @ Lx @ Ry ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_110_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 0.59/0.77 ! [Lx: nat,Rx: nat,Ry: nat] :
% 0.59/0.77 ( ( times_times_nat @ Lx @ ( times_times_nat @ Rx @ Ry ) )
% 0.59/0.77 = ( times_times_nat @ Rx @ ( times_times_nat @ Lx @ Ry ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_111_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom,
% 0.59/0.77 ! [Lx: real,Rx: real,Ry: real] :
% 0.59/0.77 ( ( times_times_real @ Lx @ ( times_times_real @ Rx @ Ry ) )
% 0.59/0.77 = ( times_times_real @ Rx @ ( times_times_real @ Lx @ Ry ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_112_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 0.59/0.77 ! [A_126: int,B_73: int] :
% 0.59/0.77 ( ( times_times_int @ A_126 @ B_73 )
% 0.59/0.77 = ( times_times_int @ B_73 @ A_126 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_113_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 0.59/0.77 ! [A_126: nat,B_73: nat] :
% 0.59/0.77 ( ( times_times_nat @ A_126 @ B_73 )
% 0.59/0.77 = ( times_times_nat @ B_73 @ A_126 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_114_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom,
% 0.59/0.77 ! [A_126: real,B_73: real] :
% 0.59/0.77 ( ( times_times_real @ A_126 @ B_73 )
% 0.59/0.77 = ( times_times_real @ B_73 @ A_126 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_115_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 0.59/0.77 ! [A_125: int,B_72: int,C_39: int,D_11: int] :
% 0.59/0.77 ( ( plus_plus_int @ ( plus_plus_int @ A_125 @ B_72 ) @ ( plus_plus_int @ C_39 @ D_11 ) )
% 0.59/0.77 = ( plus_plus_int @ ( plus_plus_int @ A_125 @ C_39 ) @ ( plus_plus_int @ B_72 @ D_11 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_116_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 0.59/0.77 ! [A_125: nat,B_72: nat,C_39: nat,D_11: nat] :
% 0.59/0.77 ( ( plus_plus_nat @ ( plus_plus_nat @ A_125 @ B_72 ) @ ( plus_plus_nat @ C_39 @ D_11 ) )
% 0.59/0.77 = ( plus_plus_nat @ ( plus_plus_nat @ A_125 @ C_39 ) @ ( plus_plus_nat @ B_72 @ D_11 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_117_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom,
% 0.59/0.77 ! [A_125: real,B_72: real,C_39: real,D_11: real] :
% 0.59/0.77 ( ( plus_plus_real @ ( plus_plus_real @ A_125 @ B_72 ) @ ( plus_plus_real @ C_39 @ D_11 ) )
% 0.59/0.77 = ( plus_plus_real @ ( plus_plus_real @ A_125 @ C_39 ) @ ( plus_plus_real @ B_72 @ D_11 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_118_mem__def,axiom,
% 0.59/0.77 ! [X_36: int,A_124: int > $o] :
% 0.59/0.77 ( ( member_int @ X_36 @ A_124 )
% 0.59/0.77 <=> ( A_124 @ X_36 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_119_Collect__def,axiom,
% 0.59/0.77 ! [P_4: int > $o] :
% 0.59/0.77 ( ( collect_int @ P_4 )
% 0.59/0.77 = P_4 ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_120_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 0.59/0.77 ! [A_123: int,B_71: int,C_38: int] :
% 0.59/0.77 ( ( plus_plus_int @ ( plus_plus_int @ A_123 @ B_71 ) @ C_38 )
% 0.59/0.77 = ( plus_plus_int @ ( plus_plus_int @ A_123 @ C_38 ) @ B_71 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_121_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 0.59/0.77 ! [A_123: nat,B_71: nat,C_38: nat] :
% 0.59/0.77 ( ( plus_plus_nat @ ( plus_plus_nat @ A_123 @ B_71 ) @ C_38 )
% 0.59/0.77 = ( plus_plus_nat @ ( plus_plus_nat @ A_123 @ C_38 ) @ B_71 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_122_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom,
% 0.59/0.77 ! [A_123: real,B_71: real,C_38: real] :
% 0.59/0.77 ( ( plus_plus_real @ ( plus_plus_real @ A_123 @ B_71 ) @ C_38 )
% 0.59/0.77 = ( plus_plus_real @ ( plus_plus_real @ A_123 @ C_38 ) @ B_71 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_123_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 0.59/0.77 ! [A_122: int,B_70: int,C_37: int] :
% 0.59/0.77 ( ( plus_plus_int @ ( plus_plus_int @ A_122 @ B_70 ) @ C_37 )
% 0.59/0.77 = ( plus_plus_int @ A_122 @ ( plus_plus_int @ B_70 @ C_37 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_124_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 0.59/0.77 ! [A_122: nat,B_70: nat,C_37: nat] :
% 0.59/0.77 ( ( plus_plus_nat @ ( plus_plus_nat @ A_122 @ B_70 ) @ C_37 )
% 0.59/0.77 = ( plus_plus_nat @ A_122 @ ( plus_plus_nat @ B_70 @ C_37 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_125_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom,
% 0.59/0.77 ! [A_122: real,B_70: real,C_37: real] :
% 0.59/0.77 ( ( plus_plus_real @ ( plus_plus_real @ A_122 @ B_70 ) @ C_37 )
% 0.59/0.77 = ( plus_plus_real @ A_122 @ ( plus_plus_real @ B_70 @ C_37 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_126_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 0.59/0.77 ! [A_121: int,C_36: int,D_10: int] :
% 0.59/0.77 ( ( plus_plus_int @ A_121 @ ( plus_plus_int @ C_36 @ D_10 ) )
% 0.59/0.77 = ( plus_plus_int @ ( plus_plus_int @ A_121 @ C_36 ) @ D_10 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_127_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 0.59/0.77 ! [A_121: nat,C_36: nat,D_10: nat] :
% 0.59/0.77 ( ( plus_plus_nat @ A_121 @ ( plus_plus_nat @ C_36 @ D_10 ) )
% 0.59/0.77 = ( plus_plus_nat @ ( plus_plus_nat @ A_121 @ C_36 ) @ D_10 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_128_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom,
% 0.59/0.77 ! [A_121: real,C_36: real,D_10: real] :
% 0.59/0.77 ( ( plus_plus_real @ A_121 @ ( plus_plus_real @ C_36 @ D_10 ) )
% 0.59/0.77 = ( plus_plus_real @ ( plus_plus_real @ A_121 @ C_36 ) @ D_10 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_129_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 0.59/0.77 ! [A_120: int,C_35: int,D_9: int] :
% 0.59/0.77 ( ( plus_plus_int @ A_120 @ ( plus_plus_int @ C_35 @ D_9 ) )
% 0.59/0.77 = ( plus_plus_int @ C_35 @ ( plus_plus_int @ A_120 @ D_9 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_130_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 0.59/0.77 ! [A_120: nat,C_35: nat,D_9: nat] :
% 0.59/0.77 ( ( plus_plus_nat @ A_120 @ ( plus_plus_nat @ C_35 @ D_9 ) )
% 0.59/0.77 = ( plus_plus_nat @ C_35 @ ( plus_plus_nat @ A_120 @ D_9 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_131_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom,
% 0.59/0.77 ! [A_120: real,C_35: real,D_9: real] :
% 0.59/0.77 ( ( plus_plus_real @ A_120 @ ( plus_plus_real @ C_35 @ D_9 ) )
% 0.59/0.77 = ( plus_plus_real @ C_35 @ ( plus_plus_real @ A_120 @ D_9 ) ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_132_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 0.59/0.77 ! [A_119: int,C_34: int] :
% 0.59/0.77 ( ( plus_plus_int @ A_119 @ C_34 )
% 0.59/0.77 = ( plus_plus_int @ C_34 @ A_119 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_133_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 0.59/0.77 ! [A_119: nat,C_34: nat] :
% 0.59/0.77 ( ( plus_plus_nat @ A_119 @ C_34 )
% 0.59/0.77 = ( plus_plus_nat @ C_34 @ A_119 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_134_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom,
% 0.59/0.77 ! [A_119: real,C_34: real] :
% 0.59/0.77 ( ( plus_plus_real @ A_119 @ C_34 )
% 0.59/0.77 = ( plus_plus_real @ C_34 @ A_119 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_135_eq__number__of,axiom,
% 0.59/0.77 ! [X_35: int,Y_31: int] :
% 0.59/0.77 ( ( ( number_number_of_int @ X_35 )
% 0.59/0.77 = ( number_number_of_int @ Y_31 ) )
% 0.59/0.77 <=> ( X_35 = Y_31 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_136_eq__number__of,axiom,
% 0.59/0.77 ! [X_35: int,Y_31: int] :
% 0.59/0.77 ( ( ( number267125858f_real @ X_35 )
% 0.59/0.77 = ( number267125858f_real @ Y_31 ) )
% 0.59/0.77 <=> ( X_35 = Y_31 ) ) ).
% 0.59/0.77
% 0.59/0.77 thf(fact_137_number__of__reorient,axiom,
% 0.59/0.78 ! [W_15: int,X_34: nat] :
% 0.59/0.78 ( ( ( number_number_of_nat @ W_15 )
% 0.59/0.78 = X_34 )
% 0.59/0.78 <=> ( X_34
% 0.59/0.78 = ( number_number_of_nat @ W_15 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_138_number__of__reorient,axiom,
% 0.59/0.78 ! [W_15: int,X_34: int] :
% 0.59/0.78 ( ( ( number_number_of_int @ W_15 )
% 0.59/0.78 = X_34 )
% 0.59/0.78 <=> ( X_34
% 0.59/0.78 = ( number_number_of_int @ W_15 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_139_number__of__reorient,axiom,
% 0.59/0.78 ! [W_15: int,X_34: real] :
% 0.59/0.78 ( ( ( number267125858f_real @ W_15 )
% 0.59/0.78 = X_34 )
% 0.59/0.78 <=> ( X_34
% 0.59/0.78 = ( number267125858f_real @ W_15 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_140_rel__simps_I51_J,axiom,
% 0.59/0.78 ! [K: int,L: int] :
% 0.59/0.78 ( ( ( bit1 @ K )
% 0.59/0.78 = ( bit1 @ L ) )
% 0.59/0.78 <=> ( K = L ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_141_rel__simps_I48_J,axiom,
% 0.59/0.78 ! [K: int,L: int] :
% 0.59/0.78 ( ( ( bit0 @ K )
% 0.59/0.78 = ( bit0 @ L ) )
% 0.59/0.78 <=> ( K = L ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_142_zmult__assoc,axiom,
% 0.59/0.78 ! [Z1: int,Z2: int,Z3: int] :
% 0.59/0.78 ( ( times_times_int @ ( times_times_int @ Z1 @ Z2 ) @ Z3 )
% 0.59/0.78 = ( times_times_int @ Z1 @ ( times_times_int @ Z2 @ Z3 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_143_zmult__commute,axiom,
% 0.59/0.78 ! [Z: int,W: int] :
% 0.59/0.78 ( ( times_times_int @ Z @ W )
% 0.59/0.78 = ( times_times_int @ W @ Z ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_144_number__of__is__id,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( number_number_of_int @ K )
% 0.59/0.78 = K ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_145_zadd__assoc,axiom,
% 0.59/0.78 ! [Z1: int,Z2: int,Z3: int] :
% 0.59/0.78 ( ( plus_plus_int @ ( plus_plus_int @ Z1 @ Z2 ) @ Z3 )
% 0.59/0.78 = ( plus_plus_int @ Z1 @ ( plus_plus_int @ Z2 @ Z3 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_146_zadd__left__commute,axiom,
% 0.59/0.78 ! [X_1: int,Y_1: int,Z: int] :
% 0.59/0.78 ( ( plus_plus_int @ X_1 @ ( plus_plus_int @ Y_1 @ Z ) )
% 0.59/0.78 = ( plus_plus_int @ Y_1 @ ( plus_plus_int @ X_1 @ Z ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_147_zadd__commute,axiom,
% 0.59/0.78 ! [Z: int,W: int] :
% 0.59/0.78 ( ( plus_plus_int @ Z @ W )
% 0.59/0.78 = ( plus_plus_int @ W @ Z ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_148_rel__simps_I12_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( ord_less_int @ ( bit1 @ K ) @ pls )
% 0.59/0.78 <=> ( ord_less_int @ K @ pls ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_149_less__int__code_I15_J,axiom,
% 0.59/0.78 ! [K1: int,K2: int] :
% 0.59/0.78 ( ( ord_less_int @ ( bit1 @ K1 ) @ ( bit0 @ K2 ) )
% 0.59/0.78 <=> ( ord_less_int @ K1 @ K2 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_150_rel__simps_I16_J,axiom,
% 0.59/0.78 ! [K: int,L: int] :
% 0.59/0.78 ( ( ord_less_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
% 0.59/0.78 <=> ( ord_less_int @ K @ L ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_151_rel__simps_I10_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( ord_less_int @ ( bit0 @ K ) @ pls )
% 0.59/0.78 <=> ( ord_less_int @ K @ pls ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_152_rel__simps_I4_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( ord_less_int @ pls @ ( bit0 @ K ) )
% 0.59/0.78 <=> ( ord_less_int @ pls @ K ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_153_rel__simps_I22_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ pls @ ( bit1 @ K ) )
% 0.59/0.78 <=> ( ord_less_eq_int @ pls @ K ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_154_less__eq__int__code_I14_J,axiom,
% 0.59/0.78 ! [K1: int,K2: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ ( bit0 @ K1 ) @ ( bit1 @ K2 ) )
% 0.59/0.78 <=> ( ord_less_eq_int @ K1 @ K2 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_155_rel__simps_I32_J,axiom,
% 0.59/0.78 ! [K: int,L: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
% 0.59/0.78 <=> ( ord_less_eq_int @ K @ L ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_156_rel__simps_I27_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ ( bit0 @ K ) @ pls )
% 0.59/0.78 <=> ( ord_less_eq_int @ K @ pls ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_157_rel__simps_I21_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ pls @ ( bit0 @ K ) )
% 0.59/0.78 <=> ( ord_less_eq_int @ pls @ K ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_158_zless__add1__eq,axiom,
% 0.59/0.78 ! [W: int,Z: int] :
% 0.59/0.78 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 0.59/0.78 <=> ( ( ord_less_int @ W @ Z )
% 0.59/0.78 | ( W = Z ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_159_power__even__eq,axiom,
% 0.59/0.78 ! [A_118: int,N_40: nat] :
% 0.59/0.78 ( ( power_power_int @ A_118 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_40 ) )
% 0.59/0.78 = ( power_power_int @ ( power_power_int @ A_118 @ N_40 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_160_power__even__eq,axiom,
% 0.59/0.78 ! [A_118: real,N_40: nat] :
% 0.59/0.78 ( ( power_power_real @ A_118 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_40 ) )
% 0.59/0.78 = ( power_power_real @ ( power_power_real @ A_118 @ N_40 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_161_power__even__eq,axiom,
% 0.59/0.78 ! [A_118: nat,N_40: nat] :
% 0.59/0.78 ( ( power_power_nat @ A_118 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_40 ) )
% 0.59/0.78 = ( power_power_nat @ ( power_power_nat @ A_118 @ N_40 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_162_less__special_I4_J,axiom,
% 0.59/0.78 ! [X_33: int] :
% 0.59/0.78 ( ( ord_less_int @ ( number_number_of_int @ X_33 ) @ one_one_int )
% 0.59/0.78 <=> ( ord_less_int @ X_33 @ ( bit1 @ pls ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_163_less__special_I4_J,axiom,
% 0.59/0.78 ! [X_33: int] :
% 0.59/0.78 ( ( ord_less_real @ ( number267125858f_real @ X_33 ) @ one_one_real )
% 0.59/0.78 <=> ( ord_less_int @ X_33 @ ( bit1 @ pls ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_164_less__special_I2_J,axiom,
% 0.59/0.78 ! [Y_30: int] :
% 0.59/0.78 ( ( ord_less_int @ one_one_int @ ( number_number_of_int @ Y_30 ) )
% 0.59/0.78 <=> ( ord_less_int @ ( bit1 @ pls ) @ Y_30 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_165_less__special_I2_J,axiom,
% 0.59/0.78 ! [Y_30: int] :
% 0.59/0.78 ( ( ord_less_real @ one_one_real @ ( number267125858f_real @ Y_30 ) )
% 0.59/0.78 <=> ( ord_less_int @ ( bit1 @ pls ) @ Y_30 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_166_le__special_I4_J,axiom,
% 0.59/0.78 ! [X_32: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ ( number_number_of_int @ X_32 ) @ one_one_int )
% 0.59/0.78 <=> ( ord_less_eq_int @ X_32 @ ( bit1 @ pls ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_167_le__special_I4_J,axiom,
% 0.59/0.78 ! [X_32: int] :
% 0.59/0.78 ( ( ord_less_eq_real @ ( number267125858f_real @ X_32 ) @ one_one_real )
% 0.59/0.78 <=> ( ord_less_eq_int @ X_32 @ ( bit1 @ pls ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_168_le__special_I2_J,axiom,
% 0.59/0.78 ! [Y_29: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ one_one_int @ ( number_number_of_int @ Y_29 ) )
% 0.59/0.78 <=> ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_29 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_169_le__special_I2_J,axiom,
% 0.59/0.78 ! [Y_29: int] :
% 0.59/0.78 ( ( ord_less_eq_real @ one_one_real @ ( number267125858f_real @ Y_29 ) )
% 0.59/0.78 <=> ( ord_less_eq_int @ ( bit1 @ pls ) @ Y_29 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_170_crossproduct__eq,axiom,
% 0.59/0.78 ! [W_14: int,Y_28: int,X_31: int,Z_9: int] :
% 0.59/0.78 ( ( ( plus_plus_int @ ( times_times_int @ W_14 @ Y_28 ) @ ( times_times_int @ X_31 @ Z_9 ) )
% 0.59/0.78 = ( plus_plus_int @ ( times_times_int @ W_14 @ Z_9 ) @ ( times_times_int @ X_31 @ Y_28 ) ) )
% 0.59/0.78 <=> ( ( W_14 = X_31 )
% 0.59/0.78 | ( Y_28 = Z_9 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_171_crossproduct__eq,axiom,
% 0.59/0.78 ! [W_14: nat,Y_28: nat,X_31: nat,Z_9: nat] :
% 0.59/0.78 ( ( ( plus_plus_nat @ ( times_times_nat @ W_14 @ Y_28 ) @ ( times_times_nat @ X_31 @ Z_9 ) )
% 0.59/0.78 = ( plus_plus_nat @ ( times_times_nat @ W_14 @ Z_9 ) @ ( times_times_nat @ X_31 @ Y_28 ) ) )
% 0.59/0.78 <=> ( ( W_14 = X_31 )
% 0.59/0.78 | ( Y_28 = Z_9 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_172_crossproduct__eq,axiom,
% 0.59/0.78 ! [W_14: real,Y_28: real,X_31: real,Z_9: real] :
% 0.59/0.78 ( ( ( plus_plus_real @ ( times_times_real @ W_14 @ Y_28 ) @ ( times_times_real @ X_31 @ Z_9 ) )
% 0.59/0.78 = ( plus_plus_real @ ( times_times_real @ W_14 @ Z_9 ) @ ( times_times_real @ X_31 @ Y_28 ) ) )
% 0.59/0.78 <=> ( ( W_14 = X_31 )
% 0.59/0.78 | ( Y_28 = Z_9 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_173_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 0.59/0.78 ! [A_117: int,M_14: int,B_69: int] :
% 0.59/0.78 ( ( plus_plus_int @ ( times_times_int @ A_117 @ M_14 ) @ ( times_times_int @ B_69 @ M_14 ) )
% 0.59/0.78 = ( times_times_int @ ( plus_plus_int @ A_117 @ B_69 ) @ M_14 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_174_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 0.59/0.78 ! [A_117: nat,M_14: nat,B_69: nat] :
% 0.59/0.78 ( ( plus_plus_nat @ ( times_times_nat @ A_117 @ M_14 ) @ ( times_times_nat @ B_69 @ M_14 ) )
% 0.59/0.78 = ( times_times_nat @ ( plus_plus_nat @ A_117 @ B_69 ) @ M_14 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_175_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom,
% 0.59/0.78 ! [A_117: real,M_14: real,B_69: real] :
% 0.59/0.78 ( ( plus_plus_real @ ( times_times_real @ A_117 @ M_14 ) @ ( times_times_real @ B_69 @ M_14 ) )
% 0.59/0.78 = ( times_times_real @ ( plus_plus_real @ A_117 @ B_69 ) @ M_14 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_176_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 0.59/0.78 ! [A_116: int,B_68: int,C_33: int] :
% 0.59/0.78 ( ( times_times_int @ ( plus_plus_int @ A_116 @ B_68 ) @ C_33 )
% 0.59/0.78 = ( plus_plus_int @ ( times_times_int @ A_116 @ C_33 ) @ ( times_times_int @ B_68 @ C_33 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_177_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 0.59/0.78 ! [A_116: nat,B_68: nat,C_33: nat] :
% 0.59/0.78 ( ( times_times_nat @ ( plus_plus_nat @ A_116 @ B_68 ) @ C_33 )
% 0.59/0.78 = ( plus_plus_nat @ ( times_times_nat @ A_116 @ C_33 ) @ ( times_times_nat @ B_68 @ C_33 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_178_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom,
% 0.59/0.78 ! [A_116: real,B_68: real,C_33: real] :
% 0.59/0.78 ( ( times_times_real @ ( plus_plus_real @ A_116 @ B_68 ) @ C_33 )
% 0.59/0.78 = ( plus_plus_real @ ( times_times_real @ A_116 @ C_33 ) @ ( times_times_real @ B_68 @ C_33 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_179_crossproduct__noteq,axiom,
% 0.59/0.78 ! [C_32: int,D_8: int,A_115: int,B_67: int] :
% 0.59/0.78 ( ( ( A_115 != B_67 )
% 0.59/0.78 & ( C_32 != D_8 ) )
% 0.59/0.78 <=> ( ( plus_plus_int @ ( times_times_int @ A_115 @ C_32 ) @ ( times_times_int @ B_67 @ D_8 ) )
% 0.59/0.78 != ( plus_plus_int @ ( times_times_int @ A_115 @ D_8 ) @ ( times_times_int @ B_67 @ C_32 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_180_crossproduct__noteq,axiom,
% 0.59/0.78 ! [C_32: nat,D_8: nat,A_115: nat,B_67: nat] :
% 0.59/0.78 ( ( ( A_115 != B_67 )
% 0.59/0.78 & ( C_32 != D_8 ) )
% 0.59/0.78 <=> ( ( plus_plus_nat @ ( times_times_nat @ A_115 @ C_32 ) @ ( times_times_nat @ B_67 @ D_8 ) )
% 0.59/0.78 != ( plus_plus_nat @ ( times_times_nat @ A_115 @ D_8 ) @ ( times_times_nat @ B_67 @ C_32 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_181_crossproduct__noteq,axiom,
% 0.59/0.78 ! [C_32: real,D_8: real,A_115: real,B_67: real] :
% 0.59/0.78 ( ( ( A_115 != B_67 )
% 0.59/0.78 & ( C_32 != D_8 ) )
% 0.59/0.78 <=> ( ( plus_plus_real @ ( times_times_real @ A_115 @ C_32 ) @ ( times_times_real @ B_67 @ D_8 ) )
% 0.59/0.78 != ( plus_plus_real @ ( times_times_real @ A_115 @ D_8 ) @ ( times_times_real @ B_67 @ C_32 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_182_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 0.59/0.78 ! [X_30: int,Y_27: int,Z_8: int] :
% 0.59/0.78 ( ( times_times_int @ X_30 @ ( plus_plus_int @ Y_27 @ Z_8 ) )
% 0.59/0.78 = ( plus_plus_int @ ( times_times_int @ X_30 @ Y_27 ) @ ( times_times_int @ X_30 @ Z_8 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_183_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 0.59/0.78 ! [X_30: nat,Y_27: nat,Z_8: nat] :
% 0.59/0.78 ( ( times_times_nat @ X_30 @ ( plus_plus_nat @ Y_27 @ Z_8 ) )
% 0.59/0.78 = ( plus_plus_nat @ ( times_times_nat @ X_30 @ Y_27 ) @ ( times_times_nat @ X_30 @ Z_8 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_184_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom,
% 0.59/0.78 ! [X_30: real,Y_27: real,Z_8: real] :
% 0.59/0.78 ( ( times_times_real @ X_30 @ ( plus_plus_real @ Y_27 @ Z_8 ) )
% 0.59/0.78 = ( plus_plus_real @ ( times_times_real @ X_30 @ Y_27 ) @ ( times_times_real @ X_30 @ Z_8 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_185_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 0.59/0.78 ! [A_114: int] :
% 0.59/0.78 ( ( times_times_int @ A_114 @ one_one_int )
% 0.59/0.78 = A_114 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_186_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 0.59/0.78 ! [A_114: nat] :
% 0.59/0.78 ( ( times_times_nat @ A_114 @ one_one_nat )
% 0.59/0.78 = A_114 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_187_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom,
% 0.59/0.78 ! [A_114: real] :
% 0.59/0.78 ( ( times_times_real @ A_114 @ one_one_real )
% 0.59/0.78 = A_114 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_188_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 0.59/0.78 ! [A_113: int] :
% 0.59/0.78 ( ( times_times_int @ one_one_int @ A_113 )
% 0.59/0.78 = A_113 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_189_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 0.59/0.78 ! [A_113: nat] :
% 0.59/0.78 ( ( times_times_nat @ one_one_nat @ A_113 )
% 0.59/0.78 = A_113 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_190_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom,
% 0.59/0.78 ! [A_113: real] :
% 0.59/0.78 ( ( times_times_real @ one_one_real @ A_113 )
% 0.59/0.78 = A_113 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_191_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 0.59/0.78 ! [X_29: int,Y_26: int,Q_4: nat] :
% 0.59/0.78 ( ( power_power_int @ ( times_times_int @ X_29 @ Y_26 ) @ Q_4 )
% 0.59/0.78 = ( times_times_int @ ( power_power_int @ X_29 @ Q_4 ) @ ( power_power_int @ Y_26 @ Q_4 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 0.59/0.78 ! [X_29: real,Y_26: real,Q_4: nat] :
% 0.59/0.78 ( ( power_power_real @ ( times_times_real @ X_29 @ Y_26 ) @ Q_4 )
% 0.59/0.78 = ( times_times_real @ ( power_power_real @ X_29 @ Q_4 ) @ ( power_power_real @ Y_26 @ Q_4 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom,
% 0.59/0.78 ! [X_29: nat,Y_26: nat,Q_4: nat] :
% 0.59/0.78 ( ( power_power_nat @ ( times_times_nat @ X_29 @ Y_26 ) @ Q_4 )
% 0.59/0.78 = ( times_times_nat @ ( power_power_nat @ X_29 @ Q_4 ) @ ( power_power_nat @ Y_26 @ Q_4 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_194_rel__simps_I46_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( bit1 @ K )
% 0.59/0.78 != pls ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_195_rel__simps_I39_J,axiom,
% 0.59/0.78 ! [L: int] :
% 0.59/0.78 ( pls
% 0.59/0.78 != ( bit1 @ L ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_196_rel__simps_I50_J,axiom,
% 0.59/0.78 ! [K: int,L: int] :
% 0.59/0.78 ( ( bit1 @ K )
% 0.59/0.78 != ( bit0 @ L ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_197_rel__simps_I49_J,axiom,
% 0.59/0.78 ! [K: int,L: int] :
% 0.59/0.78 ( ( bit0 @ K )
% 0.59/0.78 != ( bit1 @ L ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_198_rel__simps_I44_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( ( bit0 @ K )
% 0.59/0.78 = pls )
% 0.59/0.78 <=> ( K = pls ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_199_rel__simps_I38_J,axiom,
% 0.59/0.78 ! [L: int] :
% 0.59/0.78 ( ( pls
% 0.59/0.78 = ( bit0 @ L ) )
% 0.59/0.78 <=> ( pls = L ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_200_Bit0__Pls,axiom,
% 0.59/0.78 ( ( bit0 @ pls )
% 0.59/0.78 = pls ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_201_mult__Pls,axiom,
% 0.59/0.78 ! [W: int] :
% 0.59/0.78 ( ( times_times_int @ pls @ W )
% 0.59/0.78 = pls ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_202_mult__Bit0,axiom,
% 0.59/0.78 ! [K: int,L: int] :
% 0.59/0.78 ( ( times_times_int @ ( bit0 @ K ) @ L )
% 0.59/0.78 = ( bit0 @ ( times_times_int @ K @ L ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_203_add__Pls__right,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( plus_plus_int @ K @ pls )
% 0.59/0.78 = K ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_204_add__Pls,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( plus_plus_int @ pls @ K )
% 0.59/0.78 = K ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_205_add__Bit0__Bit0,axiom,
% 0.59/0.78 ! [K: int,L: int] :
% 0.59/0.78 ( ( plus_plus_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
% 0.59/0.78 = ( bit0 @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_206_Bit0__def,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( bit0 @ K )
% 0.59/0.78 = ( plus_plus_int @ K @ K ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_207_zmult__1__right,axiom,
% 0.59/0.78 ! [Z: int] :
% 0.59/0.78 ( ( times_times_int @ Z @ one_one_int )
% 0.59/0.78 = Z ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_208_zmult__1,axiom,
% 0.59/0.78 ! [Z: int] :
% 0.59/0.78 ( ( times_times_int @ one_one_int @ Z )
% 0.59/0.78 = Z ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_209_times__numeral__code_I5_J,axiom,
% 0.59/0.78 ! [V: int,W: int] :
% 0.59/0.78 ( ( times_times_int @ ( number_number_of_int @ V ) @ ( number_number_of_int @ W ) )
% 0.59/0.78 = ( number_number_of_int @ ( times_times_int @ V @ W ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_210_zadd__zmult__distrib,axiom,
% 0.59/0.78 ! [Z1: int,Z2: int,W: int] :
% 0.59/0.78 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z2 ) @ W )
% 0.59/0.78 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z2 @ W ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_211_zadd__zmult__distrib2,axiom,
% 0.59/0.78 ! [W: int,Z1: int,Z2: int] :
% 0.59/0.78 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z2 ) )
% 0.59/0.78 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z2 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_212_plus__numeral__code_I9_J,axiom,
% 0.59/0.78 ! [V: int,W: int] :
% 0.59/0.78 ( ( plus_plus_int @ ( number_number_of_int @ V ) @ ( number_number_of_int @ W ) )
% 0.59/0.78 = ( number_number_of_int @ ( plus_plus_int @ V @ W ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_213_semiring__mult__number__of,axiom,
% 0.59/0.78 ! [V_18: int,V_17: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ pls @ V_17 )
% 0.59/0.78 => ( ( ord_less_eq_int @ pls @ V_18 )
% 0.59/0.78 => ( ( times_times_int @ ( number_number_of_int @ V_17 ) @ ( number_number_of_int @ V_18 ) )
% 0.59/0.78 = ( number_number_of_int @ ( times_times_int @ V_17 @ V_18 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_214_semiring__mult__number__of,axiom,
% 0.59/0.78 ! [V_18: int,V_17: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ pls @ V_17 )
% 0.59/0.78 => ( ( ord_less_eq_int @ pls @ V_18 )
% 0.59/0.78 => ( ( times_times_nat @ ( number_number_of_nat @ V_17 ) @ ( number_number_of_nat @ V_18 ) )
% 0.59/0.78 = ( number_number_of_nat @ ( times_times_int @ V_17 @ V_18 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_215_semiring__mult__number__of,axiom,
% 0.59/0.78 ! [V_18: int,V_17: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ pls @ V_17 )
% 0.59/0.78 => ( ( ord_less_eq_int @ pls @ V_18 )
% 0.59/0.78 => ( ( times_times_real @ ( number267125858f_real @ V_17 ) @ ( number267125858f_real @ V_18 ) )
% 0.59/0.78 = ( number267125858f_real @ ( times_times_int @ V_17 @ V_18 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_216_semiring__add__number__of,axiom,
% 0.59/0.78 ! [V_16: int,V_15: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ pls @ V_15 )
% 0.59/0.78 => ( ( ord_less_eq_int @ pls @ V_16 )
% 0.59/0.78 => ( ( plus_plus_int @ ( number_number_of_int @ V_15 ) @ ( number_number_of_int @ V_16 ) )
% 0.59/0.78 = ( number_number_of_int @ ( plus_plus_int @ V_15 @ V_16 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_217_semiring__add__number__of,axiom,
% 0.59/0.78 ! [V_16: int,V_15: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ pls @ V_15 )
% 0.59/0.78 => ( ( ord_less_eq_int @ pls @ V_16 )
% 0.59/0.78 => ( ( plus_plus_nat @ ( number_number_of_nat @ V_15 ) @ ( number_number_of_nat @ V_16 ) )
% 0.59/0.78 = ( number_number_of_nat @ ( plus_plus_int @ V_15 @ V_16 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_218_semiring__add__number__of,axiom,
% 0.59/0.78 ! [V_16: int,V_15: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ pls @ V_15 )
% 0.59/0.78 => ( ( ord_less_eq_int @ pls @ V_16 )
% 0.59/0.78 => ( ( plus_plus_real @ ( number267125858f_real @ V_15 ) @ ( number267125858f_real @ V_16 ) )
% 0.59/0.78 = ( number267125858f_real @ ( plus_plus_int @ V_15 @ V_16 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_219_power2__ge__self,axiom,
% 0.59/0.78 ! [X_1: int] : ( ord_less_eq_int @ X_1 @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_220_left__distrib__number__of,axiom,
% 0.59/0.78 ! [A_112: int,B_66: int,V_14: int] :
% 0.59/0.78 ( ( times_times_int @ ( plus_plus_int @ A_112 @ B_66 ) @ ( number_number_of_int @ V_14 ) )
% 0.59/0.78 = ( plus_plus_int @ ( times_times_int @ A_112 @ ( number_number_of_int @ V_14 ) ) @ ( times_times_int @ B_66 @ ( number_number_of_int @ V_14 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_221_left__distrib__number__of,axiom,
% 0.59/0.78 ! [A_112: nat,B_66: nat,V_14: int] :
% 0.59/0.78 ( ( times_times_nat @ ( plus_plus_nat @ A_112 @ B_66 ) @ ( number_number_of_nat @ V_14 ) )
% 0.59/0.78 = ( plus_plus_nat @ ( times_times_nat @ A_112 @ ( number_number_of_nat @ V_14 ) ) @ ( times_times_nat @ B_66 @ ( number_number_of_nat @ V_14 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_222_left__distrib__number__of,axiom,
% 0.59/0.78 ! [A_112: real,B_66: real,V_14: int] :
% 0.59/0.78 ( ( times_times_real @ ( plus_plus_real @ A_112 @ B_66 ) @ ( number267125858f_real @ V_14 ) )
% 0.59/0.78 = ( plus_plus_real @ ( times_times_real @ A_112 @ ( number267125858f_real @ V_14 ) ) @ ( times_times_real @ B_66 @ ( number267125858f_real @ V_14 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_223_right__distrib__number__of,axiom,
% 0.59/0.78 ! [V_13: int,B_65: int,C_31: int] :
% 0.59/0.78 ( ( times_times_int @ ( number_number_of_int @ V_13 ) @ ( plus_plus_int @ B_65 @ C_31 ) )
% 0.59/0.78 = ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ V_13 ) @ B_65 ) @ ( times_times_int @ ( number_number_of_int @ V_13 ) @ C_31 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_224_right__distrib__number__of,axiom,
% 0.59/0.78 ! [V_13: int,B_65: nat,C_31: nat] :
% 0.59/0.78 ( ( times_times_nat @ ( number_number_of_nat @ V_13 ) @ ( plus_plus_nat @ B_65 @ C_31 ) )
% 0.59/0.78 = ( plus_plus_nat @ ( times_times_nat @ ( number_number_of_nat @ V_13 ) @ B_65 ) @ ( times_times_nat @ ( number_number_of_nat @ V_13 ) @ C_31 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_225_right__distrib__number__of,axiom,
% 0.59/0.78 ! [V_13: int,B_65: real,C_31: real] :
% 0.59/0.78 ( ( times_times_real @ ( number267125858f_real @ V_13 ) @ ( plus_plus_real @ B_65 @ C_31 ) )
% 0.59/0.78 = ( plus_plus_real @ ( times_times_real @ ( number267125858f_real @ V_13 ) @ B_65 ) @ ( times_times_real @ ( number267125858f_real @ V_13 ) @ C_31 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 0.59/0.78 ! [A_111: int,M_13: int] :
% 0.59/0.78 ( ( plus_plus_int @ ( times_times_int @ A_111 @ M_13 ) @ M_13 )
% 0.59/0.78 = ( times_times_int @ ( plus_plus_int @ A_111 @ one_one_int ) @ M_13 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 0.59/0.78 ! [A_111: nat,M_13: nat] :
% 0.59/0.78 ( ( plus_plus_nat @ ( times_times_nat @ A_111 @ M_13 ) @ M_13 )
% 0.59/0.78 = ( times_times_nat @ ( plus_plus_nat @ A_111 @ one_one_nat ) @ M_13 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_228_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom,
% 0.59/0.78 ! [A_111: real,M_13: real] :
% 0.59/0.78 ( ( plus_plus_real @ ( times_times_real @ A_111 @ M_13 ) @ M_13 )
% 0.59/0.78 = ( times_times_real @ ( plus_plus_real @ A_111 @ one_one_real ) @ M_13 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_229_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 0.59/0.78 ! [M_12: int,A_110: int] :
% 0.59/0.78 ( ( plus_plus_int @ M_12 @ ( times_times_int @ A_110 @ M_12 ) )
% 0.59/0.78 = ( times_times_int @ ( plus_plus_int @ A_110 @ one_one_int ) @ M_12 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_230_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 0.59/0.78 ! [M_12: nat,A_110: nat] :
% 0.59/0.78 ( ( plus_plus_nat @ M_12 @ ( times_times_nat @ A_110 @ M_12 ) )
% 0.59/0.78 = ( times_times_nat @ ( plus_plus_nat @ A_110 @ one_one_nat ) @ M_12 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_231_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom,
% 0.59/0.78 ! [M_12: real,A_110: real] :
% 0.59/0.78 ( ( plus_plus_real @ M_12 @ ( times_times_real @ A_110 @ M_12 ) )
% 0.59/0.78 = ( times_times_real @ ( plus_plus_real @ A_110 @ one_one_real ) @ M_12 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_232_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 0.59/0.78 ! [M_11: int] :
% 0.59/0.78 ( ( plus_plus_int @ M_11 @ M_11 )
% 0.59/0.78 = ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ M_11 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_233_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 0.59/0.78 ! [M_11: nat] :
% 0.59/0.78 ( ( plus_plus_nat @ M_11 @ M_11 )
% 0.59/0.78 = ( times_times_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) @ M_11 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_234_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
% 0.59/0.78 ! [M_11: real] :
% 0.59/0.78 ( ( plus_plus_real @ M_11 @ M_11 )
% 0.59/0.78 = ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ M_11 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_235_add__numeral__0,axiom,
% 0.59/0.78 ! [A_109: int] :
% 0.59/0.78 ( ( plus_plus_int @ ( number_number_of_int @ pls ) @ A_109 )
% 0.59/0.78 = A_109 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_236_add__numeral__0,axiom,
% 0.59/0.78 ! [A_109: real] :
% 0.59/0.78 ( ( plus_plus_real @ ( number267125858f_real @ pls ) @ A_109 )
% 0.59/0.78 = A_109 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_237_add__numeral__0__right,axiom,
% 0.59/0.78 ! [A_108: int] :
% 0.59/0.78 ( ( plus_plus_int @ A_108 @ ( number_number_of_int @ pls ) )
% 0.59/0.78 = A_108 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_238_add__numeral__0__right,axiom,
% 0.59/0.78 ! [A_108: real] :
% 0.59/0.78 ( ( plus_plus_real @ A_108 @ ( number267125858f_real @ pls ) )
% 0.59/0.78 = A_108 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_239_mult__number__of__left,axiom,
% 0.59/0.78 ! [V_12: int,W_13: int,Z_7: int] :
% 0.59/0.78 ( ( times_times_int @ ( number_number_of_int @ V_12 ) @ ( times_times_int @ ( number_number_of_int @ W_13 ) @ Z_7 ) )
% 0.59/0.78 = ( times_times_int @ ( number_number_of_int @ ( times_times_int @ V_12 @ W_13 ) ) @ Z_7 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_240_mult__number__of__left,axiom,
% 0.59/0.78 ! [V_12: int,W_13: int,Z_7: real] :
% 0.59/0.78 ( ( times_times_real @ ( number267125858f_real @ V_12 ) @ ( times_times_real @ ( number267125858f_real @ W_13 ) @ Z_7 ) )
% 0.59/0.78 = ( times_times_real @ ( number267125858f_real @ ( times_times_int @ V_12 @ W_13 ) ) @ Z_7 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_241_arith__simps_I32_J,axiom,
% 0.59/0.78 ! [V_11: int,W_12: int] :
% 0.59/0.78 ( ( times_times_int @ ( number_number_of_int @ V_11 ) @ ( number_number_of_int @ W_12 ) )
% 0.59/0.78 = ( number_number_of_int @ ( times_times_int @ V_11 @ W_12 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_242_arith__simps_I32_J,axiom,
% 0.59/0.78 ! [V_11: int,W_12: int] :
% 0.59/0.78 ( ( times_times_real @ ( number267125858f_real @ V_11 ) @ ( number267125858f_real @ W_12 ) )
% 0.59/0.78 = ( number267125858f_real @ ( times_times_int @ V_11 @ W_12 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_243_number__of__mult,axiom,
% 0.59/0.78 ! [V_10: int,W_11: int] :
% 0.59/0.78 ( ( number_number_of_int @ ( times_times_int @ V_10 @ W_11 ) )
% 0.59/0.78 = ( times_times_int @ ( number_number_of_int @ V_10 ) @ ( number_number_of_int @ W_11 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_244_number__of__mult,axiom,
% 0.59/0.78 ! [V_10: int,W_11: int] :
% 0.59/0.78 ( ( number267125858f_real @ ( times_times_int @ V_10 @ W_11 ) )
% 0.59/0.78 = ( times_times_real @ ( number267125858f_real @ V_10 ) @ ( number267125858f_real @ W_11 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_245_add__number__of__left,axiom,
% 0.59/0.78 ! [V_9: int,W_10: int,Z_6: int] :
% 0.59/0.78 ( ( plus_plus_int @ ( number_number_of_int @ V_9 ) @ ( plus_plus_int @ ( number_number_of_int @ W_10 ) @ Z_6 ) )
% 0.59/0.78 = ( plus_plus_int @ ( number_number_of_int @ ( plus_plus_int @ V_9 @ W_10 ) ) @ Z_6 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_246_add__number__of__left,axiom,
% 0.59/0.78 ! [V_9: int,W_10: int,Z_6: real] :
% 0.59/0.78 ( ( plus_plus_real @ ( number267125858f_real @ V_9 ) @ ( plus_plus_real @ ( number267125858f_real @ W_10 ) @ Z_6 ) )
% 0.59/0.78 = ( plus_plus_real @ ( number267125858f_real @ ( plus_plus_int @ V_9 @ W_10 ) ) @ Z_6 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_247_add__number__of__eq,axiom,
% 0.59/0.78 ! [V_8: int,W_9: int] :
% 0.59/0.78 ( ( plus_plus_int @ ( number_number_of_int @ V_8 ) @ ( number_number_of_int @ W_9 ) )
% 0.59/0.78 = ( number_number_of_int @ ( plus_plus_int @ V_8 @ W_9 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_248_add__number__of__eq,axiom,
% 0.59/0.78 ! [V_8: int,W_9: int] :
% 0.59/0.78 ( ( plus_plus_real @ ( number267125858f_real @ V_8 ) @ ( number267125858f_real @ W_9 ) )
% 0.59/0.78 = ( number267125858f_real @ ( plus_plus_int @ V_8 @ W_9 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_249_number__of__add,axiom,
% 0.59/0.78 ! [V_7: int,W_8: int] :
% 0.59/0.78 ( ( number_number_of_int @ ( plus_plus_int @ V_7 @ W_8 ) )
% 0.59/0.78 = ( plus_plus_int @ ( number_number_of_int @ V_7 ) @ ( number_number_of_int @ W_8 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_250_number__of__add,axiom,
% 0.59/0.78 ! [V_7: int,W_8: int] :
% 0.59/0.78 ( ( number267125858f_real @ ( plus_plus_int @ V_7 @ W_8 ) )
% 0.59/0.78 = ( plus_plus_real @ ( number267125858f_real @ V_7 ) @ ( number267125858f_real @ W_8 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_251_add__Bit1__Bit0,axiom,
% 0.59/0.78 ! [K: int,L: int] :
% 0.59/0.78 ( ( plus_plus_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
% 0.59/0.78 = ( bit1 @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_252_add__Bit0__Bit1,axiom,
% 0.59/0.78 ! [K: int,L: int] :
% 0.59/0.78 ( ( plus_plus_int @ ( bit0 @ K ) @ ( bit1 @ L ) )
% 0.59/0.78 = ( bit1 @ ( plus_plus_int @ K @ L ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_253_Bit1__def,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( bit1 @ K )
% 0.59/0.78 = ( plus_plus_int @ ( plus_plus_int @ one_one_int @ K ) @ K ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_254_number__of__Bit1,axiom,
% 0.59/0.78 ! [W_7: int] :
% 0.59/0.78 ( ( number_number_of_int @ ( bit1 @ W_7 ) )
% 0.59/0.78 = ( plus_plus_int @ ( plus_plus_int @ one_one_int @ ( number_number_of_int @ W_7 ) ) @ ( number_number_of_int @ W_7 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_255_number__of__Bit1,axiom,
% 0.59/0.78 ! [W_7: int] :
% 0.59/0.78 ( ( number267125858f_real @ ( bit1 @ W_7 ) )
% 0.59/0.78 = ( plus_plus_real @ ( plus_plus_real @ one_one_real @ ( number267125858f_real @ W_7 ) ) @ ( number267125858f_real @ W_7 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_256_mult__numeral__1,axiom,
% 0.59/0.78 ! [A_107: int] :
% 0.59/0.78 ( ( times_times_int @ ( number_number_of_int @ ( bit1 @ pls ) ) @ A_107 )
% 0.59/0.78 = A_107 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_257_mult__numeral__1,axiom,
% 0.59/0.78 ! [A_107: real] :
% 0.59/0.78 ( ( times_times_real @ ( number267125858f_real @ ( bit1 @ pls ) ) @ A_107 )
% 0.59/0.78 = A_107 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_258_mult__numeral__1__right,axiom,
% 0.59/0.78 ! [A_106: int] :
% 0.59/0.78 ( ( times_times_int @ A_106 @ ( number_number_of_int @ ( bit1 @ pls ) ) )
% 0.59/0.78 = A_106 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_259_mult__numeral__1__right,axiom,
% 0.59/0.78 ! [A_106: real] :
% 0.59/0.78 ( ( times_times_real @ A_106 @ ( number267125858f_real @ ( bit1 @ pls ) ) )
% 0.59/0.78 = A_106 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_260_semiring__numeral__1__eq__1,axiom,
% 0.59/0.78 ( ( number_number_of_int @ ( bit1 @ pls ) )
% 0.59/0.78 = one_one_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_261_semiring__numeral__1__eq__1,axiom,
% 0.59/0.78 ( ( number_number_of_nat @ ( bit1 @ pls ) )
% 0.59/0.78 = one_one_nat ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_262_semiring__numeral__1__eq__1,axiom,
% 0.59/0.78 ( ( number267125858f_real @ ( bit1 @ pls ) )
% 0.59/0.78 = one_one_real ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_263_numeral__1__eq__1,axiom,
% 0.59/0.78 ( ( number_number_of_int @ ( bit1 @ pls ) )
% 0.59/0.78 = one_one_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_264_numeral__1__eq__1,axiom,
% 0.59/0.78 ( ( number267125858f_real @ ( bit1 @ pls ) )
% 0.59/0.78 = one_one_real ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_265_semiring__norm_I110_J,axiom,
% 0.59/0.78 ( one_one_int
% 0.59/0.78 = ( number_number_of_int @ ( bit1 @ pls ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_266_semiring__norm_I110_J,axiom,
% 0.59/0.78 ( one_one_real
% 0.59/0.78 = ( number267125858f_real @ ( bit1 @ pls ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_267_one__is__num__one,axiom,
% 0.59/0.78 ( one_one_int
% 0.59/0.78 = ( number_number_of_int @ ( bit1 @ pls ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_268_mult__Bit1,axiom,
% 0.59/0.78 ! [K: int,L: int] :
% 0.59/0.78 ( ( times_times_int @ ( bit1 @ K ) @ L )
% 0.59/0.78 = ( plus_plus_int @ ( bit0 @ ( times_times_int @ K @ L ) ) @ L ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_269_double__number__of__Bit0,axiom,
% 0.59/0.78 ! [W_6: int] :
% 0.59/0.78 ( ( times_times_int @ ( plus_plus_int @ one_one_int @ one_one_int ) @ ( number_number_of_int @ W_6 ) )
% 0.59/0.78 = ( number_number_of_int @ ( bit0 @ W_6 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_270_double__number__of__Bit0,axiom,
% 0.59/0.78 ! [W_6: int] :
% 0.59/0.78 ( ( times_times_real @ ( plus_plus_real @ one_one_real @ one_one_real ) @ ( number267125858f_real @ W_6 ) )
% 0.59/0.78 = ( number267125858f_real @ ( bit0 @ W_6 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_271_power3__eq__cube,axiom,
% 0.59/0.78 ! [A_105: int] :
% 0.59/0.78 ( ( power_power_int @ A_105 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = ( times_times_int @ ( times_times_int @ A_105 @ A_105 ) @ A_105 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_272_power3__eq__cube,axiom,
% 0.59/0.78 ! [A_105: real] :
% 0.59/0.78 ( ( power_power_real @ A_105 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = ( times_times_real @ ( times_times_real @ A_105 @ A_105 ) @ A_105 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_273_power3__eq__cube,axiom,
% 0.59/0.78 ! [A_105: nat] :
% 0.59/0.78 ( ( power_power_nat @ A_105 @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = ( times_times_nat @ ( times_times_nat @ A_105 @ A_105 ) @ A_105 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_274_quartic__square__square,axiom,
% 0.59/0.78 ! [X_1: int] :
% 0.59/0.78 ( ( power_power_int @ ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = ( power_power_int @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_275_semiring__mult__2,axiom,
% 0.59/0.78 ! [Z_5: int] :
% 0.59/0.78 ( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_5 )
% 0.59/0.78 = ( plus_plus_int @ Z_5 @ Z_5 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_276_semiring__mult__2,axiom,
% 0.59/0.78 ! [Z_5: nat] :
% 0.59/0.78 ( ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_5 )
% 0.59/0.78 = ( plus_plus_nat @ Z_5 @ Z_5 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_277_semiring__mult__2,axiom,
% 0.59/0.78 ! [Z_5: real] :
% 0.59/0.78 ( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_5 )
% 0.59/0.78 = ( plus_plus_real @ Z_5 @ Z_5 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_278_mult__2,axiom,
% 0.59/0.78 ! [Z_4: int] :
% 0.59/0.78 ( ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_4 )
% 0.59/0.78 = ( plus_plus_int @ Z_4 @ Z_4 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_279_mult__2,axiom,
% 0.59/0.78 ! [Z_4: real] :
% 0.59/0.78 ( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ Z_4 )
% 0.59/0.78 = ( plus_plus_real @ Z_4 @ Z_4 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_280_semiring__mult__2__right,axiom,
% 0.59/0.78 ! [Z_3: int] :
% 0.59/0.78 ( ( times_times_int @ Z_3 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = ( plus_plus_int @ Z_3 @ Z_3 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_281_semiring__mult__2__right,axiom,
% 0.59/0.78 ! [Z_3: nat] :
% 0.59/0.78 ( ( times_times_nat @ Z_3 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = ( plus_plus_nat @ Z_3 @ Z_3 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_282_semiring__mult__2__right,axiom,
% 0.59/0.78 ! [Z_3: real] :
% 0.59/0.78 ( ( times_times_real @ Z_3 @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = ( plus_plus_real @ Z_3 @ Z_3 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_283_mult__2__right,axiom,
% 0.59/0.78 ! [Z_2: int] :
% 0.59/0.78 ( ( times_times_int @ Z_2 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = ( plus_plus_int @ Z_2 @ Z_2 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_284_mult__2__right,axiom,
% 0.59/0.78 ! [Z_2: real] :
% 0.59/0.78 ( ( times_times_real @ Z_2 @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = ( plus_plus_real @ Z_2 @ Z_2 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_285_semiring__one__add__one__is__two,axiom,
% 0.59/0.78 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 0.59/0.78 = ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_286_semiring__one__add__one__is__two,axiom,
% 0.59/0.78 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 0.59/0.78 = ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_287_semiring__one__add__one__is__two,axiom,
% 0.59/0.78 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 0.59/0.78 = ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_288_p0,axiom,
% 0.59/0.78 ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_289__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_L_A1_096,axiom,
% 0.59/0.78 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 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_290_prime__g__5,axiom,
% 0.59/0.78 ! [P: int] :
% 0.59/0.78 ( ( zprime @ P )
% 0.59/0.78 => ( ( P
% 0.59/0.78 != ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 => ( ( P
% 0.59/0.78 != ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 => ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ P ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_291__096sum2sq_A_Is_M_A1_J_A_061_A_I4_A_K_Am_A_L_A1_J_A_K_At_096,axiom,
% 0.59/0.78 ( ( twoSqu2057625106sum2sq @ ( product_Pair_int_int @ s @ one_one_int ) )
% 0.59/0.78 = ( times_times_int @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ t ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_292_real__sum__squared__expand,axiom,
% 0.59/0.78 ! [X_1: real,Y_1: real] :
% 0.59/0.78 ( ( power_power_real @ ( plus_plus_real @ X_1 @ Y_1 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_1 ) @ Y_1 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_293_four__x__squared,axiom,
% 0.59/0.78 ! [X_1: real] :
% 0.59/0.78 ( ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.78 = ( power_power_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_1 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_294_power__less__power__Suc,axiom,
% 0.59/0.78 ! [N_39: nat,A_104: int] :
% 0.59/0.78 ( ( ord_less_int @ one_one_int @ A_104 )
% 0.59/0.78 => ( ord_less_int @ ( power_power_int @ A_104 @ N_39 ) @ ( times_times_int @ A_104 @ ( power_power_int @ A_104 @ N_39 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_295_power__less__power__Suc,axiom,
% 0.59/0.78 ! [N_39: nat,A_104: nat] :
% 0.59/0.78 ( ( ord_less_nat @ one_one_nat @ A_104 )
% 0.59/0.78 => ( ord_less_nat @ ( power_power_nat @ A_104 @ N_39 ) @ ( times_times_nat @ A_104 @ ( power_power_nat @ A_104 @ N_39 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_296_power__less__power__Suc,axiom,
% 0.59/0.78 ! [N_39: nat,A_104: real] :
% 0.59/0.78 ( ( ord_less_real @ one_one_real @ A_104 )
% 0.59/0.78 => ( ord_less_real @ ( power_power_real @ A_104 @ N_39 ) @ ( times_times_real @ A_104 @ ( power_power_real @ A_104 @ N_39 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_297_power__gt1__lemma,axiom,
% 0.59/0.78 ! [N_38: nat,A_103: int] :
% 0.59/0.78 ( ( ord_less_int @ one_one_int @ A_103 )
% 0.59/0.78 => ( ord_less_int @ one_one_int @ ( times_times_int @ A_103 @ ( power_power_int @ A_103 @ N_38 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_298_power__gt1__lemma,axiom,
% 0.59/0.78 ! [N_38: nat,A_103: nat] :
% 0.59/0.78 ( ( ord_less_nat @ one_one_nat @ A_103 )
% 0.59/0.78 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A_103 @ ( power_power_nat @ A_103 @ N_38 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_299_power__gt1__lemma,axiom,
% 0.59/0.78 ! [N_38: nat,A_103: real] :
% 0.59/0.78 ( ( ord_less_real @ one_one_real @ A_103 )
% 0.59/0.78 => ( ord_less_real @ one_one_real @ ( times_times_real @ A_103 @ ( power_power_real @ A_103 @ N_38 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_300_power__le__imp__le__exp,axiom,
% 0.59/0.78 ! [M_10: nat,N_37: nat,A_102: int] :
% 0.59/0.78 ( ( ord_less_int @ one_one_int @ A_102 )
% 0.59/0.78 => ( ( ord_less_eq_int @ ( power_power_int @ A_102 @ M_10 ) @ ( power_power_int @ A_102 @ N_37 ) )
% 0.59/0.78 => ( ord_less_eq_nat @ M_10 @ N_37 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_301_power__le__imp__le__exp,axiom,
% 0.59/0.78 ! [M_10: nat,N_37: nat,A_102: nat] :
% 0.59/0.78 ( ( ord_less_nat @ one_one_nat @ A_102 )
% 0.59/0.78 => ( ( ord_less_eq_nat @ ( power_power_nat @ A_102 @ M_10 ) @ ( power_power_nat @ A_102 @ N_37 ) )
% 0.59/0.78 => ( ord_less_eq_nat @ M_10 @ N_37 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_302_power__le__imp__le__exp,axiom,
% 0.59/0.78 ! [M_10: nat,N_37: nat,A_102: real] :
% 0.59/0.78 ( ( ord_less_real @ one_one_real @ A_102 )
% 0.59/0.78 => ( ( ord_less_eq_real @ ( power_power_real @ A_102 @ M_10 ) @ ( power_power_real @ A_102 @ N_37 ) )
% 0.59/0.78 => ( ord_less_eq_nat @ M_10 @ N_37 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_303_power__increasing__iff,axiom,
% 0.59/0.78 ! [X_28: nat,Y_25: nat,B_64: int] :
% 0.59/0.78 ( ( ord_less_int @ one_one_int @ B_64 )
% 0.59/0.78 => ( ( ord_less_eq_int @ ( power_power_int @ B_64 @ X_28 ) @ ( power_power_int @ B_64 @ Y_25 ) )
% 0.59/0.78 <=> ( ord_less_eq_nat @ X_28 @ Y_25 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_304_power__increasing__iff,axiom,
% 0.59/0.78 ! [X_28: nat,Y_25: nat,B_64: nat] :
% 0.59/0.78 ( ( ord_less_nat @ one_one_nat @ B_64 )
% 0.59/0.78 => ( ( ord_less_eq_nat @ ( power_power_nat @ B_64 @ X_28 ) @ ( power_power_nat @ B_64 @ Y_25 ) )
% 0.59/0.78 <=> ( ord_less_eq_nat @ X_28 @ Y_25 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_305_power__increasing__iff,axiom,
% 0.59/0.78 ! [X_28: nat,Y_25: nat,B_64: real] :
% 0.59/0.78 ( ( ord_less_real @ one_one_real @ B_64 )
% 0.59/0.78 => ( ( ord_less_eq_real @ ( power_power_real @ B_64 @ X_28 ) @ ( power_power_real @ B_64 @ Y_25 ) )
% 0.59/0.78 <=> ( ord_less_eq_nat @ X_28 @ Y_25 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_306__096_091s_A_094_A2_A_061_As1_A_094_A2_093_A_Imod_A4_A_K_Am_A_L_A1_J_096,axiom,
% 0.59/0.78 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 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_307_s0p,axiom,
% 0.59/0.78 ( ( ord_less_eq_int @ zero_zero_int @ s )
% 0.59/0.78 & ( ord_less_int @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
% 0.59/0.78 & ( zcong @ s1 @ s @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_308__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1,axiom,
% 0.59/0.78 ? [X: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.59/0.78 & ( ord_less_int @ X @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
% 0.59/0.78 & ( zcong @ s1 @ X @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
% 0.59/0.78 & ! [Y: int] :
% 0.59/0.78 ( ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.59/0.78 & ( ord_less_int @ Y @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
% 0.59/0.78 & ( zcong @ s1 @ Y @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) )
% 0.59/0.78 => ( Y = X ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_309__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,
% 0.59/0.78 ~ ! [S_1: int] :
% 0.59/0.78 ~ ( ( ord_less_eq_int @ zero_zero_int @ S_1 )
% 0.59/0.78 & ( ord_less_int @ S_1 @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
% 0.59/0.78 & ( zcong @ s1 @ S_1 @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_310_s1,axiom,
% 0.59/0.78 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 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_311_power__eq__0__iff,axiom,
% 0.59/0.78 ! [A_101: int,N_36: nat] :
% 0.59/0.78 ( ( ( power_power_int @ A_101 @ N_36 )
% 0.59/0.78 = zero_zero_int )
% 0.59/0.78 <=> ( ( A_101 = zero_zero_int )
% 0.59/0.78 & ( N_36 != zero_zero_nat ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_312_power__eq__0__iff,axiom,
% 0.59/0.78 ! [A_101: nat,N_36: nat] :
% 0.59/0.78 ( ( ( power_power_nat @ A_101 @ N_36 )
% 0.59/0.78 = zero_zero_nat )
% 0.59/0.78 <=> ( ( A_101 = zero_zero_nat )
% 0.59/0.78 & ( N_36 != zero_zero_nat ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_313_power__eq__0__iff,axiom,
% 0.59/0.78 ! [A_101: real,N_36: nat] :
% 0.59/0.78 ( ( ( power_power_real @ A_101 @ N_36 )
% 0.59/0.78 = zero_zero_real )
% 0.59/0.78 <=> ( ( A_101 = zero_zero_real )
% 0.59/0.78 & ( N_36 != zero_zero_nat ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_314_le__imp__power__dvd,axiom,
% 0.59/0.78 ! [A_100: real,M_9: nat,N_35: nat] :
% 0.59/0.78 ( ( ord_less_eq_nat @ M_9 @ N_35 )
% 0.59/0.78 => ( dvd_dvd_real @ ( power_power_real @ A_100 @ M_9 ) @ ( power_power_real @ A_100 @ N_35 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_315_le__imp__power__dvd,axiom,
% 0.59/0.78 ! [A_100: int,M_9: nat,N_35: nat] :
% 0.59/0.78 ( ( ord_less_eq_nat @ M_9 @ N_35 )
% 0.59/0.78 => ( dvd_dvd_int @ ( power_power_int @ A_100 @ M_9 ) @ ( power_power_int @ A_100 @ N_35 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_316_le__imp__power__dvd,axiom,
% 0.59/0.78 ! [A_100: nat,M_9: nat,N_35: nat] :
% 0.59/0.78 ( ( ord_less_eq_nat @ M_9 @ N_35 )
% 0.59/0.78 => ( dvd_dvd_nat @ ( power_power_nat @ A_100 @ M_9 ) @ ( power_power_nat @ A_100 @ N_35 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_317_dvd__power__le,axiom,
% 0.59/0.78 ! [N_34: nat,M_8: nat,X_27: real,Y_24: real] :
% 0.59/0.78 ( ( dvd_dvd_real @ X_27 @ Y_24 )
% 0.59/0.78 => ( ( ord_less_eq_nat @ N_34 @ M_8 )
% 0.59/0.78 => ( dvd_dvd_real @ ( power_power_real @ X_27 @ N_34 ) @ ( power_power_real @ Y_24 @ M_8 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_318_dvd__power__le,axiom,
% 0.59/0.78 ! [N_34: nat,M_8: nat,X_27: int,Y_24: int] :
% 0.59/0.78 ( ( dvd_dvd_int @ X_27 @ Y_24 )
% 0.59/0.78 => ( ( ord_less_eq_nat @ N_34 @ M_8 )
% 0.59/0.78 => ( dvd_dvd_int @ ( power_power_int @ X_27 @ N_34 ) @ ( power_power_int @ Y_24 @ M_8 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_319_dvd__power__le,axiom,
% 0.59/0.78 ! [N_34: nat,M_8: nat,X_27: nat,Y_24: nat] :
% 0.59/0.78 ( ( dvd_dvd_nat @ X_27 @ Y_24 )
% 0.59/0.78 => ( ( ord_less_eq_nat @ N_34 @ M_8 )
% 0.59/0.78 => ( dvd_dvd_nat @ ( power_power_nat @ X_27 @ N_34 ) @ ( power_power_nat @ Y_24 @ M_8 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_320_power__le__dvd,axiom,
% 0.59/0.78 ! [M_7: nat,A_99: real,N_33: nat,B_63: real] :
% 0.59/0.78 ( ( dvd_dvd_real @ ( power_power_real @ A_99 @ N_33 ) @ B_63 )
% 0.59/0.78 => ( ( ord_less_eq_nat @ M_7 @ N_33 )
% 0.59/0.78 => ( dvd_dvd_real @ ( power_power_real @ A_99 @ M_7 ) @ B_63 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_321_power__le__dvd,axiom,
% 0.59/0.78 ! [M_7: nat,A_99: int,N_33: nat,B_63: int] :
% 0.59/0.78 ( ( dvd_dvd_int @ ( power_power_int @ A_99 @ N_33 ) @ B_63 )
% 0.59/0.78 => ( ( ord_less_eq_nat @ M_7 @ N_33 )
% 0.59/0.78 => ( dvd_dvd_int @ ( power_power_int @ A_99 @ M_7 ) @ B_63 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_322_power__le__dvd,axiom,
% 0.59/0.78 ! [M_7: nat,A_99: nat,N_33: nat,B_63: nat] :
% 0.59/0.78 ( ( dvd_dvd_nat @ ( power_power_nat @ A_99 @ N_33 ) @ B_63 )
% 0.59/0.78 => ( ( ord_less_eq_nat @ M_7 @ N_33 )
% 0.59/0.78 => ( dvd_dvd_nat @ ( power_power_nat @ A_99 @ M_7 ) @ B_63 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_323_power__eq__imp__eq__base,axiom,
% 0.59/0.78 ! [A_98: int,N_32: nat,B_62: int] :
% 0.59/0.78 ( ( ( power_power_int @ A_98 @ N_32 )
% 0.59/0.78 = ( power_power_int @ B_62 @ N_32 ) )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ A_98 )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ B_62 )
% 0.59/0.78 => ( ( ord_less_nat @ zero_zero_nat @ N_32 )
% 0.59/0.78 => ( A_98 = B_62 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_324_power__eq__imp__eq__base,axiom,
% 0.59/0.78 ! [A_98: nat,N_32: nat,B_62: nat] :
% 0.59/0.78 ( ( ( power_power_nat @ A_98 @ N_32 )
% 0.59/0.78 = ( power_power_nat @ B_62 @ N_32 ) )
% 0.59/0.78 => ( ( ord_less_eq_nat @ zero_zero_nat @ A_98 )
% 0.59/0.78 => ( ( ord_less_eq_nat @ zero_zero_nat @ B_62 )
% 0.59/0.78 => ( ( ord_less_nat @ zero_zero_nat @ N_32 )
% 0.59/0.78 => ( A_98 = B_62 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_325_power__eq__imp__eq__base,axiom,
% 0.59/0.78 ! [A_98: real,N_32: nat,B_62: real] :
% 0.59/0.78 ( ( ( power_power_real @ A_98 @ N_32 )
% 0.59/0.78 = ( power_power_real @ B_62 @ N_32 ) )
% 0.59/0.78 => ( ( ord_less_eq_real @ zero_zero_real @ A_98 )
% 0.59/0.78 => ( ( ord_less_eq_real @ zero_zero_real @ B_62 )
% 0.59/0.78 => ( ( ord_less_nat @ zero_zero_nat @ N_32 )
% 0.59/0.78 => ( A_98 = B_62 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_326_zdvd__not__zless,axiom,
% 0.59/0.78 ! [N: int,M: int] :
% 0.59/0.78 ( ( ord_less_int @ zero_zero_int @ M )
% 0.59/0.78 => ( ( ord_less_int @ M @ N )
% 0.59/0.78 => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_327_zdvd__antisym__nonneg,axiom,
% 0.59/0.78 ! [N: int,M: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 0.59/0.78 => ( ( dvd_dvd_int @ M @ N )
% 0.59/0.78 => ( ( dvd_dvd_int @ N @ M )
% 0.59/0.78 => ( M = N ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_328_zdvd__mult__cancel,axiom,
% 0.59/0.78 ! [K: int,M: int,N: int] :
% 0.59/0.78 ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 0.59/0.78 => ( ( K != zero_zero_int )
% 0.59/0.78 => ( dvd_dvd_int @ M @ N ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_329_dvd__power__same,axiom,
% 0.59/0.78 ! [N_31: nat,X_26: real,Y_23: real] :
% 0.59/0.78 ( ( dvd_dvd_real @ X_26 @ Y_23 )
% 0.59/0.78 => ( dvd_dvd_real @ ( power_power_real @ X_26 @ N_31 ) @ ( power_power_real @ Y_23 @ N_31 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_330_dvd__power__same,axiom,
% 0.59/0.78 ! [N_31: nat,X_26: int,Y_23: int] :
% 0.59/0.78 ( ( dvd_dvd_int @ X_26 @ Y_23 )
% 0.59/0.78 => ( dvd_dvd_int @ ( power_power_int @ X_26 @ N_31 ) @ ( power_power_int @ Y_23 @ N_31 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_331_dvd__power__same,axiom,
% 0.59/0.78 ! [N_31: nat,X_26: nat,Y_23: nat] :
% 0.59/0.78 ( ( dvd_dvd_nat @ X_26 @ Y_23 )
% 0.59/0.78 => ( dvd_dvd_nat @ ( power_power_nat @ X_26 @ N_31 ) @ ( power_power_nat @ Y_23 @ N_31 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_332_field__power__not__zero,axiom,
% 0.59/0.78 ! [N_30: nat,A_97: int] :
% 0.59/0.78 ( ( A_97 != zero_zero_int )
% 0.59/0.78 => ( ( power_power_int @ A_97 @ N_30 )
% 0.59/0.78 != zero_zero_int ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_333_field__power__not__zero,axiom,
% 0.59/0.78 ! [N_30: nat,A_97: real] :
% 0.59/0.78 ( ( A_97 != zero_zero_real )
% 0.59/0.78 => ( ( power_power_real @ A_97 @ N_30 )
% 0.59/0.78 != zero_zero_real ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_334_power__0__left,axiom,
% 0.59/0.78 ! [N_29: nat] :
% 0.59/0.78 ( ( ( N_29 = zero_zero_nat )
% 0.59/0.78 => ( ( power_power_int @ zero_zero_int @ N_29 )
% 0.59/0.78 = one_one_int ) )
% 0.59/0.78 & ( ( N_29 != zero_zero_nat )
% 0.59/0.78 => ( ( power_power_int @ zero_zero_int @ N_29 )
% 0.59/0.78 = zero_zero_int ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_335_power__0__left,axiom,
% 0.59/0.78 ! [N_29: nat] :
% 0.59/0.78 ( ( ( N_29 = zero_zero_nat )
% 0.59/0.78 => ( ( power_power_nat @ zero_zero_nat @ N_29 )
% 0.59/0.78 = one_one_nat ) )
% 0.59/0.78 & ( ( N_29 != zero_zero_nat )
% 0.59/0.78 => ( ( power_power_nat @ zero_zero_nat @ N_29 )
% 0.59/0.78 = zero_zero_nat ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_336_power__0__left,axiom,
% 0.59/0.78 ! [N_29: nat] :
% 0.59/0.78 ( ( ( N_29 = zero_zero_nat )
% 0.59/0.78 => ( ( power_power_real @ zero_zero_real @ N_29 )
% 0.59/0.78 = one_one_real ) )
% 0.59/0.78 & ( ( N_29 != zero_zero_nat )
% 0.59/0.78 => ( ( power_power_real @ zero_zero_real @ N_29 )
% 0.59/0.78 = zero_zero_real ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_337_zdvd__imp__le,axiom,
% 0.59/0.78 ! [Z: int,N: int] :
% 0.59/0.78 ( ( dvd_dvd_int @ Z @ N )
% 0.59/0.78 => ( ( ord_less_int @ zero_zero_int @ N )
% 0.59/0.78 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_338_power__strict__mono,axiom,
% 0.59/0.78 ! [N_28: nat,A_96: int,B_61: int] :
% 0.59/0.78 ( ( ord_less_int @ A_96 @ B_61 )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ A_96 )
% 0.59/0.78 => ( ( ord_less_nat @ zero_zero_nat @ N_28 )
% 0.59/0.78 => ( ord_less_int @ ( power_power_int @ A_96 @ N_28 ) @ ( power_power_int @ B_61 @ N_28 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_339_power__strict__mono,axiom,
% 0.59/0.78 ! [N_28: nat,A_96: nat,B_61: nat] :
% 0.59/0.78 ( ( ord_less_nat @ A_96 @ B_61 )
% 0.59/0.78 => ( ( ord_less_eq_nat @ zero_zero_nat @ A_96 )
% 0.59/0.78 => ( ( ord_less_nat @ zero_zero_nat @ N_28 )
% 0.59/0.78 => ( ord_less_nat @ ( power_power_nat @ A_96 @ N_28 ) @ ( power_power_nat @ B_61 @ N_28 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_340_power__strict__mono,axiom,
% 0.59/0.78 ! [N_28: nat,A_96: real,B_61: real] :
% 0.59/0.78 ( ( ord_less_real @ A_96 @ B_61 )
% 0.59/0.78 => ( ( ord_less_eq_real @ zero_zero_real @ A_96 )
% 0.59/0.78 => ( ( ord_less_nat @ zero_zero_nat @ N_28 )
% 0.59/0.78 => ( ord_less_real @ ( power_power_real @ A_96 @ N_28 ) @ ( power_power_real @ B_61 @ N_28 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_341_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 0.59/0.78 ! [A_95: int] :
% 0.59/0.78 ( ( times_times_int @ zero_zero_int @ A_95 )
% 0.59/0.78 = zero_zero_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_342_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 0.59/0.78 ! [A_95: nat] :
% 0.59/0.78 ( ( times_times_nat @ zero_zero_nat @ A_95 )
% 0.59/0.78 = zero_zero_nat ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_343_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom,
% 0.59/0.78 ! [A_95: real] :
% 0.59/0.78 ( ( times_times_real @ zero_zero_real @ A_95 )
% 0.59/0.78 = zero_zero_real ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_344_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 0.59/0.78 ! [A_94: int] :
% 0.59/0.78 ( ( times_times_int @ A_94 @ zero_zero_int )
% 0.59/0.78 = zero_zero_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_345_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 0.59/0.78 ! [A_94: nat] :
% 0.59/0.78 ( ( times_times_nat @ A_94 @ zero_zero_nat )
% 0.59/0.78 = zero_zero_nat ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_346_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom,
% 0.59/0.78 ! [A_94: real] :
% 0.59/0.78 ( ( times_times_real @ A_94 @ zero_zero_real )
% 0.59/0.78 = zero_zero_real ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_347_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 0.59/0.78 ! [A_93: int] :
% 0.59/0.78 ( ( plus_plus_int @ zero_zero_int @ A_93 )
% 0.59/0.78 = A_93 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_348_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 0.59/0.78 ! [A_93: nat] :
% 0.59/0.78 ( ( plus_plus_nat @ zero_zero_nat @ A_93 )
% 0.59/0.78 = A_93 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_349_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom,
% 0.59/0.78 ! [A_93: real] :
% 0.59/0.78 ( ( plus_plus_real @ zero_zero_real @ A_93 )
% 0.59/0.78 = A_93 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_350_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 0.59/0.78 ! [A_92: int] :
% 0.59/0.78 ( ( plus_plus_int @ A_92 @ zero_zero_int )
% 0.59/0.78 = A_92 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_351_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 0.59/0.78 ! [A_92: nat] :
% 0.59/0.78 ( ( plus_plus_nat @ A_92 @ zero_zero_nat )
% 0.59/0.78 = A_92 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_352_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom,
% 0.59/0.78 ! [A_92: real] :
% 0.59/0.78 ( ( plus_plus_real @ A_92 @ zero_zero_real )
% 0.59/0.78 = A_92 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_353_add__0__iff,axiom,
% 0.59/0.78 ! [B_60: int,A_91: int] :
% 0.59/0.78 ( ( B_60
% 0.59/0.78 = ( plus_plus_int @ B_60 @ A_91 ) )
% 0.59/0.78 <=> ( A_91 = zero_zero_int ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_354_add__0__iff,axiom,
% 0.59/0.78 ! [B_60: nat,A_91: nat] :
% 0.59/0.78 ( ( B_60
% 0.59/0.78 = ( plus_plus_nat @ B_60 @ A_91 ) )
% 0.59/0.78 <=> ( A_91 = zero_zero_nat ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_355_add__0__iff,axiom,
% 0.59/0.78 ! [B_60: real,A_91: real] :
% 0.59/0.78 ( ( B_60
% 0.59/0.78 = ( plus_plus_real @ B_60 @ A_91 ) )
% 0.59/0.78 <=> ( A_91 = zero_zero_real ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_356_double__eq__0__iff,axiom,
% 0.59/0.78 ! [A_90: int] :
% 0.59/0.78 ( ( ( plus_plus_int @ A_90 @ A_90 )
% 0.59/0.78 = zero_zero_int )
% 0.59/0.78 <=> ( A_90 = zero_zero_int ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_357_double__eq__0__iff,axiom,
% 0.59/0.78 ! [A_90: real] :
% 0.59/0.78 ( ( ( plus_plus_real @ A_90 @ A_90 )
% 0.59/0.78 = zero_zero_real )
% 0.59/0.78 <=> ( A_90 = zero_zero_real ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_358_Pls__def,axiom,
% 0.59/0.78 pls = zero_zero_int ).
% 0.59/0.78
% 0.59/0.78 thf(fact_359_int__0__neq__1,axiom,
% 0.59/0.78 zero_zero_int != one_one_int ).
% 0.59/0.78
% 0.59/0.78 thf(fact_360_zadd__0,axiom,
% 0.59/0.78 ! [Z: int] :
% 0.59/0.78 ( ( plus_plus_int @ zero_zero_int @ Z )
% 0.59/0.78 = Z ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_361_zadd__0__right,axiom,
% 0.59/0.78 ! [Z: int] :
% 0.59/0.78 ( ( plus_plus_int @ Z @ zero_zero_int )
% 0.59/0.78 = Z ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_362_zero__le__power,axiom,
% 0.59/0.78 ! [N_27: nat,A_89: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ zero_zero_int @ A_89 )
% 0.59/0.78 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A_89 @ N_27 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_363_zero__le__power,axiom,
% 0.59/0.78 ! [N_27: nat,A_89: nat] :
% 0.59/0.78 ( ( ord_less_eq_nat @ zero_zero_nat @ A_89 )
% 0.59/0.78 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A_89 @ N_27 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_364_zero__le__power,axiom,
% 0.59/0.78 ! [N_27: nat,A_89: real] :
% 0.59/0.78 ( ( ord_less_eq_real @ zero_zero_real @ A_89 )
% 0.59/0.78 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A_89 @ N_27 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_365_power__mono,axiom,
% 0.59/0.78 ! [N_26: nat,A_88: int,B_59: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ A_88 @ B_59 )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ A_88 )
% 0.59/0.78 => ( ord_less_eq_int @ ( power_power_int @ A_88 @ N_26 ) @ ( power_power_int @ B_59 @ N_26 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_366_power__mono,axiom,
% 0.59/0.78 ! [N_26: nat,A_88: nat,B_59: nat] :
% 0.59/0.78 ( ( ord_less_eq_nat @ A_88 @ B_59 )
% 0.59/0.78 => ( ( ord_less_eq_nat @ zero_zero_nat @ A_88 )
% 0.59/0.78 => ( ord_less_eq_nat @ ( power_power_nat @ A_88 @ N_26 ) @ ( power_power_nat @ B_59 @ N_26 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_367_power__mono,axiom,
% 0.59/0.78 ! [N_26: nat,A_88: real,B_59: real] :
% 0.59/0.78 ( ( ord_less_eq_real @ A_88 @ B_59 )
% 0.59/0.78 => ( ( ord_less_eq_real @ zero_zero_real @ A_88 )
% 0.59/0.78 => ( ord_less_eq_real @ ( power_power_real @ A_88 @ N_26 ) @ ( power_power_real @ B_59 @ N_26 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_368_zero__less__power,axiom,
% 0.59/0.78 ! [N_25: nat,A_87: int] :
% 0.59/0.78 ( ( ord_less_int @ zero_zero_int @ A_87 )
% 0.59/0.78 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_87 @ N_25 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_369_zero__less__power,axiom,
% 0.59/0.78 ! [N_25: nat,A_87: nat] :
% 0.59/0.78 ( ( ord_less_nat @ zero_zero_nat @ A_87 )
% 0.59/0.78 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A_87 @ N_25 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_370_zero__less__power,axiom,
% 0.59/0.78 ! [N_25: nat,A_87: real] :
% 0.59/0.78 ( ( ord_less_real @ zero_zero_real @ A_87 )
% 0.59/0.78 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A_87 @ N_25 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_371_zcong__zpower__zmult,axiom,
% 0.59/0.78 ! [Z: nat,X_1: int,Y_1: nat,P: int] :
% 0.59/0.78 ( ( zcong @ ( power_power_int @ X_1 @ Y_1 ) @ one_one_int @ P )
% 0.59/0.78 => ( zcong @ ( power_power_int @ X_1 @ ( times_times_nat @ Y_1 @ Z ) ) @ one_one_int @ P ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_372_zdvd__reduce,axiom,
% 0.59/0.78 ! [K: int,N: int,M: int] :
% 0.59/0.78 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 0.59/0.78 <=> ( dvd_dvd_int @ K @ N ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_373_zdvd__period,axiom,
% 0.59/0.78 ! [C: int,X_1: int,T: int,A: int,D: int] :
% 0.59/0.78 ( ( dvd_dvd_int @ A @ D )
% 0.59/0.78 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X_1 @ T ) )
% 0.59/0.78 <=> ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X_1 @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_374_power__less__imp__less__base,axiom,
% 0.59/0.78 ! [A_86: int,N_24: nat,B_58: int] :
% 0.59/0.78 ( ( ord_less_int @ ( power_power_int @ A_86 @ N_24 ) @ ( power_power_int @ B_58 @ N_24 ) )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ B_58 )
% 0.59/0.78 => ( ord_less_int @ A_86 @ B_58 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_375_power__less__imp__less__base,axiom,
% 0.59/0.78 ! [A_86: nat,N_24: nat,B_58: nat] :
% 0.59/0.78 ( ( ord_less_nat @ ( power_power_nat @ A_86 @ N_24 ) @ ( power_power_nat @ B_58 @ N_24 ) )
% 0.59/0.78 => ( ( ord_less_eq_nat @ zero_zero_nat @ B_58 )
% 0.59/0.78 => ( ord_less_nat @ A_86 @ B_58 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_376_power__less__imp__less__base,axiom,
% 0.59/0.78 ! [A_86: real,N_24: nat,B_58: real] :
% 0.59/0.78 ( ( ord_less_real @ ( power_power_real @ A_86 @ N_24 ) @ ( power_power_real @ B_58 @ N_24 ) )
% 0.59/0.78 => ( ( ord_less_eq_real @ zero_zero_real @ B_58 )
% 0.59/0.78 => ( ord_less_real @ A_86 @ B_58 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_377_power__decreasing,axiom,
% 0.59/0.78 ! [A_85: int,N_23: nat,N_22: nat] :
% 0.59/0.78 ( ( ord_less_eq_nat @ N_23 @ N_22 )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ A_85 )
% 0.59/0.78 => ( ( ord_less_eq_int @ A_85 @ one_one_int )
% 0.59/0.78 => ( ord_less_eq_int @ ( power_power_int @ A_85 @ N_22 ) @ ( power_power_int @ A_85 @ N_23 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_378_power__decreasing,axiom,
% 0.59/0.78 ! [A_85: nat,N_23: nat,N_22: nat] :
% 0.59/0.78 ( ( ord_less_eq_nat @ N_23 @ N_22 )
% 0.59/0.78 => ( ( ord_less_eq_nat @ zero_zero_nat @ A_85 )
% 0.59/0.78 => ( ( ord_less_eq_nat @ A_85 @ one_one_nat )
% 0.59/0.78 => ( ord_less_eq_nat @ ( power_power_nat @ A_85 @ N_22 ) @ ( power_power_nat @ A_85 @ N_23 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_379_power__decreasing,axiom,
% 0.59/0.78 ! [A_85: real,N_23: nat,N_22: nat] :
% 0.59/0.78 ( ( ord_less_eq_nat @ N_23 @ N_22 )
% 0.59/0.78 => ( ( ord_less_eq_real @ zero_zero_real @ A_85 )
% 0.59/0.78 => ( ( ord_less_eq_real @ A_85 @ one_one_real )
% 0.59/0.78 => ( ord_less_eq_real @ ( power_power_real @ A_85 @ N_22 ) @ ( power_power_real @ A_85 @ N_23 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_380_power__strict__decreasing,axiom,
% 0.59/0.78 ! [A_84: int,N_21: nat,N_20: nat] :
% 0.59/0.78 ( ( ord_less_nat @ N_21 @ N_20 )
% 0.59/0.78 => ( ( ord_less_int @ zero_zero_int @ A_84 )
% 0.59/0.78 => ( ( ord_less_int @ A_84 @ one_one_int )
% 0.59/0.78 => ( ord_less_int @ ( power_power_int @ A_84 @ N_20 ) @ ( power_power_int @ A_84 @ N_21 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_381_power__strict__decreasing,axiom,
% 0.59/0.78 ! [A_84: nat,N_21: nat,N_20: nat] :
% 0.59/0.78 ( ( ord_less_nat @ N_21 @ N_20 )
% 0.59/0.78 => ( ( ord_less_nat @ zero_zero_nat @ A_84 )
% 0.59/0.78 => ( ( ord_less_nat @ A_84 @ one_one_nat )
% 0.59/0.78 => ( ord_less_nat @ ( power_power_nat @ A_84 @ N_20 ) @ ( power_power_nat @ A_84 @ N_21 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_382_power__strict__decreasing,axiom,
% 0.59/0.78 ! [A_84: real,N_21: nat,N_20: nat] :
% 0.59/0.78 ( ( ord_less_nat @ N_21 @ N_20 )
% 0.59/0.78 => ( ( ord_less_real @ zero_zero_real @ A_84 )
% 0.59/0.78 => ( ( ord_less_real @ A_84 @ one_one_real )
% 0.59/0.78 => ( ord_less_real @ ( power_power_real @ A_84 @ N_20 ) @ ( power_power_real @ A_84 @ N_21 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_383_even__less__0__iff,axiom,
% 0.59/0.78 ! [A_83: int] :
% 0.59/0.78 ( ( ord_less_int @ ( plus_plus_int @ A_83 @ A_83 ) @ zero_zero_int )
% 0.59/0.78 <=> ( ord_less_int @ A_83 @ zero_zero_int ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_384_even__less__0__iff,axiom,
% 0.59/0.78 ! [A_83: real] :
% 0.59/0.78 ( ( ord_less_real @ ( plus_plus_real @ A_83 @ A_83 ) @ zero_zero_real )
% 0.59/0.78 <=> ( ord_less_real @ A_83 @ zero_zero_real ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_385_sum__squares__eq__zero__iff,axiom,
% 0.59/0.78 ! [X_25: int,Y_22: int] :
% 0.59/0.78 ( ( ( plus_plus_int @ ( times_times_int @ X_25 @ X_25 ) @ ( times_times_int @ Y_22 @ Y_22 ) )
% 0.59/0.78 = zero_zero_int )
% 0.59/0.78 <=> ( ( X_25 = zero_zero_int )
% 0.59/0.78 & ( Y_22 = zero_zero_int ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_386_sum__squares__eq__zero__iff,axiom,
% 0.59/0.78 ! [X_25: real,Y_22: real] :
% 0.59/0.78 ( ( ( plus_plus_real @ ( times_times_real @ X_25 @ X_25 ) @ ( times_times_real @ Y_22 @ Y_22 ) )
% 0.59/0.78 = zero_zero_real )
% 0.59/0.78 <=> ( ( X_25 = zero_zero_real )
% 0.59/0.78 & ( Y_22 = zero_zero_real ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_387_add__scale__eq__noteq,axiom,
% 0.59/0.78 ! [C_30: int,D_7: int,A_82: int,B_57: int,R_3: int] :
% 0.59/0.78 ( ( R_3 != zero_zero_int )
% 0.59/0.78 => ( ( ( A_82 = B_57 )
% 0.59/0.78 & ( C_30 != D_7 ) )
% 0.59/0.78 => ( ( plus_plus_int @ A_82 @ ( times_times_int @ R_3 @ C_30 ) )
% 0.59/0.78 != ( plus_plus_int @ B_57 @ ( times_times_int @ R_3 @ D_7 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_388_add__scale__eq__noteq,axiom,
% 0.59/0.78 ! [C_30: nat,D_7: nat,A_82: nat,B_57: nat,R_3: nat] :
% 0.59/0.78 ( ( R_3 != zero_zero_nat )
% 0.59/0.78 => ( ( ( A_82 = B_57 )
% 0.59/0.78 & ( C_30 != D_7 ) )
% 0.59/0.78 => ( ( plus_plus_nat @ A_82 @ ( times_times_nat @ R_3 @ C_30 ) )
% 0.59/0.78 != ( plus_plus_nat @ B_57 @ ( times_times_nat @ R_3 @ D_7 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_389_add__scale__eq__noteq,axiom,
% 0.59/0.78 ! [C_30: real,D_7: real,A_82: real,B_57: real,R_3: real] :
% 0.59/0.78 ( ( R_3 != zero_zero_real )
% 0.59/0.78 => ( ( ( A_82 = B_57 )
% 0.59/0.78 & ( C_30 != D_7 ) )
% 0.59/0.78 => ( ( plus_plus_real @ A_82 @ ( times_times_real @ R_3 @ C_30 ) )
% 0.59/0.78 != ( plus_plus_real @ B_57 @ ( times_times_real @ R_3 @ D_7 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_390_zprime__zdvd__power,axiom,
% 0.59/0.78 ! [A: int,N: nat,P: int] :
% 0.59/0.78 ( ( zprime @ P )
% 0.59/0.78 => ( ( dvd_dvd_int @ P @ ( power_power_int @ A @ N ) )
% 0.59/0.78 => ( dvd_dvd_int @ P @ A ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_391_semiring__norm_I112_J,axiom,
% 0.59/0.78 ( zero_zero_int
% 0.59/0.78 = ( number_number_of_int @ pls ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_392_semiring__norm_I112_J,axiom,
% 0.59/0.78 ( zero_zero_real
% 0.59/0.78 = ( number267125858f_real @ pls ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_393_number__of__Pls,axiom,
% 0.59/0.78 ( ( number_number_of_int @ pls )
% 0.59/0.78 = zero_zero_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_394_number__of__Pls,axiom,
% 0.59/0.78 ( ( number267125858f_real @ pls )
% 0.59/0.78 = zero_zero_real ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_395_semiring__numeral__0__eq__0,axiom,
% 0.59/0.78 ( ( number_number_of_int @ pls )
% 0.59/0.78 = zero_zero_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_396_semiring__numeral__0__eq__0,axiom,
% 0.59/0.78 ( ( number_number_of_nat @ pls )
% 0.59/0.78 = zero_zero_nat ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_397_semiring__numeral__0__eq__0,axiom,
% 0.59/0.78 ( ( number267125858f_real @ pls )
% 0.59/0.78 = zero_zero_real ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_398_bin__less__0__simps_I4_J,axiom,
% 0.59/0.78 ! [W: int] :
% 0.59/0.78 ( ( ord_less_int @ ( bit1 @ W ) @ zero_zero_int )
% 0.59/0.78 <=> ( ord_less_int @ W @ zero_zero_int ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_399_bin__less__0__simps_I1_J,axiom,
% 0.59/0.78 ~ ( ord_less_int @ pls @ zero_zero_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_400_bin__less__0__simps_I3_J,axiom,
% 0.59/0.78 ! [W: int] :
% 0.59/0.78 ( ( ord_less_int @ ( bit0 @ W ) @ zero_zero_int )
% 0.59/0.78 <=> ( ord_less_int @ W @ zero_zero_int ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_401_zero__is__num__zero,axiom,
% 0.59/0.78 ( zero_zero_int
% 0.59/0.78 = ( number_number_of_int @ pls ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_402_int__0__less__1,axiom,
% 0.59/0.78 ord_less_int @ zero_zero_int @ one_one_int ).
% 0.59/0.78
% 0.59/0.78 thf(fact_403_pos__zmult__pos,axiom,
% 0.59/0.78 ! [B: int,A: int] :
% 0.59/0.78 ( ( ord_less_int @ zero_zero_int @ A )
% 0.59/0.78 => ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 0.59/0.78 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_404_zmult__zless__mono2,axiom,
% 0.59/0.78 ! [K: int,I_1: int,J_1: int] :
% 0.59/0.78 ( ( ord_less_int @ I_1 @ J_1 )
% 0.59/0.78 => ( ( ord_less_int @ zero_zero_int @ K )
% 0.59/0.78 => ( ord_less_int @ ( times_times_int @ K @ I_1 ) @ ( times_times_int @ K @ J_1 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_405_odd__nonzero,axiom,
% 0.59/0.78 ! [Z: int] :
% 0.59/0.78 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 0.59/0.78 != zero_zero_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_406_power__Suc__less,axiom,
% 0.59/0.78 ! [N_19: nat,A_81: int] :
% 0.59/0.78 ( ( ord_less_int @ zero_zero_int @ A_81 )
% 0.59/0.78 => ( ( ord_less_int @ A_81 @ one_one_int )
% 0.59/0.78 => ( ord_less_int @ ( times_times_int @ A_81 @ ( power_power_int @ A_81 @ N_19 ) ) @ ( power_power_int @ A_81 @ N_19 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_407_power__Suc__less,axiom,
% 0.59/0.78 ! [N_19: nat,A_81: nat] :
% 0.59/0.78 ( ( ord_less_nat @ zero_zero_nat @ A_81 )
% 0.59/0.78 => ( ( ord_less_nat @ A_81 @ one_one_nat )
% 0.59/0.78 => ( ord_less_nat @ ( times_times_nat @ A_81 @ ( power_power_nat @ A_81 @ N_19 ) ) @ ( power_power_nat @ A_81 @ N_19 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_408_power__Suc__less,axiom,
% 0.59/0.78 ! [N_19: nat,A_81: real] :
% 0.59/0.78 ( ( ord_less_real @ zero_zero_real @ A_81 )
% 0.59/0.78 => ( ( ord_less_real @ A_81 @ one_one_real )
% 0.59/0.78 => ( ord_less_real @ ( times_times_real @ A_81 @ ( power_power_real @ A_81 @ N_19 ) ) @ ( power_power_real @ A_81 @ N_19 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_409_zprime__power__zdvd__cancel__left,axiom,
% 0.59/0.78 ! [N: nat,B: int,A: int,P: int] :
% 0.59/0.78 ( ( zprime @ P )
% 0.59/0.78 => ( ~ ( dvd_dvd_int @ P @ A )
% 0.59/0.78 => ( ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ ( times_times_int @ A @ B ) )
% 0.59/0.78 => ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ B ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_410_zprime__power__zdvd__cancel__right,axiom,
% 0.59/0.78 ! [N: nat,A: int,B: int,P: int] :
% 0.59/0.78 ( ( zprime @ P )
% 0.59/0.78 => ( ~ ( dvd_dvd_int @ P @ B )
% 0.59/0.78 => ( ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ ( times_times_int @ A @ B ) )
% 0.59/0.78 => ( dvd_dvd_int @ ( power_power_int @ P @ N ) @ A ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_411_sum__squares__ge__zero,axiom,
% 0.59/0.78 ! [X_24: int,Y_21: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_24 @ X_24 ) @ ( times_times_int @ Y_21 @ Y_21 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_412_sum__squares__ge__zero,axiom,
% 0.59/0.78 ! [X_24: real,Y_21: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X_24 @ X_24 ) @ ( times_times_real @ Y_21 @ Y_21 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_413_sum__squares__le__zero__iff,axiom,
% 0.59/0.78 ! [X_23: int,Y_20: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X_23 @ X_23 ) @ ( times_times_int @ Y_20 @ Y_20 ) ) @ zero_zero_int )
% 0.59/0.78 <=> ( ( X_23 = zero_zero_int )
% 0.59/0.78 & ( Y_20 = zero_zero_int ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_414_sum__squares__le__zero__iff,axiom,
% 0.59/0.78 ! [X_23: real,Y_20: real] :
% 0.59/0.78 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X_23 @ X_23 ) @ ( times_times_real @ Y_20 @ Y_20 ) ) @ zero_zero_real )
% 0.59/0.78 <=> ( ( X_23 = zero_zero_real )
% 0.59/0.78 & ( Y_20 = zero_zero_real ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_415_less__nat__number__of,axiom,
% 0.59/0.78 ! [V: int,V_6: int] :
% 0.59/0.78 ( ( ord_less_nat @ ( number_number_of_nat @ V ) @ ( number_number_of_nat @ V_6 ) )
% 0.59/0.78 <=> ( ( ( ord_less_int @ V @ V_6 )
% 0.59/0.78 => ( ord_less_int @ pls @ V_6 ) )
% 0.59/0.78 & ( ord_less_int @ V @ V_6 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_416_not__sum__squares__lt__zero,axiom,
% 0.59/0.78 ! [X_22: int,Y_19: int] :
% 0.59/0.78 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X_22 @ X_22 ) @ ( times_times_int @ Y_19 @ Y_19 ) ) @ zero_zero_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_417_not__sum__squares__lt__zero,axiom,
% 0.59/0.78 ! [X_22: real,Y_19: real] :
% 0.59/0.78 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X_22 @ X_22 ) @ ( times_times_real @ Y_19 @ Y_19 ) ) @ zero_zero_real ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_418_sum__squares__gt__zero__iff,axiom,
% 0.59/0.78 ! [X_21: int,Y_18: int] :
% 0.59/0.78 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X_21 @ X_21 ) @ ( times_times_int @ Y_18 @ Y_18 ) ) )
% 0.59/0.78 <=> ( ( X_21 != zero_zero_int )
% 0.59/0.78 | ( Y_18 != zero_zero_int ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_419_sum__squares__gt__zero__iff,axiom,
% 0.59/0.78 ! [X_21: real,Y_18: real] :
% 0.59/0.78 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X_21 @ X_21 ) @ ( times_times_real @ Y_18 @ Y_18 ) ) )
% 0.59/0.78 <=> ( ( X_21 != zero_zero_real )
% 0.59/0.78 | ( Y_18 != zero_zero_real ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_420_le__nat__number__of,axiom,
% 0.59/0.78 ! [V: int,V_6: int] :
% 0.59/0.78 ( ( ord_less_eq_nat @ ( number_number_of_nat @ V ) @ ( number_number_of_nat @ V_6 ) )
% 0.59/0.78 <=> ( ~ ( ord_less_eq_int @ V @ V_6 )
% 0.59/0.78 => ( ord_less_eq_int @ V @ pls ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_421_number__of__Bit0,axiom,
% 0.59/0.78 ! [W_5: int] :
% 0.59/0.78 ( ( number_number_of_int @ ( bit0 @ W_5 ) )
% 0.59/0.78 = ( plus_plus_int @ ( plus_plus_int @ zero_zero_int @ ( number_number_of_int @ W_5 ) ) @ ( number_number_of_int @ W_5 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_422_number__of__Bit0,axiom,
% 0.59/0.78 ! [W_5: int] :
% 0.59/0.78 ( ( number267125858f_real @ ( bit0 @ W_5 ) )
% 0.59/0.78 = ( plus_plus_real @ ( plus_plus_real @ zero_zero_real @ ( number267125858f_real @ W_5 ) ) @ ( number267125858f_real @ W_5 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_423_power__one__right,axiom,
% 0.59/0.78 ! [A_80: int] :
% 0.59/0.78 ( ( power_power_int @ A_80 @ one_one_nat )
% 0.59/0.78 = A_80 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_424_power__one__right,axiom,
% 0.59/0.78 ! [A_80: real] :
% 0.59/0.78 ( ( power_power_real @ A_80 @ one_one_nat )
% 0.59/0.78 = A_80 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_425_power__one__right,axiom,
% 0.59/0.78 ! [A_80: nat] :
% 0.59/0.78 ( ( power_power_nat @ A_80 @ one_one_nat )
% 0.59/0.78 = A_80 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_426_int__one__le__iff__zero__less,axiom,
% 0.59/0.78 ! [Z: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ one_one_int @ Z )
% 0.59/0.78 <=> ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_427_pos__zmult__eq__1__iff,axiom,
% 0.59/0.78 ! [N: int,M: int] :
% 0.59/0.78 ( ( ord_less_int @ zero_zero_int @ M )
% 0.59/0.78 => ( ( ( times_times_int @ M @ N )
% 0.59/0.78 = one_one_int )
% 0.59/0.78 <=> ( ( M = one_one_int )
% 0.59/0.78 & ( N = one_one_int ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_428_odd__less__0,axiom,
% 0.59/0.78 ! [Z: int] :
% 0.59/0.78 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 0.59/0.78 <=> ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_429_less__special_I1_J,axiom,
% 0.59/0.78 ! [Y_17: int] :
% 0.59/0.78 ( ( ord_less_int @ zero_zero_int @ ( number_number_of_int @ Y_17 ) )
% 0.59/0.78 <=> ( ord_less_int @ pls @ Y_17 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_430_less__special_I1_J,axiom,
% 0.59/0.78 ! [Y_17: int] :
% 0.59/0.78 ( ( ord_less_real @ zero_zero_real @ ( number267125858f_real @ Y_17 ) )
% 0.59/0.78 <=> ( ord_less_int @ pls @ Y_17 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_431_less__special_I3_J,axiom,
% 0.59/0.78 ! [X_20: int] :
% 0.59/0.78 ( ( ord_less_int @ ( number_number_of_int @ X_20 ) @ zero_zero_int )
% 0.59/0.78 <=> ( ord_less_int @ X_20 @ pls ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_432_less__special_I3_J,axiom,
% 0.59/0.78 ! [X_20: int] :
% 0.59/0.78 ( ( ord_less_real @ ( number267125858f_real @ X_20 ) @ zero_zero_real )
% 0.59/0.78 <=> ( ord_less_int @ X_20 @ pls ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_433_le__special_I1_J,axiom,
% 0.59/0.78 ! [Y_16: int] :
% 0.59/0.78 ( ( ord_less_eq_real @ zero_zero_real @ ( number267125858f_real @ Y_16 ) )
% 0.59/0.78 <=> ( ord_less_eq_int @ pls @ Y_16 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_434_le__special_I1_J,axiom,
% 0.59/0.78 ! [Y_16: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ Y_16 ) )
% 0.59/0.78 <=> ( ord_less_eq_int @ pls @ Y_16 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_435_le__special_I3_J,axiom,
% 0.59/0.78 ! [X_19: int] :
% 0.59/0.78 ( ( ord_less_eq_real @ ( number267125858f_real @ X_19 ) @ zero_zero_real )
% 0.59/0.78 <=> ( ord_less_eq_int @ X_19 @ pls ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_436_le__special_I3_J,axiom,
% 0.59/0.78 ! [X_19: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ ( number_number_of_int @ X_19 ) @ zero_zero_int )
% 0.59/0.78 <=> ( ord_less_eq_int @ X_19 @ pls ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_437_le__imp__0__less,axiom,
% 0.59/0.78 ! [Z: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 0.59/0.78 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_438_zero__power2,axiom,
% 0.59/0.78 ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = zero_zero_real ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_439_zero__power2,axiom,
% 0.59/0.78 ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = zero_zero_nat ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_440_zero__power2,axiom,
% 0.59/0.78 ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = zero_zero_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_441_zero__eq__power2,axiom,
% 0.59/0.78 ! [A_79: real] :
% 0.59/0.78 ( ( ( power_power_real @ A_79 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = zero_zero_real )
% 0.59/0.78 <=> ( A_79 = zero_zero_real ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_442_zero__eq__power2,axiom,
% 0.59/0.78 ! [A_79: int] :
% 0.59/0.78 ( ( ( power_power_int @ A_79 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = zero_zero_int )
% 0.59/0.78 <=> ( A_79 = zero_zero_int ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_443_zero__le__power2,axiom,
% 0.59/0.78 ! [A_78: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A_78 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_444_zero__le__power2,axiom,
% 0.59/0.78 ! [A_78: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A_78 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_445_power2__le__imp__le,axiom,
% 0.59/0.78 ! [X_18: real,Y_15: real] :
% 0.59/0.78 ( ( ord_less_eq_real @ ( power_power_real @ X_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_15 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.78 => ( ( ord_less_eq_real @ zero_zero_real @ Y_15 )
% 0.59/0.78 => ( ord_less_eq_real @ X_18 @ Y_15 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_446_power2__le__imp__le,axiom,
% 0.59/0.78 ! [X_18: nat,Y_15: nat] :
% 0.59/0.78 ( ( ord_less_eq_nat @ ( power_power_nat @ X_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y_15 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.78 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y_15 )
% 0.59/0.78 => ( ord_less_eq_nat @ X_18 @ Y_15 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_447_power2__le__imp__le,axiom,
% 0.59/0.78 ! [X_18: int,Y_15: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ ( power_power_int @ X_18 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_15 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ Y_15 )
% 0.59/0.78 => ( ord_less_eq_int @ X_18 @ Y_15 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_448_power2__eq__imp__eq,axiom,
% 0.59/0.78 ! [X_17: real,Y_14: real] :
% 0.59/0.78 ( ( ( power_power_real @ X_17 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = ( power_power_real @ Y_14 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.78 => ( ( ord_less_eq_real @ zero_zero_real @ X_17 )
% 0.59/0.78 => ( ( ord_less_eq_real @ zero_zero_real @ Y_14 )
% 0.59/0.78 => ( X_17 = Y_14 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_449_power2__eq__imp__eq,axiom,
% 0.59/0.78 ! [X_17: nat,Y_14: nat] :
% 0.59/0.78 ( ( ( power_power_nat @ X_17 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = ( power_power_nat @ Y_14 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.78 => ( ( ord_less_eq_nat @ zero_zero_nat @ X_17 )
% 0.59/0.78 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y_14 )
% 0.59/0.78 => ( X_17 = Y_14 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_450_power2__eq__imp__eq,axiom,
% 0.59/0.78 ! [X_17: int,Y_14: int] :
% 0.59/0.78 ( ( ( power_power_int @ X_17 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = ( power_power_int @ Y_14 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ X_17 )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ Y_14 )
% 0.59/0.78 => ( X_17 = Y_14 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_451_power2__less__0,axiom,
% 0.59/0.78 ! [A_77: real] :
% 0.59/0.78 ~ ( ord_less_real @ ( power_power_real @ A_77 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_real ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_452_power2__less__0,axiom,
% 0.59/0.78 ! [A_77: int] :
% 0.59/0.78 ~ ( ord_less_int @ ( power_power_int @ A_77 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ zero_zero_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_453_zero__less__power2,axiom,
% 0.59/0.78 ! [A_76: real] :
% 0.59/0.78 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A_76 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.78 <=> ( A_76 != zero_zero_real ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_454_zero__less__power2,axiom,
% 0.59/0.78 ! [A_76: int] :
% 0.59/0.78 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A_76 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.78 <=> ( A_76 != zero_zero_int ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_455_sum__power2__eq__zero__iff,axiom,
% 0.59/0.78 ! [X_16: real,Y_13: real] :
% 0.59/0.78 ( ( ( plus_plus_real @ ( power_power_real @ X_16 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_13 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.78 = zero_zero_real )
% 0.59/0.78 <=> ( ( X_16 = zero_zero_real )
% 0.59/0.78 & ( Y_13 = zero_zero_real ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_456_sum__power2__eq__zero__iff,axiom,
% 0.59/0.78 ! [X_16: int,Y_13: int] :
% 0.59/0.78 ( ( ( plus_plus_int @ ( power_power_int @ X_16 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_13 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.78 = zero_zero_int )
% 0.59/0.78 <=> ( ( X_16 = zero_zero_int )
% 0.59/0.78 & ( Y_13 = zero_zero_int ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_457_power__commutes,axiom,
% 0.59/0.78 ! [A_75: nat,N_18: nat] :
% 0.59/0.78 ( ( times_times_nat @ ( power_power_nat @ A_75 @ N_18 ) @ A_75 )
% 0.59/0.78 = ( times_times_nat @ A_75 @ ( power_power_nat @ A_75 @ N_18 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_458_power__commutes,axiom,
% 0.59/0.78 ! [A_75: real,N_18: nat] :
% 0.59/0.78 ( ( times_times_real @ ( power_power_real @ A_75 @ N_18 ) @ A_75 )
% 0.59/0.78 = ( times_times_real @ A_75 @ ( power_power_real @ A_75 @ N_18 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_459_power__commutes,axiom,
% 0.59/0.78 ! [A_75: int,N_18: nat] :
% 0.59/0.78 ( ( times_times_int @ ( power_power_int @ A_75 @ N_18 ) @ A_75 )
% 0.59/0.78 = ( times_times_int @ A_75 @ ( power_power_int @ A_75 @ N_18 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_460_power__mult__distrib,axiom,
% 0.59/0.78 ! [A_74: nat,B_56: nat,N_17: nat] :
% 0.59/0.78 ( ( power_power_nat @ ( times_times_nat @ A_74 @ B_56 ) @ N_17 )
% 0.59/0.78 = ( times_times_nat @ ( power_power_nat @ A_74 @ N_17 ) @ ( power_power_nat @ B_56 @ N_17 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_461_power__mult__distrib,axiom,
% 0.59/0.78 ! [A_74: real,B_56: real,N_17: nat] :
% 0.59/0.78 ( ( power_power_real @ ( times_times_real @ A_74 @ B_56 ) @ N_17 )
% 0.59/0.78 = ( times_times_real @ ( power_power_real @ A_74 @ N_17 ) @ ( power_power_real @ B_56 @ N_17 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_462_power__mult__distrib,axiom,
% 0.59/0.78 ! [A_74: int,B_56: int,N_17: nat] :
% 0.59/0.78 ( ( power_power_int @ ( times_times_int @ A_74 @ B_56 ) @ N_17 )
% 0.59/0.78 = ( times_times_int @ ( power_power_int @ A_74 @ N_17 ) @ ( power_power_int @ B_56 @ N_17 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_463_power__add,axiom,
% 0.59/0.78 ! [A_73: nat,M_6: nat,N_16: nat] :
% 0.59/0.78 ( ( power_power_nat @ A_73 @ ( plus_plus_nat @ M_6 @ N_16 ) )
% 0.59/0.78 = ( times_times_nat @ ( power_power_nat @ A_73 @ M_6 ) @ ( power_power_nat @ A_73 @ N_16 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_464_power__add,axiom,
% 0.59/0.78 ! [A_73: real,M_6: nat,N_16: nat] :
% 0.59/0.78 ( ( power_power_real @ A_73 @ ( plus_plus_nat @ M_6 @ N_16 ) )
% 0.59/0.78 = ( times_times_real @ ( power_power_real @ A_73 @ M_6 ) @ ( power_power_real @ A_73 @ N_16 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_465_power__add,axiom,
% 0.59/0.78 ! [A_73: int,M_6: nat,N_16: nat] :
% 0.59/0.78 ( ( power_power_int @ A_73 @ ( plus_plus_nat @ M_6 @ N_16 ) )
% 0.59/0.78 = ( times_times_int @ ( power_power_int @ A_73 @ M_6 ) @ ( power_power_int @ A_73 @ N_16 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_466_power__one,axiom,
% 0.59/0.78 ! [N_15: nat] :
% 0.59/0.78 ( ( power_power_real @ one_one_real @ N_15 )
% 0.59/0.78 = one_one_real ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_467_power__one,axiom,
% 0.59/0.78 ! [N_15: nat] :
% 0.59/0.78 ( ( power_power_nat @ one_one_nat @ N_15 )
% 0.59/0.78 = one_one_nat ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_468_power__one,axiom,
% 0.59/0.78 ! [N_15: nat] :
% 0.59/0.78 ( ( power_power_int @ one_one_int @ N_15 )
% 0.59/0.78 = one_one_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_469_power__mult,axiom,
% 0.59/0.78 ! [A_72: nat,M_5: nat,N_14: nat] :
% 0.59/0.78 ( ( power_power_nat @ A_72 @ ( times_times_nat @ M_5 @ N_14 ) )
% 0.59/0.78 = ( power_power_nat @ ( power_power_nat @ A_72 @ M_5 ) @ N_14 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_470_power__mult,axiom,
% 0.59/0.78 ! [A_72: real,M_5: nat,N_14: nat] :
% 0.59/0.78 ( ( power_power_real @ A_72 @ ( times_times_nat @ M_5 @ N_14 ) )
% 0.59/0.78 = ( power_power_real @ ( power_power_real @ A_72 @ M_5 ) @ N_14 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_471_power__mult,axiom,
% 0.59/0.78 ! [A_72: int,M_5: nat,N_14: nat] :
% 0.59/0.78 ( ( power_power_int @ A_72 @ ( times_times_nat @ M_5 @ N_14 ) )
% 0.59/0.78 = ( power_power_int @ ( power_power_int @ A_72 @ M_5 ) @ N_14 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_472_power2__less__imp__less,axiom,
% 0.59/0.78 ! [X_15: real,Y_12: real] :
% 0.59/0.78 ( ( ord_less_real @ ( power_power_real @ X_15 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_12 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.78 => ( ( ord_less_eq_real @ zero_zero_real @ Y_12 )
% 0.59/0.78 => ( ord_less_real @ X_15 @ Y_12 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_473_power2__less__imp__less,axiom,
% 0.59/0.78 ! [X_15: nat,Y_12: nat] :
% 0.59/0.78 ( ( ord_less_nat @ ( power_power_nat @ X_15 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y_12 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.78 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y_12 )
% 0.59/0.78 => ( ord_less_nat @ X_15 @ Y_12 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_474_power2__less__imp__less,axiom,
% 0.59/0.78 ! [X_15: int,Y_12: int] :
% 0.59/0.78 ( ( ord_less_int @ ( power_power_int @ X_15 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_12 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ Y_12 )
% 0.59/0.78 => ( ord_less_int @ X_15 @ Y_12 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_475_sum__power2__ge__zero,axiom,
% 0.59/0.78 ! [X_14: real,Y_11: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X_14 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_11 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_476_sum__power2__ge__zero,axiom,
% 0.59/0.78 ! [X_14: int,Y_11: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_14 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_11 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_477_sum__power2__le__zero__iff,axiom,
% 0.59/0.78 ! [X_13: real,Y_10: real] :
% 0.59/0.78 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X_13 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_10 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real )
% 0.59/0.78 <=> ( ( X_13 = zero_zero_real )
% 0.59/0.78 & ( Y_10 = zero_zero_real ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_478_sum__power2__le__zero__iff,axiom,
% 0.59/0.78 ! [X_13: int,Y_10: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X_13 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_10 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int )
% 0.59/0.78 <=> ( ( X_13 = zero_zero_int )
% 0.59/0.78 & ( Y_10 = zero_zero_int ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_479_not__sum__power2__lt__zero,axiom,
% 0.59/0.78 ! [X_12: real,Y_9: real] :
% 0.59/0.78 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X_12 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_9 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_real ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_480_not__sum__power2__lt__zero,axiom,
% 0.59/0.78 ! [X_12: int,Y_9: int] :
% 0.59/0.78 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X_12 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_9 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ zero_zero_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_481_sum__power2__gt__zero__iff,axiom,
% 0.59/0.78 ! [X_11: real,Y_8: real] :
% 0.59/0.78 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X_11 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_8 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
% 0.59/0.78 <=> ( ( X_11 != zero_zero_real )
% 0.59/0.78 | ( Y_8 != zero_zero_real ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_482_sum__power2__gt__zero__iff,axiom,
% 0.59/0.78 ! [X_11: int,Y_8: int] :
% 0.59/0.78 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X_11 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_8 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) )
% 0.59/0.78 <=> ( ( X_11 != zero_zero_int )
% 0.59/0.78 | ( Y_8 != zero_zero_int ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_483_zero__le__even__power_H,axiom,
% 0.59/0.78 ! [A_71: real,N_13: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A_71 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_13 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_484_zero__le__even__power_H,axiom,
% 0.59/0.78 ! [A_71: int,N_13: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A_71 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_13 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_485_one__le__power,axiom,
% 0.59/0.78 ! [N_12: nat,A_70: real] :
% 0.59/0.78 ( ( ord_less_eq_real @ one_one_real @ A_70 )
% 0.59/0.78 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A_70 @ N_12 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_486_one__le__power,axiom,
% 0.59/0.78 ! [N_12: nat,A_70: nat] :
% 0.59/0.78 ( ( ord_less_eq_nat @ one_one_nat @ A_70 )
% 0.59/0.78 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A_70 @ N_12 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_487_one__le__power,axiom,
% 0.59/0.78 ! [N_12: nat,A_70: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ one_one_int @ A_70 )
% 0.59/0.78 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A_70 @ N_12 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_488_power__increasing,axiom,
% 0.59/0.78 ! [A_69: real,N_11: nat,N_10: nat] :
% 0.59/0.78 ( ( ord_less_eq_nat @ N_11 @ N_10 )
% 0.59/0.78 => ( ( ord_less_eq_real @ one_one_real @ A_69 )
% 0.59/0.78 => ( ord_less_eq_real @ ( power_power_real @ A_69 @ N_11 ) @ ( power_power_real @ A_69 @ N_10 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_489_power__increasing,axiom,
% 0.59/0.78 ! [A_69: nat,N_11: nat,N_10: nat] :
% 0.59/0.78 ( ( ord_less_eq_nat @ N_11 @ N_10 )
% 0.59/0.78 => ( ( ord_less_eq_nat @ one_one_nat @ A_69 )
% 0.59/0.78 => ( ord_less_eq_nat @ ( power_power_nat @ A_69 @ N_11 ) @ ( power_power_nat @ A_69 @ N_10 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_490_power__increasing,axiom,
% 0.59/0.78 ! [A_69: int,N_11: nat,N_10: nat] :
% 0.59/0.78 ( ( ord_less_eq_nat @ N_11 @ N_10 )
% 0.59/0.78 => ( ( ord_less_eq_int @ one_one_int @ A_69 )
% 0.59/0.78 => ( ord_less_eq_int @ ( power_power_int @ A_69 @ N_11 ) @ ( power_power_int @ A_69 @ N_10 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_491_power__inject__exp,axiom,
% 0.59/0.78 ! [M_4: nat,N_9: nat,A_68: real] :
% 0.59/0.78 ( ( ord_less_real @ one_one_real @ A_68 )
% 0.59/0.78 => ( ( ( power_power_real @ A_68 @ M_4 )
% 0.59/0.78 = ( power_power_real @ A_68 @ N_9 ) )
% 0.59/0.78 <=> ( M_4 = N_9 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_492_power__inject__exp,axiom,
% 0.59/0.78 ! [M_4: nat,N_9: nat,A_68: nat] :
% 0.59/0.78 ( ( ord_less_nat @ one_one_nat @ A_68 )
% 0.59/0.78 => ( ( ( power_power_nat @ A_68 @ M_4 )
% 0.59/0.78 = ( power_power_nat @ A_68 @ N_9 ) )
% 0.59/0.78 <=> ( M_4 = N_9 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_493_power__inject__exp,axiom,
% 0.59/0.78 ! [M_4: nat,N_9: nat,A_68: int] :
% 0.59/0.78 ( ( ord_less_int @ one_one_int @ A_68 )
% 0.59/0.78 => ( ( ( power_power_int @ A_68 @ M_4 )
% 0.59/0.78 = ( power_power_int @ A_68 @ N_9 ) )
% 0.59/0.78 <=> ( M_4 = N_9 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_494_power__strict__increasing__iff,axiom,
% 0.59/0.78 ! [X_10: nat,Y_7: nat,B_55: real] :
% 0.59/0.78 ( ( ord_less_real @ one_one_real @ B_55 )
% 0.59/0.78 => ( ( ord_less_real @ ( power_power_real @ B_55 @ X_10 ) @ ( power_power_real @ B_55 @ Y_7 ) )
% 0.59/0.78 <=> ( ord_less_nat @ X_10 @ Y_7 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_495_power__strict__increasing__iff,axiom,
% 0.59/0.78 ! [X_10: nat,Y_7: nat,B_55: nat] :
% 0.59/0.78 ( ( ord_less_nat @ one_one_nat @ B_55 )
% 0.59/0.78 => ( ( ord_less_nat @ ( power_power_nat @ B_55 @ X_10 ) @ ( power_power_nat @ B_55 @ Y_7 ) )
% 0.59/0.78 <=> ( ord_less_nat @ X_10 @ Y_7 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_496_power__strict__increasing__iff,axiom,
% 0.59/0.78 ! [X_10: nat,Y_7: nat,B_55: int] :
% 0.59/0.78 ( ( ord_less_int @ one_one_int @ B_55 )
% 0.59/0.78 => ( ( ord_less_int @ ( power_power_int @ B_55 @ X_10 ) @ ( power_power_int @ B_55 @ Y_7 ) )
% 0.59/0.78 <=> ( ord_less_nat @ X_10 @ Y_7 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_497_power__less__imp__less__exp,axiom,
% 0.59/0.78 ! [M_3: nat,N_8: nat,A_67: real] :
% 0.59/0.78 ( ( ord_less_real @ one_one_real @ A_67 )
% 0.59/0.78 => ( ( ord_less_real @ ( power_power_real @ A_67 @ M_3 ) @ ( power_power_real @ A_67 @ N_8 ) )
% 0.59/0.78 => ( ord_less_nat @ M_3 @ N_8 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_498_power__less__imp__less__exp,axiom,
% 0.59/0.78 ! [M_3: nat,N_8: nat,A_67: nat] :
% 0.59/0.78 ( ( ord_less_nat @ one_one_nat @ A_67 )
% 0.59/0.78 => ( ( ord_less_nat @ ( power_power_nat @ A_67 @ M_3 ) @ ( power_power_nat @ A_67 @ N_8 ) )
% 0.59/0.78 => ( ord_less_nat @ M_3 @ N_8 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_499_power__less__imp__less__exp,axiom,
% 0.59/0.78 ! [M_3: nat,N_8: nat,A_67: int] :
% 0.59/0.78 ( ( ord_less_int @ one_one_int @ A_67 )
% 0.59/0.78 => ( ( ord_less_int @ ( power_power_int @ A_67 @ M_3 ) @ ( power_power_int @ A_67 @ N_8 ) )
% 0.59/0.78 => ( ord_less_nat @ M_3 @ N_8 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_500_power__strict__increasing,axiom,
% 0.59/0.78 ! [A_66: real,N_7: nat,N_6: nat] :
% 0.59/0.78 ( ( ord_less_nat @ N_7 @ N_6 )
% 0.59/0.78 => ( ( ord_less_real @ one_one_real @ A_66 )
% 0.59/0.78 => ( ord_less_real @ ( power_power_real @ A_66 @ N_7 ) @ ( power_power_real @ A_66 @ N_6 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_501_power__strict__increasing,axiom,
% 0.59/0.78 ! [A_66: nat,N_7: nat,N_6: nat] :
% 0.59/0.78 ( ( ord_less_nat @ N_7 @ N_6 )
% 0.59/0.78 => ( ( ord_less_nat @ one_one_nat @ A_66 )
% 0.59/0.78 => ( ord_less_nat @ ( power_power_nat @ A_66 @ N_7 ) @ ( power_power_nat @ A_66 @ N_6 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_502_power__strict__increasing,axiom,
% 0.59/0.78 ! [A_66: int,N_7: nat,N_6: nat] :
% 0.59/0.78 ( ( ord_less_nat @ N_7 @ N_6 )
% 0.59/0.78 => ( ( ord_less_int @ one_one_int @ A_66 )
% 0.59/0.78 => ( ord_less_int @ ( power_power_int @ A_66 @ N_7 ) @ ( power_power_int @ A_66 @ N_6 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_503_s,axiom,
% 0.59/0.78 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 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_504_Euler_Oaux____1,axiom,
% 0.59/0.78 ! [Y_1: int,X_1: int,P: int] :
% 0.59/0.78 ( ~ ( zcong @ X_1 @ zero_zero_int @ P )
% 0.59/0.78 => ( ( zcong @ ( power_power_int @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X_1 @ P )
% 0.59/0.78 => ~ ( dvd_dvd_int @ P @ Y_1 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_505_int__pos__lt__two__imp__zero__or__one,axiom,
% 0.59/0.78 ! [X_1: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.59/0.78 => ( ( ord_less_int @ X_1 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 => ( ( X_1 = zero_zero_int )
% 0.59/0.78 | ( X_1 = one_one_int ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_506_even__power__le__0__imp__0,axiom,
% 0.59/0.78 ! [A_65: real,K_3: nat] :
% 0.59/0.78 ( ( ord_less_eq_real @ ( power_power_real @ A_65 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ K_3 ) ) @ zero_zero_real )
% 0.59/0.78 => ( A_65 = zero_zero_real ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_507_even__power__le__0__imp__0,axiom,
% 0.59/0.78 ! [A_65: int,K_3: nat] :
% 0.59/0.78 ( ( ord_less_eq_int @ ( power_power_int @ A_65 @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ K_3 ) ) @ zero_zero_int )
% 0.59/0.78 => ( A_65 = zero_zero_int ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_508_zprime__def,axiom,
% 0.59/0.78 ! [P: int] :
% 0.59/0.78 ( ( zprime @ P )
% 0.59/0.78 <=> ( ( ord_less_int @ one_one_int @ P )
% 0.59/0.78 & ! [M_2: int] :
% 0.59/0.78 ( ( ( ord_less_eq_int @ zero_zero_int @ M_2 )
% 0.59/0.78 & ( dvd_dvd_int @ M_2 @ P ) )
% 0.59/0.78 => ( ( M_2 = one_one_int )
% 0.59/0.78 | ( M_2 = P ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_509_self__quotient__aux2,axiom,
% 0.59/0.78 ! [R: int,Q: int,A: int] :
% 0.59/0.78 ( ( ord_less_int @ zero_zero_int @ A )
% 0.59/0.78 => ( ( A
% 0.59/0.78 = ( plus_plus_int @ R @ ( times_times_int @ A @ Q ) ) )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.59/0.78 => ( ord_less_eq_int @ Q @ one_one_int ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_510_self__quotient__aux1,axiom,
% 0.59/0.78 ! [R: int,Q: int,A: int] :
% 0.59/0.78 ( ( ord_less_int @ zero_zero_int @ A )
% 0.59/0.78 => ( ( A
% 0.59/0.78 = ( plus_plus_int @ R @ ( times_times_int @ A @ Q ) ) )
% 0.59/0.78 => ( ( ord_less_int @ R @ A )
% 0.59/0.78 => ( ord_less_eq_int @ one_one_int @ Q ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_511_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom,
% 0.59/0.78 ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_512__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_,axiom,
% 0.59/0.78 ~ ! [S1: int] :
% 0.59/0.78 ~ ( 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 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_513__096Legendre_A_N1_A_I4_A_K_Am_A_L_A1_J_A_061_A1_096,axiom,
% 0.59/0.78 ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
% 0.59/0.78 = one_one_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_514_nat__zero__less__power__iff,axiom,
% 0.59/0.78 ! [X_1: nat,N: nat] :
% 0.59/0.78 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X_1 @ N ) )
% 0.59/0.78 <=> ( ( ord_less_nat @ zero_zero_nat @ X_1 )
% 0.59/0.78 | ( N = zero_zero_nat ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_515_zero__less__power__nat__eq,axiom,
% 0.59/0.78 ! [X_1: nat,N: nat] :
% 0.59/0.78 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X_1 @ N ) )
% 0.59/0.78 <=> ( ( N = zero_zero_nat )
% 0.59/0.78 | ( ord_less_nat @ zero_zero_nat @ X_1 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_516_zero__less__power__nat__eq__number__of,axiom,
% 0.59/0.78 ! [X_1: nat,W: int] :
% 0.59/0.78 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X_1 @ ( number_number_of_nat @ W ) ) )
% 0.59/0.78 <=> ( ( ( number_number_of_nat @ W )
% 0.59/0.78 = zero_zero_nat )
% 0.59/0.78 | ( ord_less_nat @ zero_zero_nat @ X_1 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_517_nat__power__less__imp__less,axiom,
% 0.59/0.78 ! [M: nat,N: nat,I_1: nat] :
% 0.59/0.78 ( ( ord_less_nat @ zero_zero_nat @ I_1 )
% 0.59/0.78 => ( ( ord_less_nat @ ( power_power_nat @ I_1 @ M ) @ ( power_power_nat @ I_1 @ N ) )
% 0.59/0.78 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_518_rel__simps_I47_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( ( bit1 @ K )
% 0.59/0.78 = min )
% 0.59/0.78 <=> ( K = min ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_519_rel__simps_I43_J,axiom,
% 0.59/0.78 ! [L: int] :
% 0.59/0.78 ( ( min
% 0.59/0.78 = ( bit1 @ L ) )
% 0.59/0.78 <=> ( min = L ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_520_Bit1__Min,axiom,
% 0.59/0.78 ( ( bit1 @ min )
% 0.59/0.78 = min ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_521_rel__simps_I37_J,axiom,
% 0.59/0.78 pls != min ).
% 0.59/0.78
% 0.59/0.78 thf(fact_522_rel__simps_I40_J,axiom,
% 0.59/0.78 min != pls ).
% 0.59/0.78
% 0.59/0.78 thf(fact_523_rel__simps_I45_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( bit0 @ K )
% 0.59/0.78 != min ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_524_rel__simps_I42_J,axiom,
% 0.59/0.78 ! [L: int] :
% 0.59/0.78 ( min
% 0.59/0.78 != ( bit0 @ L ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_525_rel__simps_I7_J,axiom,
% 0.59/0.78 ~ ( ord_less_int @ min @ min ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_526_rel__simps_I24_J,axiom,
% 0.59/0.78 ord_less_eq_int @ min @ min ).
% 0.59/0.78
% 0.59/0.78 thf(fact_527_not__real__square__gt__zero,axiom,
% 0.59/0.78 ! [X_1: real] :
% 0.59/0.78 ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X_1 @ X_1 ) )
% 0.59/0.78 <=> ( X_1 = zero_zero_real ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_528_rel__simps_I13_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( ord_less_int @ ( bit1 @ K ) @ min )
% 0.59/0.78 <=> ( ord_less_int @ K @ min ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_529_rel__simps_I9_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( ord_less_int @ min @ ( bit1 @ K ) )
% 0.59/0.78 <=> ( ord_less_int @ min @ K ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_530_rel__simps_I3_J,axiom,
% 0.59/0.78 ~ ( ord_less_int @ pls @ min ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_531_rel__simps_I6_J,axiom,
% 0.59/0.78 ord_less_int @ min @ pls ).
% 0.59/0.78
% 0.59/0.78 thf(fact_532_rel__simps_I8_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( ord_less_int @ min @ ( bit0 @ K ) )
% 0.59/0.78 <=> ( ord_less_int @ min @ K ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_533_bin__less__0__simps_I2_J,axiom,
% 0.59/0.78 ord_less_int @ min @ zero_zero_int ).
% 0.59/0.78
% 0.59/0.78 thf(fact_534_rel__simps_I30_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ ( bit1 @ K ) @ min )
% 0.59/0.78 <=> ( ord_less_eq_int @ K @ min ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_535_rel__simps_I26_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ min @ ( bit1 @ K ) )
% 0.59/0.78 <=> ( ord_less_eq_int @ min @ K ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_536_rel__simps_I20_J,axiom,
% 0.59/0.78 ~ ( ord_less_eq_int @ pls @ min ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_537_rel__simps_I23_J,axiom,
% 0.59/0.78 ord_less_eq_int @ min @ pls ).
% 0.59/0.78
% 0.59/0.78 thf(fact_538_rel__simps_I28_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ ( bit0 @ K ) @ min )
% 0.59/0.78 <=> ( ord_less_eq_int @ K @ min ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_539_eq__number__of__Pls__Min,axiom,
% 0.59/0.78 ( ( number_number_of_int @ pls )
% 0.59/0.78 != ( number_number_of_int @ min ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_540_power__dvd__imp__le,axiom,
% 0.59/0.78 ! [I_1: nat,M: nat,N: nat] :
% 0.59/0.78 ( ( dvd_dvd_nat @ ( power_power_nat @ I_1 @ M ) @ ( power_power_nat @ I_1 @ N ) )
% 0.59/0.78 => ( ( ord_less_nat @ one_one_nat @ I_1 )
% 0.59/0.78 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_541_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 0.59/0.78 ! [X_9: real] :
% 0.59/0.78 ( ( power_power_real @ X_9 @ zero_zero_nat )
% 0.59/0.78 = one_one_real ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_542_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 0.59/0.78 ! [X_9: nat] :
% 0.59/0.78 ( ( power_power_nat @ X_9 @ zero_zero_nat )
% 0.59/0.78 = one_one_nat ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_543_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom,
% 0.59/0.78 ! [X_9: int] :
% 0.59/0.78 ( ( power_power_int @ X_9 @ zero_zero_nat )
% 0.59/0.78 = one_one_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_544_power__0,axiom,
% 0.59/0.78 ! [A_64: real] :
% 0.59/0.78 ( ( power_power_real @ A_64 @ zero_zero_nat )
% 0.59/0.78 = one_one_real ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_545_power__0,axiom,
% 0.59/0.78 ! [A_64: nat] :
% 0.59/0.78 ( ( power_power_nat @ A_64 @ zero_zero_nat )
% 0.59/0.78 = one_one_nat ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_546_power__0,axiom,
% 0.59/0.78 ! [A_64: int] :
% 0.59/0.78 ( ( power_power_int @ A_64 @ zero_zero_nat )
% 0.59/0.78 = one_one_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_547_nat__number__of__Pls,axiom,
% 0.59/0.78 ( ( number_number_of_nat @ pls )
% 0.59/0.78 = zero_zero_nat ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_548_semiring__norm_I113_J,axiom,
% 0.59/0.78 ( zero_zero_nat
% 0.59/0.78 = ( number_number_of_nat @ pls ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_549_rel__simps_I25_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ min @ ( bit0 @ K ) )
% 0.59/0.78 <=> ( ord_less_int @ min @ K ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_550_rel__simps_I11_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( ord_less_int @ ( bit0 @ K ) @ min )
% 0.59/0.78 <=> ( ord_less_eq_int @ K @ min ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_551_pos__zmult__eq__1__iff__lemma,axiom,
% 0.59/0.78 ! [M: int,N: int] :
% 0.59/0.78 ( ( ( times_times_int @ M @ N )
% 0.59/0.78 = one_one_int )
% 0.59/0.78 => ( ( M = one_one_int )
% 0.59/0.78 | ( M
% 0.59/0.78 = ( number_number_of_int @ min ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_552_zmult__eq__1__iff,axiom,
% 0.59/0.78 ! [M: int,N: int] :
% 0.59/0.78 ( ( ( times_times_int @ M @ N )
% 0.59/0.78 = one_one_int )
% 0.59/0.78 <=> ( ( ( M = one_one_int )
% 0.59/0.78 & ( N = one_one_int ) )
% 0.59/0.78 | ( ( M
% 0.59/0.78 = ( number_number_of_int @ min ) )
% 0.59/0.78 & ( N
% 0.59/0.78 = ( number_number_of_int @ min ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_553_one__less__power,axiom,
% 0.59/0.78 ! [N_5: nat,A_63: real] :
% 0.59/0.78 ( ( ord_less_real @ one_one_real @ A_63 )
% 0.59/0.78 => ( ( ord_less_nat @ zero_zero_nat @ N_5 )
% 0.59/0.78 => ( ord_less_real @ one_one_real @ ( power_power_real @ A_63 @ N_5 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_554_one__less__power,axiom,
% 0.59/0.78 ! [N_5: nat,A_63: nat] :
% 0.59/0.78 ( ( ord_less_nat @ one_one_nat @ A_63 )
% 0.59/0.78 => ( ( ord_less_nat @ zero_zero_nat @ N_5 )
% 0.59/0.78 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A_63 @ N_5 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_555_one__less__power,axiom,
% 0.59/0.78 ! [N_5: nat,A_63: int] :
% 0.59/0.78 ( ( ord_less_int @ one_one_int @ A_63 )
% 0.59/0.78 => ( ( ord_less_nat @ zero_zero_nat @ N_5 )
% 0.59/0.78 => ( ord_less_int @ one_one_int @ ( power_power_int @ A_63 @ N_5 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_556_dvd__power,axiom,
% 0.59/0.78 ! [X_8: real,N_4: nat] :
% 0.59/0.78 ( ( ( ord_less_nat @ zero_zero_nat @ N_4 )
% 0.59/0.78 | ( X_8 = one_one_real ) )
% 0.59/0.78 => ( dvd_dvd_real @ X_8 @ ( power_power_real @ X_8 @ N_4 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_557_dvd__power,axiom,
% 0.59/0.78 ! [X_8: nat,N_4: nat] :
% 0.59/0.78 ( ( ( ord_less_nat @ zero_zero_nat @ N_4 )
% 0.59/0.78 | ( X_8 = one_one_nat ) )
% 0.59/0.78 => ( dvd_dvd_nat @ X_8 @ ( power_power_nat @ X_8 @ N_4 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_558_dvd__power,axiom,
% 0.59/0.78 ! [X_8: int,N_4: nat] :
% 0.59/0.78 ( ( ( ord_less_nat @ zero_zero_nat @ N_4 )
% 0.59/0.78 | ( X_8 = one_one_int ) )
% 0.59/0.78 => ( dvd_dvd_int @ X_8 @ ( power_power_int @ X_8 @ N_4 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_559_less__0__number__of,axiom,
% 0.59/0.78 ! [V: int] :
% 0.59/0.78 ( ( ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ V ) )
% 0.59/0.78 <=> ( ord_less_int @ pls @ V ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_560_eq__number__of__0,axiom,
% 0.59/0.78 ! [V: int] :
% 0.59/0.78 ( ( ( number_number_of_nat @ V )
% 0.59/0.78 = zero_zero_nat )
% 0.59/0.78 <=> ( ord_less_eq_int @ V @ pls ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_561_eq__0__number__of,axiom,
% 0.59/0.78 ! [V: int] :
% 0.59/0.78 ( ( zero_zero_nat
% 0.59/0.78 = ( number_number_of_nat @ V ) )
% 0.59/0.78 <=> ( ord_less_eq_int @ V @ pls ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_562_zcong__sym,axiom,
% 0.59/0.78 ! [A: int,B: int,M: int] :
% 0.59/0.78 ( ( zcong @ A @ B @ M )
% 0.59/0.78 <=> ( zcong @ B @ A @ M ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_563_zcong__refl,axiom,
% 0.59/0.78 ! [K: int,M: int] : ( zcong @ K @ K @ M ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_564_zcong__trans,axiom,
% 0.59/0.78 ! [C: int,A: int,B: int,M: int] :
% 0.59/0.78 ( ( zcong @ A @ B @ M )
% 0.59/0.78 => ( ( zcong @ B @ C @ M )
% 0.59/0.78 => ( zcong @ A @ C @ M ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_565_pos2,axiom,
% 0.59/0.78 ord_less_nat @ zero_zero_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_566_nat__number__of__mult__left,axiom,
% 0.59/0.78 ! [V_6: int,K: nat,V: int] :
% 0.59/0.78 ( ( ( ord_less_int @ V @ pls )
% 0.59/0.78 => ( ( times_times_nat @ ( number_number_of_nat @ V ) @ ( times_times_nat @ ( number_number_of_nat @ V_6 ) @ K ) )
% 0.59/0.78 = zero_zero_nat ) )
% 0.59/0.78 & ( ~ ( ord_less_int @ V @ pls )
% 0.59/0.78 => ( ( times_times_nat @ ( number_number_of_nat @ V ) @ ( times_times_nat @ ( number_number_of_nat @ V_6 ) @ K ) )
% 0.59/0.78 = ( times_times_nat @ ( number_number_of_nat @ ( times_times_int @ V @ V_6 ) ) @ K ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_567_mult__nat__number__of,axiom,
% 0.59/0.78 ! [V_6: int,V: int] :
% 0.59/0.78 ( ( ( ord_less_int @ V @ pls )
% 0.59/0.78 => ( ( times_times_nat @ ( number_number_of_nat @ V ) @ ( number_number_of_nat @ V_6 ) )
% 0.59/0.78 = zero_zero_nat ) )
% 0.59/0.78 & ( ~ ( ord_less_int @ V @ pls )
% 0.59/0.78 => ( ( times_times_nat @ ( number_number_of_nat @ V ) @ ( number_number_of_nat @ V_6 ) )
% 0.59/0.78 = ( number_number_of_nat @ ( times_times_int @ V @ V_6 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_568_order__le__neq__implies__less,axiom,
% 0.59/0.78 ! [X_7: real,Y_6: real] :
% 0.59/0.78 ( ( ord_less_eq_real @ X_7 @ Y_6 )
% 0.59/0.78 => ( ( X_7 != Y_6 )
% 0.59/0.78 => ( ord_less_real @ X_7 @ Y_6 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_569_order__le__neq__implies__less,axiom,
% 0.59/0.78 ! [X_7: nat,Y_6: nat] :
% 0.59/0.78 ( ( ord_less_eq_nat @ X_7 @ Y_6 )
% 0.59/0.78 => ( ( X_7 != Y_6 )
% 0.59/0.78 => ( ord_less_nat @ X_7 @ Y_6 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_570_order__le__neq__implies__less,axiom,
% 0.59/0.78 ! [X_7: int,Y_6: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ X_7 @ Y_6 )
% 0.59/0.78 => ( ( X_7 != Y_6 )
% 0.59/0.78 => ( ord_less_int @ X_7 @ Y_6 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_571_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom,
% 0.59/0.78 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 0.59/0.78
% 0.59/0.78 thf(fact_572_Euler_Oaux2,axiom,
% 0.59/0.78 ! [B: int,A: int,C: int] :
% 0.59/0.78 ( ( ord_less_int @ A @ C )
% 0.59/0.78 => ( ( ord_less_int @ B @ C )
% 0.59/0.78 => ( ( ord_less_eq_int @ A @ B )
% 0.59/0.78 | ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_573_IntPrimes_Ozcong__zero,axiom,
% 0.59/0.78 ! [A: int,B: int] :
% 0.59/0.78 ( ( zcong @ A @ B @ zero_zero_int )
% 0.59/0.78 <=> ( A = B ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_574_zcong__1,axiom,
% 0.59/0.78 ! [A: int,B: int] : ( zcong @ A @ B @ one_one_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_575_zcong__zmult,axiom,
% 0.59/0.78 ! [C: int,D: int,A: int,B: int,M: int] :
% 0.59/0.78 ( ( zcong @ A @ B @ M )
% 0.59/0.78 => ( ( zcong @ C @ D @ M )
% 0.59/0.78 => ( zcong @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) @ M ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_576_zcong__scalar2,axiom,
% 0.59/0.78 ! [K: int,A: int,B: int,M: int] :
% 0.59/0.78 ( ( zcong @ A @ B @ M )
% 0.59/0.78 => ( zcong @ ( times_times_int @ K @ A ) @ ( times_times_int @ K @ B ) @ M ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_577_zcong__scalar,axiom,
% 0.59/0.78 ! [K: int,A: int,B: int,M: int] :
% 0.59/0.78 ( ( zcong @ A @ B @ M )
% 0.59/0.78 => ( zcong @ ( times_times_int @ A @ K ) @ ( times_times_int @ B @ K ) @ M ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_578_zcong__zmult__self,axiom,
% 0.59/0.78 ! [A: int,M: int,B: int] : ( zcong @ ( times_times_int @ A @ M ) @ ( times_times_int @ B @ M ) @ M ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_579_zcong__zadd,axiom,
% 0.59/0.78 ! [C: int,D: int,A: int,B: int,M: int] :
% 0.59/0.78 ( ( zcong @ A @ B @ M )
% 0.59/0.78 => ( ( zcong @ C @ D @ M )
% 0.59/0.78 => ( zcong @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) @ M ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_580_power__m1__even,axiom,
% 0.59/0.78 ! [N_3: nat] :
% 0.59/0.78 ( ( power_power_real @ ( number267125858f_real @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_3 ) )
% 0.59/0.78 = one_one_real ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_581_power__m1__even,axiom,
% 0.59/0.78 ! [N_3: nat] :
% 0.59/0.78 ( ( power_power_int @ ( number_number_of_int @ min ) @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N_3 ) )
% 0.59/0.78 = one_one_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_582_power__eq__0__iff__number__of,axiom,
% 0.59/0.78 ! [A_62: real,W_4: int] :
% 0.59/0.78 ( ( ( power_power_real @ A_62 @ ( number_number_of_nat @ W_4 ) )
% 0.59/0.78 = zero_zero_real )
% 0.59/0.78 <=> ( ( A_62 = zero_zero_real )
% 0.59/0.78 & ( ( number_number_of_nat @ W_4 )
% 0.59/0.78 != zero_zero_nat ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_583_power__eq__0__iff__number__of,axiom,
% 0.59/0.78 ! [A_62: nat,W_4: int] :
% 0.59/0.78 ( ( ( power_power_nat @ A_62 @ ( number_number_of_nat @ W_4 ) )
% 0.59/0.78 = zero_zero_nat )
% 0.59/0.78 <=> ( ( A_62 = zero_zero_nat )
% 0.59/0.78 & ( ( number_number_of_nat @ W_4 )
% 0.59/0.78 != zero_zero_nat ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_584_power__eq__0__iff__number__of,axiom,
% 0.59/0.78 ! [A_62: int,W_4: int] :
% 0.59/0.78 ( ( ( power_power_int @ A_62 @ ( number_number_of_nat @ W_4 ) )
% 0.59/0.78 = zero_zero_int )
% 0.59/0.78 <=> ( ( A_62 = zero_zero_int )
% 0.59/0.78 & ( ( number_number_of_nat @ W_4 )
% 0.59/0.78 != zero_zero_nat ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_585_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom,
% 0.59/0.78 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 0.59/0.78
% 0.59/0.78 thf(fact_586_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom,
% 0.59/0.78 ! [Y_1: int,X_1: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ Y_1 )
% 0.59/0.78 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ X_1 @ Y_1 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_587_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom,
% 0.59/0.78 ! [Y_1: int,X_1: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ Y_1 )
% 0.59/0.78 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ X_1 @ Y_1 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_588_zcong__not,axiom,
% 0.59/0.78 ! [B: int,M: int,A: int] :
% 0.59/0.78 ( ( ord_less_int @ zero_zero_int @ A )
% 0.59/0.78 => ( ( ord_less_int @ A @ M )
% 0.59/0.78 => ( ( ord_less_int @ zero_zero_int @ B )
% 0.59/0.78 => ( ( ord_less_int @ B @ A )
% 0.59/0.78 => ~ ( zcong @ A @ B @ M ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_589_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom,
% 0.59/0.78 ! [N: nat,X_1: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.59/0.78 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ X_1 @ N ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_590_zcong__iff__lin,axiom,
% 0.59/0.78 ! [A: int,B: int,M: int] :
% 0.59/0.78 ( ( zcong @ A @ B @ M )
% 0.59/0.78 <=> ? [K_1: int] :
% 0.59/0.78 ( B
% 0.59/0.78 = ( plus_plus_int @ A @ ( times_times_int @ M @ K_1 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_591_power__0__left__number__of,axiom,
% 0.59/0.78 ! [W_3: int] :
% 0.59/0.78 ( ( ( ( number_number_of_nat @ W_3 )
% 0.59/0.78 = zero_zero_nat )
% 0.59/0.78 => ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ W_3 ) )
% 0.59/0.78 = one_one_real ) )
% 0.59/0.78 & ( ( ( number_number_of_nat @ W_3 )
% 0.59/0.78 != zero_zero_nat )
% 0.59/0.78 => ( ( power_power_real @ zero_zero_real @ ( number_number_of_nat @ W_3 ) )
% 0.59/0.78 = zero_zero_real ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_592_power__0__left__number__of,axiom,
% 0.59/0.78 ! [W_3: int] :
% 0.59/0.78 ( ( ( ( number_number_of_nat @ W_3 )
% 0.59/0.78 = zero_zero_nat )
% 0.59/0.78 => ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_3 ) )
% 0.59/0.78 = one_one_nat ) )
% 0.59/0.78 & ( ( ( number_number_of_nat @ W_3 )
% 0.59/0.78 != zero_zero_nat )
% 0.59/0.78 => ( ( power_power_nat @ zero_zero_nat @ ( number_number_of_nat @ W_3 ) )
% 0.59/0.78 = zero_zero_nat ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_593_power__0__left__number__of,axiom,
% 0.59/0.78 ! [W_3: int] :
% 0.59/0.78 ( ( ( ( number_number_of_nat @ W_3 )
% 0.59/0.78 = zero_zero_nat )
% 0.59/0.78 => ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_3 ) )
% 0.59/0.78 = one_one_int ) )
% 0.59/0.78 & ( ( ( number_number_of_nat @ W_3 )
% 0.59/0.78 != zero_zero_nat )
% 0.59/0.78 => ( ( power_power_int @ zero_zero_int @ ( number_number_of_nat @ W_3 ) )
% 0.59/0.78 = zero_zero_int ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_594_zcong__zless__imp__eq,axiom,
% 0.59/0.78 ! [B: int,M: int,A: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.59/0.78 => ( ( ord_less_int @ A @ M )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 0.59/0.78 => ( ( ord_less_int @ B @ M )
% 0.59/0.78 => ( ( zcong @ A @ B @ M )
% 0.59/0.78 => ( A = B ) ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_595_zcong__zless__0,axiom,
% 0.59/0.78 ! [M: int,A: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.59/0.78 => ( ( ord_less_int @ A @ M )
% 0.59/0.78 => ( ( zcong @ A @ zero_zero_int @ M )
% 0.59/0.78 => ( A = zero_zero_int ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_596_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom,
% 0.59/0.78 ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ ( bit1 @ pls ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_597_zdiv__mono2__neg__lemma,axiom,
% 0.59/0.78 ! [B: int,Q: int,R: int,B_54: int,Q_3: int,R_2: int] :
% 0.59/0.78 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R )
% 0.59/0.78 = ( plus_plus_int @ ( times_times_int @ B_54 @ Q_3 ) @ R_2 ) )
% 0.59/0.78 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B_54 @ Q_3 ) @ R_2 ) @ zero_zero_int )
% 0.59/0.78 => ( ( ord_less_int @ R @ B )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ R_2 )
% 0.59/0.78 => ( ( ord_less_int @ zero_zero_int @ B_54 )
% 0.59/0.78 => ( ( ord_less_eq_int @ B_54 @ B )
% 0.59/0.78 => ( ord_less_eq_int @ Q_3 @ Q ) ) ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_598_unique__quotient__lemma__neg,axiom,
% 0.59/0.78 ! [B: int,Q_3: int,R_2: int,Q: int,R: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q_3 ) @ R_2 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R ) )
% 0.59/0.78 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 0.59/0.78 => ( ( ord_less_int @ B @ R )
% 0.59/0.78 => ( ( ord_less_int @ B @ R_2 )
% 0.59/0.78 => ( ord_less_eq_int @ Q @ Q_3 ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_599_zdiv__mono2__lemma,axiom,
% 0.59/0.78 ! [B: int,Q: int,R: int,B_54: int,Q_3: int,R_2: int] :
% 0.59/0.78 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R )
% 0.59/0.78 = ( plus_plus_int @ ( times_times_int @ B_54 @ Q_3 ) @ R_2 ) )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B_54 @ Q_3 ) @ R_2 ) )
% 0.59/0.78 => ( ( ord_less_int @ R_2 @ B_54 )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.59/0.78 => ( ( ord_less_int @ zero_zero_int @ B_54 )
% 0.59/0.78 => ( ( ord_less_eq_int @ B_54 @ B )
% 0.59/0.78 => ( ord_less_eq_int @ Q @ Q_3 ) ) ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_600_unique__quotient__lemma,axiom,
% 0.59/0.78 ! [B: int,Q_3: int,R_2: int,Q: int,R: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q_3 ) @ R_2 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q ) @ R ) )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ R_2 )
% 0.59/0.78 => ( ( ord_less_int @ R_2 @ B )
% 0.59/0.78 => ( ( ord_less_int @ R @ B )
% 0.59/0.78 => ( ord_less_eq_int @ Q_3 @ Q ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_601_q__neg__lemma,axiom,
% 0.59/0.78 ! [B_54: int,Q_3: int,R_2: int] :
% 0.59/0.78 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B_54 @ Q_3 ) @ R_2 ) @ zero_zero_int )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ R_2 )
% 0.59/0.78 => ( ( ord_less_int @ zero_zero_int @ B_54 )
% 0.59/0.78 => ( ord_less_eq_int @ Q_3 @ zero_zero_int ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_602_q__pos__lemma,axiom,
% 0.59/0.78 ! [B_54: int,Q_3: int,R_2: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B_54 @ Q_3 ) @ R_2 ) )
% 0.59/0.78 => ( ( ord_less_int @ R_2 @ B_54 )
% 0.59/0.78 => ( ( ord_less_int @ zero_zero_int @ B_54 )
% 0.59/0.78 => ( ord_less_eq_int @ zero_zero_int @ Q_3 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_603_zprime__zdvd__zmult,axiom,
% 0.59/0.78 ! [N: int,P: int,M: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 0.59/0.78 => ( ( zprime @ P )
% 0.59/0.78 => ( ( dvd_dvd_int @ P @ ( times_times_int @ M @ N ) )
% 0.59/0.78 => ( ( dvd_dvd_int @ P @ M )
% 0.59/0.78 | ( dvd_dvd_int @ P @ N ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_604__096QuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_096,axiom,
% 0.59/0.78 quadRes @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( number_number_of_int @ min ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_605__0964_A_K_Am_A_L_A1_Advd_As_A_094_A2_A_N_A_N1_096,axiom,
% 0.59/0.78 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 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_606_neg__one__power__eq__mod__m,axiom,
% 0.59/0.78 ! [J_1: nat,K: nat,M: int] :
% 0.59/0.78 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ M )
% 0.59/0.78 => ( ( zcong @ ( power_power_int @ ( number_number_of_int @ min ) @ J_1 ) @ ( power_power_int @ ( number_number_of_int @ min ) @ K ) @ M )
% 0.59/0.78 => ( ( power_power_int @ ( number_number_of_int @ min ) @ J_1 )
% 0.59/0.78 = ( power_power_int @ ( number_number_of_int @ min ) @ K ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_607_zcong__neg__1__impl__ne__1,axiom,
% 0.59/0.78 ! [X_1: int,P: int] :
% 0.59/0.78 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
% 0.59/0.78 => ( ( zcong @ X_1 @ ( number_number_of_int @ min ) @ P )
% 0.59/0.78 => ~ ( zcong @ X_1 @ one_one_int @ P ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_608_one__not__neg__one__mod__m,axiom,
% 0.59/0.78 ! [M: int] :
% 0.59/0.78 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ M )
% 0.59/0.78 => ~ ( zcong @ one_one_int @ ( number_number_of_int @ min ) @ M ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_609__096s_A_094_A2_A_N_A_N1_A_061_As_A_094_A2_A_L_A1_096,axiom,
% 0.59/0.78 ( ( minus_minus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( number_number_of_int @ min ) )
% 0.59/0.78 = ( plus_plus_int @ ( power_power_int @ s @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ one_one_int ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_610__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N,axiom,
% 0.59/0.78 ( ~ ( quadRes @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) @ ( number_number_of_int @ min ) )
% 0.59/0.78 => ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) )
% 0.59/0.78 != one_one_int ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_611_Int2_Oaux1,axiom,
% 0.59/0.78 ! [A: int,B: int,C: int] :
% 0.59/0.78 ( ( ( minus_minus_int @ A @ B )
% 0.59/0.78 = C )
% 0.59/0.78 => ( A
% 0.59/0.78 = ( plus_plus_int @ C @ B ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_612_number__of__diff,axiom,
% 0.59/0.78 ! [V_5: int,W_2: int] :
% 0.59/0.78 ( ( number267125858f_real @ ( minus_minus_int @ V_5 @ W_2 ) )
% 0.59/0.78 = ( minus_minus_real @ ( number267125858f_real @ V_5 ) @ ( number267125858f_real @ W_2 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_613_number__of__diff,axiom,
% 0.59/0.78 ! [V_5: int,W_2: int] :
% 0.59/0.78 ( ( number_number_of_int @ ( minus_minus_int @ V_5 @ W_2 ) )
% 0.59/0.78 = ( minus_minus_int @ ( number_number_of_int @ V_5 ) @ ( number_number_of_int @ W_2 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_614_diff__bin__simps_I1_J,axiom,
% 0.59/0.78 ! [K: int] :
% 0.59/0.78 ( ( minus_minus_int @ K @ pls )
% 0.59/0.78 = K ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_615_diff__bin__simps_I7_J,axiom,
% 0.59/0.78 ! [K: int,L: int] :
% 0.59/0.78 ( ( minus_minus_int @ ( bit0 @ K ) @ ( bit0 @ L ) )
% 0.59/0.78 = ( bit0 @ ( minus_minus_int @ K @ L ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_616_zdiff__zmult__distrib2,axiom,
% 0.59/0.78 ! [W: int,Z1: int,Z2: int] :
% 0.59/0.78 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z2 ) )
% 0.59/0.78 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z2 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_617_zdiff__zmult__distrib,axiom,
% 0.59/0.78 ! [Z1: int,Z2: int,W: int] :
% 0.59/0.78 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z2 ) @ W )
% 0.59/0.78 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z2 @ W ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_618_zcong__zdiff,axiom,
% 0.59/0.78 ! [C: int,D: int,A: int,B: int,M: int] :
% 0.59/0.78 ( ( zcong @ A @ B @ M )
% 0.59/0.78 => ( ( zcong @ C @ D @ M )
% 0.59/0.78 => ( zcong @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) @ M ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_619_zdvd__zdiffD,axiom,
% 0.59/0.78 ! [K: int,M: int,N: int] :
% 0.59/0.78 ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
% 0.59/0.78 => ( ( dvd_dvd_int @ K @ N )
% 0.59/0.78 => ( dvd_dvd_int @ K @ M ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_620_right__diff__distrib__number__of,axiom,
% 0.59/0.78 ! [V_4: int,B_53: real,C_29: real] :
% 0.59/0.78 ( ( times_times_real @ ( number267125858f_real @ V_4 ) @ ( minus_minus_real @ B_53 @ C_29 ) )
% 0.59/0.78 = ( minus_minus_real @ ( times_times_real @ ( number267125858f_real @ V_4 ) @ B_53 ) @ ( times_times_real @ ( number267125858f_real @ V_4 ) @ C_29 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_621_right__diff__distrib__number__of,axiom,
% 0.59/0.78 ! [V_4: int,B_53: int,C_29: int] :
% 0.59/0.78 ( ( times_times_int @ ( number_number_of_int @ V_4 ) @ ( minus_minus_int @ B_53 @ C_29 ) )
% 0.59/0.78 = ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ V_4 ) @ B_53 ) @ ( times_times_int @ ( number_number_of_int @ V_4 ) @ C_29 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_622_left__diff__distrib__number__of,axiom,
% 0.59/0.78 ! [A_61: real,B_52: real,V_3: int] :
% 0.59/0.78 ( ( times_times_real @ ( minus_minus_real @ A_61 @ B_52 ) @ ( number267125858f_real @ V_3 ) )
% 0.59/0.78 = ( minus_minus_real @ ( times_times_real @ A_61 @ ( number267125858f_real @ V_3 ) ) @ ( times_times_real @ B_52 @ ( number267125858f_real @ V_3 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_623_left__diff__distrib__number__of,axiom,
% 0.59/0.78 ! [A_61: int,B_52: int,V_3: int] :
% 0.59/0.78 ( ( times_times_int @ ( minus_minus_int @ A_61 @ B_52 ) @ ( number_number_of_int @ V_3 ) )
% 0.59/0.78 = ( minus_minus_int @ ( times_times_int @ A_61 @ ( number_number_of_int @ V_3 ) ) @ ( times_times_int @ B_52 @ ( number_number_of_int @ V_3 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_624_diff__bin__simps_I9_J,axiom,
% 0.59/0.78 ! [K: int,L: int] :
% 0.59/0.78 ( ( minus_minus_int @ ( bit1 @ K ) @ ( bit0 @ L ) )
% 0.59/0.78 = ( bit1 @ ( minus_minus_int @ K @ L ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_625_diff__bin__simps_I10_J,axiom,
% 0.59/0.78 ! [K: int,L: int] :
% 0.59/0.78 ( ( minus_minus_int @ ( bit1 @ K ) @ ( bit1 @ L ) )
% 0.59/0.78 = ( bit0 @ ( minus_minus_int @ K @ L ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_626_diff__bin__simps_I3_J,axiom,
% 0.59/0.78 ! [L: int] :
% 0.59/0.78 ( ( minus_minus_int @ pls @ ( bit0 @ L ) )
% 0.59/0.78 = ( bit0 @ ( minus_minus_int @ pls @ L ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_627_less__bin__lemma,axiom,
% 0.59/0.78 ! [K: int,L: int] :
% 0.59/0.78 ( ( ord_less_int @ K @ L )
% 0.59/0.78 <=> ( ord_less_int @ ( minus_minus_int @ K @ L ) @ zero_zero_int ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_628_xzgcda__linear__aux1,axiom,
% 0.59/0.78 ! [A: int,R: int,B: int,M: int,C: int,D: int,N: int] :
% 0.59/0.78 ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ ( times_times_int @ R @ B ) ) @ M ) @ ( times_times_int @ ( minus_minus_int @ C @ ( times_times_int @ R @ D ) ) @ N ) )
% 0.59/0.78 = ( minus_minus_int @ ( plus_plus_int @ ( times_times_int @ A @ M ) @ ( times_times_int @ C @ N ) ) @ ( times_times_int @ R @ ( plus_plus_int @ ( times_times_int @ B @ M ) @ ( times_times_int @ D @ N ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_629_zcong__def,axiom,
% 0.59/0.78 ! [A: int,B: int,M: int] :
% 0.59/0.78 ( ( zcong @ A @ B @ M )
% 0.59/0.78 <=> ( dvd_dvd_int @ M @ ( minus_minus_int @ A @ B ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_630_add__number__of__diff1,axiom,
% 0.59/0.78 ! [V_2: int,W_1: int,C_28: real] :
% 0.59/0.78 ( ( plus_plus_real @ ( number267125858f_real @ V_2 ) @ ( minus_minus_real @ ( number267125858f_real @ W_1 ) @ C_28 ) )
% 0.59/0.78 = ( minus_minus_real @ ( number267125858f_real @ ( plus_plus_int @ V_2 @ W_1 ) ) @ C_28 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_631_add__number__of__diff1,axiom,
% 0.59/0.78 ! [V_2: int,W_1: int,C_28: int] :
% 0.59/0.78 ( ( plus_plus_int @ ( number_number_of_int @ V_2 ) @ ( minus_minus_int @ ( number_number_of_int @ W_1 ) @ C_28 ) )
% 0.59/0.78 = ( minus_minus_int @ ( number_number_of_int @ ( plus_plus_int @ V_2 @ W_1 ) ) @ C_28 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_632_Euler_Oaux1,axiom,
% 0.59/0.78 ! [A: int,X_1: int] :
% 0.59/0.78 ( ( ord_less_int @ zero_zero_int @ X_1 )
% 0.59/0.78 => ( ( ord_less_int @ X_1 @ A )
% 0.59/0.78 => ( ( X_1
% 0.59/0.78 != ( minus_minus_int @ A @ one_one_int ) )
% 0.59/0.78 => ( ord_less_int @ X_1 @ ( minus_minus_int @ A @ one_one_int ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_633_zle__diff1__eq,axiom,
% 0.59/0.78 ! [W: int,Z: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 0.59/0.78 <=> ( ord_less_int @ W @ Z ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_634_diff__bin__simps_I4_J,axiom,
% 0.59/0.78 ! [L: int] :
% 0.59/0.78 ( ( minus_minus_int @ pls @ ( bit1 @ L ) )
% 0.59/0.78 = ( bit1 @ ( minus_minus_int @ min @ L ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_635_diff__bin__simps_I5_J,axiom,
% 0.59/0.78 ! [L: int] :
% 0.59/0.78 ( ( minus_minus_int @ min @ ( bit0 @ L ) )
% 0.59/0.78 = ( bit1 @ ( minus_minus_int @ min @ L ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_636_diff__bin__simps_I6_J,axiom,
% 0.59/0.78 ! [L: int] :
% 0.59/0.78 ( ( minus_minus_int @ min @ ( bit1 @ L ) )
% 0.59/0.78 = ( bit0 @ ( minus_minus_int @ min @ L ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_637_inv__not__p__minus__1__aux,axiom,
% 0.59/0.78 ! [A: int,P: int] :
% 0.59/0.78 ( ( zcong @ ( times_times_int @ A @ ( minus_minus_int @ P @ one_one_int ) ) @ one_one_int @ P )
% 0.59/0.78 <=> ( zcong @ A @ ( minus_minus_int @ P @ one_one_int ) @ P ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_638_zcong__eq__trans,axiom,
% 0.59/0.78 ! [D: int,C: int,A: int,B: int,M: int] :
% 0.59/0.78 ( ( zcong @ A @ B @ M )
% 0.59/0.78 => ( ( B = C )
% 0.59/0.78 => ( ( zcong @ C @ D @ M )
% 0.59/0.78 => ( zcong @ A @ D @ M ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_639_mult__sum2sq,axiom,
% 0.59/0.78 ! [A: int,B: int,P: int,Q: int] :
% 0.59/0.78 ( ( times_times_int @ ( twoSqu2057625106sum2sq @ ( product_Pair_int_int @ A @ B ) ) @ ( twoSqu2057625106sum2sq @ ( product_Pair_int_int @ P @ Q ) ) )
% 0.59/0.78 = ( twoSqu2057625106sum2sq @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A @ P ) @ ( times_times_int @ B @ Q ) ) @ ( minus_minus_int @ ( times_times_int @ A @ Q ) @ ( times_times_int @ B @ P ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_640_zcong__square,axiom,
% 0.59/0.78 ! [A: int,P: int] :
% 0.59/0.78 ( ( zprime @ P )
% 0.59/0.78 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.59/0.78 => ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ P )
% 0.59/0.78 => ( ( zcong @ A @ one_one_int @ P )
% 0.59/0.78 | ( zcong @ A @ ( minus_minus_int @ P @ one_one_int ) @ P ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_641_zcong__square__zless,axiom,
% 0.59/0.78 ! [A: int,P: int] :
% 0.59/0.78 ( ( zprime @ P )
% 0.59/0.78 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.59/0.78 => ( ( ord_less_int @ A @ P )
% 0.59/0.78 => ( ( zcong @ ( times_times_int @ A @ A ) @ one_one_int @ P )
% 0.59/0.78 => ( ( A = one_one_int )
% 0.59/0.78 | ( A
% 0.59/0.78 = ( minus_minus_int @ P @ one_one_int ) ) ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_642_zspecial__product,axiom,
% 0.59/0.78 ! [A: int,B: int] :
% 0.59/0.78 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( minus_minus_int @ A @ B ) )
% 0.59/0.78 = ( 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 ) ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_643_zcong__id,axiom,
% 0.59/0.78 ! [M: int] : ( zcong @ M @ zero_zero_int @ M ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_644_zcong__zmult__prop1,axiom,
% 0.59/0.78 ! [C: int,D: int,A: int,B: int,M: int] :
% 0.59/0.78 ( ( zcong @ A @ B @ M )
% 0.59/0.78 => ( ( zcong @ C @ ( times_times_int @ A @ D ) @ M )
% 0.59/0.78 <=> ( zcong @ C @ ( times_times_int @ B @ D ) @ M ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_645_zcong__zmult__prop2,axiom,
% 0.59/0.78 ! [C: int,D: int,A: int,B: int,M: int] :
% 0.59/0.78 ( ( zcong @ A @ B @ M )
% 0.59/0.78 => ( ( zcong @ C @ ( times_times_int @ D @ A ) @ M )
% 0.59/0.78 <=> ( zcong @ C @ ( times_times_int @ D @ B ) @ M ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_646_zcong__shift,axiom,
% 0.59/0.78 ! [C: int,A: int,B: int,M: int] :
% 0.59/0.78 ( ( zcong @ A @ B @ M )
% 0.59/0.78 => ( zcong @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) @ M ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_647_zcong__zpower,axiom,
% 0.59/0.78 ! [Z: nat,X_1: int,Y_1: int,M: int] :
% 0.59/0.78 ( ( zcong @ X_1 @ Y_1 @ M )
% 0.59/0.78 => ( zcong @ ( power_power_int @ X_1 @ Z ) @ ( power_power_int @ Y_1 @ Z ) @ M ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_648_power2__diff,axiom,
% 0.59/0.78 ! [X_6: real,Y_5: real] :
% 0.59/0.78 ( ( power_power_real @ ( minus_minus_real @ X_6 @ Y_5 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X_6 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_5 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_6 ) @ Y_5 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_649_power2__diff,axiom,
% 0.59/0.78 ! [X_6: int,Y_5: int] :
% 0.59/0.78 ( ( power_power_int @ ( minus_minus_int @ X_6 @ Y_5 ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X_6 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_int @ Y_5 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ X_6 ) @ Y_5 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_650_zdiff__power2,axiom,
% 0.59/0.78 ! [A: int,B: int] :
% 0.59/0.78 ( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = ( 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 ) ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_651_zdiff__power3,axiom,
% 0.59/0.78 ! [A: int,B: int] :
% 0.59/0.78 ( ( power_power_int @ ( minus_minus_int @ A @ B ) @ ( number_number_of_nat @ ( bit1 @ ( bit1 @ pls ) ) ) )
% 0.59/0.78 = ( 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 ) ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_652_zcong__less__eq,axiom,
% 0.59/0.78 ! [M: int,Y_1: int,X_1: int] :
% 0.59/0.78 ( ( ord_less_int @ zero_zero_int @ X_1 )
% 0.59/0.78 => ( ( ord_less_int @ zero_zero_int @ Y_1 )
% 0.59/0.78 => ( ( ord_less_int @ zero_zero_int @ M )
% 0.59/0.78 => ( ( zcong @ X_1 @ Y_1 @ M )
% 0.59/0.78 => ( ( ord_less_int @ X_1 @ M )
% 0.59/0.78 => ( ( ord_less_int @ Y_1 @ M )
% 0.59/0.78 => ( X_1 = Y_1 ) ) ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_653_zcong__not__zero,axiom,
% 0.59/0.78 ! [M: int,X_1: int] :
% 0.59/0.78 ( ( ord_less_int @ zero_zero_int @ X_1 )
% 0.59/0.78 => ( ( ord_less_int @ X_1 @ M )
% 0.59/0.78 => ~ ( zcong @ X_1 @ zero_zero_int @ M ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_654_zdvd__bounds,axiom,
% 0.59/0.78 ! [N: int,M: int] :
% 0.59/0.78 ( ( dvd_dvd_int @ N @ M )
% 0.59/0.78 => ( ( ord_less_eq_int @ M @ zero_zero_int )
% 0.59/0.78 | ( ord_less_eq_int @ N @ M ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_655_zcong__eq__zdvd__prop,axiom,
% 0.59/0.78 ! [X_1: int,P: int] :
% 0.59/0.78 ( ( zcong @ X_1 @ zero_zero_int @ P )
% 0.59/0.78 <=> ( dvd_dvd_int @ P @ X_1 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_656_zcong__zero__equiv__div,axiom,
% 0.59/0.78 ! [A: int,M: int] :
% 0.59/0.78 ( ( zcong @ A @ zero_zero_int @ M )
% 0.59/0.78 <=> ( dvd_dvd_int @ M @ A ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_657_zprime__zdvd__zmult__better,axiom,
% 0.59/0.78 ! [M: int,N: int,P: int] :
% 0.59/0.78 ( ( zprime @ P )
% 0.59/0.78 => ( ( dvd_dvd_int @ P @ ( times_times_int @ M @ N ) )
% 0.59/0.78 => ( ( dvd_dvd_int @ P @ M )
% 0.59/0.78 | ( dvd_dvd_int @ P @ N ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_658_Int2_Ozcong__zero,axiom,
% 0.59/0.78 ! [M: int,X_1: int] :
% 0.59/0.78 ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.59/0.78 => ( ( ord_less_int @ X_1 @ M )
% 0.59/0.78 => ( ( zcong @ X_1 @ zero_zero_int @ M )
% 0.59/0.78 => ( X_1 = zero_zero_int ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_659_zpower__zdvd__prop1,axiom,
% 0.59/0.78 ! [P: int,Y_1: int,N: nat] :
% 0.59/0.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.59/0.78 => ( ( dvd_dvd_int @ P @ Y_1 )
% 0.59/0.78 => ( dvd_dvd_int @ P @ ( power_power_int @ Y_1 @ N ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_660_neg__one__power,axiom,
% 0.59/0.78 ! [N: nat] :
% 0.59/0.78 ( ( ( power_power_int @ ( number_number_of_int @ min ) @ N )
% 0.59/0.78 = one_one_int )
% 0.59/0.78 | ( ( power_power_int @ ( number_number_of_int @ min ) @ N )
% 0.59/0.78 = ( number_number_of_int @ min ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_661_zcong__zmult__prop3,axiom,
% 0.59/0.78 ! [Y_1: int,X_1: int,P: int] :
% 0.59/0.78 ( ( zprime @ P )
% 0.59/0.78 => ( ~ ( zcong @ X_1 @ zero_zero_int @ P )
% 0.59/0.78 => ( ~ ( zcong @ Y_1 @ zero_zero_int @ P )
% 0.59/0.78 => ~ ( zcong @ ( times_times_int @ X_1 @ Y_1 ) @ zero_zero_int @ P ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_662_zcong__zprime__prod__zero,axiom,
% 0.59/0.78 ! [B: int,A: int,P: int] :
% 0.59/0.78 ( ( zprime @ P )
% 0.59/0.78 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.59/0.78 => ( ( zcong @ ( times_times_int @ A @ B ) @ zero_zero_int @ P )
% 0.59/0.78 => ( ( zcong @ A @ zero_zero_int @ P )
% 0.59/0.78 | ( zcong @ B @ zero_zero_int @ P ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_663_zcong__zprime__prod__zero__contra,axiom,
% 0.59/0.78 ! [B: int,A: int,P: int] :
% 0.59/0.78 ( ( zprime @ P )
% 0.59/0.78 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.59/0.78 => ( ( ~ ( zcong @ A @ zero_zero_int @ P )
% 0.59/0.78 & ~ ( zcong @ B @ zero_zero_int @ P ) )
% 0.59/0.78 => ~ ( zcong @ ( times_times_int @ A @ B ) @ zero_zero_int @ P ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_664_zpower__zdvd__prop2,axiom,
% 0.59/0.78 ! [Y_1: int,N: nat,P: int] :
% 0.59/0.78 ( ( zprime @ P )
% 0.59/0.78 => ( ( dvd_dvd_int @ P @ ( power_power_int @ Y_1 @ N ) )
% 0.59/0.78 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.59/0.78 => ( dvd_dvd_int @ P @ Y_1 ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_665_Legendre__1mod4,axiom,
% 0.59/0.78 ! [M: int] :
% 0.59/0.78 ( ( zprime @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ M ) @ one_one_int ) )
% 0.59/0.78 => ( ( legendre @ ( number_number_of_int @ min ) @ ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ M ) @ one_one_int ) )
% 0.59/0.78 = one_one_int ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_666_Legendre__def,axiom,
% 0.59/0.78 ! [A: int,P: int] :
% 0.59/0.78 ( ( ( zcong @ A @ zero_zero_int @ P )
% 0.59/0.78 => ( ( legendre @ A @ P )
% 0.59/0.78 = zero_zero_int ) )
% 0.59/0.78 & ( ~ ( zcong @ A @ zero_zero_int @ P )
% 0.59/0.78 => ( ( ( quadRes @ P @ A )
% 0.59/0.78 => ( ( legendre @ A @ P )
% 0.59/0.78 = one_one_int ) )
% 0.59/0.78 & ( ~ ( quadRes @ P @ A )
% 0.59/0.78 => ( ( legendre @ A @ P )
% 0.59/0.78 = ( number_number_of_int @ min ) ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_667_divides__cases,axiom,
% 0.59/0.78 ! [N: nat,M: nat] :
% 0.59/0.78 ( ( dvd_dvd_nat @ N @ M )
% 0.59/0.78 => ( ( M = zero_zero_nat )
% 0.59/0.78 | ( M = N )
% 0.59/0.78 | ( ord_less_eq_nat @ ( times_times_nat @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) @ M ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_668_QuadRes__def,axiom,
% 0.59/0.78 ! [M: int,X_1: int] :
% 0.59/0.78 ( ( quadRes @ M @ X_1 )
% 0.59/0.78 <=> ? [Y: int] : ( zcong @ ( power_power_int @ Y @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ X_1 @ M ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_669_realpow__two__sum__zero__iff,axiom,
% 0.59/0.78 ! [X_1: real,Y_1: real] :
% 0.59/0.78 ( ( ( plus_plus_real @ ( power_power_real @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_real @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.78 = zero_zero_real )
% 0.59/0.78 <=> ( ( X_1 = zero_zero_real )
% 0.59/0.78 & ( Y_1 = zero_zero_real ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_670_convex__bound__lt,axiom,
% 0.59/0.78 ! [V_1: real,U_1: real,Y_4: real,X_5: real,A_60: real] :
% 0.59/0.78 ( ( ord_less_real @ X_5 @ A_60 )
% 0.59/0.78 => ( ( ord_less_real @ Y_4 @ A_60 )
% 0.59/0.78 => ( ( ord_less_eq_real @ zero_zero_real @ U_1 )
% 0.59/0.78 => ( ( ord_less_eq_real @ zero_zero_real @ V_1 )
% 0.59/0.78 => ( ( ( plus_plus_real @ U_1 @ V_1 )
% 0.59/0.78 = one_one_real )
% 0.59/0.78 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U_1 @ X_5 ) @ ( times_times_real @ V_1 @ Y_4 ) ) @ A_60 ) ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_671_convex__bound__lt,axiom,
% 0.59/0.78 ! [V_1: int,U_1: int,Y_4: int,X_5: int,A_60: int] :
% 0.59/0.78 ( ( ord_less_int @ X_5 @ A_60 )
% 0.59/0.78 => ( ( ord_less_int @ Y_4 @ A_60 )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ U_1 )
% 0.59/0.78 => ( ( ord_less_eq_int @ zero_zero_int @ V_1 )
% 0.59/0.78 => ( ( ( plus_plus_int @ U_1 @ V_1 )
% 0.59/0.78 = one_one_int )
% 0.59/0.78 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U_1 @ X_5 ) @ ( times_times_int @ V_1 @ Y_4 ) ) @ A_60 ) ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_672_dvd__0__right,axiom,
% 0.59/0.78 ! [A_59: real] : ( dvd_dvd_real @ A_59 @ zero_zero_real ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_673_dvd__0__right,axiom,
% 0.59/0.78 ! [A_59: nat] : ( dvd_dvd_nat @ A_59 @ zero_zero_nat ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_674_dvd__0__right,axiom,
% 0.59/0.78 ! [A_59: int] : ( dvd_dvd_int @ A_59 @ zero_zero_int ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_675_real__le__eq__diff,axiom,
% 0.59/0.78 ! [X_1: real,Y_1: real] :
% 0.59/0.78 ( ( ord_less_eq_real @ X_1 @ Y_1 )
% 0.59/0.78 <=> ( ord_less_eq_real @ ( minus_minus_real @ X_1 @ Y_1 ) @ zero_zero_real ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_676_linorder__neqE__linordered__idom,axiom,
% 0.59/0.78 ! [X_4: real,Y_3: real] :
% 0.59/0.78 ( ( X_4 != Y_3 )
% 0.59/0.78 => ( ~ ( ord_less_real @ X_4 @ Y_3 )
% 0.59/0.78 => ( ord_less_real @ Y_3 @ X_4 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_677_linorder__neqE__linordered__idom,axiom,
% 0.59/0.78 ! [X_4: int,Y_3: int] :
% 0.59/0.78 ( ( X_4 != Y_3 )
% 0.59/0.78 => ( ~ ( ord_less_int @ X_4 @ Y_3 )
% 0.59/0.78 => ( ord_less_int @ Y_3 @ X_4 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_678_dvd__refl,axiom,
% 0.59/0.78 ! [A_58: real] : ( dvd_dvd_real @ A_58 @ A_58 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_679_dvd__refl,axiom,
% 0.59/0.78 ! [A_58: nat] : ( dvd_dvd_nat @ A_58 @ A_58 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_680_dvd__refl,axiom,
% 0.59/0.78 ! [A_58: int] : ( dvd_dvd_int @ A_58 @ A_58 ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_681_dvd__trans,axiom,
% 0.59/0.78 ! [C_27: real,A_57: real,B_51: real] :
% 0.59/0.78 ( ( dvd_dvd_real @ A_57 @ B_51 )
% 0.59/0.78 => ( ( dvd_dvd_real @ B_51 @ C_27 )
% 0.59/0.78 => ( dvd_dvd_real @ A_57 @ C_27 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_682_dvd__trans,axiom,
% 0.59/0.78 ! [C_27: nat,A_57: nat,B_51: nat] :
% 0.59/0.78 ( ( dvd_dvd_nat @ A_57 @ B_51 )
% 0.59/0.78 => ( ( dvd_dvd_nat @ B_51 @ C_27 )
% 0.59/0.78 => ( dvd_dvd_nat @ A_57 @ C_27 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_683_dvd__trans,axiom,
% 0.59/0.78 ! [C_27: int,A_57: int,B_51: int] :
% 0.59/0.78 ( ( dvd_dvd_int @ A_57 @ B_51 )
% 0.59/0.78 => ( ( dvd_dvd_int @ B_51 @ C_27 )
% 0.59/0.78 => ( dvd_dvd_int @ A_57 @ C_27 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_684_real__zero__not__eq__one,axiom,
% 0.59/0.78 zero_zero_real != one_one_real ).
% 0.59/0.78
% 0.59/0.78 thf(fact_685_less__eq__real__def,axiom,
% 0.59/0.78 ! [X_1: real,Y_1: real] :
% 0.59/0.78 ( ( ord_less_eq_real @ X_1 @ Y_1 )
% 0.59/0.78 <=> ( ( ord_less_real @ X_1 @ Y_1 )
% 0.59/0.78 | ( X_1 = Y_1 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_686_real__less__def,axiom,
% 0.59/0.78 ! [X_1: real,Y_1: real] :
% 0.59/0.78 ( ( ord_less_real @ X_1 @ Y_1 )
% 0.59/0.78 <=> ( ( ord_less_eq_real @ X_1 @ Y_1 )
% 0.59/0.78 & ( X_1 != Y_1 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_687_divides__antisym,axiom,
% 0.59/0.78 ! [X_1: nat,Y_1: nat] :
% 0.59/0.78 ( ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.78 & ( dvd_dvd_nat @ Y_1 @ X_1 ) )
% 0.59/0.78 <=> ( X_1 = Y_1 ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_688_real__mult__assoc,axiom,
% 0.59/0.78 ! [Z1: real,Z2: real,Z3: real] :
% 0.59/0.78 ( ( times_times_real @ ( times_times_real @ Z1 @ Z2 ) @ Z3 )
% 0.59/0.78 = ( times_times_real @ Z1 @ ( times_times_real @ Z2 @ Z3 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_689_real__mult__commute,axiom,
% 0.59/0.78 ! [Z: real,W: real] :
% 0.59/0.78 ( ( times_times_real @ Z @ W )
% 0.59/0.78 = ( times_times_real @ W @ Z ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_690_real__mult__1,axiom,
% 0.59/0.78 ! [Z: real] :
% 0.59/0.78 ( ( times_times_real @ one_one_real @ Z )
% 0.59/0.78 = Z ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_691_real__add__left__mono,axiom,
% 0.59/0.78 ! [Z: real,X_1: real,Y_1: real] :
% 0.59/0.78 ( ( ord_less_eq_real @ X_1 @ Y_1 )
% 0.59/0.78 => ( ord_less_eq_real @ ( plus_plus_real @ Z @ X_1 ) @ ( plus_plus_real @ Z @ Y_1 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_692_realpow__minus__mult,axiom,
% 0.59/0.78 ! [X_3: nat,N_2: nat] :
% 0.59/0.78 ( ( ord_less_nat @ zero_zero_nat @ N_2 )
% 0.59/0.78 => ( ( times_times_nat @ ( power_power_nat @ X_3 @ ( minus_minus_nat @ N_2 @ one_one_nat ) ) @ X_3 )
% 0.59/0.78 = ( power_power_nat @ X_3 @ N_2 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_693_realpow__minus__mult,axiom,
% 0.59/0.78 ! [X_3: real,N_2: nat] :
% 0.59/0.78 ( ( ord_less_nat @ zero_zero_nat @ N_2 )
% 0.59/0.78 => ( ( times_times_real @ ( power_power_real @ X_3 @ ( minus_minus_nat @ N_2 @ one_one_nat ) ) @ X_3 )
% 0.59/0.78 = ( power_power_real @ X_3 @ N_2 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_694_realpow__minus__mult,axiom,
% 0.59/0.78 ! [X_3: int,N_2: nat] :
% 0.59/0.78 ( ( ord_less_nat @ zero_zero_nat @ N_2 )
% 0.59/0.78 => ( ( times_times_int @ ( power_power_int @ X_3 @ ( minus_minus_nat @ N_2 @ one_one_nat ) ) @ X_3 )
% 0.59/0.78 = ( power_power_int @ X_3 @ N_2 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_695_mult__eq__if,axiom,
% 0.59/0.78 ! [N: nat,M: nat] :
% 0.59/0.78 ( ( ( M = zero_zero_nat )
% 0.59/0.78 => ( ( times_times_nat @ M @ N )
% 0.59/0.78 = zero_zero_nat ) )
% 0.59/0.78 & ( ( M != zero_zero_nat )
% 0.59/0.78 => ( ( times_times_nat @ M @ N )
% 0.59/0.78 = ( plus_plus_nat @ N @ ( times_times_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_696_power__eq__if,axiom,
% 0.59/0.78 ! [P: nat,M: nat] :
% 0.59/0.78 ( ( ( M = zero_zero_nat )
% 0.59/0.78 => ( ( power_power_nat @ P @ M )
% 0.59/0.78 = one_one_nat ) )
% 0.59/0.78 & ( ( M != zero_zero_nat )
% 0.59/0.78 => ( ( power_power_nat @ P @ M )
% 0.59/0.78 = ( times_times_nat @ P @ ( power_power_nat @ P @ ( minus_minus_nat @ M @ one_one_nat ) ) ) ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_697_diff__square,axiom,
% 0.59/0.78 ! [X_1: nat,Y_1: nat] :
% 0.59/0.78 ( ( minus_minus_nat @ ( power_power_nat @ X_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ ( power_power_nat @ Y_1 @ ( number_number_of_nat @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.78 = ( times_times_nat @ ( plus_plus_nat @ X_1 @ Y_1 ) @ ( minus_minus_nat @ X_1 @ Y_1 ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_698_divisors__zero,axiom,
% 0.59/0.78 ! [A_56: real,B_50: real] :
% 0.59/0.78 ( ( ( times_times_real @ A_56 @ B_50 )
% 0.59/0.78 = zero_zero_real )
% 0.59/0.78 => ( ( A_56 = zero_zero_real )
% 0.59/0.78 | ( B_50 = zero_zero_real ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_699_divisors__zero,axiom,
% 0.59/0.78 ! [A_56: nat,B_50: nat] :
% 0.59/0.78 ( ( ( times_times_nat @ A_56 @ B_50 )
% 0.59/0.78 = zero_zero_nat )
% 0.59/0.78 => ( ( A_56 = zero_zero_nat )
% 0.59/0.78 | ( B_50 = zero_zero_nat ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_700_divisors__zero,axiom,
% 0.59/0.78 ! [A_56: int,B_50: int] :
% 0.59/0.78 ( ( ( times_times_int @ A_56 @ B_50 )
% 0.59/0.78 = zero_zero_int )
% 0.59/0.78 => ( ( A_56 = zero_zero_int )
% 0.59/0.78 | ( B_50 = zero_zero_int ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_701_no__zero__divisors,axiom,
% 0.59/0.78 ! [B_49: real,A_55: real] :
% 0.59/0.78 ( ( A_55 != zero_zero_real )
% 0.59/0.78 => ( ( B_49 != zero_zero_real )
% 0.59/0.78 => ( ( times_times_real @ A_55 @ B_49 )
% 0.59/0.78 != zero_zero_real ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_702_no__zero__divisors,axiom,
% 0.59/0.78 ! [B_49: nat,A_55: nat] :
% 0.59/0.78 ( ( A_55 != zero_zero_nat )
% 0.59/0.78 => ( ( B_49 != zero_zero_nat )
% 0.59/0.78 => ( ( times_times_nat @ A_55 @ B_49 )
% 0.59/0.78 != zero_zero_nat ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_703_no__zero__divisors,axiom,
% 0.59/0.78 ! [B_49: int,A_55: int] :
% 0.59/0.78 ( ( A_55 != zero_zero_int )
% 0.59/0.78 => ( ( B_49 != zero_zero_int )
% 0.59/0.78 => ( ( times_times_int @ A_55 @ B_49 )
% 0.59/0.78 != zero_zero_int ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_704_mult__eq__0__iff,axiom,
% 0.59/0.78 ! [A_54: real,B_48: real] :
% 0.59/0.78 ( ( ( times_times_real @ A_54 @ B_48 )
% 0.59/0.78 = zero_zero_real )
% 0.59/0.78 <=> ( ( A_54 = zero_zero_real )
% 0.59/0.78 | ( B_48 = zero_zero_real ) ) ) ).
% 0.59/0.78
% 0.59/0.78 thf(fact_705_mult__eq__0__iff,axiom,
% 0.59/0.78 ! [A_54: int,B_48: int] :
% 0.59/0.78 ( ( ( times_times_int @ A_54 @ B_48 )
% 0.59/0.78 = zero_zero_int )
% 0.59/0.78 <=> ( ( A_54 = zero_zero_int )
% 0.59/0.78 | ( B_48 = zero_zero_int ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_706_mult__zero__right,axiom,
% 0.59/0.79 ! [A_53: real] :
% 0.59/0.79 ( ( times_times_real @ A_53 @ zero_zero_real )
% 0.59/0.79 = zero_zero_real ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_707_mult__zero__right,axiom,
% 0.59/0.79 ! [A_53: nat] :
% 0.59/0.79 ( ( times_times_nat @ A_53 @ zero_zero_nat )
% 0.59/0.79 = zero_zero_nat ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_708_mult__zero__right,axiom,
% 0.59/0.79 ! [A_53: int] :
% 0.59/0.79 ( ( times_times_int @ A_53 @ zero_zero_int )
% 0.59/0.79 = zero_zero_int ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_709_mult__zero__left,axiom,
% 0.59/0.79 ! [A_52: real] :
% 0.59/0.79 ( ( times_times_real @ zero_zero_real @ A_52 )
% 0.59/0.79 = zero_zero_real ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_710_mult__zero__left,axiom,
% 0.59/0.79 ! [A_52: nat] :
% 0.59/0.79 ( ( times_times_nat @ zero_zero_nat @ A_52 )
% 0.59/0.79 = zero_zero_nat ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_711_mult__zero__left,axiom,
% 0.59/0.79 ! [A_52: int] :
% 0.59/0.79 ( ( times_times_int @ zero_zero_int @ A_52 )
% 0.59/0.79 = zero_zero_int ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_712_zero__neq__one,axiom,
% 0.59/0.79 zero_zero_real != one_one_real ).
% 0.59/0.79
% 0.59/0.79 thf(fact_713_zero__neq__one,axiom,
% 0.59/0.79 zero_zero_nat != one_one_nat ).
% 0.59/0.79
% 0.59/0.79 thf(fact_714_zero__neq__one,axiom,
% 0.59/0.79 zero_zero_int != one_one_int ).
% 0.59/0.79
% 0.59/0.79 thf(fact_715_one__neq__zero,axiom,
% 0.59/0.79 one_one_real != zero_zero_real ).
% 0.59/0.79
% 0.59/0.79 thf(fact_716_one__neq__zero,axiom,
% 0.59/0.79 one_one_nat != zero_zero_nat ).
% 0.59/0.79
% 0.59/0.79 thf(fact_717_one__neq__zero,axiom,
% 0.59/0.79 one_one_int != zero_zero_int ).
% 0.59/0.79
% 0.59/0.79 thf(fact_718_combine__common__factor,axiom,
% 0.59/0.79 ! [A_51: real,E: real,B_47: real,C_26: real] :
% 0.59/0.79 ( ( plus_plus_real @ ( times_times_real @ A_51 @ E ) @ ( plus_plus_real @ ( times_times_real @ B_47 @ E ) @ C_26 ) )
% 0.59/0.79 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A_51 @ B_47 ) @ E ) @ C_26 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_719_combine__common__factor,axiom,
% 0.59/0.79 ! [A_51: nat,E: nat,B_47: nat,C_26: nat] :
% 0.59/0.79 ( ( plus_plus_nat @ ( times_times_nat @ A_51 @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B_47 @ E ) @ C_26 ) )
% 0.59/0.79 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A_51 @ B_47 ) @ E ) @ C_26 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_720_combine__common__factor,axiom,
% 0.59/0.79 ! [A_51: int,E: int,B_47: int,C_26: int] :
% 0.59/0.79 ( ( plus_plus_int @ ( times_times_int @ A_51 @ E ) @ ( plus_plus_int @ ( times_times_int @ B_47 @ E ) @ C_26 ) )
% 0.59/0.79 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A_51 @ B_47 ) @ E ) @ C_26 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_721_comm__semiring__class_Odistrib,axiom,
% 0.59/0.79 ! [A_50: real,B_46: real,C_25: real] :
% 0.59/0.79 ( ( times_times_real @ ( plus_plus_real @ A_50 @ B_46 ) @ C_25 )
% 0.59/0.79 = ( plus_plus_real @ ( times_times_real @ A_50 @ C_25 ) @ ( times_times_real @ B_46 @ C_25 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_722_comm__semiring__class_Odistrib,axiom,
% 0.59/0.79 ! [A_50: nat,B_46: nat,C_25: nat] :
% 0.59/0.79 ( ( times_times_nat @ ( plus_plus_nat @ A_50 @ B_46 ) @ C_25 )
% 0.59/0.79 = ( plus_plus_nat @ ( times_times_nat @ A_50 @ C_25 ) @ ( times_times_nat @ B_46 @ C_25 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_723_comm__semiring__class_Odistrib,axiom,
% 0.59/0.79 ! [A_50: int,B_46: int,C_25: int] :
% 0.59/0.79 ( ( times_times_int @ ( plus_plus_int @ A_50 @ B_46 ) @ C_25 )
% 0.59/0.79 = ( plus_plus_int @ ( times_times_int @ A_50 @ C_25 ) @ ( times_times_int @ B_46 @ C_25 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_724_dvd__0__left,axiom,
% 0.59/0.79 ! [A_49: real] :
% 0.59/0.79 ( ( dvd_dvd_real @ zero_zero_real @ A_49 )
% 0.59/0.79 => ( A_49 = zero_zero_real ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_725_dvd__0__left,axiom,
% 0.59/0.79 ! [A_49: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ zero_zero_nat @ A_49 )
% 0.59/0.79 => ( A_49 = zero_zero_nat ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_726_dvd__0__left,axiom,
% 0.59/0.79 ! [A_49: int] :
% 0.59/0.79 ( ( dvd_dvd_int @ zero_zero_int @ A_49 )
% 0.59/0.79 => ( A_49 = zero_zero_int ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_727_add__diff__add,axiom,
% 0.59/0.79 ! [A_48: real,C_24: real,B_45: real,D_6: real] :
% 0.59/0.79 ( ( minus_minus_real @ ( plus_plus_real @ A_48 @ C_24 ) @ ( plus_plus_real @ B_45 @ D_6 ) )
% 0.59/0.79 = ( plus_plus_real @ ( minus_minus_real @ A_48 @ B_45 ) @ ( minus_minus_real @ C_24 @ D_6 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_728_add__diff__add,axiom,
% 0.59/0.79 ! [A_48: int,C_24: int,B_45: int,D_6: int] :
% 0.59/0.79 ( ( minus_minus_int @ ( plus_plus_int @ A_48 @ C_24 ) @ ( plus_plus_int @ B_45 @ D_6 ) )
% 0.59/0.79 = ( plus_plus_int @ ( minus_minus_int @ A_48 @ B_45 ) @ ( minus_minus_int @ C_24 @ D_6 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_729_dvd__mult__right,axiom,
% 0.59/0.79 ! [A_47: real,B_44: real,C_23: real] :
% 0.59/0.79 ( ( dvd_dvd_real @ ( times_times_real @ A_47 @ B_44 ) @ C_23 )
% 0.59/0.79 => ( dvd_dvd_real @ B_44 @ C_23 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_730_dvd__mult__right,axiom,
% 0.59/0.79 ! [A_47: nat,B_44: nat,C_23: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ ( times_times_nat @ A_47 @ B_44 ) @ C_23 )
% 0.59/0.79 => ( dvd_dvd_nat @ B_44 @ C_23 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_731_dvd__mult__right,axiom,
% 0.59/0.79 ! [A_47: int,B_44: int,C_23: int] :
% 0.59/0.79 ( ( dvd_dvd_int @ ( times_times_int @ A_47 @ B_44 ) @ C_23 )
% 0.59/0.79 => ( dvd_dvd_int @ B_44 @ C_23 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_732_dvd__mult__left,axiom,
% 0.59/0.79 ! [A_46: real,B_43: real,C_22: real] :
% 0.59/0.79 ( ( dvd_dvd_real @ ( times_times_real @ A_46 @ B_43 ) @ C_22 )
% 0.59/0.79 => ( dvd_dvd_real @ A_46 @ C_22 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_733_dvd__mult__left,axiom,
% 0.59/0.79 ! [A_46: nat,B_43: nat,C_22: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ ( times_times_nat @ A_46 @ B_43 ) @ C_22 )
% 0.59/0.79 => ( dvd_dvd_nat @ A_46 @ C_22 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_734_dvd__mult__left,axiom,
% 0.59/0.79 ! [A_46: int,B_43: int,C_22: int] :
% 0.59/0.79 ( ( dvd_dvd_int @ ( times_times_int @ A_46 @ B_43 ) @ C_22 )
% 0.59/0.79 => ( dvd_dvd_int @ A_46 @ C_22 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_735_dvdI,axiom,
% 0.59/0.79 ! [A_45: real,B_42: real,K_2: real] :
% 0.59/0.79 ( ( A_45
% 0.59/0.79 = ( times_times_real @ B_42 @ K_2 ) )
% 0.59/0.79 => ( dvd_dvd_real @ B_42 @ A_45 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_736_dvdI,axiom,
% 0.59/0.79 ! [A_45: nat,B_42: nat,K_2: nat] :
% 0.59/0.79 ( ( A_45
% 0.59/0.79 = ( times_times_nat @ B_42 @ K_2 ) )
% 0.59/0.79 => ( dvd_dvd_nat @ B_42 @ A_45 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_737_dvdI,axiom,
% 0.59/0.79 ! [A_45: int,B_42: int,K_2: int] :
% 0.59/0.79 ( ( A_45
% 0.59/0.79 = ( times_times_int @ B_42 @ K_2 ) )
% 0.59/0.79 => ( dvd_dvd_int @ B_42 @ A_45 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_738_mult__dvd__mono,axiom,
% 0.59/0.79 ! [C_21: real,D_5: real,A_44: real,B_41: real] :
% 0.59/0.79 ( ( dvd_dvd_real @ A_44 @ B_41 )
% 0.59/0.79 => ( ( dvd_dvd_real @ C_21 @ D_5 )
% 0.59/0.79 => ( dvd_dvd_real @ ( times_times_real @ A_44 @ C_21 ) @ ( times_times_real @ B_41 @ D_5 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_739_mult__dvd__mono,axiom,
% 0.59/0.79 ! [C_21: nat,D_5: nat,A_44: nat,B_41: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ A_44 @ B_41 )
% 0.59/0.79 => ( ( dvd_dvd_nat @ C_21 @ D_5 )
% 0.59/0.79 => ( dvd_dvd_nat @ ( times_times_nat @ A_44 @ C_21 ) @ ( times_times_nat @ B_41 @ D_5 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_740_mult__dvd__mono,axiom,
% 0.59/0.79 ! [C_21: int,D_5: int,A_44: int,B_41: int] :
% 0.59/0.79 ( ( dvd_dvd_int @ A_44 @ B_41 )
% 0.59/0.79 => ( ( dvd_dvd_int @ C_21 @ D_5 )
% 0.59/0.79 => ( dvd_dvd_int @ ( times_times_int @ A_44 @ C_21 ) @ ( times_times_int @ B_41 @ D_5 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_741_dvd__mult,axiom,
% 0.59/0.79 ! [B_40: real,A_43: real,C_20: real] :
% 0.59/0.79 ( ( dvd_dvd_real @ A_43 @ C_20 )
% 0.59/0.79 => ( dvd_dvd_real @ A_43 @ ( times_times_real @ B_40 @ C_20 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_742_dvd__mult,axiom,
% 0.59/0.79 ! [B_40: nat,A_43: nat,C_20: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ A_43 @ C_20 )
% 0.59/0.79 => ( dvd_dvd_nat @ A_43 @ ( times_times_nat @ B_40 @ C_20 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_743_dvd__mult,axiom,
% 0.59/0.79 ! [B_40: int,A_43: int,C_20: int] :
% 0.59/0.79 ( ( dvd_dvd_int @ A_43 @ C_20 )
% 0.59/0.79 => ( dvd_dvd_int @ A_43 @ ( times_times_int @ B_40 @ C_20 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_744_dvd__mult2,axiom,
% 0.59/0.79 ! [C_19: real,A_42: real,B_39: real] :
% 0.59/0.79 ( ( dvd_dvd_real @ A_42 @ B_39 )
% 0.59/0.79 => ( dvd_dvd_real @ A_42 @ ( times_times_real @ B_39 @ C_19 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_745_dvd__mult2,axiom,
% 0.59/0.79 ! [C_19: nat,A_42: nat,B_39: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ A_42 @ B_39 )
% 0.59/0.79 => ( dvd_dvd_nat @ A_42 @ ( times_times_nat @ B_39 @ C_19 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_746_dvd__mult2,axiom,
% 0.59/0.79 ! [C_19: int,A_42: int,B_39: int] :
% 0.59/0.79 ( ( dvd_dvd_int @ A_42 @ B_39 )
% 0.59/0.79 => ( dvd_dvd_int @ A_42 @ ( times_times_int @ B_39 @ C_19 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_747_dvd__triv__right,axiom,
% 0.59/0.79 ! [A_41: real,B_38: real] : ( dvd_dvd_real @ A_41 @ ( times_times_real @ B_38 @ A_41 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_748_dvd__triv__right,axiom,
% 0.59/0.79 ! [A_41: nat,B_38: nat] : ( dvd_dvd_nat @ A_41 @ ( times_times_nat @ B_38 @ A_41 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_749_dvd__triv__right,axiom,
% 0.59/0.79 ! [A_41: int,B_38: int] : ( dvd_dvd_int @ A_41 @ ( times_times_int @ B_38 @ A_41 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_750_dvd__triv__left,axiom,
% 0.59/0.79 ! [A_40: real,B_37: real] : ( dvd_dvd_real @ A_40 @ ( times_times_real @ A_40 @ B_37 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_751_dvd__triv__left,axiom,
% 0.59/0.79 ! [A_40: nat,B_37: nat] : ( dvd_dvd_nat @ A_40 @ ( times_times_nat @ A_40 @ B_37 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_752_dvd__triv__left,axiom,
% 0.59/0.79 ! [A_40: int,B_37: int] : ( dvd_dvd_int @ A_40 @ ( times_times_int @ A_40 @ B_37 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_753_dvd__add,axiom,
% 0.59/0.79 ! [C_18: real,A_39: real,B_36: real] :
% 0.59/0.79 ( ( dvd_dvd_real @ A_39 @ B_36 )
% 0.59/0.79 => ( ( dvd_dvd_real @ A_39 @ C_18 )
% 0.59/0.79 => ( dvd_dvd_real @ A_39 @ ( plus_plus_real @ B_36 @ C_18 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_754_dvd__add,axiom,
% 0.59/0.79 ! [C_18: nat,A_39: nat,B_36: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ A_39 @ B_36 )
% 0.59/0.79 => ( ( dvd_dvd_nat @ A_39 @ C_18 )
% 0.59/0.79 => ( dvd_dvd_nat @ A_39 @ ( plus_plus_nat @ B_36 @ C_18 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_755_dvd__add,axiom,
% 0.59/0.79 ! [C_18: int,A_39: int,B_36: int] :
% 0.59/0.79 ( ( dvd_dvd_int @ A_39 @ B_36 )
% 0.59/0.79 => ( ( dvd_dvd_int @ A_39 @ C_18 )
% 0.59/0.79 => ( dvd_dvd_int @ A_39 @ ( plus_plus_int @ B_36 @ C_18 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_756_one__dvd,axiom,
% 0.59/0.79 ! [A_38: real] : ( dvd_dvd_real @ one_one_real @ A_38 ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_757_one__dvd,axiom,
% 0.59/0.79 ! [A_38: nat] : ( dvd_dvd_nat @ one_one_nat @ A_38 ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_758_one__dvd,axiom,
% 0.59/0.79 ! [A_38: int] : ( dvd_dvd_int @ one_one_int @ A_38 ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_759_dvd__diff,axiom,
% 0.59/0.79 ! [Z_1: real,X_2: real,Y_2: real] :
% 0.59/0.79 ( ( dvd_dvd_real @ X_2 @ Y_2 )
% 0.59/0.79 => ( ( dvd_dvd_real @ X_2 @ Z_1 )
% 0.59/0.79 => ( dvd_dvd_real @ X_2 @ ( minus_minus_real @ Y_2 @ Z_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_760_dvd__diff,axiom,
% 0.59/0.79 ! [Z_1: int,X_2: int,Y_2: int] :
% 0.59/0.79 ( ( dvd_dvd_int @ X_2 @ Y_2 )
% 0.59/0.79 => ( ( dvd_dvd_int @ X_2 @ Z_1 )
% 0.59/0.79 => ( dvd_dvd_int @ X_2 @ ( minus_minus_int @ Y_2 @ Z_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_761_real__mult__right__cancel,axiom,
% 0.59/0.79 ! [A: real,B: real,C: real] :
% 0.59/0.79 ( ( C != zero_zero_real )
% 0.59/0.79 => ( ( ( times_times_real @ A @ C )
% 0.59/0.79 = ( times_times_real @ B @ C ) )
% 0.59/0.79 <=> ( A = B ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_762_real__mult__left__cancel,axiom,
% 0.59/0.79 ! [A: real,B: real,C: real] :
% 0.59/0.79 ( ( C != zero_zero_real )
% 0.59/0.79 => ( ( ( times_times_real @ C @ A )
% 0.59/0.79 = ( times_times_real @ C @ B ) )
% 0.59/0.79 <=> ( A = B ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_763_divides__add__revr,axiom,
% 0.59/0.79 ! [B: nat,D: nat,A: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ D @ A )
% 0.59/0.79 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 0.59/0.79 => ( dvd_dvd_nat @ D @ B ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_764_divides__mul__l,axiom,
% 0.59/0.79 ! [C: nat,A: nat,B: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ A @ B )
% 0.59/0.79 => ( dvd_dvd_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_765_divides__mul__r,axiom,
% 0.59/0.79 ! [C: nat,A: nat,B: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ A @ B )
% 0.59/0.79 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_766_nat__mult__eq__one,axiom,
% 0.59/0.79 ! [N: nat,M: nat] :
% 0.59/0.79 ( ( ( times_times_nat @ N @ M )
% 0.59/0.79 = one_one_nat )
% 0.59/0.79 <=> ( ( N = one_one_nat )
% 0.59/0.79 & ( M = one_one_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_767_real__add__mult__distrib,axiom,
% 0.59/0.79 ! [Z1: real,Z2: real,W: real] :
% 0.59/0.79 ( ( times_times_real @ ( plus_plus_real @ Z1 @ Z2 ) @ W )
% 0.59/0.79 = ( plus_plus_real @ ( times_times_real @ Z1 @ W ) @ ( times_times_real @ Z2 @ W ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_768_nat__power__eq__0__iff,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ( power_power_nat @ M @ N )
% 0.59/0.79 = zero_zero_nat )
% 0.59/0.79 <=> ( ( N != zero_zero_nat )
% 0.59/0.79 & ( M = zero_zero_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_769_divides__exp,axiom,
% 0.59/0.79 ! [N: nat,X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 => ( dvd_dvd_nat @ ( power_power_nat @ X_1 @ N ) @ ( power_power_nat @ Y_1 @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_770_split__mult__neg__le,axiom,
% 0.59/0.79 ! [B_35: real,A_37: real] :
% 0.59/0.79 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A_37 )
% 0.59/0.79 & ( ord_less_eq_real @ B_35 @ zero_zero_real ) )
% 0.59/0.79 | ( ( ord_less_eq_real @ A_37 @ zero_zero_real )
% 0.59/0.79 & ( ord_less_eq_real @ zero_zero_real @ B_35 ) ) )
% 0.59/0.79 => ( ord_less_eq_real @ ( times_times_real @ A_37 @ B_35 ) @ zero_zero_real ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_771_split__mult__neg__le,axiom,
% 0.59/0.79 ! [B_35: nat,A_37: nat] :
% 0.59/0.79 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A_37 )
% 0.59/0.79 & ( ord_less_eq_nat @ B_35 @ zero_zero_nat ) )
% 0.59/0.79 | ( ( ord_less_eq_nat @ A_37 @ zero_zero_nat )
% 0.59/0.79 & ( ord_less_eq_nat @ zero_zero_nat @ B_35 ) ) )
% 0.59/0.79 => ( ord_less_eq_nat @ ( times_times_nat @ A_37 @ B_35 ) @ zero_zero_nat ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_772_split__mult__neg__le,axiom,
% 0.59/0.79 ! [B_35: int,A_37: int] :
% 0.59/0.79 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A_37 )
% 0.59/0.79 & ( ord_less_eq_int @ B_35 @ zero_zero_int ) )
% 0.59/0.79 | ( ( ord_less_eq_int @ A_37 @ zero_zero_int )
% 0.59/0.79 & ( ord_less_eq_int @ zero_zero_int @ B_35 ) ) )
% 0.59/0.79 => ( ord_less_eq_int @ ( times_times_int @ A_37 @ B_35 ) @ zero_zero_int ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_773_split__mult__pos__le,axiom,
% 0.59/0.79 ! [B_34: real,A_36: real] :
% 0.59/0.79 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A_36 )
% 0.59/0.79 & ( ord_less_eq_real @ zero_zero_real @ B_34 ) )
% 0.59/0.79 | ( ( ord_less_eq_real @ A_36 @ zero_zero_real )
% 0.59/0.79 & ( ord_less_eq_real @ B_34 @ zero_zero_real ) ) )
% 0.59/0.79 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A_36 @ B_34 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_774_split__mult__pos__le,axiom,
% 0.59/0.79 ! [B_34: int,A_36: int] :
% 0.59/0.79 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A_36 )
% 0.59/0.79 & ( ord_less_eq_int @ zero_zero_int @ B_34 ) )
% 0.59/0.79 | ( ( ord_less_eq_int @ A_36 @ zero_zero_int )
% 0.59/0.79 & ( ord_less_eq_int @ B_34 @ zero_zero_int ) ) )
% 0.59/0.79 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A_36 @ B_34 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_775_mult__mono,axiom,
% 0.59/0.79 ! [C_17: real,D_4: real,A_35: real,B_33: real] :
% 0.59/0.79 ( ( ord_less_eq_real @ A_35 @ B_33 )
% 0.59/0.79 => ( ( ord_less_eq_real @ C_17 @ D_4 )
% 0.59/0.79 => ( ( ord_less_eq_real @ zero_zero_real @ B_33 )
% 0.59/0.79 => ( ( ord_less_eq_real @ zero_zero_real @ C_17 )
% 0.59/0.79 => ( ord_less_eq_real @ ( times_times_real @ A_35 @ C_17 ) @ ( times_times_real @ B_33 @ D_4 ) ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_776_mult__mono,axiom,
% 0.59/0.79 ! [C_17: nat,D_4: nat,A_35: nat,B_33: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ A_35 @ B_33 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ C_17 @ D_4 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ B_33 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ C_17 )
% 0.59/0.79 => ( ord_less_eq_nat @ ( times_times_nat @ A_35 @ C_17 ) @ ( times_times_nat @ B_33 @ D_4 ) ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_777_mult__mono,axiom,
% 0.59/0.79 ! [C_17: int,D_4: int,A_35: int,B_33: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ A_35 @ B_33 )
% 0.59/0.79 => ( ( ord_less_eq_int @ C_17 @ D_4 )
% 0.59/0.79 => ( ( ord_less_eq_int @ zero_zero_int @ B_33 )
% 0.59/0.79 => ( ( ord_less_eq_int @ zero_zero_int @ C_17 )
% 0.59/0.79 => ( ord_less_eq_int @ ( times_times_int @ A_35 @ C_17 ) @ ( times_times_int @ B_33 @ D_4 ) ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_778_mult__mono_H,axiom,
% 0.59/0.79 ! [C_16: real,D_3: real,A_34: real,B_32: real] :
% 0.59/0.79 ( ( ord_less_eq_real @ A_34 @ B_32 )
% 0.59/0.79 => ( ( ord_less_eq_real @ C_16 @ D_3 )
% 0.59/0.79 => ( ( ord_less_eq_real @ zero_zero_real @ A_34 )
% 0.59/0.79 => ( ( ord_less_eq_real @ zero_zero_real @ C_16 )
% 0.59/0.79 => ( ord_less_eq_real @ ( times_times_real @ A_34 @ C_16 ) @ ( times_times_real @ B_32 @ D_3 ) ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_779_mult__mono_H,axiom,
% 0.59/0.79 ! [C_16: nat,D_3: nat,A_34: nat,B_32: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ A_34 @ B_32 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ C_16 @ D_3 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ A_34 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ C_16 )
% 0.59/0.79 => ( ord_less_eq_nat @ ( times_times_nat @ A_34 @ C_16 ) @ ( times_times_nat @ B_32 @ D_3 ) ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_780_mult__mono_H,axiom,
% 0.59/0.79 ! [C_16: int,D_3: int,A_34: int,B_32: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ A_34 @ B_32 )
% 0.59/0.79 => ( ( ord_less_eq_int @ C_16 @ D_3 )
% 0.59/0.79 => ( ( ord_less_eq_int @ zero_zero_int @ A_34 )
% 0.59/0.79 => ( ( ord_less_eq_int @ zero_zero_int @ C_16 )
% 0.59/0.79 => ( ord_less_eq_int @ ( times_times_int @ A_34 @ C_16 ) @ ( times_times_int @ B_32 @ D_3 ) ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_781_mult__left__mono__neg,axiom,
% 0.59/0.79 ! [C_15: real,B_31: real,A_33: real] :
% 0.59/0.79 ( ( ord_less_eq_real @ B_31 @ A_33 )
% 0.59/0.79 => ( ( ord_less_eq_real @ C_15 @ zero_zero_real )
% 0.59/0.79 => ( ord_less_eq_real @ ( times_times_real @ C_15 @ A_33 ) @ ( times_times_real @ C_15 @ B_31 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_782_mult__left__mono__neg,axiom,
% 0.59/0.79 ! [C_15: int,B_31: int,A_33: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ B_31 @ A_33 )
% 0.59/0.79 => ( ( ord_less_eq_int @ C_15 @ zero_zero_int )
% 0.59/0.79 => ( ord_less_eq_int @ ( times_times_int @ C_15 @ A_33 ) @ ( times_times_int @ C_15 @ B_31 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_783_mult__right__mono__neg,axiom,
% 0.59/0.79 ! [C_14: real,B_30: real,A_32: real] :
% 0.59/0.79 ( ( ord_less_eq_real @ B_30 @ A_32 )
% 0.59/0.79 => ( ( ord_less_eq_real @ C_14 @ zero_zero_real )
% 0.59/0.79 => ( ord_less_eq_real @ ( times_times_real @ A_32 @ C_14 ) @ ( times_times_real @ B_30 @ C_14 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_784_mult__right__mono__neg,axiom,
% 0.59/0.79 ! [C_14: int,B_30: int,A_32: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ B_30 @ A_32 )
% 0.59/0.79 => ( ( ord_less_eq_int @ C_14 @ zero_zero_int )
% 0.59/0.79 => ( ord_less_eq_int @ ( times_times_int @ A_32 @ C_14 ) @ ( times_times_int @ B_30 @ C_14 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_785_comm__mult__left__mono,axiom,
% 0.59/0.79 ! [C_13: real,A_31: real,B_29: real] :
% 0.59/0.79 ( ( ord_less_eq_real @ A_31 @ B_29 )
% 0.59/0.79 => ( ( ord_less_eq_real @ zero_zero_real @ C_13 )
% 0.59/0.79 => ( ord_less_eq_real @ ( times_times_real @ C_13 @ A_31 ) @ ( times_times_real @ C_13 @ B_29 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_786_comm__mult__left__mono,axiom,
% 0.59/0.79 ! [C_13: nat,A_31: nat,B_29: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ A_31 @ B_29 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ C_13 )
% 0.59/0.79 => ( ord_less_eq_nat @ ( times_times_nat @ C_13 @ A_31 ) @ ( times_times_nat @ C_13 @ B_29 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_787_comm__mult__left__mono,axiom,
% 0.59/0.79 ! [C_13: int,A_31: int,B_29: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ A_31 @ B_29 )
% 0.59/0.79 => ( ( ord_less_eq_int @ zero_zero_int @ C_13 )
% 0.59/0.79 => ( ord_less_eq_int @ ( times_times_int @ C_13 @ A_31 ) @ ( times_times_int @ C_13 @ B_29 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_788_mult__left__mono,axiom,
% 0.59/0.79 ! [C_12: real,A_30: real,B_28: real] :
% 0.59/0.79 ( ( ord_less_eq_real @ A_30 @ B_28 )
% 0.59/0.79 => ( ( ord_less_eq_real @ zero_zero_real @ C_12 )
% 0.59/0.79 => ( ord_less_eq_real @ ( times_times_real @ C_12 @ A_30 ) @ ( times_times_real @ C_12 @ B_28 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_789_mult__left__mono,axiom,
% 0.59/0.79 ! [C_12: nat,A_30: nat,B_28: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ A_30 @ B_28 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ C_12 )
% 0.59/0.79 => ( ord_less_eq_nat @ ( times_times_nat @ C_12 @ A_30 ) @ ( times_times_nat @ C_12 @ B_28 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_790_mult__left__mono,axiom,
% 0.59/0.79 ! [C_12: int,A_30: int,B_28: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ A_30 @ B_28 )
% 0.59/0.79 => ( ( ord_less_eq_int @ zero_zero_int @ C_12 )
% 0.59/0.79 => ( ord_less_eq_int @ ( times_times_int @ C_12 @ A_30 ) @ ( times_times_int @ C_12 @ B_28 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_791_mult__right__mono,axiom,
% 0.59/0.79 ! [C_11: real,A_29: real,B_27: real] :
% 0.59/0.79 ( ( ord_less_eq_real @ A_29 @ B_27 )
% 0.59/0.79 => ( ( ord_less_eq_real @ zero_zero_real @ C_11 )
% 0.59/0.79 => ( ord_less_eq_real @ ( times_times_real @ A_29 @ C_11 ) @ ( times_times_real @ B_27 @ C_11 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_792_mult__right__mono,axiom,
% 0.59/0.79 ! [C_11: nat,A_29: nat,B_27: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ A_29 @ B_27 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ C_11 )
% 0.59/0.79 => ( ord_less_eq_nat @ ( times_times_nat @ A_29 @ C_11 ) @ ( times_times_nat @ B_27 @ C_11 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_793_mult__right__mono,axiom,
% 0.59/0.79 ! [C_11: int,A_29: int,B_27: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ A_29 @ B_27 )
% 0.59/0.79 => ( ( ord_less_eq_int @ zero_zero_int @ C_11 )
% 0.59/0.79 => ( ord_less_eq_int @ ( times_times_int @ A_29 @ C_11 ) @ ( times_times_int @ B_27 @ C_11 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_794_mult__nonpos__nonpos,axiom,
% 0.59/0.79 ! [B_26: real,A_28: real] :
% 0.59/0.79 ( ( ord_less_eq_real @ A_28 @ zero_zero_real )
% 0.59/0.79 => ( ( ord_less_eq_real @ B_26 @ zero_zero_real )
% 0.59/0.79 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A_28 @ B_26 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_795_mult__nonpos__nonpos,axiom,
% 0.59/0.79 ! [B_26: int,A_28: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ A_28 @ zero_zero_int )
% 0.59/0.79 => ( ( ord_less_eq_int @ B_26 @ zero_zero_int )
% 0.59/0.79 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A_28 @ B_26 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_796_mult__nonpos__nonneg,axiom,
% 0.59/0.79 ! [B_25: real,A_27: real] :
% 0.59/0.79 ( ( ord_less_eq_real @ A_27 @ zero_zero_real )
% 0.59/0.79 => ( ( ord_less_eq_real @ zero_zero_real @ B_25 )
% 0.59/0.79 => ( ord_less_eq_real @ ( times_times_real @ A_27 @ B_25 ) @ zero_zero_real ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_797_mult__nonpos__nonneg,axiom,
% 0.59/0.79 ! [B_25: nat,A_27: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ A_27 @ zero_zero_nat )
% 0.59/0.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ B_25 )
% 0.59/0.79 => ( ord_less_eq_nat @ ( times_times_nat @ A_27 @ B_25 ) @ zero_zero_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_798_mult__nonpos__nonneg,axiom,
% 0.59/0.79 ! [B_25: int,A_27: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ A_27 @ zero_zero_int )
% 0.59/0.79 => ( ( ord_less_eq_int @ zero_zero_int @ B_25 )
% 0.59/0.79 => ( ord_less_eq_int @ ( times_times_int @ A_27 @ B_25 ) @ zero_zero_int ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_799_mult__nonneg__nonpos2,axiom,
% 0.59/0.79 ! [B_24: real,A_26: real] :
% 0.59/0.79 ( ( ord_less_eq_real @ zero_zero_real @ A_26 )
% 0.59/0.79 => ( ( ord_less_eq_real @ B_24 @ zero_zero_real )
% 0.59/0.79 => ( ord_less_eq_real @ ( times_times_real @ B_24 @ A_26 ) @ zero_zero_real ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_800_mult__nonneg__nonpos2,axiom,
% 0.59/0.79 ! [B_24: nat,A_26: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ zero_zero_nat @ A_26 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ B_24 @ zero_zero_nat )
% 0.59/0.79 => ( ord_less_eq_nat @ ( times_times_nat @ B_24 @ A_26 ) @ zero_zero_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_801_mult__nonneg__nonpos2,axiom,
% 0.59/0.79 ! [B_24: int,A_26: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ zero_zero_int @ A_26 )
% 0.59/0.79 => ( ( ord_less_eq_int @ B_24 @ zero_zero_int )
% 0.59/0.79 => ( ord_less_eq_int @ ( times_times_int @ B_24 @ A_26 ) @ zero_zero_int ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_802_mult__nonneg__nonpos,axiom,
% 0.59/0.79 ! [B_23: real,A_25: real] :
% 0.59/0.79 ( ( ord_less_eq_real @ zero_zero_real @ A_25 )
% 0.59/0.79 => ( ( ord_less_eq_real @ B_23 @ zero_zero_real )
% 0.59/0.79 => ( ord_less_eq_real @ ( times_times_real @ A_25 @ B_23 ) @ zero_zero_real ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_803_mult__nonneg__nonpos,axiom,
% 0.59/0.79 ! [B_23: nat,A_25: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ zero_zero_nat @ A_25 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ B_23 @ zero_zero_nat )
% 0.59/0.79 => ( ord_less_eq_nat @ ( times_times_nat @ A_25 @ B_23 ) @ zero_zero_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_804_mult__nonneg__nonpos,axiom,
% 0.59/0.79 ! [B_23: int,A_25: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ zero_zero_int @ A_25 )
% 0.59/0.79 => ( ( ord_less_eq_int @ B_23 @ zero_zero_int )
% 0.59/0.79 => ( ord_less_eq_int @ ( times_times_int @ A_25 @ B_23 ) @ zero_zero_int ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_805_mult__nonneg__nonneg,axiom,
% 0.59/0.79 ! [B_22: real,A_24: real] :
% 0.59/0.79 ( ( ord_less_eq_real @ zero_zero_real @ A_24 )
% 0.59/0.79 => ( ( ord_less_eq_real @ zero_zero_real @ B_22 )
% 0.59/0.79 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A_24 @ B_22 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_806_mult__nonneg__nonneg,axiom,
% 0.59/0.79 ! [B_22: nat,A_24: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ zero_zero_nat @ A_24 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ zero_zero_nat @ B_22 )
% 0.59/0.79 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A_24 @ B_22 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_807_mult__nonneg__nonneg,axiom,
% 0.59/0.79 ! [B_22: int,A_24: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ zero_zero_int @ A_24 )
% 0.59/0.79 => ( ( ord_less_eq_int @ zero_zero_int @ B_22 )
% 0.59/0.79 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A_24 @ B_22 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_808_mult__le__0__iff,axiom,
% 0.59/0.79 ! [A_23: real,B_21: real] :
% 0.59/0.79 ( ( ord_less_eq_real @ ( times_times_real @ A_23 @ B_21 ) @ zero_zero_real )
% 0.59/0.79 <=> ( ( ( ord_less_eq_real @ zero_zero_real @ A_23 )
% 0.59/0.79 & ( ord_less_eq_real @ B_21 @ zero_zero_real ) )
% 0.59/0.79 | ( ( ord_less_eq_real @ A_23 @ zero_zero_real )
% 0.59/0.79 & ( ord_less_eq_real @ zero_zero_real @ B_21 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_809_mult__le__0__iff,axiom,
% 0.59/0.79 ! [A_23: int,B_21: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ ( times_times_int @ A_23 @ B_21 ) @ zero_zero_int )
% 0.59/0.79 <=> ( ( ( ord_less_eq_int @ zero_zero_int @ A_23 )
% 0.59/0.79 & ( ord_less_eq_int @ B_21 @ zero_zero_int ) )
% 0.59/0.79 | ( ( ord_less_eq_int @ A_23 @ zero_zero_int )
% 0.59/0.79 & ( ord_less_eq_int @ zero_zero_int @ B_21 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_810_zero__le__mult__iff,axiom,
% 0.59/0.79 ! [A_22: real,B_20: real] :
% 0.59/0.79 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A_22 @ B_20 ) )
% 0.59/0.79 <=> ( ( ( ord_less_eq_real @ zero_zero_real @ A_22 )
% 0.59/0.79 & ( ord_less_eq_real @ zero_zero_real @ B_20 ) )
% 0.59/0.79 | ( ( ord_less_eq_real @ A_22 @ zero_zero_real )
% 0.59/0.79 & ( ord_less_eq_real @ B_20 @ zero_zero_real ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_811_zero__le__mult__iff,axiom,
% 0.59/0.79 ! [A_22: int,B_20: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A_22 @ B_20 ) )
% 0.59/0.79 <=> ( ( ( ord_less_eq_int @ zero_zero_int @ A_22 )
% 0.59/0.79 & ( ord_less_eq_int @ zero_zero_int @ B_20 ) )
% 0.59/0.79 | ( ( ord_less_eq_int @ A_22 @ zero_zero_int )
% 0.59/0.79 & ( ord_less_eq_int @ B_20 @ zero_zero_int ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_812_zero__le__square,axiom,
% 0.59/0.79 ! [A_21: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A_21 @ A_21 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_813_zero__le__square,axiom,
% 0.59/0.79 ! [A_21: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A_21 @ A_21 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_814_mult__strict__left__mono__neg,axiom,
% 0.59/0.79 ! [C_10: real,B_19: real,A_20: real] :
% 0.59/0.79 ( ( ord_less_real @ B_19 @ A_20 )
% 0.59/0.79 => ( ( ord_less_real @ C_10 @ zero_zero_real )
% 0.59/0.79 => ( ord_less_real @ ( times_times_real @ C_10 @ A_20 ) @ ( times_times_real @ C_10 @ B_19 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_815_mult__strict__left__mono__neg,axiom,
% 0.59/0.79 ! [C_10: int,B_19: int,A_20: int] :
% 0.59/0.79 ( ( ord_less_int @ B_19 @ A_20 )
% 0.59/0.79 => ( ( ord_less_int @ C_10 @ zero_zero_int )
% 0.59/0.79 => ( ord_less_int @ ( times_times_int @ C_10 @ A_20 ) @ ( times_times_int @ C_10 @ B_19 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_816_mult__strict__right__mono__neg,axiom,
% 0.59/0.79 ! [C_9: real,B_18: real,A_19: real] :
% 0.59/0.79 ( ( ord_less_real @ B_18 @ A_19 )
% 0.59/0.79 => ( ( ord_less_real @ C_9 @ zero_zero_real )
% 0.59/0.79 => ( ord_less_real @ ( times_times_real @ A_19 @ C_9 ) @ ( times_times_real @ B_18 @ C_9 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_817_mult__strict__right__mono__neg,axiom,
% 0.59/0.79 ! [C_9: int,B_18: int,A_19: int] :
% 0.59/0.79 ( ( ord_less_int @ B_18 @ A_19 )
% 0.59/0.79 => ( ( ord_less_int @ C_9 @ zero_zero_int )
% 0.59/0.79 => ( ord_less_int @ ( times_times_int @ A_19 @ C_9 ) @ ( times_times_int @ B_18 @ C_9 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_818_comm__mult__strict__left__mono,axiom,
% 0.59/0.79 ! [C_8: real,A_18: real,B_17: real] :
% 0.59/0.79 ( ( ord_less_real @ A_18 @ B_17 )
% 0.59/0.79 => ( ( ord_less_real @ zero_zero_real @ C_8 )
% 0.59/0.79 => ( ord_less_real @ ( times_times_real @ C_8 @ A_18 ) @ ( times_times_real @ C_8 @ B_17 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_819_comm__mult__strict__left__mono,axiom,
% 0.59/0.79 ! [C_8: nat,A_18: nat,B_17: nat] :
% 0.59/0.79 ( ( ord_less_nat @ A_18 @ B_17 )
% 0.59/0.79 => ( ( ord_less_nat @ zero_zero_nat @ C_8 )
% 0.59/0.79 => ( ord_less_nat @ ( times_times_nat @ C_8 @ A_18 ) @ ( times_times_nat @ C_8 @ B_17 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_820_comm__mult__strict__left__mono,axiom,
% 0.59/0.79 ! [C_8: int,A_18: int,B_17: int] :
% 0.59/0.79 ( ( ord_less_int @ A_18 @ B_17 )
% 0.59/0.79 => ( ( ord_less_int @ zero_zero_int @ C_8 )
% 0.59/0.79 => ( ord_less_int @ ( times_times_int @ C_8 @ A_18 ) @ ( times_times_int @ C_8 @ B_17 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_821_mult__strict__left__mono,axiom,
% 0.59/0.79 ! [C_7: real,A_17: real,B_16: real] :
% 0.59/0.79 ( ( ord_less_real @ A_17 @ B_16 )
% 0.59/0.79 => ( ( ord_less_real @ zero_zero_real @ C_7 )
% 0.59/0.79 => ( ord_less_real @ ( times_times_real @ C_7 @ A_17 ) @ ( times_times_real @ C_7 @ B_16 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_822_mult__strict__left__mono,axiom,
% 0.59/0.79 ! [C_7: nat,A_17: nat,B_16: nat] :
% 0.59/0.79 ( ( ord_less_nat @ A_17 @ B_16 )
% 0.59/0.79 => ( ( ord_less_nat @ zero_zero_nat @ C_7 )
% 0.59/0.79 => ( ord_less_nat @ ( times_times_nat @ C_7 @ A_17 ) @ ( times_times_nat @ C_7 @ B_16 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_823_mult__strict__left__mono,axiom,
% 0.59/0.79 ! [C_7: int,A_17: int,B_16: int] :
% 0.59/0.79 ( ( ord_less_int @ A_17 @ B_16 )
% 0.59/0.79 => ( ( ord_less_int @ zero_zero_int @ C_7 )
% 0.59/0.79 => ( ord_less_int @ ( times_times_int @ C_7 @ A_17 ) @ ( times_times_int @ C_7 @ B_16 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_824_mult__strict__right__mono,axiom,
% 0.59/0.79 ! [C_6: real,A_16: real,B_15: real] :
% 0.59/0.79 ( ( ord_less_real @ A_16 @ B_15 )
% 0.59/0.79 => ( ( ord_less_real @ zero_zero_real @ C_6 )
% 0.59/0.79 => ( ord_less_real @ ( times_times_real @ A_16 @ C_6 ) @ ( times_times_real @ B_15 @ C_6 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_825_mult__strict__right__mono,axiom,
% 0.59/0.79 ! [C_6: nat,A_16: nat,B_15: nat] :
% 0.59/0.79 ( ( ord_less_nat @ A_16 @ B_15 )
% 0.59/0.79 => ( ( ord_less_nat @ zero_zero_nat @ C_6 )
% 0.59/0.79 => ( ord_less_nat @ ( times_times_nat @ A_16 @ C_6 ) @ ( times_times_nat @ B_15 @ C_6 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_826_mult__strict__right__mono,axiom,
% 0.59/0.79 ! [C_6: int,A_16: int,B_15: int] :
% 0.59/0.79 ( ( ord_less_int @ A_16 @ B_15 )
% 0.59/0.79 => ( ( ord_less_int @ zero_zero_int @ C_6 )
% 0.59/0.79 => ( ord_less_int @ ( times_times_int @ A_16 @ C_6 ) @ ( times_times_int @ B_15 @ C_6 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_827_mult__neg__neg,axiom,
% 0.59/0.79 ! [B_14: real,A_15: real] :
% 0.59/0.79 ( ( ord_less_real @ A_15 @ zero_zero_real )
% 0.59/0.79 => ( ( ord_less_real @ B_14 @ zero_zero_real )
% 0.59/0.79 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A_15 @ B_14 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_828_mult__neg__neg,axiom,
% 0.59/0.79 ! [B_14: int,A_15: int] :
% 0.59/0.79 ( ( ord_less_int @ A_15 @ zero_zero_int )
% 0.59/0.79 => ( ( ord_less_int @ B_14 @ zero_zero_int )
% 0.59/0.79 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A_15 @ B_14 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_829_mult__neg__pos,axiom,
% 0.59/0.79 ! [B_13: real,A_14: real] :
% 0.59/0.79 ( ( ord_less_real @ A_14 @ zero_zero_real )
% 0.59/0.79 => ( ( ord_less_real @ zero_zero_real @ B_13 )
% 0.59/0.79 => ( ord_less_real @ ( times_times_real @ A_14 @ B_13 ) @ zero_zero_real ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_830_mult__neg__pos,axiom,
% 0.59/0.79 ! [B_13: nat,A_14: nat] :
% 0.59/0.79 ( ( ord_less_nat @ A_14 @ zero_zero_nat )
% 0.59/0.79 => ( ( ord_less_nat @ zero_zero_nat @ B_13 )
% 0.59/0.79 => ( ord_less_nat @ ( times_times_nat @ A_14 @ B_13 ) @ zero_zero_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_831_mult__neg__pos,axiom,
% 0.59/0.79 ! [B_13: int,A_14: int] :
% 0.59/0.79 ( ( ord_less_int @ A_14 @ zero_zero_int )
% 0.59/0.79 => ( ( ord_less_int @ zero_zero_int @ B_13 )
% 0.59/0.79 => ( ord_less_int @ ( times_times_int @ A_14 @ B_13 ) @ zero_zero_int ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_832_mult__less__cancel__left__neg,axiom,
% 0.59/0.79 ! [A_13: real,B_12: real,C_5: real] :
% 0.59/0.79 ( ( ord_less_real @ C_5 @ zero_zero_real )
% 0.59/0.79 => ( ( ord_less_real @ ( times_times_real @ C_5 @ A_13 ) @ ( times_times_real @ C_5 @ B_12 ) )
% 0.59/0.79 <=> ( ord_less_real @ B_12 @ A_13 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_833_mult__less__cancel__left__neg,axiom,
% 0.59/0.79 ! [A_13: int,B_12: int,C_5: int] :
% 0.59/0.79 ( ( ord_less_int @ C_5 @ zero_zero_int )
% 0.59/0.79 => ( ( ord_less_int @ ( times_times_int @ C_5 @ A_13 ) @ ( times_times_int @ C_5 @ B_12 ) )
% 0.59/0.79 <=> ( ord_less_int @ B_12 @ A_13 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_834_zero__less__mult__pos2,axiom,
% 0.59/0.79 ! [B_11: real,A_12: real] :
% 0.59/0.79 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B_11 @ A_12 ) )
% 0.59/0.79 => ( ( ord_less_real @ zero_zero_real @ A_12 )
% 0.59/0.79 => ( ord_less_real @ zero_zero_real @ B_11 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_835_zero__less__mult__pos2,axiom,
% 0.59/0.79 ! [B_11: nat,A_12: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B_11 @ A_12 ) )
% 0.59/0.79 => ( ( ord_less_nat @ zero_zero_nat @ A_12 )
% 0.59/0.79 => ( ord_less_nat @ zero_zero_nat @ B_11 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_836_zero__less__mult__pos2,axiom,
% 0.59/0.79 ! [B_11: int,A_12: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B_11 @ A_12 ) )
% 0.59/0.79 => ( ( ord_less_int @ zero_zero_int @ A_12 )
% 0.59/0.79 => ( ord_less_int @ zero_zero_int @ B_11 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_837_zero__less__mult__pos,axiom,
% 0.59/0.79 ! [A_11: real,B_10: real] :
% 0.59/0.79 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A_11 @ B_10 ) )
% 0.59/0.79 => ( ( ord_less_real @ zero_zero_real @ A_11 )
% 0.59/0.79 => ( ord_less_real @ zero_zero_real @ B_10 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_838_zero__less__mult__pos,axiom,
% 0.59/0.79 ! [A_11: nat,B_10: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A_11 @ B_10 ) )
% 0.59/0.79 => ( ( ord_less_nat @ zero_zero_nat @ A_11 )
% 0.59/0.79 => ( ord_less_nat @ zero_zero_nat @ B_10 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_839_zero__less__mult__pos,axiom,
% 0.59/0.79 ! [A_11: int,B_10: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A_11 @ B_10 ) )
% 0.59/0.79 => ( ( ord_less_int @ zero_zero_int @ A_11 )
% 0.59/0.79 => ( ord_less_int @ zero_zero_int @ B_10 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_840_mult__pos__neg2,axiom,
% 0.59/0.79 ! [B_9: real,A_10: real] :
% 0.59/0.79 ( ( ord_less_real @ zero_zero_real @ A_10 )
% 0.59/0.79 => ( ( ord_less_real @ B_9 @ zero_zero_real )
% 0.59/0.79 => ( ord_less_real @ ( times_times_real @ B_9 @ A_10 ) @ zero_zero_real ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_841_mult__pos__neg2,axiom,
% 0.59/0.79 ! [B_9: nat,A_10: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ A_10 )
% 0.59/0.79 => ( ( ord_less_nat @ B_9 @ zero_zero_nat )
% 0.59/0.79 => ( ord_less_nat @ ( times_times_nat @ B_9 @ A_10 ) @ zero_zero_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_842_mult__pos__neg2,axiom,
% 0.59/0.79 ! [B_9: int,A_10: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ A_10 )
% 0.59/0.79 => ( ( ord_less_int @ B_9 @ zero_zero_int )
% 0.59/0.79 => ( ord_less_int @ ( times_times_int @ B_9 @ A_10 ) @ zero_zero_int ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_843_mult__pos__neg,axiom,
% 0.59/0.79 ! [B_8: real,A_9: real] :
% 0.59/0.79 ( ( ord_less_real @ zero_zero_real @ A_9 )
% 0.59/0.79 => ( ( ord_less_real @ B_8 @ zero_zero_real )
% 0.59/0.79 => ( ord_less_real @ ( times_times_real @ A_9 @ B_8 ) @ zero_zero_real ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_844_mult__pos__neg,axiom,
% 0.59/0.79 ! [B_8: nat,A_9: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ A_9 )
% 0.59/0.79 => ( ( ord_less_nat @ B_8 @ zero_zero_nat )
% 0.59/0.79 => ( ord_less_nat @ ( times_times_nat @ A_9 @ B_8 ) @ zero_zero_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_845_mult__pos__neg,axiom,
% 0.59/0.79 ! [B_8: int,A_9: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ A_9 )
% 0.59/0.79 => ( ( ord_less_int @ B_8 @ zero_zero_int )
% 0.59/0.79 => ( ord_less_int @ ( times_times_int @ A_9 @ B_8 ) @ zero_zero_int ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_846_mult__pos__pos,axiom,
% 0.59/0.79 ! [B_7: real,A_8: real] :
% 0.59/0.79 ( ( ord_less_real @ zero_zero_real @ A_8 )
% 0.59/0.79 => ( ( ord_less_real @ zero_zero_real @ B_7 )
% 0.59/0.79 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A_8 @ B_7 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_847_mult__pos__pos,axiom,
% 0.59/0.79 ! [B_7: nat,A_8: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ A_8 )
% 0.59/0.79 => ( ( ord_less_nat @ zero_zero_nat @ B_7 )
% 0.59/0.79 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A_8 @ B_7 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_848_mult__pos__pos,axiom,
% 0.59/0.79 ! [B_7: int,A_8: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ A_8 )
% 0.59/0.79 => ( ( ord_less_int @ zero_zero_int @ B_7 )
% 0.59/0.79 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A_8 @ B_7 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_849_mult__less__cancel__left__pos,axiom,
% 0.59/0.79 ! [A_7: real,B_6: real,C_4: real] :
% 0.59/0.79 ( ( ord_less_real @ zero_zero_real @ C_4 )
% 0.59/0.79 => ( ( ord_less_real @ ( times_times_real @ C_4 @ A_7 ) @ ( times_times_real @ C_4 @ B_6 ) )
% 0.59/0.79 <=> ( ord_less_real @ A_7 @ B_6 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_850_mult__less__cancel__left__pos,axiom,
% 0.59/0.79 ! [A_7: int,B_6: int,C_4: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ C_4 )
% 0.59/0.79 => ( ( ord_less_int @ ( times_times_int @ C_4 @ A_7 ) @ ( times_times_int @ C_4 @ B_6 ) )
% 0.59/0.79 <=> ( ord_less_int @ A_7 @ B_6 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_851_mult__less__cancel__left__disj,axiom,
% 0.59/0.79 ! [C_3: real,A_6: real,B_5: real] :
% 0.59/0.79 ( ( ord_less_real @ ( times_times_real @ C_3 @ A_6 ) @ ( times_times_real @ C_3 @ B_5 ) )
% 0.59/0.79 <=> ( ( ( ord_less_real @ zero_zero_real @ C_3 )
% 0.59/0.79 & ( ord_less_real @ A_6 @ B_5 ) )
% 0.59/0.79 | ( ( ord_less_real @ C_3 @ zero_zero_real )
% 0.59/0.79 & ( ord_less_real @ B_5 @ A_6 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_852_mult__less__cancel__left__disj,axiom,
% 0.59/0.79 ! [C_3: int,A_6: int,B_5: int] :
% 0.59/0.79 ( ( ord_less_int @ ( times_times_int @ C_3 @ A_6 ) @ ( times_times_int @ C_3 @ B_5 ) )
% 0.59/0.79 <=> ( ( ( ord_less_int @ zero_zero_int @ C_3 )
% 0.59/0.79 & ( ord_less_int @ A_6 @ B_5 ) )
% 0.59/0.79 | ( ( ord_less_int @ C_3 @ zero_zero_int )
% 0.59/0.79 & ( ord_less_int @ B_5 @ A_6 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_853_mult__less__cancel__right__disj,axiom,
% 0.59/0.79 ! [A_5: real,C_2: real,B_4: real] :
% 0.59/0.79 ( ( ord_less_real @ ( times_times_real @ A_5 @ C_2 ) @ ( times_times_real @ B_4 @ C_2 ) )
% 0.59/0.79 <=> ( ( ( ord_less_real @ zero_zero_real @ C_2 )
% 0.59/0.79 & ( ord_less_real @ A_5 @ B_4 ) )
% 0.59/0.79 | ( ( ord_less_real @ C_2 @ zero_zero_real )
% 0.59/0.79 & ( ord_less_real @ B_4 @ A_5 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_854_mult__less__cancel__right__disj,axiom,
% 0.59/0.79 ! [A_5: int,C_2: int,B_4: int] :
% 0.59/0.79 ( ( ord_less_int @ ( times_times_int @ A_5 @ C_2 ) @ ( times_times_int @ B_4 @ C_2 ) )
% 0.59/0.79 <=> ( ( ( ord_less_int @ zero_zero_int @ C_2 )
% 0.59/0.79 & ( ord_less_int @ A_5 @ B_4 ) )
% 0.59/0.79 | ( ( ord_less_int @ C_2 @ zero_zero_int )
% 0.59/0.79 & ( ord_less_int @ B_4 @ A_5 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_855_not__square__less__zero,axiom,
% 0.59/0.79 ! [A_4: real] :
% 0.59/0.79 ~ ( ord_less_real @ ( times_times_real @ A_4 @ A_4 ) @ zero_zero_real ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_856_not__square__less__zero,axiom,
% 0.59/0.79 ! [A_4: int] :
% 0.59/0.79 ~ ( ord_less_int @ ( times_times_int @ A_4 @ A_4 ) @ zero_zero_int ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_857_pos__add__strict,axiom,
% 0.59/0.79 ! [B_3: nat,C_1: nat,A_3: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ A_3 )
% 0.59/0.79 => ( ( ord_less_nat @ B_3 @ C_1 )
% 0.59/0.79 => ( ord_less_nat @ B_3 @ ( plus_plus_nat @ A_3 @ C_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_858_pos__add__strict,axiom,
% 0.59/0.79 ! [B_3: int,C_1: int,A_3: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ A_3 )
% 0.59/0.79 => ( ( ord_less_int @ B_3 @ C_1 )
% 0.59/0.79 => ( ord_less_int @ B_3 @ ( plus_plus_int @ A_3 @ C_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_859_divides__ge,axiom,
% 0.59/0.79 ! [A: nat,B: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ A @ B )
% 0.59/0.79 => ( ( B = zero_zero_nat )
% 0.59/0.79 | ( ord_less_eq_nat @ A @ B ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_860_nat__mult__dvd__cancel__disj_H,axiom,
% 0.59/0.79 ! [M: nat,K: nat,N: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.59/0.79 <=> ( ( K = zero_zero_nat )
% 0.59/0.79 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_861_real__mult__less__iff1,axiom,
% 0.59/0.79 ! [X_1: real,Y_1: real,Z: real] :
% 0.59/0.79 ( ( ord_less_real @ zero_zero_real @ Z )
% 0.59/0.79 => ( ( ord_less_real @ ( times_times_real @ X_1 @ Z ) @ ( times_times_real @ Y_1 @ Z ) )
% 0.59/0.79 <=> ( ord_less_real @ X_1 @ Y_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_862_real__mult__le__cancel__iff1,axiom,
% 0.59/0.79 ! [X_1: real,Y_1: real,Z: real] :
% 0.59/0.79 ( ( ord_less_real @ zero_zero_real @ Z )
% 0.59/0.79 => ( ( ord_less_eq_real @ ( times_times_real @ X_1 @ Z ) @ ( times_times_real @ Y_1 @ Z ) )
% 0.59/0.79 <=> ( ord_less_eq_real @ X_1 @ Y_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_863_real__mult__le__cancel__iff2,axiom,
% 0.59/0.79 ! [X_1: real,Y_1: real,Z: real] :
% 0.59/0.79 ( ( ord_less_real @ zero_zero_real @ Z )
% 0.59/0.79 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X_1 ) @ ( times_times_real @ Z @ Y_1 ) )
% 0.59/0.79 <=> ( ord_less_eq_real @ X_1 @ Y_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_864_real__mult__order,axiom,
% 0.59/0.79 ! [Y_1: real,X_1: real] :
% 0.59/0.79 ( ( ord_less_real @ zero_zero_real @ X_1 )
% 0.59/0.79 => ( ( ord_less_real @ zero_zero_real @ Y_1 )
% 0.59/0.79 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ X_1 @ Y_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_865_real__mult__less__mono2,axiom,
% 0.59/0.79 ! [X_1: real,Y_1: real,Z: real] :
% 0.59/0.79 ( ( ord_less_real @ zero_zero_real @ Z )
% 0.59/0.79 => ( ( ord_less_real @ X_1 @ Y_1 )
% 0.59/0.79 => ( ord_less_real @ ( times_times_real @ Z @ X_1 ) @ ( times_times_real @ Z @ Y_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_866_real__two__squares__add__zero__iff,axiom,
% 0.59/0.79 ! [X_1: real,Y_1: real] :
% 0.59/0.79 ( ( ( plus_plus_real @ ( times_times_real @ X_1 @ X_1 ) @ ( times_times_real @ Y_1 @ Y_1 ) )
% 0.59/0.79 = zero_zero_real )
% 0.59/0.79 <=> ( ( X_1 = zero_zero_real )
% 0.59/0.79 & ( Y_1 = zero_zero_real ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_867_divides__exp2,axiom,
% 0.59/0.79 ! [X_1: nat,Y_1: nat,N: nat] :
% 0.59/0.79 ( ( N != zero_zero_nat )
% 0.59/0.79 => ( ( dvd_dvd_nat @ ( power_power_nat @ X_1 @ N ) @ Y_1 )
% 0.59/0.79 => ( dvd_dvd_nat @ X_1 @ Y_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_868_divides__rev,axiom,
% 0.59/0.79 ! [A: nat,N: nat,B: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.59/0.79 => ( ( N != zero_zero_nat )
% 0.59/0.79 => ( dvd_dvd_nat @ A @ B ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_869_exp__eq__1,axiom,
% 0.59/0.79 ! [X_1: nat,N: nat] :
% 0.59/0.79 ( ( ( power_power_nat @ X_1 @ N )
% 0.59/0.79 = one_one_nat )
% 0.59/0.79 <=> ( ( X_1 = one_one_nat )
% 0.59/0.79 | ( N = zero_zero_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_870_divides__div__not,axiom,
% 0.59/0.79 ! [X_1: nat,Q: nat,N: nat,R: nat] :
% 0.59/0.79 ( ( X_1
% 0.59/0.79 = ( plus_plus_nat @ ( times_times_nat @ Q @ N ) @ R ) )
% 0.59/0.79 => ( ( ord_less_nat @ zero_zero_nat @ R )
% 0.59/0.79 => ( ( ord_less_nat @ R @ N )
% 0.59/0.79 => ~ ( dvd_dvd_nat @ N @ X_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_871_two__realpow__ge__one,axiom,
% 0.59/0.79 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( number267125858f_real @ ( bit0 @ ( bit1 @ pls ) ) ) @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_872_realpow__pos__nth,axiom,
% 0.59/0.79 ! [A: real,N: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.59/0.79 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.59/0.79 => ? [R_1: real] :
% 0.59/0.79 ( ( ord_less_real @ zero_zero_real @ R_1 )
% 0.59/0.79 & ( ( power_power_real @ R_1 @ N )
% 0.59/0.79 = A ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_873_realpow__pos__nth__unique,axiom,
% 0.59/0.79 ! [A: real,N: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.59/0.79 => ( ( ord_less_real @ zero_zero_real @ A )
% 0.59/0.79 => ? [X: real] :
% 0.59/0.79 ( ( ord_less_real @ zero_zero_real @ X )
% 0.59/0.79 & ( ( power_power_real @ X @ N )
% 0.59/0.79 = A )
% 0.59/0.79 & ! [Y: real] :
% 0.59/0.79 ( ( ( ord_less_real @ zero_zero_real @ Y )
% 0.59/0.79 & ( ( power_power_real @ Y @ N )
% 0.59/0.79 = A ) )
% 0.59/0.79 => ( Y = X ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_874_dvd__mult__cancel2,axiom,
% 0.59/0.79 ! [N: nat,M: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.59/0.79 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 0.59/0.79 <=> ( N = one_one_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_875_dvd__mult__cancel1,axiom,
% 0.59/0.79 ! [N: nat,M: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.59/0.79 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 0.59/0.79 <=> ( N = one_one_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_876_le0,axiom,
% 0.59/0.79 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_877_dvd_Oorder__refl,axiom,
% 0.59/0.79 ! [X_1: nat] : ( dvd_dvd_nat @ X_1 @ X_1 ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_878_less__zeroE,axiom,
% 0.59/0.79 ! [N: nat] :
% 0.59/0.79 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_879_diff__commute,axiom,
% 0.59/0.79 ! [I_1: nat,J_1: nat,K: nat] :
% 0.59/0.79 ( ( minus_minus_nat @ ( minus_minus_nat @ I_1 @ J_1 ) @ K )
% 0.59/0.79 = ( minus_minus_nat @ ( minus_minus_nat @ I_1 @ K ) @ J_1 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_880_real__le__refl,axiom,
% 0.59/0.79 ! [W: real] : ( ord_less_eq_real @ W @ W ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_881_real__le__linear,axiom,
% 0.59/0.79 ! [Z: real,W: real] :
% 0.59/0.79 ( ( ord_less_eq_real @ Z @ W )
% 0.59/0.79 | ( ord_less_eq_real @ W @ Z ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_882_real__le__trans,axiom,
% 0.59/0.79 ! [K: real,I_1: real,J_1: real] :
% 0.59/0.79 ( ( ord_less_eq_real @ I_1 @ J_1 )
% 0.59/0.79 => ( ( ord_less_eq_real @ J_1 @ K )
% 0.59/0.79 => ( ord_less_eq_real @ I_1 @ K ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_883_real__le__antisym,axiom,
% 0.59/0.79 ! [Z: real,W: real] :
% 0.59/0.79 ( ( ord_less_eq_real @ Z @ W )
% 0.59/0.79 => ( ( ord_less_eq_real @ W @ Z )
% 0.59/0.79 => ( Z = W ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_884_diff__0__eq__0,axiom,
% 0.59/0.79 ! [N: nat] :
% 0.59/0.79 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 0.59/0.79 = zero_zero_nat ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_885_minus__nat_Odiff__0,axiom,
% 0.59/0.79 ! [M: nat] :
% 0.59/0.79 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 0.59/0.79 = M ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_886_diff__self__eq__0,axiom,
% 0.59/0.79 ! [M: nat] :
% 0.59/0.79 ( ( minus_minus_nat @ M @ M )
% 0.59/0.79 = zero_zero_nat ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_887_diffs0__imp__equal,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ( minus_minus_nat @ M @ N )
% 0.59/0.79 = zero_zero_nat )
% 0.59/0.79 => ( ( ( minus_minus_nat @ N @ M )
% 0.59/0.79 = zero_zero_nat )
% 0.59/0.79 => ( M = N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_888_nat__less__cases,axiom,
% 0.59/0.79 ! [P_1: nat > nat > $o,M: nat,N: nat] :
% 0.59/0.79 ( ( ( ord_less_nat @ M @ N )
% 0.59/0.79 => ( P_1 @ N @ M ) )
% 0.59/0.79 => ( ( ( M = N )
% 0.59/0.79 => ( P_1 @ N @ M ) )
% 0.59/0.79 => ( ( ( ord_less_nat @ N @ M )
% 0.59/0.79 => ( P_1 @ N @ M ) )
% 0.59/0.79 => ( P_1 @ N @ M ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_889_less__not__refl3,axiom,
% 0.59/0.79 ! [S: nat,T: nat] :
% 0.59/0.79 ( ( ord_less_nat @ S @ T )
% 0.59/0.79 => ( S != T ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_890_less__not__refl2,axiom,
% 0.59/0.79 ! [N: nat,M: nat] :
% 0.59/0.79 ( ( ord_less_nat @ N @ M )
% 0.59/0.79 => ( M != N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_891_less__irrefl__nat,axiom,
% 0.59/0.79 ! [N: nat] :
% 0.59/0.79 ~ ( ord_less_nat @ N @ N ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_892_linorder__neqE__nat,axiom,
% 0.59/0.79 ! [X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( X_1 != Y_1 )
% 0.59/0.79 => ( ~ ( ord_less_nat @ X_1 @ Y_1 )
% 0.59/0.79 => ( ord_less_nat @ Y_1 @ X_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_893_nat__neq__iff,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( M != N )
% 0.59/0.79 <=> ( ( ord_less_nat @ M @ N )
% 0.59/0.79 | ( ord_less_nat @ N @ M ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_894_less__not__refl,axiom,
% 0.59/0.79 ! [N: nat] :
% 0.59/0.79 ~ ( ord_less_nat @ N @ N ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_895_diff__less__mono2,axiom,
% 0.59/0.79 ! [L: nat,M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_nat @ M @ N )
% 0.59/0.79 => ( ( ord_less_nat @ M @ L )
% 0.59/0.79 => ( ord_less_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_896_less__imp__diff__less,axiom,
% 0.59/0.79 ! [N: nat,J_1: nat,K: nat] :
% 0.59/0.79 ( ( ord_less_nat @ J_1 @ K )
% 0.59/0.79 => ( ord_less_nat @ ( minus_minus_nat @ J_1 @ N ) @ K ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_897_dvd_Oless__asym,axiom,
% 0.59/0.79 ! [X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Y_1 @ X_1 ) )
% 0.59/0.79 => ~ ( ( dvd_dvd_nat @ Y_1 @ X_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ X_1 @ Y_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_898_dvd_Oless__trans,axiom,
% 0.59/0.79 ! [Z: nat,X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Y_1 @ X_1 ) )
% 0.59/0.79 => ( ( ( dvd_dvd_nat @ Y_1 @ Z )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Z @ Y_1 ) )
% 0.59/0.79 => ( ( dvd_dvd_nat @ X_1 @ Z )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Z @ X_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_899_dvd_Oless__asym_H,axiom,
% 0.59/0.79 ! [A: nat,B: nat] :
% 0.59/0.79 ( ( ( dvd_dvd_nat @ A @ B )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ B @ A ) )
% 0.59/0.79 => ~ ( ( dvd_dvd_nat @ B @ A )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ A @ B ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_900_dvd_Oless__le__trans,axiom,
% 0.59/0.79 ! [Z: nat,X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Y_1 @ X_1 ) )
% 0.59/0.79 => ( ( dvd_dvd_nat @ Y_1 @ Z )
% 0.59/0.79 => ( ( dvd_dvd_nat @ X_1 @ Z )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Z @ X_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_901_dvd_Oord__less__eq__trans,axiom,
% 0.59/0.79 ! [C: nat,A: nat,B: nat] :
% 0.59/0.79 ( ( ( dvd_dvd_nat @ A @ B )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ B @ A ) )
% 0.59/0.79 => ( ( B = C )
% 0.59/0.79 => ( ( dvd_dvd_nat @ A @ C )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ C @ A ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_902_dvd_Oless__imp__triv,axiom,
% 0.59/0.79 ! [P_1: $o,X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Y_1 @ X_1 ) )
% 0.59/0.79 => ( ( ( dvd_dvd_nat @ Y_1 @ X_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ X_1 @ Y_1 ) )
% 0.59/0.79 => P_1 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_903_dvd_Oless__imp__not__eq2,axiom,
% 0.59/0.79 ! [X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Y_1 @ X_1 ) )
% 0.59/0.79 => ( Y_1 != X_1 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_904_dvd_Oless__imp__not__eq,axiom,
% 0.59/0.79 ! [X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Y_1 @ X_1 ) )
% 0.59/0.79 => ( X_1 != Y_1 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_905_dvd_Oless__imp__not__less,axiom,
% 0.59/0.79 ! [X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Y_1 @ X_1 ) )
% 0.59/0.79 => ~ ( ( dvd_dvd_nat @ Y_1 @ X_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ X_1 @ Y_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_906_dvd_Oless__imp__le,axiom,
% 0.59/0.79 ! [X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Y_1 @ X_1 ) )
% 0.59/0.79 => ( dvd_dvd_nat @ X_1 @ Y_1 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_907_dvd_Oless__not__sym,axiom,
% 0.59/0.79 ! [X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Y_1 @ X_1 ) )
% 0.59/0.79 => ~ ( ( dvd_dvd_nat @ Y_1 @ X_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ X_1 @ Y_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_908_dvd_Oless__imp__neq,axiom,
% 0.59/0.79 ! [X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Y_1 @ X_1 ) )
% 0.59/0.79 => ( X_1 != Y_1 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_909_dvd_Ole__less__trans,axiom,
% 0.59/0.79 ! [Z: nat,X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 => ( ( ( dvd_dvd_nat @ Y_1 @ Z )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Z @ Y_1 ) )
% 0.59/0.79 => ( ( dvd_dvd_nat @ X_1 @ Z )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Z @ X_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_910_dvd_Oord__eq__less__trans,axiom,
% 0.59/0.79 ! [C: nat,A: nat,B: nat] :
% 0.59/0.79 ( ( A = B )
% 0.59/0.79 => ( ( ( dvd_dvd_nat @ B @ C )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ C @ B ) )
% 0.59/0.79 => ( ( dvd_dvd_nat @ A @ C )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ C @ A ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_911_dvd_Oorder__trans,axiom,
% 0.59/0.79 ! [Z: nat,X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 => ( ( dvd_dvd_nat @ Y_1 @ Z )
% 0.59/0.79 => ( dvd_dvd_nat @ X_1 @ Z ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_912_dvd_Oantisym,axiom,
% 0.59/0.79 ! [X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 => ( ( dvd_dvd_nat @ Y_1 @ X_1 )
% 0.59/0.79 => ( X_1 = Y_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_913_dvd__antisym,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ M @ N )
% 0.59/0.79 => ( ( dvd_dvd_nat @ N @ M )
% 0.59/0.79 => ( M = N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_914_dvd_Oord__le__eq__trans,axiom,
% 0.59/0.79 ! [C: nat,A: nat,B: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ A @ B )
% 0.59/0.79 => ( ( B = C )
% 0.59/0.79 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_915_dvd_Oord__eq__le__trans,axiom,
% 0.59/0.79 ! [C: nat,A: nat,B: nat] :
% 0.59/0.79 ( ( A = B )
% 0.59/0.79 => ( ( dvd_dvd_nat @ B @ C )
% 0.59/0.79 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_916_dvd_Ole__neq__trans,axiom,
% 0.59/0.79 ! [A: nat,B: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ A @ B )
% 0.59/0.79 => ( ( A != B )
% 0.59/0.79 => ( ( dvd_dvd_nat @ A @ B )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_917_dvd_Ole__imp__less__or__eq,axiom,
% 0.59/0.79 ! [X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 => ( ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Y_1 @ X_1 ) )
% 0.59/0.79 | ( X_1 = Y_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_918_dvd_Oantisym__conv,axiom,
% 0.59/0.79 ! [Y_1: nat,X_1: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ Y_1 @ X_1 )
% 0.59/0.79 => ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 <=> ( X_1 = Y_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_919_dvd_Oeq__refl,axiom,
% 0.59/0.79 ! [X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( X_1 = Y_1 )
% 0.59/0.79 => ( dvd_dvd_nat @ X_1 @ Y_1 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_920_dvd_Oneq__le__trans,axiom,
% 0.59/0.79 ! [A: nat,B: nat] :
% 0.59/0.79 ( ( A != B )
% 0.59/0.79 => ( ( dvd_dvd_nat @ A @ B )
% 0.59/0.79 => ( ( dvd_dvd_nat @ A @ B )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_921_dvd_Oless__le__not__le,axiom,
% 0.59/0.79 ! [X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Y_1 @ X_1 ) )
% 0.59/0.79 <=> ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Y_1 @ X_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_922_dvd_Oless__le,axiom,
% 0.59/0.79 ! [X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Y_1 @ X_1 ) )
% 0.59/0.79 <=> ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 & ( X_1 != Y_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_923_dvd_Ole__less,axiom,
% 0.59/0.79 ! [X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 <=> ( ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ Y_1 @ X_1 ) )
% 0.59/0.79 | ( X_1 = Y_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_924_dvd_Oeq__iff,axiom,
% 0.59/0.79 ! [X_1: nat,Y_1: nat] :
% 0.59/0.79 ( ( X_1 = Y_1 )
% 0.59/0.79 <=> ( ( dvd_dvd_nat @ X_1 @ Y_1 )
% 0.59/0.79 & ( dvd_dvd_nat @ Y_1 @ X_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_925_dvd_Oless__irrefl,axiom,
% 0.59/0.79 ! [X_1: nat] :
% 0.59/0.79 ~ ( ( dvd_dvd_nat @ X_1 @ X_1 )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ X_1 @ X_1 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_926_dvd__diff__nat,axiom,
% 0.59/0.79 ! [N: nat,K: nat,M: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ K @ M )
% 0.59/0.79 => ( ( dvd_dvd_nat @ K @ N )
% 0.59/0.79 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_927_nat__add__commute,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( plus_plus_nat @ M @ N )
% 0.59/0.79 = ( plus_plus_nat @ N @ M ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_928_nat__add__left__commute,axiom,
% 0.59/0.79 ! [X_1: nat,Y_1: nat,Z: nat] :
% 0.59/0.79 ( ( plus_plus_nat @ X_1 @ ( plus_plus_nat @ Y_1 @ Z ) )
% 0.59/0.79 = ( plus_plus_nat @ Y_1 @ ( plus_plus_nat @ X_1 @ Z ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_929_nat__add__assoc,axiom,
% 0.59/0.79 ! [M: nat,N: nat,K: nat] :
% 0.59/0.79 ( ( plus_plus_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 0.59/0.79 = ( plus_plus_nat @ M @ ( plus_plus_nat @ N @ K ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_930_nat__add__left__cancel,axiom,
% 0.59/0.79 ! [K: nat,M: nat,N: nat] :
% 0.59/0.79 ( ( ( plus_plus_nat @ K @ M )
% 0.59/0.79 = ( plus_plus_nat @ K @ N ) )
% 0.59/0.79 <=> ( M = N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_931_nat__add__right__cancel,axiom,
% 0.59/0.79 ! [M: nat,K: nat,N: nat] :
% 0.59/0.79 ( ( ( plus_plus_nat @ M @ K )
% 0.59/0.79 = ( plus_plus_nat @ N @ K ) )
% 0.59/0.79 <=> ( M = N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_932_diff__add__inverse2,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 0.59/0.79 = M ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_933_diff__add__inverse,axiom,
% 0.59/0.79 ! [N: nat,M: nat] :
% 0.59/0.79 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 0.59/0.79 = M ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_934_diff__diff__left,axiom,
% 0.59/0.79 ! [I_1: nat,J_1: nat,K: nat] :
% 0.59/0.79 ( ( minus_minus_nat @ ( minus_minus_nat @ I_1 @ J_1 ) @ K )
% 0.59/0.79 = ( minus_minus_nat @ I_1 @ ( plus_plus_nat @ J_1 @ K ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_935_Nat_Odiff__cancel,axiom,
% 0.59/0.79 ! [K: nat,M: nat,N: nat] :
% 0.59/0.79 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.59/0.79 = ( minus_minus_nat @ M @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_936_diff__cancel2,axiom,
% 0.59/0.79 ! [M: nat,K: nat,N: nat] :
% 0.59/0.79 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 0.59/0.79 = ( minus_minus_nat @ M @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_937_le__refl,axiom,
% 0.59/0.79 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_938_nat__le__linear,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ M @ N )
% 0.59/0.79 | ( ord_less_eq_nat @ N @ M ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_939_eq__imp__le,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( M = N )
% 0.59/0.79 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_940_le__trans,axiom,
% 0.59/0.79 ! [K: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ J_1 @ K )
% 0.59/0.79 => ( ord_less_eq_nat @ I_1 @ K ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_941_le__antisym,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ M @ N )
% 0.59/0.79 => ( ( ord_less_eq_nat @ N @ M )
% 0.59/0.79 => ( M = N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_942_Nat_Odiff__le__self,axiom,
% 0.59/0.79 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_943_diff__le__mono2,axiom,
% 0.59/0.79 ! [L: nat,M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ M @ N )
% 0.59/0.79 => ( ord_less_eq_nat @ ( minus_minus_nat @ L @ N ) @ ( minus_minus_nat @ L @ M ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_944_diff__le__mono,axiom,
% 0.59/0.79 ! [L: nat,M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ M @ N )
% 0.59/0.79 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L ) @ ( minus_minus_nat @ N @ L ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_945_diff__diff__cancel,axiom,
% 0.59/0.79 ! [I_1: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ I_1 @ N )
% 0.59/0.79 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I_1 ) )
% 0.59/0.79 = I_1 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_946_eq__diff__iff,axiom,
% 0.59/0.79 ! [N: nat,K: nat,M: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ K @ M )
% 0.59/0.79 => ( ( ord_less_eq_nat @ K @ N )
% 0.59/0.79 => ( ( ( minus_minus_nat @ M @ K )
% 0.59/0.79 = ( minus_minus_nat @ N @ K ) )
% 0.59/0.79 <=> ( M = N ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_947_Nat_Odiff__diff__eq,axiom,
% 0.59/0.79 ! [N: nat,K: nat,M: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ K @ M )
% 0.59/0.79 => ( ( ord_less_eq_nat @ K @ N )
% 0.59/0.79 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.59/0.79 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_948_le__diff__iff,axiom,
% 0.59/0.79 ! [N: nat,K: nat,M: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ K @ M )
% 0.59/0.79 => ( ( ord_less_eq_nat @ K @ N )
% 0.59/0.79 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.59/0.79 <=> ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_949_nat__mult__assoc,axiom,
% 0.59/0.79 ! [M: nat,N: nat,K: nat] :
% 0.59/0.79 ( ( times_times_nat @ ( times_times_nat @ M @ N ) @ K )
% 0.59/0.79 = ( times_times_nat @ M @ ( times_times_nat @ N @ K ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_950_nat__mult__commute,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( times_times_nat @ M @ N )
% 0.59/0.79 = ( times_times_nat @ N @ M ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_951_diff__mult__distrib,axiom,
% 0.59/0.79 ! [M: nat,N: nat,K: nat] :
% 0.59/0.79 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 0.59/0.79 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_952_diff__mult__distrib2,axiom,
% 0.59/0.79 ! [K: nat,M: nat,N: nat] :
% 0.59/0.79 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.59/0.79 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_953_gr0I,axiom,
% 0.59/0.79 ! [N: nat] :
% 0.59/0.79 ( ( N != zero_zero_nat )
% 0.59/0.79 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_954_gr__implies__not0,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_nat @ M @ N )
% 0.59/0.79 => ( N != zero_zero_nat ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_955_less__nat__zero__code,axiom,
% 0.59/0.79 ! [N: nat] :
% 0.59/0.79 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_956_neq0__conv,axiom,
% 0.59/0.79 ! [N: nat] :
% 0.59/0.79 ( ( N != zero_zero_nat )
% 0.59/0.79 <=> ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_957_not__less0,axiom,
% 0.59/0.79 ! [N: nat] :
% 0.59/0.79 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_958_diff__less,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.59/0.79 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.59/0.79 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_959_zero__less__diff,axiom,
% 0.59/0.79 ! [N: nat,M: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 0.59/0.79 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_960_add__eq__self__zero,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ( plus_plus_nat @ M @ N )
% 0.59/0.79 = M )
% 0.59/0.79 => ( N = zero_zero_nat ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_961_add__is__0,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ( plus_plus_nat @ M @ N )
% 0.59/0.79 = zero_zero_nat )
% 0.59/0.79 <=> ( ( M = zero_zero_nat )
% 0.59/0.79 & ( N = zero_zero_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_962_Nat_Oadd__0__right,axiom,
% 0.59/0.79 ! [M: nat] :
% 0.59/0.79 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 0.59/0.79 = M ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_963_plus__nat_Oadd__0,axiom,
% 0.59/0.79 ! [N: nat] :
% 0.59/0.79 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 0.59/0.79 = N ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_964_diff__add__0,axiom,
% 0.59/0.79 ! [N: nat,M: nat] :
% 0.59/0.79 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 0.59/0.79 = zero_zero_nat ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_965_le__0__eq,axiom,
% 0.59/0.79 ! [N: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 0.59/0.79 <=> ( N = zero_zero_nat ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_966_less__eq__nat_Osimps_I1_J,axiom,
% 0.59/0.79 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_967_diff__is__0__eq_H,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ M @ N )
% 0.59/0.79 => ( ( minus_minus_nat @ M @ N )
% 0.59/0.79 = zero_zero_nat ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_968_diff__is__0__eq,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ( minus_minus_nat @ M @ N )
% 0.59/0.79 = zero_zero_nat )
% 0.59/0.79 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_969_mult__0,axiom,
% 0.59/0.79 ! [N: nat] :
% 0.59/0.79 ( ( times_times_nat @ zero_zero_nat @ N )
% 0.59/0.79 = zero_zero_nat ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_970_mult__0__right,axiom,
% 0.59/0.79 ! [M: nat] :
% 0.59/0.79 ( ( times_times_nat @ M @ zero_zero_nat )
% 0.59/0.79 = zero_zero_nat ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_971_mult__is__0,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ( times_times_nat @ M @ N )
% 0.59/0.79 = zero_zero_nat )
% 0.59/0.79 <=> ( ( M = zero_zero_nat )
% 0.59/0.79 | ( N = zero_zero_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_972_mult__cancel1,axiom,
% 0.59/0.79 ! [K: nat,M: nat,N: nat] :
% 0.59/0.79 ( ( ( times_times_nat @ K @ M )
% 0.59/0.79 = ( times_times_nat @ K @ N ) )
% 0.59/0.79 <=> ( ( M = N )
% 0.59/0.79 | ( K = zero_zero_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_973_mult__cancel2,axiom,
% 0.59/0.79 ! [M: nat,K: nat,N: nat] :
% 0.59/0.79 ( ( ( times_times_nat @ M @ K )
% 0.59/0.79 = ( times_times_nat @ N @ K ) )
% 0.59/0.79 <=> ( ( M = N )
% 0.59/0.79 | ( K = zero_zero_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_974_not__add__less1,axiom,
% 0.59/0.79 ! [I_1: nat,J_1: nat] :
% 0.59/0.79 ~ ( ord_less_nat @ ( plus_plus_nat @ I_1 @ J_1 ) @ I_1 ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_975_not__add__less2,axiom,
% 0.59/0.79 ! [J_1: nat,I_1: nat] :
% 0.59/0.79 ~ ( ord_less_nat @ ( plus_plus_nat @ J_1 @ I_1 ) @ I_1 ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_976_nat__add__left__cancel__less,axiom,
% 0.59/0.79 ! [K: nat,M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.59/0.79 <=> ( ord_less_nat @ M @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_977_trans__less__add1,axiom,
% 0.59/0.79 ! [M: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ord_less_nat @ I_1 @ ( plus_plus_nat @ J_1 @ M ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_978_trans__less__add2,axiom,
% 0.59/0.79 ! [M: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ord_less_nat @ I_1 @ ( plus_plus_nat @ M @ J_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_979_add__less__mono1,axiom,
% 0.59/0.79 ! [K: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ord_less_nat @ ( plus_plus_nat @ I_1 @ K ) @ ( plus_plus_nat @ J_1 @ K ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_980_add__less__mono,axiom,
% 0.59/0.79 ! [K: nat,L: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ( ord_less_nat @ K @ L )
% 0.59/0.79 => ( ord_less_nat @ ( plus_plus_nat @ I_1 @ K ) @ ( plus_plus_nat @ J_1 @ L ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_981_less__add__eq__less,axiom,
% 0.59/0.79 ! [M: nat,N: nat,K: nat,L: nat] :
% 0.59/0.79 ( ( ord_less_nat @ K @ L )
% 0.59/0.79 => ( ( ( plus_plus_nat @ M @ L )
% 0.59/0.79 = ( plus_plus_nat @ K @ N ) )
% 0.59/0.79 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_982_add__lessD1,axiom,
% 0.59/0.79 ! [I_1: nat,J_1: nat,K: nat] :
% 0.59/0.79 ( ( ord_less_nat @ ( plus_plus_nat @ I_1 @ J_1 ) @ K )
% 0.59/0.79 => ( ord_less_nat @ I_1 @ K ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_983_add__diff__inverse,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ~ ( ord_less_nat @ M @ N )
% 0.59/0.79 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 0.59/0.79 = M ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_984_less__diff__conv,axiom,
% 0.59/0.79 ! [I_1: nat,J_1: nat,K: nat] :
% 0.59/0.79 ( ( ord_less_nat @ I_1 @ ( minus_minus_nat @ J_1 @ K ) )
% 0.59/0.79 <=> ( ord_less_nat @ ( plus_plus_nat @ I_1 @ K ) @ J_1 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_985_nat__less__le,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_nat @ M @ N )
% 0.59/0.79 <=> ( ( ord_less_eq_nat @ M @ N )
% 0.59/0.79 & ( M != N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_986_le__eq__less__or__eq,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ M @ N )
% 0.59/0.79 <=> ( ( ord_less_nat @ M @ N )
% 0.59/0.79 | ( M = N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_987_less__imp__le__nat,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_nat @ M @ N )
% 0.59/0.79 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_988_le__neq__implies__less,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ M @ N )
% 0.59/0.79 => ( ( M != N )
% 0.59/0.79 => ( ord_less_nat @ M @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_989_less__or__eq__imp__le,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ( ord_less_nat @ M @ N )
% 0.59/0.79 | ( M = N ) )
% 0.59/0.79 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_990_less__diff__iff,axiom,
% 0.59/0.79 ! [N: nat,K: nat,M: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ K @ M )
% 0.59/0.79 => ( ( ord_less_eq_nat @ K @ N )
% 0.59/0.79 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 0.59/0.79 <=> ( ord_less_nat @ M @ N ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_991_diff__less__mono,axiom,
% 0.59/0.79 ! [C: nat,A: nat,B: nat] :
% 0.59/0.79 ( ( ord_less_nat @ A @ B )
% 0.59/0.79 => ( ( ord_less_eq_nat @ C @ A )
% 0.59/0.79 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_992_dvd__reduce,axiom,
% 0.59/0.79 ! [K: nat,N: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ K @ ( plus_plus_nat @ N @ K ) )
% 0.59/0.79 <=> ( dvd_dvd_nat @ K @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_993_dvd__diffD1,axiom,
% 0.59/0.79 ! [K: nat,M: nat,N: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.59/0.79 => ( ( dvd_dvd_nat @ K @ M )
% 0.59/0.79 => ( ( ord_less_eq_nat @ N @ M )
% 0.59/0.79 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_994_dvd__diffD,axiom,
% 0.59/0.79 ! [K: nat,M: nat,N: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 0.59/0.79 => ( ( dvd_dvd_nat @ K @ N )
% 0.59/0.79 => ( ( ord_less_eq_nat @ N @ M )
% 0.59/0.79 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_995_le__add2,axiom,
% 0.59/0.79 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_996_le__add1,axiom,
% 0.59/0.79 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_997_le__iff__add,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ M @ N )
% 0.59/0.79 <=> ? [K_1: nat] :
% 0.59/0.79 ( N
% 0.59/0.79 = ( plus_plus_nat @ M @ K_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_998_nat__add__left__cancel__le,axiom,
% 0.59/0.79 ! [K: nat,M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 0.59/0.79 <=> ( ord_less_eq_nat @ M @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_999_trans__le__add1,axiom,
% 0.59/0.79 ! [M: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ord_less_eq_nat @ I_1 @ ( plus_plus_nat @ J_1 @ M ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1000_trans__le__add2,axiom,
% 0.59/0.79 ! [M: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ord_less_eq_nat @ I_1 @ ( plus_plus_nat @ M @ J_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1001_add__le__mono1,axiom,
% 0.59/0.79 ! [K: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ord_less_eq_nat @ ( plus_plus_nat @ I_1 @ K ) @ ( plus_plus_nat @ J_1 @ K ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1002_add__le__mono,axiom,
% 0.59/0.79 ! [K: nat,L: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ K @ L )
% 0.59/0.79 => ( ord_less_eq_nat @ ( plus_plus_nat @ I_1 @ K ) @ ( plus_plus_nat @ J_1 @ L ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1003_add__leD2,axiom,
% 0.59/0.79 ! [M: nat,K: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.59/0.79 => ( ord_less_eq_nat @ K @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1004_add__leD1,axiom,
% 0.59/0.79 ! [M: nat,K: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.59/0.79 => ( ord_less_eq_nat @ M @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1005_add__leE,axiom,
% 0.59/0.79 ! [M: nat,K: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 0.59/0.79 => ~ ( ( ord_less_eq_nat @ M @ N )
% 0.59/0.79 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1006_diff__diff__right,axiom,
% 0.59/0.79 ! [I_1: nat,K: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.59/0.79 => ( ( minus_minus_nat @ I_1 @ ( minus_minus_nat @ J_1 @ K ) )
% 0.59/0.79 = ( minus_minus_nat @ ( plus_plus_nat @ I_1 @ K ) @ J_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1007_le__diff__conv,axiom,
% 0.59/0.79 ! [J_1: nat,K: nat,I_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J_1 @ K ) @ I_1 )
% 0.59/0.79 <=> ( ord_less_eq_nat @ J_1 @ ( plus_plus_nat @ I_1 @ K ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1008_le__add__diff,axiom,
% 0.59/0.79 ! [M: nat,K: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ K @ N )
% 0.59/0.79 => ( ord_less_eq_nat @ M @ ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ K ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1009_le__add__diff__inverse,axiom,
% 0.59/0.79 ! [N: nat,M: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ N @ M )
% 0.59/0.79 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 0.59/0.79 = M ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1010_add__diff__assoc,axiom,
% 0.59/0.79 ! [I_1: nat,K: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.59/0.79 => ( ( plus_plus_nat @ I_1 @ ( minus_minus_nat @ J_1 @ K ) )
% 0.59/0.79 = ( minus_minus_nat @ ( plus_plus_nat @ I_1 @ J_1 ) @ K ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1011_le__diff__conv2,axiom,
% 0.59/0.79 ! [I_1: nat,K: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ I_1 @ ( minus_minus_nat @ J_1 @ K ) )
% 0.59/0.79 <=> ( ord_less_eq_nat @ ( plus_plus_nat @ I_1 @ K ) @ J_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1012_le__add__diff__inverse2,axiom,
% 0.59/0.79 ! [N: nat,M: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ N @ M )
% 0.59/0.79 => ( ( plus_plus_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 0.59/0.79 = M ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1013_le__imp__diff__is__add,axiom,
% 0.59/0.79 ! [K: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ( ( minus_minus_nat @ J_1 @ I_1 )
% 0.59/0.79 = K )
% 0.59/0.79 <=> ( J_1
% 0.59/0.79 = ( plus_plus_nat @ K @ I_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1014_diff__add__assoc,axiom,
% 0.59/0.79 ! [I_1: nat,K: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.59/0.79 => ( ( minus_minus_nat @ ( plus_plus_nat @ I_1 @ J_1 ) @ K )
% 0.59/0.79 = ( plus_plus_nat @ I_1 @ ( minus_minus_nat @ J_1 @ K ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1015_add__diff__assoc2,axiom,
% 0.59/0.79 ! [I_1: nat,K: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.59/0.79 => ( ( plus_plus_nat @ ( minus_minus_nat @ J_1 @ K ) @ I_1 )
% 0.59/0.79 = ( minus_minus_nat @ ( plus_plus_nat @ J_1 @ I_1 ) @ K ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1016_diff__add__assoc2,axiom,
% 0.59/0.79 ! [I_1: nat,K: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ K @ J_1 )
% 0.59/0.79 => ( ( minus_minus_nat @ ( plus_plus_nat @ J_1 @ I_1 ) @ K )
% 0.59/0.79 = ( plus_plus_nat @ ( minus_minus_nat @ J_1 @ K ) @ I_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1017_add__mult__distrib,axiom,
% 0.59/0.79 ! [M: nat,N: nat,K: nat] :
% 0.59/0.79 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 0.59/0.79 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1018_add__mult__distrib2,axiom,
% 0.59/0.79 ! [K: nat,M: nat,N: nat] :
% 0.59/0.79 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 0.59/0.79 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1019_nat__dvd__1__iff__1,axiom,
% 0.59/0.79 ! [M: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 0.59/0.79 <=> ( M = one_one_nat ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1020_mult__le__mono,axiom,
% 0.59/0.79 ! [K: nat,L: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ K @ L )
% 0.59/0.79 => ( ord_less_eq_nat @ ( times_times_nat @ I_1 @ K ) @ ( times_times_nat @ J_1 @ L ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1021_mult__le__mono2,axiom,
% 0.59/0.79 ! [K: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I_1 ) @ ( times_times_nat @ K @ J_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1022_mult__le__mono1,axiom,
% 0.59/0.79 ! [K: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ord_less_eq_nat @ ( times_times_nat @ I_1 @ K ) @ ( times_times_nat @ J_1 @ K ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1023_le__cube,axiom,
% 0.59/0.79 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1024_le__square,axiom,
% 0.59/0.79 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1025_nat__mult__eq__1__iff,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ( times_times_nat @ M @ N )
% 0.59/0.79 = one_one_nat )
% 0.59/0.79 <=> ( ( M = one_one_nat )
% 0.59/0.79 & ( N = one_one_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1026_nat__mult__1__right,axiom,
% 0.59/0.79 ! [N: nat] :
% 0.59/0.79 ( ( times_times_nat @ N @ one_one_nat )
% 0.59/0.79 = N ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1027_nat__1__eq__mult__iff,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( one_one_nat
% 0.59/0.79 = ( times_times_nat @ M @ N ) )
% 0.59/0.79 <=> ( ( M = one_one_nat )
% 0.59/0.79 & ( N = one_one_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1028_nat__mult__1,axiom,
% 0.59/0.79 ! [N: nat] :
% 0.59/0.79 ( ( times_times_nat @ one_one_nat @ N )
% 0.59/0.79 = N ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1029_nat__dvd__not__less,axiom,
% 0.59/0.79 ! [N: nat,M: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.59/0.79 => ( ( ord_less_nat @ M @ N )
% 0.59/0.79 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1030_add__gr__0,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 0.59/0.79 <=> ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.59/0.79 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1031_nat__diff__split,axiom,
% 0.59/0.79 ! [P_1: nat > $o,A: nat,B: nat] :
% 0.59/0.79 ( ( P_1 @ ( minus_minus_nat @ A @ B ) )
% 0.59/0.79 <=> ( ( ( ord_less_nat @ A @ B )
% 0.59/0.79 => ( P_1 @ zero_zero_nat ) )
% 0.59/0.79 & ! [D_2: nat] :
% 0.59/0.79 ( ( A
% 0.59/0.79 = ( plus_plus_nat @ B @ D_2 ) )
% 0.59/0.79 => ( P_1 @ D_2 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1032_nat__diff__split__asm,axiom,
% 0.59/0.79 ! [P_1: nat > $o,A: nat,B: nat] :
% 0.59/0.79 ( ( P_1 @ ( minus_minus_nat @ A @ B ) )
% 0.59/0.79 <=> ~ ( ( ( ord_less_nat @ A @ B )
% 0.59/0.79 & ~ ( P_1 @ zero_zero_nat ) )
% 0.59/0.79 | ? [D_2: nat] :
% 0.59/0.79 ( ( A
% 0.59/0.79 = ( plus_plus_nat @ B @ D_2 ) )
% 0.59/0.79 & ~ ( P_1 @ D_2 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1033_mult__less__mono2,axiom,
% 0.59/0.79 ! [K: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.59/0.79 => ( ord_less_nat @ ( times_times_nat @ K @ I_1 ) @ ( times_times_nat @ K @ J_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1034_mult__less__mono1,axiom,
% 0.59/0.79 ! [K: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.59/0.79 => ( ord_less_nat @ ( times_times_nat @ I_1 @ K ) @ ( times_times_nat @ J_1 @ K ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1035_mult__less__cancel2,axiom,
% 0.59/0.79 ! [M: nat,K: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.59/0.79 <=> ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.59/0.79 & ( ord_less_nat @ M @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1036_mult__less__cancel1,axiom,
% 0.59/0.79 ! [K: nat,M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.59/0.79 <=> ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.59/0.79 & ( ord_less_nat @ M @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1037_nat__0__less__mult__iff,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 0.59/0.79 <=> ( ( ord_less_nat @ zero_zero_nat @ M )
% 0.59/0.79 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1038_mult__eq__self__implies__10,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( M
% 0.59/0.79 = ( times_times_nat @ M @ N ) )
% 0.59/0.79 => ( ( N = one_one_nat )
% 0.59/0.79 | ( M = zero_zero_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1039_dvd__imp__le,axiom,
% 0.59/0.79 ! [K: nat,N: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ K @ N )
% 0.59/0.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.59/0.79 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1040_dvd__mult__cancel,axiom,
% 0.59/0.79 ! [K: nat,M: nat,N: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.59/0.79 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.59/0.79 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1041_mult__le__cancel1,axiom,
% 0.59/0.79 ! [K: nat,M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.59/0.79 <=> ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.59/0.79 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1042_mult__le__cancel2,axiom,
% 0.59/0.79 ! [M: nat,K: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 0.59/0.79 <=> ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.59/0.79 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1043_ex__least__nat__less,axiom,
% 0.59/0.79 ! [N: nat,P_1: nat > $o] :
% 0.59/0.79 ( ~ ( P_1 @ zero_zero_nat )
% 0.59/0.79 => ( ( P_1 @ N )
% 0.59/0.79 => ? [K_1: nat] :
% 0.59/0.79 ( ( ord_less_nat @ K_1 @ N )
% 0.59/0.79 & ! [I: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ I @ K_1 )
% 0.59/0.79 => ~ ( P_1 @ I ) )
% 0.59/0.79 & ( P_1 @ ( plus_plus_nat @ K_1 @ one_one_nat ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1044_nat__less__add__iff2,axiom,
% 0.59/0.79 ! [U: nat,M: nat,N: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J_1 @ U ) @ N ) )
% 0.59/0.79 <=> ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J_1 @ I_1 ) @ U ) @ N ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1045_nat__mult__eq__cancel__disj,axiom,
% 0.59/0.79 ! [K: nat,M: nat,N: nat] :
% 0.59/0.79 ( ( ( times_times_nat @ K @ M )
% 0.59/0.79 = ( times_times_nat @ K @ N ) )
% 0.59/0.79 <=> ( ( K = zero_zero_nat )
% 0.59/0.79 | ( M = N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1046_left__add__mult__distrib,axiom,
% 0.59/0.79 ! [I_1: nat,U: nat,J_1: nat,K: nat] :
% 0.59/0.79 ( ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J_1 @ U ) @ K ) )
% 0.59/0.79 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I_1 @ J_1 ) @ U ) @ K ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1047_nat__mult__eq__cancel1,axiom,
% 0.59/0.79 ! [M: nat,N: nat,K: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.59/0.79 => ( ( ( times_times_nat @ K @ M )
% 0.59/0.79 = ( times_times_nat @ K @ N ) )
% 0.59/0.79 <=> ( M = N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1048_nat__mult__less__cancel1,axiom,
% 0.59/0.79 ! [M: nat,N: nat,K: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.59/0.79 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.59/0.79 <=> ( ord_less_nat @ M @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1049_nat__mult__dvd__cancel__disj,axiom,
% 0.59/0.79 ! [K: nat,M: nat,N: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.59/0.79 <=> ( ( K = zero_zero_nat )
% 0.59/0.79 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1050_nat__mult__dvd__cancel1,axiom,
% 0.59/0.79 ! [M: nat,N: nat,K: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.59/0.79 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.59/0.79 <=> ( dvd_dvd_nat @ M @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1051_nat__mult__le__cancel1,axiom,
% 0.59/0.79 ! [M: nat,N: nat,K: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.59/0.79 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 0.59/0.79 <=> ( ord_less_eq_nat @ M @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1052_nat__le__add__iff1,axiom,
% 0.59/0.79 ! [U: nat,M: nat,N: nat,J_1: nat,I_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ J_1 @ I_1 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J_1 @ U ) @ N ) )
% 0.59/0.79 <=> ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I_1 @ J_1 ) @ U ) @ M ) @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1053_nat__diff__add__eq1,axiom,
% 0.59/0.79 ! [U: nat,M: nat,N: nat,J_1: nat,I_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ J_1 @ I_1 )
% 0.59/0.79 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J_1 @ U ) @ N ) )
% 0.59/0.79 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I_1 @ J_1 ) @ U ) @ M ) @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1054_nat__eq__add__iff1,axiom,
% 0.59/0.79 ! [U: nat,M: nat,N: nat,J_1: nat,I_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ J_1 @ I_1 )
% 0.59/0.79 => ( ( ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M )
% 0.59/0.79 = ( plus_plus_nat @ ( times_times_nat @ J_1 @ U ) @ N ) )
% 0.59/0.79 <=> ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I_1 @ J_1 ) @ U ) @ M )
% 0.59/0.79 = N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1055_nat__le__add__iff2,axiom,
% 0.59/0.79 ! [U: nat,M: nat,N: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J_1 @ U ) @ N ) )
% 0.59/0.79 <=> ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J_1 @ I_1 ) @ U ) @ N ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1056_nat__diff__add__eq2,axiom,
% 0.59/0.79 ! [U: nat,M: nat,N: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J_1 @ U ) @ N ) )
% 0.59/0.79 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J_1 @ I_1 ) @ U ) @ N ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1057_nat__eq__add__iff2,axiom,
% 0.59/0.79 ! [U: nat,M: nat,N: nat,I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ I_1 @ J_1 )
% 0.59/0.79 => ( ( ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M )
% 0.59/0.79 = ( plus_plus_nat @ ( times_times_nat @ J_1 @ U ) @ N ) )
% 0.59/0.79 <=> ( M
% 0.59/0.79 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J_1 @ I_1 ) @ U ) @ N ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1058_nat__less__add__iff1,axiom,
% 0.59/0.79 ! [U: nat,M: nat,N: nat,J_1: nat,I_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ J_1 @ I_1 )
% 0.59/0.79 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I_1 @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J_1 @ U ) @ N ) )
% 0.59/0.79 <=> ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I_1 @ J_1 ) @ U ) @ M ) @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1059_number__of1,axiom,
% 0.59/0.79 ! [N: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ N ) )
% 0.59/0.79 => ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit0 @ N ) ) )
% 0.59/0.79 & ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ ( bit1 @ N ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1060_is__sum2sq__def,axiom,
% 0.59/0.79 ! [X_1: int] :
% 0.59/0.79 ( ( twoSqu919416604sum2sq @ X_1 )
% 0.59/0.79 <=> ? [A_2: int,B_2: int] :
% 0.59/0.79 ( ( twoSqu2057625106sum2sq @ ( product_Pair_int_int @ A_2 @ B_2 ) )
% 0.59/0.79 = X_1 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1061_imp__le__cong,axiom,
% 0.59/0.79 ! [P_3: $o,P_1: $o,X_1: int] :
% 0.59/0.79 ( ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.59/0.79 => ( P_1
% 0.59/0.79 <=> P_3 ) )
% 0.59/0.79 => ( ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.59/0.79 => P_1 )
% 0.59/0.79 <=> ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.59/0.79 => P_3 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1062_conj__le__cong,axiom,
% 0.59/0.79 ! [P_3: $o,P_1: $o,X_1: int] :
% 0.59/0.79 ( ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.59/0.79 => ( P_1
% 0.59/0.79 <=> P_3 ) )
% 0.59/0.79 => ( ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.59/0.79 & P_1 )
% 0.59/0.79 <=> ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.59/0.79 & P_3 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1063_zdvd__mono,axiom,
% 0.59/0.79 ! [M: int,T: int,K: int] :
% 0.59/0.79 ( ( K != zero_zero_int )
% 0.59/0.79 => ( ( dvd_dvd_int @ M @ T )
% 0.59/0.79 <=> ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1064_number__of2,axiom,
% 0.59/0.79 ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ pls ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1065_decr__mult__lemma,axiom,
% 0.59/0.79 ! [K: int,P_1: int > $o,D: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ D )
% 0.59/0.79 => ( ! [X: int] :
% 0.59/0.79 ( ( P_1 @ X )
% 0.59/0.79 => ( P_1 @ ( minus_minus_int @ X @ D ) ) )
% 0.59/0.79 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.59/0.79 => ! [X: int] :
% 0.59/0.79 ( ( P_1 @ X )
% 0.59/0.79 => ( P_1 @ ( minus_minus_int @ X @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1066_incr__mult__lemma,axiom,
% 0.59/0.79 ! [K: int,P_1: int > $o,D: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ D )
% 0.59/0.79 => ( ! [X: int] :
% 0.59/0.79 ( ( P_1 @ X )
% 0.59/0.79 => ( P_1 @ ( plus_plus_int @ X @ D ) ) )
% 0.59/0.79 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 0.59/0.79 => ! [X: int] :
% 0.59/0.79 ( ( P_1 @ X )
% 0.59/0.79 => ( P_1 @ ( plus_plus_int @ X @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1067_zprime__factor__exists,axiom,
% 0.59/0.79 ! [A: int] :
% 0.59/0.79 ( ( ord_less_int @ one_one_int @ A )
% 0.59/0.79 => ? [P_2: int] :
% 0.59/0.79 ( ( zprime @ P_2 )
% 0.59/0.79 & ( dvd_dvd_int @ P_2 @ A ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1068_zcong__zless__unique,axiom,
% 0.59/0.79 ! [A: int,M: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ M )
% 0.59/0.79 => ? [X: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 0.59/0.79 & ( ord_less_int @ X @ M )
% 0.59/0.79 & ( zcong @ A @ X @ M )
% 0.59/0.79 & ! [Y: int] :
% 0.59/0.79 ( ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 0.59/0.79 & ( ord_less_int @ Y @ M )
% 0.59/0.79 & ( zcong @ A @ Y @ M ) )
% 0.59/0.79 => ( Y = X ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1069_norR__mem__unique__aux,axiom,
% 0.59/0.79 ! [A: int,B: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ B @ one_one_int ) )
% 0.59/0.79 => ( ord_less_int @ A @ B ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1070_Wilson__Russ,axiom,
% 0.59/0.79 ! [P: int] :
% 0.59/0.79 ( ( zprime @ P )
% 0.59/0.79 => ( zcong @ ( zfact @ ( minus_minus_int @ P @ one_one_int ) ) @ ( number_number_of_int @ min ) @ P ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1071_zfact_Osimps,axiom,
% 0.59/0.79 ! [N: int] :
% 0.59/0.79 ( ( ( ord_less_eq_int @ N @ zero_zero_int )
% 0.59/0.79 => ( ( zfact @ N )
% 0.59/0.79 = one_one_int ) )
% 0.59/0.79 & ( ~ ( ord_less_eq_int @ N @ zero_zero_int )
% 0.59/0.79 => ( ( zfact @ N )
% 0.59/0.79 = ( times_times_int @ N @ ( zfact @ ( minus_minus_int @ N @ one_one_int ) ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1072_inv__inv,axiom,
% 0.59/0.79 ! [A: int,P: int] :
% 0.59/0.79 ( ( zprime @ P )
% 0.59/0.79 => ( ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ P )
% 0.59/0.79 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.59/0.79 => ( ( ord_less_int @ A @ P )
% 0.59/0.79 => ( ( inv @ P @ ( inv @ P @ A ) )
% 0.59/0.79 = A ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1073_MultInvPair__distinct,axiom,
% 0.59/0.79 ! [J_1: int,A: int,P: int] :
% 0.59/0.79 ( ( zprime @ P )
% 0.59/0.79 => ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
% 0.59/0.79 => ( ~ ( zcong @ A @ zero_zero_int @ P )
% 0.59/0.79 => ( ~ ( zcong @ J_1 @ zero_zero_int @ P )
% 0.59/0.79 => ( ~ ( quadRes @ P @ A )
% 0.59/0.79 => ~ ( zcong @ J_1 @ ( times_times_int @ A @ ( multInv @ P @ J_1 ) ) @ P ) ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1074_aux______3,axiom,
% 0.59/0.79 ! [J_1: int,K: int,A: int,P: int] :
% 0.59/0.79 ( ( zcong @ ( times_times_int @ J_1 @ K ) @ A @ P )
% 0.59/0.79 => ( zcong @ ( times_times_int @ ( times_times_int @ ( multInv @ P @ J_1 ) @ J_1 ) @ K ) @ ( times_times_int @ ( multInv @ P @ J_1 ) @ A ) @ P ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1075_aux______1,axiom,
% 0.59/0.79 ! [J_1: int,A: int,P: int,K: int] :
% 0.59/0.79 ( ( zcong @ J_1 @ ( times_times_int @ A @ ( multInv @ P @ K ) ) @ P )
% 0.59/0.79 => ( zcong @ ( times_times_int @ J_1 @ K ) @ ( times_times_int @ ( times_times_int @ A @ ( multInv @ P @ K ) ) @ K ) @ P ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1076_inv__distinct,axiom,
% 0.59/0.79 ! [A: int,P: int] :
% 0.59/0.79 ( ( zprime @ P )
% 0.59/0.79 => ( ( ord_less_int @ one_one_int @ A )
% 0.59/0.79 => ( ( ord_less_int @ A @ ( minus_minus_int @ P @ one_one_int ) )
% 0.59/0.79 => ( A
% 0.59/0.79 != ( inv @ P @ A ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1077_inv__not__1,axiom,
% 0.59/0.79 ! [A: int,P: int] :
% 0.59/0.79 ( ( zprime @ P )
% 0.59/0.79 => ( ( ord_less_int @ one_one_int @ A )
% 0.59/0.79 => ( ( ord_less_int @ A @ ( minus_minus_int @ P @ one_one_int ) )
% 0.59/0.79 => ( ( inv @ P @ A )
% 0.59/0.79 != one_one_int ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1078_inv__not__p__minus__1,axiom,
% 0.59/0.79 ! [A: int,P: int] :
% 0.59/0.79 ( ( zprime @ P )
% 0.59/0.79 => ( ( ord_less_int @ one_one_int @ A )
% 0.59/0.79 => ( ( ord_less_int @ A @ ( minus_minus_int @ P @ one_one_int ) )
% 0.59/0.79 => ( ( inv @ P @ A )
% 0.59/0.79 != ( minus_minus_int @ P @ one_one_int ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1079_inv__g__1,axiom,
% 0.59/0.79 ! [A: int,P: int] :
% 0.59/0.79 ( ( zprime @ P )
% 0.59/0.79 => ( ( ord_less_int @ one_one_int @ A )
% 0.59/0.79 => ( ( ord_less_int @ A @ ( minus_minus_int @ P @ one_one_int ) )
% 0.59/0.79 => ( ord_less_int @ one_one_int @ ( inv @ P @ A ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1080_inv__less__p__minus__1,axiom,
% 0.59/0.79 ! [A: int,P: int] :
% 0.59/0.79 ( ( zprime @ P )
% 0.59/0.79 => ( ( ord_less_int @ one_one_int @ A )
% 0.59/0.79 => ( ( ord_less_int @ A @ ( minus_minus_int @ P @ one_one_int ) )
% 0.59/0.79 => ( ord_less_int @ ( inv @ P @ A ) @ ( minus_minus_int @ P @ one_one_int ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1081_MultInv__prop1,axiom,
% 0.59/0.79 ! [X_1: int,Y_1: int,P: int] :
% 0.59/0.79 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
% 0.59/0.79 => ( ( zcong @ X_1 @ Y_1 @ P )
% 0.59/0.79 => ( zcong @ ( multInv @ P @ X_1 ) @ ( multInv @ P @ Y_1 ) @ P ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1082_inv__not__0,axiom,
% 0.59/0.79 ! [A: int,P: int] :
% 0.59/0.79 ( ( zprime @ P )
% 0.59/0.79 => ( ( ord_less_int @ one_one_int @ A )
% 0.59/0.79 => ( ( ord_less_int @ A @ ( minus_minus_int @ P @ one_one_int ) )
% 0.59/0.79 => ( ( inv @ P @ A )
% 0.59/0.79 != zero_zero_int ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1083_MultInv__zcong__prop1,axiom,
% 0.59/0.79 ! [A: int,J_1: int,K: int,P: int] :
% 0.59/0.79 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
% 0.59/0.79 => ( ( zcong @ J_1 @ K @ P )
% 0.59/0.79 => ( zcong @ ( times_times_int @ A @ ( multInv @ P @ J_1 ) ) @ ( times_times_int @ A @ ( multInv @ P @ K ) ) @ P ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1084_MultInv__prop5,axiom,
% 0.59/0.79 ! [Y_1: int,X_1: int,P: int] :
% 0.59/0.79 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
% 0.59/0.79 => ( ( zprime @ P )
% 0.59/0.79 => ( ~ ( zcong @ X_1 @ zero_zero_int @ P )
% 0.59/0.79 => ( ~ ( zcong @ Y_1 @ zero_zero_int @ P )
% 0.59/0.79 => ( ( zcong @ ( multInv @ P @ X_1 ) @ ( multInv @ P @ Y_1 ) @ P )
% 0.59/0.79 => ( zcong @ X_1 @ Y_1 @ P ) ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1085_MultInv__prop4,axiom,
% 0.59/0.79 ! [X_1: int,P: int] :
% 0.59/0.79 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
% 0.59/0.79 => ( ( zprime @ P )
% 0.59/0.79 => ( ~ ( zcong @ X_1 @ zero_zero_int @ P )
% 0.59/0.79 => ( zcong @ ( multInv @ P @ ( multInv @ P @ X_1 ) ) @ X_1 @ P ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1086_MultInv__prop3,axiom,
% 0.59/0.79 ! [X_1: int,P: int] :
% 0.59/0.79 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
% 0.59/0.79 => ( ( zprime @ P )
% 0.59/0.79 => ( ~ ( zcong @ X_1 @ zero_zero_int @ P )
% 0.59/0.79 => ~ ( zcong @ ( multInv @ P @ X_1 ) @ zero_zero_int @ P ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1087_inv__is__inv,axiom,
% 0.59/0.79 ! [A: int,P: int] :
% 0.59/0.79 ( ( zprime @ P )
% 0.59/0.79 => ( ( ord_less_int @ zero_zero_int @ A )
% 0.59/0.79 => ( ( ord_less_int @ A @ P )
% 0.59/0.79 => ( zcong @ ( times_times_int @ A @ ( inv @ P @ A ) ) @ one_one_int @ P ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1088_aux______4,axiom,
% 0.59/0.79 ! [K: int,A: int,J_1: int,P: int] :
% 0.59/0.79 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
% 0.59/0.79 => ( ( zprime @ P )
% 0.59/0.79 => ( ~ ( zcong @ J_1 @ zero_zero_int @ P )
% 0.59/0.79 => ( ( zcong @ ( times_times_int @ ( times_times_int @ ( multInv @ P @ J_1 ) @ J_1 ) @ K ) @ ( times_times_int @ ( multInv @ P @ J_1 ) @ A ) @ P )
% 0.59/0.79 => ( zcong @ K @ ( times_times_int @ A @ ( multInv @ P @ J_1 ) ) @ P ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1089_aux______2,axiom,
% 0.59/0.79 ! [J_1: int,A: int,K: int,P: int] :
% 0.59/0.79 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
% 0.59/0.79 => ( ( zprime @ P )
% 0.59/0.79 => ( ~ ( zcong @ K @ zero_zero_int @ P )
% 0.59/0.79 => ( ( zcong @ ( times_times_int @ J_1 @ K ) @ ( times_times_int @ ( times_times_int @ A @ ( multInv @ P @ K ) ) @ K ) @ P )
% 0.59/0.79 => ( zcong @ ( times_times_int @ J_1 @ K ) @ A @ P ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1090_MultInv__zcong__prop2,axiom,
% 0.59/0.79 ! [A: int,J_1: int,K: int,P: int] :
% 0.59/0.79 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
% 0.59/0.79 => ( ( zprime @ P )
% 0.59/0.79 => ( ~ ( zcong @ K @ zero_zero_int @ P )
% 0.59/0.79 => ( ~ ( zcong @ J_1 @ zero_zero_int @ P )
% 0.59/0.79 => ( ( zcong @ J_1 @ ( times_times_int @ A @ ( multInv @ P @ K ) ) @ P )
% 0.59/0.79 => ( zcong @ K @ ( times_times_int @ A @ ( multInv @ P @ J_1 ) ) @ P ) ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1091_MultInv__zcong__prop3,axiom,
% 0.59/0.79 ! [J_1: int,K: int,A: int,P: int] :
% 0.59/0.79 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
% 0.59/0.79 => ( ( zprime @ P )
% 0.59/0.79 => ( ~ ( zcong @ A @ zero_zero_int @ P )
% 0.59/0.79 => ( ~ ( zcong @ K @ zero_zero_int @ P )
% 0.59/0.79 => ( ~ ( zcong @ J_1 @ zero_zero_int @ P )
% 0.59/0.79 => ( ( zcong @ ( times_times_int @ A @ ( multInv @ P @ J_1 ) ) @ ( times_times_int @ A @ ( multInv @ P @ K ) ) @ P )
% 0.59/0.79 => ( zcong @ J_1 @ K @ P ) ) ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1092_Int2_Oaux____2,axiom,
% 0.59/0.79 ! [X_1: int,P: int] :
% 0.59/0.79 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
% 0.59/0.79 => ( ( zprime @ P )
% 0.59/0.79 => ( ~ ( zcong @ X_1 @ zero_zero_int @ P )
% 0.59/0.79 => ( zcong @ ( times_times_int @ ( times_times_int @ X_1 @ ( multInv @ P @ X_1 ) ) @ ( multInv @ P @ ( multInv @ P @ X_1 ) ) ) @ X_1 @ P ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1093_Int2_Oaux____1,axiom,
% 0.59/0.79 ! [X_1: int,P: int] :
% 0.59/0.79 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
% 0.59/0.79 => ( ( zprime @ P )
% 0.59/0.79 => ( ~ ( zcong @ X_1 @ zero_zero_int @ P )
% 0.59/0.79 => ( zcong @ ( multInv @ P @ ( multInv @ P @ X_1 ) ) @ ( times_times_int @ ( times_times_int @ X_1 @ ( multInv @ P @ X_1 ) ) @ ( multInv @ P @ ( multInv @ P @ X_1 ) ) ) @ P ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1094_MultInv__prop2a,axiom,
% 0.59/0.79 ! [X_1: int,P: int] :
% 0.59/0.79 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
% 0.59/0.79 => ( ( zprime @ P )
% 0.59/0.79 => ( ~ ( zcong @ X_1 @ zero_zero_int @ P )
% 0.59/0.79 => ( zcong @ ( times_times_int @ ( multInv @ P @ X_1 ) @ X_1 ) @ one_one_int @ P ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1095_MultInv__prop2,axiom,
% 0.59/0.79 ! [X_1: int,P: int] :
% 0.59/0.79 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ P )
% 0.59/0.79 => ( ( zprime @ P )
% 0.59/0.79 => ( ~ ( zcong @ X_1 @ zero_zero_int @ P )
% 0.59/0.79 => ( zcong @ ( times_times_int @ X_1 @ ( multInv @ P @ X_1 ) ) @ one_one_int @ P ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1096_wset__mem__inv__mem,axiom,
% 0.59/0.79 ! [B: int,A: int,P: int] :
% 0.59/0.79 ( ( zprime @ P )
% 0.59/0.79 => ( ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ P )
% 0.59/0.79 => ( ( ord_less_int @ A @ ( minus_minus_int @ P @ one_one_int ) )
% 0.59/0.79 => ( ( member_int @ B @ ( wset @ A @ P ) )
% 0.59/0.79 => ( member_int @ ( inv @ P @ B ) @ ( wset @ A @ P ) ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1097_wset__inv__mem__mem,axiom,
% 0.59/0.79 ! [B: int,A: int,P: int] :
% 0.59/0.79 ( ( zprime @ P )
% 0.59/0.79 => ( ( ord_less_eq_int @ ( number_number_of_int @ ( bit1 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ P )
% 0.59/0.79 => ( ( ord_less_int @ A @ ( minus_minus_int @ P @ one_one_int ) )
% 0.59/0.79 => ( ( ord_less_int @ one_one_int @ B )
% 0.59/0.79 => ( ( ord_less_int @ B @ ( minus_minus_int @ P @ one_one_int ) )
% 0.59/0.79 => ( ( member_int @ ( inv @ P @ B ) @ ( wset @ A @ P ) )
% 0.59/0.79 => ( member_int @ B @ ( wset @ A @ P ) ) ) ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1098_wset__mem__mem,axiom,
% 0.59/0.79 ! [P: int,A: int] :
% 0.59/0.79 ( ( ord_less_int @ one_one_int @ A )
% 0.59/0.79 => ( member_int @ A @ ( wset @ A @ P ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1099_wset__subset,axiom,
% 0.59/0.79 ! [B: int,P: int,A: int] :
% 0.59/0.79 ( ( ord_less_int @ one_one_int @ A )
% 0.59/0.79 => ( ( member_int @ B @ ( wset @ ( minus_minus_int @ A @ one_one_int ) @ P ) )
% 0.59/0.79 => ( member_int @ B @ ( wset @ A @ P ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1100_wset__less,axiom,
% 0.59/0.79 ! [B: int,A: int,P: int] :
% 0.59/0.79 ( ( zprime @ P )
% 0.59/0.79 => ( ( ord_less_int @ A @ ( minus_minus_int @ P @ one_one_int ) )
% 0.59/0.79 => ( ( member_int @ B @ ( wset @ A @ P ) )
% 0.59/0.79 => ( ord_less_int @ B @ ( minus_minus_int @ P @ one_one_int ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1101_wset__g__1,axiom,
% 0.59/0.79 ! [B: int,A: int,P: int] :
% 0.59/0.79 ( ( zprime @ P )
% 0.59/0.79 => ( ( ord_less_int @ A @ ( minus_minus_int @ P @ one_one_int ) )
% 0.59/0.79 => ( ( member_int @ B @ ( wset @ A @ P ) )
% 0.59/0.79 => ( ord_less_int @ one_one_int @ B ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1102_wset__mem__imp__or,axiom,
% 0.59/0.79 ! [B: int,P: int,A: int] :
% 0.59/0.79 ( ( ord_less_int @ one_one_int @ A )
% 0.59/0.79 => ( ~ ( member_int @ B @ ( wset @ ( minus_minus_int @ A @ one_one_int ) @ P ) )
% 0.59/0.79 => ( ( member_int @ B @ ( wset @ A @ P ) )
% 0.59/0.79 => ( ( B = A )
% 0.59/0.79 | ( B
% 0.59/0.79 = ( inv @ P @ A ) ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1103_wset__mem,axiom,
% 0.59/0.79 ! [B: int,A: int,P: int] :
% 0.59/0.79 ( ( zprime @ P )
% 0.59/0.79 => ( ( ord_less_int @ A @ ( minus_minus_int @ P @ one_one_int ) )
% 0.59/0.79 => ( ( ord_less_int @ one_one_int @ B )
% 0.59/0.79 => ( ( ord_less_eq_int @ B @ A )
% 0.59/0.79 => ( member_int @ B @ ( wset @ A @ P ) ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1104_int__le__induct,axiom,
% 0.59/0.79 ! [P_1: int > $o,I_1: int,K: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ I_1 @ K )
% 0.59/0.79 => ( ( P_1 @ K )
% 0.59/0.79 => ( ! [I: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ I @ K )
% 0.59/0.79 => ( ( P_1 @ I )
% 0.59/0.79 => ( P_1 @ ( minus_minus_int @ I @ one_one_int ) ) ) )
% 0.59/0.79 => ( P_1 @ I_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1105_int__less__induct,axiom,
% 0.59/0.79 ! [P_1: int > $o,I_1: int,K: int] :
% 0.59/0.79 ( ( ord_less_int @ I_1 @ K )
% 0.59/0.79 => ( ( P_1 @ ( minus_minus_int @ K @ one_one_int ) )
% 0.59/0.79 => ( ! [I: int] :
% 0.59/0.79 ( ( ord_less_int @ I @ K )
% 0.59/0.79 => ( ( P_1 @ I )
% 0.59/0.79 => ( P_1 @ ( minus_minus_int @ I @ one_one_int ) ) ) )
% 0.59/0.79 => ( P_1 @ I_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1106_d22set__induct__old,axiom,
% 0.59/0.79 ! [X_1: int,P_1: int > $o] :
% 0.59/0.79 ( ! [A_2: int] :
% 0.59/0.79 ( ( ( ord_less_int @ one_one_int @ A_2 )
% 0.59/0.79 => ( P_1 @ ( minus_minus_int @ A_2 @ one_one_int ) ) )
% 0.59/0.79 => ( P_1 @ A_2 ) )
% 0.59/0.79 => ( P_1 @ X_1 ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1107_int__ge__induct,axiom,
% 0.59/0.79 ! [P_1: int > $o,K: int,I_1: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ K @ I_1 )
% 0.59/0.79 => ( ( P_1 @ K )
% 0.59/0.79 => ( ! [I: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ K @ I )
% 0.59/0.79 => ( ( P_1 @ I )
% 0.59/0.79 => ( P_1 @ ( plus_plus_int @ I @ one_one_int ) ) ) )
% 0.59/0.79 => ( P_1 @ I_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1108_int__gr__induct,axiom,
% 0.59/0.79 ! [P_1: int > $o,K: int,I_1: int] :
% 0.59/0.79 ( ( ord_less_int @ K @ I_1 )
% 0.59/0.79 => ( ( P_1 @ ( plus_plus_int @ K @ one_one_int ) )
% 0.59/0.79 => ( ! [I: int] :
% 0.59/0.79 ( ( ord_less_int @ K @ I )
% 0.59/0.79 => ( ( P_1 @ I )
% 0.59/0.79 => ( P_1 @ ( plus_plus_int @ I @ one_one_int ) ) ) )
% 0.59/0.79 => ( P_1 @ I_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1109_mono__nat__linear__lb,axiom,
% 0.59/0.79 ! [M: nat,K: nat,F: nat > nat] :
% 0.59/0.79 ( ! [M_2: nat,N_1: nat] :
% 0.59/0.79 ( ( ord_less_nat @ M_2 @ N_1 )
% 0.59/0.79 => ( ord_less_nat @ ( F @ M_2 ) @ ( F @ N_1 ) ) )
% 0.59/0.79 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1110_d22set__eq__wset,axiom,
% 0.59/0.79 ! [P: int] :
% 0.59/0.79 ( ( zprime @ P )
% 0.59/0.79 => ( ( d22set @ ( minus_minus_int @ P @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) )
% 0.59/0.79 = ( wset @ ( minus_minus_int @ P @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ P ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1111_ex__least__nat__le,axiom,
% 0.59/0.79 ! [N: nat,P_1: nat > $o] :
% 0.59/0.79 ( ~ ( P_1 @ zero_zero_nat )
% 0.59/0.79 => ( ( P_1 @ N )
% 0.59/0.79 => ? [K_1: nat] :
% 0.59/0.79 ( ( ord_less_eq_nat @ K_1 @ N )
% 0.59/0.79 & ! [I: nat] :
% 0.59/0.79 ( ( ord_less_nat @ I @ K_1 )
% 0.59/0.79 => ~ ( P_1 @ I ) )
% 0.59/0.79 & ( P_1 @ K_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1112_d22set__le,axiom,
% 0.59/0.79 ! [B: int,A: int] :
% 0.59/0.79 ( ( member_int @ B @ ( d22set @ A ) )
% 0.59/0.79 => ( ord_less_eq_int @ B @ A ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1113_d22set__le__swap,axiom,
% 0.59/0.79 ! [A: int,B: int] :
% 0.59/0.79 ( ( ord_less_int @ A @ B )
% 0.59/0.79 => ~ ( member_int @ B @ ( d22set @ A ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1114_d22set__g__1,axiom,
% 0.59/0.79 ! [B: int,A: int] :
% 0.59/0.79 ( ( member_int @ B @ ( d22set @ A ) )
% 0.59/0.79 => ( ord_less_int @ one_one_int @ B ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1115_d22set__mem,axiom,
% 0.59/0.79 ! [A: int,B: int] :
% 0.59/0.79 ( ( ord_less_int @ one_one_int @ B )
% 0.59/0.79 => ( ( ord_less_eq_int @ B @ A )
% 0.59/0.79 => ( member_int @ B @ ( d22set @ A ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1116_less__imp__add__positive,axiom,
% 0.59/0.79 ! [I_1: nat,J_1: nat] :
% 0.59/0.79 ( ( ord_less_nat @ I_1 @ J_1 )
% 0.59/0.79 => ? [K_1: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ K_1 )
% 0.59/0.79 & ( ( plus_plus_nat @ I_1 @ K_1 )
% 0.59/0.79 = J_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1117_pow__divides__eq__int,axiom,
% 0.59/0.79 ! [A: int,B: int,N: nat] :
% 0.59/0.79 ( ( N != zero_zero_nat )
% 0.59/0.79 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.59/0.79 <=> ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1118_gcd__lcm__complete__lattice__nat_Otop__le,axiom,
% 0.59/0.79 ! [A: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.59/0.79 => ( A = zero_zero_nat ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1119_gcd__lcm__complete__lattice__nat_Otop__unique,axiom,
% 0.59/0.79 ! [A: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.59/0.79 <=> ( A = zero_zero_nat ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1120_gcd__lcm__complete__lattice__nat_Oless__top,axiom,
% 0.59/0.79 ! [A: nat] :
% 0.59/0.79 ( ( A != zero_zero_nat )
% 0.59/0.79 <=> ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ zero_zero_nat @ A ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1121_gcd__lcm__complete__lattice__nat_Otop__greatest,axiom,
% 0.59/0.79 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1122_gcd__lcm__complete__lattice__nat_Onot__top__less,axiom,
% 0.59/0.79 ! [A: nat] :
% 0.59/0.79 ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ A @ zero_zero_nat ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1123_gcd__lcm__complete__lattice__nat_Onot__less__bot,axiom,
% 0.59/0.79 ! [A: nat] :
% 0.59/0.79 ~ ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ one_one_nat @ A ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1124_gcd__lcm__complete__lattice__nat_Obot__least,axiom,
% 0.59/0.79 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1125_gcd__lcm__complete__lattice__nat_Obot__less,axiom,
% 0.59/0.79 ! [A: nat] :
% 0.59/0.79 ( ( A != one_one_nat )
% 0.59/0.79 <=> ( ( dvd_dvd_nat @ one_one_nat @ A )
% 0.59/0.79 & ~ ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1126_gcd__lcm__complete__lattice__nat_Obot__unique,axiom,
% 0.59/0.79 ! [A: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.59/0.79 <=> ( A = one_one_nat ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1127_gcd__lcm__complete__lattice__nat_Ole__bot,axiom,
% 0.59/0.79 ! [A: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 0.59/0.79 => ( A = one_one_nat ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1128_dvd__pos__nat,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.59/0.79 => ( ( dvd_dvd_nat @ M @ N )
% 0.59/0.79 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1129_pow__divides__eq__nat,axiom,
% 0.59/0.79 ! [A: nat,B: nat,N: nat] :
% 0.59/0.79 ( ( N != zero_zero_nat )
% 0.59/0.79 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 0.59/0.79 <=> ( dvd_dvd_nat @ A @ B ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1130_pow__divides__pow__int,axiom,
% 0.59/0.79 ! [A: int,N: nat,B: int] :
% 0.59/0.79 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 0.59/0.79 => ( ( N != zero_zero_nat )
% 0.59/0.79 => ( dvd_dvd_int @ A @ B ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1131_divides__le,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( dvd_dvd_nat @ M @ N )
% 0.59/0.79 => ( ( ord_less_eq_nat @ M @ N )
% 0.59/0.79 | ( N = zero_zero_nat ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1132_mult__left__cancel,axiom,
% 0.59/0.79 ! [N: nat,M: nat,K: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ K )
% 0.59/0.79 => ( ( ( times_times_nat @ K @ N )
% 0.59/0.79 = ( times_times_nat @ K @ M ) )
% 0.59/0.79 => ( N = M ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1133_SR__def,axiom,
% 0.59/0.79 ! [P: int] :
% 0.59/0.79 ( ( sr @ P )
% 0.59/0.79 = ( collect_int
% 0.59/0.79 @ ^ [X: int] : ( (&) @ ( ord_less_eq_int @ zero_zero_int @ X ) @ ( ord_less_int @ X @ P ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1134_neg__zmod__mult__2,axiom,
% 0.59/0.79 ! [B: int,A: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.59/0.79 => ( ( div_mod_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
% 0.59/0.79 = ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( div_mod_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) @ one_one_int ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1135_zmod__number__of__Bit1,axiom,
% 0.59/0.79 ! [V: int,W: int] :
% 0.59/0.79 ( ( ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ W ) )
% 0.59/0.79 => ( ( div_mod_int @ ( number_number_of_int @ ( bit1 @ V ) ) @ ( number_number_of_int @ ( bit0 @ W ) ) )
% 0.59/0.79 = ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( div_mod_int @ ( number_number_of_int @ V ) @ ( number_number_of_int @ W ) ) ) @ one_one_int ) ) )
% 0.59/0.79 & ( ~ ( ord_less_eq_int @ zero_zero_int @ ( number_number_of_int @ W ) )
% 0.59/0.79 => ( ( div_mod_int @ ( number_number_of_int @ ( bit1 @ V ) ) @ ( number_number_of_int @ ( bit0 @ W ) ) )
% 0.59/0.79 = ( minus_minus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( div_mod_int @ ( plus_plus_int @ ( number_number_of_int @ V ) @ one_one_int ) @ ( number_number_of_int @ W ) ) ) @ one_one_int ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1136_zdvd__iff__zmod__eq__0__number__of,axiom,
% 0.59/0.79 ! [X_1: int,Y_1: int] :
% 0.59/0.79 ( ( dvd_dvd_int @ ( number_number_of_int @ X_1 ) @ ( number_number_of_int @ Y_1 ) )
% 0.59/0.79 <=> ( ( div_mod_int @ ( number_number_of_int @ Y_1 ) @ ( number_number_of_int @ X_1 ) )
% 0.59/0.79 = zero_zero_int ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1137_neg__mod__bound,axiom,
% 0.59/0.79 ! [A: int,B: int] :
% 0.59/0.79 ( ( ord_less_int @ B @ zero_zero_int )
% 0.59/0.79 => ( ord_less_int @ B @ ( div_mod_int @ A @ B ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1138_pos__mod__bound,axiom,
% 0.59/0.79 ! [A: int,B: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ B )
% 0.59/0.79 => ( ord_less_int @ ( div_mod_int @ A @ B ) @ B ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1139_Divides_Otransfer__nat__int__function__closures_I2_J,axiom,
% 0.59/0.79 ! [Y_1: int,X_1: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ zero_zero_int @ X_1 )
% 0.59/0.79 => ( ( ord_less_eq_int @ zero_zero_int @ Y_1 )
% 0.59/0.79 => ( ord_less_eq_int @ zero_zero_int @ ( div_mod_int @ X_1 @ Y_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1140_zmod__le__nonneg__dividend,axiom,
% 0.59/0.79 ! [K: int,M: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 0.59/0.79 => ( ord_less_eq_int @ ( div_mod_int @ M @ K ) @ M ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1141_zmod__eq__0__iff,axiom,
% 0.59/0.79 ! [M: int,D: int] :
% 0.59/0.79 ( ( ( div_mod_int @ M @ D )
% 0.59/0.79 = zero_zero_int )
% 0.59/0.79 <=> ? [Q_1: int] :
% 0.59/0.79 ( M
% 0.59/0.79 = ( times_times_int @ D @ Q_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1142_zmod__eq__dvd__iff,axiom,
% 0.59/0.79 ! [X_1: int,N: int,Y_1: int] :
% 0.59/0.79 ( ( ( div_mod_int @ X_1 @ N )
% 0.59/0.79 = ( div_mod_int @ Y_1 @ N ) )
% 0.59/0.79 <=> ( dvd_dvd_int @ N @ ( minus_minus_int @ X_1 @ Y_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1143_Residues_Oaux,axiom,
% 0.59/0.79 ! [X_1: int,M: int,Y_1: int] :
% 0.59/0.79 ( ( ( div_mod_int @ X_1 @ M )
% 0.59/0.79 = ( div_mod_int @ Y_1 @ M ) )
% 0.59/0.79 => ( zcong @ X_1 @ Y_1 @ M ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1144_mod__mod__is__mod,axiom,
% 0.59/0.79 ! [X_1: int,M: int] : ( zcong @ X_1 @ ( div_mod_int @ X_1 @ M ) @ M ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1145_zcong__zmod,axiom,
% 0.59/0.79 ! [A: int,B: int,M: int] :
% 0.59/0.79 ( ( zcong @ A @ B @ M )
% 0.59/0.79 <=> ( zcong @ ( div_mod_int @ A @ M ) @ ( div_mod_int @ B @ M ) @ M ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1146_zdvd__zmod__imp__zdvd,axiom,
% 0.59/0.79 ! [K: int,M: int,N: int] :
% 0.59/0.79 ( ( dvd_dvd_int @ K @ ( div_mod_int @ M @ N ) )
% 0.59/0.79 => ( ( dvd_dvd_int @ K @ N )
% 0.59/0.79 => ( dvd_dvd_int @ K @ M ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1147_zdvd__zmod,axiom,
% 0.59/0.79 ! [N: int,F: int,M: int] :
% 0.59/0.79 ( ( dvd_dvd_int @ F @ M )
% 0.59/0.79 => ( ( dvd_dvd_int @ F @ N )
% 0.59/0.79 => ( dvd_dvd_int @ F @ ( div_mod_int @ M @ N ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1148_zpower__zmod,axiom,
% 0.59/0.79 ! [X_1: int,M: int,Y_1: nat] :
% 0.59/0.79 ( ( div_mod_int @ ( power_power_int @ ( div_mod_int @ X_1 @ M ) @ Y_1 ) @ M )
% 0.59/0.79 = ( div_mod_int @ ( power_power_int @ X_1 @ Y_1 ) @ M ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1149_zmod__zmult1__eq,axiom,
% 0.59/0.79 ! [A: int,B: int,C: int] :
% 0.59/0.79 ( ( div_mod_int @ ( times_times_int @ A @ B ) @ C )
% 0.59/0.79 = ( div_mod_int @ ( times_times_int @ A @ ( div_mod_int @ B @ C ) ) @ C ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1150_zmod__simps_I3_J,axiom,
% 0.59/0.79 ! [A: int,B: int,C: int] :
% 0.59/0.79 ( ( div_mod_int @ ( times_times_int @ A @ ( div_mod_int @ B @ C ) ) @ C )
% 0.59/0.79 = ( div_mod_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1151_zmod__self,axiom,
% 0.59/0.79 ! [A: int] :
% 0.59/0.79 ( ( div_mod_int @ A @ A )
% 0.59/0.79 = zero_zero_int ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1152_zmod__zero,axiom,
% 0.59/0.79 ! [B: int] :
% 0.59/0.79 ( ( div_mod_int @ zero_zero_int @ B )
% 0.59/0.79 = zero_zero_int ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1153_zdiff__zmod__right,axiom,
% 0.59/0.79 ! [X_1: int,Y_1: int,M: int] :
% 0.59/0.79 ( ( div_mod_int @ ( minus_minus_int @ X_1 @ ( div_mod_int @ Y_1 @ M ) ) @ M )
% 0.59/0.79 = ( div_mod_int @ ( minus_minus_int @ X_1 @ Y_1 ) @ M ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1154_zdiff__zmod__left,axiom,
% 0.59/0.79 ! [X_1: int,M: int,Y_1: int] :
% 0.59/0.79 ( ( div_mod_int @ ( minus_minus_int @ ( div_mod_int @ X_1 @ M ) @ Y_1 ) @ M )
% 0.59/0.79 = ( div_mod_int @ ( minus_minus_int @ X_1 @ Y_1 ) @ M ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1155_zmod__minus1__right,axiom,
% 0.59/0.79 ! [A: int] :
% 0.59/0.79 ( ( div_mod_int @ A @ ( number_number_of_int @ min ) )
% 0.59/0.79 = zero_zero_int ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1156_zmod__zdvd__zmod,axiom,
% 0.59/0.79 ! [A: int,B: int,M: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ M )
% 0.59/0.79 => ( ( dvd_dvd_int @ M @ B )
% 0.59/0.79 => ( ( div_mod_int @ ( div_mod_int @ A @ B ) @ M )
% 0.59/0.79 = ( div_mod_int @ A @ M ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1157_zcong__zmod__eq,axiom,
% 0.59/0.79 ! [A: int,B: int,M: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ M )
% 0.59/0.79 => ( ( zcong @ A @ B @ M )
% 0.59/0.79 <=> ( ( div_mod_int @ A @ M )
% 0.59/0.79 = ( div_mod_int @ B @ M ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1158_pos__mod__sign,axiom,
% 0.59/0.79 ! [A: int,B: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ B )
% 0.59/0.79 => ( ord_less_eq_int @ zero_zero_int @ ( div_mod_int @ A @ B ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1159_pos__mod__conj,axiom,
% 0.59/0.79 ! [A: int,B: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ B )
% 0.59/0.79 => ( ( ord_less_eq_int @ zero_zero_int @ ( div_mod_int @ A @ B ) )
% 0.59/0.79 & ( ord_less_int @ ( div_mod_int @ A @ B ) @ B ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1160_mod__pos__pos__trivial,axiom,
% 0.59/0.79 ! [B: int,A: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.59/0.79 => ( ( ord_less_int @ A @ B )
% 0.59/0.79 => ( ( div_mod_int @ A @ B )
% 0.59/0.79 = A ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1161_neg__mod__sign,axiom,
% 0.59/0.79 ! [A: int,B: int] :
% 0.59/0.79 ( ( ord_less_int @ B @ zero_zero_int )
% 0.59/0.79 => ( ord_less_eq_int @ ( div_mod_int @ A @ B ) @ zero_zero_int ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1162_neg__mod__conj,axiom,
% 0.59/0.79 ! [A: int,B: int] :
% 0.59/0.79 ( ( ord_less_int @ B @ zero_zero_int )
% 0.59/0.79 => ( ( ord_less_eq_int @ ( div_mod_int @ A @ B ) @ zero_zero_int )
% 0.59/0.79 & ( ord_less_int @ B @ ( div_mod_int @ A @ B ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1163_mod__neg__neg__trivial,axiom,
% 0.59/0.79 ! [B: int,A: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 0.59/0.79 => ( ( ord_less_int @ B @ A )
% 0.59/0.79 => ( ( div_mod_int @ A @ B )
% 0.59/0.79 = A ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1164_mod__pos__neg__trivial,axiom,
% 0.59/0.79 ! [B: int,A: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ A )
% 0.59/0.79 => ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int )
% 0.59/0.79 => ( ( div_mod_int @ A @ B )
% 0.59/0.79 = ( plus_plus_int @ A @ B ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1165_zmod__number__of__Bit0,axiom,
% 0.59/0.79 ! [V: int,W: int] :
% 0.59/0.79 ( ( div_mod_int @ ( number_number_of_int @ ( bit0 @ V ) ) @ ( number_number_of_int @ ( bit0 @ W ) ) )
% 0.59/0.79 = ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( div_mod_int @ ( number_number_of_int @ V ) @ ( number_number_of_int @ W ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1166_split__zmod,axiom,
% 0.59/0.79 ! [P_1: int > $o,N: int,K: int] :
% 0.59/0.79 ( ( P_1 @ ( div_mod_int @ N @ K ) )
% 0.59/0.79 <=> ( ( ( K = zero_zero_int )
% 0.59/0.79 => ( P_1 @ N ) )
% 0.59/0.79 & ( ( ord_less_int @ zero_zero_int @ K )
% 0.59/0.79 => ! [I: int,J: int] :
% 0.59/0.79 ( ( ( ord_less_eq_int @ zero_zero_int @ J )
% 0.59/0.79 & ( ord_less_int @ J @ K )
% 0.59/0.79 & ( N
% 0.59/0.79 = ( plus_plus_int @ ( times_times_int @ K @ I ) @ J ) ) )
% 0.59/0.79 => ( P_1 @ J ) ) )
% 0.59/0.79 & ( ( ord_less_int @ K @ zero_zero_int )
% 0.59/0.79 => ! [I: int,J: int] :
% 0.59/0.79 ( ( ( ord_less_int @ K @ J )
% 0.59/0.79 & ( ord_less_eq_int @ J @ zero_zero_int )
% 0.59/0.79 & ( N
% 0.59/0.79 = ( plus_plus_int @ ( times_times_int @ K @ I ) @ J ) ) )
% 0.59/0.79 => ( P_1 @ J ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1167_zmult2__lemma__aux3,axiom,
% 0.59/0.79 ! [Q: int,B: int,R: int,C: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ C )
% 0.59/0.79 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.59/0.79 => ( ( ord_less_int @ R @ B )
% 0.59/0.79 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B @ ( div_mod_int @ Q @ C ) ) @ R ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1168_zmult2__lemma__aux4,axiom,
% 0.59/0.79 ! [Q: int,B: int,R: int,C: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ C )
% 0.59/0.79 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 0.59/0.79 => ( ( ord_less_int @ R @ B )
% 0.59/0.79 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B @ ( div_mod_int @ Q @ C ) ) @ R ) @ ( times_times_int @ B @ C ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1169_zmult2__lemma__aux1,axiom,
% 0.59/0.79 ! [Q: int,B: int,R: int,C: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ C )
% 0.59/0.79 => ( ( ord_less_int @ B @ R )
% 0.59/0.79 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 0.59/0.79 => ( ord_less_int @ ( times_times_int @ B @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ ( div_mod_int @ Q @ C ) ) @ R ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1170_zmult2__lemma__aux2,axiom,
% 0.59/0.79 ! [Q: int,B: int,R: int,C: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ C )
% 0.59/0.79 => ( ( ord_less_int @ B @ R )
% 0.59/0.79 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 0.59/0.79 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ ( div_mod_int @ Q @ C ) ) @ R ) @ zero_zero_int ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1171_divmod__int__rel__mod__eq,axiom,
% 0.59/0.79 ! [A_1: int,B_1: int,Q_2: int,Y_1: int] :
% 0.59/0.79 ( ( A_1
% 0.59/0.79 = ( plus_plus_int @ ( times_times_int @ B_1 @ Q_2 ) @ Y_1 ) )
% 0.59/0.79 => ( ( ( ( ord_less_int @ zero_zero_int @ B_1 )
% 0.59/0.79 => ( ( ord_less_eq_int @ zero_zero_int @ Y_1 )
% 0.59/0.79 & ( ord_less_int @ Y_1 @ B_1 ) ) )
% 0.59/0.79 & ( ~ ( ord_less_int @ zero_zero_int @ B_1 )
% 0.59/0.79 => ( ( ord_less_int @ B_1 @ Y_1 )
% 0.59/0.79 & ( ord_less_eq_int @ Y_1 @ zero_zero_int ) ) ) )
% 0.59/0.79 => ( ( B_1 != zero_zero_int )
% 0.59/0.79 => ( ( div_mod_int @ A_1 @ B_1 )
% 0.59/0.79 = Y_1 ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1172_neq__one__mod__two,axiom,
% 0.59/0.79 ! [X_1: int] :
% 0.59/0.79 ( ( ( div_mod_int @ X_1 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.79 != zero_zero_int )
% 0.59/0.79 <=> ( ( div_mod_int @ X_1 @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) )
% 0.59/0.79 = one_one_int ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1173_zmod__minus1,axiom,
% 0.59/0.79 ! [B: int] :
% 0.59/0.79 ( ( ord_less_int @ zero_zero_int @ B )
% 0.59/0.79 => ( ( div_mod_int @ ( number_number_of_int @ min ) @ B )
% 0.59/0.79 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1174_pos__zmod__mult__2,axiom,
% 0.59/0.79 ! [B: int,A: int] :
% 0.59/0.79 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 0.59/0.79 => ( ( div_mod_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ B ) ) @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ A ) )
% 0.59/0.79 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ ( div_mod_int @ B @ A ) ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1175_zmod__eq__0D,axiom,
% 0.59/0.79 ! [M_1: int,D_1: int] :
% 0.59/0.79 ( ( ( div_mod_int @ M_1 @ D_1 )
% 0.59/0.79 = zero_zero_int )
% 0.59/0.79 => ? [Q_1: int] :
% 0.59/0.79 ( M_1
% 0.59/0.79 = ( times_times_int @ D_1 @ Q_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1176_StandardRes__prop4,axiom,
% 0.59/0.79 ! [X_1: int,Y_1: int,M: int] :
% 0.59/0.79 ( ( ord_less_int @ ( number_number_of_int @ ( bit0 @ ( bit1 @ pls ) ) ) @ M )
% 0.59/0.79 => ( zcong @ ( times_times_int @ ( standardRes @ M @ X_1 ) @ ( standardRes @ M @ Y_1 ) ) @ ( times_times_int @ X_1 @ Y_1 ) @ M ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1177_mod__le__divisor,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.59/0.79 => ( ord_less_eq_nat @ ( div_mod_nat @ M @ N ) @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1178_mod__less__divisor,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 0.59/0.79 => ( ord_less_nat @ ( div_mod_nat @ M @ N ) @ N ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1179_mod__eq__0__iff,axiom,
% 0.59/0.79 ! [M: nat,D: nat] :
% 0.59/0.79 ( ( ( div_mod_nat @ M @ D )
% 0.59/0.79 = zero_zero_nat )
% 0.59/0.79 <=> ? [Q_1: nat] :
% 0.59/0.79 ( M
% 0.59/0.79 = ( times_times_nat @ D @ Q_1 ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1180_mod__geq,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ~ ( ord_less_nat @ M @ N )
% 0.59/0.79 => ( ( div_mod_nat @ M @ N )
% 0.59/0.79 = ( div_mod_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1181_mod__if,axiom,
% 0.59/0.79 ! [M: nat,N: nat] :
% 0.59/0.79 ( ( ( ord_less_nat @ M @ N )
% 0.59/0.79 => ( ( div_mod_nat @ M @ N )
% 0.59/0.79 = M ) )
% 0.59/0.79 & ( ~ ( ord_less_nat @ M @ N )
% 0.59/0.79 => ( ( div_mod_nat @ M @ N )
% 0.59/0.79 = ( div_mod_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ).
% 0.59/0.79
% 0.59/0.79 thf(fact_1182_mod__mult__self3,axiom,
% 0.60/0.99 ! [K: nat,N: nat,M: nat] :
% 0.60/0.99 ( ( div_mod_nat @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) @ N )
% 0.60/0.99 = ( div_mod_nat @ M @ N ) ) ).
% 0.60/0.99
% 0.60/0.99 thf(fact_1183_le__mod__geq,axiom,
% 0.60/0.99 ! [N: nat,M: nat] :
% 0.60/0.99 ( ( ord_less_eq_nat @ N @ M )
% 0.60/0.99 => ( ( div_mod_nat @ M @ N )
% 0.60/0.99 = ( div_mod_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 0.60/0.99
% 0.60/0.99 thf(fact_1184_StandardRes__def,axiom,
% 0.60/0.99 ! [M: int,X_1: int] :
% 0.60/0.99 ( ( standardRes @ M @ X_1 )
% 0.60/0.99 = ( div_mod_int @ X_1 @ M ) ) ).
% 0.60/0.99
% 0.60/0.99 thf(fact_1185_mod__mult__distrib,axiom,
% 0.60/0.99 ! [M: nat,N: nat,K: nat] :
% 0.60/0.99 ( ( times_times_nat @ ( div_mod_nat @ M @ N ) @ K )
% 0.60/0.99 = ( div_mod_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 0.60/0.99
% 0.60/0.99 thf(fact_1186_mod__mult__distrib2,axiom,
% 0.60/0.99 ! [K: nat,M: nat,N: nat] :
% 0.60/0.99 ( ( times_times_nat @ K @ ( div_mod_nat @ M @ N ) )
% 0.60/0.99 = ( div_mod_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 0.60/0.99
% 0.60/0.99 thf(fact_1187_mod__less,axiom,
% 0.60/0.99 ! [M: nat,N: nat] :
% 0.60/0.99 ( ( ord_less_nat @ M @ N )
% 0.60/0.99 => ( ( div_mod_nat @ M @ N )
% 0.60/0.99 = M ) ) ).
% 0.60/0.99
% 0.60/0.99 thf(fact_1188_mod__less__eq__dividend,axiom,
% 0.60/0.99 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( div_mod_nat @ M @ N ) @ M ) ).
% 0.60/0.99
% 0.60/0.99 thf(fact_1189_StandardRes__eq__zcong,axiom,
% 0.60/0.99 ! [M: int,X_1: int] :
% 0.60/0.99 ( ( ( standardRes @ M @ X_1 )
% 0.60/0.99 = zero_zero_int )
% 0.60/0.99 <=> ( zcong @ X_1 @ zero_zero_int @ M ) ) ).
% 0.60/0.99
% 0.60/0.99 thf(fact_1190_StandardRes__prop3,axiom,
% 0.60/0.99 ! [X_1: int,P: int] :
% 0.60/0.99 ( ~ ( zcong @ X_1 @ zero_zero_int @ P )
% 0.60/0.99 <=> ( ( standardRes @ P @ X_1 )
% 0.60/0.99 != zero_zero_int ) ) ).
% 0.60/0.99
% 0.60/0.99 thf(fact_1191_StandardRes__prop1,axiom,
% 0.60/0.99 ! [X_1: int,M: int] : ( zcong @ X_1 @ ( standardRes @ M @ X_1 ) @ M ) ).
% 0.60/0.99
% 0.60/0.99 thf(fact_1192_StandardRes__ubound,axiom,
% 0.60/0.99 ! [X_1: int,P: int] :
% 0.60/0.99 ( ( ord_less_int @ zero_zero_int @ P )
% 0.60/0.99 => ( ord_less_int @ ( standardRes @ P @ X_1 ) @ P ) ) ).
% 0.60/0.99
% 0.60/0.99 thf(fact_1193_StandardRes__SR__prop,axiom,
% 0.60/0.99 ! [X_1: int,P: int] :
% 0.60/0.99 ( ( member_int @ X_1 @ ( sr @ P ) )
% 0.60/0.99 => ( ( standardRes @ P @ X_1 )
% 0.60/0.99 = X_1 ) ) ).
% 0.60/0.99
% 0.60/0.99 thf(fact_1194_split__mod,axiom,
% 0.60/0.99 ! [P_1: nat > $o,N: nat,K: nat] :
% 0.60/0.99 ( ( P_1 @ ( div_mod_nat @ N @ K ) )
% 0.60/0.99 <=> ( ( ( K = zero_zero_nat )
% 0.60/0.99 => ( P_1 @ N ) )
% 0.60/0.99 & ( ( K != zero_zero_nat )
% 0.60/0.99 => ! [I: nat,J: nat] :
% 0.60/0.99 ( ( ord_less_nat @ J @ K )
% 0.60/0.99 => ( ( N
% 0.60/0.99 = ( plus_plus_nat @ ( times_times_nat @ K @ I ) @ J ) )
% 0.60/0.99 => ( P_1 @ J ) ) ) ) ) ) ).
% 0.60/0.99
% 0.60/0.99 thf(fact_1195_mod__lemma,axiom,
% 0.60/0.99 ! [Q: nat,R: nat,B: nat,C: nat] :
% 0.60/0.99 ( ( ord_less_nat @ zero_zero_nat @ C )
% 0.60/0.99 => ( ( ord_less_nat @ R @ B )
% 0.60/0.99 => ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( div_mod_nat @ Q @ C ) ) @ R ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 0.60/0.99
% 0.60/0.99 thf(fact_1196_StandardRes__lbound,axiom,
% 0.60/0.99 ! [X_1: int,P: int] :
% 0.60/0.99 ( ( ord_less_int @ zero_zero_int @ P )
% 0.60/0.99 => ( ord_less_eq_int @ zero_zero_int @ ( standardRes @ P @ X_1 ) ) ) ).
% 0.60/0.99
% 0.60/0.99 thf(fact_1197_StandardRes__prop2,axiom,
% 0.60/0.99 ! [X1: int,X2: int,M: int] :
% 0.60/0.99 ( ( ord_less_int @ zero_zero_int @ M )
% 0.60/0.99 => ( ( ( standardRes @ M @ X1 )
% 0.60/0.99 = ( standardRes @ M @ X2 ) )
% 0.60/0.99 <=> ( zcong @ X1 @ X2 @ M ) ) ) ).
% 0.60/0.99
% 0.60/0.99 %----Conjectures (1)
% 0.60/0.99 thf(conj_0,conjecture,
% 0.60/0.99 ? [X: int,Y: int] :
% 0.60/0.99 ( ( 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 ) ) ) ) )
% 0.60/0.99 = ( plus_plus_int @ ( times_times_int @ ( number_number_of_int @ ( bit0 @ ( bit0 @ ( bit1 @ pls ) ) ) ) @ m ) @ one_one_int ) ) ).
% 0.60/0.99
% 0.60/0.99 %------------------------------------------------------------------------------
% 0.60/0.99 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.W8d7nP8V33/cvc5---1.0.5_4968.p...
% 0.60/0.99 (declare-sort $$unsorted 0)
% 0.60/0.99 (declare-sort tptp.int 0)
% 0.60/0.99 (declare-sort tptp.nat 0)
% 0.60/0.99 (declare-sort tptp.real 0)
% 0.60/0.99 (declare-sort tptp.product_prod_int_int 0)
% 0.60/0.99 (declare-fun tptp.div_mod_int (tptp.int tptp.int) tptp.int)
% 0.60/0.99 (declare-fun tptp.div_mod_nat (tptp.nat tptp.nat) tptp.nat)
% 0.60/0.99 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 0.60/0.99 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.60/0.99 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 0.60/0.99 (declare-fun tptp.one_one_int () tptp.int)
% 0.60/0.99 (declare-fun tptp.one_one_nat () tptp.nat)
% 0.60/0.99 (declare-fun tptp.one_one_real () tptp.real)
% 0.60/0.99 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 0.60/0.99 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 0.60/0.99 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 0.60/0.99 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 0.60/0.99 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 0.60/0.99 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 0.60/0.99 (declare-fun tptp.zero_zero_int () tptp.int)
% 0.60/0.99 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 0.60/0.99 (declare-fun tptp.zero_zero_real () tptp.real)
% 0.60/0.99 (declare-fun tptp.multInv (tptp.int tptp.int) tptp.int)
% 0.60/0.99 (declare-fun tptp.d22set (tptp.int tptp.int) Bool)
% 0.60/0.99 (declare-fun tptp.zfact (tptp.int) tptp.int)
% 0.60/0.99 (declare-fun tptp.zcong (tptp.int tptp.int tptp.int) Bool)
% 0.60/0.99 (declare-fun tptp.zprime (tptp.int) Bool)
% 0.60/0.99 (declare-fun tptp.bit0 (tptp.int) tptp.int)
% 0.60/0.99 (declare-fun tptp.bit1 (tptp.int) tptp.int)
% 0.60/0.99 (declare-fun tptp.min () tptp.int)
% 0.60/0.99 (declare-fun tptp.pls () tptp.int)
% 0.60/0.99 (declare-fun tptp.number_number_of_int (tptp.int) tptp.int)
% 0.60/0.99 (declare-fun tptp.number_number_of_nat (tptp.int) tptp.nat)
% 0.60/0.99 (declare-fun tptp.number267125858f_real (tptp.int) tptp.real)
% 0.60/0.99 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 0.60/0.99 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 0.60/0.99 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 0.60/0.99 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 0.60/0.99 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 0.60/0.99 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 0.60/0.99 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 0.60/0.99 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 0.60/0.99 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 0.60/0.99 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 0.60/0.99 (declare-fun tptp.legendre (tptp.int tptp.int) tptp.int)
% 0.60/0.99 (declare-fun tptp.quadRes (tptp.int tptp.int) Bool)
% 0.60/0.99 (declare-fun tptp.sr (tptp.int tptp.int) Bool)
% 0.60/0.99 (declare-fun tptp.standardRes (tptp.int tptp.int) tptp.int)
% 0.60/0.99 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 0.60/0.99 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 0.60/0.99 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 0.60/0.99 (declare-fun tptp.collect_int ((-> tptp.int Bool) tptp.int) Bool)
% 0.60/0.99 (declare-fun tptp.twoSqu919416604sum2sq (tptp.int) Bool)
% 0.60/0.99 (declare-fun tptp.twoSqu2057625106sum2sq (tptp.product_prod_int_int) tptp.int)
% 0.60/0.99 (declare-fun tptp.inv (tptp.int tptp.int) tptp.int)
% 0.60/0.99 (declare-fun tptp.wset (tptp.int tptp.int tptp.int) Bool)
% 0.60/0.99 (declare-fun tptp.member_int (tptp.int (-> tptp.int Bool)) Bool)
% 0.60/0.99 (declare-fun tptp.m () tptp.int)
% 0.60/0.99 (declare-fun tptp.s1 () tptp.int)
% 0.60/0.99 (declare-fun tptp.s () tptp.int)
% 0.60/0.99 (declare-fun tptp.t () tptp.int)
% 0.60/0.99 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.t))
% 0.60/0.99 (assert (=> (= tptp.t tptp.one_one_int) (exists ((X tptp.int) (Y 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) _let_2)) (@ (@ tptp.power_power_int Y) _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)))))))
% 0.60/0.99 (assert (=> (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.t) (exists ((X tptp.int) (Y 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) _let_2)) (@ (@ tptp.power_power_int Y) _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)))))))
% 0.60/0.99 (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)))
% 0.60/0.99 (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)))
% 0.60/0.99 (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))))
% 0.60/0.99 (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)))
% 0.60/0.99 (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)))))))
% 0.60/0.99 (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))))))))))))
% 0.60/0.99 (assert (forall ((X_44 tptp.int) (Y_34 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 X_44) Y_34)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_44) _let_2)) (@ (@ tptp.power_power_int Y_34) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int _let_1)) X_44)) Y_34)))))))
% 0.60/0.99 (assert (forall ((X_44 tptp.nat) (Y_34 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X_44) Y_34)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X_44) _let_1)) (@ (@ tptp.power_power_nat Y_34) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X_44)) Y_34))))))
% 0.60/0.99 (assert (forall ((X_44 tptp.real) (Y_34 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_44) Y_34)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X_44) _let_2)) (@ (@ tptp.power_power_real Y_34) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.number267125858f_real _let_1)) X_44)) Y_34)))))))
% 0.60/0.99 (assert (forall ((W_19 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W_19))) (= (@ (@ tptp.power_power_int _let_1) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_int _let_1) _let_1)))))
% 0.60/0.99 (assert (forall ((W_19 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real W_19))) (= (@ (@ tptp.power_power_real _let_1) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_real _let_1) _let_1)))))
% 0.60/0.99 (assert (forall ((W_19 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_19))) (= (@ (@ tptp.power_power_nat _let_1) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_nat _let_1) _let_1)))))
% 0.60/0.99 (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))))))))
% 0.60/0.99 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.one_one_int))
% 0.60/0.99 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.one_one_nat))
% 0.60/0.99 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.one_one_real))
% 0.60/0.99 (assert (forall ((X_43 tptp.int)) (= (@ (@ tptp.times_times_int X_43) X_43) (@ (@ tptp.power_power_int X_43) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))))
% 0.60/0.99 (assert (forall ((X_43 tptp.real)) (= (@ (@ tptp.times_times_real X_43) X_43) (@ (@ tptp.power_power_real X_43) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))))
% 0.60/0.99 (assert (forall ((X_43 tptp.nat)) (= (@ (@ tptp.times_times_nat X_43) X_43) (@ (@ tptp.power_power_nat X_43) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))))
% 0.60/0.99 (assert (forall ((A_127 tptp.int)) (= (@ (@ tptp.power_power_int A_127) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_int A_127) A_127))))
% 0.60/0.99 (assert (forall ((A_127 tptp.real)) (= (@ (@ tptp.power_power_real A_127) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_real A_127) A_127))))
% 0.60/0.99 (assert (forall ((A_127 tptp.nat)) (= (@ (@ tptp.power_power_nat A_127) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_nat A_127) A_127))))
% 0.60/0.99 (assert (forall ((X_42 tptp.int) (N_41 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X_42))) (let ((_let_2 (@ _let_1 N_41))) (= (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_41)) (@ (@ tptp.times_times_int _let_2) _let_2))))))
% 0.60/0.99 (assert (forall ((X_42 tptp.real) (N_41 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X_42))) (let ((_let_2 (@ _let_1 N_41))) (= (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_41)) (@ (@ tptp.times_times_real _let_2) _let_2))))))
% 0.60/0.99 (assert (forall ((X_42 tptp.nat) (N_41 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X_42))) (let ((_let_2 (@ _let_1 N_41))) (= (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_41)) (@ (@ tptp.times_times_nat _let_2) _let_2))))))
% 0.60/0.99 (assert (forall ((W_18 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.number_number_of_int W_18)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int (@ tptp.bit1 tptp.pls)) W_18)))))
% 0.60/0.99 (assert (forall ((W_18 tptp.int)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.number267125858f_real W_18)) (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int (@ tptp.bit1 tptp.pls)) W_18)))))
% 0.60/0.99 (assert (forall ((V_20 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_20)) tptp.one_one_int) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_20) (@ tptp.bit1 tptp.pls))))))
% 0.60/0.99 (assert (forall ((V_20 tptp.int)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_20)) tptp.one_one_real) (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_20) (@ tptp.bit1 tptp.pls))))))
% 0.60/0.99 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.60/0.99 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.number267125858f_real (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.60/0.99 (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)))))))
% 0.60/0.99 (assert (forall ((W tptp.int)) (@ (@ tptp.ord_less_eq_int W) W)))
% 0.60/1.00 (assert (forall ((Z tptp.int) (W tptp.int)) (or (@ (@ tptp.ord_less_eq_int Z) W) (@ (@ tptp.ord_less_eq_int W) Z))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (Y_1 tptp.int)) (or (@ (@ tptp.ord_less_int X_1) Y_1) (= X_1 Y_1) (@ (@ tptp.ord_less_int Y_1) X_1))))
% 0.60/1.00 (assert (forall ((K tptp.int) (I_1 tptp.int) (J_1 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int I_1))) (=> (@ _let_1 J_1) (=> (@ (@ tptp.ord_less_eq_int J_1) K) (@ _let_1 K))))))
% 0.60/1.00 (assert (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) W) (=> (@ (@ tptp.ord_less_eq_int W) Z) (= Z W)))))
% 0.60/1.00 (assert (forall ((X_41 tptp.int) (P_6 tptp.nat) (Q_6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X_41))) (= (@ (@ tptp.power_power_int (@ _let_1 P_6)) Q_6) (@ _let_1 (@ (@ tptp.times_times_nat P_6) Q_6))))))
% 0.60/1.00 (assert (forall ((X_41 tptp.real) (P_6 tptp.nat) (Q_6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X_41))) (= (@ (@ tptp.power_power_real (@ _let_1 P_6)) Q_6) (@ _let_1 (@ (@ tptp.times_times_nat P_6) Q_6))))))
% 0.60/1.00 (assert (forall ((X_41 tptp.nat) (P_6 tptp.nat) (Q_6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X_41))) (= (@ (@ tptp.power_power_nat (@ _let_1 P_6)) Q_6) (@ _let_1 (@ (@ tptp.times_times_nat P_6) Q_6))))))
% 0.60/1.00 (assert (forall ((X_40 tptp.int)) (= (@ (@ tptp.power_power_int X_40) tptp.one_one_nat) X_40)))
% 0.60/1.00 (assert (forall ((X_40 tptp.real)) (= (@ (@ tptp.power_power_real X_40) tptp.one_one_nat) X_40)))
% 0.60/1.00 (assert (forall ((X_40 tptp.nat)) (= (@ (@ tptp.power_power_nat X_40) tptp.one_one_nat) X_40)))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (Y_1 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X_1))) (= (@ (@ tptp.power_power_int (@ _let_1 Y_1)) Z) (@ _let_1 (@ (@ tptp.times_times_nat Y_1) Z))))))
% 0.60/1.00 (assert (forall ((V_19 tptp.int) (W_17 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V_19))) (let ((_let_2 (@ tptp.number_number_of_int W_17))) (= (@ (@ tptp.ord_less_eq_int _let_1) _let_2) (not (@ (@ tptp.ord_less_int _let_2) _let_1)))))))
% 0.60/1.00 (assert (forall ((V_19 tptp.int) (W_17 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V_19))) (let ((_let_2 (@ tptp.number_number_of_nat W_17))) (= (@ (@ tptp.ord_less_eq_nat _let_1) _let_2) (not (@ (@ tptp.ord_less_nat _let_2) _let_1)))))))
% 0.60/1.00 (assert (forall ((V_19 tptp.int) (W_17 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real V_19))) (let ((_let_2 (@ tptp.number267125858f_real W_17))) (= (@ (@ tptp.ord_less_eq_real _let_1) _let_2) (not (@ (@ tptp.ord_less_real _let_2) _let_1)))))))
% 0.60/1.00 (assert (forall ((X_39 tptp.int) (Y_33 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int X_39)) (@ tptp.number_number_of_int Y_33)) (@ (@ tptp.ord_less_int X_39) Y_33))))
% 0.60/1.00 (assert (forall ((X_39 tptp.int) (Y_33 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.number267125858f_real X_39)) (@ tptp.number267125858f_real Y_33)) (@ (@ tptp.ord_less_int X_39) Y_33))))
% 0.60/1.00 (assert (forall ((X_38 tptp.int) (Y_32 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_38)) (@ tptp.number_number_of_int Y_32)) (@ (@ tptp.ord_less_eq_int X_38) Y_32))))
% 0.60/1.00 (assert (forall ((X_38 tptp.int) (Y_32 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.number267125858f_real X_38)) (@ tptp.number267125858f_real Y_32)) (@ (@ tptp.ord_less_eq_int X_38) Y_32))))
% 0.60/1.00 (assert (forall ((Z_10 tptp.int) (Z tptp.int) (W_16 tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int W_16) W) (=> (@ (@ tptp.ord_less_eq_int Z_10) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int W_16) Z_10)) (@ (@ tptp.plus_plus_int W) Z))))))
% 0.60/1.00 (assert (forall ((X_37 tptp.int) (P_5 tptp.nat) (Q_5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X_37))) (= (@ (@ tptp.times_times_int (@ _let_1 P_5)) (@ _let_1 Q_5)) (@ _let_1 (@ (@ tptp.plus_plus_nat P_5) Q_5))))))
% 0.60/1.00 (assert (forall ((X_37 tptp.real) (P_5 tptp.nat) (Q_5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X_37))) (= (@ (@ tptp.times_times_real (@ _let_1 P_5)) (@ _let_1 Q_5)) (@ _let_1 (@ (@ tptp.plus_plus_nat P_5) Q_5))))))
% 0.60/1.00 (assert (forall ((X_37 tptp.nat) (P_5 tptp.nat) (Q_5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X_37))) (= (@ (@ tptp.times_times_nat (@ _let_1 P_5)) (@ _let_1 Q_5)) (@ _let_1 (@ (@ tptp.plus_plus_nat P_5) Q_5))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (Y_1 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X_1))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat Y_1) Z)) (@ (@ tptp.times_times_int (@ _let_1 Y_1)) (@ _let_1 Z))))))
% 0.60/1.00 (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))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.60/1.00 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_int K1) K2))))
% 0.60/1.00 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_int K) L))))
% 0.60/1.00 (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))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (not (@ (@ tptp.ord_less_int tptp.pls) tptp.pls)))
% 0.60/1.00 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K1)) (@ tptp.bit0 K2)) (@ (@ tptp.ord_less_int K1) K2))))
% 0.60/1.00 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K)) (@ tptp.bit0 L)) (@ (@ tptp.ord_less_int K) L))))
% 0.60/1.00 (assert (@ (@ tptp.ord_less_eq_int tptp.pls) tptp.pls))
% 0.60/1.00 (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))))
% 0.60/1.00 (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))))
% 0.60/1.00 (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))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((K tptp.int) (I_1 tptp.int) (J_1 tptp.int)) (=> (@ (@ tptp.ord_less_int I_1) J_1) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I_1) K)) (@ (@ tptp.plus_plus_int J_1) K)))))
% 0.60/1.00 (assert (forall ((K tptp.int) (I_1 tptp.int) (J_1 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (@ (@ tptp.ord_less_eq_int I_1) J_1) (@ (@ tptp.ord_less_eq_int (@ _let_1 I_1)) (@ _let_1 J_1))))))
% 0.60/1.00 (assert (forall ((V_6 tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V_6))) (let ((_let_2 (@ tptp.number_number_of_nat V))) (let ((_let_3 (@ (@ tptp.plus_plus_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_int V_6) tptp.pls))) (let ((_let_5 (@ (@ tptp.ord_less_int V) 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) V_6))))))))))))))
% 0.60/1.00 (assert (= (@ tptp.number_number_of_nat (@ tptp.bit1 tptp.pls)) tptp.one_one_nat))
% 0.60/1.00 (assert (= tptp.one_one_nat (@ tptp.number_number_of_nat (@ tptp.bit1 tptp.pls))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) tptp.pls) (@ (@ tptp.ord_less_int K) tptp.pls))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int tptp.pls) (@ tptp.bit1 K)) (@ (@ tptp.ord_less_eq_int tptp.pls) K))))
% 0.60/1.00 (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))))
% 0.60/1.00 (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))))
% 0.60/1.00 (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))))
% 0.60/1.00 (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))))
% 0.60/1.00 (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))))
% 0.60/1.00 (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))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (@ tptp.zprime (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.60/1.00 (assert (forall ((Y_1 tptp.int) (X_1 tptp.int)) (=> (@ tptp.twoSqu919416604sum2sq X_1) (=> (@ tptp.twoSqu919416604sum2sq Y_1) (@ tptp.twoSqu919416604sum2sq (@ (@ tptp.times_times_int X_1) Y_1))))))
% 0.60/1.00 (assert (forall ((Lx_6 tptp.int) (Ly_4 tptp.int) (Rx_6 tptp.int) (Ry_4 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_6))) (= (@ (@ tptp.times_times_int (@ _let_1 Ly_4)) (@ (@ tptp.times_times_int Rx_6) Ry_4)) (@ (@ tptp.times_times_int (@ _let_1 Rx_6)) (@ (@ tptp.times_times_int Ly_4) Ry_4))))))
% 0.60/1.00 (assert (forall ((Lx_6 tptp.nat) (Ly_4 tptp.nat) (Rx_6 tptp.nat) (Ry_4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx_6))) (= (@ (@ tptp.times_times_nat (@ _let_1 Ly_4)) (@ (@ tptp.times_times_nat Rx_6) Ry_4)) (@ (@ tptp.times_times_nat (@ _let_1 Rx_6)) (@ (@ tptp.times_times_nat Ly_4) Ry_4))))))
% 0.60/1.00 (assert (forall ((Lx_6 tptp.real) (Ly_4 tptp.real) (Rx_6 tptp.real) (Ry_4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx_6))) (= (@ (@ tptp.times_times_real (@ _let_1 Ly_4)) (@ (@ tptp.times_times_real Rx_6) Ry_4)) (@ (@ tptp.times_times_real (@ _let_1 Rx_6)) (@ (@ tptp.times_times_real Ly_4) Ry_4))))))
% 0.60/1.00 (assert (forall ((Lx_5 tptp.int) (Ly_3 tptp.int) (Rx_5 tptp.int) (Ry_3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.times_times_int Lx_5) Ly_3)))) (let ((_let_2 (@ tptp.times_times_int Rx_5))) (= (@ _let_1 (@ _let_2 Ry_3)) (@ _let_2 (@ _let_1 Ry_3)))))))
% 0.60/1.00 (assert (forall ((Lx_5 tptp.nat) (Ly_3 tptp.nat) (Rx_5 tptp.nat) (Ry_3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ (@ tptp.times_times_nat Lx_5) Ly_3)))) (let ((_let_2 (@ tptp.times_times_nat Rx_5))) (= (@ _let_1 (@ _let_2 Ry_3)) (@ _let_2 (@ _let_1 Ry_3)))))))
% 0.60/1.00 (assert (forall ((Lx_5 tptp.real) (Ly_3 tptp.real) (Rx_5 tptp.real) (Ry_3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.times_times_real Lx_5) Ly_3)))) (let ((_let_2 (@ tptp.times_times_real Rx_5))) (= (@ _let_1 (@ _let_2 Ry_3)) (@ _let_2 (@ _let_1 Ry_3)))))))
% 0.60/1.00 (assert (forall ((Lx_4 tptp.int) (Ly_2 tptp.int) (Rx_4 tptp.int) (Ry_2 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int Rx_4) Ry_2))) (let ((_let_2 (@ tptp.times_times_int Lx_4))) (= (@ (@ tptp.times_times_int (@ _let_2 Ly_2)) _let_1) (@ _let_2 (@ (@ tptp.times_times_int Ly_2) _let_1)))))))
% 0.60/1.00 (assert (forall ((Lx_4 tptp.nat) (Ly_2 tptp.nat) (Rx_4 tptp.nat) (Ry_2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat Rx_4) Ry_2))) (let ((_let_2 (@ tptp.times_times_nat Lx_4))) (= (@ (@ tptp.times_times_nat (@ _let_2 Ly_2)) _let_1) (@ _let_2 (@ (@ tptp.times_times_nat Ly_2) _let_1)))))))
% 0.60/1.00 (assert (forall ((Lx_4 tptp.real) (Ly_2 tptp.real) (Rx_4 tptp.real) (Ry_2 tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real Rx_4) Ry_2))) (let ((_let_2 (@ tptp.times_times_real Lx_4))) (= (@ (@ tptp.times_times_real (@ _let_2 Ly_2)) _let_1) (@ _let_2 (@ (@ tptp.times_times_real Ly_2) _let_1)))))))
% 0.60/1.00 (assert (forall ((Lx_3 tptp.int) (Ly_1 tptp.int) (Rx_3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_3))) (= (@ (@ tptp.times_times_int (@ _let_1 Ly_1)) Rx_3) (@ (@ tptp.times_times_int (@ _let_1 Rx_3)) Ly_1)))))
% 0.60/1.00 (assert (forall ((Lx_3 tptp.nat) (Ly_1 tptp.nat) (Rx_3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx_3))) (= (@ (@ tptp.times_times_nat (@ _let_1 Ly_1)) Rx_3) (@ (@ tptp.times_times_nat (@ _let_1 Rx_3)) Ly_1)))))
% 0.60/1.00 (assert (forall ((Lx_3 tptp.real) (Ly_1 tptp.real) (Rx_3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx_3))) (= (@ (@ tptp.times_times_real (@ _let_1 Ly_1)) Rx_3) (@ (@ tptp.times_times_real (@ _let_1 Rx_3)) Ly_1)))))
% 0.60/1.00 (assert (forall ((Lx_2 tptp.int) (Ly tptp.int) (Rx_2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_2))) (= (@ (@ tptp.times_times_int (@ _let_1 Ly)) Rx_2) (@ _let_1 (@ (@ tptp.times_times_int Ly) Rx_2))))))
% 0.60/1.00 (assert (forall ((Lx_2 tptp.nat) (Ly tptp.nat) (Rx_2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx_2))) (= (@ (@ tptp.times_times_nat (@ _let_1 Ly)) Rx_2) (@ _let_1 (@ (@ tptp.times_times_nat Ly) Rx_2))))))
% 0.60/1.00 (assert (forall ((Lx_2 tptp.real) (Ly tptp.real) (Rx_2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx_2))) (= (@ (@ tptp.times_times_real (@ _let_1 Ly)) Rx_2) (@ _let_1 (@ (@ tptp.times_times_real Ly) Rx_2))))))
% 0.60/1.00 (assert (forall ((Lx_1 tptp.int) (Rx_1 tptp.int) (Ry_1 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_1))) (= (@ _let_1 (@ (@ tptp.times_times_int Rx_1) Ry_1)) (@ (@ tptp.times_times_int (@ _let_1 Rx_1)) Ry_1)))))
% 0.60/1.00 (assert (forall ((Lx_1 tptp.nat) (Rx_1 tptp.nat) (Ry_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx_1))) (= (@ _let_1 (@ (@ tptp.times_times_nat Rx_1) Ry_1)) (@ (@ tptp.times_times_nat (@ _let_1 Rx_1)) Ry_1)))))
% 0.60/1.00 (assert (forall ((Lx_1 tptp.real) (Rx_1 tptp.real) (Ry_1 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx_1))) (= (@ _let_1 (@ (@ tptp.times_times_real Rx_1) Ry_1)) (@ (@ tptp.times_times_real (@ _let_1 Rx_1)) Ry_1)))))
% 0.60/1.00 (assert (forall ((Lx tptp.int) (Rx tptp.int) (Ry tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx))) (let ((_let_2 (@ tptp.times_times_int Rx))) (= (@ _let_1 (@ _let_2 Ry)) (@ _let_2 (@ _let_1 Ry)))))))
% 0.60/1.00 (assert (forall ((Lx tptp.nat) (Rx tptp.nat) (Ry tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx))) (let ((_let_2 (@ tptp.times_times_nat Rx))) (= (@ _let_1 (@ _let_2 Ry)) (@ _let_2 (@ _let_1 Ry)))))))
% 0.60/1.00 (assert (forall ((Lx tptp.real) (Rx tptp.real) (Ry tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx))) (let ((_let_2 (@ tptp.times_times_real Rx))) (= (@ _let_1 (@ _let_2 Ry)) (@ _let_2 (@ _let_1 Ry)))))))
% 0.60/1.00 (assert (forall ((A_126 tptp.int) (B_73 tptp.int)) (= (@ (@ tptp.times_times_int A_126) B_73) (@ (@ tptp.times_times_int B_73) A_126))))
% 0.60/1.00 (assert (forall ((A_126 tptp.nat) (B_73 tptp.nat)) (= (@ (@ tptp.times_times_nat A_126) B_73) (@ (@ tptp.times_times_nat B_73) A_126))))
% 0.60/1.00 (assert (forall ((A_126 tptp.real) (B_73 tptp.real)) (= (@ (@ tptp.times_times_real A_126) B_73) (@ (@ tptp.times_times_real B_73) A_126))))
% 0.60/1.00 (assert (forall ((A_125 tptp.int) (B_72 tptp.int) (C_39 tptp.int) (D_11 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_125))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_72)) (@ (@ tptp.plus_plus_int C_39) D_11)) (@ (@ tptp.plus_plus_int (@ _let_1 C_39)) (@ (@ tptp.plus_plus_int B_72) D_11))))))
% 0.60/1.00 (assert (forall ((A_125 tptp.nat) (B_72 tptp.nat) (C_39 tptp.nat) (D_11 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_125))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_72)) (@ (@ tptp.plus_plus_nat C_39) D_11)) (@ (@ tptp.plus_plus_nat (@ _let_1 C_39)) (@ (@ tptp.plus_plus_nat B_72) D_11))))))
% 0.60/1.00 (assert (forall ((A_125 tptp.real) (B_72 tptp.real) (C_39 tptp.real) (D_11 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_125))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B_72)) (@ (@ tptp.plus_plus_real C_39) D_11)) (@ (@ tptp.plus_plus_real (@ _let_1 C_39)) (@ (@ tptp.plus_plus_real B_72) D_11))))))
% 0.60/1.00 (assert (forall ((X_36 tptp.int) (A_124 (-> tptp.int Bool))) (= (@ (@ tptp.member_int X_36) A_124) (@ A_124 X_36))))
% 0.60/1.00 (assert (forall ((P_4 (-> tptp.int Bool))) (= (@ tptp.collect_int P_4) P_4)))
% 0.60/1.00 (assert (forall ((A_123 tptp.int) (B_71 tptp.int) (C_38 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_123))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_71)) C_38) (@ (@ tptp.plus_plus_int (@ _let_1 C_38)) B_71)))))
% 0.60/1.00 (assert (forall ((A_123 tptp.nat) (B_71 tptp.nat) (C_38 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_123))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_71)) C_38) (@ (@ tptp.plus_plus_nat (@ _let_1 C_38)) B_71)))))
% 0.60/1.00 (assert (forall ((A_123 tptp.real) (B_71 tptp.real) (C_38 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_123))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B_71)) C_38) (@ (@ tptp.plus_plus_real (@ _let_1 C_38)) B_71)))))
% 0.60/1.00 (assert (forall ((A_122 tptp.int) (B_70 tptp.int) (C_37 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_122))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_70)) C_37) (@ _let_1 (@ (@ tptp.plus_plus_int B_70) C_37))))))
% 0.60/1.00 (assert (forall ((A_122 tptp.nat) (B_70 tptp.nat) (C_37 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_122))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_70)) C_37) (@ _let_1 (@ (@ tptp.plus_plus_nat B_70) C_37))))))
% 0.60/1.00 (assert (forall ((A_122 tptp.real) (B_70 tptp.real) (C_37 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_122))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B_70)) C_37) (@ _let_1 (@ (@ tptp.plus_plus_real B_70) C_37))))))
% 0.60/1.00 (assert (forall ((A_121 tptp.int) (C_36 tptp.int) (D_10 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_121))) (= (@ _let_1 (@ (@ tptp.plus_plus_int C_36) D_10)) (@ (@ tptp.plus_plus_int (@ _let_1 C_36)) D_10)))))
% 0.60/1.00 (assert (forall ((A_121 tptp.nat) (C_36 tptp.nat) (D_10 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_121))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat C_36) D_10)) (@ (@ tptp.plus_plus_nat (@ _let_1 C_36)) D_10)))))
% 0.60/1.00 (assert (forall ((A_121 tptp.real) (C_36 tptp.real) (D_10 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_121))) (= (@ _let_1 (@ (@ tptp.plus_plus_real C_36) D_10)) (@ (@ tptp.plus_plus_real (@ _let_1 C_36)) D_10)))))
% 0.60/1.00 (assert (forall ((A_120 tptp.int) (C_35 tptp.int) (D_9 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_120))) (let ((_let_2 (@ tptp.plus_plus_int C_35))) (= (@ _let_1 (@ _let_2 D_9)) (@ _let_2 (@ _let_1 D_9)))))))
% 0.60/1.00 (assert (forall ((A_120 tptp.nat) (C_35 tptp.nat) (D_9 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_120))) (let ((_let_2 (@ tptp.plus_plus_nat C_35))) (= (@ _let_1 (@ _let_2 D_9)) (@ _let_2 (@ _let_1 D_9)))))))
% 0.60/1.00 (assert (forall ((A_120 tptp.real) (C_35 tptp.real) (D_9 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_120))) (let ((_let_2 (@ tptp.plus_plus_real C_35))) (= (@ _let_1 (@ _let_2 D_9)) (@ _let_2 (@ _let_1 D_9)))))))
% 0.60/1.00 (assert (forall ((A_119 tptp.int) (C_34 tptp.int)) (= (@ (@ tptp.plus_plus_int A_119) C_34) (@ (@ tptp.plus_plus_int C_34) A_119))))
% 0.60/1.00 (assert (forall ((A_119 tptp.nat) (C_34 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_119) C_34) (@ (@ tptp.plus_plus_nat C_34) A_119))))
% 0.60/1.00 (assert (forall ((A_119 tptp.real) (C_34 tptp.real)) (= (@ (@ tptp.plus_plus_real A_119) C_34) (@ (@ tptp.plus_plus_real C_34) A_119))))
% 0.60/1.00 (assert (forall ((X_35 tptp.int) (Y_31 tptp.int)) (= (= (@ tptp.number_number_of_int X_35) (@ tptp.number_number_of_int Y_31)) (= X_35 Y_31))))
% 0.60/1.00 (assert (forall ((X_35 tptp.int) (Y_31 tptp.int)) (= (= (@ tptp.number267125858f_real X_35) (@ tptp.number267125858f_real Y_31)) (= X_35 Y_31))))
% 0.60/1.00 (assert (forall ((W_15 tptp.int) (X_34 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat W_15))) (= (= _let_1 X_34) (= X_34 _let_1)))))
% 0.60/1.00 (assert (forall ((W_15 tptp.int) (X_34 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W_15))) (= (= _let_1 X_34) (= X_34 _let_1)))))
% 0.60/1.00 (assert (forall ((W_15 tptp.int) (X_34 tptp.real)) (let ((_let_1 (@ tptp.number267125858f_real W_15))) (= (= _let_1 X_34) (= X_34 _let_1)))))
% 0.60/1.00 (assert (forall ((K tptp.int) (L tptp.int)) (= (= (@ tptp.bit1 K) (@ tptp.bit1 L)) (= K L))))
% 0.60/1.00 (assert (forall ((K tptp.int) (L tptp.int)) (= (= (@ tptp.bit0 K) (@ tptp.bit0 L)) (= K L))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int Z) W) (@ (@ tptp.times_times_int W) Z))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (@ tptp.number_number_of_int K) K)))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (Y_1 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X_1))) (let ((_let_2 (@ tptp.plus_plus_int Y_1))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.60/1.00 (assert (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.plus_plus_int Z) W) (@ (@ tptp.plus_plus_int W) Z))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K)) tptp.pls) (@ (@ tptp.ord_less_int K) tptp.pls))))
% 0.60/1.00 (assert (forall ((K1 tptp.int) (K2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K1)) (@ tptp.bit0 K2)) (@ (@ tptp.ord_less_int K1) K2))))
% 0.60/1.00 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K)) (@ tptp.bit0 L)) (@ (@ tptp.ord_less_int K) L))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K)) tptp.pls) (@ (@ tptp.ord_less_int K) tptp.pls))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.pls))) (= (@ _let_1 (@ tptp.bit0 K)) (@ _let_1 K)))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (= (@ _let_1 (@ tptp.bit1 K)) (@ _let_1 K)))))
% 0.60/1.00 (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))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) tptp.pls) (@ (@ tptp.ord_less_eq_int K) tptp.pls))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (= (@ _let_1 (@ tptp.bit0 K)) (@ _let_1 K)))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((A_118 tptp.int) (N_40 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (let ((_let_2 (@ tptp.power_power_int A_118))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N_40)) (@ (@ tptp.power_power_int (@ _let_2 N_40)) _let_1))))))
% 0.60/1.00 (assert (forall ((A_118 tptp.real) (N_40 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (let ((_let_2 (@ tptp.power_power_real A_118))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N_40)) (@ (@ tptp.power_power_real (@ _let_2 N_40)) _let_1))))))
% 0.60/1.00 (assert (forall ((A_118 tptp.nat) (N_40 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (let ((_let_2 (@ tptp.power_power_nat A_118))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N_40)) (@ (@ tptp.power_power_nat (@ _let_2 N_40)) _let_1))))))
% 0.60/1.00 (assert (forall ((X_33 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int X_33)) tptp.one_one_int) (@ (@ tptp.ord_less_int X_33) (@ tptp.bit1 tptp.pls)))))
% 0.60/1.00 (assert (forall ((X_33 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.number267125858f_real X_33)) tptp.one_one_real) (@ (@ tptp.ord_less_int X_33) (@ tptp.bit1 tptp.pls)))))
% 0.60/1.00 (assert (forall ((Y_30 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.number_number_of_int Y_30)) (@ (@ tptp.ord_less_int (@ tptp.bit1 tptp.pls)) Y_30))))
% 0.60/1.00 (assert (forall ((Y_30 tptp.int)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.number267125858f_real Y_30)) (@ (@ tptp.ord_less_int (@ tptp.bit1 tptp.pls)) Y_30))))
% 0.60/1.00 (assert (forall ((X_32 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_32)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int X_32) (@ tptp.bit1 tptp.pls)))))
% 0.60/1.00 (assert (forall ((X_32 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.number267125858f_real X_32)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_int X_32) (@ tptp.bit1 tptp.pls)))))
% 0.60/1.00 (assert (forall ((Y_29 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.number_number_of_int Y_29)) (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 tptp.pls)) Y_29))))
% 0.60/1.00 (assert (forall ((Y_29 tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.number267125858f_real Y_29)) (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 tptp.pls)) Y_29))))
% 0.60/1.00 (assert (forall ((W_14 tptp.int) (Y_28 tptp.int) (X_31 tptp.int) (Z_9 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X_31))) (let ((_let_2 (@ tptp.times_times_int W_14))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y_28)) (@ _let_1 Z_9)) (@ (@ tptp.plus_plus_int (@ _let_2 Z_9)) (@ _let_1 Y_28))) (or (= W_14 X_31) (= Y_28 Z_9)))))))
% 0.60/1.00 (assert (forall ((W_14 tptp.nat) (Y_28 tptp.nat) (X_31 tptp.nat) (Z_9 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X_31))) (let ((_let_2 (@ tptp.times_times_nat W_14))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y_28)) (@ _let_1 Z_9)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z_9)) (@ _let_1 Y_28))) (or (= W_14 X_31) (= Y_28 Z_9)))))))
% 0.60/1.00 (assert (forall ((W_14 tptp.real) (Y_28 tptp.real) (X_31 tptp.real) (Z_9 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X_31))) (let ((_let_2 (@ tptp.times_times_real W_14))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y_28)) (@ _let_1 Z_9)) (@ (@ tptp.plus_plus_real (@ _let_2 Z_9)) (@ _let_1 Y_28))) (or (= W_14 X_31) (= Y_28 Z_9)))))))
% 0.60/1.00 (assert (forall ((A_117 tptp.int) (M_14 tptp.int) (B_69 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_117) M_14)) (@ (@ tptp.times_times_int B_69) M_14)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_117) B_69)) M_14))))
% 0.60/1.00 (assert (forall ((A_117 tptp.nat) (M_14 tptp.nat) (B_69 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_117) M_14)) (@ (@ tptp.times_times_nat B_69) M_14)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_117) B_69)) M_14))))
% 0.60/1.00 (assert (forall ((A_117 tptp.real) (M_14 tptp.real) (B_69 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_117) M_14)) (@ (@ tptp.times_times_real B_69) M_14)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_117) B_69)) M_14))))
% 0.60/1.00 (assert (forall ((A_116 tptp.int) (B_68 tptp.int) (C_33 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_116) B_68)) C_33) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_116) C_33)) (@ (@ tptp.times_times_int B_68) C_33)))))
% 0.60/1.00 (assert (forall ((A_116 tptp.nat) (B_68 tptp.nat) (C_33 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_116) B_68)) C_33) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_116) C_33)) (@ (@ tptp.times_times_nat B_68) C_33)))))
% 0.60/1.00 (assert (forall ((A_116 tptp.real) (B_68 tptp.real) (C_33 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_116) B_68)) C_33) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_116) C_33)) (@ (@ tptp.times_times_real B_68) C_33)))))
% 0.60/1.00 (assert (forall ((C_32 tptp.int) (D_8 tptp.int) (A_115 tptp.int) (B_67 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B_67))) (let ((_let_2 (@ tptp.times_times_int A_115))) (= (and (not (= A_115 B_67)) (not (= C_32 D_8))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C_32)) (@ _let_1 D_8)) (@ (@ tptp.plus_plus_int (@ _let_2 D_8)) (@ _let_1 C_32)))))))))
% 0.60/1.00 (assert (forall ((C_32 tptp.nat) (D_8 tptp.nat) (A_115 tptp.nat) (B_67 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B_67))) (let ((_let_2 (@ tptp.times_times_nat A_115))) (= (and (not (= A_115 B_67)) (not (= C_32 D_8))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C_32)) (@ _let_1 D_8)) (@ (@ tptp.plus_plus_nat (@ _let_2 D_8)) (@ _let_1 C_32)))))))))
% 0.60/1.00 (assert (forall ((C_32 tptp.real) (D_8 tptp.real) (A_115 tptp.real) (B_67 tptp.real)) (let ((_let_1 (@ tptp.times_times_real B_67))) (let ((_let_2 (@ tptp.times_times_real A_115))) (= (and (not (= A_115 B_67)) (not (= C_32 D_8))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C_32)) (@ _let_1 D_8)) (@ (@ tptp.plus_plus_real (@ _let_2 D_8)) (@ _let_1 C_32)))))))))
% 0.60/1.00 (assert (forall ((X_30 tptp.int) (Y_27 tptp.int) (Z_8 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X_30))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Y_27) Z_8)) (@ (@ tptp.plus_plus_int (@ _let_1 Y_27)) (@ _let_1 Z_8))))))
% 0.60/1.00 (assert (forall ((X_30 tptp.nat) (Y_27 tptp.nat) (Z_8 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X_30))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat Y_27) Z_8)) (@ (@ tptp.plus_plus_nat (@ _let_1 Y_27)) (@ _let_1 Z_8))))))
% 0.60/1.00 (assert (forall ((X_30 tptp.real) (Y_27 tptp.real) (Z_8 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X_30))) (= (@ _let_1 (@ (@ tptp.plus_plus_real Y_27) Z_8)) (@ (@ tptp.plus_plus_real (@ _let_1 Y_27)) (@ _let_1 Z_8))))))
% 0.60/1.00 (assert (forall ((A_114 tptp.int)) (= (@ (@ tptp.times_times_int A_114) tptp.one_one_int) A_114)))
% 0.60/1.00 (assert (forall ((A_114 tptp.nat)) (= (@ (@ tptp.times_times_nat A_114) tptp.one_one_nat) A_114)))
% 0.60/1.00 (assert (forall ((A_114 tptp.real)) (= (@ (@ tptp.times_times_real A_114) tptp.one_one_real) A_114)))
% 0.60/1.00 (assert (forall ((A_113 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A_113) A_113)))
% 0.60/1.00 (assert (forall ((A_113 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A_113) A_113)))
% 0.60/1.00 (assert (forall ((A_113 tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A_113) A_113)))
% 0.60/1.00 (assert (forall ((X_29 tptp.int) (Y_26 tptp.int) (Q_4 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int X_29) Y_26)) Q_4) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X_29) Q_4)) (@ (@ tptp.power_power_int Y_26) Q_4)))))
% 0.60/1.00 (assert (forall ((X_29 tptp.real) (Y_26 tptp.real) (Q_4 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real X_29) Y_26)) Q_4) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X_29) Q_4)) (@ (@ tptp.power_power_real Y_26) Q_4)))))
% 0.60/1.00 (assert (forall ((X_29 tptp.nat) (Y_26 tptp.nat) (Q_4 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat X_29) Y_26)) Q_4) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X_29) Q_4)) (@ (@ tptp.power_power_nat Y_26) Q_4)))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (not (= (@ tptp.bit1 K) tptp.pls))))
% 0.60/1.00 (assert (forall ((L tptp.int)) (not (= tptp.pls (@ tptp.bit1 L)))))
% 0.60/1.00 (assert (forall ((K tptp.int) (L tptp.int)) (not (= (@ tptp.bit1 K) (@ tptp.bit0 L)))))
% 0.60/1.00 (assert (forall ((K tptp.int) (L tptp.int)) (not (= (@ tptp.bit0 K) (@ tptp.bit1 L)))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (= (@ tptp.bit0 K) tptp.pls) (= K tptp.pls))))
% 0.60/1.00 (assert (forall ((L tptp.int)) (= (= tptp.pls (@ tptp.bit0 L)) (= tptp.pls L))))
% 0.60/1.00 (assert (= (@ tptp.bit0 tptp.pls) tptp.pls))
% 0.60/1.00 (assert (forall ((W tptp.int)) (= (@ (@ tptp.times_times_int tptp.pls) W) tptp.pls)))
% 0.60/1.00 (assert (forall ((K tptp.int) (L tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.bit0 K)) L) (@ tptp.bit0 (@ (@ tptp.times_times_int K) L)))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.pls) K)))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.pls) K) K)))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (@ tptp.bit0 K) (@ (@ tptp.plus_plus_int K) K))))
% 0.60/1.00 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) tptp.one_one_int) Z)))
% 0.60/1.00 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) Z) Z)))
% 0.60/1.00 (assert (forall ((V tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V)) (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V) W)))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((V tptp.int) (W tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V)) (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V) W)))))
% 0.60/1.00 (assert (forall ((V_18 tptp.int) (V_17 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_17) (=> (@ _let_1 V_18) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_17)) (@ tptp.number_number_of_int V_18)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_17) V_18))))))))
% 0.60/1.00 (assert (forall ((V_18 tptp.int) (V_17 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_17) (=> (@ _let_1 V_18) (= (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V_17)) (@ tptp.number_number_of_nat V_18)) (@ tptp.number_number_of_nat (@ (@ tptp.times_times_int V_17) V_18))))))))
% 0.60/1.00 (assert (forall ((V_18 tptp.int) (V_17 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_17) (=> (@ _let_1 V_18) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real V_17)) (@ tptp.number267125858f_real V_18)) (@ tptp.number267125858f_real (@ (@ tptp.times_times_int V_17) V_18))))))))
% 0.60/1.00 (assert (forall ((V_16 tptp.int) (V_15 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_15) (=> (@ _let_1 V_16) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_15)) (@ tptp.number_number_of_int V_16)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_15) V_16))))))))
% 0.60/1.00 (assert (forall ((V_16 tptp.int) (V_15 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_15) (=> (@ _let_1 V_16) (= (@ (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat V_15)) (@ tptp.number_number_of_nat V_16)) (@ tptp.number_number_of_nat (@ (@ tptp.plus_plus_int V_15) V_16))))))))
% 0.60/1.00 (assert (forall ((V_16 tptp.int) (V_15 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_15) (=> (@ _let_1 V_16) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_15)) (@ tptp.number267125858f_real V_16)) (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_15) V_16))))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int)) (@ (@ tptp.ord_less_eq_int X_1) (@ (@ tptp.power_power_int X_1) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))))
% 0.60/1.00 (assert (forall ((A_112 tptp.int) (B_66 tptp.int) (V_14 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V_14))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_112) B_66)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_112) _let_1)) (@ (@ tptp.times_times_int B_66) _let_1))))))
% 0.60/1.00 (assert (forall ((A_112 tptp.nat) (B_66 tptp.nat) (V_14 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V_14))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_112) B_66)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_112) _let_1)) (@ (@ tptp.times_times_nat B_66) _let_1))))))
% 0.60/1.00 (assert (forall ((A_112 tptp.real) (B_66 tptp.real) (V_14 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real V_14))) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_112) B_66)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_112) _let_1)) (@ (@ tptp.times_times_real B_66) _let_1))))))
% 0.60/1.00 (assert (forall ((V_13 tptp.int) (B_65 tptp.int) (C_31 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.number_number_of_int V_13)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B_65) C_31)) (@ (@ tptp.plus_plus_int (@ _let_1 B_65)) (@ _let_1 C_31))))))
% 0.60/1.00 (assert (forall ((V_13 tptp.int) (B_65 tptp.nat) (C_31 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.number_number_of_nat V_13)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B_65) C_31)) (@ (@ tptp.plus_plus_nat (@ _let_1 B_65)) (@ _let_1 C_31))))))
% 0.60/1.00 (assert (forall ((V_13 tptp.int) (B_65 tptp.real) (C_31 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.number267125858f_real V_13)))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B_65) C_31)) (@ (@ tptp.plus_plus_real (@ _let_1 B_65)) (@ _let_1 C_31))))))
% 0.60/1.00 (assert (forall ((A_111 tptp.int) (M_13 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_111) M_13)) M_13) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_111) tptp.one_one_int)) M_13))))
% 0.60/1.00 (assert (forall ((A_111 tptp.nat) (M_13 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_111) M_13)) M_13) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_111) tptp.one_one_nat)) M_13))))
% 0.60/1.00 (assert (forall ((A_111 tptp.real) (M_13 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_111) M_13)) M_13) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_111) tptp.one_one_real)) M_13))))
% 0.60/1.00 (assert (forall ((M_12 tptp.int) (A_110 tptp.int)) (= (@ (@ tptp.plus_plus_int M_12) (@ (@ tptp.times_times_int A_110) M_12)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_110) tptp.one_one_int)) M_12))))
% 0.60/1.00 (assert (forall ((M_12 tptp.nat) (A_110 tptp.nat)) (= (@ (@ tptp.plus_plus_nat M_12) (@ (@ tptp.times_times_nat A_110) M_12)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_110) tptp.one_one_nat)) M_12))))
% 0.60/1.00 (assert (forall ((M_12 tptp.real) (A_110 tptp.real)) (= (@ (@ tptp.plus_plus_real M_12) (@ (@ tptp.times_times_real A_110) M_12)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_110) tptp.one_one_real)) M_12))))
% 0.60/1.00 (assert (forall ((M_11 tptp.int)) (= (@ (@ tptp.plus_plus_int M_11) M_11) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)) M_11))))
% 0.60/1.00 (assert (forall ((M_11 tptp.nat)) (= (@ (@ tptp.plus_plus_nat M_11) M_11) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)) M_11))))
% 0.60/1.00 (assert (forall ((M_11 tptp.real)) (= (@ (@ tptp.plus_plus_real M_11) M_11) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)) M_11))))
% 0.60/1.00 (assert (forall ((A_109 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int tptp.pls)) A_109) A_109)))
% 0.60/1.00 (assert (forall ((A_109 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real tptp.pls)) A_109) A_109)))
% 0.60/1.00 (assert (forall ((A_108 tptp.int)) (= (@ (@ tptp.plus_plus_int A_108) (@ tptp.number_number_of_int tptp.pls)) A_108)))
% 0.60/1.00 (assert (forall ((A_108 tptp.real)) (= (@ (@ tptp.plus_plus_real A_108) (@ tptp.number267125858f_real tptp.pls)) A_108)))
% 0.60/1.00 (assert (forall ((V_12 tptp.int) (W_13 tptp.int) (Z_7 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_12)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int W_13)) Z_7)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_12) W_13))) Z_7))))
% 0.60/1.00 (assert (forall ((V_12 tptp.int) (W_13 tptp.int) (Z_7 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real V_12)) (@ (@ tptp.times_times_real (@ tptp.number267125858f_real W_13)) Z_7)) (@ (@ tptp.times_times_real (@ tptp.number267125858f_real (@ (@ tptp.times_times_int V_12) W_13))) Z_7))))
% 0.60/1.00 (assert (forall ((V_11 tptp.int) (W_12 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_11)) (@ tptp.number_number_of_int W_12)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_11) W_12)))))
% 0.60/1.00 (assert (forall ((V_11 tptp.int) (W_12 tptp.int)) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real V_11)) (@ tptp.number267125858f_real W_12)) (@ tptp.number267125858f_real (@ (@ tptp.times_times_int V_11) W_12)))))
% 0.60/1.00 (assert (forall ((V_10 tptp.int) (W_11 tptp.int)) (= (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_10) W_11)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_10)) (@ tptp.number_number_of_int W_11)))))
% 0.60/1.00 (assert (forall ((V_10 tptp.int) (W_11 tptp.int)) (= (@ tptp.number267125858f_real (@ (@ tptp.times_times_int V_10) W_11)) (@ (@ tptp.times_times_real (@ tptp.number267125858f_real V_10)) (@ tptp.number267125858f_real W_11)))))
% 0.60/1.00 (assert (forall ((V_9 tptp.int) (W_10 tptp.int) (Z_6 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_9)) (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int W_10)) Z_6)) (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_9) W_10))) Z_6))))
% 0.60/1.00 (assert (forall ((V_9 tptp.int) (W_10 tptp.int) (Z_6 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_9)) (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real W_10)) Z_6)) (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_9) W_10))) Z_6))))
% 0.60/1.00 (assert (forall ((V_8 tptp.int) (W_9 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_8)) (@ tptp.number_number_of_int W_9)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_8) W_9)))))
% 0.60/1.00 (assert (forall ((V_8 tptp.int) (W_9 tptp.int)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_8)) (@ tptp.number267125858f_real W_9)) (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_8) W_9)))))
% 0.60/1.00 (assert (forall ((V_7 tptp.int) (W_8 tptp.int)) (= (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_7) W_8)) (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_7)) (@ tptp.number_number_of_int W_8)))))
% 0.60/1.00 (assert (forall ((V_7 tptp.int) (W_8 tptp.int)) (= (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_7) W_8)) (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_7)) (@ tptp.number267125858f_real W_8)))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (@ tptp.bit1 K) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) K)) K))))
% 0.60/1.00 (assert (forall ((W_7 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W_7))) (= (@ tptp.number_number_of_int (@ tptp.bit1 W_7)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1)) _let_1)))))
% 0.60/1.00 (assert (forall ((W_7 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real W_7))) (= (@ tptp.number267125858f_real (@ tptp.bit1 W_7)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1)) _let_1)))))
% 0.60/1.00 (assert (forall ((A_107 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit1 tptp.pls))) A_107) A_107)))
% 0.60/1.00 (assert (forall ((A_107 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real (@ tptp.bit1 tptp.pls))) A_107) A_107)))
% 0.60/1.00 (assert (forall ((A_106 tptp.int)) (= (@ (@ tptp.times_times_int A_106) (@ tptp.number_number_of_int (@ tptp.bit1 tptp.pls))) A_106)))
% 0.60/1.00 (assert (forall ((A_106 tptp.real)) (= (@ (@ tptp.times_times_real A_106) (@ tptp.number267125858f_real (@ tptp.bit1 tptp.pls))) A_106)))
% 0.60/1.00 (assert (= (@ tptp.number_number_of_int (@ tptp.bit1 tptp.pls)) tptp.one_one_int))
% 0.60/1.00 (assert (= (@ tptp.number_number_of_nat (@ tptp.bit1 tptp.pls)) tptp.one_one_nat))
% 0.60/1.00 (assert (= (@ tptp.number267125858f_real (@ tptp.bit1 tptp.pls)) tptp.one_one_real))
% 0.60/1.00 (assert (= (@ tptp.number_number_of_int (@ tptp.bit1 tptp.pls)) tptp.one_one_int))
% 0.60/1.00 (assert (= (@ tptp.number267125858f_real (@ tptp.bit1 tptp.pls)) tptp.one_one_real))
% 0.60/1.00 (assert (= tptp.one_one_int (@ tptp.number_number_of_int (@ tptp.bit1 tptp.pls))))
% 0.60/1.00 (assert (= tptp.one_one_real (@ tptp.number267125858f_real (@ tptp.bit1 tptp.pls))))
% 0.60/1.00 (assert (= tptp.one_one_int (@ tptp.number_number_of_int (@ tptp.bit1 tptp.pls))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((W_6 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)) (@ tptp.number_number_of_int W_6)) (@ tptp.number_number_of_int (@ tptp.bit0 W_6)))))
% 0.60/1.00 (assert (forall ((W_6 tptp.int)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)) (@ tptp.number267125858f_real W_6)) (@ tptp.number267125858f_real (@ tptp.bit0 W_6)))))
% 0.60/1.00 (assert (forall ((A_105 tptp.int)) (= (@ (@ tptp.power_power_int A_105) (@ tptp.number_number_of_nat (@ tptp.bit1 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A_105) A_105)) A_105))))
% 0.60/1.00 (assert (forall ((A_105 tptp.real)) (= (@ (@ tptp.power_power_real A_105) (@ tptp.number_number_of_nat (@ tptp.bit1 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real A_105) A_105)) A_105))))
% 0.60/1.00 (assert (forall ((A_105 tptp.nat)) (= (@ (@ tptp.power_power_nat A_105) (@ tptp.number_number_of_nat (@ tptp.bit1 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat A_105) A_105)) A_105))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.power_power_int X_1))) (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)))))))))
% 0.60/1.00 (assert (forall ((Z_5 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) Z_5) (@ (@ tptp.plus_plus_int Z_5) Z_5))))
% 0.60/1.00 (assert (forall ((Z_5 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) Z_5) (@ (@ tptp.plus_plus_nat Z_5) Z_5))))
% 0.60/1.00 (assert (forall ((Z_5 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) Z_5) (@ (@ tptp.plus_plus_real Z_5) Z_5))))
% 0.60/1.00 (assert (forall ((Z_4 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) Z_4) (@ (@ tptp.plus_plus_int Z_4) Z_4))))
% 0.60/1.00 (assert (forall ((Z_4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) Z_4) (@ (@ tptp.plus_plus_real Z_4) Z_4))))
% 0.60/1.00 (assert (forall ((Z_3 tptp.int)) (= (@ (@ tptp.times_times_int Z_3) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.plus_plus_int Z_3) Z_3))))
% 0.60/1.00 (assert (forall ((Z_3 tptp.nat)) (= (@ (@ tptp.times_times_nat Z_3) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.plus_plus_nat Z_3) Z_3))))
% 0.60/1.00 (assert (forall ((Z_3 tptp.real)) (= (@ (@ tptp.times_times_real Z_3) (@ tptp.number267125858f_real (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.plus_plus_real Z_3) Z_3))))
% 0.60/1.00 (assert (forall ((Z_2 tptp.int)) (= (@ (@ tptp.times_times_int Z_2) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.plus_plus_int Z_2) Z_2))))
% 0.60/1.00 (assert (forall ((Z_2 tptp.real)) (= (@ (@ tptp.times_times_real Z_2) (@ tptp.number267125858f_real (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.plus_plus_real Z_2) Z_2))))
% 0.60/1.00 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.60/1.00 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.60/1.00 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.number267125858f_real (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.60/1.00 (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)))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((P tptp.int)) (let ((_let_1 (@ tptp.bit1 tptp.pls))) (let ((_let_2 (@ tptp.bit0 _let_1))) (=> (@ tptp.zprime P) (=> (not (= P (@ tptp.number_number_of_int _let_2))) (=> (not (= P (@ tptp.number_number_of_int (@ tptp.bit1 _let_1)))) (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int (@ tptp.bit1 _let_2))) P))))))))
% 0.60/1.00 (assert (= (@ tptp.twoSqu2057625106sum2sq (@ (@ tptp.product_Pair_int_int tptp.s) tptp.one_one_int)) (@ (@ 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)))
% 0.60/1.00 (assert (forall ((X_1 tptp.real) (Y_1 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_1) Y_1)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X_1) _let_2)) (@ (@ tptp.power_power_real Y_1) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.number267125858f_real _let_1)) X_1)) Y_1)))))))
% 0.60/1.00 (assert (forall ((X_1 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_1) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.number267125858f_real _let_1)) X_1)) _let_2))))))
% 0.60/1.00 (assert (forall ((N_39 tptp.nat) (A_104 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A_104) N_39))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_104) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A_104) _let_1))))))
% 0.60/1.00 (assert (forall ((N_39 tptp.nat) (A_104 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A_104) N_39))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_104) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A_104) _let_1))))))
% 0.60/1.00 (assert (forall ((N_39 tptp.nat) (A_104 tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A_104) N_39))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_104) (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.times_times_real A_104) _let_1))))))
% 0.60/1.00 (assert (forall ((N_38 tptp.nat) (A_103 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A_103) (@ _let_1 (@ (@ tptp.times_times_int A_103) (@ (@ tptp.power_power_int A_103) N_38)))))))
% 0.60/1.00 (assert (forall ((N_38 tptp.nat) (A_103 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A_103) (@ _let_1 (@ (@ tptp.times_times_nat A_103) (@ (@ tptp.power_power_nat A_103) N_38)))))))
% 0.60/1.00 (assert (forall ((N_38 tptp.nat) (A_103 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A_103) (@ _let_1 (@ (@ tptp.times_times_real A_103) (@ (@ tptp.power_power_real A_103) N_38)))))))
% 0.60/1.00 (assert (forall ((M_10 tptp.nat) (N_37 tptp.nat) (A_102 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A_102))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_102) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M_10)) (@ _let_1 N_37)) (@ (@ tptp.ord_less_eq_nat M_10) N_37))))))
% 0.60/1.00 (assert (forall ((M_10 tptp.nat) (N_37 tptp.nat) (A_102 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_102))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_102) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M_10)) (@ _let_1 N_37)) (@ (@ tptp.ord_less_eq_nat M_10) N_37))))))
% 0.60/1.00 (assert (forall ((M_10 tptp.nat) (N_37 tptp.nat) (A_102 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A_102))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_102) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 M_10)) (@ _let_1 N_37)) (@ (@ tptp.ord_less_eq_nat M_10) N_37))))))
% 0.60/1.00 (assert (forall ((X_28 tptp.nat) (Y_25 tptp.nat) (B_64 tptp.int)) (let ((_let_1 (@ tptp.power_power_int B_64))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B_64) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X_28)) (@ _let_1 Y_25)) (@ (@ tptp.ord_less_eq_nat X_28) Y_25))))))
% 0.60/1.00 (assert (forall ((X_28 tptp.nat) (Y_25 tptp.nat) (B_64 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B_64))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B_64) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X_28)) (@ _let_1 Y_25)) (@ (@ tptp.ord_less_eq_nat X_28) Y_25))))))
% 0.60/1.00 (assert (forall ((X_28 tptp.nat) (Y_25 tptp.nat) (B_64 tptp.real)) (let ((_let_1 (@ tptp.power_power_real B_64))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B_64) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X_28)) (@ _let_1 Y_25)) (@ (@ tptp.ord_less_eq_nat X_28) Y_25))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (exists ((X 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) (@ (@ tptp.ord_less_int X) _let_1) (@ (@ (@ tptp.zcong tptp.s1) X) _let_1) (forall ((Y 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) (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ (@ tptp.zcong tptp.s1) Y) _let_1)) (= Y X))))))))
% 0.60/1.00 (assert (not (forall ((S_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))) (not (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) S_1) (@ (@ tptp.ord_less_int S_1) _let_1) (@ (@ (@ tptp.zcong tptp.s1) S_1) _let_1)))))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((A_101 tptp.int) (N_36 tptp.nat)) (= (= (@ (@ tptp.power_power_int A_101) N_36) tptp.zero_zero_int) (and (= A_101 tptp.zero_zero_int) (not (= N_36 tptp.zero_zero_nat))))))
% 0.60/1.00 (assert (forall ((A_101 tptp.nat) (N_36 tptp.nat)) (= (= (@ (@ tptp.power_power_nat A_101) N_36) tptp.zero_zero_nat) (and (= A_101 tptp.zero_zero_nat) (not (= N_36 tptp.zero_zero_nat))))))
% 0.60/1.00 (assert (forall ((A_101 tptp.real) (N_36 tptp.nat)) (= (= (@ (@ tptp.power_power_real A_101) N_36) tptp.zero_zero_real) (and (= A_101 tptp.zero_zero_real) (not (= N_36 tptp.zero_zero_nat))))))
% 0.60/1.00 (assert (forall ((A_100 tptp.real) (M_9 tptp.nat) (N_35 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_100))) (=> (@ (@ tptp.ord_less_eq_nat M_9) N_35) (@ (@ tptp.dvd_dvd_real (@ _let_1 M_9)) (@ _let_1 N_35))))))
% 0.60/1.00 (assert (forall ((A_100 tptp.int) (M_9 tptp.nat) (N_35 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_100))) (=> (@ (@ tptp.ord_less_eq_nat M_9) N_35) (@ (@ tptp.dvd_dvd_int (@ _let_1 M_9)) (@ _let_1 N_35))))))
% 0.60/1.00 (assert (forall ((A_100 tptp.nat) (M_9 tptp.nat) (N_35 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_100))) (=> (@ (@ tptp.ord_less_eq_nat M_9) N_35) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M_9)) (@ _let_1 N_35))))))
% 0.60/1.00 (assert (forall ((N_34 tptp.nat) (M_8 tptp.nat) (X_27 tptp.real) (Y_24 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real X_27) Y_24) (=> (@ (@ tptp.ord_less_eq_nat N_34) M_8) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X_27) N_34)) (@ (@ tptp.power_power_real Y_24) M_8))))))
% 0.60/1.00 (assert (forall ((N_34 tptp.nat) (M_8 tptp.nat) (X_27 tptp.int) (Y_24 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int X_27) Y_24) (=> (@ (@ tptp.ord_less_eq_nat N_34) M_8) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X_27) N_34)) (@ (@ tptp.power_power_int Y_24) M_8))))))
% 0.60/1.00 (assert (forall ((N_34 tptp.nat) (M_8 tptp.nat) (X_27 tptp.nat) (Y_24 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X_27) Y_24) (=> (@ (@ tptp.ord_less_eq_nat N_34) M_8) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X_27) N_34)) (@ (@ tptp.power_power_nat Y_24) M_8))))))
% 0.60/1.00 (assert (forall ((M_7 tptp.nat) (A_99 tptp.real) (N_33 tptp.nat) (B_63 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A_99))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N_33)) B_63) (=> (@ (@ tptp.ord_less_eq_nat M_7) N_33) (@ (@ tptp.dvd_dvd_real (@ _let_1 M_7)) B_63))))))
% 0.60/1.00 (assert (forall ((M_7 tptp.nat) (A_99 tptp.int) (N_33 tptp.nat) (B_63 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A_99))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N_33)) B_63) (=> (@ (@ tptp.ord_less_eq_nat M_7) N_33) (@ (@ tptp.dvd_dvd_int (@ _let_1 M_7)) B_63))))))
% 0.60/1.00 (assert (forall ((M_7 tptp.nat) (A_99 tptp.nat) (N_33 tptp.nat) (B_63 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_99))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N_33)) B_63) (=> (@ (@ tptp.ord_less_eq_nat M_7) N_33) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M_7)) B_63))))))
% 0.60/1.00 (assert (forall ((A_98 tptp.int) (N_32 tptp.nat) (B_62 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A_98) N_32) (@ (@ tptp.power_power_int B_62) N_32)) (=> (@ _let_1 A_98) (=> (@ _let_1 B_62) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_32) (= A_98 B_62))))))))
% 0.60/1.00 (assert (forall ((A_98 tptp.nat) (N_32 tptp.nat) (B_62 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A_98) N_32) (@ (@ tptp.power_power_nat B_62) N_32)) (=> (@ _let_1 A_98) (=> (@ _let_1 B_62) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_32) (= A_98 B_62))))))))
% 0.60/1.00 (assert (forall ((A_98 tptp.real) (N_32 tptp.nat) (B_62 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A_98) N_32) (@ (@ tptp.power_power_real B_62) N_32)) (=> (@ _let_1 A_98) (=> (@ _let_1 B_62) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_32) (= A_98 B_62))))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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))))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((N_31 tptp.nat) (X_26 tptp.real) (Y_23 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real X_26) Y_23) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X_26) N_31)) (@ (@ tptp.power_power_real Y_23) N_31)))))
% 0.60/1.00 (assert (forall ((N_31 tptp.nat) (X_26 tptp.int) (Y_23 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int X_26) Y_23) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X_26) N_31)) (@ (@ tptp.power_power_int Y_23) N_31)))))
% 0.60/1.00 (assert (forall ((N_31 tptp.nat) (X_26 tptp.nat) (Y_23 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X_26) Y_23) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X_26) N_31)) (@ (@ tptp.power_power_nat Y_23) N_31)))))
% 0.60/1.00 (assert (forall ((N_30 tptp.nat) (A_97 tptp.int)) (=> (not (= A_97 tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A_97) N_30) tptp.zero_zero_int)))))
% 0.60/1.00 (assert (forall ((N_30 tptp.nat) (A_97 tptp.real)) (=> (not (= A_97 tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A_97) N_30) tptp.zero_zero_real)))))
% 0.60/1.00 (assert (forall ((N_29 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N_29))) (let ((_let_2 (= N_29 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 0.60/1.00 (assert (forall ((N_29 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N_29))) (let ((_let_2 (= N_29 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 0.60/1.00 (assert (forall ((N_29 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real tptp.zero_zero_real) N_29))) (let ((_let_2 (= N_29 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((N_28 tptp.nat) (A_96 tptp.int) (B_61 tptp.int)) (=> (@ (@ tptp.ord_less_int A_96) B_61) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_96) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_28) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A_96) N_28)) (@ (@ tptp.power_power_int B_61) N_28)))))))
% 0.60/1.00 (assert (forall ((N_28 tptp.nat) (A_96 tptp.nat) (B_61 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_96) B_61) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_96) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_28) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A_96) N_28)) (@ (@ tptp.power_power_nat B_61) N_28)))))))
% 0.60/1.00 (assert (forall ((N_28 tptp.nat) (A_96 tptp.real) (B_61 tptp.real)) (=> (@ (@ tptp.ord_less_real A_96) B_61) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_96) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_28) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A_96) N_28)) (@ (@ tptp.power_power_real B_61) N_28)))))))
% 0.60/1.00 (assert (forall ((A_95 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A_95) tptp.zero_zero_int)))
% 0.60/1.00 (assert (forall ((A_95 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A_95) tptp.zero_zero_nat)))
% 0.60/1.00 (assert (forall ((A_95 tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A_95) tptp.zero_zero_real)))
% 0.60/1.00 (assert (forall ((A_94 tptp.int)) (= (@ (@ tptp.times_times_int A_94) tptp.zero_zero_int) tptp.zero_zero_int)))
% 0.60/1.00 (assert (forall ((A_94 tptp.nat)) (= (@ (@ tptp.times_times_nat A_94) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 0.60/1.00 (assert (forall ((A_94 tptp.real)) (= (@ (@ tptp.times_times_real A_94) tptp.zero_zero_real) tptp.zero_zero_real)))
% 0.60/1.00 (assert (forall ((A_93 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A_93) A_93)))
% 0.60/1.00 (assert (forall ((A_93 tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A_93) A_93)))
% 0.60/1.00 (assert (forall ((A_93 tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A_93) A_93)))
% 0.60/1.00 (assert (forall ((A_92 tptp.int)) (= (@ (@ tptp.plus_plus_int A_92) tptp.zero_zero_int) A_92)))
% 0.60/1.00 (assert (forall ((A_92 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_92) tptp.zero_zero_nat) A_92)))
% 0.60/1.00 (assert (forall ((A_92 tptp.real)) (= (@ (@ tptp.plus_plus_real A_92) tptp.zero_zero_real) A_92)))
% 0.60/1.00 (assert (forall ((B_60 tptp.int) (A_91 tptp.int)) (= (= B_60 (@ (@ tptp.plus_plus_int B_60) A_91)) (= A_91 tptp.zero_zero_int))))
% 0.60/1.00 (assert (forall ((B_60 tptp.nat) (A_91 tptp.nat)) (= (= B_60 (@ (@ tptp.plus_plus_nat B_60) A_91)) (= A_91 tptp.zero_zero_nat))))
% 0.60/1.00 (assert (forall ((B_60 tptp.real) (A_91 tptp.real)) (= (= B_60 (@ (@ tptp.plus_plus_real B_60) A_91)) (= A_91 tptp.zero_zero_real))))
% 0.60/1.00 (assert (forall ((A_90 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A_90) A_90) tptp.zero_zero_int) (= A_90 tptp.zero_zero_int))))
% 0.60/1.00 (assert (forall ((A_90 tptp.real)) (= (= (@ (@ tptp.plus_plus_real A_90) A_90) tptp.zero_zero_real) (= A_90 tptp.zero_zero_real))))
% 0.60/1.00 (assert (= tptp.pls tptp.zero_zero_int))
% 0.60/1.00 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 0.60/1.00 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) Z) Z)))
% 0.60/1.00 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.plus_plus_int Z) tptp.zero_zero_int) Z)))
% 0.60/1.00 (assert (forall ((N_27 tptp.nat) (A_89 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A_89) (@ _let_1 (@ (@ tptp.power_power_int A_89) N_27))))))
% 0.60/1.00 (assert (forall ((N_27 tptp.nat) (A_89 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A_89) (@ _let_1 (@ (@ tptp.power_power_nat A_89) N_27))))))
% 0.60/1.00 (assert (forall ((N_27 tptp.nat) (A_89 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A_89) (@ _let_1 (@ (@ tptp.power_power_real A_89) N_27))))))
% 0.60/1.00 (assert (forall ((N_26 tptp.nat) (A_88 tptp.int) (B_59 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_88) B_59) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_88) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A_88) N_26)) (@ (@ tptp.power_power_int B_59) N_26))))))
% 0.60/1.00 (assert (forall ((N_26 tptp.nat) (A_88 tptp.nat) (B_59 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_88) B_59) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_88) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A_88) N_26)) (@ (@ tptp.power_power_nat B_59) N_26))))))
% 0.60/1.00 (assert (forall ((N_26 tptp.nat) (A_88 tptp.real) (B_59 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_88) B_59) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_88) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A_88) N_26)) (@ (@ tptp.power_power_real B_59) N_26))))))
% 0.60/1.00 (assert (forall ((N_25 tptp.nat) (A_87 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A_87) (@ _let_1 (@ (@ tptp.power_power_int A_87) N_25))))))
% 0.60/1.00 (assert (forall ((N_25 tptp.nat) (A_87 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A_87) (@ _let_1 (@ (@ tptp.power_power_nat A_87) N_25))))))
% 0.60/1.00 (assert (forall ((N_25 tptp.nat) (A_87 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A_87) (@ _let_1 (@ (@ tptp.power_power_real A_87) N_25))))))
% 0.60/1.00 (assert (forall ((Z tptp.nat) (X_1 tptp.int) (Y_1 tptp.nat) (P tptp.int)) (let ((_let_1 (@ tptp.power_power_int X_1))) (=> (@ (@ (@ tptp.zcong (@ _let_1 Y_1)) tptp.one_one_int) P) (@ (@ (@ tptp.zcong (@ _let_1 (@ (@ tptp.times_times_nat Y_1) Z))) tptp.one_one_int) P)))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((C tptp.int) (X_1 tptp.int) (T tptp.int) (A tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X_1))) (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))))))))
% 0.60/1.00 (assert (forall ((A_86 tptp.int) (N_24 tptp.nat) (B_58 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A_86) N_24)) (@ (@ tptp.power_power_int B_58) N_24)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B_58) (@ (@ tptp.ord_less_int A_86) B_58)))))
% 0.60/1.00 (assert (forall ((A_86 tptp.nat) (N_24 tptp.nat) (B_58 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A_86) N_24)) (@ (@ tptp.power_power_nat B_58) N_24)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B_58) (@ (@ tptp.ord_less_nat A_86) B_58)))))
% 0.60/1.00 (assert (forall ((A_86 tptp.real) (N_24 tptp.nat) (B_58 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A_86) N_24)) (@ (@ tptp.power_power_real B_58) N_24)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B_58) (@ (@ tptp.ord_less_real A_86) B_58)))))
% 0.60/1.00 (assert (forall ((A_85 tptp.int) (N_23 tptp.nat) (N_22 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_85))) (=> (@ (@ tptp.ord_less_eq_nat N_23) N_22) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_85) (=> (@ (@ tptp.ord_less_eq_int A_85) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N_22)) (@ _let_1 N_23))))))))
% 0.60/1.00 (assert (forall ((A_85 tptp.nat) (N_23 tptp.nat) (N_22 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_85))) (=> (@ (@ tptp.ord_less_eq_nat N_23) N_22) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_85) (=> (@ (@ tptp.ord_less_eq_nat A_85) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N_22)) (@ _let_1 N_23))))))))
% 0.60/1.00 (assert (forall ((A_85 tptp.real) (N_23 tptp.nat) (N_22 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_85))) (=> (@ (@ tptp.ord_less_eq_nat N_23) N_22) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_85) (=> (@ (@ tptp.ord_less_eq_real A_85) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N_22)) (@ _let_1 N_23))))))))
% 0.60/1.00 (assert (forall ((A_84 tptp.int) (N_21 tptp.nat) (N_20 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_84))) (=> (@ (@ tptp.ord_less_nat N_21) N_20) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_84) (=> (@ (@ tptp.ord_less_int A_84) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N_20)) (@ _let_1 N_21))))))))
% 0.60/1.00 (assert (forall ((A_84 tptp.nat) (N_21 tptp.nat) (N_20 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_84))) (=> (@ (@ tptp.ord_less_nat N_21) N_20) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_84) (=> (@ (@ tptp.ord_less_nat A_84) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N_20)) (@ _let_1 N_21))))))))
% 0.60/1.00 (assert (forall ((A_84 tptp.real) (N_21 tptp.nat) (N_20 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_84))) (=> (@ (@ tptp.ord_less_nat N_21) N_20) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A_84) (=> (@ (@ tptp.ord_less_real A_84) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N_20)) (@ _let_1 N_21))))))))
% 0.60/1.00 (assert (forall ((A_83 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_83) A_83)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A_83) tptp.zero_zero_int))))
% 0.60/1.00 (assert (forall ((A_83 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A_83) A_83)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A_83) tptp.zero_zero_real))))
% 0.60/1.00 (assert (forall ((X_25 tptp.int) (Y_22 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_25) X_25)) (@ (@ tptp.times_times_int Y_22) Y_22)) tptp.zero_zero_int) (and (= X_25 tptp.zero_zero_int) (= Y_22 tptp.zero_zero_int)))))
% 0.60/1.00 (assert (forall ((X_25 tptp.real) (Y_22 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X_25) X_25)) (@ (@ tptp.times_times_real Y_22) Y_22)) tptp.zero_zero_real) (and (= X_25 tptp.zero_zero_real) (= Y_22 tptp.zero_zero_real)))))
% 0.60/1.00 (assert (forall ((C_30 tptp.int) (D_7 tptp.int) (A_82 tptp.int) (B_57 tptp.int) (R_3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int R_3))) (=> (not (= R_3 tptp.zero_zero_int)) (=> (and (= A_82 B_57) (not (= C_30 D_7))) (not (= (@ (@ tptp.plus_plus_int A_82) (@ _let_1 C_30)) (@ (@ tptp.plus_plus_int B_57) (@ _let_1 D_7)))))))))
% 0.60/1.00 (assert (forall ((C_30 tptp.nat) (D_7 tptp.nat) (A_82 tptp.nat) (B_57 tptp.nat) (R_3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R_3))) (=> (not (= R_3 tptp.zero_zero_nat)) (=> (and (= A_82 B_57) (not (= C_30 D_7))) (not (= (@ (@ tptp.plus_plus_nat A_82) (@ _let_1 C_30)) (@ (@ tptp.plus_plus_nat B_57) (@ _let_1 D_7)))))))))
% 0.60/1.00 (assert (forall ((C_30 tptp.real) (D_7 tptp.real) (A_82 tptp.real) (B_57 tptp.real) (R_3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R_3))) (=> (not (= R_3 tptp.zero_zero_real)) (=> (and (= A_82 B_57) (not (= C_30 D_7))) (not (= (@ (@ tptp.plus_plus_real A_82) (@ _let_1 C_30)) (@ (@ tptp.plus_plus_real B_57) (@ _let_1 D_7)))))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (N tptp.nat) (P tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int P))) (=> (@ tptp.zprime P) (=> (@ _let_1 (@ (@ tptp.power_power_int A) N)) (@ _let_1 A))))))
% 0.60/1.00 (assert (= tptp.zero_zero_int (@ tptp.number_number_of_int tptp.pls)))
% 0.60/1.00 (assert (= tptp.zero_zero_real (@ tptp.number267125858f_real tptp.pls)))
% 0.60/1.00 (assert (= (@ tptp.number_number_of_int tptp.pls) tptp.zero_zero_int))
% 0.60/1.00 (assert (= (@ tptp.number267125858f_real tptp.pls) tptp.zero_zero_real))
% 0.60/1.00 (assert (= (@ tptp.number_number_of_int tptp.pls) tptp.zero_zero_int))
% 0.60/1.00 (assert (= (@ tptp.number_number_of_nat tptp.pls) tptp.zero_zero_nat))
% 0.60/1.00 (assert (= (@ tptp.number267125858f_real tptp.pls) tptp.zero_zero_real))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (not (@ (@ tptp.ord_less_int tptp.pls) tptp.zero_zero_int)))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (= tptp.zero_zero_int (@ tptp.number_number_of_int tptp.pls)))
% 0.60/1.00 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((K tptp.int) (I_1 tptp.int) (J_1 tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I_1) J_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I_1)) (@ _let_1 J_1)))))))
% 0.60/1.00 (assert (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))))
% 0.60/1.00 (assert (forall ((N_19 tptp.nat) (A_81 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A_81) N_19))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_81) (=> (@ (@ tptp.ord_less_int A_81) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_81) _let_1)) _let_1))))))
% 0.60/1.00 (assert (forall ((N_19 tptp.nat) (A_81 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A_81) N_19))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_81) (=> (@ (@ tptp.ord_less_nat A_81) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_81) _let_1)) _let_1))))))
% 0.60/1.00 (assert (forall ((N_19 tptp.nat) (A_81 tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A_81) N_19))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A_81) (=> (@ (@ tptp.ord_less_real A_81) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_81) _let_1)) _let_1))))))
% 0.60/1.00 (assert (forall ((N tptp.nat) (B tptp.int) (A tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int P) N)))) (=> (@ tptp.zprime P) (=> (not (@ (@ tptp.dvd_dvd_int P) A)) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (@ _let_1 B)))))))
% 0.60/1.00 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int P) N)))) (=> (@ tptp.zprime P) (=> (not (@ (@ tptp.dvd_dvd_int P) B)) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (@ _let_1 A)))))))
% 0.60/1.00 (assert (forall ((X_24 tptp.int) (Y_21 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_24) X_24)) (@ (@ tptp.times_times_int Y_21) Y_21)))))
% 0.60/1.00 (assert (forall ((X_24 tptp.real) (Y_21 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X_24) X_24)) (@ (@ tptp.times_times_real Y_21) Y_21)))))
% 0.60/1.00 (assert (forall ((X_23 tptp.int) (Y_20 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_23) X_23)) (@ (@ tptp.times_times_int Y_20) Y_20))) tptp.zero_zero_int) (and (= X_23 tptp.zero_zero_int) (= Y_20 tptp.zero_zero_int)))))
% 0.60/1.00 (assert (forall ((X_23 tptp.real) (Y_20 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X_23) X_23)) (@ (@ tptp.times_times_real Y_20) Y_20))) tptp.zero_zero_real) (and (= X_23 tptp.zero_zero_real) (= Y_20 tptp.zero_zero_real)))))
% 0.60/1.00 (assert (forall ((V tptp.int) (V_6 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_int V) V_6))) (= (@ (@ tptp.ord_less_nat (@ tptp.number_number_of_nat V)) (@ tptp.number_number_of_nat V_6)) (and (=> _let_1 (@ (@ tptp.ord_less_int tptp.pls) V_6)) _let_1)))))
% 0.60/1.00 (assert (forall ((X_22 tptp.int) (Y_19 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_22) X_22)) (@ (@ tptp.times_times_int Y_19) Y_19))) tptp.zero_zero_int))))
% 0.60/1.00 (assert (forall ((X_22 tptp.real) (Y_19 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X_22) X_22)) (@ (@ tptp.times_times_real Y_19) Y_19))) tptp.zero_zero_real))))
% 0.60/1.00 (assert (forall ((X_21 tptp.int) (Y_18 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_21) X_21)) (@ (@ tptp.times_times_int Y_18) Y_18))) (or (not (= X_21 tptp.zero_zero_int)) (not (= Y_18 tptp.zero_zero_int))))))
% 0.60/1.00 (assert (forall ((X_21 tptp.real) (Y_18 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X_21) X_21)) (@ (@ tptp.times_times_real Y_18) Y_18))) (or (not (= X_21 tptp.zero_zero_real)) (not (= Y_18 tptp.zero_zero_real))))))
% 0.60/1.00 (assert (forall ((V tptp.int) (V_6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int V))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.number_number_of_nat V)) (@ tptp.number_number_of_nat V_6)) (=> (not (@ _let_1 V_6)) (@ _let_1 tptp.pls))))))
% 0.60/1.00 (assert (forall ((W_5 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W_5))) (= (@ tptp.number_number_of_int (@ tptp.bit0 W_5)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.zero_zero_int) _let_1)) _let_1)))))
% 0.60/1.00 (assert (forall ((W_5 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real W_5))) (= (@ tptp.number267125858f_real (@ tptp.bit0 W_5)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.zero_zero_real) _let_1)) _let_1)))))
% 0.60/1.00 (assert (forall ((A_80 tptp.int)) (= (@ (@ tptp.power_power_int A_80) tptp.one_one_nat) A_80)))
% 0.60/1.00 (assert (forall ((A_80 tptp.real)) (= (@ (@ tptp.power_power_real A_80) tptp.one_one_nat) A_80)))
% 0.60/1.00 (assert (forall ((A_80 tptp.nat)) (= (@ (@ tptp.power_power_nat A_80) tptp.one_one_nat) A_80)))
% 0.60/1.00 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((Y_17 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.number_number_of_int Y_17)) (@ (@ tptp.ord_less_int tptp.pls) Y_17))))
% 0.60/1.00 (assert (forall ((Y_17 tptp.int)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.number267125858f_real Y_17)) (@ (@ tptp.ord_less_int tptp.pls) Y_17))))
% 0.60/1.00 (assert (forall ((X_20 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int X_20)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int X_20) tptp.pls))))
% 0.60/1.00 (assert (forall ((X_20 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.number267125858f_real X_20)) tptp.zero_zero_real) (@ (@ tptp.ord_less_int X_20) tptp.pls))))
% 0.60/1.00 (assert (forall ((Y_16 tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.number267125858f_real Y_16)) (@ (@ tptp.ord_less_eq_int tptp.pls) Y_16))))
% 0.60/1.00 (assert (forall ((Y_16 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.number_number_of_int Y_16)) (@ (@ tptp.ord_less_eq_int tptp.pls) Y_16))))
% 0.60/1.00 (assert (forall ((X_19 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.number267125858f_real X_19)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_int X_19) tptp.pls))))
% 0.60/1.00 (assert (forall ((X_19 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_19)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int X_19) tptp.pls))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_real))
% 0.60/1.00 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_nat))
% 0.60/1.00 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_int))
% 0.60/1.00 (assert (forall ((A_79 tptp.real)) (= (= (@ (@ tptp.power_power_real A_79) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_real) (= A_79 tptp.zero_zero_real))))
% 0.60/1.00 (assert (forall ((A_79 tptp.int)) (= (= (@ (@ tptp.power_power_int A_79) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_int) (= A_79 tptp.zero_zero_int))))
% 0.60/1.00 (assert (forall ((A_78 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A_78) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))))
% 0.60/1.00 (assert (forall ((A_78 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A_78) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))))
% 0.60/1.00 (assert (forall ((X_18 tptp.real) (Y_15 tptp.real)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X_18) _let_1)) (@ (@ tptp.power_power_real Y_15) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y_15) (@ (@ tptp.ord_less_eq_real X_18) Y_15))))))
% 0.60/1.00 (assert (forall ((X_18 tptp.nat) (Y_15 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X_18) _let_1)) (@ (@ tptp.power_power_nat Y_15) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y_15) (@ (@ tptp.ord_less_eq_nat X_18) Y_15))))))
% 0.60/1.00 (assert (forall ((X_18 tptp.int) (Y_15 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X_18) _let_1)) (@ (@ tptp.power_power_int Y_15) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y_15) (@ (@ tptp.ord_less_eq_int X_18) Y_15))))))
% 0.60/1.00 (assert (forall ((X_17 tptp.real) (Y_14 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (= (@ (@ tptp.power_power_real X_17) _let_2) (@ (@ tptp.power_power_real Y_14) _let_2)) (=> (@ _let_1 X_17) (=> (@ _let_1 Y_14) (= X_17 Y_14))))))))
% 0.60/1.00 (assert (forall ((X_17 tptp.nat) (Y_14 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (= (@ (@ tptp.power_power_nat X_17) _let_2) (@ (@ tptp.power_power_nat Y_14) _let_2)) (=> (@ _let_1 X_17) (=> (@ _let_1 Y_14) (= X_17 Y_14))))))))
% 0.60/1.00 (assert (forall ((X_17 tptp.int) (Y_14 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (= (@ (@ tptp.power_power_int X_17) _let_2) (@ (@ tptp.power_power_int Y_14) _let_2)) (=> (@ _let_1 X_17) (=> (@ _let_1 Y_14) (= X_17 Y_14))))))))
% 0.60/1.00 (assert (forall ((A_77 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A_77) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.zero_zero_real))))
% 0.60/1.00 (assert (forall ((A_77 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A_77) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.zero_zero_int))))
% 0.60/1.00 (assert (forall ((A_76 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A_76) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (not (= A_76 tptp.zero_zero_real)))))
% 0.60/1.00 (assert (forall ((A_76 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A_76) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (not (= A_76 tptp.zero_zero_int)))))
% 0.60/1.00 (assert (forall ((X_16 tptp.real) (Y_13 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_16) _let_1)) (@ (@ tptp.power_power_real Y_13) _let_1)) tptp.zero_zero_real) (and (= X_16 tptp.zero_zero_real) (= Y_13 tptp.zero_zero_real))))))
% 0.60/1.00 (assert (forall ((X_16 tptp.int) (Y_13 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_16) _let_1)) (@ (@ tptp.power_power_int Y_13) _let_1)) tptp.zero_zero_int) (and (= X_16 tptp.zero_zero_int) (= Y_13 tptp.zero_zero_int))))))
% 0.60/1.00 (assert (forall ((A_75 tptp.nat) (N_18 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A_75) N_18))) (= (@ (@ tptp.times_times_nat _let_1) A_75) (@ (@ tptp.times_times_nat A_75) _let_1)))))
% 0.60/1.00 (assert (forall ((A_75 tptp.real) (N_18 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A_75) N_18))) (= (@ (@ tptp.times_times_real _let_1) A_75) (@ (@ tptp.times_times_real A_75) _let_1)))))
% 0.60/1.00 (assert (forall ((A_75 tptp.int) (N_18 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A_75) N_18))) (= (@ (@ tptp.times_times_int _let_1) A_75) (@ (@ tptp.times_times_int A_75) _let_1)))))
% 0.60/1.00 (assert (forall ((A_74 tptp.nat) (B_56 tptp.nat) (N_17 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A_74) B_56)) N_17) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A_74) N_17)) (@ (@ tptp.power_power_nat B_56) N_17)))))
% 0.60/1.00 (assert (forall ((A_74 tptp.real) (B_56 tptp.real) (N_17 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A_74) B_56)) N_17) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A_74) N_17)) (@ (@ tptp.power_power_real B_56) N_17)))))
% 0.60/1.00 (assert (forall ((A_74 tptp.int) (B_56 tptp.int) (N_17 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A_74) B_56)) N_17) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A_74) N_17)) (@ (@ tptp.power_power_int B_56) N_17)))))
% 0.60/1.00 (assert (forall ((A_73 tptp.nat) (M_6 tptp.nat) (N_16 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_73))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M_6) N_16)) (@ (@ tptp.times_times_nat (@ _let_1 M_6)) (@ _let_1 N_16))))))
% 0.60/1.00 (assert (forall ((A_73 tptp.real) (M_6 tptp.nat) (N_16 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_73))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M_6) N_16)) (@ (@ tptp.times_times_real (@ _let_1 M_6)) (@ _let_1 N_16))))))
% 0.60/1.00 (assert (forall ((A_73 tptp.int) (M_6 tptp.nat) (N_16 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_73))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M_6) N_16)) (@ (@ tptp.times_times_int (@ _let_1 M_6)) (@ _let_1 N_16))))))
% 0.60/1.00 (assert (forall ((N_15 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N_15) tptp.one_one_real)))
% 0.60/1.00 (assert (forall ((N_15 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N_15) tptp.one_one_nat)))
% 0.60/1.00 (assert (forall ((N_15 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N_15) tptp.one_one_int)))
% 0.60/1.00 (assert (forall ((A_72 tptp.nat) (M_5 tptp.nat) (N_14 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_72))) (= (@ _let_1 (@ (@ tptp.times_times_nat M_5) N_14)) (@ (@ tptp.power_power_nat (@ _let_1 M_5)) N_14)))))
% 0.60/1.00 (assert (forall ((A_72 tptp.real) (M_5 tptp.nat) (N_14 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_72))) (= (@ _let_1 (@ (@ tptp.times_times_nat M_5) N_14)) (@ (@ tptp.power_power_real (@ _let_1 M_5)) N_14)))))
% 0.60/1.00 (assert (forall ((A_72 tptp.int) (M_5 tptp.nat) (N_14 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_72))) (= (@ _let_1 (@ (@ tptp.times_times_nat M_5) N_14)) (@ (@ tptp.power_power_int (@ _let_1 M_5)) N_14)))))
% 0.60/1.00 (assert (forall ((X_15 tptp.real) (Y_12 tptp.real)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X_15) _let_1)) (@ (@ tptp.power_power_real Y_12) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y_12) (@ (@ tptp.ord_less_real X_15) Y_12))))))
% 0.60/1.00 (assert (forall ((X_15 tptp.nat) (Y_12 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X_15) _let_1)) (@ (@ tptp.power_power_nat Y_12) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y_12) (@ (@ tptp.ord_less_nat X_15) Y_12))))))
% 0.60/1.00 (assert (forall ((X_15 tptp.int) (Y_12 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X_15) _let_1)) (@ (@ tptp.power_power_int Y_12) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y_12) (@ (@ tptp.ord_less_int X_15) Y_12))))))
% 0.60/1.00 (assert (forall ((X_14 tptp.real) (Y_11 tptp.real)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X_14) _let_1)) (@ (@ tptp.power_power_real Y_11) _let_1))))))
% 0.60/1.00 (assert (forall ((X_14 tptp.int) (Y_11 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_14) _let_1)) (@ (@ tptp.power_power_int Y_11) _let_1))))))
% 0.60/1.00 (assert (forall ((X_13 tptp.real) (Y_10 tptp.real)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X_13) _let_1)) (@ (@ tptp.power_power_real Y_10) _let_1))) tptp.zero_zero_real) (and (= X_13 tptp.zero_zero_real) (= Y_10 tptp.zero_zero_real))))))
% 0.60/1.00 (assert (forall ((X_13 tptp.int) (Y_10 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_13) _let_1)) (@ (@ tptp.power_power_int Y_10) _let_1))) tptp.zero_zero_int) (and (= X_13 tptp.zero_zero_int) (= Y_10 tptp.zero_zero_int))))))
% 0.60/1.00 (assert (forall ((X_12 tptp.real) (Y_9 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_12) _let_1)) (@ (@ tptp.power_power_real Y_9) _let_1))) tptp.zero_zero_real)))))
% 0.60/1.00 (assert (forall ((X_12 tptp.int) (Y_9 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_12) _let_1)) (@ (@ tptp.power_power_int Y_9) _let_1))) tptp.zero_zero_int)))))
% 0.60/1.00 (assert (forall ((X_11 tptp.real) (Y_8 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_11) _let_1)) (@ (@ tptp.power_power_real Y_8) _let_1))) (or (not (= X_11 tptp.zero_zero_real)) (not (= Y_8 tptp.zero_zero_real)))))))
% 0.60/1.00 (assert (forall ((X_11 tptp.int) (Y_8 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_11) _let_1)) (@ (@ tptp.power_power_int Y_8) _let_1))) (or (not (= X_11 tptp.zero_zero_int)) (not (= Y_8 tptp.zero_zero_int)))))))
% 0.60/1.00 (assert (forall ((A_71 tptp.real) (N_13 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A_71) (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_13)))))
% 0.60/1.00 (assert (forall ((A_71 tptp.int) (N_13 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A_71) (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_13)))))
% 0.60/1.00 (assert (forall ((N_12 tptp.nat) (A_70 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A_70) (@ _let_1 (@ (@ tptp.power_power_real A_70) N_12))))))
% 0.60/1.00 (assert (forall ((N_12 tptp.nat) (A_70 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A_70) (@ _let_1 (@ (@ tptp.power_power_nat A_70) N_12))))))
% 0.60/1.00 (assert (forall ((N_12 tptp.nat) (A_70 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A_70) (@ _let_1 (@ (@ tptp.power_power_int A_70) N_12))))))
% 0.60/1.00 (assert (forall ((A_69 tptp.real) (N_11 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_69))) (=> (@ (@ tptp.ord_less_eq_nat N_11) N_10) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A_69) (@ (@ tptp.ord_less_eq_real (@ _let_1 N_11)) (@ _let_1 N_10)))))))
% 0.60/1.00 (assert (forall ((A_69 tptp.nat) (N_11 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_69))) (=> (@ (@ tptp.ord_less_eq_nat N_11) N_10) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A_69) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N_11)) (@ _let_1 N_10)))))))
% 0.60/1.00 (assert (forall ((A_69 tptp.int) (N_11 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_69))) (=> (@ (@ tptp.ord_less_eq_nat N_11) N_10) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A_69) (@ (@ tptp.ord_less_eq_int (@ _let_1 N_11)) (@ _let_1 N_10)))))))
% 0.60/1.00 (assert (forall ((M_4 tptp.nat) (N_9 tptp.nat) (A_68 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A_68))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_68) (= (= (@ _let_1 M_4) (@ _let_1 N_9)) (= M_4 N_9))))))
% 0.60/1.00 (assert (forall ((M_4 tptp.nat) (N_9 tptp.nat) (A_68 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_68))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_68) (= (= (@ _let_1 M_4) (@ _let_1 N_9)) (= M_4 N_9))))))
% 0.60/1.00 (assert (forall ((M_4 tptp.nat) (N_9 tptp.nat) (A_68 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A_68))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_68) (= (= (@ _let_1 M_4) (@ _let_1 N_9)) (= M_4 N_9))))))
% 0.60/1.00 (assert (forall ((X_10 tptp.nat) (Y_7 tptp.nat) (B_55 tptp.real)) (let ((_let_1 (@ tptp.power_power_real B_55))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B_55) (= (@ (@ tptp.ord_less_real (@ _let_1 X_10)) (@ _let_1 Y_7)) (@ (@ tptp.ord_less_nat X_10) Y_7))))))
% 0.60/1.00 (assert (forall ((X_10 tptp.nat) (Y_7 tptp.nat) (B_55 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B_55))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B_55) (= (@ (@ tptp.ord_less_nat (@ _let_1 X_10)) (@ _let_1 Y_7)) (@ (@ tptp.ord_less_nat X_10) Y_7))))))
% 0.60/1.00 (assert (forall ((X_10 tptp.nat) (Y_7 tptp.nat) (B_55 tptp.int)) (let ((_let_1 (@ tptp.power_power_int B_55))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B_55) (= (@ (@ tptp.ord_less_int (@ _let_1 X_10)) (@ _let_1 Y_7)) (@ (@ tptp.ord_less_nat X_10) Y_7))))))
% 0.60/1.00 (assert (forall ((M_3 tptp.nat) (N_8 tptp.nat) (A_67 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A_67))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_67) (=> (@ (@ tptp.ord_less_real (@ _let_1 M_3)) (@ _let_1 N_8)) (@ (@ tptp.ord_less_nat M_3) N_8))))))
% 0.60/1.00 (assert (forall ((M_3 tptp.nat) (N_8 tptp.nat) (A_67 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_67))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_67) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M_3)) (@ _let_1 N_8)) (@ (@ tptp.ord_less_nat M_3) N_8))))))
% 0.60/1.00 (assert (forall ((M_3 tptp.nat) (N_8 tptp.nat) (A_67 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A_67))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_67) (=> (@ (@ tptp.ord_less_int (@ _let_1 M_3)) (@ _let_1 N_8)) (@ (@ tptp.ord_less_nat M_3) N_8))))))
% 0.60/1.00 (assert (forall ((A_66 tptp.real) (N_7 tptp.nat) (N_6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_66))) (=> (@ (@ tptp.ord_less_nat N_7) N_6) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_66) (@ (@ tptp.ord_less_real (@ _let_1 N_7)) (@ _let_1 N_6)))))))
% 0.60/1.00 (assert (forall ((A_66 tptp.nat) (N_7 tptp.nat) (N_6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_66))) (=> (@ (@ tptp.ord_less_nat N_7) N_6) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_66) (@ (@ tptp.ord_less_nat (@ _let_1 N_7)) (@ _let_1 N_6)))))))
% 0.60/1.00 (assert (forall ((A_66 tptp.int) (N_7 tptp.nat) (N_6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_66))) (=> (@ (@ tptp.ord_less_nat N_7) N_6) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_66) (@ (@ tptp.ord_less_int (@ _let_1 N_7)) (@ _let_1 N_6)))))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((Y_1 tptp.int) (X_1 tptp.int) (P tptp.int)) (=> (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int Y_1) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) X_1) P) (not (@ (@ tptp.dvd_dvd_int P) Y_1))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (=> (@ (@ tptp.ord_less_int X_1) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (or (= X_1 tptp.zero_zero_int) (= X_1 tptp.one_one_int))))))
% 0.60/1.00 (assert (forall ((A_65 tptp.real) (K_3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A_65) (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) K_3))) tptp.zero_zero_real) (= A_65 tptp.zero_zero_real))))
% 0.60/1.00 (assert (forall ((A_65 tptp.int) (K_3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A_65) (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) K_3))) tptp.zero_zero_int) (= A_65 tptp.zero_zero_int))))
% 0.60/1.00 (assert (forall ((P tptp.int)) (= (@ tptp.zprime P) (and (@ (@ tptp.ord_less_int tptp.one_one_int) P) (forall ((M_2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M_2) (@ (@ tptp.dvd_dvd_int M_2) P)) (or (= M_2 tptp.one_one_int) (= M_2 P))))))))
% 0.60/1.00 (assert (forall ((R tptp.int) (Q tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (= A (@ (@ tptp.plus_plus_int R) (@ (@ tptp.times_times_int A) Q))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (@ (@ tptp.ord_less_eq_int Q) tptp.one_one_int))))))
% 0.60/1.00 (assert (forall ((R tptp.int) (Q tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (= A (@ (@ tptp.plus_plus_int R) (@ (@ tptp.times_times_int A) Q))) (=> (@ (@ tptp.ord_less_int R) A) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Q))))))
% 0.60/1.00 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.60/1.00 (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)))))))
% 0.60/1.00 (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))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X_1) N)) (or (@ _let_1 X_1) (= N tptp.zero_zero_nat))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X_1) N)) (or (= N tptp.zero_zero_nat) (@ _let_1 X_1))))))
% 0.60/1.00 (assert (forall ((X_1 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_1) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (@ _let_1 X_1)))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (= (@ tptp.bit1 K) tptp.min) (= K tptp.min))))
% 0.60/1.00 (assert (forall ((L tptp.int)) (= (= tptp.min (@ tptp.bit1 L)) (= tptp.min L))))
% 0.60/1.00 (assert (= (@ tptp.bit1 tptp.min) tptp.min))
% 0.60/1.00 (assert (not (= tptp.pls tptp.min)))
% 0.60/1.00 (assert (not (= tptp.min tptp.pls)))
% 0.60/1.00 (assert (forall ((K tptp.int)) (not (= (@ tptp.bit0 K) tptp.min))))
% 0.60/1.00 (assert (forall ((L tptp.int)) (not (= tptp.min (@ tptp.bit0 L)))))
% 0.60/1.00 (assert (not (@ (@ tptp.ord_less_int tptp.min) tptp.min)))
% 0.60/1.00 (assert (@ (@ tptp.ord_less_eq_int tptp.min) tptp.min))
% 0.60/1.00 (assert (forall ((X_1 tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X_1) X_1))) (= X_1 tptp.zero_zero_real))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K)) tptp.min) (@ (@ tptp.ord_less_int K) tptp.min))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.min))) (= (@ _let_1 (@ tptp.bit1 K)) (@ _let_1 K)))))
% 0.60/1.00 (assert (not (@ (@ tptp.ord_less_int tptp.pls) tptp.min)))
% 0.60/1.00 (assert (@ (@ tptp.ord_less_int tptp.min) tptp.pls))
% 0.60/1.00 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.min))) (= (@ _let_1 (@ tptp.bit0 K)) (@ _let_1 K)))))
% 0.60/1.00 (assert (@ (@ tptp.ord_less_int tptp.min) tptp.zero_zero_int))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) tptp.min) (@ (@ tptp.ord_less_eq_int K) tptp.min))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.min))) (= (@ _let_1 (@ tptp.bit1 K)) (@ _let_1 K)))))
% 0.60/1.00 (assert (not (@ (@ tptp.ord_less_eq_int tptp.pls) tptp.min)))
% 0.60/1.00 (assert (@ (@ tptp.ord_less_eq_int tptp.min) tptp.pls))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) tptp.min) (@ (@ tptp.ord_less_eq_int K) tptp.min))))
% 0.60/1.00 (assert (not (= (@ tptp.number_number_of_int tptp.pls) (@ tptp.number_number_of_int tptp.min))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((X_9 tptp.real)) (= (@ (@ tptp.power_power_real X_9) tptp.zero_zero_nat) tptp.one_one_real)))
% 0.60/1.00 (assert (forall ((X_9 tptp.nat)) (= (@ (@ tptp.power_power_nat X_9) tptp.zero_zero_nat) tptp.one_one_nat)))
% 0.60/1.00 (assert (forall ((X_9 tptp.int)) (= (@ (@ tptp.power_power_int X_9) tptp.zero_zero_nat) tptp.one_one_int)))
% 0.60/1.00 (assert (forall ((A_64 tptp.real)) (= (@ (@ tptp.power_power_real A_64) tptp.zero_zero_nat) tptp.one_one_real)))
% 0.60/1.00 (assert (forall ((A_64 tptp.nat)) (= (@ (@ tptp.power_power_nat A_64) tptp.zero_zero_nat) tptp.one_one_nat)))
% 0.60/1.00 (assert (forall ((A_64 tptp.int)) (= (@ (@ tptp.power_power_int A_64) tptp.zero_zero_nat) tptp.one_one_int)))
% 0.60/1.00 (assert (= (@ tptp.number_number_of_nat tptp.pls) tptp.zero_zero_nat))
% 0.60/1.00 (assert (= tptp.zero_zero_nat (@ tptp.number_number_of_nat tptp.pls)))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.min) (@ tptp.bit0 K)) (@ (@ tptp.ord_less_int tptp.min) K))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit0 K)) tptp.min) (@ (@ tptp.ord_less_eq_int K) tptp.min))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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)))))))
% 0.60/1.00 (assert (forall ((N_5 tptp.nat) (A_63 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A_63) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (@ _let_1 (@ (@ tptp.power_power_real A_63) N_5)))))))
% 0.60/1.00 (assert (forall ((N_5 tptp.nat) (A_63 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A_63) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (@ _let_1 (@ (@ tptp.power_power_nat A_63) N_5)))))))
% 0.60/1.00 (assert (forall ((N_5 tptp.nat) (A_63 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A_63) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (@ _let_1 (@ (@ tptp.power_power_int A_63) N_5)))))))
% 0.60/1.00 (assert (forall ((X_8 tptp.real) (N_4 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_4) (= X_8 tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X_8) (@ (@ tptp.power_power_real X_8) N_4)))))
% 0.60/1.00 (assert (forall ((X_8 tptp.nat) (N_4 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_4) (= X_8 tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X_8) (@ (@ tptp.power_power_nat X_8) N_4)))))
% 0.60/1.00 (assert (forall ((X_8 tptp.int) (N_4 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_4) (= X_8 tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X_8) (@ (@ tptp.power_power_int X_8) N_4)))))
% 0.60/1.00 (assert (forall ((V tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.number_number_of_nat V)) (@ (@ tptp.ord_less_int tptp.pls) V))))
% 0.60/1.00 (assert (forall ((V tptp.int)) (= (= (@ tptp.number_number_of_nat V) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int V) tptp.pls))))
% 0.60/1.00 (assert (forall ((V tptp.int)) (= (= tptp.zero_zero_nat (@ tptp.number_number_of_nat V)) (@ (@ tptp.ord_less_eq_int V) tptp.pls))))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int) (M tptp.int)) (= (@ (@ (@ tptp.zcong A) B) M) (@ (@ (@ tptp.zcong B) A) M))))
% 0.60/1.00 (assert (forall ((K tptp.int) (M tptp.int)) (@ (@ (@ tptp.zcong K) K) M)))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))
% 0.60/1.00 (assert (forall ((V_6 tptp.int) (K tptp.nat) (V tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V)) (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V_6)) K)))) (let ((_let_2 (@ (@ tptp.ord_less_int V) 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) V_6))) K))))))))
% 0.60/1.00 (assert (forall ((V_6 tptp.int) (V tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V)) (@ tptp.number_number_of_nat V_6)))) (let ((_let_2 (@ (@ tptp.ord_less_int V) 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) V_6)))))))))
% 0.60/1.00 (assert (forall ((X_7 tptp.real) (Y_6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X_7) Y_6) (=> (not (= X_7 Y_6)) (@ (@ tptp.ord_less_real X_7) Y_6)))))
% 0.60/1.00 (assert (forall ((X_7 tptp.nat) (Y_6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X_7) Y_6) (=> (not (= X_7 Y_6)) (@ (@ tptp.ord_less_nat X_7) Y_6)))))
% 0.60/1.00 (assert (forall ((X_7 tptp.int) (Y_6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X_7) Y_6) (=> (not (= X_7 Y_6)) (@ (@ tptp.ord_less_int X_7) Y_6)))))
% 0.60/1.00 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ (@ tptp.zcong A) B) tptp.zero_zero_int) (= A B))))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ (@ tptp.zcong A) B) tptp.one_one_int)))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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))))
% 0.60/1.00 (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)))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((N_3 tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.number267125858f_real tptp.min)) (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_3)) tptp.one_one_real)))
% 0.60/1.00 (assert (forall ((N_3 tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.number_number_of_int tptp.min)) (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_3)) tptp.one_one_int)))
% 0.60/1.00 (assert (forall ((A_62 tptp.real) (W_4 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_4))) (= (= (@ (@ tptp.power_power_real A_62) _let_1) tptp.zero_zero_real) (and (= A_62 tptp.zero_zero_real) (not (= _let_1 tptp.zero_zero_nat)))))))
% 0.60/1.00 (assert (forall ((A_62 tptp.nat) (W_4 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_4))) (= (= (@ (@ tptp.power_power_nat A_62) _let_1) tptp.zero_zero_nat) (and (= A_62 tptp.zero_zero_nat) (not (= _let_1 tptp.zero_zero_nat)))))))
% 0.60/1.00 (assert (forall ((A_62 tptp.int) (W_4 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_4))) (= (= (@ (@ tptp.power_power_int A_62) _let_1) tptp.zero_zero_int) (and (= A_62 tptp.zero_zero_int) (not (= _let_1 tptp.zero_zero_nat)))))))
% 0.60/1.00 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 0.60/1.00 (assert (forall ((Y_1 tptp.int) (X_1 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X_1) (=> (@ _let_1 Y_1) (@ _let_1 (@ (@ tptp.times_times_int X_1) Y_1)))))))
% 0.60/1.00 (assert (forall ((Y_1 tptp.int) (X_1 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X_1) (=> (@ _let_1 Y_1) (@ _let_1 (@ (@ tptp.plus_plus_int X_1) Y_1)))))))
% 0.60/1.00 (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)))))))))
% 0.60/1.00 (assert (forall ((N tptp.nat) (X_1 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X_1) (@ _let_1 (@ (@ tptp.power_power_int X_1) N))))))
% 0.60/1.00 (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)))))))
% 0.60/1.00 (assert (forall ((W_3 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_3))) (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))))))))
% 0.60/1.00 (assert (forall ((W_3 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_3))) (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))))))))
% 0.60/1.00 (assert (forall ((W_3 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_3))) (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))))))))
% 0.60/1.00 (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)))))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.number_number_of_int (@ tptp.bit1 (@ tptp.bit1 tptp.pls)))))
% 0.60/1.00 (assert (forall ((B tptp.int) (Q tptp.int) (R tptp.int) (B_54 tptp.int) (Q_3 tptp.int) (R_2 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_54) Q_3)) R_2))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q)) R) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R_2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_54) (=> (@ (@ tptp.ord_less_eq_int B_54) B) (@ (@ tptp.ord_less_eq_int Q_3) Q))))))))))
% 0.60/1.00 (assert (forall ((B tptp.int) (Q_3 tptp.int) (R_2 tptp.int) (Q tptp.int) (R 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_3)) R_2)) (@ (@ tptp.plus_plus_int (@ _let_2 Q)) R)) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (=> (@ _let_1 R) (=> (@ _let_1 R_2) (@ (@ tptp.ord_less_eq_int Q) Q_3)))))))))
% 0.60/1.00 (assert (forall ((B tptp.int) (Q tptp.int) (R tptp.int) (B_54 tptp.int) (Q_3 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_54) Q_3)) R_2))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q)) R) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R_2) B_54) (=> (@ _let_1 R) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_54) (=> (@ (@ tptp.ord_less_eq_int B_54) B) (@ (@ tptp.ord_less_eq_int Q) Q_3)))))))))))
% 0.60/1.00 (assert (forall ((B tptp.int) (Q_3 tptp.int) (R_2 tptp.int) (Q tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q_3)) R_2)) (@ (@ tptp.plus_plus_int (@ _let_1 Q)) R)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R_2) (=> (@ (@ tptp.ord_less_int R_2) B) (=> (@ (@ tptp.ord_less_int R) B) (@ (@ tptp.ord_less_eq_int Q_3) Q))))))))
% 0.60/1.00 (assert (forall ((B_54 tptp.int) (Q_3 tptp.int) (R_2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_54) Q_3)) 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_54) (@ (@ tptp.ord_less_eq_int Q_3) tptp.zero_zero_int))))))
% 0.60/1.00 (assert (forall ((B_54 tptp.int) (Q_3 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_54) Q_3)) R_2)) (=> (@ (@ tptp.ord_less_int R_2) B_54) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_54) (@ _let_1 Q_3)))))))
% 0.60/1.00 (assert (forall ((N tptp.int) (P tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int P))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M) (=> (@ tptp.zprime P) (=> (@ _let_1 (@ (@ tptp.times_times_int M) N)) (or (@ _let_1 M) (@ _let_1 N))))))))
% 0.60/1.00 (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)))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((J_1 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_1))) (=> (@ (@ 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))))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.zcong X_1))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ (@ _let_1 (@ tptp.number_number_of_int tptp.min)) P) (not (@ (@ _let_1 tptp.one_one_int) P)))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((V_5 tptp.int) (W_2 tptp.int)) (= (@ tptp.number267125858f_real (@ (@ tptp.minus_minus_int V_5) W_2)) (@ (@ tptp.minus_minus_real (@ tptp.number267125858f_real V_5)) (@ tptp.number267125858f_real W_2)))))
% 0.60/1.00 (assert (forall ((V_5 tptp.int) (W_2 tptp.int)) (= (@ tptp.number_number_of_int (@ (@ tptp.minus_minus_int V_5) W_2)) (@ (@ tptp.minus_minus_int (@ tptp.number_number_of_int V_5)) (@ tptp.number_number_of_int W_2)))))
% 0.60/1.00 (assert (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.pls) K)))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((V_4 tptp.int) (B_53 tptp.real) (C_29 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.number267125858f_real V_4)))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B_53) C_29)) (@ (@ tptp.minus_minus_real (@ _let_1 B_53)) (@ _let_1 C_29))))))
% 0.60/1.00 (assert (forall ((V_4 tptp.int) (B_53 tptp.int) (C_29 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.number_number_of_int V_4)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B_53) C_29)) (@ (@ tptp.minus_minus_int (@ _let_1 B_53)) (@ _let_1 C_29))))))
% 0.60/1.00 (assert (forall ((A_61 tptp.real) (B_52 tptp.real) (V_3 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real V_3))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A_61) B_52)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A_61) _let_1)) (@ (@ tptp.times_times_real B_52) _let_1))))))
% 0.60/1.00 (assert (forall ((A_61 tptp.int) (B_52 tptp.int) (V_3 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V_3))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A_61) B_52)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A_61) _let_1)) (@ (@ tptp.times_times_int B_52) _let_1))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((L tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int tptp.pls))) (= (@ _let_1 (@ tptp.bit0 L)) (@ tptp.bit0 (@ _let_1 L))))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((A tptp.int) (R 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))) (= (@ (@ 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))))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((V_2 tptp.int) (W_1 tptp.int) (C_28 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_2)) (@ (@ tptp.minus_minus_real (@ tptp.number267125858f_real W_1)) C_28)) (@ (@ tptp.minus_minus_real (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_2) W_1))) C_28))))
% 0.60/1.00 (assert (forall ((V_2 tptp.int) (W_1 tptp.int) (C_28 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_2)) (@ (@ tptp.minus_minus_int (@ tptp.number_number_of_int W_1)) C_28)) (@ (@ tptp.minus_minus_int (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_2) W_1))) C_28))))
% 0.60/1.00 (assert (forall ((A tptp.int) (X_1 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int A) tptp.one_one_int))) (let ((_let_2 (@ tptp.ord_less_int X_1))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X_1) (=> (@ _let_2 A) (=> (not (= X_1 _let_1)) (@ _let_2 _let_1))))))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((L tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.pls) (@ tptp.bit1 L)) (@ tptp.bit1 (@ (@ tptp.minus_minus_int tptp.min) L)))))
% 0.60/1.00 (assert (forall ((L tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int tptp.min))) (= (@ _let_1 (@ tptp.bit0 L)) (@ tptp.bit1 (@ _let_1 L))))))
% 0.60/1.00 (assert (forall ((L tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int tptp.min))) (= (@ _let_1 (@ tptp.bit1 L)) (@ tptp.bit0 (@ _let_1 L))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (P tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int P) tptp.one_one_int))) (= (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) _let_1)) tptp.one_one_int) P) (@ (@ (@ tptp.zcong A) _let_1) P)))))
% 0.60/1.00 (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)))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int) (P tptp.int) (Q tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ tptp.twoSqu2057625106sum2sq (@ (@ tptp.product_Pair_int_int A) B))) (@ tptp.twoSqu2057625106sum2sq (@ (@ tptp.product_Pair_int_int P) Q))) (@ tptp.twoSqu2057625106sum2sq (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ _let_2 P)) (@ _let_1 Q))) (@ (@ tptp.minus_minus_int (@ _let_2 Q)) (@ _let_1 P)))))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.zcong A))) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) A)) tptp.one_one_int) P) (or (@ (@ _let_1 tptp.one_one_int) P) (@ (@ _let_1 (@ (@ tptp.minus_minus_int P) tptp.one_one_int)) P))))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) P) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) A)) tptp.one_one_int) P) (or (= A tptp.one_one_int) (= A (@ (@ tptp.minus_minus_int P) tptp.one_one_int)))))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((M tptp.int)) (@ (@ (@ tptp.zcong M) tptp.zero_zero_int) M)))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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)))))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((Z tptp.nat) (X_1 tptp.int) (Y_1 tptp.int) (M tptp.int)) (=> (@ (@ (@ tptp.zcong X_1) Y_1) M) (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int X_1) Z)) (@ (@ tptp.power_power_int Y_1) Z)) M))))
% 0.60/1.00 (assert (forall ((X_6 tptp.real) (Y_5 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.minus_minus_real X_6) Y_5)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X_6) _let_2)) (@ (@ tptp.power_power_real Y_5) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.number267125858f_real _let_1)) X_6)) Y_5)))))))
% 0.60/1.00 (assert (forall ((X_6 tptp.int) (Y_5 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 X_6) Y_5)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_6) _let_2)) (@ (@ tptp.power_power_int Y_5) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int _let_1)) X_6)) Y_5)))))))
% 0.60/1.00 (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)))))))
% 0.60/1.00 (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))))))))))))
% 0.60/1.00 (assert (forall ((M tptp.int) (Y_1 tptp.int) (X_1 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X_1) (=> (@ _let_1 Y_1) (=> (@ _let_1 M) (=> (@ (@ (@ tptp.zcong X_1) Y_1) M) (=> (@ (@ tptp.ord_less_int X_1) M) (=> (@ (@ tptp.ord_less_int Y_1) M) (= X_1 Y_1))))))))))
% 0.60/1.00 (assert (forall ((M tptp.int) (X_1 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X_1) (=> (@ (@ tptp.ord_less_int X_1) M) (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) M))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (P tptp.int)) (= (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P) (@ (@ tptp.dvd_dvd_int P) X_1))))
% 0.60/1.00 (assert (forall ((A tptp.int) (M tptp.int)) (= (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) M) (@ (@ tptp.dvd_dvd_int M) A))))
% 0.60/1.00 (assert (forall ((M tptp.int) (N tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int P))) (=> (@ tptp.zprime P) (=> (@ _let_1 (@ (@ tptp.times_times_int M) N)) (or (@ _let_1 M) (@ _let_1 N)))))))
% 0.60/1.00 (assert (forall ((M tptp.int) (X_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (=> (@ (@ tptp.ord_less_int X_1) M) (=> (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) M) (= X_1 tptp.zero_zero_int))))))
% 0.60/1.00 (assert (forall ((P tptp.int) (Y_1 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int P))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 Y_1) (@ _let_1 (@ (@ tptp.power_power_int Y_1) N)))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((Y_1 tptp.int) (X_1 tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (=> (not (@ (@ (@ tptp.zcong Y_1) tptp.zero_zero_int) P)) (not (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int X_1) Y_1)) tptp.zero_zero_int) P)))))))
% 0.60/1.00 (assert (forall ((B tptp.int) (A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) P) (or (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) P) (@ (@ (@ tptp.zcong B) tptp.zero_zero_int) P)))))))
% 0.60/1.00 (assert (forall ((B tptp.int) (A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (and (not (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) P)) (not (@ (@ (@ tptp.zcong B) tptp.zero_zero_int) P))) (not (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) P)))))))
% 0.60/1.00 (assert (forall ((Y_1 tptp.int) (N tptp.nat) (P tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int P))) (=> (@ tptp.zprime P) (=> (@ _let_1 (@ (@ tptp.power_power_int Y_1) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 Y_1)))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((A tptp.int) (P tptp.int)) (let ((_let_1 (@ (@ tptp.legendre A) P))) (let ((_let_2 (@ (@ tptp.quadRes P) A))) (let ((_let_3 (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) P))) (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)))))))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((M tptp.int) (X_1 tptp.int)) (= (@ (@ tptp.quadRes M) X_1) (exists ((Y tptp.int)) (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int Y) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) X_1) M)))))
% 0.60/1.00 (assert (forall ((X_1 tptp.real) (Y_1 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_1) _let_1)) (@ (@ tptp.power_power_real Y_1) _let_1)) tptp.zero_zero_real) (and (= X_1 tptp.zero_zero_real) (= Y_1 tptp.zero_zero_real))))))
% 0.60/1.00 (assert (forall ((V_1 tptp.real) (U_1 tptp.real) (Y_4 tptp.real) (X_5 tptp.real) (A_60 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X_5) A_60) (=> (@ (@ tptp.ord_less_real Y_4) A_60) (=> (@ _let_1 U_1) (=> (@ _let_1 V_1) (=> (= (@ (@ tptp.plus_plus_real U_1) V_1) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U_1) X_5)) (@ (@ tptp.times_times_real V_1) Y_4))) A_60)))))))))
% 0.60/1.00 (assert (forall ((V_1 tptp.int) (U_1 tptp.int) (Y_4 tptp.int) (X_5 tptp.int) (A_60 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X_5) A_60) (=> (@ (@ tptp.ord_less_int Y_4) A_60) (=> (@ _let_1 U_1) (=> (@ _let_1 V_1) (=> (= (@ (@ tptp.plus_plus_int U_1) V_1) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U_1) X_5)) (@ (@ tptp.times_times_int V_1) Y_4))) A_60)))))))))
% 0.60/1.00 (assert (forall ((A_59 tptp.real)) (@ (@ tptp.dvd_dvd_real A_59) tptp.zero_zero_real)))
% 0.60/1.00 (assert (forall ((A_59 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A_59) tptp.zero_zero_nat)))
% 0.60/1.00 (assert (forall ((A_59 tptp.int)) (@ (@ tptp.dvd_dvd_int A_59) tptp.zero_zero_int)))
% 0.60/1.00 (assert (forall ((X_1 tptp.real) (Y_1 tptp.real)) (= (@ (@ tptp.ord_less_eq_real X_1) Y_1) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X_1) Y_1)) tptp.zero_zero_real))))
% 0.60/1.00 (assert (forall ((X_4 tptp.real) (Y_3 tptp.real)) (=> (not (= X_4 Y_3)) (=> (not (@ (@ tptp.ord_less_real X_4) Y_3)) (@ (@ tptp.ord_less_real Y_3) X_4)))))
% 0.60/1.00 (assert (forall ((X_4 tptp.int) (Y_3 tptp.int)) (=> (not (= X_4 Y_3)) (=> (not (@ (@ tptp.ord_less_int X_4) Y_3)) (@ (@ tptp.ord_less_int Y_3) X_4)))))
% 0.60/1.00 (assert (forall ((A_58 tptp.real)) (@ (@ tptp.dvd_dvd_real A_58) A_58)))
% 0.60/1.00 (assert (forall ((A_58 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A_58) A_58)))
% 0.60/1.00 (assert (forall ((A_58 tptp.int)) (@ (@ tptp.dvd_dvd_int A_58) A_58)))
% 0.60/1.00 (assert (forall ((C_27 tptp.real) (A_57 tptp.real) (B_51 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A_57))) (=> (@ _let_1 B_51) (=> (@ (@ tptp.dvd_dvd_real B_51) C_27) (@ _let_1 C_27))))))
% 0.60/1.00 (assert (forall ((C_27 tptp.nat) (A_57 tptp.nat) (B_51 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A_57))) (=> (@ _let_1 B_51) (=> (@ (@ tptp.dvd_dvd_nat B_51) C_27) (@ _let_1 C_27))))))
% 0.60/1.00 (assert (forall ((C_27 tptp.int) (A_57 tptp.int) (B_51 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A_57))) (=> (@ _let_1 B_51) (=> (@ (@ tptp.dvd_dvd_int B_51) C_27) (@ _let_1 C_27))))))
% 0.60/1.00 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 0.60/1.00 (assert (forall ((X_1 tptp.real) (Y_1 tptp.real)) (= (@ (@ tptp.ord_less_eq_real X_1) Y_1) (or (@ (@ tptp.ord_less_real X_1) Y_1) (= X_1 Y_1)))))
% 0.60/1.00 (assert (forall ((X_1 tptp.real) (Y_1 tptp.real)) (= (@ (@ tptp.ord_less_real X_1) Y_1) (and (@ (@ tptp.ord_less_eq_real X_1) Y_1) (not (= X_1 Y_1))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (= (and (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (@ (@ tptp.dvd_dvd_nat Y_1) X_1)) (= X_1 Y_1))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real Z) W) (@ (@ tptp.times_times_real W) Z))))
% 0.60/1.00 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) Z) Z)))
% 0.60/1.00 (assert (forall ((Z tptp.real) (X_1 tptp.real) (Y_1 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real Z))) (=> (@ (@ tptp.ord_less_eq_real X_1) Y_1) (@ (@ tptp.ord_less_eq_real (@ _let_1 X_1)) (@ _let_1 Y_1))))))
% 0.60/1.00 (assert (forall ((X_3 tptp.nat) (N_2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X_3))) (=> (@ (@ 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_3) (@ _let_1 N_2))))))
% 0.60/1.00 (assert (forall ((X_3 tptp.real) (N_2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X_3))) (=> (@ (@ 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_3) (@ _let_1 N_2))))))
% 0.60/1.00 (assert (forall ((X_3 tptp.int) (N_2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X_3))) (=> (@ (@ 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_3) (@ _let_1 N_2))))))
% 0.60/1.00 (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)))))))))
% 0.60/1.00 (assert (forall ((P tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat P))) (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) (@ _let_1 (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 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_1) _let_1)) (@ (@ tptp.power_power_nat Y_1) _let_1)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat X_1) Y_1)) (@ (@ tptp.minus_minus_nat X_1) Y_1))))))
% 0.60/1.00 (assert (forall ((A_56 tptp.real) (B_50 tptp.real)) (=> (= (@ (@ tptp.times_times_real A_56) B_50) tptp.zero_zero_real) (or (= A_56 tptp.zero_zero_real) (= B_50 tptp.zero_zero_real)))))
% 0.60/1.00 (assert (forall ((A_56 tptp.nat) (B_50 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A_56) B_50) tptp.zero_zero_nat) (or (= A_56 tptp.zero_zero_nat) (= B_50 tptp.zero_zero_nat)))))
% 0.60/1.00 (assert (forall ((A_56 tptp.int) (B_50 tptp.int)) (=> (= (@ (@ tptp.times_times_int A_56) B_50) tptp.zero_zero_int) (or (= A_56 tptp.zero_zero_int) (= B_50 tptp.zero_zero_int)))))
% 0.60/1.00 (assert (forall ((B_49 tptp.real) (A_55 tptp.real)) (=> (not (= A_55 tptp.zero_zero_real)) (=> (not (= B_49 tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A_55) B_49) tptp.zero_zero_real))))))
% 0.60/1.00 (assert (forall ((B_49 tptp.nat) (A_55 tptp.nat)) (=> (not (= A_55 tptp.zero_zero_nat)) (=> (not (= B_49 tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A_55) B_49) tptp.zero_zero_nat))))))
% 0.60/1.00 (assert (forall ((B_49 tptp.int) (A_55 tptp.int)) (=> (not (= A_55 tptp.zero_zero_int)) (=> (not (= B_49 tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A_55) B_49) tptp.zero_zero_int))))))
% 0.60/1.00 (assert (forall ((A_54 tptp.real) (B_48 tptp.real)) (= (= (@ (@ tptp.times_times_real A_54) B_48) tptp.zero_zero_real) (or (= A_54 tptp.zero_zero_real) (= B_48 tptp.zero_zero_real)))))
% 0.60/1.00 (assert (forall ((A_54 tptp.int) (B_48 tptp.int)) (= (= (@ (@ tptp.times_times_int A_54) B_48) tptp.zero_zero_int) (or (= A_54 tptp.zero_zero_int) (= B_48 tptp.zero_zero_int)))))
% 0.60/1.00 (assert (forall ((A_53 tptp.real)) (= (@ (@ tptp.times_times_real A_53) tptp.zero_zero_real) tptp.zero_zero_real)))
% 0.60/1.00 (assert (forall ((A_53 tptp.nat)) (= (@ (@ tptp.times_times_nat A_53) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 0.60/1.00 (assert (forall ((A_53 tptp.int)) (= (@ (@ tptp.times_times_int A_53) tptp.zero_zero_int) tptp.zero_zero_int)))
% 0.60/1.00 (assert (forall ((A_52 tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A_52) tptp.zero_zero_real)))
% 0.60/1.00 (assert (forall ((A_52 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A_52) tptp.zero_zero_nat)))
% 0.60/1.00 (assert (forall ((A_52 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A_52) tptp.zero_zero_int)))
% 0.60/1.00 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 0.60/1.00 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 0.60/1.00 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 0.60/1.00 (assert (not (= tptp.one_one_real tptp.zero_zero_real)))
% 0.60/1.00 (assert (not (= tptp.one_one_nat tptp.zero_zero_nat)))
% 0.60/1.00 (assert (not (= tptp.one_one_int tptp.zero_zero_int)))
% 0.60/1.00 (assert (forall ((A_51 tptp.real) (E tptp.real) (B_47 tptp.real) (C_26 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_51) E)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B_47) E)) C_26)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_51) B_47)) E)) C_26))))
% 0.60/1.00 (assert (forall ((A_51 tptp.nat) (E tptp.nat) (B_47 tptp.nat) (C_26 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_51) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B_47) E)) C_26)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_51) B_47)) E)) C_26))))
% 0.60/1.00 (assert (forall ((A_51 tptp.int) (E tptp.int) (B_47 tptp.int) (C_26 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_51) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_47) E)) C_26)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_51) B_47)) E)) C_26))))
% 0.60/1.00 (assert (forall ((A_50 tptp.real) (B_46 tptp.real) (C_25 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_50) B_46)) C_25) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_50) C_25)) (@ (@ tptp.times_times_real B_46) C_25)))))
% 0.60/1.00 (assert (forall ((A_50 tptp.nat) (B_46 tptp.nat) (C_25 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_50) B_46)) C_25) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_50) C_25)) (@ (@ tptp.times_times_nat B_46) C_25)))))
% 0.60/1.00 (assert (forall ((A_50 tptp.int) (B_46 tptp.int) (C_25 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_50) B_46)) C_25) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_50) C_25)) (@ (@ tptp.times_times_int B_46) C_25)))))
% 0.60/1.00 (assert (forall ((A_49 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A_49) (= A_49 tptp.zero_zero_real))))
% 0.60/1.00 (assert (forall ((A_49 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A_49) (= A_49 tptp.zero_zero_nat))))
% 0.60/1.00 (assert (forall ((A_49 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A_49) (= A_49 tptp.zero_zero_int))))
% 0.60/1.00 (assert (forall ((A_48 tptp.real) (C_24 tptp.real) (B_45 tptp.real) (D_6 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A_48) C_24)) (@ (@ tptp.plus_plus_real B_45) D_6)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A_48) B_45)) (@ (@ tptp.minus_minus_real C_24) D_6)))))
% 0.60/1.00 (assert (forall ((A_48 tptp.int) (C_24 tptp.int) (B_45 tptp.int) (D_6 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A_48) C_24)) (@ (@ tptp.plus_plus_int B_45) D_6)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A_48) B_45)) (@ (@ tptp.minus_minus_int C_24) D_6)))))
% 0.60/1.00 (assert (forall ((A_47 tptp.real) (B_44 tptp.real) (C_23 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A_47) B_44)) C_23) (@ (@ tptp.dvd_dvd_real B_44) C_23))))
% 0.60/1.00 (assert (forall ((A_47 tptp.nat) (B_44 tptp.nat) (C_23 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A_47) B_44)) C_23) (@ (@ tptp.dvd_dvd_nat B_44) C_23))))
% 0.60/1.00 (assert (forall ((A_47 tptp.int) (B_44 tptp.int) (C_23 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A_47) B_44)) C_23) (@ (@ tptp.dvd_dvd_int B_44) C_23))))
% 0.60/1.00 (assert (forall ((A_46 tptp.real) (B_43 tptp.real) (C_22 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A_46) B_43)) C_22) (@ (@ tptp.dvd_dvd_real A_46) C_22))))
% 0.60/1.00 (assert (forall ((A_46 tptp.nat) (B_43 tptp.nat) (C_22 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A_46) B_43)) C_22) (@ (@ tptp.dvd_dvd_nat A_46) C_22))))
% 0.60/1.00 (assert (forall ((A_46 tptp.int) (B_43 tptp.int) (C_22 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A_46) B_43)) C_22) (@ (@ tptp.dvd_dvd_int A_46) C_22))))
% 0.60/1.00 (assert (forall ((A_45 tptp.real) (B_42 tptp.real) (K_2 tptp.real)) (=> (= A_45 (@ (@ tptp.times_times_real B_42) K_2)) (@ (@ tptp.dvd_dvd_real B_42) A_45))))
% 0.60/1.00 (assert (forall ((A_45 tptp.nat) (B_42 tptp.nat) (K_2 tptp.nat)) (=> (= A_45 (@ (@ tptp.times_times_nat B_42) K_2)) (@ (@ tptp.dvd_dvd_nat B_42) A_45))))
% 0.60/1.00 (assert (forall ((A_45 tptp.int) (B_42 tptp.int) (K_2 tptp.int)) (=> (= A_45 (@ (@ tptp.times_times_int B_42) K_2)) (@ (@ tptp.dvd_dvd_int B_42) A_45))))
% 0.60/1.00 (assert (forall ((C_21 tptp.real) (D_5 tptp.real) (A_44 tptp.real) (B_41 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A_44) B_41) (=> (@ (@ tptp.dvd_dvd_real C_21) D_5) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A_44) C_21)) (@ (@ tptp.times_times_real B_41) D_5))))))
% 0.60/1.00 (assert (forall ((C_21 tptp.nat) (D_5 tptp.nat) (A_44 tptp.nat) (B_41 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A_44) B_41) (=> (@ (@ tptp.dvd_dvd_nat C_21) D_5) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A_44) C_21)) (@ (@ tptp.times_times_nat B_41) D_5))))))
% 0.60/1.00 (assert (forall ((C_21 tptp.int) (D_5 tptp.int) (A_44 tptp.int) (B_41 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A_44) B_41) (=> (@ (@ tptp.dvd_dvd_int C_21) D_5) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A_44) C_21)) (@ (@ tptp.times_times_int B_41) D_5))))))
% 0.60/1.00 (assert (forall ((B_40 tptp.real) (A_43 tptp.real) (C_20 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A_43))) (=> (@ _let_1 C_20) (@ _let_1 (@ (@ tptp.times_times_real B_40) C_20))))))
% 0.60/1.00 (assert (forall ((B_40 tptp.nat) (A_43 tptp.nat) (C_20 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A_43))) (=> (@ _let_1 C_20) (@ _let_1 (@ (@ tptp.times_times_nat B_40) C_20))))))
% 0.60/1.00 (assert (forall ((B_40 tptp.int) (A_43 tptp.int) (C_20 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A_43))) (=> (@ _let_1 C_20) (@ _let_1 (@ (@ tptp.times_times_int B_40) C_20))))))
% 0.60/1.00 (assert (forall ((C_19 tptp.real) (A_42 tptp.real) (B_39 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A_42))) (=> (@ _let_1 B_39) (@ _let_1 (@ (@ tptp.times_times_real B_39) C_19))))))
% 0.60/1.00 (assert (forall ((C_19 tptp.nat) (A_42 tptp.nat) (B_39 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A_42))) (=> (@ _let_1 B_39) (@ _let_1 (@ (@ tptp.times_times_nat B_39) C_19))))))
% 0.60/1.00 (assert (forall ((C_19 tptp.int) (A_42 tptp.int) (B_39 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A_42))) (=> (@ _let_1 B_39) (@ _let_1 (@ (@ tptp.times_times_int B_39) C_19))))))
% 0.60/1.00 (assert (forall ((A_41 tptp.real) (B_38 tptp.real)) (@ (@ tptp.dvd_dvd_real A_41) (@ (@ tptp.times_times_real B_38) A_41))))
% 0.60/1.00 (assert (forall ((A_41 tptp.nat) (B_38 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A_41) (@ (@ tptp.times_times_nat B_38) A_41))))
% 0.60/1.00 (assert (forall ((A_41 tptp.int) (B_38 tptp.int)) (@ (@ tptp.dvd_dvd_int A_41) (@ (@ tptp.times_times_int B_38) A_41))))
% 0.60/1.00 (assert (forall ((A_40 tptp.real) (B_37 tptp.real)) (@ (@ tptp.dvd_dvd_real A_40) (@ (@ tptp.times_times_real A_40) B_37))))
% 0.60/1.00 (assert (forall ((A_40 tptp.nat) (B_37 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A_40) (@ (@ tptp.times_times_nat A_40) B_37))))
% 0.60/1.00 (assert (forall ((A_40 tptp.int) (B_37 tptp.int)) (@ (@ tptp.dvd_dvd_int A_40) (@ (@ tptp.times_times_int A_40) B_37))))
% 0.60/1.00 (assert (forall ((C_18 tptp.real) (A_39 tptp.real) (B_36 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A_39))) (=> (@ _let_1 B_36) (=> (@ _let_1 C_18) (@ _let_1 (@ (@ tptp.plus_plus_real B_36) C_18)))))))
% 0.60/1.00 (assert (forall ((C_18 tptp.nat) (A_39 tptp.nat) (B_36 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A_39))) (=> (@ _let_1 B_36) (=> (@ _let_1 C_18) (@ _let_1 (@ (@ tptp.plus_plus_nat B_36) C_18)))))))
% 0.60/1.00 (assert (forall ((C_18 tptp.int) (A_39 tptp.int) (B_36 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A_39))) (=> (@ _let_1 B_36) (=> (@ _let_1 C_18) (@ _let_1 (@ (@ tptp.plus_plus_int B_36) C_18)))))))
% 0.60/1.00 (assert (forall ((A_38 tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A_38)))
% 0.60/1.00 (assert (forall ((A_38 tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A_38)))
% 0.60/1.00 (assert (forall ((A_38 tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A_38)))
% 0.60/1.00 (assert (forall ((Z_1 tptp.real) (X_2 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X_2))) (=> (@ _let_1 Y_2) (=> (@ _let_1 Z_1) (@ _let_1 (@ (@ tptp.minus_minus_real Y_2) Z_1)))))))
% 0.60/1.00 (assert (forall ((Z_1 tptp.int) (X_2 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X_2))) (=> (@ _let_1 Y_2) (=> (@ _let_1 Z_1) (@ _let_1 (@ (@ tptp.minus_minus_int Y_2) Z_1)))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((N tptp.nat) (X_1 tptp.nat) (Y_1 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X_1) N)) (@ (@ tptp.power_power_nat Y_1) N)))))
% 0.60/1.00 (assert (forall ((B_35 tptp.real) (A_37 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A_37) (@ (@ tptp.ord_less_eq_real B_35) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A_37) tptp.zero_zero_real) (@ _let_1 B_35))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_37) B_35)) tptp.zero_zero_real)))))
% 0.60/1.00 (assert (forall ((B_35 tptp.nat) (A_37 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A_37) (@ (@ tptp.ord_less_eq_nat B_35) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A_37) tptp.zero_zero_nat) (@ _let_1 B_35))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_37) B_35)) tptp.zero_zero_nat)))))
% 0.60/1.00 (assert (forall ((B_35 tptp.int) (A_37 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A_37) (@ (@ tptp.ord_less_eq_int B_35) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A_37) tptp.zero_zero_int) (@ _let_1 B_35))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_37) B_35)) tptp.zero_zero_int)))))
% 0.60/1.00 (assert (forall ((B_34 tptp.real) (A_36 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A_36) (@ _let_1 B_34)) (and (@ (@ tptp.ord_less_eq_real A_36) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B_34) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.times_times_real A_36) B_34))))))
% 0.60/1.00 (assert (forall ((B_34 tptp.int) (A_36 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A_36) (@ _let_1 B_34)) (and (@ (@ tptp.ord_less_eq_int A_36) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B_34) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A_36) B_34))))))
% 0.60/1.00 (assert (forall ((C_17 tptp.real) (D_4 tptp.real) (A_35 tptp.real) (B_33 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A_35) B_33) (=> (@ (@ tptp.ord_less_eq_real C_17) D_4) (=> (@ _let_1 B_33) (=> (@ _let_1 C_17) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_35) C_17)) (@ (@ tptp.times_times_real B_33) D_4)))))))))
% 0.60/1.00 (assert (forall ((C_17 tptp.nat) (D_4 tptp.nat) (A_35 tptp.nat) (B_33 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A_35) B_33) (=> (@ (@ tptp.ord_less_eq_nat C_17) D_4) (=> (@ _let_1 B_33) (=> (@ _let_1 C_17) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_35) C_17)) (@ (@ tptp.times_times_nat B_33) D_4)))))))))
% 0.60/1.00 (assert (forall ((C_17 tptp.int) (D_4 tptp.int) (A_35 tptp.int) (B_33 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A_35) B_33) (=> (@ (@ tptp.ord_less_eq_int C_17) D_4) (=> (@ _let_1 B_33) (=> (@ _let_1 C_17) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_35) C_17)) (@ (@ tptp.times_times_int B_33) D_4)))))))))
% 0.60/1.00 (assert (forall ((C_16 tptp.real) (D_3 tptp.real) (A_34 tptp.real) (B_32 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A_34) B_32) (=> (@ (@ tptp.ord_less_eq_real C_16) D_3) (=> (@ _let_1 A_34) (=> (@ _let_1 C_16) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_34) C_16)) (@ (@ tptp.times_times_real B_32) D_3)))))))))
% 0.60/1.00 (assert (forall ((C_16 tptp.nat) (D_3 tptp.nat) (A_34 tptp.nat) (B_32 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A_34) B_32) (=> (@ (@ tptp.ord_less_eq_nat C_16) D_3) (=> (@ _let_1 A_34) (=> (@ _let_1 C_16) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_34) C_16)) (@ (@ tptp.times_times_nat B_32) D_3)))))))))
% 0.60/1.00 (assert (forall ((C_16 tptp.int) (D_3 tptp.int) (A_34 tptp.int) (B_32 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A_34) B_32) (=> (@ (@ tptp.ord_less_eq_int C_16) D_3) (=> (@ _let_1 A_34) (=> (@ _let_1 C_16) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_34) C_16)) (@ (@ tptp.times_times_int B_32) D_3)))))))))
% 0.60/1.00 (assert (forall ((C_15 tptp.real) (B_31 tptp.real) (A_33 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_15))) (=> (@ (@ tptp.ord_less_eq_real B_31) A_33) (=> (@ (@ tptp.ord_less_eq_real C_15) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A_33)) (@ _let_1 B_31)))))))
% 0.60/1.00 (assert (forall ((C_15 tptp.int) (B_31 tptp.int) (A_33 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_15))) (=> (@ (@ tptp.ord_less_eq_int B_31) A_33) (=> (@ (@ tptp.ord_less_eq_int C_15) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A_33)) (@ _let_1 B_31)))))))
% 0.60/1.00 (assert (forall ((C_14 tptp.real) (B_30 tptp.real) (A_32 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B_30) A_32) (=> (@ (@ tptp.ord_less_eq_real C_14) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_32) C_14)) (@ (@ tptp.times_times_real B_30) C_14))))))
% 0.60/1.00 (assert (forall ((C_14 tptp.int) (B_30 tptp.int) (A_32 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B_30) A_32) (=> (@ (@ tptp.ord_less_eq_int C_14) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_32) C_14)) (@ (@ tptp.times_times_int B_30) C_14))))))
% 0.60/1.00 (assert (forall ((C_13 tptp.real) (A_31 tptp.real) (B_29 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_13))) (=> (@ (@ tptp.ord_less_eq_real A_31) B_29) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_13) (@ (@ tptp.ord_less_eq_real (@ _let_1 A_31)) (@ _let_1 B_29)))))))
% 0.60/1.00 (assert (forall ((C_13 tptp.nat) (A_31 tptp.nat) (B_29 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_13))) (=> (@ (@ tptp.ord_less_eq_nat A_31) B_29) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_13) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_31)) (@ _let_1 B_29)))))))
% 0.60/1.00 (assert (forall ((C_13 tptp.int) (A_31 tptp.int) (B_29 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_13))) (=> (@ (@ tptp.ord_less_eq_int A_31) B_29) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_13) (@ (@ tptp.ord_less_eq_int (@ _let_1 A_31)) (@ _let_1 B_29)))))))
% 0.60/1.00 (assert (forall ((C_12 tptp.real) (A_30 tptp.real) (B_28 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_12))) (=> (@ (@ tptp.ord_less_eq_real A_30) B_28) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_12) (@ (@ tptp.ord_less_eq_real (@ _let_1 A_30)) (@ _let_1 B_28)))))))
% 0.60/1.00 (assert (forall ((C_12 tptp.nat) (A_30 tptp.nat) (B_28 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_12))) (=> (@ (@ tptp.ord_less_eq_nat A_30) B_28) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_12) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_30)) (@ _let_1 B_28)))))))
% 0.60/1.00 (assert (forall ((C_12 tptp.int) (A_30 tptp.int) (B_28 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_12))) (=> (@ (@ tptp.ord_less_eq_int A_30) B_28) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_12) (@ (@ tptp.ord_less_eq_int (@ _let_1 A_30)) (@ _let_1 B_28)))))))
% 0.60/1.00 (assert (forall ((C_11 tptp.real) (A_29 tptp.real) (B_27 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_29) B_27) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_11) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_29) C_11)) (@ (@ tptp.times_times_real B_27) C_11))))))
% 0.60/1.00 (assert (forall ((C_11 tptp.nat) (A_29 tptp.nat) (B_27 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_29) B_27) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_11) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_29) C_11)) (@ (@ tptp.times_times_nat B_27) C_11))))))
% 0.60/1.00 (assert (forall ((C_11 tptp.int) (A_29 tptp.int) (B_27 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_29) B_27) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_11) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_29) C_11)) (@ (@ tptp.times_times_int B_27) C_11))))))
% 0.60/1.00 (assert (forall ((B_26 tptp.real) (A_28 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_28) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B_26) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A_28) B_26))))))
% 0.60/1.00 (assert (forall ((B_26 tptp.int) (A_28 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_28) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B_26) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A_28) B_26))))))
% 0.60/1.00 (assert (forall ((B_25 tptp.real) (A_27 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_27) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B_25) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_27) B_25)) tptp.zero_zero_real)))))
% 0.60/1.00 (assert (forall ((B_25 tptp.nat) (A_27 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_27) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B_25) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_27) B_25)) tptp.zero_zero_nat)))))
% 0.60/1.00 (assert (forall ((B_25 tptp.int) (A_27 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_27) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B_25) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_27) B_25)) tptp.zero_zero_int)))))
% 0.60/1.00 (assert (forall ((B_24 tptp.real) (A_26 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_26) (=> (@ (@ tptp.ord_less_eq_real B_24) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real B_24) A_26)) tptp.zero_zero_real)))))
% 0.60/1.00 (assert (forall ((B_24 tptp.nat) (A_26 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_26) (=> (@ (@ tptp.ord_less_eq_nat B_24) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B_24) A_26)) tptp.zero_zero_nat)))))
% 0.60/1.00 (assert (forall ((B_24 tptp.int) (A_26 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_26) (=> (@ (@ tptp.ord_less_eq_int B_24) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B_24) A_26)) tptp.zero_zero_int)))))
% 0.60/1.00 (assert (forall ((B_23 tptp.real) (A_25 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_25) (=> (@ (@ tptp.ord_less_eq_real B_23) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_25) B_23)) tptp.zero_zero_real)))))
% 0.60/1.00 (assert (forall ((B_23 tptp.nat) (A_25 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_25) (=> (@ (@ tptp.ord_less_eq_nat B_23) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_25) B_23)) tptp.zero_zero_nat)))))
% 0.60/1.00 (assert (forall ((B_23 tptp.int) (A_25 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_25) (=> (@ (@ tptp.ord_less_eq_int B_23) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_25) B_23)) tptp.zero_zero_int)))))
% 0.60/1.00 (assert (forall ((B_22 tptp.real) (A_24 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A_24) (=> (@ _let_1 B_22) (@ _let_1 (@ (@ tptp.times_times_real A_24) B_22)))))))
% 0.60/1.00 (assert (forall ((B_22 tptp.nat) (A_24 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A_24) (=> (@ _let_1 B_22) (@ _let_1 (@ (@ tptp.times_times_nat A_24) B_22)))))))
% 0.60/1.00 (assert (forall ((B_22 tptp.int) (A_24 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A_24) (=> (@ _let_1 B_22) (@ _let_1 (@ (@ tptp.times_times_int A_24) B_22)))))))
% 0.60/1.00 (assert (forall ((A_23 tptp.real) (B_21 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_23) B_21)) tptp.zero_zero_real) (or (and (@ _let_1 A_23) (@ (@ tptp.ord_less_eq_real B_21) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A_23) tptp.zero_zero_real) (@ _let_1 B_21)))))))
% 0.60/1.00 (assert (forall ((A_23 tptp.int) (B_21 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_23) B_21)) tptp.zero_zero_int) (or (and (@ _let_1 A_23) (@ (@ tptp.ord_less_eq_int B_21) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A_23) tptp.zero_zero_int) (@ _let_1 B_21)))))))
% 0.60/1.00 (assert (forall ((A_22 tptp.real) (B_20 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A_22) B_20)) (or (and (@ _let_1 A_22) (@ _let_1 B_20)) (and (@ (@ tptp.ord_less_eq_real A_22) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B_20) tptp.zero_zero_real)))))))
% 0.60/1.00 (assert (forall ((A_22 tptp.int) (B_20 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A_22) B_20)) (or (and (@ _let_1 A_22) (@ _let_1 B_20)) (and (@ (@ tptp.ord_less_eq_int A_22) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B_20) tptp.zero_zero_int)))))))
% 0.60/1.00 (assert (forall ((A_21 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A_21) A_21))))
% 0.60/1.00 (assert (forall ((A_21 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A_21) A_21))))
% 0.60/1.00 (assert (forall ((C_10 tptp.real) (B_19 tptp.real) (A_20 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_10))) (=> (@ (@ tptp.ord_less_real B_19) A_20) (=> (@ (@ tptp.ord_less_real C_10) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ _let_1 A_20)) (@ _let_1 B_19)))))))
% 0.60/1.00 (assert (forall ((C_10 tptp.int) (B_19 tptp.int) (A_20 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_10))) (=> (@ (@ tptp.ord_less_int B_19) A_20) (=> (@ (@ tptp.ord_less_int C_10) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A_20)) (@ _let_1 B_19)))))))
% 0.60/1.00 (assert (forall ((C_9 tptp.real) (B_18 tptp.real) (A_19 tptp.real)) (=> (@ (@ tptp.ord_less_real B_18) A_19) (=> (@ (@ tptp.ord_less_real C_9) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_19) C_9)) (@ (@ tptp.times_times_real B_18) C_9))))))
% 0.60/1.00 (assert (forall ((C_9 tptp.int) (B_18 tptp.int) (A_19 tptp.int)) (=> (@ (@ tptp.ord_less_int B_18) A_19) (=> (@ (@ tptp.ord_less_int C_9) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_19) C_9)) (@ (@ tptp.times_times_int B_18) C_9))))))
% 0.60/1.00 (assert (forall ((C_8 tptp.real) (A_18 tptp.real) (B_17 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_8))) (=> (@ (@ tptp.ord_less_real A_18) B_17) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_8) (@ (@ tptp.ord_less_real (@ _let_1 A_18)) (@ _let_1 B_17)))))))
% 0.60/1.00 (assert (forall ((C_8 tptp.nat) (A_18 tptp.nat) (B_17 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_8))) (=> (@ (@ tptp.ord_less_nat A_18) B_17) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C_8) (@ (@ tptp.ord_less_nat (@ _let_1 A_18)) (@ _let_1 B_17)))))))
% 0.60/1.00 (assert (forall ((C_8 tptp.int) (A_18 tptp.int) (B_17 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_8))) (=> (@ (@ tptp.ord_less_int A_18) B_17) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_8) (@ (@ tptp.ord_less_int (@ _let_1 A_18)) (@ _let_1 B_17)))))))
% 0.60/1.00 (assert (forall ((C_7 tptp.real) (A_17 tptp.real) (B_16 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_7))) (=> (@ (@ tptp.ord_less_real A_17) B_16) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_7) (@ (@ tptp.ord_less_real (@ _let_1 A_17)) (@ _let_1 B_16)))))))
% 0.60/1.00 (assert (forall ((C_7 tptp.nat) (A_17 tptp.nat) (B_16 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_7))) (=> (@ (@ tptp.ord_less_nat A_17) B_16) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C_7) (@ (@ tptp.ord_less_nat (@ _let_1 A_17)) (@ _let_1 B_16)))))))
% 0.60/1.00 (assert (forall ((C_7 tptp.int) (A_17 tptp.int) (B_16 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_7))) (=> (@ (@ tptp.ord_less_int A_17) B_16) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_7) (@ (@ tptp.ord_less_int (@ _let_1 A_17)) (@ _let_1 B_16)))))))
% 0.60/1.00 (assert (forall ((C_6 tptp.real) (A_16 tptp.real) (B_15 tptp.real)) (=> (@ (@ tptp.ord_less_real A_16) B_15) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_6) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_16) C_6)) (@ (@ tptp.times_times_real B_15) C_6))))))
% 0.60/1.00 (assert (forall ((C_6 tptp.nat) (A_16 tptp.nat) (B_15 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_16) B_15) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C_6) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_16) C_6)) (@ (@ tptp.times_times_nat B_15) C_6))))))
% 0.60/1.00 (assert (forall ((C_6 tptp.int) (A_16 tptp.int) (B_15 tptp.int)) (=> (@ (@ tptp.ord_less_int A_16) B_15) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_6) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_16) C_6)) (@ (@ tptp.times_times_int B_15) C_6))))))
% 0.60/1.00 (assert (forall ((B_14 tptp.real) (A_15 tptp.real)) (=> (@ (@ tptp.ord_less_real A_15) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B_14) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A_15) B_14))))))
% 0.60/1.00 (assert (forall ((B_14 tptp.int) (A_15 tptp.int)) (=> (@ (@ tptp.ord_less_int A_15) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B_14) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A_15) B_14))))))
% 0.60/1.00 (assert (forall ((B_13 tptp.real) (A_14 tptp.real)) (=> (@ (@ tptp.ord_less_real A_14) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B_13) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_14) B_13)) tptp.zero_zero_real)))))
% 0.60/1.00 (assert (forall ((B_13 tptp.nat) (A_14 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_14) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B_13) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_14) B_13)) tptp.zero_zero_nat)))))
% 0.60/1.00 (assert (forall ((B_13 tptp.int) (A_14 tptp.int)) (=> (@ (@ tptp.ord_less_int A_14) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_13) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_14) B_13)) tptp.zero_zero_int)))))
% 0.60/1.00 (assert (forall ((A_13 tptp.real) (B_12 tptp.real) (C_5 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_5))) (=> (@ (@ tptp.ord_less_real C_5) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ _let_1 A_13)) (@ _let_1 B_12)) (@ (@ tptp.ord_less_real B_12) A_13))))))
% 0.60/1.00 (assert (forall ((A_13 tptp.int) (B_12 tptp.int) (C_5 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_5))) (=> (@ (@ tptp.ord_less_int C_5) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A_13)) (@ _let_1 B_12)) (@ (@ tptp.ord_less_int B_12) A_13))))))
% 0.60/1.00 (assert (forall ((B_11 tptp.real) (A_12 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real B_11) A_12)) (=> (@ _let_1 A_12) (@ _let_1 B_11))))))
% 0.60/1.00 (assert (forall ((B_11 tptp.nat) (A_12 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B_11) A_12)) (=> (@ _let_1 A_12) (@ _let_1 B_11))))))
% 0.60/1.00 (assert (forall ((B_11 tptp.int) (A_12 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B_11) A_12)) (=> (@ _let_1 A_12) (@ _let_1 B_11))))))
% 0.60/1.00 (assert (forall ((A_11 tptp.real) (B_10 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real A_11) B_10)) (=> (@ _let_1 A_11) (@ _let_1 B_10))))))
% 0.60/1.00 (assert (forall ((A_11 tptp.nat) (B_10 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A_11) B_10)) (=> (@ _let_1 A_11) (@ _let_1 B_10))))))
% 0.60/1.00 (assert (forall ((A_11 tptp.int) (B_10 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A_11) B_10)) (=> (@ _let_1 A_11) (@ _let_1 B_10))))))
% 0.60/1.00 (assert (forall ((B_9 tptp.real) (A_10 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A_10) (=> (@ (@ tptp.ord_less_real B_9) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real B_9) A_10)) tptp.zero_zero_real)))))
% 0.60/1.00 (assert (forall ((B_9 tptp.nat) (A_10 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_10) (=> (@ (@ tptp.ord_less_nat B_9) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B_9) A_10)) tptp.zero_zero_nat)))))
% 0.60/1.00 (assert (forall ((B_9 tptp.int) (A_10 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_10) (=> (@ (@ tptp.ord_less_int B_9) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B_9) A_10)) tptp.zero_zero_int)))))
% 0.60/1.00 (assert (forall ((B_8 tptp.real) (A_9 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A_9) (=> (@ (@ tptp.ord_less_real B_8) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_9) B_8)) tptp.zero_zero_real)))))
% 0.60/1.00 (assert (forall ((B_8 tptp.nat) (A_9 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_9) (=> (@ (@ tptp.ord_less_nat B_8) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_9) B_8)) tptp.zero_zero_nat)))))
% 0.60/1.00 (assert (forall ((B_8 tptp.int) (A_9 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_9) (=> (@ (@ tptp.ord_less_int B_8) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_9) B_8)) tptp.zero_zero_int)))))
% 0.60/1.00 (assert (forall ((B_7 tptp.real) (A_8 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A_8) (=> (@ _let_1 B_7) (@ _let_1 (@ (@ tptp.times_times_real A_8) B_7)))))))
% 0.60/1.00 (assert (forall ((B_7 tptp.nat) (A_8 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A_8) (=> (@ _let_1 B_7) (@ _let_1 (@ (@ tptp.times_times_nat A_8) B_7)))))))
% 0.60/1.00 (assert (forall ((B_7 tptp.int) (A_8 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A_8) (=> (@ _let_1 B_7) (@ _let_1 (@ (@ tptp.times_times_int A_8) B_7)))))))
% 0.60/1.00 (assert (forall ((A_7 tptp.real) (B_6 tptp.real) (C_4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_4) (= (@ (@ tptp.ord_less_real (@ _let_1 A_7)) (@ _let_1 B_6)) (@ (@ tptp.ord_less_real A_7) B_6))))))
% 0.60/1.00 (assert (forall ((A_7 tptp.int) (B_6 tptp.int) (C_4 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_4))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_4) (= (@ (@ tptp.ord_less_int (@ _let_1 A_7)) (@ _let_1 B_6)) (@ (@ tptp.ord_less_int A_7) B_6))))))
% 0.60/1.00 (assert (forall ((C_3 tptp.real) (A_6 tptp.real) (B_5 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_3))) (= (@ (@ tptp.ord_less_real (@ _let_1 A_6)) (@ _let_1 B_5)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_3) (@ (@ tptp.ord_less_real A_6) B_5)) (and (@ (@ tptp.ord_less_real C_3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B_5) A_6)))))))
% 0.60/1.00 (assert (forall ((C_3 tptp.int) (A_6 tptp.int) (B_5 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_3))) (= (@ (@ tptp.ord_less_int (@ _let_1 A_6)) (@ _let_1 B_5)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_3) (@ (@ tptp.ord_less_int A_6) B_5)) (and (@ (@ tptp.ord_less_int C_3) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B_5) A_6)))))))
% 0.60/1.00 (assert (forall ((A_5 tptp.real) (C_2 tptp.real) (B_4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_5) C_2)) (@ (@ tptp.times_times_real B_4) C_2)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_2) (@ (@ tptp.ord_less_real A_5) B_4)) (and (@ (@ tptp.ord_less_real C_2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B_4) A_5))))))
% 0.60/1.00 (assert (forall ((A_5 tptp.int) (C_2 tptp.int) (B_4 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_5) C_2)) (@ (@ tptp.times_times_int B_4) C_2)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_2) (@ (@ tptp.ord_less_int A_5) B_4)) (and (@ (@ tptp.ord_less_int C_2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B_4) A_5))))))
% 0.60/1.00 (assert (forall ((A_4 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_4) A_4)) tptp.zero_zero_real))))
% 0.60/1.00 (assert (forall ((A_4 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_4) A_4)) tptp.zero_zero_int))))
% 0.60/1.00 (assert (forall ((B_3 tptp.nat) (C_1 tptp.nat) (A_3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B_3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_3) (=> (@ _let_1 C_1) (@ _let_1 (@ (@ tptp.plus_plus_nat A_3) C_1)))))))
% 0.60/1.00 (assert (forall ((B_3 tptp.int) (C_1 tptp.int) (A_3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B_3))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_3) (=> (@ _let_1 C_1) (@ _let_1 (@ (@ tptp.plus_plus_int A_3) C_1)))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((X_1 tptp.real) (Y_1 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X_1) Z)) (@ (@ tptp.times_times_real Y_1) Z)) (@ (@ tptp.ord_less_real X_1) Y_1)))))
% 0.60/1.00 (assert (forall ((X_1 tptp.real) (Y_1 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X_1) Z)) (@ (@ tptp.times_times_real Y_1) Z)) (@ (@ tptp.ord_less_eq_real X_1) Y_1)))))
% 0.60/1.00 (assert (forall ((X_1 tptp.real) (Y_1 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_1)) (@ _let_1 Y_1)) (@ (@ tptp.ord_less_eq_real X_1) Y_1))))))
% 0.60/1.00 (assert (forall ((Y_1 tptp.real) (X_1 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X_1) (=> (@ _let_1 Y_1) (@ _let_1 (@ (@ tptp.times_times_real X_1) Y_1)))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.real) (Y_1 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_1) Y_1) (@ (@ tptp.ord_less_real (@ _let_1 X_1)) (@ _let_1 Y_1)))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.real) (Y_1 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X_1) X_1)) (@ (@ tptp.times_times_real Y_1) Y_1)) tptp.zero_zero_real) (and (= X_1 tptp.zero_zero_real) (= Y_1 tptp.zero_zero_real)))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat) (N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X_1) N)) Y_1) (@ (@ tptp.dvd_dvd_nat X_1) Y_1)))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat X_1) N) tptp.one_one_nat) (or (= X_1 tptp.one_one_nat) (= N tptp.zero_zero_nat)))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Q tptp.nat) (N tptp.nat) (R tptp.nat)) (=> (= X_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Q) N)) R)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) R) (=> (@ (@ tptp.ord_less_nat R) N) (not (@ (@ tptp.dvd_dvd_nat N) X_1)))))))
% 0.60/1.00 (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))))
% 0.60/1.00 (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_1 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R_1) (= (@ (@ tptp.power_power_real R_1) N) A)))))))
% 0.60/1.00 (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 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real X) N) A) (forall ((Y tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.power_power_real Y) N) A)) (= Y X)))))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat)) (@ (@ tptp.dvd_dvd_nat X_1) X_1)))
% 0.60/1.00 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.60/1.00 (assert (forall ((I_1 tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I_1))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J_1)))))
% 0.60/1.00 (assert (forall ((W tptp.real)) (@ (@ tptp.ord_less_eq_real W) W)))
% 0.60/1.00 (assert (forall ((Z tptp.real) (W tptp.real)) (or (@ (@ tptp.ord_less_eq_real Z) W) (@ (@ tptp.ord_less_eq_real W) Z))))
% 0.60/1.00 (assert (forall ((K tptp.real) (I_1 tptp.real) (J_1 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real I_1))) (=> (@ _let_1 J_1) (=> (@ (@ tptp.ord_less_eq_real J_1) K) (@ _let_1 K))))))
% 0.60/1.00 (assert (forall ((Z tptp.real) (W tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Z) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (= Z W)))))
% 0.60/1.00 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 0.60/1.00 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 0.60/1.00 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((P_1 (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ P_1 N) M))) (=> (=> (@ (@ tptp.ord_less_nat M) N) _let_1) (=> (=> (= M N) _let_1) (=> (=> (@ (@ tptp.ord_less_nat N) M) _let_1) _let_1))))))
% 0.60/1.00 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 0.60/1.00 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 0.60/1.00 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (not (= X_1 Y_1)) (=> (not (@ (@ tptp.ord_less_nat X_1) Y_1)) (@ (@ tptp.ord_less_nat Y_1) X_1)))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 0.60/1.00 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 0.60/1.00 (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))))))))
% 0.60/1.00 (assert (forall ((N tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat J_1) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J_1) N)) K))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) Y_1))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))))
% 0.60/1.00 (assert (forall ((Z tptp.nat) (X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat Z))) (let ((_let_2 (@ tptp.dvd_dvd_nat X_1))) (let ((_let_3 (@ tptp.dvd_dvd_nat Y_1))) (=> (and (@ _let_2 Y_1) (not (@ _let_3 X_1))) (=> (and (@ _let_3 Z) (not (@ _let_1 Y_1))) (and (@ _let_2 Z) (not (@ _let_1 X_1))))))))))
% 0.60/1.00 (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))))))))
% 0.60/1.00 (assert (forall ((Z tptp.nat) (X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat X_1))) (let ((_let_2 (@ tptp.dvd_dvd_nat Y_1))) (=> (and (@ _let_1 Y_1) (not (@ _let_2 X_1))) (=> (@ _let_2 Z) (and (@ _let_1 Z) (not (@ (@ tptp.dvd_dvd_nat Z) X_1)))))))))
% 0.60/1.00 (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))))))))
% 0.60/1.00 (assert (forall ((P_1 Bool) (X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) Y_1))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (=> (and _let_1 (not _let_2)) (=> (and _let_2 (not _let_1)) P_1))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (and (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (not (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (not (= Y_1 X_1)))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (and (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (not (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (not (= X_1 Y_1)))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) Y_1))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) Y_1))) (=> (and _let_1 (not (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) _let_1))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) Y_1))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (and (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (not (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (not (= X_1 Y_1)))))
% 0.60/1.00 (assert (forall ((Z tptp.nat) (X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat Z))) (let ((_let_2 (@ tptp.dvd_dvd_nat X_1))) (=> (@ _let_2 Y_1) (=> (and (@ (@ tptp.dvd_dvd_nat Y_1) Z) (not (@ _let_1 Y_1))) (and (@ _let_2 Z) (not (@ _let_1 X_1)))))))))
% 0.60/1.00 (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))))))))
% 0.60/1.00 (assert (forall ((Z tptp.nat) (X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat X_1))) (=> (@ _let_1 Y_1) (=> (@ (@ tptp.dvd_dvd_nat Y_1) Z) (@ _let_1 Z))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (=> (@ (@ tptp.dvd_dvd_nat Y_1) X_1) (= X_1 Y_1)))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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))))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) Y_1))) (=> _let_1 (or (and _let_1 (not (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (= X_1 Y_1))))))
% 0.60/1.00 (assert (forall ((Y_1 tptp.nat) (X_1 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat Y_1) X_1) (= (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (= X_1 Y_1)))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (= X_1 Y_1) (@ (@ tptp.dvd_dvd_nat X_1) Y_1))))
% 0.60/1.00 (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))))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (and (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (not (@ (@ tptp.dvd_dvd_nat Y_1) X_1))))) (= _let_1 _let_1))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) Y_1))) (= (and _let_1 (not (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (and _let_1 (not (= X_1 Y_1)))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) Y_1))) (= _let_1 (or (and _let_1 (not (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (= X_1 Y_1))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (= (= X_1 Y_1) (and (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (@ (@ tptp.dvd_dvd_nat Y_1) X_1)))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) X_1))) (not (and _let_1 (not _let_1))))))
% 0.60/1.00 (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)))))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) N) (@ (@ tptp.plus_plus_nat N) M))))
% 0.60/1.00 (assert (forall ((X_1 tptp.nat) (Y_1 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X_1))) (let ((_let_2 (@ tptp.plus_plus_nat Y_1))) (= (@ _let_1 (@ _let_2 Z)) (@ _let_2 (@ _let_1 Z)))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 0.60/1.00 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 0.60/1.00 (assert (forall ((I_1 tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I_1))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J_1) K))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.60/1.00 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J_1) (=> (@ (@ tptp.ord_less_eq_nat J_1) K) (@ _let_1 K))))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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)))))))
% 0.60/1.00 (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))))))))
% 0.60/1.00 (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)))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat M) N) (@ (@ tptp.times_times_nat N) M))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 0.60/1.00 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.60/1.00 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 0.60/1.00 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 0.60/1.00 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 0.60/1.00 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 0.60/1.00 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 0.60/1.00 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 0.60/1.00 (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))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 0.60/1.00 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((I_1 tptp.nat) (J_1 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) J_1)) I_1))))
% 0.60/1.00 (assert (forall ((J_1 tptp.nat) (I_1 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J_1) I_1)) I_1))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I_1))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat J_1) M))))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I_1))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J_1))))))
% 0.60/1.00 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J_1) K)))))
% 0.60/1.00 (assert (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J_1) L))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((I_1 tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) J_1)) K) (@ (@ tptp.ord_less_nat I_1) K))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((I_1 tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat I_1) (@ (@ tptp.minus_minus_nat J_1) K)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K)) J_1))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat M) N) (or (@ (@ tptp.ord_less_nat M) N) (= M N)))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 0.60/1.00 (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)))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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)))))))
% 0.60/1.00 (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)))))))
% 0.60/1.00 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 0.60/1.00 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat J_1) M))))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J_1))))))
% 0.60/1.00 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J_1) K)))))
% 0.60/1.00 (assert (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J_1) L))))))
% 0.60/1.00 (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))))
% 0.60/1.00 (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))))
% 0.60/1.00 (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)))))))
% 0.60/1.00 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.minus_minus_nat I_1) (@ (@ tptp.minus_minus_nat J_1) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I_1) K)) J_1)))))
% 0.60/1.00 (assert (forall ((J_1 tptp.nat) (K tptp.nat) (I_1 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J_1) K)) I_1) (@ (@ tptp.ord_less_eq_nat J_1) (@ (@ tptp.plus_plus_nat I_1) K)))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I_1))) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J_1) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K))))))
% 0.60/1.00 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.ord_less_eq_nat I_1) (@ (@ tptp.minus_minus_nat J_1) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) J_1)))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (= (= (@ (@ tptp.minus_minus_nat J_1) I_1) K) (= J_1 (@ (@ tptp.plus_plus_nat K) I_1))))))
% 0.60/1.00 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I_1))) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J_1) K)))))))
% 0.60/1.00 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J_1) K)) I_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J_1) I_1)) K)))))
% 0.60/1.00 (assert (forall ((I_1 tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J_1) I_1)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J_1) K)) I_1)))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 0.60/1.00 (assert (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I_1) K)) (@ (@ tptp.times_times_nat J_1) L))))))
% 0.60/1.00 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I_1)) (@ _let_1 J_1))))))
% 0.60/1.00 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I_1) K)) (@ (@ tptp.times_times_nat J_1) K)))))
% 0.60/1.00 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 0.60/1.00 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((P_1 (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P_1 (@ (@ tptp.minus_minus_nat A) B)) (and (=> (@ (@ tptp.ord_less_nat A) B) (@ P_1 tptp.zero_zero_nat)) (forall ((D_2 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D_2)) (@ P_1 D_2)))))))
% 0.60/1.00 (assert (forall ((P_1 (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P_1 (@ (@ tptp.minus_minus_nat A) B)) (not (or (and (@ (@ tptp.ord_less_nat A) B) (not (@ P_1 tptp.zero_zero_nat))) (exists ((D_2 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D_2)) (not (@ P_1 D_2)))))))))
% 0.60/1.00 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I_1)) (@ _let_1 J_1)))))))
% 0.60/1.00 (assert (forall ((K tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (=> (@ (@ 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_1) K))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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)))))
% 0.60/1.00 (assert (forall ((N tptp.nat) (P_1 (-> tptp.nat Bool))) (=> (not (@ P_1 tptp.zero_zero_nat)) (=> (@ P_1 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_1 I)))) (@ P_1 (@ (@ tptp.plus_plus_nat K_1) tptp.one_one_nat))))))))
% 0.60/1.00 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_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_1) U)) N)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J_1) I_1)) U)) N))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((I_1 tptp.nat) (U tptp.nat) (J_1 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_1) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I_1) J_1)) U)) K))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (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))))))
% 0.60/1.00 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J_1 tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J_1) 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_1) U)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J_1)) U)) M)) N)))))
% 0.60/1.00 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J_1 tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J_1) 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_1) U)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J_1)) U)) M)) N)))))
% 0.60/1.00 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J_1 tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J_1) I_1) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J_1) U)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J_1)) U)) M) N)))))
% 0.60/1.00 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_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_1) U)) N)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J_1) I_1)) U)) N))))))
% 0.60/1.00 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_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_1) U)) N)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J_1) I_1)) U)) N))))))
% 0.60/1.00 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J_1) U)) N)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J_1) I_1)) U)) N))))))
% 0.60/1.00 (assert (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J_1 tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J_1) 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_1) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J_1)) U)) M)) N)))))
% 0.60/1.00 (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))))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int)) (= (@ tptp.twoSqu919416604sum2sq X_1) (exists ((A_2 tptp.int) (B_2 tptp.int)) (= (@ tptp.twoSqu2057625106sum2sq (@ (@ tptp.product_Pair_int_int A_2) B_2)) X_1)))))
% 0.60/1.00 (assert (forall ((P_3 Bool) (P_1 Bool) (X_1 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1))) (=> (=> _let_1 (= P_1 P_3)) (= (=> _let_1 P_1) (=> _let_1 P_3))))))
% 0.60/1.00 (assert (forall ((P_3 Bool) (P_1 Bool) (X_1 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1))) (=> (=> _let_1 (= P_1 P_3)) (= (and _let_1 P_1) (and _let_1 P_3))))))
% 0.60/1.00 (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)))))))
% 0.60/1.00 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.number_number_of_int tptp.pls)))
% 0.60/1.00 (assert (forall ((K tptp.int) (P_1 (-> tptp.int Bool)) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X tptp.int)) (=> (@ P_1 X) (@ P_1 (@ (@ tptp.minus_minus_int X) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X tptp.int)) (=> (@ P_1 X) (@ P_1 (@ (@ tptp.minus_minus_int X) (@ (@ tptp.times_times_int K) D))))))))))
% 0.60/1.00 (assert (forall ((K tptp.int) (P_1 (-> tptp.int Bool)) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X tptp.int)) (=> (@ P_1 X) (@ P_1 (@ (@ tptp.plus_plus_int X) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X tptp.int)) (=> (@ P_1 X) (@ P_1 (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int K) D))))))))))
% 0.60/1.00 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (exists ((P_2 tptp.int)) (and (@ tptp.zprime P_2) (@ (@ tptp.dvd_dvd_int P_2) A))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (M tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (exists ((X tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_int X) M) (@ (@ (@ tptp.zcong A) X) M) (forall ((Y tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int Y) M) (@ (@ (@ tptp.zcong A) Y) M)) (= Y X))))))))
% 0.60/1.00 (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))))
% 0.60/1.00 (assert (forall ((P tptp.int)) (=> (@ tptp.zprime P) (@ (@ (@ tptp.zcong (@ tptp.zfact (@ (@ tptp.minus_minus_int P) tptp.one_one_int))) (@ tptp.number_number_of_int tptp.min)) P))))
% 0.60/1.00 (assert (forall ((N tptp.int)) (let ((_let_1 (@ tptp.zfact N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int N) tptp.zero_zero_int))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (@ (@ tptp.times_times_int N) (@ tptp.zfact (@ (@ tptp.minus_minus_int N) tptp.one_one_int))))))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.inv P))) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) P) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) P) (= (@ _let_1 (@ _let_1 A)) A))))))))
% 0.60/1.00 (assert (forall ((J_1 tptp.int) (A tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.zcong J_1))) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (not (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) P)) (=> (not (@ (@ _let_1 tptp.zero_zero_int) P)) (=> (not (@ (@ tptp.quadRes P) A)) (not (@ (@ _let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.multInv P) J_1))) P))))))))))
% 0.60/1.00 (assert (forall ((J_1 tptp.int) (K tptp.int) (A tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.multInv P) J_1)))) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int J_1) K)) A) P) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int (@ _let_1 J_1)) K)) (@ _let_1 A)) P)))))
% 0.60/1.00 (assert (forall ((J_1 tptp.int) (A tptp.int) (P tptp.int) (K tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.multInv P) K)))) (=> (@ (@ (@ tptp.zcong J_1) _let_1) P) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int J_1) K)) (@ (@ tptp.times_times_int _let_1) K)) P)))))
% 0.60/1.00 (assert (forall ((A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int P) tptp.one_one_int)) (not (= A (@ (@ tptp.inv P) A))))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int P) tptp.one_one_int)) (not (= (@ (@ tptp.inv P) A) tptp.one_one_int)))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (P tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int P) tptp.one_one_int))) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int A) _let_1) (not (= (@ (@ tptp.inv P) A) _let_1))))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.zprime P) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int P) tptp.one_one_int)) (@ _let_1 (@ (@ tptp.inv P) A))))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (P tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int P) tptp.one_one_int))) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int A) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.inv P) A)) _let_1)))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (Y_1 tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.multInv P))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ (@ (@ tptp.zcong X_1) Y_1) P) (@ (@ (@ tptp.zcong (@ _let_1 X_1)) (@ _let_1 Y_1)) P))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int P) tptp.one_one_int)) (not (= (@ (@ tptp.inv P) A) tptp.zero_zero_int)))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (J_1 tptp.int) (K tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.multInv P))) (let ((_let_2 (@ tptp.times_times_int A))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ (@ (@ tptp.zcong J_1) K) P) (@ (@ (@ tptp.zcong (@ _let_2 (@ _let_1 J_1))) (@ _let_2 (@ _let_1 K))) P)))))))
% 0.60/1.00 (assert (forall ((Y_1 tptp.int) (X_1 tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.zcong X_1))) (let ((_let_2 (@ tptp.multInv P))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ _let_1 tptp.zero_zero_int) P)) (=> (not (@ (@ (@ tptp.zcong Y_1) tptp.zero_zero_int) P)) (=> (@ (@ (@ tptp.zcong (@ _let_2 X_1)) (@ _let_2 Y_1)) P) (@ (@ _let_1 Y_1) P))))))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.multInv P))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (@ (@ (@ tptp.zcong (@ _let_1 (@ _let_1 X_1))) X_1) P)))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (P tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (not (@ (@ (@ tptp.zcong (@ (@ tptp.multInv P) X_1)) tptp.zero_zero_int) P)))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) P) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) (@ (@ tptp.inv P) A))) tptp.one_one_int) P))))))
% 0.60/1.00 (assert (forall ((K tptp.int) (A tptp.int) (J_1 tptp.int) (P tptp.int)) (let ((_let_1 (@ (@ tptp.multInv P) J_1))) (let ((_let_2 (@ tptp.times_times_int _let_1))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong J_1) tptp.zero_zero_int) P)) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int (@ _let_2 J_1)) K)) (@ _let_2 A)) P) (@ (@ (@ tptp.zcong K) (@ (@ tptp.times_times_int A) _let_1)) P)))))))))
% 0.60/1.00 (assert (forall ((J_1 tptp.int) (A tptp.int) (K tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.zcong (@ (@ tptp.times_times_int J_1) K)))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong K) tptp.zero_zero_int) P)) (=> (@ (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) (@ (@ tptp.multInv P) K))) K)) P) (@ (@ _let_1 A) P))))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (J_1 tptp.int) (K tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.multInv P))) (let ((_let_2 (@ tptp.times_times_int A))) (let ((_let_3 (@ tptp.zcong K))) (let ((_let_4 (@ tptp.zcong J_1))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ _let_3 tptp.zero_zero_int) P)) (=> (not (@ (@ _let_4 tptp.zero_zero_int) P)) (=> (@ (@ _let_4 (@ _let_2 (@ _let_1 K))) P) (@ (@ _let_3 (@ _let_2 (@ _let_1 J_1))) P))))))))))))
% 0.60/1.00 (assert (forall ((J_1 tptp.int) (K tptp.int) (A tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.zcong J_1))) (let ((_let_2 (@ tptp.multInv P))) (let ((_let_3 (@ tptp.times_times_int A))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) P)) (=> (not (@ (@ (@ tptp.zcong K) tptp.zero_zero_int) P)) (=> (not (@ (@ _let_1 tptp.zero_zero_int) P)) (=> (@ (@ (@ tptp.zcong (@ _let_3 (@ _let_2 J_1))) (@ _let_3 (@ _let_2 K))) P) (@ (@ _let_1 K) P))))))))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.multInv P))) (let ((_let_2 (@ _let_1 X_1))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X_1) _let_2)) (@ _let_1 _let_2))) X_1) P))))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.multInv P))) (let ((_let_2 (@ _let_1 X_1))) (let ((_let_3 (@ _let_1 _let_2))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (@ (@ (@ tptp.zcong _let_3) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X_1) _let_2)) _let_3)) P)))))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (P tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int (@ (@ tptp.multInv P) X_1)) X_1)) tptp.one_one_int) P))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (P tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int X_1) (@ (@ tptp.multInv P) X_1))) tptp.one_one_int) P))))))
% 0.60/1.00 (assert (forall ((B tptp.int) (A tptp.int) (P tptp.int)) (let ((_let_1 (@ (@ tptp.wset A) P))) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) P) (=> (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int P) tptp.one_one_int)) (=> (@ (@ tptp.member_int B) _let_1) (@ (@ tptp.member_int (@ (@ tptp.inv P) B)) _let_1))))))))
% 0.60/1.00 (assert (forall ((B tptp.int) (A tptp.int) (P tptp.int)) (let ((_let_1 (@ (@ tptp.wset A) P))) (let ((_let_2 (@ (@ tptp.minus_minus_int P) tptp.one_one_int))) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) P) (=> (@ (@ tptp.ord_less_int A) _let_2) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (=> (@ (@ tptp.ord_less_int B) _let_2) (=> (@ (@ tptp.member_int (@ (@ tptp.inv P) B)) _let_1) (@ (@ tptp.member_int B) _let_1)))))))))))
% 0.60/1.00 (assert (forall ((P tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.member_int A) (@ (@ tptp.wset A) P)))))
% 0.60/1.00 (assert (forall ((B tptp.int) (P tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.member_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ _let_1 (@ (@ tptp.wset (@ (@ tptp.minus_minus_int A) tptp.one_one_int)) P)) (@ _let_1 (@ (@ tptp.wset A) P)))))))
% 0.60/1.00 (assert (forall ((B tptp.int) (A tptp.int) (P tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int P) tptp.one_one_int))) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int A) _let_1) (=> (@ (@ tptp.member_int B) (@ (@ tptp.wset A) P)) (@ (@ tptp.ord_less_int B) _let_1)))))))
% 0.60/1.00 (assert (forall ((B tptp.int) (A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int P) tptp.one_one_int)) (=> (@ (@ tptp.member_int B) (@ (@ tptp.wset A) P)) (@ (@ tptp.ord_less_int tptp.one_one_int) B))))))
% 0.60/1.00 (assert (forall ((B tptp.int) (P tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.member_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (not (@ _let_1 (@ (@ tptp.wset (@ (@ tptp.minus_minus_int A) tptp.one_one_int)) P))) (=> (@ _let_1 (@ (@ tptp.wset A) P)) (or (= B A) (= B (@ (@ tptp.inv P) A)))))))))
% 0.60/1.00 (assert (forall ((B tptp.int) (A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int P) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.member_int B) (@ (@ tptp.wset A) P))))))))
% 0.60/1.00 (assert (forall ((P_1 (-> tptp.int Bool)) (I_1 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I_1) K) (=> (@ P_1 K) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I) K) (=> (@ P_1 I) (@ P_1 (@ (@ tptp.minus_minus_int I) tptp.one_one_int))))) (@ P_1 I_1))))))
% 0.60/1.00 (assert (forall ((P_1 (-> tptp.int Bool)) (I_1 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int I_1) K) (=> (@ P_1 (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_int I) K) (=> (@ P_1 I) (@ P_1 (@ (@ tptp.minus_minus_int I) tptp.one_one_int))))) (@ P_1 I_1))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (P_1 (-> tptp.int Bool))) (=> (forall ((A_2 tptp.int)) (=> (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_2) (@ P_1 (@ (@ tptp.minus_minus_int A_2) tptp.one_one_int))) (@ P_1 A_2))) (@ P_1 X_1))))
% 0.60/1.00 (assert (forall ((P_1 (-> tptp.int Bool)) (K tptp.int) (I_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I_1) (=> (@ P_1 K) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I) (=> (@ P_1 I) (@ P_1 (@ (@ tptp.plus_plus_int I) tptp.one_one_int))))) (@ P_1 I_1))))))
% 0.60/1.00 (assert (forall ((P_1 (-> tptp.int Bool)) (K tptp.int) (I_1 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I_1) (=> (@ P_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_int K) I) (=> (@ P_1 I) (@ P_1 (@ (@ tptp.plus_plus_int I) tptp.one_one_int))))) (@ P_1 I_1))))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (K tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M_2) N_1) (@ (@ tptp.ord_less_nat (@ F M_2)) (@ F N_1)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 0.60/1.00 (assert (forall ((P tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int P) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (=> (@ tptp.zprime P) (= (@ tptp.d22set _let_1) (@ (@ tptp.wset _let_1) P))))))
% 0.60/1.00 (assert (forall ((N tptp.nat) (P_1 (-> tptp.nat Bool))) (=> (not (@ P_1 tptp.zero_zero_nat)) (=> (@ P_1 N) (exists ((K_1 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K_1) N) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K_1) (not (@ P_1 I)))) (@ P_1 K_1)))))))
% 0.60/1.00 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.member_int B) (@ tptp.d22set A)) (@ (@ tptp.ord_less_eq_int B) A))))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.member_int B) (@ tptp.d22set A))))))
% 0.60/1.00 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.member_int B) (@ tptp.d22set A)) (@ (@ tptp.ord_less_int tptp.one_one_int) B))))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.member_int B) (@ tptp.d22set A))))))
% 0.60/1.00 (assert (forall ((I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (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_1))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.dvd_dvd_int A) B)))))
% 0.60/1.00 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 0.60/1.00 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 0.60/1.00 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (and (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A))))))
% 0.60/1.00 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 0.60/1.00 (assert (forall ((A tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (not (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat))))))
% 0.60/1.00 (assert (forall ((A tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A))))))
% 0.60/1.00 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 0.60/1.00 (assert (forall ((A tptp.nat)) (= (not (= A tptp.one_one_nat)) (and (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A) (not (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat))))))
% 0.60/1.00 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= A tptp.one_one_nat))))
% 0.60/1.00 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= A tptp.one_one_nat))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_nat M) N) (@ _let_1 M))))))
% 0.60/1.00 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.dvd_dvd_nat A) B)))))
% 0.60/1.00 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.dvd_dvd_int A) B)))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (or (@ (@ tptp.ord_less_eq_nat M) N) (= N tptp.zero_zero_nat)))))
% 0.60/1.00 (assert (forall ((N tptp.nat) (M tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (=> (= (@ _let_1 N) (@ _let_1 M)) (= N M))))))
% 0.60/1.00 (assert (forall ((P tptp.int)) (= (@ tptp.sr P) (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_int X) P)))))))
% 0.60/1.00 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.div_mod_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.minus_minus_int (@ _let_1 (@ (@ tptp.div_mod_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))) tptp.one_one_int))))))
% 0.60/1.00 (assert (forall ((V tptp.int) (W tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W))) (let ((_let_2 (@ tptp.number_number_of_int V))) (let ((_let_3 (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (let ((_let_4 (@ (@ tptp.div_mod_int (@ tptp.number_number_of_int (@ tptp.bit1 V))) (@ tptp.number_number_of_int (@ tptp.bit0 W))))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1))) (and (=> _let_5 (= _let_4 (@ (@ tptp.plus_plus_int (@ _let_3 (@ (@ tptp.div_mod_int _let_2) _let_1))) tptp.one_one_int))) (=> (not _let_5) (= _let_4 (@ (@ tptp.minus_minus_int (@ _let_3 (@ (@ tptp.div_mod_int (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1))) tptp.one_one_int)))))))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (Y_1 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int X_1))) (let ((_let_2 (@ tptp.number_number_of_int Y_1))) (= (@ (@ tptp.dvd_dvd_int _let_1) _let_2) (= (@ (@ tptp.div_mod_int _let_2) _let_1) tptp.zero_zero_int))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ _let_1 tptp.zero_zero_int) (@ _let_1 (@ (@ tptp.div_mod_int A) B))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.div_mod_int A) B)) B))))
% 0.60/1.00 (assert (forall ((Y_1 tptp.int) (X_1 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X_1) (=> (@ _let_1 Y_1) (@ _let_1 (@ (@ tptp.div_mod_int X_1) Y_1)))))))
% 0.60/1.00 (assert (forall ((K tptp.int) (M tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.div_mod_int M) K)) M))))
% 0.60/1.00 (assert (forall ((M tptp.int) (D tptp.int)) (= (= (@ (@ tptp.div_mod_int M) D) tptp.zero_zero_int) (exists ((Q_1 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q_1))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (N tptp.int) (Y_1 tptp.int)) (= (= (@ (@ tptp.div_mod_int X_1) N) (@ (@ tptp.div_mod_int Y_1) N)) (@ (@ tptp.dvd_dvd_int N) (@ (@ tptp.minus_minus_int X_1) Y_1)))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (M tptp.int) (Y_1 tptp.int)) (=> (= (@ (@ tptp.div_mod_int X_1) M) (@ (@ tptp.div_mod_int Y_1) M)) (@ (@ (@ tptp.zcong X_1) Y_1) M))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (M tptp.int)) (@ (@ (@ tptp.zcong X_1) (@ (@ tptp.div_mod_int X_1) M)) M)))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int) (M tptp.int)) (= (@ (@ (@ tptp.zcong A) B) M) (@ (@ (@ tptp.zcong (@ (@ tptp.div_mod_int A) M)) (@ (@ tptp.div_mod_int B) M)) M))))
% 0.60/1.00 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 (@ (@ tptp.div_mod_int M) N)) (=> (@ _let_1 N) (@ _let_1 M))))))
% 0.60/1.00 (assert (forall ((N tptp.int) (F tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int F))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.div_mod_int M) N)))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (M tptp.int) (Y_1 tptp.nat)) (= (@ (@ tptp.div_mod_int (@ (@ tptp.power_power_int (@ (@ tptp.div_mod_int X_1) M)) Y_1)) M) (@ (@ tptp.div_mod_int (@ (@ tptp.power_power_int X_1) Y_1)) M))))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.div_mod_int (@ _let_1 B)) C) (@ (@ tptp.div_mod_int (@ _let_1 (@ (@ tptp.div_mod_int B) C))) C)))))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.div_mod_int (@ _let_1 (@ (@ tptp.div_mod_int B) C))) C) (@ (@ tptp.div_mod_int (@ _let_1 B)) C)))))
% 0.60/1.00 (assert (forall ((A tptp.int)) (= (@ (@ tptp.div_mod_int A) A) tptp.zero_zero_int)))
% 0.60/1.00 (assert (forall ((B tptp.int)) (= (@ (@ tptp.div_mod_int tptp.zero_zero_int) B) tptp.zero_zero_int)))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (Y_1 tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X_1))) (= (@ (@ tptp.div_mod_int (@ _let_1 (@ (@ tptp.div_mod_int Y_1) M))) M) (@ (@ tptp.div_mod_int (@ _let_1 Y_1)) M)))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (M tptp.int) (Y_1 tptp.int)) (= (@ (@ tptp.div_mod_int (@ (@ tptp.minus_minus_int (@ (@ tptp.div_mod_int X_1) M)) Y_1)) M) (@ (@ tptp.div_mod_int (@ (@ tptp.minus_minus_int X_1) Y_1)) M))))
% 0.60/1.00 (assert (forall ((A tptp.int)) (= (@ (@ tptp.div_mod_int A) (@ tptp.number_number_of_int tptp.min)) tptp.zero_zero_int)))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.div_mod_int A))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.dvd_dvd_int M) B) (= (@ (@ tptp.div_mod_int (@ _let_1 B)) M) (@ _let_1 M)))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int) (M tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (@ (@ (@ tptp.zcong A) B) M) (= (@ (@ tptp.div_mod_int A) M) (@ (@ tptp.div_mod_int B) M))))))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.div_mod_int A) B)))))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.div_mod_int A) B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_int _let_1) B))))))
% 0.60/1.00 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.div_mod_int A) B) A)))))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.div_mod_int A) B)) tptp.zero_zero_int))))
% 0.60/1.00 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.div_mod_int A) B))) (let ((_let_2 (@ tptp.ord_less_int B))) (=> (@ _let_2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (@ _let_2 _let_1)))))))
% 0.60/1.00 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.div_mod_int A) B) A)))))
% 0.60/1.00 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int A) B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (= (@ (@ tptp.div_mod_int A) B) _let_1))))))
% 0.60/1.00 (assert (forall ((V tptp.int) (W tptp.int)) (= (@ (@ tptp.div_mod_int (@ tptp.number_number_of_int (@ tptp.bit0 V))) (@ tptp.number_number_of_int (@ tptp.bit0 W))) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.div_mod_int (@ tptp.number_number_of_int V)) (@ tptp.number_number_of_int W))))))
% 0.60/1.00 (assert (forall ((P_1 (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P_1 (@ (@ tptp.div_mod_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P_1 N)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J) (@ (@ tptp.ord_less_int J) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I)) J))) (@ P_1 J)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J) (@ (@ tptp.ord_less_eq_int J) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I)) J))) (@ P_1 J))))))))
% 0.60/1.00 (assert (forall ((Q tptp.int) (B tptp.int) (R tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (=> (@ _let_1 R) (=> (@ (@ tptp.ord_less_int R) B) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.div_mod_int Q) C))) R))))))))
% 0.60/1.00 (assert (forall ((Q tptp.int) (B tptp.int) (R tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (=> (@ (@ tptp.ord_less_int R) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.div_mod_int Q) C))) R)) (@ _let_1 C))))))))
% 0.60/1.00 (assert (forall ((Q tptp.int) (B tptp.int) (R tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (=> (@ (@ tptp.ord_less_int B) R) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 C)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.div_mod_int Q) C))) R))))))))
% 0.60/1.00 (assert (forall ((Q tptp.int) (B tptp.int) (R tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (=> (@ (@ tptp.ord_less_int B) R) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.div_mod_int Q) C))) R)) tptp.zero_zero_int))))))
% 0.60/1.00 (assert (forall ((A_1 tptp.int) (B_1 tptp.int) (Q_2 tptp.int) (Y_1 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1))) (=> (= A_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q_2)) Y_1)) (=> (and (=> _let_1 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y_1) (@ (@ tptp.ord_less_int Y_1) B_1))) (=> (not _let_1) (and (@ (@ tptp.ord_less_int B_1) Y_1) (@ (@ tptp.ord_less_eq_int Y_1) tptp.zero_zero_int)))) (=> (not (= B_1 tptp.zero_zero_int)) (= (@ (@ tptp.div_mod_int A_1) B_1) Y_1)))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int)) (let ((_let_1 (@ (@ tptp.div_mod_int X_1) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))))
% 0.60/1.00 (assert (forall ((B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.div_mod_int (@ tptp.number_number_of_int tptp.min)) B) (@ (@ tptp.minus_minus_int B) tptp.one_one_int)))))
% 0.60/1.00 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.div_mod_int (@ _let_2 (@ _let_1 B))) (@ _let_1 A)) (@ _let_2 (@ _let_1 (@ (@ tptp.div_mod_int B) A)))))))))
% 0.60/1.00 (assert (forall ((M_1 tptp.int) (D_1 tptp.int)) (=> (= (@ (@ tptp.div_mod_int M_1) D_1) tptp.zero_zero_int) (exists ((Q_1 tptp.int)) (= M_1 (@ (@ tptp.times_times_int D_1) Q_1))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (Y_1 tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.standardRes M))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) M) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int (@ _let_1 X_1)) (@ _let_1 Y_1))) (@ (@ tptp.times_times_int X_1) Y_1)) M)))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.div_mod_nat M) N)) N))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.div_mod_nat M) N)) N))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (D tptp.nat)) (= (= (@ (@ tptp.div_mod_nat M) D) tptp.zero_zero_nat) (exists ((Q_1 tptp.nat)) (= M (@ (@ tptp.times_times_nat D) Q_1))))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.div_mod_nat M) N) (@ (@ tptp.div_mod_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.div_mod_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_nat M) N))) (and (=> _let_2 (= _let_1 M)) (=> (not _let_2) (= _let_1 (@ (@ tptp.div_mod_nat (@ (@ tptp.minus_minus_nat M) N)) N))))))))
% 0.60/1.00 (assert (forall ((K tptp.nat) (N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.div_mod_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N)) M)) N) (@ (@ tptp.div_mod_nat M) N))))
% 0.60/1.00 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.div_mod_nat M) N) (@ (@ tptp.div_mod_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))
% 0.60/1.00 (assert (forall ((M tptp.int) (X_1 tptp.int)) (= (@ (@ tptp.standardRes M) X_1) (@ (@ tptp.div_mod_int X_1) M))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.div_mod_nat M) N)) K) (@ (@ tptp.div_mod_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))))
% 0.60/1.00 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.div_mod_nat M) N)) (@ (@ tptp.div_mod_nat (@ _let_1 M)) (@ _let_1 N))))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.div_mod_nat M) N) M))))
% 0.60/1.00 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.div_mod_nat M) N)) M)))
% 0.60/1.00 (assert (forall ((M tptp.int) (X_1 tptp.int)) (= (= (@ (@ tptp.standardRes M) X_1) tptp.zero_zero_int) (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) M))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (P tptp.int)) (= (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (not (= (@ (@ tptp.standardRes P) X_1) tptp.zero_zero_int)))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (M tptp.int)) (@ (@ (@ tptp.zcong X_1) (@ (@ tptp.standardRes M) X_1)) M)))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (P tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) P) (@ (@ tptp.ord_less_int (@ (@ tptp.standardRes P) X_1)) P))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (P tptp.int)) (=> (@ (@ tptp.member_int X_1) (@ tptp.sr P)) (= (@ (@ tptp.standardRes P) X_1) X_1))))
% 0.60/1.00 (assert (forall ((P_1 (-> tptp.nat Bool)) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (= K tptp.zero_zero_nat))) (= (@ P_1 (@ (@ tptp.div_mod_nat N) K)) (and (=> _let_1 (@ P_1 N)) (=> (not _let_1) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (=> (= N (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) I)) J)) (@ P_1 J))))))))))
% 0.60/1.00 (assert (forall ((Q tptp.nat) (R tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (=> (@ (@ tptp.ord_less_nat R) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.div_mod_nat Q) C))) R)) (@ _let_1 C)))))))
% 0.60/1.00 (assert (forall ((X_1 tptp.int) (P tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) P) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.standardRes P) X_1)))))
% 0.60/1.00 (assert (forall ((X1 tptp.int) (X2 tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.standardRes M))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ _let_1 X1) (@ _let_1 X2)) (@ (@ (@ tptp.zcong X1) X2) M))))))
% 0.60/1.00 (assert (not (exists ((X tptp.int) (Y 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) _let_2)) (@ (@ tptp.power_power_int Y) _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)))))))
% 1.17/1.43 (set-info :filename cvc5---1.0.5_4968)
% 1.17/1.43 (check-sat-assuming ( true ))
% 1.17/1.43 ------- get file name : TPTP file name is NUM926^3
% 1.17/1.43 ------- cvc5-thf : /export/starexec/sandbox2/solver/bin/cvc5---1.0.5_4968.smt2...
% 1.17/1.43 --- Run --ho-elim --full-saturate-quant at 10...
% 1.17/1.43 % SZS status Theorem for NUM926^3
% 1.17/1.43 % SZS output start Proof for NUM926^3
% 1.17/1.43 (
% 1.17/1.43 (let ((_let_1 (not (exists ((X tptp.int) (Y 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) _let_2)) (@ (@ tptp.power_power_int Y) _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)))))))) (let ((_let_2 (@ tptp.number_number_of_int tptp.pls))) (let ((_let_3 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_4 (not (= tptp.zero_zero_int tptp.one_one_int)))) (let ((_let_5 (not (= tptp.zero_zero_real tptp.one_one_real)))) (let ((_let_6 (@ tptp.bit1 tptp.pls))) (let ((_let_7 (@ tptp.bit0 _let_6))) (let ((_let_8 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_7))) tptp.m)) tptp.one_one_int))) (let ((_let_9 (@ tptp.number_number_of_int tptp.min))) (let ((_let_10 (= (@ (@ tptp.legendre _let_9) _let_8) tptp.one_one_int))) (let ((_let_11 (@ (@ tptp.quadRes _let_8) _let_9))) (let ((_let_12 (@ tptp.number_number_of_nat _let_7))) (let ((_let_13 (@ (@ tptp.power_power_int tptp.s) _let_12))) (let ((_let_14 (@ (@ tptp.plus_plus_int _let_13) tptp.one_one_int))) (let ((_let_15 (@ (@ tptp.minus_minus_int _let_13) _let_9))) (let ((_let_16 (@ tptp.dvd_dvd_int _let_8))) (let ((_let_17 (@ tptp.number_number_of_nat tptp.pls))) (let ((_let_18 (= tptp.zero_zero_nat _let_17))) (let ((_let_19 (= _let_17 tptp.zero_zero_nat))) (let ((_let_20 (@ tptp.ord_less_eq_int tptp.min))) (let ((_let_21 (@ tptp.ord_less_eq_int tptp.pls))) (let ((_let_22 (@ tptp.ord_less_int tptp.min))) (let ((_let_23 (@ tptp.ord_less_int tptp.pls))) (let ((_let_24 (@ tptp.number_number_of_int _let_7))) (let ((_let_25 (@ tptp.zcong _let_13))) (let ((_let_26 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_27 (= tptp.zero_zero_int _let_2))) (let ((_let_28 (@ tptp.number267125858f_real tptp.pls))) (let ((_let_29 (= _let_28 tptp.zero_zero_real))) (let ((_let_30 (= _let_2 tptp.zero_zero_int))) (let ((_let_31 (= tptp.zero_zero_real _let_28))) (let ((_let_32 (= tptp.pls tptp.zero_zero_int))) (let ((_let_33 (@ (@ tptp.power_power_int tptp.s1) _let_12))) (let ((_let_34 (@ (@ tptp.times_times_int _let_8) tptp.t))) (let ((_let_35 (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.number267125858f_real _let_7)))) (let ((_let_36 (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) _let_12))) (let ((_let_37 (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) _let_24))) (let ((_let_38 (@ tptp.number_number_of_int _let_6))) (let ((_let_39 (= tptp.one_one_int _let_38))) (let ((_let_40 (@ tptp.number267125858f_real _let_6))) (let ((_let_41 (= tptp.one_one_real _let_40))) (let ((_let_42 (= _let_40 tptp.one_one_real))) (let ((_let_43 (= _let_38 tptp.one_one_int))) (let ((_let_44 (@ tptp.number_number_of_nat _let_6))) (let ((_let_45 (= _let_44 tptp.one_one_nat))) (let ((_let_46 (= tptp.one_one_nat _let_44))) (let ((_let_47 (forall ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.ord_less_int Z) W) (and (@ (@ tptp.ord_less_eq_int Z) W) (not (= Z W))))))) (let ((_let_48 (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.t))) (let ((_let_49 (=> _let_48 (exists ((X tptp.int) (Y 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) _let_2)) (@ (@ tptp.power_power_int Y) _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)))))))) (let ((_let_50 (=> (= tptp.t tptp.one_one_int) (exists ((X tptp.int) (Y 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) _let_2)) (@ (@ tptp.power_power_int Y) _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)))))))) (let ((_let_51 (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.t))) (let ((_let_52 (ho_9 k_10 (ho_9 k_8 tptp.pls)))) (let ((_let_53 (ho_5 (ho_4 k_6 _let_52) tptp.t))) (let ((_let_54 (= tptp.t _let_52))) (let ((_let_55 (not _let_54))) (let ((_let_56 (ho_5 (ho_4 k_7 _let_52) tptp.t))) (let ((_let_57 (and _let_56 _let_55))) (let ((_let_58 (= _let_53 _let_57))) (let ((_let_59 (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (ho_9 k_8 tptp.pls))) (let ((_let_2 (ho_9 k_11 _let_1))) (let ((_let_3 (ho_16 k_15 _let_2))) (not (= (ho_9 (ho_13 k_14 (ho_9 (ho_13 k_12 (ho_9 k_10 (ho_9 k_11 _let_2))) tptp.m)) (ho_9 k_10 _let_1)) (ho_9 (ho_13 k_14 (ho_19 (ho_18 k_17 X) _let_3)) (ho_19 (ho_18 k_17 Y) _let_3)))))))))) (let ((_let_60 (not _let_53))) (let ((_let_61 (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (ho_9 k_8 tptp.pls))) (let ((_let_2 (ho_9 k_11 _let_1))) (let ((_let_3 (ho_16 k_15 _let_2))) (not (= (ho_9 (ho_13 k_14 (ho_9 (ho_13 k_12 (ho_9 k_10 (ho_9 k_11 _let_2))) tptp.m)) (ho_9 k_10 _let_1)) (ho_9 (ho_13 k_14 (ho_19 (ho_18 k_17 X) _let_3)) (ho_19 (ho_18 k_17 Y) _let_3)))))))))) (let ((_let_62 (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (ho_9 k_8 tptp.pls))) (let ((_let_2 (ho_9 k_11 _let_1))) (let ((_let_3 (ho_16 k_15 _let_2))) (not (= (ho_9 (ho_13 k_14 (ho_9 (ho_13 k_12 (ho_9 k_10 (ho_9 k_11 _let_2))) tptp.m)) (ho_9 k_10 _let_1)) (ho_9 (ho_13 k_14 (ho_19 (ho_18 k_17 X) _let_3)) (ho_19 (ho_18 k_17 Y) _let_3)))))))))) (let ((_let_63 (AND_INTRO (ASSUME :args (_let_18)) (ASSUME :args (_let_31)) (SYMM (ASSUME :args (_let_32))) (ASSUME :args (_let_41)) (ASSUME :args (_let_39)) (ASSUME :args (_let_46))))) (let ((_let_64 (MACRO_RESOLUTION_TRUST (EQUIV_ELIM2 (ALPHA_EQUIV :args (_let_61 (= X X) (= Y Y)))) (EQ_RESOLVE (ASSUME :args (_let_1)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_1 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_63 :args ((forall ((X tptp.int) (Y 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.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 X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit1 tptp.pls))) (let ((_let_2 (@ tptp.bit0 _let_1))) (let ((_let_3 (@ tptp.number_number_of_nat _let_2))) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_3)) (@ (@ tptp.power_power_int Y) _let_3)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_2))) tptp.m)) (@ tptp.number_number_of_int _let_1)))))))) _let_62))))) :args (_let_61 false _let_62)))) (let ((_let_65 (not _let_59))) (let ((_let_66 (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_30 v ii) (ite (= i ii) e (ho_30 u ii)))))))))) (let ((_let_67 (forall ((x |u_(-> tptp.real tptp.real tptp.real)|) (y |u_(-> tptp.real tptp.real tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_30 x z) (ho_30 y z)))) (= x y))))) (let ((_let_68 (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_31 v ii) (ite (= i ii) e (ho_31 u ii)))))))))) (let ((_let_69 (forall ((x |u_(-> tptp.real tptp.real)|) (y |u_(-> tptp.real tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_31 x z) (ho_31 y z)))) (= x y))))) (let ((_let_70 (forall ((u |u_(-> _u_(-> tptp.int Bool)_ Bool)|) (e Bool) (i |u_(-> tptp.int Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.int Bool)_ Bool)|)) (not (forall ((ii |u_(-> tptp.int Bool)|)) (= (ho_46 v ii) (ite (= i ii) e (ho_46 u ii)))))))))) (let ((_let_71 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_46 x z) (ho_46 y z)))) (= x y))))) (let ((_let_72 (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_56 v ii) (ite (= i ii) e (ho_56 u ii)))))))))) (let ((_let_73 (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_56 x z) (ho_56 y z)))) (= x y))))) (let ((_let_74 (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_23 v ii) (ite (= i ii) e (ho_23 u ii)))))))))) (let ((_let_75 (forall ((x |u_(-> tptp.nat tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_23 x z) (ho_23 y z)))) (= x y))))) (let ((_let_76 (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_19 v ii) (ite (= i ii) e (ho_19 u ii)))))))))) (let ((_let_77 (forall ((x |u_(-> tptp.nat tptp.int)|) (y |u_(-> tptp.nat tptp.int)|)) (or (not (forall ((z tptp.nat)) (= (ho_19 x z) (ho_19 y z)))) (= x y))))) (let ((_let_78 (forall ((u |u_(-> _u_(-> tptp.int Bool)_ tptp.int Bool)|) (e |u_(-> tptp.int Bool)|) (i |u_(-> tptp.int Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (not (forall ((ii |u_(-> tptp.int Bool)|)) (= (ho_48 v ii) (ite (= i ii) e (ho_48 u ii)))))))))) (let ((_let_79 (forall ((x |u_(-> _u_(-> tptp.int Bool)_ tptp.int Bool)|) (y |u_(-> _u_(-> tptp.int Bool)_ tptp.int Bool)|)) (or (not (forall ((z |u_(-> tptp.int Bool)|)) (= (ho_48 x z) (ho_48 y z)))) (= x y))))) (let ((_let_80 (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_18 v ii) (ite (= i ii) e (ho_18 u ii)))))))))) (let ((_let_81 (forall ((x |u_(-> tptp.int tptp.nat tptp.int)|) (y |u_(-> tptp.int tptp.nat tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_18 x z) (ho_18 y z)))) (= x y))))) (let ((_let_82 (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_24 v ii) (ite (= i ii) e (ho_24 u ii)))))))))) (let ((_let_83 (forall ((x |u_(-> tptp.nat tptp.nat)|) (y |u_(-> tptp.nat tptp.nat)|)) (or (not (forall ((z tptp.nat)) (= (ho_24 x z) (ho_24 y z)))) (= x y))))) (let ((_let_84 (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_13 v ii) (ite (= i ii) e (ho_13 u ii)))))))))) (let ((_let_85 (forall ((x |u_(-> tptp.int tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_13 x z) (ho_13 y z)))) (= x y))))) (let ((_let_86 (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_28 v ii) (ite (= i ii) e (ho_28 u ii)))))))))) (let ((_let_87 (forall ((x |u_(-> tptp.int tptp.real)|) (y |u_(-> tptp.int tptp.real)|)) (or (not (forall ((z tptp.int)) (= (ho_28 x z) (ho_28 y z)))) (= x y))))) (let ((_let_88 (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_9 v ii) (ite (= i ii) e (ho_9 u ii)))))))))) (let ((_let_89 (forall ((x |u_(-> tptp.int tptp.int)|) (y |u_(-> tptp.int tptp.int)|)) (or (not (forall ((z tptp.int)) (= (ho_9 x z) (ho_9 y z)))) (= x y))))) (let ((_let_90 (forall ((u |u_(-> tptp.int tptp.product_prod_int_int)|) (e tptp.product_prod_int_int) (i tptp.int)) (not (forall ((v |u_(-> tptp.int tptp.product_prod_int_int)|)) (not (forall ((ii tptp.int)) (= (ho_52 v ii) (ite (= i ii) e (ho_52 u ii)))))))))) (let ((_let_91 (forall ((x |u_(-> tptp.int tptp.product_prod_int_int)|) (y |u_(-> tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.int)) (= (ho_52 x z) (ho_52 y z)))) (= x y))))) (let ((_let_92 (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_34 v ii) (ite (= i ii) e (ho_34 u ii)))))))))) (let ((_let_93 (forall ((x |u_(-> tptp.nat tptp.real)|) (y |u_(-> tptp.nat tptp.real)|)) (or (not (forall ((z tptp.nat)) (= (ho_34 x z) (ho_34 y z)))) (= x y))))) (let ((_let_94 (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_16 v ii) (ite (= i ii) e (ho_16 u ii)))))))))) (let ((_let_95 (forall ((x |u_(-> tptp.int tptp.nat)|) (y |u_(-> tptp.int tptp.nat)|)) (or (not (forall ((z tptp.int)) (= (ho_16 x z) (ho_16 y z)))) (= x y))))) (let ((_let_96 (forall ((u |u_(-> tptp.product_prod_int_int tptp.int)|) (e tptp.int) (i tptp.product_prod_int_int)) (not (forall ((v |u_(-> tptp.product_prod_int_int tptp.int)|)) (not (forall ((ii tptp.product_prod_int_int)) (= (ho_54 v ii) (ite (= i ii) e (ho_54 u ii)))))))))) (let ((_let_97 (forall ((x |u_(-> tptp.product_prod_int_int tptp.int)|) (y |u_(-> tptp.product_prod_int_int tptp.int)|)) (or (not (forall ((z tptp.product_prod_int_int)) (= (ho_54 x z) (ho_54 y z)))) (= x y))))) (let ((_let_98 (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_4 v ii) (ite (= i ii) e (ho_4 u ii)))))))))) (let ((_let_99 (forall ((x |u_(-> tptp.int tptp.int Bool)|) (y |u_(-> tptp.int tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_4 x z) (ho_4 y z)))) (= x y))))) (let ((_let_100 (forall ((u |u_(-> tptp.int Bool)|) (e Bool) (i tptp.int)) (not (forall ((v |u_(-> tptp.int Bool)|)) (not (forall ((ii tptp.int)) (= (ho_5 v ii) (ite (= i ii) e (ho_5 u ii)))))))))) (let ((_let_101 (forall ((x |u_(-> tptp.int Bool)|) (y |u_(-> tptp.int Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_5 x z) (ho_5 y z)))) (= x y))))) (let ((_let_102 (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_33 v ii) (ite (= i ii) e (ho_33 u ii)))))))))) (let ((_let_103 (forall ((x |u_(-> tptp.real tptp.nat tptp.real)|) (y |u_(-> tptp.real tptp.nat tptp.real)|)) (or (not (forall ((z tptp.real)) (= (ho_33 x z) (ho_33 y z)))) (= x y))))) (let ((_let_104 (forall ((u |u_(-> tptp.nat Bool)|) (e Bool) (i tptp.nat)) (not (forall ((v |u_(-> tptp.nat Bool)|)) (not (forall ((ii tptp.nat)) (= (ho_38 v ii) (ite (= i ii) e (ho_38 u ii)))))))))) (let ((_let_105 (forall ((x |u_(-> tptp.nat Bool)|) (y |u_(-> tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_38 x z) (ho_38 y z)))) (= x y))))) (let ((_let_106 (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_37 v ii) (ite (= i ii) e (ho_37 u ii)))))))))) (let ((_let_107 (forall ((x |u_(-> tptp.nat tptp.nat Bool)|) (y |u_(-> tptp.nat tptp.nat Bool)|)) (or (not (forall ((z tptp.nat)) (= (ho_37 x z) (ho_37 y z)))) (= x y))))) (let ((_let_108 (forall ((u |u_(-> tptp.real Bool)|) (e Bool) (i tptp.real)) (not (forall ((v |u_(-> tptp.real Bool)|)) (not (forall ((ii tptp.real)) (= (ho_42 v ii) (ite (= i ii) e (ho_42 u ii)))))))))) (let ((_let_109 (forall ((x |u_(-> tptp.real Bool)|) (y |u_(-> tptp.real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_42 x z) (ho_42 y z)))) (= x y))))) (let ((_let_110 (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_41 v ii) (ite (= i ii) e (ho_41 u ii)))))))))) (let ((_let_111 (forall ((x |u_(-> tptp.real tptp.real Bool)|) (y |u_(-> tptp.real tptp.real Bool)|)) (or (not (forall ((z tptp.real)) (= (ho_41 x z) (ho_41 y z)))) (= x y))))) (let ((_let_112 (forall ((u |u_(-> tptp.int _u_(-> tptp.int Bool)_ Bool)|) (e |u_(-> _u_(-> tptp.int Bool)_ Bool)|) (i tptp.int)) (not (forall ((v |u_(-> tptp.int _u_(-> tptp.int Bool)_ Bool)|)) (not (forall ((ii tptp.int)) (= (ho_45 v ii) (ite (= i ii) e (ho_45 u ii)))))))))) (let ((_let_113 (forall ((x |u_(-> tptp.int _u_(-> tptp.int Bool)_ Bool)|) (y |u_(-> tptp.int _u_(-> tptp.int Bool)_ Bool)|)) (or (not (forall ((z tptp.int)) (= (ho_45 x z) (ho_45 y z)))) (= x y))))) (let ((_let_114 (forall ((u |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|) (e |u_(-> tptp.int tptp.product_prod_int_int)|) (i tptp.int)) (not (forall ((v |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (not (forall ((ii tptp.int)) (= (ho_51 v ii) (ite (= i ii) e (ho_51 u ii)))))))))) (let ((_let_115 (forall ((x |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|) (y |u_(-> tptp.int tptp.int tptp.product_prod_int_int)|)) (or (not (forall ((z tptp.int)) (= (ho_51 x z) (ho_51 y z)))) (= x y))))) (let ((_let_116 (forall ((BOUND_VARIABLE_25239 tptp.int) (BOUND_VARIABLE_25240 tptp.int)) (= (ho_5 (ho_4 k_3 BOUND_VARIABLE_25239) BOUND_VARIABLE_25240) (and (ho_5 (ho_4 k_7 tptp.pls) BOUND_VARIABLE_25240) (ho_5 (ho_4 k_6 BOUND_VARIABLE_25240) BOUND_VARIABLE_25239)))))) (let ((_let_117 (forall ((BOUND_VARIABLE_25239 tptp.int) (BOUND_VARIABLE_25240 tptp.int)) (= (and (@ (@ tptp.ord_less_eq_int tptp.pls) BOUND_VARIABLE_25240) (@ (@ tptp.ord_less_int BOUND_VARIABLE_25240) BOUND_VARIABLE_25239)) (ll_2 BOUND_VARIABLE_25239 BOUND_VARIABLE_25240))))) (let ((_let_118 (not _let_61))) (let ((_let_119 (not _let_56))) (let ((_let_120 (_let_57))) (let ((_let_121 (forall ((Z tptp.int) (W tptp.int)) (= (and (ho_5 (ho_4 k_7 Z) W) (not (= Z W))) (ho_5 (ho_4 k_6 Z) W))))) (let ((_let_122 (EQ_RESOLVE (ASSUME :args (_let_47)) (PREPROCESS :args ((= _let_47 _let_121)))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_58)) :args ((or _let_53 (not _let_57) (not _let_58)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_122 :args (_let_52 tptp.t QUANTIFIERS_INST_CBQI_CONFLICT)) :args (_let_121)))) _let_122 :args (_let_58 false _let_121)) (MACRO_RESOLUTION_TRUST (REORDERING (EQ_RESOLVE (CNF_AND_NEG :args _let_120) (CONG (REFL :args _let_120) (REFL :args (_let_119)) (MACRO_SR_PRED_INTRO :args ((= (not _let_55) _let_54))) :args (or))) :args ((or _let_54 _let_119 _let_57))) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_50)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_50 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_63 :args ((=> (= tptp.one_one_int tptp.t) (not (forall ((X tptp.int) (Y 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) _let_2)) (@ (@ tptp.power_power_int Y) _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)))))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (=> (= tptp.t _let_38) (not (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit1 tptp.pls))) (let ((_let_2 (@ tptp.bit0 _let_1))) (let ((_let_3 (@ tptp.number_number_of_nat _let_2))) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_3)) (@ (@ tptp.power_power_int Y) _let_3)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_2))) tptp.m)) (@ tptp.number_number_of_int _let_1)))))))))) (=> _let_54 _let_118))))))) :args ((or _let_118 _let_55))) _let_64 :args (_let_55 false _let_61)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_51)) (MACRO_SR_EQ_INTRO _let_63 :args (_let_51 SB_DEFAULT SBA_FIXPOINT))) (PREPROCESS :args (_let_117))) (PREPROCESS :args ((= (and (@ (@ tptp.ord_less_eq_int _let_38) tptp.t) _let_117) (and _let_56 _let_116))))) (PREPROCESS :args ((and _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66)))) :args ((and _let_56 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66))) :args (0)) :args (_let_57 true _let_54 false _let_56)) (MACRO_RESOLUTION_TRUST (REORDERING (IMPLIES_ELIM (EQ_RESOLVE (ASSUME :args (_let_49)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_49 SB_DEFAULT SBA_FIXPOINT)) (MACRO_SR_EQ_INTRO _let_63 :args ((=> _let_48 (not (forall ((X tptp.int) (Y 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.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 X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))))))))) SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (=> (@ (@ tptp.ord_less_int _let_38) tptp.t) (not (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit1 tptp.pls))) (let ((_let_2 (@ tptp.bit0 _let_1))) (let ((_let_3 (@ tptp.number_number_of_nat _let_2))) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_3)) (@ (@ tptp.power_power_int Y) _let_3)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 _let_2))) tptp.m)) (@ tptp.number_number_of_int _let_1)))))))))) (=> _let_53 _let_65))))))) :args ((or _let_65 _let_60))) (MACRO_RESOLUTION_TRUST (EQUIV_ELIM1 (ALPHA_EQUIV :args (_let_61 (= X X) (= Y Y)))) _let_64 :args (_let_59 false _let_61)) :args (_let_60 false _let_59)) :args (false false _let_58 false _let_57 true _let_53)) :args (_let_51 _let_50 _let_49 (@ (@ tptp.ord_less_int tptp.t) _let_8) (@ tptp.zprime _let_8) (= _let_14 _let_34) (@ tptp.twoSqu919416604sum2sq _let_34) (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)))))) (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 ((X_44 tptp.int) (Y_34 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 X_44) Y_34)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_44) _let_2)) (@ (@ tptp.power_power_int Y_34) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int _let_1)) X_44)) Y_34)))))) (forall ((X_44 tptp.nat) (Y_34 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X_44) Y_34)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X_44) _let_1)) (@ (@ tptp.power_power_nat Y_34) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X_44)) Y_34))))) (forall ((X_44 tptp.real) (Y_34 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_44) Y_34)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X_44) _let_2)) (@ (@ tptp.power_power_real Y_34) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.number267125858f_real _let_1)) X_44)) Y_34)))))) (forall ((W_19 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W_19))) (= (@ (@ tptp.power_power_int _let_1) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_int _let_1) _let_1)))) (forall ((W_19 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real W_19))) (= (@ (@ tptp.power_power_real _let_1) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_real _let_1) _let_1)))) (forall ((W_19 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_19))) (= (@ (@ tptp.power_power_nat _let_1) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_nat _let_1) _let_1)))) (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))))))) (= (@ (@ tptp.power_power_int tptp.one_one_int) _let_12) tptp.one_one_int) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) _let_12) tptp.one_one_nat) (= (@ (@ tptp.power_power_real tptp.one_one_real) _let_12) tptp.one_one_real) (forall ((X_43 tptp.int)) (= (@ (@ tptp.times_times_int X_43) X_43) (@ (@ tptp.power_power_int X_43) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (forall ((X_43 tptp.real)) (= (@ (@ tptp.times_times_real X_43) X_43) (@ (@ tptp.power_power_real X_43) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (forall ((X_43 tptp.nat)) (= (@ (@ tptp.times_times_nat X_43) X_43) (@ (@ tptp.power_power_nat X_43) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (forall ((A_127 tptp.int)) (= (@ (@ tptp.power_power_int A_127) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_int A_127) A_127))) (forall ((A_127 tptp.real)) (= (@ (@ tptp.power_power_real A_127) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_real A_127) A_127))) (forall ((A_127 tptp.nat)) (= (@ (@ tptp.power_power_nat A_127) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_nat A_127) A_127))) (forall ((X_42 tptp.int) (N_41 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X_42))) (let ((_let_2 (@ _let_1 N_41))) (= (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_41)) (@ (@ tptp.times_times_int _let_2) _let_2))))) (forall ((X_42 tptp.real) (N_41 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X_42))) (let ((_let_2 (@ _let_1 N_41))) (= (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_41)) (@ (@ tptp.times_times_real _let_2) _let_2))))) (forall ((X_42 tptp.nat) (N_41 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X_42))) (let ((_let_2 (@ _let_1 N_41))) (= (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_41)) (@ (@ tptp.times_times_nat _let_2) _let_2))))) (forall ((W_18 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.number_number_of_int W_18)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int (@ tptp.bit1 tptp.pls)) W_18)))) (forall ((W_18 tptp.int)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.number267125858f_real W_18)) (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int (@ tptp.bit1 tptp.pls)) W_18)))) (forall ((V_20 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_20)) tptp.one_one_int) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_20) (@ tptp.bit1 tptp.pls))))) (forall ((V_20 tptp.int)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_20)) tptp.one_one_real) (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_20) (@ tptp.bit1 tptp.pls))))) _let_37 _let_35 (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.int)) (@ (@ tptp.ord_less_eq_int W) W)) (forall ((Z tptp.int) (W tptp.int)) (or (@ (@ tptp.ord_less_eq_int Z) W) (@ (@ tptp.ord_less_eq_int W) Z))) _let_47 (forall ((X_1 tptp.int) (Y_1 tptp.int)) (or (@ (@ tptp.ord_less_int X_1) Y_1) (= X_1 Y_1) (@ (@ tptp.ord_less_int Y_1) X_1))) (forall ((K tptp.int) (I_1 tptp.int) (J_1 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int I_1))) (=> (@ _let_1 J_1) (=> (@ (@ tptp.ord_less_eq_int J_1) 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_41 tptp.int) (P_6 tptp.nat) (Q_6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X_41))) (= (@ (@ tptp.power_power_int (@ _let_1 P_6)) Q_6) (@ _let_1 (@ (@ tptp.times_times_nat P_6) Q_6))))) (forall ((X_41 tptp.real) (P_6 tptp.nat) (Q_6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X_41))) (= (@ (@ tptp.power_power_real (@ _let_1 P_6)) Q_6) (@ _let_1 (@ (@ tptp.times_times_nat P_6) Q_6))))) (forall ((X_41 tptp.nat) (P_6 tptp.nat) (Q_6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X_41))) (= (@ (@ tptp.power_power_nat (@ _let_1 P_6)) Q_6) (@ _let_1 (@ (@ tptp.times_times_nat P_6) Q_6))))) (forall ((X_40 tptp.int)) (= (@ (@ tptp.power_power_int X_40) tptp.one_one_nat) X_40)) (forall ((X_40 tptp.real)) (= (@ (@ tptp.power_power_real X_40) tptp.one_one_nat) X_40)) (forall ((X_40 tptp.nat)) (= (@ (@ tptp.power_power_nat X_40) tptp.one_one_nat) X_40)) (forall ((X_1 tptp.int) (Y_1 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X_1))) (= (@ (@ tptp.power_power_int (@ _let_1 Y_1)) Z) (@ _let_1 (@ (@ tptp.times_times_nat Y_1) Z))))) (forall ((V_19 tptp.int) (W_17 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V_19))) (let ((_let_2 (@ tptp.number_number_of_int W_17))) (= (@ (@ tptp.ord_less_eq_int _let_1) _let_2) (not (@ (@ tptp.ord_less_int _let_2) _let_1)))))) (forall ((V_19 tptp.int) (W_17 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V_19))) (let ((_let_2 (@ tptp.number_number_of_nat W_17))) (= (@ (@ tptp.ord_less_eq_nat _let_1) _let_2) (not (@ (@ tptp.ord_less_nat _let_2) _let_1)))))) (forall ((V_19 tptp.int) (W_17 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real V_19))) (let ((_let_2 (@ tptp.number267125858f_real W_17))) (= (@ (@ tptp.ord_less_eq_real _let_1) _let_2) (not (@ (@ tptp.ord_less_real _let_2) _let_1)))))) (forall ((X_39 tptp.int) (Y_33 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int X_39)) (@ tptp.number_number_of_int Y_33)) (@ (@ tptp.ord_less_int X_39) Y_33))) (forall ((X_39 tptp.int) (Y_33 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.number267125858f_real X_39)) (@ tptp.number267125858f_real Y_33)) (@ (@ tptp.ord_less_int X_39) Y_33))) (forall ((X_38 tptp.int) (Y_32 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_38)) (@ tptp.number_number_of_int Y_32)) (@ (@ tptp.ord_less_eq_int X_38) Y_32))) (forall ((X_38 tptp.int) (Y_32 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.number267125858f_real X_38)) (@ tptp.number267125858f_real Y_32)) (@ (@ tptp.ord_less_eq_int X_38) Y_32))) (forall ((Z_10 tptp.int) (Z tptp.int) (W_16 tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int W_16) W) (=> (@ (@ tptp.ord_less_eq_int Z_10) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int W_16) Z_10)) (@ (@ tptp.plus_plus_int W) Z))))) (forall ((X_37 tptp.int) (P_5 tptp.nat) (Q_5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X_37))) (= (@ (@ tptp.times_times_int (@ _let_1 P_5)) (@ _let_1 Q_5)) (@ _let_1 (@ (@ tptp.plus_plus_nat P_5) Q_5))))) (forall ((X_37 tptp.real) (P_5 tptp.nat) (Q_5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X_37))) (= (@ (@ tptp.times_times_real (@ _let_1 P_5)) (@ _let_1 Q_5)) (@ _let_1 (@ (@ tptp.plus_plus_nat P_5) Q_5))))) (forall ((X_37 tptp.nat) (P_5 tptp.nat) (Q_5 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X_37))) (= (@ (@ tptp.times_times_nat (@ _let_1 P_5)) (@ _let_1 Q_5)) (@ _let_1 (@ (@ tptp.plus_plus_nat P_5) Q_5))))) (forall ((X_1 tptp.int) (Y_1 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X_1))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat Y_1) Z)) (@ (@ tptp.times_times_int (@ _let_1 Y_1)) (@ _let_1 Z))))) (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))) _let_36 (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))) (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))) (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))) (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))) (@ _let_21 tptp.pls) (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))) (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 ((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 ((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 ((K tptp.int) (I_1 tptp.int) (J_1 tptp.int)) (=> (@ (@ tptp.ord_less_int I_1) J_1) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I_1) K)) (@ (@ tptp.plus_plus_int J_1) K)))) (forall ((K tptp.int) (I_1 tptp.int) (J_1 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (@ (@ tptp.ord_less_eq_int I_1) J_1) (@ (@ tptp.ord_less_eq_int (@ _let_1 I_1)) (@ _let_1 J_1))))) (forall ((V_6 tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V_6))) (let ((_let_2 (@ tptp.number_number_of_nat V))) (let ((_let_3 (@ (@ tptp.plus_plus_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_int V_6) tptp.pls))) (let ((_let_5 (@ (@ tptp.ord_less_int V) 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) V_6))))))))))))) _let_45 _let_46 (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)) (= (@ (@ tptp.ord_less_int tptp.pls) (@ tptp.bit1 K)) (@ (@ tptp.ord_less_eq_int tptp.pls) K))) (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.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_int (@ tptp.bit0 K1)) (@ tptp.bit1 K2)) (@ (@ tptp.ord_less_eq_int K1) K2))) (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 ((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 ((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) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W) Z))) (@ tptp.zprime _let_24) (forall ((Y_1 tptp.int) (X_1 tptp.int)) (=> (@ tptp.twoSqu919416604sum2sq X_1) (=> (@ tptp.twoSqu919416604sum2sq Y_1) (@ tptp.twoSqu919416604sum2sq (@ (@ tptp.times_times_int X_1) Y_1))))) (forall ((Lx_6 tptp.int) (Ly_4 tptp.int) (Rx_6 tptp.int) (Ry_4 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_6))) (= (@ (@ tptp.times_times_int (@ _let_1 Ly_4)) (@ (@ tptp.times_times_int Rx_6) Ry_4)) (@ (@ tptp.times_times_int (@ _let_1 Rx_6)) (@ (@ tptp.times_times_int Ly_4) Ry_4))))) (forall ((Lx_6 tptp.nat) (Ly_4 tptp.nat) (Rx_6 tptp.nat) (Ry_4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx_6))) (= (@ (@ tptp.times_times_nat (@ _let_1 Ly_4)) (@ (@ tptp.times_times_nat Rx_6) Ry_4)) (@ (@ tptp.times_times_nat (@ _let_1 Rx_6)) (@ (@ tptp.times_times_nat Ly_4) Ry_4))))) (forall ((Lx_6 tptp.real) (Ly_4 tptp.real) (Rx_6 tptp.real) (Ry_4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx_6))) (= (@ (@ tptp.times_times_real (@ _let_1 Ly_4)) (@ (@ tptp.times_times_real Rx_6) Ry_4)) (@ (@ tptp.times_times_real (@ _let_1 Rx_6)) (@ (@ tptp.times_times_real Ly_4) Ry_4))))) (forall ((Lx_5 tptp.int) (Ly_3 tptp.int) (Rx_5 tptp.int) (Ry_3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.times_times_int Lx_5) Ly_3)))) (let ((_let_2 (@ tptp.times_times_int Rx_5))) (= (@ _let_1 (@ _let_2 Ry_3)) (@ _let_2 (@ _let_1 Ry_3)))))) (forall ((Lx_5 tptp.nat) (Ly_3 tptp.nat) (Rx_5 tptp.nat) (Ry_3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ (@ tptp.times_times_nat Lx_5) Ly_3)))) (let ((_let_2 (@ tptp.times_times_nat Rx_5))) (= (@ _let_1 (@ _let_2 Ry_3)) (@ _let_2 (@ _let_1 Ry_3)))))) (forall ((Lx_5 tptp.real) (Ly_3 tptp.real) (Rx_5 tptp.real) (Ry_3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.times_times_real Lx_5) Ly_3)))) (let ((_let_2 (@ tptp.times_times_real Rx_5))) (= (@ _let_1 (@ _let_2 Ry_3)) (@ _let_2 (@ _let_1 Ry_3)))))) (forall ((Lx_4 tptp.int) (Ly_2 tptp.int) (Rx_4 tptp.int) (Ry_2 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int Rx_4) Ry_2))) (let ((_let_2 (@ tptp.times_times_int Lx_4))) (= (@ (@ tptp.times_times_int (@ _let_2 Ly_2)) _let_1) (@ _let_2 (@ (@ tptp.times_times_int Ly_2) _let_1)))))) (forall ((Lx_4 tptp.nat) (Ly_2 tptp.nat) (Rx_4 tptp.nat) (Ry_2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat Rx_4) Ry_2))) (let ((_let_2 (@ tptp.times_times_nat Lx_4))) (= (@ (@ tptp.times_times_nat (@ _let_2 Ly_2)) _let_1) (@ _let_2 (@ (@ tptp.times_times_nat Ly_2) _let_1)))))) (forall ((Lx_4 tptp.real) (Ly_2 tptp.real) (Rx_4 tptp.real) (Ry_2 tptp.real)) (let ((_let_1 (@ (@ tptp.times_times_real Rx_4) Ry_2))) (let ((_let_2 (@ tptp.times_times_real Lx_4))) (= (@ (@ tptp.times_times_real (@ _let_2 Ly_2)) _let_1) (@ _let_2 (@ (@ tptp.times_times_real Ly_2) _let_1)))))) (forall ((Lx_3 tptp.int) (Ly_1 tptp.int) (Rx_3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_3))) (= (@ (@ tptp.times_times_int (@ _let_1 Ly_1)) Rx_3) (@ (@ tptp.times_times_int (@ _let_1 Rx_3)) Ly_1)))) (forall ((Lx_3 tptp.nat) (Ly_1 tptp.nat) (Rx_3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx_3))) (= (@ (@ tptp.times_times_nat (@ _let_1 Ly_1)) Rx_3) (@ (@ tptp.times_times_nat (@ _let_1 Rx_3)) Ly_1)))) (forall ((Lx_3 tptp.real) (Ly_1 tptp.real) (Rx_3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx_3))) (= (@ (@ tptp.times_times_real (@ _let_1 Ly_1)) Rx_3) (@ (@ tptp.times_times_real (@ _let_1 Rx_3)) Ly_1)))) (forall ((Lx_2 tptp.int) (Ly tptp.int) (Rx_2 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_2))) (= (@ (@ tptp.times_times_int (@ _let_1 Ly)) Rx_2) (@ _let_1 (@ (@ tptp.times_times_int Ly) Rx_2))))) (forall ((Lx_2 tptp.nat) (Ly tptp.nat) (Rx_2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx_2))) (= (@ (@ tptp.times_times_nat (@ _let_1 Ly)) Rx_2) (@ _let_1 (@ (@ tptp.times_times_nat Ly) Rx_2))))) (forall ((Lx_2 tptp.real) (Ly tptp.real) (Rx_2 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx_2))) (= (@ (@ tptp.times_times_real (@ _let_1 Ly)) Rx_2) (@ _let_1 (@ (@ tptp.times_times_real Ly) Rx_2))))) (forall ((Lx_1 tptp.int) (Rx_1 tptp.int) (Ry_1 tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx_1))) (= (@ _let_1 (@ (@ tptp.times_times_int Rx_1) Ry_1)) (@ (@ tptp.times_times_int (@ _let_1 Rx_1)) Ry_1)))) (forall ((Lx_1 tptp.nat) (Rx_1 tptp.nat) (Ry_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx_1))) (= (@ _let_1 (@ (@ tptp.times_times_nat Rx_1) Ry_1)) (@ (@ tptp.times_times_nat (@ _let_1 Rx_1)) Ry_1)))) (forall ((Lx_1 tptp.real) (Rx_1 tptp.real) (Ry_1 tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx_1))) (= (@ _let_1 (@ (@ tptp.times_times_real Rx_1) Ry_1)) (@ (@ tptp.times_times_real (@ _let_1 Rx_1)) Ry_1)))) (forall ((Lx tptp.int) (Rx tptp.int) (Ry tptp.int)) (let ((_let_1 (@ tptp.times_times_int Lx))) (let ((_let_2 (@ tptp.times_times_int Rx))) (= (@ _let_1 (@ _let_2 Ry)) (@ _let_2 (@ _let_1 Ry)))))) (forall ((Lx tptp.nat) (Rx tptp.nat) (Ry tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Lx))) (let ((_let_2 (@ tptp.times_times_nat Rx))) (= (@ _let_1 (@ _let_2 Ry)) (@ _let_2 (@ _let_1 Ry)))))) (forall ((Lx tptp.real) (Rx tptp.real) (Ry tptp.real)) (let ((_let_1 (@ tptp.times_times_real Lx))) (let ((_let_2 (@ tptp.times_times_real Rx))) (= (@ _let_1 (@ _let_2 Ry)) (@ _let_2 (@ _let_1 Ry)))))) (forall ((A_126 tptp.int) (B_73 tptp.int)) (= (@ (@ tptp.times_times_int A_126) B_73) (@ (@ tptp.times_times_int B_73) A_126))) (forall ((A_126 tptp.nat) (B_73 tptp.nat)) (= (@ (@ tptp.times_times_nat A_126) B_73) (@ (@ tptp.times_times_nat B_73) A_126))) (forall ((A_126 tptp.real) (B_73 tptp.real)) (= (@ (@ tptp.times_times_real A_126) B_73) (@ (@ tptp.times_times_real B_73) A_126))) (forall ((A_125 tptp.int) (B_72 tptp.int) (C_39 tptp.int) (D_11 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_125))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_72)) (@ (@ tptp.plus_plus_int C_39) D_11)) (@ (@ tptp.plus_plus_int (@ _let_1 C_39)) (@ (@ tptp.plus_plus_int B_72) D_11))))) (forall ((A_125 tptp.nat) (B_72 tptp.nat) (C_39 tptp.nat) (D_11 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_125))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_72)) (@ (@ tptp.plus_plus_nat C_39) D_11)) (@ (@ tptp.plus_plus_nat (@ _let_1 C_39)) (@ (@ tptp.plus_plus_nat B_72) D_11))))) (forall ((A_125 tptp.real) (B_72 tptp.real) (C_39 tptp.real) (D_11 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_125))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B_72)) (@ (@ tptp.plus_plus_real C_39) D_11)) (@ (@ tptp.plus_plus_real (@ _let_1 C_39)) (@ (@ tptp.plus_plus_real B_72) D_11))))) (forall ((X_36 tptp.int) (A_124 (-> tptp.int Bool))) (= (@ (@ tptp.member_int X_36) A_124) (@ A_124 X_36))) (forall ((P_4 (-> tptp.int Bool))) (= (@ tptp.collect_int P_4) P_4)) (forall ((A_123 tptp.int) (B_71 tptp.int) (C_38 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_123))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_71)) C_38) (@ (@ tptp.plus_plus_int (@ _let_1 C_38)) B_71)))) (forall ((A_123 tptp.nat) (B_71 tptp.nat) (C_38 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_123))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_71)) C_38) (@ (@ tptp.plus_plus_nat (@ _let_1 C_38)) B_71)))) (forall ((A_123 tptp.real) (B_71 tptp.real) (C_38 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_123))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B_71)) C_38) (@ (@ tptp.plus_plus_real (@ _let_1 C_38)) B_71)))) (forall ((A_122 tptp.int) (B_70 tptp.int) (C_37 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_122))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B_70)) C_37) (@ _let_1 (@ (@ tptp.plus_plus_int B_70) C_37))))) (forall ((A_122 tptp.nat) (B_70 tptp.nat) (C_37 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_122))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B_70)) C_37) (@ _let_1 (@ (@ tptp.plus_plus_nat B_70) C_37))))) (forall ((A_122 tptp.real) (B_70 tptp.real) (C_37 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_122))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B_70)) C_37) (@ _let_1 (@ (@ tptp.plus_plus_real B_70) C_37))))) (forall ((A_121 tptp.int) (C_36 tptp.int) (D_10 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_121))) (= (@ _let_1 (@ (@ tptp.plus_plus_int C_36) D_10)) (@ (@ tptp.plus_plus_int (@ _let_1 C_36)) D_10)))) (forall ((A_121 tptp.nat) (C_36 tptp.nat) (D_10 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_121))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat C_36) D_10)) (@ (@ tptp.plus_plus_nat (@ _let_1 C_36)) D_10)))) (forall ((A_121 tptp.real) (C_36 tptp.real) (D_10 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_121))) (= (@ _let_1 (@ (@ tptp.plus_plus_real C_36) D_10)) (@ (@ tptp.plus_plus_real (@ _let_1 C_36)) D_10)))) (forall ((A_120 tptp.int) (C_35 tptp.int) (D_9 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A_120))) (let ((_let_2 (@ tptp.plus_plus_int C_35))) (= (@ _let_1 (@ _let_2 D_9)) (@ _let_2 (@ _let_1 D_9)))))) (forall ((A_120 tptp.nat) (C_35 tptp.nat) (D_9 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A_120))) (let ((_let_2 (@ tptp.plus_plus_nat C_35))) (= (@ _let_1 (@ _let_2 D_9)) (@ _let_2 (@ _let_1 D_9)))))) (forall ((A_120 tptp.real) (C_35 tptp.real) (D_9 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A_120))) (let ((_let_2 (@ tptp.plus_plus_real C_35))) (= (@ _let_1 (@ _let_2 D_9)) (@ _let_2 (@ _let_1 D_9)))))) (forall ((A_119 tptp.int) (C_34 tptp.int)) (= (@ (@ tptp.plus_plus_int A_119) C_34) (@ (@ tptp.plus_plus_int C_34) A_119))) (forall ((A_119 tptp.nat) (C_34 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_119) C_34) (@ (@ tptp.plus_plus_nat C_34) A_119))) (forall ((A_119 tptp.real) (C_34 tptp.real)) (= (@ (@ tptp.plus_plus_real A_119) C_34) (@ (@ tptp.plus_plus_real C_34) A_119))) (forall ((X_35 tptp.int) (Y_31 tptp.int)) (= (= (@ tptp.number_number_of_int X_35) (@ tptp.number_number_of_int Y_31)) (= X_35 Y_31))) (forall ((X_35 tptp.int) (Y_31 tptp.int)) (= (= (@ tptp.number267125858f_real X_35) (@ tptp.number267125858f_real Y_31)) (= X_35 Y_31))) (forall ((W_15 tptp.int) (X_34 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat W_15))) (= (= _let_1 X_34) (= X_34 _let_1)))) (forall ((W_15 tptp.int) (X_34 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W_15))) (= (= _let_1 X_34) (= X_34 _let_1)))) (forall ((W_15 tptp.int) (X_34 tptp.real)) (let ((_let_1 (@ tptp.number267125858f_real W_15))) (= (= _let_1 X_34) (= X_34 _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 ((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 ((Z tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int Z) W) (@ (@ tptp.times_times_int W) Z))) (forall ((K tptp.int)) (= (@ tptp.number_number_of_int K) K)) (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_1 tptp.int) (Y_1 tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X_1))) (let ((_let_2 (@ tptp.plus_plus_int Y_1))) (= (@ _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 ((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 ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (= (@ _let_1 (@ tptp.bit1 K)) (@ _let_1 K)))) (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) (L tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) (@ tptp.bit1 L)) (@ (@ tptp.ord_less_eq_int K) L))) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) tptp.pls) (@ (@ tptp.ord_less_eq_int K) tptp.pls))) (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (= (@ _let_1 (@ tptp.bit0 K)) (@ _let_1 K)))) (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 ((A_118 tptp.int) (N_40 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (let ((_let_2 (@ tptp.power_power_int A_118))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N_40)) (@ (@ tptp.power_power_int (@ _let_2 N_40)) _let_1))))) (forall ((A_118 tptp.real) (N_40 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (let ((_let_2 (@ tptp.power_power_real A_118))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N_40)) (@ (@ tptp.power_power_real (@ _let_2 N_40)) _let_1))))) (forall ((A_118 tptp.nat) (N_40 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (let ((_let_2 (@ tptp.power_power_nat A_118))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N_40)) (@ (@ tptp.power_power_nat (@ _let_2 N_40)) _let_1))))) (forall ((X_33 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int X_33)) tptp.one_one_int) (@ (@ tptp.ord_less_int X_33) (@ tptp.bit1 tptp.pls)))) (forall ((X_33 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.number267125858f_real X_33)) tptp.one_one_real) (@ (@ tptp.ord_less_int X_33) (@ tptp.bit1 tptp.pls)))) (forall ((Y_30 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.number_number_of_int Y_30)) (@ (@ tptp.ord_less_int (@ tptp.bit1 tptp.pls)) Y_30))) (forall ((Y_30 tptp.int)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.number267125858f_real Y_30)) (@ (@ tptp.ord_less_int (@ tptp.bit1 tptp.pls)) Y_30))) (forall ((X_32 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_32)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int X_32) (@ tptp.bit1 tptp.pls)))) (forall ((X_32 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.number267125858f_real X_32)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_int X_32) (@ tptp.bit1 tptp.pls)))) (forall ((Y_29 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.number_number_of_int Y_29)) (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 tptp.pls)) Y_29))) (forall ((Y_29 tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.number267125858f_real Y_29)) (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 tptp.pls)) Y_29))) (forall ((W_14 tptp.int) (Y_28 tptp.int) (X_31 tptp.int) (Z_9 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X_31))) (let ((_let_2 (@ tptp.times_times_int W_14))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y_28)) (@ _let_1 Z_9)) (@ (@ tptp.plus_plus_int (@ _let_2 Z_9)) (@ _let_1 Y_28))) (or (= W_14 X_31) (= Y_28 Z_9)))))) (forall ((W_14 tptp.nat) (Y_28 tptp.nat) (X_31 tptp.nat) (Z_9 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X_31))) (let ((_let_2 (@ tptp.times_times_nat W_14))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y_28)) (@ _let_1 Z_9)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z_9)) (@ _let_1 Y_28))) (or (= W_14 X_31) (= Y_28 Z_9)))))) (forall ((W_14 tptp.real) (Y_28 tptp.real) (X_31 tptp.real) (Z_9 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X_31))) (let ((_let_2 (@ tptp.times_times_real W_14))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y_28)) (@ _let_1 Z_9)) (@ (@ tptp.plus_plus_real (@ _let_2 Z_9)) (@ _let_1 Y_28))) (or (= W_14 X_31) (= Y_28 Z_9)))))) (forall ((A_117 tptp.int) (M_14 tptp.int) (B_69 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_117) M_14)) (@ (@ tptp.times_times_int B_69) M_14)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_117) B_69)) M_14))) (forall ((A_117 tptp.nat) (M_14 tptp.nat) (B_69 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_117) M_14)) (@ (@ tptp.times_times_nat B_69) M_14)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_117) B_69)) M_14))) (forall ((A_117 tptp.real) (M_14 tptp.real) (B_69 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_117) M_14)) (@ (@ tptp.times_times_real B_69) M_14)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_117) B_69)) M_14))) (forall ((A_116 tptp.int) (B_68 tptp.int) (C_33 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_116) B_68)) C_33) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_116) C_33)) (@ (@ tptp.times_times_int B_68) C_33)))) (forall ((A_116 tptp.nat) (B_68 tptp.nat) (C_33 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_116) B_68)) C_33) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_116) C_33)) (@ (@ tptp.times_times_nat B_68) C_33)))) (forall ((A_116 tptp.real) (B_68 tptp.real) (C_33 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_116) B_68)) C_33) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_116) C_33)) (@ (@ tptp.times_times_real B_68) C_33)))) (forall ((C_32 tptp.int) (D_8 tptp.int) (A_115 tptp.int) (B_67 tptp.int)) (let ((_let_1 (@ tptp.times_times_int B_67))) (let ((_let_2 (@ tptp.times_times_int A_115))) (= (and (not (= A_115 B_67)) (not (= C_32 D_8))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C_32)) (@ _let_1 D_8)) (@ (@ tptp.plus_plus_int (@ _let_2 D_8)) (@ _let_1 C_32)))))))) (forall ((C_32 tptp.nat) (D_8 tptp.nat) (A_115 tptp.nat) (B_67 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B_67))) (let ((_let_2 (@ tptp.times_times_nat A_115))) (= (and (not (= A_115 B_67)) (not (= C_32 D_8))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C_32)) (@ _let_1 D_8)) (@ (@ tptp.plus_plus_nat (@ _let_2 D_8)) (@ _let_1 C_32)))))))) (forall ((C_32 tptp.real) (D_8 tptp.real) (A_115 tptp.real) (B_67 tptp.real)) (let ((_let_1 (@ tptp.times_times_real B_67))) (let ((_let_2 (@ tptp.times_times_real A_115))) (= (and (not (= A_115 B_67)) (not (= C_32 D_8))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C_32)) (@ _let_1 D_8)) (@ (@ tptp.plus_plus_real (@ _let_2 D_8)) (@ _let_1 C_32)))))))) (forall ((X_30 tptp.int) (Y_27 tptp.int) (Z_8 tptp.int)) (let ((_let_1 (@ tptp.times_times_int X_30))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Y_27) Z_8)) (@ (@ tptp.plus_plus_int (@ _let_1 Y_27)) (@ _let_1 Z_8))))) (forall ((X_30 tptp.nat) (Y_27 tptp.nat) (Z_8 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X_30))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat Y_27) Z_8)) (@ (@ tptp.plus_plus_nat (@ _let_1 Y_27)) (@ _let_1 Z_8))))) (forall ((X_30 tptp.real) (Y_27 tptp.real) (Z_8 tptp.real)) (let ((_let_1 (@ tptp.times_times_real X_30))) (= (@ _let_1 (@ (@ tptp.plus_plus_real Y_27) Z_8)) (@ (@ tptp.plus_plus_real (@ _let_1 Y_27)) (@ _let_1 Z_8))))) (forall ((A_114 tptp.int)) (= (@ (@ tptp.times_times_int A_114) tptp.one_one_int) A_114)) (forall ((A_114 tptp.nat)) (= (@ (@ tptp.times_times_nat A_114) tptp.one_one_nat) A_114)) (forall ((A_114 tptp.real)) (= (@ (@ tptp.times_times_real A_114) tptp.one_one_real) A_114)) (forall ((A_113 tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A_113) A_113)) (forall ((A_113 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A_113) A_113)) (forall ((A_113 tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A_113) A_113)) (forall ((X_29 tptp.int) (Y_26 tptp.int) (Q_4 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int X_29) Y_26)) Q_4) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X_29) Q_4)) (@ (@ tptp.power_power_int Y_26) Q_4)))) (forall ((X_29 tptp.real) (Y_26 tptp.real) (Q_4 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real X_29) Y_26)) Q_4) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X_29) Q_4)) (@ (@ tptp.power_power_real Y_26) Q_4)))) (forall ((X_29 tptp.nat) (Y_26 tptp.nat) (Q_4 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat X_29) Y_26)) Q_4) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X_29) Q_4)) (@ (@ tptp.power_power_nat Y_26) Q_4)))) (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) (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)) (= (@ (@ 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.times_times_int Z) tptp.one_one_int) Z)) (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) Z) Z)) (forall ((V tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V)) (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V) W)))) (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 ((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 ((V tptp.int) (W tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V)) (@ tptp.number_number_of_int W)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V) W)))) (forall ((V_18 tptp.int) (V_17 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_17) (=> (@ _let_1 V_18) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_17)) (@ tptp.number_number_of_int V_18)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_17) V_18))))))) (forall ((V_18 tptp.int) (V_17 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_17) (=> (@ _let_1 V_18) (= (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V_17)) (@ tptp.number_number_of_nat V_18)) (@ tptp.number_number_of_nat (@ (@ tptp.times_times_int V_17) V_18))))))) (forall ((V_18 tptp.int) (V_17 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_17) (=> (@ _let_1 V_18) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real V_17)) (@ tptp.number267125858f_real V_18)) (@ tptp.number267125858f_real (@ (@ tptp.times_times_int V_17) V_18))))))) (forall ((V_16 tptp.int) (V_15 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_15) (=> (@ _let_1 V_16) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_15)) (@ tptp.number_number_of_int V_16)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_15) V_16))))))) (forall ((V_16 tptp.int) (V_15 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_15) (=> (@ _let_1 V_16) (= (@ (@ tptp.plus_plus_nat (@ tptp.number_number_of_nat V_15)) (@ tptp.number_number_of_nat V_16)) (@ tptp.number_number_of_nat (@ (@ tptp.plus_plus_int V_15) V_16))))))) (forall ((V_16 tptp.int) (V_15 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.pls))) (=> (@ _let_1 V_15) (=> (@ _let_1 V_16) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_15)) (@ tptp.number267125858f_real V_16)) (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_15) V_16))))))) (forall ((X_1 tptp.int)) (@ (@ tptp.ord_less_eq_int X_1) (@ (@ tptp.power_power_int X_1) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (forall ((A_112 tptp.int) (B_66 tptp.int) (V_14 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V_14))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_112) B_66)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_112) _let_1)) (@ (@ tptp.times_times_int B_66) _let_1))))) (forall ((A_112 tptp.nat) (B_66 tptp.nat) (V_14 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat V_14))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_112) B_66)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_112) _let_1)) (@ (@ tptp.times_times_nat B_66) _let_1))))) (forall ((A_112 tptp.real) (B_66 tptp.real) (V_14 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real V_14))) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_112) B_66)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_112) _let_1)) (@ (@ tptp.times_times_real B_66) _let_1))))) (forall ((V_13 tptp.int) (B_65 tptp.int) (C_31 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.number_number_of_int V_13)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B_65) C_31)) (@ (@ tptp.plus_plus_int (@ _let_1 B_65)) (@ _let_1 C_31))))) (forall ((V_13 tptp.int) (B_65 tptp.nat) (C_31 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.number_number_of_nat V_13)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B_65) C_31)) (@ (@ tptp.plus_plus_nat (@ _let_1 B_65)) (@ _let_1 C_31))))) (forall ((V_13 tptp.int) (B_65 tptp.real) (C_31 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.number267125858f_real V_13)))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B_65) C_31)) (@ (@ tptp.plus_plus_real (@ _let_1 B_65)) (@ _let_1 C_31))))) (forall ((A_111 tptp.int) (M_13 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_111) M_13)) M_13) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_111) tptp.one_one_int)) M_13))) (forall ((A_111 tptp.nat) (M_13 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_111) M_13)) M_13) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_111) tptp.one_one_nat)) M_13))) (forall ((A_111 tptp.real) (M_13 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_111) M_13)) M_13) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_111) tptp.one_one_real)) M_13))) (forall ((M_12 tptp.int) (A_110 tptp.int)) (= (@ (@ tptp.plus_plus_int M_12) (@ (@ tptp.times_times_int A_110) M_12)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_110) tptp.one_one_int)) M_12))) (forall ((M_12 tptp.nat) (A_110 tptp.nat)) (= (@ (@ tptp.plus_plus_nat M_12) (@ (@ tptp.times_times_nat A_110) M_12)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_110) tptp.one_one_nat)) M_12))) (forall ((M_12 tptp.real) (A_110 tptp.real)) (= (@ (@ tptp.plus_plus_real M_12) (@ (@ tptp.times_times_real A_110) M_12)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_110) tptp.one_one_real)) M_12))) (forall ((M_11 tptp.int)) (= (@ (@ tptp.plus_plus_int M_11) M_11) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)) M_11))) (forall ((M_11 tptp.nat)) (= (@ (@ tptp.plus_plus_nat M_11) M_11) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)) M_11))) (forall ((M_11 tptp.real)) (= (@ (@ tptp.plus_plus_real M_11) M_11) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)) M_11))) (forall ((A_109 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int tptp.pls)) A_109) A_109)) (forall ((A_109 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real tptp.pls)) A_109) A_109)) (forall ((A_108 tptp.int)) (= (@ (@ tptp.plus_plus_int A_108) (@ tptp.number_number_of_int tptp.pls)) A_108)) (forall ((A_108 tptp.real)) (= (@ (@ tptp.plus_plus_real A_108) (@ tptp.number267125858f_real tptp.pls)) A_108)) (forall ((V_12 tptp.int) (W_13 tptp.int) (Z_7 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_12)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int W_13)) Z_7)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_12) W_13))) Z_7))) (forall ((V_12 tptp.int) (W_13 tptp.int) (Z_7 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real V_12)) (@ (@ tptp.times_times_real (@ tptp.number267125858f_real W_13)) Z_7)) (@ (@ tptp.times_times_real (@ tptp.number267125858f_real (@ (@ tptp.times_times_int V_12) W_13))) Z_7))) (forall ((V_11 tptp.int) (W_12 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_11)) (@ tptp.number_number_of_int W_12)) (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_11) W_12)))) (forall ((V_11 tptp.int) (W_12 tptp.int)) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real V_11)) (@ tptp.number267125858f_real W_12)) (@ tptp.number267125858f_real (@ (@ tptp.times_times_int V_11) W_12)))) (forall ((V_10 tptp.int) (W_11 tptp.int)) (= (@ tptp.number_number_of_int (@ (@ tptp.times_times_int V_10) W_11)) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int V_10)) (@ tptp.number_number_of_int W_11)))) (forall ((V_10 tptp.int) (W_11 tptp.int)) (= (@ tptp.number267125858f_real (@ (@ tptp.times_times_int V_10) W_11)) (@ (@ tptp.times_times_real (@ tptp.number267125858f_real V_10)) (@ tptp.number267125858f_real W_11)))) (forall ((V_9 tptp.int) (W_10 tptp.int) (Z_6 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_9)) (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int W_10)) Z_6)) (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_9) W_10))) Z_6))) (forall ((V_9 tptp.int) (W_10 tptp.int) (Z_6 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_9)) (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real W_10)) Z_6)) (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_9) W_10))) Z_6))) (forall ((V_8 tptp.int) (W_9 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_8)) (@ tptp.number_number_of_int W_9)) (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_8) W_9)))) (forall ((V_8 tptp.int) (W_9 tptp.int)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_8)) (@ tptp.number267125858f_real W_9)) (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_8) W_9)))) (forall ((V_7 tptp.int) (W_8 tptp.int)) (= (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_7) W_8)) (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_7)) (@ tptp.number_number_of_int W_8)))) (forall ((V_7 tptp.int) (W_8 tptp.int)) (= (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_7) W_8)) (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_7)) (@ tptp.number267125858f_real W_8)))) (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 ((W_7 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W_7))) (= (@ tptp.number_number_of_int (@ tptp.bit1 W_7)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1)) _let_1)))) (forall ((W_7 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real W_7))) (= (@ tptp.number267125858f_real (@ tptp.bit1 W_7)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1)) _let_1)))) (forall ((A_107 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit1 tptp.pls))) A_107) A_107)) (forall ((A_107 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real (@ tptp.bit1 tptp.pls))) A_107) A_107)) (forall ((A_106 tptp.int)) (= (@ (@ tptp.times_times_int A_106) (@ tptp.number_number_of_int (@ tptp.bit1 tptp.pls))) A_106)) (forall ((A_106 tptp.real)) (= (@ (@ tptp.times_times_real A_106) (@ tptp.number267125858f_real (@ tptp.bit1 tptp.pls))) A_106)) _let_43 _let_45 _let_42 _let_43 _let_42 _let_39 _let_41 _let_39 (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 ((W_6 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)) (@ tptp.number_number_of_int W_6)) (@ tptp.number_number_of_int (@ tptp.bit0 W_6)))) (forall ((W_6 tptp.int)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)) (@ tptp.number267125858f_real W_6)) (@ tptp.number267125858f_real (@ tptp.bit0 W_6)))) (forall ((A_105 tptp.int)) (= (@ (@ tptp.power_power_int A_105) (@ tptp.number_number_of_nat (@ tptp.bit1 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A_105) A_105)) A_105))) (forall ((A_105 tptp.real)) (= (@ (@ tptp.power_power_real A_105) (@ tptp.number_number_of_nat (@ tptp.bit1 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real A_105) A_105)) A_105))) (forall ((A_105 tptp.nat)) (= (@ (@ tptp.power_power_nat A_105) (@ tptp.number_number_of_nat (@ tptp.bit1 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat A_105) A_105)) A_105))) (forall ((X_1 tptp.int)) (let ((_let_1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (let ((_let_2 (@ tptp.power_power_int X_1))) (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 ((Z_5 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) Z_5) (@ (@ tptp.plus_plus_int Z_5) Z_5))) (forall ((Z_5 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) Z_5) (@ (@ tptp.plus_plus_nat Z_5) Z_5))) (forall ((Z_5 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) Z_5) (@ (@ tptp.plus_plus_real Z_5) Z_5))) (forall ((Z_4 tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) Z_4) (@ (@ tptp.plus_plus_int Z_4) Z_4))) (forall ((Z_4 tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.number267125858f_real (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) Z_4) (@ (@ tptp.plus_plus_real Z_4) Z_4))) (forall ((Z_3 tptp.int)) (= (@ (@ tptp.times_times_int Z_3) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.plus_plus_int Z_3) Z_3))) (forall ((Z_3 tptp.nat)) (= (@ (@ tptp.times_times_nat Z_3) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.plus_plus_nat Z_3) Z_3))) (forall ((Z_3 tptp.real)) (= (@ (@ tptp.times_times_real Z_3) (@ tptp.number267125858f_real (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.plus_plus_real Z_3) Z_3))) (forall ((Z_2 tptp.int)) (= (@ (@ tptp.times_times_int Z_2) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.plus_plus_int Z_2) Z_2))) (forall ((Z_2 tptp.real)) (= (@ (@ tptp.times_times_real Z_2) (@ tptp.number267125858f_real (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.plus_plus_real Z_2) Z_2))) _let_37 _let_36 _let_35 (@ _let_26 _let_8) (@ _let_16 _let_14) (forall ((P tptp.int)) (let ((_let_1 (@ tptp.bit1 tptp.pls))) (let ((_let_2 (@ tptp.bit0 _let_1))) (=> (@ tptp.zprime P) (=> (not (= P (@ tptp.number_number_of_int _let_2))) (=> (not (= P (@ tptp.number_number_of_int (@ tptp.bit1 _let_1)))) (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int (@ tptp.bit1 _let_2))) P))))))) (= (@ tptp.twoSqu2057625106sum2sq (@ (@ tptp.product_Pair_int_int tptp.s) tptp.one_one_int)) _let_34) (forall ((X_1 tptp.real) (Y_1 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_1) Y_1)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X_1) _let_2)) (@ (@ tptp.power_power_real Y_1) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.number267125858f_real _let_1)) X_1)) Y_1)))))) (forall ((X_1 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_1) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.number267125858f_real _let_1)) X_1)) _let_2))))) (forall ((N_39 tptp.nat) (A_104 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A_104) N_39))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_104) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A_104) _let_1))))) (forall ((N_39 tptp.nat) (A_104 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A_104) N_39))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_104) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A_104) _let_1))))) (forall ((N_39 tptp.nat) (A_104 tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A_104) N_39))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_104) (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.times_times_real A_104) _let_1))))) (forall ((N_38 tptp.nat) (A_103 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A_103) (@ _let_1 (@ (@ tptp.times_times_int A_103) (@ (@ tptp.power_power_int A_103) N_38)))))) (forall ((N_38 tptp.nat) (A_103 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A_103) (@ _let_1 (@ (@ tptp.times_times_nat A_103) (@ (@ tptp.power_power_nat A_103) N_38)))))) (forall ((N_38 tptp.nat) (A_103 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A_103) (@ _let_1 (@ (@ tptp.times_times_real A_103) (@ (@ tptp.power_power_real A_103) N_38)))))) (forall ((M_10 tptp.nat) (N_37 tptp.nat) (A_102 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A_102))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_102) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M_10)) (@ _let_1 N_37)) (@ (@ tptp.ord_less_eq_nat M_10) N_37))))) (forall ((M_10 tptp.nat) (N_37 tptp.nat) (A_102 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_102))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_102) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M_10)) (@ _let_1 N_37)) (@ (@ tptp.ord_less_eq_nat M_10) N_37))))) (forall ((M_10 tptp.nat) (N_37 tptp.nat) (A_102 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A_102))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_102) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 M_10)) (@ _let_1 N_37)) (@ (@ tptp.ord_less_eq_nat M_10) N_37))))) (forall ((X_28 tptp.nat) (Y_25 tptp.nat) (B_64 tptp.int)) (let ((_let_1 (@ tptp.power_power_int B_64))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B_64) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X_28)) (@ _let_1 Y_25)) (@ (@ tptp.ord_less_eq_nat X_28) Y_25))))) (forall ((X_28 tptp.nat) (Y_25 tptp.nat) (B_64 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B_64))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B_64) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X_28)) (@ _let_1 Y_25)) (@ (@ tptp.ord_less_eq_nat X_28) Y_25))))) (forall ((X_28 tptp.nat) (Y_25 tptp.nat) (B_64 tptp.real)) (let ((_let_1 (@ tptp.power_power_real B_64))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B_64) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X_28)) (@ _let_1 Y_25)) (@ (@ tptp.ord_less_eq_nat X_28) Y_25))))) (@ (@ _let_25 _let_33) _let_8) (and (@ _let_3 tptp.s) (@ (@ tptp.ord_less_int tptp.s) _let_8) (@ (@ (@ tptp.zcong tptp.s1) tptp.s) _let_8)) (exists ((X 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) (@ (@ tptp.ord_less_int X) _let_1) (@ (@ (@ tptp.zcong tptp.s1) X) _let_1) (forall ((Y 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) (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ (@ tptp.zcong tptp.s1) Y) _let_1)) (= Y X))))))) (not (forall ((S_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))) (not (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) S_1) (@ (@ tptp.ord_less_int S_1) _let_1) (@ (@ (@ tptp.zcong tptp.s1) S_1) _let_1)))))) (@ (@ (@ tptp.zcong _let_33) _let_9) _let_8) (forall ((A_101 tptp.int) (N_36 tptp.nat)) (= (= (@ (@ tptp.power_power_int A_101) N_36) tptp.zero_zero_int) (and (= A_101 tptp.zero_zero_int) (not (= N_36 tptp.zero_zero_nat))))) (forall ((A_101 tptp.nat) (N_36 tptp.nat)) (= (= (@ (@ tptp.power_power_nat A_101) N_36) tptp.zero_zero_nat) (and (= A_101 tptp.zero_zero_nat) (not (= N_36 tptp.zero_zero_nat))))) (forall ((A_101 tptp.real) (N_36 tptp.nat)) (= (= (@ (@ tptp.power_power_real A_101) N_36) tptp.zero_zero_real) (and (= A_101 tptp.zero_zero_real) (not (= N_36 tptp.zero_zero_nat))))) (forall ((A_100 tptp.real) (M_9 tptp.nat) (N_35 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_100))) (=> (@ (@ tptp.ord_less_eq_nat M_9) N_35) (@ (@ tptp.dvd_dvd_real (@ _let_1 M_9)) (@ _let_1 N_35))))) (forall ((A_100 tptp.int) (M_9 tptp.nat) (N_35 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_100))) (=> (@ (@ tptp.ord_less_eq_nat M_9) N_35) (@ (@ tptp.dvd_dvd_int (@ _let_1 M_9)) (@ _let_1 N_35))))) (forall ((A_100 tptp.nat) (M_9 tptp.nat) (N_35 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_100))) (=> (@ (@ tptp.ord_less_eq_nat M_9) N_35) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M_9)) (@ _let_1 N_35))))) (forall ((N_34 tptp.nat) (M_8 tptp.nat) (X_27 tptp.real) (Y_24 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real X_27) Y_24) (=> (@ (@ tptp.ord_less_eq_nat N_34) M_8) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X_27) N_34)) (@ (@ tptp.power_power_real Y_24) M_8))))) (forall ((N_34 tptp.nat) (M_8 tptp.nat) (X_27 tptp.int) (Y_24 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int X_27) Y_24) (=> (@ (@ tptp.ord_less_eq_nat N_34) M_8) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X_27) N_34)) (@ (@ tptp.power_power_int Y_24) M_8))))) (forall ((N_34 tptp.nat) (M_8 tptp.nat) (X_27 tptp.nat) (Y_24 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X_27) Y_24) (=> (@ (@ tptp.ord_less_eq_nat N_34) M_8) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X_27) N_34)) (@ (@ tptp.power_power_nat Y_24) M_8))))) (forall ((M_7 tptp.nat) (A_99 tptp.real) (N_33 tptp.nat) (B_63 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A_99))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N_33)) B_63) (=> (@ (@ tptp.ord_less_eq_nat M_7) N_33) (@ (@ tptp.dvd_dvd_real (@ _let_1 M_7)) B_63))))) (forall ((M_7 tptp.nat) (A_99 tptp.int) (N_33 tptp.nat) (B_63 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A_99))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N_33)) B_63) (=> (@ (@ tptp.ord_less_eq_nat M_7) N_33) (@ (@ tptp.dvd_dvd_int (@ _let_1 M_7)) B_63))))) (forall ((M_7 tptp.nat) (A_99 tptp.nat) (N_33 tptp.nat) (B_63 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_99))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N_33)) B_63) (=> (@ (@ tptp.ord_less_eq_nat M_7) N_33) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M_7)) B_63))))) (forall ((A_98 tptp.int) (N_32 tptp.nat) (B_62 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A_98) N_32) (@ (@ tptp.power_power_int B_62) N_32)) (=> (@ _let_1 A_98) (=> (@ _let_1 B_62) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_32) (= A_98 B_62))))))) (forall ((A_98 tptp.nat) (N_32 tptp.nat) (B_62 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A_98) N_32) (@ (@ tptp.power_power_nat B_62) N_32)) (=> (@ _let_1 A_98) (=> (@ _let_1 B_62) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_32) (= A_98 B_62))))))) (forall ((A_98 tptp.real) (N_32 tptp.nat) (B_62 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A_98) N_32) (@ (@ tptp.power_power_real B_62) N_32)) (=> (@ _let_1 A_98) (=> (@ _let_1 B_62) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_32) (= A_98 B_62))))))) (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 ((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) (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_31 tptp.nat) (X_26 tptp.real) (Y_23 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real X_26) Y_23) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X_26) N_31)) (@ (@ tptp.power_power_real Y_23) N_31)))) (forall ((N_31 tptp.nat) (X_26 tptp.int) (Y_23 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int X_26) Y_23) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X_26) N_31)) (@ (@ tptp.power_power_int Y_23) N_31)))) (forall ((N_31 tptp.nat) (X_26 tptp.nat) (Y_23 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X_26) Y_23) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X_26) N_31)) (@ (@ tptp.power_power_nat Y_23) N_31)))) (forall ((N_30 tptp.nat) (A_97 tptp.int)) (=> (not (= A_97 tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A_97) N_30) tptp.zero_zero_int)))) (forall ((N_30 tptp.nat) (A_97 tptp.real)) (=> (not (= A_97 tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A_97) N_30) tptp.zero_zero_real)))) (forall ((N_29 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N_29))) (let ((_let_2 (= N_29 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))) (forall ((N_29 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N_29))) (let ((_let_2 (= N_29 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))) (forall ((N_29 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real tptp.zero_zero_real) N_29))) (let ((_let_2 (= N_29 tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))) (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 ((N_28 tptp.nat) (A_96 tptp.int) (B_61 tptp.int)) (=> (@ (@ tptp.ord_less_int A_96) B_61) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_96) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_28) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A_96) N_28)) (@ (@ tptp.power_power_int B_61) N_28)))))) (forall ((N_28 tptp.nat) (A_96 tptp.nat) (B_61 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_96) B_61) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_96) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_28) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A_96) N_28)) (@ (@ tptp.power_power_nat B_61) N_28)))))) (forall ((N_28 tptp.nat) (A_96 tptp.real) (B_61 tptp.real)) (=> (@ (@ tptp.ord_less_real A_96) B_61) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_96) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_28) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A_96) N_28)) (@ (@ tptp.power_power_real B_61) N_28)))))) (forall ((A_95 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A_95) tptp.zero_zero_int)) (forall ((A_95 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A_95) tptp.zero_zero_nat)) (forall ((A_95 tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A_95) tptp.zero_zero_real)) (forall ((A_94 tptp.int)) (= (@ (@ tptp.times_times_int A_94) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A_94 tptp.nat)) (= (@ (@ tptp.times_times_nat A_94) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A_94 tptp.real)) (= (@ (@ tptp.times_times_real A_94) tptp.zero_zero_real) tptp.zero_zero_real)) (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 ((A_92 tptp.int)) (= (@ (@ tptp.plus_plus_int A_92) tptp.zero_zero_int) A_92)) (forall ((A_92 tptp.nat)) (= (@ (@ tptp.plus_plus_nat A_92) tptp.zero_zero_nat) A_92)) (forall ((A_92 tptp.real)) (= (@ (@ tptp.plus_plus_real A_92) tptp.zero_zero_real) A_92)) (forall ((B_60 tptp.int) (A_91 tptp.int)) (= (= B_60 (@ (@ tptp.plus_plus_int B_60) A_91)) (= A_91 tptp.zero_zero_int))) (forall ((B_60 tptp.nat) (A_91 tptp.nat)) (= (= B_60 (@ (@ tptp.plus_plus_nat B_60) A_91)) (= A_91 tptp.zero_zero_nat))) (forall ((B_60 tptp.real) (A_91 tptp.real)) (= (= B_60 (@ (@ tptp.plus_plus_real B_60) A_91)) (= A_91 tptp.zero_zero_real))) (forall ((A_90 tptp.int)) (= (= (@ (@ tptp.plus_plus_int A_90) A_90) tptp.zero_zero_int) (= A_90 tptp.zero_zero_int))) (forall ((A_90 tptp.real)) (= (= (@ (@ tptp.plus_plus_real A_90) A_90) tptp.zero_zero_real) (= A_90 tptp.zero_zero_real))) _let_32 _let_4 (forall ((Z tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) Z) Z)) (forall ((Z tptp.int)) (= (@ (@ tptp.plus_plus_int Z) tptp.zero_zero_int) Z)) (forall ((N_27 tptp.nat) (A_89 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A_89) (@ _let_1 (@ (@ tptp.power_power_int A_89) N_27))))) (forall ((N_27 tptp.nat) (A_89 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A_89) (@ _let_1 (@ (@ tptp.power_power_nat A_89) N_27))))) (forall ((N_27 tptp.nat) (A_89 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A_89) (@ _let_1 (@ (@ tptp.power_power_real A_89) N_27))))) (forall ((N_26 tptp.nat) (A_88 tptp.int) (B_59 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_88) B_59) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_88) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A_88) N_26)) (@ (@ tptp.power_power_int B_59) N_26))))) (forall ((N_26 tptp.nat) (A_88 tptp.nat) (B_59 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_88) B_59) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_88) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A_88) N_26)) (@ (@ tptp.power_power_nat B_59) N_26))))) (forall ((N_26 tptp.nat) (A_88 tptp.real) (B_59 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_88) B_59) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_88) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A_88) N_26)) (@ (@ tptp.power_power_real B_59) N_26))))) (forall ((N_25 tptp.nat) (A_87 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A_87) (@ _let_1 (@ (@ tptp.power_power_int A_87) N_25))))) (forall ((N_25 tptp.nat) (A_87 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A_87) (@ _let_1 (@ (@ tptp.power_power_nat A_87) N_25))))) (forall ((N_25 tptp.nat) (A_87 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A_87) (@ _let_1 (@ (@ tptp.power_power_real A_87) N_25))))) (forall ((Z tptp.nat) (X_1 tptp.int) (Y_1 tptp.nat) (P tptp.int)) (let ((_let_1 (@ tptp.power_power_int X_1))) (=> (@ (@ (@ tptp.zcong (@ _let_1 Y_1)) tptp.one_one_int) P) (@ (@ (@ tptp.zcong (@ _let_1 (@ (@ tptp.times_times_nat Y_1) Z))) tptp.one_one_int) P)))) (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_1 tptp.int) (T tptp.int) (A tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X_1))) (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 ((A_86 tptp.int) (N_24 tptp.nat) (B_58 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A_86) N_24)) (@ (@ tptp.power_power_int B_58) N_24)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B_58) (@ (@ tptp.ord_less_int A_86) B_58)))) (forall ((A_86 tptp.nat) (N_24 tptp.nat) (B_58 tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A_86) N_24)) (@ (@ tptp.power_power_nat B_58) N_24)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B_58) (@ (@ tptp.ord_less_nat A_86) B_58)))) (forall ((A_86 tptp.real) (N_24 tptp.nat) (B_58 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A_86) N_24)) (@ (@ tptp.power_power_real B_58) N_24)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B_58) (@ (@ tptp.ord_less_real A_86) B_58)))) (forall ((A_85 tptp.int) (N_23 tptp.nat) (N_22 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_85))) (=> (@ (@ tptp.ord_less_eq_nat N_23) N_22) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_85) (=> (@ (@ tptp.ord_less_eq_int A_85) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N_22)) (@ _let_1 N_23))))))) (forall ((A_85 tptp.nat) (N_23 tptp.nat) (N_22 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_85))) (=> (@ (@ tptp.ord_less_eq_nat N_23) N_22) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_85) (=> (@ (@ tptp.ord_less_eq_nat A_85) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N_22)) (@ _let_1 N_23))))))) (forall ((A_85 tptp.real) (N_23 tptp.nat) (N_22 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_85))) (=> (@ (@ tptp.ord_less_eq_nat N_23) N_22) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_85) (=> (@ (@ tptp.ord_less_eq_real A_85) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N_22)) (@ _let_1 N_23))))))) (forall ((A_84 tptp.int) (N_21 tptp.nat) (N_20 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_84))) (=> (@ (@ tptp.ord_less_nat N_21) N_20) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_84) (=> (@ (@ tptp.ord_less_int A_84) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N_20)) (@ _let_1 N_21))))))) (forall ((A_84 tptp.nat) (N_21 tptp.nat) (N_20 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_84))) (=> (@ (@ tptp.ord_less_nat N_21) N_20) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_84) (=> (@ (@ tptp.ord_less_nat A_84) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N_20)) (@ _let_1 N_21))))))) (forall ((A_84 tptp.real) (N_21 tptp.nat) (N_20 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_84))) (=> (@ (@ tptp.ord_less_nat N_21) N_20) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A_84) (=> (@ (@ tptp.ord_less_real A_84) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N_20)) (@ _let_1 N_21))))))) (forall ((A_83 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A_83) A_83)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A_83) tptp.zero_zero_int))) (forall ((A_83 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A_83) A_83)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A_83) tptp.zero_zero_real))) (forall ((X_25 tptp.int) (Y_22 tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_25) X_25)) (@ (@ tptp.times_times_int Y_22) Y_22)) tptp.zero_zero_int) (and (= X_25 tptp.zero_zero_int) (= Y_22 tptp.zero_zero_int)))) (forall ((X_25 tptp.real) (Y_22 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X_25) X_25)) (@ (@ tptp.times_times_real Y_22) Y_22)) tptp.zero_zero_real) (and (= X_25 tptp.zero_zero_real) (= Y_22 tptp.zero_zero_real)))) (forall ((C_30 tptp.int) (D_7 tptp.int) (A_82 tptp.int) (B_57 tptp.int) (R_3 tptp.int)) (let ((_let_1 (@ tptp.times_times_int R_3))) (=> (not (= R_3 tptp.zero_zero_int)) (=> (and (= A_82 B_57) (not (= C_30 D_7))) (not (= (@ (@ tptp.plus_plus_int A_82) (@ _let_1 C_30)) (@ (@ tptp.plus_plus_int B_57) (@ _let_1 D_7)))))))) (forall ((C_30 tptp.nat) (D_7 tptp.nat) (A_82 tptp.nat) (B_57 tptp.nat) (R_3 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R_3))) (=> (not (= R_3 tptp.zero_zero_nat)) (=> (and (= A_82 B_57) (not (= C_30 D_7))) (not (= (@ (@ tptp.plus_plus_nat A_82) (@ _let_1 C_30)) (@ (@ tptp.plus_plus_nat B_57) (@ _let_1 D_7)))))))) (forall ((C_30 tptp.real) (D_7 tptp.real) (A_82 tptp.real) (B_57 tptp.real) (R_3 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R_3))) (=> (not (= R_3 tptp.zero_zero_real)) (=> (and (= A_82 B_57) (not (= C_30 D_7))) (not (= (@ (@ tptp.plus_plus_real A_82) (@ _let_1 C_30)) (@ (@ tptp.plus_plus_real B_57) (@ _let_1 D_7)))))))) (forall ((A tptp.int) (N tptp.nat) (P tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int P))) (=> (@ tptp.zprime P) (=> (@ _let_1 (@ (@ tptp.power_power_int A) N)) (@ _let_1 A))))) _let_27 _let_31 _let_30 _let_29 _let_30 _let_19 _let_29 (forall ((W tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 W)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int W) tptp.zero_zero_int))) (not (@ _let_23 tptp.zero_zero_int)) (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_27 (@ _let_26 tptp.one_one_int) (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_1 tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.ord_less_int I_1) J_1) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int (@ _let_1 I_1)) (@ _let_1 J_1)))))) (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_19 tptp.nat) (A_81 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A_81) N_19))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_81) (=> (@ (@ tptp.ord_less_int A_81) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_81) _let_1)) _let_1))))) (forall ((N_19 tptp.nat) (A_81 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A_81) N_19))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_81) (=> (@ (@ tptp.ord_less_nat A_81) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_81) _let_1)) _let_1))))) (forall ((N_19 tptp.nat) (A_81 tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A_81) N_19))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A_81) (=> (@ (@ tptp.ord_less_real A_81) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_81) _let_1)) _let_1))))) (forall ((N tptp.nat) (B tptp.int) (A tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int P) N)))) (=> (@ tptp.zprime P) (=> (not (@ (@ tptp.dvd_dvd_int P) A)) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (@ _let_1 B)))))) (forall ((N tptp.nat) (A tptp.int) (B tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int P) N)))) (=> (@ tptp.zprime P) (=> (not (@ (@ tptp.dvd_dvd_int P) B)) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (@ _let_1 A)))))) (forall ((X_24 tptp.int) (Y_21 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_24) X_24)) (@ (@ tptp.times_times_int Y_21) Y_21)))) (forall ((X_24 tptp.real) (Y_21 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X_24) X_24)) (@ (@ tptp.times_times_real Y_21) Y_21)))) (forall ((X_23 tptp.int) (Y_20 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_23) X_23)) (@ (@ tptp.times_times_int Y_20) Y_20))) tptp.zero_zero_int) (and (= X_23 tptp.zero_zero_int) (= Y_20 tptp.zero_zero_int)))) (forall ((X_23 tptp.real) (Y_20 tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X_23) X_23)) (@ (@ tptp.times_times_real Y_20) Y_20))) tptp.zero_zero_real) (and (= X_23 tptp.zero_zero_real) (= Y_20 tptp.zero_zero_real)))) (forall ((V tptp.int) (V_6 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_int V) V_6))) (= (@ (@ tptp.ord_less_nat (@ tptp.number_number_of_nat V)) (@ tptp.number_number_of_nat V_6)) (and (=> _let_1 (@ (@ tptp.ord_less_int tptp.pls) V_6)) _let_1)))) (forall ((X_22 tptp.int) (Y_19 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_22) X_22)) (@ (@ tptp.times_times_int Y_19) Y_19))) tptp.zero_zero_int))) (forall ((X_22 tptp.real) (Y_19 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X_22) X_22)) (@ (@ tptp.times_times_real Y_19) Y_19))) tptp.zero_zero_real))) (forall ((X_21 tptp.int) (Y_18 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X_21) X_21)) (@ (@ tptp.times_times_int Y_18) Y_18))) (or (not (= X_21 tptp.zero_zero_int)) (not (= Y_18 tptp.zero_zero_int))))) (forall ((X_21 tptp.real) (Y_18 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X_21) X_21)) (@ (@ tptp.times_times_real Y_18) Y_18))) (or (not (= X_21 tptp.zero_zero_real)) (not (= Y_18 tptp.zero_zero_real))))) (forall ((V tptp.int) (V_6 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int V))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.number_number_of_nat V)) (@ tptp.number_number_of_nat V_6)) (=> (not (@ _let_1 V_6)) (@ _let_1 tptp.pls))))) (forall ((W_5 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W_5))) (= (@ tptp.number_number_of_int (@ tptp.bit0 W_5)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.zero_zero_int) _let_1)) _let_1)))) (forall ((W_5 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real W_5))) (= (@ tptp.number267125858f_real (@ tptp.bit0 W_5)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.zero_zero_real) _let_1)) _let_1)))) (forall ((A_80 tptp.int)) (= (@ (@ tptp.power_power_int A_80) tptp.one_one_nat) A_80)) (forall ((A_80 tptp.real)) (= (@ (@ tptp.power_power_real A_80) tptp.one_one_nat) A_80)) (forall ((A_80 tptp.nat)) (= (@ (@ tptp.power_power_nat A_80) tptp.one_one_nat) A_80)) (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.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_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 ((Y_17 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.number_number_of_int Y_17)) (@ (@ tptp.ord_less_int tptp.pls) Y_17))) (forall ((Y_17 tptp.int)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.number267125858f_real Y_17)) (@ (@ tptp.ord_less_int tptp.pls) Y_17))) (forall ((X_20 tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int X_20)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int X_20) tptp.pls))) (forall ((X_20 tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.number267125858f_real X_20)) tptp.zero_zero_real) (@ (@ tptp.ord_less_int X_20) tptp.pls))) (forall ((Y_16 tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.number267125858f_real Y_16)) (@ (@ tptp.ord_less_eq_int tptp.pls) Y_16))) (forall ((Y_16 tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.number_number_of_int Y_16)) (@ (@ tptp.ord_less_eq_int tptp.pls) Y_16))) (forall ((X_19 tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.number267125858f_real X_19)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_int X_19) tptp.pls))) (forall ((X_19 tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int X_19)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int X_19) tptp.pls))) (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)))) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) _let_12) tptp.zero_zero_real) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) _let_12) tptp.zero_zero_nat) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) _let_12) tptp.zero_zero_int) (forall ((A_79 tptp.real)) (= (= (@ (@ tptp.power_power_real A_79) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_real) (= A_79 tptp.zero_zero_real))) (forall ((A_79 tptp.int)) (= (= (@ (@ tptp.power_power_int A_79) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) tptp.zero_zero_int) (= A_79 tptp.zero_zero_int))) (forall ((A_78 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A_78) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (forall ((A_78 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A_78) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (forall ((X_18 tptp.real) (Y_15 tptp.real)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X_18) _let_1)) (@ (@ tptp.power_power_real Y_15) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y_15) (@ (@ tptp.ord_less_eq_real X_18) Y_15))))) (forall ((X_18 tptp.nat) (Y_15 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X_18) _let_1)) (@ (@ tptp.power_power_nat Y_15) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y_15) (@ (@ tptp.ord_less_eq_nat X_18) Y_15))))) (forall ((X_18 tptp.int) (Y_15 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X_18) _let_1)) (@ (@ tptp.power_power_int Y_15) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y_15) (@ (@ tptp.ord_less_eq_int X_18) Y_15))))) (forall ((X_17 tptp.real) (Y_14 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (= (@ (@ tptp.power_power_real X_17) _let_2) (@ (@ tptp.power_power_real Y_14) _let_2)) (=> (@ _let_1 X_17) (=> (@ _let_1 Y_14) (= X_17 Y_14))))))) (forall ((X_17 tptp.nat) (Y_14 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (= (@ (@ tptp.power_power_nat X_17) _let_2) (@ (@ tptp.power_power_nat Y_14) _let_2)) (=> (@ _let_1 X_17) (=> (@ _let_1 Y_14) (= X_17 Y_14))))))) (forall ((X_17 tptp.int) (Y_14 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (= (@ (@ tptp.power_power_int X_17) _let_2) (@ (@ tptp.power_power_int Y_14) _let_2)) (=> (@ _let_1 X_17) (=> (@ _let_1 Y_14) (= X_17 Y_14))))))) (forall ((A_77 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A_77) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.zero_zero_real))) (forall ((A_77 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A_77) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) tptp.zero_zero_int))) (forall ((A_76 tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A_76) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (not (= A_76 tptp.zero_zero_real)))) (forall ((A_76 tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A_76) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (not (= A_76 tptp.zero_zero_int)))) (forall ((X_16 tptp.real) (Y_13 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_16) _let_1)) (@ (@ tptp.power_power_real Y_13) _let_1)) tptp.zero_zero_real) (and (= X_16 tptp.zero_zero_real) (= Y_13 tptp.zero_zero_real))))) (forall ((X_16 tptp.int) (Y_13 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_16) _let_1)) (@ (@ tptp.power_power_int Y_13) _let_1)) tptp.zero_zero_int) (and (= X_16 tptp.zero_zero_int) (= Y_13 tptp.zero_zero_int))))) (forall ((A_75 tptp.nat) (N_18 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A_75) N_18))) (= (@ (@ tptp.times_times_nat _let_1) A_75) (@ (@ tptp.times_times_nat A_75) _let_1)))) (forall ((A_75 tptp.real) (N_18 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A_75) N_18))) (= (@ (@ tptp.times_times_real _let_1) A_75) (@ (@ tptp.times_times_real A_75) _let_1)))) (forall ((A_75 tptp.int) (N_18 tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A_75) N_18))) (= (@ (@ tptp.times_times_int _let_1) A_75) (@ (@ tptp.times_times_int A_75) _let_1)))) (forall ((A_74 tptp.nat) (B_56 tptp.nat) (N_17 tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A_74) B_56)) N_17) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A_74) N_17)) (@ (@ tptp.power_power_nat B_56) N_17)))) (forall ((A_74 tptp.real) (B_56 tptp.real) (N_17 tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A_74) B_56)) N_17) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A_74) N_17)) (@ (@ tptp.power_power_real B_56) N_17)))) (forall ((A_74 tptp.int) (B_56 tptp.int) (N_17 tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A_74) B_56)) N_17) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A_74) N_17)) (@ (@ tptp.power_power_int B_56) N_17)))) (forall ((A_73 tptp.nat) (M_6 tptp.nat) (N_16 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_73))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M_6) N_16)) (@ (@ tptp.times_times_nat (@ _let_1 M_6)) (@ _let_1 N_16))))) (forall ((A_73 tptp.real) (M_6 tptp.nat) (N_16 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_73))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M_6) N_16)) (@ (@ tptp.times_times_real (@ _let_1 M_6)) (@ _let_1 N_16))))) (forall ((A_73 tptp.int) (M_6 tptp.nat) (N_16 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_73))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M_6) N_16)) (@ (@ tptp.times_times_int (@ _let_1 M_6)) (@ _let_1 N_16))))) (forall ((N_15 tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N_15) tptp.one_one_real)) (forall ((N_15 tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N_15) tptp.one_one_nat)) (forall ((N_15 tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N_15) tptp.one_one_int)) (forall ((A_72 tptp.nat) (M_5 tptp.nat) (N_14 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_72))) (= (@ _let_1 (@ (@ tptp.times_times_nat M_5) N_14)) (@ (@ tptp.power_power_nat (@ _let_1 M_5)) N_14)))) (forall ((A_72 tptp.real) (M_5 tptp.nat) (N_14 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_72))) (= (@ _let_1 (@ (@ tptp.times_times_nat M_5) N_14)) (@ (@ tptp.power_power_real (@ _let_1 M_5)) N_14)))) (forall ((A_72 tptp.int) (M_5 tptp.nat) (N_14 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_72))) (= (@ _let_1 (@ (@ tptp.times_times_nat M_5) N_14)) (@ (@ tptp.power_power_int (@ _let_1 M_5)) N_14)))) (forall ((X_15 tptp.real) (Y_12 tptp.real)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X_15) _let_1)) (@ (@ tptp.power_power_real Y_12) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y_12) (@ (@ tptp.ord_less_real X_15) Y_12))))) (forall ((X_15 tptp.nat) (Y_12 tptp.nat)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X_15) _let_1)) (@ (@ tptp.power_power_nat Y_12) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y_12) (@ (@ tptp.ord_less_nat X_15) Y_12))))) (forall ((X_15 tptp.int) (Y_12 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X_15) _let_1)) (@ (@ tptp.power_power_int Y_12) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y_12) (@ (@ tptp.ord_less_int X_15) Y_12))))) (forall ((X_14 tptp.real) (Y_11 tptp.real)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X_14) _let_1)) (@ (@ tptp.power_power_real Y_11) _let_1))))) (forall ((X_14 tptp.int) (Y_11 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_14) _let_1)) (@ (@ tptp.power_power_int Y_11) _let_1))))) (forall ((X_13 tptp.real) (Y_10 tptp.real)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X_13) _let_1)) (@ (@ tptp.power_power_real Y_10) _let_1))) tptp.zero_zero_real) (and (= X_13 tptp.zero_zero_real) (= Y_10 tptp.zero_zero_real))))) (forall ((X_13 tptp.int) (Y_10 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_13) _let_1)) (@ (@ tptp.power_power_int Y_10) _let_1))) tptp.zero_zero_int) (and (= X_13 tptp.zero_zero_int) (= Y_10 tptp.zero_zero_int))))) (forall ((X_12 tptp.real) (Y_9 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_12) _let_1)) (@ (@ tptp.power_power_real Y_9) _let_1))) tptp.zero_zero_real)))) (forall ((X_12 tptp.int) (Y_9 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_12) _let_1)) (@ (@ tptp.power_power_int Y_9) _let_1))) tptp.zero_zero_int)))) (forall ((X_11 tptp.real) (Y_8 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_11) _let_1)) (@ (@ tptp.power_power_real Y_8) _let_1))) (or (not (= X_11 tptp.zero_zero_real)) (not (= Y_8 tptp.zero_zero_real)))))) (forall ((X_11 tptp.int) (Y_8 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_11) _let_1)) (@ (@ tptp.power_power_int Y_8) _let_1))) (or (not (= X_11 tptp.zero_zero_int)) (not (= Y_8 tptp.zero_zero_int)))))) (forall ((A_71 tptp.real) (N_13 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A_71) (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_13)))) (forall ((A_71 tptp.int) (N_13 tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A_71) (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_13)))) (forall ((N_12 tptp.nat) (A_70 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A_70) (@ _let_1 (@ (@ tptp.power_power_real A_70) N_12))))) (forall ((N_12 tptp.nat) (A_70 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A_70) (@ _let_1 (@ (@ tptp.power_power_nat A_70) N_12))))) (forall ((N_12 tptp.nat) (A_70 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A_70) (@ _let_1 (@ (@ tptp.power_power_int A_70) N_12))))) (forall ((A_69 tptp.real) (N_11 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_69))) (=> (@ (@ tptp.ord_less_eq_nat N_11) N_10) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A_69) (@ (@ tptp.ord_less_eq_real (@ _let_1 N_11)) (@ _let_1 N_10)))))) (forall ((A_69 tptp.nat) (N_11 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_69))) (=> (@ (@ tptp.ord_less_eq_nat N_11) N_10) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A_69) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N_11)) (@ _let_1 N_10)))))) (forall ((A_69 tptp.int) (N_11 tptp.nat) (N_10 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_69))) (=> (@ (@ tptp.ord_less_eq_nat N_11) N_10) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A_69) (@ (@ tptp.ord_less_eq_int (@ _let_1 N_11)) (@ _let_1 N_10)))))) (forall ((M_4 tptp.nat) (N_9 tptp.nat) (A_68 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A_68))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_68) (= (= (@ _let_1 M_4) (@ _let_1 N_9)) (= M_4 N_9))))) (forall ((M_4 tptp.nat) (N_9 tptp.nat) (A_68 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_68))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_68) (= (= (@ _let_1 M_4) (@ _let_1 N_9)) (= M_4 N_9))))) (forall ((M_4 tptp.nat) (N_9 tptp.nat) (A_68 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A_68))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_68) (= (= (@ _let_1 M_4) (@ _let_1 N_9)) (= M_4 N_9))))) (forall ((X_10 tptp.nat) (Y_7 tptp.nat) (B_55 tptp.real)) (let ((_let_1 (@ tptp.power_power_real B_55))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B_55) (= (@ (@ tptp.ord_less_real (@ _let_1 X_10)) (@ _let_1 Y_7)) (@ (@ tptp.ord_less_nat X_10) Y_7))))) (forall ((X_10 tptp.nat) (Y_7 tptp.nat) (B_55 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B_55))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B_55) (= (@ (@ tptp.ord_less_nat (@ _let_1 X_10)) (@ _let_1 Y_7)) (@ (@ tptp.ord_less_nat X_10) Y_7))))) (forall ((X_10 tptp.nat) (Y_7 tptp.nat) (B_55 tptp.int)) (let ((_let_1 (@ tptp.power_power_int B_55))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B_55) (= (@ (@ tptp.ord_less_int (@ _let_1 X_10)) (@ _let_1 Y_7)) (@ (@ tptp.ord_less_nat X_10) Y_7))))) (forall ((M_3 tptp.nat) (N_8 tptp.nat) (A_67 tptp.real)) (let ((_let_1 (@ tptp.power_power_real A_67))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_67) (=> (@ (@ tptp.ord_less_real (@ _let_1 M_3)) (@ _let_1 N_8)) (@ (@ tptp.ord_less_nat M_3) N_8))))) (forall ((M_3 tptp.nat) (N_8 tptp.nat) (A_67 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_67))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_67) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M_3)) (@ _let_1 N_8)) (@ (@ tptp.ord_less_nat M_3) N_8))))) (forall ((M_3 tptp.nat) (N_8 tptp.nat) (A_67 tptp.int)) (let ((_let_1 (@ tptp.power_power_int A_67))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_67) (=> (@ (@ tptp.ord_less_int (@ _let_1 M_3)) (@ _let_1 N_8)) (@ (@ tptp.ord_less_nat M_3) N_8))))) (forall ((A_66 tptp.real) (N_7 tptp.nat) (N_6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A_66))) (=> (@ (@ tptp.ord_less_nat N_7) N_6) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A_66) (@ (@ tptp.ord_less_real (@ _let_1 N_7)) (@ _let_1 N_6)))))) (forall ((A_66 tptp.nat) (N_7 tptp.nat) (N_6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A_66))) (=> (@ (@ tptp.ord_less_nat N_7) N_6) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A_66) (@ (@ tptp.ord_less_nat (@ _let_1 N_7)) (@ _let_1 N_6)))))) (forall ((A_66 tptp.int) (N_7 tptp.nat) (N_6 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A_66))) (=> (@ (@ tptp.ord_less_nat N_7) N_6) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_66) (@ (@ tptp.ord_less_int (@ _let_1 N_7)) (@ _let_1 N_6)))))) (@ (@ _let_25 _let_9) _let_8) (forall ((Y_1 tptp.int) (X_1 tptp.int) (P tptp.int)) (=> (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int Y_1) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) X_1) P) (not (@ (@ tptp.dvd_dvd_int P) Y_1))))) (forall ((X_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (=> (@ (@ tptp.ord_less_int X_1) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (or (= X_1 tptp.zero_zero_int) (= X_1 tptp.one_one_int))))) (forall ((A_65 tptp.real) (K_3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A_65) (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) K_3))) tptp.zero_zero_real) (= A_65 tptp.zero_zero_real))) (forall ((A_65 tptp.int) (K_3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A_65) (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) K_3))) tptp.zero_zero_int) (= A_65 tptp.zero_zero_int))) (forall ((P tptp.int)) (= (@ tptp.zprime P) (and (@ (@ tptp.ord_less_int tptp.one_one_int) P) (forall ((M_2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M_2) (@ (@ tptp.dvd_dvd_int M_2) P)) (or (= M_2 tptp.one_one_int) (= M_2 P))))))) (forall ((R tptp.int) (Q tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (= A (@ (@ tptp.plus_plus_int R) (@ (@ tptp.times_times_int A) Q))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (@ (@ tptp.ord_less_eq_int Q) tptp.one_one_int))))) (forall ((R tptp.int) (Q tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (= A (@ (@ tptp.plus_plus_int R) (@ (@ tptp.times_times_int A) Q))) (=> (@ (@ tptp.ord_less_int R) A) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Q))))) (@ _let_3 _let_24) (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)))))) _let_10 (forall ((X_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X_1) N)) (or (@ _let_1 X_1) (= N tptp.zero_zero_nat))))) (forall ((X_1 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X_1) N)) (or (= N tptp.zero_zero_nat) (@ _let_1 X_1))))) (forall ((X_1 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_1) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (@ _let_1 X_1)))))) (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 ((K tptp.int)) (= (= (@ tptp.bit1 K) tptp.min) (= K tptp.min))) (forall ((L tptp.int)) (= (= tptp.min (@ tptp.bit1 L)) (= tptp.min L))) (= (@ tptp.bit1 tptp.min) tptp.min) (not (= tptp.pls tptp.min)) (not (= tptp.min tptp.pls)) (forall ((K tptp.int)) (not (= (@ tptp.bit0 K) tptp.min))) (forall ((L tptp.int)) (not (= tptp.min (@ tptp.bit0 L)))) (not (@ _let_22 tptp.min)) (@ _let_20 tptp.min) (forall ((X_1 tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X_1) X_1))) (= X_1 tptp.zero_zero_real))) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit1 K)) tptp.min) (@ (@ tptp.ord_less_int K) tptp.min))) (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.min))) (= (@ _let_1 (@ tptp.bit1 K)) (@ _let_1 K)))) (not (@ _let_23 tptp.min)) (@ _let_22 tptp.pls) (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.min))) (= (@ _let_1 (@ tptp.bit0 K)) (@ _let_1 K)))) (@ _let_22 tptp.zero_zero_int) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit1 K)) tptp.min) (@ (@ tptp.ord_less_eq_int K) tptp.min))) (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.min))) (= (@ _let_1 (@ tptp.bit1 K)) (@ _let_1 K)))) (not (@ _let_21 tptp.min)) (@ _let_20 tptp.pls) (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.bit0 K)) tptp.min) (@ (@ tptp.ord_less_eq_int K) tptp.min))) (not (= _let_2 _let_9)) (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 ((X_9 tptp.real)) (= (@ (@ tptp.power_power_real X_9) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((X_9 tptp.nat)) (= (@ (@ tptp.power_power_nat X_9) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((X_9 tptp.int)) (= (@ (@ tptp.power_power_int X_9) tptp.zero_zero_nat) tptp.one_one_int)) (forall ((A_64 tptp.real)) (= (@ (@ tptp.power_power_real A_64) tptp.zero_zero_nat) tptp.one_one_real)) (forall ((A_64 tptp.nat)) (= (@ (@ tptp.power_power_nat A_64) tptp.zero_zero_nat) tptp.one_one_nat)) (forall ((A_64 tptp.int)) (= (@ (@ tptp.power_power_int A_64) tptp.zero_zero_nat) tptp.one_one_int)) _let_19 _let_18 (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 ((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 ((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 ((N_5 tptp.nat) (A_63 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A_63) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (@ _let_1 (@ (@ tptp.power_power_real A_63) N_5)))))) (forall ((N_5 tptp.nat) (A_63 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A_63) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (@ _let_1 (@ (@ tptp.power_power_nat A_63) N_5)))))) (forall ((N_5 tptp.nat) (A_63 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A_63) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_5) (@ _let_1 (@ (@ tptp.power_power_int A_63) N_5)))))) (forall ((X_8 tptp.real) (N_4 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_4) (= X_8 tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X_8) (@ (@ tptp.power_power_real X_8) N_4)))) (forall ((X_8 tptp.nat) (N_4 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_4) (= X_8 tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X_8) (@ (@ tptp.power_power_nat X_8) N_4)))) (forall ((X_8 tptp.int) (N_4 tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N_4) (= X_8 tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X_8) (@ (@ tptp.power_power_int X_8) N_4)))) (forall ((V tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.number_number_of_nat V)) (@ (@ tptp.ord_less_int tptp.pls) V))) (forall ((V tptp.int)) (= (= (@ tptp.number_number_of_nat V) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int V) tptp.pls))) (forall ((V tptp.int)) (= (= tptp.zero_zero_nat (@ tptp.number_number_of_nat V)) (@ (@ tptp.ord_less_eq_int V) tptp.pls))) (forall ((A tptp.int) (B tptp.int) (M tptp.int)) (= (@ (@ (@ tptp.zcong A) B) M) (@ (@ (@ tptp.zcong B) A) M))) (forall ((K tptp.int) (M tptp.int)) (@ (@ (@ tptp.zcong K) K) M)) (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))))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_12) (forall ((V_6 tptp.int) (K tptp.nat) (V tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V)) (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V_6)) K)))) (let ((_let_2 (@ (@ tptp.ord_less_int V) 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) V_6))) K))))))) (forall ((V_6 tptp.int) (V tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat V)) (@ tptp.number_number_of_nat V_6)))) (let ((_let_2 (@ (@ tptp.ord_less_int V) 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) V_6)))))))) (forall ((X_7 tptp.real) (Y_6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X_7) Y_6) (=> (not (= X_7 Y_6)) (@ (@ tptp.ord_less_real X_7) Y_6)))) (forall ((X_7 tptp.nat) (Y_6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X_7) Y_6) (=> (not (= X_7 Y_6)) (@ (@ tptp.ord_less_nat X_7) Y_6)))) (forall ((X_7 tptp.int) (Y_6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X_7) Y_6) (=> (not (= X_7 Y_6)) (@ (@ tptp.ord_less_int X_7) Y_6)))) (@ _let_3 tptp.zero_zero_int) (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)) (= (@ (@ (@ 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 ((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 ((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 ((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 ((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 ((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 ((N_3 tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.number267125858f_real tptp.min)) (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_3)) tptp.one_one_real)) (forall ((N_3 tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.number_number_of_int tptp.min)) (@ (@ tptp.times_times_nat (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) N_3)) tptp.one_one_int)) (forall ((A_62 tptp.real) (W_4 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_4))) (= (= (@ (@ tptp.power_power_real A_62) _let_1) tptp.zero_zero_real) (and (= A_62 tptp.zero_zero_real) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A_62 tptp.nat) (W_4 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_4))) (= (= (@ (@ tptp.power_power_nat A_62) _let_1) tptp.zero_zero_nat) (and (= A_62 tptp.zero_zero_nat) (not (= _let_1 tptp.zero_zero_nat)))))) (forall ((A_62 tptp.int) (W_4 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_4))) (= (= (@ (@ tptp.power_power_int A_62) _let_1) tptp.zero_zero_int) (and (= A_62 tptp.zero_zero_int) (not (= _let_1 tptp.zero_zero_nat)))))) (@ _let_3 tptp.one_one_int) (forall ((Y_1 tptp.int) (X_1 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X_1) (=> (@ _let_1 Y_1) (@ _let_1 (@ (@ tptp.times_times_int X_1) Y_1)))))) (forall ((Y_1 tptp.int) (X_1 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X_1) (=> (@ _let_1 Y_1) (@ _let_1 (@ (@ tptp.plus_plus_int X_1) Y_1)))))) (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 ((N tptp.nat) (X_1 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X_1) (@ _let_1 (@ (@ tptp.power_power_int X_1) 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 ((W_3 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_3))) (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))))))) (forall ((W_3 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_3))) (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_3 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_nat W_3))) (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 ((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 ((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))))) (@ _let_3 (@ tptp.number_number_of_int (@ tptp.bit1 _let_6))) (forall ((B tptp.int) (Q tptp.int) (R tptp.int) (B_54 tptp.int) (Q_3 tptp.int) (R_2 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_54) Q_3)) R_2))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q)) R) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R_2) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_54) (=> (@ (@ tptp.ord_less_eq_int B_54) B) (@ (@ tptp.ord_less_eq_int Q_3) Q))))))))) (forall ((B tptp.int) (Q_3 tptp.int) (R_2 tptp.int) (Q tptp.int) (R 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_3)) R_2)) (@ (@ tptp.plus_plus_int (@ _let_2 Q)) R)) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (=> (@ _let_1 R) (=> (@ _let_1 R_2) (@ (@ tptp.ord_less_eq_int Q) Q_3)))))))) (forall ((B tptp.int) (Q tptp.int) (R tptp.int) (B_54 tptp.int) (Q_3 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_54) Q_3)) R_2))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q)) R) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R_2) B_54) (=> (@ _let_1 R) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_54) (=> (@ (@ tptp.ord_less_eq_int B_54) B) (@ (@ tptp.ord_less_eq_int Q) Q_3)))))))))) (forall ((B tptp.int) (Q_3 tptp.int) (R_2 tptp.int) (Q tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q_3)) R_2)) (@ (@ tptp.plus_plus_int (@ _let_1 Q)) R)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R_2) (=> (@ (@ tptp.ord_less_int R_2) B) (=> (@ (@ tptp.ord_less_int R) B) (@ (@ tptp.ord_less_eq_int Q_3) Q))))))) (forall ((B_54 tptp.int) (Q_3 tptp.int) (R_2 tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_54) Q_3)) 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_54) (@ (@ tptp.ord_less_eq_int Q_3) tptp.zero_zero_int))))) (forall ((B_54 tptp.int) (Q_3 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_54) Q_3)) R_2)) (=> (@ (@ tptp.ord_less_int R_2) B_54) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_54) (@ _let_1 Q_3)))))) (forall ((N tptp.int) (P tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int P))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M) (=> (@ tptp.zprime P) (=> (@ _let_1 (@ (@ tptp.times_times_int M) N)) (or (@ _let_1 M) (@ _let_1 N))))))) _let_11 (@ _let_16 _let_15) (forall ((J_1 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_1))) (=> (@ (@ 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 ((X_1 tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.zcong X_1))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ (@ _let_1 (@ tptp.number_number_of_int tptp.min)) P) (not (@ (@ _let_1 tptp.one_one_int) P)))))) (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)))) (= _let_15 _let_14) (=> (not _let_11) (not _let_10)) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) C) (= A (@ (@ tptp.plus_plus_int C) B)))) (forall ((V_5 tptp.int) (W_2 tptp.int)) (= (@ tptp.number267125858f_real (@ (@ tptp.minus_minus_int V_5) W_2)) (@ (@ tptp.minus_minus_real (@ tptp.number267125858f_real V_5)) (@ tptp.number267125858f_real W_2)))) (forall ((V_5 tptp.int) (W_2 tptp.int)) (= (@ tptp.number_number_of_int (@ (@ tptp.minus_minus_int V_5) W_2)) (@ (@ tptp.minus_minus_int (@ tptp.number_number_of_int V_5)) (@ tptp.number_number_of_int W_2)))) (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 ((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 ((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 ((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 ((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 ((V_4 tptp.int) (B_53 tptp.real) (C_29 tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.number267125858f_real V_4)))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B_53) C_29)) (@ (@ tptp.minus_minus_real (@ _let_1 B_53)) (@ _let_1 C_29))))) (forall ((V_4 tptp.int) (B_53 tptp.int) (C_29 tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.number_number_of_int V_4)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B_53) C_29)) (@ (@ tptp.minus_minus_int (@ _let_1 B_53)) (@ _let_1 C_29))))) (forall ((A_61 tptp.real) (B_52 tptp.real) (V_3 tptp.int)) (let ((_let_1 (@ tptp.number267125858f_real V_3))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A_61) B_52)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A_61) _let_1)) (@ (@ tptp.times_times_real B_52) _let_1))))) (forall ((A_61 tptp.int) (B_52 tptp.int) (V_3 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int V_3))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A_61) B_52)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A_61) _let_1)) (@ (@ tptp.times_times_int B_52) _let_1))))) (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 ((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 ((L tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int tptp.pls))) (= (@ _let_1 (@ tptp.bit0 L)) (@ tptp.bit0 (@ _let_1 L))))) (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 ((A tptp.int) (R 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))) (= (@ (@ 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) (@ (@ tptp.dvd_dvd_int M) (@ (@ tptp.minus_minus_int A) B)))) (forall ((V_2 tptp.int) (W_1 tptp.int) (C_28 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.number267125858f_real V_2)) (@ (@ tptp.minus_minus_real (@ tptp.number267125858f_real W_1)) C_28)) (@ (@ tptp.minus_minus_real (@ tptp.number267125858f_real (@ (@ tptp.plus_plus_int V_2) W_1))) C_28))) (forall ((V_2 tptp.int) (W_1 tptp.int) (C_28 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.number_number_of_int V_2)) (@ (@ tptp.minus_minus_int (@ tptp.number_number_of_int W_1)) C_28)) (@ (@ tptp.minus_minus_int (@ tptp.number_number_of_int (@ (@ tptp.plus_plus_int V_2) W_1))) C_28))) (forall ((A tptp.int) (X_1 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int A) tptp.one_one_int))) (let ((_let_2 (@ tptp.ord_less_int X_1))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X_1) (=> (@ _let_2 A) (=> (not (= X_1 _let_1)) (@ _let_2 _let_1))))))) (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 ((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.bit0 L)) (@ tptp.bit1 (@ _let_1 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 ((A tptp.int) (P tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int P) tptp.one_one_int))) (= (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) _let_1)) tptp.one_one_int) P) (@ (@ (@ tptp.zcong A) _let_1) P)))) (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 ((A tptp.int) (B tptp.int) (P tptp.int) (Q tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ tptp.twoSqu2057625106sum2sq (@ (@ tptp.product_Pair_int_int A) B))) (@ tptp.twoSqu2057625106sum2sq (@ (@ tptp.product_Pair_int_int P) Q))) (@ tptp.twoSqu2057625106sum2sq (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ _let_2 P)) (@ _let_1 Q))) (@ (@ tptp.minus_minus_int (@ _let_2 Q)) (@ _let_1 P)))))))) (forall ((A tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.zcong A))) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) A)) tptp.one_one_int) P) (or (@ (@ _let_1 tptp.one_one_int) P) (@ (@ _let_1 (@ (@ tptp.minus_minus_int P) tptp.one_one_int)) P))))))) (forall ((A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) P) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) A)) tptp.one_one_int) P) (or (= A tptp.one_one_int) (= A (@ (@ tptp.minus_minus_int P) tptp.one_one_int)))))))) (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 ((M tptp.int)) (@ (@ (@ tptp.zcong M) 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 ((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 ((Z tptp.nat) (X_1 tptp.int) (Y_1 tptp.int) (M tptp.int)) (=> (@ (@ (@ tptp.zcong X_1) Y_1) M) (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int X_1) Z)) (@ (@ tptp.power_power_int Y_1) Z)) M))) (forall ((X_6 tptp.real) (Y_5 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.minus_minus_real X_6) Y_5)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X_6) _let_2)) (@ (@ tptp.power_power_real Y_5) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.number267125858f_real _let_1)) X_6)) Y_5)))))) (forall ((X_6 tptp.int) (Y_5 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 X_6) Y_5)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X_6) _let_2)) (@ (@ tptp.power_power_int Y_5) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.number_number_of_int _let_1)) X_6)) Y_5)))))) (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 ((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 ((M tptp.int) (Y_1 tptp.int) (X_1 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 X_1) (=> (@ _let_1 Y_1) (=> (@ _let_1 M) (=> (@ (@ (@ tptp.zcong X_1) Y_1) M) (=> (@ (@ tptp.ord_less_int X_1) M) (=> (@ (@ tptp.ord_less_int Y_1) M) (= X_1 Y_1))))))))) (forall ((M tptp.int) (X_1 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X_1) (=> (@ (@ tptp.ord_less_int X_1) M) (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) M))))) (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 ((X_1 tptp.int) (P tptp.int)) (= (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P) (@ (@ tptp.dvd_dvd_int P) X_1))) (forall ((A tptp.int) (M tptp.int)) (= (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) M) (@ (@ tptp.dvd_dvd_int M) A))) (forall ((M tptp.int) (N tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int P))) (=> (@ tptp.zprime P) (=> (@ _let_1 (@ (@ tptp.times_times_int M) N)) (or (@ _let_1 M) (@ _let_1 N)))))) (forall ((M tptp.int) (X_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1) (=> (@ (@ tptp.ord_less_int X_1) M) (=> (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) M) (= X_1 tptp.zero_zero_int))))) (forall ((P tptp.int) (Y_1 tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int P))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 Y_1) (@ _let_1 (@ (@ tptp.power_power_int Y_1) N)))))) (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 ((Y_1 tptp.int) (X_1 tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (=> (not (@ (@ (@ tptp.zcong Y_1) tptp.zero_zero_int) P)) (not (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int X_1) Y_1)) tptp.zero_zero_int) P)))))) (forall ((B tptp.int) (A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) P) (or (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) P) (@ (@ (@ tptp.zcong B) tptp.zero_zero_int) P)))))) (forall ((B tptp.int) (A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (and (not (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) P)) (not (@ (@ (@ tptp.zcong B) tptp.zero_zero_int) P))) (not (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) P)))))) (forall ((Y_1 tptp.int) (N tptp.nat) (P tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int P))) (=> (@ tptp.zprime P) (=> (@ _let_1 (@ (@ tptp.power_power_int Y_1) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 Y_1)))))) (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)))) (forall ((A tptp.int) (P tptp.int)) (let ((_let_1 (@ (@ tptp.legendre A) P))) (let ((_let_2 (@ (@ tptp.quadRes P) A))) (let ((_let_3 (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) P))) (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 ((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) (X_1 tptp.int)) (= (@ (@ tptp.quadRes M) X_1) (exists ((Y tptp.int)) (@ (@ (@ tptp.zcong (@ (@ tptp.power_power_int Y) (@ tptp.number_number_of_nat (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) X_1) M)))) (forall ((X_1 tptp.real) (Y_1 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_1) _let_1)) (@ (@ tptp.power_power_real Y_1) _let_1)) tptp.zero_zero_real) (and (= X_1 tptp.zero_zero_real) (= Y_1 tptp.zero_zero_real))))) (forall ((V_1 tptp.real) (U_1 tptp.real) (Y_4 tptp.real) (X_5 tptp.real) (A_60 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X_5) A_60) (=> (@ (@ tptp.ord_less_real Y_4) A_60) (=> (@ _let_1 U_1) (=> (@ _let_1 V_1) (=> (= (@ (@ tptp.plus_plus_real U_1) V_1) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U_1) X_5)) (@ (@ tptp.times_times_real V_1) Y_4))) A_60)))))))) (forall ((V_1 tptp.int) (U_1 tptp.int) (Y_4 tptp.int) (X_5 tptp.int) (A_60 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X_5) A_60) (=> (@ (@ tptp.ord_less_int Y_4) A_60) (=> (@ _let_1 U_1) (=> (@ _let_1 V_1) (=> (= (@ (@ tptp.plus_plus_int U_1) V_1) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U_1) X_5)) (@ (@ tptp.times_times_int V_1) Y_4))) A_60)))))))) (forall ((A_59 tptp.real)) (@ (@ tptp.dvd_dvd_real A_59) tptp.zero_zero_real)) (forall ((A_59 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A_59) tptp.zero_zero_nat)) (forall ((A_59 tptp.int)) (@ (@ tptp.dvd_dvd_int A_59) tptp.zero_zero_int)) (forall ((X_1 tptp.real) (Y_1 tptp.real)) (= (@ (@ tptp.ord_less_eq_real X_1) Y_1) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X_1) Y_1)) tptp.zero_zero_real))) (forall ((X_4 tptp.real) (Y_3 tptp.real)) (=> (not (= X_4 Y_3)) (=> (not (@ (@ tptp.ord_less_real X_4) Y_3)) (@ (@ tptp.ord_less_real Y_3) X_4)))) (forall ((X_4 tptp.int) (Y_3 tptp.int)) (=> (not (= X_4 Y_3)) (=> (not (@ (@ tptp.ord_less_int X_4) Y_3)) (@ (@ tptp.ord_less_int Y_3) X_4)))) (forall ((A_58 tptp.real)) (@ (@ tptp.dvd_dvd_real A_58) A_58)) (forall ((A_58 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A_58) A_58)) (forall ((A_58 tptp.int)) (@ (@ tptp.dvd_dvd_int A_58) A_58)) (forall ((C_27 tptp.real) (A_57 tptp.real) (B_51 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A_57))) (=> (@ _let_1 B_51) (=> (@ (@ tptp.dvd_dvd_real B_51) C_27) (@ _let_1 C_27))))) (forall ((C_27 tptp.nat) (A_57 tptp.nat) (B_51 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A_57))) (=> (@ _let_1 B_51) (=> (@ (@ tptp.dvd_dvd_nat B_51) C_27) (@ _let_1 C_27))))) (forall ((C_27 tptp.int) (A_57 tptp.int) (B_51 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A_57))) (=> (@ _let_1 B_51) (=> (@ (@ tptp.dvd_dvd_int B_51) C_27) (@ _let_1 C_27))))) _let_5 (forall ((X_1 tptp.real) (Y_1 tptp.real)) (= (@ (@ tptp.ord_less_eq_real X_1) Y_1) (or (@ (@ tptp.ord_less_real X_1) Y_1) (= X_1 Y_1)))) (forall ((X_1 tptp.real) (Y_1 tptp.real)) (= (@ (@ tptp.ord_less_real X_1) Y_1) (and (@ (@ tptp.ord_less_eq_real X_1) Y_1) (not (= X_1 Y_1))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (= (and (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (@ (@ tptp.dvd_dvd_nat Y_1) X_1)) (= X_1 Y_1))) (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 ((Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real Z) W) (@ (@ tptp.times_times_real W) Z))) (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) Z) Z)) (forall ((Z tptp.real) (X_1 tptp.real) (Y_1 tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real Z))) (=> (@ (@ tptp.ord_less_eq_real X_1) Y_1) (@ (@ tptp.ord_less_eq_real (@ _let_1 X_1)) (@ _let_1 Y_1))))) (forall ((X_3 tptp.nat) (N_2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X_3))) (=> (@ (@ 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_3) (@ _let_1 N_2))))) (forall ((X_3 tptp.real) (N_2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X_3))) (=> (@ (@ 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_3) (@ _let_1 N_2))))) (forall ((X_3 tptp.int) (N_2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X_3))) (=> (@ (@ 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_3) (@ _let_1 N_2))))) (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 ((P tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat P))) (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) (@ _let_1 (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))))))))) (forall ((X_1 tptp.nat) (Y_1 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_1) _let_1)) (@ (@ tptp.power_power_nat Y_1) _let_1)) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat X_1) Y_1)) (@ (@ tptp.minus_minus_nat X_1) Y_1))))) (forall ((A_56 tptp.real) (B_50 tptp.real)) (=> (= (@ (@ tptp.times_times_real A_56) B_50) tptp.zero_zero_real) (or (= A_56 tptp.zero_zero_real) (= B_50 tptp.zero_zero_real)))) (forall ((A_56 tptp.nat) (B_50 tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A_56) B_50) tptp.zero_zero_nat) (or (= A_56 tptp.zero_zero_nat) (= B_50 tptp.zero_zero_nat)))) (forall ((A_56 tptp.int) (B_50 tptp.int)) (=> (= (@ (@ tptp.times_times_int A_56) B_50) tptp.zero_zero_int) (or (= A_56 tptp.zero_zero_int) (= B_50 tptp.zero_zero_int)))) (forall ((B_49 tptp.real) (A_55 tptp.real)) (=> (not (= A_55 tptp.zero_zero_real)) (=> (not (= B_49 tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A_55) B_49) tptp.zero_zero_real))))) (forall ((B_49 tptp.nat) (A_55 tptp.nat)) (=> (not (= A_55 tptp.zero_zero_nat)) (=> (not (= B_49 tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A_55) B_49) tptp.zero_zero_nat))))) (forall ((B_49 tptp.int) (A_55 tptp.int)) (=> (not (= A_55 tptp.zero_zero_int)) (=> (not (= B_49 tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A_55) B_49) tptp.zero_zero_int))))) (forall ((A_54 tptp.real) (B_48 tptp.real)) (= (= (@ (@ tptp.times_times_real A_54) B_48) tptp.zero_zero_real) (or (= A_54 tptp.zero_zero_real) (= B_48 tptp.zero_zero_real)))) (forall ((A_54 tptp.int) (B_48 tptp.int)) (= (= (@ (@ tptp.times_times_int A_54) B_48) tptp.zero_zero_int) (or (= A_54 tptp.zero_zero_int) (= B_48 tptp.zero_zero_int)))) (forall ((A_53 tptp.real)) (= (@ (@ tptp.times_times_real A_53) tptp.zero_zero_real) tptp.zero_zero_real)) (forall ((A_53 tptp.nat)) (= (@ (@ tptp.times_times_nat A_53) tptp.zero_zero_nat) tptp.zero_zero_nat)) (forall ((A_53 tptp.int)) (= (@ (@ tptp.times_times_int A_53) tptp.zero_zero_int) tptp.zero_zero_int)) (forall ((A_52 tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A_52) tptp.zero_zero_real)) (forall ((A_52 tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A_52) tptp.zero_zero_nat)) (forall ((A_52 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A_52) tptp.zero_zero_int)) _let_5 (not (= tptp.zero_zero_nat tptp.one_one_nat)) _let_4 (not (= tptp.one_one_real tptp.zero_zero_real)) (not (= tptp.one_one_nat tptp.zero_zero_nat)) (not (= tptp.one_one_int tptp.zero_zero_int)) (forall ((A_51 tptp.real) (E tptp.real) (B_47 tptp.real) (C_26 tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_51) E)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B_47) E)) C_26)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_51) B_47)) E)) C_26))) (forall ((A_51 tptp.nat) (E tptp.nat) (B_47 tptp.nat) (C_26 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_51) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B_47) E)) C_26)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_51) B_47)) E)) C_26))) (forall ((A_51 tptp.int) (E tptp.int) (B_47 tptp.int) (C_26 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_51) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_47) E)) C_26)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_51) B_47)) E)) C_26))) (forall ((A_50 tptp.real) (B_46 tptp.real) (C_25 tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A_50) B_46)) C_25) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A_50) C_25)) (@ (@ tptp.times_times_real B_46) C_25)))) (forall ((A_50 tptp.nat) (B_46 tptp.nat) (C_25 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A_50) B_46)) C_25) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A_50) C_25)) (@ (@ tptp.times_times_nat B_46) C_25)))) (forall ((A_50 tptp.int) (B_46 tptp.int) (C_25 tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A_50) B_46)) C_25) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A_50) C_25)) (@ (@ tptp.times_times_int B_46) C_25)))) (forall ((A_49 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A_49) (= A_49 tptp.zero_zero_real))) (forall ((A_49 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A_49) (= A_49 tptp.zero_zero_nat))) (forall ((A_49 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A_49) (= A_49 tptp.zero_zero_int))) (forall ((A_48 tptp.real) (C_24 tptp.real) (B_45 tptp.real) (D_6 tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A_48) C_24)) (@ (@ tptp.plus_plus_real B_45) D_6)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A_48) B_45)) (@ (@ tptp.minus_minus_real C_24) D_6)))) (forall ((A_48 tptp.int) (C_24 tptp.int) (B_45 tptp.int) (D_6 tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A_48) C_24)) (@ (@ tptp.plus_plus_int B_45) D_6)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A_48) B_45)) (@ (@ tptp.minus_minus_int C_24) D_6)))) (forall ((A_47 tptp.real) (B_44 tptp.real) (C_23 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A_47) B_44)) C_23) (@ (@ tptp.dvd_dvd_real B_44) C_23))) (forall ((A_47 tptp.nat) (B_44 tptp.nat) (C_23 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A_47) B_44)) C_23) (@ (@ tptp.dvd_dvd_nat B_44) C_23))) (forall ((A_47 tptp.int) (B_44 tptp.int) (C_23 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A_47) B_44)) C_23) (@ (@ tptp.dvd_dvd_int B_44) C_23))) (forall ((A_46 tptp.real) (B_43 tptp.real) (C_22 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A_46) B_43)) C_22) (@ (@ tptp.dvd_dvd_real A_46) C_22))) (forall ((A_46 tptp.nat) (B_43 tptp.nat) (C_22 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A_46) B_43)) C_22) (@ (@ tptp.dvd_dvd_nat A_46) C_22))) (forall ((A_46 tptp.int) (B_43 tptp.int) (C_22 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A_46) B_43)) C_22) (@ (@ tptp.dvd_dvd_int A_46) C_22))) (forall ((A_45 tptp.real) (B_42 tptp.real) (K_2 tptp.real)) (=> (= A_45 (@ (@ tptp.times_times_real B_42) K_2)) (@ (@ tptp.dvd_dvd_real B_42) A_45))) (forall ((A_45 tptp.nat) (B_42 tptp.nat) (K_2 tptp.nat)) (=> (= A_45 (@ (@ tptp.times_times_nat B_42) K_2)) (@ (@ tptp.dvd_dvd_nat B_42) A_45))) (forall ((A_45 tptp.int) (B_42 tptp.int) (K_2 tptp.int)) (=> (= A_45 (@ (@ tptp.times_times_int B_42) K_2)) (@ (@ tptp.dvd_dvd_int B_42) A_45))) (forall ((C_21 tptp.real) (D_5 tptp.real) (A_44 tptp.real) (B_41 tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A_44) B_41) (=> (@ (@ tptp.dvd_dvd_real C_21) D_5) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A_44) C_21)) (@ (@ tptp.times_times_real B_41) D_5))))) (forall ((C_21 tptp.nat) (D_5 tptp.nat) (A_44 tptp.nat) (B_41 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A_44) B_41) (=> (@ (@ tptp.dvd_dvd_nat C_21) D_5) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A_44) C_21)) (@ (@ tptp.times_times_nat B_41) D_5))))) (forall ((C_21 tptp.int) (D_5 tptp.int) (A_44 tptp.int) (B_41 tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A_44) B_41) (=> (@ (@ tptp.dvd_dvd_int C_21) D_5) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A_44) C_21)) (@ (@ tptp.times_times_int B_41) D_5))))) (forall ((B_40 tptp.real) (A_43 tptp.real) (C_20 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A_43))) (=> (@ _let_1 C_20) (@ _let_1 (@ (@ tptp.times_times_real B_40) C_20))))) (forall ((B_40 tptp.nat) (A_43 tptp.nat) (C_20 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A_43))) (=> (@ _let_1 C_20) (@ _let_1 (@ (@ tptp.times_times_nat B_40) C_20))))) (forall ((B_40 tptp.int) (A_43 tptp.int) (C_20 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A_43))) (=> (@ _let_1 C_20) (@ _let_1 (@ (@ tptp.times_times_int B_40) C_20))))) (forall ((C_19 tptp.real) (A_42 tptp.real) (B_39 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A_42))) (=> (@ _let_1 B_39) (@ _let_1 (@ (@ tptp.times_times_real B_39) C_19))))) (forall ((C_19 tptp.nat) (A_42 tptp.nat) (B_39 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A_42))) (=> (@ _let_1 B_39) (@ _let_1 (@ (@ tptp.times_times_nat B_39) C_19))))) (forall ((C_19 tptp.int) (A_42 tptp.int) (B_39 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A_42))) (=> (@ _let_1 B_39) (@ _let_1 (@ (@ tptp.times_times_int B_39) C_19))))) (forall ((A_41 tptp.real) (B_38 tptp.real)) (@ (@ tptp.dvd_dvd_real A_41) (@ (@ tptp.times_times_real B_38) A_41))) (forall ((A_41 tptp.nat) (B_38 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A_41) (@ (@ tptp.times_times_nat B_38) A_41))) (forall ((A_41 tptp.int) (B_38 tptp.int)) (@ (@ tptp.dvd_dvd_int A_41) (@ (@ tptp.times_times_int B_38) A_41))) (forall ((A_40 tptp.real) (B_37 tptp.real)) (@ (@ tptp.dvd_dvd_real A_40) (@ (@ tptp.times_times_real A_40) B_37))) (forall ((A_40 tptp.nat) (B_37 tptp.nat)) (@ (@ tptp.dvd_dvd_nat A_40) (@ (@ tptp.times_times_nat A_40) B_37))) (forall ((A_40 tptp.int) (B_37 tptp.int)) (@ (@ tptp.dvd_dvd_int A_40) (@ (@ tptp.times_times_int A_40) B_37))) (forall ((C_18 tptp.real) (A_39 tptp.real) (B_36 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A_39))) (=> (@ _let_1 B_36) (=> (@ _let_1 C_18) (@ _let_1 (@ (@ tptp.plus_plus_real B_36) C_18)))))) (forall ((C_18 tptp.nat) (A_39 tptp.nat) (B_36 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A_39))) (=> (@ _let_1 B_36) (=> (@ _let_1 C_18) (@ _let_1 (@ (@ tptp.plus_plus_nat B_36) C_18)))))) (forall ((C_18 tptp.int) (A_39 tptp.int) (B_36 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A_39))) (=> (@ _let_1 B_36) (=> (@ _let_1 C_18) (@ _let_1 (@ (@ tptp.plus_plus_int B_36) C_18)))))) (forall ((A_38 tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A_38)) (forall ((A_38 tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A_38)) (forall ((A_38 tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A_38)) (forall ((Z_1 tptp.real) (X_2 tptp.real) (Y_2 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X_2))) (=> (@ _let_1 Y_2) (=> (@ _let_1 Z_1) (@ _let_1 (@ (@ tptp.minus_minus_real Y_2) Z_1)))))) (forall ((Z_1 tptp.int) (X_2 tptp.int) (Y_2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X_2))) (=> (@ _let_1 Y_2) (=> (@ _let_1 Z_1) (@ _let_1 (@ (@ tptp.minus_minus_int Y_2) Z_1)))))) (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 ((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 ((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 ((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 ((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 ((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 ((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 ((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 ((N tptp.nat) (X_1 tptp.nat) (Y_1 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X_1) N)) (@ (@ tptp.power_power_nat Y_1) N)))) (forall ((B_35 tptp.real) (A_37 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A_37) (@ (@ tptp.ord_less_eq_real B_35) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A_37) tptp.zero_zero_real) (@ _let_1 B_35))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_37) B_35)) tptp.zero_zero_real)))) (forall ((B_35 tptp.nat) (A_37 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A_37) (@ (@ tptp.ord_less_eq_nat B_35) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A_37) tptp.zero_zero_nat) (@ _let_1 B_35))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_37) B_35)) tptp.zero_zero_nat)))) (forall ((B_35 tptp.int) (A_37 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A_37) (@ (@ tptp.ord_less_eq_int B_35) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A_37) tptp.zero_zero_int) (@ _let_1 B_35))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_37) B_35)) tptp.zero_zero_int)))) (forall ((B_34 tptp.real) (A_36 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A_36) (@ _let_1 B_34)) (and (@ (@ tptp.ord_less_eq_real A_36) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B_34) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.times_times_real A_36) B_34))))) (forall ((B_34 tptp.int) (A_36 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A_36) (@ _let_1 B_34)) (and (@ (@ tptp.ord_less_eq_int A_36) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B_34) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A_36) B_34))))) (forall ((C_17 tptp.real) (D_4 tptp.real) (A_35 tptp.real) (B_33 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A_35) B_33) (=> (@ (@ tptp.ord_less_eq_real C_17) D_4) (=> (@ _let_1 B_33) (=> (@ _let_1 C_17) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_35) C_17)) (@ (@ tptp.times_times_real B_33) D_4)))))))) (forall ((C_17 tptp.nat) (D_4 tptp.nat) (A_35 tptp.nat) (B_33 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A_35) B_33) (=> (@ (@ tptp.ord_less_eq_nat C_17) D_4) (=> (@ _let_1 B_33) (=> (@ _let_1 C_17) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_35) C_17)) (@ (@ tptp.times_times_nat B_33) D_4)))))))) (forall ((C_17 tptp.int) (D_4 tptp.int) (A_35 tptp.int) (B_33 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A_35) B_33) (=> (@ (@ tptp.ord_less_eq_int C_17) D_4) (=> (@ _let_1 B_33) (=> (@ _let_1 C_17) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_35) C_17)) (@ (@ tptp.times_times_int B_33) D_4)))))))) (forall ((C_16 tptp.real) (D_3 tptp.real) (A_34 tptp.real) (B_32 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A_34) B_32) (=> (@ (@ tptp.ord_less_eq_real C_16) D_3) (=> (@ _let_1 A_34) (=> (@ _let_1 C_16) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_34) C_16)) (@ (@ tptp.times_times_real B_32) D_3)))))))) (forall ((C_16 tptp.nat) (D_3 tptp.nat) (A_34 tptp.nat) (B_32 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A_34) B_32) (=> (@ (@ tptp.ord_less_eq_nat C_16) D_3) (=> (@ _let_1 A_34) (=> (@ _let_1 C_16) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_34) C_16)) (@ (@ tptp.times_times_nat B_32) D_3)))))))) (forall ((C_16 tptp.int) (D_3 tptp.int) (A_34 tptp.int) (B_32 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A_34) B_32) (=> (@ (@ tptp.ord_less_eq_int C_16) D_3) (=> (@ _let_1 A_34) (=> (@ _let_1 C_16) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_34) C_16)) (@ (@ tptp.times_times_int B_32) D_3)))))))) (forall ((C_15 tptp.real) (B_31 tptp.real) (A_33 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_15))) (=> (@ (@ tptp.ord_less_eq_real B_31) A_33) (=> (@ (@ tptp.ord_less_eq_real C_15) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A_33)) (@ _let_1 B_31)))))) (forall ((C_15 tptp.int) (B_31 tptp.int) (A_33 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_15))) (=> (@ (@ tptp.ord_less_eq_int B_31) A_33) (=> (@ (@ tptp.ord_less_eq_int C_15) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A_33)) (@ _let_1 B_31)))))) (forall ((C_14 tptp.real) (B_30 tptp.real) (A_32 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B_30) A_32) (=> (@ (@ tptp.ord_less_eq_real C_14) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_32) C_14)) (@ (@ tptp.times_times_real B_30) C_14))))) (forall ((C_14 tptp.int) (B_30 tptp.int) (A_32 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B_30) A_32) (=> (@ (@ tptp.ord_less_eq_int C_14) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_32) C_14)) (@ (@ tptp.times_times_int B_30) C_14))))) (forall ((C_13 tptp.real) (A_31 tptp.real) (B_29 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_13))) (=> (@ (@ tptp.ord_less_eq_real A_31) B_29) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_13) (@ (@ tptp.ord_less_eq_real (@ _let_1 A_31)) (@ _let_1 B_29)))))) (forall ((C_13 tptp.nat) (A_31 tptp.nat) (B_29 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_13))) (=> (@ (@ tptp.ord_less_eq_nat A_31) B_29) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_13) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_31)) (@ _let_1 B_29)))))) (forall ((C_13 tptp.int) (A_31 tptp.int) (B_29 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_13))) (=> (@ (@ tptp.ord_less_eq_int A_31) B_29) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_13) (@ (@ tptp.ord_less_eq_int (@ _let_1 A_31)) (@ _let_1 B_29)))))) (forall ((C_12 tptp.real) (A_30 tptp.real) (B_28 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_12))) (=> (@ (@ tptp.ord_less_eq_real A_30) B_28) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_12) (@ (@ tptp.ord_less_eq_real (@ _let_1 A_30)) (@ _let_1 B_28)))))) (forall ((C_12 tptp.nat) (A_30 tptp.nat) (B_28 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_12))) (=> (@ (@ tptp.ord_less_eq_nat A_30) B_28) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_12) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A_30)) (@ _let_1 B_28)))))) (forall ((C_12 tptp.int) (A_30 tptp.int) (B_28 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_12))) (=> (@ (@ tptp.ord_less_eq_int A_30) B_28) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_12) (@ (@ tptp.ord_less_eq_int (@ _let_1 A_30)) (@ _let_1 B_28)))))) (forall ((C_11 tptp.real) (A_29 tptp.real) (B_27 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_29) B_27) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C_11) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_29) C_11)) (@ (@ tptp.times_times_real B_27) C_11))))) (forall ((C_11 tptp.nat) (A_29 tptp.nat) (B_27 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_29) B_27) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C_11) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_29) C_11)) (@ (@ tptp.times_times_nat B_27) C_11))))) (forall ((C_11 tptp.int) (A_29 tptp.int) (B_27 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_29) B_27) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C_11) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_29) C_11)) (@ (@ tptp.times_times_int B_27) C_11))))) (forall ((B_26 tptp.real) (A_28 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_28) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B_26) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A_28) B_26))))) (forall ((B_26 tptp.int) (A_28 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_28) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B_26) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A_28) B_26))))) (forall ((B_25 tptp.real) (A_27 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A_27) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B_25) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_27) B_25)) tptp.zero_zero_real)))) (forall ((B_25 tptp.nat) (A_27 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A_27) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B_25) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_27) B_25)) tptp.zero_zero_nat)))) (forall ((B_25 tptp.int) (A_27 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A_27) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B_25) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_27) B_25)) tptp.zero_zero_int)))) (forall ((B_24 tptp.real) (A_26 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_26) (=> (@ (@ tptp.ord_less_eq_real B_24) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real B_24) A_26)) tptp.zero_zero_real)))) (forall ((B_24 tptp.nat) (A_26 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_26) (=> (@ (@ tptp.ord_less_eq_nat B_24) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B_24) A_26)) tptp.zero_zero_nat)))) (forall ((B_24 tptp.int) (A_26 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_26) (=> (@ (@ tptp.ord_less_eq_int B_24) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B_24) A_26)) tptp.zero_zero_int)))) (forall ((B_23 tptp.real) (A_25 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A_25) (=> (@ (@ tptp.ord_less_eq_real B_23) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_25) B_23)) tptp.zero_zero_real)))) (forall ((B_23 tptp.nat) (A_25 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A_25) (=> (@ (@ tptp.ord_less_eq_nat B_23) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A_25) B_23)) tptp.zero_zero_nat)))) (forall ((B_23 tptp.int) (A_25 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A_25) (=> (@ (@ tptp.ord_less_eq_int B_23) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_25) B_23)) tptp.zero_zero_int)))) (forall ((B_22 tptp.real) (A_24 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A_24) (=> (@ _let_1 B_22) (@ _let_1 (@ (@ tptp.times_times_real A_24) B_22)))))) (forall ((B_22 tptp.nat) (A_24 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A_24) (=> (@ _let_1 B_22) (@ _let_1 (@ (@ tptp.times_times_nat A_24) B_22)))))) (forall ((B_22 tptp.int) (A_24 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A_24) (=> (@ _let_1 B_22) (@ _let_1 (@ (@ tptp.times_times_int A_24) B_22)))))) (forall ((A_23 tptp.real) (B_21 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A_23) B_21)) tptp.zero_zero_real) (or (and (@ _let_1 A_23) (@ (@ tptp.ord_less_eq_real B_21) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A_23) tptp.zero_zero_real) (@ _let_1 B_21)))))) (forall ((A_23 tptp.int) (B_21 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A_23) B_21)) tptp.zero_zero_int) (or (and (@ _let_1 A_23) (@ (@ tptp.ord_less_eq_int B_21) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A_23) tptp.zero_zero_int) (@ _let_1 B_21)))))) (forall ((A_22 tptp.real) (B_20 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A_22) B_20)) (or (and (@ _let_1 A_22) (@ _let_1 B_20)) (and (@ (@ tptp.ord_less_eq_real A_22) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B_20) tptp.zero_zero_real)))))) (forall ((A_22 tptp.int) (B_20 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A_22) B_20)) (or (and (@ _let_1 A_22) (@ _let_1 B_20)) (and (@ (@ tptp.ord_less_eq_int A_22) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B_20) tptp.zero_zero_int)))))) (forall ((A_21 tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A_21) A_21))) (forall ((A_21 tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A_21) A_21))) (forall ((C_10 tptp.real) (B_19 tptp.real) (A_20 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_10))) (=> (@ (@ tptp.ord_less_real B_19) A_20) (=> (@ (@ tptp.ord_less_real C_10) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ _let_1 A_20)) (@ _let_1 B_19)))))) (forall ((C_10 tptp.int) (B_19 tptp.int) (A_20 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_10))) (=> (@ (@ tptp.ord_less_int B_19) A_20) (=> (@ (@ tptp.ord_less_int C_10) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A_20)) (@ _let_1 B_19)))))) (forall ((C_9 tptp.real) (B_18 tptp.real) (A_19 tptp.real)) (=> (@ (@ tptp.ord_less_real B_18) A_19) (=> (@ (@ tptp.ord_less_real C_9) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_19) C_9)) (@ (@ tptp.times_times_real B_18) C_9))))) (forall ((C_9 tptp.int) (B_18 tptp.int) (A_19 tptp.int)) (=> (@ (@ tptp.ord_less_int B_18) A_19) (=> (@ (@ tptp.ord_less_int C_9) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_19) C_9)) (@ (@ tptp.times_times_int B_18) C_9))))) (forall ((C_8 tptp.real) (A_18 tptp.real) (B_17 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_8))) (=> (@ (@ tptp.ord_less_real A_18) B_17) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_8) (@ (@ tptp.ord_less_real (@ _let_1 A_18)) (@ _let_1 B_17)))))) (forall ((C_8 tptp.nat) (A_18 tptp.nat) (B_17 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_8))) (=> (@ (@ tptp.ord_less_nat A_18) B_17) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C_8) (@ (@ tptp.ord_less_nat (@ _let_1 A_18)) (@ _let_1 B_17)))))) (forall ((C_8 tptp.int) (A_18 tptp.int) (B_17 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_8))) (=> (@ (@ tptp.ord_less_int A_18) B_17) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_8) (@ (@ tptp.ord_less_int (@ _let_1 A_18)) (@ _let_1 B_17)))))) (forall ((C_7 tptp.real) (A_17 tptp.real) (B_16 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_7))) (=> (@ (@ tptp.ord_less_real A_17) B_16) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_7) (@ (@ tptp.ord_less_real (@ _let_1 A_17)) (@ _let_1 B_16)))))) (forall ((C_7 tptp.nat) (A_17 tptp.nat) (B_16 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C_7))) (=> (@ (@ tptp.ord_less_nat A_17) B_16) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C_7) (@ (@ tptp.ord_less_nat (@ _let_1 A_17)) (@ _let_1 B_16)))))) (forall ((C_7 tptp.int) (A_17 tptp.int) (B_16 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_7))) (=> (@ (@ tptp.ord_less_int A_17) B_16) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_7) (@ (@ tptp.ord_less_int (@ _let_1 A_17)) (@ _let_1 B_16)))))) (forall ((C_6 tptp.real) (A_16 tptp.real) (B_15 tptp.real)) (=> (@ (@ tptp.ord_less_real A_16) B_15) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_6) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_16) C_6)) (@ (@ tptp.times_times_real B_15) C_6))))) (forall ((C_6 tptp.nat) (A_16 tptp.nat) (B_15 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_16) B_15) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C_6) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_16) C_6)) (@ (@ tptp.times_times_nat B_15) C_6))))) (forall ((C_6 tptp.int) (A_16 tptp.int) (B_15 tptp.int)) (=> (@ (@ tptp.ord_less_int A_16) B_15) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_6) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_16) C_6)) (@ (@ tptp.times_times_int B_15) C_6))))) (forall ((B_14 tptp.real) (A_15 tptp.real)) (=> (@ (@ tptp.ord_less_real A_15) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B_14) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A_15) B_14))))) (forall ((B_14 tptp.int) (A_15 tptp.int)) (=> (@ (@ tptp.ord_less_int A_15) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B_14) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A_15) B_14))))) (forall ((B_13 tptp.real) (A_14 tptp.real)) (=> (@ (@ tptp.ord_less_real A_14) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B_13) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_14) B_13)) tptp.zero_zero_real)))) (forall ((B_13 tptp.nat) (A_14 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A_14) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B_13) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_14) B_13)) tptp.zero_zero_nat)))) (forall ((B_13 tptp.int) (A_14 tptp.int)) (=> (@ (@ tptp.ord_less_int A_14) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_13) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_14) B_13)) tptp.zero_zero_int)))) (forall ((A_13 tptp.real) (B_12 tptp.real) (C_5 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_5))) (=> (@ (@ tptp.ord_less_real C_5) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ _let_1 A_13)) (@ _let_1 B_12)) (@ (@ tptp.ord_less_real B_12) A_13))))) (forall ((A_13 tptp.int) (B_12 tptp.int) (C_5 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_5))) (=> (@ (@ tptp.ord_less_int C_5) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A_13)) (@ _let_1 B_12)) (@ (@ tptp.ord_less_int B_12) A_13))))) (forall ((B_11 tptp.real) (A_12 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real B_11) A_12)) (=> (@ _let_1 A_12) (@ _let_1 B_11))))) (forall ((B_11 tptp.nat) (A_12 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B_11) A_12)) (=> (@ _let_1 A_12) (@ _let_1 B_11))))) (forall ((B_11 tptp.int) (A_12 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B_11) A_12)) (=> (@ _let_1 A_12) (@ _let_1 B_11))))) (forall ((A_11 tptp.real) (B_10 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real A_11) B_10)) (=> (@ _let_1 A_11) (@ _let_1 B_10))))) (forall ((A_11 tptp.nat) (B_10 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A_11) B_10)) (=> (@ _let_1 A_11) (@ _let_1 B_10))))) (forall ((A_11 tptp.int) (B_10 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A_11) B_10)) (=> (@ _let_1 A_11) (@ _let_1 B_10))))) (forall ((B_9 tptp.real) (A_10 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A_10) (=> (@ (@ tptp.ord_less_real B_9) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real B_9) A_10)) tptp.zero_zero_real)))) (forall ((B_9 tptp.nat) (A_10 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_10) (=> (@ (@ tptp.ord_less_nat B_9) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B_9) A_10)) tptp.zero_zero_nat)))) (forall ((B_9 tptp.int) (A_10 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_10) (=> (@ (@ tptp.ord_less_int B_9) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B_9) A_10)) tptp.zero_zero_int)))) (forall ((B_8 tptp.real) (A_9 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A_9) (=> (@ (@ tptp.ord_less_real B_8) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_9) B_8)) tptp.zero_zero_real)))) (forall ((B_8 tptp.nat) (A_9 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_9) (=> (@ (@ tptp.ord_less_nat B_8) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A_9) B_8)) tptp.zero_zero_nat)))) (forall ((B_8 tptp.int) (A_9 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_9) (=> (@ (@ tptp.ord_less_int B_8) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_9) B_8)) tptp.zero_zero_int)))) (forall ((B_7 tptp.real) (A_8 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A_8) (=> (@ _let_1 B_7) (@ _let_1 (@ (@ tptp.times_times_real A_8) B_7)))))) (forall ((B_7 tptp.nat) (A_8 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A_8) (=> (@ _let_1 B_7) (@ _let_1 (@ (@ tptp.times_times_nat A_8) B_7)))))) (forall ((B_7 tptp.int) (A_8 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A_8) (=> (@ _let_1 B_7) (@ _let_1 (@ (@ tptp.times_times_int A_8) B_7)))))) (forall ((A_7 tptp.real) (B_6 tptp.real) (C_4 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_4) (= (@ (@ tptp.ord_less_real (@ _let_1 A_7)) (@ _let_1 B_6)) (@ (@ tptp.ord_less_real A_7) B_6))))) (forall ((A_7 tptp.int) (B_6 tptp.int) (C_4 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_4))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_4) (= (@ (@ tptp.ord_less_int (@ _let_1 A_7)) (@ _let_1 B_6)) (@ (@ tptp.ord_less_int A_7) B_6))))) (forall ((C_3 tptp.real) (A_6 tptp.real) (B_5 tptp.real)) (let ((_let_1 (@ tptp.times_times_real C_3))) (= (@ (@ tptp.ord_less_real (@ _let_1 A_6)) (@ _let_1 B_5)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_3) (@ (@ tptp.ord_less_real A_6) B_5)) (and (@ (@ tptp.ord_less_real C_3) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B_5) A_6)))))) (forall ((C_3 tptp.int) (A_6 tptp.int) (B_5 tptp.int)) (let ((_let_1 (@ tptp.times_times_int C_3))) (= (@ (@ tptp.ord_less_int (@ _let_1 A_6)) (@ _let_1 B_5)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_3) (@ (@ tptp.ord_less_int A_6) B_5)) (and (@ (@ tptp.ord_less_int C_3) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B_5) A_6)))))) (forall ((A_5 tptp.real) (C_2 tptp.real) (B_4 tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_5) C_2)) (@ (@ tptp.times_times_real B_4) C_2)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C_2) (@ (@ tptp.ord_less_real A_5) B_4)) (and (@ (@ tptp.ord_less_real C_2) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B_4) A_5))))) (forall ((A_5 tptp.int) (C_2 tptp.int) (B_4 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_5) C_2)) (@ (@ tptp.times_times_int B_4) C_2)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C_2) (@ (@ tptp.ord_less_int A_5) B_4)) (and (@ (@ tptp.ord_less_int C_2) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B_4) A_5))))) (forall ((A_4 tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A_4) A_4)) tptp.zero_zero_real))) (forall ((A_4 tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A_4) A_4)) tptp.zero_zero_int))) (forall ((B_3 tptp.nat) (C_1 tptp.nat) (A_3 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B_3))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A_3) (=> (@ _let_1 C_1) (@ _let_1 (@ (@ tptp.plus_plus_nat A_3) C_1)))))) (forall ((B_3 tptp.int) (C_1 tptp.int) (A_3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B_3))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A_3) (=> (@ _let_1 C_1) (@ _let_1 (@ (@ tptp.plus_plus_int A_3) C_1)))))) (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 ((X_1 tptp.real) (Y_1 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X_1) Z)) (@ (@ tptp.times_times_real Y_1) Z)) (@ (@ tptp.ord_less_real X_1) Y_1)))) (forall ((X_1 tptp.real) (Y_1 tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X_1) Z)) (@ (@ tptp.times_times_real Y_1) Z)) (@ (@ tptp.ord_less_eq_real X_1) Y_1)))) (forall ((X_1 tptp.real) (Y_1 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_1)) (@ _let_1 Y_1)) (@ (@ tptp.ord_less_eq_real X_1) Y_1))))) (forall ((Y_1 tptp.real) (X_1 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X_1) (=> (@ _let_1 Y_1) (@ _let_1 (@ (@ tptp.times_times_real X_1) Y_1)))))) (forall ((X_1 tptp.real) (Y_1 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_1) Y_1) (@ (@ tptp.ord_less_real (@ _let_1 X_1)) (@ _let_1 Y_1)))))) (forall ((X_1 tptp.real) (Y_1 tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X_1) X_1)) (@ (@ tptp.times_times_real Y_1) Y_1)) tptp.zero_zero_real) (and (= X_1 tptp.zero_zero_real) (= Y_1 tptp.zero_zero_real)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat) (N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X_1) N)) Y_1) (@ (@ tptp.dvd_dvd_nat X_1) Y_1)))) (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_1 tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat X_1) N) tptp.one_one_nat) (or (= X_1 tptp.one_one_nat) (= N tptp.zero_zero_nat)))) (forall ((X_1 tptp.nat) (Q tptp.nat) (N tptp.nat) (R tptp.nat)) (=> (= X_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Q) N)) R)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) R) (=> (@ (@ tptp.ord_less_nat R) N) (not (@ (@ tptp.dvd_dvd_nat N) X_1)))))) (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 ((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_1 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R_1) (= (@ (@ tptp.power_power_real R_1) N) A)))))) (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 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real X) N) A) (forall ((Y tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.power_power_real Y) N) A)) (= Y 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 N) M)) 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 M) N)) M) (= N tptp.one_one_nat)))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)) (forall ((X_1 tptp.nat)) (@ (@ tptp.dvd_dvd_nat X_1) X_1)) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))) (forall ((I_1 tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I_1))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) J_1)))) (forall ((W tptp.real)) (@ (@ tptp.ord_less_eq_real W) W)) (forall ((Z tptp.real) (W tptp.real)) (or (@ (@ tptp.ord_less_eq_real Z) W) (@ (@ tptp.ord_less_eq_real W) Z))) (forall ((K tptp.real) (I_1 tptp.real) (J_1 tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real I_1))) (=> (@ _let_1 J_1) (=> (@ (@ tptp.ord_less_eq_real J_1) 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)))) (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)) (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)) (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 ((P_1 (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ P_1 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 ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (not (= X_1 Y_1)) (=> (not (@ (@ tptp.ord_less_nat X_1) Y_1)) (@ (@ tptp.ord_less_nat Y_1) X_1)))) (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))) (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))) (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 ((N tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat J_1) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J_1) N)) K))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) Y_1))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((Z tptp.nat) (X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat Z))) (let ((_let_2 (@ tptp.dvd_dvd_nat X_1))) (let ((_let_3 (@ tptp.dvd_dvd_nat Y_1))) (=> (and (@ _let_2 Y_1) (not (@ _let_3 X_1))) (=> (and (@ _let_3 Z) (not (@ _let_1 Y_1))) (and (@ _let_2 Z) (not (@ _let_1 X_1))))))))) (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_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat X_1))) (let ((_let_2 (@ tptp.dvd_dvd_nat Y_1))) (=> (and (@ _let_1 Y_1) (not (@ _let_2 X_1))) (=> (@ _let_2 Z) (and (@ _let_1 Z) (not (@ (@ tptp.dvd_dvd_nat Z) X_1)))))))) (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_1 Bool) (X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) Y_1))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (=> (and _let_1 (not _let_2)) (=> (and _let_2 (not _let_1)) P_1))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (and (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (not (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (not (= Y_1 X_1)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (and (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (not (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (not (= X_1 Y_1)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) Y_1))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) Y_1))) (=> (and _let_1 (not (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) _let_1))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) Y_1))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (=> (and _let_1 (not _let_2)) (not (and _let_2 (not _let_1))))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (and (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (not (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (not (= X_1 Y_1)))) (forall ((Z tptp.nat) (X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat Z))) (let ((_let_2 (@ tptp.dvd_dvd_nat X_1))) (=> (@ _let_2 Y_1) (=> (and (@ (@ tptp.dvd_dvd_nat Y_1) Z) (not (@ _let_1 Y_1))) (and (@ _let_2 Z) (not (@ _let_1 X_1)))))))) (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_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat X_1))) (=> (@ _let_1 Y_1) (=> (@ (@ tptp.dvd_dvd_nat Y_1) Z) (@ _let_1 Z))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (=> (@ (@ tptp.dvd_dvd_nat Y_1) X_1) (= X_1 Y_1)))) (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_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) Y_1))) (=> _let_1 (or (and _let_1 (not (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (= X_1 Y_1))))) (forall ((Y_1 tptp.nat) (X_1 tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat Y_1) X_1) (= (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (= X_1 Y_1)))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (=> (= X_1 Y_1) (@ (@ tptp.dvd_dvd_nat X_1) Y_1))) (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_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (and (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (not (@ (@ tptp.dvd_dvd_nat Y_1) X_1))))) (= _let_1 _let_1))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) Y_1))) (= (and _let_1 (not (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (and _let_1 (not (= X_1 Y_1)))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) Y_1))) (= _let_1 (or (and _let_1 (not (@ (@ tptp.dvd_dvd_nat Y_1) X_1))) (= X_1 Y_1))))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat)) (= (= X_1 Y_1) (and (@ (@ tptp.dvd_dvd_nat X_1) Y_1) (@ (@ tptp.dvd_dvd_nat Y_1) X_1)))) (forall ((X_1 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat X_1) X_1))) (not (and _let_1 (not _let_1))))) (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 ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) N) (@ (@ tptp.plus_plus_nat N) M))) (forall ((X_1 tptp.nat) (Y_1 tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X_1))) (let ((_let_2 (@ tptp.plus_plus_nat Y_1))) (= (@ _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 ((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_1 tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat I_1))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K) (@ _let_1 (@ (@ tptp.plus_plus_nat J_1) 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 ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)) (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)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))) (forall ((K tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J_1) (=> (@ (@ tptp.ord_less_eq_nat J_1) 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 ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)) (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 ((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 ((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 ((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 ((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.ord_less_eq_nat (@ (@ 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tptp.plus_plus_nat tptp.zero_zero_nat) N) N)) (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)) (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))) (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) 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 ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))) (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 ((I_1 tptp.nat) (J_1 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) J_1)) I_1))) (forall ((J_1 tptp.nat) (I_1 tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J_1) I_1)) I_1))) (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 ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I_1))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat J_1) M))))) (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I_1))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J_1))))) (forall ((K tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J_1) K)))) (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (=> (@ (@ tptp.ord_less_nat K) L) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J_1) 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_1 tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I_1) J_1)) K) (@ (@ tptp.ord_less_nat I_1) K))) (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 ((I_1 tptp.nat) (J_1 tptp.nat) (K tptp.nat)) (= (@ (@ 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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 ((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 ((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 ((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 ((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.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))) (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 ((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) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat J_1) M))))) (forall ((M tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I_1))) (=> (@ _let_1 J_1) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J_1))))) (forall ((K tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J_1) K)))) (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) (@ (@ tptp.plus_plus_nat J_1) L))))) (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 ((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) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))) (forall ((I_1 tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.minus_minus_nat I_1) (@ (@ tptp.minus_minus_nat J_1) K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat I_1) K)) J_1)))) (forall ((J_1 tptp.nat) (K tptp.nat) (I_1 tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat J_1) K)) I_1) (@ (@ tptp.ord_less_eq_nat J_1) (@ (@ 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_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I_1))) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ _let_1 (@ (@ tptp.minus_minus_nat J_1) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K))))) (forall ((I_1 tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.ord_less_eq_nat I_1) (@ (@ tptp.minus_minus_nat J_1) K)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I_1) K)) J_1)))) (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_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (= (= (@ (@ tptp.minus_minus_nat J_1) I_1) K) (= J_1 (@ (@ tptp.plus_plus_nat K) I_1))))) (forall ((I_1 tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat I_1))) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.minus_minus_nat (@ _let_1 J_1)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat J_1) K)))))) (forall ((I_1 tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J_1) K)) I_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J_1) I_1)) K)))) (forall ((I_1 tptp.nat) (K tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) J_1) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat J_1) I_1)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat J_1) K)) I_1)))) (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)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))) (forall ((K tptp.nat) (L tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (=> (@ (@ tptp.ord_less_eq_nat K) L) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I_1) K)) (@ (@ tptp.times_times_nat J_1) L))))) (forall ((K tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (@ (@ tptp.ord_less_eq_nat (@ _let_1 I_1)) (@ _let_1 J_1))))) (forall ((K tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I_1) K)) (@ (@ tptp.times_times_nat J_1) K)))) (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)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))) (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 ((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 ((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 ((P_1 (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P_1 (@ (@ tptp.minus_minus_nat A) B)) (and (=> (@ (@ tptp.ord_less_nat A) B) (@ P_1 tptp.zero_zero_nat)) (forall ((D_2 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D_2)) (@ P_1 D_2)))))) (forall ((P_1 (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P_1 (@ (@ tptp.minus_minus_nat A) B)) (not (or (and (@ (@ tptp.ord_less_nat A) B) (not (@ P_1 tptp.zero_zero_nat))) (exists ((D_2 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D_2)) (not (@ P_1 D_2)))))))) (forall ((K tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat (@ _let_1 I_1)) (@ _let_1 J_1)))))) (forall ((K tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (=> (@ (@ 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_1) 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 ((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 ((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 ((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 ((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 ((N tptp.nat) (P_1 (-> tptp.nat Bool))) (=> (not (@ P_1 tptp.zero_zero_nat)) (=> (@ P_1 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_1 I)))) (@ P_1 (@ (@ tptp.plus_plus_nat K_1) tptp.one_one_nat))))))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_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_1) U)) N)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J_1) 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_1 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_1) U)) K)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat I_1) J_1)) 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) (= (= (@ _let_1 M) (@ _let_1 N)) (= 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_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ 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.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_1 tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J_1) 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_1) U)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J_1)) U)) M)) N)))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J_1 tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J_1) 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_1) U)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J_1)) U)) M)) N)))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J_1 tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J_1) I_1) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J_1) U)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J_1)) U)) M) N)))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_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_1) U)) N)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J_1) I_1)) U)) N))))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_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_1) U)) N)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J_1) I_1)) U)) N))))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I_1) J_1) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I_1) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J_1) U)) N)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J_1) I_1)) U)) N))))) (forall ((U tptp.nat) (M tptp.nat) (N tptp.nat) (J_1 tptp.nat) (I_1 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J_1) 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_1) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I_1) J_1)) U)) M)) N)))) (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))))))) (forall ((X_1 tptp.int)) (= (@ tptp.twoSqu919416604sum2sq X_1) (exists ((A_2 tptp.int) (B_2 tptp.int)) (= (@ tptp.twoSqu2057625106sum2sq (@ (@ tptp.product_Pair_int_int A_2) B_2)) X_1)))) (forall ((P_3 Bool) (P_1 Bool) (X_1 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1))) (=> (=> _let_1 (= P_1 P_3)) (= (=> _let_1 P_1) (=> _let_1 P_3))))) (forall ((P_3 Bool) (P_1 Bool) (X_1 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X_1))) (=> (=> _let_1 (= P_1 P_3)) (= (and _let_1 P_1) (and _let_1 P_3))))) (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_3 _let_2) (forall ((K tptp.int) (P_1 (-> tptp.int Bool)) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X tptp.int)) (=> (@ P_1 X) (@ P_1 (@ (@ tptp.minus_minus_int X) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X tptp.int)) (=> (@ P_1 X) (@ P_1 (@ (@ tptp.minus_minus_int X) (@ (@ tptp.times_times_int K) D))))))))) (forall ((K tptp.int) (P_1 (-> tptp.int Bool)) (D tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X tptp.int)) (=> (@ P_1 X) (@ P_1 (@ (@ tptp.plus_plus_int X) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X tptp.int)) (=> (@ P_1 X) (@ P_1 (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int K) D))))))))) (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (exists ((P_2 tptp.int)) (and (@ tptp.zprime P_2) (@ (@ tptp.dvd_dvd_int P_2) A))))) (forall ((A tptp.int) (M tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (exists ((X tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_int X) M) (@ (@ (@ tptp.zcong A) X) M) (forall ((Y tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int Y) M) (@ (@ (@ tptp.zcong A) Y) M)) (= Y X))))))) (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 ((P tptp.int)) (=> (@ tptp.zprime P) (@ (@ (@ tptp.zcong (@ tptp.zfact (@ (@ tptp.minus_minus_int P) tptp.one_one_int))) (@ tptp.number_number_of_int tptp.min)) P))) (forall ((N tptp.int)) (let ((_let_1 (@ tptp.zfact N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int N) tptp.zero_zero_int))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 (@ (@ tptp.times_times_int N) (@ tptp.zfact (@ (@ tptp.minus_minus_int N) tptp.one_one_int))))))))) (forall ((A tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.inv P))) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) P) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) P) (= (@ _let_1 (@ _let_1 A)) A))))))) (forall ((J_1 tptp.int) (A tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.zcong J_1))) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (not (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) P)) (=> (not (@ (@ _let_1 tptp.zero_zero_int) P)) (=> (not (@ (@ tptp.quadRes P) A)) (not (@ (@ _let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.multInv P) J_1))) P))))))))) (forall ((J_1 tptp.int) (K tptp.int) (A tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.multInv P) J_1)))) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int J_1) K)) A) P) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int (@ _let_1 J_1)) K)) (@ _let_1 A)) P)))) (forall ((J_1 tptp.int) (A tptp.int) (P tptp.int) (K tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.multInv P) K)))) (=> (@ (@ (@ tptp.zcong J_1) _let_1) P) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int J_1) K)) (@ (@ tptp.times_times_int _let_1) K)) P)))) (forall ((A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int P) tptp.one_one_int)) (not (= A (@ (@ tptp.inv P) A))))))) (forall ((A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int P) tptp.one_one_int)) (not (= (@ (@ tptp.inv P) A) tptp.one_one_int)))))) (forall ((A tptp.int) (P tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int P) tptp.one_one_int))) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int A) _let_1) (not (= (@ (@ tptp.inv P) A) _let_1))))))) (forall ((A tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ tptp.zprime P) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int P) tptp.one_one_int)) (@ _let_1 (@ (@ tptp.inv P) A))))))) (forall ((A tptp.int) (P tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int P) tptp.one_one_int))) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int A) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.inv P) A)) _let_1)))))) (forall ((X_1 tptp.int) (Y_1 tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.multInv P))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ (@ (@ tptp.zcong X_1) Y_1) P) (@ (@ (@ tptp.zcong (@ _let_1 X_1)) (@ _let_1 Y_1)) P))))) (forall ((A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int P) tptp.one_one_int)) (not (= (@ (@ tptp.inv P) A) tptp.zero_zero_int)))))) (forall ((A tptp.int) (J_1 tptp.int) (K tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.multInv P))) (let ((_let_2 (@ tptp.times_times_int A))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ (@ (@ tptp.zcong J_1) K) P) (@ (@ (@ tptp.zcong (@ _let_2 (@ _let_1 J_1))) (@ _let_2 (@ _let_1 K))) P)))))) (forall ((Y_1 tptp.int) (X_1 tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.zcong X_1))) (let ((_let_2 (@ tptp.multInv P))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ _let_1 tptp.zero_zero_int) P)) (=> (not (@ (@ (@ tptp.zcong Y_1) tptp.zero_zero_int) P)) (=> (@ (@ (@ tptp.zcong (@ _let_2 X_1)) (@ _let_2 Y_1)) P) (@ (@ _let_1 Y_1) P))))))))) (forall ((X_1 tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.multInv P))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (@ (@ (@ tptp.zcong (@ _let_1 (@ _let_1 X_1))) X_1) P)))))) (forall ((X_1 tptp.int) (P tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (not (@ (@ (@ tptp.zcong (@ (@ tptp.multInv P) X_1)) tptp.zero_zero_int) P)))))) (forall ((A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) P) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int A) (@ (@ tptp.inv P) A))) tptp.one_one_int) P))))) (forall ((K tptp.int) (A tptp.int) (J_1 tptp.int) (P tptp.int)) (let ((_let_1 (@ (@ tptp.multInv P) J_1))) (let ((_let_2 (@ tptp.times_times_int _let_1))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong J_1) tptp.zero_zero_int) P)) (=> (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int (@ _let_2 J_1)) K)) (@ _let_2 A)) P) (@ (@ (@ tptp.zcong K) (@ (@ tptp.times_times_int A) _let_1)) P)))))))) (forall ((J_1 tptp.int) (A tptp.int) (K tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.zcong (@ (@ tptp.times_times_int J_1) K)))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong K) tptp.zero_zero_int) P)) (=> (@ (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) (@ (@ tptp.multInv P) K))) K)) P) (@ (@ _let_1 A) P))))))) (forall ((A tptp.int) (J_1 tptp.int) (K tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.multInv P))) (let ((_let_2 (@ tptp.times_times_int A))) (let ((_let_3 (@ tptp.zcong K))) (let ((_let_4 (@ tptp.zcong J_1))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ _let_3 tptp.zero_zero_int) P)) (=> (not (@ (@ _let_4 tptp.zero_zero_int) P)) (=> (@ (@ _let_4 (@ _let_2 (@ _let_1 K))) P) (@ (@ _let_3 (@ _let_2 (@ _let_1 J_1))) P))))))))))) (forall ((J_1 tptp.int) (K tptp.int) (A tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.zcong J_1))) (let ((_let_2 (@ tptp.multInv P))) (let ((_let_3 (@ tptp.times_times_int A))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong A) tptp.zero_zero_int) P)) (=> (not (@ (@ (@ tptp.zcong K) tptp.zero_zero_int) P)) (=> (not (@ (@ _let_1 tptp.zero_zero_int) P)) (=> (@ (@ (@ tptp.zcong (@ _let_3 (@ _let_2 J_1))) (@ _let_3 (@ _let_2 K))) P) (@ (@ _let_1 K) P))))))))))) (forall ((X_1 tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.multInv P))) (let ((_let_2 (@ _let_1 X_1))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X_1) _let_2)) (@ _let_1 _let_2))) X_1) P))))))) (forall ((X_1 tptp.int) (P tptp.int)) (let ((_let_1 (@ tptp.multInv P))) (let ((_let_2 (@ _let_1 X_1))) (let ((_let_3 (@ _let_1 _let_2))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (@ (@ (@ tptp.zcong _let_3) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X_1) _let_2)) _let_3)) P)))))))) (forall ((X_1 tptp.int) (P tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int (@ (@ tptp.multInv P) X_1)) X_1)) tptp.one_one_int) P))))) (forall ((X_1 tptp.int) (P tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) P) (=> (@ tptp.zprime P) (=> (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int X_1) (@ (@ tptp.multInv P) X_1))) tptp.one_one_int) P))))) (forall ((B tptp.int) (A tptp.int) (P tptp.int)) (let ((_let_1 (@ (@ tptp.wset A) P))) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) P) (=> (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int P) tptp.one_one_int)) (=> (@ (@ tptp.member_int B) _let_1) (@ (@ tptp.member_int (@ (@ tptp.inv P) B)) _let_1))))))) (forall ((B tptp.int) (A tptp.int) (P tptp.int)) (let ((_let_1 (@ (@ tptp.wset A) P))) (let ((_let_2 (@ (@ tptp.minus_minus_int P) tptp.one_one_int))) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.number_number_of_int (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 tptp.pls))))) P) (=> (@ (@ tptp.ord_less_int A) _let_2) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (=> (@ (@ tptp.ord_less_int B) _let_2) (=> (@ (@ tptp.member_int (@ (@ tptp.inv P) B)) _let_1) (@ (@ tptp.member_int B) _let_1)))))))))) (forall ((P tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.member_int A) (@ (@ tptp.wset A) P)))) (forall ((B tptp.int) (P tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.member_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ _let_1 (@ (@ tptp.wset (@ (@ tptp.minus_minus_int A) tptp.one_one_int)) P)) (@ _let_1 (@ (@ tptp.wset A) P)))))) (forall ((B tptp.int) (A tptp.int) (P tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int P) tptp.one_one_int))) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int A) _let_1) (=> (@ (@ tptp.member_int B) (@ (@ tptp.wset A) P)) (@ (@ tptp.ord_less_int B) _let_1)))))) (forall ((B tptp.int) (A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int P) tptp.one_one_int)) (=> (@ (@ tptp.member_int B) (@ (@ tptp.wset A) P)) (@ (@ tptp.ord_less_int tptp.one_one_int) B))))) (forall ((B tptp.int) (P tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.member_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (not (@ _let_1 (@ (@ tptp.wset (@ (@ tptp.minus_minus_int A) tptp.one_one_int)) P))) (=> (@ _let_1 (@ (@ tptp.wset A) P)) (or (= B A) (= B (@ (@ tptp.inv P) A)))))))) (forall ((B tptp.int) (A tptp.int) (P tptp.int)) (=> (@ tptp.zprime P) (=> (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int P) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.member_int B) (@ (@ tptp.wset A) P))))))) (forall ((P_1 (-> tptp.int Bool)) (I_1 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I_1) K) (=> (@ P_1 K) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_eq_int I) K) (=> (@ P_1 I) (@ P_1 (@ (@ tptp.minus_minus_int I) tptp.one_one_int))))) (@ P_1 I_1))))) (forall ((P_1 (-> tptp.int Bool)) (I_1 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int I_1) K) (=> (@ P_1 (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_int I) K) (=> (@ P_1 I) (@ P_1 (@ (@ tptp.minus_minus_int I) tptp.one_one_int))))) (@ P_1 I_1))))) (forall ((X_1 tptp.int) (P_1 (-> tptp.int Bool))) (=> (forall ((A_2 tptp.int)) (=> (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A_2) (@ P_1 (@ (@ tptp.minus_minus_int A_2) tptp.one_one_int))) (@ P_1 A_2))) (@ P_1 X_1))) (forall ((P_1 (-> tptp.int Bool)) (K tptp.int) (I_1 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I_1) (=> (@ P_1 K) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) I) (=> (@ P_1 I) (@ P_1 (@ (@ tptp.plus_plus_int I) tptp.one_one_int))))) (@ P_1 I_1))))) (forall ((P_1 (-> tptp.int Bool)) (K tptp.int) (I_1 tptp.int)) (=> (@ (@ tptp.ord_less_int K) I_1) (=> (@ P_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (=> (forall ((I tptp.int)) (=> (@ (@ tptp.ord_less_int K) I) (=> (@ P_1 I) (@ P_1 (@ (@ tptp.plus_plus_int I) tptp.one_one_int))))) (@ P_1 I_1))))) (forall ((M tptp.nat) (K tptp.nat) (F (-> tptp.nat tptp.nat))) (=> (forall ((M_2 tptp.nat) (N_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M_2) N_1) (@ (@ tptp.ord_less_nat (@ F M_2)) (@ F N_1)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))) (forall ((P tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int P) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (=> (@ tptp.zprime P) (= (@ tptp.d22set _let_1) (@ (@ tptp.wset _let_1) P))))) (forall ((N tptp.nat) (P_1 (-> tptp.nat Bool))) (=> (not (@ P_1 tptp.zero_zero_nat)) (=> (@ P_1 N) (exists ((K_1 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K_1) N) (forall ((I tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K_1) (not (@ P_1 I)))) (@ P_1 K_1)))))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.member_int B) (@ tptp.d22set A)) (@ (@ tptp.ord_less_eq_int B) A))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.member_int B) (@ tptp.d22set A))))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.member_int B) (@ tptp.d22set A)) (@ (@ tptp.ord_less_int tptp.one_one_int) B))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.member_int B) (@ tptp.d22set A))))) (forall ((I_1 tptp.nat) (J_1 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I_1) J_1) (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_1))))) (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.dvd_dvd_int A) B)))) (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))) (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))) (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (and (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat) (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A))))) (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)) (forall ((A tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (not (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat))))) (forall ((A tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A))))) (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)) (forall ((A tptp.nat)) (= (not (= A tptp.one_one_nat)) (and (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A) (not (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat))))) (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= A tptp.one_one_nat))) (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= A tptp.one_one_nat))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_nat M) N) (@ _let_1 M))))) (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.dvd_dvd_nat A) B)))) (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.dvd_dvd_int A) B)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (or (@ (@ tptp.ord_less_eq_nat M) N) (= N tptp.zero_zero_nat)))) (forall ((N tptp.nat) (M tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (=> (= (@ _let_1 N) (@ _let_1 M)) (= N M))))) (forall ((P tptp.int)) (= (@ tptp.sr P) (@ tptp.collect_int (lambda ((X tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_int X) P)))))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.div_mod_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.minus_minus_int (@ _let_1 (@ (@ tptp.div_mod_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))) tptp.one_one_int))))) (forall ((V tptp.int) (W tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int W))) (let ((_let_2 (@ tptp.number_number_of_int V))) (let ((_let_3 (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (let ((_let_4 (@ (@ tptp.div_mod_int (@ tptp.number_number_of_int (@ tptp.bit1 V))) (@ tptp.number_number_of_int (@ tptp.bit0 W))))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1))) (and (=> _let_5 (= _let_4 (@ (@ tptp.plus_plus_int (@ _let_3 (@ (@ tptp.div_mod_int _let_2) _let_1))) tptp.one_one_int))) (=> (not _let_5) (= _let_4 (@ (@ tptp.minus_minus_int (@ _let_3 (@ (@ tptp.div_mod_int (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1))) tptp.one_one_int)))))))))) (forall ((X_1 tptp.int) (Y_1 tptp.int)) (let ((_let_1 (@ tptp.number_number_of_int X_1))) (let ((_let_2 (@ tptp.number_number_of_int Y_1))) (= (@ (@ tptp.dvd_dvd_int _let_1) _let_2) (= (@ (@ tptp.div_mod_int _let_2) _let_1) tptp.zero_zero_int))))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ _let_1 tptp.zero_zero_int) (@ _let_1 (@ (@ tptp.div_mod_int A) B))))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.div_mod_int A) B)) B))) (forall ((Y_1 tptp.int) (X_1 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X_1) (=> (@ _let_1 Y_1) (@ _let_1 (@ (@ tptp.div_mod_int X_1) Y_1)))))) (forall ((K tptp.int) (M tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.div_mod_int M) K)) M))) (forall ((M tptp.int) (D tptp.int)) (= (= (@ (@ tptp.div_mod_int M) D) tptp.zero_zero_int) (exists ((Q_1 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q_1))))) (forall ((X_1 tptp.int) (N tptp.int) (Y_1 tptp.int)) (= (= (@ (@ tptp.div_mod_int X_1) N) (@ (@ tptp.div_mod_int Y_1) N)) (@ (@ tptp.dvd_dvd_int N) (@ (@ tptp.minus_minus_int X_1) Y_1)))) (forall ((X_1 tptp.int) (M tptp.int) (Y_1 tptp.int)) (=> (= (@ (@ tptp.div_mod_int X_1) M) (@ (@ tptp.div_mod_int Y_1) M)) (@ (@ (@ tptp.zcong X_1) Y_1) M))) (forall ((X_1 tptp.int) (M tptp.int)) (@ (@ (@ tptp.zcong X_1) (@ (@ tptp.div_mod_int X_1) M)) M)) (forall ((A tptp.int) (B tptp.int) (M tptp.int)) (= (@ (@ (@ tptp.zcong A) B) M) (@ (@ (@ tptp.zcong (@ (@ tptp.div_mod_int A) M)) (@ (@ tptp.div_mod_int B) M)) M))) (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 (@ (@ tptp.div_mod_int M) N)) (=> (@ _let_1 N) (@ _let_1 M))))) (forall ((N tptp.int) (F tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int F))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.div_mod_int M) N)))))) (forall ((X_1 tptp.int) (M tptp.int) (Y_1 tptp.nat)) (= (@ (@ tptp.div_mod_int (@ (@ tptp.power_power_int (@ (@ tptp.div_mod_int X_1) M)) Y_1)) M) (@ (@ tptp.div_mod_int (@ (@ tptp.power_power_int X_1) Y_1)) M))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.div_mod_int (@ _let_1 B)) C) (@ (@ tptp.div_mod_int (@ _let_1 (@ (@ tptp.div_mod_int B) C))) C)))) (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.div_mod_int (@ _let_1 (@ (@ tptp.div_mod_int B) C))) C) (@ (@ tptp.div_mod_int (@ _let_1 B)) C)))) (forall ((A tptp.int)) (= (@ (@ tptp.div_mod_int A) A) tptp.zero_zero_int)) (forall ((B tptp.int)) (= (@ (@ tptp.div_mod_int tptp.zero_zero_int) B) tptp.zero_zero_int)) (forall ((X_1 tptp.int) (Y_1 tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X_1))) (= (@ (@ tptp.div_mod_int (@ _let_1 (@ (@ tptp.div_mod_int Y_1) M))) M) (@ (@ tptp.div_mod_int (@ _let_1 Y_1)) M)))) (forall ((X_1 tptp.int) (M tptp.int) (Y_1 tptp.int)) (= (@ (@ tptp.div_mod_int (@ (@ tptp.minus_minus_int (@ (@ tptp.div_mod_int X_1) M)) Y_1)) M) (@ (@ tptp.div_mod_int (@ (@ tptp.minus_minus_int X_1) Y_1)) M))) (forall ((A tptp.int)) (= (@ (@ tptp.div_mod_int A) (@ tptp.number_number_of_int tptp.min)) tptp.zero_zero_int)) (forall ((A tptp.int) (B tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.div_mod_int A))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.dvd_dvd_int M) B) (= (@ (@ tptp.div_mod_int (@ _let_1 B)) M) (@ _let_1 M)))))) (forall ((A tptp.int) (B tptp.int) (M tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (@ (@ (@ tptp.zcong A) B) M) (= (@ (@ tptp.div_mod_int A) M) (@ (@ tptp.div_mod_int B) M))))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.div_mod_int A) B)))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.div_mod_int A) B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_int _let_1) B))))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.div_mod_int A) B) A)))) (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.div_mod_int A) B)) tptp.zero_zero_int))) (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.div_mod_int A) B))) (let ((_let_2 (@ tptp.ord_less_int B))) (=> (@ _let_2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (@ _let_2 _let_1)))))) (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.div_mod_int A) B) A)))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int A) B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (= (@ (@ tptp.div_mod_int A) B) _let_1))))) (forall ((V tptp.int) (W tptp.int)) (= (@ (@ tptp.div_mod_int (@ tptp.number_number_of_int (@ tptp.bit0 V))) (@ tptp.number_number_of_int (@ tptp.bit0 W))) (@ (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) (@ (@ tptp.div_mod_int (@ tptp.number_number_of_int V)) (@ tptp.number_number_of_int W))))) (forall ((P_1 (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P_1 (@ (@ tptp.div_mod_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P_1 N)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J) (@ (@ tptp.ord_less_int J) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I)) J))) (@ P_1 J)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I tptp.int) (J tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J) (@ (@ tptp.ord_less_eq_int J) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I)) J))) (@ P_1 J))))))) (forall ((Q tptp.int) (B tptp.int) (R tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (=> (@ _let_1 R) (=> (@ (@ tptp.ord_less_int R) B) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.div_mod_int Q) C))) R))))))) (forall ((Q tptp.int) (B tptp.int) (R tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (=> (@ (@ tptp.ord_less_int R) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.div_mod_int Q) C))) R)) (@ _let_1 C))))))) (forall ((Q tptp.int) (B tptp.int) (R tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (=> (@ (@ tptp.ord_less_int B) R) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 C)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.div_mod_int Q) C))) R))))))) (forall ((Q tptp.int) (B tptp.int) (R tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (=> (@ (@ tptp.ord_less_int B) R) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.div_mod_int Q) C))) R)) tptp.zero_zero_int))))) (forall ((A_1 tptp.int) (B_1 tptp.int) (Q_2 tptp.int) (Y_1 tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_int tptp.zero_zero_int) B_1))) (=> (= A_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B_1) Q_2)) Y_1)) (=> (and (=> _let_1 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y_1) (@ (@ tptp.ord_less_int Y_1) B_1))) (=> (not _let_1) (and (@ (@ tptp.ord_less_int B_1) Y_1) (@ (@ tptp.ord_less_eq_int Y_1) tptp.zero_zero_int)))) (=> (not (= B_1 tptp.zero_zero_int)) (= (@ (@ tptp.div_mod_int A_1) B_1) Y_1)))))) (forall ((X_1 tptp.int)) (let ((_let_1 (@ (@ tptp.div_mod_int X_1) (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))) (forall ((B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.div_mod_int (@ tptp.number_number_of_int tptp.min)) B) (@ (@ tptp.minus_minus_int B) tptp.one_one_int)))) (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.div_mod_int (@ _let_2 (@ _let_1 B))) (@ _let_1 A)) (@ _let_2 (@ _let_1 (@ (@ tptp.div_mod_int B) A)))))))) (forall ((M_1 tptp.int) (D_1 tptp.int)) (=> (= (@ (@ tptp.div_mod_int M_1) D_1) tptp.zero_zero_int) (exists ((Q_1 tptp.int)) (= M_1 (@ (@ tptp.times_times_int D_1) Q_1))))) (forall ((X_1 tptp.int) (Y_1 tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.standardRes M))) (=> (@ (@ tptp.ord_less_int (@ tptp.number_number_of_int (@ tptp.bit0 (@ tptp.bit1 tptp.pls)))) M) (@ (@ (@ tptp.zcong (@ (@ tptp.times_times_int (@ _let_1 X_1)) (@ _let_1 Y_1))) (@ (@ tptp.times_times_int X_1) Y_1)) M)))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.div_mod_nat M) N)) N))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.div_mod_nat M) N)) N))) (forall ((M tptp.nat) (D tptp.nat)) (= (= (@ (@ tptp.div_mod_nat M) D) tptp.zero_zero_nat) (exists ((Q_1 tptp.nat)) (= M (@ (@ tptp.times_times_nat D) Q_1))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.div_mod_nat M) N) (@ (@ tptp.div_mod_nat (@ (@ tptp.minus_minus_nat M) N)) N)))) (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.div_mod_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_nat M) N))) (and (=> _let_2 (= _let_1 M)) (=> (not _let_2) (= _let_1 (@ (@ tptp.div_mod_nat (@ (@ tptp.minus_minus_nat M) N)) N))))))) (forall ((K tptp.nat) (N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.div_mod_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N)) M)) N) (@ (@ tptp.div_mod_nat M) N))) (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.div_mod_nat M) N) (@ (@ tptp.div_mod_nat (@ (@ tptp.minus_minus_nat M) N)) N)))) (forall ((M tptp.int) (X_1 tptp.int)) (= (@ (@ tptp.standardRes M) X_1) (@ (@ tptp.div_mod_int X_1) M))) (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.div_mod_nat M) N)) K) (@ (@ tptp.div_mod_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.div_mod_nat M) N)) (@ (@ tptp.div_mod_nat (@ _let_1 M)) (@ _let_1 N))))) (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.div_mod_nat M) N) M))) (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.div_mod_nat M) N)) M)) (forall ((M tptp.int) (X_1 tptp.int)) (= (= (@ (@ tptp.standardRes M) X_1) tptp.zero_zero_int) (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) M))) (forall ((X_1 tptp.int) (P tptp.int)) (= (not (@ (@ (@ tptp.zcong X_1) tptp.zero_zero_int) P)) (not (= (@ (@ tptp.standardRes P) X_1) tptp.zero_zero_int)))) (forall ((X_1 tptp.int) (M tptp.int)) (@ (@ (@ tptp.zcong X_1) (@ (@ tptp.standardRes M) X_1)) M)) (forall ((X_1 tptp.int) (P tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) P) (@ (@ tptp.ord_less_int (@ (@ tptp.standardRes P) X_1)) P))) (forall ((X_1 tptp.int) (P tptp.int)) (=> (@ (@ tptp.member_int X_1) (@ tptp.sr P)) (= (@ (@ tptp.standardRes P) X_1) X_1))) (forall ((P_1 (-> tptp.nat Bool)) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (= K tptp.zero_zero_nat))) (= (@ P_1 (@ (@ tptp.div_mod_nat N) K)) (and (=> _let_1 (@ P_1 N)) (=> (not _let_1) (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (=> (= N (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) I)) J)) (@ P_1 J))))))))) (forall ((Q tptp.nat) (R tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (=> (@ (@ tptp.ord_less_nat R) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.div_mod_nat Q) C))) R)) (@ _let_1 C)))))) (forall ((X_1 tptp.int) (P tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) P) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.standardRes P) X_1)))) (forall ((X1 tptp.int) (X2 tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.standardRes M))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ _let_1 X1) (@ _let_1 X2)) (@ (@ (@ tptp.zcong X1) X2) M))))) _let_1 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 1.24/1.44 )
% 1.24/1.44 % SZS output end Proof for NUM926^3
% 1.24/1.44 % cvc5---1.0.5 exiting
% 1.24/1.44 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------